LMFDB - Embedded newform 504.3.l.h.181.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(181,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.181"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.26
Character	$\chi$	$=$	504.181
Dual form			504.3.l.h.181.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.81702 - 0.835731i) q^{2} +(2.60311 - 3.03707i) q^{4} +7.31322 q^{5} +(0.0227120 + 6.99996i) q^{7} +(2.19172 - 7.69392i) q^{8} +(13.2882 - 6.11188i) q^{10} +15.8808i q^{11} +12.2995 q^{13} +(5.89135 + 12.7001i) q^{14} +(-2.44765 - 15.8117i) q^{16} +8.41229i q^{17} +8.46170 q^{19} +(19.0371 - 22.2108i) q^{20} +(13.2720 + 28.8557i) q^{22} -45.5755 q^{23} +28.4831 q^{25} +(22.3484 - 10.2790i) q^{26} +(21.3185 + 18.1527i) q^{28} -15.5738i q^{29} -41.0781i q^{31} +(-17.6617 - 26.6845i) q^{32} +(7.03040 + 15.2853i) q^{34} +(0.166098 + 51.1922i) q^{35} +11.2257i q^{37} +(15.3751 - 7.07170i) q^{38} +(16.0285 - 56.2673i) q^{40} -22.8018i q^{41} -46.2778i q^{43} +(48.2311 + 41.3394i) q^{44} +(-82.8114 + 38.0888i) q^{46} +62.8287i q^{47} +(-48.9990 + 0.317966i) q^{49} +(51.7543 - 23.8042i) q^{50} +(32.0169 - 37.3544i) q^{52} -79.7103i q^{53} +116.140i q^{55} +(53.9069 + 15.1672i) q^{56} +(-13.0155 - 28.2979i) q^{58} -27.2534 q^{59} +15.7029 q^{61} +(-34.3302 - 74.6396i) q^{62} +(-54.3927 - 33.7258i) q^{64} +89.9487 q^{65} -55.8440i q^{67} +(25.5487 + 21.8981i) q^{68} +(43.0847 + 92.8784i) q^{70} +37.3473 q^{71} -105.242i q^{73} +(9.38165 + 20.3973i) q^{74} +(22.0267 - 25.6988i) q^{76} +(-111.165 + 0.360684i) q^{77} +92.1093 q^{79} +(-17.9002 - 115.634i) q^{80} +(-19.0562 - 41.4313i) q^{82} -38.3882 q^{83} +61.5208i q^{85} +(-38.6758 - 84.0877i) q^{86} +(122.185 + 34.8062i) q^{88} +90.6203i q^{89} +(0.279345 + 86.0959i) q^{91} +(-118.638 + 138.416i) q^{92} +(52.5078 + 114.161i) q^{94} +61.8822 q^{95} +26.7589i q^{97} +(-88.7663 + 41.5277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.81702	−	0.835731i	0.908509	−	0.417865i
$2$	1.81702	−	0.835731i	0.908509	−	0.417865i
$3$		0			0
$3$		0			0
$4$	2.60311	−	3.03707i	0.650777	−	0.759269i
$5$	7.31322			1.46264			0.731322	−	0.682033i	$-0.238904\pi$
$5$	7.31322			1.46264			0.731322	+	0.682033i	$0.238904\pi$
$6$		0			0
$7$	0.0227120	+	6.99996i	0.00324457	+	0.999995i
$7$	0.0227120	+	6.99996i	0.00324457	+	0.999995i
$8$	2.19172	−	7.69392i	0.273965	−	0.961740i
$9$		0			0
$10$	13.2882	−	6.11188i	1.32882	−	0.611188i
$11$			15.8808i			1.44371i	0.692046	+	0.721853i	$0.256710\pi$
$11$			15.8808i			1.44371i	−0.692046	+	0.721853i	$0.743290\pi$
$12$		0			0
$13$	12.2995			0.946114			0.473057	−	0.881032i	$-0.343151\pi$
$13$	12.2995			0.946114			0.473057	+	0.881032i	$0.343151\pi$
$14$	5.89135	+	12.7001i	0.420811	+	0.907148i
$15$		0			0
$16$	−2.44765	−	15.8117i	−0.152978	−	0.988230i
$17$			8.41229i			0.494840i	0.968908	+	0.247420i	$0.0795828\pi$
$17$			8.41229i			0.494840i	−0.968908	+	0.247420i	$0.920417\pi$
$18$		0			0
$19$	8.46170			0.445353			0.222676	−	0.974892i	$-0.428521\pi$
$19$	8.46170			0.445353			0.222676	+	0.974892i	$0.428521\pi$
$20$	19.0371	−	22.2108i	0.951855	−	1.11054i
$21$		0			0
$22$	13.2720	+	28.8557i	0.603275	+	1.31162i
$23$	−45.5755			−1.98154			−0.990771	−	0.135547i	$-0.956721\pi$
$23$	−45.5755			−1.98154			−0.990771	+	0.135547i	$0.956721\pi$
$24$		0			0
$25$	28.4831			1.13932
$26$	22.3484	−	10.2790i	0.859553	−	0.395348i
$27$		0			0
$28$	21.3185	+	18.1527i	0.761376	+	0.648310i
$29$		−	15.5738i		−	0.537028i	−0.963276	−	0.268514i	$-0.913467\pi$
$29$		−	15.5738i		−	0.537028i	0.963276	−	0.268514i	$-0.0865325\pi$
$30$		0			0
$31$		−	41.0781i		−	1.32510i	−0.749018	−	0.662549i	$-0.769475\pi$
$31$		−	41.0781i		−	1.32510i	0.749018	−	0.662549i	$-0.230525\pi$
$32$	−17.6617	−	26.6845i	−0.551929	−	0.833891i
$33$		0			0
$34$	7.03040	+	15.2853i	0.206777	+	0.449567i
$35$	0.166098	+	51.1922i	0.00474564	+	1.46264i
$36$		0			0
$37$			11.2257i			0.303397i	0.988427	+	0.151698i	$0.0484743\pi$
$37$			11.2257i			0.303397i	−0.988427	+	0.151698i	$0.951526\pi$
$38$	15.3751	−	7.07170i	0.404607	−	0.186097i
$39$		0			0
$40$	16.0285	−	56.2673i	0.400713	−	1.40668i
$41$		−	22.8018i		−	0.556141i	−0.960561	−	0.278071i	$-0.910305\pi$
$41$		−	22.8018i		−	0.556141i	0.960561	−	0.278071i	$-0.0896949\pi$
$42$		0			0
$43$		−	46.2778i		−	1.07623i	−0.842872	−	0.538114i	$-0.819137\pi$
$43$		−	46.2778i		−	1.07623i	0.842872	−	0.538114i	$-0.180863\pi$
$44$	48.2311	+	41.3394i	1.09616	+	0.939532i
$45$		0			0
$46$	−82.8114	+	38.0888i	−1.80025	+	0.828018i
$47$			62.8287i			1.33678i	0.743811	+	0.668390i	$0.233016\pi$
$47$			62.8287i			1.33678i	−0.743811	+	0.668390i	$0.766984\pi$
$48$		0			0
$49$	−48.9990	+	0.317966i	−0.999979	+	0.00648910i
$50$	51.7543	−	23.8042i	1.03509	−	0.476084i
$51$		0			0
$52$	32.0169	−	37.3544i	0.615709	−	0.718354i
$53$		−	79.7103i		−	1.50397i	−0.659181	−	0.751984i	$-0.729097\pi$
$53$		−	79.7103i		−	1.50397i	0.659181	−	0.751984i	$-0.270903\pi$
$54$		0			0
$55$			116.140i			2.11163i
$56$	53.9069	+	15.1672i	0.962624	+	0.270843i
$57$		0			0
$58$	−13.0155	−	28.2979i	−0.224405	−	0.487895i
$59$	−27.2534			−0.461923			−0.230961	−	0.972963i	$-0.574187\pi$
$59$	−27.2534			−0.461923			−0.230961	+	0.972963i	$0.574187\pi$
$60$		0			0
$61$	15.7029			0.257424			0.128712	−	0.991682i	$-0.458916\pi$
$61$	15.7029			0.257424			0.128712	+	0.991682i	$0.458916\pi$
$62$	−34.3302	−	74.6396i	−0.553713	−	1.20386i
$63$		0			0
$64$	−54.3927	−	33.7258i	−0.849886	−	0.526966i
$65$	89.9487			1.38383
$66$		0			0
$67$		−	55.8440i		−	0.833493i	−0.909023	−	0.416746i	$-0.863170\pi$
$67$		−	55.8440i		−	0.833493i	0.909023	−	0.416746i	$-0.136830\pi$
$68$	25.5487	+	21.8981i	0.375717	+	0.322031i
$69$		0			0
$70$	43.0847	+	92.8784i	0.615496	+	1.32683i
$71$	37.3473			0.526018			0.263009	−	0.964793i	$-0.415285\pi$
$71$	37.3473			0.526018			0.263009	+	0.964793i	$0.415285\pi$
$72$		0			0
$73$		−	105.242i		−	1.44168i	−0.693103	−	0.720839i	$-0.743757\pi$
$73$		−	105.242i		−	1.44168i	0.693103	−	0.720839i	$-0.256243\pi$
$74$	9.38165	+	20.3973i	0.126779	+	0.275639i
$75$		0			0
$76$	22.0267	−	25.6988i	0.289825	−	0.338142i
$77$	−111.165	+	0.360684i	−1.44370	+	0.00468420i
$78$		0			0
$79$	92.1093			1.16594			0.582970	−	0.812494i	$-0.301890\pi$
$79$	92.1093			1.16594			0.582970	+	0.812494i	$0.301890\pi$
$80$	−17.9002	−	115.634i	−0.223752	−	1.44543i
$81$		0			0
$82$	−19.0562	−	41.4313i	−0.232392	−	0.505259i
$83$	−38.3882			−0.462508			−0.231254	−	0.972893i	$-0.574283\pi$
$83$	−38.3882			−0.462508			−0.231254	+	0.972893i	$0.574283\pi$
$84$		0			0
$85$			61.5208i			0.723775i
$86$	−38.6758	−	84.0877i	−0.449719	−	0.977764i
$87$		0			0
$88$	122.185	+	34.8062i	1.38847	+	0.395525i
$89$			90.6203i			1.01821i	0.860706	+	0.509103i	$0.170023\pi$
$89$			90.6203i			1.01821i	−0.860706	+	0.509103i	$0.829977\pi$
$90$		0			0
$91$	0.279345	+	86.0959i	0.00306973	+	0.946109i
$92$	−118.638	+	138.416i	−1.28954	+	1.50452i
$93$		0			0
$94$	52.5078	+	114.161i	0.558594	+	1.21448i
$95$	61.8822			0.651392
$96$		0			0
$97$			26.7589i			0.275865i	0.990442	+	0.137932i	$0.0440457\pi$
$97$			26.7589i			0.275865i	−0.990442	+	0.137932i	$0.955954\pi$
$98$	−88.7663	+	41.5277i	−0.905778	+	0.423752i
$99$		0			0
$100$	74.1446	−	86.5054i	0.741446	−	0.865054i
$101$	1.38519			0.0137148			0.00685738	−	0.999976i	$-0.497817\pi$
$101$	1.38519			0.0137148			0.00685738	+	0.999976i	$0.497817\pi$
$102$		0			0
$103$			126.743i			1.23051i	0.788328	+	0.615255i	$0.210947\pi$
$103$			126.743i			1.23051i	−0.788328	+	0.615255i	$0.789053\pi$
$104$	26.9570	−	94.6312i	0.259202	−	0.909915i
$105$		0			0
$106$	−66.6164	−	144.835i	−0.628456	−	1.36637i
$107$		−	2.01251i		−	0.0188085i	−0.999956	−	0.00940423i	$-0.997006\pi$
$107$		−	2.01251i		−	0.0188085i	0.999956	−	0.00940423i	$-0.00299350\pi$
$108$		0			0
$109$			4.45196i			0.0408436i	0.999791	+	0.0204218i	$0.00650092\pi$
$109$			4.45196i			0.0408436i	−0.999791	+	0.0204218i	$0.993499\pi$
$110$	97.0614	+	211.028i	0.882376	+	1.91843i
$111$		0			0
$112$	110.626	−	17.4926i	0.987728	−	0.156184i
$113$	−172.799			−1.52919			−0.764596	−	0.644510i	$-0.777061\pi$
$113$	−172.799			−1.52919			−0.764596	+	0.644510i	$0.777061\pi$
$114$		0			0
$115$	−333.303			−2.89829
$116$	−47.2988	−	40.5403i	−0.407748	−	0.349485i
$117$		0			0
$118$	−49.5200	+	22.7765i	−0.419661	+	0.193021i
$119$	−58.8857	+	0.191060i	−0.494838	+	0.00160554i
$120$		0			0
$121$	−131.199			−1.08429
$122$	28.5324	−	13.1234i	0.233872	−	0.107569i
$123$		0			0
$124$	−124.757	−	106.931i	−1.00611	−	0.862344i
$125$	25.4728			0.203782
$126$		0			0
$127$	−77.1696			−0.607635			−0.303818	−	0.952730i	$-0.598261\pi$
$127$	−77.1696			−0.607635			−0.303818	+	0.952730i	$0.598261\pi$
$128$	−127.018	−	15.8227i	−0.992330	−	0.123615i
$129$		0			0
$130$	163.438	−	75.1729i	1.25722	−	0.578253i
$131$	−245.145			−1.87134			−0.935669	−	0.352879i	$-0.885203\pi$
$131$	−245.145			−1.87134			−0.935669	+	0.352879i	$0.885203\pi$
$132$		0			0
$133$	0.192182	+	59.2316i	0.00144498	+	0.445350i
$134$	−46.6705	−	101.470i	−0.348288	−	0.757236i
$135$		0			0
$136$	64.7234	+	18.4374i	0.475908	+	0.135569i
$137$	72.7244			0.530835			0.265418	−	0.964134i	$-0.414490\pi$
$137$	72.7244			0.530835			0.265418	+	0.964134i	$0.414490\pi$
$138$		0			0
$139$	150.950			1.08597			0.542984	−	0.839743i	$-0.317294\pi$
$139$	150.950			1.08597			0.542984	+	0.839743i	$0.317294\pi$
$140$	155.907	+	132.755i	1.11362	+	0.948247i
$141$		0			0
$142$	67.8607	−	31.2123i	0.477892	−	0.219805i
$143$			195.325i			1.36591i
$144$		0			0
$145$		−	113.895i		−	0.785480i
$146$	−87.9543	−	191.227i	−0.602427	−	1.30978i
$147$		0			0
$148$	34.0932	+	29.2217i	0.230360	+	0.197444i
$149$			249.152i			1.67216i	0.548607	+	0.836081i	$0.315158\pi$
$149$			249.152i			1.67216i	−0.548607	+	0.836081i	$0.684842\pi$
$150$		0			0
$151$	−108.996			−0.721828			−0.360914	−	0.932599i	$-0.617535\pi$
$151$	−108.996			−0.721828			−0.360914	+	0.932599i	$0.617535\pi$
$152$	18.5457	−	65.1036i	0.122011	−	0.428313i
$153$		0			0
$154$	−201.687	+	93.5592i	−1.30966	+	0.607527i
$155$		−	300.413i		−	1.93815i
$156$		0			0
$157$	4.46627			0.0284476			0.0142238	−	0.999899i	$-0.495472\pi$
$157$	4.46627			0.0284476			0.0142238	+	0.999899i	$0.495472\pi$
$158$	167.364	−	76.9786i	1.05927	−	0.487206i
$159$		0			0
$160$	−129.164	−	195.150i	−0.807275	−	1.21969i
$161$	−1.03511	−	319.027i	−0.00642925	−	1.98153i
$162$		0			0
$163$			60.6259i			0.371938i	0.982556	+	0.185969i	$0.0595424\pi$
$163$			60.6259i			0.371938i	−0.982556	+	0.185969i	$0.940458\pi$
$164$	−69.2508	−	59.3556i	−0.422261	−	0.361924i
$165$		0			0
$166$	−69.7520	+	32.0822i	−0.420193	+	0.193266i
$167$			234.030i			1.40138i	0.713466	+	0.700690i	$0.247124\pi$
$167$			234.030i			1.40138i	−0.713466	+	0.700690i	$0.752876\pi$
$168$		0			0
$169$	−17.7229			−0.104869
$170$	51.4149	+	111.784i	0.302440	+	0.657556i
$171$		0			0
$172$	−140.549	−	120.466i	−0.817147	−	0.700385i
$173$	146.553			0.847129			0.423564	−	0.905866i	$-0.360779\pi$
$173$	146.553			0.847129			0.423564	+	0.905866i	$0.360779\pi$
$174$		0			0
$175$	0.646908	+	199.381i	0.00369662	+	1.13932i
$176$	251.102	−	38.8706i	1.42671	−	0.220855i
$177$		0			0
$178$	75.7342	+	164.659i	0.425473	+	0.925049i
$179$		−	4.20304i		−	0.0234807i	−0.999931	−	0.0117403i	$-0.996263\pi$
$179$		−	4.20304i		−	0.0234807i	0.999931	−	0.0117403i	$-0.00373715\pi$
$180$		0			0
$181$	−142.881			−0.789396			−0.394698	−	0.918811i	$-0.629151\pi$
$181$	−142.881			−0.789396			−0.394698	+	0.918811i	$0.629151\pi$
$182$	72.4605	+	156.204i	0.398135	+	0.858265i
$183$		0			0
$184$	−99.8886	+	350.654i	−0.542873	+	1.90573i
$185$			82.0958i			0.443761i
$186$		0			0
$187$	−133.594			−0.714404
$188$	190.815	+	163.550i	1.01498	+	0.869946i
$189$		0			0
$190$	112.441	−	51.7169i	0.591795	−	0.272194i
$191$	215.929			1.13052			0.565258	−	0.824914i	$-0.308777\pi$
$191$	215.929			1.13052			0.565258	+	0.824914i	$0.308777\pi$
$192$		0			0
$193$	178.327			0.923975			0.461987	−	0.886887i	$-0.347137\pi$
$193$	178.327			0.923975			0.461987	+	0.886887i	$0.347137\pi$
$194$	22.3632	+	48.6214i	0.115274	+	0.250626i
$195$		0			0
$196$	−126.584	+	149.641i	−0.645837	+	0.763476i
$197$		−	8.37478i		−	0.0425116i	−0.999774	−	0.0212558i	$-0.993234\pi$
$197$		−	8.37478i		−	0.0425116i	0.999774	−	0.0212558i	$-0.00676644\pi$
$198$		0			0
$199$		−	57.4302i		−	0.288594i	−0.989534	−	0.144297i	$-0.953908\pi$
$199$		−	57.4302i		−	0.288594i	0.989534	−	0.144297i	$-0.0460921\pi$
$200$	62.4270	−	219.147i	0.312135	−	1.09573i
$201$		0			0
$202$	2.51692	−	1.15765i	0.0124600	−	0.00573092i
$203$	109.016	−	0.353712i	0.537025	−	0.00174242i
$204$		0			0
$205$		−	166.754i		−	0.813436i
$206$	105.923	+	230.294i	0.514188	+	1.11793i
$207$		0			0
$208$	−30.1048	−	194.475i	−0.144735	−	0.934977i
$209$			134.378i			0.642958i
$210$		0			0
$211$		−	306.750i		−	1.45379i	−0.686748	−	0.726895i	$-0.740963\pi$
$211$		−	306.750i		−	1.45379i	0.686748	−	0.726895i	$-0.259037\pi$
$212$	−242.086	−	207.495i	−1.14192	−	0.978749i
$213$		0			0
$214$	−1.68191	−	3.65676i	−0.00785940	−	0.0170877i
$215$		−	338.440i		−	1.57414i
$216$		0			0
$217$	287.545	−	0.932964i	1.32509	−	0.00429937i
$218$	3.72064	+	8.08929i	0.0170671	+	0.0371068i
$219$		0			0
$220$	352.724	+	302.324i	1.60329	+	1.37420i
$221$			103.467i			0.468175i
$222$		0			0
$223$			320.455i			1.43702i	0.695517	+	0.718510i	$0.255176\pi$
$223$			320.455i			1.43702i	−0.695517	+	0.718510i	$0.744824\pi$
$224$	186.390	−	124.237i	0.832096	−	0.554631i
$225$		0			0
$226$	−313.978	+	144.413i	−1.38928	+	0.638996i
$227$	235.456			1.03725			0.518626	−	0.855001i	$-0.326444\pi$
$227$	235.456			1.03725			0.518626	+	0.855001i	$0.326444\pi$
$228$		0			0
$229$	303.138			1.32375			0.661874	−	0.749615i	$-0.269761\pi$
$229$	303.138			1.32375			0.661874	+	0.749615i	$0.269761\pi$
$230$	−605.618	+	278.552i	−2.63312	+	1.21109i
$231$		0			0
$232$	−119.824	−	34.1334i	−0.516481	−	0.147127i
$233$	−200.433			−0.860229			−0.430115	−	0.902774i	$-0.641527\pi$
$233$	−200.433			−0.860229			−0.430115	+	0.902774i	$0.641527\pi$
$234$		0			0
$235$			459.480i			1.95523i
$236$	−70.9437	+	82.7707i	−0.300609	+	0.350723i
$237$		0			0
$238$	−106.837	+	49.5597i	−0.448894	+	0.208234i
$239$	−172.580			−0.722090			−0.361045	−	0.932548i	$-0.617580\pi$
$239$	−172.580			−0.722090			−0.361045	+	0.932548i	$0.617580\pi$
$240$		0			0
$241$		−	235.213i		−	0.975989i	−0.872847	−	0.487995i	$-0.837729\pi$
$241$		−	235.213i		−	0.975989i	0.872847	−	0.487995i	$-0.162271\pi$
$242$	−238.391	+	109.647i	−0.985087	+	0.453087i
$243$		0			0
$244$	40.8763	−	47.6909i	0.167526	−	0.195454i
$245$	−358.340	+	2.32535i	−1.46261	+	0.00949124i
$246$		0			0
$247$	104.074			0.421354
$248$	−316.051	−	90.0316i	−1.27440	−	0.363030i
$249$		0			0
$250$	46.2845	−	21.2884i	0.185138	−	0.0851535i
$251$	164.929			0.657087			0.328543	−	0.944489i	$-0.393442\pi$
$251$	164.929			0.657087			0.328543	+	0.944489i	$0.393442\pi$
$252$		0			0
$253$		−	723.774i		−	2.86077i
$254$	−140.219	+	64.4930i	−0.552042	+	0.253910i
$255$		0			0
$256$	−244.018	+	77.4028i	−0.953195	+	0.302355i
$257$		−	344.374i		−	1.33998i	−0.742371	−	0.669989i	$-0.766299\pi$
$257$		−	344.374i		−	1.33998i	0.742371	−	0.669989i	$-0.233701\pi$
$258$		0			0
$259$	−78.5794	+	0.254957i	−0.303395	+	0.000984391i
$260$	234.146	−	273.181i	0.900563	−	1.05070i
$261$		0			0
$262$	−445.433	+	204.875i	−1.70013	+	0.781967i
$263$	−317.186			−1.20603			−0.603016	−	0.797729i	$-0.706034\pi$
$263$	−317.186			−1.20603			−0.603016	+	0.797729i	$0.706034\pi$
$264$		0			0
$265$		−	582.939i		−	2.19977i
$266$	49.8508	+	107.464i	0.187409	+	0.404001i
$267$		0			0
$268$	−169.602	−	145.368i	−0.632845	−	0.542418i
$269$	215.901			0.802604			0.401302	−	0.915946i	$-0.368558\pi$
$269$	215.901			0.802604			0.401302	+	0.915946i	$0.368558\pi$
$270$		0			0
$271$			2.35354i			0.00868464i	0.999991	+	0.00434232i	$0.00138221\pi$
$271$			2.35354i			0.00868464i	−0.999991	+	0.00434232i	$0.998618\pi$
$272$	133.012	−	20.5903i	0.489016	−	0.0756997i
$273$		0			0
$274$	132.142	−	60.7780i	0.482269	−	0.221818i
$275$			452.334i			1.64485i
$276$		0			0
$277$			216.483i			0.781528i	0.920491	+	0.390764i	$0.127789\pi$
$277$			216.483i			0.781528i	−0.920491	+	0.390764i	$0.872211\pi$
$278$	274.278	−	126.153i	0.986612	−	0.453789i
$279$		0			0
$280$	394.233	+	110.921i	1.40797	+	0.396147i
$281$	264.456			0.941126			0.470563	−	0.882366i	$-0.344051\pi$
$281$	264.456			0.941126			0.470563	+	0.882366i	$0.344051\pi$
$282$		0			0
$283$	−114.488			−0.404550			−0.202275	−	0.979329i	$-0.564833\pi$
$283$	−114.488			−0.404550			−0.202275	+	0.979329i	$0.564833\pi$
$284$	97.2191	−	113.427i	0.342321	−	0.399389i
$285$		0			0
$286$	163.239	+	354.909i	0.570767	+	1.24094i
$287$	159.612	−	0.517874i	0.556138	−	0.00180444i
$288$		0			0
$289$	218.233			0.755133
$290$	−95.1852	−	206.949i	−0.328225	−	0.713616i
$291$		0			0
$292$	−319.629	−	273.957i	−1.09462	−	0.938211i
$293$	257.014			0.877182			0.438591	−	0.898687i	$-0.355478\pi$
$293$	257.014			0.877182			0.438591	+	0.898687i	$0.355478\pi$
$294$		0			0
$295$	−199.310			−0.675628
$296$	86.3695	+	24.6035i	0.291789	+	0.0831201i
$297$		0			0
$298$	208.224	+	452.714i	0.698738	+	1.51917i
$299$	−560.554			−1.87476
$300$		0			0
$301$	323.943	−	1.05106i	1.07622	−	0.00349190i
$302$	−198.048	+	91.0913i	−0.655787	+	0.301627i
$303$		0			0
$304$	−20.7113	−	133.794i	−0.0681292	−	0.440111i
$305$	114.839			0.376520
$306$		0			0
$307$	378.989			1.23449			0.617246	−	0.786770i	$-0.288248\pi$
$307$	378.989			1.23449			0.617246	+	0.786770i	$0.288248\pi$
$308$	−288.279	+	338.555i	−0.935970	+	1.09920i
$309$		0			0
$310$	−251.064	−	545.855i	−0.809884	−	1.76082i
$311$			230.962i			0.742642i	0.928504	+	0.371321i	$0.121095\pi$
$311$			230.962i			0.742642i	−0.928504	+	0.371321i	$0.878905\pi$
$312$		0			0
$313$			328.672i			1.05007i	0.851080	+	0.525035i	$0.175948\pi$
$313$			328.672i			1.05007i	−0.851080	+	0.525035i	$0.824052\pi$
$314$	8.11530	−	3.73260i	0.0258449	−	0.0118873i
$315$		0			0
$316$	239.771	−	279.743i	0.758767	−	0.885262i
$317$		−	153.186i		−	0.483237i	−0.970371	−	0.241618i	$-0.922322\pi$
$317$		−	153.186i		−	0.483237i	0.970371	−	0.241618i	$-0.0776782\pi$
$318$		0			0
$319$	247.324			0.775311
$320$	−397.786	−	246.644i	−1.24308	−	0.770763i
$321$		0			0
$322$	−268.501	−	578.812i	−0.833854	−	1.79755i
$323$			71.1822i			0.220378i
$324$		0			0
$325$	350.327			1.07793
$326$	50.6669	+	110.158i	0.155420	+	0.337909i
$327$		0			0
$328$	−175.435	−	49.9751i	−0.534863	−	0.152363i
$329$	−439.798	+	1.42696i	−1.33677	+	0.00433727i
$330$		0			0
$331$			395.271i			1.19417i	0.802177	+	0.597087i	$0.203675\pi$
$331$			395.271i			1.19417i	−0.802177	+	0.597087i	$0.796325\pi$
$332$	−99.9286	+	116.588i	−0.300990	+	0.351168i
$333$		0			0
$334$	195.586	+	425.238i	0.585588	+	1.27317i
$335$		−	408.399i		−	1.21910i
$336$		0			0
$337$	−155.326			−0.460908			−0.230454	−	0.973083i	$-0.574021\pi$
$337$	−155.326			−0.460908			−0.230454	+	0.973083i	$0.574021\pi$
$338$	−32.2028	+	14.8115i	−0.0952745	+	0.0438211i
$339$		0			0
$340$	186.843	+	160.145i	0.549540	+	0.471016i
$341$	652.351			1.91305
$342$		0			0
$343$	−3.33861	−	342.984i	−0.00973357	−	0.999953i
$344$	−356.058	−	101.428i	−1.03505	−	0.294849i
$345$		0			0
$346$	266.290	−	122.479i	0.769624	−	0.353986i
$347$		−	309.937i		−	0.893191i	−0.894736	−	0.446596i	$-0.852636\pi$
$347$		−	309.937i		−	0.893191i	0.894736	−	0.446596i	$-0.147364\pi$
$348$		0			0
$349$	−533.429			−1.52845			−0.764226	−	0.644949i	$-0.776879\pi$
$349$	−533.429			−1.52845			−0.764226	+	0.644949i	$0.776879\pi$
$350$	167.804	+	361.738i	0.479440	+	1.03354i
$351$		0			0
$352$	423.771	−	280.482i	1.20389	−	0.796823i
$353$		−	317.324i		−	0.898934i	−0.893297	−	0.449467i	$-0.851614\pi$
$353$		−	317.324i		−	0.898934i	0.893297	−	0.449467i	$-0.148386\pi$
$354$		0			0
$355$	273.129			0.769377
$356$	275.221	+	235.895i	0.773092	+	0.662625i
$357$		0			0
$358$	−3.51261	−	7.63700i	−0.00981176	−	0.0213324i
$359$	228.679			0.636988			0.318494	−	0.947925i	$-0.396823\pi$
$359$	228.679			0.636988			0.318494	+	0.947925i	$0.396823\pi$
$360$		0			0
$361$	−289.400			−0.801661
$362$	−259.617	+	119.410i	−0.717174	+	0.329861i
$363$		0			0
$364$	262.207	+	223.269i	0.720348	+	0.613375i
$365$		−	769.661i		−	2.10866i
$366$		0			0
$367$		−	127.971i		−	0.348694i	−0.984684	−	0.174347i	$-0.944219\pi$
$367$		−	127.971i		−	0.348694i	0.984684	−	0.174347i	$-0.0557814\pi$
$368$	111.553	+	720.624i	0.303132	+	1.95822i
$369$		0			0
$370$	68.6100	+	149.170i	0.185432	+	0.403161i
$371$	557.970	−	1.81038i	1.50396	−	0.00487973i
$372$		0			0
$373$			622.385i			1.66859i	0.551317	+	0.834296i	$0.314126\pi$
$373$			622.385i			1.66859i	−0.551317	+	0.834296i	$0.685874\pi$
$374$	−242.742	+	111.648i	−0.649043	+	0.298525i
$375$		0			0
$376$	483.399	+	137.703i	1.28563	+	0.366231i
$377$		−	191.550i		−	0.508089i
$378$		0			0
$379$		−	211.256i		−	0.557405i	−0.960377	−	0.278702i	$-0.910096\pi$
$379$		−	211.256i		−	0.557405i	0.960377	−	0.278702i	$-0.0899043\pi$
$380$	161.086	−	187.941i	0.423911	−	0.494581i
$381$		0			0
$382$	392.346	−	180.458i	1.02708	−	0.472403i
$383$		−	310.998i		−	0.812006i	−0.913872	−	0.406003i	$-0.866922\pi$
$383$		−	310.998i		−	0.812006i	0.913872	−	0.406003i	$-0.133078\pi$
$384$		0			0
$385$	−812.972	+	2.63776i	−2.11162	+	0.00685132i
$386$	324.024	−	149.033i	0.839439	−	0.386097i
$387$		0			0
$388$	81.2687	+	69.6563i	0.209455	+	0.179526i
$389$			557.569i			1.43334i	0.697412	+	0.716670i	$0.254335\pi$
$389$			557.569i			1.43334i	−0.697412	+	0.716670i	$0.745665\pi$
$390$		0			0
$391$		−	383.394i		−	0.980547i
$392$	−104.946	+	377.691i	−0.267718	+	0.963497i
$393$		0			0
$394$	−6.99906	−	15.2171i	−0.0177641	−	0.0386221i
$395$	673.615			1.70535
$396$		0			0
$397$	343.293			0.864718			0.432359	−	0.901702i	$-0.357681\pi$
$397$	343.293			0.864718			0.432359	+	0.901702i	$0.357681\pi$
$398$	−47.9962	−	104.352i	−0.120593	−	0.262190i
$399$		0			0
$400$	−69.7167	−	450.366i	−0.174292	−	1.12591i
$401$	544.592			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$401$	544.592			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$402$		0			0
$403$		−	505.239i		−	1.25369i
$404$	3.60580	−	4.20693i	0.00892525	−	0.0104132i
$405$		0			0
$406$	197.789	−	91.7508i	0.487164	−	0.225987i
$407$	−178.273			−0.438016
$408$		0			0
$409$			419.631i			1.02599i	0.858391	+	0.512997i	$0.171465\pi$
$409$			419.631i			1.02599i	−0.858391	+	0.512997i	$0.828535\pi$
$410$	−139.362	−	302.996i	−0.339907	−	0.739014i
$411$		0			0
$412$	384.927	+	329.925i	0.934288	+	0.800788i
$413$	−0.618979	−	190.773i	−0.00149874	−	0.461920i
$414$		0			0
$415$	−280.741			−0.676484
$416$	−217.230	−	328.206i	−0.522187	−	0.788956i
$417$		0			0
$418$	112.304	+	244.168i	0.268670	+	0.584134i
$419$	−435.089			−1.03840			−0.519199	−	0.854653i	$-0.673770\pi$
$419$	−435.089			−1.03840			−0.519199	+	0.854653i	$0.673770\pi$
$420$		0			0
$421$			219.731i			0.521927i	0.965349	+	0.260963i	$0.0840402\pi$
$421$			219.731i			0.521927i	−0.965349	+	0.260963i	$0.915960\pi$
$422$	−256.360	−	557.370i	−0.607489	−	1.32078i
$423$		0			0
$424$	−613.285	−	174.703i	−1.44643	−	0.412035i
$425$			239.608i			0.563784i
$426$		0			0
$427$	0.356644	+	109.920i	0.000835231	+	0.257423i
$428$	−6.11213	−	5.23877i	−0.0142807	−	0.0122401i
$429$		0			0
$430$	−282.845	−	614.951i	−0.657778	−	1.43012i
$431$	297.775			0.690894			0.345447	−	0.938438i	$-0.387727\pi$
$431$	297.775			0.690894			0.345447	+	0.938438i	$0.387727\pi$
$432$		0			0
$433$		−	425.481i		−	0.982635i	−0.870980	−	0.491318i	$-0.836515\pi$
$433$		−	425.481i		−	0.982635i	0.870980	−	0.491318i	$-0.163485\pi$
$434$	521.694	−	242.005i	1.20206	−	0.557616i
$435$		0			0
$436$	13.5209	+	11.5889i	0.0310113	+	0.0265801i
$437$	−385.646			−0.882485
$438$		0			0
$439$			376.609i			0.857878i	0.903333	+	0.428939i	$0.141113\pi$
$439$			376.609i			0.857878i	−0.903333	+	0.428939i	$0.858887\pi$
$440$	893.568	+	254.545i	2.03084	+	0.578512i
$441$		0			0
$442$	86.4703	+	188.001i	0.195634	+	0.425341i
$443$		−	8.28153i		−	0.0186942i	−0.999956	−	0.00934710i	$-0.997025\pi$
$443$		−	8.28153i		−	0.0186942i	0.999956	−	0.00934710i	$-0.00297532\pi$
$444$		0			0
$445$			662.726i			1.48927i
$446$	267.814	+	582.273i	0.600481	+	1.30555i
$447$		0			0
$448$	234.844	−	381.513i	0.524206	−	0.851592i
$449$	−438.457			−0.976520			−0.488260	−	0.872698i	$-0.662368\pi$
$449$	−438.457			−0.976520			−0.488260	+	0.872698i	$0.662368\pi$
$450$		0			0
$451$	362.110			0.802905
$452$	−449.814	+	524.802i	−0.995163	+	1.16107i
$453$		0			0
$454$	427.828	−	196.778i	0.942353	−	0.433432i
$455$	2.04291	+	629.638i	0.00448992	+	1.38382i
$456$		0			0
$457$	−75.2427			−0.164645			−0.0823224	−	0.996606i	$-0.526234\pi$
$457$	−75.2427			−0.164645			−0.0823224	+	0.996606i	$0.526234\pi$
$458$	550.808	−	253.342i	1.20264	−	0.553148i
$459$		0			0
$460$	−867.624	+	1012.27i	−1.88614	+	2.20058i
$461$	258.818			0.561428			0.280714	−	0.959791i	$-0.409429\pi$
$461$	258.818			0.561428			0.280714	+	0.959791i	$0.409429\pi$
$462$		0			0
$463$	−70.5104			−0.152290			−0.0761452	−	0.997097i	$-0.524261\pi$
$463$	−70.5104			−0.152290			−0.0761452	+	0.997097i	$0.524261\pi$
$464$	−246.248	+	38.1192i	−0.530707	+	0.0821535i
$465$		0			0
$466$	−364.191	+	167.508i	−0.781526	+	0.359460i
$467$	547.216			1.17177			0.585885	−	0.810394i	$-0.300747\pi$
$467$	547.216			1.17177			0.585885	+	0.810394i	$0.300747\pi$
$468$		0			0
$469$	390.906	−	1.26833i	0.833488	−	0.00270432i
$470$	384.001	+	834.883i	0.817024	+	1.77635i
$471$		0			0
$472$	−59.7319	+	209.686i	−0.126551	+	0.444249i
$473$	734.928			1.55376
$474$		0			0
$475$	241.016			0.507401
$476$	−152.706	+	179.338i	−0.320810	+	0.376760i
$477$		0			0
$478$	−313.580	+	144.230i	−0.656025	+	0.301736i
$479$		−	256.765i		−	0.536043i	−0.963413	−	0.268021i	$-0.913630\pi$
$479$		−	256.765i		−	0.536043i	0.963413	−	0.268021i	$-0.0863698\pi$
$480$		0			0
$481$			138.070i			0.287048i
$482$	−196.575	−	427.387i	−0.407832	−	0.886695i
$483$		0			0
$484$	−341.525	+	398.461i	−0.705631	+	0.823267i
$485$			195.693i			0.403492i
$486$		0			0
$487$	−226.766			−0.465638			−0.232819	−	0.972520i	$-0.574795\pi$
$487$	−226.766			−0.465638			−0.232819	+	0.972520i	$0.574795\pi$
$488$	34.4163	−	120.817i	0.0705253	−	0.247575i
$489$		0			0
$490$	−649.167	+	303.701i	−1.32483	+	0.619798i
$491$		−	265.821i		−	0.541386i	−0.962666	−	0.270693i	$-0.912747\pi$
$491$		−	265.821i		−	0.541386i	0.962666	−	0.270693i	$-0.0872529\pi$
$492$		0			0
$493$	131.011			0.265743
$494$	189.105	−	86.9782i	0.382804	−	0.176069i
$495$		0			0
$496$	−649.513	+	100.545i	−1.30950	+	0.202711i
$497$	0.848231	+	261.430i	0.00170670	+	0.526016i
$498$		0			0
$499$		−	701.805i		−	1.40642i	−0.710980	−	0.703212i	$-0.751749\pi$
$499$		−	701.805i		−	1.40642i	0.710980	−	0.703212i	$-0.248251\pi$
$500$	66.3084	−	77.3627i	0.132617	−	0.154725i
$501$		0			0
$502$	299.679	−	137.836i	0.596969	−	0.274574i
$503$		−	297.395i		−	0.591243i	−0.955305	−	0.295622i	$-0.904473\pi$
$503$		−	297.395i		−	0.591243i	0.955305	−	0.295622i	$-0.0955267\pi$
$504$		0			0
$505$	10.1302			0.0200598
$506$	−604.880	−	1315.11i	−1.19541	−	2.59903i
$507$		0			0
$508$	−200.881	+	234.370i	−0.395435	+	0.461358i
$509$	−470.194			−0.923760			−0.461880	−	0.886942i	$-0.652825\pi$
$509$	−470.194			−0.923760			−0.461880	+	0.886942i	$0.652825\pi$
$510$		0			0
$511$	736.693	−	2.39026i	1.44167	−	0.00467762i
$512$	−378.697	+	344.576i	−0.739643	+	0.672999i
$513$		0			0
$514$	−287.804	−	625.734i	−0.559930	−	1.21738i
$515$			926.896i			1.79980i
$516$		0			0
$517$	−997.768			−1.92992
$518$	−142.567	+	66.1344i	−0.275226	+	0.127673i
$519$		0			0
$520$	197.142	−	692.058i	0.379120	−	1.33088i
$521$			357.911i			0.686970i	0.939158	+	0.343485i	$0.111607\pi$
$521$			357.911i			0.686970i	−0.939158	+	0.343485i	$0.888393\pi$
$522$		0			0
$523$	−356.189			−0.681049			−0.340524	−	0.940236i	$-0.610605\pi$
$523$	−356.189			−0.681049			−0.340524	+	0.940236i	$0.610605\pi$
$524$	−638.140	+	744.524i	−1.21782	+	1.42085i
$525$		0			0
$526$	−576.333	+	265.082i	−1.09569	+	0.503959i
$527$	345.560			0.655712
$528$		0			0
$529$	1548.12			2.92651
$530$	−487.180	−	1059.21i	−0.919207	−	1.99851i
$531$		0			0
$532$	180.391	+	153.603i	0.339081	+	0.288727i
$533$		−	280.450i		−	0.526173i
$534$		0			0
$535$		−	14.7179i		−	0.0275101i
$536$	−429.659	−	122.394i	−0.801603	−	0.228348i
$537$		0			0
$538$	392.295	−	180.435i	0.729173	−	0.335380i
$539$	−5.04955	−	778.142i	−0.00936836	−	1.44368i
$540$		0			0
$541$		−	473.636i		−	0.875483i	−0.899101	−	0.437742i	$-0.855778\pi$
$541$		−	473.636i		−	0.875483i	0.899101	−	0.437742i	$-0.144222\pi$
$542$	1.96692	+	4.27642i	0.00362901	+	0.00789007i
$543$		0			0
$544$	224.478	−	148.575i	0.412643	−	0.273117i
$545$			32.5581i			0.0597397i
$546$		0			0
$547$		−	437.249i		−	0.799359i	−0.916655	−	0.399679i	$-0.869121\pi$
$547$		−	437.249i		−	0.799359i	0.916655	−	0.399679i	$-0.130879\pi$
$548$	189.310	−	220.870i	0.345456	−	0.403047i
$549$		0			0
$550$	378.029	+	821.899i	0.687326	+	1.49436i
$551$		−	131.781i		−	0.239167i
$552$		0			0
$553$	2.09198	+	644.762i	0.00378297	+	1.16593i
$554$	180.922	+	393.354i	0.326573	+	0.710025i
$555$		0			0
$556$	392.938	−	458.445i	0.706724	−	0.824542i
$557$			498.479i			0.894936i	0.894300	+	0.447468i	$0.147674\pi$
$557$			498.479i			0.894936i	−0.894300	+	0.447468i	$0.852326\pi$
$558$		0			0
$559$		−	569.193i		−	1.01823i
$560$	809.028	−	127.927i	1.44469	−	0.228441i
$561$		0			0
$562$	480.522	−	221.014i	0.855022	−	0.393264i
$563$	−665.619			−1.18227			−0.591136	−	0.806572i	$-0.701320\pi$
$563$	−665.619			−1.18227			−0.591136	+	0.806572i	$0.701320\pi$
$564$		0			0
$565$	−1263.71			−2.23666
$566$	−208.026	+	95.6807i	−0.367537	+	0.169047i
$567$		0			0
$568$	81.8548	−	287.347i	0.144111	−	0.505893i
$569$	−310.711			−0.546065			−0.273033	−	0.962005i	$-0.588027\pi$
$569$	−310.711			−0.546065			−0.273033	+	0.962005i	$0.588027\pi$
$570$		0			0
$571$		−	170.411i		−	0.298443i	−0.988804	−	0.149222i	$-0.952323\pi$
$571$		−	170.411i		−	0.298443i	0.988804	−	0.149222i	$-0.0476768\pi$
$572$	593.217	+	508.453i	1.03709	+	0.888904i
$573$		0			0
$574$	289.585	−	134.333i	0.504503	−	0.234030i
$575$	−1298.13			−2.25762
$576$		0			0
$577$			499.500i			0.865685i	0.901470	+	0.432842i	$0.142489\pi$
$577$			499.500i			0.865685i	−0.901470	+	0.432842i	$0.857511\pi$
$578$	396.534	−	182.384i	0.686045	−	0.315544i
$579$		0			0
$580$	−345.906	−	296.480i	−0.596390	−	0.511172i
$581$	−0.871871	−	268.716i	−0.00150064	−	0.462506i
$582$		0			0
$583$	1265.86			2.17129
$584$	−809.727	−	230.662i	−1.38652	−	0.394969i
$585$		0			0
$586$	466.999	−	214.795i	0.796927	−	0.366544i
$587$	−716.411			−1.22046			−0.610231	−	0.792224i	$-0.708923\pi$
$587$	−716.411			−1.22046			−0.610231	+	0.792224i	$0.708923\pi$
$588$		0			0
$589$		−	347.590i		−	0.590136i
$590$	−362.150	+	166.570i	−0.613814	+	0.282321i
$591$		0			0
$592$	177.497	−	27.4765i	0.299826	−	0.0464131i
$593$			668.608i			1.12750i	0.825945	+	0.563750i	$0.190642\pi$
$593$			668.608i			1.12750i	−0.825945	+	0.563750i	$0.809358\pi$
$594$		0			0
$595$	−430.644	+	1.39726i	−0.723771	+	0.00234834i
$596$	756.693	+	648.570i	1.26962	+	1.08820i
$597$		0			0
$598$	−1018.54	+	468.472i	−1.70324	+	0.783399i
$599$	67.1144			0.112044			0.0560220	−	0.998430i	$-0.482158\pi$
$599$	67.1144			0.112044			0.0560220	+	0.998430i	$0.482158\pi$
$600$		0			0
$601$			1070.97i			1.78198i	0.454026	+	0.890988i	$0.349987\pi$
$601$			1070.97i			1.78198i	−0.454026	+	0.890988i	$0.650013\pi$
$602$	587.732	−	272.639i	0.976299	−	0.452889i
$603$		0			0
$604$	−283.729	+	331.029i	−0.469749	+	0.548062i
$605$	−959.487			−1.58593
$606$		0			0
$607$		−	877.198i		−	1.44514i	−0.691300	−	0.722568i	$-0.742961\pi$
$607$		−	877.198i		−	1.44514i	0.691300	−	0.722568i	$-0.257039\pi$
$608$	−149.448	−	225.796i	−0.245803	−	0.371376i
$609$		0			0
$610$	208.664	−	95.9742i	0.342072	−	0.157335i
$611$			772.760i			1.26475i
$612$		0			0
$613$			230.762i			0.376446i	0.982126	+	0.188223i	$0.0602728\pi$
$613$			230.762i			0.376446i	−0.982126	+	0.188223i	$0.939727\pi$
$614$	688.630	−	316.733i	1.12155	−	0.515852i
$615$		0			0
$616$	−240.867	+	856.084i	−0.391018	+	1.38975i
$617$	−134.978			−0.218765			−0.109382	−	0.994000i	$-0.534887\pi$
$617$	−134.978			−0.218765			−0.109382	+	0.994000i	$0.534887\pi$
$618$		0			0
$619$	−665.757			−1.07554			−0.537769	−	0.843093i	$-0.680733\pi$
$619$	−665.757			−1.07554			−0.537769	+	0.843093i	$0.680733\pi$
$620$	−912.376	−	782.007i	−1.47157	−	1.26130i
$621$		0			0
$622$	193.022	+	419.662i	0.310324	+	0.674697i
$623$	−634.339	+	2.05817i	−1.01820	+	0.00330364i
$624$		0			0
$625$	−525.790			−0.841264
$626$	274.681	+	597.203i	0.438788	+	0.953999i
$627$		0			0
$628$	11.6262	−	13.5644i	0.0185130	−	0.0215994i
$629$	−94.4336			−0.150133
$630$		0			0
$631$	−73.9832			−0.117248			−0.0586238	−	0.998280i	$-0.518671\pi$
$631$	−73.9832			−0.117248			−0.0586238	+	0.998280i	$0.518671\pi$
$632$	201.878	−	708.681i	0.319427	−	1.12133i
$633$		0			0
$634$	−128.022	−	278.342i	−0.201928	−	0.439025i
$635$	−564.358			−0.888753
$636$		0			0
$637$	−602.662	+	3.91081i	−0.946094	+	0.00613943i
$638$	449.392	−	206.696i	0.704377	−	0.323975i
$639$		0			0
$640$	−928.912	−	115.715i	−1.45142	−	0.180805i
$641$	−1069.94			−1.66917			−0.834587	−	0.550877i	$-0.814293\pi$
$641$	−1069.94			−1.66917			−0.834587	+	0.550877i	$0.814293\pi$
$642$		0			0
$643$	−389.931			−0.606424			−0.303212	−	0.952923i	$-0.598059\pi$
$643$	−389.931			−0.606424			−0.303212	+	0.952923i	$0.598059\pi$
$644$	−971.602	−	827.317i	−1.50870	−	1.28465i
$645$		0			0
$646$	59.4891	+	129.339i	0.0920885	+	0.200216i
$647$		−	547.457i		−	0.846147i	−0.906095	−	0.423073i	$-0.860951\pi$
$647$		−	547.457i		−	0.846147i	0.906095	−	0.423073i	$-0.139049\pi$
$648$		0			0
$649$		−	432.806i		−	0.666881i
$650$	636.551	−	292.779i	0.979310	−	0.450430i
$651$		0			0
$652$	184.125	+	157.816i	0.282401	+	0.242049i
$653$			296.513i			0.454078i	0.973886	+	0.227039i	$0.0729046\pi$
$653$			296.513i			0.454078i	−0.973886	+	0.227039i	$0.927095\pi$
$654$		0			0
$655$	−1792.80			−2.73710
$656$	−360.535	+	55.8108i	−0.549595	+	0.0850774i
$657$		0			0
$658$	−797.929	+	370.146i	−1.21266	+	0.562531i
$659$		−	104.860i		−	0.159120i	−0.996830	−	0.0795599i	$-0.974648\pi$
$659$		−	104.860i		−	0.159120i	0.996830	−	0.0795599i	$-0.0253515\pi$
$660$		0			0
$661$	484.516			0.733005			0.366503	−	0.930417i	$-0.380555\pi$
$661$	484.516			0.733005			0.366503	+	0.930417i	$0.380555\pi$
$662$	330.340	+	718.215i	0.499004	+	1.08492i
$663$		0			0
$664$	−84.1361	+	295.355i	−0.126711	+	0.444812i
$665$	1.40547	+	433.173i	0.00211348	+	0.651388i
$666$		0			0
$667$			709.784i			1.06414i
$668$	710.768	+	609.207i	1.06402	+	0.911986i
$669$		0			0
$670$	−341.312	−	742.069i	−0.509420	−	1.10757i
$671$			249.374i			0.371646i
$672$		0			0
$673$	−270.376			−0.401747			−0.200874	−	0.979617i	$-0.564378\pi$
$673$	−270.376			−0.401747			−0.200874	+	0.979617i	$0.564378\pi$
$674$	−282.230	+	129.811i	−0.418740	+	0.192598i
$675$		0			0
$676$	−46.1346	+	53.8257i	−0.0682464	+	0.0796238i
$677$	−522.418			−0.771666			−0.385833	−	0.922569i	$-0.626086\pi$
$677$	−522.418			−0.771666			−0.385833	+	0.922569i	$0.626086\pi$
$678$		0			0
$679$	−187.311	+	0.607747i	−0.275863	+	0.000895062i
$680$	473.336	+	134.836i	0.696083	+	0.198289i
$681$		0			0
$682$	1185.33	−	545.190i	1.73803	−	0.799399i
$683$			244.752i			0.358348i	0.983817	+	0.179174i	$0.0573425\pi$
$683$			244.752i			0.358348i	−0.983817	+	0.179174i	$0.942658\pi$
$684$		0			0
$685$	531.850			0.776423
$686$	−292.708	−	620.417i	−0.426689	−	0.904399i
$687$		0			0
$688$	−731.730	+	113.272i	−1.06356	+	0.164639i
$689$		−	980.396i		−	1.42293i
$690$		0			0
$691$	852.260			1.23337			0.616686	−	0.787209i	$-0.288475\pi$
$691$	852.260			1.23337			0.616686	+	0.787209i	$0.288475\pi$
$692$	381.494	−	445.093i	0.551292	−	0.643198i
$693$		0			0
$694$	−259.024	−	563.162i	−0.373234	−	0.811472i
$695$	1103.93			1.58838
$696$		0			0
$697$	191.815			0.275201
$698$	−969.251	+	445.803i	−1.38861	+	0.638687i
$699$		0			0
$700$	607.218	+	517.045i	0.867455	+	0.738636i
$701$			146.007i			0.208284i	0.994562	+	0.104142i	$0.0332097\pi$
$701$			146.007i			0.208284i	−0.994562	+	0.104142i	$0.966790\pi$
$702$		0			0
$703$			94.9883i			0.135119i
$704$	535.592	−	863.799i	0.760784	−	1.22699i
$705$		0			0
$706$	−265.197	−	576.583i	−0.375633	−	0.816690i
$707$	0.0314604	+	9.69628i	4.44984e−5	+	0.0137147i
$708$		0			0
$709$		−	1086.30i		−	1.53216i	−0.642745	−	0.766080i	$-0.722204\pi$
$709$		−	1086.30i		−	1.53216i	0.642745	−	0.766080i	$-0.277796\pi$
$710$	496.280	−	228.262i	0.698986	−	0.321496i
$711$		0			0
$712$	697.225	+	198.614i	0.979249	+	0.278953i
$713$			1872.15i			2.62574i
$714$		0			0
$715$			1428.46i			1.99784i
$716$	−12.7649	−	10.9410i	−0.0178281	−	0.0152807i
$717$		0			0
$718$	415.513	−	191.114i	0.578709	−	0.266175i
$719$			1358.50i			1.88943i	0.327898	+	0.944713i	$0.393660\pi$
$719$			1358.50i			1.88943i	−0.327898	+	0.944713i	$0.606340\pi$
$720$		0			0
$721$	−887.193	+	2.87857i	−1.23050	+	0.00399247i
$722$	−525.844	+	241.860i	−0.728316	+	0.334986i
$723$		0			0
$724$	−371.934	+	433.940i	−0.513721	+	0.599364i
$725$		−	443.591i		−	0.611849i
$726$		0			0
$727$			1020.19i			1.40329i	0.712527	+	0.701645i	$0.247551\pi$
$727$			1020.19i			1.40329i	−0.712527	+	0.701645i	$0.752449\pi$
$728$	663.027	+	186.549i	0.910751	+	0.256248i
$729$		0			0
$730$	−643.229	−	1398.49i	−0.881135	−	1.91574i
$731$	389.302			0.532561
$732$		0			0
$733$	−1151.72			−1.57125			−0.785624	−	0.618704i	$-0.787658\pi$
$733$	−1151.72			−1.57125			−0.785624	+	0.618704i	$0.787658\pi$
$734$	−106.949	−	232.525i	−0.145707	−	0.316792i
$735$		0			0
$736$	804.941	+	1216.16i	1.09367	+	1.65239i
$737$	886.846			1.20332
$738$		0			0
$739$			308.708i			0.417738i	0.977944	+	0.208869i	$0.0669782\pi$
$739$			308.708i			0.417738i	−0.977944	+	0.208869i	$0.933022\pi$
$740$	249.331	+	213.704i	0.336934	+	0.288790i
$741$		0			0
$742$	1012.33	−	469.602i	1.36432	−	0.632886i
$743$	733.205			0.986817			0.493408	−	0.869798i	$-0.335751\pi$
$743$	733.205			0.986817			0.493408	+	0.869798i	$0.335751\pi$
$744$		0			0
$745$			1822.10i			2.44577i
$746$	520.146	+	1130.88i	0.697247	+	1.51593i
$747$		0			0
$748$	−347.759	+	405.734i	−0.464918	+	0.542425i
$749$	14.0875	−	0.0457080i	0.0188084	−	6.10253e-5i
$750$		0			0
$751$	1018.66			1.35640			0.678199	−	0.734878i	$-0.262761\pi$
$751$	1018.66			1.35640			0.678199	+	0.734878i	$0.262761\pi$
$752$	993.426	−	153.783i	1.32105	−	0.204498i
$753$		0			0
$754$	−160.084	−	348.049i	−0.212313	−	0.461604i
$755$	−797.112			−1.05578
$756$		0			0
$757$			508.650i			0.671929i	0.941875	+	0.335965i	$0.109062\pi$
$757$			508.650i			0.671929i	−0.941875	+	0.335965i	$0.890938\pi$
$758$	−176.553	−	383.857i	−0.232920	−	0.506407i
$759$		0			0
$760$	135.628	−	476.117i	0.178458	−	0.626469i
$761$		−	51.1261i		−	0.0671827i	−0.999436	−	0.0335914i	$-0.989306\pi$
$761$		−	51.1261i		−	0.0671827i	0.999436	−	0.0335914i	$-0.0106945\pi$
$762$		0			0
$763$	−31.1635	+	0.101113i	−0.0408434	+	0.000132520i
$764$	562.085	−	655.791i	0.735714	−	0.858365i
$765$		0			0
$766$	−259.911	−	565.089i	−0.339309	−	0.737714i
$767$	−335.203			−0.437031
$768$		0			0
$769$		−	155.922i		−	0.202759i	−0.994848	−	0.101380i	$-0.967674\pi$
$769$		−	155.922i		−	0.202759i	0.994848	−	0.101380i	$-0.0323256\pi$
$770$	−1474.98	+	684.219i	−1.91556	+	0.888596i
$771$		0			0
$772$	464.205	−	541.593i	0.601302	−	0.701545i
$773$	−546.448			−0.706918			−0.353459	−	0.935450i	$-0.614995\pi$
$773$	−546.448			−0.706918			−0.353459	+	0.935450i	$0.614995\pi$
$774$		0			0
$775$		−	1170.03i		−	1.50972i
$776$	205.881	+	58.6479i	0.265310	+	0.0755772i
$777$		0			0
$778$	465.978	+	1013.11i	0.598943	+	1.30220i
$779$		−	192.942i		−	0.247679i
$780$		0			0
$781$			593.104i			0.759416i
$782$	−320.414	−	696.633i	−0.409736	−	0.890836i
$783$		0			0
$784$	124.960	+	773.977i	0.159388	+	0.987216i
$785$	32.6628			0.0416087
$786$		0			0
$787$	313.116			0.397860			0.198930	−	0.980014i	$-0.436253\pi$
$787$	313.116			0.397860			0.198930	+	0.980014i	$0.436253\pi$
$788$	−25.4348	−	21.8005i	−0.0322777	−	0.0276656i
$789$		0			0
$790$	1223.97	−	562.961i	1.54933	−	0.712609i
$791$	−3.92460	−	1209.58i	−0.00496156	−	1.52918i
$792$		0			0
$793$	193.137			0.243553
$794$	623.770	−	286.900i	0.785604	−	0.361336i
$795$		0			0
$796$	−174.420	−	149.497i	−0.219120	−	0.187810i
$797$	305.648			0.383499			0.191749	−	0.981444i	$-0.438584\pi$
$797$	305.648			0.383499			0.191749	+	0.981444i	$0.438584\pi$
$798$		0			0
$799$	−528.533			−0.661493
$800$	−503.061	−	760.058i	−0.628826	−	0.950073i
$801$		0			0
$802$	989.534	−	455.132i	1.23383	−	0.567497i
$803$	1671.33			2.08136
$804$		0			0
$805$	−7.56997	−	2333.11i	−0.00940369	−	2.89827i
$806$	−422.243	−	918.028i	−0.523875	−	1.13899i
$807$		0			0
$808$	3.03595	−	10.6575i	0.00375736	−	0.0131900i
$809$	922.426			1.14020			0.570102	−	0.821574i	$-0.306903\pi$
$809$	922.426			1.14020			0.570102	+	0.821574i	$0.306903\pi$
$810$		0			0
$811$	1571.20			1.93736			0.968680	−	0.248311i	$-0.0798753\pi$
$811$	1571.20			1.93736			0.968680	+	0.248311i	$0.0798753\pi$
$812$	282.706	−	332.011i	0.348161	−	0.408880i
$813$		0			0
$814$	−323.924	+	148.988i	−0.397942	+	0.183032i
$815$			443.370i			0.544013i
$816$		0			0
$817$		−	391.589i		−	0.479301i
$818$	350.699	+	762.478i	0.428727	+	0.932124i
$819$		0			0
$820$	−506.446	−	434.080i	−0.617617	−	0.529366i
$821$		−	550.756i		−	0.670836i	−0.942069	−	0.335418i	$-0.891122\pi$
$821$		−	550.756i		−	0.670836i	0.942069	−	0.335418i	$-0.108878\pi$
$822$		0			0
$823$	−816.633			−0.992263			−0.496132	−	0.868247i	$-0.665247\pi$
$823$	−816.633			−0.992263			−0.496132	+	0.868247i	$0.665247\pi$
$824$	975.147	+	277.784i	1.18343	+	0.337117i
$825$		0			0
$826$	−160.560	−	346.121i	−0.194382	−	0.419032i
$827$		−	1141.58i		−	1.38039i	−0.723623	−	0.690195i	$-0.757525\pi$
$827$		−	1141.58i		−	1.38039i	0.723623	−	0.690195i	$-0.242475\pi$
$828$		0			0
$829$	−272.762			−0.329025			−0.164513	−	0.986375i	$-0.552605\pi$
$829$	−272.762			−0.329025			−0.164513	+	0.986375i	$0.552605\pi$
$830$	−510.111	+	234.624i	−0.614592	+	0.282679i
$831$		0			0
$832$	−669.002	−	414.810i	−0.804089	−	0.498570i
$833$	−2.67482	−	412.193i	−0.00321107	−	0.494830i
$834$		0			0
$835$			1711.51i			2.04972i
$836$	408.117	+	349.801i	0.488178	+	0.418423i
$837$		0			0
$838$	−790.564	+	363.617i	−0.943394	+	0.433910i
$839$		−	1021.76i		−	1.21783i	−0.793237	−	0.608913i	$-0.791606\pi$
$839$		−	1021.76i		−	1.21783i	0.793237	−	0.608913i	$-0.208394\pi$
$840$		0			0
$841$	598.457			0.711601
$842$	183.636	+	399.256i	0.218095	+	0.474175i
$843$		0			0
$844$	−931.622	−	798.503i	−1.10382	−	0.946094i
$845$	−129.611			−0.153386
$846$		0			0
$847$	−2.97979	−	918.388i	−0.00351805	−	1.08428i
$848$	−1260.35	+	195.103i	−1.48627	+	0.230074i
$849$		0			0
$850$	200.248	+	435.372i	0.235586	+	0.512203i
$851$		−	511.616i		−	0.601194i
$852$		0			0
$853$	487.521			0.571537			0.285769	−	0.958299i	$-0.407751\pi$
$853$	487.521			0.571537			0.285769	+	0.958299i	$0.407751\pi$
$854$	92.5113	+	199.428i	0.108327	+	0.233522i
$855$		0			0
$856$	−15.4841	−	4.41085i	−0.0180888	−	0.00515286i
$857$			1253.85i			1.46307i	0.681806	+	0.731533i	$0.261195\pi$
$857$			1253.85i			1.46307i	−0.681806	+	0.731533i	$0.738805\pi$
$858$		0			0
$859$	−550.565			−0.640937			−0.320469	−	0.947259i	$-0.603840\pi$
$859$	−550.565			−0.640937			−0.320469	+	0.947259i	$0.603840\pi$
$860$	−1027.87	−	880.996i	−1.19519	−	1.02441i
$861$		0			0
$862$	541.063	−	248.860i	0.627684	−	0.288701i
$863$	878.436			1.01789			0.508943	−	0.860800i	$-0.330036\pi$
$863$	878.436			1.01789			0.508943	+	0.860800i	$0.330036\pi$
$864$		0			0
$865$	1071.78			1.23905
$866$	−355.588	−	773.107i	−0.410609	−	0.892733i
$867$		0			0
$868$	745.677	−	875.724i	0.859075	−	1.00890i
$869$			1462.77i			1.68328i
$870$		0			0
$871$		−	686.852i		−	0.788579i
$872$	34.2530	+	9.75744i	0.0392810	+	0.0111897i
$873$		0			0
$874$	−700.725	+	322.296i	−0.801745	+	0.368760i
$875$	0.578537	+	178.308i	0.000661185	+	0.203781i
$876$		0			0
$877$			1006.35i			1.14749i	0.819033	+	0.573746i	$0.194510\pi$
$877$			1006.35i			1.14749i	−0.819033	+	0.573746i	$0.805490\pi$
$878$	314.743	+	684.305i	0.358478	+	0.779390i
$879$		0			0
$880$	1836.36	−	284.269i	2.08677	−	0.323033i
$881$		−	1531.22i		−	1.73805i	−0.494766	−	0.869026i	$-0.664746\pi$
$881$		−	1531.22i		−	1.73805i	0.494766	−	0.869026i	$-0.335254\pi$
$882$		0			0
$883$		−	1607.37i		−	1.82035i	−0.414225	−	0.910174i	$-0.635947\pi$
$883$		−	1607.37i		−	1.82035i	0.414225	−	0.910174i	$-0.364053\pi$
$884$	314.236	+	269.335i	0.355471	+	0.304678i
$885$		0			0
$886$	−6.92113	−	15.0477i	−0.00781165	−	0.0169838i
$887$			1334.50i			1.50451i	0.658873	+	0.752254i	$0.271033\pi$
$887$			1334.50i			1.50451i	−0.658873	+	0.752254i	$0.728967\pi$
$888$		0			0
$889$	−1.75267	−	540.185i	−0.00197151	−	0.607632i
$890$	553.860	+	1204.18i	0.622315	+	1.35302i
$891$		0			0
$892$	973.247	+	834.180i	1.09108	+	0.935180i
$893$			531.637i			0.595338i
$894$		0			0
$895$		−	30.7377i		−	0.0343438i
$896$	107.874	−	889.483i	0.120395	−	0.992726i
$897$		0			0
$898$	−796.685	+	366.432i	−0.887177	+	0.408054i
$899$	−639.742			−0.711615
$900$		0			0
$901$	670.546			0.744224
$902$	657.961	−	302.627i	0.729446	−	0.335506i
$903$		0			0
$904$	−378.726	+	1329.50i	−0.418945	+	1.47068i
$905$	−1044.92			−1.15461
$906$		0			0
$907$		−	111.912i		−	0.123387i	−0.998095	−	0.0616937i	$-0.980350\pi$
$907$		−	111.912i		−	0.123387i	0.998095	−	0.0616937i	$-0.0196502\pi$
$908$	612.918	−	715.098i	0.675020	−	0.787553i
$909$		0			0
$910$	529.919	+	1142.36i	0.582329	+	1.25534i
$911$	743.108			0.815705			0.407853	−	0.913048i	$-0.366278\pi$
$911$	743.108			0.815705			0.407853	+	0.913048i	$0.366278\pi$
$912$		0			0
$913$		−	609.634i		−	0.667726i
$914$	−136.717	+	62.8826i	−0.149581	+	0.0687994i
$915$		0			0
$916$	789.102	−	920.654i	0.861465	−	1.00508i
$917$	−5.56773	−	1716.01i	−0.00607168	−	1.87133i
$918$		0			0
$919$	728.424			0.792627			0.396313	−	0.918115i	$-0.370289\pi$
$919$	728.424			0.792627			0.396313	+	0.918115i	$0.370289\pi$
$920$	−730.507	+	2564.41i	−0.794029	+	2.78740i
$921$		0			0
$922$	470.277	−	216.302i	0.510062	−	0.234601i
$923$	459.352			0.497673
$924$		0			0
$925$			319.742i			0.345667i
$926$	−128.119	+	58.9277i	−0.138357	+	0.0636368i
$927$		0			0
$928$	−415.580	+	275.060i	−0.447823	+	0.296401i
$929$		−	118.370i		−	0.127416i	−0.997969	−	0.0637081i	$-0.979707\pi$
$929$		−	118.370i		−	0.127416i	0.997969	−	0.0637081i	$-0.0202927\pi$
$930$		0			0
$931$	−414.614	+	2.69053i	−0.445343	+	0.00288994i
$932$	−521.750	+	608.731i	−0.559818	+	0.653145i
$933$		0			0
$934$	994.302	−	457.325i	1.06456	−	0.489642i
$935$	−976.999			−1.04492
$936$		0			0
$937$			1452.60i			1.55026i	0.631800	+	0.775132i	$0.282316\pi$
$937$			1452.60i			1.55026i	−0.631800	+	0.775132i	$0.717684\pi$
$938$	709.223	−	328.997i	0.756102	−	0.350743i
$939$		0			0
$940$	1395.47	+	1196.08i	1.48455	+	1.27242i
$941$	953.864			1.01367			0.506835	−	0.862043i	$-0.330815\pi$
$941$	953.864			1.01367			0.506835	+	0.862043i	$0.330815\pi$
$942$		0			0
$943$			1039.20i			1.10202i
$944$	66.7068	+	430.922i	0.0706640	+	0.456486i
$945$		0			0
$946$	1335.38	−	614.202i	1.41160	−	0.649262i
$947$		−	360.912i		−	0.381111i	−0.981676	−	0.190556i	$-0.938971\pi$
$947$		−	360.912i		−	0.381111i	0.981676	−	0.190556i	$-0.0610289\pi$
$948$		0			0
$949$		−	1294.43i		−	1.36399i
$950$	437.930	−	201.424i	0.460978	−	0.212025i
$951$		0			0
$952$	−127.591	+	453.480i	−0.134024	+	0.476345i
$953$	−356.487			−0.374069			−0.187034	−	0.982353i	$-0.559888\pi$
$953$	−356.487			−0.374069			−0.187034	+	0.982353i	$0.559888\pi$
$954$		0			0
$955$	1579.13			1.65354
$956$	−449.243	+	524.137i	−0.469920	+	0.548260i
$957$		0			0
$958$	−214.586	−	466.546i	−0.223994	−	0.487000i
$959$	1.65172	+	509.068i	0.00172233	+	0.530833i
$960$		0			0
$961$	−726.406			−0.755886
$962$	115.389	+	250.876i	0.119947	+	0.260786i
$963$		0			0
$964$	−714.361	−	612.286i	−0.741038	−	0.635152i
$965$	1304.14			1.35145
$966$		0			0
$967$	−1231.14			−1.27315			−0.636577	−	0.771213i	$-0.719650\pi$
$967$	−1231.14			−1.27315			−0.636577	+	0.771213i	$0.719650\pi$
$968$	−287.551	+	1009.43i	−0.297057	+	1.04280i
$969$		0			0
$970$	163.547	+	355.578i	0.168605	+	0.366576i
$971$	1439.10			1.48208			0.741040	−	0.671461i	$-0.234333\pi$
$971$	1439.10			1.48208			0.741040	+	0.671461i	$0.234333\pi$
$972$		0			0
$973$	3.42836	+	1056.64i	0.00352350	+	1.08596i
$974$	−412.037	+	189.515i	−0.423036	+	0.194574i
$975$		0			0
$976$	−38.4352	−	248.289i	−0.0393803	−	0.254394i
$977$	862.621			0.882928			0.441464	−	0.897279i	$-0.354459\pi$
$977$	862.621			0.882928			0.441464	+	0.897279i	$0.354459\pi$
$978$		0			0
$979$	−1439.12			−1.46999
$980$	−925.736	+	1094.36i	−0.944628	+	1.11669i
$981$		0			0
$982$	−222.155	−	483.001i	−0.226227	−	0.491854i
$983$		−	221.577i		−	0.225409i	−0.993629	−	0.112705i	$-0.964049\pi$
$983$		−	221.577i		−	0.225409i	0.993629	−	0.112705i	$-0.0359514\pi$
$984$		0			0
$985$		−	61.2466i		−	0.0621793i
$986$	238.050	−	109.490i	0.241430	−	0.111045i
$987$		0			0
$988$	270.917	−	316.082i	0.274208	−	0.319921i
$989$			2109.13i			2.13259i
$990$		0			0
$991$	503.835			0.508411			0.254205	−	0.967150i	$-0.418186\pi$
$991$	503.835			0.508411			0.254205	+	0.967150i	$0.418186\pi$
$992$	−1096.15	+	725.509i	−1.10499	+	0.731360i
$993$		0			0
$994$	220.026	+	474.314i	0.221354	+	0.477177i
$995$		−	419.999i		−	0.422110i
$996$		0			0
$997$	453.120			0.454483			0.227242	−	0.973838i	$-0.427029\pi$
$997$	453.120			0.454483			0.227242	+	0.973838i	$0.427029\pi$
$998$	−586.520	−	1275.19i	−0.587696	−	1.27775i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.l.h.181.26		32
3.2	odd	2		168.3.l.a.13.7	yes	32
4.3	odd	2		2016.3.l.h.433.30		32
7.6	odd	2	inner	504.3.l.h.181.25		32
8.3	odd	2		2016.3.l.h.433.3		32
8.5	even	2	inner	504.3.l.h.181.27		32
12.11	even	2		672.3.l.a.433.32		32
21.20	even	2		168.3.l.a.13.8	yes	32
24.5	odd	2		168.3.l.a.13.6	yes	32
24.11	even	2		672.3.l.a.433.1		32
28.27	even	2		2016.3.l.h.433.4		32
56.13	odd	2	inner	504.3.l.h.181.28		32
56.27	even	2		2016.3.l.h.433.29		32
84.83	odd	2		672.3.l.a.433.16		32
168.83	odd	2		672.3.l.a.433.17		32
168.125	even	2		168.3.l.a.13.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.l.a.13.5	✓	32	168.125	even	2
168.3.l.a.13.6	yes	32	24.5	odd	2
168.3.l.a.13.7	yes	32	3.2	odd	2
168.3.l.a.13.8	yes	32	21.20	even	2
504.3.l.h.181.25		32	7.6	odd	2	inner
504.3.l.h.181.26		32	1.1	even	1	trivial
504.3.l.h.181.27		32	8.5	even	2	inner
504.3.l.h.181.28		32	56.13	odd	2	inner
672.3.l.a.433.1		32	24.11	even	2
672.3.l.a.433.16		32	84.83	odd	2
672.3.l.a.433.17		32	168.83	odd	2
672.3.l.a.433.32		32	12.11	even	2
2016.3.l.h.433.3		32	8.3	odd	2
2016.3.l.h.433.4		32	28.27	even	2
2016.3.l.h.433.29		32	56.27	even	2
2016.3.l.h.433.30		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81702 - 0.835731i) q^{2} +(2.60311 - 3.03707i) q^{4} +7.31322 q^{5} +(0.0227120 + 6.99996i) q^{7} +(2.19172 - 7.69392i) q^{8} +(13.2882 - 6.11188i) q^{10} +15.8808i q^{11} +12.2995 q^{13} +(5.89135 + 12.7001i) q^{14} +(-2.44765 - 15.8117i) q^{16} +8.41229i q^{17} +8.46170 q^{19} +(19.0371 - 22.2108i) q^{20} +(13.2720 + 28.8557i) q^{22} -45.5755 q^{23} +28.4831 q^{25} +(22.3484 - 10.2790i) q^{26} +(21.3185 + 18.1527i) q^{28} -15.5738i q^{29} -41.0781i q^{31} +(-17.6617 - 26.6845i) q^{32} +(7.03040 + 15.2853i) q^{34} +(0.166098 + 51.1922i) q^{35} +11.2257i q^{37} +(15.3751 - 7.07170i) q^{38} +(16.0285 - 56.2673i) q^{40} -22.8018i q^{41} -46.2778i q^{43} +(48.2311 + 41.3394i) q^{44} +(-82.8114 + 38.0888i) q^{46} +62.8287i q^{47} +(-48.9990 + 0.317966i) q^{49} +(51.7543 - 23.8042i) q^{50} +(32.0169 - 37.3544i) q^{52} -79.7103i q^{53} +116.140i q^{55} +(53.9069 + 15.1672i) q^{56} +(-13.0155 - 28.2979i) q^{58} -27.2534 q^{59} +15.7029 q^{61} +(-34.3302 - 74.6396i) q^{62} +(-54.3927 - 33.7258i) q^{64} +89.9487 q^{65} -55.8440i q^{67} +(25.5487 + 21.8981i) q^{68} +(43.0847 + 92.8784i) q^{70} +37.3473 q^{71} -105.242i q^{73} +(9.38165 + 20.3973i) q^{74} +(22.0267 - 25.6988i) q^{76} +(-111.165 + 0.360684i) q^{77} +92.1093 q^{79} +(-17.9002 - 115.634i) q^{80} +(-19.0562 - 41.4313i) q^{82} -38.3882 q^{83} +61.5208i q^{85} +(-38.6758 - 84.0877i) q^{86} +(122.185 + 34.8062i) q^{88} +90.6203i q^{89} +(0.279345 + 86.0959i) q^{91} +(-118.638 + 138.416i) q^{92} +(52.5078 + 114.161i) q^{94} +61.8822 q^{95} +26.7589i q^{97} +(-88.7663 + 41.5277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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