LMFDB - Embedded newform 1064.2.q.l.457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, degree $2$, 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:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.1
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	1064.457
Dual form			1064.2.q.l.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.63746 + 4.56821i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(0.137459 + 0.238085i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-2.27492 - 4.77753i) q^{21} +(-3.77492 + 6.53835i) q^{23} +(2.00000 + 3.46410i) q^{25} +4.00000 q^{27} -4.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-5.27492 + 9.13642i) q^{33} +(-1.50000 + 2.17945i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{39} +10.5498 q^{41} -1.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(-2.63746 + 4.56821i) q^{47} +(6.91238 + 1.10411i) q^{49} +(-0.274917 + 0.476171i) q^{51} +(-4.27492 - 7.40437i) q^{53} +5.27492 q^{55} +2.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-2.36254 + 4.09204i) q^{61} +(1.50000 - 2.17945i) q^{63} +(1.00000 - 1.73205i) q^{65} -15.0997 q^{69} -4.54983 q^{71} +(-5.63746 - 9.76436i) q^{73} +(-4.00000 + 6.92820i) q^{75} +(-6.00000 - 12.6005i) q^{77} +(7.27492 - 12.6005i) q^{79} +(5.50000 + 9.52628i) q^{81} -3.54983 q^{83} +0.274917 q^{85} +(-4.00000 - 6.92820i) q^{87} +(-0.725083 + 1.25588i) q^{89} +(-5.27492 - 0.418627i) q^{91} +(-4.00000 + 6.92820i) q^{93} +(-0.500000 - 0.866025i) q^{95} -6.54983 q^{97} -5.27492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 + 2 * q^5 - 3 * q^7 - 2 * q^9	$ 4 q + 4 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9} + 3 q^{11} + 8 q^{13} + 8 q^{15} - 7 q^{17} + 2 q^{19} + 6 q^{21} + 8 q^{25} + 16 q^{27} - 16 q^{29} + 8 q^{31} - 6 q^{33} - 6 q^{35} - 4 q^{37} + 8 q^{39} + 12 q^{41} - 4 q^{43} + 2 q^{45} - 3 q^{47} + 5 q^{49} + 14 q^{51} - 2 q^{53} + 6 q^{55} + 8 q^{57} + 8 q^{59} - 17 q^{61} + 6 q^{63} + 4 q^{65} + 12 q^{71} - 15 q^{73} - 16 q^{75} - 24 q^{77} + 14 q^{79} + 22 q^{81} + 16 q^{83} - 14 q^{85} - 16 q^{87} - 18 q^{89} - 6 q^{91} - 16 q^{93} - 2 q^{95} + 4 q^{97} - 6 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 + 2 * q^5 - 3 * q^7 - 2 * q^9 + 3 * q^11 + 8 * q^13 + 8 * q^15 - 7 * q^17 + 2 * q^19 + 6 * q^21 + 8 * q^25 + 16 * q^27 - 16 * q^29 + 8 * q^31 - 6 * q^33 - 6 * q^35 - 4 * q^37 + 8 * q^39 + 12 * q^41 - 4 * q^43 + 2 * q^45 - 3 * q^47 + 5 * q^49 + 14 * q^51 - 2 * q^53 + 6 * q^55 + 8 * q^57 + 8 * q^59 - 17 * q^61 + 6 * q^63 + 4 * q^65 + 12 * q^71 - 15 * q^73 - 16 * q^75 - 24 * q^77 + 14 * q^79 + 22 * q^81 + 16 * q^83 - 14 * q^85 - 16 * q^87 - 18 * q^89 - 6 * q^91 - 16 * q^93 - 2 * q^95 + 4 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	0.995782	+	0.0917517i	$0.0292466\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	−0.418432	+	0.908248i	$0.637420\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	−2.63746	−	0.209313i	−0.996866	−	0.0791130i
$7$	−2.63746	−	0.209313i	−0.996866	−	0.0791130i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.63746	+	4.56821i	0.795224	+	1.37737i	0.922697	+	0.385526i	$0.125980\pi$
$11$	2.63746	+	4.56821i	0.795224	+	1.37737i	−0.127473	+	0.991842i	$0.540687\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$	0.137459	+	0.238085i	0.0333386	+	0.0577442i	0.882213	−	0.470850i	$-0.156053\pi$
$17$	0.137459	+	0.238085i	0.0333386	+	0.0577442i	−0.848875	+	0.528594i	$0.822719\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$		0			0
$21$	−2.27492	−	4.77753i	−0.496428	−	1.04254i
$22$		0			0
$23$	−3.77492	+	6.53835i	−0.787125	+	1.36334i	0.140597	+	0.990067i	$0.455098\pi$
$23$	−3.77492	+	6.53835i	−0.787125	+	1.36334i	−0.927722	+	0.373273i	$0.878235\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	−5.27492	+	9.13642i	−0.918245	+	1.59045i
$34$		0			0
$35$	−1.50000	+	2.17945i	−0.253546	+	0.368394i
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	10.5498			1.64761			0.823804	−	0.566875i	$-0.191848\pi$
$41$	10.5498			1.64761			0.823804	+	0.566875i	$0.191848\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	−2.63746	+	4.56821i	−0.384713	+	0.666342i	−0.991729	−	0.128347i	$-0.959033\pi$
$47$	−2.63746	+	4.56821i	−0.384713	+	0.666342i	0.607016	+	0.794689i	$0.292366\pi$
$48$		0			0
$49$	6.91238	+	1.10411i	0.987482	+	0.157730i
$50$		0			0
$51$	−0.274917	+	0.476171i	−0.0384961	+	0.0666772i
$52$		0			0
$53$	−4.27492	−	7.40437i	−0.587205	−	1.01707i	−0.994597	−	0.103815i	$-0.966895\pi$
$53$	−4.27492	−	7.40437i	−0.587205	−	1.01707i	0.407392	−	0.913254i	$-0.366438\pi$
$54$		0			0
$55$	5.27492			0.711270
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−2.36254	+	4.09204i	−0.302492	+	0.523932i	−0.976700	−	0.214610i	$-0.931152\pi$
$61$	−2.36254	+	4.09204i	−0.302492	+	0.523932i	0.674207	+	0.738542i	$0.264485\pi$
$62$		0			0
$63$	1.50000	−	2.17945i	0.188982	−	0.274585i
$64$		0			0
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$		0			0
$69$	−15.0997			−1.81779
$70$		0			0
$71$	−4.54983			−0.539966			−0.269983	−	0.962865i	$-0.587018\pi$
$71$	−4.54983			−0.539966			−0.269983	+	0.962865i	$0.587018\pi$
$72$		0			0
$73$	−5.63746	−	9.76436i	−0.659815	−	1.14283i	−0.980663	−	0.195702i	$-0.937301\pi$
$73$	−5.63746	−	9.76436i	−0.659815	−	1.14283i	0.320849	−	0.947130i	$-0.396032\pi$
$74$		0			0
$75$	−4.00000	+	6.92820i	−0.461880	+	0.800000i
$76$		0			0
$77$	−6.00000	−	12.6005i	−0.683763	−	1.43596i
$78$		0			0
$79$	7.27492	−	12.6005i	0.818492	−	1.41767i	−0.0883009	−	0.996094i	$-0.528144\pi$
$79$	7.27492	−	12.6005i	0.818492	−	1.41767i	0.906793	−	0.421576i	$-0.138523\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	−3.54983			−0.389645			−0.194822	−	0.980839i	$-0.562413\pi$
$83$	−3.54983			−0.389645			−0.194822	+	0.980839i	$0.562413\pi$
$84$		0			0
$85$	0.274917			0.0298190
$86$		0			0
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$		0			0
$89$	−0.725083	+	1.25588i	−0.0768586	+	0.133123i	−0.901893	−	0.431959i	$-0.857822\pi$
$89$	−0.725083	+	1.25588i	−0.0768586	+	0.133123i	0.825034	+	0.565083i	$0.191156\pi$
$90$		0			0
$91$	−5.27492	−	0.418627i	−0.552962	−	0.0438840i
$92$		0			0
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$		0			0
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	−6.54983			−0.665035			−0.332517	−	0.943097i	$-0.607898\pi$
$97$	−6.54983			−0.665035			−0.332517	+	0.943097i	$0.607898\pi$
$98$		0			0
$99$	−5.27492			−0.530149
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	−0.999964	−	0.00844953i	$-0.997310\pi$
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	0.507300	+	0.861770i	$0.330644\pi$
$104$		0			0
$105$	−5.27492	−	0.418627i	−0.514779	−	0.0408538i
$106$		0			0
$107$	9.27492	−	16.0646i	0.896640	−	1.55303i	0.0648785	−	0.997893i	$-0.479334\pi$
$107$	9.27492	−	16.0646i	0.896640	−	1.55303i	0.831762	−	0.555133i	$-0.187333\pi$
$108$		0			0
$109$	−2.27492	−	3.94027i	−0.217898	−	0.377410i	0.736267	−	0.676691i	$-0.236587\pi$
$109$	−2.27492	−	3.94027i	−0.217898	−	0.377410i	−0.954165	+	0.299281i	$0.903253\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$		0			0
$113$	3.45017			0.324564			0.162282	−	0.986744i	$-0.448115\pi$
$113$	3.45017			0.324564			0.162282	+	0.986744i	$0.448115\pi$
$114$		0			0
$115$	3.77492	+	6.53835i	0.352013	+	0.609704i
$116$		0			0
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$		0			0
$119$	−0.312707	−	0.656712i	−0.0286658	−	0.0602007i
$120$		0			0
$121$	−8.41238	+	14.5707i	−0.764761	+	1.32461i
$122$		0			0
$123$	10.5498	+	18.2728i	0.951247	+	1.64761i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	15.0997			1.33988			0.669939	−	0.742416i	$-0.266320\pi$
$127$	15.0997			1.33988			0.669939	+	0.742416i	$0.266320\pi$
$128$		0			0
$129$	−1.00000	−	1.73205i	−0.0880451	−	0.152499i
$130$		0			0
$131$	−3.41238	+	5.91041i	−0.298141	+	0.516395i	−0.975711	−	0.219064i	$-0.929700\pi$
$131$	−3.41238	+	5.91041i	−0.298141	+	0.516395i	0.677570	+	0.735458i	$0.263033\pi$
$132$		0			0
$133$	−1.50000	+	2.17945i	−0.130066	+	0.188982i
$134$		0			0
$135$	2.00000	−	3.46410i	0.172133	−	0.298142i
$136$		0			0
$137$	−5.63746	−	9.76436i	−0.481641	−	0.834226i	0.518137	−	0.855297i	$-0.326626\pi$
$137$	−5.63746	−	9.76436i	−0.481641	−	0.834226i	−0.999778	+	0.0210714i	$0.993292\pi$
$138$		0			0
$139$	11.8248			1.00296			0.501481	−	0.865169i	$-0.332789\pi$
$139$	11.8248			1.00296			0.501481	+	0.865169i	$0.332789\pi$
$140$		0			0
$141$	−10.5498			−0.888456
$142$		0			0
$143$	5.27492	+	9.13642i	0.441111	+	0.764026i
$144$		0			0
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$		0			0
$147$	5.00000	+	13.0767i	0.412393	+	1.07855i
$148$		0			0
$149$	8.04983	−	13.9427i	0.659468	−	1.14223i	−0.321285	−	0.946982i	$-0.604115\pi$
$149$	8.04983	−	13.9427i	0.659468	−	1.14223i	0.980754	−	0.195250i	$-0.0625518\pi$
$150$		0			0
$151$	−3.27492	−	5.67232i	−0.266509	−	0.461607i	0.701449	−	0.712720i	$-0.252537\pi$
$151$	−3.27492	−	5.67232i	−0.266509	−	0.461607i	−0.967958	+	0.251113i	$0.919204\pi$
$152$		0			0
$153$	−0.274917			−0.0222257
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	−7.04983	−	12.2107i	−0.562638	−	0.974518i	−0.997265	−	0.0739072i	$-0.976453\pi$
$157$	−7.04983	−	12.2107i	−0.562638	−	0.974518i	0.434627	−	0.900611i	$-0.356880\pi$
$158$		0			0
$159$	8.54983	−	14.8087i	0.678046	−	1.17441i
$160$		0			0
$161$	11.3248	−	16.4545i	0.892515	−	1.29679i
$162$		0			0
$163$	10.7749	−	18.6627i	0.843957	−	1.46178i	−0.0425676	−	0.999094i	$-0.513554\pi$
$163$	10.7749	−	18.6627i	0.843957	−	1.46178i	0.886524	−	0.462682i	$-0.153113\pi$
$164$		0			0
$165$	5.27492	+	9.13642i	0.410652	+	0.711270i
$166$		0			0
$167$	13.0997			1.01368			0.506841	−	0.862039i	$-0.330813\pi$
$167$	13.0997			1.01368			0.506841	+	0.862039i	$0.330813\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$		0			0
$173$	−10.2749	+	17.7967i	−0.781187	+	1.35306i	0.150063	+	0.988676i	$0.452052\pi$
$173$	−10.2749	+	17.7967i	−0.781187	+	1.35306i	−0.931250	+	0.364380i	$0.881281\pi$
$174$		0			0
$175$	−4.54983	−	9.55505i	−0.343935	−	0.722294i
$176$		0			0
$177$	−4.00000	+	6.92820i	−0.300658	+	0.520756i
$178$		0			0
$179$	7.54983	+	13.0767i	0.564301	+	0.977398i	0.997114	+	0.0759146i	$0.0241876\pi$
$179$	7.54983	+	13.0767i	0.564301	+	0.977398i	−0.432813	+	0.901484i	$0.642479\pi$
$180$		0			0
$181$	0.549834			0.0408689			0.0204344	−	0.999791i	$-0.493495\pi$
$181$	0.549834			0.0408689			0.0204344	+	0.999791i	$0.493495\pi$
$182$		0			0
$183$	−9.45017			−0.698576
$184$		0			0
$185$	1.00000	+	1.73205i	0.0735215	+	0.127343i
$186$		0			0
$187$	−0.725083	+	1.25588i	−0.0530233	+	0.0918391i
$188$		0			0
$189$	−10.5498	−	0.837253i	−0.767388	−	0.0609012i
$190$		0			0
$191$	10.5000	−	18.1865i	0.759753	−	1.31593i	−0.183223	−	0.983071i	$-0.558653\pi$
$191$	10.5000	−	18.1865i	0.759753	−	1.31593i	0.942976	−	0.332860i	$-0.108014\pi$
$192$		0			0
$193$	1.54983	+	2.68439i	0.111560	+	0.193227i	0.916399	−	0.400265i	$-0.131082\pi$
$193$	1.54983	+	2.68439i	0.111560	+	0.193227i	−0.804840	+	0.593492i	$0.797749\pi$
$194$		0			0
$195$	4.00000			0.286446
$196$		0			0
$197$	12.0997			0.862066			0.431033	−	0.902336i	$-0.358149\pi$
$197$	12.0997			0.862066			0.431033	+	0.902336i	$0.358149\pi$
$198$		0			0
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	0.807950	−	0.589252i	$-0.200577\pi$
$199$	−1.50000	−	2.59808i	−0.106332	−	0.184173i	−0.914282	+	0.405079i	$0.867244\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.5498	+	0.837253i	0.740453	+	0.0587637i
$204$		0			0
$205$	5.27492	−	9.13642i	0.368416	−	0.638116i
$206$		0			0
$207$	−3.77492	−	6.53835i	−0.262375	−	0.454447i
$208$		0			0
$209$	5.27492			0.364874
$210$		0			0
$211$	−25.6495			−1.76578			−0.882892	−	0.469576i	$-0.844407\pi$
$211$	−25.6495			−1.76578			−0.882892	+	0.469576i	$0.844407\pi$
$212$		0			0
$213$	−4.54983	−	7.88054i	−0.311750	−	0.539966i
$214$		0			0
$215$	−0.500000	+	0.866025i	−0.0340997	+	0.0590624i
$216$		0			0
$217$	−4.54983	−	9.55505i	−0.308863	−	0.648639i
$218$		0			0
$219$	11.2749	−	19.5287i	0.761888	−	1.31963i
$220$		0			0
$221$	0.274917	+	0.476171i	0.0184929	+	0.0320307i
$222$		0			0
$223$	−17.0997			−1.14508			−0.572539	−	0.819877i	$-0.694042\pi$
$223$	−17.0997			−1.14508			−0.572539	+	0.819877i	$0.694042\pi$
$224$		0			0
$225$	−4.00000			−0.266667
$226$		0			0
$227$	4.72508	+	8.18408i	0.313615	+	0.543197i	0.979142	−	0.203177i	$-0.0651266\pi$
$227$	4.72508	+	8.18408i	0.313615	+	0.543197i	−0.665527	+	0.746374i	$0.731793\pi$
$228$		0			0
$229$	8.13746	−	14.0945i	0.537738	−	0.931390i	−0.461287	−	0.887251i	$-0.652612\pi$
$229$	8.13746	−	14.0945i	0.537738	−	0.931390i	0.999025	−	0.0441392i	$-0.0140545\pi$
$230$		0			0
$231$	15.8248	−	22.9928i	1.04119	−	1.51282i
$232$		0			0
$233$	−2.13746	+	3.70219i	−0.140030	+	0.242538i	−0.927508	−	0.373804i	$-0.878053\pi$
$233$	−2.13746	+	3.70219i	−0.140030	+	0.242538i	0.787478	+	0.616343i	$0.211386\pi$
$234$		0			0
$235$	2.63746	+	4.56821i	0.172049	+	0.297997i
$236$		0			0
$237$	29.0997			1.89023
$238$		0			0
$239$	23.3746			1.51198			0.755988	−	0.654585i	$-0.227157\pi$
$239$	23.3746			1.51198			0.755988	+	0.654585i	$0.227157\pi$
$240$		0			0
$241$	−5.27492	−	9.13642i	−0.339787	−	0.588529i	0.644605	−	0.764516i	$-0.277022\pi$
$241$	−5.27492	−	9.13642i	−0.339787	−	0.588529i	−0.984393	+	0.175987i	$0.943688\pi$
$242$		0			0
$243$	−5.00000	+	8.66025i	−0.320750	+	0.555556i
$244$		0			0
$245$	4.41238	−	5.43424i	0.281896	−	0.347181i
$246$		0			0
$247$	1.00000	−	1.73205i	0.0636285	−	0.110208i
$248$		0			0
$249$	−3.54983	−	6.14849i	−0.224962	−	0.389645i
$250$		0			0
$251$	−28.0997			−1.77364			−0.886818	−	0.462119i	$-0.847089\pi$
$251$	−28.0997			−1.77364			−0.886818	+	0.462119i	$0.847089\pi$
$252$		0			0
$253$	−39.8248			−2.50376
$254$		0			0
$255$	0.274917	+	0.476171i	0.0172160	+	0.0298190i
$256$		0			0
$257$	11.2749	−	19.5287i	0.703310	−	1.21817i	−0.263988	−	0.964526i	$-0.585038\pi$
$257$	11.2749	−	19.5287i	0.703310	−	1.21817i	0.967298	−	0.253643i	$-0.0816287\pi$
$258$		0			0
$259$	3.00000	−	4.35890i	0.186411	−	0.270849i
$260$		0			0
$261$	2.00000	−	3.46410i	0.123797	−	0.214423i
$262$		0			0
$263$	−11.4124	−	19.7668i	−0.703717	−	1.21887i	−0.967152	−	0.254197i	$-0.918189\pi$
$263$	−11.4124	−	19.7668i	−0.703717	−	1.21887i	0.263435	−	0.964677i	$-0.415144\pi$
$264$		0			0
$265$	−8.54983			−0.525212
$266$		0			0
$267$	−2.90033			−0.177497
$268$		0			0
$269$	12.2749	+	21.2608i	0.748415	+	1.29629i	0.948582	+	0.316531i	$0.102518\pi$
$269$	12.2749	+	21.2608i	0.748415	+	1.29629i	−0.200167	+	0.979762i	$0.564149\pi$
$270$		0			0
$271$	−8.77492	+	15.1986i	−0.533038	+	0.923249i	0.466217	+	0.884670i	$0.345616\pi$
$271$	−8.77492	+	15.1986i	−0.533038	+	0.923249i	−0.999256	+	0.0385791i	$0.987717\pi$
$272$		0			0
$273$	−4.54983	−	9.55505i	−0.275369	−	0.578298i
$274$		0			0
$275$	−10.5498	+	18.2728i	−0.636179	+	1.10189i
$276$		0			0
$277$	0.362541	+	0.627940i	0.0217830	+	0.0377293i	0.876711	−	0.481017i	$-0.159732\pi$
$277$	0.362541	+	0.627940i	0.0217830	+	0.0377293i	−0.854928	+	0.518746i	$0.826399\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	0.549834			0.0328004			0.0164002	−	0.999866i	$-0.494779\pi$
$281$	0.549834			0.0328004			0.0164002	+	0.999866i	$0.494779\pi$
$282$		0			0
$283$	8.50000	+	14.7224i	0.505273	+	0.875158i	0.999981	+	0.00609896i	$0.00194137\pi$
$283$	8.50000	+	14.7224i	0.505273	+	0.875158i	−0.494709	+	0.869059i	$0.664725\pi$
$284$		0			0
$285$	1.00000	−	1.73205i	0.0592349	−	0.102598i
$286$		0			0
$287$	−27.8248	−	2.20822i	−1.64244	−	0.130347i
$288$		0			0
$289$	8.46221	−	14.6570i	0.497777	−	0.862175i
$290$		0			0
$291$	−6.54983	−	11.3446i	−0.383958	−	0.665035i
$292$		0			0
$293$	27.6495			1.61530			0.807651	−	0.589661i	$-0.200739\pi$
$293$	27.6495			1.61530			0.807651	+	0.589661i	$0.200739\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$		0			0
$297$	10.5498	+	18.2728i	0.612163	+	1.06030i
$298$		0			0
$299$	−7.54983	+	13.0767i	−0.436618	+	0.756245i
$300$		0			0
$301$	2.63746	+	0.209313i	0.152021	+	0.0120646i
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		0			0
$305$	2.36254	+	4.09204i	0.135279	+	0.234310i
$306$		0			0
$307$	−26.0000			−1.48390			−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000			−1.48390			−0.741949	+	0.670456i	$0.766098\pi$
$308$		0			0
$309$	−20.0000			−1.13776
$310$		0			0
$311$	5.13746	+	8.89834i	0.291319	+	0.504579i	0.974122	−	0.226024i	$-0.0725727\pi$
$311$	5.13746	+	8.89834i	0.291319	+	0.504579i	−0.682803	+	0.730602i	$0.739239\pi$
$312$		0			0
$313$	15.5997	−	27.0194i	0.881745	−	1.52723i	0.0323464	−	0.999477i	$-0.489702\pi$
$313$	15.5997	−	27.0194i	0.881745	−	1.52723i	0.849399	−	0.527751i	$-0.176965\pi$
$314$		0			0
$315$	−1.13746	−	2.38876i	−0.0640885	−	0.134592i
$316$		0			0
$317$	−4.54983	+	7.88054i	−0.255544	+	0.442615i	−0.965043	−	0.262091i	$-0.915588\pi$
$317$	−4.54983	+	7.88054i	−0.255544	+	0.442615i	0.709499	+	0.704706i	$0.248921\pi$
$318$		0			0
$319$	−10.5498	−	18.2728i	−0.590677	−	1.02308i
$320$		0			0
$321$	37.0997			2.07070
$322$		0			0
$323$	0.274917			0.0152968
$324$		0			0
$325$	4.00000	+	6.92820i	0.221880	+	0.384308i
$326$		0			0
$327$	4.54983	−	7.88054i	0.251606	−	0.435795i
$328$		0			0
$329$	7.91238	−	11.4964i	0.436223	−	0.633818i
$330$		0			0
$331$	7.00000	−	12.1244i	0.384755	−	0.666415i	−0.606980	−	0.794717i	$-0.707619\pi$
$331$	7.00000	−	12.1244i	0.384755	−	0.666415i	0.991735	+	0.128302i	$0.0409527\pi$
$332$		0			0
$333$	−1.00000	−	1.73205i	−0.0547997	−	0.0949158i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.09967			0.495691			0.247845	−	0.968800i	$-0.420278\pi$
$337$	9.09967			0.495691			0.247845	+	0.968800i	$0.420278\pi$
$338$		0			0
$339$	3.45017	+	5.97586i	0.187387	+	0.324564i
$340$		0			0
$341$	−10.5498	+	18.2728i	−0.571306	+	0.989530i
$342$		0			0
$343$	−18.0000	−	4.35890i	−0.971909	−	0.235358i
$344$		0			0
$345$	−7.54983	+	13.0767i	−0.406469	+	0.704026i
$346$		0			0
$347$	−13.5997	−	23.5553i	−0.730068	−	1.26452i	−0.956853	−	0.290571i	$-0.906155\pi$
$347$	−13.5997	−	23.5553i	−0.730068	−	1.26452i	0.226785	−	0.973945i	$-0.427179\pi$
$348$		0			0
$349$	−9.37459			−0.501810			−0.250905	−	0.968012i	$-0.580728\pi$
$349$	−9.37459			−0.501810			−0.250905	+	0.968012i	$0.580728\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	3.54983	+	6.14849i	0.188939	+	0.327251i	0.944897	−	0.327369i	$-0.106162\pi$
$353$	3.54983	+	6.14849i	0.188939	+	0.327251i	−0.755958	+	0.654620i	$0.772829\pi$
$354$		0			0
$355$	−2.27492	+	3.94027i	−0.120740	+	0.209128i
$356$		0			0
$357$	0.824752	−	1.19834i	0.0436505	−	0.0634227i
$358$		0			0
$359$	12.6375	−	21.8887i	0.666980	−	1.15524i	−0.311765	−	0.950159i	$-0.600920\pi$
$359$	12.6375	−	21.8887i	0.666980	−	1.15524i	0.978745	−	0.205083i	$-0.0657465\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	−33.6495			−1.76614
$364$		0			0
$365$	−11.2749			−0.590156
$366$		0			0
$367$	−17.0997	−	29.6175i	−0.892595	−	1.54602i	−0.836753	−	0.547581i	$-0.815549\pi$
$367$	−17.0997	−	29.6175i	−0.892595	−	1.54602i	−0.0558428	−	0.998440i	$-0.517785\pi$
$368$		0			0
$369$	−5.27492	+	9.13642i	−0.274601	+	0.475623i
$370$		0			0
$371$	9.72508	+	20.4235i	0.504901	+	1.06034i
$372$		0			0
$373$	−4.27492	+	7.40437i	−0.221347	+	0.383384i	−0.955217	−	0.295906i	$-0.904379\pi$
$373$	−4.27492	+	7.40437i	−0.221347	+	0.383384i	0.733870	+	0.679290i	$0.237712\pi$
$374$		0			0
$375$	9.00000	+	15.5885i	0.464758	+	0.804984i
$376$		0			0
$377$	−8.00000			−0.412021
$378$		0			0
$379$	−27.0997			−1.39202			−0.696008	−	0.718034i	$-0.745042\pi$
$379$	−27.0997			−1.39202			−0.696008	+	0.718034i	$0.745042\pi$
$380$		0			0
$381$	15.0997	+	26.1534i	0.773579	+	1.33988i
$382$		0			0
$383$	−11.0000	+	19.0526i	−0.562074	+	0.973540i	0.435242	+	0.900314i	$0.356663\pi$
$383$	−11.0000	+	19.0526i	−0.562074	+	0.973540i	−0.997315	+	0.0732266i	$0.976670\pi$
$384$		0			0
$385$	−13.9124	−	1.10411i	−0.709040	−	0.0562707i
$386$		0			0
$387$	0.500000	−	0.866025i	0.0254164	−	0.0440225i
$388$		0			0
$389$	−7.58762	−	13.1422i	−0.384708	−	0.666333i	0.607021	−	0.794686i	$-0.292364\pi$
$389$	−7.58762	−	13.1422i	−0.384708	−	0.666333i	−0.991729	+	0.128352i	$0.959031\pi$
$390$		0			0
$391$	−2.07558			−0.104967
$392$		0			0
$393$	−13.6495			−0.688526
$394$		0			0
$395$	−7.27492	−	12.6005i	−0.366041	−	0.634001i
$396$		0			0
$397$	14.1375	−	24.4868i	0.709539	−	1.22896i	−0.255490	−	0.966812i	$-0.582237\pi$
$397$	14.1375	−	24.4868i	0.709539	−	1.22896i	0.965028	−	0.262145i	$-0.0844300\pi$
$398$		0			0
$399$	−5.27492	−	0.418627i	−0.264076	−	0.0209576i
$400$		0			0
$401$	4.54983	−	7.88054i	0.227208	−	0.393536i	−0.729772	−	0.683691i	$-0.760374\pi$
$401$	4.54983	−	7.88054i	0.227208	−	0.393536i	0.956980	+	0.290155i	$0.0937070\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$		0			0
$405$	11.0000			0.546594
$406$		0			0
$407$	−10.5498			−0.522936
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$		0			0
$411$	11.2749	−	19.5287i	0.556151	−	0.963281i
$412$		0			0
$413$	−4.54983	−	9.55505i	−0.223883	−	0.470173i
$414$		0			0
$415$	−1.77492	+	3.07425i	−0.0871273	+	0.150909i
$416$		0			0
$417$	11.8248	+	20.4811i	0.579061	+	1.00296i
$418$		0			0
$419$	4.45017			0.217405			0.108702	−	0.994074i	$-0.465330\pi$
$419$	4.45017			0.217405			0.108702	+	0.994074i	$0.465330\pi$
$420$		0			0
$421$	3.45017			0.168151			0.0840754	−	0.996459i	$-0.473206\pi$
$421$	3.45017			0.168151			0.0840754	+	0.996459i	$0.473206\pi$
$422$		0			0
$423$	−2.63746	−	4.56821i	−0.128238	−	0.222114i
$424$		0			0
$425$	−0.549834	+	0.952341i	−0.0266709	+	0.0461953i
$426$		0			0
$427$	7.08762	−	10.2981i	0.342994	−	0.498359i
$428$		0			0
$429$	−10.5498	+	18.2728i	−0.509351	+	0.882221i
$430$		0			0
$431$	10.5498	+	18.2728i	0.508168	+	0.880172i	0.999955	+	0.00945700i	$0.00301030\pi$
$431$	10.5498	+	18.2728i	0.508168	+	0.880172i	−0.491788	+	0.870715i	$0.663656\pi$
$432$		0			0
$433$	−5.09967			−0.245074			−0.122537	−	0.992464i	$-0.539103\pi$
$433$	−5.09967			−0.245074			−0.122537	+	0.992464i	$0.539103\pi$
$434$		0			0
$435$	−8.00000			−0.383571
$436$		0			0
$437$	3.77492	+	6.53835i	0.180579	+	0.312772i
$438$		0			0
$439$	13.0997	−	22.6893i	0.625213	−	1.08290i	−0.363287	−	0.931677i	$-0.618345\pi$
$439$	13.0997	−	22.6893i	0.625213	−	1.08290i	0.988500	−	0.151223i	$-0.0483213\pi$
$440$		0			0
$441$	−4.41238	+	5.43424i	−0.210113	+	0.258773i
$442$		0			0
$443$	−11.4124	+	19.7668i	−0.542218	+	0.939150i	0.456558	+	0.889694i	$0.349082\pi$
$443$	−11.4124	+	19.7668i	−0.542218	+	0.939150i	−0.998776	+	0.0494560i	$0.984251\pi$
$444$		0			0
$445$	0.725083	+	1.25588i	0.0343722	+	0.0595344i
$446$		0			0
$447$	32.1993			1.52298
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	27.8248	+	48.1939i	1.31022	+	2.26936i
$452$		0			0
$453$	6.54983	−	11.3446i	0.307738	−	0.533018i
$454$		0			0
$455$	−3.00000	+	4.35890i	−0.140642	+	0.204348i
$456$		0			0
$457$	−2.36254	+	4.09204i	−0.110515	+	0.191418i	−0.915978	−	0.401228i	$-0.868583\pi$
$457$	−2.36254	+	4.09204i	−0.110515	+	0.191418i	0.805463	+	0.592646i	$0.201917\pi$
$458$		0			0
$459$	0.549834	+	0.952341i	0.0256641	+	0.0444515i
$460$		0			0
$461$	23.2749			1.08402			0.542010	−	0.840372i	$-0.317663\pi$
$461$	23.2749			1.08402			0.542010	+	0.840372i	$0.317663\pi$
$462$		0			0
$463$	−19.8248			−0.921334			−0.460667	−	0.887573i	$-0.652390\pi$
$463$	−19.8248			−0.921334			−0.460667	+	0.887573i	$0.652390\pi$
$464$		0			0
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$		0			0
$467$	5.36254	−	9.28819i	0.248149	−	0.429806i	−0.714863	−	0.699264i	$-0.753511\pi$
$467$	5.36254	−	9.28819i	0.248149	−	0.429806i	0.963012	+	0.269458i	$0.0868445\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	14.0997	−	24.4213i	0.649678	−	1.12528i
$472$		0			0
$473$	−2.63746	−	4.56821i	−0.121270	−	0.210047i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	8.54983			0.391470
$478$		0			0
$479$	7.22508	+	12.5142i	0.330122	+	0.571789i	0.982536	−	0.186075i	$-0.0595766\pi$
$479$	7.22508	+	12.5142i	0.330122	+	0.571789i	−0.652413	+	0.757863i	$0.726243\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$		0			0
$483$	39.8248	+	3.16056i	1.81209	+	0.143811i
$484$		0			0
$485$	−3.27492	+	5.67232i	−0.148706	+	0.257567i
$486$		0			0
$487$	−3.54983	−	6.14849i	−0.160858	−	0.278615i	0.774318	−	0.632796i	$-0.218093\pi$
$487$	−3.54983	−	6.14849i	−0.160858	−	0.278615i	−0.935177	+	0.354181i	$0.884760\pi$
$488$		0			0
$489$	43.0997			1.94903
$490$		0			0
$491$	5.54983			0.250461			0.125230	−	0.992128i	$-0.460033\pi$
$491$	5.54983			0.250461			0.125230	+	0.992128i	$0.460033\pi$
$492$		0			0
$493$	−0.549834	−	0.952341i	−0.0247633	−	0.0428913i
$494$		0			0
$495$	−2.63746	+	4.56821i	−0.118545	+	0.205326i
$496$		0			0
$497$	12.0000	+	0.952341i	0.538274	+	0.0427183i
$498$		0			0
$499$	−15.5997	+	27.0194i	−0.698337	+	1.20956i	0.270706	+	0.962662i	$0.412743\pi$
$499$	−15.5997	+	27.0194i	−0.698337	+	1.20956i	−0.969043	+	0.246893i	$0.920590\pi$
$500$		0			0
$501$	13.0997	+	22.6893i	0.585250	+	1.01368i
$502$		0			0
$503$	−10.6495			−0.474838			−0.237419	−	0.971407i	$-0.576301\pi$
$503$	−10.6495			−0.474838			−0.237419	+	0.971407i	$0.576301\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$		0			0
$507$	−9.00000	−	15.5885i	−0.399704	−	0.692308i
$508$		0			0
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	−0.843012	−	0.537895i	$-0.819220\pi$
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	0.887336	+	0.461123i	$0.152553\pi$
$510$		0			0
$511$	12.8248	+	26.9331i	0.567334	+	1.19145i
$512$		0			0
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$		0			0
$515$	5.00000	+	8.66025i	0.220326	+	0.381616i
$516$		0			0
$517$	−27.8248			−1.22373
$518$		0			0
$519$	−41.0997			−1.80408
$520$		0			0
$521$	13.0000	+	22.5167i	0.569540	+	0.986473i	0.996611	+	0.0822547i	$0.0262121\pi$
$521$	13.0000	+	22.5167i	0.569540	+	0.986473i	−0.427071	+	0.904218i	$0.640455\pi$
$522$		0			0
$523$	−1.82475	+	3.16056i	−0.0797908	+	0.138202i	−0.903160	−	0.429305i	$-0.858759\pi$
$523$	−1.82475	+	3.16056i	−0.0797908	+	0.138202i	0.823369	+	0.567507i	$0.192092\pi$
$524$		0			0
$525$	12.0000	−	17.4356i	0.523723	−	0.760952i
$526$		0			0
$527$	−0.549834	+	0.952341i	−0.0239512	+	0.0414846i
$528$		0			0
$529$	−17.0000	−	29.4449i	−0.739130	−	1.28021i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$	21.0997			0.913928
$534$		0			0
$535$	−9.27492	−	16.0646i	−0.400990	−	0.694534i
$536$		0			0
$537$	−15.0997	+	26.1534i	−0.651599	+	1.12860i
$538$		0			0
$539$	13.1873	+	34.4892i	0.568017	+	1.48556i
$540$		0			0
$541$	8.50000	−	14.7224i	0.365444	−	0.632967i	−0.623404	−	0.781900i	$-0.714251\pi$
$541$	8.50000	−	14.7224i	0.365444	−	0.632967i	0.988847	+	0.148933i	$0.0475840\pi$
$542$		0			0
$543$	0.549834	+	0.952341i	0.0235957	+	0.0408689i
$544$		0			0
$545$	−4.54983			−0.194893
$546$		0			0
$547$	−32.0000			−1.36822			−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000			−1.36822			−0.684111	+	0.729378i	$0.739809\pi$
$548$		0			0
$549$	−2.36254	−	4.09204i	−0.100831	−	0.174644i
$550$		0			0
$551$	−2.00000	+	3.46410i	−0.0852029	+	0.147576i
$552$		0			0
$553$	−21.8248	+	31.7106i	−0.928083	+	1.34847i
$554$		0			0
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$		0			0
$557$	14.0498	+	24.3350i	0.595311	+	1.03111i	0.993503	+	0.113806i	$0.0363043\pi$
$557$	14.0498	+	24.3350i	0.595311	+	1.03111i	−0.398192	+	0.917302i	$0.630362\pi$
$558$		0			0
$559$	−2.00000			−0.0845910
$560$		0			0
$561$	−2.90033			−0.122452
$562$		0			0
$563$	13.2749	+	22.9928i	0.559471	+	0.969032i	0.997541	+	0.0700912i	$0.0223290\pi$
$563$	13.2749	+	22.9928i	0.559471	+	0.969032i	−0.438070	+	0.898941i	$0.644338\pi$
$564$		0			0
$565$	1.72508	−	2.98793i	0.0725748	−	0.125703i
$566$		0			0
$567$	−12.5120	−	26.2764i	−0.525456	−	1.10350i
$568$		0			0
$569$	−22.0997	+	38.2777i	−0.926466	+	1.60469i	−0.137281	+	0.990532i	$0.543836\pi$
$569$	−22.0997	+	38.2777i	−0.926466	+	1.60469i	−0.789186	+	0.614155i	$0.789497\pi$
$570$		0			0
$571$	17.7749	+	30.7871i	0.743857	+	1.28840i	0.950727	+	0.310030i	$0.100339\pi$
$571$	17.7749	+	30.7871i	0.743857	+	1.28840i	−0.206870	+	0.978369i	$0.566328\pi$
$572$		0			0
$573$	42.0000			1.75458
$574$		0			0
$575$	−30.1993			−1.25940
$576$		0			0
$577$	12.1873	+	21.1090i	0.507364	+	0.878780i	0.999964	+	0.00852378i	$0.00271324\pi$
$577$	12.1873	+	21.1090i	0.507364	+	0.878780i	−0.492600	+	0.870256i	$0.663953\pi$
$578$		0			0
$579$	−3.09967	+	5.36878i	−0.128818	+	0.223119i
$580$		0			0
$581$	9.36254	+	0.743028i	0.388424	+	0.0308260i
$582$		0			0
$583$	22.5498	−	39.0575i	0.933919	−	1.61759i
$584$		0			0
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$		0			0
$587$	−10.2749			−0.424091			−0.212046	−	0.977260i	$-0.568013\pi$
$587$	−10.2749			−0.424091			−0.212046	+	0.977260i	$0.568013\pi$
$588$		0			0
$589$	4.00000			0.164817
$590$		0			0
$591$	12.0997	+	20.9572i	0.497714	+	0.862066i
$592$		0			0
$593$	−1.50000	+	2.59808i	−0.0615976	+	0.106690i	−0.895180	−	0.445705i	$-0.852953\pi$
$593$	−1.50000	+	2.59808i	−0.0615976	+	0.106690i	0.833582	+	0.552396i	$0.186286\pi$
$594$		0			0
$595$	−0.725083	−	0.0575438i	−0.0297255	−	0.00235907i
$596$		0			0
$597$	3.00000	−	5.19615i	0.122782	−	0.212664i
$598$		0			0
$599$	14.8248	+	25.6772i	0.605723	+	1.04914i	0.991937	+	0.126734i	$0.0404493\pi$
$599$	14.8248	+	25.6772i	0.605723	+	1.04914i	−0.386214	+	0.922409i	$0.626217\pi$
$600$		0			0
$601$	−26.5498			−1.08299			−0.541495	−	0.840704i	$-0.682142\pi$
$601$	−26.5498			−1.08299			−0.541495	+	0.840704i	$0.682142\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.41238	+	14.5707i	0.342012	+	0.592382i
$606$		0			0
$607$	9.82475	−	17.0170i	0.398774	−	0.690697i	−0.594801	−	0.803873i	$-0.702769\pi$
$607$	9.82475	−	17.0170i	0.398774	−	0.690697i	0.993575	+	0.113176i	$0.0361023\pi$
$608$		0			0
$609$	9.09967	+	19.1101i	0.368737	+	0.774380i
$610$		0			0
$611$	−5.27492	+	9.13642i	−0.213400	+	0.369620i
$612$		0			0
$613$	7.58762	+	13.1422i	0.306461	+	0.530806i	0.977586	−	0.210538i	$-0.0675217\pi$
$613$	7.58762	+	13.1422i	0.306461	+	0.530806i	−0.671124	+	0.741345i	$0.734188\pi$
$614$		0			0
$615$	21.0997			0.850821
$616$		0			0
$617$	6.09967			0.245563			0.122782	−	0.992434i	$-0.460818\pi$
$617$	6.09967			0.245563			0.122782	+	0.992434i	$0.460818\pi$
$618$		0			0
$619$	1.77492	+	3.07425i	0.0713399	+	0.123564i	0.899489	−	0.436944i	$-0.143939\pi$
$619$	1.77492	+	3.07425i	0.0713399	+	0.123564i	−0.828149	+	0.560508i	$0.810606\pi$
$620$		0			0
$621$	−15.0997	+	26.1534i	−0.605929	+	1.04950i
$622$		0			0
$623$	2.17525	−	3.16056i	0.0871495	−	0.126625i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$	5.27492	+	9.13642i	0.210660	+	0.364874i
$628$		0			0
$629$	−0.549834			−0.0219233
$630$		0			0
$631$	−17.0000			−0.676759			−0.338380	−	0.941010i	$-0.609879\pi$
$631$	−17.0000			−0.676759			−0.338380	+	0.941010i	$0.609879\pi$
$632$		0			0
$633$	−25.6495	−	44.4262i	−1.01948	−	1.76578i
$634$		0			0
$635$	7.54983	−	13.0767i	0.299606	−	0.518933i
$636$		0			0
$637$	13.8248	+	2.20822i	0.547757	+	0.0874929i
$638$		0			0
$639$	2.27492	−	3.94027i	0.0899943	−	0.155875i
$640$		0			0
$641$	−15.7251	−	27.2366i	−0.621103	−	1.07578i	−0.989281	−	0.146027i	$-0.953351\pi$
$641$	−15.7251	−	27.2366i	−0.621103	−	1.07578i	0.368177	−	0.929756i	$-0.379982\pi$
$642$		0			0
$643$	−22.8248			−0.900120			−0.450060	−	0.892998i	$-0.648597\pi$
$643$	−22.8248			−0.900120			−0.450060	+	0.892998i	$0.648597\pi$
$644$		0			0
$645$	−2.00000			−0.0787499
$646$		0			0
$647$	−8.04983	−	13.9427i	−0.316472	−	0.548145i	0.663278	−	0.748373i	$-0.269165\pi$
$647$	−8.04983	−	13.9427i	−0.316472	−	0.548145i	−0.979749	+	0.200228i	$0.935832\pi$
$648$		0			0
$649$	−10.5498	+	18.2728i	−0.414117	+	0.717272i
$650$		0			0
$651$	12.0000	−	17.4356i	0.470317	−	0.683355i
$652$		0			0
$653$	4.13746	−	7.16629i	0.161911	−	0.280439i	−0.773643	−	0.633622i	$-0.781567\pi$
$653$	4.13746	−	7.16629i	0.161911	−	0.280439i	0.935554	+	0.353183i	$0.114901\pi$
$654$		0			0
$655$	3.41238	+	5.91041i	0.133333	+	0.230939i
$656$		0			0
$657$	11.2749			0.439876
$658$		0			0
$659$	−40.5498			−1.57960			−0.789799	−	0.613366i	$-0.789815\pi$
$659$	−40.5498			−1.57960			−0.789799	+	0.613366i	$0.789815\pi$
$660$		0			0
$661$	14.7251	+	25.5046i	0.572739	+	0.992014i	0.996283	+	0.0861380i	$0.0274526\pi$
$661$	14.7251	+	25.5046i	0.572739	+	0.992014i	−0.423544	+	0.905876i	$0.639214\pi$
$662$		0			0
$663$	−0.549834	+	0.952341i	−0.0213538	+	0.0369859i
$664$		0			0
$665$	1.13746	+	2.38876i	0.0441088	+	0.0926322i
$666$		0			0
$667$	15.0997	−	26.1534i	0.584662	−	1.01266i
$668$		0			0
$669$	−17.0997	−	29.6175i	−0.661111	−	1.14508i
$670$		0			0
$671$	−24.9244			−0.962197
$672$		0			0
$673$	−4.54983			−0.175383			−0.0876916	−	0.996148i	$-0.527949\pi$
$673$	−4.54983			−0.175383			−0.0876916	+	0.996148i	$0.527949\pi$
$674$		0			0
$675$	8.00000	+	13.8564i	0.307920	+	0.533333i
$676$		0			0
$677$	−3.45017	+	5.97586i	−0.132601	+	0.229671i	−0.924678	−	0.380749i	$-0.875666\pi$
$677$	−3.45017	+	5.97586i	−0.132601	+	0.229671i	0.792078	+	0.610420i	$0.208999\pi$
$678$		0			0
$679$	17.2749	+	1.37097i	0.662950	+	0.0526129i
$680$		0			0
$681$	−9.45017	+	16.3682i	−0.362131	+	0.627230i
$682$		0			0
$683$	−13.8248	−	23.9452i	−0.528989	−	0.916237i	−0.999428	−	0.0338041i	$-0.989238\pi$
$683$	−13.8248	−	23.9452i	−0.528989	−	0.916237i	0.470439	−	0.882432i	$-0.344096\pi$
$684$		0			0
$685$	−11.2749			−0.430792
$686$		0			0
$687$	32.5498			1.24185
$688$		0			0
$689$	−8.54983	−	14.8087i	−0.325723	−	0.564168i
$690$		0			0
$691$	−7.96221	+	13.7910i	−0.302897	+	0.524633i	−0.976791	−	0.214195i	$-0.931287\pi$
$691$	−7.96221	+	13.7910i	−0.302897	+	0.524633i	0.673894	+	0.738828i	$0.264620\pi$
$692$		0			0
$693$	13.9124	+	1.10411i	0.528487	+	0.0419417i
$694$		0			0
$695$	5.91238	−	10.2405i	0.224269	−	0.388446i
$696$		0			0
$697$	1.45017	+	2.51176i	0.0549289	+	0.0951397i
$698$		0			0
$699$	−8.54983			−0.323384
$700$		0			0
$701$	−15.0000			−0.566542			−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000			−0.566542			−0.283271	+	0.959040i	$0.591420\pi$
$702$		0			0
$703$	1.00000	+	1.73205i	0.0377157	+	0.0653255i
$704$		0			0
$705$	−5.27492	+	9.13642i	−0.198665	+	0.344098i
$706$		0			0
$707$	−3.41238	−	7.16629i	−0.128336	−	0.269516i
$708$		0			0
$709$	7.50000	−	12.9904i	0.281668	−	0.487864i	−0.690127	−	0.723688i	$-0.742446\pi$
$709$	7.50000	−	12.9904i	0.281668	−	0.487864i	0.971796	+	0.235824i	$0.0757789\pi$
$710$		0			0
$711$	7.27492	+	12.6005i	0.272831	+	0.472557i
$712$		0			0
$713$	−30.1993			−1.13097
$714$		0			0
$715$	10.5498			0.394541
$716$		0			0
$717$	23.3746	+	40.4860i	0.872940	+	1.51198i
$718$		0			0
$719$	−17.1375	+	29.6829i	−0.639119	+	1.10699i	0.346507	+	0.938047i	$0.387368\pi$
$719$	−17.1375	+	29.6829i	−0.639119	+	1.10699i	−0.985626	+	0.168940i	$0.945966\pi$
$720$		0			0
$721$	15.0000	−	21.7945i	0.558629	−	0.811669i
$722$		0			0
$723$	10.5498	−	18.2728i	0.392353	−	0.679575i
$724$		0			0
$725$	−8.00000	−	13.8564i	−0.297113	−	0.514614i
$726$		0			0
$727$	−44.0997			−1.63557			−0.817783	−	0.575527i	$-0.804797\pi$
$727$	−44.0997			−1.63557			−0.817783	+	0.575527i	$0.804797\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−0.137459	−	0.238085i	−0.00508409	−	0.00880590i
$732$		0			0
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	0.360061	+	0.932929i	$0.382756\pi$
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	−0.987971	+	0.154642i	$0.950578\pi$
$734$		0			0
$735$	13.8248	+	2.20822i	0.509934	+	0.0814515i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	13.4124	+	23.2309i	0.493382	+	0.854563i	0.999971	−	0.00762477i	$-0.00242706\pi$
$739$	13.4124	+	23.2309i	0.493382	+	0.854563i	−0.506589	+	0.862188i	$0.669094\pi$
$740$		0			0
$741$	4.00000			0.146944
$742$		0			0
$743$	28.7492			1.05470			0.527352	−	0.849647i	$-0.323185\pi$
$743$	28.7492			1.05470			0.527352	+	0.849647i	$0.323185\pi$
$744$		0			0
$745$	−8.04983	−	13.9427i	−0.294923	−	0.510822i
$746$		0			0
$747$	1.77492	−	3.07425i	0.0649408	−	0.112481i
$748$		0			0
$749$	−27.8248	+	40.4284i	−1.01669	+	1.47722i
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$		0			0
$753$	−28.0997	−	48.6701i	−1.02401	−	1.77364i
$754$		0			0
$755$	−6.54983			−0.238373
$756$		0			0
$757$	−12.3746			−0.449762			−0.224881	−	0.974386i	$-0.572199\pi$
$757$	−12.3746			−0.449762			−0.224881	+	0.974386i	$0.572199\pi$
$758$		0			0
$759$	−39.8248	−	68.9785i	−1.44555	−	2.50376i
$760$		0			0
$761$	21.5000	−	37.2391i	0.779374	−	1.34992i	−0.152928	−	0.988237i	$-0.548870\pi$
$761$	21.5000	−	37.2391i	0.779374	−	1.34992i	0.932303	−	0.361679i	$-0.117796\pi$
$762$		0			0
$763$	5.17525	+	10.8685i	0.187357	+	0.393465i
$764$		0			0
$765$	−0.137459	+	0.238085i	−0.00496983	+	0.00860799i
$766$		0			0
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$		0			0
$769$	17.1993			0.620224			0.310112	−	0.950700i	$-0.399633\pi$
$769$	17.1993			0.620224			0.310112	+	0.950700i	$0.399633\pi$
$770$		0			0
$771$	45.0997			1.62422
$772$		0			0
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	0.964014	−	0.265852i	$-0.0856532\pi$
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	−0.712241	+	0.701935i	$0.752320\pi$
$774$		0			0
$775$	−8.00000	+	13.8564i	−0.287368	+	0.497737i
$776$		0			0
$777$	10.5498	+	0.837253i	0.378473	+	0.0300363i
$778$		0			0
$779$	5.27492	−	9.13642i	0.188994	−	0.327346i
$780$		0			0
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$		0			0
$783$	−16.0000			−0.571793
$784$		0			0
$785$	−14.0997			−0.503239
$786$		0			0
$787$	−7.00000	−	12.1244i	−0.249523	−	0.432187i	0.713871	−	0.700278i	$-0.246941\pi$
$787$	−7.00000	−	12.1244i	−0.249523	−	0.432187i	−0.963394	+	0.268091i	$0.913607\pi$
$788$		0			0
$789$	22.8248	−	39.5336i	0.812583	−	1.40743i
$790$		0			0
$791$	−9.09967	−	0.722166i	−0.323547	−	0.0256773i
$792$		0			0
$793$	−4.72508	+	8.18408i	−0.167793	+	0.290625i
$794$		0			0
$795$	−8.54983	−	14.8087i	−0.303231	−	0.525212i
$796$		0			0
$797$	−1.45017			−0.0513675			−0.0256837	−	0.999670i	$-0.508176\pi$
$797$	−1.45017			−0.0513675			−0.0256837	+	0.999670i	$0.508176\pi$
$798$		0			0
$799$	−1.45017			−0.0513032
$800$		0			0
$801$	−0.725083	−	1.25588i	−0.0256195	−	0.0443743i
$802$		0			0
$803$	29.7371	−	51.5062i	1.04940	−	1.81761i
$804$		0			0
$805$	−8.58762	−	18.0348i	−0.302674	−	0.635642i
$806$		0			0
$807$	−24.5498	+	42.5216i	−0.864195	+	1.49683i
$808$		0			0
$809$	−6.04983	−	10.4786i	−0.212701	−	0.368409i	0.739858	−	0.672763i	$-0.234893\pi$
$809$	−6.04983	−	10.4786i	−0.212701	−	0.368409i	−0.952559	+	0.304354i	$0.901559\pi$
$810$		0			0
$811$	52.7492			1.85227			0.926137	−	0.377187i	$-0.123109\pi$
$811$	52.7492			1.85227			0.926137	+	0.377187i	$0.123109\pi$
$812$		0			0
$813$	−35.0997			−1.23100
$814$		0			0
$815$	−10.7749	−	18.6627i	−0.377429	−	0.653726i
$816$		0			0
$817$	−0.500000	+	0.866025i	−0.0174928	+	0.0302984i
$818$		0			0
$819$	3.00000	−	4.35890i	0.104828	−	0.152312i
$820$		0			0
$821$	13.4622	−	23.3172i	0.469834	−	0.813777i	−0.529571	−	0.848266i	$-0.677647\pi$
$821$	13.4622	−	23.3172i	0.469834	−	0.813777i	0.999405	+	0.0344888i	$0.0109803\pi$
$822$		0			0
$823$	−2.46221	−	4.26467i	−0.0858273	−	0.148657i	0.819916	−	0.572484i	$-0.194020\pi$
$823$	−2.46221	−	4.26467i	−0.0858273	−	0.148657i	−0.905743	+	0.423826i	$0.860687\pi$
$824$		0			0
$825$	−42.1993			−1.46919
$826$		0			0
$827$	−41.6495			−1.44830			−0.724148	−	0.689645i	$-0.757767\pi$
$827$	−41.6495			−1.44830			−0.724148	+	0.689645i	$0.757767\pi$
$828$		0			0
$829$	7.45017	+	12.9041i	0.258755	+	0.448177i	0.965909	−	0.258883i	$-0.0833545\pi$
$829$	7.45017	+	12.9041i	0.258755	+	0.448177i	−0.707154	+	0.707060i	$0.750021\pi$
$830$		0			0
$831$	−0.725083	+	1.25588i	−0.0251528	+	0.0435660i
$832$		0			0
$833$	0.687293	+	1.79750i	0.0238133	+	0.0622798i
$834$		0			0
$835$	6.54983	−	11.3446i	0.226666	−	0.392598i
$836$		0			0
$837$	8.00000	+	13.8564i	0.276520	+	0.478947i
$838$		0			0
$839$	37.6495			1.29981			0.649903	−	0.760018i	$-0.274810\pi$
$839$	37.6495			1.29981			0.649903	+	0.760018i	$0.274810\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$	0.549834	+	0.952341i	0.0189373	+	0.0328004i
$844$		0			0
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$	25.2371	−	36.6687i	0.867158	−	1.25995i
$848$		0			0
$849$	−17.0000	+	29.4449i	−0.583438	+	1.01055i
$850$		0			0
$851$	−7.54983	−	13.0767i	−0.258805	−	0.448263i
$852$		0			0
$853$	−42.0997			−1.44147			−0.720733	−	0.693213i	$-0.756194\pi$
$853$	−42.0997			−1.44147			−0.720733	+	0.693213i	$0.756194\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$		0			0
$857$	−20.8248	−	36.0695i	−0.711360	−	1.23211i	−0.964347	−	0.264642i	$-0.914746\pi$
$857$	−20.8248	−	36.0695i	−0.711360	−	1.23211i	0.252987	−	0.967470i	$-0.418587\pi$
$858$		0			0
$859$	5.04983	−	8.74657i	0.172298	−	0.298429i	−0.766925	−	0.641737i	$-0.778214\pi$
$859$	5.04983	−	8.74657i	0.172298	−	0.298429i	0.939223	+	0.343308i	$0.111547\pi$
$860$		0			0
$861$	−24.0000	−	50.4021i	−0.817918	−	1.71770i
$862$		0			0
$863$	1.45017	−	2.51176i	0.0493642	−	0.0855013i	−0.840287	−	0.542141i	$-0.817614\pi$
$863$	1.45017	−	2.51176i	0.0493642	−	0.0855013i	0.889652	+	0.456640i	$0.150947\pi$
$864$		0			0
$865$	10.2749	+	17.7967i	0.349358	+	0.605105i
$866$		0			0
$867$	33.8488			1.14957
$868$		0			0
$869$	76.7492			2.60354
$870$		0			0
$871$		0			0
$872$		0			0
$873$	3.27492	−	5.67232i	0.110839	−	0.191979i
$874$		0			0
$875$	−23.7371	−	1.88382i	−0.802461	−	0.0636848i
$876$		0			0
$877$	−16.3746	+	28.3616i	−0.552930	+	0.957704i	0.445131	+	0.895466i	$0.353157\pi$
$877$	−16.3746	+	28.3616i	−0.552930	+	0.957704i	−0.998061	+	0.0622382i	$0.980176\pi$
$878$		0			0
$879$	27.6495	+	47.8903i	0.932595	+	1.61530i
$880$		0			0
$881$	49.9244			1.68200			0.840998	−	0.541038i	$-0.181968\pi$
$881$	49.9244			1.68200			0.840998	+	0.541038i	$0.181968\pi$
$882$		0			0
$883$	−41.0241			−1.38057			−0.690285	−	0.723537i	$-0.742515\pi$
$883$	−41.0241			−1.38057			−0.690285	+	0.723537i	$0.742515\pi$
$884$		0			0
$885$	4.00000	+	6.92820i	0.134459	+	0.232889i
$886$		0			0
$887$	26.0997	−	45.2060i	0.876341	−	1.51787i	0.0210139	−	0.999779i	$-0.493311\pi$
$887$	26.0997	−	45.2060i	0.876341	−	1.51787i	0.855327	−	0.518088i	$-0.173356\pi$
$888$		0			0
$889$	−39.8248	−	3.16056i	−1.33568	−	0.106002i
$890$		0			0
$891$	−29.0120	+	50.2503i	−0.971940	+	1.68345i
$892$		0			0
$893$	2.63746	+	4.56821i	0.0882592	+	0.152869i
$894$		0			0
$895$	15.0997			0.504726
$896$		0			0
$897$	−30.1993			−1.00833
$898$		0			0
$899$	−8.00000	−	13.8564i	−0.266815	−	0.462137i
$900$		0			0
$901$	1.17525	−	2.03559i	0.0391532	−	0.0678153i
$902$		0			0
$903$	2.27492	+	4.77753i	0.0757045	+	0.158986i
$904$		0			0
$905$	0.274917	−	0.476171i	0.00913856	−	0.0158284i
$906$		0			0
$907$	−3.45017	−	5.97586i	−0.114561	−	0.198425i	0.803043	−	0.595921i	$-0.203213\pi$
$907$	−3.45017	−	5.97586i	−0.114561	−	0.198425i	−0.917604	+	0.397495i	$0.869879\pi$
$908$		0			0
$909$	−3.00000			−0.0995037
$910$		0			0
$911$	11.4502			0.379361			0.189680	−	0.981846i	$-0.439255\pi$
$911$	11.4502			0.379361			0.189680	+	0.981846i	$0.439255\pi$
$912$		0			0
$913$	−9.36254	−	16.2164i	−0.309855	−	0.536684i
$914$		0			0
$915$	−4.72508	+	8.18408i	−0.156206	+	0.270557i
$916$		0			0
$917$	10.2371	−	14.8742i	0.338060	−	0.491189i
$918$		0			0
$919$	19.7749	−	34.2512i	0.652314	−	1.12984i	−0.330246	−	0.943895i	$-0.607132\pi$
$919$	19.7749	−	34.2512i	0.652314	−	1.12984i	0.982560	−	0.185947i	$-0.0595351\pi$
$920$		0			0
$921$	−26.0000	−	45.0333i	−0.856729	−	1.48390i
$922$		0			0
$923$	−9.09967			−0.299519
$924$		0			0
$925$	−8.00000			−0.263038
$926$		0			0
$927$	−5.00000	−	8.66025i	−0.164222	−	0.284440i
$928$		0			0
$929$	16.5000	−	28.5788i	0.541347	−	0.937641i	−0.457480	−	0.889220i	$-0.651248\pi$
$929$	16.5000	−	28.5788i	0.541347	−	0.937641i	0.998827	−	0.0484211i	$-0.0154190\pi$
$930$		0			0
$931$	4.41238	−	5.43424i	0.144610	−	0.178100i
$932$		0			0
$933$	−10.2749	+	17.7967i	−0.336386	+	0.582637i
$934$		0			0
$935$	0.725083	+	1.25588i	0.0237127	+	0.0410717i
$936$		0			0
$937$	−7.00000			−0.228680			−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000			−0.228680			−0.114340	+	0.993442i	$0.536475\pi$
$938$		0			0
$939$	62.3987			2.03630
$940$		0			0
$941$	−4.00000	−	6.92820i	−0.130396	−	0.225853i	0.793433	−	0.608657i	$-0.208292\pi$
$941$	−4.00000	−	6.92820i	−0.130396	−	0.225853i	−0.923829	+	0.382804i	$0.874958\pi$
$942$		0			0
$943$	−39.8248	+	68.9785i	−1.29687	+	2.24625i
$944$		0			0
$945$	−6.00000	+	8.71780i	−0.195180	+	0.283590i
$946$		0			0
$947$	−22.0000	+	38.1051i	−0.714904	+	1.23825i	0.248093	+	0.968736i	$0.420196\pi$
$947$	−22.0000	+	38.1051i	−0.714904	+	1.23825i	−0.962997	+	0.269514i	$0.913137\pi$
$948$		0			0
$949$	−11.2749	−	19.5287i	−0.365999	−	0.633929i
$950$		0			0
$951$	−18.1993			−0.590154
$952$		0			0
$953$	43.0997			1.39614			0.698068	−	0.716032i	$-0.254043\pi$
$953$	43.0997			1.39614			0.698068	+	0.716032i	$0.254043\pi$
$954$		0			0
$955$	−10.5000	−	18.1865i	−0.339772	−	0.588502i
$956$		0			0
$957$	21.0997	−	36.5457i	0.682055	−	1.18135i
$958$		0			0
$959$	12.8248	+	26.9331i	0.414133	+	0.869715i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	9.27492	+	16.0646i	0.298880	+	0.517675i
$964$		0			0
$965$	3.09967			0.0997819
$966$		0			0
$967$	42.1993			1.35704			0.678520	−	0.734582i	$-0.262622\pi$
$967$	42.1993			1.35704			0.678520	+	0.734582i	$0.262622\pi$
$968$		0			0
$969$	0.274917	+	0.476171i	0.00883161	+	0.0152968i
$970$		0			0
$971$	−10.7251	+	18.5764i	−0.344184	+	0.596145i	−0.985205	−	0.171379i	$-0.945178\pi$
$971$	−10.7251	+	18.5764i	−0.344184	+	0.596145i	0.641021	+	0.767523i	$0.278511\pi$
$972$		0			0
$973$	−31.1873	−	2.47508i	−0.999819	−	0.0793474i
$974$		0			0
$975$	−8.00000	+	13.8564i	−0.256205	+	0.443760i
$976$		0			0
$977$	17.6495	+	30.5698i	0.564658	+	0.978016i	0.997081	+	0.0763452i	$0.0243251\pi$
$977$	17.6495	+	30.5698i	0.564658	+	0.978016i	−0.432424	+	0.901670i	$0.642342\pi$
$978$		0			0
$979$	−7.64950			−0.244479
$980$		0			0
$981$	4.54983			0.145265
$982$		0			0
$983$	26.0997	+	45.2060i	0.832450	+	1.44185i	0.896090	+	0.443873i	$0.146396\pi$
$983$	26.0997	+	45.2060i	0.832450	+	1.44185i	−0.0636395	+	0.997973i	$0.520271\pi$
$984$		0			0
$985$	6.04983	−	10.4786i	0.192764	−	0.333877i
$986$		0			0
$987$	27.8248	+	2.20822i	0.885672	+	0.0702885i
$988$		0			0
$989$	3.77492	−	6.53835i	0.120035	−	0.207907i
$990$		0			0
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$		0			0
$993$	28.0000			0.888553
$994$		0			0
$995$	−3.00000			−0.0951064
$996$		0			0
$997$	3.58762	+	6.21395i	0.113621	+	0.196798i	0.917228	−	0.398363i	$-0.130422\pi$
$997$	3.58762	+	6.21395i	0.113621	+	0.196798i	−0.803607	+	0.595161i	$0.797088\pi$
$998$		0			0
$999$	−4.00000	+	6.92820i	−0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.l.457.1	yes	4
7.2	even	3		7448.2.a.w.1.1		2
7.4	even	3	inner	1064.2.q.l.305.1	✓	4
7.5	odd	6		7448.2.a.be.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.l.305.1	✓	4	7.4	even	3	inner
1064.2.q.l.457.1	yes	4	1.1	even	1	trivial
7448.2.a.w.1.1		2	7.2	even	3
7448.2.a.be.1.1		2	7.5	odd	6

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:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.63746 + 4.56821i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(0.137459 + 0.238085i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-2.27492 - 4.77753i) q^{21} +(-3.77492 + 6.53835i) q^{23} +(2.00000 + 3.46410i) q^{25} +4.00000 q^{27} -4.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-5.27492 + 9.13642i) q^{33} +(-1.50000 + 2.17945i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{39} +10.5498 q^{41} -1.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(-2.63746 + 4.56821i) q^{47} +(6.91238 + 1.10411i) q^{49} +(-0.274917 + 0.476171i) q^{51} +(-4.27492 - 7.40437i) q^{53} +5.27492 q^{55} +2.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-2.36254 + 4.09204i) q^{61} +(1.50000 - 2.17945i) q^{63} +(1.00000 - 1.73205i) q^{65} -15.0997 q^{69} -4.54983 q^{71} +(-5.63746 - 9.76436i) q^{73} +(-4.00000 + 6.92820i) q^{75} +(-6.00000 - 12.6005i) q^{77} +(7.27492 - 12.6005i) q^{79} +(5.50000 + 9.52628i) q^{81} -3.54983 q^{83} +0.274917 q^{85} +(-4.00000 - 6.92820i) q^{87} +(-0.725083 + 1.25588i) q^{89} +(-5.27492 - 0.418627i) q^{91} +(-4.00000 + 6.92820i) q^{93} +(-0.500000 - 0.866025i) q^{95} -6.54983 q^{97} -5.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 + 2 * q^5 - 3 * q^7 - 2 * q^9	\( 4 q + 4 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9} + 3 q^{11} + 8 q^{13} + 8 q^{15} - 7 q^{17} + 2 q^{19} + 6 q^{21} + 8 q^{25} + 16 q^{27} - 16 q^{29} + 8 q^{31} - 6 q^{33} - 6 q^{35} - 4 q^{37} + 8 q^{39} + 12 q^{41} - 4 q^{43} + 2 q^{45} - 3 q^{47} + 5 q^{49} + 14 q^{51} - 2 q^{53} + 6 q^{55} + 8 q^{57} + 8 q^{59} - 17 q^{61} + 6 q^{63} + 4 q^{65} + 12 q^{71} - 15 q^{73} - 16 q^{75} - 24 q^{77} + 14 q^{79} + 22 q^{81} + 16 q^{83} - 14 q^{85} - 16 q^{87} - 18 q^{89} - 6 q^{91} - 16 q^{93} - 2 q^{95} + 4 q^{97} - 6 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 + 2 * q^5 - 3 * q^7 - 2 * q^9 + 3 * q^11 + 8 * q^13 + 8 * q^15 - 7 * q^17 + 2 * q^19 + 6 * q^21 + 8 * q^25 + 16 * q^27 - 16 * q^29 + 8 * q^31 - 6 * q^33 - 6 * q^35 - 4 * q^37 + 8 * q^39 + 12 * q^41 - 4 * q^43 + 2 * q^45 - 3 * q^47 + 5 * q^49 + 14 * q^51 - 2 * q^53 + 6 * q^55 + 8 * q^57 + 8 * q^59 - 17 * q^61 + 6 * q^63 + 4 * q^65 + 12 * q^71 - 15 * q^73 - 16 * q^75 - 24 * q^77 + 14 * q^79 + 22 * q^81 + 16 * q^83 - 14 * q^85 - 16 * q^87 - 18 * q^89 - 6 * q^91 - 16 * q^93 - 2 * q^95 + 4 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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