LMFDB - Embedded newform 600.3.g.a.451.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,3,Mod(451,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.451"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$600 = 2^{3} \cdot 3 \cdot 5^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	600.g (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$16.3488158616$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.4752.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} + 3x^{2} - 6x + 6$ x^4 + 3x^2 - 6x + 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$2$
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.2
Root			$-0.866025 + 1.99551i$ of defining polynomial
Character	$\chi$	$=$	600.451
Dual form			600.3.g.a.451.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 1.46081i) q^{2} +1.73205 q^{3} +(-0.267949 - 3.99102i) q^{4} +(-2.36603 + 2.53020i) q^{6} +2.13878i q^{7} +(6.19615 + 5.06040i) q^{8} +3.00000 q^{9} -8.00000 q^{11} +(-0.464102 - 6.91264i) q^{12} +11.6865i q^{13} +(-3.12436 - 2.92163i) q^{14} +(-15.8564 + 2.13878i) q^{16} -11.8564 q^{17} +(-4.09808 + 4.38244i) q^{18} +14.9282 q^{19} +3.70447i q^{21} +(10.9282 - 11.6865i) q^{22} -4.27756i q^{23} +(10.7321 + 8.76488i) q^{24} +(-17.0718 - 15.9641i) q^{26} +5.19615 q^{27} +(8.53590 - 0.573084i) q^{28} -0.573084i q^{29} +57.4399i q^{31} +(18.5359 - 26.0849i) q^{32} -13.8564 q^{33} +(16.1962 - 17.3200i) q^{34} +(-0.803848 - 11.9730i) q^{36} +27.6506i q^{37} +(-20.3923 + 21.8073i) q^{38} +20.2416i q^{39} -31.5692 q^{41} +(-5.41154 - 5.06040i) q^{42} -28.7846 q^{43} +(2.14359 + 31.9281i) q^{44} +(6.24871 + 5.84325i) q^{46} +59.5787i q^{47} +(-27.4641 + 3.70447i) q^{48} +44.4256 q^{49} -20.5359 q^{51} +(46.6410 - 3.13139i) q^{52} +31.3550i q^{53} +(-7.09808 + 7.59061i) q^{54} +(-10.8231 + 13.2522i) q^{56} +25.8564 q^{57} +(0.837169 + 0.782847i) q^{58} -52.7846 q^{59} +59.5787i q^{61} +(-83.9090 - 78.4644i) q^{62} +6.41634i q^{63} +(12.7846 + 62.7101i) q^{64} +(18.9282 - 20.2416i) q^{66} +84.7846 q^{67} +(3.17691 + 47.3191i) q^{68} -7.40895i q^{69} +42.4685i q^{71} +(18.5885 + 15.1812i) q^{72} +5.42563 q^{73} +(-40.3923 - 37.7714i) q^{74} +(-4.00000 - 59.5787i) q^{76} -17.1102i q^{77} +(-29.5692 - 27.6506i) q^{78} -44.6072i q^{79} +9.00000 q^{81} +(43.1244 - 46.1167i) q^{82} -67.7128 q^{83} +(14.7846 - 0.992611i) q^{84} +(39.3205 - 42.0489i) q^{86} -0.992611i q^{87} +(-49.5692 - 40.4832i) q^{88} -133.138 q^{89} -24.9948 q^{91} +(-17.0718 + 1.14617i) q^{92} +99.4888i q^{93} +(-87.0333 - 81.3860i) q^{94} +(32.1051 - 45.1803i) q^{96} -97.1384 q^{97} +(-60.6865 + 64.8975i) q^{98} -24.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 2 q^{2} - 8 q^{4} - 6 q^{6} + 4 q^{8} + 12 q^{9} - 32 q^{11} + 12 q^{12} + 36 q^{14} - 8 q^{16} + 8 q^{17} - 6 q^{18} + 32 q^{19} + 16 q^{22} + 36 q^{24} - 96 q^{26} + 48 q^{28} + 88 q^{32} + 44 q^{34}+ \cdots - 96 q^{99}+O(q^{100})$ 4 * q - 2 * q^2 - 8 * q^4 - 6 * q^6 + 4 * q^8 + 12 * q^9 - 32 * q^11 + 12 * q^12 + 36 * q^14 - 8 * q^16 + 8 * q^17 - 6 * q^18 + 32 * q^19 + 16 * q^22 + 36 * q^24 - 96 * q^26 + 48 * q^28 + 88 * q^32 + 44 * q^34 - 24 * q^36 - 40 * q^38 + 40 * q^41 - 84 * q^42 - 32 * q^43 + 64 * q^44 - 72 * q^46 - 96 * q^48 - 44 * q^49 - 96 * q^51 + 48 * q^52 - 18 * q^54 - 168 * q^56 + 48 * q^57 - 156 * q^58 - 128 * q^59 - 204 * q^62 - 32 * q^64 + 48 * q^66 + 256 * q^67 - 112 * q^68 + 12 * q^72 - 200 * q^73 - 120 * q^74 - 16 * q^76 + 48 * q^78 + 36 * q^81 + 124 * q^82 - 160 * q^83 - 24 * q^84 + 88 * q^86 - 32 * q^88 - 200 * q^89 + 288 * q^91 - 96 * q^92 - 168 * q^94 - 24 * q^96 - 56 * q^97 - 170 * q^98 - 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$ .

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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

)

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

$2$	−1.36603	+	1.46081i	−0.683013	+	0.730406i
$2$	−1.36603	+	1.46081i	−0.683013	+	0.730406i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−0.267949	−	3.99102i	−0.0669873	−	0.997754i
$5$		0			0
$5$		0			0
$6$	−2.36603	+	2.53020i	−0.394338	+	0.421700i
$7$			2.13878i			0.305540i	0.988262	+	0.152770i	$0.0488193\pi$
$7$			2.13878i			0.305540i	−0.988262	+	0.152770i	$0.951181\pi$
$8$	6.19615	+	5.06040i	0.774519	+	0.632551i
$9$	3.00000			0.333333
$10$		0			0
$11$	−8.00000			−0.727273			−0.363636	−	0.931541i	$-0.618465\pi$
$11$	−8.00000			−0.727273			−0.363636	+	0.931541i	$0.618465\pi$
$12$	−0.464102	−	6.91264i	−0.0386751	−	0.576053i
$13$			11.6865i			0.898962i	0.893290	+	0.449481i	$0.148391\pi$
$13$			11.6865i			0.898962i	−0.893290	+	0.449481i	$0.851609\pi$
$14$	−3.12436	−	2.92163i	−0.223168	−	0.208688i
$15$		0			0
$16$	−15.8564	+	2.13878i	−0.991025	+	0.133674i
$17$	−11.8564			−0.697436			−0.348718	−	0.937228i	$-0.613383\pi$
$17$	−11.8564			−0.697436			−0.348718	+	0.937228i	$0.613383\pi$
$18$	−4.09808	+	4.38244i	−0.227671	+	0.243469i
$19$	14.9282			0.785695			0.392847	−	0.919604i	$-0.371490\pi$
$19$	14.9282			0.785695			0.392847	+	0.919604i	$0.371490\pi$
$20$		0			0
$21$			3.70447i			0.176403i
$22$	10.9282	−	11.6865i	0.496737	−	0.531205i
$23$		−	4.27756i		−	0.185981i	−0.995667	−	0.0929904i	$-0.970357\pi$
$23$		−	4.27756i		−	0.185981i	0.995667	−	0.0929904i	$-0.0296426\pi$
$24$	10.7321	+	8.76488i	0.447169	+	0.365203i
$25$		0			0
$26$	−17.0718	−	15.9641i	−0.656608	−	0.614002i
$27$	5.19615			0.192450
$28$	8.53590	−	0.573084i	0.304854	−	0.0204673i
$29$		−	0.573084i		−	0.0197615i	−0.999951	−	0.00988076i	$-0.996855\pi$
$29$		−	0.573084i		−	0.0197615i	0.999951	−	0.00988076i	$-0.00314519\pi$
$30$		0			0
$31$			57.4399i			1.85290i	0.376417	+	0.926450i	$0.377156\pi$
$31$			57.4399i			1.85290i	−0.376417	+	0.926450i	$0.622844\pi$
$32$	18.5359	−	26.0849i	0.579247	−	0.815152i
$33$	−13.8564			−0.419891
$34$	16.1962	−	17.3200i	0.476357	−	0.509412i
$35$		0			0
$36$	−0.803848	−	11.9730i	−0.0223291	−	0.332585i
$37$			27.6506i			0.747313i	0.927567	+	0.373656i	$0.121896\pi$
$37$			27.6506i			0.747313i	−0.927567	+	0.373656i	$0.878104\pi$
$38$	−20.3923	+	21.8073i	−0.536640	+	0.573877i
$39$			20.2416i			0.519016i
$40$		0			0
$41$	−31.5692			−0.769981			−0.384990	−	0.922921i	$-0.625795\pi$
$41$	−31.5692			−0.769981			−0.384990	+	0.922921i	$0.625795\pi$
$42$	−5.41154	−	5.06040i	−0.128846	−	0.120486i
$43$	−28.7846			−0.669410			−0.334705	−	0.942323i	$-0.608637\pi$
$43$	−28.7846			−0.669410			−0.334705	+	0.942323i	$0.608637\pi$
$44$	2.14359	+	31.9281i	0.0487180	+	0.725639i
$45$		0			0
$46$	6.24871	+	5.84325i	0.135842	+	0.127027i
$47$			59.5787i			1.26763i	0.773484	+	0.633816i	$0.218512\pi$
$47$			59.5787i			1.26763i	−0.773484	+	0.633816i	$0.781488\pi$
$48$	−27.4641	+	3.70447i	−0.572169	+	0.0771765i
$49$	44.4256			0.906645
$50$		0			0
$51$	−20.5359			−0.402665
$52$	46.6410	−	3.13139i	0.896943	−	0.0602190i
$53$			31.3550i			0.591604i	0.955249	+	0.295802i	$0.0955869\pi$
$53$			31.3550i			0.591604i	−0.955249	+	0.295802i	$0.904413\pi$
$54$	−7.09808	+	7.59061i	−0.131446	+	0.140567i
$55$		0			0
$56$	−10.8231	+	13.2522i	−0.193269	+	0.236646i
$57$	25.8564			0.453621
$58$	0.837169	+	0.782847i	0.0144339	+	0.0134974i
$59$	−52.7846			−0.894654			−0.447327	−	0.894370i	$-0.647624\pi$
$59$	−52.7846			−0.894654			−0.447327	+	0.894370i	$0.647624\pi$
$60$		0			0
$61$			59.5787i			0.976700i	0.872648	+	0.488350i	$0.162401\pi$
$61$			59.5787i			0.976700i	−0.872648	+	0.488350i	$0.837599\pi$
$62$	−83.9090	−	78.4644i	−1.35337	−	1.26555i
$63$			6.41634i			0.101847i
$64$	12.7846	+	62.7101i	0.199760	+	0.979845i
$65$		0			0
$66$	18.9282	−	20.2416i	0.286791	−	0.306691i
$67$	84.7846			1.26544			0.632721	−	0.774380i	$-0.281938\pi$
$67$	84.7846			1.26544			0.632721	+	0.774380i	$0.281938\pi$
$68$	3.17691	+	47.3191i	0.0467193	+	0.695869i
$69$		−	7.40895i		−	0.107376i
$70$		0			0
$71$			42.4685i			0.598147i	0.954230	+	0.299074i	$0.0966776\pi$
$71$			42.4685i			0.598147i	−0.954230	+	0.299074i	$0.903322\pi$
$72$	18.5885	+	15.1812i	0.258173	+	0.210850i
$73$	5.42563			0.0743236			0.0371618	−	0.999309i	$-0.488168\pi$
$73$	5.42563			0.0743236			0.0371618	+	0.999309i	$0.488168\pi$
$74$	−40.3923	−	37.7714i	−0.545842	−	0.510424i
$75$		0			0
$76$	−4.00000	−	59.5787i	−0.0526316	−	0.783930i
$77$		−	17.1102i		−	0.222211i
$78$	−29.5692	−	27.6506i	−0.379093	−	0.354494i
$79$		−	44.6072i		−	0.564649i	−0.959319	−	0.282324i	$-0.908895\pi$
$79$		−	44.6072i		−	0.564649i	0.959319	−	0.282324i	$-0.0911054\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	43.1244	−	46.1167i	0.525907	−	0.562399i
$83$	−67.7128			−0.815817			−0.407909	−	0.913023i	$-0.633742\pi$
$83$	−67.7128			−0.815817			−0.407909	+	0.913023i	$0.633742\pi$
$84$	14.7846	−	0.992611i	0.176007	−	0.0118168i
$85$		0			0
$86$	39.3205	−	42.0489i	0.457215	−	0.488941i
$87$		−	0.992611i		−	0.0114093i
$88$	−49.5692	−	40.4832i	−0.563287	−	0.460037i
$89$	−133.138			−1.49594			−0.747969	−	0.663734i	$-0.768971\pi$
$89$	−133.138			−1.49594			−0.747969	+	0.663734i	$0.768971\pi$
$90$		0			0
$91$	−24.9948			−0.274669
$92$	−17.0718	+	1.14617i	−0.185563	+	0.0124583i
$93$			99.4888i			1.06977i
$94$	−87.0333	−	81.3860i	−0.925886	−	0.865809i
$95$		0			0
$96$	32.1051	−	45.1803i	0.334428	−	0.470628i
$97$	−97.1384			−1.00143			−0.500714	−	0.865613i	$-0.666929\pi$
$97$	−97.1384			−1.00143			−0.500714	+	0.865613i	$0.666929\pi$
$98$	−60.6865	+	64.8975i	−0.619250	+	0.662220i
$99$	−24.0000			−0.242424
$100$		0			0
$101$			62.1370i			0.615218i	0.951513	+	0.307609i	$0.0995288\pi$
$101$			62.1370i			0.615218i	−0.951513	+	0.307609i	$0.900471\pi$
$102$	28.0526	−	29.9991i	0.275025	−	0.294109i
$103$		−	27.8041i		−	0.269943i	−0.990849	−	0.134971i	$-0.956906\pi$
$103$		−	27.8041i		−	0.269943i	0.990849	−	0.134971i	$-0.0430943\pi$
$104$	−59.1384	+	72.4114i	−0.568639	+	0.696263i
$105$		0			0
$106$	−45.8038	−	42.8318i	−0.432112	−	0.404073i
$107$	−37.7795			−0.353079			−0.176540	−	0.984294i	$-0.556490\pi$
$107$	−37.7795			−0.353079			−0.176540	+	0.984294i	$0.556490\pi$
$108$	−1.39230	−	20.7379i	−0.0128917	−	0.192018i
$109$		−	141.691i		−	1.29992i	−0.759968	−	0.649960i	$-0.774786\pi$
$109$		−	141.691i		−	1.29992i	0.759968	−	0.649960i	$-0.225214\pi$
$110$		0			0
$111$			47.8922i			0.431461i
$112$	−4.57437	−	33.9133i	−0.0408426	−	0.302798i
$113$	58.2872			0.515816			0.257908	−	0.966170i	$-0.416967\pi$
$113$	58.2872			0.515816			0.257908	+	0.966170i	$0.416967\pi$
$114$	−35.3205	+	37.7714i	−0.309829	+	0.331328i
$115$		0			0
$116$	−2.28719	+	0.153557i	−0.0197171	+	0.00132377i
$117$			35.0595i			0.299654i
$118$	72.1051	−	77.1084i	0.611060	−	0.653461i
$119$		−	25.3582i		−	0.213094i
$120$		0			0
$121$	−57.0000			−0.471074
$122$	−87.0333	−	81.3860i	−0.713388	−	0.667098i
$123$	−54.6795			−0.444549
$124$	229.244	−	15.3910i	1.84874	−	0.124121i
$125$		0			0
$126$	−9.37307	−	8.76488i	−0.0743894	−	0.0695625i
$127$			185.152i			1.45789i	0.684571	+	0.728946i	$0.259990\pi$
$127$			185.152i			1.45789i	−0.684571	+	0.728946i	$0.740010\pi$
$128$	−109.072	−	66.9876i	−0.852123	−	0.523341i
$129$	−49.8564			−0.386484
$130$		0			0
$131$	125.359			0.956939			0.478469	−	0.878104i	$-0.341192\pi$
$131$	125.359			0.956939			0.478469	+	0.878104i	$0.341192\pi$
$132$	3.71281	+	55.3011i	0.0281274	+	0.418948i
$133$			31.9281i			0.240061i
$134$	−115.818	+	123.854i	−0.864313	+	0.924287i
$135$		0			0
$136$	−73.4641	−	59.9982i	−0.540177	−	0.441163i
$137$	−99.5692			−0.726783			−0.363391	−	0.931637i	$-0.618381\pi$
$137$	−99.5692			−0.726783			−0.363391	+	0.931637i	$0.618381\pi$
$138$	10.8231	+	10.1208i	0.0784282	+	0.0733392i
$139$	177.492			1.27692			0.638461	−	0.769654i	$-0.279571\pi$
$139$	177.492			1.27692			0.638461	+	0.769654i	$0.279571\pi$
$140$		0			0
$141$			103.193i			0.731867i
$142$	−62.0385	−	58.0130i	−0.436891	−	0.408542i
$143$		−	93.4920i		−	0.653790i
$144$	−47.5692	+	6.41634i	−0.330342	+	0.0445579i
$145$		0			0
$146$	−7.41154	+	7.92582i	−0.0507640	+	0.0542865i
$147$	76.9474			0.523452
$148$	110.354	−	7.40895i	0.745634	−	0.0500605i
$149$		−	87.8023i		−	0.589277i	−0.955609	−	0.294639i	$-0.904801\pi$
$149$		−	87.8023i		−	0.589277i	0.955609	−	0.294639i	$-0.0951993\pi$
$150$		0			0
$151$			219.066i			1.45077i	0.688345	+	0.725383i	$0.258337\pi$
$151$			219.066i			1.45077i	−0.688345	+	0.725383i	$0.741663\pi$
$152$	92.4974	+	75.5427i	0.608536	+	0.496992i
$153$	−35.5692			−0.232479
$154$	24.9948	+	23.3730i	0.162304	+	0.151773i
$155$		0			0
$156$	80.7846	−	5.42373i	0.517850	−	0.0347675i
$157$		−	253.440i		−	1.61427i	−0.590370	−	0.807133i	$-0.701018\pi$
$157$		−	253.440i		−	1.61427i	0.590370	−	0.807133i	$-0.298982\pi$
$158$	65.1628	+	60.9346i	0.412423	+	0.385662i
$159$			54.3085i			0.341563i
$160$		0			0
$161$	9.14875			0.0568245
$162$	−12.2942	+	13.1473i	−0.0758903	+	0.0811563i
$163$	102.354			0.627938			0.313969	−	0.949433i	$-0.398341\pi$
$163$	102.354			0.627938			0.313969	+	0.949433i	$0.398341\pi$
$164$	8.45895	+	125.993i	0.0515789	+	0.768251i
$165$		0			0
$166$	92.4974	−	98.9158i	0.557213	−	0.595878i
$167$			281.090i			1.68318i	0.540120	+	0.841588i	$0.318379\pi$
$167$			281.090i			1.68318i	−0.540120	+	0.841588i	$0.681621\pi$
$168$	−18.7461	+	22.9535i	−0.111584	+	0.136628i
$169$	32.4256			0.191868
$170$		0			0
$171$	44.7846			0.261898
$172$	7.71281	+	114.880i	0.0448419	+	0.667906i
$173$		−	242.858i		−	1.40381i	−0.712273	−	0.701903i	$-0.752334\pi$
$173$		−	242.858i		−	1.40381i	0.712273	−	0.701903i	$-0.247666\pi$
$174$	1.45002	+	1.35593i	0.00833344	+	0.00779271i
$175$		0			0
$176$	126.851	−	17.1102i	0.720746	−	0.0972172i
$177$	−91.4256			−0.516529
$178$	181.870	−	194.490i	1.02174	−	1.09264i
$179$	318.354			1.77851			0.889257	−	0.457409i	$-0.151222\pi$
$179$	318.354			1.77851			0.889257	+	0.457409i	$0.151222\pi$
$180$		0			0
$181$		−	79.5132i		−	0.439299i	−0.975579	−	0.219650i	$-0.929509\pi$
$181$		−	79.5132i		−	0.439299i	0.975579	−	0.219650i	$-0.0704914\pi$
$182$	34.1436	−	36.5128i	0.187602	−	0.200620i
$183$			103.193i			0.563898i
$184$	21.6462	−	26.5044i	0.117642	−	0.144046i
$185$		0			0
$186$	−145.335	−	135.904i	−0.781369	−	0.730668i
$187$	94.8513			0.507226
$188$	237.779	−	15.9641i	1.26478	−	0.0849152i
$189$			11.1134i			0.0588012i
$190$		0			0
$191$		−	352.887i		−	1.84758i	−0.382902	−	0.923789i	$-0.625075\pi$
$191$		−	352.887i		−	1.84758i	0.382902	−	0.923789i	$-0.374925\pi$
$192$	22.1436	+	108.617i	0.115331	+	0.565714i
$193$	284.277			1.47294			0.736469	−	0.676472i	$-0.236492\pi$
$193$	284.277			1.47294			0.736469	+	0.676472i	$0.236492\pi$
$194$	132.694	−	141.901i	0.683988	−	0.731449i
$195$		0			0
$196$	−11.9038	−	177.303i	−0.0607337	−	0.904609i
$197$			75.8087i			0.384816i	0.981315	+	0.192408i	$0.0616297\pi$
$197$			75.8087i			0.384816i	−0.981315	+	0.192408i	$0.938370\pi$
$198$	32.7846	−	35.0595i	0.165579	−	0.177068i
$199$			104.186i			0.523547i	0.965129	+	0.261774i	$0.0843074\pi$
$199$			104.186i			0.523547i	−0.965129	+	0.261774i	$0.915693\pi$
$200$		0			0
$201$	146.851			0.730603
$202$	−90.7705	−	84.8807i	−0.449359	−	0.420202i
$203$	1.22570			0.00603793
$204$	5.50258	+	81.9591i	0.0269734	+	0.401760i
$205$		0			0
$206$	40.6166	+	37.9811i	0.197168	+	0.184374i
$207$		−	12.8327i		−	0.0619936i
$208$	−24.9948	−	185.306i	−0.120168	−	0.890894i
$209$	−119.426			−0.571414
$210$		0			0
$211$	136.918			0.648900			0.324450	−	0.945903i	$-0.394821\pi$
$211$	136.918			0.648900			0.324450	+	0.945903i	$0.394821\pi$
$212$	125.138	−	8.40156i	0.590276	−	0.0396300i
$213$			73.5575i			0.345341i
$214$	51.6077	−	55.1887i	0.241157	−	0.257891i
$215$		0			0
$216$	32.1962	+	26.2946i	0.149056	+	0.121734i
$217$	−122.851			−0.566135
$218$	206.985	+	193.554i	0.949470	+	0.887862i
$219$	9.39746			0.0429108
$220$		0			0
$221$		−	138.560i		−	0.626968i
$222$	−69.9615	−	65.4219i	−0.315142	−	0.294693i
$223$		−	53.1624i		−	0.238396i	−0.992870	−	0.119198i	$-0.961968\pi$
$223$		−	53.1624i		−	0.238396i	0.992870	−	0.119198i	$-0.0380324\pi$
$224$	55.7898	+	39.6442i	0.249061	+	0.176983i
$225$		0			0
$226$	−79.6218	+	85.1467i	−0.352309	+	0.376755i
$227$	119.846			0.527956			0.263978	−	0.964529i	$-0.414965\pi$
$227$	119.846			0.527956			0.263978	+	0.964529i	$0.414965\pi$
$228$	−6.92820	−	103.193i	−0.0303869	−	0.452602i
$229$		−	214.103i		−	0.934946i	−0.884007	−	0.467473i	$-0.845164\pi$
$229$		−	214.103i		−	0.934946i	0.884007	−	0.467473i	$-0.154836\pi$
$230$		0			0
$231$		−	29.6358i		−	0.128293i
$232$	2.90004	−	3.55092i	0.0125002	−	0.0153057i
$233$	127.436			0.546935			0.273468	−	0.961881i	$-0.411829\pi$
$233$	127.436			0.546935			0.273468	+	0.961881i	$0.411829\pi$
$234$	−51.2154	−	47.8922i	−0.218869	−	0.204667i
$235$		0			0
$236$	14.1436	+	210.664i	0.0599305	+	0.892645i
$237$		−	77.2620i		−	0.326000i
$238$	37.0436	+	34.6400i	0.155646	+	0.145546i
$239$			319.281i			1.33590i	0.744204	+	0.667952i	$0.232829\pi$
$239$			319.281i			1.33590i	−0.744204	+	0.667952i	$0.767171\pi$
$240$		0			0
$241$	−247.415			−1.02662			−0.513310	−	0.858203i	$-0.671581\pi$
$241$	−247.415			−1.02662			−0.513310	+	0.858203i	$0.671581\pi$
$242$	77.8634	−	83.2663i	0.321750	−	0.344076i
$243$	15.5885			0.0641500
$244$	237.779	−	15.9641i	0.974506	−	0.0654265i
$245$		0			0
$246$	74.6936	−	79.8765i	0.303632	−	0.324701i
$247$			174.459i			0.706310i
$248$	−290.669	+	355.906i	−1.17205	+	1.43511i
$249$	−117.282			−0.471012
$250$		0			0
$251$	−214.851			−0.855981			−0.427991	−	0.903783i	$-0.640778\pi$
$251$	−214.851			−0.855981			−0.427991	+	0.903783i	$0.640778\pi$
$252$	25.6077	−	1.71925i	0.101618	−	0.00682243i
$253$			34.2205i			0.135259i
$254$	−270.473	−	252.923i	−1.06485	−	0.995759i
$255$		0			0
$256$	246.851	−	67.8267i	0.964263	−	0.264948i
$257$	84.2769			0.327926			0.163963	−	0.986467i	$-0.447572\pi$
$257$	84.2769			0.327926			0.163963	+	0.986467i	$0.447572\pi$
$258$	68.1051	−	72.8309i	0.263973	−	0.282290i
$259$	−59.1384			−0.228334
$260$		0			0
$261$		−	1.71925i		−	0.00658717i
$262$	−171.244	+	183.126i	−0.653601	+	0.698954i
$263$		−	277.120i		−	1.05369i	−0.849962	−	0.526844i	$-0.823375\pi$
$263$		−	277.120i		−	1.05369i	0.849962	−	0.526844i	$-0.176625\pi$
$264$	−85.8564	−	70.1190i	−0.325214	−	0.265602i
$265$		0			0
$266$	−46.6410	−	43.6146i	−0.175342	−	0.163965i
$267$	−230.603			−0.863680
$268$	−22.7180	−	338.377i	−0.0847685	−	1.26260i
$269$		−	123.701i		−	0.459855i	−0.973208	−	0.229927i	$-0.926151\pi$
$269$		−	123.701i		−	0.459855i	0.973208	−	0.229927i	$-0.0738489\pi$
$270$		0			0
$271$			197.985i			0.730572i	0.930895	+	0.365286i	$0.119029\pi$
$271$			197.985i			0.730572i	−0.930895	+	0.365286i	$0.880971\pi$
$272$	188.000	−	25.3582i	0.691176	−	0.0932288i
$273$	−43.2923			−0.158580
$274$	136.014	−	145.452i	0.496402	−	0.530847i
$275$		0			0
$276$	−29.5692	+	1.98522i	−0.107135	+	0.00719283i
$277$		−	247.709i		−	0.894256i	−0.894470	−	0.447128i	$-0.852447\pi$
$277$		−	247.709i		−	0.894256i	0.894470	−	0.447128i	$-0.147553\pi$
$278$	−242.459	+	259.283i	−0.872154	+	0.932673i
$279$			172.320i			0.617633i
$280$		0			0
$281$	443.128			1.57697			0.788484	−	0.615055i	$-0.210866\pi$
$281$	443.128			1.57697			0.788484	+	0.615055i	$0.210866\pi$
$282$	−150.746	−	140.965i	−0.534561	−	0.499875i
$283$	294.620			1.04106			0.520531	−	0.853843i	$-0.325734\pi$
$283$	294.620			1.04106			0.520531	+	0.853843i	$0.325734\pi$
$284$	169.492	−	11.3794i	0.596804	−	0.0400683i
$285$		0			0
$286$	136.574	+	127.712i	0.477533	+	0.446547i
$287$		−	67.5196i		−	0.235260i
$288$	55.6077	−	78.2546i	0.193082	−	0.271717i
$289$	−148.426			−0.513583
$290$		0			0
$291$	−168.249			−0.578174
$292$	−1.45379	−	21.6538i	−0.00497874	−	0.0741567i
$293$		−	66.7217i		−	0.227719i	−0.993497	−	0.113859i	$-0.963679\pi$
$293$		−	66.7217i		−	0.227719i	0.993497	−	0.113859i	$-0.0363214\pi$
$294$	−105.112	+	112.406i	−0.357524	+	0.382333i
$295$		0			0
$296$	−139.923	+	171.327i	−0.472713	+	0.578808i
$297$	−41.5692			−0.139964
$298$	128.263	+	119.940i	0.430412	+	0.402484i
$299$	49.9897			0.167190
$300$		0			0
$301$		−	61.5639i		−	0.204531i
$302$	−320.014	−	299.249i	−1.05965	−	0.990892i
$303$			107.624i			0.355196i
$304$	−236.708	+	31.9281i	−0.778644	+	0.105027i
$305$		0			0
$306$	48.5885	−	51.9600i	0.158786	−	0.169804i
$307$	524.210			1.70753			0.853763	−	0.520662i	$-0.174315\pi$
$307$	524.210			1.70753			0.853763	+	0.520662i	$0.174315\pi$
$308$	−68.2872	+	4.58467i	−0.221712	+	0.0148853i
$309$		−	48.1582i		−	0.155852i
$310$		0			0
$311$		−	362.057i		−	1.16417i	−0.813128	−	0.582085i	$-0.802237\pi$
$311$		−	362.057i		−	1.16417i	0.813128	−	0.582085i	$-0.197763\pi$
$312$	−102.431	+	125.420i	−0.328304	+	0.401988i
$313$	−252.277			−0.805996			−0.402998	−	0.915201i	$-0.632032\pi$
$313$	−252.277			−0.805996			−0.402998	+	0.915201i	$0.632032\pi$
$314$	370.228	+	346.205i	1.17907	+	1.10256i
$315$		0			0
$316$	−178.028	+	11.9525i	−0.563380	+	0.0378243i
$317$		−	80.3934i		−	0.253607i	−0.991928	−	0.126803i	$-0.959528\pi$
$317$		−	80.3934i		−	0.253607i	0.991928	−	0.126803i	$-0.0404717\pi$
$318$	−79.3346	−	74.1868i	−0.249480	−	0.233292i
$319$			4.58467i			0.0143720i
$320$		0			0
$321$	−65.4359			−0.203850
$322$	−12.4974	+	13.3646i	−0.0388119	+	0.0415050i
$323$	−176.995			−0.547972
$324$	−2.41154	−	35.9191i	−0.00744303	−	0.110862i
$325$		0			0
$326$	−139.818	+	149.520i	−0.428889	+	0.458650i
$327$		−	245.417i		−	0.750509i
$328$	−195.608	−	159.753i	−0.596365	−	0.487052i
$329$	−127.426			−0.387312
$330$		0			0
$331$	172.056			0.519808			0.259904	−	0.965635i	$-0.416309\pi$
$331$	172.056			0.519808			0.259904	+	0.965635i	$0.416309\pi$
$332$	18.1436	+	270.243i	0.0546494	+	0.813985i
$333$			82.9517i			0.249104i
$334$	−410.620	−	383.977i	−1.22940	−	1.14963i
$335$		0			0
$336$	−7.92305	−	58.7396i	−0.0235805	−	0.174820i
$337$	−564.277			−1.67441			−0.837206	−	0.546888i	$-0.815813\pi$
$337$	−564.277			−1.67441			−0.837206	+	0.546888i	$0.815813\pi$
$338$	−44.2942	+	47.3678i	−0.131048	+	0.140141i
$339$	100.956			0.297806
$340$		0			0
$341$		−	459.519i		−	1.34756i
$342$	−61.1769	+	65.4219i	−0.178880	+	0.191292i
$343$			199.817i			0.582556i
$344$	−178.354	−	145.662i	−0.518470	−	0.423435i
$345$		0			0
$346$	354.771	+	331.751i	1.02535	+	0.958817i
$347$	286.123			0.824562			0.412281	−	0.911057i	$-0.364732\pi$
$347$	286.123			0.824562			0.412281	+	0.911057i	$0.364732\pi$
$348$	−3.96152	+	0.265969i	−0.0113837	+	0.000764279i
$349$			421.021i			1.20636i	0.797603	+	0.603182i	$0.206101\pi$
$349$			421.021i			1.20636i	−0.797603	+	0.603182i	$0.793899\pi$
$350$		0			0
$351$			60.7249i			0.173005i
$352$	−148.287	+	208.679i	−0.421270	+	0.592838i
$353$	−429.138			−1.21569			−0.607845	−	0.794056i	$-0.707966\pi$
$353$	−429.138			−1.21569			−0.607845	+	0.794056i	$0.707966\pi$
$354$	124.890	−	133.556i	0.352796	−	0.377276i
$355$		0			0
$356$	35.6743	+	531.358i	0.100209	+	1.49258i
$357$		−	43.9217i		−	0.123030i
$358$	−434.879	+	465.055i	−1.21475	+	1.29904i
$359$			263.673i			0.734465i	0.930129	+	0.367233i	$0.119695\pi$
$359$			263.673i			0.734465i	−0.930129	+	0.367233i	$0.880305\pi$
$360$		0			0
$361$	−138.149			−0.382684
$362$	116.154	+	108.617i	0.320867	+	0.300047i
$363$	−98.7269			−0.271975
$364$	6.69735	+	99.7548i	0.0183993	+	0.274052i
$365$		0			0
$366$	−150.746	−	140.965i	−0.411875	−	0.385149i
$367$			129.544i			0.352981i	0.984302	+	0.176491i	$0.0564745\pi$
$367$			129.544i			0.352981i	−0.984302	+	0.176491i	$0.943525\pi$
$368$	9.14875	+	67.8267i	0.0248607	+	0.184312i
$369$	−94.7077			−0.256660
$370$		0			0
$371$	−67.0615			−0.180759
$372$	397.061	−	26.6580i	1.06737	−	0.0716612i
$373$			302.478i			0.810933i	0.914110	+	0.405467i	$0.132891\pi$
$373$			302.478i			0.810933i	−0.914110	+	0.405467i	$0.867109\pi$
$374$	−129.569	+	138.560i	−0.346442	+	0.370481i
$375$		0			0
$376$	−301.492	+	369.159i	−0.801841	+	0.981805i
$377$	6.69735			0.0177649
$378$	−16.2346	−	15.1812i	−0.0429488	−	0.0401619i
$379$	−116.210			−0.306623			−0.153312	−	0.988178i	$-0.548994\pi$
$379$	−116.210			−0.306623			−0.153312	+	0.988178i	$0.548994\pi$
$380$		0			0
$381$			320.693i			0.841715i
$382$	515.503	+	482.053i	1.34948	+	1.26192i
$383$		−	566.151i		−	1.47820i	−0.673595	−	0.739101i	$-0.735251\pi$
$383$		−	566.151i		−	1.47820i	0.673595	−	0.739101i	$-0.264749\pi$
$384$	−188.918	−	116.026i	−0.491974	−	0.302151i
$385$		0			0
$386$	−388.329	+	415.275i	−1.00603	+	1.07584i
$387$	−86.3538			−0.223137
$388$	26.0282	+	387.681i	0.0670829	+	0.999178i
$389$		−	350.104i		−	0.900011i	−0.893026	−	0.450006i	$-0.851422\pi$
$389$		−	350.104i		−	0.900011i	0.893026	−	0.450006i	$-0.148578\pi$
$390$		0			0
$391$			50.7165i			0.129710i
$392$	275.268	+	224.812i	0.702214	+	0.573499i
$393$	217.128			0.552489
$394$	−110.742	−	103.557i	−0.281072	−	0.262834i
$395$		0			0
$396$	6.43078	+	95.7844i	0.0162393	+	0.241880i
$397$		−	544.149i		−	1.37065i	−0.728236	−	0.685326i	$-0.759660\pi$
$397$		−	544.149i		−	1.37065i	0.728236	−	0.685326i	$-0.240340\pi$
$398$	−152.196	−	142.321i	−0.382402	−	0.357589i
$399$			55.3011i			0.138599i
$400$		0			0
$401$	−296.431			−0.739229			−0.369614	−	0.929185i	$-0.620510\pi$
$401$	−296.431			−0.739229			−0.369614	+	0.929185i	$0.620510\pi$
$402$	−200.603	+	214.522i	−0.499011	+	0.533637i
$403$	−671.272			−1.66569
$404$	247.990	−	16.6496i	0.613836	−	0.0412118i
$405$		0			0
$406$	−1.67434	+	1.79052i	−0.00412398	+	0.00441014i
$407$		−	221.205i		−	0.543500i
$408$	−127.244	−	103.920i	−0.311871	−	0.254706i
$409$	−247.415			−0.604927			−0.302464	−	0.953161i	$-0.597809\pi$
$409$	−247.415			−0.604927			−0.302464	+	0.953161i	$0.597809\pi$
$410$		0			0
$411$	−172.459			−0.419608
$412$	−110.967	+	7.45009i	−0.269337	+	0.0180827i
$413$		−	112.895i		−	0.273353i
$414$	18.7461	+	17.5298i	0.0452805	+	0.0423424i
$415$		0			0
$416$	304.841	+	216.620i	0.732791	+	0.520721i
$417$	307.426			0.737232
$418$	163.138	−	174.459i	0.390283	−	0.417365i
$419$	−92.1333			−0.219889			−0.109944	−	0.993938i	$-0.535067\pi$
$419$	−92.1333			−0.219889			−0.109944	+	0.993938i	$0.535067\pi$
$420$		0			0
$421$		−	445.540i		−	1.05829i	−0.848531	−	0.529145i	$-0.822513\pi$
$421$		−	445.540i		−	1.05829i	0.848531	−	0.529145i	$-0.177487\pi$
$422$	−187.033	+	200.011i	−0.443207	+	0.473961i
$423$			178.736i			0.422544i
$424$	−158.669	+	194.281i	−0.374220	+	0.458209i
$425$		0			0
$426$	−107.454	−	100.481i	−0.252239	−	0.235872i
$427$	−127.426			−0.298421
$428$	10.1230	+	150.778i	0.0236518	+	0.352286i
$429$		−	161.933i		−	0.377466i
$430$		0			0
$431$		−	186.677i		−	0.433125i	−0.976269	−	0.216563i	$-0.930515\pi$
$431$		−	186.677i		−	0.433125i	0.976269	−	0.216563i	$-0.0694845\pi$
$432$	−82.3923	+	11.1134i	−0.190723	+	0.0257255i
$433$	−291.128			−0.672351			−0.336176	−	0.941799i	$-0.609134\pi$
$433$	−291.128			−0.672351			−0.336176	+	0.941799i	$0.609134\pi$
$434$	167.818	−	179.463i	0.386677	−	0.413509i
$435$		0			0
$436$	−565.492	+	37.9661i	−1.29700	+	0.0870782i
$437$		−	63.8562i		−	0.146124i
$438$	−12.8372	+	13.7279i	−0.0293086	+	0.0313423i
$439$			87.6899i			0.199749i	0.995000	+	0.0998746i	$0.0318442\pi$
$439$			87.6899i			0.199749i	−0.995000	+	0.0998746i	$0.968156\pi$
$440$		0			0
$441$	133.277			0.302215
$442$	202.410	+	189.276i	0.457942	+	0.428227i
$443$	−20.7077			−0.0467441			−0.0233721	−	0.999727i	$-0.507440\pi$
$443$	−20.7077			−0.0467441			−0.0233721	+	0.999727i	$0.507440\pi$
$444$	191.138	−	12.8327i	0.430492	−	0.0289024i
$445$		0			0
$446$	77.6603	+	72.6211i	0.174126	+	0.162828i
$447$		−	152.078i		−	0.340219i
$448$	−134.123	+	27.3435i	−0.299382	+	0.0610345i
$449$	584.410			1.30158			0.650791	−	0.759257i	$-0.274437\pi$
$449$	584.410			1.30158			0.650791	+	0.759257i	$0.274437\pi$
$450$		0			0
$451$	252.554			0.559986
$452$	−15.6180	−	232.625i	−0.0345531	−	0.514657i
$453$			379.433i			0.837600i
$454$	−163.713	+	175.073i	−0.360601	+	0.385623i
$455$		0			0
$456$	160.210	+	130.844i	0.351338	+	0.286938i
$457$	269.692			0.590136			0.295068	−	0.955476i	$-0.404658\pi$
$457$	269.692			0.590136			0.295068	+	0.955476i	$0.404658\pi$
$458$	312.764	+	292.470i	0.682891	+	0.638580i
$459$	−61.6077			−0.134222
$460$		0			0
$461$		−	44.4948i		−	0.0965181i	−0.998835	−	0.0482590i	$-0.984633\pi$
$461$		−	44.4948i		−	0.0965181i	0.998835	−	0.0482590i	$-0.0153673\pi$
$462$	43.2923	+	40.4832i	0.0937064	+	0.0876261i
$463$			611.065i			1.31980i	0.751355	+	0.659898i	$0.229400\pi$
$463$			611.065i			1.31980i	−0.751355	+	0.659898i	$0.770600\pi$
$464$	1.22570	+	9.08705i	0.00264159	+	0.0195842i
$465$		0			0
$466$	−174.081	+	186.160i	−0.373564	+	0.399485i
$467$	−146.410			−0.313512			−0.156756	−	0.987637i	$-0.550104\pi$
$467$	−146.410			−0.313512			−0.156756	+	0.987637i	$0.550104\pi$
$468$	139.923	−	9.39417i	0.298981	−	0.0200730i
$469$			181.336i			0.386643i
$470$		0			0
$471$		−	438.971i		−	0.931997i
$472$	−327.061	−	267.111i	−0.692927	−	0.565914i
$473$	230.277			0.486843
$474$	112.865	+	105.542i	0.238113	+	0.222662i
$475$		0			0
$476$	−101.205	+	6.79472i	−0.212616	+	0.0142746i
$477$			94.0651i			0.197201i
$478$	−466.410	−	436.146i	−0.975753	−	0.912440i
$479$		−	191.876i		−	0.400576i	−0.979737	−	0.200288i	$-0.935812\pi$
$479$		−	191.876i		−	0.400576i	0.979737	−	0.200288i	$-0.0641878\pi$
$480$		0			0
$481$	−323.138			−0.671805
$482$	337.976	−	361.428i	0.701194	−	0.749850i
$483$	15.8461			0.0328077
$484$	15.2731	+	227.488i	0.0315560	+	0.470016i
$485$		0			0
$486$	−21.2942	+	22.7718i	−0.0438153	+	0.0468556i
$487$		−	610.758i		−	1.25412i	−0.778969	−	0.627062i	$-0.784257\pi$
$487$		−	610.758i		−	1.25412i	0.778969	−	0.627062i	$-0.215743\pi$
$488$	−301.492	+	369.159i	−0.617812	+	0.756473i
$489$	177.282			0.362540
$490$		0			0
$491$	−142.354			−0.289926			−0.144963	−	0.989437i	$-0.546306\pi$
$491$	−142.354			−0.289926			−0.144963	+	0.989437i	$0.546306\pi$
$492$	14.6513	+	218.227i	0.0297791	+	0.443550i
$493$			6.79472i			0.0137824i
$494$	−254.851	−	238.315i	−0.515893	−	0.482419i
$495$		0			0
$496$	−122.851	−	910.791i	−0.247684	−	1.83627i
$497$	−90.8306			−0.182758
$498$	160.210	−	171.327i	0.321707	−	0.344030i
$499$	91.3693			0.183105			0.0915524	−	0.995800i	$-0.470817\pi$
$499$	91.3693			0.183105			0.0915524	+	0.995800i	$0.470817\pi$
$500$		0			0
$501$			486.863i			0.971782i
$502$	293.492	−	313.857i	0.584646	−	0.625214i
$503$			230.067i			0.457389i	0.973498	+	0.228695i	$0.0734457\pi$
$503$			230.067i			0.457389i	−0.973498	+	0.228695i	$0.926554\pi$
$504$	−32.4693	+	39.7566i	−0.0644231	+	0.0788821i
$505$		0			0
$506$	−49.9897	−	46.7460i	−0.0987939	−	0.0923834i
$507$	56.1628			0.110775
$508$	738.946	−	49.6114i	1.45462	−	0.0976603i
$509$			527.387i			1.03612i	0.855343	+	0.518062i	$0.173346\pi$
$509$			527.387i			1.03612i	−0.855343	+	0.518062i	$0.826654\pi$
$510$		0			0
$511$			11.6042i			0.0227088i
$512$	−238.123	+	453.256i	−0.465084	+	0.885267i
$513$	77.5692			0.151207
$514$	−115.124	+	123.113i	−0.223977	+	0.239519i
$515$		0			0
$516$	13.3590	+	198.978i	0.0258895	+	0.385616i
$517$		−	476.630i		−	0.921914i
$518$	80.7846	−	86.3902i	0.155955	−	0.166776i
$519$		−	420.643i		−	0.810487i
$520$		0			0
$521$	191.856			0.368246			0.184123	−	0.982903i	$-0.441055\pi$
$521$	191.856			0.368246			0.184123	+	0.982903i	$0.441055\pi$
$522$	2.51151	+	2.34854i	0.00481131	+	0.00449912i
$523$	−105.492			−0.201706			−0.100853	−	0.994901i	$-0.532157\pi$
$523$	−105.492			−0.201706			−0.100853	+	0.994901i	$0.532157\pi$
$524$	−33.5898	−	500.310i	−0.0641027	−	0.954789i
$525$		0			0
$526$	404.820	+	378.553i	0.769620	+	0.719682i
$527$		−	681.031i		−	1.29228i
$528$	219.713	−	29.6358i	0.416123	−	0.0561284i
$529$	510.703			0.965411
$530$		0			0
$531$	−158.354			−0.298218
$532$	127.426	−	8.55511i	0.239522	−	0.0160810i
$533$		−	368.934i		−	0.692184i
$534$	315.009	−	336.867i	0.589904	−	0.630837i
$535$		0			0
$536$	525.338	+	429.044i	0.980109	+	0.800456i
$537$	551.405			1.02682
$538$	180.704	+	168.979i	0.335881	+	0.314087i
$539$	−355.405			−0.659378
$540$		0			0
$541$		−	459.744i		−	0.849804i	−0.905239	−	0.424902i	$-0.860309\pi$
$541$		−	459.744i		−	0.849804i	0.905239	−	0.424902i	$-0.139691\pi$
$542$	−289.219	−	270.453i	−0.533615	−	0.498990i
$543$		−	137.721i		−	0.253630i
$544$	−219.769	+	309.273i	−0.403987	+	0.568516i
$545$		0			0
$546$	59.1384	−	63.2420i	0.108312	−	0.115828i
$547$	−67.3693			−0.123161			−0.0615807	−	0.998102i	$-0.519614\pi$
$547$	−67.3693			−0.123161			−0.0615807	+	0.998102i	$0.519614\pi$
$548$	26.6795	+	397.382i	0.0486852	+	0.725150i
$549$			178.736i			0.325567i
$550$		0			0
$551$		−	8.55511i		−	0.0155265i
$552$	37.4923	−	45.9070i	0.0679208	−	0.0831648i
$553$	95.4050			0.172523
$554$	361.856	+	338.377i	0.653170	+	0.610788i
$555$		0			0
$556$	−47.5589	−	708.374i	−0.0855376	−	1.27405i
$557$			476.671i			0.855782i	0.903830	+	0.427891i	$0.140743\pi$
$557$			476.671i			0.855782i	−0.903830	+	0.427891i	$0.859257\pi$
$558$	−251.727	−	235.393i	−0.451123	−	0.421851i
$559$		−	336.391i		−	0.601774i
$560$		0			0
$561$	164.287			0.292847
$562$	−605.324	+	647.327i	−1.07709	+	1.15183i
$563$	910.123			1.61656			0.808280	−	0.588799i	$-0.200399\pi$
$563$	910.123			1.61656			0.808280	+	0.588799i	$0.200399\pi$
$564$	411.846	−	27.6506i	0.730224	−	0.0490258i
$565$		0			0
$566$	−402.459	+	430.385i	−0.711058	+	0.760398i
$567$			19.2490i			0.0339489i
$568$	−214.908	+	263.141i	−0.378358	+	0.463276i
$569$	−124.123			−0.218142			−0.109071	−	0.994034i	$-0.534788\pi$
$569$	−124.123			−0.218142			−0.109071	+	0.994034i	$0.534788\pi$
$570$		0			0
$571$	945.031			1.65504			0.827522	−	0.561433i	$-0.189750\pi$
$571$	945.031			1.65504			0.827522	+	0.561433i	$0.189750\pi$
$572$	−373.128	+	25.0511i	−0.652322	+	0.0437957i
$573$		−	611.219i		−	1.06670i
$574$	98.6335	+	92.2335i	0.171835	+	0.160685i
$575$		0			0
$576$	38.3538	+	188.130i	0.0665865	+	0.326615i
$577$	−215.682			−0.373799			−0.186899	−	0.982379i	$-0.559844\pi$
$577$	−215.682			−0.373799			−0.186899	+	0.982379i	$0.559844\pi$
$578$	202.753	−	216.822i	0.350784	−	0.375125i
$579$	492.382			0.850401
$580$		0			0
$581$		−	144.823i		−	0.249265i
$582$	229.832	−	245.780i	0.394900	−	0.422302i
$583$		−	250.840i		−	0.430258i
$584$	33.6180	+	27.4559i	0.0575651	+	0.0470135i
$585$		0			0
$586$	97.4679	+	91.1435i	0.166327	+	0.155535i
$587$	−900.785			−1.53456			−0.767278	−	0.641314i	$-0.778389\pi$
$587$	−900.785			−1.53456			−0.767278	+	0.641314i	$0.778389\pi$
$588$	−20.6180	−	307.098i	−0.0350646	−	0.522276i
$589$			857.475i			1.45581i
$590$		0			0
$591$			131.305i			0.222174i
$592$	−59.1384	−	438.439i	−0.0998960	−	0.740606i
$593$	508.585			0.857647			0.428824	−	0.903388i	$-0.358928\pi$
$593$	508.585			0.857647			0.428824	+	0.903388i	$0.358928\pi$
$594$	56.7846	−	60.7249i	0.0955970	−	0.102230i
$595$		0			0
$596$	−350.420	+	23.5266i	−0.587954	+	0.0394741i
$597$			180.455i			0.302270i
$598$	−68.2872	+	73.0256i	−0.114193	+	0.122116i
$599$		−	846.934i		−	1.41391i	−0.707257	−	0.706957i	$-0.750067\pi$
$599$		−	846.934i		−	1.41391i	0.707257	−	0.706957i	$-0.249933\pi$
$600$		0			0
$601$	−406.000			−0.675541			−0.337770	−	0.941229i	$-0.609673\pi$
$601$	−406.000			−0.675541			−0.337770	+	0.941229i	$0.609673\pi$
$602$	89.9334	+	84.0979i	0.149391	+	0.139697i
$603$	254.354			0.421814
$604$	874.295	−	58.6985i	1.44751	−	0.0971829i
$605$		0			0
$606$	−157.219	−	147.018i	−0.259438	−	0.242603i
$607$			771.156i			1.27044i	0.772332	+	0.635219i	$0.219090\pi$
$607$			771.156i			1.27044i	−0.772332	+	0.635219i	$0.780910\pi$
$608$	276.708	−	389.400i	0.455111	−	0.640461i
$609$	2.12297			0.00348600
$610$		0			0
$611$	−696.267			−1.13955
$612$	9.53074	+	141.957i	0.0155731	+	0.231956i
$613$			336.699i			0.549264i	0.961549	+	0.274632i	$0.0885560\pi$
$613$			336.699i			0.549264i	−0.961549	+	0.274632i	$0.911444\pi$
$614$	−716.084	+	765.773i	−1.16626	+	1.24719i
$615$		0			0
$616$	86.5847	−	106.018i	0.140560	−	0.172106i
$617$	908.831			1.47298			0.736492	−	0.676447i	$-0.236481\pi$
$617$	908.831			1.47298			0.736492	+	0.676447i	$0.236481\pi$
$618$	70.3501	+	65.7853i	0.113835	+	0.106449i
$619$	−1047.77			−1.69268			−0.846340	−	0.532643i	$-0.821199\pi$
$619$	−1047.77			−1.69268			−0.846340	+	0.532643i	$0.821199\pi$
$620$		0			0
$621$		−	22.2268i		−	0.0357920i
$622$	528.897	+	494.579i	0.850317	+	0.795143i
$623$		−	284.754i		−	0.457068i
$624$	−43.2923	−	320.959i	−0.0693788	−	0.514358i
$625$		0			0
$626$	344.617	−	368.529i	0.550506	−	0.588705i
$627$	−206.851			−0.329906
$628$	−1011.48	+	67.9090i	−1.61064	+	0.108135i
$629$		−	327.836i		−	0.521202i
$630$		0			0
$631$			610.758i			0.967921i	0.875090	+	0.483961i	$0.160802\pi$
$631$			610.758i			0.967921i	−0.875090	+	0.483961i	$0.839198\pi$
$632$	225.731	−	276.393i	0.357169	−	0.437331i
$633$	237.149			0.374643
$634$	117.440	+	109.819i	0.185236	+	0.173217i
$635$		0			0
$636$	216.746	−	14.5519i	0.340796	−	0.0228804i
$637$			519.180i			0.815040i
$638$	−6.69735	−	6.26278i	−0.0104974	−	0.00981627i
$639$			127.405i			0.199382i
$640$		0			0
$641$	9.60015			0.0149768			0.00748842	−	0.999972i	$-0.497616\pi$
$641$	9.60015			0.0149768			0.00748842	+	0.999972i	$0.497616\pi$
$642$	89.3872	−	95.5897i	0.139232	−	0.148894i
$643$	−86.1999			−0.134059			−0.0670295	−	0.997751i	$-0.521352\pi$
$643$	−86.1999			−0.134059			−0.0670295	+	0.997751i	$0.521352\pi$
$644$	−2.45140	−	36.5128i	−0.00380652	−	0.0566969i
$645$		0			0
$646$	241.779	−	258.556i	0.374272	−	0.400242i
$647$			352.580i			0.544946i	0.962163	+	0.272473i	$0.0878416\pi$
$647$			352.580i			0.544946i	−0.962163	+	0.272473i	$0.912158\pi$
$648$	55.7654	+	45.5436i	0.0860577	+	0.0702834i
$649$	422.277			0.650658
$650$		0			0
$651$	−212.785			−0.326858
$652$	−27.4256	−	408.496i	−0.0420638	−	0.626527i
$653$			319.322i			0.489008i	0.969648	+	0.244504i	$0.0786252\pi$
$653$			319.322i			0.489008i	−0.969648	+	0.244504i	$0.921375\pi$
$654$	358.508	+	335.245i	0.548177	+	0.512607i
$655$		0			0
$656$	500.574	−	67.5196i	0.763071	−	0.102926i
$657$	16.2769			0.0247745
$658$	174.067	−	186.145i	0.264539	−	0.282895i
$659$	275.328			0.417797			0.208898	−	0.977937i	$-0.433012\pi$
$659$	275.328			0.417797			0.208898	+	0.977937i	$0.433012\pi$
$660$		0			0
$661$		−	133.668i		−	0.202221i	−0.994875	−	0.101111i	$-0.967760\pi$
$661$		−	133.668i		−	0.202221i	0.994875	−	0.101111i	$-0.0322396\pi$
$662$	−235.033	+	251.342i	−0.355035	+	0.379671i
$663$		−	239.993i		−	0.361980i
$664$	−419.559	−	342.654i	−0.631866	−	0.516046i
$665$		0			0
$666$	−121.177	−	113.314i	−0.181947	−	0.170141i
$667$	−2.45140			−0.00367526
$668$	1121.84	−	75.3179i	1.67939	−	0.112751i
$669$		−	92.0799i		−	0.137638i
$670$		0			0
$671$		−	476.630i		−	0.710327i
$672$	96.6307	+	68.6657i	0.143796	+	0.102181i
$673$	−187.703			−0.278904			−0.139452	−	0.990229i	$-0.544534\pi$
$673$	−187.703			−0.278904			−0.139452	+	0.990229i	$0.544534\pi$
$674$	770.817	−	824.303i	1.14364	−	1.22300i
$675$		0			0
$676$	−8.68842	−	129.411i	−0.0128527	−	0.191437i
$677$			1169.84i			1.72797i	0.503515	+	0.863986i	$0.332040\pi$
$677$			1169.84i			1.72797i	−0.503515	+	0.863986i	$0.667960\pi$
$678$	−137.909	+	147.478i	−0.203406	+	0.217520i
$679$		−	207.758i		−	0.305976i
$680$		0			0
$681$	207.580			0.304816
$682$	671.272	+	627.715i	0.984269	+	0.920403i
$683$	−89.4566			−0.130976			−0.0654880	−	0.997853i	$-0.520860\pi$
$683$	−89.4566			−0.130976			−0.0654880	+	0.997853i	$0.520860\pi$
$684$	−12.0000	−	178.736i	−0.0175439	−	0.261310i
$685$		0			0
$686$	−291.895	−	272.955i	−0.425503	−	0.397893i
$687$		−	370.837i		−	0.539791i
$688$	456.420	−	61.5639i	0.663402	−	0.0894824i
$689$	−366.431			−0.531830
$690$		0			0
$691$	139.103			0.201306			0.100653	−	0.994922i	$-0.467907\pi$
$691$	139.103			0.201306			0.100653	+	0.994922i	$0.467907\pi$
$692$	−969.251	+	65.0737i	−1.40065	+	0.0940371i
$693$		−	51.3307i		−	0.0740703i
$694$	−390.851	+	417.972i	−0.563186	+	0.602265i
$695$		0			0
$696$	5.02301	−	6.15037i	0.00721697	−	0.00883673i
$697$	374.297			0.537012
$698$	−615.033	−	575.126i	−0.881137	−	0.823962i
$699$	220.726			0.315773
$700$		0			0
$701$			1218.34i			1.73801i	0.494804	+	0.869004i	$0.335240\pi$
$701$			1218.34i			1.73801i	−0.494804	+	0.869004i	$0.664760\pi$
$702$	−88.7077	−	82.9517i	−0.126364	−	0.118165i
$703$			412.773i			0.587160i
$704$	−102.277	−	501.681i	−0.145280	−	0.712615i
$705$		0			0
$706$	586.214	−	626.891i	0.830331	−	0.887948i
$707$	−132.897			−0.187974
$708$	24.4974	+	364.881i	0.0346009	+	0.515369i
$709$			1080.13i			1.52346i	0.647895	+	0.761730i	$0.275649\pi$
$709$			1080.13i			1.52346i	−0.647895	+	0.761730i	$0.724351\pi$
$710$		0			0
$711$		−	133.822i		−	0.188216i
$712$	−824.946	−	673.734i	−1.15863	−	0.946256i
$713$	245.703			0.344604
$714$	64.1615	+	59.9982i	0.0898620	+	0.0840311i
$715$		0			0
$716$	−85.3027	−	1270.56i	−0.119138	−	1.77452i
$717$			553.011i			0.771285i
$718$	−385.177	−	360.184i	−0.536458	−	0.501649i
$719$			20.7736i			0.0288923i	0.999896	+	0.0144461i	$0.00459851\pi$
$719$			20.7736i			0.0288923i	−0.999896	+	0.0144461i	$0.995401\pi$
$720$		0			0
$721$	59.4669			0.0824783
$722$	188.715	−	201.809i	0.261378	−	0.279515i
$723$	−428.536			−0.592719
$724$	−317.338	+	21.3055i	−0.438313	+	0.0294275i
$725$		0			0
$726$	134.863	−	144.222i	0.185762	−	0.198652i
$727$			1031.17i			1.41838i	0.705015	+	0.709192i	$0.250940\pi$
$727$			1031.17i			1.41838i	−0.705015	+	0.709192i	$0.749060\pi$
$728$	−154.872	−	126.484i	−0.212736	−	0.173742i
$729$	27.0000			0.0370370
$730$		0			0
$731$	341.282			0.466870
$732$	411.846	−	27.6506i	0.562631	−	0.0377740i
$733$		−	881.072i		−	1.20201i	−0.799246	−	0.601004i	$-0.794767\pi$
$733$		−	881.072i		−	1.20201i	0.799246	−	0.601004i	$-0.205233\pi$
$734$	−189.240	−	176.961i	−0.257820	−	0.241091i
$735$		0			0
$736$	−111.580	−	79.2884i	−0.151603	−	0.107729i
$737$	−678.277			−0.920321
$738$	129.373	−	138.350i	0.175302	−	0.187466i
$739$	−671.195			−0.908247			−0.454124	−	0.890939i	$-0.650048\pi$
$739$	−671.195			−0.908247			−0.454124	+	0.890939i	$0.650048\pi$
$740$		0			0
$741$			302.171i			0.407788i
$742$	91.6077	−	97.9643i	0.123461	−	0.132027i
$743$		−	254.197i		−	0.342122i	−0.985260	−	0.171061i	$-0.945281\pi$
$743$		−	254.197i		−	0.342122i	0.985260	−	0.171061i	$-0.0547195\pi$
$744$	−503.454	+	616.448i	−0.676685	+	0.828559i
$745$		0			0
$746$	−441.864	−	413.193i	−0.592311	−	0.553878i
$747$	−203.138			−0.271939
$748$	−25.4153	−	378.553i	−0.0339777	−	0.506087i
$749$		−	80.8019i		−	0.107880i
$750$		0			0
$751$			728.994i			0.970698i	0.874320	+	0.485349i	$0.161307\pi$
$751$			728.994i			0.970698i	−0.874320	+	0.485349i	$0.838693\pi$
$752$	−127.426	−	944.704i	−0.169449	−	1.25626i
$753$	−372.133			−0.494201
$754$	−9.14875	+	9.78357i	−0.0121336	+	0.0129756i
$755$		0			0
$756$	44.3538	−	2.97783i	0.0586691	−	0.00393893i
$757$			372.679i			0.492311i	0.969230	+	0.246155i	$0.0791674\pi$
$757$			372.679i			0.492311i	−0.969230	+	0.246155i	$0.920833\pi$
$758$	158.746	−	169.761i	0.209428	−	0.223960i
$759$			59.2716i			0.0780917i
$760$		0			0
$761$	1257.80			1.65283			0.826416	−	0.563060i	$-0.190376\pi$
$761$	1257.80			1.65283			0.826416	+	0.563060i	$0.190376\pi$
$762$	−468.473	−	438.075i	−0.614794	−	0.574902i
$763$	303.046			0.397177
$764$	−1408.38	+	94.5559i	−1.84343	+	0.123764i
$765$		0			0
$766$	827.041	+	773.377i	1.07969	+	1.00963i
$767$		−	616.868i		−	0.804260i
$768$	427.559	−	117.479i	0.556717	−	0.152968i
$769$	247.703			0.322110			0.161055	−	0.986945i	$-0.448510\pi$
$769$	247.703			0.322110			0.161055	+	0.986945i	$0.448510\pi$
$770$		0			0
$771$	145.972			0.189328
$772$	−76.1718	−	1134.55i	−0.0986681	−	1.46963i
$773$		−	587.805i		−	0.760420i	−0.924900	−	0.380210i	$-0.875852\pi$
$773$		−	587.805i		−	0.760420i	0.924900	−	0.380210i	$-0.124148\pi$
$774$	117.962	−	126.147i	0.152405	−	0.162980i
$775$		0			0
$776$	−601.885	−	491.560i	−0.775624	−	0.633453i
$777$	−102.431			−0.131829
$778$	511.437	+	478.251i	0.657374	+	0.614719i
$779$	−471.272			−0.604970
$780$		0			0
$781$		−	339.748i		−	0.435016i
$782$	−74.0873	−	69.2800i	−0.0947407	−	0.0885933i
$783$		−	2.97783i		−	0.00380311i
$784$	−704.431	+	95.0166i	−0.898509	+	0.121195i
$785$		0			0
$786$	−296.603	+	317.184i	−0.377357	+	0.403541i
$787$	31.0821			0.0394944			0.0197472	−	0.999805i	$-0.493714\pi$
$787$	31.0821			0.0394944			0.0197472	+	0.999805i	$0.493714\pi$
$788$	302.554	−	20.3129i	0.383951	−	0.0257778i
$789$		−	479.986i		−	0.608347i
$790$		0			0
$791$			124.663i			0.157602i
$792$	−148.708	−	121.450i	−0.187762	−	0.153346i
$793$	−696.267			−0.878016
$794$	794.900	+	743.321i	1.00113	+	0.936173i
$795$		0			0
$796$	415.808	−	27.9165i	0.522371	−	0.0350710i
$797$			490.260i			0.615132i	0.951527	+	0.307566i	$0.0995145\pi$
$797$			490.260i			0.615132i	−0.951527	+	0.307566i	$0.900486\pi$
$798$	−80.7846	−	75.5427i	−0.101234	−	0.0946651i
$799$		−	706.389i		−	0.884092i
$800$		0			0
$801$	−399.415			−0.498646
$802$	404.932	−	433.030i	0.504903	−	0.539938i
$803$	−43.4050			−0.0540536
$804$	−39.3487	−	586.086i	−0.0489411	−	0.728962i
$805$		0			0
$806$	916.974	−	980.602i	1.13769	−	1.21663i
$807$		−	214.256i		−	0.265497i
$808$	−314.438	+	385.010i	−0.389156	+	0.476498i
$809$	676.102			0.835726			0.417863	−	0.908510i	$-0.362779\pi$
$809$	676.102			0.835726			0.417863	+	0.908510i	$0.362779\pi$
$810$		0			0
$811$	−74.1793			−0.0914665			−0.0457332	−	0.998954i	$-0.514562\pi$
$811$	−74.1793			−0.0914665			−0.0457332	+	0.998954i	$0.514562\pi$
$812$	−0.328425	−	4.89179i	−0.000404465	−	0.00602437i
$813$			342.920i			0.421796i
$814$	323.138	+	302.171i	0.396976	+	0.371217i
$815$		0			0
$816$	325.626	−	43.9217i	0.399051	−	0.0538257i
$817$	−429.703			−0.525952
$818$	337.976	−	361.428i	0.413173	−	0.441843i
$819$	−74.9845			−0.0915562
$820$		0			0
$821$			1130.58i			1.37708i	0.725198	+	0.688540i	$0.241748\pi$
$821$			1130.58i			1.37708i	−0.725198	+	0.688540i	$0.758252\pi$
$822$	235.583	−	251.930i	0.286598	−	0.306485i
$823$		−	82.1839i		−	0.0998589i	−0.998753	−	0.0499295i	$-0.984100\pi$
$823$		−	82.1839i		−	0.0998589i	0.998753	−	0.0499295i	$-0.0158997\pi$
$824$	140.700	−	172.279i	0.170753	−	0.209076i
$825$		0			0
$826$	164.918	+	154.217i	0.199658	+	0.186703i
$827$	−1504.57			−1.81931			−0.909655	−	0.415365i	$-0.863654\pi$
$827$	−1504.57			−1.81931			−0.909655	+	0.415365i	$0.863654\pi$
$828$	−51.2154	+	3.43850i	−0.0618543	+	0.00415278i
$829$		−	1409.65i		−	1.70042i	−0.526445	−	0.850209i	$-0.676475\pi$
$829$		−	1409.65i		−	1.70042i	0.526445	−	0.850209i	$-0.323525\pi$
$830$		0			0
$831$		−	429.044i		−	0.516299i
$832$	−732.862	+	149.407i	−0.880843	+	0.179576i
$833$	−526.728			−0.632327
$834$	−419.951	+	449.091i	−0.503539	+	0.538479i
$835$		0			0
$836$	32.0000	+	476.630i	0.0382775	+	0.570131i
$837$			298.467i			0.356591i
$838$	125.856	−	134.589i	0.150187	−	0.160608i
$839$			288.110i			0.343397i	0.985150	+	0.171698i	$0.0549254\pi$
$839$			288.110i			0.343397i	−0.985150	+	0.171698i	$0.945075\pi$
$840$		0			0
$841$	840.672			0.999609
$842$	650.851	+	608.620i	0.772982	+	0.722826i
$843$	767.520			0.910463
$844$	−36.6870	−	546.441i	−0.0434681	−	0.647442i
$845$		0			0
$846$	−261.100	−	244.158i	−0.308629	−	0.288603i
$847$		−	121.910i		−	0.143932i
$848$	−67.0615	−	497.178i	−0.0790819	−	0.586295i
$849$	510.297			0.601057
$850$		0			0
$851$	118.277			0.138986
$852$	293.569	−	19.7097i	0.344565	−	0.0231334i
$853$		−	645.132i		−	0.756310i	−0.925742	−	0.378155i	$-0.876559\pi$
$853$		−	645.132i		−	0.756310i	0.925742	−	0.378155i	$-0.123441\pi$
$854$	174.067	−	186.145i	0.203825	−	0.217968i
$855$		0			0
$856$	−234.087	−	191.179i	−0.273466	−	0.223340i
$857$	995.549			1.16167			0.580833	−	0.814022i	$-0.302727\pi$
$857$	995.549			1.16167			0.580833	+	0.814022i	$0.302727\pi$
$858$	236.554	+	221.205i	0.275704	+	0.257814i
$859$	−774.354			−0.901460			−0.450730	−	0.892660i	$-0.648836\pi$
$859$	−774.354			−0.901460			−0.450730	+	0.892660i	$0.648836\pi$
$860$		0			0
$861$		−	116.947i		−	0.135827i
$862$	272.700	+	255.005i	0.316357	+	0.295830i
$863$			1007.33i			1.16724i	0.812025	+	0.583622i	$0.198365\pi$
$863$			1007.33i			1.16724i	−0.812025	+	0.583622i	$0.801635\pi$
$864$	96.3154	−	135.541i	0.111476	−	0.156876i
$865$		0			0
$866$	397.688	−	425.284i	0.459225	−	0.491090i
$867$	−257.081			−0.296518
$868$	32.9179	+	490.301i	0.0379238	+	0.564863i
$869$			356.858i			0.410654i
$870$		0			0
$871$			990.836i			1.13758i
$872$	717.015	−	877.941i	0.822265	−	1.00681i
$873$	−291.415			−0.333809
$874$	93.2820	+	87.2293i	0.106730	+	0.0998046i
$875$		0			0
$876$	−2.51804	−	37.5054i	−0.00287448	−	0.0428144i
$877$			681.645i			0.777246i	0.921397	+	0.388623i	$0.127049\pi$
$877$			681.645i			0.777246i	−0.921397	+	0.388623i	$0.872951\pi$
$878$	−128.099	−	119.787i	−0.145898	−	0.136431i
$879$		−	115.565i		−	0.131474i
$880$		0			0
$881$	−679.108			−0.770837			−0.385419	−	0.922742i	$-0.625943\pi$
$881$	−679.108			−0.770837			−0.385419	+	0.922742i	$0.625943\pi$
$882$	−182.060	+	194.693i	−0.206417	+	0.220740i
$883$	1059.44			1.19982			0.599910	−	0.800068i	$-0.295203\pi$
$883$	1059.44			1.19982			0.599910	+	0.800068i	$0.295203\pi$
$884$	−552.995	+	37.1270i	−0.625560	+	0.0419989i
$885$		0			0
$886$	28.2872	−	30.2500i	0.0319268	−	0.0341422i
$887$		−	856.411i		−	0.965514i	−0.875754	−	0.482757i	$-0.839635\pi$
$887$		−	856.411i		−	0.965514i	0.875754	−	0.482757i	$-0.160365\pi$
$888$	−242.354	+	296.747i	−0.272921	+	0.334175i
$889$	−396.000			−0.445444
$890$		0			0
$891$	−72.0000			−0.0808081
$892$	−212.172	+	14.2448i	−0.237861	+	0.0159695i
$893$			889.403i			0.995972i
$894$	222.158	+	207.743i	0.248499	+	0.232374i
$895$		0			0
$896$	143.272	−	233.280i	0.159901	−	0.260358i
$897$	86.5847			0.0965270
$898$	−798.319	+	853.714i	−0.888997	+	0.950684i
$899$	32.9179			0.0366161
$900$		0			0
$901$		−	371.758i		−	0.412606i
$902$	−344.995	+	368.934i	−0.382478	+	0.409018i
$903$		−	106.632i		−	0.118086i
$904$	361.156	+	294.957i	0.399509	+	0.326280i
$905$		0			0
$906$	−554.281	−	518.315i	−0.611789	−	0.572092i
$907$	761.492			0.839573			0.419786	−	0.907623i	$-0.362105\pi$
$907$	761.492			0.839573			0.419786	+	0.907623i	$0.362105\pi$
$908$	−32.1127	−	478.308i	−0.0353664	−	0.526770i
$909$			186.411i			0.205073i
$910$		0			0
$911$			897.344i			0.985009i	0.870310	+	0.492505i	$0.163919\pi$
$911$			897.344i			0.985009i	−0.870310	+	0.492505i	$0.836081\pi$
$912$	−409.990	+	55.3011i	−0.449550	+	0.0606372i
$913$	541.703			0.593321
$914$	−368.406	+	393.970i	−0.403070	+	0.431039i
$915$		0			0
$916$	−854.487	+	57.3686i	−0.932846	+	0.0626295i
$917$			268.115i			0.292383i
$918$	84.1577	−	89.9973i	0.0916750	−	0.0980363i
$919$		−	62.6388i		−	0.0681598i	−0.999419	−	0.0340799i	$-0.989150\pi$
$919$		−	62.6388i		−	0.0681598i	0.999419	−	0.0340799i	$-0.0108501\pi$
$920$		0			0
$921$	907.959			0.985840
$922$	64.9986	+	60.7811i	0.0704974	+	0.0659231i
$923$	−496.308			−0.537712
$924$	−118.277	+	7.94089i	−0.128005	+	0.00859403i
$925$		0			0
$926$	−892.652	−	834.731i	−0.963987	−	0.901437i
$927$		−	83.4124i		−	0.0899810i
$928$	−14.9488	−	10.6226i	−0.0161086	−	0.0114468i
$929$	253.313			0.272673			0.136336	−	0.990663i	$-0.456467\pi$
$929$	253.313			0.272673			0.136336	+	0.990663i	$0.456467\pi$
$930$		0			0
$931$	663.195			0.712347
$932$	−34.1464	−	508.599i	−0.0366377	−	0.545707i
$933$		−	627.101i		−	0.672134i
$934$	200.000	−	213.878i	0.214133	−	0.228991i
$935$		0			0
$936$	−177.415	+	217.234i	−0.189546	+	0.232088i
$937$	30.5538			0.0326081			0.0163040	−	0.999867i	$-0.494810\pi$
$937$	30.5538			0.0326081			0.0163040	+	0.999867i	$0.494810\pi$
$938$	−264.897	−	247.709i	−0.282406	−	0.264082i
$939$	−436.956			−0.465342
$940$		0			0
$941$			388.745i			0.413119i	0.978434	+	0.206559i	$0.0662267\pi$
$941$			388.745i			0.413119i	−0.978434	+	0.206559i	$0.933773\pi$
$942$	641.254	+	599.645i	0.680737	+	0.636566i
$943$			135.039i			0.143202i
$944$	836.974	−	112.895i	0.886625	−	0.119592i
$945$		0			0
$946$	−314.564	+	336.391i	−0.332520	+	0.355594i
$947$	263.615			0.278369			0.139184	−	0.990266i	$-0.455552\pi$
$947$	263.615			0.278369			0.139184	+	0.990266i	$0.455552\pi$
$948$	−308.354	+	20.7023i	−0.325268	+	0.0218379i
$949$			63.4066i			0.0668141i
$950$		0			0
$951$		−	139.245i		−	0.146420i
$952$	128.323	−	157.123i	0.134793	−	0.165046i
$953$	−1292.41			−1.35615			−0.678075	−	0.734993i	$-0.737185\pi$
$953$	−1292.41			−1.35615			−0.678075	+	0.734993i	$0.737185\pi$
$954$	−137.412	−	128.495i	−0.144037	−	0.134691i
$955$		0			0
$956$	1274.26	−	85.5511i	1.33290	−	0.0894886i
$957$			7.94089i			0.00829769i
$958$	280.295	+	262.107i	0.292583	+	0.273598i
$959$		−	212.957i		−	0.222061i
$960$		0			0
$961$	−2338.34			−2.43324
$962$	441.415	−	472.045i	0.458852	−	0.490691i
$963$	−113.338			−0.117693
$964$	66.2947	+	987.438i	0.0687705	+	1.02431i
$965$		0			0
$966$	−21.6462	+	23.1482i	−0.0224080	+	0.0239629i
$967$		−	1110.00i		−	1.14788i	−0.818896	−	0.573942i	$-0.805413\pi$
$967$		−	1110.00i		−	1.14788i	0.818896	−	0.573942i	$-0.194587\pi$
$968$	−353.181	−	288.443i	−0.364856	−	0.297978i
$969$	−306.564			−0.316372
$970$		0			0
$971$	−1341.66			−1.38173			−0.690866	−	0.722983i	$-0.742770\pi$
$971$	−1341.66			−1.38173			−0.690866	+	0.722983i	$0.742770\pi$
$972$	−4.17691	−	62.2138i	−0.00429724	−	0.0640059i
$973$			379.617i			0.390151i
$974$	892.204	+	834.311i	0.916020	+	0.856583i
$975$		0			0
$976$	−127.426	−	944.704i	−0.130559	−	0.967934i
$977$	920.431			0.942099			0.471050	−	0.882107i	$-0.343875\pi$
$977$	920.431			0.942099			0.471050	+	0.882107i	$0.343875\pi$
$978$	−242.172	+	258.976i	−0.247619	+	0.264802i
$979$	1065.11			1.08795
$980$		0			0
$981$		−	425.074i		−	0.433307i
$982$	194.459	−	207.952i	0.198023	−	0.211764i
$983$			1697.84i			1.72720i	0.504176	+	0.863601i	$0.331796\pi$
$983$			1697.84i			1.72720i	−0.504176	+	0.863601i	$0.668204\pi$
$984$	−338.802	−	276.700i	−0.344311	−	0.281200i
$985$		0			0
$986$	−9.92581	−	9.28176i	−0.0100667	−	0.00941355i
$987$	−220.708			−0.223615
$988$	696.267	−	46.7460i	0.704723	−	0.0473138i
$989$			123.128i			0.124497i
$990$		0			0
$991$		−	284.765i		−	0.287351i	−0.989625	−	0.143675i	$-0.954108\pi$
$991$		−	284.765i		−	0.287351i	0.989625	−	0.143675i	$-0.0458921\pi$
$992$	1498.31	+	1064.70i	1.51040	+	1.07329i
$993$	298.010			0.300111
$994$	124.077	−	132.687i	0.124826	−	0.133487i
$995$		0			0
$996$	31.4256	+	468.074i	0.0315518	+	0.469954i
$997$			1093.80i			1.09710i	0.836119	+	0.548548i	$0.184819\pi$
$997$			1093.80i			1.09710i	−0.836119	+	0.548548i	$0.815181\pi$
$998$	−124.813	+	133.473i	−0.125063	+	0.133741i
$999$			143.677i			0.143820i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.3.g.a.451.2		4
4.3	odd	2		2400.3.g.a.751.1		4
5.2	odd	4		600.3.p.a.499.3		8
5.3	odd	4		600.3.p.a.499.6		8
5.4	even	2		24.3.b.a.19.3	✓	4
8.3	odd	2	inner	600.3.g.a.451.1		4
8.5	even	2		2400.3.g.a.751.2		4
15.14	odd	2		72.3.b.b.19.2		4
20.3	even	4		2400.3.p.a.1999.2		8
20.7	even	4		2400.3.p.a.1999.7		8
20.19	odd	2		96.3.b.a.79.4		4
40.3	even	4		600.3.p.a.499.4		8
40.13	odd	4		2400.3.p.a.1999.3		8
40.19	odd	2		24.3.b.a.19.4	yes	4
40.27	even	4		600.3.p.a.499.5		8
40.29	even	2		96.3.b.a.79.3		4
40.37	odd	4		2400.3.p.a.1999.6		8
60.59	even	2		288.3.b.b.271.1		4
80.19	odd	4		768.3.g.h.511.8		8
80.29	even	4		768.3.g.h.511.4		8
80.59	odd	4		768.3.g.h.511.1		8
80.69	even	4		768.3.g.h.511.5		8
120.29	odd	2		288.3.b.b.271.4		4
120.59	even	2		72.3.b.b.19.1		4
240.29	odd	4		2304.3.g.z.1279.2		8
240.59	even	4		2304.3.g.z.1279.7		8
240.149	odd	4		2304.3.g.z.1279.8		8
240.179	even	4		2304.3.g.z.1279.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.3.b.a.19.3	✓	4	5.4	even	2
24.3.b.a.19.4	yes	4	40.19	odd	2
72.3.b.b.19.1		4	120.59	even	2
72.3.b.b.19.2		4	15.14	odd	2
96.3.b.a.79.3		4	40.29	even	2
96.3.b.a.79.4		4	20.19	odd	2
288.3.b.b.271.1		4	60.59	even	2
288.3.b.b.271.4		4	120.29	odd	2
600.3.g.a.451.1		4	8.3	odd	2	inner
600.3.g.a.451.2		4	1.1	even	1	trivial
600.3.p.a.499.3		8	5.2	odd	4
600.3.p.a.499.4		8	40.3	even	4
600.3.p.a.499.5		8	40.27	even	4
600.3.p.a.499.6		8	5.3	odd	4
768.3.g.h.511.1		8	80.59	odd	4
768.3.g.h.511.4		8	80.29	even	4
768.3.g.h.511.5		8	80.69	even	4
768.3.g.h.511.8		8	80.19	odd	4
2304.3.g.z.1279.1		8	240.179	even	4
2304.3.g.z.1279.2		8	240.29	odd	4
2304.3.g.z.1279.7		8	240.59	even	4
2304.3.g.z.1279.8		8	240.149	odd	4
2400.3.g.a.751.1		4	4.3	odd	2
2400.3.g.a.751.2		4	8.5	even	2
2400.3.p.a.1999.2		8	20.3	even	4
2400.3.p.a.1999.3		8	40.13	odd	4
2400.3.p.a.1999.6		8	40.37	odd	4
2400.3.p.a.1999.7		8	20.7	even	4

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	600.3.g.a.451.2

Level	$600$
Weight	$3$
Character	600.451
Analytic conductor	$16.349$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$