LMFDB - Embedded newform 400.2.u.f.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 24 x^{9} + 93 x^{8} - 6 x^{7} + 342 x^{6} + 786 x^{5} + 1473 x^{4} + \cdots + 16 $ x^12 - 3x^11 + 13x^10 - 24x^9 + 93x^8 - 6x^7 + 342x^6 + 786x^5 + 1473x^4 + 84x^3 + 688x^2 + 168*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			161.3
Root			$-1.25005 + 0.908212i$ of defining polynomial
Character	$\chi$	$=$	400.161
Dual form			400.2.u.f.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.477475 - 1.46952i) q^{3} +(1.08159 + 1.95708i) q^{5} +2.43270 q^{7} +(0.495552 + 0.360039i) q^{9} +O(q^{10})$	\(q+(0.477475 - 1.46952i) q^{3} +(1.08159 + 1.95708i) q^{5} +2.43270 q^{7} +(0.495552 + 0.360039i) q^{9} +(-2.41187 + 1.75233i) q^{11} +(2.27986 + 1.65642i) q^{13} +(3.39240 - 0.654955i) q^{15} +(-1.89061 - 5.81868i) q^{17} +(1.61119 + 4.95872i) q^{19} +(1.16155 - 3.57489i) q^{21} +(-1.19552 + 0.868599i) q^{23} +(-2.66033 + 4.23351i) q^{25} +(4.51584 - 3.28095i) q^{27} +(2.72499 - 8.38665i) q^{29} +(-2.06767 - 6.36362i) q^{31} +(1.42347 + 4.38098i) q^{33} +(2.63118 + 4.76099i) q^{35} +(3.78784 + 2.75203i) q^{37} +(3.52271 - 2.55940i) q^{39} +(-2.92980 - 2.12862i) q^{41} -3.60984 q^{43} +(-0.168643 + 1.35925i) q^{45} +(1.69382 - 5.21306i) q^{47} -1.08197 q^{49} -9.45338 q^{51} +(0.366346 - 1.12750i) q^{53} +(-6.03810 - 2.82493i) q^{55} +8.05623 q^{57} +(-6.70876 - 4.87420i) q^{59} +(-12.2455 + 8.89689i) q^{61} +(1.20553 + 0.875867i) q^{63} +(-0.775870 + 6.25343i) q^{65} +(4.56011 + 14.0346i) q^{67} +(0.705588 + 2.17158i) q^{69} +(-1.80837 + 5.56558i) q^{71} +(-4.84077 + 3.51703i) q^{73} +(4.95098 + 5.93080i) q^{75} +(-5.86736 + 4.26289i) q^{77} +(3.75202 - 11.5475i) q^{79} +(-2.09736 - 6.45500i) q^{81} +(3.78995 + 11.6643i) q^{83} +(9.34278 - 9.99349i) q^{85} +(-11.0232 - 8.00884i) q^{87} +(-2.12213 + 1.54182i) q^{89} +(5.54622 + 4.02956i) q^{91} -10.3387 q^{93} +(-7.96198 + 8.51652i) q^{95} +(2.93972 - 9.04752i) q^{97} -1.82612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9	$ 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9} + 5 q^{11} - 2 q^{13} - 18 q^{15} + q^{17} + 8 q^{19} + 2 q^{21} + 6 q^{23} - 26 q^{25} + 34 q^{27} - 18 q^{29} - 12 q^{31} - 35 q^{33} + 3 q^{35} + 13 q^{37} - 22 q^{39} - 23 q^{41} - 50 q^{43} + 71 q^{45} - q^{47} + 34 q^{49} - 14 q^{51} + 21 q^{53} - 5 q^{55} + 72 q^{57} - 9 q^{59} - 26 q^{61} + 32 q^{63} - 18 q^{65} + 37 q^{67} - 44 q^{69} - 21 q^{71} + 18 q^{73} + 73 q^{75} - 60 q^{77} + 24 q^{79} + 18 q^{81} + 46 q^{83} - 16 q^{85} - 57 q^{87} - 2 q^{89} + 32 q^{91} + 22 q^{93} - 6 q^{95} - 7 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9 + 5 * q^11 - 2 * q^13 - 18 * q^15 + q^17 + 8 * q^19 + 2 * q^21 + 6 * q^23 - 26 * q^25 + 34 * q^27 - 18 * q^29 - 12 * q^31 - 35 * q^33 + 3 * q^35 + 13 * q^37 - 22 * q^39 - 23 * q^41 - 50 * q^43 + 71 * q^45 - q^47 + 34 * q^49 - 14 * q^51 + 21 * q^53 - 5 * q^55 + 72 * q^57 - 9 * q^59 - 26 * q^61 + 32 * q^63 - 18 * q^65 + 37 * q^67 - 44 * q^69 - 21 * q^71 + 18 * q^73 + 73 * q^75 - 60 * q^77 + 24 * q^79 + 18 * q^81 + 46 * q^83 - 16 * q^85 - 57 * q^87 - 2 * q^89 + 32 * q^91 + 22 * q^93 - 6 * q^95 - 7 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.477475	−	1.46952i	0.275670	−	0.848426i	−0.713371	−	0.700787i	$-0.752832\pi$
$3$	0.477475	−	1.46952i	0.275670	−	0.848426i	0.989041	−	0.147640i	$-0.0471676\pi$
$4$		0			0
$5$	1.08159	+	1.95708i	0.483701	+	0.875233i
$5$	1.08159	+	1.95708i	0.483701	+	0.875233i
$6$		0			0
$7$	2.43270			0.919474			0.459737	−	0.888055i	$-0.347944\pi$
$7$	2.43270			0.919474			0.459737	+	0.888055i	$0.347944\pi$
$8$		0			0
$9$	0.495552	+	0.360039i	0.165184	+	0.120013i
$10$		0			0
$11$	−2.41187	+	1.75233i	−0.727207	+	0.528347i	−0.888679	−	0.458530i	$-0.848376\pi$
$11$	−2.41187	+	1.75233i	−0.727207	+	0.528347i	0.161471	+	0.986877i	$0.448376\pi$
$12$		0			0
$13$	2.27986	+	1.65642i	0.632320	+	0.459407i	0.857203	−	0.514978i	$-0.172200\pi$
$13$	2.27986	+	1.65642i	0.632320	+	0.459407i	−0.224883	+	0.974386i	$0.572200\pi$
$14$		0			0
$15$	3.39240	−	0.654955i	0.875913	−	0.169109i
$16$		0			0
$17$	−1.89061	−	5.81868i	−0.458539	−	1.41124i	−0.866929	−	0.498431i	$-0.833910\pi$
$17$	−1.89061	−	5.81868i	−0.458539	−	1.41124i	0.408390	−	0.912807i	$-0.366090\pi$
$18$		0			0
$19$	1.61119	+	4.95872i	0.369632	+	1.13761i	0.947030	+	0.321146i	$0.104068\pi$
$19$	1.61119	+	4.95872i	0.369632	+	1.13761i	−0.577398	+	0.816463i	$0.695932\pi$
$20$		0			0
$21$	1.16155	−	3.57489i	0.253472	−	0.780106i
$22$		0			0
$23$	−1.19552	+	0.868599i	−0.249284	+	0.181115i	−0.705409	−	0.708800i	$-0.749237\pi$
$23$	−1.19552	+	0.868599i	−0.249284	+	0.181115i	0.456125	+	0.889915i	$0.349237\pi$
$24$		0			0
$25$	−2.66033	+	4.23351i	−0.532067	+	0.846702i
$26$		0			0
$27$	4.51584	−	3.28095i	0.869073	−	0.631419i
$28$		0			0
$29$	2.72499	−	8.38665i	0.506018	−	1.55736i	−0.293035	−	0.956102i	$-0.594665\pi$
$29$	2.72499	−	8.38665i	0.506018	−	1.55736i	0.799053	−	0.601261i	$-0.205335\pi$
$30$		0			0
$31$	−2.06767	−	6.36362i	−0.371364	−	1.14294i	−0.945899	−	0.324461i	$-0.894817\pi$
$31$	−2.06767	−	6.36362i	−0.371364	−	1.14294i	0.574535	−	0.818480i	$-0.305183\pi$
$32$		0			0
$33$	1.42347	+	4.38098i	0.247794	+	0.762631i
$34$		0			0
$35$	2.63118	+	4.76099i	0.444750	+	0.804754i
$36$		0			0
$37$	3.78784	+	2.75203i	0.622717	+	0.452431i	0.853870	−	0.520487i	$-0.174250\pi$
$37$	3.78784	+	2.75203i	0.622717	+	0.452431i	−0.231152	+	0.972918i	$0.574250\pi$
$38$		0			0
$39$	3.52271	−	2.55940i	0.564085	−	0.409832i
$40$		0			0
$41$	−2.92980	−	2.12862i	−0.457558	−	0.332435i	0.335015	−	0.942213i	$-0.391259\pi$
$41$	−2.92980	−	2.12862i	−0.457558	−	0.332435i	−0.792573	+	0.609778i	$0.791259\pi$
$42$		0			0
$43$	−3.60984			−0.550495			−0.275248	−	0.961373i	$-0.588760\pi$
$43$	−3.60984			−0.550495			−0.275248	+	0.961373i	$0.588760\pi$
$44$		0			0
$45$	−0.168643	+	1.35925i	−0.0251399	+	0.202625i
$46$		0			0
$47$	1.69382	−	5.21306i	0.247070	−	0.760403i	−0.748219	−	0.663451i	$-0.769091\pi$
$47$	1.69382	−	5.21306i	0.247070	−	0.760403i	0.995289	−	0.0969511i	$-0.0309091\pi$
$48$		0			0
$49$	−1.08197			−0.154568
$50$		0			0
$51$	−9.45338			−1.32374
$52$		0			0
$53$	0.366346	−	1.12750i	0.0503215	−	0.154874i	−0.922738	−	0.385428i	$-0.874054\pi$
$53$	0.366346	−	1.12750i	0.0503215	−	0.154874i	0.973059	+	0.230554i	$0.0740539\pi$
$54$		0			0
$55$	−6.03810	−	2.82493i	−0.814178	−	0.380914i
$56$		0			0
$57$	8.05623			1.06707
$58$		0			0
$59$	−6.70876	−	4.87420i	−0.873406	−	0.634567i	0.0580925	−	0.998311i	$-0.481498\pi$
$59$	−6.70876	−	4.87420i	−0.873406	−	0.634567i	−0.931499	+	0.363744i	$0.881498\pi$
$60$		0			0
$61$	−12.2455	+	8.89689i	−1.56788	+	1.13913i	−0.638724	+	0.769436i	$0.720537\pi$
$61$	−12.2455	+	8.89689i	−1.56788	+	1.13913i	−0.929154	+	0.369694i	$0.879463\pi$
$62$		0			0
$63$	1.20553	+	0.875867i	0.151882	+	0.110349i
$64$		0			0
$65$	−0.775870	+	6.25343i	−0.0962349	+	0.775643i
$66$		0			0
$67$	4.56011	+	14.0346i	0.557107	+	1.71460i	0.690314	+	0.723509i	$0.257472\pi$
$67$	4.56011	+	14.0346i	0.557107	+	1.71460i	−0.133208	+	0.991088i	$0.542528\pi$
$68$		0			0
$69$	0.705588	+	2.17158i	0.0849429	+	0.261427i
$70$		0			0
$71$	−1.80837	+	5.56558i	−0.214614	+	0.660513i	0.784567	+	0.620044i	$0.212885\pi$
$71$	−1.80837	+	5.56558i	−0.214614	+	0.660513i	−0.999181	+	0.0404693i	$0.987115\pi$
$72$		0			0
$73$	−4.84077	+	3.51703i	−0.566570	+	0.411637i	−0.833858	−	0.551980i	$-0.813873\pi$
$73$	−4.84077	+	3.51703i	−0.566570	+	0.411637i	0.267288	+	0.963617i	$0.413873\pi$
$74$		0			0
$75$	4.95098	+	5.93080i	0.571689	+	0.684830i
$76$		0			0
$77$	−5.86736	+	4.26289i	−0.668648	+	0.485801i
$78$		0			0
$79$	3.75202	−	11.5475i	0.422135	−	1.29920i	−0.483576	−	0.875302i	$-0.660662\pi$
$79$	3.75202	−	11.5475i	0.422135	−	1.29920i	0.905711	−	0.423896i	$-0.139338\pi$
$80$		0			0
$81$	−2.09736	−	6.45500i	−0.233040	−	0.717223i
$82$		0			0
$83$	3.78995	+	11.6643i	0.416001	+	1.28032i	0.911353	+	0.411626i	$0.135039\pi$
$83$	3.78995	+	11.6643i	0.416001	+	1.28032i	−0.495352	+	0.868692i	$0.664961\pi$
$84$		0			0
$85$	9.34278	−	9.99349i	1.01337	−	1.08395i
$86$		0			0
$87$	−11.0232	−	8.00884i	−1.18181	−	0.858638i
$88$		0			0
$89$	−2.12213	+	1.54182i	−0.224946	+	0.163433i	−0.694550	−	0.719444i	$-0.744397\pi$
$89$	−2.12213	+	1.54182i	−0.224946	+	0.163433i	0.469605	+	0.882877i	$0.344397\pi$
$90$		0			0
$91$	5.54622	+	4.02956i	0.581402	+	0.422413i
$92$		0			0
$93$	−10.3387			−1.07208
$94$		0			0
$95$	−7.96198	+	8.51652i	−0.816882	+	0.873776i
$96$		0			0
$97$	2.93972	−	9.04752i	0.298483	−	0.918636i	−0.683546	−	0.729907i	$-0.739563\pi$
$97$	2.93972	−	9.04752i	0.298483	−	0.918636i	0.982029	−	0.188729i	$-0.0604367\pi$
$98$		0			0
$99$	−1.82612			−0.183531
$100$		0			0
$101$	−1.44518			−0.143801			−0.0719004	−	0.997412i	$-0.522906\pi$
$101$	−1.44518			−0.143801			−0.0719004	+	0.997412i	$0.522906\pi$
$102$		0			0
$103$	−1.71543	+	5.27956i	−0.169027	+	0.520211i	−0.999310	−	0.0371303i	$-0.988178\pi$
$103$	−1.71543	+	5.27956i	−0.169027	+	0.520211i	0.830284	+	0.557341i	$0.188178\pi$
$104$		0			0
$105$	8.25268	−	1.59331i	0.805379	−	0.155491i
$106$		0			0
$107$	−7.44078			−0.719327			−0.359664	−	0.933082i	$-0.617109\pi$
$107$	−7.44078			−0.719327			−0.359664	+	0.933082i	$0.617109\pi$
$108$		0			0
$109$	−7.52018	−	5.46373i	−0.720302	−	0.523330i	0.166178	−	0.986096i	$-0.446857\pi$
$109$	−7.52018	−	5.46373i	−0.720302	−	0.523330i	−0.886481	+	0.462765i	$0.846857\pi$
$110$		0			0
$111$	5.85275	−	4.25227i	0.555519	−	0.403608i
$112$		0			0
$113$	−13.5068	−	9.81326i	−1.27061	−	0.923154i	−0.271385	−	0.962471i	$-0.587482\pi$
$113$	−13.5068	−	9.81326i	−1.27061	−	0.923154i	−0.999227	+	0.0393171i	$0.987482\pi$
$114$		0			0
$115$	−2.99298	−	1.40027i	−0.279097	−	0.130576i
$116$		0			0
$117$	0.533414	+	1.64168i	0.0493141	+	0.151773i
$118$		0			0
$119$	−4.59927	−	14.1551i	−0.421615	−	1.29760i
$120$		0			0
$121$	−0.652708	+	2.00883i	−0.0593371	+	0.182621i
$122$		0			0
$123$	−4.52696	+	3.28903i	−0.408182	+	0.296562i
$124$		0			0
$125$	−11.1627	−	0.627575i	−0.998423	−	0.0561320i
$126$		0			0
$127$	9.72353	−	7.06456i	0.862824	−	0.626878i	−0.0658279	−	0.997831i	$-0.520969\pi$
$127$	9.72353	−	7.06456i	0.862824	−	0.626878i	0.928652	+	0.370953i	$0.120969\pi$
$128$		0			0
$129$	−1.72361	+	5.30472i	−0.151755	+	0.467055i
$130$		0			0
$131$	−5.50078	−	16.9297i	−0.480605	−	1.47915i	−0.838247	−	0.545291i	$-0.816419\pi$
$131$	−5.50078	−	16.9297i	−0.480605	−	1.47915i	0.357641	−	0.933859i	$-0.383581\pi$
$132$		0			0
$133$	3.91953	+	12.0631i	0.339867	+	1.04600i
$134$		0			0
$135$	11.3054	+	5.28923i	0.973010	+	0.455224i
$136$		0			0
$137$	12.7004	+	9.22736i	1.08507	+	0.788347i	0.978559	−	0.205965i	$-0.0660334\pi$
$137$	12.7004	+	9.22736i	1.08507	+	0.788347i	0.106507	+	0.994312i	$0.466033\pi$
$138$		0			0
$139$	−4.91371	+	3.57002i	−0.416775	+	0.302805i	−0.776339	−	0.630316i	$-0.782925\pi$
$139$	−4.91371	+	3.57002i	−0.416775	+	0.302805i	0.359564	+	0.933120i	$0.382925\pi$
$140$		0			0
$141$	−6.85192	−	4.97821i	−0.577036	−	0.419241i
$142$		0			0
$143$	−8.40132			−0.702554
$144$		0			0
$145$	19.3607	−	3.73788i	1.60782	−	0.310414i
$146$		0			0
$147$	−0.516616	+	1.58998i	−0.0426097	+	0.131139i
$148$		0			0
$149$	3.55995			0.291642			0.145821	−	0.989311i	$-0.453418\pi$
$149$	3.55995			0.291642			0.145821	+	0.989311i	$0.453418\pi$
$150$		0			0
$151$	10.3185			0.839704			0.419852	−	0.907593i	$-0.362082\pi$
$151$	10.3185			0.839704			0.419852	+	0.907593i	$0.362082\pi$
$152$		0			0
$153$	1.15806	−	3.56415i	0.0936238	−	0.288145i
$154$		0			0
$155$	10.2178	−	10.9294i	0.820711	−	0.877872i
$156$		0			0
$157$	19.6148			1.56543			0.782714	−	0.622382i	$-0.213835\pi$
$157$	19.6148			1.56543			0.782714	+	0.622382i	$0.213835\pi$
$158$		0			0
$159$	−1.48195	−	1.07670i	−0.117527	−	0.0853881i
$160$		0			0
$161$	−2.90835	+	2.11304i	−0.229210	+	0.166531i
$162$		0			0
$163$	−12.3545	−	8.97608i	−0.967681	−	0.703061i	−0.0127589	−	0.999919i	$-0.504061\pi$
$163$	−12.3545	−	8.97608i	−0.967681	−	0.703061i	−0.954922	+	0.296857i	$0.904061\pi$
$164$		0			0
$165$	−7.03434	+	7.52426i	−0.547622	+	0.585763i
$166$		0			0
$167$	−0.349377	−	1.07527i	−0.0270356	−	0.0832070i	0.936628	−	0.350325i	$-0.113929\pi$
$167$	−0.349377	−	1.07527i	−0.0270356	−	0.0832070i	−0.963664	+	0.267118i	$0.913929\pi$
$168$		0			0
$169$	−1.56317	−	4.81094i	−0.120244	−	0.370072i
$170$		0			0
$171$	−0.986909	+	3.03739i	−0.0754708	+	0.232275i
$172$		0			0
$173$	2.72385	−	1.97899i	0.207090	−	0.150460i	−0.479406	−	0.877593i	$-0.659148\pi$
$173$	2.72385	−	1.97899i	0.207090	−	0.150460i	0.686496	+	0.727133i	$0.259148\pi$
$174$		0			0
$175$	−6.47179	+	10.2989i	−0.489222	+	0.778521i
$176$		0			0
$177$	−10.3660	+	7.53133i	−0.779156	+	0.566090i
$178$		0			0
$179$	−0.0143068	+	0.0440317i	−0.00106934	+	0.00329108i	−0.951590	−	0.307371i	$-0.900551\pi$
$179$	−0.0143068	+	0.0440317i	−0.00106934	+	0.00329108i	0.950520	+	0.310662i	$0.100551\pi$
$180$		0			0
$181$	3.69146	+	11.3611i	0.274384	+	0.844468i	0.989382	+	0.145341i	$0.0464278\pi$
$181$	3.69146	+	11.3611i	0.274384	+	0.844468i	−0.714998	+	0.699127i	$0.753572\pi$
$182$		0			0
$183$	7.22720	+	22.2430i	0.534250	+	1.64425i
$184$		0			0
$185$	−1.28906	+	10.3897i	−0.0947734	+	0.763864i
$186$		0			0
$187$	14.7561	+	10.7210i	1.07908	+	0.783995i
$188$		0			0
$189$	10.9857	−	7.98156i	0.799090	−	0.580573i
$190$		0			0
$191$	7.00775	+	5.09143i	0.507063	+	0.368403i	0.811708	−	0.584063i	$-0.198538\pi$
$191$	7.00775	+	5.09143i	0.507063	+	0.368403i	−0.304645	+	0.952466i	$0.598538\pi$
$192$		0			0
$193$	−3.47620			−0.250222			−0.125111	−	0.992143i	$-0.539929\pi$
$193$	−3.47620			−0.250222			−0.125111	+	0.992143i	$0.539929\pi$
$194$		0			0
$195$	8.81907	+	4.12601i	0.631547	+	0.295470i
$196$		0			0
$197$	−0.910753	+	2.80301i	−0.0648885	+	0.199706i	−0.978244	−	0.207456i	$-0.933482\pi$
$197$	−0.910753	+	2.80301i	−0.0648885	+	0.199706i	0.913356	+	0.407162i	$0.133482\pi$
$198$		0			0
$199$	15.9228			1.12874			0.564369	−	0.825523i	$-0.309119\pi$
$199$	15.9228			1.12874			0.564369	+	0.825523i	$0.309119\pi$
$200$		0			0
$201$	22.8014			1.60829
$202$		0			0
$203$	6.62908	−	20.4022i	0.465270	−	1.43195i
$204$		0			0
$205$	0.997054	−	8.03615i	0.0696373	−	0.561269i
$206$		0			0
$207$	−0.905174			−0.0629139
$208$		0			0
$209$	−12.5753	−	9.13648i	−0.869851	−	0.631984i
$210$		0			0
$211$	−9.72209	+	7.06351i	−0.669296	+	0.486272i	−0.869790	−	0.493423i	$-0.835746\pi$
$211$	−9.72209	+	7.06351i	−0.669296	+	0.486272i	0.200493	+	0.979695i	$0.435746\pi$
$212$		0			0
$213$	7.31527	+	5.31486i	0.501234	+	0.364168i
$214$		0			0
$215$	−3.90436	−	7.06475i	−0.266275	−	0.481812i
$216$		0			0
$217$	−5.03001	−	15.4808i	−0.341459	−	1.05090i
$218$		0			0
$219$	2.85699	+	8.79290i	0.193057	+	0.594169i
$220$		0			0
$221$	5.32785	−	16.3974i	0.358390	−	1.10301i
$222$		0			0
$223$	4.04587	−	2.93949i	0.270931	−	0.196843i	−0.444021	−	0.896016i	$-0.646448\pi$
$223$	4.04587	−	2.93949i	0.270931	−	0.196843i	0.714952	+	0.699173i	$0.246448\pi$
$224$		0			0
$225$	−2.84256	+	1.14010i	−0.189504	+	0.0760066i
$226$		0			0
$227$	11.1259	−	8.08342i	0.738450	−	0.536516i	−0.153775	−	0.988106i	$-0.549143\pi$
$227$	11.1259	−	8.08342i	0.738450	−	0.536516i	0.892225	+	0.451590i	$0.149143\pi$
$228$		0			0
$229$	2.31025	−	7.11022i	0.152666	−	0.469857i	−0.845251	−	0.534369i	$-0.820549\pi$
$229$	2.31025	−	7.11022i	0.152666	−	0.469857i	0.997917	+	0.0645124i	$0.0205492\pi$
$230$		0			0
$231$	3.46287	+	10.6576i	0.227840	+	0.701220i
$232$		0			0
$233$	5.16070	+	15.8830i	0.338089	+	1.04053i	0.965181	+	0.261585i	$0.0842451\pi$
$233$	5.16070	+	15.8830i	0.338089	+	1.04053i	−0.627092	+	0.778945i	$0.715755\pi$
$234$		0			0
$235$	12.0344	−	2.32343i	0.785038	−	0.151564i
$236$		0			0
$237$	−15.1778	−	11.0273i	−0.985904	−	0.716301i
$238$		0			0
$239$	−8.36778	+	6.07955i	−0.541267	+	0.393253i	−0.824555	−	0.565781i	$-0.808575\pi$
$239$	−8.36778	+	6.07955i	−0.541267	+	0.393253i	0.283288	+	0.959035i	$0.408575\pi$
$240$		0			0
$241$	6.22944	+	4.52595i	0.401273	+	0.291542i	0.770059	−	0.637972i	$-0.220227\pi$
$241$	6.22944	+	4.52595i	0.401273	+	0.291542i	−0.368786	+	0.929514i	$0.620227\pi$
$242$		0			0
$243$	6.25846			0.401481
$244$		0			0
$245$	−1.17025	−	2.11751i	−0.0747645	−	0.135283i
$246$		0			0
$247$	−4.54043	+	13.9740i	−0.288900	+	0.889144i
$248$		0			0
$249$	18.9504			1.20094
$250$		0			0
$251$	−13.0605			−0.824372			−0.412186	−	0.911100i	$-0.635235\pi$
$251$	−13.0605			−0.824372			−0.412186	+	0.911100i	$0.635235\pi$
$252$		0			0
$253$	1.36138	−	4.18990i	0.0855893	−	0.263417i
$254$		0			0
$255$	−10.2247	−	18.5010i	−0.640293	−	1.15858i
$256$		0			0
$257$	−22.1683			−1.38282			−0.691411	−	0.722461i	$-0.743011\pi$
$257$	−22.1683			−1.38282			−0.691411	+	0.722461i	$0.743011\pi$
$258$		0			0
$259$	9.21468	+	6.69486i	0.572572	+	0.415998i
$260$		0			0
$261$	4.36990	−	3.17492i	0.270490	−	0.196522i
$262$		0			0
$263$	1.09287	+	0.794015i	0.0673891	+	0.0489611i	0.620970	−	0.783834i	$-0.286739\pi$
$263$	1.09287	+	0.794015i	0.0673891	+	0.0489611i	−0.553581	+	0.832796i	$0.686739\pi$
$264$		0			0
$265$	2.60284	−	0.502518i	0.159891	−	0.0308694i
$266$		0			0
$267$	1.25246	+	3.85469i	0.0766496	+	0.235903i
$268$		0			0
$269$	4.77819	+	14.7057i	0.291331	+	0.896625i	0.984429	+	0.175782i	$0.0562453\pi$
$269$	4.77819	+	14.7057i	0.291331	+	0.896625i	−0.693098	+	0.720843i	$0.743755\pi$
$270$		0			0
$271$	0.740383	−	2.27866i	0.0449750	−	0.138419i	−0.926047	−	0.377407i	$-0.876816\pi$
$271$	0.740383	−	2.27866i	0.0449750	−	0.138419i	0.971022	+	0.238988i	$0.0768157\pi$
$272$		0			0
$273$	8.56969	−	6.22625i	0.518662	−	0.376830i
$274$		0			0
$275$	−1.00211	−	14.8725i	−0.0604298	−	0.896844i
$276$		0			0
$277$	6.35533	−	4.61742i	0.381855	−	0.277434i	−0.380255	−	0.924882i	$-0.624164\pi$
$277$	6.35533	−	4.61742i	0.381855	−	0.277434i	0.762110	+	0.647448i	$0.224164\pi$
$278$		0			0
$279$	1.26652	−	3.89795i	0.0758245	−	0.233364i
$280$		0			0
$281$	−2.70559	−	8.32694i	−0.161402	−	0.496743i	0.837351	−	0.546665i	$-0.184103\pi$
$281$	−2.70559	−	8.32694i	−0.161402	−	0.496743i	−0.998753	+	0.0499216i	$0.984103\pi$
$282$		0			0
$283$	−8.25156	−	25.3957i	−0.490504	−	1.50962i	−0.823847	−	0.566812i	$-0.808177\pi$
$283$	−8.25156	−	25.3957i	−0.490504	−	1.50962i	0.333343	−	0.942806i	$-0.391823\pi$
$284$		0			0
$285$	8.71352	+	15.7667i	0.516145	+	0.933939i
$286$		0			0
$287$	−7.12732	−	5.17830i	−0.420713	−	0.305666i
$288$		0			0
$289$	−16.5294	+	12.0093i	−0.972318	+	0.706431i
$290$		0			0
$291$	−11.8918	−	8.63993i	−0.697112	−	0.506482i
$292$		0			0
$293$	13.7472			0.803118			0.401559	−	0.915833i	$-0.368469\pi$
$293$	13.7472			0.803118			0.401559	+	0.915833i	$0.368469\pi$
$294$		0			0
$295$	2.28309	−	18.4015i	0.132927	−	1.07137i
$296$		0			0
$297$	−5.14233	+	15.8265i	−0.298388	+	0.918344i
$298$		0			0
$299$	−4.16439			−0.240833
$300$		0			0
$301$	−8.78165			−0.506166
$302$		0			0
$303$	−0.690037	+	2.12372i	−0.0396416	+	0.122004i
$304$		0			0
$305$	−30.6565	−	14.3427i	−1.75539	−	0.821261i
$306$		0			0
$307$	5.41804			0.309224			0.154612	−	0.987975i	$-0.450587\pi$
$307$	5.41804			0.309224			0.154612	+	0.987975i	$0.450587\pi$
$308$		0			0
$309$	6.93933	+	5.04172i	0.394765	+	0.286813i
$310$		0			0
$311$	−9.70149	+	7.04854i	−0.550121	+	0.399686i	−0.827830	−	0.560979i	$-0.810425\pi$
$311$	−9.70149	+	7.04854i	−0.550121	+	0.399686i	0.277709	+	0.960665i	$0.410425\pi$
$312$		0			0
$313$	4.12496	+	2.99696i	0.233156	+	0.169398i	0.698229	−	0.715875i	$-0.253972\pi$
$313$	4.12496	+	2.99696i	0.233156	+	0.169398i	−0.465073	+	0.885273i	$0.653972\pi$
$314$		0			0
$315$	−0.410259	+	3.30664i	−0.0231155	+	0.186308i
$316$		0			0
$317$	2.18248	+	6.71698i	0.122580	+	0.377263i	0.993452	−	0.114246i	$-0.0364453\pi$
$317$	2.18248	+	6.71698i	0.122580	+	0.377263i	−0.870872	+	0.491509i	$0.836445\pi$
$318$		0			0
$319$	8.12385	+	25.0026i	0.454848	+	1.39988i
$320$		0			0
$321$	−3.55279	+	10.9344i	−0.198297	+	0.610296i
$322$		0			0
$323$	25.8071	−	18.7500i	1.43595	−	1.04328i
$324$		0			0
$325$	−13.0777	+	5.24520i	−0.725418	+	0.290951i
$326$		0			0
$327$	−11.6197	+	8.44224i	−0.642573	+	0.466857i
$328$		0			0
$329$	4.12057	−	12.6818i	0.227174	−	0.699170i
$330$		0			0
$331$	−1.79401	−	5.52140i	−0.0986077	−	0.303483i	0.889569	−	0.456800i	$-0.151005\pi$
$331$	−1.79401	−	5.52140i	−0.0986077	−	0.303483i	−0.988177	+	0.153317i	$0.951005\pi$
$332$		0			0
$333$	0.886233	+	2.72754i	0.0485652	+	0.149468i
$334$		0			0
$335$	−22.5347	+	24.1042i	−1.23120	+	1.31695i
$336$		0			0
$337$	−1.10613	−	0.803650i	−0.0602547	−	0.0437776i	0.557250	−	0.830345i	$-0.311856\pi$
$337$	−1.10613	−	0.803650i	−0.0602547	−	0.0437776i	−0.617505	+	0.786567i	$0.711856\pi$
$338$		0			0
$339$	−20.8699	+	15.1629i	−1.13350	+	0.823535i
$340$		0			0
$341$	16.1381	+	11.7250i	0.873928	+	0.634946i
$342$		0			0
$343$	−19.6610			−1.06159
$344$		0			0
$345$	−3.48680	+	3.72965i	−0.187723	+	0.200797i
$346$		0			0
$347$	0.308138	−	0.948350i	0.0165417	−	0.0509101i	−0.942445	−	0.334361i	$-0.891479\pi$
$347$	0.308138	−	0.948350i	0.0165417	−	0.0509101i	0.958987	+	0.283451i	$0.0914794\pi$
$348$		0			0
$349$	−12.5266			−0.670534			−0.335267	−	0.942123i	$-0.608827\pi$
$349$	−12.5266			−0.670534			−0.335267	+	0.942123i	$0.608827\pi$
$350$		0			0
$351$	15.7301			0.839610
$352$		0			0
$353$	5.97697	−	18.3952i	0.318122	−	0.979079i	−0.656328	−	0.754476i	$-0.727891\pi$
$353$	5.97697	−	18.3952i	0.318122	−	0.979079i	0.974450	−	0.224604i	$-0.0721088\pi$
$354$		0			0
$355$	−12.8482	+	2.48055i	−0.681912	+	0.131654i
$356$		0			0
$357$	−22.9972			−1.21714
$358$		0			0
$359$	−4.66127	−	3.38661i	−0.246013	−	0.178739i	0.457945	−	0.888980i	$-0.348586\pi$
$359$	−4.66127	−	3.38661i	−0.246013	−	0.178739i	−0.703958	+	0.710242i	$0.748586\pi$
$360$		0			0
$361$	−6.62169	+	4.81094i	−0.348510	+	0.253207i
$362$		0			0
$363$	2.64036	+	1.91833i	0.138583	+	0.100686i
$364$		0			0
$365$	−12.1188	−	5.66981i	−0.634329	−	0.296772i
$366$		0			0
$367$	−10.6509	−	32.7802i	−0.555975	−	1.71111i	−0.693355	−	0.720596i	$-0.743868\pi$
$367$	−10.6509	−	32.7802i	−0.555975	−	1.71111i	0.137380	−	0.990518i	$-0.456132\pi$
$368$		0			0
$369$	−0.685479	−	2.10969i	−0.0356846	−	0.109826i
$370$		0			0
$371$	0.891209	−	2.74286i	0.0462693	−	0.142402i
$372$		0			0
$373$	20.6588	−	15.0095i	1.06967	−	0.777163i	0.0938202	−	0.995589i	$-0.470092\pi$
$373$	20.6588	−	15.0095i	1.06967	−	0.777163i	0.975854	+	0.218426i	$0.0700921\pi$
$374$		0			0
$375$	−6.25215	+	16.1042i	−0.322860	+	0.831615i
$376$		0			0
$377$	20.1044	−	14.6067i	1.03543	−	0.752283i
$378$		0			0
$379$	−4.13595	+	12.7291i	−0.212449	+	0.653852i	0.786876	+	0.617112i	$0.211697\pi$
$379$	−4.13595	+	12.7291i	−0.212449	+	0.653852i	−0.999325	+	0.0367400i	$0.988303\pi$
$380$		0			0
$381$	−5.73875	−	17.6621i	−0.294005	−	0.904854i
$382$		0			0
$383$	11.4948	+	35.3772i	0.587354	+	1.80769i	0.589602	+	0.807694i	$0.299284\pi$
$383$	11.4948	+	35.3772i	0.587354	+	1.80769i	−0.00224788	+	0.999997i	$0.500716\pi$
$384$		0			0
$385$	−14.6889	−	6.87222i	−0.748615	−	0.350241i
$386$		0			0
$387$	−1.78886	−	1.29968i	−0.0909329	−	0.0660666i
$388$		0			0
$389$	−29.3114	+	21.2960i	−1.48615	+	1.07975i	−0.510638	+	0.859796i	$0.670591\pi$
$389$	−29.3114	+	21.2960i	−1.48615	+	1.07975i	−0.975510	+	0.219954i	$0.929409\pi$
$390$		0			0
$391$	7.31437	+	5.31420i	0.369903	+	0.268751i
$392$		0			0
$393$	−27.5049			−1.38744
$394$		0			0
$395$	26.6576	−	5.14666i	1.34129	−	0.258957i
$396$		0			0
$397$	0.838720	−	2.58132i	0.0420942	−	0.129552i	−0.927801	−	0.373076i	$-0.878303\pi$
$397$	0.838720	−	2.58132i	0.0420942	−	0.129552i	0.969895	+	0.243523i	$0.0783032\pi$
$398$		0			0
$399$	19.5984			0.981147
$400$		0			0
$401$	−11.6883			−0.583686			−0.291843	−	0.956466i	$-0.594269\pi$
$401$	−11.6883			−0.583686			−0.291843	+	0.956466i	$0.594269\pi$
$402$		0			0
$403$	5.82682	−	17.9331i	0.290254	−	0.893311i
$404$		0			0
$405$	10.3645	−	11.0864i	0.515016	−	0.550886i
$406$		0			0
$407$	−13.9583			−0.691885
$408$		0			0
$409$	21.1020	+	15.3315i	1.04343	+	0.758094i	0.970952	−	0.239276i	$-0.0769101\pi$
$409$	21.1020	+	15.3315i	1.04343	+	0.758094i	0.0724753	+	0.997370i	$0.476910\pi$
$410$		0			0
$411$	19.6239	−	14.2576i	0.967975	−	0.703275i
$412$		0			0
$413$	−16.3204	−	11.8575i	−0.803074	−	0.583468i
$414$		0			0
$415$	−18.7287	+	20.0332i	−0.919358	+	0.983389i
$416$		0			0
$417$	2.90003	+	8.92537i	0.142015	+	0.437077i
$418$		0			0
$419$	2.20300	+	6.78014i	0.107624	+	0.331232i	0.990337	−	0.138680i	$-0.0442859\pi$
$419$	2.20300	+	6.78014i	0.107624	+	0.331232i	−0.882714	+	0.469911i	$0.844286\pi$
$420$		0			0
$421$	−5.67304	+	17.4598i	−0.276487	+	0.850940i	0.712335	+	0.701840i	$0.247638\pi$
$421$	−5.67304	+	17.4598i	−0.276487	+	0.850940i	−0.988822	+	0.149100i	$0.952362\pi$
$422$		0			0
$423$	2.71628	−	1.97350i	0.132070	−	0.0959546i
$424$		0			0
$425$	29.6631	+	7.47575i	1.43887	+	0.362627i
$426$		0			0
$427$	−29.7897	+	21.6435i	−1.44162	+	1.04740i
$428$		0			0
$429$	−4.01142	+	12.3459i	−0.193673	+	0.596065i
$430$		0			0
$431$	9.48261	+	29.1845i	0.456761	+	1.40577i	0.869055	+	0.494716i	$0.164728\pi$
$431$	9.48261	+	29.1845i	0.456761	+	1.40577i	−0.412294	+	0.911051i	$0.635272\pi$
$432$		0			0
$433$	0.963040	+	2.96393i	0.0462808	+	0.142438i	0.971527	−	0.236931i	$-0.0761414\pi$
$433$	0.963040	+	2.96393i	0.0462808	+	0.142438i	−0.925246	+	0.379368i	$0.876141\pi$
$434$		0			0
$435$	3.75136	−	30.2356i	0.179864	−	1.44969i
$436$		0			0
$437$	−6.23335	−	4.52880i	−0.298182	−	0.216642i
$438$		0			0
$439$	12.1537	−	8.83019i	0.580065	−	0.421442i	−0.258682	−	0.965962i	$-0.583288\pi$
$439$	12.1537	−	8.83019i	0.580065	−	0.421442i	0.838748	+	0.544520i	$0.183288\pi$
$440$		0			0
$441$	−0.536174	−	0.389553i	−0.0255321	−	0.0185501i
$442$		0			0
$443$	−25.6976			−1.22093			−0.610466	−	0.792043i	$-0.709018\pi$
$443$	−25.6976			−1.22093			−0.610466	+	0.792043i	$0.709018\pi$
$444$		0			0
$445$	−5.31274	−	2.48557i	−0.251848	−	0.117827i
$446$		0			0
$447$	1.69979	−	5.23141i	0.0803972	−	0.247437i
$448$		0			0
$449$	31.0378			1.46476			0.732382	−	0.680894i	$-0.238408\pi$
$449$	31.0378			1.46476			0.732382	+	0.680894i	$0.238408\pi$
$450$		0			0
$451$	10.7964			0.508381
$452$		0			0
$453$	4.92681	−	15.1632i	0.231482	−	0.712427i
$454$		0			0
$455$	−1.88746	+	15.2127i	−0.0884855	+	0.713184i
$456$		0			0
$457$	−11.0889			−0.518716			−0.259358	−	0.965781i	$-0.583511\pi$
$457$	−11.0889			−0.518716			−0.259358	+	0.965781i	$0.583511\pi$
$458$		0			0
$459$	−27.6285	−	20.0733i	−1.28959	−	0.936939i
$460$		0			0
$461$	19.1196	−	13.8912i	0.890490	−	0.646979i	−0.0455158	−	0.998964i	$-0.514493\pi$
$461$	19.1196	−	13.8912i	0.890490	−	0.646979i	0.936006	+	0.351985i	$0.114493\pi$
$462$		0			0
$463$	13.4389	+	9.76393i	0.624558	+	0.453768i	0.854511	−	0.519434i	$-0.173857\pi$
$463$	13.4389	+	9.76393i	0.624558	+	0.453768i	−0.229952	+	0.973202i	$0.573857\pi$
$464$		0			0
$465$	−11.1822	−	20.2337i	−0.518564	−	0.938316i
$466$		0			0
$467$	0.412338	+	1.26905i	0.0190807	+	0.0587245i	0.960144	−	0.279507i	$-0.0901712\pi$
$467$	0.412338	+	1.26905i	0.0190807	+	0.0587245i	−0.941063	+	0.338232i	$0.890171\pi$
$468$		0			0
$469$	11.0934	+	34.1419i	0.512245	+	1.57653i
$470$		0			0
$471$	9.36556	−	28.8242i	0.431542	−	1.32815i
$472$		0			0
$473$	8.70647	−	6.32562i	0.400324	−	0.290852i
$474$		0			0
$475$	−25.2791	−	6.37088i	−1.15988	−	0.292316i
$476$		0			0
$477$	0.587486	−	0.426834i	0.0268992	−	0.0195434i
$478$		0			0
$479$	1.53880	−	4.73594i	0.0703095	−	0.216390i	−0.909727	−	0.415206i	$-0.863709\pi$
$479$	1.53880	−	4.73594i	0.0703095	−	0.216390i	0.980037	+	0.198816i	$0.0637095\pi$
$480$		0			0
$481$	4.07725	+	12.5485i	0.185907	+	0.572162i
$482$		0			0
$483$	1.71648	+	5.28280i	0.0781028	+	0.240376i
$484$		0			0
$485$	20.8863	−	4.03242i	0.948397	−	0.183103i
$486$		0			0
$487$	−6.66836	−	4.84485i	−0.302172	−	0.219541i	0.426358	−	0.904554i	$-0.359796\pi$
$487$	−6.66836	−	4.84485i	−0.302172	−	0.219541i	−0.728530	+	0.685013i	$0.759796\pi$
$488$		0			0
$489$	−19.0895	+	13.8693i	−0.863257	+	0.627193i
$490$		0			0
$491$	2.09586	+	1.52273i	0.0945849	+	0.0687199i	0.634073	−	0.773274i	$-0.281382\pi$
$491$	2.09586	+	1.52273i	0.0945849	+	0.0687199i	−0.539488	+	0.841994i	$0.681382\pi$
$492$		0			0
$493$	−53.9512			−2.42984
$494$		0			0
$495$	−1.97510	−	3.57386i	−0.0887743	−	0.160633i
$496$		0			0
$497$	−4.39922	+	13.5394i	−0.197332	+	0.607325i
$498$		0			0
$499$	10.7285			0.480272			0.240136	−	0.970739i	$-0.422808\pi$
$499$	10.7285			0.480272			0.240136	+	0.970739i	$0.422808\pi$
$500$		0			0
$501$	−1.74695			−0.0780479
$502$		0			0
$503$	7.41971	−	22.8355i	0.330829	−	1.01819i	−0.637912	−	0.770109i	$-0.720202\pi$
$503$	7.41971	−	22.8355i	0.330829	−	1.01819i	0.968740	−	0.248077i	$-0.0797984\pi$
$504$		0			0
$505$	−1.56309	−	2.82833i	−0.0695566	−	0.125859i
$506$		0			0
$507$	−7.81613			−0.347126
$508$		0			0
$509$	−11.0394	−	8.02058i	−0.489312	−	0.355506i	0.315608	−	0.948890i	$-0.397792\pi$
$509$	−11.0394	−	8.02058i	−0.489312	−	0.355506i	−0.804920	+	0.593384i	$0.797792\pi$
$510$		0			0
$511$	−11.7761	+	8.55587i	−0.520946	+	0.378489i
$512$		0			0
$513$	23.5452	+	17.1066i	1.03954	+	0.755273i
$514$		0			0
$515$	−12.1879	+	2.35307i	−0.537064	+	0.103689i
$516$		0			0
$517$	5.04970	+	15.5414i	0.222085	+	0.683509i
$518$		0			0
$519$	−1.60759	−	4.94766i	−0.0705654	−	0.217178i
$520$		0			0
$521$	−0.739568	+	2.27616i	−0.0324011	+	0.0997202i	−0.965949	−	0.258732i	$-0.916695\pi$
$521$	−0.739568	+	2.27616i	−0.0324011	+	0.0997202i	0.933548	+	0.358452i	$0.116695\pi$
$522$		0			0
$523$	18.4575	−	13.4101i	0.807089	−	0.586385i	−0.105896	−	0.994377i	$-0.533771\pi$
$523$	18.4575	−	13.4101i	0.807089	−	0.586385i	0.912985	+	0.407992i	$0.133771\pi$
$524$		0			0
$525$	12.0442	+	14.4279i	0.525654	+	0.629684i
$526$		0			0
$527$	−33.1188	+	24.0622i	−1.44268	+	1.04817i
$528$		0			0
$529$	−6.43258	+	19.7974i	−0.279677	+	0.860758i
$530$		0			0
$531$	−1.56963	−	4.83084i	−0.0681163	−	0.209640i
$532$		0			0
$533$	−3.15365	−	9.70594i	−0.136600	−	0.420411i
$534$		0			0
$535$	−8.04786	−	14.5622i	−0.347939	−	0.629579i
$536$		0			0
$537$	0.0578742	+	0.0420481i	0.00249746	+	0.00181451i
$538$		0			0
$539$	2.60958	−	1.89597i	0.112403	−	0.0816654i
$540$		0			0
$541$	7.85249	+	5.70517i	0.337605	+	0.245284i	0.743651	−	0.668568i	$-0.233093\pi$
$541$	7.85249	+	5.70517i	0.337605	+	0.245284i	−0.406046	+	0.913853i	$0.633093\pi$
$542$		0			0
$543$	18.4580			0.792108
$544$		0			0
$545$	2.55923	−	20.6271i	0.109625	−	0.883568i
$546$		0			0
$547$	8.42533	−	25.9305i	0.360241	−	1.10871i	−0.592667	−	0.805448i	$-0.701925\pi$
$547$	8.42533	−	25.9305i	0.360241	−	1.10871i	0.952908	−	0.303260i	$-0.0980752\pi$
$548$		0			0
$549$	−9.27152			−0.395699
$550$		0			0
$551$	45.9776			1.95871
$552$		0			0
$553$	9.12753	−	28.0917i	0.388142	−	1.19458i
$554$		0			0
$555$	14.6523	+	6.85510i	0.621956	+	0.290983i
$556$		0			0
$557$	−1.20057			−0.0508700			−0.0254350	−	0.999676i	$-0.508097\pi$
$557$	−1.20057			−0.0508700			−0.0254350	+	0.999676i	$0.508097\pi$
$558$		0			0
$559$	−8.22993	−	5.97939i	−0.348089	−	0.252901i
$560$		0			0
$561$	22.8003	−	16.5654i	0.962631	−	0.699393i
$562$		0			0
$563$	13.7727	+	10.0065i	0.580451	+	0.421722i	0.838887	−	0.544306i	$-0.183207\pi$
$563$	13.7727	+	10.0065i	0.580451	+	0.421722i	−0.258436	+	0.966028i	$0.583207\pi$
$564$		0			0
$565$	4.59656	−	37.0478i	0.193379	−	1.55861i
$566$		0			0
$567$	−5.10224	−	15.7031i	−0.214274	−	0.659468i
$568$		0			0
$569$	−2.11398	−	6.50617i	−0.0886227	−	0.272753i	0.896917	−	0.442200i	$-0.145802\pi$
$569$	−2.11398	−	6.50617i	−0.0886227	−	0.272753i	−0.985539	+	0.169447i	$0.945802\pi$
$570$		0			0
$571$	−8.05817	+	24.8005i	−0.337224	+	1.03787i	0.628392	+	0.777897i	$0.283713\pi$
$571$	−8.05817	+	24.8005i	−0.337224	+	1.03787i	−0.965616	+	0.259972i	$0.916287\pi$
$572$		0			0
$573$	10.8280	−	7.86698i	0.452345	−	0.328648i
$574$		0			0
$575$	−0.496731	−	7.37203i	−0.0207151	−	0.307435i
$576$		0			0
$577$	13.7137	−	9.96356i	0.570907	−	0.414789i	−0.264527	−	0.964378i	$-0.585216\pi$
$577$	13.7137	−	9.96356i	0.570907	−	0.414789i	0.835435	+	0.549590i	$0.185216\pi$
$578$		0			0
$579$	−1.65980	+	5.10834i	−0.0689789	+	0.212295i
$580$		0			0
$581$	9.21980	+	28.3756i	0.382502	+	1.17722i
$582$		0			0
$583$	1.09216	+	3.36134i	0.0452328	+	0.139212i
$584$		0			0
$585$	−2.63597	+	2.81956i	−0.108984	+	0.116574i
$586$		0			0
$587$	36.1035	+	26.2307i	1.49015	+	1.08266i	0.974105	+	0.226097i	$0.0725967\pi$
$587$	36.1035	+	26.2307i	1.49015	+	1.08266i	0.516046	+	0.856561i	$0.327403\pi$
$588$		0			0
$589$	28.2241	−	20.5060i	1.16295	−	0.844934i
$590$		0			0
$591$	3.68421	+	2.67673i	0.151548	+	0.110106i
$592$		0			0
$593$	37.7787			1.55139			0.775694	−	0.631110i	$-0.217400\pi$
$593$	37.7787			1.55139			0.775694	+	0.631110i	$0.217400\pi$
$594$		0			0
$595$	22.7282	−	24.3112i	0.931765	−	0.996660i
$596$		0			0
$597$	7.60275	−	23.3989i	0.311160	−	0.957651i
$598$		0			0
$599$	−8.06719			−0.329617			−0.164808	−	0.986326i	$-0.552701\pi$
$599$	−8.06719			−0.329617			−0.164808	+	0.986326i	$0.552701\pi$
$600$		0			0
$601$	−23.5962			−0.962509			−0.481255	−	0.876581i	$-0.659819\pi$
$601$	−23.5962			−0.962509			−0.481255	+	0.876581i	$0.659819\pi$
$602$		0			0
$603$	−2.79323	+	8.59668i	−0.113749	+	0.350084i
$604$		0			0
$605$	−4.63741	+	0.895323i	−0.188537	+	0.0364001i
$606$		0			0
$607$	47.5160			1.92861			0.964307	−	0.264788i	$-0.0853019\pi$
$607$	47.5160			1.92861			0.964307	+	0.264788i	$0.0853019\pi$
$608$		0			0
$609$	−26.8162	−	19.4831i	−1.08665	−	0.789495i
$610$		0			0
$611$	12.4967	−	9.07937i	0.505561	−	0.367312i
$612$		0			0
$613$	−4.57226	−	3.32194i	−0.184672	−	0.134172i	0.491608	−	0.870816i	$-0.336409\pi$
$613$	−4.57226	−	3.32194i	−0.184672	−	0.134172i	−0.676280	+	0.736644i	$0.736409\pi$
$614$		0			0
$615$	−11.3332	−	5.30225i	−0.456999	−	0.213807i
$616$		0			0
$617$	12.9382	+	39.8198i	0.520874	+	1.60308i	0.772334	+	0.635216i	$0.219089\pi$
$617$	12.9382	+	39.8198i	0.520874	+	1.60308i	−0.251461	+	0.967868i	$0.580911\pi$
$618$		0			0
$619$	5.52654	+	17.0089i	0.222130	+	0.683647i	0.998570	+	0.0534558i	$0.0170236\pi$
$619$	5.52654	+	17.0089i	0.222130	+	0.683647i	−0.776440	+	0.630191i	$0.782976\pi$
$620$		0			0
$621$	−2.54896	+	7.84490i	−0.102286	+	0.314805i
$622$		0			0
$623$	−5.16251	+	3.75078i	−0.206832	+	0.150272i
$624$		0			0
$625$	−10.8452	−	22.5251i	−0.433810	−	0.901005i
$626$		0			0
$627$	−19.4306	+	14.1172i	−0.775984	+	0.563785i
$628$		0			0
$629$	8.85187	−	27.2432i	0.352947	−	1.08626i
$630$		0			0
$631$	11.8982	+	36.6189i	0.473660	+	1.45778i	0.847756	+	0.530386i	$0.177953\pi$
$631$	11.8982	+	36.6189i	0.473660	+	1.45778i	−0.374096	+	0.927390i	$0.622047\pi$
$632$		0			0
$633$	5.73790	+	17.6594i	0.228061	+	0.701900i
$634$		0			0
$635$	24.3428	+	11.3888i	0.966013	+	0.451951i
$636$		0			0
$637$	−2.46675	−	1.79220i	−0.0977362	−	0.0710095i
$638$		0			0
$639$	−2.89997	+	2.10695i	−0.114721	+	0.0833497i
$640$		0			0
$641$	4.32064	+	3.13913i	0.170655	+	0.123988i	0.669834	−	0.742511i	$-0.266365\pi$
$641$	4.32064	+	3.13913i	0.170655	+	0.123988i	−0.499179	+	0.866499i	$0.666365\pi$
$642$		0			0
$643$	−25.3417			−0.999381			−0.499690	−	0.866204i	$-0.666553\pi$
$643$	−25.3417			−0.999381			−0.499690	+	0.866204i	$0.666553\pi$
$644$		0			0
$645$	−12.2460	+	2.36428i	−0.482186	+	0.0930935i
$646$		0			0
$647$	−9.96127	+	30.6576i	−0.391618	+	1.20528i	0.539946	+	0.841700i	$0.318445\pi$
$647$	−9.96127	+	30.6576i	−0.391618	+	1.20528i	−0.931564	+	0.363577i	$0.881555\pi$
$648$		0			0
$649$	24.7219			0.970419
$650$		0			0
$651$	−25.1510			−0.985745
$652$		0			0
$653$	−13.1684	+	40.5282i	−0.515319	+	1.58599i	0.267382	+	0.963591i	$0.413842\pi$
$653$	−13.1684	+	40.5282i	−0.515319	+	1.58599i	−0.782701	+	0.622398i	$0.786158\pi$
$654$		0			0
$655$	27.1831	−	29.0764i	1.06213	−	1.13611i
$656$		0			0
$657$	−3.66512			−0.142990
$658$		0			0
$659$	18.7933	+	13.6541i	0.732082	+	0.531889i	0.890221	−	0.455528i	$-0.150550\pi$
$659$	18.7933	+	13.6541i	0.732082	+	0.531889i	−0.158139	+	0.987417i	$0.550550\pi$
$660$		0			0
$661$	25.5558	−	18.5674i	0.994004	−	0.722186i	0.0332099	−	0.999448i	$-0.489427\pi$
$661$	25.5558	−	18.5674i	0.994004	−	0.722186i	0.960794	+	0.277262i	$0.0894270\pi$
$662$		0			0
$663$	−21.5524	−	15.6587i	−0.837025	−	0.608134i
$664$		0			0
$665$	−19.3691	+	20.7181i	−0.751102	+	0.803415i
$666$		0			0
$667$	4.02685	+	12.3934i	0.155920	+	0.479873i
$668$		0			0
$669$	−2.38784	−	7.34901i	−0.0923191	−	0.284129i
$670$		0			0
$671$	13.9444	−	42.9163i	0.538316	−	1.65677i
$672$		0			0
$673$	6.06059	−	4.40327i	0.233618	−	0.169734i	−0.464817	−	0.885407i	$-0.653880\pi$
$673$	6.06059	−	4.40327i	0.233618	−	0.169734i	0.698435	+	0.715673i	$0.253880\pi$
$674$		0			0
$675$	1.87629	+	27.8463i	0.0722186	+	1.07180i
$676$		0			0
$677$	−21.3719	+	15.5276i	−0.821389	+	0.596774i	−0.917110	−	0.398634i	$-0.869484\pi$
$677$	−21.3719	+	15.5276i	−0.821389	+	0.596774i	0.0957209	+	0.995408i	$0.469484\pi$
$678$		0			0
$679$	7.15144	−	22.0099i	0.274447	−	0.844662i
$680$		0			0
$681$	−6.56640	−	20.2093i	−0.251625	−	0.774422i
$682$		0			0
$683$	1.87077	+	5.75763i	0.0715829	+	0.220310i	0.980447	−	0.196782i	$-0.0630493\pi$
$683$	1.87077	+	5.75763i	0.0715829	+	0.220310i	−0.908864	+	0.417092i	$0.863049\pi$
$684$		0			0
$685$	−4.32212	+	34.8359i	−0.165140	+	1.33101i
$686$		0			0
$687$	−9.34551	−	6.78991i	−0.356553	−	0.259051i
$688$		0			0
$689$	2.70282	−	1.96371i	0.102969	−	0.0748116i
$690$		0			0
$691$	−30.3719	−	22.0665i	−1.15540	−	0.839449i	−0.166212	−	0.986090i	$-0.553154\pi$
$691$	−30.3719	−	22.0665i	−1.15540	−	0.839449i	−0.989190	+	0.146641i	$0.953154\pi$
$692$		0			0
$693$	−4.44239			−0.168752
$694$		0			0
$695$	−12.3014	−	5.75523i	−0.466619	−	0.218308i
$696$		0			0
$697$	−6.84670	+	21.0720i	−0.259337	+	0.798158i
$698$		0			0
$699$	25.8045			0.976014
$700$		0			0
$701$	14.9151			0.563334			0.281667	−	0.959512i	$-0.409113\pi$
$701$	14.9151			0.563334			0.281667	+	0.959512i	$0.409113\pi$
$702$		0			0
$703$	−7.54362	+	23.2169i	−0.284513	+	0.875641i
$704$		0			0
$705$	2.33181	−	18.7941i	0.0878210	−	0.707828i
$706$		0			0
$707$	−3.51569			−0.132221
$708$		0			0
$709$	−3.79990	−	2.76079i	−0.142708	−	0.103684i	0.514140	−	0.857706i	$-0.328111\pi$
$709$	−3.79990	−	2.76079i	−0.142708	−	0.103684i	−0.656849	+	0.754022i	$0.728111\pi$
$710$		0			0
$711$	6.01688	−	4.37152i	0.225651	−	0.163945i
$712$		0			0
$713$	7.99938	+	5.81189i	0.299579	+	0.217657i
$714$		0			0
$715$	−9.08677	−	16.4421i	−0.339826	−	0.614899i
$716$		0			0
$717$	4.93860	+	15.1994i	0.184435	+	0.567633i
$718$		0			0
$719$	1.84285	+	5.67172i	0.0687268	+	0.211519i	0.979521	−	0.201341i	$-0.0645299\pi$
$719$	1.84285	+	5.67172i	0.0687268	+	0.211519i	−0.910794	+	0.412860i	$0.864530\pi$
$720$		0			0
$721$	−4.17313	+	12.8436i	−0.155416	+	0.478320i
$722$		0			0
$723$	9.62537	−	6.99324i	0.357971	−	0.260081i
$724$		0			0
$725$	28.2556	+	33.8476i	1.04939	+	1.25707i
$726$		0			0
$727$	34.3640	−	24.9669i	1.27449	−	0.925972i	0.275120	−	0.961410i	$-0.411282\pi$
$727$	34.3640	−	24.9669i	1.27449	−	0.925972i	0.999372	+	0.0354375i	$0.0112825\pi$
$728$		0			0
$729$	9.28034	−	28.5619i	0.343716	−	1.05785i
$730$		0			0
$731$	6.82478	+	21.0045i	0.252424	+	0.776880i
$732$		0			0
$733$	4.05041	+	12.4659i	0.149605	+	0.460438i	0.997574	−	0.0696075i	$-0.0221747\pi$
$733$	4.05041	+	12.4659i	0.149605	+	0.460438i	−0.847969	+	0.530046i	$0.822175\pi$
$734$		0			0
$735$	−3.67048	+	0.708644i	−0.135388	+	0.0261387i
$736$		0			0
$737$	−35.5916	−	25.8588i	−1.31103	−	0.952522i
$738$		0			0
$739$	−39.7715	+	28.8957i	−1.46302	+	1.06295i	−0.480456	+	0.877019i	$0.659529\pi$
$739$	−39.7715	+	28.8957i	−1.46302	+	1.06295i	−0.982564	+	0.185927i	$0.940471\pi$
$740$		0			0
$741$	18.3671	+	13.3445i	0.674732	+	0.490221i
$742$		0			0
$743$	−22.2935			−0.817869			−0.408934	−	0.912564i	$-0.634099\pi$
$743$	−22.2935			−0.817869			−0.408934	+	0.912564i	$0.634099\pi$
$744$		0			0
$745$	3.85040	+	6.96711i	0.141068	+	0.255255i
$746$		0			0
$747$	−2.32148	+	7.14477i	−0.0849384	+	0.261414i
$748$		0			0
$749$	−18.1012			−0.661403
$750$		0			0
$751$	−40.0656			−1.46202			−0.731008	−	0.682369i	$-0.760950\pi$
$751$	−40.0656			−1.46202			−0.731008	+	0.682369i	$0.760950\pi$
$752$		0			0
$753$	−6.23607	+	19.1927i	−0.227255	+	0.699419i
$754$		0			0
$755$	11.1603	+	20.1941i	0.406166	+	0.734937i
$756$		0			0
$757$	8.47793			0.308136			0.154068	−	0.988060i	$-0.450763\pi$
$757$	8.47793			0.308136			0.154068	+	0.988060i	$0.450763\pi$
$758$		0			0
$759$	−5.50711	−	4.00115i	−0.199895	−	0.145233i
$760$		0			0
$761$	4.94790	−	3.59486i	0.179361	−	0.130313i	−0.494482	−	0.869188i	$-0.664642\pi$
$761$	4.94790	−	3.59486i	0.179361	−	0.130313i	0.673843	+	0.738874i	$0.264642\pi$
$762$		0			0
$763$	−18.2943	−	13.2916i	−0.662299	−	0.481189i
$764$		0			0
$765$	8.22788	−	1.58852i	0.297480	−	0.0574331i
$766$		0			0
$767$	−7.22134	−	22.2250i	−0.260748	−	0.802498i
$768$		0			0
$769$	4.57999	+	14.0958i	0.165159	+	0.508306i	0.999048	−	0.0436258i	$-0.0138909\pi$
$769$	4.57999	+	14.0958i	0.165159	+	0.508306i	−0.833889	+	0.551932i	$0.813891\pi$
$770$		0			0
$771$	−10.5848	+	32.5768i	−0.381203	+	1.17322i
$772$		0			0
$773$	−15.8625	+	11.5248i	−0.570534	+	0.414517i	−0.835299	−	0.549796i	$-0.814706\pi$
$773$	−15.8625	+	11.5248i	−0.570534	+	0.414517i	0.264765	+	0.964313i	$0.414706\pi$
$774$		0			0
$775$	32.4412	+	8.17588i	1.16532	+	0.293686i
$776$		0			0
$777$	14.2380	−	10.3445i	0.510785	−	0.371107i
$778$		0			0
$779$	5.83480	−	17.9577i	0.209054	−	0.643401i
$780$		0			0
$781$	−5.39118	−	16.5923i	−0.192912	−	0.593721i
$782$		0			0
$783$	−15.2106	−	46.8133i	−0.543581	−	1.67297i
$784$		0			0
$785$	21.2151	+	38.3877i	0.757199	+	1.37011i
$786$		0			0
$787$	11.2403	+	8.16654i	0.400673	+	0.291106i	0.769815	−	0.638267i	$-0.220348\pi$
$787$	11.2403	+	8.16654i	0.400673	+	0.291106i	−0.369142	+	0.929373i	$0.620348\pi$
$788$		0			0
$789$	1.68864	−	1.22687i	0.0601170	−	0.0436776i
$790$		0			0
$791$	−32.8580	−	23.8727i	−1.16829	−	0.848816i
$792$		0			0
$793$	−42.6550			−1.51472
$794$		0			0
$795$	0.504331	−	4.06486i	0.0178868	−	0.144166i
$796$		0			0
$797$	9.06395	−	27.8960i	0.321062	−	0.988126i	−0.652125	−	0.758111i	$-0.726122\pi$
$797$	9.06395	−	27.8960i	0.321062	−	0.988126i	0.973187	−	0.230015i	$-0.0738776\pi$
$798$		0			0
$799$	−33.5355			−1.18640
$800$		0			0
$801$	−1.60674			−0.0567714
$802$		0			0
$803$	5.51235	−	16.9653i	0.194526	−	0.598691i
$804$		0			0
$805$	−7.28103	−	3.40644i	−0.256623	−	0.120061i
$806$		0			0
$807$	23.8918			0.841032
$808$		0			0
$809$	−20.2613	−	14.7207i	−0.712349	−	0.517552i	0.171582	−	0.985170i	$-0.445112\pi$
$809$	−20.2613	−	14.7207i	−0.712349	−	0.517552i	−0.883931	+	0.467618i	$0.845112\pi$
$810$		0			0
$811$	−4.89268	+	3.55474i	−0.171805	+	0.124824i	−0.670365	−	0.742032i	$-0.733862\pi$
$811$	−4.89268	+	3.55474i	−0.171805	+	0.124824i	0.498560	+	0.866855i	$0.333862\pi$
$812$		0			0
$813$	−2.99502	−	2.17601i	−0.105040	−	0.0763160i
$814$		0			0
$815$	4.20442	−	33.8872i	0.147275	−	1.18702i
$816$		0			0
$817$	−5.81612	−	17.9002i	−0.203480	−	0.626248i
$818$		0			0
$819$	1.29764	+	3.99371i	0.0453431	+	0.139552i
$820$		0			0
$821$	7.36777	−	22.6757i	0.257137	−	0.791386i	−0.736264	−	0.676694i	$-0.763412\pi$
$821$	7.36777	−	22.6757i	0.257137	−	0.791386i	0.993401	−	0.114692i	$-0.0365881\pi$
$822$		0			0
$823$	−1.82288	+	1.32440i	−0.0635414	+	0.0461656i	−0.619103	−	0.785310i	$-0.712503\pi$
$823$	−1.82288	+	1.32440i	−0.0635414	+	0.0461656i	0.555561	+	0.831476i	$0.312503\pi$
$824$		0			0
$825$	−22.3338	−	5.62861i	−0.777565	−	0.195963i
$826$		0			0
$827$	18.2058	−	13.2273i	0.633079	−	0.459959i	−0.224387	−	0.974500i	$-0.572038\pi$
$827$	18.2058	−	13.2273i	0.633079	−	0.459959i	0.857465	+	0.514542i	$0.172038\pi$
$828$		0			0
$829$	4.64584	−	14.2984i	0.161357	−	0.496605i	−0.837393	−	0.546602i	$-0.815921\pi$
$829$	4.64584	−	14.2984i	0.161357	−	0.496605i	0.998749	+	0.0499970i	$0.0159212\pi$
$830$		0			0
$831$	−3.75086	−	11.5440i	−0.130116	−	0.400456i
$832$		0			0
$833$	2.04559	+	6.29566i	0.0708753	+	0.218132i
$834$		0			0
$835$	1.72651	−	1.84676i	0.0597484	−	0.0639097i
$836$		0			0
$837$	−30.2160	−	21.9532i	−1.04442	−	0.758813i
$838$		0			0
$839$	17.2255	−	12.5150i	0.594689	−	0.432067i	−0.249301	−	0.968426i	$-0.580201\pi$
$839$	17.2255	−	12.5150i	0.594689	−	0.432067i	0.843990	+	0.536359i	$0.180201\pi$
$840$		0			0
$841$	−39.4489	−	28.6613i	−1.36031	−	0.988321i
$842$		0			0
$843$	−13.5284			−0.465944
$844$		0			0
$845$	7.72469	−	8.26270i	0.265737	−	0.284245i
$846$		0			0
$847$	−1.58784	+	4.88688i	−0.0545589	+	0.167915i
$848$		0			0
$849$	−41.2593			−1.41602
$850$		0			0
$851$	−6.91886			−0.237176
$852$		0			0
$853$	10.6164	−	32.6740i	0.363500	−	1.11874i	−0.587416	−	0.809285i	$-0.699855\pi$
$853$	10.6164	−	32.6740i	0.363500	−	1.11874i	0.950915	−	0.309452i	$-0.100145\pi$
$854$		0			0
$855$	−7.01186	+	1.35375i	−0.239800	+	0.0462972i
$856$		0			0
$857$	−0.0100587			−0.000343599			−0.000171800	−	1.00000i	$-0.500055\pi$
$857$	−0.0100587			−0.000343599			−0.000171800		1.00000i	$0.500055\pi$
$858$		0			0
$859$	12.0260	+	8.73743i	0.410323	+	0.298117i	0.773733	−	0.633512i	$-0.218387\pi$
$859$	12.0260	+	8.73743i	0.410323	+	0.298117i	−0.363410	+	0.931629i	$0.618387\pi$
$860$		0			0
$861$	−11.0127	+	8.00122i	−0.375313	+	0.272681i
$862$		0			0
$863$	24.2578	+	17.6243i	0.825744	+	0.599938i	0.918352	−	0.395765i	$-0.129520\pi$
$863$	24.2578	+	17.6243i	0.825744	+	0.599938i	−0.0926084	+	0.995703i	$0.529520\pi$
$864$		0			0
$865$	6.81912	+	3.19034i	0.231857	+	0.108475i
$866$		0			0
$867$	9.75552	+	30.0244i	0.331315	+	1.01968i
$868$		0			0
$869$	11.1857	+	34.4259i	0.379448	+	1.16782i
$870$		0			0
$871$	−12.8507	+	39.5504i	−0.435429	+	1.34011i
$872$		0			0
$873$	4.71424	−	3.42510i	0.159553	−	0.115922i
$874$		0			0
$875$	−27.1555	−	1.52670i	−0.918024	−	0.0516119i
$876$		0			0
$877$	4.67426	−	3.39605i	0.157839	−	0.114676i	−0.506063	−	0.862497i	$-0.668900\pi$
$877$	4.67426	−	3.39605i	0.157839	−	0.114676i	0.663901	+	0.747820i	$0.268900\pi$
$878$		0			0
$879$	6.56393	−	20.2017i	0.221396	−	0.681386i
$880$		0			0
$881$	13.2887	+	40.8983i	0.447706	+	1.37790i	0.879489	+	0.475920i	$0.157885\pi$
$881$	13.2887	+	40.8983i	0.447706	+	1.37790i	−0.431783	+	0.901978i	$0.642115\pi$
$882$		0			0
$883$	11.1993	+	34.4679i	0.376886	+	1.15994i	0.942197	+	0.335058i	$0.108756\pi$
$883$	11.1993	+	34.4679i	0.376886	+	1.15994i	−0.565311	+	0.824878i	$0.691244\pi$
$884$		0			0
$885$	−25.9512	−	12.1413i	−0.872339	−	0.408125i
$886$		0			0
$887$	4.08529	+	2.96814i	0.137171	+	0.0996602i	0.654255	−	0.756274i	$-0.272983\pi$
$887$	4.08529	+	2.96814i	0.137171	+	0.0996602i	−0.517084	+	0.855935i	$0.672983\pi$
$888$		0			0
$889$	23.6544	−	17.1859i	0.793344	−	0.576398i
$890$		0			0
$891$	16.3699	+	11.8934i	0.548411	+	0.398444i
$892$		0			0
$893$	28.5792			0.956366
$894$		0			0
$895$	−0.101648	+	0.0196247i	−0.00339771	+	0.000655980i
$896$		0			0
$897$	−1.98839	+	6.11965i	−0.0663905	+	0.204329i
$898$		0			0
$899$	−59.0039			−1.96789
$900$		0			0
$901$	−7.25316			−0.241638
$902$		0			0
$903$	−4.19302	+	12.9048i	−0.139535	+	0.429445i
$904$		0			0
$905$	−18.2421	+	19.5126i	−0.606386	+	0.648620i
$906$		0			0
$907$	−36.2922			−1.20506			−0.602532	−	0.798095i	$-0.705841\pi$
$907$	−36.2922			−1.20506			−0.602532	+	0.798095i	$0.705841\pi$
$908$		0			0
$909$	−0.716161	−	0.520322i	−0.0237536	−	0.0172580i
$910$		0			0
$911$	0.782203	−	0.568304i	0.0259155	−	0.0188287i	−0.574752	−	0.818328i	$-0.694902\pi$
$911$	0.782203	−	0.568304i	0.0259155	−	0.0188287i	0.600668	+	0.799499i	$0.294902\pi$
$912$		0			0
$913$	−29.5805	−	21.4915i	−0.978971	−	0.711264i
$914$		0			0
$915$	−35.7146	+	38.2020i	−1.18069	+	1.26292i
$916$		0			0
$917$	−13.3817	−	41.1848i	−0.441904	−	1.36004i
$918$		0			0
$919$	2.44217	+	7.51624i	0.0805599	+	0.247938i	0.983222	−	0.182412i	$-0.0583903\pi$
$919$	2.44217	+	7.51624i	0.0805599	+	0.247938i	−0.902662	+	0.430349i	$0.858390\pi$
$920$		0			0
$921$	2.58698	−	7.96190i	0.0852439	−	0.262354i
$922$		0			0
$923$	−13.3418	+	9.69335i	−0.439149	+	0.319061i
$924$		0			0
$925$	−21.7277	+	8.71456i	−0.714401	+	0.286533i
$926$		0			0
$927$	−2.75094	+	1.99867i	−0.0903526	+	0.0656450i
$928$		0			0
$929$	−5.33760	+	16.4275i	−0.175121	+	0.538967i	−0.999639	−	0.0268686i	$-0.991446\pi$
$929$	−5.33760	+	16.4275i	−0.175121	+	0.538967i	0.824518	+	0.565836i	$0.191446\pi$
$930$		0			0
$931$	−1.74326	−	5.36521i	−0.0571331	−	0.175838i
$932$		0			0
$933$	5.72574	+	17.6220i	0.187452	+	0.576919i
$934$		0			0
$935$	−5.02173	+	40.4747i	−0.164228	+	1.32366i
$936$		0			0
$937$	32.2197	+	23.4090i	1.05257	+	0.764738i	0.972700	−	0.232067i	$-0.0745488\pi$
$937$	32.2197	+	23.4090i	1.05257	+	0.764738i	0.0798723	+	0.996805i	$0.474549\pi$
$938$		0			0
$939$	6.37365	−	4.63073i	0.207996	−	0.151118i
$940$		0			0
$941$	−40.6179	−	29.5106i	−1.32411	−	0.962019i	−0.999871	−	0.0160420i	$-0.994893\pi$
$941$	−40.6179	−	29.5106i	−1.32411	−	0.962019i	−0.324234	−	0.945977i	$-0.605107\pi$
$942$		0			0
$943$	5.35157			0.174271
$944$		0			0
$945$	27.5025	+	12.8671i	0.894657	+	0.418567i
$946$		0			0
$947$	14.6528	−	45.0966i	0.476151	−	1.46544i	−0.368248	−	0.929727i	$-0.620042\pi$
$947$	14.6528	−	45.0966i	0.476151	−	1.46544i	0.844399	−	0.535714i	$-0.179958\pi$
$948$		0			0
$949$	−16.8620			−0.547362
$950$		0			0
$951$	10.9128			0.353872
$952$		0			0
$953$	−18.2380	+	56.1307i	−0.590786	+	1.81825i	−0.0161122	+	0.999870i	$0.505129\pi$
$953$	−18.2380	+	56.1307i	−0.590786	+	1.81825i	−0.574674	+	0.818382i	$0.694871\pi$
$954$		0			0
$955$	−2.38484	+	19.2216i	−0.0771716	+	0.621995i
$956$		0			0
$957$	40.6207			1.31308
$958$		0			0
$959$	30.8962	+	22.4474i	0.997690	+	0.724864i
$960$		0			0
$961$	−11.1409	+	8.09437i	−0.359385	+	0.261109i
$962$		0			0
$963$	−3.68729	−	2.67897i	−0.118821	−	0.0863287i
$964$		0			0
$965$	−3.75982	−	6.80321i	−0.121033	−	0.219003i
$966$		0			0
$967$	−15.6390	−	48.1319i	−0.502917	−	1.54782i	−0.804245	−	0.594298i	$-0.797430\pi$
$967$	−15.6390	−	48.1319i	−0.502917	−	1.54782i	0.301328	−	0.953520i	$-0.402570\pi$
$968$		0			0
$969$	−15.2312	−	46.8767i	−0.489295	−	1.50590i
$970$		0			0
$971$	15.5600	−	47.8887i	0.499343	−	1.53682i	−0.310734	−	0.950497i	$-0.600575\pi$
$971$	15.5600	−	47.8887i	0.499343	−	1.53682i	0.810077	−	0.586324i	$-0.199425\pi$
$972$		0			0
$973$	−11.9536	+	8.68478i	−0.383214	+	0.278421i
$974$		0			0
$975$	1.46366	+	21.7223i	0.0468746	+	0.695670i
$976$		0			0
$977$	−8.16192	+	5.92998i	−0.261123	+	0.189717i	−0.710642	−	0.703554i	$-0.751595\pi$
$977$	−8.16192	+	5.92998i	−0.261123	+	0.189717i	0.449519	+	0.893271i	$0.351595\pi$
$978$		0			0
$979$	2.41654	−	7.43735i	0.0772330	−	0.237699i
$980$		0			0
$981$	−1.75948	−	5.41512i	−0.0561758	−	0.172891i
$982$		0			0
$983$	9.47888	+	29.1730i	0.302329	+	0.930474i	0.980660	+	0.195718i	$0.0627036\pi$
$983$	9.47888	+	29.1730i	0.302329	+	0.930474i	−0.678331	+	0.734757i	$0.737296\pi$
$984$		0			0
$985$	−6.47078	+	1.24928i	−0.206176	+	0.0398055i
$986$		0			0
$987$	−16.6687	−	12.1105i	−0.530569	−	0.385481i
$988$		0			0
$989$	4.31565	−	3.13550i	0.137230	−	0.0997032i
$990$		0			0
$991$	−34.3611	−	24.9648i	−1.09152	−	0.793034i	−0.111863	−	0.993724i	$-0.535682\pi$
$991$	−34.3611	−	24.9648i	−1.09152	−	0.793034i	−0.979655	+	0.200690i	$0.935682\pi$
$992$		0			0
$993$	−8.97038			−0.284667
$994$		0			0
$995$	17.2219	+	31.1622i	0.545972	+	0.987909i
$996$		0			0
$997$	−1.13204	+	3.48407i	−0.0358522	+	0.110342i	−0.967381	−	0.253326i	$-0.918476\pi$
$997$	−1.13204	+	3.48407i	−0.0358522	+	0.110342i	0.931529	+	0.363667i	$0.118476\pi$
$998$		0			0
$999$	26.1345			0.826860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.f.161.3		12
4.3	odd	2		100.2.g.a.61.1	yes	12
12.11	even	2		900.2.n.c.361.1		12
20.3	even	4		500.2.i.b.449.2		24
20.7	even	4		500.2.i.b.449.5		24
20.19	odd	2		500.2.g.a.301.3		12
25.4	even	10		10000.2.a.bd.1.2		6
25.16	even	5	inner	400.2.u.f.241.3		12
25.21	even	5		10000.2.a.bc.1.5		6
100.3	even	20		2500.2.c.c.1249.4		12
100.47	even	20		2500.2.c.c.1249.9		12
100.59	odd	10		500.2.g.a.201.3		12
100.63	even	20		500.2.i.b.49.5		24
100.71	odd	10		2500.2.a.d.1.2		6
100.79	odd	10		2500.2.a.c.1.5		6
100.87	even	20		500.2.i.b.49.2		24
100.91	odd	10		100.2.g.a.41.1	✓	12
300.191	even	10		900.2.n.c.541.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.g.a.41.1	✓	12	100.91	odd	10
100.2.g.a.61.1	yes	12	4.3	odd	2
400.2.u.f.161.3		12	1.1	even	1	trivial
400.2.u.f.241.3		12	25.16	even	5	inner
500.2.g.a.201.3		12	100.59	odd	10
500.2.g.a.301.3		12	20.19	odd	2
500.2.i.b.49.2		24	100.87	even	20
500.2.i.b.49.5		24	100.63	even	20
500.2.i.b.449.2		24	20.3	even	4
500.2.i.b.449.5		24	20.7	even	4
900.2.n.c.361.1		12	12.11	even	2
900.2.n.c.541.1		12	300.191	even	10
2500.2.a.c.1.5		6	100.79	odd	10
2500.2.a.d.1.2		6	100.71	odd	10
2500.2.c.c.1249.4		12	100.3	even	20
2500.2.c.c.1249.9		12	100.47	even	20
10000.2.a.bc.1.5		6	25.21	even	5
10000.2.a.bd.1.2		6	25.4	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.477475 - 1.46952i) q^{3} +(1.08159 + 1.95708i) q^{5} +2.43270 q^{7} +(0.495552 + 0.360039i) q^{9} +O(q^{10})\)	\(q+(0.477475 - 1.46952i) q^{3} +(1.08159 + 1.95708i) q^{5} +2.43270 q^{7} +(0.495552 + 0.360039i) q^{9} +(-2.41187 + 1.75233i) q^{11} +(2.27986 + 1.65642i) q^{13} +(3.39240 - 0.654955i) q^{15} +(-1.89061 - 5.81868i) q^{17} +(1.61119 + 4.95872i) q^{19} +(1.16155 - 3.57489i) q^{21} +(-1.19552 + 0.868599i) q^{23} +(-2.66033 + 4.23351i) q^{25} +(4.51584 - 3.28095i) q^{27} +(2.72499 - 8.38665i) q^{29} +(-2.06767 - 6.36362i) q^{31} +(1.42347 + 4.38098i) q^{33} +(2.63118 + 4.76099i) q^{35} +(3.78784 + 2.75203i) q^{37} +(3.52271 - 2.55940i) q^{39} +(-2.92980 - 2.12862i) q^{41} -3.60984 q^{43} +(-0.168643 + 1.35925i) q^{45} +(1.69382 - 5.21306i) q^{47} -1.08197 q^{49} -9.45338 q^{51} +(0.366346 - 1.12750i) q^{53} +(-6.03810 - 2.82493i) q^{55} +8.05623 q^{57} +(-6.70876 - 4.87420i) q^{59} +(-12.2455 + 8.89689i) q^{61} +(1.20553 + 0.875867i) q^{63} +(-0.775870 + 6.25343i) q^{65} +(4.56011 + 14.0346i) q^{67} +(0.705588 + 2.17158i) q^{69} +(-1.80837 + 5.56558i) q^{71} +(-4.84077 + 3.51703i) q^{73} +(4.95098 + 5.93080i) q^{75} +(-5.86736 + 4.26289i) q^{77} +(3.75202 - 11.5475i) q^{79} +(-2.09736 - 6.45500i) q^{81} +(3.78995 + 11.6643i) q^{83} +(9.34278 - 9.99349i) q^{85} +(-11.0232 - 8.00884i) q^{87} +(-2.12213 + 1.54182i) q^{89} +(5.54622 + 4.02956i) q^{91} -10.3387 q^{93} +(-7.96198 + 8.51652i) q^{95} +(2.93972 - 9.04752i) q^{97} -1.82612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9	\( 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9} + 5 q^{11} - 2 q^{13} - 18 q^{15} + q^{17} + 8 q^{19} + 2 q^{21} + 6 q^{23} - 26 q^{25} + 34 q^{27} - 18 q^{29} - 12 q^{31} - 35 q^{33} + 3 q^{35} + 13 q^{37} - 22 q^{39} - 23 q^{41} - 50 q^{43} + 71 q^{45} - q^{47} + 34 q^{49} - 14 q^{51} + 21 q^{53} - 5 q^{55} + 72 q^{57} - 9 q^{59} - 26 q^{61} + 32 q^{63} - 18 q^{65} + 37 q^{67} - 44 q^{69} - 21 q^{71} + 18 q^{73} + 73 q^{75} - 60 q^{77} + 24 q^{79} + 18 q^{81} + 46 q^{83} - 16 q^{85} - 57 q^{87} - 2 q^{89} + 32 q^{91} + 22 q^{93} - 6 q^{95} - 7 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9 + 5 * q^11 - 2 * q^13 - 18 * q^15 + q^17 + 8 * q^19 + 2 * q^21 + 6 * q^23 - 26 * q^25 + 34 * q^27 - 18 * q^29 - 12 * q^31 - 35 * q^33 + 3 * q^35 + 13 * q^37 - 22 * q^39 - 23 * q^41 - 50 * q^43 + 71 * q^45 - q^47 + 34 * q^49 - 14 * q^51 + 21 * q^53 - 5 * q^55 + 72 * q^57 - 9 * q^59 - 26 * q^61 + 32 * q^63 - 18 * q^65 + 37 * q^67 - 44 * q^69 - 21 * q^71 + 18 * q^73 + 73 * q^75 - 60 * q^77 + 24 * q^79 + 18 * q^81 + 46 * q^83 - 16 * q^85 - 57 * q^87 - 2 * q^89 + 32 * q^91 + 22 * q^93 - 6 * q^95 - 7 * q^97 - 40 * q^99

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