LMFDB - Embedded newform 512.2.k.a.497.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			497.13
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.98645 - 1.06178i) q^{3} +(2.06545 + 2.51675i) q^{5} +(-3.55182 + 2.37325i) q^{7} +(1.15189 - 1.72393i) q^{9} +(4.79412 - 1.45428i) q^{11} +(0.194397 + 0.159538i) q^{13} +(6.77513 + 2.80635i) q^{15} +(-2.23193 + 0.924497i) q^{17} +(0.0645615 + 0.655504i) q^{19} +(-4.53564 + 8.48559i) q^{21} +(5.38519 - 1.07118i) q^{23} +(-1.09253 + 5.49251i) q^{25} +(-0.204582 + 2.07715i) q^{27} +(1.65805 - 5.46586i) q^{29} +(-1.88212 - 1.88212i) q^{31} +(7.97915 - 7.97915i) q^{33} +(-13.3090 - 4.03724i) q^{35} +(-5.31555 - 0.523536i) q^{37} +(0.555554 + 0.110507i) q^{39} +(-1.06625 - 5.36040i) q^{41} +(-3.35872 - 1.79527i) q^{43} +(6.71786 - 0.661652i) q^{45} +(-2.40646 - 5.80970i) q^{47} +(4.30433 - 10.3916i) q^{49} +(-3.45201 + 4.20628i) q^{51} +(2.52084 + 8.31009i) q^{53} +(13.5621 + 9.06189i) q^{55} +(0.824248 + 1.23357i) q^{57} +(4.78714 - 3.92870i) q^{59} +(-2.32093 - 4.34215i) q^{61} +8.85680i q^{63} +0.818767i q^{65} +(-3.94942 - 7.38884i) q^{67} +(9.56004 - 7.84572i) q^{69} +(-1.89286 - 2.83287i) q^{71} +(2.61962 + 1.75037i) q^{73} +(3.66158 + 12.0706i) q^{75} +(-13.5765 + 16.5430i) q^{77} +(-4.38565 + 10.5879i) q^{79} +(4.17939 + 10.0899i) q^{81} +(-11.3812 + 1.12095i) q^{83} +(-6.93667 - 3.70773i) q^{85} +(-2.50990 - 12.6181i) q^{87} +(4.78690 + 0.952173i) q^{89} +(-1.06909 - 0.105296i) q^{91} +(-5.73713 - 1.74034i) q^{93} +(-1.51639 + 1.51639i) q^{95} +(7.32752 + 7.32752i) q^{97} +(3.01523 - 9.93988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

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
$3$	1.98645	−	1.06178i	1.14688	−	0.613018i	0.215294	−	0.976549i	$-0.430929\pi$
$3$	1.98645	−	1.06178i	1.14688	−	0.613018i	0.931582	+	0.363531i	$0.118429\pi$
$4$		0			0
$5$	2.06545	+	2.51675i	0.923696	+	1.12553i	0.991794	+	0.127848i	$0.0408069\pi$
$5$	2.06545	+	2.51675i	0.923696	+	1.12553i	−0.0680982	+	0.997679i	$0.521693\pi$
$6$		0			0
$7$	−3.55182	+	2.37325i	−1.34246	+	0.897005i	−0.999109	−	0.0422012i	$-0.986563\pi$
$7$	−3.55182	+	2.37325i	−1.34246	+	0.897005i	−0.343354	+	0.939206i	$0.611563\pi$
$8$		0			0
$9$	1.15189	−	1.72393i	0.383963	−	0.574642i
$10$		0			0
$11$	4.79412	−	1.45428i	1.44548	−	0.438482i	0.532482	−	0.846441i	$-0.321259\pi$
$11$	4.79412	−	1.45428i	1.44548	−	0.438482i	0.913000	+	0.407959i	$0.133759\pi$
$12$		0			0
$13$	0.194397	+	0.159538i	0.0539161	+	0.0442478i	0.660965	−	0.750416i	$-0.270147\pi$
$13$	0.194397	+	0.159538i	0.0539161	+	0.0442478i	−0.607049	+	0.794664i	$0.707647\pi$
$14$		0			0
$15$	6.77513	+	2.80635i	1.74933	+	0.724597i
$16$		0			0
$17$	−2.23193	+	0.924497i	−0.541323	+	0.224223i	−0.636554	−	0.771232i	$-0.719641\pi$
$17$	−2.23193	+	0.924497i	−0.541323	+	0.224223i	0.0952312	+	0.995455i	$0.469641\pi$
$18$		0			0
$19$	0.0645615	+	0.655504i	0.0148114	+	0.150383i	0.999746	−	0.0225455i	$-0.00717706\pi$
$19$	0.0645615	+	0.655504i	0.0148114	+	0.150383i	−0.984934	+	0.172928i	$0.944677\pi$
$20$		0			0
$21$	−4.53564	+	8.48559i	−0.989758	+	1.85171i
$22$		0			0
$23$	5.38519	−	1.07118i	1.12289	−	0.223357i	0.401481	−	0.915867i	$-0.368495\pi$
$23$	5.38519	−	1.07118i	1.12289	−	0.223357i	0.721408	+	0.692511i	$0.243495\pi$
$24$		0			0
$25$	−1.09253	+	5.49251i	−0.218506	+	1.09850i
$26$		0			0
$27$	−0.204582	+	2.07715i	−0.0393717	+	0.399748i
$28$		0			0
$29$	1.65805	−	5.46586i	0.307892	−	1.01498i	−0.657341	−	0.753594i	$-0.728319\pi$
$29$	1.65805	−	5.46586i	0.307892	−	1.01498i	0.965233	−	0.261391i	$-0.0841813\pi$
$30$		0			0
$31$	−1.88212	−	1.88212i	−0.338039	−	0.338039i	0.517590	−	0.855629i	$-0.326829\pi$
$31$	−1.88212	−	1.88212i	−0.338039	−	0.338039i	−0.855629	+	0.517590i	$0.826829\pi$
$32$		0			0
$33$	7.97915	−	7.97915i	1.38899	−	1.38899i
$34$		0			0
$35$	−13.3090	−	4.03724i	−2.24963	−	0.682418i
$36$		0			0
$37$	−5.31555	−	0.523536i	−0.873871	−	0.0860688i	−0.348871	−	0.937171i	$-0.613435\pi$
$37$	−5.31555	−	0.523536i	−0.873871	−	0.0860688i	−0.525000	+	0.851102i	$0.675935\pi$
$38$		0			0
$39$	0.555554	+	0.110507i	0.0889598	+	0.0176952i
$40$		0			0
$41$	−1.06625	−	5.36040i	−0.166520	−	0.837154i	−0.970240	−	0.242146i	$-0.922149\pi$
$41$	−1.06625	−	5.36040i	−0.166520	−	0.837154i	0.803720	−	0.595008i	$-0.202851\pi$
$42$		0			0
$43$	−3.35872	−	1.79527i	−0.512200	−	0.273777i	0.194984	−	0.980807i	$-0.437535\pi$
$43$	−3.35872	−	1.79527i	−0.512200	−	0.273777i	−0.707184	+	0.707030i	$0.750035\pi$
$44$		0			0
$45$	6.71786	−	0.661652i	1.00144	−	0.0986332i
$46$		0			0
$47$	−2.40646	−	5.80970i	−0.351018	−	0.847432i	−0.996495	−	0.0836523i	$-0.973342\pi$
$47$	−2.40646	−	5.80970i	−0.351018	−	0.847432i	0.645477	−	0.763779i	$-0.276658\pi$
$48$		0			0
$49$	4.30433	−	10.3916i	0.614905	−	1.48451i
$50$		0			0
$51$	−3.45201	+	4.20628i	−0.483378	+	0.588997i
$52$		0			0
$53$	2.52084	+	8.31009i	0.346264	+	1.14148i	0.941241	+	0.337736i	$0.109661\pi$
$53$	2.52084	+	8.31009i	0.346264	+	1.14148i	−0.594977	+	0.803743i	$0.702839\pi$
$54$		0			0
$55$	13.5621	+	9.06189i	1.82871	+	1.22190i
$56$		0			0
$57$	0.824248	+	1.23357i	0.109174	+	0.163391i
$58$		0			0
$59$	4.78714	−	3.92870i	0.623232	−	0.511473i	−0.268947	−	0.963155i	$-0.586676\pi$
$59$	4.78714	−	3.92870i	0.623232	−	0.511473i	0.892179	+	0.451682i	$0.149176\pi$
$60$		0			0
$61$	−2.32093	−	4.34215i	−0.297164	−	0.555955i	0.688385	−	0.725346i	$-0.258320\pi$
$61$	−2.32093	−	4.34215i	−0.297164	−	0.555955i	−0.985549	+	0.169391i	$0.945820\pi$
$62$		0			0
$63$			8.85680i			1.11585i
$64$		0			0
$65$			0.818767i			0.101556i
$66$		0			0
$67$	−3.94942	−	7.38884i	−0.482498	−	0.902690i	−0.998925	−	0.0463589i	$-0.985238\pi$
$67$	−3.94942	−	7.38884i	−0.482498	−	0.902690i	0.516427	−	0.856331i	$-0.327262\pi$
$68$		0			0
$69$	9.56004	−	7.84572i	1.15089	−	0.944514i
$70$		0			0
$71$	−1.89286	−	2.83287i	−0.224642	−	0.336200i	0.701979	−	0.712198i	$-0.252300\pi$
$71$	−1.89286	−	2.83287i	−0.224642	−	0.336200i	−0.926621	+	0.375998i	$0.877300\pi$
$72$		0			0
$73$	2.61962	+	1.75037i	0.306603	+	0.204866i	0.699347	−	0.714782i	$-0.253474\pi$
$73$	2.61962	+	1.75037i	0.306603	+	0.204866i	−0.392744	+	0.919648i	$0.628474\pi$
$74$		0			0
$75$	3.66158	+	12.0706i	0.422803	+	1.39379i
$76$		0			0
$77$	−13.5765	+	16.5430i	−1.54719	+	1.88525i
$78$		0			0
$79$	−4.38565	+	10.5879i	−0.493424	+	1.19123i	0.459542	+	0.888156i	$0.348014\pi$
$79$	−4.38565	+	10.5879i	−0.493424	+	1.19123i	−0.952966	+	0.303076i	$0.901986\pi$
$80$		0			0
$81$	4.17939	+	10.0899i	0.464377	+	1.12110i
$82$		0			0
$83$	−11.3812	+	1.12095i	−1.24925	+	0.123040i	−0.700931	−	0.713229i	$-0.747232\pi$
$83$	−11.3812	+	1.12095i	−1.24925	+	0.123040i	−0.548319	+	0.836269i	$0.684732\pi$
$84$		0			0
$85$	−6.93667	−	3.70773i	−0.752387	−	0.402159i
$86$		0			0
$87$	−2.50990	−	12.6181i	−0.269090	−	1.35281i
$88$		0			0
$89$	4.78690	+	0.952173i	0.507410	+	0.100930i	0.442155	−	0.896939i	$-0.354214\pi$
$89$	4.78690	+	0.952173i	0.507410	+	0.100930i	0.0652547	+	0.997869i	$0.479214\pi$
$90$		0			0
$91$	−1.06909	−	0.105296i	−0.112071	−	0.0110380i
$92$		0			0
$93$	−5.73713	−	1.74034i	−0.594913	−	0.180465i
$94$		0			0
$95$	−1.51639	+	1.51639i	−0.155579	+	0.155579i
$96$		0			0
$97$	7.32752	+	7.32752i	0.743996	+	0.743996i	0.973344	−	0.229348i	$-0.0736594\pi$
$97$	7.32752	+	7.32752i	0.743996	+	0.743996i	−0.229348	+	0.973344i	$0.573659\pi$
$98$		0			0
$99$	3.01523	−	9.93988i	0.303042	−	0.998996i
$100$		0			0
$101$	0.424290	−	4.30789i	0.0422184	−	0.428651i	−0.950723	−	0.310043i	$-0.899657\pi$
$101$	0.424290	−	4.30789i	0.0422184	−	0.428651i	0.992941	−	0.118608i	$-0.0378433\pi$
$102$		0			0
$103$	2.80522	−	14.1028i	0.276406	−	1.38959i	−0.554040	−	0.832490i	$-0.686915\pi$
$103$	2.80522	−	14.1028i	0.276406	−	1.38959i	0.830447	−	0.557098i	$-0.188085\pi$
$104$		0			0
$105$	−30.7243	+	6.11144i	−2.99838	+	0.596415i
$106$		0			0
$107$	−4.86971	+	9.11058i	−0.470773	+	0.880753i	0.528717	+	0.848798i	$0.322673\pi$
$107$	−4.86971	+	9.11058i	−0.470773	+	0.880753i	−0.999489	+	0.0319552i	$0.989827\pi$
$108$		0			0
$109$	−1.43240	−	14.5434i	−0.137199	−	1.39301i	−0.779427	−	0.626494i	$-0.784489\pi$
$109$	−1.43240	−	14.5434i	−0.137199	−	1.39301i	0.642227	−	0.766514i	$-0.278011\pi$
$110$		0			0
$111$	−11.1149	+	4.60396i	−1.05498	+	0.436988i
$112$		0			0
$113$	−12.7313	−	5.27349i	−1.19766	−	0.496088i	−0.307420	−	0.951574i	$-0.599466\pi$
$113$	−12.7313	−	5.27349i	−1.19766	−	0.496088i	−0.890243	+	0.455486i	$0.849466\pi$
$114$		0			0
$115$	13.8187	+	11.3407i	1.28860	+	1.05753i
$116$		0			0
$117$	0.498956	−	0.151357i	0.0461285	−	0.0139929i
$118$		0			0
$119$	5.73337	−	8.58059i	0.525577	−	0.786581i
$120$		0			0
$121$	11.7225	−	7.83274i	1.06568	−	0.712067i
$122$		0			0
$123$	−7.80961	−	9.51603i	−0.704169	−	0.858032i
$124$		0			0
$125$	−1.72314	+	0.921037i	−0.154122	+	0.0823800i
$126$		0			0
$127$	−2.35088			−0.208607			−0.104303	−	0.994546i	$-0.533261\pi$
$127$	−2.35088			−0.208607			−0.104303	+	0.994546i	$0.533261\pi$
$128$		0			0
$129$	−8.57811			−0.755260
$130$		0			0
$131$	−0.925434	+	0.494655i	−0.0808555	+	0.0432182i	−0.511329	−	0.859385i	$-0.670847\pi$
$131$	−0.925434	+	0.494655i	−0.0808555	+	0.0432182i	0.430473	+	0.902603i	$0.358347\pi$
$132$		0			0
$133$	−1.78499	−	2.17501i	−0.154778	−	0.188598i
$134$		0			0
$135$	−5.65023	+	3.77536i	−0.486294	+	0.324931i
$136$		0			0
$137$	−5.20818	+	7.79459i	−0.444965	+	0.665937i	−0.984371	−	0.176109i	$-0.943649\pi$
$137$	−5.20818	+	7.79459i	−0.444965	+	0.665937i	0.539406	+	0.842046i	$0.318649\pi$
$138$		0			0
$139$	10.9869	−	3.33284i	0.931896	−	0.282688i	0.212399	−	0.977183i	$-0.431872\pi$
$139$	10.9869	−	3.33284i	0.931896	−	0.282688i	0.719497	+	0.694495i	$0.244372\pi$
$140$		0			0
$141$	−10.9489	−	8.98554i	−0.922065	−	0.756719i
$142$		0			0
$143$	1.16398	+	0.482135i	0.0973367	+	0.0403182i
$144$		0			0
$145$	17.1808	−	7.11654i	1.42679	−	0.590996i
$146$		0			0
$147$	−2.48322	−	25.2126i	−0.204813	−	2.07950i
$148$		0			0
$149$	−6.45252	+	12.0718i	−0.528611	+	0.988962i	0.465950	+	0.884811i	$0.345713\pi$
$149$	−6.45252	+	12.0718i	−0.528611	+	0.988962i	−0.994561	+	0.104151i	$0.966787\pi$
$150$		0			0
$151$	−2.46881	+	0.491077i	−0.200909	+	0.0399633i	−0.294519	−	0.955646i	$-0.595159\pi$
$151$	−2.46881	+	0.491077i	−0.200909	+	0.0399633i	0.0936098	+	0.995609i	$0.470159\pi$
$152$		0			0
$153$	−0.977178	+	4.91260i	−0.0790001	+	0.397161i
$154$		0			0
$155$	0.849415	−	8.62425i	0.0682267	−	0.692717i
$156$		0			0
$157$	−2.24587	+	7.40365i	−0.179240	+	0.590875i	0.820573	+	0.571542i	$0.193654\pi$
$157$	−2.24587	+	7.40365i	−0.179240	+	0.590875i	−0.999813	+	0.0193336i	$0.993846\pi$
$158$		0			0
$159$	13.8310	+	13.8310i	1.09687	+	1.09687i
$160$		0			0
$161$	−16.5850	+	16.5850i	−1.30709	+	1.30709i
$162$		0			0
$163$	21.5873	+	6.54844i	1.69085	+	0.512913i	0.981421	−	0.191866i	$-0.0614538\pi$
$163$	21.5873	+	6.54844i	1.69085	+	0.512913i	0.709427	+	0.704779i	$0.248954\pi$
$164$		0			0
$165$	36.5621	+	3.60105i	2.84635	+	0.280341i
$166$		0			0
$167$	−11.2529	−	2.23834i	−0.870774	−	0.173208i	−0.260573	−	0.965454i	$-0.583911\pi$
$167$	−11.2529	−	2.23834i	−0.870774	−	0.173208i	−0.610201	+	0.792246i	$0.708911\pi$
$168$		0			0
$169$	−2.52384	−	12.6882i	−0.194141	−	0.976014i
$170$		0			0
$171$	1.20441	+	0.643769i	0.0921034	+	0.0492303i
$172$		0			0
$173$	13.6901	−	1.34836i	1.04084	−	0.102514i	0.436872	−	0.899524i	$-0.356086\pi$
$173$	13.6901	−	1.34836i	1.04084	−	0.102514i	0.603966	+	0.797010i	$0.293586\pi$
$174$		0			0
$175$	−9.15465	−	22.1013i	−0.692026	−	1.67070i
$176$		0			0
$177$	5.33798	−	12.8870i	0.401228	−	0.968649i
$178$		0			0
$179$	−7.22561	+	8.80444i	−0.540068	+	0.658074i	−0.969519	−	0.245016i	$-0.921207\pi$
$179$	−7.22561	+	8.80444i	−0.540068	+	0.658074i	0.429451	+	0.903090i	$0.358707\pi$
$180$		0			0
$181$	0.325681	+	1.07363i	0.0242077	+	0.0798021i	0.968212	−	0.250131i	$-0.0804737\pi$
$181$	0.325681	+	1.07363i	0.0242077	+	0.0798021i	−0.944004	+	0.329933i	$0.892974\pi$
$182$		0			0
$183$	−9.22079	−	6.16114i	−0.681621	−	0.455444i
$184$		0			0
$185$	−9.66137	−	14.4593i	−0.710318	−	1.06307i
$186$		0			0
$187$	−9.35569	+	7.67801i	−0.684155	+	0.561472i
$188$		0			0
$189$	−4.20297	−	7.86320i	−0.305721	−	0.571963i
$190$		0			0
$191$			9.84999i			0.712720i	0.934349	+	0.356360i	$0.115982\pi$
$191$			9.84999i			0.712720i	−0.934349	+	0.356360i	$0.884018\pi$
$192$		0			0
$193$			9.47713i			0.682178i	0.940031	+	0.341089i	$0.110796\pi$
$193$			9.47713i			0.682178i	−0.940031	+	0.341089i	$0.889204\pi$
$194$		0			0
$195$	0.869349	+	1.62644i	0.0622554	+	0.116472i
$196$		0			0
$197$	−14.1251	+	11.5922i	−1.00637	+	0.825907i	−0.984770	−	0.173859i	$-0.944376\pi$
$197$	−14.1251	+	11.5922i	−1.00637	+	0.825907i	−0.0216005	+	0.999767i	$0.506876\pi$
$198$		0			0
$199$	−3.49233	−	5.22664i	−0.247565	−	0.370507i	0.686787	−	0.726859i	$-0.259020\pi$
$199$	−3.49233	−	5.22664i	−0.247565	−	0.370507i	−0.934352	+	0.356352i	$0.884020\pi$
$200$		0			0
$201$	−15.6906	−	10.4841i	−1.10673	−	0.739494i
$202$		0			0
$203$	7.08276	+	23.3487i	0.497112	+	1.63876i
$204$		0			0
$205$	11.2885	−	13.7551i	0.788425	−	0.960698i
$206$		0			0
$207$	4.35651	−	10.5175i	0.302798	−	0.731020i
$208$		0			0
$209$	1.26280	+	3.04868i	0.0873500	+	0.210881i
$210$		0			0
$211$	−10.3523	+	1.01961i	−0.712683	+	0.0701932i	−0.447860	−	0.894104i	$-0.647814\pi$
$211$	−10.3523	+	1.01961i	−0.712683	+	0.0701932i	−0.264823	+	0.964297i	$0.585314\pi$
$212$		0			0
$213$	−6.76796	−	3.61755i	−0.463733	−	0.247870i
$214$		0			0
$215$	−2.41900	−	12.1611i	−0.164974	−	0.829381i
$216$		0			0
$217$	11.1517	+	2.21821i	0.757027	+	0.150582i
$218$		0			0
$219$	7.06225	+	0.695571i	0.477222	+	0.0470023i
$220$		0			0
$221$	−0.581374	−	0.176358i	−0.0391075	−	0.0118631i
$222$		0			0
$223$	1.22989	−	1.22989i	0.0823592	−	0.0823592i	−0.664727	−	0.747086i	$-0.731452\pi$
$223$	1.22989	−	1.22989i	0.0823592	−	0.0823592i	0.747086	+	0.664727i	$0.231452\pi$
$224$		0			0
$225$	8.21021	+	8.21021i	0.547347	+	0.547347i
$226$		0			0
$227$	−4.04265	+	13.3268i	−0.268320	+	0.884534i	0.714447	+	0.699689i	$0.246678\pi$
$227$	−4.04265	+	13.3268i	−0.268320	+	0.884534i	−0.982768	+	0.184845i	$0.940822\pi$
$228$		0			0
$229$	−0.881724	+	8.95229i	−0.0582660	+	0.591584i	0.921077	+	0.389380i	$0.127311\pi$
$229$	−0.881724	+	8.95229i	−0.0582660	+	0.591584i	−0.979343	+	0.202205i	$0.935189\pi$
$230$		0			0
$231$	−9.40399	+	47.2771i	−0.618737	+	3.11060i
$232$		0			0
$233$	27.9034	−	5.55032i	1.82801	−	0.363614i	0.843248	−	0.537525i	$-0.180641\pi$
$233$	27.9034	−	5.55032i	1.82801	−	0.363614i	0.984761	+	0.173911i	$0.0556406\pi$
$234$		0			0
$235$	9.65117	−	18.0561i	0.629573	−	1.17785i
$236$		0			0
$237$	2.53014	+	25.6889i	0.164350	+	1.66867i
$238$		0			0
$239$	−7.46771	+	3.09323i	−0.483046	+	0.200084i	−0.610898	−	0.791709i	$-0.709192\pi$
$239$	−7.46771	+	3.09323i	−0.483046	+	0.200084i	0.127852	+	0.991793i	$0.459192\pi$
$240$		0			0
$241$	−5.38398	−	2.23012i	−0.346812	−	0.143654i	0.202476	−	0.979287i	$-0.435101\pi$
$241$	−5.38398	−	2.23012i	−0.346812	−	0.143654i	−0.549288	+	0.835633i	$0.685101\pi$
$242$		0			0
$243$	14.1751	+	11.6332i	0.909335	+	0.746272i
$244$		0			0
$245$	35.0434	−	10.6303i	2.23884	−	0.679145i
$246$		0			0
$247$	−0.0920271	+	0.137728i	−0.00585554	+	0.00876344i
$248$		0			0
$249$	−21.4180	+	14.3110i	−1.35731	+	0.906925i
$250$		0			0
$251$	−5.85487	−	7.13418i	−0.369556	−	0.450306i	0.554716	−	0.832040i	$-0.312827\pi$
$251$	−5.85487	−	7.13418i	−0.369556	−	0.450306i	−0.924272	+	0.381734i	$0.875327\pi$
$252$		0			0
$253$	24.2595	−	12.9670i	1.52518	−	0.815225i
$254$		0			0
$255$	−17.7161			−1.10943
$256$		0			0
$257$	27.1263			1.69209			0.846047	−	0.533108i	$-0.178976\pi$
$257$	27.1263			1.69209			0.846047	+	0.533108i	$0.178976\pi$
$258$		0			0
$259$	20.1224	−	10.7556i	1.25034	−	0.668322i
$260$		0			0
$261$	−7.51284	−	9.15443i	−0.465033	−	0.566645i
$262$		0			0
$263$	19.3926	−	12.9577i	1.19580	−	0.799008i	0.211823	−	0.977308i	$-0.432060\pi$
$263$	19.3926	−	12.9577i	1.19580	−	0.799008i	0.983976	+	0.178300i	$0.0570599\pi$
$264$		0			0
$265$	−15.7078	+	23.5084i	−0.964922	+	1.44411i
$266$		0			0
$267$	10.5199	−	3.19118i	0.643808	−	0.195297i
$268$		0			0
$269$	15.5258	+	12.7417i	0.946625	+	0.776875i	0.974881	−	0.222726i	$-0.0714954\pi$
$269$	15.5258	+	12.7417i	0.946625	+	0.776875i	−0.0282561	+	0.999601i	$0.508995\pi$
$270$		0			0
$271$	3.72011	+	1.54092i	0.225981	+	0.0936043i	0.492801	−	0.870142i	$-0.335973\pi$
$271$	3.72011	+	1.54092i	0.225981	+	0.0936043i	−0.266820	+	0.963746i	$0.585973\pi$
$272$		0			0
$273$	−2.23549	+	0.925970i	−0.135298	+	0.0560422i
$274$		0			0
$275$	2.74994	+	27.9206i	0.165828	+	1.68368i
$276$		0			0
$277$	5.14175	−	9.61953i	0.308938	−	0.577981i	−0.678760	−	0.734361i	$-0.737482\pi$
$277$	5.14175	−	9.61953i	0.308938	−	0.577981i	0.987697	+	0.156379i	$0.0499822\pi$
$278$		0			0
$279$	−5.41263	+	1.07664i	−0.324046	+	0.0644567i
$280$		0			0
$281$	−0.539150	+	2.71049i	−0.0321630	+	0.161694i	−0.993529	−	0.113579i	$-0.963768\pi$
$281$	−0.539150	+	2.71049i	−0.0321630	+	0.161694i	0.961366	+	0.275273i	$0.0887684\pi$
$282$		0			0
$283$	−0.536914	+	5.45138i	−0.0319162	+	0.324051i	0.965948	+	0.258735i	$0.0833056\pi$
$283$	−0.536914	+	5.45138i	−0.0319162	+	0.324051i	−0.997865	+	0.0653161i	$0.979194\pi$
$284$		0			0
$285$	−1.40216	+	4.62231i	−0.0830570	+	0.273802i
$286$		0			0
$287$	16.5087	+	16.5087i	0.974479	+	0.974479i
$288$		0			0
$289$	−7.89398	+	7.89398i	−0.464352	+	0.464352i
$290$		0			0
$291$	22.3359	+	6.77553i	1.30935	+	0.397188i
$292$		0			0
$293$	−16.7155	−	1.64633i	−0.976530	−	0.0961798i	−0.402856	−	0.915263i	$-0.631982\pi$
$293$	−16.7155	−	1.64633i	−0.976530	−	0.0961798i	−0.573674	+	0.819084i	$0.694482\pi$
$294$		0			0
$295$	19.7751	+	3.93352i	1.15135	+	0.229018i
$296$		0			0
$297$	2.03997	+	10.2556i	0.118371	+	0.595092i
$298$		0			0
$299$	1.21776	+	0.650906i	0.0704249	+	0.0376429i
$300$		0			0
$301$	16.1902	−	1.59460i	0.933189	−	0.0919111i
$302$		0			0
$303$	−3.73119	−	9.00790i	−0.214351	−	0.517490i
$304$		0			0
$305$	6.13437	−	14.8097i	0.351253	−	0.847999i
$306$		0			0
$307$	−0.0541551	+	0.0659882i	−0.00309079	+	0.00376614i	−0.774554	−	0.632508i	$-0.782025\pi$
$307$	−0.0541551	+	0.0659882i	−0.00309079	+	0.00376614i	0.771463	+	0.636274i	$0.219525\pi$
$308$		0			0
$309$	−9.40161	−	30.9929i	−0.534839	−	1.76313i
$310$		0			0
$311$	19.3728	+	12.9445i	1.09853	+	0.734014i	0.966355	−	0.257213i	$-0.0828041\pi$
$311$	19.3728	+	12.9445i	1.09853	+	0.734014i	0.132174	+	0.991226i	$0.457804\pi$
$312$		0			0
$313$	8.54186	+	12.7838i	0.482815	+	0.722583i	0.990280	−	0.139089i	$-0.0444174\pi$
$313$	8.54186	+	12.7838i	0.482815	+	0.722583i	−0.507465	+	0.861672i	$0.669417\pi$
$314$		0			0
$315$	−22.2904	+	18.2932i	−1.25592	+	1.03071i
$316$		0			0
$317$	−16.0811	−	30.0857i	−0.903206	−	1.68978i	−0.704478	−	0.709726i	$-0.748819\pi$
$317$	−16.0811	−	30.0857i	−0.903206	−	1.68978i	−0.198728	−	0.980055i	$-0.563681\pi$
$318$		0			0
$319$		−	28.6153i		−	1.60215i
$320$		0			0
$321$			23.2683i			1.29871i
$322$		0			0
$323$	−0.750109	−	1.40335i	−0.0417372	−	0.0780847i
$324$		0			0
$325$	−1.08865	+	0.893430i	−0.0603873	+	0.0495586i
$326$		0			0
$327$	−18.2873	−	27.3689i	−1.01129	−	1.51350i
$328$		0			0
$329$	22.3352	+	14.9239i	1.23138	+	0.822781i
$330$		0			0
$331$	−4.70553	−	15.5121i	−0.258640	−	0.852620i	−0.986055	−	0.166422i	$-0.946778\pi$
$331$	−4.70553	−	15.5121i	−0.258640	−	0.852620i	0.727415	−	0.686198i	$-0.240722\pi$
$332$		0			0
$333$	−7.02546	+	8.56055i	−0.384993	+	0.469115i
$334$		0			0
$335$	10.4386	−	25.2010i	0.570320	−	1.37688i
$336$		0			0
$337$	2.57370	+	6.21347i	0.140198	+	0.338469i	0.978346	−	0.206974i	$-0.0663615\pi$
$337$	2.57370	+	6.21347i	0.140198	+	0.338469i	−0.838148	+	0.545443i	$0.816361\pi$
$338$		0			0
$339$	−30.8894	+	3.04234i	−1.67768	+	0.165237i
$340$		0			0
$341$	−11.7603	−	6.28599i	−0.636854	−	0.340405i
$342$		0			0
$343$	3.53999	+	17.7967i	0.191141	+	0.960932i
$344$		0			0
$345$	39.4915	+	7.85534i	2.12615	+	0.422918i
$346$		0			0
$347$	19.9305	+	1.96298i	1.06992	+	0.105378i	0.617613	−	0.786482i	$-0.288100\pi$
$347$	19.9305	+	1.96298i	1.06992	+	0.105378i	0.452311	+	0.891860i	$0.350600\pi$
$348$		0			0
$349$	−25.6998	−	7.79594i	−1.37568	−	0.417307i	−0.486025	−	0.873945i	$-0.661554\pi$
$349$	−25.6998	−	7.79594i	−1.37568	−	0.417307i	−0.889653	+	0.456638i	$0.849054\pi$
$350$		0			0
$351$	−0.371154	+	0.371154i	−0.0198107	+	0.0198107i
$352$		0			0
$353$	−21.9292	−	21.9292i	−1.16717	−	1.16717i	−0.982869	−	0.184305i	$-0.940997\pi$
$353$	−21.9292	−	21.9292i	−1.16717	−	1.16717i	−0.184305	−	0.982869i	$-0.559003\pi$
$354$		0			0
$355$	3.22003	−	10.6150i	0.170901	−	0.563386i
$356$		0			0
$357$	2.27835	−	23.1325i	0.120583	−	1.22430i
$358$		0			0
$359$	−2.31645	+	11.6456i	−0.122258	+	0.614630i	0.870267	+	0.492581i	$0.163947\pi$
$359$	−2.31645	+	11.6456i	−0.122258	+	0.614630i	−0.992524	+	0.122049i	$0.961053\pi$
$360$		0			0
$361$	18.2094	−	3.62208i	0.958390	−	0.190636i
$362$		0			0
$363$	14.9695	−	28.0060i	0.785697	−	1.46994i
$364$		0			0
$365$	1.00542	+	10.2082i	0.0526263	+	0.534324i
$366$		0			0
$367$	21.9794	−	9.10417i	1.14732	−	0.475234i	0.273683	−	0.961820i	$-0.411758\pi$
$367$	21.9794	−	9.10417i	1.14732	−	0.475234i	0.873633	+	0.486586i	$0.161758\pi$
$368$		0			0
$369$	−10.4691	−	4.33646i	−0.545001	−	0.225747i
$370$		0			0
$371$	−28.6755	−	23.5334i	−1.48876	−	1.22179i
$372$		0			0
$373$	−24.7620	+	7.51146i	−1.28213	+	0.388929i	−0.856583	−	0.516010i	$-0.827417\pi$
$373$	−24.7620	+	7.51146i	−1.28213	+	0.388929i	−0.425543	+	0.904938i	$0.639917\pi$
$374$		0			0
$375$	−2.44499	+	3.65918i	−0.126259	+	0.188959i
$376$		0			0
$377$	1.19433	−	0.798027i	0.0615112	−	0.0411005i
$378$		0			0
$379$	1.07262	+	1.30699i	0.0550969	+	0.0671357i	0.799830	−	0.600227i	$-0.204923\pi$
$379$	1.07262	+	1.30699i	0.0550969	+	0.0671357i	−0.744733	+	0.667363i	$0.767423\pi$
$380$		0			0
$381$	−4.66990	+	2.49611i	−0.239246	+	0.127880i
$382$		0			0
$383$	14.7934			0.755909			0.377954	−	0.925824i	$-0.376628\pi$
$383$	14.7934			0.755909			0.377954	+	0.925824i	$0.376628\pi$
$384$		0			0
$385$	−69.6762			−3.55103
$386$		0			0
$387$	−6.96380	+	3.72223i	−0.353990	+	0.189211i
$388$		0			0
$389$	−5.91015	−	7.20154i	−0.299657	−	0.365133i	0.601314	−	0.799013i	$-0.294644\pi$
$389$	−5.91015	−	7.20154i	−0.299657	−	0.365133i	−0.900971	+	0.433880i	$0.857144\pi$
$390$		0			0
$391$	−11.0291	+	7.36939i	−0.557764	+	0.372686i
$392$		0			0
$393$	−1.31311	+	1.96521i	−0.0662378	+	0.0991318i
$394$		0			0
$395$	−35.7055	+	10.8311i	−1.79654	+	0.544974i
$396$		0			0
$397$	20.0120	+	16.4234i	1.00437	+	0.824266i	0.984473	−	0.175536i	$-0.0561657\pi$
$397$	20.0120	+	16.4234i	1.00437	+	0.824266i	0.0198985	+	0.999802i	$0.493666\pi$
$398$		0			0
$399$	−5.85517	−	2.42529i	−0.293125	−	0.121416i
$400$		0			0
$401$	−19.2755	+	7.98419i	−0.962575	+	0.398712i	−0.807943	−	0.589261i	$-0.799419\pi$
$401$	−19.2755	+	7.98419i	−0.962575	+	0.398712i	−0.154632	+	0.987972i	$0.549419\pi$
$402$		0			0
$403$	−0.0656099	−	0.666149i	−0.00326826	−	0.0331832i
$404$		0			0
$405$	−16.7616	+	31.3587i	−0.832890	+	1.55823i
$406$		0			0
$407$	−26.2448	+	5.22041i	−1.30090	+	0.258766i
$408$		0			0
$409$	6.70284	−	33.6975i	0.331434	−	1.66623i	−0.351832	−	0.936063i	$-0.614441\pi$
$409$	6.70284	−	33.6975i	0.331434	−	1.66623i	0.683266	−	0.730169i	$-0.260559\pi$
$410$		0			0
$411$	−2.06965	+	21.0135i	−0.102088	+	1.03652i
$412$		0			0
$413$	−7.67926	+	25.3151i	−0.377872	+	1.24568i
$414$		0			0
$415$	−26.3284	−	26.3284i	−1.29241	−	1.29241i
$416$		0			0
$417$	18.2862	−	18.2862i	0.895477	−	0.895477i
$418$		0			0
$419$	−27.7420	−	8.41544i	−1.35528	−	0.411121i	−0.472678	−	0.881235i	$-0.656713\pi$
$419$	−27.7420	−	8.41544i	−1.35528	−	0.411121i	−0.882606	+	0.470114i	$0.844213\pi$
$420$		0			0
$421$	29.4565	+	2.90121i	1.43562	+	0.141396i	0.785700	−	0.618607i	$-0.212303\pi$
$421$	29.4565	+	2.90121i	1.43562	+	0.141396i	0.649919	+	0.760003i	$0.274803\pi$
$422$		0			0
$423$	−12.7875	−	2.54358i	−0.621748	−	0.123673i
$424$		0			0
$425$	−2.63936	−	13.2690i	−0.128028	−	0.643639i
$426$		0			0
$427$	18.5485	+	9.91439i	0.897626	+	0.479791i
$428$		0			0
$429$	2.82410	−	0.278150i	0.136349	−	0.0134292i
$430$		0			0
$431$	−0.581270	−	1.40331i	−0.0279988	−	0.0675951i	0.909262	−	0.416225i	$-0.136647\pi$
$431$	−0.581270	−	1.40331i	−0.0279988	−	0.0675951i	−0.937261	+	0.348630i	$0.886647\pi$
$432$		0			0
$433$	−7.71150	+	18.6172i	−0.370591	+	0.894686i	0.623059	+	0.782175i	$0.285889\pi$
$433$	−7.71150	+	18.6172i	−0.370591	+	0.894686i	−0.993650	+	0.112511i	$0.964111\pi$
$434$		0			0
$435$	26.5726	−	32.3789i	1.27406	−	1.55245i
$436$		0			0
$437$	1.04984	+	3.46086i	0.0502206	+	0.165555i
$438$		0			0
$439$	26.9257	+	17.9912i	1.28509	+	0.858672i	0.995150	−	0.0983714i	$-0.0313633\pi$
$439$	26.9257	+	17.9912i	1.28509	+	0.858672i	0.289944	+	0.957044i	$0.406363\pi$
$440$		0			0
$441$	−12.9562	−	19.3903i	−0.616962	−	0.923348i
$442$		0			0
$443$	−15.0177	+	12.3247i	−0.713515	+	0.585566i	−0.919548	−	0.392979i	$-0.871445\pi$
$443$	−15.0177	+	12.3247i	−0.713515	+	0.585566i	0.206033	+	0.978545i	$0.433945\pi$
$444$		0			0
$445$	7.49069	+	14.0141i	0.355093	+	0.664332i
$446$		0			0
$447$			30.8312i			1.45827i
$448$		0			0
$449$		−	32.6162i		−	1.53925i	−0.638495	−	0.769626i	$-0.720443\pi$
$449$		−	32.6162i		−	1.53925i	0.638495	−	0.769626i	$-0.279557\pi$
$450$		0			0
$451$	−12.9073	−	24.1478i	−0.607780	−	1.13708i
$452$		0			0
$453$	−4.38275	+	3.59683i	−0.205920	+	0.168994i
$454$		0			0
$455$	−1.94314	−	2.90811i	−0.0910958	−	0.136335i
$456$		0			0
$457$	−5.57294	−	3.72372i	−0.260691	−	0.174188i	0.418355	−	0.908283i	$-0.362607\pi$
$457$	−5.57294	−	3.72372i	−0.260691	−	0.174188i	−0.679047	+	0.734095i	$0.737607\pi$
$458$		0			0
$459$	−1.46371	−	4.82520i	−0.0683200	−	0.225221i
$460$		0			0
$461$	−0.00108412	+	0.00132100i	−5.04924e−5	+	6.15252e-5i	−0.773036	−	0.634363i	$-0.781263\pi$
$461$	−0.00108412	+	0.00132100i	−5.04924e−5	+	6.15252e-5i	0.772985	+	0.634424i	$0.218763\pi$
$462$		0			0
$463$	−8.13838	+	19.6478i	−0.378222	+	0.913110i	0.614077	+	0.789246i	$0.289529\pi$
$463$	−8.13838	+	19.6478i	−0.378222	+	0.913110i	−0.992299	+	0.123864i	$0.960471\pi$
$464$		0			0
$465$	−7.46973	−	18.0335i	−0.346400	−	0.836284i
$466$		0			0
$467$	35.2578	−	3.47259i	1.63154	−	0.160692i	0.759627	−	0.650359i	$-0.225381\pi$
$467$	35.2578	−	3.47259i	1.63154	−	0.160692i	0.871910	+	0.489666i	$0.162881\pi$
$468$		0			0
$469$	31.5632	+	16.8709i	1.45745	+	0.779025i
$470$		0			0
$471$	3.39973	+	17.0916i	0.156651	+	0.787538i
$472$		0			0
$473$	−18.7130	−	3.72224i	−0.860423	−	0.171149i
$474$		0			0
$475$	−3.67090	−	0.361552i	−0.168432	−	0.0165891i
$476$		0			0
$477$	17.2297	+	5.22657i	0.788894	+	0.239308i
$478$		0			0
$479$	12.1308	−	12.1308i	0.554272	−	0.554272i	−0.373399	−	0.927671i	$-0.621808\pi$
$479$	12.1308	−	12.1308i	0.554272	−	0.554272i	0.927671	+	0.373399i	$0.121808\pi$
$480$		0			0
$481$	−0.949805	−	0.949805i	−0.0433074	−	0.0433074i
$482$		0			0
$483$	−15.3357	+	50.5550i	−0.697798	+	2.30033i
$484$		0			0
$485$	−3.30696	+	33.5761i	−0.150161	+	1.52461i
$486$		0			0
$487$	−3.15527	+	15.8626i	−0.142979	+	0.718803i	0.841073	+	0.540921i	$0.181924\pi$
$487$	−3.15527	+	15.8626i	−0.142979	+	0.718803i	−0.984052	+	0.177882i	$0.943076\pi$
$488$		0			0
$489$	49.8350	−	9.91281i	2.25362	−	0.448273i
$490$		0			0
$491$	7.66795	−	14.3457i	0.346050	−	0.647414i	−0.647340	−	0.762201i	$-0.724119\pi$
$491$	7.66795	−	14.3457i	0.346050	−	0.647414i	0.993390	+	0.114787i	$0.0366187\pi$
$492$		0			0
$493$	1.35251	+	13.7323i	0.0609141	+	0.618472i
$494$		0			0
$495$	31.2440	−	12.9417i	1.40431	−	0.581686i
$496$		0			0
$497$	13.4462	+	5.56961i	0.603146	+	0.249831i
$498$		0			0
$499$	27.1441	+	22.2766i	1.21514	+	0.997237i	0.999786	+	0.0207001i	$0.00658952\pi$
$499$	27.1441	+	22.2766i	1.21514	+	0.997237i	0.215351	+	0.976537i	$0.430910\pi$
$500$		0			0
$501$	−24.7299	+	7.50173i	−1.10485	+	0.335152i
$502$		0			0
$503$	7.27348	−	10.8855i	0.324308	−	0.485362i	−0.633112	−	0.774061i	$-0.718223\pi$
$503$	7.27348	−	10.8855i	0.324308	−	0.485362i	0.957420	+	0.288699i	$0.0932226\pi$
$504$		0			0
$505$	11.7182	−	7.82988i	0.521455	−	0.348425i
$506$		0			0
$507$	−18.4855	−	22.5247i	−0.820970	−	1.00035i
$508$		0			0
$509$	−16.8926	+	9.02931i	−0.748753	+	0.400217i	−0.801192	−	0.598407i	$-0.795801\pi$
$509$	−16.8926	+	9.02931i	−0.748753	+	0.400217i	0.0524388	+	0.998624i	$0.483301\pi$
$510$		0			0
$511$	−13.4585			−0.595369
$512$		0			0
$513$	−1.37479			−0.0606984
$514$		0			0
$515$	41.2872	−	22.0685i	1.81933	−	0.972454i
$516$		0			0
$517$	−19.9858	−	24.3528i	−0.878974	−	1.07103i
$518$		0			0
$519$	25.7630	−	17.2143i	1.13087	−	0.755623i
$520$		0			0
$521$	−12.2596	+	18.3477i	−0.537101	+	0.803829i	−0.996429	−	0.0844382i	$-0.973090\pi$
$521$	−12.2596	+	18.3477i	−0.537101	+	0.803829i	0.459327	+	0.888267i	$0.348090\pi$
$522$		0			0
$523$	−36.3720	+	11.0333i	−1.59044	+	0.482454i	−0.956695	−	0.291092i	$-0.905982\pi$
$523$	−36.3720	+	11.0333i	−1.59044	+	0.482454i	−0.633741	+	0.773545i	$0.718482\pi$
$524$		0			0
$525$	−41.6519	−	34.1828i	−1.81784	−	1.49186i
$526$		0			0
$527$	5.94078	+	2.46075i	0.258785	+	0.107192i
$528$		0			0
$529$	6.60359	−	2.73530i	0.287112	−	0.118926i
$530$		0			0
$531$	−1.25853	−	12.7781i	−0.0546157	−	0.554522i
$532$		0			0
$533$	0.647910	−	1.21215i	0.0280641	−	0.0525043i
$534$		0			0
$535$	−32.9872	+	6.56157i	−1.42616	+	0.283681i
$536$		0			0
$537$	−5.00494	+	25.1616i	−0.215979	+	1.08580i
$538$		0			0
$539$	5.52323	−	56.0783i	0.237902	−	2.41546i
$540$		0			0
$541$	−3.26500	+	10.7633i	−0.140373	+	0.462749i	−0.998734	−	0.0502971i	$-0.983983\pi$
$541$	−3.26500	+	10.7633i	−0.140373	+	0.462749i	0.858361	+	0.513047i	$0.171483\pi$
$542$		0			0
$543$	1.78690	+	1.78690i	0.0766834	+	0.0766834i
$544$		0			0
$545$	33.6437	−	33.6437i	1.44114	−	1.44114i
$546$		0			0
$547$	−26.3758	−	8.00100i	−1.12775	−	0.342098i	−0.329336	−	0.944213i	$-0.606825\pi$
$547$	−26.3758	−	8.00100i	−1.12775	−	0.342098i	−0.798410	+	0.602115i	$0.794325\pi$
$548$		0			0
$549$	−10.1590	−	1.00057i	−0.433575	−	0.0427034i
$550$		0			0
$551$	3.68994	+	0.733975i	0.157197	+	0.0312684i
$552$		0			0
$553$	−9.55070	−	48.0146i	−0.406137	−	2.04179i
$554$		0			0
$555$	−34.5443	−	18.4643i	−1.46633	−	0.783767i
$556$		0			0
$557$	−8.84139	+	0.870801i	−0.374622	+	0.0368970i	−0.283576	−	0.958950i	$-0.591521\pi$
$557$	−8.84139	+	0.870801i	−0.374622	+	0.0368970i	−0.0910456	+	0.995847i	$0.529021\pi$
$558$		0			0
$559$	−0.366513	−	0.884839i	−0.0155018	−	0.0374247i
$560$		0			0
$561$	−10.4322	+	25.1856i	−0.440449	+	1.06334i
$562$		0			0
$563$	−23.9330	+	29.1624i	−1.00865	+	1.22905i	−0.0353867	+	0.999374i	$0.511266\pi$
$563$	−23.9330	+	29.1624i	−1.00865	+	1.22905i	−0.973267	+	0.229675i	$0.926234\pi$
$564$		0			0
$565$	−13.0238	−	42.9337i	−0.547916	−	1.80624i
$566$		0			0
$567$	−38.7904	−	25.9189i	−1.62904	−	1.08849i
$568$		0			0
$569$	−19.0773	−	28.5513i	−0.799764	−	1.19693i	−0.977100	−	0.212781i	$-0.931748\pi$
$569$	−19.0773	−	28.5513i	−0.799764	−	1.19693i	0.177336	−	0.984150i	$-0.443252\pi$
$570$		0			0
$571$	−7.06166	+	5.79535i	−0.295521	+	0.242528i	−0.770456	−	0.637493i	$-0.779972\pi$
$571$	−7.06166	+	5.79535i	−0.295521	+	0.242528i	0.474935	+	0.880021i	$0.342472\pi$
$572$		0			0
$573$	10.4585	+	19.5665i	0.436910	+	0.817402i
$574$		0			0
$575$			30.7485i			1.28230i
$576$		0			0
$577$			47.2816i			1.96836i	0.177175	+	0.984179i	$0.443304\pi$
$577$			47.2816i			1.96836i	−0.177175	+	0.984179i	$0.556696\pi$
$578$		0			0
$579$	10.0626	+	18.8258i	0.418188	+	0.782374i
$580$		0			0
$581$	37.7637	−	30.9919i	1.56670	−	1.28576i
$582$		0			0
$583$	24.1704	+	36.1736i	1.00104	+	1.49816i
$584$		0			0
$585$	1.41149	+	0.943129i	0.0583580	+	0.0389936i
$586$		0			0
$587$	4.51962	+	14.8992i	0.186545	+	0.614955i	0.999469	+	0.0325858i	$0.0103742\pi$
$587$	4.51962	+	14.8992i	0.186545	+	0.614955i	−0.812924	+	0.582369i	$0.802126\pi$
$588$		0			0
$589$	1.11223	−	1.35525i	0.0458285	−	0.0558421i
$590$		0			0
$591$	−15.7504	+	38.0249i	−0.647887	+	1.56414i
$592$		0			0
$593$	−7.24552	−	17.4922i	−0.297538	−	0.718320i	−0.999978	−	0.00657744i	$-0.997906\pi$
$593$	−7.24552	−	17.4922i	−0.297538	−	0.718320i	0.702441	−	0.711742i	$-0.252094\pi$
$594$		0			0
$595$	33.4372	−	3.29328i	1.37079	−	0.135011i
$596$		0			0
$597$	−12.4869	−	6.67437i	−0.511053	−	0.273164i
$598$		0			0
$599$	3.41910	+	17.1890i	0.139701	+	0.702323i	0.985615	+	0.169005i	$0.0540553\pi$
$599$	3.41910	+	17.1890i	0.139701	+	0.702323i	−0.845915	+	0.533318i	$0.820945\pi$
$600$		0			0
$601$	14.2232	+	2.82918i	0.580178	+	0.115405i	0.476451	−	0.879201i	$-0.341923\pi$
$601$	14.2232	+	2.82918i	0.580178	+	0.115405i	0.103727	+	0.994606i	$0.466923\pi$
$602$		0			0
$603$	−17.2871	−	1.70263i	−0.703985	−	0.0693365i
$604$		0			0
$605$	43.9253	+	13.3246i	1.78582	+	0.541722i
$606$		0			0
$607$	23.6529	−	23.6529i	0.960042	−	0.960042i	−0.0391894	−	0.999232i	$-0.512478\pi$
$607$	23.6529	−	23.6529i	0.960042	−	0.960042i	0.999232	+	0.0391894i	$0.0124776\pi$
$608$		0			0
$609$	38.8607	+	38.8607i	1.57472	+	1.57472i
$610$		0			0
$611$	0.459058	−	1.51331i	0.0185715	−	0.0612220i
$612$		0			0
$613$	−1.90704	+	19.3625i	−0.0770246	+	0.782044i	0.876635	+	0.481156i	$0.159783\pi$
$613$	−1.90704	+	19.3625i	−0.0770246	+	0.782044i	−0.953659	+	0.300888i	$0.902717\pi$
$614$		0			0
$615$	7.81919	−	39.3097i	0.315300	−	1.58512i
$616$		0			0
$617$	−20.6296	+	4.10349i	−0.830517	+	0.165200i	−0.592000	−	0.805938i	$-0.701661\pi$
$617$	−20.6296	+	4.10349i	−0.830517	+	0.165200i	−0.238517	+	0.971138i	$0.576661\pi$
$618$		0			0
$619$	−14.1798	+	26.5285i	−0.569932	+	1.06627i	0.417567	+	0.908646i	$0.362883\pi$
$619$	−14.1798	+	26.5285i	−0.569932	+	1.06627i	−0.987499	+	0.157622i	$0.949617\pi$
$620$		0			0
$621$	1.12329	+	11.4050i	0.0450762	+	0.457667i
$622$		0			0
$623$	−19.2620	+	7.97856i	−0.771714	+	0.319654i
$624$		0			0
$625$	19.9921	+	8.28099i	0.799684	+	0.331240i
$626$		0			0
$627$	5.74551	+	4.71522i	0.229454	+	0.188308i
$628$		0			0
$629$	12.3480	−	3.74571i	0.492345	−	0.149351i
$630$		0			0
$631$	−5.29776	+	7.92865i	−0.210900	+	0.315635i	−0.921805	−	0.387654i	$-0.873286\pi$
$631$	−5.29776	+	7.92865i	−0.210900	+	0.315635i	0.710905	+	0.703288i	$0.248286\pi$
$632$		0			0
$633$	−19.4817	+	13.0173i	−0.774330	+	0.517391i
$634$		0			0
$635$	−4.85562	−	5.91659i	−0.192689	−	0.234793i
$636$		0			0
$637$	2.49460	−	1.33339i	0.0988397	−	0.0528309i
$638$		0			0
$639$	−7.06403			−0.279449
$640$		0			0
$641$	−0.551919			−0.0217995			−0.0108997	−	0.999941i	$-0.503470\pi$
$641$	−0.551919			−0.0217995			−0.0108997	+	0.999941i	$0.503470\pi$
$642$		0			0
$643$	−36.5660	+	19.5449i	−1.44202	+	0.770776i	−0.992471	−	0.122479i	$-0.960916\pi$
$643$	−36.5660	+	19.5449i	−1.44202	+	0.770776i	−0.449550	+	0.893255i	$0.648416\pi$
$644$		0			0
$645$	−17.7176	−	21.5890i	−0.697631	−	0.850065i
$646$		0			0
$647$	−6.46099	+	4.31709i	−0.254008	+	0.169722i	−0.676055	−	0.736851i	$-0.736312\pi$
$647$	−6.46099	+	4.31709i	−0.254008	+	0.169722i	0.422047	+	0.906574i	$0.361312\pi$
$648$		0			0
$649$	17.2367	−	25.7965i	0.676599	−	1.01260i
$650$		0			0
$651$	24.5075	−	7.43428i	0.960526	−	0.291372i
$652$		0			0
$653$	−23.4027	−	19.2061i	−0.915820	−	0.751594i	0.0531981	−	0.998584i	$-0.483059\pi$
$653$	−23.4027	−	19.2061i	−0.915820	−	0.751594i	−0.969018	+	0.246990i	$0.920559\pi$
$654$		0			0
$655$	−3.15636	−	1.30741i	−0.123329	−	0.0510846i
$656$		0			0
$657$	6.03503	−	2.49979i	0.235449	−	0.0975261i
$658$		0			0
$659$	2.46187	+	24.9958i	0.0959007	+	0.973696i	0.915920	+	0.401361i	$0.131463\pi$
$659$	2.46187	+	24.9958i	0.0959007	+	0.973696i	−0.820019	+	0.572336i	$0.806037\pi$
$660$		0			0
$661$	4.42487	−	8.27836i	0.172108	−	0.321991i	−0.781048	−	0.624471i	$-0.785315\pi$
$661$	4.42487	−	8.27836i	0.172108	−	0.321991i	0.953156	+	0.302480i	$0.0978146\pi$
$662$		0			0
$663$	−1.34212	+	0.266965i	−0.0521237	+	0.0103680i
$664$		0			0
$665$	1.78718	−	8.98475i	0.0693038	−	0.348414i
$666$		0			0
$667$	3.07399	−	31.2108i	0.119025	−	1.20849i
$668$		0			0
$669$	1.13724	−	3.74897i	0.0439681	−	0.144944i
$670$		0			0
$671$	−17.4415	−	17.4415i	−0.673322	−	0.673322i
$672$		0			0
$673$	13.4865	−	13.4865i	0.519867	−	0.519867i	−0.397664	−	0.917531i	$-0.630179\pi$
$673$	13.4865	−	13.4865i	0.519867	−	0.519867i	0.917531	+	0.397664i	$0.130179\pi$
$674$		0			0
$675$	−11.1853	−	3.39301i	−0.430521	−	0.130597i
$676$		0			0
$677$	7.00798	+	0.690226i	0.269339	+	0.0265276i	0.231785	−	0.972767i	$-0.425543\pi$
$677$	7.00798	+	0.690226i	0.269339	+	0.0265276i	0.0375538	+	0.999295i	$0.488043\pi$
$678$		0			0
$679$	−43.4161	−	8.63599i	−1.66616	−	0.331419i
$680$		0			0
$681$	6.11964	+	30.7655i	0.234505	+	1.17894i
$682$		0			0
$683$	−38.8150	−	20.7470i	−1.48521	−	0.793863i	−0.488322	−	0.872663i	$-0.662391\pi$
$683$	−38.8150	−	20.7470i	−1.48521	−	0.793863i	−0.996890	+	0.0788005i	$0.974891\pi$
$684$		0			0
$685$	−30.3743	+	2.99161i	−1.16054	+	0.114303i
$686$		0			0
$687$	7.75385	+	18.7195i	0.295828	+	0.714192i
$688$		0			0
$689$	−0.835729	+	2.01763i	−0.0318387	+	0.0768655i
$690$		0			0
$691$	28.5458	−	34.7832i	1.08593	−	1.32321i	0.143190	−	0.989695i	$-0.454264\pi$
$691$	28.5458	−	34.7832i	1.08593	−	1.32321i	0.942743	−	0.333519i	$-0.108236\pi$
$692$		0			0
$693$	12.8803	+	42.4606i	0.489282	+	1.61294i
$694$		0			0
$695$	31.0808	+	20.7675i	1.17896	+	0.787757i
$696$		0			0
$697$	7.33547	+	10.9783i	0.277851	+	0.415833i
$698$		0			0
$699$	49.5353	−	40.6526i	1.87360	−	1.53762i
$700$		0			0
$701$	0.0331947	+	0.0621028i	0.00125374	+	0.00234559i	0.882547	−	0.470224i	$-0.155827\pi$
$701$	0.0331947	+	0.0621028i	0.00125374	+	0.00234559i	−0.881294	+	0.472569i	$0.843327\pi$
$702$		0			0
$703$		−	3.51816i		−	0.132690i
$704$		0			0
$705$		−	46.1149i		−	1.73679i
$706$		0			0
$707$	8.71670	+	16.3078i	0.327825	+	0.613318i
$708$		0			0
$709$	−15.6475	+	12.8416i	−0.587654	+	0.482275i	−0.880604	−	0.473852i	$-0.842863\pi$
$709$	−15.6475	+	12.8416i	−0.587654	+	0.482275i	0.292950	+	0.956128i	$0.405363\pi$
$710$		0			0
$711$	13.2010	+	19.7566i	0.495075	+	0.740932i
$712$		0			0
$713$	−12.1517	−	8.11948i	−0.455083	−	0.304077i
$714$		0			0
$715$	1.19072	+	3.92527i	0.0445303	+	0.146797i
$716$		0			0
$717$	−11.5499	+	14.0736i	−0.431339	+	0.525588i
$718$		0			0
$719$	9.86945	−	23.8270i	0.368069	−	0.888596i	−0.625998	−	0.779824i	$-0.715308\pi$
$719$	9.86945	−	23.8270i	0.368069	−	0.888596i	0.994067	−	0.108772i	$-0.0346917\pi$
$720$		0			0
$721$	23.5058	+	56.7481i	0.875402	+	2.11341i
$722$		0			0
$723$	−13.0629	+	1.28658i	−0.485814	+	0.0478485i
$724$		0			0
$725$	28.2098	+	15.0785i	1.04769	+	0.560000i
$726$		0			0
$727$	−5.61845	−	28.2459i	−0.208377	−	1.04758i	−0.933395	−	0.358851i	$-0.883169\pi$
$727$	−5.61845	−	28.2459i	−0.208377	−	1.04758i	0.725018	−	0.688730i	$-0.241831\pi$
$728$		0			0
$729$	8.37580	+	1.66605i	0.310215	+	0.0617056i
$730$		0			0
$731$	9.15617	+	0.901804i	0.338653	+	0.0333544i
$732$		0			0
$733$	29.8725	+	9.06172i	1.10337	+	0.334702i	0.788872	−	0.614558i	$-0.210665\pi$
$733$	29.8725	+	9.06172i	1.10337	+	0.334702i	0.314493	+	0.949260i	$0.398165\pi$
$734$		0			0
$735$	58.3249	−	58.3249i	2.15135	−	2.15135i
$736$		0			0
$737$	−29.6794	−	29.6794i	−1.09326	−	1.09326i
$738$		0			0
$739$	−5.09388	+	16.7923i	−0.187382	+	0.617714i	0.812037	+	0.583606i	$0.198359\pi$
$739$	−5.09388	+	16.7923i	−0.187382	+	0.617714i	−0.999418	+	0.0341077i	$0.989141\pi$
$740$		0			0
$741$	−0.0365701	+	0.371302i	−0.00134344	+	0.0136401i
$742$		0			0
$743$	−4.76524	+	23.9565i	−0.174820	+	0.878878i	0.789421	+	0.613852i	$0.210381\pi$
$743$	−4.76524	+	23.9565i	−0.174820	+	0.878878i	−0.964241	+	0.265026i	$0.914619\pi$
$744$		0			0
$745$	−43.7091	+	8.69429i	−1.60138	+	0.318534i
$746$		0			0
$747$	−11.1775	+	20.9116i	−0.408962	+	0.765114i
$748$		0			0
$749$	−4.32537	−	43.9162i	−0.158046	−	1.60466i
$750$		0			0
$751$	0.251570	−	0.104204i	0.00917992	−	0.00380245i	−0.378089	−	0.925769i	$-0.623419\pi$
$751$	0.251570	−	0.104204i	0.00917992	−	0.00380245i	0.387269	+	0.921967i	$0.373419\pi$
$752$		0			0
$753$	−19.2053	−	7.95510i	−0.699881	−	0.289900i
$754$		0			0
$755$	−6.33512	−	5.19910i	−0.230559	−	0.189215i
$756$		0			0
$757$	14.7825	−	4.48421i	0.537278	−	0.162981i	−0.00997291	−	0.999950i	$-0.503175\pi$
$757$	14.7825	−	4.48421i	0.537278	−	0.162981i	0.547250	+	0.836969i	$0.315675\pi$
$758$		0			0
$759$	34.4221	−	51.5163i	1.24944	−	1.86992i
$760$		0			0
$761$	−15.9856	+	10.6813i	−0.579479	+	0.387196i	−0.810487	−	0.585756i	$-0.800798\pi$
$761$	−15.9856	+	10.6813i	−0.579479	+	0.387196i	0.231008	+	0.972952i	$0.425798\pi$
$762$		0			0
$763$	39.6029	+	48.2562i	1.43372	+	1.74699i
$764$		0			0
$765$	−14.3821	+	7.68740i	−0.519987	+	0.277939i
$766$		0			0
$767$	1.55738			0.0562338
$768$		0			0
$769$	−3.60596			−0.130034			−0.0650171	−	0.997884i	$-0.520710\pi$
$769$	−3.60596			−0.130034			−0.0650171	+	0.997884i	$0.520710\pi$
$770$		0			0
$771$	53.8851	−	28.8022i	1.94062	−	1.03728i
$772$		0			0
$773$	20.7798	+	25.3202i	0.747396	+	0.910704i	0.998357	−	0.0572926i	$-0.0182468\pi$
$773$	20.7798	+	25.3202i	0.747396	+	0.910704i	−0.250962	+	0.967997i	$0.580747\pi$
$774$		0			0
$775$	12.3938	−	8.28130i	0.445200	−	0.297473i
$776$		0			0
$777$	28.5519	−	42.7310i	1.02429	−	1.53297i
$778$		0			0
$779$	3.44493	−	1.04501i	0.123427	−	0.0374413i
$780$		0			0
$781$	−13.1944	−	10.8284i	−0.472133	−	0.387470i
$782$		0			0
$783$	11.0142	+	4.56224i	0.393616	+	0.163041i
$784$		0			0
$785$	−23.2719	+	9.63953i	−0.830609	+	0.344050i
$786$		0			0
$787$	−0.312848	−	3.17640i	−0.0111518	−	0.113227i	0.987997	−	0.154472i	$-0.0493675\pi$
$787$	−0.312848	−	3.17640i	−0.0111518	−	0.113227i	−0.999149	+	0.0412451i	$0.986868\pi$
$788$		0			0
$789$	24.7642	−	46.3305i	0.881628	−	1.64941i
$790$		0			0
$791$	57.7348	−	11.4842i	2.05281	−	0.408330i
$792$		0			0
$793$	0.241555	−	1.21438i	0.00857786	−	0.0431238i
$794$		0			0
$795$	−6.24202	+	63.3763i	−0.221382	+	2.24773i
$796$		0			0
$797$	−6.00384	+	19.7920i	−0.212667	+	0.701068i	0.784094	+	0.620642i	$0.213128\pi$
$797$	−6.00384	+	19.7920i	−0.212667	+	0.701068i	−0.996761	+	0.0804261i	$0.974372\pi$
$798$		0			0
$799$	10.7421	+	10.7421i	0.380028	+	0.380028i
$800$		0			0
$801$	7.15545	−	7.15545i	0.252825	−	0.252825i
$802$		0			0
$803$	15.1043	+	4.58185i	0.533020	+	0.161690i
$804$		0			0
$805$	−75.9960	−	7.48495i	−2.67851	−	0.263810i
$806$		0			0
$807$	44.3701	+	8.82575i	1.56190	+	0.310681i
$808$		0			0
$809$	8.82541	+	44.3684i	0.310285	+	1.55991i	0.749795	+	0.661670i	$0.230152\pi$
$809$	8.82541	+	44.3684i	0.310285	+	1.55991i	−0.439510	+	0.898238i	$0.644848\pi$
$810$		0			0
$811$	−0.0935689	−	0.0500136i	−0.00328565	−	0.00175622i	0.469753	−	0.882798i	$-0.344343\pi$
$811$	−0.0935689	−	0.0500136i	−0.00328565	−	0.00175622i	−0.473039	+	0.881042i	$0.656843\pi$
$812$		0			0
$813$	9.02593	−	0.888976i	0.316553	−	0.0311778i
$814$		0			0
$815$	28.1066	+	67.8554i	0.984532	+	2.37687i
$816$		0			0
$817$	0.959966	−	2.31756i	0.0335849	−	0.0810812i
$818$		0			0
$819$	−1.41299	+	1.72174i	−0.0493740	+	0.0601624i
$820$		0			0
$821$	3.93801	+	12.9819i	0.137438	+	0.453071i	0.998459	−	0.0554982i	$-0.0176747\pi$
$821$	3.93801	+	12.9819i	0.137438	+	0.453071i	−0.861021	+	0.508569i	$0.830175\pi$
$822$		0			0
$823$	−18.5566	−	12.3991i	−0.646841	−	0.432206i	0.188398	−	0.982093i	$-0.439671\pi$
$823$	−18.5566	−	12.3991i	−0.646841	−	0.432206i	−0.835239	+	0.549887i	$0.814671\pi$
$824$		0			0
$825$	35.1081	+	52.5430i	1.22231	+	1.82931i
$826$		0			0
$827$	−0.636009	+	0.521959i	−0.0221162	+	0.0181503i	−0.645386	−	0.763856i	$-0.723304\pi$
$827$	−0.636009	+	0.521959i	−0.0221162	+	0.0181503i	0.623270	+	0.782007i	$0.285804\pi$
$828$		0			0
$829$	−4.34393	−	8.12692i	−0.150871	−	0.282259i	0.795120	−	0.606452i	$-0.207408\pi$
$829$	−4.34393	−	8.12692i	−0.150871	−	0.282259i	−0.945991	+	0.324192i	$0.894908\pi$
$830$		0			0
$831$		−	24.5681i		−	0.852257i
$832$		0			0
$833$			27.1727i			0.941477i
$834$		0			0
$835$	−17.6089	−	32.9439i	−0.609380	−	1.14007i
$836$		0			0
$837$	4.29450	−	3.52440i	0.148440	−	0.121821i
$838$		0			0
$839$	−24.3059	−	36.3764i	−0.839134	−	1.25585i	−0.964590	−	0.263754i	$-0.915039\pi$
$839$	−24.3059	−	36.3764i	−0.839134	−	1.25585i	0.125456	−	0.992099i	$-0.459961\pi$
$840$		0			0
$841$	−3.01388	−	2.01381i	−0.103927	−	0.0694418i
$842$		0			0
$843$	1.80695	+	5.95670i	0.0622345	+	0.205160i
$844$		0			0
$845$	26.7202	−	32.5586i	0.919202	−	1.12005i
$846$		0			0
$847$	−23.0473	+	55.6410i	−0.791913	+	1.91185i
$848$		0			0
$849$	4.72160	+	11.3990i	0.162045	+	0.391211i
$850$		0			0
$851$	−29.1860	+	2.87457i	−1.00048	+	0.0985391i
$852$		0			0
$853$	1.21273	+	0.648217i	0.0415230	+	0.0221945i	0.492028	−	0.870580i	$-0.336256\pi$
$853$	1.21273	+	0.648217i	0.0415230	+	0.0221945i	−0.450505	+	0.892774i	$0.648756\pi$
$854$		0			0
$855$	0.867431	+	4.36087i	0.0296655	+	0.149139i
$856$		0			0
$857$	−9.69737	−	1.92893i	−0.331256	−	0.0658909i	0.0266604	−	0.999645i	$-0.491513\pi$
$857$	−9.69737	−	1.92893i	−0.331256	−	0.0658909i	−0.357916	+	0.933754i	$0.616513\pi$
$858$		0			0
$859$	20.9471	+	2.06311i	0.714706	+	0.0703924i	0.448833	−	0.893616i	$-0.351840\pi$
$859$	20.9471	+	2.06311i	0.714706	+	0.0703924i	0.265873	+	0.964008i	$0.414340\pi$
$860$		0			0
$861$	50.3223	+	15.2651i	1.71498	+	0.520233i
$862$		0			0
$863$	−18.6960	+	18.6960i	−0.636420	+	0.636420i	−0.949671	−	0.313250i	$-0.898582\pi$
$863$	−18.6960	+	18.6960i	−0.636420	+	0.636420i	0.313250	+	0.949671i	$0.398582\pi$
$864$		0			0
$865$	31.6696	+	31.6696i	1.07680	+	1.07680i
$866$		0			0
$867$	−7.29932	+	24.0626i	−0.247898	+	0.817210i
$868$		0			0
$869$	−5.62757	+	57.1377i	−0.190902	+	1.93826i
$870$		0			0
$871$	0.411043	−	2.06645i	0.0139277	−	0.0700190i
$872$		0			0
$873$	21.0726	−	4.19160i	0.713199	−	0.141864i
$874$		0			0
$875$	3.93443	−	7.36080i	0.133008	−	0.248840i
$876$		0			0
$877$	1.71024	+	17.3643i	0.0577506	+	0.586352i	0.979896	+	0.199509i	$0.0639346\pi$
$877$	1.71024	+	17.3643i	0.0577506	+	0.586352i	−0.922145	+	0.386843i	$0.873565\pi$
$878$		0			0
$879$	−34.9525	+	14.4778i	−1.17892	+	0.488324i
$880$		0			0
$881$	16.0947	+	6.66664i	0.542244	+	0.224605i	0.636956	−	0.770900i	$-0.280193\pi$
$881$	16.0947	+	6.66664i	0.542244	+	0.224605i	−0.0947122	+	0.995505i	$0.530193\pi$
$882$		0			0
$883$	−32.1840	−	26.4128i	−1.08308	−	0.888860i	−0.0888401	−	0.996046i	$-0.528316\pi$
$883$	−32.1840	−	26.4128i	−1.08308	−	0.888860i	−0.994239	+	0.107186i	$0.965816\pi$
$884$		0			0
$885$	43.4588	−	13.1831i	1.46085	−	0.443145i
$886$		0			0
$887$	−20.3916	+	30.5182i	−0.684684	+	1.02470i	0.312515	+	0.949913i	$0.398828\pi$
$887$	−20.3916	+	30.5182i	−0.684684	+	1.02470i	−0.997199	+	0.0747894i	$0.976172\pi$
$888$		0			0
$889$	8.34991	−	5.57923i	0.280047	−	0.187121i
$890$		0			0
$891$	34.7101	+	42.2944i	1.16283	+	1.41692i
$892$		0			0
$893$	3.65292	−	1.95253i	0.122240	−	0.0653388i
$894$		0			0
$895$	−37.0827			−1.23954
$896$		0			0
$897$	3.11013			0.103844
$898$		0			0
$899$	−13.4081	+	7.16676i	−0.447184	+	0.239025i
$900$		0			0
$901$	−13.3090	−	16.2171i	−0.443387	−	0.540268i
$902$		0			0
$903$	30.4679	−	20.3580i	1.01391	−	0.677472i
$904$		0			0
$905$	−2.02938	+	3.03718i	−0.0674588	+	0.100959i
$906$		0			0
$907$	−27.3877	+	8.30796i	−0.909393	+	0.275861i	−0.710118	−	0.704082i	$-0.751359\pi$
$907$	−27.3877	+	8.30796i	−0.909393	+	0.275861i	−0.199275	+	0.979944i	$0.563859\pi$
$908$		0			0
$909$	−6.93774	−	5.69366i	−0.230110	−	0.188847i
$910$		0			0
$911$	7.01846	+	2.90714i	0.232532	+	0.0963179i	0.495907	−	0.868376i	$-0.334836\pi$
$911$	7.01846	+	2.90714i	0.232532	+	0.0963179i	−0.263375	+	0.964694i	$0.584836\pi$
$912$		0			0
$913$	−52.9327	+	21.9255i	−1.75182	+	0.725627i
$914$		0			0
$915$	−3.53899	−	35.9320i	−0.116995	−	1.18787i
$916$		0			0
$917$	2.11304	−	3.95321i	0.0697786	−	0.130547i
$918$		0			0
$919$	15.6670	−	3.11635i	0.516805	−	0.102799i	0.0702050	−	0.997533i	$-0.477635\pi$
$919$	15.6670	−	3.11635i	0.516805	−	0.102799i	0.446600	+	0.894734i	$0.352635\pi$
$920$		0			0
$921$	−0.0375114	+	0.188583i	−0.00123604	+	0.00621401i
$922$		0			0
$923$	0.0839822	−	0.852686i	0.00276431	−	0.0280665i
$924$		0			0
$925$	8.68291	−	28.6237i	0.285492	−	0.941142i
$926$		0			0
$927$	−21.0808	−	21.0808i	−0.692385	−	0.692385i
$928$		0			0
$929$	3.29668	−	3.29668i	0.108161	−	0.108161i	−0.650955	−	0.759116i	$-0.725632\pi$
$929$	3.29668	−	3.29668i	0.108161	−	0.108161i	0.759116	+	0.650955i	$0.225632\pi$
$930$		0			0
$931$	7.08962	+	2.15061i	0.232353	+	0.0704835i
$932$		0			0
$933$	52.2272	+	5.14393i	1.70984	+	0.168405i
$934$		0			0
$935$	−38.6473	−	7.68743i	−1.26390	−	0.251406i
$936$		0			0
$937$	2.22998	+	11.2109i	0.0728503	+	0.366243i	0.999964	−	0.00853809i	$-0.00271779\pi$
$937$	2.22998	+	11.2109i	0.0728503	+	0.366243i	−0.927113	+	0.374781i	$0.877718\pi$
$938$		0			0
$939$	30.5415	+	16.3248i	0.996685	+	0.532739i
$940$		0			0
$941$	9.88718	−	0.973802i	0.322313	−	0.0317450i	0.0644330	−	0.997922i	$-0.479476\pi$
$941$	9.88718	−	0.973802i	0.322313	−	0.0317450i	0.257880	+	0.966177i	$0.416976\pi$
$942$		0			0
$943$	−11.4839	−	27.7246i	−0.373968	−	0.902838i
$944$		0			0
$945$	11.1087	−	26.8188i	0.361367	−	0.872417i
$946$		0			0
$947$	−15.2393	+	18.5691i	−0.495210	+	0.603415i	−0.959306	−	0.282370i	$-0.908879\pi$
$947$	−15.2393	+	18.5691i	−0.495210	+	0.603415i	0.464096	+	0.885785i	$0.346379\pi$
$948$		0			0
$949$	0.229996	+	0.758196i	0.00746600	+	0.0246121i
$950$		0			0
$951$	−63.8887	−	42.6890i	−2.07173	−	1.38429i
$952$		0			0
$953$	8.35307	+	12.5012i	0.270582	+	0.404955i	0.941731	−	0.336368i	$-0.109199\pi$
$953$	8.35307	+	12.5012i	0.270582	+	0.404955i	−0.671148	+	0.741323i	$0.734199\pi$
$954$		0			0
$955$	−24.7900	+	20.3446i	−0.802185	+	0.658337i
$956$		0			0
$957$	−30.3831	−	56.8428i	−0.982146	−	1.83747i
$958$		0			0
$959$		−	40.0453i		−	1.29313i
$960$		0			0
$961$		−	23.9152i		−	0.771459i
$962$		0			0
$963$	10.0966	+	18.8894i	0.325358	+	0.608703i
$964$		0			0
$965$	−23.8516	+	19.5745i	−0.767810	+	0.630125i
$966$		0			0
$967$	15.4548	+	23.1297i	0.496992	+	0.743800i	0.992157	−	0.124998i	$-0.0398925\pi$
$967$	15.4548	+	23.1297i	0.496992	+	0.743800i	−0.495165	+	0.868799i	$0.664893\pi$
$968$		0			0
$969$	−2.98010	−	1.99124i	−0.0957347	−	0.0639679i
$970$		0			0
$971$	−2.98002	−	9.82382i	−0.0956335	−	0.315261i	0.896052	−	0.443950i	$-0.146423\pi$
$971$	−2.98002	−	9.82382i	−0.0956335	−	0.315261i	−0.991685	+	0.128689i	$0.958923\pi$
$972$		0			0
$973$	−31.1138	+	37.9123i	−0.997464	+	1.21541i
$974$		0			0
$975$	−1.21392	+	2.93065i	−0.0388765	+	0.0938561i
$976$		0			0
$977$	−8.55307	−	20.6489i	−0.273637	−	0.660618i	0.725996	−	0.687699i	$-0.241379\pi$
$977$	−8.55307	−	20.6489i	−0.273637	−	0.660618i	−0.999633	+	0.0270805i	$0.991379\pi$
$978$		0			0
$979$	24.3337	−	2.39666i	0.777708	−	0.0765976i
$980$		0			0
$981$	−26.7218	−	14.2831i	−0.853160	−	0.456024i
$982$		0			0
$983$	−4.20609	−	21.1454i	−0.134153	−	0.674434i	−0.988068	−	0.154021i	$-0.950778\pi$
$983$	−4.20609	−	21.1454i	−0.134153	−	0.674434i	0.853914	−	0.520414i	$-0.174222\pi$
$984$		0			0
$985$	−58.3492	−	11.6064i	−1.85916	−	0.369810i
$986$		0			0
$987$	60.2135	+	5.93052i	1.91662	+	0.188770i
$988$		0			0
$989$	−20.0104	−	6.07009i	−0.636294	−	0.193018i
$990$		0			0
$991$	−32.6004	+	32.6004i	−1.03559	+	1.03559i	−0.0362439	+	0.999343i	$0.511539\pi$
$991$	−32.6004	+	32.6004i	−1.03559	+	1.03559i	−0.999343	+	0.0362439i	$0.988461\pi$
$992$		0			0
$993$	−25.8177	−	25.8177i	−0.819299	−	0.819299i
$994$		0			0
$995$	5.94095	−	19.5847i	0.188341	−	0.620876i
$996$		0			0
$997$	4.12052	−	41.8363i	0.130498	−	1.32497i	−0.677386	−	0.735628i	$-0.736887\pi$
$997$	4.12052	−	41.8363i	0.130498	−	1.32497i	0.807884	−	0.589341i	$-0.200613\pi$
$998$		0			0
$999$	2.17493	−	10.9341i	0.0688116	−	0.345939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.13		240
4.3	odd	2		128.2.k.a.101.13	✓	240
128.19	odd	32		128.2.k.a.109.13	yes	240
128.109	even	32	inner	512.2.k.a.273.13		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.13	✓	240	4.3	odd	2
128.2.k.a.109.13	yes	240	128.19	odd	32
512.2.k.a.273.13		240	128.109	even	32	inner
512.2.k.a.497.13		240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.98645 - 1.06178i) q^{3} +(2.06545 + 2.51675i) q^{5} +(-3.55182 + 2.37325i) q^{7} +(1.15189 - 1.72393i) q^{9} +(4.79412 - 1.45428i) q^{11} +(0.194397 + 0.159538i) q^{13} +(6.77513 + 2.80635i) q^{15} +(-2.23193 + 0.924497i) q^{17} +(0.0645615 + 0.655504i) q^{19} +(-4.53564 + 8.48559i) q^{21} +(5.38519 - 1.07118i) q^{23} +(-1.09253 + 5.49251i) q^{25} +(-0.204582 + 2.07715i) q^{27} +(1.65805 - 5.46586i) q^{29} +(-1.88212 - 1.88212i) q^{31} +(7.97915 - 7.97915i) q^{33} +(-13.3090 - 4.03724i) q^{35} +(-5.31555 - 0.523536i) q^{37} +(0.555554 + 0.110507i) q^{39} +(-1.06625 - 5.36040i) q^{41} +(-3.35872 - 1.79527i) q^{43} +(6.71786 - 0.661652i) q^{45} +(-2.40646 - 5.80970i) q^{47} +(4.30433 - 10.3916i) q^{49} +(-3.45201 + 4.20628i) q^{51} +(2.52084 + 8.31009i) q^{53} +(13.5621 + 9.06189i) q^{55} +(0.824248 + 1.23357i) q^{57} +(4.78714 - 3.92870i) q^{59} +(-2.32093 - 4.34215i) q^{61} +8.85680i q^{63} +0.818767i q^{65} +(-3.94942 - 7.38884i) q^{67} +(9.56004 - 7.84572i) q^{69} +(-1.89286 - 2.83287i) q^{71} +(2.61962 + 1.75037i) q^{73} +(3.66158 + 12.0706i) q^{75} +(-13.5765 + 16.5430i) q^{77} +(-4.38565 + 10.5879i) q^{79} +(4.17939 + 10.0899i) q^{81} +(-11.3812 + 1.12095i) q^{83} +(-6.93667 - 3.70773i) q^{85} +(-2.50990 - 12.6181i) q^{87} +(4.78690 + 0.952173i) q^{89} +(-1.06909 - 0.105296i) q^{91} +(-5.73713 - 1.74034i) q^{93} +(-1.51639 + 1.51639i) q^{95} +(7.32752 + 7.32752i) q^{97} +(3.01523 - 9.93988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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