LMFDB - Embedded newform 684.3.s.a.445.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.37
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.94477 - 0.573008i) q^{3} +(1.51878 + 2.63060i) q^{5} +(-4.58926 - 7.94883i) q^{7} +(8.34332 - 3.37475i) q^{9} +O(q^{10})$	\(q+(2.94477 - 0.573008i) q^{3} +(1.51878 + 2.63060i) q^{5} +(-4.58926 - 7.94883i) q^{7} +(8.34332 - 3.37475i) q^{9} +(8.59704 + 14.8905i) q^{11} +16.7261i q^{13} +(5.97981 + 6.87625i) q^{15} +(-2.67174 + 4.62759i) q^{17} +(5.04896 + 18.3169i) q^{19} +(-18.0690 - 20.7778i) q^{21} +3.30087 q^{23} +(7.88662 - 13.6600i) q^{25} +(22.6354 - 14.7186i) q^{27} +(43.0837 + 24.8744i) q^{29} +(-22.3214 - 12.8873i) q^{31} +(33.8487 + 38.9229i) q^{33} +(13.9401 - 24.1450i) q^{35} -66.3367i q^{37} +(9.58421 + 49.2546i) q^{39} +(62.8325 - 36.2763i) q^{41} +31.5007 q^{43} +(21.5493 + 16.8225i) q^{45} +(-17.1505 + 29.7056i) q^{47} +(-17.6225 + 30.5232i) q^{49} +(-5.21601 + 15.1581i) q^{51} +(-9.05628 + 5.22865i) q^{53} +(-26.1140 + 45.2308i) q^{55} +(25.3637 + 51.0459i) q^{57} +(-6.59670 + 3.80861i) q^{59} +(3.93471 - 6.81513i) q^{61} +(-65.1150 - 50.8320i) q^{63} +(-43.9999 + 25.4033i) q^{65} +106.716i q^{67} +(9.72031 - 1.89143i) q^{69} +(-63.9663 - 36.9310i) q^{71} +(-4.59392 + 7.95690i) q^{73} +(15.3970 - 44.7447i) q^{75} +(78.9080 - 136.673i) q^{77} +129.531i q^{79} +(58.2221 - 56.3133i) q^{81} +(-62.6598 - 108.530i) q^{83} -16.2311 q^{85} +(141.125 + 48.5620i) q^{87} +(-98.3402 + 56.7767i) q^{89} +(132.953 - 76.7606i) q^{91} +(-73.1158 - 25.1597i) q^{93} +(-40.5162 + 41.1011i) q^{95} +27.3005i q^{97} +(121.980 + 95.2235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	2.94477	−	0.573008i	0.981590	−	0.191003i
$3$	2.94477	−	0.573008i	0.981590	−	0.191003i
$4$		0			0
$5$	1.51878	+	2.63060i	0.303756	+	0.526121i	0.976984	−	0.213315i	$-0.0684259\pi$
$5$	1.51878	+	2.63060i	0.303756	+	0.526121i	−0.673228	+	0.739435i	$0.735093\pi$
$6$		0			0
$7$	−4.58926	−	7.94883i	−0.655608	−	1.13555i	−0.981741	−	0.190223i	$-0.939079\pi$
$7$	−4.58926	−	7.94883i	−0.655608	−	1.13555i	0.326133	−	0.945324i	$-0.394254\pi$
$8$		0			0
$9$	8.34332	−	3.37475i	0.927036	−	0.374972i
$10$		0			0
$11$	8.59704	+	14.8905i	0.781549	+	1.35368i	0.931039	+	0.364919i	$0.118903\pi$
$11$	8.59704	+	14.8905i	0.781549	+	1.35368i	−0.149490	+	0.988763i	$0.547763\pi$
$12$		0			0
$13$			16.7261i			1.28663i	0.765603	+	0.643313i	$0.222441\pi$
$13$			16.7261i			1.28663i	−0.765603	+	0.643313i	$0.777559\pi$
$14$		0			0
$15$	5.97981	+	6.87625i	0.398654	+	0.458416i
$16$		0			0
$17$	−2.67174	+	4.62759i	−0.157161	+	0.272211i	−0.933844	−	0.357681i	$-0.883568\pi$
$17$	−2.67174	+	4.62759i	−0.157161	+	0.272211i	0.776683	+	0.629892i	$0.216901\pi$
$18$		0			0
$19$	5.04896	+	18.3169i	0.265734	+	0.964046i
$19$	5.04896	+	18.3169i	0.265734	+	0.964046i
$20$		0			0
$21$	−18.0690	−	20.7778i	−0.860430	−	0.989418i
$22$		0			0
$23$	3.30087			0.143516			0.0717581	−	0.997422i	$-0.477139\pi$
$23$	3.30087			0.143516			0.0717581	+	0.997422i	$0.477139\pi$
$24$		0			0
$25$	7.88662	−	13.6600i	0.315465	−	0.546401i
$26$		0			0
$27$	22.6354	−	14.7186i	0.838348	−	0.545135i
$28$		0			0
$29$	43.0837	+	24.8744i	1.48564	+	0.857737i	0.999866	−	0.0163447i	$-0.00520291\pi$
$29$	43.0837	+	24.8744i	1.48564	+	0.857737i	0.485778	+	0.874082i	$0.338536\pi$
$30$		0			0
$31$	−22.3214	−	12.8873i	−0.720045	−	0.415718i	0.0947243	−	0.995504i	$-0.469803\pi$
$31$	−22.3214	−	12.8873i	−0.720045	−	0.415718i	−0.814769	+	0.579785i	$0.803136\pi$
$32$		0			0
$33$	33.8487	+	38.9229i	1.02572	+	1.17948i
$34$		0			0
$35$	13.9401	−	24.1450i	0.398290	−	0.689858i
$36$		0			0
$37$		−	66.3367i		−	1.79288i	−0.443162	−	0.896441i	$-0.646144\pi$
$37$		−	66.3367i		−	1.79288i	0.443162	−	0.896441i	$-0.353856\pi$
$38$		0			0
$39$	9.58421	+	49.2546i	0.245749	+	1.26294i
$40$		0			0
$41$	62.8325	−	36.2763i	1.53250	−	0.884789i	0.533253	−	0.845956i	$-0.320969\pi$
$41$	62.8325	−	36.2763i	1.53250	−	0.884789i	0.999246	−	0.0388329i	$-0.0123640\pi$
$42$		0			0
$43$	31.5007			0.732574			0.366287	−	0.930502i	$-0.380629\pi$
$43$	31.5007			0.732574			0.366287	+	0.930502i	$0.380629\pi$
$44$		0			0
$45$	21.5493	+	16.8225i	0.478873	+	0.373833i
$46$		0			0
$47$	−17.1505	+	29.7056i	−0.364905	+	0.632033i	−0.988761	−	0.149506i	$-0.952232\pi$
$47$	−17.1505	+	29.7056i	−0.364905	+	0.632033i	0.623856	+	0.781539i	$0.285565\pi$
$48$		0			0
$49$	−17.6225	+	30.5232i	−0.359644	+	0.622921i
$50$		0			0
$51$	−5.21601	+	15.1581i	−0.102275	+	0.297218i
$52$		0			0
$53$	−9.05628	+	5.22865i	−0.170873	+	0.0986537i	−0.582998	−	0.812474i	$-0.698120\pi$
$53$	−9.05628	+	5.22865i	−0.170873	+	0.0986537i	0.412124	+	0.911128i	$0.364787\pi$
$54$		0			0
$55$	−26.1140	+	45.2308i	−0.474800	+	0.822378i
$56$		0			0
$57$	25.3637	+	51.0459i	0.444977	+	0.895542i
$58$		0			0
$59$	−6.59670	+	3.80861i	−0.111808	+	0.0645526i	−0.554861	−	0.831943i	$-0.687229\pi$
$59$	−6.59670	+	3.80861i	−0.111808	+	0.0645526i	0.443053	+	0.896495i	$0.353895\pi$
$60$		0			0
$61$	3.93471	−	6.81513i	0.0645035	−	0.111723i	−0.831970	−	0.554820i	$-0.812787\pi$
$61$	3.93471	−	6.81513i	0.0645035	−	0.111723i	0.896474	+	0.443097i	$0.146120\pi$
$62$		0			0
$63$	−65.1150	−	50.8320i	−1.03357	−	0.806858i
$64$		0			0
$65$	−43.9999	+	25.4033i	−0.676921	+	0.390820i
$66$		0			0
$67$			106.716i			1.59277i	0.604789	+	0.796386i	$0.293257\pi$
$67$			106.716i			1.59277i	−0.604789	+	0.796386i	$0.706743\pi$
$68$		0			0
$69$	9.72031	−	1.89143i	0.140874	−	0.0274120i
$70$		0			0
$71$	−63.9663	−	36.9310i	−0.900934	−	0.520154i	−0.0234308	−	0.999725i	$-0.507459\pi$
$71$	−63.9663	−	36.9310i	−0.900934	−	0.520154i	−0.877503	+	0.479571i	$0.840792\pi$
$72$		0			0
$73$	−4.59392	+	7.95690i	−0.0629304	+	0.108999i	−0.895774	−	0.444510i	$-0.853378\pi$
$73$	−4.59392	+	7.95690i	−0.0629304	+	0.108999i	0.832844	+	0.553508i	$0.186711\pi$
$74$		0			0
$75$	15.3970	−	44.7447i	0.205293	−	0.596596i
$76$		0			0
$77$	78.9080	−	136.673i	1.02478	−	1.77497i
$78$		0			0
$79$			129.531i			1.63963i	0.572630	+	0.819814i	$0.305923\pi$
$79$			129.531i			1.63963i	−0.572630	+	0.819814i	$0.694077\pi$
$80$		0			0
$81$	58.2221	−	56.3133i	0.718792	−	0.695225i
$82$		0			0
$83$	−62.6598	−	108.530i	−0.754937	−	1.30759i	−0.945406	−	0.325896i	$-0.894334\pi$
$83$	−62.6598	−	108.530i	−0.754937	−	1.30759i	0.190469	−	0.981693i	$-0.438999\pi$
$84$		0			0
$85$	−16.2311			−0.190954
$86$		0			0
$87$	141.125	+	48.5620i	1.62212	+	0.558184i
$88$		0			0
$89$	−98.3402	+	56.7767i	−1.10495	+	0.637941i	−0.937516	−	0.347943i	$-0.886880\pi$
$89$	−98.3402	+	56.7767i	−1.10495	+	0.637941i	−0.167430	+	0.985884i	$0.553547\pi$
$90$		0			0
$91$	132.953	−	76.7606i	1.46102	−	0.843523i
$92$		0			0
$93$	−73.1158	−	25.1597i	−0.786192	−	0.270534i
$94$		0			0
$95$	−40.5162	+	41.1011i	−0.426486	+	0.432643i
$96$		0			0
$97$			27.3005i			0.281448i	0.990049	+	0.140724i	$0.0449430\pi$
$97$			27.3005i			0.281448i	−0.990049	+	0.140724i	$0.955057\pi$
$98$		0			0
$99$	121.980	+	95.2235i	1.23212	+	0.961853i
$100$		0			0
$101$	−7.89347	+	13.6719i	−0.0781532	+	0.135365i	−0.902453	−	0.430788i	$-0.858236\pi$
$101$	−7.89347	+	13.6719i	−0.0781532	+	0.135365i	0.824300	+	0.566153i	$0.191569\pi$
$102$		0			0
$103$	80.7901	+	46.6442i	0.784370	+	0.452856i	0.837977	−	0.545706i	$-0.183738\pi$
$103$	80.7901	+	46.6442i	0.784370	+	0.452856i	−0.0536067	+	0.998562i	$0.517072\pi$
$104$		0			0
$105$	27.2152	−	79.0893i	0.259192	−	0.753232i
$106$		0			0
$107$		−	209.984i		−	1.96247i	−0.192815	−	0.981235i	$-0.561762\pi$
$107$		−	209.984i		−	1.96247i	0.192815	−	0.981235i	$-0.438238\pi$
$108$		0			0
$109$	−123.665	−	71.3980i	−1.13454	−	0.655028i	−0.189468	−	0.981887i	$-0.560676\pi$
$109$	−123.665	−	71.3980i	−1.13454	−	0.655028i	−0.945073	+	0.326859i	$0.894010\pi$
$110$		0			0
$111$	−38.0114	−	195.346i	−0.342445	−	1.75987i
$112$		0			0
$113$	29.1674	+	16.8398i	0.258119	+	0.149025i	0.623476	−	0.781842i	$-0.285720\pi$
$113$	29.1674	+	16.8398i	0.258119	+	0.149025i	−0.365357	+	0.930867i	$0.619053\pi$
$114$		0			0
$115$	5.01330	+	8.68329i	0.0435939	+	0.0755069i
$116$		0			0
$117$	56.4466	+	139.552i	0.482449	+	1.19275i
$118$		0			0
$119$	49.0452			0.412144
$120$		0			0
$121$	−87.3181	+	151.239i	−0.721637	+	1.24991i
$122$		0			0
$123$	164.240	−	142.829i	1.33529	−	1.16121i
$124$		0			0
$125$	123.851			0.990809
$126$		0			0
$127$	−115.264	+	66.5480i	−0.907594	+	0.524000i	−0.879656	−	0.475610i	$-0.842227\pi$
$127$	−115.264	+	66.5480i	−0.907594	+	0.524000i	−0.0279380	+	0.999610i	$0.508894\pi$
$128$		0			0
$129$	92.7623	−	18.0501i	0.719087	−	0.139924i
$130$		0			0
$131$	72.5164	+	125.602i	0.553561	+	0.958795i	0.998014	+	0.0629930i	$0.0200646\pi$
$131$	72.5164	+	125.602i	0.553561	+	0.958795i	−0.444453	+	0.895802i	$0.646602\pi$
$132$		0			0
$133$	122.427	−	124.194i	0.920502	−	0.933790i
$134$		0			0
$135$	73.0971	+	37.1904i	0.541460	+	0.275484i
$136$		0			0
$137$	−11.3287	+	19.6219i	−0.0826913	+	0.143226i	−0.904405	−	0.426675i	$-0.859685\pi$
$137$	−11.3287	+	19.6219i	−0.0826913	+	0.143226i	0.821714	+	0.569900i	$0.193018\pi$
$138$		0			0
$139$	92.4156			0.664860			0.332430	−	0.943128i	$-0.392131\pi$
$139$	92.4156			0.664860			0.332430	+	0.943128i	$0.392131\pi$
$140$		0			0
$141$	−33.4828	+	97.3034i	−0.237467	+	0.690095i
$142$		0			0
$143$	−249.061	+	143.795i	−1.74168	+	1.00556i
$144$		0			0
$145$			151.115i			1.04217i
$146$		0			0
$147$	−34.4043	+	99.9815i	−0.234043	+	0.680146i
$148$		0			0
$149$	−69.5743	−	120.506i	−0.466942	−	0.808767i	0.532345	−	0.846528i	$-0.321311\pi$
$149$	−69.5743	−	120.506i	−0.466942	−	0.808767i	−0.999287	+	0.0377605i	$0.987978\pi$
$150$		0			0
$151$	−147.309	+	85.0489i	−0.975557	+	0.563238i	−0.900926	−	0.433973i	$-0.857111\pi$
$151$	−147.309	+	85.0489i	−0.975557	+	0.563238i	−0.0746309	+	0.997211i	$0.523778\pi$
$152$		0			0
$153$	−6.67424	+	47.6259i	−0.0436225	+	0.311280i
$154$		0			0
$155$		−	78.2916i		−	0.505107i
$156$		0			0
$157$	38.8426	+	67.2773i	0.247405	+	0.428518i	0.962805	−	0.270197i	$-0.0870889\pi$
$157$	38.8426	+	67.2773i	0.247405	+	0.428518i	−0.715400	+	0.698715i	$0.753756\pi$
$158$		0			0
$159$	−23.6726	+	20.5865i	−0.148884	+	0.129475i
$160$		0			0
$161$	−15.1486	−	26.2381i	−0.0940904	−	0.162969i
$162$		0			0
$163$	−292.299			−1.79324			−0.896622	−	0.442797i	$-0.853986\pi$
$163$	−292.299			−1.79324			−0.896622	+	0.442797i	$0.853986\pi$
$164$		0			0
$165$	−50.9821	+	148.158i	−0.308983	+	0.897926i
$166$		0			0
$167$		−	201.218i		−	1.20490i	−0.798158	−	0.602448i	$-0.794192\pi$
$167$		−	201.218i		−	1.20490i	0.798158	−	0.602448i	$-0.205808\pi$
$168$		0			0
$169$	−110.764			−0.655408
$170$		0			0
$171$	103.940	+	135.785i	0.607836	+	0.794063i
$172$		0			0
$173$		−	165.266i		−	0.955296i	−0.878551	−	0.477648i	$-0.841489\pi$
$173$		−	165.266i		−	0.955296i	0.878551	−	0.477648i	$-0.158511\pi$
$174$		0			0
$175$	−144.775			−0.827285
$176$		0			0
$177$	−17.2434	+	14.9954i	−0.0974203	+	0.0847199i
$178$		0			0
$179$			145.201i			0.811178i	0.914055	+	0.405589i	$0.132934\pi$
$179$			145.201i			0.811178i	−0.914055	+	0.405589i	$0.867066\pi$
$180$		0			0
$181$	−68.2196	+	39.3866i	−0.376904	+	0.217605i	−0.676470	−	0.736470i	$-0.736491\pi$
$181$	−68.2196	+	39.3866i	−0.376904	+	0.217605i	0.299567	+	0.954075i	$0.403158\pi$
$182$		0			0
$183$	7.68171	−	22.3236i	0.0419765	−	0.121987i
$184$		0			0
$185$	174.505	−	100.751i	0.943273	−	0.544599i
$186$		0			0
$187$	−91.8761			−0.491316
$188$		0			0
$189$	−220.876	−	112.377i	−1.16865	−	0.594589i
$190$		0			0
$191$	−116.080	−	201.057i	−0.607751	−	1.05266i	−0.991610	−	0.129264i	$-0.958739\pi$
$191$	−116.080	−	201.057i	−0.607751	−	1.05266i	0.383860	−	0.923391i	$-0.374595\pi$
$192$		0			0
$193$	313.526	−	181.014i	1.62449	−	0.937898i	0.638789	−	0.769382i	$-0.279436\pi$
$193$	313.526	−	181.014i	1.62449	−	0.937898i	0.985699	−	0.168516i	$-0.0538975\pi$
$194$		0			0
$195$	−115.013	+	100.019i	−0.589811	+	0.512919i
$196$		0			0
$197$	43.5251			0.220940			0.110470	−	0.993879i	$-0.464764\pi$
$197$	43.5251			0.220940			0.110470	+	0.993879i	$0.464764\pi$
$198$		0			0
$199$	−177.033	−	306.630i	−0.889612	−	1.54085i	−0.840335	−	0.542068i	$-0.817642\pi$
$199$	−177.033	−	306.630i	−0.889612	−	1.54085i	−0.0492772	−	0.998785i	$-0.515692\pi$
$200$		0			0
$201$	61.1489	+	314.253i	0.304223	+	1.56345i
$202$		0			0
$203$		−	456.620i		−	2.24936i
$204$		0			0
$205$	190.857	+	110.192i	0.931011	+	0.537520i
$206$		0			0
$207$	27.5403	−	11.1396i	0.133045	−	0.0538146i
$208$		0			0
$209$	−229.342	+	232.652i	−1.09733	+	1.11317i
$210$		0			0
$211$	−121.067	+	69.8983i	−0.573779	+	0.331272i	−0.758657	−	0.651490i	$-0.774144\pi$
$211$	−121.067	+	69.8983i	−0.573779	+	0.331272i	0.184878	+	0.982761i	$0.440811\pi$
$212$		0			0
$213$	−209.528	−	72.1000i	−0.983698	−	0.338497i
$214$		0			0
$215$	47.8426	+	82.8659i	0.222524	+	0.385423i
$216$		0			0
$217$			236.572i			1.09019i
$218$		0			0
$219$	−8.96867	+	26.0636i	−0.0409528	+	0.119012i
$220$		0			0
$221$	−77.4017	−	44.6879i	−0.350234	−	0.202208i
$222$		0			0
$223$		−	212.053i		−	0.950910i	−0.879740	−	0.475455i	$-0.842283\pi$
$223$		−	212.053i		−	0.950910i	0.879740	−	0.475455i	$-0.157717\pi$
$224$		0			0
$225$	19.7015	−	140.585i	0.0875620	−	0.624824i
$226$		0			0
$227$	203.767	−	117.645i	0.897654	−	0.518261i	0.0212155	−	0.999775i	$-0.493246\pi$
$227$	203.767	−	117.645i	0.897654	−	0.518261i	0.876438	+	0.481514i	$0.159913\pi$
$228$		0			0
$229$	64.0833	−	110.996i	0.279840	−	0.484697i	−0.691505	−	0.722372i	$-0.743052\pi$
$229$	64.0833	−	110.996i	0.279840	−	0.484697i	0.971345	+	0.237675i	$0.0763853\pi$
$230$		0			0
$231$	154.051	−	447.684i	0.666889	−	1.93803i
$232$		0			0
$233$	5.70487	−	9.88112i	0.0244844	−	0.0424082i	−0.853524	−	0.521054i	$-0.825539\pi$
$233$	5.70487	−	9.88112i	0.0244844	−	0.0424082i	0.878008	+	0.478646i	$0.158872\pi$
$234$		0			0
$235$	−104.191			−0.443368
$236$		0			0
$237$	74.2220	+	381.438i	0.313173	+	1.60944i
$238$		0			0
$239$	10.8199	−	18.7407i	0.0452717	−	0.0784129i	−0.842502	−	0.538694i	$-0.818918\pi$
$239$	10.8199	−	18.7407i	0.0452717	−	0.0784129i	0.887773	+	0.460281i	$0.152251\pi$
$240$		0			0
$241$	54.7221	+	31.5938i	0.227063	+	0.131095i	0.609216	−	0.793004i	$-0.291484\pi$
$241$	54.7221	+	31.5938i	0.227063	+	0.131095i	−0.382153	+	0.924099i	$0.624817\pi$
$242$		0			0
$243$	139.183	−	199.191i	0.572769	−	0.819717i
$244$		0			0
$245$	−107.059			−0.436976
$246$		0			0
$247$	−306.371	+	84.4496i	−1.24037	+	0.341901i
$248$		0			0
$249$	−246.707	−	283.691i	−0.990791	−	1.13932i
$250$		0			0
$251$	5.30322	+	9.18545i	0.0211284	+	0.0365954i	0.876396	−	0.481591i	$-0.159941\pi$
$251$	5.30322	+	9.18545i	0.0211284	+	0.0365954i	−0.855268	+	0.518186i	$0.826607\pi$
$252$		0			0
$253$	28.3777	+	49.1517i	0.112165	+	0.194275i
$254$		0			0
$255$	−47.7969	+	9.30056i	−0.187439	+	0.0364728i
$256$		0			0
$257$		−	137.036i		−	0.533215i	−0.963805	−	0.266607i	$-0.914097\pi$
$257$		−	137.036i		−	0.533215i	0.963805	−	0.266607i	$-0.0859027\pi$
$258$		0			0
$259$	−527.299	+	304.436i	−2.03590	+	1.17543i
$260$		0			0
$261$	443.406	+	62.1384i	1.69887	+	0.238078i
$262$		0			0
$263$	−384.616			−1.46242			−0.731209	−	0.682154i	$-0.761044\pi$
$263$	−384.616			−1.46242			−0.731209	+	0.682154i	$0.761044\pi$
$264$		0			0
$265$	−27.5090	−	15.8823i	−0.103808	−	0.0599333i
$266$		0			0
$267$	−257.056	+	223.544i	−0.962755	+	0.837243i
$268$		0			0
$269$	176.772	+	102.060i	0.657147	+	0.379404i	0.791189	−	0.611572i	$-0.209462\pi$
$269$	176.772	+	102.060i	0.657147	+	0.379404i	−0.134042	+	0.990976i	$0.542796\pi$
$270$		0			0
$271$	139.752	−	242.057i	0.515689	−	0.893200i	−0.484145	−	0.874988i	$-0.660869\pi$
$271$	139.752	−	242.057i	0.515689	−	0.893200i	0.999834	−	0.0182122i	$-0.00579743\pi$
$272$		0			0
$273$	347.532	−	302.225i	1.27301	−	1.10705i
$274$		0			0
$275$	271.206			0.986204
$276$		0			0
$277$	−43.4726	−	75.2967i	−0.156941	−	0.271829i	0.776823	−	0.629719i	$-0.216830\pi$
$277$	−43.4726	−	75.2967i	−0.156941	−	0.271829i	−0.933764	+	0.357889i	$0.883497\pi$
$278$		0			0
$279$	−229.726	−	32.1935i	−0.823390	−	0.115389i
$280$		0			0
$281$	−217.817	−	125.757i	−0.775149	−	0.447532i	0.0595594	−	0.998225i	$-0.481030\pi$
$281$	−217.817	−	125.757i	−0.775149	−	0.447532i	−0.834708	+	0.550692i	$0.814364\pi$
$282$		0			0
$283$	−45.6510	−	79.0699i	−0.161311	−	0.279399i	0.774028	−	0.633151i	$-0.218239\pi$
$283$	−45.6510	−	79.0699i	−0.161311	−	0.279399i	−0.935339	+	0.353752i	$0.884906\pi$
$284$		0			0
$285$	−95.7596	+	144.249i	−0.335999	+	0.506138i
$286$		0			0
$287$	−576.708	−	332.963i	−2.00944	−	1.16015i
$288$		0			0
$289$	130.224	+	225.554i	0.450601	+	0.780463i
$290$		0			0
$291$	15.6434	+	80.3935i	0.0537573	+	0.276266i
$292$		0			0
$293$	−38.3512	−	22.1421i	−0.130891	−	0.0755702i	0.433124	−	0.901334i	$-0.357411\pi$
$293$	−38.3512	−	22.1421i	−0.130891	−	0.0755702i	−0.564016	+	0.825764i	$0.690744\pi$
$294$		0			0
$295$	−20.0379	−	11.5689i	−0.0679250	−	0.0392165i
$296$		0			0
$297$	413.765	+	210.516i	1.39315	+	0.708808i
$298$		0			0
$299$			55.2109i			0.184652i
$300$		0			0
$301$	−144.565	−	250.394i	−0.480282	−	0.831872i
$302$		0			0
$303$	−15.4104	+	44.7836i	−0.0508592	+	0.147801i
$304$		0			0
$305$	23.9039			0.0783733
$306$		0			0
$307$	−346.732	−	200.186i	−1.12942	−	0.652070i	−0.185630	−	0.982620i	$-0.559433\pi$
$307$	−346.732	−	200.186i	−1.12942	−	0.652070i	−0.943789	+	0.330549i	$0.892766\pi$
$308$		0			0
$309$	264.636	+	91.0630i	0.856426	+	0.294702i
$310$		0			0
$311$	−212.272	+	367.665i	−0.682546	+	1.18220i	0.291656	+	0.956523i	$0.405794\pi$
$311$	−212.272	+	367.665i	−0.682546	+	1.18220i	−0.974201	+	0.225680i	$0.927540\pi$
$312$		0			0
$313$	183.712	−	318.198i	0.586938	−	1.01661i	−0.407693	−	0.913119i	$-0.633667\pi$
$313$	183.712	−	318.198i	0.586938	−	1.01661i	0.994631	−	0.103487i	$-0.0330001\pi$
$314$		0			0
$315$	34.8237	−	248.494i	0.110551	−	0.788871i
$316$		0			0
$317$	−11.0988	−	6.40791i	−0.0350120	−	0.0202142i	0.482392	−	0.875956i	$-0.339768\pi$
$317$	−11.0988	−	6.40791i	−0.0350120	−	0.0202142i	−0.517404	+	0.855741i	$0.673101\pi$
$318$		0			0
$319$			855.384i			2.68145i
$320$		0			0
$321$	−120.323	−	618.355i	−0.374837	−	1.92634i
$322$		0			0
$323$	−98.2524	−	25.5734i	−0.304187	−	0.0791747i
$324$		0			0
$325$	228.480	+	131.913i	0.703014	+	0.405885i
$326$		0			0
$327$	−405.076	−	139.390i	−1.23877	−	0.426268i
$328$		0			0
$329$	314.832			0.956937
$330$		0			0
$331$	−95.5088	+	55.1420i	−0.288546	+	0.166592i	−0.637286	−	0.770627i	$-0.719943\pi$
$331$	−95.5088	+	55.1420i	−0.288546	+	0.166592i	0.348740	+	0.937220i	$0.386610\pi$
$332$		0			0
$333$	−223.870	−	553.468i	−0.672281	−	1.66207i
$334$		0			0
$335$	−280.727	+	162.078i	−0.837990	+	0.483814i
$336$		0			0
$337$	−479.582	+	276.887i	−1.42309	+	0.821623i	−0.996562	−	0.0828509i	$-0.973597\pi$
$337$	−479.582	+	276.887i	−1.42309	+	0.821623i	−0.426530	+	0.904473i	$0.640264\pi$
$338$		0			0
$339$	95.5406	+	32.8762i	0.281831	+	0.0969800i
$340$		0			0
$341$		−	443.169i		−	1.29962i
$342$		0			0
$343$	−126.250			−0.368074
$344$		0			0
$345$	19.7386	+	22.6976i	0.0572134	+	0.0657902i
$346$		0			0
$347$	59.7869	+	103.554i	0.172297	+	0.298427i	0.939222	−	0.343309i	$-0.111548\pi$
$347$	59.7869	+	103.554i	0.172297	+	0.298427i	−0.766926	+	0.641736i	$0.778215\pi$
$348$		0			0
$349$	241.912	+	419.003i	0.693157	+	1.20058i	0.970798	+	0.239898i	$0.0771139\pi$
$349$	241.912	+	419.003i	0.693157	+	1.20058i	−0.277642	+	0.960685i	$0.589553\pi$
$350$		0			0
$351$	246.186	+	378.603i	0.701385	+	1.07864i
$352$		0			0
$353$	300.837	+	521.065i	0.852229	+	1.47610i	0.879192	+	0.476467i	$0.158083\pi$
$353$	300.837	+	521.065i	0.852229	+	1.47610i	−0.0269636	+	0.999636i	$0.508584\pi$
$354$		0			0
$355$		−	224.360i		−	0.632000i
$356$		0			0
$357$	144.427	−	28.1033i	0.404557	−	0.0787206i
$358$		0			0
$359$	62.5595	−	108.356i	0.174260	−	0.301828i	−0.765645	−	0.643264i	$-0.777580\pi$
$359$	62.5595	−	108.356i	0.174260	−	0.301828i	0.939905	+	0.341436i	$0.110913\pi$
$360$		0			0
$361$	−310.016	+	184.962i	−0.858770	+	0.512361i
$362$		0			0
$363$	−170.470	+	495.399i	−0.469615	+	1.36474i
$364$		0			0
$365$	−27.9086			−0.0764620
$366$		0			0
$367$	249.861	−	432.772i	0.680820	−	1.17922i	−0.293911	−	0.955833i	$-0.594957\pi$
$367$	249.861	−	432.772i	0.680820	−	1.17922i	0.974731	−	0.223382i	$-0.0717098\pi$
$368$		0			0
$369$	401.808	−	514.709i	1.08891	−	1.39488i
$370$		0			0
$371$	83.1232	+	47.9912i	0.224052	+	0.129356i
$372$		0			0
$373$	210.652	+	121.620i	0.564750	+	0.326058i	0.755050	−	0.655668i	$-0.227613\pi$
$373$	210.652	+	121.620i	0.564750	+	0.326058i	−0.190300	+	0.981726i	$0.560946\pi$
$374$		0			0
$375$	364.713	−	70.9676i	0.972568	−	0.189247i
$376$		0			0
$377$	−416.053	+	720.624i	−1.10359	+	1.91147i
$378$		0			0
$379$			557.003i			1.46966i	0.678249	+	0.734832i	$0.262739\pi$
$379$			557.003i			1.46966i	−0.678249	+	0.734832i	$0.737261\pi$
$380$		0			0
$381$	−301.295	+	262.016i	−0.790800	+	0.687706i
$382$		0			0
$383$	−58.4933	+	33.7711i	−0.152724	+	0.0881753i	−0.574415	−	0.818565i	$-0.694770\pi$
$383$	−58.4933	+	33.7711i	−0.152724	+	0.0881753i	0.421690	+	0.906740i	$0.361437\pi$
$384$		0			0
$385$	479.376			1.24513
$386$		0			0
$387$	262.821	−	106.307i	0.679123	−	0.274695i
$388$		0			0
$389$	−203.050	+	351.693i	−0.521980	+	0.904096i	0.477693	+	0.878527i	$0.341473\pi$
$389$	−203.050	+	351.693i	−0.521980	+	0.904096i	−0.999673	+	0.0255691i	$0.991860\pi$
$390$		0			0
$391$	−8.81908	+	15.2751i	−0.0225552	+	0.0390667i
$392$		0			0
$393$	285.515	+	328.317i	0.726501	+	0.835412i
$394$		0			0
$395$	−340.744	+	196.728i	−0.862642	+	0.498047i
$396$		0			0
$397$	53.1939	−	92.1345i	0.133990	−	0.232077i	−0.791221	−	0.611530i	$-0.790554\pi$
$397$	53.1939	−	92.1345i	0.133990	−	0.232077i	0.925211	+	0.379453i	$0.123888\pi$
$398$		0			0
$399$	289.354	−	435.874i	0.725198	−	1.09242i
$400$		0			0
$401$	326.343	−	188.414i	0.813823	−	0.469861i	−0.0344587	−	0.999406i	$-0.510971\pi$
$401$	326.343	−	188.414i	0.813823	−	0.469861i	0.848282	+	0.529545i	$0.177637\pi$
$402$		0			0
$403$	215.554	−	373.351i	0.534874	−	0.926429i
$404$		0			0
$405$	236.564	+	67.6319i	0.584110	+	0.166992i
$406$		0			0
$407$	987.786	−	570.299i	2.42699	−	1.40123i
$408$		0			0
$409$		−	7.89988i		−	0.0193151i	−0.999953	−	0.00965756i	$-0.996926\pi$
$409$		−	7.89988i		−	0.0193151i	0.999953	−	0.00965756i	$-0.00307414\pi$
$410$		0			0
$411$	−22.1169	+	64.2734i	−0.0538125	+	0.156383i
$412$		0			0
$413$	60.5479	+	34.9573i	0.146605	+	0.0846425i
$414$		0			0
$415$	190.333	−	329.666i	0.458633	−	0.794376i
$416$		0			0
$417$	272.143	−	52.9548i	0.652620	−	0.126990i
$418$		0			0
$419$	227.346	−	393.774i	0.542591	−	0.939795i	−0.456163	−	0.889896i	$-0.650777\pi$
$419$	227.346	−	393.774i	0.542591	−	0.939795i	0.998754	−	0.0498989i	$-0.0158899\pi$
$420$		0			0
$421$		−	227.531i		−	0.540454i	−0.962797	−	0.270227i	$-0.912901\pi$
$421$		−	227.531i		−	0.540454i	0.962797	−	0.270227i	$-0.0870988\pi$
$422$		0			0
$423$	−42.8435	+	305.722i	−0.101285	+	0.722747i
$424$		0			0
$425$	42.1420	+	72.9920i	0.0991576	+	0.171746i
$426$		0			0
$427$	−72.2297			−0.169156
$428$		0			0
$429$	−651.031	+	566.158i	−1.51755	+	1.31971i
$430$		0			0
$431$	675.810	−	390.179i	1.56800	−	0.905288i	0.571603	−	0.820530i	$-0.306322\pi$
$431$	675.810	−	390.179i	1.56800	−	0.905288i	0.996402	−	0.0847573i	$-0.0270115\pi$
$432$		0			0
$433$	141.387	−	81.6296i	0.326528	−	0.188521i	−0.327771	−	0.944757i	$-0.606297\pi$
$433$	141.387	−	81.6296i	0.326528	−	0.188521i	0.654299	+	0.756236i	$0.272964\pi$
$434$		0			0
$435$	86.5899	+	444.998i	0.199057	+	1.02298i
$436$		0			0
$437$	16.6660	+	60.4617i	0.0381372	+	0.138356i
$438$		0			0
$439$			367.486i			0.837098i	0.908194	+	0.418549i	$0.137461\pi$
$439$			367.486i			0.837098i	−0.908194	+	0.418549i	$0.862539\pi$
$440$		0			0
$441$	−44.0227	+	314.136i	−0.0998246	+	0.712327i
$442$		0			0
$443$	−284.017	+	491.932i	−0.641122	+	1.11046i	0.344060	+	0.938948i	$0.388198\pi$
$443$	−284.017	+	491.932i	−0.641122	+	1.11046i	−0.985183	+	0.171509i	$0.945136\pi$
$444$		0			0
$445$	−298.714	−	172.463i	−0.671268	−	0.387557i
$446$		0			0
$447$	−273.931	−	314.996i	−0.612822	−	0.704690i
$448$		0			0
$449$		−	589.964i		−	1.31395i	−0.753912	−	0.656975i	$-0.771836\pi$
$449$		−	589.964i		−	1.31395i	0.753912	−	0.656975i	$-0.228164\pi$
$450$		0			0
$451$	1080.35	+	623.738i	2.39545	+	1.38301i
$452$		0			0
$453$	−385.057	+	334.859i	−0.850016	+	0.739202i
$454$		0			0
$455$	403.853	+	233.165i	0.887590	+	0.512450i
$456$		0			0
$457$	−175.806	−	304.505i	−0.384696	−	0.666313i	0.607031	−	0.794678i	$-0.292360\pi$
$457$	−175.806	−	304.505i	−0.384696	−	0.666313i	−0.991727	+	0.128365i	$0.959027\pi$
$458$		0			0
$459$	7.63593	+	144.072i	0.0166360	+	0.313882i
$460$		0			0
$461$	747.602			1.62170			0.810848	−	0.585257i	$-0.199006\pi$
$461$	747.602			1.62170			0.810848	+	0.585257i	$0.199006\pi$
$462$		0			0
$463$	−64.0550	+	110.947i	−0.138348	+	0.239625i	−0.926871	−	0.375379i	$-0.877512\pi$
$463$	−64.0550	+	110.947i	−0.138348	+	0.239625i	0.788524	+	0.615005i	$0.210846\pi$
$464$		0			0
$465$	−44.8617	−	230.551i	−0.0964768	−	0.495808i
$466$		0			0
$467$	−258.903			−0.554397			−0.277198	−	0.960813i	$-0.589406\pi$
$467$	−258.903			−0.554397			−0.277198	+	0.960813i	$0.589406\pi$
$468$		0			0
$469$	848.264	−	489.746i	1.80867	−	1.04423i
$470$		0			0
$471$	152.933	+	175.859i	0.324698	+	0.373374i
$472$		0			0
$473$	270.813	+	469.061i	0.572543	+	0.991673i
$474$		0			0
$475$	290.028	+	75.4894i	0.610586	+	0.158925i
$476$		0			0
$477$	−57.9141	+	74.1870i	−0.121413	+	0.155528i
$478$		0			0
$479$	354.767	−	614.474i	0.740640	−	1.28283i	−0.211564	−	0.977364i	$-0.567856\pi$
$479$	354.767	−	614.474i	0.740640	−	1.28283i	0.952204	−	0.305463i	$-0.0988111\pi$
$480$		0			0
$481$	1109.56			2.30677
$482$		0			0
$483$	−59.6436	−	68.5848i	−0.123486	−	0.141998i
$484$		0			0
$485$	−71.8167	+	41.4634i	−0.148076	+	0.0854915i
$486$		0			0
$487$		−	74.4123i		−	0.152797i	−0.997077	−	0.0763987i	$-0.975658\pi$
$487$		−	74.4123i		−	0.152797i	0.997077	−	0.0763987i	$-0.0243422\pi$
$488$		0			0
$489$	−860.752	+	167.489i	−1.76023	+	0.342514i
$490$		0			0
$491$	−408.049	−	706.761i	−0.831057	−	1.43943i	−0.897201	−	0.441622i	$-0.854403\pi$
$491$	−408.049	−	706.761i	−0.831057	−	1.43943i	0.0661442	−	0.997810i	$-0.478930\pi$
$492$		0			0
$493$	−230.217	+	132.916i	−0.466971	+	0.269606i
$494$		0			0
$495$	−65.2351	+	465.503i	−0.131788	+	0.940411i
$496$		0			0
$497$			677.943i			1.36407i
$498$		0			0
$499$	−213.282	−	369.415i	−0.427418	−	0.740310i	0.569225	−	0.822182i	$-0.307243\pi$
$499$	−213.282	−	369.415i	−0.427418	−	0.740310i	−0.996643	+	0.0818722i	$0.973910\pi$
$500$		0			0
$501$	−115.299	−	592.540i	−0.230138	−	1.18271i
$502$		0			0
$503$	−258.876	−	448.386i	−0.514663	−	0.891423i	−0.999855	−	0.0170153i	$-0.994584\pi$
$503$	−258.876	−	448.386i	−0.514663	−	0.891423i	0.485192	−	0.874408i	$-0.338750\pi$
$504$		0			0
$505$	−47.9538			−0.0949580
$506$		0			0
$507$	−326.174	+	63.4686i	−0.643342	+	0.125185i
$508$		0			0
$509$			263.703i			0.518080i	0.965867	+	0.259040i	$0.0834061\pi$
$509$			263.703i			0.518080i	−0.965867	+	0.259040i	$0.916594\pi$
$510$		0			0
$511$	84.3307			0.165031
$512$		0			0
$513$	383.885	+	340.296i	0.748313	+	0.663345i
$514$		0			0
$515$			283.369i			0.550231i
$516$		0			0
$517$	−589.774			−1.14076
$518$		0			0
$519$	−94.6988	−	486.671i	−0.182464	−	0.937708i
$520$		0			0
$521$		−	99.1573i		−	0.190321i	−0.995462	−	0.0951606i	$-0.969664\pi$
$521$		−	99.1573i		−	0.190321i	0.995462	−	0.0951606i	$-0.0303365\pi$
$522$		0			0
$523$	256.105	−	147.862i	0.489684	−	0.282719i	−0.234759	−	0.972054i	$-0.575430\pi$
$523$	256.105	−	147.862i	0.489684	−	0.282719i	0.724444	+	0.689334i	$0.242097\pi$
$524$		0			0
$525$	−426.328	+	82.9571i	−0.812054	+	0.158013i
$526$		0			0
$527$	119.274	−	68.8628i	0.226326	−	0.130669i
$528$		0			0
$529$	−518.104			−0.979403
$530$		0			0
$531$	−42.1853	+	54.0386i	−0.0794450	+	0.101768i
$532$		0			0
$533$	606.763	+	1050.94i	1.13839	+	1.97175i
$534$		0			0
$535$	552.385	−	318.920i	1.03250	−	0.596112i
$536$		0			0
$537$	83.2012	+	427.583i	0.154937	+	0.796244i
$538$		0			0
$539$	−606.007			−1.12432
$540$		0			0
$541$	−385.570	−	667.827i	−0.712699	−	1.23443i	−0.963840	−	0.266480i	$-0.914139\pi$
$541$	−385.570	−	667.827i	−0.712699	−	1.23443i	0.251142	−	0.967950i	$-0.419194\pi$
$542$		0			0
$543$	−178.322	+	155.075i	−0.328402	+	0.285589i
$544$		0			0
$545$		−	433.751i		−	0.795874i
$546$		0			0
$547$	565.647	+	326.577i	1.03409	+	0.597032i	0.918154	−	0.396224i	$-0.129680\pi$
$547$	565.647	+	326.577i	1.03409	+	0.597032i	0.115936	+	0.993257i	$0.463013\pi$
$548$		0			0
$549$	9.82926	−	70.1395i	0.0179039	−	0.127759i
$550$		0			0
$551$	−238.093	+	914.748i	−0.432111	+	1.66016i
$552$		0			0
$553$	1029.62	−	594.449i	1.86187	−	1.07495i
$554$		0			0
$555$	456.147	−	396.681i	0.821887	−	0.714740i
$556$		0			0
$557$	−45.8653	−	79.4411i	−0.0823435	−	0.142623i	0.821913	−	0.569614i	$-0.192907\pi$
$557$	−45.8653	−	79.4411i	−0.0823435	−	0.142623i	−0.904256	+	0.426990i	$0.859574\pi$
$558$		0			0
$559$			526.885i			0.942550i
$560$		0			0
$561$	−270.554	+	52.6457i	−0.482271	+	0.0938427i
$562$		0			0
$563$	−145.572	−	84.0459i	−0.258565	−	0.149282i	0.365115	−	0.930962i	$-0.381030\pi$
$563$	−145.572	−	84.0459i	−0.258565	−	0.149282i	−0.623680	+	0.781680i	$0.714363\pi$
$564$		0			0
$565$			102.304i			0.181069i
$566$		0			0
$567$	−714.821	−	204.362i	−1.26071	−	0.360426i
$568$		0			0
$569$	−116.931	+	67.5103i	−0.205503	+	0.118647i	−0.599220	−	0.800585i	$-0.704522\pi$
$569$	−116.931	+	67.5103i	−0.205503	+	0.118647i	0.393717	+	0.919232i	$0.371189\pi$
$570$		0			0
$571$	95.2078	−	164.905i	0.166739	−	0.288800i	−0.770533	−	0.637400i	$-0.780010\pi$
$571$	95.2078	−	164.905i	0.166739	−	0.288800i	0.937271	+	0.348601i	$0.113343\pi$
$572$		0			0
$573$	−457.037	−	525.552i	−0.797622	−	0.917193i
$574$		0			0
$575$	26.0327	−	45.0900i	0.0452743	−	0.0784174i
$576$		0			0
$577$	−451.628			−0.782717			−0.391359	−	0.920238i	$-0.627995\pi$
$577$	−451.628			−0.782717			−0.391359	+	0.920238i	$0.627995\pi$
$578$		0			0
$579$	819.539	−	712.698i	1.41544	−	1.23091i
$580$		0			0
$581$	−575.123	+	996.143i	−0.989886	+	1.71453i
$582$		0			0
$583$	−155.714	−	89.9017i	−0.267092	−	0.154205i
$584$		0			0
$585$	−281.375	+	360.437i	−0.480983	+	0.616131i
$586$		0			0
$587$	119.218			0.203097			0.101549	−	0.994831i	$-0.467620\pi$
$587$	119.218			0.203097			0.101549	+	0.994831i	$0.467620\pi$
$588$		0			0
$589$	123.355	−	473.925i	0.209431	−	0.804627i
$590$		0			0
$591$	128.171	−	24.9402i	0.216872	−	0.0422000i
$592$		0			0
$593$	303.979	+	526.507i	0.512612	+	0.887870i	0.999893	+	0.0146245i	$0.00465529\pi$
$593$	303.979	+	526.507i	0.512612	+	0.887870i	−0.487281	+	0.873245i	$0.662011\pi$
$594$		0			0
$595$	74.4888	+	129.018i	0.125191	+	0.216838i
$596$		0			0
$597$	−697.022	−	801.513i	−1.16754	−	1.34257i
$598$		0			0
$599$			502.476i			0.838858i	0.907788	+	0.419429i	$0.137770\pi$
$599$			502.476i			0.838858i	−0.907788	+	0.419429i	$0.862230\pi$
$600$		0			0
$601$	−394.576	+	227.808i	−0.656532	+	0.379049i	−0.790954	−	0.611875i	$-0.790416\pi$
$601$	−394.576	+	227.808i	−0.656532	+	0.379049i	0.134422	+	0.990924i	$0.457082\pi$
$602$		0			0
$603$	360.139	+	890.364i	0.597245	+	1.47656i
$604$		0			0
$605$	−530.468			−0.876806
$606$		0			0
$607$	−650.368	−	375.490i	−1.07145	−	0.618600i	−0.142870	−	0.989741i	$-0.545633\pi$
$607$	−650.368	−	375.490i	−1.07145	−	0.618600i	−0.928576	+	0.371141i	$0.878967\pi$
$608$		0			0
$609$	−261.647	−	1344.64i	−0.429633	−	2.20795i
$610$		0			0
$611$	−496.860	−	286.862i	−0.813191	−	0.469496i
$612$		0			0
$613$	−282.155	+	488.706i	−0.460285	+	0.797237i	−0.998975	−	0.0452673i	$-0.985586\pi$
$613$	−282.155	+	488.706i	−0.460285	+	0.797237i	0.538690	+	0.842504i	$0.318919\pi$
$614$		0			0
$615$	625.171	+	215.126i	1.01654	+	0.349798i
$616$		0			0
$617$	393.306			0.637449			0.318725	−	0.947847i	$-0.396745\pi$
$617$	393.306			0.637449			0.318725	+	0.947847i	$0.396745\pi$
$618$		0			0
$619$	−90.1452	−	156.136i	−0.145630	−	0.252239i	0.783978	−	0.620789i	$-0.213188\pi$
$619$	−90.1452	−	156.136i	−0.145630	−	0.252239i	−0.929608	+	0.368550i	$0.879854\pi$
$620$		0			0
$621$	74.7166	−	48.5844i	0.120317	−	0.0782358i
$622$		0			0
$623$	902.616	+	521.126i	1.44882	+	0.836478i
$624$		0			0
$625$	−9.06287	−	15.6974i	−0.0145006	−	0.0251158i
$626$		0			0
$627$	−542.046	+	816.522i	−0.864507	+	1.30227i
$628$		0			0
$629$	306.979	+	177.234i	0.488042	+	0.281771i
$630$		0			0
$631$	−394.729	−	683.692i	−0.625562	−	1.08350i	−0.988432	−	0.151665i	$-0.951536\pi$
$631$	−394.729	−	683.692i	−0.625562	−	1.08350i	0.362870	−	0.931840i	$-0.381797\pi$
$632$		0			0
$633$	−316.463	+	275.207i	−0.499942	+	0.434766i
$634$		0			0
$635$	−350.123	−	202.143i	−0.551374	−	0.318336i
$636$		0			0
$637$	−510.535	−	294.757i	−0.801467	−	0.462727i
$638$		0			0
$639$	−658.324	−	92.2568i	−1.03024	−	0.144377i
$640$		0			0
$641$			275.451i			0.429721i	0.976645	+	0.214861i	$0.0689298\pi$
$641$			275.451i			0.429721i	−0.976645	+	0.214861i	$0.931070\pi$
$642$		0			0
$643$	195.008	+	337.763i	0.303278	+	0.525293i	0.976876	−	0.213805i	$-0.0685856\pi$
$643$	195.008	+	337.763i	0.303278	+	0.525293i	−0.673598	+	0.739098i	$0.735252\pi$
$644$		0			0
$645$	188.368	+	216.607i	0.292044	+	0.335824i
$646$		0			0
$647$	−259.940			−0.401763			−0.200881	−	0.979616i	$-0.564381\pi$
$647$	−259.940			−0.401763			−0.200881	+	0.979616i	$0.564381\pi$
$648$		0			0
$649$	−113.424	−	65.4854i	−0.174768	−	0.100902i
$650$		0			0
$651$	135.557	+	696.649i	0.208230	+	1.07012i
$652$		0			0
$653$	395.996	−	685.884i	0.606425	−	1.05036i	−0.385399	−	0.922750i	$-0.625936\pi$
$653$	395.996	−	685.884i	0.606425	−	1.05036i	0.991825	−	0.127609i	$-0.0407303\pi$
$654$		0			0
$655$	−220.273	+	381.524i	−0.336295	+	0.582479i
$656$		0			0
$657$	−11.4760	+	81.8904i	−0.0174673	+	0.124643i
$658$		0			0
$659$	1007.30	+	581.566i	1.52853	+	0.882498i	0.999424	+	0.0339434i	$0.0108066\pi$
$659$	1007.30	+	581.566i	1.52853	+	0.882498i	0.529108	+	0.848555i	$0.322527\pi$
$660$		0			0
$661$		−	619.896i		−	0.937816i	−0.883247	−	0.468908i	$-0.844648\pi$
$661$		−	619.896i		−	0.937816i	0.883247	−	0.468908i	$-0.155352\pi$
$662$		0			0
$663$	−253.537	−	87.2437i	−0.382408	−	0.131589i
$664$		0			0
$665$	512.645	+	133.433i	0.770894	+	0.200651i
$666$		0			0
$667$	142.214	+	82.1072i	0.213214	+	0.123099i
$668$		0			0
$669$	−121.508	−	624.447i	−0.181626	−	0.933403i
$670$		0			0
$671$	135.308			0.201651
$672$		0			0
$673$	654.752	−	378.021i	0.972885	−	0.561695i	0.0727704	−	0.997349i	$-0.476816\pi$
$673$	654.752	−	378.021i	0.972885	−	0.561695i	0.900115	+	0.435653i	$0.143483\pi$
$674$		0			0
$675$	−22.5402	−	425.280i	−0.0333930	−	0.630045i
$676$		0			0
$677$	236.104	−	136.315i	0.348750	−	0.201351i	−0.315385	−	0.948964i	$-0.602134\pi$
$677$	236.104	−	136.315i	0.348750	−	0.201351i	0.664135	+	0.747613i	$0.268800\pi$
$678$		0			0
$679$	217.007	−	125.289i	0.319597	−	0.184520i
$680$		0			0
$681$	532.636	−	463.198i	0.782138	−	0.680173i
$682$		0			0
$683$		−	1028.19i		−	1.50541i	−0.658361	−	0.752703i	$-0.728750\pi$
$683$		−	1028.19i		−	1.50541i	0.658361	−	0.752703i	$-0.271250\pi$
$684$		0			0
$685$	−68.8233			−0.100472
$686$		0			0
$687$	125.109	−	363.577i	0.182110	−	0.529224i
$688$		0			0
$689$	−87.4551	−	151.477i	−0.126930	−	0.219850i
$690$		0			0
$691$	528.528	+	915.437i	0.764874	+	1.32480i	0.940313	+	0.340311i	$0.110532\pi$
$691$	528.528	+	915.437i	0.764874	+	1.32480i	−0.175439	+	0.984490i	$0.556134\pi$
$692$		0			0
$693$	197.119	−	1406.60i	0.284443	−	2.02972i
$694$		0			0
$695$	140.359	+	243.109i	0.201955	+	0.349797i
$696$		0			0
$697$			387.684i			0.556217i
$698$		0			0
$699$	11.1376	−	32.3665i	0.0159336	−	0.0463041i
$700$		0			0
$701$	−88.1596	+	152.697i	−0.125763	+	0.217827i	−0.922031	−	0.387117i	$-0.873471\pi$
$701$	−88.1596	+	152.697i	−0.125763	+	0.217827i	0.796268	+	0.604944i	$0.206804\pi$
$702$		0			0
$703$	1215.08	−	334.931i	1.72842	−	0.476431i
$704$		0			0
$705$	−306.820	+	59.7025i	−0.435205	+	0.0846843i
$706$		0			0
$707$	144.901			0.204951
$708$		0			0
$709$	320.348	−	554.858i	0.451830	−	0.782593i	−0.546670	−	0.837348i	$-0.684105\pi$
$709$	320.348	−	554.858i	0.451830	−	0.782593i	0.998500	+	0.0547555i	$0.0174379\pi$
$710$		0			0
$711$	437.133	+	1080.72i	0.614815	+	1.51999i
$712$		0			0
$713$	−73.6801	−	42.5392i	−0.103338	−	0.0596623i
$714$		0			0
$715$	−756.537	−	436.787i	−1.05809	−	0.610891i
$716$		0			0
$717$	21.1237	−	61.3869i	0.0294612	−	0.0856163i
$718$		0			0
$719$	−250.658	+	434.152i	−0.348620	+	0.603828i	−0.986005	−	0.166718i	$-0.946683\pi$
$719$	−250.658	+	434.152i	−0.348620	+	0.603828i	0.637384	+	0.770546i	$0.280016\pi$
$720$		0			0
$721$		−	856.249i		−	1.18759i
$722$		0			0
$723$	179.248	+	61.6804i	0.247922	+	0.0853117i
$724$		0			0
$725$	679.569	−	392.349i	0.937337	−	0.541172i
$726$		0			0
$727$	−1151.35			−1.58371			−0.791853	−	0.610712i	$-0.790883\pi$
$727$	−1151.35			−1.58371			−0.791853	+	0.610712i	$0.790883\pi$
$728$		0			0
$729$	295.723	−	666.325i	0.405656	−	0.914026i
$730$		0			0
$731$	−84.1616	+	145.772i	−0.115132	+	0.199415i
$732$		0			0
$733$	241.659	−	418.565i	0.329685	−	0.571030i	−0.652765	−	0.757561i	$-0.726391\pi$
$733$	241.659	−	418.565i	0.329685	−	0.571030i	0.982449	+	0.186530i	$0.0597243\pi$
$734$		0			0
$735$	−315.264	+	61.3457i	−0.428931	+	0.0834635i
$736$		0			0
$737$	−1589.05	+	917.439i	−2.15611	+	1.24483i
$738$		0			0
$739$	−117.129	+	202.874i	−0.158497	+	0.274525i	−0.934327	−	0.356417i	$-0.883998\pi$
$739$	−117.129	+	202.874i	−0.158497	+	0.274525i	0.775830	+	0.630942i	$0.217331\pi$
$740$		0			0
$741$	−853.801	+	424.237i	−1.15223	+	0.572520i
$742$		0			0
$743$	366.009	−	211.316i	0.492610	−	0.284409i	−0.233046	−	0.972466i	$-0.574869\pi$
$743$	366.009	−	211.316i	0.492610	−	0.284409i	0.725657	+	0.688057i	$0.241536\pi$
$744$		0			0
$745$	211.336	−	366.045i	0.283673	−	0.491336i
$746$		0			0
$747$	−889.052	−	694.039i	−1.19016	−	0.929102i
$748$		0			0
$749$	−1669.13	+	963.672i	−2.22848	+	1.28661i
$750$		0			0
$751$		−	79.8535i		−	0.106330i	−0.998586	−	0.0531648i	$-0.983069\pi$
$751$		−	79.8535i		−	0.106330i	0.998586	−	0.0531648i	$-0.0169309\pi$
$752$		0			0
$753$	20.8801	+	24.0102i	0.0277292	+	0.0318861i
$754$		0			0
$755$	−447.460	−	258.341i	−0.592662	−	0.342174i
$756$		0			0
$757$	−157.885	+	273.465i	−0.208567	+	0.361248i	−0.951263	−	0.308380i	$-0.900213\pi$
$757$	−157.885	+	273.465i	−0.208567	+	0.361248i	0.742697	+	0.669628i	$0.233546\pi$
$758$		0			0
$759$	111.730	+	128.480i	0.147207	+	0.169275i
$760$		0			0
$761$	80.7321	−	139.832i	0.106087	−	0.183748i	−0.808095	−	0.589052i	$-0.799501\pi$
$761$	80.7321	−	139.832i	0.106087	−	0.183748i	0.914182	+	0.405304i	$0.132834\pi$
$762$		0			0
$763$			1310.66i			1.71777i
$764$		0			0
$765$	−135.422	+	54.7760i	−0.177022	+	0.0716026i
$766$		0			0
$767$	−63.7033	−	110.337i	−0.0830551	−	0.143856i
$768$		0			0
$769$	385.778			0.501662			0.250831	−	0.968031i	$-0.419296\pi$
$769$	385.778			0.501662			0.250831	+	0.968031i	$0.419296\pi$
$770$		0			0
$771$	−78.5228	−	403.540i	−0.101845	−	0.523398i
$772$		0			0
$773$	−1019.23	+	588.452i	−1.31854	+	0.761257i	−0.983493	−	0.180946i	$-0.942084\pi$
$773$	−1019.23	+	588.452i	−1.31854	+	0.761257i	−0.335042	+	0.942203i	$0.608751\pi$
$774$		0			0
$775$	−352.081	+	203.274i	−0.454297	+	0.262289i
$776$		0			0
$777$	−1378.33	+	1198.64i	−1.77391	+	1.54265i
$778$		0			0
$779$	981.707	+	967.737i	1.26021	+	1.24228i
$780$		0			0
$781$		−	1269.99i		−	1.62610i
$782$		0			0
$783$	1341.33	−	71.0919i	1.71307	−	0.0907943i
$784$		0			0
$785$	−117.987	+	204.359i	−0.150301	+	0.260330i
$786$		0			0
$787$	−417.513	−	241.051i	−0.530511	−	0.306291i	0.210713	−	0.977548i	$-0.432421\pi$
$787$	−417.513	−	241.051i	−0.530511	−	0.306291i	−0.741225	+	0.671257i	$0.765755\pi$
$788$		0			0
$789$	−1132.60	+	220.388i	−1.43549	+	0.279326i
$790$		0			0
$791$		−	309.129i		−	0.390808i
$792$		0			0
$793$	113.991	+	65.8126i	0.143746	+	0.0829919i
$794$		0			0
$795$	−90.1083	−	31.0069i	−0.113344	−	0.0390024i
$796$		0			0
$797$	529.152	+	305.506i	0.663930	+	0.383320i	0.793773	−	0.608214i	$-0.208114\pi$
$797$	529.152	+	305.506i	0.663930	+	0.383320i	−0.129843	+	0.991535i	$0.541447\pi$
$798$		0			0
$799$	−91.6434	−	158.731i	−0.114698	−	0.198662i
$800$		0			0
$801$	−628.877	+	805.580i	−0.785115	+	1.00572i
$802$		0			0
$803$	−157.976			−0.196733
$804$		0			0
$805$	46.0147	−	79.6997i	0.0571611	−	0.0990059i
$806$		0			0
$807$	579.035	+	199.250i	0.717515	+	0.246902i
$808$		0			0
$809$	−161.765			−0.199957			−0.0999784	−	0.994990i	$-0.531877\pi$
$809$	−161.765			−0.199957			−0.0999784	+	0.994990i	$0.531877\pi$
$810$		0			0
$811$	−336.253	+	194.136i	−0.414616	+	0.239379i	−0.692771	−	0.721158i	$-0.743610\pi$
$811$	−336.253	+	194.136i	−0.414616	+	0.239379i	0.278155	+	0.960536i	$0.410277\pi$
$812$		0			0
$813$	272.836	−	792.881i	0.335592	−	0.975254i
$814$		0			0
$815$	−443.937	−	768.922i	−0.544708	−	0.943462i
$816$		0			0
$817$	159.046	+	576.995i	0.194670	+	0.706236i
$818$		0			0
$819$	850.224	−	1089.12i	1.03812	−	1.32982i
$820$		0			0
$821$	501.020	−	867.792i	0.610256	−	1.05699i	−0.380941	−	0.924599i	$-0.624400\pi$
$821$	501.020	−	867.792i	0.610256	−	1.05699i	0.991197	−	0.132395i	$-0.0422667\pi$
$822$		0			0
$823$	−155.121			−0.188483			−0.0942414	−	0.995549i	$-0.530043\pi$
$823$	−155.121			−0.188483			−0.0942414	+	0.995549i	$0.530043\pi$
$824$		0			0
$825$	798.639	−	155.403i	0.968048	−	0.188367i
$826$		0			0
$827$	863.503	−	498.544i	1.04414	−	0.602834i	0.123136	−	0.992390i	$-0.460705\pi$
$827$	863.503	−	498.544i	1.04414	−	0.602834i	0.921003	+	0.389556i	$0.127371\pi$
$828$		0			0
$829$		−	117.909i		−	0.142230i	−0.997468	−	0.0711152i	$-0.977344\pi$
$829$		−	117.909i		−	0.142230i	0.997468	−	0.0711152i	$-0.0226558\pi$
$830$		0			0
$831$	−171.162	−	196.821i	−0.205972	−	0.236849i
$832$		0			0
$833$	−94.1657	−	163.100i	−0.113044	−	0.195798i
$834$		0			0
$835$	529.324	−	305.605i	0.633921	−	0.365994i
$836$		0			0
$837$	−694.937	+	36.8323i	−0.830271	+	0.0440051i
$838$		0			0
$839$			1139.15i			1.35774i	0.734257	+	0.678872i	$0.237531\pi$
$839$			1139.15i			1.35774i	−0.734257	+	0.678872i	$0.762469\pi$
$840$		0			0
$841$	816.970	+	1415.03i	0.971427	+	1.68256i
$842$		0			0
$843$	−713.480	−	245.513i	−0.846358	−	0.291238i
$844$		0			0
$845$	−168.226	−	291.376i	−0.199084	−	0.344824i
$846$		0			0
$847$	1602.90			1.89244
$848$		0			0
$849$	−179.739	−	206.684i	−0.211707	−	0.243444i
$850$		0			0
$851$		−	218.969i		−	0.257308i
$852$		0			0
$853$	−768.793			−0.901281			−0.450641	−	0.892706i	$-0.648804\pi$
$853$	−768.793			−0.901281			−0.450641	+	0.892706i	$0.648804\pi$
$854$		0			0
$855$	−199.334	+	479.652i	−0.233139	+	0.560996i
$856$		0			0
$857$		−	431.377i		−	0.503357i	−0.967811	−	0.251678i	$-0.919018\pi$
$857$		−	431.377i		−	0.503357i	0.967811	−	0.251678i	$-0.0809825\pi$
$858$		0			0
$859$	1204.68			1.40242			0.701211	−	0.712954i	$-0.252643\pi$
$859$	1204.68			1.40242			0.701211	+	0.712954i	$0.252643\pi$
$860$		0			0
$861$	−1889.06	−	650.040i	−2.19403	−	0.754983i
$862$		0			0
$863$			691.413i			0.801174i	0.916259	+	0.400587i	$0.131194\pi$
$863$			691.413i			0.801174i	−0.916259	+	0.400587i	$0.868806\pi$
$864$		0			0
$865$	434.750	−	251.003i	0.502601	−	0.290177i
$866$		0			0
$867$	512.723	+	589.585i	0.591375	+	0.680029i
$868$		0			0
$869$	−1928.78	+	1113.58i	−2.21953	+	1.28145i
$870$		0			0
$871$	−1784.94			−2.04930
$872$		0			0
$873$	92.1322	+	227.777i	0.105535	+	0.260912i
$874$		0			0
$875$	−568.385	−	984.471i	−0.649582	−	1.12511i
$876$		0			0
$877$	−192.164	+	110.946i	−0.219115	+	0.126506i	−0.605540	−	0.795815i	$-0.707043\pi$
$877$	−192.164	+	110.946i	−0.219115	+	0.126506i	0.386425	+	0.922321i	$0.373710\pi$
$878$		0			0
$879$	−125.623	−	43.2278i	−0.142916	−	0.0491783i
$880$		0			0
$881$	665.909			0.755856			0.377928	−	0.925835i	$-0.376637\pi$
$881$	665.909			0.755856			0.377928	+	0.925835i	$0.376637\pi$
$882$		0			0
$883$	339.730	+	588.429i	0.384745	+	0.666398i	0.991734	−	0.128312i	$-0.0409560\pi$
$883$	339.730	+	588.429i	0.384745	+	0.666398i	−0.606989	+	0.794710i	$0.707623\pi$
$884$		0			0
$885$	−65.6359	−	22.5858i	−0.0741649	−	0.0255207i
$886$		0			0
$887$			1564.74i			1.76409i	0.471168	+	0.882043i	$0.343832\pi$
$887$			1564.74i			1.76409i	−0.471168	+	0.882043i	$0.656168\pi$
$888$		0			0
$889$	1057.96	+	610.812i	1.19005	+	0.687077i
$890$		0			0
$891$	1339.07	+	382.830i	1.50289	+	0.429663i
$892$		0			0
$893$	−630.705	−	164.162i	−0.706277	−	0.183832i
$894$		0			0
$895$	−381.966	+	220.528i	−0.426778	+	0.246400i
$896$		0			0
$897$	31.6363	+	162.583i	0.0352690	+	0.181252i
$898$		0			0
$899$	−641.125	−	1110.46i	−0.713154	−	1.23522i
$900$		0			0
$901$		−	55.8783i		−	0.0620181i
$902$		0			0
$903$	−569.187	−	654.514i	−0.630329	−	0.724822i
$904$		0			0
$905$	−207.221	−	119.639i	−0.228973	−	0.132198i
$906$		0			0
$907$			1370.09i			1.51057i	0.655394	+	0.755287i	$0.272503\pi$
$907$			1370.09i			1.51057i	−0.655394	+	0.755287i	$0.727497\pi$
$908$		0			0
$909$	−19.7186	+	140.708i	−0.0216926	+	0.154794i
$910$		0			0
$911$	−1122.02	+	647.796i	−1.23163	+	0.711083i	−0.967370	−	0.253369i	$-0.918461\pi$
$911$	−1122.02	+	647.796i	−1.23163	+	0.711083i	−0.264261	+	0.964451i	$0.585128\pi$
$912$		0			0
$913$	1077.38	−	1866.07i	1.18004	−	2.04389i
$914$		0			0
$915$	70.3913	−	13.6971i	0.0769304	−	0.0149695i
$916$		0			0
$917$	665.593	−	1152.84i	0.725837	−	1.25719i
$918$		0			0
$919$	−142.924			−0.155522			−0.0777608	−	0.996972i	$-0.524777\pi$
$919$	−142.924			−0.155522			−0.0777608	+	0.996972i	$0.524777\pi$
$920$		0			0
$921$	−1135.75	−	390.820i	−1.23317	−	0.424344i
$922$		0			0
$923$	617.713	−	1069.91i	0.669245	−	1.15917i
$924$		0			0
$925$	−906.160	−	523.172i	−0.979633	−	0.565591i
$926$		0			0
$927$	831.471	+	116.521i	0.896948	+	0.125697i
$928$		0			0
$929$	405.181			0.436148			0.218074	−	0.975932i	$-0.430023\pi$
$929$	405.181			0.436148			0.218074	+	0.975932i	$0.430023\pi$
$930$		0			0
$931$	−648.064	−	168.680i	−0.696095	−	0.181182i
$932$		0			0
$933$	−414.416	+	1204.32i	−0.444176	+	1.29081i
$934$		0			0
$935$	−139.540	−	241.690i	−0.149240	−	0.258492i
$936$		0			0
$937$	−115.023	−	199.226i	−0.122757	−	0.212621i	0.798097	−	0.602529i	$-0.205840\pi$
$937$	−115.023	−	199.226i	−0.122757	−	0.212621i	−0.920854	+	0.389908i	$0.872507\pi$
$938$		0			0
$939$	358.658	−	1042.29i	0.381958	−	1.11000i
$940$		0			0
$941$		−	777.835i		−	0.826605i	−0.910594	−	0.413302i	$-0.864375\pi$
$941$		−	777.835i		−	0.826605i	0.910594	−	0.413302i	$-0.135625\pi$
$942$		0			0
$943$	207.402	−	119.744i	0.219939	−	0.126982i
$944$		0			0
$945$	−39.8414	−	751.712i	−0.0421602	−	0.795463i
$946$		0			0
$947$	−705.817			−0.745318			−0.372659	−	0.927968i	$-0.621554\pi$
$947$	−705.817			−0.745318			−0.372659	+	0.927968i	$0.621554\pi$
$948$		0			0
$949$	−133.088	−	76.8386i	−0.140241	−	0.0809680i
$950$		0			0
$951$	−36.3552	−	12.5101i	−0.0382284	−	0.0131547i
$952$		0			0
$953$	971.095	+	560.662i	1.01899	+	0.588312i	0.913810	−	0.406141i	$-0.133126\pi$
$953$	971.095	+	560.662i	1.01899	+	0.588312i	0.105177	+	0.994454i	$0.466459\pi$
$954$		0			0
$955$	352.601	−	610.723i	0.369216	−	0.639500i
$956$		0			0
$957$	490.142	+	2518.91i	0.512165	+	2.63209i
$958$		0			0
$959$	207.961			0.216852
$960$		0			0
$961$	−148.337	−	256.927i	−0.154357	−	0.267354i
$962$		0			0
$963$	−708.644	−	1751.97i	−0.735872	−	1.81928i
$964$		0			0
$965$	952.354	+	549.842i	0.986895	+	0.569784i
$966$		0			0
$967$	−664.306	−	1150.61i	−0.686976	−	1.18988i	−0.972811	−	0.231599i	$-0.925604\pi$
$967$	−664.306	−	1150.61i	−0.686976	−	1.18988i	0.285835	−	0.958279i	$-0.407729\pi$
$968$		0			0
$969$	−303.984	−	19.0085i	−0.313709	−	0.0196166i
$970$		0			0
$971$	183.805	+	106.120i	0.189295	+	0.109289i	0.591652	−	0.806193i	$-0.298476\pi$
$971$	183.805	+	106.120i	0.189295	+	0.109289i	−0.402358	+	0.915483i	$0.631809\pi$
$972$		0			0
$973$	−424.119	−	734.595i	−0.435888	−	0.754980i
$974$		0			0
$975$	748.406	+	257.532i	0.767596	+	0.264135i
$976$		0			0
$977$	−129.948	−	75.0254i	−0.133007	−	0.0767916i	0.432020	−	0.901864i	$-0.357801\pi$
$977$	−129.948	−	75.0254i	−0.133007	−	0.0767916i	−0.565027	+	0.825072i	$0.691134\pi$
$978$		0			0
$979$	−1690.87	−	976.223i	−1.72714	−	0.997164i
$980$		0			0
$981$	−1272.73	−	178.358i	−1.29738	−	0.181813i
$982$		0			0
$983$			150.314i			0.152913i	0.997073	+	0.0764565i	$0.0243606\pi$
$983$			150.314i			0.152913i	−0.997073	+	0.0764565i	$0.975639\pi$
$984$		0			0
$985$	66.1050	+	114.497i	0.0671117	+	0.116241i
$986$		0			0
$987$	927.109	−	180.401i	0.939320	−	0.182777i
$988$		0			0
$989$	103.980			0.105136
$990$		0			0
$991$	607.427	+	350.698i	0.612943	+	0.353883i	0.774117	−	0.633043i	$-0.218194\pi$
$991$	607.427	+	350.698i	0.612943	+	0.353883i	−0.161173	+	0.986926i	$0.551528\pi$
$992$		0			0
$993$	−249.654	+	217.108i	−0.251414	+	0.218638i
$994$		0			0
$995$	537.748	−	931.406i	0.540450	−	0.936086i
$996$		0			0
$997$	359.870	−	623.313i	0.360953	−	0.625189i	−0.627165	−	0.778886i	$-0.715785\pi$
$997$	359.870	−	623.313i	0.360953	−	0.625189i	0.988118	+	0.153698i	$0.0491181\pi$
$998$		0			0
$999$	−976.386	−	1501.56i	−0.977363	−	1.50306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.37	✓	80
3.2	odd	2		2052.3.s.a.901.14		80
9.2	odd	6		2052.3.bl.a.1585.27		80
9.7	even	3		684.3.bl.a.673.25	yes	80
19.12	odd	6		684.3.bl.a.373.25	yes	80
57.50	even	6		2052.3.bl.a.145.27		80
171.88	odd	6	inner	684.3.s.a.601.37	yes	80
171.164	even	6		2052.3.s.a.829.14		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.37	✓	80	1.1	even	1	trivial
684.3.s.a.601.37	yes	80	171.88	odd	6	inner
684.3.bl.a.373.25	yes	80	19.12	odd	6
684.3.bl.a.673.25	yes	80	9.7	even	3
2052.3.s.a.829.14		80	171.164	even	6
2052.3.s.a.901.14		80	3.2	odd	2
2052.3.bl.a.145.27		80	57.50	even	6
2052.3.bl.a.1585.27		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.94477 - 0.573008i) q^{3} +(1.51878 + 2.63060i) q^{5} +(-4.58926 - 7.94883i) q^{7} +(8.34332 - 3.37475i) q^{9} +O(q^{10})\)	\(q+(2.94477 - 0.573008i) q^{3} +(1.51878 + 2.63060i) q^{5} +(-4.58926 - 7.94883i) q^{7} +(8.34332 - 3.37475i) q^{9} +(8.59704 + 14.8905i) q^{11} +16.7261i q^{13} +(5.97981 + 6.87625i) q^{15} +(-2.67174 + 4.62759i) q^{17} +(5.04896 + 18.3169i) q^{19} +(-18.0690 - 20.7778i) q^{21} +3.30087 q^{23} +(7.88662 - 13.6600i) q^{25} +(22.6354 - 14.7186i) q^{27} +(43.0837 + 24.8744i) q^{29} +(-22.3214 - 12.8873i) q^{31} +(33.8487 + 38.9229i) q^{33} +(13.9401 - 24.1450i) q^{35} -66.3367i q^{37} +(9.58421 + 49.2546i) q^{39} +(62.8325 - 36.2763i) q^{41} +31.5007 q^{43} +(21.5493 + 16.8225i) q^{45} +(-17.1505 + 29.7056i) q^{47} +(-17.6225 + 30.5232i) q^{49} +(-5.21601 + 15.1581i) q^{51} +(-9.05628 + 5.22865i) q^{53} +(-26.1140 + 45.2308i) q^{55} +(25.3637 + 51.0459i) q^{57} +(-6.59670 + 3.80861i) q^{59} +(3.93471 - 6.81513i) q^{61} +(-65.1150 - 50.8320i) q^{63} +(-43.9999 + 25.4033i) q^{65} +106.716i q^{67} +(9.72031 - 1.89143i) q^{69} +(-63.9663 - 36.9310i) q^{71} +(-4.59392 + 7.95690i) q^{73} +(15.3970 - 44.7447i) q^{75} +(78.9080 - 136.673i) q^{77} +129.531i q^{79} +(58.2221 - 56.3133i) q^{81} +(-62.6598 - 108.530i) q^{83} -16.2311 q^{85} +(141.125 + 48.5620i) q^{87} +(-98.3402 + 56.7767i) q^{89} +(132.953 - 76.7606i) q^{91} +(-73.1158 - 25.1597i) q^{93} +(-40.5162 + 41.1011i) q^{95} +27.3005i q^{97} +(121.980 + 95.2235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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