LMFDB - Embedded newform 1064.2.q.l.305.2

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			305.2
Root			$2.13746 - 0.656712i$ of defining polynomial
Character	$\chi$	$=$	1064.305
Dual form			1064.2.q.l.457.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.13746 + 2.38876i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.13746 + 2.38876i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.13746 + 1.97014i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(-3.63746 + 6.30026i) q^{17} +(0.500000 + 0.866025i) q^{19} +(5.27492 + 0.418627i) q^{21} +(3.77492 + 6.53835i) q^{23} +(2.00000 - 3.46410i) q^{25} +4.00000 q^{27} -4.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(2.27492 + 3.94027i) q^{33} +(-1.50000 + 2.17945i) q^{35} +(-1.00000 - 1.73205i) q^{37} +(2.00000 - 3.46410i) q^{39} -4.54983 q^{41} -1.00000 q^{43} +(0.500000 - 0.866025i) q^{45} +(1.13746 + 1.97014i) q^{47} +(-4.41238 + 5.43424i) q^{49} +(7.27492 + 12.6005i) q^{51} +(3.27492 - 5.67232i) q^{53} -2.27492 q^{55} +2.00000 q^{57} +(2.00000 - 3.46410i) q^{59} +(-6.13746 - 10.6304i) q^{61} +(1.50000 - 2.17945i) q^{63} +(1.00000 + 1.73205i) q^{65} +15.0997 q^{69} +10.5498 q^{71} +(-1.86254 + 3.22602i) q^{73} +(-4.00000 - 6.92820i) q^{75} +(-6.00000 - 0.476171i) q^{77} +(-0.274917 - 0.476171i) q^{79} +(5.50000 - 9.52628i) q^{81} +11.5498 q^{83} -7.27492 q^{85} +(-4.00000 + 6.92820i) q^{87} +(-8.27492 - 14.3326i) q^{89} +(2.27492 + 4.77753i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(-0.500000 + 0.866025i) q^{95} +8.54983 q^{97} +2.27492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	1.13746	+	2.38876i	0.429919	+	0.902867i
$7$	1.13746	+	2.38876i	0.429919	+	0.902867i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.13746	+	1.97014i	−0.342957	+	0.594018i	−0.984980	−	0.172666i	$-0.944762\pi$
$11$	−1.13746	+	1.97014i	−0.342957	+	0.594018i	0.642024	+	0.766685i	$0.278095\pi$
$12$		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
$17$	−3.63746	+	6.30026i	−0.882213	+	1.52804i	−0.0333386	+	0.999444i	$0.510614\pi$
$17$	−3.63746	+	6.30026i	−0.882213	+	1.52804i	−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
$21$	5.27492	+	0.418627i	1.15108	+	0.0913518i
$22$		0			0
$23$	3.77492	+	6.53835i	0.787125	+	1.36334i	0.927722	+	0.373273i	$0.121765\pi$
$23$	3.77492	+	6.53835i	0.787125	+	1.36334i	−0.140597	+	0.990067i	$0.544902\pi$
$24$		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	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$		0			0
$33$	2.27492	+	3.94027i	0.396012	+	0.685913i
$34$		0			0
$35$	−1.50000	+	2.17945i	−0.253546	+	0.368394i
$36$		0			0
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$		0			0
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$		0			0
$41$	−4.54983			−0.710565			−0.355282	−	0.934759i	$-0.615615\pi$
$41$	−4.54983			−0.710565			−0.355282	+	0.934759i	$0.615615\pi$
$42$		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
$47$	1.13746	+	1.97014i	0.165915	+	0.287374i	0.936980	−	0.349383i	$-0.113609\pi$
$47$	1.13746	+	1.97014i	0.165915	+	0.287374i	−0.771065	+	0.636757i	$0.780275\pi$
$48$		0			0
$49$	−4.41238	+	5.43424i	−0.630339	+	0.776320i
$50$		0			0
$51$	7.27492	+	12.6005i	1.01869	+	1.76443i
$52$		0			0
$53$	3.27492	−	5.67232i	0.449844	−	0.779153i	−0.548531	−	0.836130i	$-0.684813\pi$
$53$	3.27492	−	5.67232i	0.449844	−	0.779153i	0.998376	+	0.0569767i	$0.0181461\pi$
$54$		0			0
$55$	−2.27492			−0.306750
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	−6.13746	−	10.6304i	−0.785821	−	1.36108i	−0.928507	−	0.371314i	$-0.878907\pi$
$61$	−6.13746	−	10.6304i	−0.785821	−	1.36108i	0.142686	−	0.989768i	$-0.454426\pi$
$62$		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	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$		0			0
$69$	15.0997			1.81779
$70$		0			0
$71$	10.5498			1.25204			0.626018	−	0.779809i	$-0.284684\pi$
$71$	10.5498			1.25204			0.626018	+	0.779809i	$0.284684\pi$
$72$		0			0
$73$	−1.86254	+	3.22602i	−0.217994	+	0.377577i	−0.954195	−	0.299187i	$-0.903285\pi$
$73$	−1.86254	+	3.22602i	−0.217994	+	0.377577i	0.736201	+	0.676763i	$0.236618\pi$
$74$		0			0
$75$	−4.00000	−	6.92820i	−0.461880	−	0.800000i
$76$		0			0
$77$	−6.00000	−	0.476171i	−0.683763	−	0.0542647i
$78$		0			0
$79$	−0.274917	−	0.476171i	−0.0309306	−	0.0535734i	0.850146	−	0.526547i	$-0.176514\pi$
$79$	−0.274917	−	0.476171i	−0.0309306	−	0.0535734i	−0.881076	+	0.472974i	$0.843180\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	11.5498			1.26776			0.633880	−	0.773432i	$-0.281462\pi$
$83$	11.5498			1.26776			0.633880	+	0.773432i	$0.281462\pi$
$84$		0			0
$85$	−7.27492			−0.789076
$86$		0			0
$87$	−4.00000	+	6.92820i	−0.428845	+	0.742781i
$88$		0			0
$89$	−8.27492	−	14.3326i	−0.877139	−	1.51925i	−0.854466	−	0.519507i	$-0.826116\pi$
$89$	−8.27492	−	14.3326i	−0.877139	−	1.51925i	−0.0226734	−	0.999743i	$-0.507218\pi$
$90$		0			0
$91$	2.27492	+	4.77753i	0.238476	+	0.500821i
$92$		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
$97$	8.54983			0.868104			0.434052	−	0.900888i	$-0.357083\pi$
$97$	8.54983			0.868104			0.434052	+	0.900888i	$0.357083\pi$
$98$		0			0
$99$	2.27492			0.228638
$100$		0			0
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	0.507300	−	0.861770i	$-0.330644\pi$
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	−0.999964	+	0.00844953i	$0.997310\pi$
$104$		0			0
$105$	2.27492	+	4.77753i	0.222009	+	0.466239i
$106$		0			0
$107$	1.72508	+	2.98793i	0.166770	+	0.288854i	0.937282	−	0.348571i	$-0.113333\pi$
$107$	1.72508	+	2.98793i	0.166770	+	0.288854i	−0.770512	+	0.637425i	$0.780000\pi$
$108$		0			0
$109$	5.27492	−	9.13642i	0.505245	−	0.875111i	−0.494736	−	0.869043i	$-0.664735\pi$
$109$	5.27492	−	9.13642i	0.505245	−	0.875111i	0.999982	−	0.00606754i	$-0.00193137\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$		0			0
$113$	18.5498			1.74502			0.872511	−	0.488595i	$-0.162490\pi$
$113$	18.5498			1.74502			0.872511	+	0.488595i	$0.162490\pi$
$114$		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
$119$	−19.1873	−	1.52274i	−1.75890	−	0.139589i
$120$		0			0
$121$	2.91238	+	5.04438i	0.264761	+	0.458580i
$122$		0			0
$123$	−4.54983	+	7.88054i	−0.410245	+	0.710565i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−15.0997			−1.33988			−0.669939	−	0.742416i	$-0.733680\pi$
$127$	−15.0997			−1.33988			−0.669939	+	0.742416i	$0.733680\pi$
$128$		0			0
$129$	−1.00000	+	1.73205i	−0.0880451	+	0.152499i
$130$		0			0
$131$	7.91238	+	13.7046i	0.691307	+	1.19738i	0.971410	+	0.237409i	$0.0762983\pi$
$131$	7.91238	+	13.7046i	0.691307	+	1.19738i	−0.280102	+	0.959970i	$0.590368\pi$
$132$		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
$137$	−1.86254	+	3.22602i	−0.159128	+	0.275617i	−0.934554	−	0.355820i	$-0.884201\pi$
$137$	−1.86254	+	3.22602i	−0.159128	+	0.275617i	0.775427	+	0.631438i	$0.217535\pi$
$138$		0			0
$139$	−10.8248			−0.918143			−0.459072	−	0.888399i	$-0.651818\pi$
$139$	−10.8248			−0.918143			−0.459072	+	0.888399i	$0.651818\pi$
$140$		0			0
$141$	4.54983			0.383165
$142$		0			0
$143$	−2.27492	+	3.94027i	−0.190238	+	0.329502i
$144$		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
$149$	−7.04983	−	12.2107i	−0.577545	−	1.00034i	−0.995760	−	0.0919891i	$-0.970677\pi$
$149$	−7.04983	−	12.2107i	−0.577545	−	1.00034i	0.418215	−	0.908348i	$-0.362656\pi$
$150$		0			0
$151$	4.27492	−	7.40437i	0.347888	−	0.602559i	−0.637986	−	0.770048i	$-0.720232\pi$
$151$	4.27492	−	7.40437i	0.347888	−	0.602559i	0.985874	+	0.167488i	$0.0535657\pi$
$152$		0			0
$153$	7.27492			0.588142
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	8.04983	−	13.9427i	0.642447	−	1.11275i	−0.342438	−	0.939540i	$-0.611253\pi$
$157$	8.04983	−	13.9427i	0.642447	−	1.11275i	0.984885	−	0.173210i	$-0.0554139\pi$
$158$		0			0
$159$	−6.54983	−	11.3446i	−0.519436	−	0.899689i
$160$		0			0
$161$	−11.3248	+	16.4545i	−0.892515	+	1.29679i
$162$		0			0
$163$	3.22508	+	5.58601i	0.252608	+	0.437530i	0.964243	−	0.265019i	$-0.0853784\pi$
$163$	3.22508	+	5.58601i	0.252608	+	0.437530i	−0.711635	+	0.702549i	$0.752045\pi$
$164$		0			0
$165$	−2.27492	+	3.94027i	−0.177102	+	0.306750i
$166$		0			0
$167$	−17.0997			−1.32321			−0.661606	−	0.749852i	$-0.730125\pi$
$167$	−17.0997			−1.32321			−0.661606	+	0.749852i	$0.730125\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$		0			0
$173$	−2.72508	−	4.71998i	−0.207184	−	0.358854i	0.743642	−	0.668578i	$-0.233097\pi$
$173$	−2.72508	−	4.71998i	−0.207184	−	0.358854i	−0.950826	+	0.309724i	$0.899763\pi$
$174$		0			0
$175$	10.5498	+	0.837253i	0.797493	+	0.0632904i
$176$		0			0
$177$	−4.00000	−	6.92820i	−0.300658	−	0.520756i
$178$		0			0
$179$	−7.54983	+	13.0767i	−0.564301	+	0.977398i	0.432813	+	0.901484i	$0.357521\pi$
$179$	−7.54983	+	13.0767i	−0.564301	+	0.977398i	−0.997114	+	0.0759146i	$0.975812\pi$
$180$		0			0
$181$	−14.5498			−1.08148			−0.540740	−	0.841190i	$-0.681856\pi$
$181$	−14.5498			−1.08148			−0.540740	+	0.841190i	$0.681856\pi$
$182$		0			0
$183$	−24.5498			−1.81478
$184$		0			0
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$		0			0
$187$	−8.27492	−	14.3326i	−0.605122	−	1.04810i
$188$		0			0
$189$	4.54983	+	9.55505i	0.330952	+	0.695028i
$190$		0			0
$191$	10.5000	+	18.1865i	0.759753	+	1.31593i	0.942976	+	0.332860i	$0.108014\pi$
$191$	10.5000	+	18.1865i	0.759753	+	1.31593i	−0.183223	+	0.983071i	$0.558653\pi$
$192$		0			0
$193$	−13.5498	+	23.4690i	−0.975338	+	1.68934i	−0.296525	+	0.955025i	$0.595828\pi$
$193$	−13.5498	+	23.4690i	−0.975338	+	1.68934i	−0.678814	+	0.734311i	$0.737506\pi$
$194$		0			0
$195$	4.00000			0.286446
$196$		0			0
$197$	−18.0997			−1.28955			−0.644774	−	0.764373i	$-0.723049\pi$
$197$	−18.0997			−1.28955			−0.644774	+	0.764373i	$0.723049\pi$
$198$		0			0
$199$	−1.50000	+	2.59808i	−0.106332	+	0.184173i	−0.914282	−	0.405079i	$-0.867244\pi$
$199$	−1.50000	+	2.59808i	−0.106332	+	0.184173i	0.807950	+	0.589252i	$0.200577\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.54983	−	9.55505i	−0.319336	−	0.670633i
$204$		0			0
$205$	−2.27492	−	3.94027i	−0.158887	−	0.275201i
$206$		0			0
$207$	3.77492	−	6.53835i	0.262375	−	0.454447i
$208$		0			0
$209$	−2.27492			−0.157359
$210$		0			0
$211$	19.6495			1.35273			0.676364	−	0.736568i	$-0.263555\pi$
$211$	19.6495			1.35273			0.676364	+	0.736568i	$0.263555\pi$
$212$		0			0
$213$	10.5498	−	18.2728i	0.722863	−	1.25204i
$214$		0			0
$215$	−0.500000	−	0.866025i	−0.0340997	−	0.0590624i
$216$		0			0
$217$	10.5498	+	0.837253i	0.716169	+	0.0568365i
$218$		0			0
$219$	3.72508	+	6.45203i	0.251718	+	0.435988i
$220$		0			0
$221$	−7.27492	+	12.6005i	−0.489364	+	0.847603i
$222$		0			0
$223$	13.0997			0.877219			0.438609	−	0.898678i	$-0.355471\pi$
$223$	13.0997			0.877219			0.438609	+	0.898678i	$0.355471\pi$
$224$		0			0
$225$	−4.00000			−0.266667
$226$		0			0
$227$	12.2749	−	21.2608i	0.814715	−	1.41113i	−0.0948176	−	0.995495i	$-0.530227\pi$
$227$	12.2749	−	21.2608i	0.814715	−	1.41113i	0.909532	−	0.415633i	$-0.136440\pi$
$228$		0			0
$229$	4.36254	+	7.55614i	0.288285	+	0.499324i	0.973400	−	0.229110i	$-0.0735817\pi$
$229$	4.36254	+	7.55614i	0.288285	+	0.499324i	−0.685116	+	0.728434i	$0.740248\pi$
$230$		0			0
$231$	−6.82475	+	9.91613i	−0.449036	+	0.652434i
$232$		0			0
$233$	1.63746	+	2.83616i	0.107273	+	0.185803i	0.914665	−	0.404213i	$-0.132455\pi$
$233$	1.63746	+	2.83616i	0.107273	+	0.185803i	−0.807391	+	0.590016i	$0.799121\pi$
$234$		0			0
$235$	−1.13746	+	1.97014i	−0.0741996	+	0.128518i
$236$		0			0
$237$	−1.09967			−0.0714312
$238$		0			0
$239$	−14.3746			−0.929815			−0.464907	−	0.885359i	$-0.653912\pi$
$239$	−14.3746			−0.929815			−0.464907	+	0.885359i	$0.653912\pi$
$240$		0			0
$241$	2.27492	−	3.94027i	0.146540	−	0.253815i	−0.783406	−	0.621510i	$-0.786520\pi$
$241$	2.27492	−	3.94027i	0.146540	−	0.253815i	0.929947	+	0.367695i	$0.119853\pi$
$242$		0			0
$243$	−5.00000	−	8.66025i	−0.320750	−	0.555556i
$244$		0			0
$245$	−6.91238	−	1.10411i	−0.441615	−	0.0705390i
$246$		0			0
$247$	1.00000	+	1.73205i	0.0636285	+	0.110208i
$248$		0			0
$249$	11.5498	−	20.0049i	0.731941	−	1.26776i
$250$		0			0
$251$	2.09967			0.132530			0.0662650	−	0.997802i	$-0.478892\pi$
$251$	2.09967			0.132530			0.0662650	+	0.997802i	$0.478892\pi$
$252$		0			0
$253$	−17.1752			−1.07980
$254$		0			0
$255$	−7.27492	+	12.6005i	−0.455573	+	0.789076i
$256$		0			0
$257$	3.72508	+	6.45203i	0.232364	+	0.402467i	0.958503	−	0.285081i	$-0.0920205\pi$
$257$	3.72508	+	6.45203i	0.232364	+	0.402467i	−0.726139	+	0.687548i	$0.758687\pi$
$258$		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
$263$	−0.0876242	+	0.151770i	−0.00540314	+	0.00935851i	−0.868714	−	0.495313i	$-0.835053\pi$
$263$	−0.0876242	+	0.151770i	−0.00540314	+	0.00935851i	0.863311	+	0.504672i	$0.168387\pi$
$264$		0			0
$265$	6.54983			0.402353
$266$		0			0
$267$	−33.0997			−2.02567
$268$		0			0
$269$	4.72508	−	8.18408i	0.288093	−	0.498992i	−0.685261	−	0.728297i	$-0.740312\pi$
$269$	4.72508	−	8.18408i	0.288093	−	0.498992i	0.973355	+	0.229305i	$0.0736453\pi$
$270$		0			0
$271$	−1.22508	−	2.12191i	−0.0744185	−	0.128897i	0.826415	−	0.563062i	$-0.190377\pi$
$271$	−1.22508	−	2.12191i	−0.0744185	−	0.128897i	−0.900833	+	0.434165i	$0.857043\pi$
$272$		0			0
$273$	10.5498	+	0.837253i	0.638505	+	0.0506729i
$274$		0			0
$275$	4.54983	+	7.88054i	0.274365	+	0.475215i
$276$		0			0
$277$	4.13746	−	7.16629i	0.248596	−	0.430581i	−0.714541	−	0.699594i	$-0.753364\pi$
$277$	4.13746	−	7.16629i	0.248596	−	0.430581i	0.963136	+	0.269013i	$0.0866976\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−14.5498			−0.867970			−0.433985	−	0.900920i	$-0.642893\pi$
$281$	−14.5498			−0.867970			−0.433985	+	0.900920i	$0.642893\pi$
$282$		0			0
$283$	8.50000	−	14.7224i	0.505273	−	0.875158i	−0.494709	−	0.869059i	$-0.664725\pi$
$283$	8.50000	−	14.7224i	0.505273	−	0.875158i	0.999981	−	0.00609896i	$-0.00194137\pi$
$284$		0			0
$285$	1.00000	+	1.73205i	0.0592349	+	0.102598i
$286$		0			0
$287$	−5.17525	−	10.8685i	−0.305485	−	0.641546i
$288$		0			0
$289$	−17.9622	−	31.1115i	−1.05660	−	1.83009i
$290$		0			0
$291$	8.54983	−	14.8087i	0.501200	−	0.868104i
$292$		0			0
$293$	−17.6495			−1.03109			−0.515547	−	0.856861i	$-0.672411\pi$
$293$	−17.6495			−1.03109			−0.515547	+	0.856861i	$0.672411\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$		0			0
$297$	−4.54983	+	7.88054i	−0.264008	+	0.457276i
$298$		0			0
$299$	7.54983	+	13.0767i	0.436618	+	0.756245i
$300$		0			0
$301$	−1.13746	−	2.38876i	−0.0655620	−	0.137686i
$302$		0			0
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$		0			0
$305$	6.13746	−	10.6304i	0.351430	−	0.608694i
$306$		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
$311$	1.36254	−	2.35999i	0.0772626	−	0.133823i	−0.824805	−	0.565417i	$-0.808715\pi$
$311$	1.36254	−	2.35999i	0.0772626	−	0.133823i	0.902068	+	0.431594i	$0.142049\pi$
$312$		0			0
$313$	−14.5997	−	25.2874i	−0.825222	−	1.42933i	−0.901749	−	0.432259i	$-0.857717\pi$
$313$	−14.5997	−	25.2874i	−0.825222	−	1.42933i	0.0765274	−	0.997067i	$-0.475617\pi$
$314$		0			0
$315$	2.63746	+	0.209313i	0.148604	+	0.0117935i
$316$		0			0
$317$	10.5498	+	18.2728i	0.592538	+	1.02631i	0.993889	+	0.110381i	$0.0352072\pi$
$317$	10.5498	+	18.2728i	0.592538	+	1.02631i	−0.401352	+	0.915924i	$0.631459\pi$
$318$		0			0
$319$	4.54983	−	7.88054i	0.254742	−	0.441226i
$320$		0			0
$321$	6.90033			0.385139
$322$		0			0
$323$	−7.27492			−0.404787
$324$		0			0
$325$	4.00000	−	6.92820i	0.221880	−	0.384308i
$326$		0			0
$327$	−10.5498	−	18.2728i	−0.583407	−	1.01049i
$328$		0			0
$329$	−3.41238	+	4.95807i	−0.188130	+	0.273347i
$330$		0			0
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	0.991735	−	0.128302i	$-0.0409527\pi$
$331$	7.00000	+	12.1244i	0.384755	+	0.666415i	−0.606980	+	0.794717i	$0.707619\pi$
$332$		0			0
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−21.0997			−1.14937			−0.574686	−	0.818374i	$-0.694876\pi$
$337$	−21.0997			−1.14937			−0.574686	+	0.818374i	$0.694876\pi$
$338$		0			0
$339$	18.5498	−	32.1293i	1.00749	−	1.74502i
$340$		0			0
$341$	4.54983	+	7.88054i	0.246387	+	0.426755i
$342$		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
$347$	16.5997	−	28.7515i	0.891117	−	1.54346i	0.0525788	−	0.998617i	$-0.483256\pi$
$347$	16.5997	−	28.7515i	0.891117	−	1.54346i	0.838538	−	0.544843i	$-0.183411\pi$
$348$		0			0
$349$	28.3746			1.51886			0.759428	−	0.650591i	$-0.225479\pi$
$349$	28.3746			1.51886			0.759428	+	0.650591i	$0.225479\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	−11.5498	+	20.0049i	−0.614736	+	1.06475i	0.375695	+	0.926743i	$0.377404\pi$
$353$	−11.5498	+	20.0049i	−0.614736	+	1.06475i	−0.990431	+	0.138010i	$0.955929\pi$
$354$		0			0
$355$	5.27492	+	9.13642i	0.279964	+	0.484911i
$356$		0			0
$357$	−21.8248	+	31.7106i	−1.15509	+	1.67830i
$358$		0			0
$359$	8.86254	+	15.3504i	0.467747	+	0.810162i	0.999321	−	0.0368504i	$-0.0117325\pi$
$359$	8.86254	+	15.3504i	0.467747	+	0.810162i	−0.531574	+	0.847012i	$0.678399\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		0			0
$363$	11.6495			0.611440
$364$		0			0
$365$	−3.72508			−0.194980
$366$		0			0
$367$	13.0997	−	22.6893i	0.683797	−	1.18437i	−0.290016	−	0.957022i	$-0.593661\pi$
$367$	13.0997	−	22.6893i	0.683797	−	1.18437i	0.973813	−	0.227350i	$-0.0730060\pi$
$368$		0			0
$369$	2.27492	+	3.94027i	0.118427	+	0.205122i
$370$		0			0
$371$	17.2749	+	1.37097i	0.896869	+	0.0711771i
$372$		0			0
$373$	3.27492	+	5.67232i	0.169569	+	0.293702i	0.938268	−	0.345908i	$-0.112429\pi$
$373$	3.27492	+	5.67232i	0.169569	+	0.293702i	−0.768700	+	0.639610i	$0.779096\pi$
$374$		0			0
$375$	9.00000	−	15.5885i	0.464758	−	0.804984i
$376$		0			0
$377$	−8.00000			−0.412021
$378$		0			0
$379$	3.09967			0.159219			0.0796096	−	0.996826i	$-0.474633\pi$
$379$	3.09967			0.159219			0.0796096	+	0.996826i	$0.474633\pi$
$380$		0			0
$381$	−15.0997	+	26.1534i	−0.773579	+	1.33988i
$382$		0			0
$383$	−11.0000	−	19.0526i	−0.562074	−	0.973540i	−0.997315	−	0.0732266i	$-0.976670\pi$
$383$	−11.0000	−	19.0526i	−0.562074	−	0.973540i	0.435242	−	0.900314i	$-0.356663\pi$
$384$		0			0
$385$	−2.58762	−	5.43424i	−0.131878	−	0.276954i
$386$		0			0
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$		0			0
$389$	−18.9124	+	32.7572i	−0.958896	+	1.66086i	−0.233705	+	0.972308i	$0.575085\pi$
$389$	−18.9124	+	32.7572i	−0.958896	+	1.66086i	−0.725191	+	0.688548i	$0.758248\pi$
$390$		0			0
$391$	−54.9244			−2.77765
$392$		0			0
$393$	31.6495			1.59651
$394$		0			0
$395$	0.274917	−	0.476171i	0.0138326	−	0.0239587i
$396$		0			0
$397$	10.3625	+	17.9484i	0.520081	+	0.900807i	0.999727	+	0.0233449i	$0.00743160\pi$
$397$	10.3625	+	17.9484i	0.520081	+	0.900807i	−0.479646	+	0.877462i	$0.659235\pi$
$398$		0			0
$399$	2.27492	+	4.77753i	0.113888	+	0.239175i
$400$		0			0
$401$	−10.5498	−	18.2728i	−0.526834	−	0.912503i	−0.999511	−	0.0312670i	$-0.990046\pi$
$401$	−10.5498	−	18.2728i	−0.526834	−	0.912503i	0.472677	−	0.881235i	$-0.343288\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$		0			0
$405$	11.0000			0.546594
$406$		0			0
$407$	4.54983			0.225527
$408$		0			0
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$		0			0
$411$	3.72508	+	6.45203i	0.183745	+	0.318255i
$412$		0			0
$413$	10.5498	+	0.837253i	0.519123	+	0.0411986i
$414$		0			0
$415$	5.77492	+	10.0025i	0.283480	+	0.491001i
$416$		0			0
$417$	−10.8248	+	18.7490i	−0.530090	+	0.918143i
$418$		0			0
$419$	19.5498			0.955072			0.477536	−	0.878612i	$-0.341530\pi$
$419$	19.5498			0.955072			0.477536	+	0.878612i	$0.341530\pi$
$420$		0			0
$421$	18.5498			0.904064			0.452032	−	0.892002i	$-0.350699\pi$
$421$	18.5498			0.904064			0.452032	+	0.892002i	$0.350699\pi$
$422$		0			0
$423$	1.13746	−	1.97014i	0.0553051	−	0.0957913i
$424$		0			0
$425$	14.5498	+	25.2011i	0.705771	+	1.22243i
$426$		0			0
$427$	18.4124	−	26.7526i	0.891037	−	1.29465i
$428$		0			0
$429$	4.54983	+	7.88054i	0.219668	+	0.380476i
$430$		0			0
$431$	−4.54983	+	7.88054i	−0.219158	+	0.379592i	−0.954551	−	0.298048i	$-0.903664\pi$
$431$	−4.54983	+	7.88054i	−0.219158	+	0.379592i	0.735393	+	0.677641i	$0.236998\pi$
$432$		0			0
$433$	25.0997			1.20621			0.603107	−	0.797661i	$-0.293929\pi$
$433$	25.0997			1.20621			0.603107	+	0.797661i	$0.293929\pi$
$434$		0			0
$435$	−8.00000			−0.383571
$436$		0			0
$437$	−3.77492	+	6.53835i	−0.180579	+	0.312772i
$438$		0			0
$439$	−17.0997	−	29.6175i	−0.816123	−	1.41357i	−0.908519	−	0.417844i	$-0.862786\pi$
$439$	−17.0997	−	29.6175i	−0.816123	−	1.41357i	0.0923963	−	0.995722i	$-0.470547\pi$
$440$		0			0
$441$	6.91238	+	1.10411i	0.329161	+	0.0525767i
$442$		0			0
$443$	−0.0876242	−	0.151770i	−0.00416315	−	0.00721079i	0.863936	−	0.503601i	$-0.167992\pi$
$443$	−0.0876242	−	0.151770i	−0.00416315	−	0.00721079i	−0.868099	+	0.496390i	$0.834659\pi$
$444$		0			0
$445$	8.27492	−	14.3326i	0.392269	−	0.679429i
$446$		0			0
$447$	−28.1993			−1.33378
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	5.17525	−	8.96379i	0.243693	−	0.422089i
$452$		0			0
$453$	−8.54983	−	14.8087i	−0.401706	−	0.695776i
$454$		0			0
$455$	−3.00000	+	4.35890i	−0.140642	+	0.204348i
$456$		0			0
$457$	−6.13746	−	10.6304i	−0.287098	−	0.497269i	0.686018	−	0.727585i	$-0.259357\pi$
$457$	−6.13746	−	10.6304i	−0.287098	−	0.497269i	−0.973116	+	0.230316i	$0.926024\pi$
$458$		0			0
$459$	−14.5498	+	25.2011i	−0.679128	+	1.17628i
$460$		0			0
$461$	15.7251			0.732390			0.366195	−	0.930538i	$-0.380660\pi$
$461$	15.7251			0.732390			0.366195	+	0.930538i	$0.380660\pi$
$462$		0			0
$463$	2.82475			0.131277			0.0656387	−	0.997843i	$-0.479092\pi$
$463$	2.82475			0.131277			0.0656387	+	0.997843i	$0.479092\pi$
$464$		0			0
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$		0			0
$467$	9.13746	+	15.8265i	0.422831	+	0.732365i	0.996215	−	0.0869217i	$-0.0277030\pi$
$467$	9.13746	+	15.8265i	0.422831	+	0.732365i	−0.573384	+	0.819287i	$0.694370\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−16.0997	−	27.8854i	−0.741834	−	1.28489i
$472$		0			0
$473$	1.13746	−	1.97014i	0.0523004	−	0.0905870i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	−6.54983			−0.299896
$478$		0			0
$479$	14.7749	−	25.5909i	0.675083	−	1.16928i	−0.301361	−	0.953510i	$-0.597441\pi$
$479$	14.7749	−	25.5909i	0.675083	−	1.16928i	0.976445	−	0.215768i	$-0.0692256\pi$
$480$		0			0
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$		0			0
$483$	17.1752	+	36.0695i	0.781501	+	1.64122i
$484$		0			0
$485$	4.27492	+	7.40437i	0.194114	+	0.336215i
$486$		0			0
$487$	11.5498	−	20.0049i	0.523373	−	0.906509i	−0.476257	−	0.879306i	$-0.658007\pi$
$487$	11.5498	−	20.0049i	0.523373	−	0.906509i	0.999630	−	0.0272024i	$-0.00865987\pi$
$488$		0			0
$489$	12.9003			0.583373
$490$		0			0
$491$	−9.54983			−0.430978			−0.215489	−	0.976506i	$-0.569135\pi$
$491$	−9.54983			−0.430978			−0.215489	+	0.976506i	$0.569135\pi$
$492$		0			0
$493$	14.5498	−	25.2011i	0.655292	−	1.13500i
$494$		0			0
$495$	1.13746	+	1.97014i	0.0511250	+	0.0885510i
$496$		0			0
$497$	12.0000	+	25.2011i	0.538274	+	1.13042i
$498$		0			0
$499$	14.5997	+	25.2874i	0.653571	+	1.13202i	0.982250	+	0.187576i	$0.0600632\pi$
$499$	14.5997	+	25.2874i	0.653571	+	1.13202i	−0.328679	+	0.944442i	$0.606603\pi$
$500$		0			0
$501$	−17.0997	+	29.6175i	−0.763957	+	1.32321i
$502$		0			0
$503$	34.6495			1.54494			0.772472	−	0.635048i	$-0.219020\pi$
$503$	34.6495			1.54494			0.772472	+	0.635048i	$0.219020\pi$
$504$		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	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$		0			0
$511$	−9.82475	−	0.779710i	−0.434621	−	0.0344923i
$512$		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
$517$	−5.17525			−0.227607
$518$		0			0
$519$	−10.9003			−0.478471
$520$		0			0
$521$	13.0000	−	22.5167i	0.569540	−	0.986473i	−0.427071	−	0.904218i	$-0.640455\pi$
$521$	13.0000	−	22.5167i	0.569540	−	0.986473i	0.996611	−	0.0822547i	$-0.0262121\pi$
$522$		0			0
$523$	20.8248	+	36.0695i	0.910603	+	1.57721i	0.813215	+	0.581964i	$0.197715\pi$
$523$	20.8248	+	36.0695i	0.910603	+	1.57721i	0.0973882	+	0.995246i	$0.468951\pi$
$524$		0			0
$525$	12.0000	−	17.4356i	0.523723	−	0.760952i
$526$		0			0
$527$	14.5498	+	25.2011i	0.633801	+	1.09778i
$528$		0			0
$529$	−17.0000	+	29.4449i	−0.739130	+	1.28021i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$	−9.09967			−0.394150
$534$		0			0
$535$	−1.72508	+	2.98793i	−0.0745818	+	0.129180i
$536$		0			0
$537$	15.0997	+	26.1534i	0.651599	+	1.12860i
$538$		0			0
$539$	−5.68729	−	14.8742i	−0.244969	−	0.640677i
$540$		0			0
$541$	8.50000	+	14.7224i	0.365444	+	0.632967i	0.988847	−	0.148933i	$-0.0475840\pi$
$541$	8.50000	+	14.7224i	0.365444	+	0.632967i	−0.623404	+	0.781900i	$0.714251\pi$
$542$		0			0
$543$	−14.5498	+	25.2011i	−0.624393	+	1.08148i
$544$		0			0
$545$	10.5498			0.451905
$546$		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
$549$	−6.13746	+	10.6304i	−0.261940	+	0.453694i
$550$		0			0
$551$	−2.00000	−	3.46410i	−0.0852029	−	0.147576i
$552$		0			0
$553$	0.824752	−	1.19834i	0.0350720	−	0.0509584i
$554$		0			0
$555$	−2.00000	−	3.46410i	−0.0848953	−	0.147043i
$556$		0			0
$557$	−1.04983	+	1.81837i	−0.0444829	+	0.0770467i	−0.887410	−	0.460982i	$-0.847497\pi$
$557$	−1.04983	+	1.81837i	−0.0444829	+	0.0770467i	0.842927	+	0.538028i	$0.180831\pi$
$558$		0			0
$559$	−2.00000			−0.0845910
$560$		0			0
$561$	−33.0997			−1.39747
$562$		0			0
$563$	5.72508	−	9.91613i	0.241283	−	0.417915i	−0.719797	−	0.694185i	$-0.755765\pi$
$563$	5.72508	−	9.91613i	0.241283	−	0.417915i	0.961080	+	0.276270i	$0.0890983\pi$
$564$		0			0
$565$	9.27492	+	16.0646i	0.390199	+	0.675844i
$566$		0			0
$567$	29.0120	+	2.30245i	1.21839	+	0.0966937i
$568$		0			0
$569$	8.09967	+	14.0290i	0.339556	+	0.588128i	0.984349	−	0.176229i	$-0.0563899\pi$
$569$	8.09967	+	14.0290i	0.339556	+	0.588128i	−0.644793	+	0.764357i	$0.723057\pi$
$570$		0			0
$571$	10.2251	−	17.7104i	0.427906	−	0.741156i	−0.568781	−	0.822489i	$-0.692585\pi$
$571$	10.2251	−	17.7104i	0.427906	−	0.741156i	0.996687	+	0.0813337i	$0.0259180\pi$
$572$		0			0
$573$	42.0000			1.75458
$574$		0			0
$575$	30.1993			1.25940
$576$		0			0
$577$	−6.68729	+	11.5827i	−0.278396	+	0.482195i	−0.970986	−	0.239136i	$-0.923136\pi$
$577$	−6.68729	+	11.5827i	−0.278396	+	0.482195i	0.692591	+	0.721331i	$0.256469\pi$
$578$		0			0
$579$	27.0997	+	46.9380i	1.12622	+	1.95068i
$580$		0			0
$581$	13.1375	+	27.5898i	0.545034	+	1.14462i
$582$		0			0
$583$	7.45017	+	12.9041i	0.308554	+	0.534432i
$584$		0			0
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$		0			0
$587$	−2.72508			−0.112476			−0.0562381	−	0.998417i	$-0.517911\pi$
$587$	−2.72508			−0.112476			−0.0562381	+	0.998417i	$0.517911\pi$
$588$		0			0
$589$	4.00000			0.164817
$590$		0			0
$591$	−18.0997	+	31.3495i	−0.744521	+	1.28955i
$592$		0			0
$593$	−1.50000	−	2.59808i	−0.0615976	−	0.106690i	0.833582	−	0.552396i	$-0.186286\pi$
$593$	−1.50000	−	2.59808i	−0.0615976	−	0.106690i	−0.895180	+	0.445705i	$0.852953\pi$
$594$		0			0
$595$	−8.27492	−	17.3781i	−0.339239	−	0.712431i
$596$		0			0
$597$	3.00000	+	5.19615i	0.122782	+	0.212664i
$598$		0			0
$599$	−7.82475	+	13.5529i	−0.319711	+	0.553755i	−0.980428	−	0.196880i	$-0.936919\pi$
$599$	−7.82475	+	13.5529i	−0.319711	+	0.553755i	0.660717	+	0.750635i	$0.270252\pi$
$600$		0			0
$601$	−11.4502			−0.467062			−0.233531	−	0.972349i	$-0.575028\pi$
$601$	−11.4502			−0.467062			−0.233531	+	0.972349i	$0.575028\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.91238	+	5.04438i	−0.118405	+	0.205083i
$606$		0			0
$607$	−12.8248	−	22.2131i	−0.520541	−	0.901603i	−0.999715	−	0.0238829i	$-0.992397\pi$
$607$	−12.8248	−	22.2131i	−0.520541	−	0.901603i	0.479174	−	0.877720i	$-0.340936\pi$
$608$		0			0
$609$	−21.0997	−	1.67451i	−0.855002	−	0.0678544i
$610$		0			0
$611$	2.27492	+	3.94027i	0.0920333	+	0.159406i
$612$		0			0
$613$	18.9124	−	32.7572i	0.763864	−	1.32305i	−0.176982	−	0.984214i	$-0.556633\pi$
$613$	18.9124	−	32.7572i	0.763864	−	1.32305i	0.940845	−	0.338837i	$-0.110033\pi$
$614$		0			0
$615$	−9.09967			−0.366934
$616$		0			0
$617$	−24.0997			−0.970216			−0.485108	−	0.874454i	$-0.661220\pi$
$617$	−24.0997			−0.970216			−0.485108	+	0.874454i	$0.661220\pi$
$618$		0			0
$619$	−5.77492	+	10.0025i	−0.232114	+	0.402032i	−0.958430	−	0.285328i	$-0.907897\pi$
$619$	−5.77492	+	10.0025i	−0.232114	+	0.402032i	0.726316	+	0.687361i	$0.241231\pi$
$620$		0			0
$621$	15.0997	+	26.1534i	0.605929	+	1.04950i
$622$		0			0
$623$	24.8248	−	36.0695i	0.994583	−	1.44510i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	−2.27492	+	3.94027i	−0.0908514	+	0.157359i
$628$		0			0
$629$	14.5498			0.580140
$630$		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
$633$	19.6495	−	34.0339i	0.780998	−	1.35273i
$634$		0			0
$635$	−7.54983	−	13.0767i	−0.299606	−	0.518933i
$636$		0			0
$637$	−8.82475	+	10.8685i	−0.349649	+	0.430625i
$638$		0			0
$639$	−5.27492	−	9.13642i	−0.208673	−	0.361431i
$640$		0			0
$641$	−23.2749	+	40.3133i	−0.919304	+	1.59228i	−0.118829	+	0.992915i	$0.537914\pi$
$641$	−23.2749	+	40.3133i	−0.919304	+	1.59228i	−0.800475	+	0.599366i	$0.795419\pi$
$642$		0			0
$643$	−0.175248			−0.00691112			−0.00345556	−	0.999994i	$-0.501100\pi$
$643$	−0.175248			−0.00691112			−0.00345556	+	0.999994i	$0.501100\pi$
$644$		0			0
$645$	−2.00000			−0.0787499
$646$		0			0
$647$	7.04983	−	12.2107i	0.277158	−	0.480051i	−0.693520	−	0.720438i	$-0.743941\pi$
$647$	7.04983	−	12.2107i	0.277158	−	0.480051i	0.970677	+	0.240387i	$0.0772743\pi$
$648$		0			0
$649$	4.54983	+	7.88054i	0.178597	+	0.309338i
$650$		0			0
$651$	12.0000	−	17.4356i	0.470317	−	0.683355i
$652$		0			0
$653$	0.362541	+	0.627940i	0.0141873	+	0.0245732i	0.873032	−	0.487663i	$-0.162151\pi$
$653$	0.362541	+	0.627940i	0.0141873	+	0.0245732i	−0.858845	+	0.512236i	$0.828817\pi$
$654$		0			0
$655$	−7.91238	+	13.7046i	−0.309162	+	0.535484i
$656$		0			0
$657$	3.72508			0.145329
$658$		0			0
$659$	−25.4502			−0.991398			−0.495699	−	0.868494i	$-0.665088\pi$
$659$	−25.4502			−0.991398			−0.495699	+	0.868494i	$0.665088\pi$
$660$		0			0
$661$	22.2749	−	38.5813i	0.866394	−	1.50064i	0.000737396	−	1.00000i	$-0.499765\pi$
$661$	22.2749	−	38.5813i	0.866394	−	1.50064i	0.865656	−	0.500638i	$-0.166901\pi$
$662$		0			0
$663$	14.5498	+	25.2011i	0.565069	+	0.978728i
$664$		0			0
$665$	−2.63746	−	0.209313i	−0.102276	−	0.00811682i
$666$		0			0
$667$	−15.0997	−	26.1534i	−0.584662	−	1.01266i
$668$		0			0
$669$	13.0997	−	22.6893i	0.506462	−	0.877219i
$670$		0			0
$671$	27.9244			1.07801
$672$		0			0
$673$	10.5498			0.406666			0.203333	−	0.979110i	$-0.434823\pi$
$673$	10.5498			0.406666			0.203333	+	0.979110i	$0.434823\pi$
$674$		0			0
$675$	8.00000	−	13.8564i	0.307920	−	0.533333i
$676$		0			0
$677$	−18.5498	−	32.1293i	−0.712928	−	1.23483i	−0.963753	−	0.266795i	$-0.914035\pi$
$677$	−18.5498	−	32.1293i	−0.712928	−	1.23483i	0.250825	−	0.968032i	$-0.419298\pi$
$678$		0			0
$679$	9.72508	+	20.4235i	0.373214	+	0.783783i
$680$		0			0
$681$	−24.5498	−	42.5216i	−0.940752	−	1.62943i
$682$		0			0
$683$	8.82475	−	15.2849i	0.337670	−	0.584861i	−0.646324	−	0.763063i	$-0.723695\pi$
$683$	8.82475	−	15.2849i	0.337670	−	0.584861i	0.983994	+	0.178202i	$0.0570280\pi$
$684$		0			0
$685$	−3.72508			−0.142328
$686$		0			0
$687$	17.4502			0.665765
$688$		0			0
$689$	6.54983	−	11.3446i	0.249529	−	0.432197i
$690$		0			0
$691$	18.4622	+	31.9775i	0.702336	+	1.21648i	0.967645	+	0.252317i	$0.0811927\pi$
$691$	18.4622	+	31.9775i	0.702336	+	1.21648i	−0.265309	+	0.964163i	$0.585474\pi$
$692$		0			0
$693$	2.58762	+	5.43424i	0.0982957	+	0.206430i
$694$		0			0
$695$	−5.41238	−	9.37451i	−0.205303	−	0.355595i
$696$		0			0
$697$	16.5498	−	28.6652i	0.626870	−	1.08577i
$698$		0			0
$699$	6.54983			0.247737
$700$		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
$705$	2.27492	+	3.94027i	0.0856783	+	0.148399i
$706$		0			0
$707$	7.91238	+	0.627940i	0.297576	+	0.0236161i
$708$		0			0
$709$	7.50000	+	12.9904i	0.281668	+	0.487864i	0.971796	−	0.235824i	$-0.0757789\pi$
$709$	7.50000	+	12.9904i	0.281668	+	0.487864i	−0.690127	+	0.723688i	$0.742446\pi$
$710$		0			0
$711$	−0.274917	+	0.476171i	−0.0103102	+	0.0178578i
$712$		0			0
$713$	30.1993			1.13097
$714$		0			0
$715$	−4.54983			−0.170154
$716$		0			0
$717$	−14.3746	+	24.8975i	−0.536829	+	0.929815i
$718$		0			0
$719$	−13.3625	−	23.1446i	−0.498339	−	0.863148i	0.501659	−	0.865065i	$-0.332723\pi$
$719$	−13.3625	−	23.1446i	−0.498339	−	0.863148i	−0.999998	+	0.00191724i	$0.999390\pi$
$720$		0			0
$721$	15.0000	−	21.7945i	0.558629	−	0.811669i
$722$		0			0
$723$	−4.54983	−	7.88054i	−0.169210	−	0.293081i
$724$		0			0
$725$	−8.00000	+	13.8564i	−0.297113	+	0.514614i
$726$		0			0
$727$	−13.9003			−0.515535			−0.257767	−	0.966207i	$-0.582987\pi$
$727$	−13.9003			−0.515535			−0.257767	+	0.966207i	$0.582987\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	3.63746	−	6.30026i	0.134536	−	0.233024i
$732$		0			0
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	−0.987971	−	0.154642i	$-0.950578\pi$
$733$	−17.0000	−	29.4449i	−0.627909	−	1.08757i	0.360061	−	0.932929i	$-0.382756\pi$
$734$		0			0
$735$	−8.82475	+	10.8685i	−0.325506	+	0.400890i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	2.08762	−	3.61587i	0.0767945	−	0.133012i	−0.825071	−	0.565029i	$-0.808865\pi$
$739$	2.08762	−	3.61587i	0.0767945	−	0.133012i	0.901865	+	0.432017i	$0.142198\pi$
$740$		0			0
$741$	4.00000			0.146944
$742$		0			0
$743$	−46.7492			−1.71506			−0.857530	−	0.514433i	$-0.828002\pi$
$743$	−46.7492			−1.71506			−0.857530	+	0.514433i	$0.828002\pi$
$744$		0			0
$745$	7.04983	−	12.2107i	0.258286	−	0.447364i
$746$		0			0
$747$	−5.77492	−	10.0025i	−0.211293	−	0.365971i
$748$		0			0
$749$	−5.17525	+	7.51946i	−0.189099	+	0.274755i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$		0			0
$753$	2.09967	−	3.63673i	0.0765162	−	0.132530i
$754$		0			0
$755$	8.54983			0.311160
$756$		0			0
$757$	25.3746			0.922255			0.461128	−	0.887334i	$-0.347445\pi$
$757$	25.3746			0.922255			0.461128	+	0.887334i	$0.347445\pi$
$758$		0			0
$759$	−17.1752	+	29.7484i	−0.623422	+	1.07980i
$760$		0			0
$761$	21.5000	+	37.2391i	0.779374	+	1.34992i	0.932303	+	0.361679i	$0.117796\pi$
$761$	21.5000	+	37.2391i	0.779374	+	1.34992i	−0.152928	+	0.988237i	$0.548870\pi$
$762$		0			0
$763$	27.8248	+	2.20822i	1.00732	+	0.0799430i
$764$		0			0
$765$	3.63746	+	6.30026i	0.131513	+	0.227786i
$766$		0			0
$767$	4.00000	−	6.92820i	0.144432	−	0.250163i
$768$		0			0
$769$	−43.1993			−1.55781			−0.778904	−	0.627143i	$-0.784224\pi$
$769$	−43.1993			−1.55781			−0.778904	+	0.627143i	$0.784224\pi$
$770$		0			0
$771$	14.9003			0.536622
$772$		0			0
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	−0.712241	−	0.701935i	$-0.752320\pi$
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$774$		0			0
$775$	−8.00000	−	13.8564i	−0.287368	−	0.497737i
$776$		0			0
$777$	−4.54983	−	9.55505i	−0.163224	−	0.342786i
$778$		0			0
$779$	−2.27492	−	3.94027i	−0.0815074	−	0.141175i
$780$		0			0
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$		0			0
$783$	−16.0000			−0.571793
$784$		0			0
$785$	16.0997			0.574622
$786$		0			0
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	−0.963394	−	0.268091i	$-0.913607\pi$
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	0.713871	+	0.700278i	$0.246941\pi$
$788$		0			0
$789$	0.175248	+	0.303539i	0.00623901	+	0.0108063i
$790$		0			0
$791$	21.0997	+	44.3112i	0.750218	+	1.57552i
$792$		0			0
$793$	−12.2749	−	21.2608i	−0.435895	−	0.754992i
$794$		0			0
$795$	6.54983	−	11.3446i	0.232299	−	0.402353i
$796$		0			0
$797$	−16.5498			−0.586225			−0.293113	−	0.956078i	$-0.594691\pi$
$797$	−16.5498			−0.586225			−0.293113	+	0.956078i	$0.594691\pi$
$798$		0			0
$799$	−16.5498			−0.585491
$800$		0			0
$801$	−8.27492	+	14.3326i	−0.292380	+	0.506417i
$802$		0			0
$803$	−4.23713	−	7.33892i	−0.149525	−	0.258985i
$804$		0			0
$805$	−19.9124	−	1.58028i	−0.701819	−	0.0556976i
$806$		0			0
$807$	−9.45017	−	16.3682i	−0.332662	−	0.576187i
$808$		0			0
$809$	9.04983	−	15.6748i	0.318175	−	0.551096i	−0.661932	−	0.749564i	$-0.730263\pi$
$809$	9.04983	−	15.6748i	0.318175	−	0.551096i	0.980107	+	0.198468i	$0.0635966\pi$
$810$		0			0
$811$	−22.7492			−0.798831			−0.399416	−	0.916770i	$-0.630787\pi$
$811$	−22.7492			−0.798831			−0.399416	+	0.916770i	$0.630787\pi$
$812$		0			0
$813$	−4.90033			−0.171862
$814$		0			0
$815$	−3.22508	+	5.58601i	−0.112970	+	0.195669i
$816$		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
$821$	−12.9622	−	22.4512i	−0.452384	−	0.783553i	0.546149	−	0.837688i	$-0.316093\pi$
$821$	−12.9622	−	22.4512i	−0.452384	−	0.783553i	−0.998534	+	0.0541353i	$0.982760\pi$
$822$		0			0
$823$	23.9622	−	41.5038i	0.835270	−	1.44673i	−0.0585402	−	0.998285i	$-0.518645\pi$
$823$	23.9622	−	41.5038i	0.835270	−	1.44673i	0.893810	−	0.448445i	$-0.148022\pi$
$824$		0			0
$825$	18.1993			0.633620
$826$		0			0
$827$	3.64950			0.126906			0.0634528	−	0.997985i	$-0.479789\pi$
$827$	3.64950			0.126906			0.0634528	+	0.997985i	$0.479789\pi$
$828$		0			0
$829$	22.5498	−	39.0575i	0.783188	−	1.35652i	−0.146887	−	0.989153i	$-0.546925\pi$
$829$	22.5498	−	39.0575i	0.783188	−	1.35652i	0.930076	−	0.367368i	$-0.119741\pi$
$830$		0			0
$831$	−8.27492	−	14.3326i	−0.287054	−	0.497192i
$832$		0			0
$833$	−18.1873	−	47.5659i	−0.630152	−	1.64806i
$834$		0			0
$835$	−8.54983	−	14.8087i	−0.295879	−	0.512478i
$836$		0			0
$837$	8.00000	−	13.8564i	0.276520	−	0.478947i
$838$		0			0
$839$	−7.64950			−0.264090			−0.132045	−	0.991244i	$-0.542154\pi$
$839$	−7.64950			−0.264090			−0.132045	+	0.991244i	$0.542154\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$	−14.5498	+	25.2011i	−0.501123	+	0.867970i
$844$		0			0
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	−8.73713	+	12.6948i	−0.300211	+	0.436197i
$848$		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
$853$	−11.9003			−0.407460			−0.203730	−	0.979027i	$-0.565306\pi$
$853$	−11.9003			−0.407460			−0.203730	+	0.979027i	$0.565306\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$		0			0
$857$	1.82475	−	3.16056i	0.0623323	−	0.107963i	−0.833175	−	0.553009i	$-0.813479\pi$
$857$	1.82475	−	3.16056i	0.0623323	−	0.107963i	0.895508	+	0.445046i	$0.146813\pi$
$858$		0			0
$859$	−10.0498	−	17.4068i	−0.342896	−	0.593913i	0.642073	−	0.766643i	$-0.278074\pi$
$859$	−10.0498	−	17.4068i	−0.342896	−	0.593913i	−0.984969	+	0.172730i	$0.944741\pi$
$860$		0			0
$861$	−24.0000	−	1.90468i	−0.817918	−	0.0649114i
$862$		0			0
$863$	16.5498	+	28.6652i	0.563363	+	0.975773i	0.997200	+	0.0747818i	$0.0238260\pi$
$863$	16.5498	+	28.6652i	0.563363	+	0.975773i	−0.433837	+	0.900991i	$0.642841\pi$
$864$		0			0
$865$	2.72508	−	4.71998i	0.0926556	−	0.160484i
$866$		0			0
$867$	−71.8488			−2.44011
$868$		0			0
$869$	1.25083			0.0424314
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−4.27492	−	7.40437i	−0.144684	−	0.250600i
$874$		0			0
$875$	10.2371	+	21.4989i	0.346078	+	0.726794i
$876$		0			0
$877$	21.3746	+	37.0219i	0.721768	+	1.25014i	0.960290	+	0.279003i	$0.0900038\pi$
$877$	21.3746	+	37.0219i	0.721768	+	1.25014i	−0.238522	+	0.971137i	$0.576663\pi$
$878$		0			0
$879$	−17.6495	+	30.5698i	−0.595303	+	1.03109i
$880$		0			0
$881$	−2.92442			−0.0985262			−0.0492631	−	0.998786i	$-0.515687\pi$
$881$	−2.92442			−0.0985262			−0.0492631	+	0.998786i	$0.515687\pi$
$882$		0			0
$883$	42.0241			1.41422			0.707112	−	0.707102i	$-0.249998\pi$
$883$	42.0241			1.41422			0.707112	+	0.707102i	$0.249998\pi$
$884$		0			0
$885$	4.00000	−	6.92820i	0.134459	−	0.232889i
$886$		0			0
$887$	−4.09967	−	7.10083i	−0.137653	−	0.238423i	0.788955	−	0.614452i	$-0.210623\pi$
$887$	−4.09967	−	7.10083i	−0.137653	−	0.238423i	−0.926608	+	0.376029i	$0.877289\pi$
$888$		0			0
$889$	−17.1752	−	36.0695i	−0.576039	−	1.20973i
$890$		0			0
$891$	12.5120	+	21.6715i	0.419169	+	0.726022i
$892$		0			0
$893$	−1.13746	+	1.97014i	−0.0380636	+	0.0659281i
$894$		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
$901$	23.8248	+	41.2657i	0.793718	+	1.37476i
$902$		0			0
$903$	−5.27492	−	0.418627i	−0.175538	−	0.0139310i
$904$		0			0
$905$	−7.27492	−	12.6005i	−0.241826	−	0.418856i
$906$		0			0
$907$	−18.5498	+	32.1293i	−0.615937	+	1.06683i	0.374282	+	0.927315i	$0.377889\pi$
$907$	−18.5498	+	32.1293i	−0.615937	+	1.06683i	−0.990219	+	0.139520i	$0.955444\pi$
$908$		0			0
$909$	−3.00000			−0.0995037
$910$		0			0
$911$	26.5498			0.879635			0.439818	−	0.898087i	$-0.355043\pi$
$911$	26.5498			0.879635			0.439818	+	0.898087i	$0.355043\pi$
$912$		0			0
$913$	−13.1375	+	22.7547i	−0.434786	+	0.753072i
$914$		0			0
$915$	−12.2749	−	21.2608i	−0.405796	−	0.702860i
$916$		0			0
$917$	−23.7371	+	34.4892i	−0.783869	+	1.13894i
$918$		0			0
$919$	12.2251	+	21.1745i	0.403268	+	0.698481i	0.994118	−	0.108300i	$-0.0345408\pi$
$919$	12.2251	+	21.1745i	0.403268	+	0.698481i	−0.590850	+	0.806781i	$0.701207\pi$
$920$		0			0
$921$	−26.0000	+	45.0333i	−0.856729	+	1.48390i
$922$		0			0
$923$	21.0997			0.694504
$924$		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	0.998827	+	0.0484211i	$0.0154190\pi$
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	−0.457480	+	0.889220i	$0.651248\pi$
$930$		0			0
$931$	−6.91238	−	1.10411i	−0.226544	−	0.0361858i
$932$		0			0
$933$	−2.72508	−	4.71998i	−0.0892152	−	0.154525i
$934$		0			0
$935$	8.27492	−	14.3326i	0.270619	−	0.468725i
$936$		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
$939$	−58.3987			−1.90577
$940$		0			0
$941$	−4.00000	+	6.92820i	−0.130396	+	0.225853i	−0.923829	−	0.382804i	$-0.874958\pi$
$941$	−4.00000	+	6.92820i	−0.130396	+	0.225853i	0.793433	+	0.608657i	$0.208292\pi$
$942$		0			0
$943$	−17.1752	−	29.7484i	−0.559303	−	0.968741i
$944$		0			0
$945$	−6.00000	+	8.71780i	−0.195180	+	0.283590i
$946$		0			0
$947$	−22.0000	−	38.1051i	−0.714904	−	1.23825i	−0.962997	−	0.269514i	$-0.913137\pi$
$947$	−22.0000	−	38.1051i	−0.714904	−	1.23825i	0.248093	−	0.968736i	$-0.420196\pi$
$948$		0			0
$949$	−3.72508	+	6.45203i	−0.120921	+	0.209442i
$950$		0			0
$951$	42.1993			1.36841
$952$		0			0
$953$	12.9003			0.417883			0.208941	−	0.977928i	$-0.432998\pi$
$953$	12.9003			0.417883			0.208941	+	0.977928i	$0.432998\pi$
$954$		0			0
$955$	−10.5000	+	18.1865i	−0.339772	+	0.588502i
$956$		0			0
$957$	−9.09967	−	15.7611i	−0.294151	−	0.509484i
$958$		0			0
$959$	−9.82475	−	0.779710i	−0.317258	−	0.0251781i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	1.72508	−	2.98793i	0.0555900	−	0.0962847i
$964$		0			0
$965$	−27.0997			−0.872369
$966$		0			0
$967$	−18.1993			−0.585251			−0.292626	−	0.956227i	$-0.594529\pi$
$967$	−18.1993			−0.585251			−0.292626	+	0.956227i	$0.594529\pi$
$968$		0			0
$969$	−7.27492	+	12.6005i	−0.233704	+	0.404787i
$970$		0			0
$971$	−18.2749	−	31.6531i	−0.586470	−	1.01580i	−0.994690	−	0.102912i	$-0.967184\pi$
$971$	−18.2749	−	31.6531i	−0.586470	−	1.01580i	0.408220	−	0.912883i	$-0.366149\pi$
$972$		0			0
$973$	−12.3127	−	25.8578i	−0.394727	−	0.828962i
$974$		0			0
$975$	−8.00000	−	13.8564i	−0.256205	−	0.443760i
$976$		0			0
$977$	−27.6495	+	47.8903i	−0.884586	+	1.53215i	−0.0383985	+	0.999263i	$0.512226\pi$
$977$	−27.6495	+	47.8903i	−0.884586	+	1.53215i	−0.846187	+	0.532885i	$0.821108\pi$
$978$		0			0
$979$	37.6495			1.20328
$980$		0			0
$981$	−10.5498			−0.336830
$982$		0			0
$983$	−4.09967	+	7.10083i	−0.130759	+	0.226481i	−0.923969	−	0.382466i	$-0.875075\pi$
$983$	−4.09967	+	7.10083i	−0.130759	+	0.226481i	0.793210	+	0.608948i	$0.208408\pi$
$984$		0			0
$985$	−9.04983	−	15.6748i	−0.288352	−	0.499440i
$986$		0			0
$987$	5.17525	+	10.8685i	0.164730	+	0.345947i
$988$		0			0
$989$	−3.77492	−	6.53835i	−0.120035	−	0.207907i
$990$		0			0
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$		0			0
$993$	28.0000			0.888553
$994$		0			0
$995$	−3.00000			−0.0951064
$996$		0			0
$997$	14.9124	−	25.8290i	0.472280	−	0.818012i	−0.527217	−	0.849731i	$-0.676765\pi$
$997$	14.9124	−	25.8290i	0.472280	−	0.818012i	0.999497	+	0.0317182i	$0.0100979\pi$
$998$		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.305.2	✓	4
7.2	even	3	inner	1064.2.q.l.457.2	yes	4
7.3	odd	6		7448.2.a.be.1.2		2
7.4	even	3		7448.2.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.l.305.2	✓	4	1.1	even	1	trivial
1064.2.q.l.457.2	yes	4	7.2	even	3	inner
7448.2.a.w.1.2		2	7.4	even	3
7448.2.a.be.1.2		2	7.3	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.13746 + 2.38876i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.13746 + 2.38876i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.13746 + 1.97014i) q^{11} +2.00000 q^{13} +2.00000 q^{15} +(-3.63746 + 6.30026i) q^{17} +(0.500000 + 0.866025i) q^{19} +(5.27492 + 0.418627i) q^{21} +(3.77492 + 6.53835i) q^{23} +(2.00000 - 3.46410i) q^{25} +4.00000 q^{27} -4.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(2.27492 + 3.94027i) q^{33} +(-1.50000 + 2.17945i) q^{35} +(-1.00000 - 1.73205i) q^{37} +(2.00000 - 3.46410i) q^{39} -4.54983 q^{41} -1.00000 q^{43} +(0.500000 - 0.866025i) q^{45} +(1.13746 + 1.97014i) q^{47} +(-4.41238 + 5.43424i) q^{49} +(7.27492 + 12.6005i) q^{51} +(3.27492 - 5.67232i) q^{53} -2.27492 q^{55} +2.00000 q^{57} +(2.00000 - 3.46410i) q^{59} +(-6.13746 - 10.6304i) q^{61} +(1.50000 - 2.17945i) q^{63} +(1.00000 + 1.73205i) q^{65} +15.0997 q^{69} +10.5498 q^{71} +(-1.86254 + 3.22602i) q^{73} +(-4.00000 - 6.92820i) q^{75} +(-6.00000 - 0.476171i) q^{77} +(-0.274917 - 0.476171i) q^{79} +(5.50000 - 9.52628i) q^{81} +11.5498 q^{83} -7.27492 q^{85} +(-4.00000 + 6.92820i) q^{87} +(-8.27492 - 14.3326i) q^{89} +(2.27492 + 4.77753i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(-0.500000 + 0.866025i) q^{95} +8.54983 q^{97} +2.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 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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