LMFDB - Embedded newform 728.2.bm.c.673.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(225,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.225"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.5
Character	$\chi$	$=$	728.673
Dual form			728.2.bm.c.225.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.509942 - 0.883245i) q^{3} +2.02001i q^{5} +(-0.866025 - 0.500000i) q^{7} +(0.979919 - 1.69727i) q^{9} +(-5.06414 + 2.92378i) q^{11} +(-2.41142 - 2.68049i) q^{13} +(1.78417 - 1.03009i) q^{15} +(3.04158 - 5.26816i) q^{17} +(-0.610163 - 0.352278i) q^{19} +1.01988i q^{21} +(-2.48413 - 4.30265i) q^{23} +0.919550 q^{25} -5.05846 q^{27} +(-4.92645 - 8.53286i) q^{29} +4.81518i q^{31} +(5.16483 + 2.98192i) q^{33} +(1.01001 - 1.74938i) q^{35} +(1.45284 - 0.838799i) q^{37} +(-1.13785 + 3.49677i) q^{39} +(-1.89288 + 1.09285i) q^{41} +(0.391141 - 0.677476i) q^{43} +(3.42850 + 1.97945i) q^{45} -5.26356i q^{47} +(0.500000 + 0.866025i) q^{49} -6.20411 q^{51} -10.0419 q^{53} +(-5.90608 - 10.2296i) q^{55} +0.718565i q^{57} +(-5.03891 - 2.90921i) q^{59} +(-3.48257 + 6.03200i) q^{61} +(-1.69727 + 0.979919i) q^{63} +(5.41463 - 4.87110i) q^{65} +(9.63479 - 5.56265i) q^{67} +(-2.53353 + 4.38820i) q^{69} +(-10.7862 - 6.22739i) q^{71} +11.4541i q^{73} +(-0.468917 - 0.812188i) q^{75} +5.84756 q^{77} +1.05083 q^{79} +(-0.360237 - 0.623949i) q^{81} +3.04409i q^{83} +(10.6418 + 6.14402i) q^{85} +(-5.02440 + 8.70252i) q^{87} +(-1.34250 + 0.775094i) q^{89} +(0.748104 + 3.52709i) q^{91} +(4.25299 - 2.45546i) q^{93} +(0.711606 - 1.23254i) q^{95} +(1.33021 + 0.767994i) q^{97} +11.4603i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} - 18 q^{9} + 12 q^{11} + 8 q^{17} - 12 q^{19} + 2 q^{23} - 28 q^{25} - 20 q^{27} + 2 q^{29} - 18 q^{33} - 8 q^{35} + 60 q^{37} + 18 q^{39} - 6 q^{41} + 24 q^{43} - 72 q^{45} + 12 q^{49} - 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 - 18 * q^9 + 12 * q^11 + 8 * q^17 - 12 * q^19 + 2 * q^23 - 28 * q^25 - 20 * q^27 + 2 * q^29 - 18 * q^33 - 8 * q^35 + 60 * q^37 + 18 * q^39 - 6 * q^41 + 24 * q^43 - 72 * q^45 + 12 * q^49 - 72 * q^51 - 48 * q^53 - 44 * q^55 - 12 * q^59 - 30 * q^61 + 12 * q^63 + 10 * q^65 + 78 * q^67 + 36 * q^69 - 36 * q^71 + 22 * q^75 + 4 * q^77 + 20 * q^79 - 40 * q^81 - 6 * q^85 - 20 * q^87 + 108 * q^89 + 6 * q^91 + 30 * q^93 + 18 * q^95 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.509942	−	0.883245i	−0.294415	−	0.509942i	0.680434	−	0.732810i	$-0.261791\pi$
$3$	−0.509942	−	0.883245i	−0.294415	−	0.509942i	−0.974849	+	0.222868i	$0.928458\pi$
$4$		0			0
$5$			2.02001i			0.903377i	0.892176	+	0.451688i	$0.149178\pi$
$5$			2.02001i			0.903377i	−0.892176	+	0.451688i	$0.850822\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		0			0
$9$	0.979919	−	1.69727i	0.326640	−	0.565756i
$10$		0			0
$11$	−5.06414	+	2.92378i	−1.52690	+	0.881553i	−0.527405	+	0.849614i	$0.676835\pi$
$11$	−5.06414	+	2.92378i	−1.52690	+	0.881553i	−0.999490	+	0.0319397i	$0.989832\pi$
$12$		0			0
$13$	−2.41142	−	2.68049i	−0.668808	−	0.743435i
$13$	−2.41142	−	2.68049i	−0.668808	−	0.743435i
$14$		0			0
$15$	1.78417	−	1.03009i	0.460670	−	0.265968i
$16$		0			0
$17$	3.04158	−	5.26816i	0.737690	−	1.27772i	−0.215842	−	0.976428i	$-0.569250\pi$
$17$	3.04158	−	5.26816i	0.737690	−	1.27772i	0.953533	−	0.301289i	$-0.0974169\pi$
$18$		0			0
$19$	−0.610163	−	0.352278i	−0.139981	−	0.0808181i	0.428374	−	0.903602i	$-0.359087\pi$
$19$	−0.610163	−	0.352278i	−0.139981	−	0.0808181i	−0.568355	+	0.822783i	$0.692420\pi$
$20$		0			0
$21$			1.01988i			0.222557i
$22$		0			0
$23$	−2.48413	−	4.30265i	−0.517978	−	0.897164i	−0.999782	−	0.0208847i	$-0.993352\pi$
$23$	−2.48413	−	4.30265i	−0.517978	−	0.897164i	0.481804	−	0.876279i	$-0.339982\pi$
$24$		0			0
$25$	0.919550			0.183910
$26$		0			0
$27$	−5.05846			−0.973501
$28$		0			0
$29$	−4.92645	−	8.53286i	−0.914818	−	1.58451i	−0.807167	−	0.590323i	$-0.799000\pi$
$29$	−4.92645	−	8.53286i	−0.914818	−	1.58451i	−0.107651	−	0.994189i	$-0.534333\pi$
$30$		0			0
$31$			4.81518i			0.864833i	0.901674	+	0.432416i	$0.142339\pi$
$31$			4.81518i			0.864833i	−0.901674	+	0.432416i	$0.857661\pi$
$32$		0			0
$33$	5.16483	+	2.98192i	0.899082	+	0.519085i
$34$		0			0
$35$	1.01001	−	1.74938i	0.170722	−	0.295700i
$36$		0			0
$37$	1.45284	−	0.838799i	0.238846	−	0.137898i	−0.375800	−	0.926701i	$-0.622632\pi$
$37$	1.45284	−	0.838799i	0.238846	−	0.137898i	0.614646	+	0.788803i	$0.289299\pi$
$38$		0			0
$39$	−1.13785	+	3.49677i	−0.182202	+	0.559932i
$40$		0			0
$41$	−1.89288	+	1.09285i	−0.295618	+	0.170675i	−0.640473	−	0.767981i	$-0.721262\pi$
$41$	−1.89288	+	1.09285i	−0.295618	+	0.170675i	0.344855	+	0.938656i	$0.387928\pi$
$42$		0			0
$43$	0.391141	−	0.677476i	0.0596485	−	0.103314i	−0.834659	−	0.550767i	$-0.814335\pi$
$43$	0.391141	−	0.677476i	0.0596485	−	0.103314i	0.894308	+	0.447453i	$0.147669\pi$
$44$		0			0
$45$	3.42850	+	1.97945i	0.511091	+	0.295079i
$46$		0			0
$47$		−	5.26356i		−	0.767769i	−0.923381	−	0.383885i	$-0.874586\pi$
$47$		−	5.26356i		−	0.767769i	0.923381	−	0.383885i	$-0.125414\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−6.20411			−0.868749
$52$		0			0
$53$	−10.0419			−1.37936			−0.689681	−	0.724114i	$-0.742249\pi$
$53$	−10.0419			−1.37936			−0.689681	+	0.724114i	$0.742249\pi$
$54$		0			0
$55$	−5.90608	−	10.2296i	−0.796375	−	1.37936i
$56$		0			0
$57$			0.718565i			0.0951763i
$58$		0			0
$59$	−5.03891	−	2.90921i	−0.656010	−	0.378747i	0.134745	−	0.990880i	$-0.456978\pi$
$59$	−5.03891	−	2.90921i	−0.656010	−	0.378747i	−0.790755	+	0.612133i	$0.790312\pi$
$60$		0			0
$61$	−3.48257	+	6.03200i	−0.445898	+	0.772318i	−0.998114	−	0.0613829i	$-0.980449\pi$
$61$	−3.48257	+	6.03200i	−0.445898	+	0.772318i	0.552216	+	0.833701i	$0.313782\pi$
$62$		0			0
$63$	−1.69727	+	0.979919i	−0.213836	+	0.123458i
$64$		0			0
$65$	5.41463	−	4.87110i	0.671602	−	0.604186i
$66$		0			0
$67$	9.63479	−	5.56265i	1.17708	−	0.679586i	0.221740	−	0.975106i	$-0.428826\pi$
$67$	9.63479	−	5.56265i	1.17708	−	0.679586i	0.955337	+	0.295520i	$0.0954929\pi$
$68$		0			0
$69$	−2.53353	+	4.38820i	−0.305001	+	0.528277i
$70$		0			0
$71$	−10.7862	−	6.22739i	−1.28008	−	0.739056i	−0.303219	−	0.952921i	$-0.598061\pi$
$71$	−10.7862	−	6.22739i	−1.28008	−	0.739056i	−0.976863	+	0.213865i	$0.931395\pi$
$72$		0			0
$73$			11.4541i			1.34060i	0.742090	+	0.670301i	$0.233835\pi$
$73$			11.4541i			1.34060i	−0.742090	+	0.670301i	$0.766165\pi$
$74$		0			0
$75$	−0.468917	−	0.812188i	−0.0541459	−	0.0937834i
$76$		0			0
$77$	5.84756			0.666392
$78$		0			0
$79$	1.05083			0.118227			0.0591136	−	0.998251i	$-0.481173\pi$
$79$	1.05083			0.118227			0.0591136	+	0.998251i	$0.481173\pi$
$80$		0			0
$81$	−0.360237	−	0.623949i	−0.0400263	−	0.0693276i
$82$		0			0
$83$			3.04409i			0.334132i	0.985946	+	0.167066i	$0.0534293\pi$
$83$			3.04409i			0.334132i	−0.985946	+	0.167066i	$0.946571\pi$
$84$		0			0
$85$	10.6418	+	6.14402i	1.15426	+	0.666413i
$86$		0			0
$87$	−5.02440	+	8.70252i	−0.538673	+	0.933008i
$88$		0			0
$89$	−1.34250	+	0.775094i	−0.142305	+	0.0821598i	−0.569462	−	0.822018i	$-0.692848\pi$
$89$	−1.34250	+	0.775094i	−0.142305	+	0.0821598i	0.427157	+	0.904177i	$0.359515\pi$
$90$		0			0
$91$	0.748104	+	3.52709i	0.0784226	+	0.369739i
$92$		0			0
$93$	4.25299	−	2.45546i	0.441014	−	0.254620i
$94$		0			0
$95$	0.711606	−	1.23254i	0.0730092	−	0.126456i
$96$		0			0
$97$	1.33021	+	0.767994i	0.135062	+	0.0779780i	0.566008	−	0.824399i	$-0.308487\pi$
$97$	1.33021	+	0.767994i	0.135062	+	0.0779780i	−0.430947	+	0.902377i	$0.641820\pi$
$98$		0			0
$99$			11.4603i			1.15180i
$100$		0			0
$101$	7.88894	+	13.6640i	0.784978	+	1.35962i	0.929012	+	0.370050i	$0.120659\pi$
$101$	7.88894	+	13.6640i	0.784978	+	1.35962i	−0.144033	+	0.989573i	$0.546007\pi$
$102$		0			0
$103$	−0.0661752			−0.00652044			−0.00326022	−	0.999995i	$-0.501038\pi$
$103$	−0.0661752			−0.00652044			−0.00326022	+	0.999995i	$0.501038\pi$
$104$		0			0
$105$	−2.06018			−0.201053
$106$		0			0
$107$	2.45244	+	4.24775i	0.237087	+	0.410646i	0.959877	−	0.280421i	$-0.0904742\pi$
$107$	2.45244	+	4.24775i	0.237087	+	0.410646i	−0.722790	+	0.691067i	$0.757141\pi$
$108$		0			0
$109$		−	13.7491i		−	1.31692i	−0.752614	−	0.658462i	$-0.771207\pi$
$109$		−	13.7491i		−	1.31692i	0.752614	−	0.658462i	$-0.228793\pi$
$110$		0			0
$111$	−1.48173	−	0.855478i	−0.140640	−	0.0811984i
$112$		0			0
$113$	1.46579	−	2.53882i	0.137890	−	0.238832i	−0.788808	−	0.614640i	$-0.789301\pi$
$113$	1.46579	−	2.53882i	0.137890	−	0.238832i	0.926698	+	0.375808i	$0.122635\pi$
$114$		0			0
$115$	8.69140	−	5.01798i	0.810477	−	0.467929i
$116$		0			0
$117$	−6.91252	+	1.46616i	−0.639062	+	0.135547i
$118$		0			0
$119$	−5.26816	+	3.04158i	−0.482932	+	0.278821i
$120$		0			0
$121$	11.5970	−	20.0866i	1.05427	−	1.82605i
$122$		0			0
$123$	1.93052	+	1.11458i	0.174069	+	0.100499i
$124$		0			0
$125$			11.9576i			1.06952i
$126$		0			0
$127$	−2.86732	−	4.96634i	−0.254433	−	0.440691i	0.710308	−	0.703891i	$-0.248556\pi$
$127$	−2.86732	−	4.96634i	−0.254433	−	0.440691i	−0.964741	+	0.263200i	$0.915222\pi$
$128$		0			0
$129$	−0.797837			−0.0702456
$130$		0			0
$131$	18.6052			1.62554			0.812772	−	0.582581i	$-0.197957\pi$
$131$	18.6052			1.62554			0.812772	+	0.582581i	$0.197957\pi$
$132$		0			0
$133$	0.352278	+	0.610163i	0.0305464	+	0.0529079i
$134$		0			0
$135$		−	10.2181i		−	0.879438i
$136$		0			0
$137$	11.4279	+	6.59793i	0.976355	+	0.563699i	0.901168	−	0.433470i	$-0.142711\pi$
$137$	11.4279	+	6.59793i	0.976355	+	0.563699i	0.0751875	+	0.997169i	$0.476044\pi$
$138$		0			0
$139$	6.03195	−	10.4476i	0.511623	−	0.886158i	−0.488286	−	0.872684i	$-0.662378\pi$
$139$	6.03195	−	10.4476i	0.511623	−	0.886158i	0.999909	−	0.0134739i	$-0.00428899\pi$
$140$		0			0
$141$	−4.64902	+	2.68411i	−0.391518	+	0.226043i
$142$		0			0
$143$	20.0489	+	6.52393i	1.67658	+	0.545558i
$144$		0			0
$145$	17.2365	−	9.95148i	1.43141	−	0.826426i
$146$		0			0
$147$	0.509942	−	0.883245i	0.0420593	−	0.0728488i
$148$		0			0
$149$	−20.5202	−	11.8473i	−1.68108	−	0.970571i	−0.960947	−	0.276734i	$-0.910748\pi$
$149$	−20.5202	−	11.8473i	−1.68108	−	0.970571i	−0.720132	−	0.693837i	$-0.755919\pi$
$150$		0			0
$151$			18.0151i			1.46605i	0.680203	+	0.733024i	$0.261892\pi$
$151$			18.0151i			1.46605i	−0.680203	+	0.733024i	$0.738108\pi$
$152$		0			0
$153$	−5.96099	−	10.3247i	−0.481918	−	0.834706i
$154$		0			0
$155$	−9.72673			−0.781270
$156$		0			0
$157$	13.3205			1.06309			0.531547	−	0.847028i	$-0.321611\pi$
$157$	13.3205			1.06309			0.531547	+	0.847028i	$0.321611\pi$
$158$		0			0
$159$	5.12079	+	8.86946i	0.406105	+	0.703394i
$160$		0			0
$161$			4.96827i			0.391554i
$162$		0			0
$163$	−10.9382	−	6.31518i	−0.856746	−	0.494643i	0.00617502	−	0.999981i	$-0.498034\pi$
$163$	−10.9382	−	6.31518i	−0.856746	−	0.494643i	−0.862921	+	0.505338i	$0.831368\pi$
$164$		0			0
$165$	−6.02351	+	10.4330i	−0.468930	+	0.812210i
$166$		0			0
$167$	16.0968	−	9.29348i	1.24561	−	0.719151i	0.275376	−	0.961336i	$-0.411198\pi$
$167$	16.0968	−	9.29348i	1.24561	−	0.719151i	0.970230	+	0.242185i	$0.0778642\pi$
$168$		0			0
$169$	−1.37010	+	12.9276i	−0.105392	+	0.994431i
$170$		0			0
$171$	−1.19582	+	0.690408i	−0.0914467	+	0.0527968i
$172$		0			0
$173$	−3.60469	+	6.24350i	−0.274059	+	0.474685i	−0.969897	−	0.243514i	$-0.921700\pi$
$173$	−3.60469	+	6.24350i	−0.274059	+	0.474685i	0.695838	+	0.718199i	$0.255033\pi$
$174$		0			0
$175$	−0.796354	−	0.459775i	−0.0601987	−	0.0347557i
$176$		0			0
$177$			5.93412i			0.446036i
$178$		0			0
$179$	10.3711	+	17.9632i	0.775170	+	1.34263i	0.934699	+	0.355440i	$0.115669\pi$
$179$	10.3711	+	17.9632i	0.775170	+	1.34263i	−0.159529	+	0.987193i	$0.550998\pi$
$180$		0			0
$181$	15.2611			1.13435			0.567173	−	0.823599i	$-0.308037\pi$
$181$	15.2611			1.13435			0.567173	+	0.823599i	$0.308037\pi$
$182$		0			0
$183$	7.10364			0.525116
$184$		0			0
$185$	1.69439	+	2.93476i	0.124574	+	0.215768i
$186$		0			0
$187$			35.5716i			2.60125i
$188$		0			0
$189$	4.38075	+	2.52923i	0.318653	+	0.183974i
$190$		0			0
$191$	−1.59564	+	2.76373i	−0.115456	+	0.199976i	−0.917962	−	0.396668i	$-0.870166\pi$
$191$	−1.59564	+	2.76373i	−0.115456	+	0.199976i	0.802506	+	0.596645i	$0.203500\pi$
$192$		0			0
$193$	9.04430	−	5.22173i	0.651023	−	0.375868i	−0.137825	−	0.990457i	$-0.544011\pi$
$193$	9.04430	−	5.22173i	0.651023	−	0.375868i	0.788848	+	0.614588i	$0.210678\pi$
$194$		0			0
$195$	−7.06352	−	2.29847i	−0.505829	−	0.164597i
$196$		0			0
$197$	−2.98736	+	1.72476i	−0.212841	+	0.122884i	−0.602631	−	0.798020i	$-0.705881\pi$
$197$	−2.98736	+	1.72476i	−0.212841	+	0.122884i	0.389790	+	0.920904i	$0.372548\pi$
$198$		0			0
$199$	−2.49808	+	4.32679i	−0.177084	+	0.306718i	−0.940880	−	0.338739i	$-0.890000\pi$
$199$	−2.49808	+	4.32679i	−0.177084	+	0.306718i	0.763797	+	0.645457i	$0.223333\pi$
$200$		0			0
$201$	−9.82636	−	5.67325i	−0.693098	−	0.400161i
$202$		0			0
$203$			9.85289i			0.691538i
$204$		0			0
$205$	−2.20758	−	3.82364i	−0.154184	−	0.267054i
$206$		0			0
$207$	−9.73699			−0.676768
$208$		0			0
$209$	4.11994			0.284982
$210$		0			0
$211$	−11.3510	−	19.6604i	−0.781432	−	1.35348i	−0.931108	−	0.364745i	$-0.881156\pi$
$211$	−11.3510	−	19.6604i	−0.781432	−	1.35348i	0.149676	−	0.988735i	$-0.452177\pi$
$212$		0			0
$213$			12.7024i			0.870356i
$214$		0			0
$215$	1.36851	+	0.790110i	0.0933316	+	0.0538850i
$216$		0			0
$217$	2.40759	−	4.17007i	0.163438	−	0.283083i
$218$		0			0
$219$	10.1168	−	5.84093i	0.683629	−	0.394693i
$220$		0			0
$221$	−21.4558	+	4.55083i	−1.44327	+	0.306122i
$222$		0			0
$223$	−7.64573	+	4.41426i	−0.511996	+	0.295601i	−0.733654	−	0.679524i	$-0.762187\pi$
$223$	−7.64573	+	4.41426i	−0.511996	+	0.295601i	0.221658	+	0.975125i	$0.428853\pi$
$224$		0			0
$225$	0.901084	−	1.56072i	0.0600723	−	0.104048i
$226$		0			0
$227$	−13.6744	−	7.89493i	−0.907603	−	0.524005i	−0.0279438	−	0.999609i	$-0.508896\pi$
$227$	−13.6744	−	7.89493i	−0.907603	−	0.524005i	−0.879659	+	0.475605i	$0.842229\pi$
$228$		0			0
$229$			7.89653i			0.521818i	0.965363	+	0.260909i	$0.0840222\pi$
$229$			7.89653i			0.521818i	−0.965363	+	0.260909i	$0.915978\pi$
$230$		0			0
$231$	−2.98192	−	5.16483i	−0.196196	−	0.339821i
$232$		0			0
$233$	−12.8845			−0.844089			−0.422045	−	0.906575i	$-0.638687\pi$
$233$	−12.8845			−0.844089			−0.422045	+	0.906575i	$0.638687\pi$
$234$		0			0
$235$	10.6325			0.693585
$236$		0			0
$237$	−0.535860	−	0.928137i	−0.0348079	−	0.0602890i
$238$		0			0
$239$		−	15.9013i		−	1.02857i	−0.857620	−	0.514283i	$-0.828058\pi$
$239$		−	15.9013i		−	1.02857i	0.857620	−	0.514283i	$-0.171942\pi$
$240$		0			0
$241$	−20.9790	−	12.1122i	−1.35137	−	0.780216i	−0.362931	−	0.931816i	$-0.618224\pi$
$241$	−20.9790	−	12.1122i	−1.35137	−	0.780216i	−0.988442	+	0.151600i	$0.951557\pi$
$242$		0			0
$243$	−7.95509	+	13.7786i	−0.510319	+	0.883898i
$244$		0			0
$245$	−1.74938	+	1.01001i	−0.111764	+	0.0645269i
$246$		0			0
$247$	0.527081	+	2.48503i	0.0335374	+	0.158119i
$248$		0			0
$249$	2.68867	−	1.55231i	0.170388	−	0.0983735i
$250$		0			0
$251$	11.8183	−	20.4699i	0.745966	−	1.29205i	−0.203777	−	0.979017i	$-0.565322\pi$
$251$	11.8183	−	20.4699i	0.745966	−	1.29205i	0.949742	−	0.313033i	$-0.101345\pi$
$252$		0			0
$253$	25.1600	+	14.5261i	1.58180	+	0.913250i
$254$		0			0
$255$		−	12.5324i		−	0.784808i
$256$		0			0
$257$	4.36835	+	7.56620i	0.272490	+	0.471966i	0.969499	−	0.245096i	$-0.0788195\pi$
$257$	4.36835	+	7.56620i	0.272490	+	0.471966i	−0.697009	+	0.717063i	$0.745486\pi$
$258$		0			0
$259$	−1.67760			−0.104241
$260$		0			0
$261$	−19.3101			−1.19526
$262$		0			0
$263$	3.71086	+	6.42740i	0.228822	+	0.396330i	0.957459	−	0.288569i	$-0.0931794\pi$
$263$	3.71086	+	6.42740i	0.228822	+	0.396330i	−0.728638	+	0.684899i	$0.759846\pi$
$264$		0			0
$265$		−	20.2848i		−	1.24608i
$266$		0			0
$267$	1.36920	+	0.790505i	0.0837934	+	0.0483782i
$268$		0			0
$269$	−14.1475	+	24.5042i	−0.862589	+	1.49405i	0.00683299	+	0.999977i	$0.497825\pi$
$269$	−14.1475	+	24.5042i	−0.862589	+	1.49405i	−0.869422	+	0.494071i	$0.835508\pi$
$270$		0			0
$271$	10.2435	−	5.91408i	0.622248	−	0.359255i	−0.155496	−	0.987837i	$-0.549698\pi$
$271$	10.2435	−	5.91408i	0.622248	−	0.359255i	0.777744	+	0.628582i	$0.216364\pi$
$272$		0			0
$273$	2.73379	−	2.45937i	0.165457	−	0.148848i
$274$		0			0
$275$	−4.65673	+	2.68856i	−0.280811	+	0.162126i
$276$		0			0
$277$	0.106240	−	0.184013i	0.00638335	−	0.0110563i	−0.862816	−	0.505518i	$-0.831301\pi$
$277$	0.106240	−	0.184013i	0.00638335	−	0.0110563i	0.869199	+	0.494462i	$0.164635\pi$
$278$		0			0
$279$	8.17266	+	4.71849i	0.489285	+	0.282489i
$280$		0			0
$281$		−	20.2326i		−	1.20698i	−0.797371	−	0.603489i	$-0.793777\pi$
$281$		−	20.2326i		−	1.20698i	0.797371	−	0.603489i	$-0.206223\pi$
$282$		0			0
$283$	10.1574	+	17.5931i	0.603793	+	1.04580i	0.992241	+	0.124330i	$0.0396781\pi$
$283$	10.1574	+	17.5931i	0.603793	+	1.04580i	−0.388448	+	0.921471i	$0.626989\pi$
$284$		0			0
$285$	−1.45151			−0.0859801
$286$		0			0
$287$	2.18571			0.129018
$288$		0			0
$289$	−10.0024	−	17.3246i	−0.588374	−	1.01909i
$290$		0			0
$291$		−	1.56653i		−	0.0918316i
$292$		0			0
$293$	−11.8479	−	6.84038i	−0.692161	−	0.399619i	0.112260	−	0.993679i	$-0.464191\pi$
$293$	−11.8479	−	6.84038i	−0.692161	−	0.399619i	−0.804421	+	0.594059i	$0.797524\pi$
$294$		0			0
$295$	5.87665	−	10.1787i	0.342152	−	0.592624i
$296$		0			0
$297$	25.6167	−	14.7898i	1.48643	−	0.858193i
$298$		0			0
$299$	−5.54293	+	17.0342i	−0.320556	+	0.985113i
$300$		0			0
$301$	−0.677476	+	0.391141i	−0.0390491	+	0.0225450i
$302$		0			0
$303$	8.04580	−	13.9357i	0.462219	−	0.800587i
$304$		0			0
$305$	−12.1847	−	7.03484i	−0.697694	−	0.402814i
$306$		0			0
$307$		−	9.17060i		−	0.523394i	−0.965150	−	0.261697i	$-0.915718\pi$
$307$		−	9.17060i		−	0.523394i	0.965150	−	0.261697i	$-0.0842821\pi$
$308$		0			0
$309$	0.0337455	+	0.0584490i	0.00191972	+	0.00332505i
$310$		0			0
$311$	−19.7022			−1.11721			−0.558604	−	0.829435i	$-0.688663\pi$
$311$	−19.7022			−1.11721			−0.558604	+	0.829435i	$0.688663\pi$
$312$		0			0
$313$	−18.7782			−1.06141			−0.530703	−	0.847558i	$-0.678072\pi$
$313$	−18.7782			−1.06141			−0.530703	+	0.847558i	$0.678072\pi$
$314$		0			0
$315$	−1.97945	−	3.42850i	−0.111529	−	0.193174i
$316$		0			0
$317$			16.5701i			0.930667i	0.885135	+	0.465334i	$0.154066\pi$
$317$			16.5701i			0.930667i	−0.885135	+	0.465334i	$0.845934\pi$
$318$		0			0
$319$	49.8964	+	28.8077i	2.79366	+	1.61292i
$320$		0			0
$321$	2.50121	−	4.33222i	0.139604	−	0.241801i
$322$		0			0
$323$	−3.71172	+	2.14296i	−0.206525	+	0.119238i
$324$		0			0
$325$	−2.21742	−	2.46485i	−0.123000	−	0.136725i
$326$		0			0
$327$	−12.1438	+	7.01124i	−0.671555	+	0.387722i
$328$		0			0
$329$	−2.63178	+	4.55838i	−0.145095	+	0.251312i
$330$		0			0
$331$	−16.7899	−	9.69363i	−0.922854	−	0.532810i	−0.0383097	−	0.999266i	$-0.512197\pi$
$331$	−16.7899	−	9.69363i	−0.922854	−	0.532810i	−0.884545	+	0.466456i	$0.845531\pi$
$332$		0			0
$333$		−	3.28782i		−	0.180171i
$334$		0			0
$335$	11.2366	+	19.4624i	0.613922	+	1.06334i
$336$		0			0
$337$	4.37084			0.238095			0.119047	−	0.992889i	$-0.462016\pi$
$337$	4.37084			0.238095			0.119047	+	0.992889i	$0.462016\pi$
$338$		0			0
$339$	−2.98987			−0.162388
$340$		0			0
$341$	−14.0786	−	24.3848i	−0.762396	−	1.32051i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	−8.86421	−	5.11776i	−0.477233	−	0.275531i
$346$		0			0
$347$	10.7824	−	18.6756i	0.578828	−	1.00256i	−0.416786	−	0.909005i	$-0.636844\pi$
$347$	10.7824	−	18.6756i	0.578828	−	1.00256i	0.995614	−	0.0935548i	$-0.0298230\pi$
$348$		0			0
$349$	16.6767	−	9.62828i	0.892682	−	0.515390i	0.0178632	−	0.999840i	$-0.494314\pi$
$349$	16.6767	−	9.62828i	0.892682	−	0.515390i	0.874819	+	0.484450i	$0.160980\pi$
$350$		0			0
$351$	12.1981	+	13.5592i	0.651085	+	0.723735i
$352$		0			0
$353$	7.66898	−	4.42769i	0.408179	−	0.235662i	−0.281828	−	0.959465i	$-0.590941\pi$
$353$	7.66898	−	4.42769i	0.408179	−	0.235662i	0.690007	+	0.723803i	$0.257607\pi$
$354$		0			0
$355$	12.5794	−	21.7882i	0.667646	−	1.15640i
$356$		0			0
$357$	5.37291	+	3.10205i	0.284365	+	0.164178i
$358$		0			0
$359$		−	24.2377i		−	1.27922i	−0.768700	−	0.639609i	$-0.779096\pi$
$359$		−	24.2377i		−	1.27922i	0.768700	−	0.639609i	$-0.220904\pi$
$360$		0			0
$361$	−9.25180	−	16.0246i	−0.486937	−	0.843399i
$362$		0			0
$363$	−23.6552			−1.24158
$364$		0			0
$365$	−23.1374			−1.21107
$366$		0			0
$367$	−1.12828	−	1.95423i	−0.0588955	−	0.102010i	0.835074	−	0.550137i	$-0.185425\pi$
$367$	−1.12828	−	1.95423i	−0.0588955	−	0.102010i	−0.893970	+	0.448127i	$0.852091\pi$
$368$		0			0
$369$			4.28363i			0.222997i
$370$		0			0
$371$	8.69654	+	5.02095i	0.451502	+	0.260675i
$372$		0			0
$373$	−1.00315	+	1.73750i	−0.0519409	+	0.0899643i	−0.890827	−	0.454343i	$-0.849874\pi$
$373$	−1.00315	+	1.73750i	−0.0519409	+	0.0899643i	0.838886	+	0.544307i	$0.183207\pi$
$374$		0			0
$375$	10.5615	−	6.09766i	0.545392	−	0.314882i
$376$		0			0
$377$	−10.9925	+	33.7816i	−0.566145	+	1.73984i
$378$		0			0
$379$	4.46530	−	2.57804i	0.229367	−	0.132425i	−0.380913	−	0.924611i	$-0.624390\pi$
$379$	4.46530	−	2.57804i	0.229367	−	0.132425i	0.610280	+	0.792186i	$0.291057\pi$
$380$		0			0
$381$	−2.92433	+	5.06509i	−0.149818	+	0.259492i
$382$		0			0
$383$	−18.5542	−	10.7123i	−0.948077	−	0.547373i	−0.0555943	−	0.998453i	$-0.517705\pi$
$383$	−18.5542	−	10.7123i	−0.948077	−	0.547373i	−0.892483	+	0.451081i	$0.851039\pi$
$384$		0			0
$385$			11.8122i			0.602003i
$386$		0			0
$387$	−0.766573	−	1.32774i	−0.0389671	−	0.0674930i
$388$		0			0
$389$	−24.3103			−1.23258			−0.616291	−	0.787518i	$-0.711366\pi$
$389$	−24.3103			−1.23258			−0.616291	+	0.787518i	$0.711366\pi$
$390$		0			0
$391$	−30.2227			−1.52843
$392$		0			0
$393$	−9.48757	−	16.4330i	−0.478585	−	0.828933i
$394$		0			0
$395$			2.12268i			0.106804i
$396$		0			0
$397$	1.43301	+	0.827347i	0.0719206	+	0.0415234i	0.535529	−	0.844517i	$-0.320112\pi$
$397$	1.43301	+	0.827347i	0.0719206	+	0.0415234i	−0.463608	+	0.886040i	$0.653446\pi$
$398$		0			0
$399$	0.359283	−	0.622296i	0.0179866	−	0.0311538i
$400$		0			0
$401$	3.33602	−	1.92605i	0.166593	−	0.0961825i	−0.414385	−	0.910102i	$-0.636003\pi$
$401$	3.33602	−	1.92605i	0.166593	−	0.0961825i	0.580978	+	0.813919i	$0.302670\pi$
$402$		0			0
$403$	12.9071	−	11.6114i	0.642947	−	0.578407i
$404$		0			0
$405$	1.26038	−	0.727683i	0.0626290	−	0.0361589i
$406$		0			0
$407$	−4.90493	+	8.49559i	−0.243129	+	0.421111i
$408$		0			0
$409$	20.7527	+	11.9816i	1.02615	+	0.592450i	0.915880	−	0.401451i	$-0.131494\pi$
$409$	20.7527	+	11.9816i	1.02615	+	0.592450i	0.110273	+	0.993901i	$0.464827\pi$
$410$		0			0
$411$		−	13.4582i		−	0.663846i
$412$		0			0
$413$	2.90921	+	5.03891i	0.143153	+	0.247948i
$414$		0			0
$415$	−6.14909			−0.301847
$416$		0			0
$417$	−12.3038			−0.602518
$418$		0			0
$419$	−16.9634	−	29.3815i	−0.828717	−	1.43538i	−0.899045	−	0.437856i	$-0.855738\pi$
$419$	−16.9634	−	29.3815i	−0.828717	−	1.43538i	0.0703279	−	0.997524i	$-0.477595\pi$
$420$		0			0
$421$		−	32.0785i		−	1.56341i	−0.623648	−	0.781705i	$-0.714350\pi$
$421$		−	32.0785i		−	1.56341i	0.623648	−	0.781705i	$-0.285650\pi$
$422$		0			0
$423$	−8.93368	−	5.15786i	−0.434370	−	0.250784i
$424$		0			0
$425$	2.79688	−	4.84434i	0.135669	−	0.234985i
$426$		0			0
$427$	6.03200	−	3.48257i	0.291909	−	0.168534i
$428$		0			0
$429$	−4.46157	−	21.0350i	−0.215407	−	1.01558i
$430$		0			0
$431$	−4.66521	+	2.69346i	−0.224715	+	0.129739i	−0.608132	−	0.793836i	$-0.708081\pi$
$431$	−4.66521	+	2.69346i	−0.224715	+	0.129739i	0.383416	+	0.923576i	$0.374747\pi$
$432$		0			0
$433$	−2.29422	+	3.97371i	−0.110253	+	0.190964i	−0.915872	−	0.401470i	$-0.868500\pi$
$433$	−2.29422	+	3.97371i	−0.110253	+	0.190964i	0.805619	+	0.592434i	$0.201833\pi$
$434$		0			0
$435$	−17.5792	−	10.1494i	−0.842858	−	0.486624i
$436$		0			0
$437$			3.50042i			0.167448i
$438$		0			0
$439$	9.95016	+	17.2342i	0.474895	+	0.822542i	0.999587	−	0.0287501i	$-0.00915269\pi$
$439$	9.95016	+	17.2342i	0.474895	+	0.822542i	−0.524692	+	0.851292i	$0.675819\pi$
$440$		0			0
$441$	1.95984			0.0933256
$442$		0			0
$443$	12.3708			0.587757			0.293878	−	0.955843i	$-0.405054\pi$
$443$	12.3708			0.587757			0.293878	+	0.955843i	$0.405054\pi$
$444$		0			0
$445$	−1.56570	−	2.71187i	−0.0742213	−	0.128555i
$446$		0			0
$447$			24.1658i			1.14300i
$448$		0			0
$449$	15.8252	+	9.13666i	0.746835	+	0.431186i	0.824549	−	0.565790i	$-0.191429\pi$
$449$	15.8252	+	9.13666i	0.746835	+	0.431186i	−0.0777140	+	0.996976i	$0.524762\pi$
$450$		0			0
$451$	6.39053	−	11.0687i	0.300918	−	0.521206i
$452$		0			0
$453$	15.9117	−	9.18665i	0.747599	−	0.431627i
$454$		0			0
$455$	−7.12476	+	1.51118i	−0.334014	+	0.0708452i
$456$		0			0
$457$	23.4033	−	13.5119i	1.09476	−	0.632060i	0.159921	−	0.987130i	$-0.448876\pi$
$457$	23.4033	−	13.5119i	1.09476	−	0.632060i	0.934840	+	0.355069i	$0.115543\pi$
$458$		0			0
$459$	−15.3857	+	26.6488i	−0.718142	+	1.24386i
$460$		0			0
$461$	−18.4766	−	10.6675i	−0.860540	−	0.496833i	0.00365309	−	0.999993i	$-0.498837\pi$
$461$	−18.4766	−	10.6675i	−0.860540	−	0.496833i	−0.864193	+	0.503160i	$0.832171\pi$
$462$		0			0
$463$			22.2481i			1.03396i	0.855998	+	0.516979i	$0.172943\pi$
$463$			22.2481i			1.03396i	−0.855998	+	0.516979i	$0.827057\pi$
$464$		0			0
$465$	4.96007	+	8.59109i	0.230018	+	0.398402i
$466$		0			0
$467$	39.4841			1.82711			0.913553	−	0.406719i	$-0.133327\pi$
$467$	39.4841			1.82711			0.913553	+	0.406719i	$0.133327\pi$
$468$		0			0
$469$	−11.1253			−0.513718
$470$		0			0
$471$	−6.79270	−	11.7653i	−0.312991	−	0.542117i
$472$		0			0
$473$			4.57444i			0.210333i
$474$		0			0
$475$	−0.561076	−	0.323937i	−0.0257439	−	0.0148633i
$476$		0			0
$477$	−9.84025	+	17.0438i	−0.450554	+	0.780382i
$478$		0			0
$479$	−32.4927	+	18.7597i	−1.48463	+	0.857151i	−0.999847	−	0.0174844i	$-0.994434\pi$
$479$	−32.4927	+	18.7597i	−1.48463	+	0.857151i	−0.484782	+	0.874635i	$0.661101\pi$
$480$		0			0
$481$	−5.75181	−	1.87164i	−0.262260	−	0.0853394i
$482$		0			0
$483$	4.38820	−	2.53353i	0.199670	−	0.115279i
$484$		0			0
$485$	−1.55136	+	2.68703i	−0.0704436	+	0.122012i
$486$		0			0
$487$	4.59317	+	2.65187i	0.208136	+	0.120168i	0.600445	−	0.799666i	$-0.294990\pi$
$487$	4.59317	+	2.65187i	0.208136	+	0.120168i	−0.392309	+	0.919834i	$0.628323\pi$
$488$		0			0
$489$			12.8815i			0.582521i
$490$		0			0
$491$	16.3430	+	28.3069i	0.737550	+	1.27747i	0.953596	+	0.301090i	$0.0973506\pi$
$491$	16.3430	+	28.3069i	0.737550	+	1.27747i	−0.216046	+	0.976383i	$0.569316\pi$
$492$		0			0
$493$	−59.9366			−2.69941
$494$		0			0
$495$	−23.1499			−1.04051
$496$		0			0
$497$	6.22739	+	10.7862i	0.279337	+	0.483825i
$498$		0			0
$499$			11.9976i			0.537086i	0.963268	+	0.268543i	$0.0865421\pi$
$499$			11.9976i			0.537086i	−0.963268	+	0.268543i	$0.913458\pi$
$500$		0			0
$501$	−16.4168	−	9.47827i	−0.733451	−	0.423458i
$502$		0			0
$503$	18.0640	−	31.2878i	0.805435	−	1.39505i	−0.110563	−	0.993869i	$-0.535265\pi$
$503$	18.0640	−	31.2878i	0.805435	−	1.39505i	0.915997	−	0.401184i	$-0.131401\pi$
$504$		0			0
$505$	−27.6015	+	15.9357i	−1.22825	+	0.709131i
$506$		0			0
$507$	12.1169	−	5.38219i	0.538131	−	0.239031i
$508$		0			0
$509$	−7.09320	+	4.09526i	−0.314401	+	0.181519i	−0.648894	−	0.760879i	$-0.724768\pi$
$509$	−7.09320	+	4.09526i	−0.314401	+	0.181519i	0.334493	+	0.942398i	$0.391435\pi$
$510$		0			0
$511$	5.72705	−	9.91954i	0.253350	−	0.438815i
$512$		0			0
$513$	3.08649	+	1.78198i	0.136272	+	0.0786765i
$514$		0			0
$515$		−	0.133675i		−	0.00589042i
$516$		0			0
$517$	15.3895	+	26.6554i	0.676830	+	1.17230i
$518$		0			0
$519$	7.35272			0.322749
$520$		0			0
$521$	−22.0138			−0.964442			−0.482221	−	0.876050i	$-0.660170\pi$
$521$	−22.0138			−0.964442			−0.482221	+	0.876050i	$0.660170\pi$
$522$		0			0
$523$	3.45843	+	5.99017i	0.151226	+	0.261932i	0.931679	−	0.363284i	$-0.118344\pi$
$523$	3.45843	+	5.99017i	0.151226	+	0.261932i	−0.780452	+	0.625215i	$0.785011\pi$
$524$		0			0
$525$			0.937834i			0.0409304i
$526$		0			0
$527$	25.3672	+	14.6457i	1.10501	+	0.637979i
$528$		0			0
$529$	−0.841838	+	1.45811i	−0.0366016	+	0.0633959i
$530$		0			0
$531$	−9.87544	+	5.70159i	−0.428557	+	0.247428i
$532$		0			0
$533$	7.49391	+	2.43852i	0.324597	+	0.105624i
$534$		0			0
$535$	−8.58052	+	4.95396i	−0.370968	+	0.214179i
$536$		0			0
$537$	10.5773	−	18.3204i	0.456443	−	0.790583i
$538$		0			0
$539$	−5.06414	−	2.92378i	−0.218128	−	0.125936i
$540$		0			0
$541$			15.6696i			0.673690i	0.941560	+	0.336845i	$0.109360\pi$
$541$			15.6696i			0.673690i	−0.941560	+	0.336845i	$0.890640\pi$
$542$		0			0
$543$	−7.78225	−	13.4793i	−0.333968	−	0.578450i
$544$		0			0
$545$	27.7733			1.18968
$546$		0			0
$547$	8.28824			0.354379			0.177190	−	0.984177i	$-0.443299\pi$
$547$	8.28824			0.354379			0.177190	+	0.984177i	$0.443299\pi$
$548$		0			0
$549$	6.82528	+	11.8217i	0.291296	+	0.504539i
$550$		0			0
$551$			6.94192i			0.295736i
$552$		0			0
$553$	−0.910042	−	0.525413i	−0.0386989	−	0.0223428i
$554$		0			0
$555$	1.72808	−	2.99312i	0.0733527	−	0.127051i
$556$		0			0
$557$	33.9659	−	19.6102i	1.43918	−	0.830911i	0.441387	−	0.897317i	$-0.354486\pi$
$557$	33.9659	−	19.6102i	1.43918	−	0.830911i	0.997793	+	0.0664056i	$0.0211531\pi$
$558$		0			0
$559$	−2.75918	+	0.585229i	−0.116701	+	0.0247525i
$560$		0			0
$561$	31.4185	−	18.1395i	1.32649	−	0.765848i
$562$		0			0
$563$	14.4692	−	25.0613i	0.609803	−	1.05621i	−0.381470	−	0.924381i	$-0.624582\pi$
$563$	14.4692	−	25.0613i	0.609803	−	1.05621i	0.991273	−	0.131828i	$-0.0420846\pi$
$564$		0			0
$565$	5.12845	+	2.96091i	0.215756	+	0.124567i
$566$		0			0
$567$			0.720474i			0.0302571i
$568$		0			0
$569$	−14.8904	−	25.7910i	−0.624240	−	1.08122i	−0.988687	−	0.149991i	$-0.952075\pi$
$569$	−14.8904	−	25.7910i	−0.624240	−	1.08122i	0.364448	−	0.931224i	$-0.381258\pi$
$570$		0			0
$571$	−2.44165			−0.102180			−0.0510900	−	0.998694i	$-0.516270\pi$
$571$	−2.44165			−0.102180			−0.0510900	+	0.998694i	$0.516270\pi$
$572$		0			0
$573$	3.25473			0.135968
$574$		0			0
$575$	−2.28429	−	3.95650i	−0.0952613	−	0.164997i
$576$		0			0
$577$		−	27.7941i		−	1.15708i	−0.815652	−	0.578542i	$-0.803622\pi$
$577$		−	27.7941i		−	1.15708i	0.815652	−	0.578542i	$-0.196378\pi$
$578$		0			0
$579$	−9.22414	−	5.32556i	−0.383342	−	0.221323i
$580$		0			0
$581$	1.52204	−	2.63626i	0.0631450	−	0.109370i
$582$		0			0
$583$	50.8536	−	29.3603i	2.10614	−	1.21598i
$584$		0			0
$585$	−2.96167	−	13.9634i	−0.122450	−	0.577314i
$586$		0			0
$587$	−18.2317	+	10.5261i	−0.752502	+	0.434457i	−0.826597	−	0.562794i	$-0.809726\pi$
$587$	−18.2317	+	10.5261i	−0.752502	+	0.434457i	0.0740954	+	0.997251i	$0.476393\pi$
$588$		0			0
$589$	1.69628	−	2.93805i	0.0698942	−	0.121060i
$590$		0			0
$591$	3.04676	+	1.75905i	0.125327	+	0.0723576i
$592$		0			0
$593$			8.12990i			0.333855i	0.985969	+	0.166927i	$0.0533846\pi$
$593$			8.12990i			0.333855i	−0.985969	+	0.166927i	$0.946615\pi$
$594$		0			0
$595$	−6.14402	−	10.6418i	−0.251880	−	0.436269i
$596$		0			0
$597$	5.09549			0.208545
$598$		0			0
$599$	−18.1382			−0.741105			−0.370552	−	0.928812i	$-0.620832\pi$
$599$	−18.1382			−0.741105			−0.370552	+	0.928812i	$0.620832\pi$
$600$		0			0
$601$	8.72037	+	15.1041i	0.355711	+	0.616110i	0.987239	−	0.159243i	$-0.0509053\pi$
$601$	8.72037	+	15.1041i	0.355711	+	0.616110i	−0.631528	+	0.775353i	$0.717572\pi$
$602$		0			0
$603$		−	21.8038i		−	0.887918i
$604$		0			0
$605$	40.5752	+	23.4261i	1.64962	+	0.952406i
$606$		0			0
$607$	−3.03573	+	5.25803i	−0.123216	+	0.213417i	−0.921034	−	0.389481i	$-0.872654\pi$
$607$	−3.03573	+	5.25803i	−0.123216	+	0.213417i	0.797818	+	0.602898i	$0.205988\pi$
$608$		0			0
$609$	8.70252	−	5.02440i	0.352644	−	0.203599i
$610$		0			0
$611$	−14.1090	+	12.6927i	−0.570787	+	0.513490i
$612$		0			0
$613$	−12.3808	+	7.14804i	−0.500054	+	0.288707i	−0.728736	−	0.684795i	$-0.759892\pi$
$613$	−12.3808	+	7.14804i	−0.500054	+	0.288707i	0.228682	+	0.973501i	$0.426559\pi$
$614$		0			0
$615$	−2.25147	+	3.89967i	−0.0907882	+	0.157250i
$616$		0			0
$617$	28.5296	+	16.4716i	1.14856	+	0.663120i	0.948535	−	0.316672i	$-0.102565\pi$
$617$	28.5296	+	16.4716i	1.14856	+	0.663120i	0.200022	+	0.979791i	$0.435899\pi$
$618$		0			0
$619$			14.2687i			0.573506i	0.958005	+	0.286753i	$0.0925759\pi$
$619$			14.2687i			0.573506i	−0.958005	+	0.286753i	$0.907424\pi$
$620$		0			0
$621$	12.5659	+	21.7647i	0.504251	+	0.873389i
$622$		0			0
$623$	1.55019			0.0621070
$624$		0			0
$625$	−19.5567			−0.782267
$626$		0			0
$627$	−2.10093	−	3.63891i	−0.0839030	−	0.145324i
$628$		0			0
$629$		−	10.2051i		−	0.406903i
$630$		0			0
$631$	−20.4636	−	11.8147i	−0.814644	−	0.470335i	0.0339220	−	0.999424i	$-0.489200\pi$
$631$	−20.4636	−	11.8147i	−0.814644	−	0.470335i	−0.848566	+	0.529090i	$0.822534\pi$
$632$		0			0
$633$	−11.5767	+	20.0514i	−0.460131	+	0.796970i
$634$		0			0
$635$	10.0321	−	5.79202i	0.398110	−	0.229849i
$636$		0			0
$637$	1.11567	−	3.42860i	0.0442043	−	0.135846i
$638$		0			0
$639$	−21.1391	+	12.2047i	−0.836251	+	0.482810i
$640$		0			0
$641$	−18.5168	+	32.0720i	−0.731368	+	1.26677i	0.224931	+	0.974375i	$0.427784\pi$
$641$	−18.5168	+	32.0720i	−0.731368	+	1.26677i	−0.956299	+	0.292392i	$0.905549\pi$
$642$		0			0
$643$	−28.9127	−	16.6927i	−1.14021	−	0.658298i	−0.193724	−	0.981056i	$-0.562057\pi$
$643$	−28.9127	−	16.6927i	−1.14021	−	0.658298i	−0.946481	+	0.322758i	$0.895390\pi$
$644$		0			0
$645$		−	1.61164i		−	0.0634583i
$646$		0			0
$647$	−12.1505	−	21.0454i	−0.477687	−	0.827379i	0.521986	−	0.852954i	$-0.325191\pi$
$647$	−12.1505	−	21.0454i	−0.477687	−	0.827379i	−0.999673	+	0.0255756i	$0.991858\pi$
$648$		0			0
$649$	34.0236			1.33554
$650$		0			0
$651$	−4.91093			−0.192474
$652$		0			0
$653$	2.73619	+	4.73922i	0.107075	+	0.185460i	0.914584	−	0.404395i	$-0.132518\pi$
$653$	2.73619	+	4.73922i	0.107075	+	0.185460i	−0.807509	+	0.589856i	$0.799185\pi$
$654$		0			0
$655$			37.5828i			1.46848i
$656$		0			0
$657$	19.4407	+	11.2241i	0.758454	+	0.437893i
$658$		0			0
$659$	−0.668430	+	1.15775i	−0.0260383	+	0.0450997i	−0.878751	−	0.477281i	$-0.841623\pi$
$659$	−0.668430	+	1.15775i	−0.0260383	+	0.0450997i	0.852713	+	0.522380i	$0.174956\pi$
$660$		0			0
$661$	36.5902	−	21.1254i	1.42319	−	0.821682i	0.426624	−	0.904429i	$-0.359703\pi$
$661$	36.5902	−	21.1254i	1.42319	−	0.821682i	0.996571	+	0.0827471i	$0.0263694\pi$
$662$		0			0
$663$	14.9607	+	16.6301i	0.581026	+	0.645859i
$664$		0			0
$665$	−1.23254	+	0.711606i	−0.0477958	+	0.0275949i
$666$		0			0
$667$	−24.4759	+	42.3935i	−0.947711	+	1.64148i
$668$		0			0
$669$	7.79775	+	4.50204i	0.301479	+	0.174059i
$670$		0			0
$671$		−	40.7292i		−	1.57233i
$672$		0			0
$673$	−1.50029	−	2.59858i	−0.0578320	−	0.100168i	0.835660	−	0.549247i	$-0.185085\pi$
$673$	−1.50029	−	2.59858i	−0.0578320	−	0.100168i	−0.893492	+	0.449079i	$0.851752\pi$
$674$		0			0
$675$	−4.65150			−0.179036
$676$		0			0
$677$	−8.36881			−0.321639			−0.160820	−	0.986984i	$-0.551414\pi$
$677$	−8.36881			−0.321639			−0.160820	+	0.986984i	$0.551414\pi$
$678$		0			0
$679$	−0.767994	−	1.33021i	−0.0294729	−	0.0510486i
$680$		0			0
$681$			16.1038i			0.617100i
$682$		0			0
$683$	27.4304	+	15.8369i	1.04959	+	0.605984i	0.922536	−	0.385911i	$-0.126113\pi$
$683$	27.4304	+	15.8369i	1.04959	+	0.605984i	0.127059	+	0.991895i	$0.459446\pi$
$684$		0			0
$685$	−13.3279	+	23.0846i	−0.509233	+	0.882017i
$686$		0			0
$687$	6.97457	−	4.02677i	0.266097	−	0.153631i
$688$		0			0
$689$	24.2153	+	26.9173i	0.922528	+	1.02547i
$690$		0			0
$691$	9.92153	−	5.72820i	0.377433	−	0.217911i	−0.299268	−	0.954169i	$-0.596742\pi$
$691$	9.92153	−	5.72820i	0.377433	−	0.217911i	0.676701	+	0.736258i	$0.263409\pi$
$692$		0			0
$693$	5.73014	−	9.92489i	0.217670	−	0.377015i
$694$		0			0
$695$	21.1044	+	12.1846i	0.800534	+	0.462189i
$696$		0			0
$697$			13.2960i			0.503622i
$698$		0			0
$699$	6.57033	+	11.3801i	0.248513	+	0.430436i
$700$		0			0
$701$	34.2672			1.29426			0.647128	−	0.762382i	$-0.275970\pi$
$701$	34.2672			1.29426			0.647128	+	0.762382i	$0.275970\pi$
$702$		0			0
$703$	−1.18196			−0.0445786
$704$		0			0
$705$	−5.42194	−	9.39107i	−0.204202	−	0.353688i
$706$		0			0
$707$		−	15.7779i		−	0.593388i
$708$		0			0
$709$	33.3838	+	19.2742i	1.25376	+	0.723857i	0.971853	−	0.235586i	$-0.0757010\pi$
$709$	33.3838	+	19.2742i	1.25376	+	0.723857i	0.281903	+	0.959443i	$0.409034\pi$
$710$		0			0
$711$	1.02972	−	1.78353i	0.0386177	−	0.0668878i
$712$		0			0
$713$	20.7180	−	11.9616i	0.775896	−	0.447964i
$714$		0			0
$715$	−13.1784	+	40.4991i	−0.492845	+	1.51458i
$716$		0			0
$717$	−14.0447	+	8.10872i	−0.524509	+	0.302826i
$718$		0			0
$719$	−16.6621	+	28.8596i	−0.621392	+	1.07628i	0.367834	+	0.929891i	$0.380099\pi$
$719$	−16.6621	+	28.8596i	−0.621392	+	1.07628i	−0.989227	+	0.146392i	$0.953234\pi$
$720$		0			0
$721$	0.0573094	+	0.0330876i	0.00213432	+	0.00123225i
$722$		0			0
$723$			24.7061i			0.918829i
$724$		0			0
$725$	−4.53011	−	7.84639i	−0.168244	−	0.291408i
$726$		0			0
$727$	1.38332			0.0513045			0.0256523	−	0.999671i	$-0.491834\pi$
$727$	1.38332			0.0513045			0.0256523	+	0.999671i	$0.491834\pi$
$728$		0			0
$729$	14.0651			0.520930
$730$		0			0
$731$	−2.37937	−	4.12119i	−0.0880042	−	0.152428i
$732$		0			0
$733$		−	1.82716i		−	0.0674877i	−0.999431	−	0.0337439i	$-0.989257\pi$
$733$		−	1.82716i		−	0.0674877i	0.999431	−	0.0337439i	$-0.0107430\pi$
$734$		0			0
$735$	1.78417	+	1.03009i	0.0658100	+	0.0379954i
$736$		0			0
$737$	−32.5279	+	56.3400i	−1.19818	+	2.07531i
$738$		0			0
$739$	6.76651	−	3.90665i	0.248910	−	0.143708i	−0.370355	−	0.928890i	$-0.620764\pi$
$739$	6.76651	−	3.90665i	0.248910	−	0.143708i	0.619265	+	0.785182i	$0.287431\pi$
$740$		0			0
$741$	1.92611	−	1.73276i	0.0707574	−	0.0636546i
$742$		0			0
$743$	14.3038	−	8.25828i	0.524754	−	0.302967i	−0.214123	−	0.976807i	$-0.568689\pi$
$743$	14.3038	−	8.25828i	0.524754	−	0.302967i	0.738878	+	0.673840i	$0.235356\pi$
$744$		0			0
$745$	23.9318	−	41.4510i	0.876792	−	1.51865i
$746$		0			0
$747$	5.16663	+	2.98296i	0.189037	+	0.109141i
$748$		0			0
$749$		−	4.90488i		−	0.179221i
$750$		0			0
$751$	3.63615	+	6.29801i	0.132685	+	0.229817i	0.924711	−	0.380670i	$-0.124307\pi$
$751$	3.63615	+	6.29801i	0.132685	+	0.229817i	−0.792026	+	0.610488i	$0.790973\pi$
$752$		0			0
$753$	−24.1066			−0.878494
$754$		0			0
$755$	−36.3907			−1.32439
$756$		0			0
$757$	−10.0239	−	17.3618i	−0.364324	−	0.631027i	0.624344	−	0.781150i	$-0.285366\pi$
$757$	−10.0239	−	17.3618i	−0.364324	−	0.631027i	−0.988667	+	0.150123i	$0.952033\pi$
$758$		0			0
$759$		−	29.6299i		−	1.07550i
$760$		0			0
$761$	−36.2244	−	20.9142i	−1.31313	−	0.758138i	−0.330520	−	0.943799i	$-0.607224\pi$
$761$	−36.2244	−	20.9142i	−1.31313	−	0.758138i	−0.982614	+	0.185661i	$0.940557\pi$
$762$		0			0
$763$	−6.87455	+	11.9071i	−0.248875	+	0.431065i
$764$		0			0
$765$	20.8561	−	12.0413i	0.754054	−	0.435353i
$766$		0			0
$767$	4.35279	+	20.5221i	0.157170	+	0.741010i
$768$		0			0
$769$	12.4644	−	7.19634i	0.449479	−	0.259507i	−0.258131	−	0.966110i	$-0.583107\pi$
$769$	12.4644	−	7.19634i	0.449479	−	0.259507i	0.707610	+	0.706603i	$0.249773\pi$
$770$		0			0
$771$	4.45521	−	7.71664i	0.160450	−	0.277908i
$772$		0			0
$773$	−0.184965	−	0.106790i	−0.00665272	−	0.00384095i	0.496670	−	0.867939i	$-0.334556\pi$
$773$	−0.184965	−	0.106790i	−0.00665272	−	0.00384095i	−0.503323	+	0.864099i	$0.667889\pi$
$774$		0			0
$775$			4.42780i			0.159051i
$776$		0			0
$777$	0.855478	+	1.48173i	0.0306901	+	0.0531568i
$778$		0			0
$779$	1.53995			0.0551746
$780$		0			0
$781$	72.8302			2.60607
$782$		0			0
$783$	24.9202	+	43.1631i	0.890576	+	1.54252i
$784$		0			0
$785$			26.9077i			0.960376i
$786$		0			0
$787$	11.5580	+	6.67299i	0.411996	+	0.237866i	0.691647	−	0.722236i	$-0.256885\pi$
$787$	11.5580	+	6.67299i	0.411996	+	0.237866i	−0.279651	+	0.960102i	$0.590219\pi$
$788$		0			0
$789$	3.78465	−	6.55520i	0.134737	−	0.233371i
$790$		0			0
$791$	−2.53882	+	1.46579i	−0.0902702	+	0.0521175i
$792$		0			0
$793$	24.5667	−	5.21066i	0.872389	−	0.185036i
$794$		0			0
$795$	−17.9164	+	10.3441i	−0.635430	+	0.366866i
$796$		0			0
$797$	21.3259	−	36.9376i	0.755403	−	1.30840i	−0.189770	−	0.981829i	$-0.560774\pi$
$797$	21.3259	−	36.9376i	0.755403	−	1.30840i	0.945174	−	0.326569i	$-0.105892\pi$
$798$		0			0
$799$	−27.7293	−	16.0095i	−0.980992	−	0.566376i
$800$		0			0
$801$			3.03812i			0.107347i
$802$		0			0
$803$	−33.4893	−	58.0052i	−1.18181	−	2.04696i
$804$		0			0
$805$	−10.0360			−0.353721
$806$		0			0
$807$	28.8576			1.01584
$808$		0			0
$809$	−19.1725	−	33.2077i	−0.674067	−	1.16752i	−0.976741	−	0.214425i	$-0.931212\pi$
$809$	−19.1725	−	33.2077i	−0.674067	−	1.16752i	0.302673	−	0.953094i	$-0.402121\pi$
$810$		0			0
$811$			16.6127i			0.583352i	0.956517	+	0.291676i	$0.0942129\pi$
$811$			16.6127i			0.583352i	−0.956517	+	0.291676i	$0.905787\pi$
$812$		0			0
$813$	−10.4472	−	6.03167i	−0.366398	−	0.211540i
$814$		0			0
$815$	12.7567	−	22.0953i	0.446849	−	0.773965i
$816$		0			0
$817$	−0.477320	+	0.275581i	−0.0166993	+	0.00964135i
$818$		0			0
$819$	6.71950	+	2.18652i	0.234798	+	0.0764033i
$820$		0			0
$821$	−14.8271	+	8.56041i	−0.517468	+	0.298760i	−0.735898	−	0.677092i	$-0.763240\pi$
$821$	−14.8271	+	8.56041i	−0.517468	+	0.298760i	0.218430	+	0.975853i	$0.429906\pi$
$822$		0			0
$823$	18.9613	−	32.8419i	0.660948	−	1.14480i	−0.319419	−	0.947614i	$-0.603488\pi$
$823$	18.9613	−	32.8419i	0.660948	−	1.14480i	0.980367	−	0.197182i	$-0.0631789\pi$
$824$		0			0
$825$	4.74932	+	2.74202i	0.165350	+	0.0954650i
$826$		0			0
$827$		−	45.5918i		−	1.58538i	−0.609624	−	0.792691i	$-0.708679\pi$
$827$		−	45.5918i		−	1.58538i	0.609624	−	0.792691i	$-0.291321\pi$
$828$		0			0
$829$	−1.04770	−	1.81467i	−0.0363882	−	0.0630262i	0.847258	−	0.531182i	$-0.178252\pi$
$829$	−1.04770	−	1.81467i	−0.0363882	−	0.0630262i	−0.883646	+	0.468156i	$0.844919\pi$
$830$		0			0
$831$	−0.216705			−0.00751742
$832$		0			0
$833$	6.08315			0.210769
$834$		0			0
$835$	18.7729	+	32.5157i	0.649665	+	1.12525i
$836$		0			0
$837$		−	24.3574i		−	0.841915i
$838$		0			0
$839$	14.3831	+	8.30408i	0.496560	+	0.286689i	0.727292	−	0.686329i	$-0.240779\pi$
$839$	14.3831	+	8.30408i	0.496560	+	0.286689i	−0.230732	+	0.973017i	$0.574112\pi$
$840$		0			0
$841$	−34.0398	+	58.9586i	−1.17378	+	2.03305i
$842$		0			0
$843$	−17.8704	+	10.3175i	−0.615489	+	0.355353i
$844$		0			0
$845$	−26.1139	−	2.76762i	−0.898346	−	0.0952091i
$846$		0			0
$847$	−20.0866	+	11.5970i	−0.690184	+	0.398478i
$848$		0			0
$849$	10.3593	−	17.9429i	0.355532	−	0.615799i
$850$		0			0
$851$	−7.21811	−	4.16738i	−0.247434	−	0.142856i
$852$		0			0
$853$			12.2314i			0.418795i	0.977831	+	0.209397i	$0.0671502\pi$
$853$			12.2314i			0.418795i	−0.977831	+	0.209397i	$0.932850\pi$
$854$		0			0
$855$	−1.39463	−	2.41557i	−0.0476954	−	0.0826109i
$856$		0			0
$857$	50.3302			1.71925			0.859623	−	0.510929i	$-0.170699\pi$
$857$	50.3302			1.71925			0.859623	+	0.510929i	$0.170699\pi$
$858$		0			0
$859$	51.4997			1.75715			0.878573	−	0.477608i	$-0.158496\pi$
$859$	51.4997			1.75715			0.878573	+	0.477608i	$0.158496\pi$
$860$		0			0
$861$	−1.11458	−	1.93052i	−0.0379849	−	0.0657918i
$862$		0			0
$863$		−	2.82545i		−	0.0961793i	−0.998843	−	0.0480896i	$-0.984687\pi$
$863$		−	2.82545i		−	0.0961793i	0.998843	−	0.0480896i	$-0.0153133\pi$
$864$		0			0
$865$	−12.6120	−	7.28151i	−0.428819	−	0.247579i
$866$		0			0
$867$	−10.2012	+	17.6691i	−0.346453	+	0.600073i
$868$		0			0
$869$	−5.32153	+	3.07239i	−0.180520	+	0.104224i
$870$		0			0
$871$	−38.1442	−	12.4121i	−1.29247	−	0.420569i
$872$		0			0
$873$	2.60699	−	1.50514i	0.0882331	−	0.0509414i
$874$		0			0
$875$	5.97878	−	10.3556i	0.202120	−	0.350082i
$876$		0			0
$877$	9.67508	+	5.58591i	0.326704	+	0.188623i	0.654377	−	0.756169i	$-0.272931\pi$
$877$	9.67508	+	5.58591i	0.326704	+	0.188623i	−0.327673	+	0.944791i	$0.606264\pi$
$878$		0			0
$879$			13.9528i			0.470616i
$880$		0			0
$881$	−10.8598	−	18.8098i	−0.365877	−	0.633718i	0.623039	−	0.782190i	$-0.285898\pi$
$881$	−10.8598	−	18.8098i	−0.365877	−	0.633718i	−0.988916	+	0.148473i	$0.952564\pi$
$882$		0			0
$883$	−48.0644			−1.61750			−0.808748	−	0.588155i	$-0.799854\pi$
$883$	−48.0644			−1.61750			−0.808748	+	0.588155i	$0.799854\pi$
$884$		0			0
$885$	−11.9870			−0.402938
$886$		0			0
$887$	−16.6014	−	28.7544i	−0.557420	−	0.965480i	−0.997711	−	0.0676244i	$-0.978458\pi$
$887$	−16.6014	−	28.7544i	−0.557420	−	0.965480i	0.440291	−	0.897855i	$-0.354875\pi$
$888$		0			0
$889$			5.73463i			0.192333i
$890$		0			0
$891$	3.64858	+	2.10651i	0.122232	+	0.0705707i
$892$		0			0
$893$	−1.85424	+	3.21163i	−0.0620497	+	0.107473i
$894$		0			0
$895$	−36.2859	+	20.9497i	−1.21290	+	0.700271i
$896$		0			0
$897$	17.8719	−	3.79068i	0.596727	−	0.126567i
$898$		0			0
$899$	41.0873	−	23.7218i	1.37034	−	0.791165i
$900$		0			0
$901$	−30.5432	+	52.9024i	−1.01754	+	1.76243i
$902$		0			0
$903$	0.690947	+	0.398918i	0.0229933	+	0.0132752i
$904$		0			0
$905$			30.8275i			1.02474i
$906$		0			0
$907$	−8.44403	−	14.6255i	−0.280379	−	0.485631i	0.691099	−	0.722760i	$-0.257127\pi$
$907$	−8.44403	−	14.6255i	−0.280379	−	0.485631i	−0.971478	+	0.237129i	$0.923794\pi$
$908$		0			0
$909$	30.9221			1.02562
$910$		0			0
$911$	3.77644			0.125119			0.0625595	−	0.998041i	$-0.480074\pi$
$911$	3.77644			0.125119			0.0625595	+	0.998041i	$0.480074\pi$
$912$		0			0
$913$	−8.90024	−	15.4157i	−0.294555	−	0.510184i
$914$		0			0
$915$			14.3494i			0.474378i
$916$		0			0
$917$	−16.1126	−	9.30260i	−0.532084	−	0.307199i
$918$		0			0
$919$	24.8491	−	43.0399i	0.819696	−	1.41976i	−0.0862102	−	0.996277i	$-0.527476\pi$
$919$	24.8491	−	43.0399i	0.819696	−	1.41976i	0.905906	−	0.423478i	$-0.139191\pi$
$920$		0			0
$921$	−8.09989	+	4.67647i	−0.266900	+	0.154095i
$922$		0			0
$923$	9.31748	+	43.9291i	0.306689	+	1.44594i
$924$		0			0
$925$	1.33596	−	0.771318i	0.0439262	−	0.0253608i
$926$		0			0
$927$	−0.0648464	+	0.112317i	−0.00212983	+	0.00368898i
$928$		0			0
$929$	−35.5455	−	20.5222i	−1.16621	−	0.673311i	−0.213425	−	0.976959i	$-0.568462\pi$
$929$	−35.5455	−	20.5222i	−1.16621	−	0.673311i	−0.952784	+	0.303648i	$0.901795\pi$
$930$		0			0
$931$		−	0.704556i		−	0.0230909i
$932$		0			0
$933$	10.0470	+	17.4018i	0.328923	+	0.569711i
$934$		0			0
$935$	−71.8551			−2.34991
$936$		0			0
$937$	24.0211			0.784735			0.392368	−	0.919808i	$-0.371656\pi$
$937$	24.0211			0.784735			0.392368	+	0.919808i	$0.371656\pi$
$938$		0			0
$939$	9.57579	+	16.5857i	0.312494	+	0.541255i
$940$		0			0
$941$		−	30.9571i		−	1.00917i	−0.863361	−	0.504586i	$-0.831645\pi$
$941$		−	30.9571i		−	1.00917i	0.863361	−	0.504586i	$-0.168355\pi$
$942$		0			0
$943$	9.40433	+	5.42959i	0.306247	+	0.176812i
$944$		0			0
$945$	−5.10907	+	8.84917i	−0.166198	+	0.287864i
$946$		0			0
$947$	−49.4060	+	28.5246i	−1.60548	+	0.926924i	−0.615115	+	0.788437i	$0.710891\pi$
$947$	−49.4060	+	28.5246i	−1.60548	+	0.926924i	−0.990364	+	0.138487i	$0.955776\pi$
$948$		0			0
$949$	30.7027	−	27.6207i	0.996650	−	0.896604i
$950$		0			0
$951$	14.6354	−	8.44977i	0.474586	−	0.274002i
$952$		0			0
$953$	−21.7078	+	37.5989i	−0.703183	+	1.21795i	0.264160	+	0.964479i	$0.414905\pi$
$953$	−21.7078	+	37.5989i	−0.703183	+	1.21795i	−0.967343	+	0.253470i	$0.918428\pi$
$954$		0			0
$955$	−5.58277	−	3.22321i	−0.180654	−	0.104301i
$956$		0			0
$957$		−	58.7610i		−	1.89947i
$958$		0			0
$959$	−6.59793	−	11.4279i	−0.213058	−	0.369028i
$960$		0			0
$961$	7.81399			0.252064
$962$		0			0
$963$	9.61278			0.309767
$964$		0			0
$965$	10.5480	+	18.2696i	0.339551	+	0.588119i
$966$		0			0
$967$		−	26.4842i		−	0.851675i	−0.904800	−	0.425837i	$-0.859980\pi$
$967$		−	26.4842i		−	0.851675i	0.904800	−	0.425837i	$-0.140020\pi$
$968$		0			0
$969$	3.78552	+	2.18557i	0.121608	+	0.0702106i
$970$		0			0
$971$	0.686676	−	1.18936i	0.0220365	−	0.0381683i	−0.854797	−	0.518963i	$-0.826318\pi$
$971$	0.686676	−	1.18936i	0.0220365	−	0.0381683i	0.876833	+	0.480794i	$0.159652\pi$
$972$		0			0
$973$	−10.4476	+	6.03195i	−0.334936	+	0.193375i
$974$		0			0
$975$	−1.04631	+	3.21546i	−0.0335087	+	0.102977i
$976$		0			0
$977$	5.57241	−	3.21723i	0.178277	−	0.102928i	−0.408206	−	0.912890i	$-0.633845\pi$
$977$	5.57241	−	3.21723i	0.178277	−	0.102928i	0.586483	+	0.809962i	$0.300512\pi$
$978$		0			0
$979$	4.53241	−	7.85036i	0.144856	−	0.250899i
$980$		0			0
$981$	−23.3359	−	13.4730i	−0.745058	−	0.430159i
$982$		0			0
$983$			25.2739i			0.806113i	0.915175	+	0.403056i	$0.132052\pi$
$983$			25.2739i			0.806113i	−0.915175	+	0.403056i	$0.867948\pi$
$984$		0			0
$985$	−3.48403	−	6.03451i	−0.111010	−	0.192276i
$986$		0			0
$987$	5.36822			0.170872
$988$		0			0
$989$	−3.88659			−0.123586
$990$		0			0
$991$	−24.2738	−	42.0434i	−0.771082	−	1.33555i	−0.936970	−	0.349409i	$-0.886382\pi$
$991$	−24.2738	−	42.0434i	−0.771082	−	1.33555i	0.165888	−	0.986145i	$-0.446951\pi$
$992$		0			0
$993$			19.7728i			0.627469i
$994$		0			0
$995$	−8.74018	−	5.04614i	−0.277082	−	0.159973i
$996$		0			0
$997$	9.21146	−	15.9547i	0.291730	−	0.505291i	−0.682489	−	0.730896i	$-0.739102\pi$
$997$	9.21146	−	15.9547i	0.291730	−	0.505291i	0.974219	+	0.225605i	$0.0724358\pi$
$998$		0			0
$999$	−7.34915	+	4.24303i	−0.232517	+	0.134244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.bm.c.673.5	yes	24
4.3	odd	2		1456.2.cc.g.673.8		24
13.2	odd	12		9464.2.a.bl.1.8		12
13.4	even	6	inner	728.2.bm.c.225.5	✓	24
13.11	odd	12		9464.2.a.bm.1.8		12
52.43	odd	6		1456.2.cc.g.225.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.5	✓	24	13.4	even	6	inner
728.2.bm.c.673.5	yes	24	1.1	even	1	trivial
1456.2.cc.g.225.8		24	52.43	odd	6
1456.2.cc.g.673.8		24	4.3	odd	2
9464.2.a.bl.1.8		12	13.2	odd	12
9464.2.a.bm.1.8		12	13.11	odd	12

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.509942 - 0.883245i) q^{3} +2.02001i q^{5} +(-0.866025 - 0.500000i) q^{7} +(0.979919 - 1.69727i) q^{9} +(-5.06414 + 2.92378i) q^{11} +(-2.41142 - 2.68049i) q^{13} +(1.78417 - 1.03009i) q^{15} +(3.04158 - 5.26816i) q^{17} +(-0.610163 - 0.352278i) q^{19} +1.01988i q^{21} +(-2.48413 - 4.30265i) q^{23} +0.919550 q^{25} -5.05846 q^{27} +(-4.92645 - 8.53286i) q^{29} +4.81518i q^{31} +(5.16483 + 2.98192i) q^{33} +(1.01001 - 1.74938i) q^{35} +(1.45284 - 0.838799i) q^{37} +(-1.13785 + 3.49677i) q^{39} +(-1.89288 + 1.09285i) q^{41} +(0.391141 - 0.677476i) q^{43} +(3.42850 + 1.97945i) q^{45} -5.26356i q^{47} +(0.500000 + 0.866025i) q^{49} -6.20411 q^{51} -10.0419 q^{53} +(-5.90608 - 10.2296i) q^{55} +0.718565i q^{57} +(-5.03891 - 2.90921i) q^{59} +(-3.48257 + 6.03200i) q^{61} +(-1.69727 + 0.979919i) q^{63} +(5.41463 - 4.87110i) q^{65} +(9.63479 - 5.56265i) q^{67} +(-2.53353 + 4.38820i) q^{69} +(-10.7862 - 6.22739i) q^{71} +11.4541i q^{73} +(-0.468917 - 0.812188i) q^{75} +5.84756 q^{77} +1.05083 q^{79} +(-0.360237 - 0.623949i) q^{81} +3.04409i q^{83} +(10.6418 + 6.14402i) q^{85} +(-5.02440 + 8.70252i) q^{87} +(-1.34250 + 0.775094i) q^{89} +(0.748104 + 3.52709i) q^{91} +(4.25299 - 2.45546i) q^{93} +(0.711606 - 1.23254i) q^{95} +(1.33021 + 0.767994i) q^{97} +11.4603i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} - 18 q^{9} + 12 q^{11} + 8 q^{17} - 12 q^{19} + 2 q^{23} - 28 q^{25} - 20 q^{27} + 2 q^{29} - 18 q^{33} - 8 q^{35} + 60 q^{37} + 18 q^{39} - 6 q^{41} + 24 q^{43} - 72 q^{45} + 12 q^{49} - 72 q^{51}+ \cdots - 54 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 - 18 * q^9 + 12 * q^11 + 8 * q^17 - 12 * q^19 + 2 * q^23 - 28 * q^25 - 20 * q^27 + 2 * q^29 - 18 * q^33 - 8 * q^35 + 60 * q^37 + 18 * q^39 - 6 * q^41 + 24 * q^43 - 72 * q^45 + 12 * q^49 - 72 * q^51 - 48 * q^53 - 44 * q^55 - 12 * q^59 - 30 * q^61 + 12 * q^63 + 10 * q^65 + 78 * q^67 + 36 * q^69 - 36 * q^71 + 22 * q^75 + 4 * q^77 + 20 * q^79 - 40 * q^81 - 6 * q^85 - 20 * q^87 + 108 * q^89 + 6 * q^91 + 30 * q^93 + 18 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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