LMFDB - Embedded newform 500.2.g.a.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [500,2,Mod(101,500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("500.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 500 = 2^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	500.g (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:	$3.99252010106$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.3
Root			$-1.25005 + 0.908212i$ of defining polynomial
Character	$\chi$	$=$	500.301
Dual form			500.2.g.a.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

$n$	$251$	$377$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			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
$5$		0			0
$5$		0			0
$6$		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	−0.161471	−	0.986877i	$-0.551624\pi$
$11$	2.41187	−	1.75233i	0.727207	−	0.528347i	0.888679	+	0.458530i	$0.151624\pi$
$12$		0			0
$13$	−2.27986	−	1.65642i	−0.632320	−	0.459407i	0.224883	−	0.974386i	$-0.427800\pi$
$13$	−2.27986	−	1.65642i	−0.632320	−	0.459407i	−0.857203	+	0.514978i	$0.827800\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.89061	+	5.81868i	0.458539	+	1.41124i	0.866929	+	0.498431i	$0.166090\pi$
$17$	1.89061	+	5.81868i	0.458539	+	1.41124i	−0.408390	+	0.912807i	$0.633910\pi$
$18$		0			0
$19$	−1.61119	−	4.95872i	−0.369632	−	1.13761i	−0.947030	−	0.321146i	$-0.895932\pi$
$19$	−1.61119	−	4.95872i	−0.369632	−	1.13761i	0.577398	−	0.816463i	$-0.304068\pi$
$20$		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
$25$		0			0
$26$		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	$0.105183\pi$
$31$	2.06767	+	6.36362i	0.371364	+	1.14294i	−0.574535	+	0.818480i	$0.694817\pi$
$32$		0			0
$33$	−1.42347	−	4.38098i	−0.247794	−	0.762631i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.78784	−	2.75203i	−0.622717	−	0.452431i	0.231152	−	0.972918i	$-0.425750\pi$
$37$	−3.78784	−	2.75203i	−0.622717	−	0.452431i	−0.853870	+	0.520487i	$0.825750\pi$
$38$		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			0
$46$		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	−0.973059	−	0.230554i	$-0.925946\pi$
$53$	−0.366346	+	1.12750i	−0.0503215	+	0.154874i	0.922738	+	0.385428i	$0.125946\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.05623			−1.06707
$58$		0			0
$59$	6.70876	+	4.87420i	0.873406	+	0.634567i	0.931499	−	0.363744i	$-0.118502\pi$
$59$	6.70876	+	4.87420i	0.873406	+	0.634567i	−0.0580925	+	0.998311i	$0.518502\pi$
$60$		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			0
$66$		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	$-0.787115\pi$
$71$	1.80837	−	5.56558i	0.214614	−	0.660513i	0.999181	−	0.0404693i	$-0.0128853\pi$
$72$		0			0
$73$	4.84077	−	3.51703i	0.566570	−	0.411637i	−0.267288	−	0.963617i	$-0.586127\pi$
$73$	4.84077	−	3.51703i	0.566570	−	0.411637i	0.833858	+	0.551980i	$0.186127\pi$
$74$		0			0
$75$		0			0
$76$		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	$0.339338\pi$
$79$	−3.75202	+	11.5475i	−0.422135	+	1.29920i	−0.905711	+	0.423896i	$0.860662\pi$
$80$		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
$85$		0			0
$86$		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
$95$		0			0
$96$		0			0
$97$	−2.93972	+	9.04752i	−0.298483	+	0.918636i	0.683546	+	0.729907i	$0.260437\pi$
$97$	−2.93972	+	9.04752i	−0.298483	+	0.918636i	−0.982029	+	0.188729i	$0.939563\pi$
$98$		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
$105$		0			0
$106$		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	0.999227	−	0.0393171i	$-0.0125182\pi$
$113$	13.5068	+	9.81326i	1.27061	+	0.923154i	0.271385	+	0.962471i	$0.412518\pi$
$114$		0			0
$115$		0			0
$116$		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
$125$		0			0
$126$		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	$0.183581\pi$
$131$	5.50078	+	16.9297i	0.480605	+	1.47915i	−0.357641	+	0.933859i	$0.616419\pi$
$132$		0			0
$133$	−3.91953	−	12.0631i	−0.339867	−	1.04600i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.7004	−	9.22736i	−1.08507	−	0.788347i	−0.106507	−	0.994312i	$-0.533967\pi$
$137$	−12.7004	−	9.22736i	−1.08507	−	0.788347i	−0.978559	+	0.205965i	$0.933967\pi$
$138$		0			0
$139$	4.91371	−	3.57002i	0.416775	−	0.302805i	−0.359564	−	0.933120i	$-0.617075\pi$
$139$	4.91371	−	3.57002i	0.416775	−	0.302805i	0.776339	+	0.630316i	$0.217075\pi$
$140$		0			0
$141$	−6.85192	−	4.97821i	−0.577036	−	0.419241i
$142$		0			0
$143$	−8.40132			−0.702554
$144$		0			0
$145$		0			0
$146$		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	$-0.637918\pi$
$151$	−10.3185			−0.839704			−0.419852	+	0.907593i	$0.637918\pi$
$152$		0			0
$153$	−1.15806	+	3.56415i	−0.0936238	+	0.288145i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−19.6148			−1.56543			−0.782714	−	0.622382i	$-0.786165\pi$
$157$	−19.6148			−1.56543			−0.782714	+	0.622382i	$0.786165\pi$
$158$		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
$165$		0			0
$166$		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	−0.686496	−	0.727133i	$-0.740852\pi$
$173$	−2.72385	+	1.97899i	−0.207090	+	0.150460i	0.479406	+	0.877593i	$0.340852\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.3660	−	7.53133i	0.779156	−	0.566090i
$178$		0			0
$179$	0.0143068	−	0.0440317i	0.00106934	−	0.00329108i	−0.950520	−	0.310662i	$-0.899449\pi$
$179$	0.0143068	−	0.0440317i	0.00106934	−	0.00329108i	0.951590	+	0.307371i	$0.0994493\pi$
$180$		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
$185$		0			0
$186$		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	0.304645	−	0.952466i	$-0.401462\pi$
$191$	−7.00775	−	5.09143i	−0.507063	−	0.368403i	−0.811708	+	0.584063i	$0.801462\pi$
$192$		0			0
$193$	3.47620			0.250222			0.125111	−	0.992143i	$-0.460071\pi$
$193$	3.47620			0.250222			0.125111	+	0.992143i	$0.460071\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.910753	−	2.80301i	0.0648885	−	0.199706i	−0.913356	−	0.407162i	$-0.866518\pi$
$197$	0.910753	−	2.80301i	0.0648885	−	0.199706i	0.978244	+	0.207456i	$0.0665184\pi$
$198$		0			0
$199$	−15.9228			−1.12874			−0.564369	−	0.825523i	$-0.690881\pi$
$199$	−15.9228			−1.12874			−0.564369	+	0.825523i	$0.690881\pi$
$200$		0			0
$201$	22.8014			1.60829
$202$		0			0
$203$	6.62908	−	20.4022i	0.465270	−	1.43195i
$204$		0			0
$205$		0			0
$206$		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	−0.200493	−	0.979695i	$-0.564254\pi$
$211$	9.72209	−	7.06351i	0.669296	−	0.486272i	0.869790	+	0.493423i	$0.164254\pi$
$212$		0			0
$213$	−7.31527	−	5.31486i	−0.501234	−	0.364168i
$214$		0			0
$215$		0			0
$216$		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
$225$		0			0
$226$		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	$-0.915755\pi$
$233$	−5.16070	−	15.8830i	−0.338089	−	1.04053i	0.627092	−	0.778945i	$-0.284245\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	15.1778	+	11.0273i	0.985904	+	0.716301i
$238$		0			0
$239$	8.36778	−	6.07955i	0.541267	−	0.393253i	−0.283288	−	0.959035i	$-0.591425\pi$
$239$	8.36778	−	6.07955i	0.541267	−	0.393253i	0.824555	+	0.565781i	$0.191425\pi$
$240$		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
$245$		0			0
$246$		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	$-0.364765\pi$
$251$	13.0605			0.824372			0.412186	+	0.911100i	$0.364765\pi$
$252$		0			0
$253$	−1.36138	+	4.18990i	−0.0855893	+	0.263417i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	22.1683			1.38282			0.691411	−	0.722461i	$-0.256989\pi$
$257$	22.1683			1.38282			0.691411	+	0.722461i	$0.256989\pi$
$258$		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
$265$		0			0
$266$		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	−0.971022	−	0.238988i	$-0.923184\pi$
$271$	−0.740383	+	2.27866i	−0.0449750	+	0.138419i	0.926047	+	0.377407i	$0.123184\pi$
$272$		0			0
$273$	−8.56969	+	6.22625i	−0.518662	+	0.376830i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.35533	+	4.61742i	−0.381855	+	0.277434i	−0.762110	−	0.647448i	$-0.775836\pi$
$277$	−6.35533	+	4.61742i	−0.381855	+	0.277434i	0.380255	+	0.924882i	$0.375836\pi$
$278$		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
$285$		0			0
$286$		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	$-0.631531\pi$
$293$	−13.7472			−0.803118			−0.401559	+	0.915833i	$0.631531\pi$
$294$		0			0
$295$		0			0
$296$		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
$305$		0			0
$306$		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	−0.277709	−	0.960665i	$-0.589575\pi$
$311$	9.70149	−	7.04854i	0.550121	−	0.399686i	0.827830	+	0.560979i	$0.189575\pi$
$312$		0			0
$313$	−4.12496	−	2.99696i	−0.233156	−	0.169398i	0.465073	−	0.885273i	$-0.346028\pi$
$313$	−4.12496	−	2.99696i	−0.233156	−	0.169398i	−0.698229	+	0.715875i	$0.746028\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.18248	−	6.71698i	−0.122580	−	0.377263i	0.870872	−	0.491509i	$-0.163555\pi$
$317$	−2.18248	−	6.71698i	−0.122580	−	0.377263i	−0.993452	+	0.114246i	$0.963555\pi$
$318$		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
$325$		0			0
$326$		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	0.988177	−	0.153317i	$-0.0489955\pi$
$331$	1.79401	+	5.52140i	0.0986077	+	0.303483i	−0.889569	+	0.456800i	$0.848995\pi$
$332$		0			0
$333$	−0.886233	−	2.72754i	−0.0485652	−	0.149468i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.10613	+	0.803650i	0.0602547	+	0.0437776i	0.617505	−	0.786567i	$-0.288144\pi$
$337$	1.10613	+	0.803650i	0.0602547	+	0.0437776i	−0.557250	+	0.830345i	$0.688144\pi$
$338$		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
$345$		0			0
$346$		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	$0.272109\pi$
$353$	−5.97697	+	18.3952i	−0.318122	+	0.979079i	−0.974450	+	0.224604i	$0.927891\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	22.9972			1.21714
$358$		0			0
$359$	4.66127	+	3.38661i	0.246013	+	0.178739i	0.703958	−	0.710242i	$-0.251414\pi$
$359$	4.66127	+	3.38661i	0.246013	+	0.178739i	−0.457945	+	0.888980i	$0.651414\pi$
$360$		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
$365$		0			0
$366$		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	−0.975854	−	0.218426i	$-0.929908\pi$
$373$	−20.6588	+	15.0095i	−1.06967	+	0.777163i	−0.0938202	+	0.995589i	$0.529908\pi$
$374$		0			0
$375$		0			0
$376$		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	$-0.788303\pi$
$379$	4.13595	−	12.7291i	0.212449	−	0.653852i	0.999325	−	0.0367400i	$-0.0116973\pi$
$380$		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
$385$		0			0
$386$		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
$395$		0			0
$396$		0			0
$397$	−0.838720	+	2.58132i	−0.0420942	+	0.129552i	−0.969895	−	0.243523i	$-0.921697\pi$
$397$	−0.838720	+	2.58132i	−0.0420942	+	0.129552i	0.927801	+	0.373076i	$0.121697\pi$
$398$		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
$405$		0			0
$406$		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
$415$		0			0
$416$		0			0
$417$	−2.90003	−	8.92537i	−0.142015	−	0.437077i
$418$		0			0
$419$	−2.20300	−	6.78014i	−0.107624	−	0.331232i	0.882714	−	0.469911i	$-0.155714\pi$
$419$	−2.20300	−	6.78014i	−0.107624	−	0.331232i	−0.990337	+	0.138680i	$0.955714\pi$
$420$		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
$425$		0			0
$426$		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	$-0.835272\pi$
$431$	−9.48261	−	29.1845i	−0.456761	−	1.40577i	0.412294	−	0.911051i	$-0.364728\pi$
$432$		0			0
$433$	−0.963040	−	2.96393i	−0.0462808	−	0.142438i	0.925246	−	0.379368i	$-0.123859\pi$
$433$	−0.963040	−	2.96393i	−0.0462808	−	0.142438i	−0.971527	+	0.236931i	$0.923859\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.23335	+	4.52880i	0.298182	+	0.216642i
$438$		0			0
$439$	−12.1537	+	8.83019i	−0.580065	+	0.421442i	−0.838748	−	0.544520i	$-0.816712\pi$
$439$	−12.1537	+	8.83019i	−0.580065	+	0.421442i	0.258682	+	0.965962i	$0.416712\pi$
$440$		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
$445$		0			0
$446$		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
$455$		0			0
$456$		0			0
$457$	11.0889			0.518716			0.259358	−	0.965781i	$-0.416489\pi$
$457$	11.0889			0.518716			0.259358	+	0.965781i	$0.416489\pi$
$458$		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
$465$		0			0
$466$		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
$475$		0			0
$476$		0			0
$477$	−0.587486	+	0.426834i	−0.0268992	+	0.0195434i
$478$		0			0
$479$	−1.53880	+	4.73594i	−0.0703095	+	0.216390i	−0.980037	−	0.198816i	$-0.936291\pi$
$479$	−1.53880	+	4.73594i	−0.0703095	+	0.216390i	0.909727	+	0.415206i	$0.136291\pi$
$480$		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
$485$		0			0
$486$		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	0.539488	−	0.841994i	$-0.318618\pi$
$491$	−2.09586	−	1.52273i	−0.0945849	−	0.0687199i	−0.634073	+	0.773274i	$0.718618\pi$
$492$		0			0
$493$	53.9512			2.42984
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.39922	−	13.5394i	0.197332	−	0.607325i
$498$		0			0
$499$	−10.7285			−0.480272			−0.240136	−	0.970739i	$-0.577192\pi$
$499$	−10.7285			−0.480272			−0.240136	+	0.970739i	$0.577192\pi$
$500$		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
$505$		0			0
$506$		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
$515$		0			0
$516$		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
$525$		0			0
$526$		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
$535$		0			0
$536$		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
$545$		0			0
$546$		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
$555$		0			0
$556$		0			0
$557$	1.20057			0.0508700			0.0254350	−	0.999676i	$-0.491903\pi$
$557$	1.20057			0.0508700			0.0254350	+	0.999676i	$0.491903\pi$
$558$		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
$565$		0			0
$566$		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	$-0.716287\pi$
$571$	8.05817	−	24.8005i	0.337224	−	1.03787i	0.965616	−	0.259972i	$-0.0837134\pi$
$572$		0			0
$573$	−10.8280	+	7.86698i	−0.452345	+	0.328648i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−13.7137	+	9.96356i	−0.570907	+	0.414789i	−0.835435	−	0.549590i	$-0.814784\pi$
$577$	−13.7137	+	9.96356i	−0.570907	+	0.414789i	0.264527	+	0.964378i	$0.414784\pi$
$578$		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
$585$		0			0
$586$		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	$-0.782600\pi$
$593$	−37.7787			−1.55139			−0.775694	+	0.631110i	$0.782600\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.60275	+	23.3989i	−0.311160	+	0.957651i
$598$		0			0
$599$	8.06719			0.329617			0.164808	−	0.986326i	$-0.447299\pi$
$599$	8.06719			0.329617			0.164808	+	0.986326i	$0.447299\pi$
$600$		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
$605$		0			0
$606$		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	0.676280	−	0.736644i	$-0.263591\pi$
$613$	4.57226	+	3.32194i	0.184672	+	0.134172i	−0.491608	+	0.870816i	$0.663591\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.9382	−	39.8198i	−0.520874	−	1.60308i	−0.772334	−	0.635216i	$-0.780911\pi$
$617$	−12.9382	−	39.8198i	−0.520874	−	1.60308i	0.251461	−	0.967868i	$-0.419089\pi$
$618$		0			0
$619$	−5.52654	−	17.0089i	−0.222130	−	0.683647i	−0.998570	−	0.0534558i	$-0.982976\pi$
$619$	−5.52654	−	17.0089i	−0.222130	−	0.683647i	0.776440	−	0.630191i	$-0.217024\pi$
$620$		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
$625$		0			0
$626$		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	$-0.822047\pi$
$631$	−11.8982	−	36.6189i	−0.473660	−	1.45778i	0.374096	−	0.927390i	$-0.377953\pi$
$632$		0			0
$633$	−5.73790	−	17.6594i	−0.228061	−	0.701900i
$634$		0			0
$635$		0			0
$636$		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
$645$		0			0
$646$		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	$-0.586158\pi$
$653$	13.1684	−	40.5282i	0.515319	−	1.58599i	0.782701	−	0.622398i	$-0.213842\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.66512			0.142990
$658$		0			0
$659$	−18.7933	−	13.6541i	−0.732082	−	0.531889i	0.158139	−	0.987417i	$-0.449450\pi$
$659$	−18.7933	−	13.6541i	−0.732082	−	0.531889i	−0.890221	+	0.455528i	$0.849450\pi$
$660$		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
$665$		0			0
$666$		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	−0.698435	−	0.715673i	$-0.746120\pi$
$673$	−6.06059	+	4.40327i	−0.233618	+	0.169734i	0.464817	+	0.885407i	$0.346120\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.3719	−	15.5276i	0.821389	−	0.596774i	−0.0957209	−	0.995408i	$-0.530516\pi$
$677$	21.3719	−	15.5276i	0.821389	−	0.596774i	0.917110	+	0.398634i	$0.130516\pi$
$678$		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
$685$		0			0
$686$		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	0.989190	−	0.146641i	$-0.0468462\pi$
$691$	30.3719	+	22.0665i	1.15540	+	0.839449i	0.166212	+	0.986090i	$0.446846\pi$
$692$		0			0
$693$	4.44239			0.168752
$694$		0			0
$695$		0			0
$696$		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
$705$		0			0
$706$		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
$715$		0			0
$716$		0			0
$717$	−4.93860	−	15.1994i	−0.184435	−	0.567633i
$718$		0			0
$719$	−1.84285	−	5.67172i	−0.0687268	−	0.211519i	0.910794	−	0.412860i	$-0.135470\pi$
$719$	−1.84285	−	5.67172i	−0.0687268	−	0.211519i	−0.979521	+	0.201341i	$0.935470\pi$
$720$		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
$725$		0			0
$726$		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	0.847969	−	0.530046i	$-0.177825\pi$
$733$	−4.05041	−	12.4659i	−0.149605	−	0.460438i	−0.997574	+	0.0696075i	$0.977825\pi$
$734$		0			0
$735$		0			0
$736$		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	$-0.340471\pi$
$739$	39.7715	−	28.8957i	1.46302	−	1.06295i	0.982564	−	0.185927i	$-0.0595288\pi$
$740$		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
$745$		0			0
$746$		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	$-0.239050\pi$
$751$	40.0656			1.46202			0.731008	+	0.682369i	$0.239050\pi$
$752$		0			0
$753$	6.23607	−	19.1927i	0.227255	−	0.699419i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−8.47793			−0.308136			−0.154068	−	0.988060i	$-0.549237\pi$
$757$	−8.47793			−0.308136			−0.154068	+	0.988060i	$0.549237\pi$
$758$		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
$765$		0			0
$766$		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	−0.264765	−	0.964313i	$-0.585294\pi$
$773$	15.8625	−	11.5248i	0.570534	−	0.414517i	0.835299	+	0.549796i	$0.185294\pi$
$774$		0			0
$775$		0			0
$776$		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
$785$		0			0
$786$		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			0
$796$		0			0
$797$	−9.06395	+	27.8960i	−0.321062	+	0.988126i	0.652125	+	0.758111i	$0.273878\pi$
$797$	−9.06395	+	27.8960i	−0.321062	+	0.988126i	−0.973187	+	0.230015i	$0.926122\pi$
$798$		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
$805$		0			0
$806$		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	−0.498560	−	0.866855i	$-0.666138\pi$
$811$	4.89268	−	3.55474i	0.171805	−	0.124824i	0.670365	+	0.742032i	$0.266138\pi$
$812$		0			0
$813$	2.99502	+	2.17601i	0.105040	+	0.0763160i
$814$		0			0
$815$		0			0
$816$		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
$825$		0			0
$826$		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
$835$		0			0
$836$		0			0
$837$	30.2160	+	21.9532i	1.04442	+	0.758813i
$838$		0			0
$839$	−17.2255	+	12.5150i	−0.594689	+	0.432067i	−0.843990	−	0.536359i	$-0.819799\pi$
$839$	−17.2255	+	12.5150i	−0.594689	+	0.432067i	0.249301	+	0.968426i	$0.419799\pi$
$840$		0			0
$841$	−39.4489	−	28.6613i	−1.36031	−	0.988321i
$842$		0			0
$843$	−13.5284			−0.465944
$844$		0			0
$845$		0			0
$846$		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	$0.300145\pi$
$853$	−10.6164	+	32.6740i	−0.363500	+	1.11874i	−0.950915	+	0.309452i	$0.899855\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.0100587			0.000343599			0.000171800	−	1.00000i	$-0.499945\pi$
$857$	0.0100587			0.000343599			0.000171800		1.00000i	$0.499945\pi$
$858$		0			0
$859$	−12.0260	−	8.73743i	−0.410323	−	0.298117i	0.363410	−	0.931629i	$-0.381613\pi$
$859$	−12.0260	−	8.73743i	−0.410323	−	0.298117i	−0.773733	+	0.633512i	$0.781613\pi$
$860$		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
$865$		0			0
$866$		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
$875$		0			0
$876$		0			0
$877$	−4.67426	+	3.39605i	−0.157839	+	0.114676i	−0.663901	−	0.747820i	$-0.731100\pi$
$877$	−4.67426	+	3.39605i	−0.157839	+	0.114676i	0.506063	+	0.862497i	$0.331100\pi$
$878$		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
$885$		0			0
$886$		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			0
$896$		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
$905$		0			0
$906$		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	−0.600668	−	0.799499i	$-0.705098\pi$
$911$	−0.782203	+	0.568304i	−0.0259155	+	0.0188287i	0.574752	+	0.818328i	$0.305098\pi$
$912$		0			0
$913$	29.5805	+	21.4915i	0.978971	+	0.711264i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.3817	+	41.1848i	0.441904	+	1.36004i
$918$		0			0
$919$	−2.44217	−	7.51624i	−0.0805599	−	0.247938i	0.902662	−	0.430349i	$-0.141610\pi$
$919$	−2.44217	−	7.51624i	−0.0805599	−	0.247938i	−0.983222	+	0.182412i	$0.941610\pi$
$920$		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
$925$		0			0
$926$		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
$935$		0			0
$936$		0			0
$937$	−32.2197	−	23.4090i	−1.05257	−	0.764738i	−0.0798723	−	0.996805i	$-0.525451\pi$
$937$	−32.2197	−	23.4090i	−1.05257	−	0.764738i	−0.972700	+	0.232067i	$0.925451\pi$
$938$		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
$945$		0			0
$946$		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	$-0.494871\pi$
$953$	18.2380	−	56.1307i	0.590786	−	1.81825i	0.574674	−	0.818382i	$-0.305129\pi$
$954$		0			0
$955$		0			0
$956$		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
$965$		0			0
$966$		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	$0.399425\pi$
$971$	−15.5600	+	47.8887i	−0.499343	+	1.53682i	−0.810077	+	0.586324i	$0.800575\pi$
$972$		0			0
$973$	11.9536	−	8.68478i	0.383214	−	0.278421i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.16192	−	5.92998i	0.261123	−	0.189717i	−0.449519	−	0.893271i	$-0.648405\pi$
$977$	8.16192	−	5.92998i	0.261123	−	0.189717i	0.710642	+	0.703554i	$0.248405\pi$
$978$		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
$985$		0			0
$986$		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	0.979655	−	0.200690i	$-0.0643183\pi$
$991$	34.3611	+	24.9648i	1.09152	+	0.793034i	0.111863	+	0.993724i	$0.464318\pi$
$992$		0			0
$993$	8.97038			0.284667
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.13204	−	3.48407i	0.0358522	−	0.110342i	−0.931529	−	0.363667i	$-0.881524\pi$
$997$	1.13204	−	3.48407i	0.0358522	−	0.110342i	0.967381	+	0.253326i	$0.0815245\pi$
$998$		0			0
$999$	−26.1345			−0.826860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.2.g.a.301.3		12
5.2	odd	4		500.2.i.b.449.2		24
5.3	odd	4		500.2.i.b.449.5		24
5.4	even	2		100.2.g.a.61.1	yes	12
15.14	odd	2		900.2.n.c.361.1		12
20.19	odd	2		400.2.u.f.161.3		12
25.3	odd	20		2500.2.c.c.1249.9		12
25.4	even	10		2500.2.a.d.1.2		6
25.9	even	10		100.2.g.a.41.1	✓	12
25.12	odd	20		500.2.i.b.49.5		24
25.13	odd	20		500.2.i.b.49.2		24
25.16	even	5	inner	500.2.g.a.201.3		12
25.21	even	5		2500.2.a.c.1.5		6
25.22	odd	20		2500.2.c.c.1249.4		12
75.59	odd	10		900.2.n.c.541.1		12
100.59	odd	10		400.2.u.f.241.3		12
100.71	odd	10		10000.2.a.bd.1.2		6
100.79	odd	10		10000.2.a.bc.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.g.a.41.1	✓	12	25.9	even	10
100.2.g.a.61.1	yes	12	5.4	even	2
400.2.u.f.161.3		12	20.19	odd	2
400.2.u.f.241.3		12	100.59	odd	10
500.2.g.a.201.3		12	25.16	even	5	inner
500.2.g.a.301.3		12	1.1	even	1	trivial
500.2.i.b.49.2		24	25.13	odd	20
500.2.i.b.49.5		24	25.12	odd	20
500.2.i.b.449.2		24	5.2	odd	4
500.2.i.b.449.5		24	5.3	odd	4
900.2.n.c.361.1		12	15.14	odd	2
900.2.n.c.541.1		12	75.59	odd	10
2500.2.a.c.1.5		6	25.21	even	5
2500.2.a.d.1.2		6	25.4	even	10
2500.2.c.c.1249.4		12	25.22	odd	20
2500.2.c.c.1249.9		12	25.3	odd	20
10000.2.a.bc.1.5		6	100.79	odd	10
10000.2.a.bd.1.2		6	100.71	odd	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:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	500.g (of order \(5\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more