LMFDB - Embedded newform 145.2.b.c.59.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,2,Mod(59,145)] 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("145.59"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.84345856.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 13x^{4} + 41x^{2} + 1 $ x^6 + 13x^4 + 41x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.4
Root			$0.156785i$ of defining polynomial
Character	$\chi$	$=$	145.59
Dual form			145.2.b.c.59.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.156785i q^{2} +2.56387i q^{3} +1.97542 q^{4} +(1.28672 - 1.82876i) q^{5} -0.401976 q^{6} -1.09364i q^{7} +0.623285i q^{8} -3.57344 q^{9} +(0.286721 + 0.201738i) q^{10} -4.40198 q^{11} +5.06472i q^{12} +3.97108i q^{13} +0.171466 q^{14} +(4.68870 + 3.29899i) q^{15} +3.85312 q^{16} -6.22138i q^{17} -0.560261i q^{18} -6.97542 q^{19} +(2.54181 - 3.61256i) q^{20} +2.80395 q^{21} -0.690163i q^{22} -0.780070i q^{23} -1.59802 q^{24} +(-1.68870 - 4.70620i) q^{25} -0.622605 q^{26} -1.47023i q^{27} -2.16040i q^{28} +1.00000 q^{29} +(-0.517231 + 0.735116i) q^{30} +6.40198 q^{31} +1.85068i q^{32} -11.2861i q^{33} +0.975419 q^{34} +(-2.00000 - 1.40721i) q^{35} -7.05904 q^{36} +1.09364i q^{37} -1.09364i q^{38} -10.1813 q^{39} +(1.13984 + 0.801994i) q^{40} +0.439617i q^{42} -0.376593i q^{43} -8.69575 q^{44} +(-4.59802 + 6.53495i) q^{45} +0.122303 q^{46} +4.75115i q^{47} +9.87890i q^{48} +5.80395 q^{49} +(0.737860 - 0.264762i) q^{50} +15.9508 q^{51} +7.84455i q^{52} -11.2861i q^{53} +0.230510 q^{54} +(-5.66412 + 8.05014i) q^{55} +0.681649 q^{56} -17.8841i q^{57} +0.156785i q^{58} -10.0000 q^{59} +(9.26214 + 6.51688i) q^{60} -1.14688 q^{61} +1.00373i q^{62} +3.90806i q^{63} +7.41607 q^{64} +(7.26214 + 5.10967i) q^{65} +1.76949 q^{66} +5.90782i q^{67} -12.2898i q^{68} +2.00000 q^{69} +(0.220629 - 0.313570i) q^{70} +2.00000 q^{71} -2.22727i q^{72} +8.72223i q^{73} -0.171466 q^{74} +(12.0661 - 4.32960i) q^{75} -13.7794 q^{76} +4.81418i q^{77} -1.59628i q^{78} +5.54886 q^{79} +(4.95789 - 7.04641i) q^{80} -6.95084 q^{81} +6.22138i q^{83} +5.53898 q^{84} +(-11.3774 - 8.00519i) q^{85} +0.0590441 q^{86} +2.56387i q^{87} -2.74369i q^{88} +10.8040 q^{89} +(-1.02458 - 0.720900i) q^{90} +4.34293 q^{91} -1.54096i q^{92} +16.4139i q^{93} -0.744908 q^{94} +(-8.97542 + 12.7563i) q^{95} -4.74491 q^{96} +17.4176i q^{97} +0.909972i q^{98} +15.7302 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 14 q^{4} + 3 q^{5} + 14 q^{6} - 12 q^{9} - 3 q^{10} - 10 q^{11} + 8 q^{14} + 7 q^{15} + 42 q^{16} - 16 q^{19} + 13 q^{20} - 16 q^{21} - 26 q^{24} + 11 q^{25} - 46 q^{26} + 6 q^{29} + 25 q^{30} + 22 q^{31}+ \cdots - 16 q^{99}+O(q^{100}) $ 6 * q - 14 * q^4 + 3 * q^5 + 14 * q^6 - 12 * q^9 - 3 * q^10 - 10 * q^11 + 8 * q^14 + 7 * q^15 + 42 * q^16 - 16 * q^19 + 13 * q^20 - 16 * q^21 - 26 * q^24 + 11 * q^25 - 46 * q^26 + 6 * q^29 + 25 * q^30 + 22 * q^31 - 20 * q^34 - 12 * q^35 - 12 * q^36 + 14 * q^39 + 21 * q^40 + 2 * q^44 - 44 * q^45 - 44 * q^46 + 2 * q^49 + 35 * q^50 + 44 * q^51 - 22 * q^54 + 13 * q^55 + 16 * q^56 - 60 * q^59 + 25 * q^60 + 12 * q^61 - 38 * q^64 + 13 * q^65 + 34 * q^66 + 12 * q^69 + 60 * q^70 + 12 * q^71 - 8 * q^74 + 9 * q^75 - 24 * q^76 - 2 * q^79 - 55 * q^80 + 10 * q^81 + 80 * q^84 - 26 * q^85 - 30 * q^86 + 32 * q^89 - 32 * q^90 + 40 * q^91 - 2 * q^94 - 28 * q^95 - 26 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.156785i			0.110864i	0.998462	+	0.0554318i	$0.0176535\pi$
$2$			0.156785i			0.110864i	−0.998462	+	0.0554318i	$0.982346\pi$
$3$			2.56387i			1.48025i	0.672468	+	0.740126i	$0.265234\pi$
$3$			2.56387i			1.48025i	−0.672468	+	0.740126i	$0.734766\pi$
$4$	1.97542			0.987709
$5$	1.28672	−	1.82876i	0.575439	−	0.817845i
$5$	1.28672	−	1.82876i	0.575439	−	0.817845i
$6$	−0.401976			−0.164106
$7$		−	1.09364i		−	0.413357i	−0.978409	−	0.206678i	$-0.933735\pi$
$7$		−	1.09364i		−	0.413357i	0.978409	−	0.206678i	$-0.0662654\pi$
$8$			0.623285i			0.220365i
$9$	−3.57344			−1.19115
$10$	0.286721	+	0.201738i	0.0906692	+	0.0637953i
$11$	−4.40198			−1.32725			−0.663623	−	0.748067i	$-0.730982\pi$
$11$	−4.40198			−1.32725			−0.663623	+	0.748067i	$0.730982\pi$
$12$			5.06472i			1.46206i
$13$			3.97108i			1.10138i	0.834710	+	0.550690i	$0.185635\pi$
$13$			3.97108i			1.10138i	−0.834710	+	0.550690i	$0.814365\pi$
$14$	0.171466			0.0458262
$15$	4.68870	+	3.29899i	1.21062	+	0.851795i
$16$	3.85312			0.963279
$17$		−	6.22138i		−	1.50891i	−0.656353	−	0.754454i	$-0.727902\pi$
$17$		−	6.22138i		−	1.50891i	0.656353	−	0.754454i	$-0.272098\pi$
$18$		−	0.560261i		−	0.132055i
$19$	−6.97542			−1.60027			−0.800135	−	0.599819i	$-0.795239\pi$
$19$	−6.97542			−1.60027			−0.800135	+	0.599819i	$0.795239\pi$
$20$	2.54181	−	3.61256i	0.568367	−	0.807793i
$21$	2.80395			0.611873
$22$		−	0.690163i		−	0.147143i
$23$		−	0.780070i		−	0.162656i	−0.996687	−	0.0813279i	$-0.974084\pi$
$23$		−	0.780070i		−	0.162656i	0.996687	−	0.0813279i	$-0.0259161\pi$
$24$	−1.59802			−0.326195
$25$	−1.68870	−	4.70620i	−0.337739	−	0.941240i
$26$	−0.622605			−0.122103
$27$		−	1.47023i		−	0.282946i
$28$		−	2.16040i		−	0.408276i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$	−0.517231	+	0.735116i	−0.0944331	+	0.134213i
$31$	6.40198			1.14983			0.574914	−	0.818214i	$-0.305035\pi$
$31$	6.40198			1.14983			0.574914	+	0.818214i	$0.305035\pi$
$32$			1.85068i			0.327157i
$33$		−	11.2861i		−	1.96466i
$34$	0.975419			0.167283
$35$	−2.00000	−	1.40721i	−0.338062	−	0.237862i
$36$	−7.05904			−1.17651
$37$			1.09364i			0.179793i	0.995951	+	0.0898966i	$0.0286537\pi$
$37$			1.09364i			0.179793i	−0.995951	+	0.0898966i	$0.971346\pi$
$38$		−	1.09364i		−	0.177412i
$39$	−10.1813			−1.63032
$40$	1.13984	+	0.801994i	0.180224	+	0.126806i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$			0.439617i			0.0678344i
$43$		−	0.376593i		−	0.0574299i	−0.999588	−	0.0287150i	$-0.990858\pi$
$43$		−	0.376593i		−	0.0574299i	0.999588	−	0.0287150i	$-0.00914152\pi$
$44$	−8.69575			−1.31093
$45$	−4.59802	+	6.53495i	−0.685433	+	0.974173i
$46$	0.122303			0.0180326
$47$			4.75115i			0.693027i	0.938045	+	0.346513i	$0.112634\pi$
$47$			4.75115i			0.693027i	−0.938045	+	0.346513i	$0.887366\pi$
$48$			9.87890i			1.42590i
$49$	5.80395			0.829136
$50$	0.737860	−	0.264762i	0.104349	−	0.0374430i
$51$	15.9508			2.23356
$52$			7.84455i			1.08784i
$53$		−	11.2861i		−	1.55027i	−0.631798	−	0.775133i	$-0.717683\pi$
$53$		−	11.2861i		−	1.55027i	0.631798	−	0.775133i	$-0.282317\pi$
$54$	0.230510			0.0313685
$55$	−5.66412	+	8.05014i	−0.763749	+	1.08548i
$56$	0.681649			0.0910892
$57$		−	17.8841i		−	2.36880i
$58$			0.156785i			0.0205869i
$59$	−10.0000			−1.30189			−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000			−1.30189			−0.650945	+	0.759125i	$0.725627\pi$
$60$	9.26214	+	6.51688i	1.19574	+	0.841326i
$61$	−1.14688			−0.146844			−0.0734218	−	0.997301i	$-0.523392\pi$
$61$	−1.14688			−0.146844			−0.0734218	+	0.997301i	$0.523392\pi$
$62$			1.00373i			0.127474i
$63$			3.90806i			0.492369i
$64$	7.41607			0.927009
$65$	7.26214	+	5.10967i	0.900758	+	0.633777i
$66$	1.76949			0.217809
$67$			5.90782i			0.721754i	0.932613	+	0.360877i	$0.117523\pi$
$67$			5.90782i			0.721754i	−0.932613	+	0.360877i	$0.882477\pi$
$68$		−	12.2898i		−	1.49036i
$69$	2.00000			0.240772
$70$	0.220629	−	0.313570i	0.0263702	−	0.0374787i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		−	2.22727i		−	0.262487i
$73$			8.72223i			1.02086i	0.859919	+	0.510430i	$0.170514\pi$
$73$			8.72223i			1.02086i	−0.859919	+	0.510430i	$0.829486\pi$
$74$	−0.171466			−0.0199325
$75$	12.0661	−	4.32960i	1.39327	−	0.499940i
$76$	−13.7794			−1.58060
$77$			4.81418i			0.548626i
$78$		−	1.59628i		−	0.180743i
$79$	5.54886			0.624296			0.312148	−	0.950034i	$-0.398952\pi$
$79$	5.54886			0.624296			0.312148	+	0.950034i	$0.398952\pi$
$80$	4.95789	−	7.04641i	0.554308	−	0.787812i
$81$	−6.95084			−0.772315
$82$		0			0
$83$			6.22138i			0.682886i	0.939903	+	0.341443i	$0.110916\pi$
$83$			6.22138i			0.682886i	−0.939903	+	0.341443i	$0.889084\pi$
$84$	5.53898			0.604352
$85$	−11.3774	−	8.00519i	−1.23405	−	0.868284i
$86$	0.0590441			0.00636689
$87$			2.56387i			0.274876i
$88$		−	2.74369i		−	0.292478i
$89$	10.8040			1.14522			0.572608	−	0.819829i	$-0.305932\pi$
$89$	10.8040			1.14522			0.572608	+	0.819829i	$0.305932\pi$
$90$	−1.02458	−	0.720900i	−0.108000	−	0.0759896i
$91$	4.34293			0.455263
$92$		−	1.54096i		−	0.160657i
$93$			16.4139i			1.70204i
$94$	−0.744908			−0.0768314
$95$	−8.97542	+	12.7563i	−0.920859	+	1.30877i
$96$	−4.74491			−0.484275
$97$			17.4176i			1.76849i	0.467026	+	0.884244i	$0.345326\pi$
$97$			17.4176i			1.76849i	−0.467026	+	0.884244i	$0.654674\pi$
$98$			0.909972i			0.0919210i
$99$	15.7302			1.58095
$100$	−3.33588	−	9.29671i	−0.333588	−	0.929671i
$101$	−12.7548			−1.26915			−0.634574	−	0.772862i	$-0.718825\pi$
$101$	−12.7548			−1.26915			−0.634574	+	0.772862i	$0.718825\pi$
$102$			2.50085i			0.247621i
$103$		−	5.15463i		−	0.507901i	−0.967217	−	0.253950i	$-0.918270\pi$
$103$		−	5.15463i		−	0.507901i	0.967217	−	0.253950i	$-0.0817300\pi$
$104$	−2.47512			−0.242705
$105$	3.60790	−	5.12775i	0.352095	−	0.500417i
$106$	1.76949			0.171868
$107$			1.09364i			0.105726i	0.998602	+	0.0528631i	$0.0168347\pi$
$107$			1.09364i			0.105726i	−0.998602	+	0.0528631i	$0.983165\pi$
$108$		−	2.90433i		−	0.279469i
$109$	−15.3282			−1.46818			−0.734089	−	0.679053i	$-0.762391\pi$
$109$	−15.3282			−1.46818			−0.734089	+	0.679053i	$0.762391\pi$
$110$	−1.26214	−	0.888047i	−0.120340	−	0.0846720i
$111$	−2.80395			−0.266139
$112$		−	4.21392i		−	0.398178i
$113$			7.28814i			0.685611i	0.939406	+	0.342805i	$0.111377\pi$
$113$			7.28814i			0.685611i	−0.939406	+	0.342805i	$0.888623\pi$
$114$	2.80395			0.262614
$115$	−1.42656	−	1.00373i	−0.133027	−	0.0935985i
$116$	1.97542			0.183413
$117$		−	14.1904i		−	1.31191i
$118$		−	1.56785i		−	0.144332i
$119$	−6.80395			−0.623717
$120$	−2.05621	+	2.92240i	−0.187706	+	0.266777i
$121$	8.37739			0.761581
$122$		−	0.179814i		−	0.0162796i
$123$		0			0
$124$	12.6466			1.13570
$125$	−10.7794	−	2.96735i	−0.964136	−	0.265408i
$126$	−0.612724			−0.0545858
$127$		−	17.7312i		−	1.57339i	−0.617345	−	0.786693i	$-0.711792\pi$
$127$		−	17.7312i		−	1.57339i	0.617345	−	0.786693i	$-0.288208\pi$
$128$			4.86409i			0.429929i
$129$	0.965537			0.0850108
$130$	−0.801119	+	1.13859i	−0.0702628	+	0.0998612i
$131$	7.31835			0.639407			0.319704	−	0.947518i	$-0.396417\pi$
$131$	7.31835			0.639407			0.319704	+	0.947518i	$0.396417\pi$
$132$		−	22.2948i		−	1.94051i
$133$			7.62859i			0.661483i
$134$	−0.926256			−0.0800163
$135$	−2.68870	−	1.89178i	−0.231406	−	0.162818i
$136$	3.87770			0.332510
$137$		−	9.78899i		−	0.836330i	−0.908371	−	0.418165i	$-0.862673\pi$
$137$		−	9.78899i		−	0.836330i	0.908371	−	0.418165i	$-0.137327\pi$
$138$			0.313570i			0.0266928i
$139$	2.75479			0.233658			0.116829	−	0.993152i	$-0.462727\pi$
$139$	2.75479			0.233658			0.116829	+	0.993152i	$0.462727\pi$
$140$	−3.95084	−	2.77983i	−0.333907	−	0.234938i
$141$	−12.1813			−1.02585
$142$			0.313570i			0.0263142i
$143$		−	17.4806i		−	1.46180i
$144$	−13.7689			−1.14741
$145$	1.28672	−	1.82876i	0.106856	−	0.151870i
$146$	−1.36751			−0.113176
$147$			14.8806i			1.22733i
$148$			2.16040i			0.177583i
$149$	4.52428			0.370643			0.185322	−	0.982678i	$-0.440667\pi$
$149$	4.52428			0.370643			0.185322	+	0.982678i	$0.440667\pi$
$150$	0.678816	+	1.89178i	0.0554251	+	0.154463i
$151$	2.80395			0.228182			0.114091	−	0.993470i	$-0.463604\pi$
$151$	2.80395			0.228182			0.114091	+	0.993470i	$0.463604\pi$
$152$		−	4.34768i		−	0.352643i
$153$			22.2318i			1.79733i
$154$	−0.754790			−0.0608227
$155$	8.23756	−	11.7077i	0.661657	−	0.940381i
$156$	−20.1124			−1.61028
$157$			4.97481i			0.397033i	0.980098	+	0.198517i	$0.0636124\pi$
$157$			4.97481i			0.397033i	−0.980098	+	0.198517i	$0.936388\pi$
$158$			0.869977i			0.0692117i
$159$	28.9361			2.29478
$160$	3.38444	+	2.38131i	0.267564	+	0.188259i
$161$	−0.853115			−0.0672349
$162$		−	1.08979i		−	0.0856216i
$163$		−	20.7615i		−	1.62617i	−0.582146	−	0.813084i	$-0.697787\pi$
$163$		−	20.7615i		−	1.62617i	0.582146	−	0.813084i	$-0.302213\pi$
$164$		0			0
$165$	−20.6395	−	14.5221i	−1.60679	−	1.13054i
$166$	−0.975419			−0.0757072
$167$			21.9182i			1.69608i	0.529932	+	0.848040i	$0.322217\pi$
$167$			21.9182i			1.69608i	−0.529932	+	0.848040i	$0.677783\pi$
$168$			1.74766i			0.134835i
$169$	−2.76949			−0.213038
$170$	1.25509	−	1.78380i	0.0962611	−	0.136811i
$171$	24.9263			1.90616
$172$		−	0.743929i		−	0.0567241i
$173$			3.25404i			0.247400i	0.992320	+	0.123700i	$0.0394760\pi$
$173$			3.25404i			0.247400i	−0.992320	+	0.123700i	$0.960524\pi$
$174$	−0.401976			−0.0304737
$175$	−5.14688	+	1.84683i	−0.389068	+	0.139607i
$176$	−16.9613			−1.27851
$177$		−	25.6387i		−	1.92712i
$178$			1.69390i			0.126963i
$179$	7.19605			0.537858			0.268929	−	0.963160i	$-0.413330\pi$
$179$	7.19605			0.537858			0.268929	+	0.963160i	$0.413330\pi$
$180$	−9.08302	+	12.9093i	−0.677008	+	0.962200i
$181$	13.0345			0.968844			0.484422	−	0.874834i	$-0.339030\pi$
$181$	13.0345			0.968844			0.484422	+	0.874834i	$0.339030\pi$
$182$			0.680906i			0.0504721i
$183$		−	2.94047i		−	0.217365i
$184$	0.486206			0.0358436
$185$	2.00000	+	1.40721i	0.147043	+	0.103460i
$186$	−2.57344			−0.188694
$187$			27.3864i			2.00269i
$188$			9.38551i			0.684509i
$189$	−1.60790			−0.116958
$190$	−2.00000	−	1.40721i	−0.145095	−	0.102090i
$191$	−10.1223			−0.732424			−0.366212	−	0.930531i	$-0.619346\pi$
$191$	−10.1223			−0.732424			−0.366212	+	0.930531i	$0.619346\pi$
$192$			19.0139i			1.37221i
$193$		−	22.8589i		−	1.64542i	−0.568462	−	0.822710i	$-0.692461\pi$
$193$		−	22.8589i		−	1.64542i	0.568462	−	0.822710i	$-0.307539\pi$
$194$	−2.73081			−0.196061
$195$	−13.1006	+	18.6192i	−0.938150	+	1.33335i
$196$	11.4652			0.818945
$197$			22.0711i			1.57250i	0.617907	+	0.786251i	$0.287981\pi$
$197$			22.0711i			1.57250i	−0.617907	+	0.786251i	$0.712019\pi$
$198$			2.46626i			0.175269i
$199$	−5.19605			−0.368338			−0.184169	−	0.982895i	$-0.558959\pi$
$199$	−5.19605			−0.368338			−0.184169	+	0.982895i	$0.558959\pi$
$200$	2.93330	−	1.05254i	0.207416	−	0.0744258i
$201$	−15.1469			−1.06838
$202$		−	1.99976i		−	0.140702i
$203$		−	1.09364i		−	0.0767585i
$204$	31.5096			2.20611
$205$		0			0
$206$	0.808167			0.0563077
$207$			2.78754i			0.193747i
$208$			15.3010i			1.06094i
$209$	30.7056			2.12395
$210$	0.803952	+	0.565665i	0.0554780	+	0.0390346i
$211$	1.64719			0.113397			0.0566985	−	0.998391i	$-0.481943\pi$
$211$	1.64719			0.113397			0.0566985	+	0.998391i	$0.481943\pi$
$212$		−	22.2948i		−	1.53121i
$213$			5.12775i			0.351347i
$214$	−0.171466			−0.0117212
$215$	−0.688697	−	0.484571i	−0.0469688	−	0.0330474i
$216$	0.916374			0.0623514
$217$		−	7.00145i		−	0.475290i
$218$		−	2.40323i		−	0.162768i
$219$	−22.3627			−1.51113
$220$	−11.1890	+	15.9024i	−0.754362	+	1.07214i
$221$	24.7056			1.66188
$222$		−	0.439617i		−	0.0295052i
$223$		−	9.47542i		−	0.634521i	−0.948338	−	0.317261i	$-0.897237\pi$
$223$		−	9.47542i		−	0.634521i	0.948338	−	0.317261i	$-0.102763\pi$
$224$	2.02398			0.135233
$225$	6.03446	+	16.8173i	0.402298	+	1.12116i
$226$	−1.14267			−0.0760093
$227$			5.72800i			0.380181i	0.981767	+	0.190090i	$0.0608781\pi$
$227$			5.72800i			0.380181i	−0.981767	+	0.190090i	$0.939122\pi$
$228$		−	35.3286i		−	2.33969i
$229$	−15.1469			−1.00093			−0.500467	−	0.865756i	$-0.666838\pi$
$229$	−15.1469			−1.00093			−0.500467	+	0.865756i	$0.666838\pi$
$230$	0.157370	−	0.223663i	0.0103767	−	0.0147479i
$231$	−12.3429			−0.812105
$232$			0.623285i			0.0409207i
$233$			0.717046i			0.0469753i	0.999724	+	0.0234876i	$0.00747703\pi$
$233$			0.717046i			0.0469753i	−0.999724	+	0.0234876i	$0.992523\pi$
$234$	2.22484			0.145443
$235$	8.68870	+	6.11341i	0.566788	+	0.398795i
$236$	−19.7542			−1.28589
$237$			14.2266i			0.924115i
$238$		−	1.06676i		−	0.0691475i
$239$	2.00000			0.129369			0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000			0.129369			0.0646846	+	0.997906i	$0.479396\pi$
$240$	18.0661	+	12.7114i	1.16616	+	0.820516i
$241$	17.3282			1.11621			0.558105	−	0.829770i	$-0.311529\pi$
$241$	17.3282			1.11621			0.558105	+	0.829770i	$0.311529\pi$
$242$			1.31345i			0.0844316i
$243$		−	22.2318i		−	1.42617i
$244$	−2.26558			−0.145039
$245$	7.46807	−	10.6140i	0.477117	−	0.678104i
$246$		0			0
$247$		−	27.7000i		−	1.76251i
$248$			3.99026i			0.253382i
$249$	−15.9508			−1.01084
$250$	0.465235	−	1.69004i	0.0294241	−	0.106888i
$251$	26.0099			1.64173			0.820865	−	0.571123i	$-0.193492\pi$
$251$	26.0099			1.64173			0.820865	+	0.571123i	$0.193492\pi$
$252$			7.72005i			0.486317i
$253$			3.43385i			0.215884i
$254$	2.77998			0.174431
$255$	20.5243	−	29.1702i	1.28528	−	1.82671i
$256$	14.0695			0.879346
$257$			15.0335i			0.937766i	0.883260	+	0.468883i	$0.155343\pi$
$257$			15.0335i			0.937766i	−0.883260	+	0.468883i	$0.844657\pi$
$258$			0.151382i			0.00942461i
$259$	1.19605			0.0743188
$260$	14.3458	+	10.0937i	0.889687	+	0.625988i
$261$	−3.57344			−0.221191
$262$			1.14741i			0.0708870i
$263$			12.0662i			0.744032i	0.928226	+	0.372016i	$0.121333\pi$
$263$			12.0662i			0.744032i	−0.928226	+	0.372016i	$0.878667\pi$
$264$	7.03446			0.432941
$265$	−20.6395	−	14.5221i	−1.26788	−	0.892084i
$266$	−1.19605			−0.0733344
$267$			27.7000i			1.69521i
$268$			11.6704i			0.712884i
$269$	10.8531			0.661726			0.330863	−	0.943679i	$-0.392660\pi$
$269$	10.8531			0.661726			0.330863	+	0.943679i	$0.392660\pi$
$270$	0.296602	−	0.421547i	0.0180506	−	0.0256545i
$271$	−12.7449			−0.774198			−0.387099	−	0.922038i	$-0.626523\pi$
$271$	−12.7449			−0.774198			−0.387099	+	0.922038i	$0.626523\pi$
$272$		−	23.9717i		−	1.45350i
$273$			11.1347i			0.673904i
$274$	1.53476			0.0927185
$275$	7.43361	+	20.7166i	0.448263	+	1.24926i
$276$	3.95084			0.237812
$277$		−	20.0714i		−	1.20597i	−0.797752	−	0.602986i	$-0.793978\pi$
$277$		−	20.0714i		−	1.20597i	0.797752	−	0.602986i	$-0.206022\pi$
$278$			0.431909i			0.0259042i
$279$	−22.8771			−1.36962
$280$	0.877093	−	1.24657i	0.0524163	−	0.0744968i
$281$	−20.9361			−1.24895			−0.624473	−	0.781047i	$-0.714686\pi$
$281$	−20.9361			−1.24895			−0.624473	+	0.781047i	$0.714686\pi$
$282$		−	1.90985i		−	0.113730i
$283$			16.9703i			1.00878i	0.863477	+	0.504389i	$0.168282\pi$
$283$			16.9703i			1.00878i	−0.863477	+	0.504389i	$0.831718\pi$
$284$	3.95084			0.234439
$285$	−32.7056	−	23.0118i	−1.93731	−	1.36310i
$286$	2.74069			0.162061
$287$		0			0
$288$		−	6.61330i		−	0.389692i
$289$	−21.7056			−1.27680
$290$	0.286721	+	0.201738i	0.0168368	+	0.0118465i
$291$	−44.6565			−2.61781
$292$			17.2301i			1.00831i
$293$		−	9.47542i		−	0.553560i	−0.960933	−	0.276780i	$-0.910733\pi$
$293$		−	9.47542i		−	0.553560i	0.960933	−	0.276780i	$-0.0892673\pi$
$294$	−2.33305			−0.136066
$295$	−12.8672	+	18.2876i	−0.749158	+	1.06474i
$296$	−0.681649			−0.0396201
$297$			6.47193i			0.375539i
$298$			0.709338i			0.0410909i
$299$	3.09772			0.179146
$300$	23.8356	−	8.55278i	1.37615	−	0.493795i
$301$	−0.411857			−0.0237391
$302$			0.439617i			0.0252971i
$303$		−	32.7017i		−	1.87866i
$304$	−26.8771			−1.54151
$305$	−1.47572	+	2.09737i	−0.0844995	+	0.120095i
$306$	−3.48560			−0.199259
$307$		−	19.3812i		−	1.10614i	−0.833134	−	0.553072i	$-0.813456\pi$
$307$		−	19.3812i		−	1.10614i	0.833134	−	0.553072i	$-0.186544\pi$
$308$			9.51001i			0.541883i
$309$	13.2158			0.751821
$310$	1.83558	+	1.29152i	0.104254	+	0.0733536i
$311$	−9.26919			−0.525607			−0.262804	−	0.964849i	$-0.584647\pi$
$311$	−9.26919			−0.525607			−0.262804	+	0.964849i	$0.584647\pi$
$312$		−	6.34588i		−	0.359265i
$313$		−	14.5324i		−	0.821422i	−0.911766	−	0.410711i	$-0.865281\pi$
$313$		−	14.5324i		−	0.821422i	0.911766	−	0.410711i	$-0.134719\pi$
$314$	−0.779975			−0.0440165
$315$	7.14688	+	5.02858i	0.402681	+	0.283328i
$316$	10.9613			0.616623
$317$			22.4116i			1.25876i	0.777098	+	0.629380i	$0.216691\pi$
$317$			22.4116i			1.25876i	−0.777098	+	0.629380i	$0.783309\pi$
$318$			4.53675i			0.254408i
$319$	−4.40198			−0.246463
$320$	9.54242	−	13.5622i	0.533437	−	0.758149i
$321$	−2.80395			−0.156501
$322$		−	0.133756i		−	0.00745390i
$323$			43.3968i			2.41466i
$324$	−13.7308			−0.762823
$325$	18.6887	−	6.70596i	1.03666	−	0.371979i
$326$	3.25509			0.180283
$327$		−	39.2996i		−	2.17327i
$328$		0			0
$329$	5.19605			0.286467
$330$	2.27684	−	3.23597i	0.125336	−	0.178134i
$331$	7.89179			0.433772			0.216886	−	0.976197i	$-0.430410\pi$
$331$	7.89179			0.433772			0.216886	+	0.976197i	$0.430410\pi$
$332$			12.2898i			0.674493i
$333$		−	3.90806i		−	0.214160i
$334$	−3.43644			−0.188034
$335$	10.8040	+	7.60171i	0.590283	+	0.415326i
$336$	10.8040			0.589404
$337$		−	33.4280i		−	1.82094i	−0.413579	−	0.910468i	$-0.635721\pi$
$337$		−	33.4280i		−	1.82094i	0.413579	−	0.910468i	$-0.364279\pi$
$338$		−	0.434214i		−	0.0236181i
$339$	−18.6859			−1.01488
$340$	−22.4751	−	15.8136i	−1.21888	−	0.857613i
$341$	−28.1813			−1.52611
$342$			3.90806i			0.211324i
$343$		−	14.0029i		−	0.756086i
$344$	0.234725			0.0126555
$345$	2.57344	−	3.65751i	0.138549	−	0.196914i
$346$	−0.510183			−0.0274276
$347$		−	31.1069i		−	1.66991i	−0.550320	−	0.834954i	$-0.685494\pi$
$347$		−	31.1069i		−	1.66991i	0.550320	−	0.834954i	$-0.314506\pi$
$348$			5.06472i			0.271498i
$349$	5.76949			0.308834			0.154417	−	0.988006i	$-0.450650\pi$
$349$	5.76949			0.308834			0.154417	+	0.988006i	$0.450650\pi$
$350$	−0.289554	−	0.806953i	−0.0154773	−	0.0431335i
$351$	5.83842			0.311632
$352$		−	8.14665i		−	0.434218i
$353$		−	13.5095i		−	0.719039i	−0.933137	−	0.359520i	$-0.882941\pi$
$353$		−	13.5095i		−	0.719039i	0.933137	−	0.359520i	$-0.117059\pi$
$354$	4.01976			0.213648
$355$	2.57344	−	3.65751i	0.136584	−	0.194121i
$356$	21.3423			1.13114
$357$		−	17.4445i		−	0.923259i
$358$			1.12823i			0.0596289i
$359$	1.15677			0.0610518			0.0305259	−	0.999534i	$-0.490282\pi$
$359$	1.15677			0.0610518			0.0305259	+	0.999534i	$0.490282\pi$
$360$	−4.07314	−	2.86588i	−0.214673	−	0.151045i
$361$	29.6565			1.56087
$362$			2.04361i			0.107410i
$363$			21.4786i			1.12733i
$364$	8.57911			0.449667
$365$	15.9508	+	11.2231i	0.834905	+	0.587443i
$366$	0.461020			0.0240979
$367$			10.5959i			0.553104i	0.960999	+	0.276552i	$0.0891918\pi$
$367$			10.5959i			0.553104i	−0.960999	+	0.276552i	$0.910808\pi$
$368$		−	3.00570i		−	0.156683i
$369$		0			0
$370$	−0.220629	+	0.313570i	−0.0114700	+	0.0163017i
$371$	−12.3429			−0.640813
$372$			32.4242i			1.68112i
$373$		−	7.09907i		−	0.367576i	−0.982966	−	0.183788i	$-0.941164\pi$
$373$		−	7.09907i		−	0.367576i	0.982966	−	0.183788i	$-0.0588360\pi$
$374$	−4.29377			−0.222026
$375$	7.60790	−	27.6369i	0.392871	−	1.42717i
$376$	−2.96132			−0.152719
$377$			3.97108i			0.204521i
$378$		−	0.252095i		−	0.0129664i
$379$	−18.1223			−0.930880			−0.465440	−	0.885079i	$-0.654104\pi$
$379$	−18.1223			−0.930880			−0.465440	+	0.885079i	$0.654104\pi$
$380$	−17.7302	+	25.1991i	−0.909540	+	1.29269i
$381$	45.4604			2.32901
$382$		−	1.58702i		−	0.0811992i
$383$		−	3.28092i		−	0.167647i	−0.996481	−	0.0838236i	$-0.973287\pi$
$383$		−	3.28092i		−	0.167647i	0.996481	−	0.0838236i	$-0.0267132\pi$
$384$	−12.4709			−0.636403
$385$	8.80395	+	6.19450i	0.448691	+	0.315701i
$386$	3.58393			0.182417
$387$			1.34573i			0.0684075i
$388$			34.4070i			1.74675i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$	−2.91921	−	2.05397i	−0.147820	−	0.104007i
$391$	−4.85312			−0.245433
$392$			3.61752i			0.182712i
$393$			18.7633i			0.946484i
$394$	−3.46042			−0.174333
$395$	7.13984	−	10.1475i	0.359244	−	0.510577i
$396$	31.0737			1.56151
$397$			36.3054i			1.82212i	0.412278	+	0.911058i	$0.364733\pi$
$397$			36.3054i			1.82212i	−0.412278	+	0.911058i	$0.635267\pi$
$398$		−	0.814661i		−	0.0408353i
$399$	−19.5587			−0.979162
$400$	−6.50675	−	18.1335i	−0.325337	−	0.906676i
$401$	26.0830			1.30252			0.651262	−	0.758853i	$-0.274240\pi$
$401$	26.0830			1.30252			0.651262	+	0.758853i	$0.274240\pi$
$402$		−	2.37480i		−	0.118444i
$403$			25.4228i			1.26640i
$404$	−25.1960			−1.25355
$405$	−8.94379	+	12.7114i	−0.444420	+	0.631634i
$406$	0.171466			0.00850972
$407$		−	4.81418i		−	0.238630i
$408$			9.94192i			0.492198i
$409$	−13.0486			−0.645210			−0.322605	−	0.946534i	$-0.604558\pi$
$409$	−13.0486			−0.645210			−0.322605	+	0.946534i	$0.604558\pi$
$410$		0			0
$411$	25.0977			1.23798
$412$		−	10.1825i		−	0.501658i
$413$			10.9364i			0.538145i
$414$	−0.437043			−0.0214795
$415$	11.3774	+	8.00519i	0.558494	+	0.392959i
$416$	−7.34920			−0.360324
$417$			7.06293i			0.345873i
$418$			4.81418i			0.235469i
$419$	−35.8525			−1.75151			−0.875755	−	0.482756i	$-0.839636\pi$
$419$	−35.8525			−1.75151			−0.875755	+	0.482756i	$0.839636\pi$
$420$	7.12712	−	10.1294i	0.347768	−	0.494266i
$421$	16.7056			0.814182			0.407091	−	0.913388i	$-0.366543\pi$
$421$	16.7056			0.814182			0.407091	+	0.913388i	$0.366543\pi$
$422$			0.258254i			0.0125716i
$423$		−	16.9780i		−	0.825497i
$424$	7.03446			0.341624
$425$	−29.2791	+	10.5060i	−1.42024	+	0.509618i
$426$	−0.803952			−0.0389516
$427$			1.25428i			0.0606988i
$428$			2.16040i			0.104427i
$429$	44.8180			2.16384
$430$	0.0759733	−	0.107977i	0.00366376	−	0.00520713i
$431$	−26.3135			−1.26748			−0.633739	−	0.773547i	$-0.718481\pi$
$431$	−26.3135			−1.26748			−0.633739	+	0.773547i	$0.718481\pi$
$432$		−	5.66498i		−	0.272556i
$433$			10.7220i			0.515266i	0.966243	+	0.257633i	$0.0829425\pi$
$433$			10.7220i			0.515266i	−0.966243	+	0.257633i	$0.917057\pi$
$434$	1.09772			0.0526923
$435$	4.68870	+	3.29899i	0.224806	+	0.158174i
$436$	−30.2797			−1.45013
$437$			5.44131i			0.260293i
$438$		−	3.50613i		−	0.167529i
$439$	−29.5587			−1.41076			−0.705381	−	0.708828i	$-0.749224\pi$
$439$	−29.5587			−1.41076			−0.705381	+	0.708828i	$0.749224\pi$
$440$	−5.01753	−	3.53036i	−0.239202	−	0.168303i
$441$	−20.7401			−0.987623
$442$			3.87347i			0.184242i
$443$		−	3.40697i		−	0.161870i	−0.996719	−	0.0809349i	$-0.974209\pi$
$443$		−	3.40697i		−	0.161870i	0.996719	−	0.0809349i	$-0.0257906\pi$
$444$	−5.53898			−0.262868
$445$	13.9017	−	19.7578i	0.659003	−	0.936609i
$446$	1.48560			0.0703453
$447$			11.5997i			0.548646i
$448$		−	8.11051i		−	0.383186i
$449$	−0.461020			−0.0217569			−0.0108784	−	0.999941i	$-0.503463\pi$
$449$	−0.461020			−0.0217569			−0.0108784	+	0.999941i	$0.503463\pi$
$450$	−2.63670	+	0.946112i	−0.124295	+	0.0446001i
$451$		0			0
$452$			14.3971i			0.677184i
$453$			7.18898i			0.337768i
$454$	−0.898063			−0.0421482
$455$	5.58814	−	7.94216i	0.261976	−	0.372334i
$456$	11.1469			0.522001
$457$		−	1.37262i		−	0.0642084i	−0.999485	−	0.0321042i	$-0.989779\pi$
$457$		−	1.37262i		−	0.0642084i	0.999485	−	0.0321042i	$-0.0102208\pi$
$458$		−	2.37480i		−	0.110967i
$459$	−9.14688			−0.426940
$460$	−2.81805	−	1.98279i	−0.131392	−	0.0924481i
$461$	14.5875			0.679409			0.339705	−	0.940532i	$-0.389673\pi$
$461$	14.5875			0.679409			0.339705	+	0.940532i	$0.389673\pi$
$462$		−	1.93518i		−	0.0900329i
$463$		−	18.8517i		−	0.876112i	−0.898948	−	0.438056i	$-0.855667\pi$
$463$		−	18.8517i		−	0.876112i	0.898948	−	0.438056i	$-0.144333\pi$
$464$	3.85312			0.178876
$465$	30.0169	+	21.1200i	1.39200	+	0.979419i
$466$	−0.112422			−0.00520785
$467$		−	29.9580i		−	1.38629i	−0.720798	−	0.693145i	$-0.756225\pi$
$467$		−	29.9580i		−	1.38629i	0.720798	−	0.693145i	$-0.243775\pi$
$468$		−	28.0320i		−	1.29578i
$469$	6.46102			0.298342
$470$	−0.958489	+	1.36226i	−0.0442118	+	0.0628362i
$471$	−12.7548			−0.587710
$472$		−	6.23285i		−	0.286890i
$473$			1.65776i			0.0762237i
$474$	−2.23051			−0.102451
$475$	11.7794	+	32.8277i	0.540475	+	1.50624i
$476$	−13.4407			−0.616051
$477$			40.3302i			1.84660i
$478$			0.313570i			0.0143423i
$479$	32.7647			1.49706			0.748528	−	0.663103i	$-0.230761\pi$
$479$	32.7647			1.49706			0.748528	+	0.663103i	$0.230761\pi$
$480$	−6.10537	+	8.67728i	−0.278671	+	0.396062i
$481$	−4.34293			−0.198021
$482$			2.71680i			0.123747i
$483$		−	2.18728i		−	0.0995246i
$484$	16.5489			0.752221
$485$	31.8525	+	22.4116i	1.44635	+	1.01766i
$486$	3.48560			0.158110
$487$			14.1098i			0.639375i	0.947523	+	0.319688i	$0.103578\pi$
$487$			14.1098i			0.639375i	−0.947523	+	0.319688i	$0.896422\pi$
$488$		−	0.714836i		−	0.0323591i
$489$	53.2299			2.40714
$490$	1.66412	+	1.17088i	0.0751771	+	0.0528949i
$491$	4.10821			0.185401			0.0927004	−	0.995694i	$-0.470450\pi$
$491$	4.10821			0.185401			0.0927004	+	0.995694i	$0.470450\pi$
$492$		0			0
$493$		−	6.22138i		−	0.280197i
$494$	4.34293			0.195398
$495$	20.2404	−	28.7667i	0.909738	−	1.29297i
$496$	24.6676			1.10761
$497$		−	2.18728i		−	0.0981129i
$498$		−	2.50085i		−	0.112066i
$499$	−30.0689			−1.34607			−0.673035	−	0.739611i	$-0.735010\pi$
$499$	−30.0689			−1.34607			−0.673035	+	0.739611i	$0.735010\pi$
$500$	−21.2938	−	5.86176i	−0.952286	−	0.262146i
$501$	−56.1954			−2.51063
$502$			4.07795i			0.182008i
$503$		−	14.8806i		−	0.663493i	−0.943369	−	0.331746i	$-0.892362\pi$
$503$		−	14.8806i		−	0.663493i	0.943369	−	0.331746i	$-0.107638\pi$
$504$	−2.43583			−0.108501
$505$	−16.4119	+	23.3254i	−0.730318	+	1.03797i
$506$	−0.538375			−0.0239337
$507$		−	7.10062i		−	0.315350i
$508$		−	35.0264i		−	1.55405i
$509$	−1.93674			−0.0858445			−0.0429223	−	0.999078i	$-0.513667\pi$
$509$	−1.93674			−0.0858445			−0.0429223	+	0.999078i	$0.513667\pi$
$510$	4.57344	+	3.21789i	0.202515	+	0.142491i
$511$	9.53898			0.421980
$512$			11.9341i			0.527416i
$513$			10.2555i			0.452791i
$514$	−2.35703			−0.103964
$515$	−9.42656	−	6.63257i	−0.415384	−	0.292266i
$516$	1.90734			0.0839660
$517$		−	20.9145i		−	0.919817i
$518$			0.187522i			0.00823925i
$519$	−8.34293			−0.366214
$520$	−3.18478	+	4.52638i	−0.139662	+	0.198495i
$521$	−4.23051			−0.185342			−0.0926710	−	0.995697i	$-0.529540\pi$
$521$	−4.23051			−0.185342			−0.0926710	+	0.995697i	$0.529540\pi$
$522$		−	0.560261i		−	0.0245220i
$523$		−	4.40144i		−	0.192462i	−0.995359	−	0.0962308i	$-0.969321\pi$
$523$		−	4.40144i		−	0.192462i	0.995359	−	0.0962308i	$-0.0306787\pi$
$524$	14.4568			0.631548
$525$	−4.73503	−	13.1960i	−0.206654	−	0.575919i
$526$	−1.89179			−0.0824861
$527$		−	39.8292i		−	1.73499i
$528$		−	43.4867i		−	1.89251i
$529$	22.3915			0.973543
$530$	2.27684	−	3.23597i	0.0988996	−	0.140561i
$531$	35.7344			1.55074
$532$			15.0697i			0.653353i
$533$		0			0
$534$	−4.34293			−0.187937
$535$	2.00000	+	1.40721i	0.0864675	+	0.0608390i
$536$	−3.68225			−0.159049
$537$			18.4497i			0.796165i
$538$			1.70160i			0.0733613i
$539$	−25.5489			−1.10047
$540$	−5.31130	−	3.73706i	−0.228562	−	0.160817i
$541$	−32.4119			−1.39349			−0.696747	−	0.717317i	$-0.745370\pi$
$541$	−32.4119			−1.39349			−0.696747	+	0.717317i	$0.745370\pi$
$542$		−	1.99821i		−	0.0858304i
$543$			33.4187i			1.43413i
$544$	11.5138			0.493650
$545$	−19.7232	+	28.0316i	−0.844847	+	1.20074i
$546$	−1.74576			−0.0747114
$547$			12.9093i			0.551961i	0.961163	+	0.275980i	$0.0890024\pi$
$547$			12.9093i			0.551961i	−0.961163	+	0.275980i	$0.910998\pi$
$548$		−	19.3374i		−	0.826051i
$549$	4.09833			0.174912
$550$	−3.24804	+	1.16548i	−0.138497	+	0.0496961i
$551$	−6.97542			−0.297163
$552$			1.24657i			0.0530576i
$553$		−	6.06845i		−	0.258057i
$554$	3.14688			0.133698
$555$	−3.60790	+	5.12775i	−0.153147	+	0.217661i
$556$	5.44186			0.230786
$557$		−	23.0195i		−	0.975369i	−0.873020	−	0.487685i	$-0.837842\pi$
$557$		−	23.0195i		−	0.975369i	0.873020	−	0.487685i	$-0.162158\pi$
$558$		−	3.58678i		−	0.151841i
$559$	1.49548			0.0632522
$560$	−7.70623	−	5.42214i	−0.325648	−	0.229127i
$561$	−70.2152			−2.96449
$562$		−	3.28247i		−	0.138463i
$563$		−	27.3234i		−	1.15154i	−0.817611	−	0.575771i	$-0.804702\pi$
$563$		−	27.3234i		−	1.15154i	0.817611	−	0.575771i	$-0.195298\pi$
$564$	−24.0633			−1.01325
$565$	13.3282	+	9.37781i	0.560723	+	0.394527i
$566$	−2.66068			−0.111837
$567$			7.60171i			0.319242i
$568$			1.24657i			0.0523049i
$569$	0.803952			0.0337034			0.0168517	−	0.999858i	$-0.494636\pi$
$569$	0.803952			0.0337034			0.0168517	+	0.999858i	$0.494636\pi$
$570$	3.60790	−	5.12775i	0.151119	−	0.214778i
$571$	43.4604			1.81876			0.909381	−	0.415964i	$-0.136556\pi$
$571$	43.4604			1.81876			0.909381	+	0.415964i	$0.136556\pi$
$572$		−	34.5315i		−	1.44384i
$573$		−	25.9523i		−	1.08417i
$574$		0			0
$575$	−3.67116	+	1.31730i	−0.153098	+	0.0549353i
$576$	−26.5009			−1.10420
$577$			1.27345i			0.0530146i	0.999649	+	0.0265073i	$0.00843852\pi$
$577$			1.27345i			0.0530146i	−0.999649	+	0.0265073i	$0.991561\pi$
$578$		−	3.40311i		−	0.141551i
$579$	58.6073			2.43564
$580$	2.54181	−	3.61256i	0.105543	−	0.150003i
$581$	6.80395			0.282276
$582$		−	7.00145i		−	0.290220i
$583$			49.6812i			2.05758i
$584$	−5.43644			−0.224961
$585$	−25.9508	−	18.2591i	−1.07294	−	0.754922i
$586$	1.48560			0.0613696
$587$		−	31.8678i		−	1.31533i	−0.753312	−	0.657663i	$-0.771545\pi$
$587$		−	31.8678i		−	1.31533i	0.753312	−	0.657663i	$-0.228455\pi$
$588$			29.3954i			1.21225i
$589$	−44.6565			−1.84004
$590$	−2.86721	−	2.01738i	−0.118041	−	0.0830543i
$591$	−56.5875			−2.32770
$592$			4.21392i			0.173191i
$593$			1.21043i			0.0497064i	0.999691	+	0.0248532i	$0.00791183\pi$
$593$			1.21043i			0.0497064i	−0.999691	+	0.0248532i	$0.992088\pi$
$594$	−1.01470			−0.0416337
$595$	−8.75479	+	12.4428i	−0.358911	+	0.510104i
$596$	8.93735			0.366088
$597$		−	13.3220i		−	0.545233i
$598$			0.485676i			0.0198608i
$599$	−24.2053			−0.989003			−0.494501	−	0.869177i	$-0.664649\pi$
$599$	−24.2053			−0.989003			−0.494501	+	0.869177i	$0.664649\pi$
$600$	2.69858	+	7.52062i	0.110169	+	0.307028i
$601$	4.68586			0.191140			0.0955702	−	0.995423i	$-0.469533\pi$
$601$	4.68586			0.191140			0.0955702	+	0.995423i	$0.469533\pi$
$602$		−	0.0645730i		−	0.00263180i
$603$		−	21.1112i		−	0.859716i
$604$	5.53898			0.225378
$605$	10.7794	−	15.3202i	0.438244	−	0.622855i
$606$	5.12712			0.208275
$607$		−	0.502641i		−	0.0204016i	−0.999948	−	0.0102008i	$-0.996753\pi$
$607$		−	0.502641i		−	0.0204016i	0.999948	−	0.0102008i	$-0.00324707\pi$
$608$		−	12.9093i		−	0.523540i
$609$	2.80395			0.113622
$610$	−0.328836	−	0.231371i	−0.0133142	−	0.00936792i
$611$	−18.8672			−0.763286
$612$			43.9170i			1.77524i
$613$		−	22.9142i		−	0.925496i	−0.886490	−	0.462748i	$-0.846863\pi$
$613$		−	22.9142i		−	0.925496i	0.886490	−	0.462748i	$-0.153137\pi$
$614$	3.03868			0.122631
$615$		0			0
$616$	−3.00060			−0.120898
$617$		−	15.8574i		−	0.638397i	−0.947688	−	0.319198i	$-0.896586\pi$
$617$		−	15.8574i		−	0.638397i	0.947688	−	0.319198i	$-0.103414\pi$
$618$			2.07204i			0.0833496i
$619$	35.4014			1.42290			0.711451	−	0.702736i	$-0.248039\pi$
$619$	35.4014			1.42290			0.711451	+	0.702736i	$0.248039\pi$
$620$	16.2726	−	23.1275i	0.653524	−	0.928823i
$621$	−1.14688			−0.0460229
$622$		−	1.45327i		−	0.0582707i
$623$		−	11.8156i		−	0.473383i
$624$	−39.2299			−1.57045
$625$	−19.2966	+	15.8947i	−0.771864	+	0.635788i
$626$	2.27846			0.0910658
$627$			78.7253i			3.14399i
$628$			9.82734i			0.392154i
$629$	6.80395			0.271291
$630$	−0.788405	+	1.12052i	−0.0314108	+	0.0446427i
$631$	44.7056			1.77970			0.889851	−	0.456250i	$-0.150808\pi$
$631$	44.7056			1.77970			0.889851	+	0.456250i	$0.150808\pi$
$632$			3.45852i			0.137573i
$633$			4.22318i			0.167856i
$634$	−3.51379			−0.139551
$635$	−32.4260	−	22.8150i	−1.28678	−	0.905388i
$636$	57.1610			2.26658
$637$			23.0480i			0.913194i
$638$		−	0.690163i		−	0.0273238i
$639$	−7.14688			−0.282726
$640$	8.89523	+	6.25872i	0.351615	+	0.247398i
$641$	10.0689			0.397699			0.198849	−	0.980030i	$-0.436280\pi$
$641$	10.0689			0.397699			0.198849	+	0.980030i	$0.436280\pi$
$642$		−	0.439617i		−	0.0173503i
$643$		−	13.9760i		−	0.551161i	−0.961278	−	0.275580i	$-0.911130\pi$
$643$		−	13.9760i		−	0.551161i	0.961278	−	0.275580i	$-0.0888700\pi$
$644$	−1.68526			−0.0664085
$645$	1.24238	−	1.76573i	0.0489186	−	0.0695256i
$646$	−6.80395			−0.267698
$647$			31.1607i			1.22505i	0.790450	+	0.612527i	$0.209847\pi$
$647$			31.1607i			1.22505i	−0.790450	+	0.612527i	$0.790153\pi$
$648$		−	4.33235i		−	0.170191i
$649$	44.0198			1.72793
$650$	1.05139	+	2.93010i	0.0412390	+	0.114928i
$651$	17.9508			0.703549
$652$		−	41.0127i		−	1.60618i
$653$			26.1129i			1.02188i	0.859617	+	0.510939i	$0.170702\pi$
$653$			26.1129i			1.02188i	−0.859617	+	0.510939i	$0.829298\pi$
$654$	6.16158			0.240937
$655$	9.41668	−	13.3835i	0.367940	−	0.522936i
$656$		0			0
$657$		−	31.1684i		−	1.21600i
$658$			0.814661i			0.0317588i
$659$	28.5974			1.11400			0.556999	−	0.830513i	$-0.311953\pi$
$659$	28.5974			1.11400			0.556999	+	0.830513i	$0.311953\pi$
$660$	−40.7717	−	28.6872i	−1.58704	−	1.11665i
$661$	−38.9994			−1.51690			−0.758450	−	0.651731i	$-0.774043\pi$
$661$	−38.9994			−1.51690			−0.758450	+	0.651731i	$0.774043\pi$
$662$			1.23731i			0.0480895i
$663$			63.3421i			2.46000i
$664$	−3.87770			−0.150484
$665$	13.9508	+	9.81587i	0.540990	+	0.380643i
$666$	0.612724			0.0237426
$667$		−	0.780070i		−	0.0302044i
$668$			43.2976i			1.67523i
$669$	24.2938			0.939251
$670$	−1.19183	+	1.69390i	−0.0460445	+	0.0654409i
$671$	5.04856			0.194897
$672$			5.18922i			0.200178i
$673$			38.6725i			1.49072i	0.666665	+	0.745358i	$0.267721\pi$
$673$			38.6725i			1.49072i	−0.666665	+	0.745358i	$0.732279\pi$
$674$	5.24100			0.201876
$675$	−6.91921	+	2.48278i	−0.266320	+	0.0955622i
$676$	−5.47090			−0.210419
$677$			28.4800i			1.09458i	0.836944	+	0.547288i	$0.184340\pi$
$677$			28.4800i			1.09458i	−0.836944	+	0.547288i	$0.815660\pi$
$678$		−	2.92966i		−	0.112513i
$679$	19.0486			0.731017
$680$	4.98951	−	7.09136i	0.191339	−	0.271941i
$681$	−14.6859			−0.562764
$682$		−	4.41841i		−	0.169190i
$683$		−	12.4159i		−	0.475081i	−0.971378	−	0.237540i	$-0.923659\pi$
$683$		−	12.4159i		−	0.475081i	0.971378	−	0.237540i	$-0.0763412\pi$
$684$	49.2398			1.88273
$685$	−17.9017	−	12.5957i	−0.683988	−	0.481257i
$686$	2.19544			0.0838224
$687$		−	38.8347i		−	1.48164i
$688$		−	1.45106i		−	0.0553211i
$689$	44.8180			1.70743
$690$	0.573442	+	0.403477i	0.0218306	+	0.0153601i
$691$	10.8040			0.411002			0.205501	−	0.978657i	$-0.434118\pi$
$691$	10.8040			0.411002			0.205501	+	0.978657i	$0.434118\pi$
$692$			6.42808i			0.244359i
$693$		−	17.2032i		−	0.653495i
$694$	4.87709			0.185132
$695$	3.54465	−	5.03784i	0.134456	−	0.191096i
$696$	−1.59802			−0.0605729
$697$		0			0
$698$			0.904568i			0.0342384i
$699$	−1.83842			−0.0695352
$700$	−10.1673	+	3.64825i	−0.384286	+	0.137891i
$701$	8.47512			0.320101			0.160050	−	0.987109i	$-0.448834\pi$
$701$	8.47512			0.320101			0.160050	+	0.987109i	$0.448834\pi$
$702$			0.915375i			0.0345486i
$703$		−	7.62859i		−	0.287718i
$704$	−32.6454			−1.23037
$705$	−15.6740	+	22.2767i	−0.590317	+	0.838990i
$706$	2.11809			0.0797153
$707$			13.9491i			0.524612i
$708$		−	50.6472i		−	1.90344i
$709$	32.8180			1.23251			0.616254	−	0.787548i	$-0.288650\pi$
$709$	32.8180			1.23251			0.616254	+	0.787548i	$0.288650\pi$
$710$	0.573442	+	0.403477i	0.0215209	+	0.0151422i
$711$	−19.8285			−0.743628
$712$			6.73394i			0.252365i
$713$		−	4.99399i		−	0.187026i
$714$	2.73503			0.102356
$715$	−31.9678	−	22.4927i	−1.19553	−	0.841178i
$716$	14.2152			0.531247
$717$			5.12775i			0.191499i
$718$			0.181363i			0.00676842i
$719$	−39.7542			−1.48258			−0.741290	−	0.671184i	$-0.765786\pi$
$719$	−39.7542			−1.48258			−0.741290	+	0.671184i	$0.765786\pi$
$720$	−17.7167	+	25.1799i	−0.660263	+	0.938401i
$721$	−5.63731			−0.209944
$722$			4.64968i			0.173043i
$723$			44.4274i			1.65227i
$724$	25.7485			0.956936
$725$	−1.68870	−	4.70620i	−0.0627166	−	0.174784i
$726$	−3.36751			−0.124980
$727$		−	49.4844i		−	1.83527i	−0.397419	−	0.917637i	$-0.630094\pi$
$727$		−	49.4844i		−	1.83527i	0.397419	−	0.917637i	$-0.369906\pi$
$728$			2.70689i			0.100324i
$729$	36.1469			1.33877
$730$	−1.75961	+	2.50085i	−0.0651260	+	0.0925606i
$731$	−2.34293			−0.0866565
$732$		−	5.80865i		−	0.214694i
$733$		−	46.2381i		−	1.70784i	−0.520403	−	0.853921i	$-0.674218\pi$
$733$		−	46.2381i		−	1.70784i	0.520403	−	0.853921i	$-0.325782\pi$
$734$	−1.66128			−0.0613191
$735$	27.2130	+	19.1472i	1.00377	+	0.706254i
$736$	1.44366			0.0532140
$737$		−	26.0061i		−	0.957946i
$738$		0			0
$739$	−28.7155			−1.05632			−0.528159	−	0.849146i	$-0.677117\pi$
$739$	−28.7155			−1.05632			−0.528159	+	0.849146i	$0.677117\pi$
$740$	3.95084	+	2.77983i	0.145236	+	0.102188i
$741$	71.0192			2.60895
$742$		−	1.93518i		−	0.0710428i
$743$			27.0536i			0.992502i	0.868179	+	0.496251i	$0.165290\pi$
$743$			27.0536i			0.992502i	−0.868179	+	0.496251i	$0.834710\pi$
$744$	−10.2305			−0.375069
$745$	5.82149	−	8.27380i	0.213283	−	0.303129i
$746$	1.11303			0.0407508
$747$		−	22.2318i		−	0.813418i
$748$			54.0996i			1.97808i
$749$	1.19605			0.0437026
$750$	4.33305	+	1.19280i	0.158221	+	0.0435550i
$751$	−26.8771			−0.980759			−0.490380	−	0.871509i	$-0.663142\pi$
$751$	−26.8771			−0.980759			−0.490380	+	0.871509i	$0.663142\pi$
$752$			18.3067i			0.667578i
$753$			66.6860i			2.43017i
$754$	−0.622605			−0.0226739
$755$	3.60790	−	5.12775i	0.131305	−	0.186618i
$756$	−3.17629			−0.115520
$757$			7.28814i			0.264892i	0.991190	+	0.132446i	$0.0422831\pi$
$757$			7.28814i			0.264892i	−0.991190	+	0.132446i	$0.957717\pi$
$758$		−	2.84130i		−	0.103201i
$759$	−8.80395			−0.319563
$760$	−7.95084	−	5.59425i	−0.288407	−	0.202925i
$761$	−31.6079			−1.14579			−0.572893	−	0.819630i	$-0.694179\pi$
$761$	−31.6079			−1.14579			−0.572893	+	0.819630i	$0.694179\pi$
$762$			7.12750i			0.258202i
$763$			16.7636i			0.606882i
$764$	−19.9958			−0.723422
$765$	40.6565	+	28.6061i	1.46994	+	1.03425i
$766$	0.514398			0.0185860
$767$		−	39.7108i		−	1.43387i
$768$			36.0725i			1.30165i
$769$	0.293769			0.0105936			0.00529679	−	0.999986i	$-0.498314\pi$
$769$	0.293769			0.0105936			0.00529679	+	0.999986i	$0.498314\pi$
$770$	−0.971204	+	1.38033i	−0.0349997	+	0.0497435i
$771$	−38.5440			−1.38813
$772$		−	45.1559i		−	1.62520i
$773$			28.4877i			1.02463i	0.858797	+	0.512316i	$0.171212\pi$
$773$			28.4877i			1.02463i	−0.858797	+	0.512316i	$0.828788\pi$
$774$	−0.210991			−0.00758391
$775$	−10.8110	−	30.1290i	−0.388343	−	1.08226i
$776$	−10.8561			−0.389712
$777$			3.06651i			0.110011i
$778$			1.88142i			0.0674521i
$779$		0			0
$780$	−25.8791	+	36.7807i	−0.926620	+	1.31696i
$781$	−8.80395			−0.315030
$782$		−	0.760895i		−	0.0272095i
$783$		−	1.47023i		−	0.0525418i
$784$	22.3633			0.798689
$785$	9.09772	+	6.40120i	0.324712	+	0.228469i
$786$	−2.94180			−0.104931
$787$			32.9883i			1.17591i	0.808895	+	0.587954i	$0.200066\pi$
$787$			32.9883i			1.17591i	−0.808895	+	0.587954i	$0.799934\pi$
$788$			43.5997i			1.55317i
$789$	−30.9361			−1.10136
$790$	1.59098	+	1.11942i	0.0566044	+	0.0398271i
$791$	7.97060			0.283402
$792$			9.80441i			0.348384i
$793$		−	4.55437i		−	0.161731i
$794$	−5.69213			−0.202006
$795$	37.2327	−	52.9171i	1.32051	−	1.87678i
$796$	−10.2644			−0.363811
$797$			30.9194i			1.09522i	0.836733	+	0.547611i	$0.184463\pi$
$797$			30.9194i			1.09522i	−0.836733	+	0.547611i	$0.815537\pi$
$798$		−	3.06651i		−	0.108553i
$799$	29.5587			1.04571
$800$	8.70967	−	3.12524i	0.307933	−	0.110494i
$801$	−38.6073			−1.36412
$802$			4.08942i			0.144402i
$803$		−	38.3951i		−	1.35493i
$804$	−29.9214			−1.05525
$805$	−1.09772	+	1.56014i	−0.0386896	+	0.0549877i
$806$	−3.98590			−0.140397
$807$			27.8260i			0.979522i
$808$		−	7.94987i		−	0.279675i
$809$	−21.0977			−0.741756			−0.370878	−	0.928682i	$-0.620943\pi$
$809$	−21.0977			−0.741756			−0.370878	+	0.928682i	$0.620943\pi$
$810$	−1.99295	−	1.40225i	−0.0700252	−	0.0492700i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		−	2.16040i		−	0.0758150i
$813$		−	32.6763i		−	1.14601i
$814$	0.754790			0.0264554
$815$	−37.9678	−	26.7143i	−1.32995	−	0.935761i
$816$	61.4604			2.15154
$817$			2.62690i			0.0919035i
$818$		−	2.04582i		−	0.0715303i
$819$	−15.5192			−0.542285
$820$		0			0
$821$	−15.2791			−0.533243			−0.266622	−	0.963801i	$-0.585907\pi$
$821$	−15.2791			−0.533243			−0.266622	+	0.963801i	$0.585907\pi$
$822$			3.93494i			0.137247i
$823$			7.78152i			0.271247i	0.990760	+	0.135623i	$0.0433037\pi$
$823$			7.78152i			0.271247i	−0.990760	+	0.135623i	$0.956696\pi$
$824$	3.21280			0.111923
$825$	−53.1147	+	19.0588i	−1.84921	+	0.663543i
$826$	−1.71466			−0.0596607
$827$		−	0.376593i		−	0.0130954i	−0.999979	−	0.00654772i	$-0.997916\pi$
$827$		−	0.376593i		−	0.0130954i	0.999979	−	0.00654772i	$-0.00208422\pi$
$828$			5.50655i			0.191366i
$829$	49.8723			1.73214			0.866068	−	0.499927i	$-0.166640\pi$
$829$	49.8723			1.73214			0.866068	+	0.499927i	$0.166640\pi$
$830$	−1.25509	+	1.78380i	−0.0435649	+	0.0619167i
$831$	51.4604			1.78514
$832$			29.4498i			1.02099i
$833$		−	36.1086i		−	1.25109i
$834$	−1.10736			−0.0383447
$835$	40.0830	+	28.2026i	1.38713	+	0.975991i
$836$	60.6565			2.09785
$837$		−	9.41240i		−	0.325340i
$838$		−	5.62113i		−	0.194179i
$839$	0.0590441			0.00203843			0.00101921	−	0.999999i	$-0.499676\pi$
$839$	0.0590441			0.00203843			0.00101921	+	0.999999i	$0.499676\pi$
$840$	3.19605	+	2.24875i	0.110274	+	0.0775894i
$841$	1.00000			0.0344828
$842$			2.61919i			0.0902632i
$843$		−	53.6776i		−	1.84875i
$844$	3.25388			0.112003
$845$	−3.56356	+	5.06472i	−0.122590	+	0.174232i
$846$	2.66189			0.0915176
$847$		−	9.16185i		−	0.314805i
$848$		−	43.4867i		−	1.49334i
$849$	−43.5096			−1.49324
$850$	−1.64719	−	4.59051i	−0.0564980	−	0.157453i
$851$	0.853115			0.0292444
$852$			10.1294i			0.347029i
$853$		−	2.77983i		−	0.0951795i	−0.998867	−	0.0475897i	$-0.984846\pi$
$853$		−	2.77983i		−	0.0951795i	0.998867	−	0.0475897i	$-0.0151540\pi$
$854$	−0.196652			−0.00672929
$855$	32.0731	−	45.5840i	1.09688	−	1.55894i
$856$	−0.681649			−0.0232983
$857$			0.850802i			0.0290628i	0.999894	+	0.0145314i	$0.00462566\pi$
$857$			0.850802i			0.0290628i	−0.999894	+	0.0145314i	$0.995374\pi$
$858$			7.02679i			0.239891i
$859$	−7.35342			−0.250895			−0.125448	−	0.992100i	$-0.540037\pi$
$859$	−7.35342			−0.250895			−0.125448	+	0.992100i	$0.540037\pi$
$860$	−1.36047	−	0.957230i	−0.0463915	−	0.0326413i
$861$		0			0
$862$		−	4.12556i		−	0.140517i
$863$		−	42.6167i		−	1.45069i	−0.688386	−	0.725345i	$-0.741680\pi$
$863$		−	42.6167i		−	1.45069i	0.688386	−	0.725345i	$-0.258320\pi$
$864$	2.72093			0.0925680
$865$	5.95084	+	4.18704i	0.202335	+	0.142364i
$866$	−1.68105			−0.0571242
$867$		−	55.6505i		−	1.88999i
$868$		−	13.8308i		−	0.469448i
$869$	−24.4260			−0.828594
$870$	−0.517231	+	0.735116i	−0.0175358	+	0.0249228i
$871$	−23.4604			−0.794926
$872$		−	9.55386i		−	0.323535i
$873$		−	62.2407i		−	2.10653i
$874$	−0.853115			−0.0288571
$875$	−3.24521	+	11.7887i	−0.109708	+	0.398532i
$876$	−44.1757			−1.49256
$877$			13.4196i			0.453148i	0.973994	+	0.226574i	$0.0727526\pi$
$877$			13.4196i			0.453148i	−0.973994	+	0.226574i	$0.927247\pi$
$878$		−	4.63436i		−	0.156402i
$879$	24.2938			0.819408
$880$	−21.8245	+	31.0181i	−0.735703	+	1.04562i
$881$	−38.3135			−1.29082			−0.645408	−	0.763838i	$-0.723313\pi$
$881$	−38.3135			−1.29082			−0.645408	+	0.763838i	$0.723313\pi$
$882$		−	3.25173i		−	0.109491i
$883$			31.5542i			1.06188i	0.847408	+	0.530942i	$0.178162\pi$
$883$			31.5542i			1.06188i	−0.847408	+	0.530942i	$0.821838\pi$
$884$	48.8040			1.64145
$885$	−46.8870	−	32.9899i	−1.57609	−	1.10894i
$886$	0.534161			0.0179455
$887$			23.3961i			0.785565i	0.919631	+	0.392783i	$0.128488\pi$
$887$			23.3961i			0.785565i	−0.919631	+	0.392783i	$0.871512\pi$
$888$		−	1.74766i		−	0.0586477i
$889$	−19.3915			−0.650370
$890$	3.09772	+	2.17957i	0.103836	+	0.0730594i
$891$	30.5974			1.02505
$892$		−	18.7179i		−	0.626722i
$893$		−	33.1413i		−	1.10903i
$894$	−1.81865			−0.0608248
$895$	9.25931	−	13.1598i	0.309504	−	0.439884i
$896$	5.31956			0.177714
$897$			7.94216i			0.265181i
$898$		−	0.0722810i		−	0.00241205i
$899$	6.40198			0.213518
$900$	11.9206	+	33.2213i	0.397353	+	1.10738i
$901$	−70.2152			−2.33921
$902$		0			0
$903$		−	1.05595i		−	0.0351398i
$904$	−4.54259			−0.151084
$905$	16.7717	−	23.8369i	0.557511	−	0.792364i
$906$	−1.12712			−0.0374461
$907$			32.4150i			1.07632i	0.842842	+	0.538161i	$0.180881\pi$
$907$			32.4150i			1.07632i	−0.842842	+	0.538161i	$0.819119\pi$
$908$			11.3152i			0.375508i
$909$	45.5785			1.51174
$910$	1.24521	+	0.876136i	0.0412783	+	0.0290436i
$911$	−45.2749			−1.50002			−0.750011	−	0.661425i	$-0.769952\pi$
$911$	−45.2749			−1.50002			−0.750011	+	0.661425i	$0.769952\pi$
$912$		−	68.9094i		−	2.28182i
$913$		−	27.3864i		−	0.906357i
$914$	0.215206			0.00711837
$915$	−5.37739	−	3.78356i	−0.177771	−	0.125081i
$916$	−29.9214			−0.988632
$917$		−	8.00364i		−	0.264303i
$918$		−	1.43409i		−	0.0473321i
$919$	5.90167			0.194678			0.0973391	−	0.995251i	$-0.468967\pi$
$919$	5.90167			0.194678			0.0973391	+	0.995251i	$0.468967\pi$
$920$	0.625612	−	0.889152i	0.0206258	−	0.0293145i
$921$	49.6909			1.63737
$922$			2.28710i			0.0753218i
$923$			7.94216i			0.261419i
$924$	−24.3825			−0.802124
$925$	5.14688	−	1.84683i	0.169229	−	0.0607233i
$926$	2.95566			0.0971289
$927$			18.4198i			0.604985i
$928$			1.85068i			0.0607516i
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$	−3.31130	+	4.70620i	−0.108582	+	0.154322i
$931$	−40.4850			−1.32684
$932$			1.41647i			0.0463979i
$933$		−	23.7650i		−	0.778032i
$934$	4.69695			0.153689
$935$	50.0830	+	35.2386i	1.63789	+	1.15243i
$936$	8.84469			0.289098
$937$			43.0755i			1.40721i	0.710589	+	0.703607i	$0.248429\pi$
$937$			43.0755i			1.40721i	−0.710589	+	0.703607i	$0.751571\pi$
$938$			1.01299i			0.0330753i
$939$	37.2593			1.21591
$940$	17.1638	+	12.0765i	0.559822	+	0.393893i
$941$	2.91637			0.0950711			0.0475355	−	0.998870i	$-0.484863\pi$
$941$	2.91637			0.0950711			0.0475355	+	0.998870i	$0.484863\pi$
$942$		−	1.99976i		−	0.0651556i
$943$		0			0
$944$	−38.5312			−1.25408
$945$	−2.06893	+	2.94047i	−0.0673021	+	0.0956534i
$946$	−0.259911			−0.00845043
$947$			0.556407i			0.0180808i	0.999959	+	0.00904041i	$0.00287769\pi$
$947$			0.556407i			0.0180808i	−0.999959	+	0.00904041i	$0.997122\pi$
$948$			28.1034i			0.912757i
$949$	−34.6367			−1.12435
$950$	−5.14688	+	1.84683i	−0.166987	+	0.0599190i
$951$	−57.4604			−1.86328
$952$		−	4.24080i		−	0.137445i
$953$			37.1661i			1.20393i	0.798523	+	0.601964i	$0.205615\pi$
$953$			37.1661i			1.20393i	−0.798523	+	0.601964i	$0.794385\pi$
$954$	−6.32317			−0.204720
$955$	−13.0246	+	18.5112i	−0.421466	+	0.599009i
$956$	3.95084			0.127779
$957$		−	11.2861i		−	0.364828i
$958$			5.13700i			0.165969i
$959$	−10.7056			−0.345703
$960$	34.7717	+	24.4655i	1.12225	+	0.789622i
$961$	9.98530			0.322106
$962$		−	0.680906i		−	0.0219533i
$963$		−	3.90806i		−	0.125935i
$964$	34.2305			1.10249
$965$	−41.8033	−	29.4130i	−1.34570	−	0.946839i
$966$	0.342932			0.0110337
$967$		−	24.2754i		−	0.780643i	−0.920679	−	0.390322i	$-0.872364\pi$
$967$		−	24.2754i		−	0.780643i	0.920679	−	0.390322i	$-0.127636\pi$
$968$			5.22151i			0.167826i
$969$	−111.264			−3.57431
$970$	−3.51379	+	4.99399i	−0.112821	+	0.160347i
$971$	−17.1709			−0.551039			−0.275520	−	0.961295i	$-0.588850\pi$
$971$	−17.1709			−0.551039			−0.275520	+	0.961295i	$0.588850\pi$
$972$		−	43.9170i		−	1.40864i
$973$		−	3.01275i		−	0.0965842i
$974$	−2.21220			−0.0708834
$975$	17.1932	+	47.9154i	0.550624	+	1.53452i
$976$	−4.41908			−0.141451
$977$		−	4.95785i		−	0.158616i	−0.996850	−	0.0793078i	$-0.974729\pi$
$977$		−	4.95785i		−	0.158616i	0.996850	−	0.0793078i	$-0.0252710\pi$
$978$			8.34564i			0.266864i
$979$	−47.5587			−1.51998
$980$	14.7526	−	20.9671i	0.471253	−	0.669770i
$981$	54.7746			1.74882
$982$			0.644104i			0.0205542i
$983$			11.5651i			0.368869i	0.982845	+	0.184434i	$0.0590453\pi$
$983$			11.5651i			0.368869i	−0.982845	+	0.184434i	$0.940955\pi$
$984$		0			0
$985$	40.3627	+	28.3994i	1.28606	+	0.904879i
$986$	0.975419			0.0310637
$987$			13.3220i			0.424044i
$988$		−	54.7190i		−	1.74084i
$989$	−0.293769			−0.00934132
$990$	4.51018	+	3.17339i	0.143343	+	0.100857i
$991$	−18.3429			−0.582682			−0.291341	−	0.956619i	$-0.594102\pi$
$991$	−18.3429			−0.582682			−0.291341	+	0.956619i	$0.594102\pi$
$992$			11.8480i			0.376175i
$993$			20.2336i			0.642092i
$994$	0.342932			0.0108771
$995$	−6.68586	+	9.50230i	−0.211956	+	0.301243i
$996$	−31.5096			−0.998419
$997$			32.2997i			1.02294i	0.859300	+	0.511471i	$0.170899\pi$
$997$			32.2997i			1.02294i	−0.859300	+	0.511471i	$0.829101\pi$
$998$		−	4.71435i		−	0.149230i
$999$	1.60790			0.0508719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.b.c.59.4	yes	6
3.2	odd	2		1305.2.c.h.784.3		6
4.3	odd	2		2320.2.d.g.929.2		6
5.2	odd	4		725.2.a.l.1.3		6
5.3	odd	4		725.2.a.l.1.4		6
5.4	even	2	inner	145.2.b.c.59.3	✓	6
15.2	even	4		6525.2.a.bt.1.4		6
15.8	even	4		6525.2.a.bt.1.3		6
15.14	odd	2		1305.2.c.h.784.4		6
20.19	odd	2		2320.2.d.g.929.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.c.59.3	✓	6	5.4	even	2	inner
145.2.b.c.59.4	yes	6	1.1	even	1	trivial
725.2.a.l.1.3		6	5.2	odd	4
725.2.a.l.1.4		6	5.3	odd	4
1305.2.c.h.784.3		6	3.2	odd	2
1305.2.c.h.784.4		6	15.14	odd	2
2320.2.d.g.929.2		6	4.3	odd	2
2320.2.d.g.929.5		6	20.19	odd	2
6525.2.a.bt.1.3		6	15.8	even	4
6525.2.a.bt.1.4		6	15.2	even	4

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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.156785i q^{2} +2.56387i q^{3} +1.97542 q^{4} +(1.28672 - 1.82876i) q^{5} -0.401976 q^{6} -1.09364i q^{7} +0.623285i q^{8} -3.57344 q^{9} +(0.286721 + 0.201738i) q^{10} -4.40198 q^{11} +5.06472i q^{12} +3.97108i q^{13} +0.171466 q^{14} +(4.68870 + 3.29899i) q^{15} +3.85312 q^{16} -6.22138i q^{17} -0.560261i q^{18} -6.97542 q^{19} +(2.54181 - 3.61256i) q^{20} +2.80395 q^{21} -0.690163i q^{22} -0.780070i q^{23} -1.59802 q^{24} +(-1.68870 - 4.70620i) q^{25} -0.622605 q^{26} -1.47023i q^{27} -2.16040i q^{28} +1.00000 q^{29} +(-0.517231 + 0.735116i) q^{30} +6.40198 q^{31} +1.85068i q^{32} -11.2861i q^{33} +0.975419 q^{34} +(-2.00000 - 1.40721i) q^{35} -7.05904 q^{36} +1.09364i q^{37} -1.09364i q^{38} -10.1813 q^{39} +(1.13984 + 0.801994i) q^{40} +0.439617i q^{42} -0.376593i q^{43} -8.69575 q^{44} +(-4.59802 + 6.53495i) q^{45} +0.122303 q^{46} +4.75115i q^{47} +9.87890i q^{48} +5.80395 q^{49} +(0.737860 - 0.264762i) q^{50} +15.9508 q^{51} +7.84455i q^{52} -11.2861i q^{53} +0.230510 q^{54} +(-5.66412 + 8.05014i) q^{55} +0.681649 q^{56} -17.8841i q^{57} +0.156785i q^{58} -10.0000 q^{59} +(9.26214 + 6.51688i) q^{60} -1.14688 q^{61} +1.00373i q^{62} +3.90806i q^{63} +7.41607 q^{64} +(7.26214 + 5.10967i) q^{65} +1.76949 q^{66} +5.90782i q^{67} -12.2898i q^{68} +2.00000 q^{69} +(0.220629 - 0.313570i) q^{70} +2.00000 q^{71} -2.22727i q^{72} +8.72223i q^{73} -0.171466 q^{74} +(12.0661 - 4.32960i) q^{75} -13.7794 q^{76} +4.81418i q^{77} -1.59628i q^{78} +5.54886 q^{79} +(4.95789 - 7.04641i) q^{80} -6.95084 q^{81} +6.22138i q^{83} +5.53898 q^{84} +(-11.3774 - 8.00519i) q^{85} +0.0590441 q^{86} +2.56387i q^{87} -2.74369i q^{88} +10.8040 q^{89} +(-1.02458 - 0.720900i) q^{90} +4.34293 q^{91} -1.54096i q^{92} +16.4139i q^{93} -0.744908 q^{94} +(-8.97542 + 12.7563i) q^{95} -4.74491 q^{96} +17.4176i q^{97} +0.909972i q^{98} +15.7302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 14 q^{4} + 3 q^{5} + 14 q^{6} - 12 q^{9} - 3 q^{10} - 10 q^{11} + 8 q^{14} + 7 q^{15} + 42 q^{16} - 16 q^{19} + 13 q^{20} - 16 q^{21} - 26 q^{24} + 11 q^{25} - 46 q^{26} + 6 q^{29} + 25 q^{30} + 22 q^{31}+ \cdots - 16 q^{99}+O(q^{100}) \) 6 * q - 14 * q^4 + 3 * q^5 + 14 * q^6 - 12 * q^9 - 3 * q^10 - 10 * q^11 + 8 * q^14 + 7 * q^15 + 42 * q^16 - 16 * q^19 + 13 * q^20 - 16 * q^21 - 26 * q^24 + 11 * q^25 - 46 * q^26 + 6 * q^29 + 25 * q^30 + 22 * q^31 - 20 * q^34 - 12 * q^35 - 12 * q^36 + 14 * q^39 + 21 * q^40 + 2 * q^44 - 44 * q^45 - 44 * q^46 + 2 * q^49 + 35 * q^50 + 44 * q^51 - 22 * q^54 + 13 * q^55 + 16 * q^56 - 60 * q^59 + 25 * q^60 + 12 * q^61 - 38 * q^64 + 13 * q^65 + 34 * q^66 + 12 * q^69 + 60 * q^70 + 12 * q^71 - 8 * q^74 + 9 * q^75 - 24 * q^76 - 2 * q^79 - 55 * q^80 + 10 * q^81 + 80 * q^84 - 26 * q^85 - 30 * q^86 + 32 * q^89 - 32 * q^90 + 40 * q^91 - 2 * q^94 - 28 * q^95 - 26 * q^96 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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