LMFDB - Embedded newform 600.3.p.a.499.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,3,Mod(499,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.499");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$600 = 2^{3} \cdot 3 \cdot 5^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	600.p (of order $2$ , degree $1$ , not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.3488158616$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16$ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{8}$
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			499.6
Root			$1.20036 - 0.747754i$ of defining polynomial
Character	$\chi$	$=$	600.499
Dual form			600.3.p.a.499.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46081 + 1.36603i) q^{2} +1.73205i q^{3} +(0.267949 + 3.99102i) q^{4} +(-2.36603 + 2.53020i) q^{6} +2.13878 q^{7} +(-5.06040 + 6.19615i) q^{8} -3.00000 q^{9} -8.00000 q^{11} +(-6.91264 + 0.464102i) q^{12} -11.6865 q^{13} +(3.12436 + 2.92163i) q^{14} +(-15.8564 + 2.13878i) q^{16} +11.8564i q^{17} +(-4.38244 - 4.09808i) q^{18} -14.9282 q^{19} +3.70447i q^{21} +(-11.6865 - 10.9282i) q^{22} +4.27756 q^{23} +(-10.7321 - 8.76488i) q^{24} +(-17.0718 - 15.9641i) q^{26} -5.19615i q^{27} +(0.573084 + 8.53590i) q^{28} +0.573084i q^{29} +57.4399i q^{31} +(-26.0849 - 18.5359i) q^{32} -13.8564i q^{33} +(-16.1962 + 17.3200i) q^{34} +(-0.803848 - 11.9730i) q^{36} +27.6506 q^{37} +(-21.8073 - 20.3923i) q^{38} -20.2416i q^{39} -31.5692 q^{41} +(-5.06040 + 5.41154i) q^{42} -28.7846i q^{43} +(-2.14359 - 31.9281i) q^{44} +(6.24871 + 5.84325i) q^{46} +59.5787 q^{47} +(-3.70447 - 27.4641i) q^{48} -44.4256 q^{49} -20.5359 q^{51} +(-3.13139 - 46.6410i) q^{52} -31.3550 q^{53} +(7.09808 - 7.59061i) q^{54} +(-10.8231 + 13.2522i) q^{56} -25.8564i q^{57} +(-0.782847 + 0.837169i) q^{58} +52.7846 q^{59} +59.5787i q^{61} +(-78.4644 + 83.9090i) q^{62} -6.41634 q^{63} +(-12.7846 - 62.7101i) q^{64} +(18.9282 - 20.2416i) q^{66} -84.7846i q^{67} +(-47.3191 + 3.17691i) q^{68} +7.40895i q^{69} +42.4685i q^{71} +(15.1812 - 18.5885i) q^{72} +5.42563i q^{73} +(40.3923 + 37.7714i) q^{74} +(-4.00000 - 59.5787i) q^{76} -17.1102 q^{77} +(27.6506 - 29.5692i) q^{78} +44.6072i q^{79} +9.00000 q^{81} +(-46.1167 - 43.1244i) q^{82} -67.7128i q^{83} +(-14.7846 + 0.992611i) q^{84} +(39.3205 - 42.0489i) q^{86} -0.992611 q^{87} +(40.4832 - 49.5692i) q^{88} +133.138 q^{89} -24.9948 q^{91} +(1.14617 + 17.0718i) q^{92} -99.4888 q^{93} +(87.0333 + 81.3860i) q^{94} +(32.1051 - 45.1803i) q^{96} +97.1384i q^{97} +(-64.8975 - 60.6865i) q^{98} +24.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 16 q^{4} - 12 q^{6} - 24 q^{9} - 64 q^{11} - 72 q^{14} - 16 q^{16} - 64 q^{19} - 72 q^{24} - 192 q^{26} - 88 q^{34} - 48 q^{36} + 80 q^{41} - 128 q^{44} - 144 q^{46} + 88 q^{49} - 192 q^{51} + 36 q^{54}+ \cdots + 192 q^{99}+O(q^{100})$ 8 * q + 16 * q^4 - 12 * q^6 - 24 * q^9 - 64 * q^11 - 72 * q^14 - 16 * q^16 - 64 * q^19 - 72 * q^24 - 192 * q^26 - 88 * q^34 - 48 * q^36 + 80 * q^41 - 128 * q^44 - 144 * q^46 + 88 * q^49 - 192 * q^51 + 36 * q^54 - 336 * q^56 + 256 * q^59 + 64 * q^64 + 96 * q^66 + 240 * q^74 - 32 * q^76 + 72 * q^81 + 48 * q^84 + 176 * q^86 + 400 * q^89 + 576 * q^91 + 336 * q^94 - 48 * q^96 + 192 * 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

)

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

$2$	1.46081	+	1.36603i	0.730406	+	0.683013i
$2$	1.46081	+	1.36603i	0.730406	+	0.683013i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	0.267949	+	3.99102i	0.0669873	+	0.997754i
$5$		0			0
$5$		0			0
$6$	−2.36603	+	2.53020i	−0.394338	+	0.421700i
$7$	2.13878			0.305540			0.152770	−	0.988262i	$-0.451181\pi$
$7$	2.13878			0.305540			0.152770	+	0.988262i	$0.451181\pi$
$8$	−5.06040	+	6.19615i	−0.632551	+	0.774519i
$9$	−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	$0.618465\pi$
$12$	−6.91264	+	0.464102i	−0.576053	+	0.0386751i
$13$	−11.6865			−0.898962			−0.449481	−	0.893290i	$-0.648391\pi$
$13$	−11.6865			−0.898962			−0.449481	+	0.893290i	$0.648391\pi$
$14$	3.12436	+	2.92163i	0.223168	+	0.208688i
$15$		0			0
$16$	−15.8564	+	2.13878i	−0.991025	+	0.133674i
$17$			11.8564i			0.697436i	0.937228	+	0.348718i	$0.113383\pi$
$17$			11.8564i			0.697436i	−0.937228	+	0.348718i	$0.886617\pi$
$18$	−4.38244	−	4.09808i	−0.243469	−	0.227671i
$19$	−14.9282			−0.785695			−0.392847	−	0.919604i	$-0.628510\pi$
$19$	−14.9282			−0.785695			−0.392847	+	0.919604i	$0.628510\pi$
$20$		0			0
$21$			3.70447i			0.176403i
$22$	−11.6865	−	10.9282i	−0.531205	−	0.496737i
$23$	4.27756			0.185981			0.0929904	−	0.995667i	$-0.470357\pi$
$23$	4.27756			0.185981			0.0929904	+	0.995667i	$0.470357\pi$
$24$	−10.7321	−	8.76488i	−0.447169	−	0.365203i
$25$		0			0
$26$	−17.0718	−	15.9641i	−0.656608	−	0.614002i
$27$		−	5.19615i		−	0.192450i
$28$	0.573084	+	8.53590i	0.0204673	+	0.304854i
$29$			0.573084i			0.0197615i	0.999951	+	0.00988076i	$0.00314519\pi$
$29$			0.573084i			0.0197615i	−0.999951	+	0.00988076i	$0.996855\pi$
$30$		0			0
$31$			57.4399i			1.85290i	0.376417	+	0.926450i	$0.377156\pi$
$31$			57.4399i			1.85290i	−0.376417	+	0.926450i	$0.622844\pi$
$32$	−26.0849	−	18.5359i	−0.815152	−	0.579247i
$33$		−	13.8564i		−	0.419891i
$34$	−16.1962	+	17.3200i	−0.476357	+	0.509412i
$35$		0			0
$36$	−0.803848	−	11.9730i	−0.0223291	−	0.332585i
$37$	27.6506			0.747313			0.373656	−	0.927567i	$-0.378104\pi$
$37$	27.6506			0.747313			0.373656	+	0.927567i	$0.378104\pi$
$38$	−21.8073	−	20.3923i	−0.573877	−	0.536640i
$39$		−	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	$0.625795\pi$
$42$	−5.06040	+	5.41154i	−0.120486	+	0.128846i
$43$		−	28.7846i		−	0.669410i	−0.942323	−	0.334705i	$-0.891363\pi$
$43$		−	28.7846i		−	0.669410i	0.942323	−	0.334705i	$-0.108637\pi$
$44$	−2.14359	−	31.9281i	−0.0487180	−	0.725639i
$45$		0			0
$46$	6.24871	+	5.84325i	0.135842	+	0.127027i
$47$	59.5787			1.26763			0.633816	−	0.773484i	$-0.281488\pi$
$47$	59.5787			1.26763			0.633816	+	0.773484i	$0.281488\pi$
$48$	−3.70447	−	27.4641i	−0.0771765	−	0.572169i
$49$	−44.4256			−0.906645
$50$		0			0
$51$	−20.5359			−0.402665
$52$	−3.13139	−	46.6410i	−0.0602190	−	0.896943i
$53$	−31.3550			−0.591604			−0.295802	−	0.955249i	$-0.595587\pi$
$53$	−31.3550			−0.591604			−0.295802	+	0.955249i	$0.595587\pi$
$54$	7.09808	−	7.59061i	0.131446	−	0.140567i
$55$		0			0
$56$	−10.8231	+	13.2522i	−0.193269	+	0.236646i
$57$		−	25.8564i		−	0.453621i
$58$	−0.782847	+	0.837169i	−0.0134974	+	0.0144339i
$59$	52.7846			0.894654			0.447327	−	0.894370i	$-0.352376\pi$
$59$	52.7846			0.894654			0.447327	+	0.894370i	$0.352376\pi$
$60$		0			0
$61$			59.5787i			0.976700i	0.872648	+	0.488350i	$0.162401\pi$
$61$			59.5787i			0.976700i	−0.872648	+	0.488350i	$0.837599\pi$
$62$	−78.4644	+	83.9090i	−1.26555	+	1.35337i
$63$	−6.41634			−0.101847
$64$	−12.7846	−	62.7101i	−0.199760	−	0.979845i
$65$		0			0
$66$	18.9282	−	20.2416i	0.286791	−	0.306691i
$67$		−	84.7846i		−	1.26544i	−0.774380	−	0.632721i	$-0.781938\pi$
$67$		−	84.7846i		−	1.26544i	0.774380	−	0.632721i	$-0.218062\pi$
$68$	−47.3191	+	3.17691i	−0.695869	+	0.0467193i
$69$			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	$0.903322\pi$
$72$	15.1812	−	18.5885i	0.210850	−	0.258173i
$73$			5.42563i			0.0743236i	0.999309	+	0.0371618i	$0.0118317\pi$
$73$			5.42563i			0.0743236i	−0.999309	+	0.0371618i	$0.988168\pi$
$74$	40.3923	+	37.7714i	0.545842	+	0.510424i
$75$		0			0
$76$	−4.00000	−	59.5787i	−0.0526316	−	0.783930i
$77$	−17.1102			−0.222211
$78$	27.6506	−	29.5692i	0.354494	−	0.379093i
$79$			44.6072i			0.564649i	0.959319	+	0.282324i	$0.0911054\pi$
$79$			44.6072i			0.564649i	−0.959319	+	0.282324i	$0.908895\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−46.1167	−	43.1244i	−0.562399	−	0.525907i
$83$		−	67.7128i		−	0.815817i	−0.913023	−	0.407909i	$-0.866258\pi$
$83$		−	67.7128i		−	0.815817i	0.913023	−	0.407909i	$-0.133742\pi$
$84$	−14.7846	+	0.992611i	−0.176007	+	0.0118168i
$85$		0			0
$86$	39.3205	−	42.0489i	0.457215	−	0.488941i
$87$	−0.992611			−0.0114093
$88$	40.4832	−	49.5692i	0.460037	−	0.563287i
$89$	133.138			1.49594			0.747969	−	0.663734i	$-0.231029\pi$
$89$	133.138			1.49594			0.747969	+	0.663734i	$0.231029\pi$
$90$		0			0
$91$	−24.9948			−0.274669
$92$	1.14617	+	17.0718i	0.0124583	+	0.185563i
$93$	−99.4888			−1.06977
$94$	87.0333	+	81.3860i	0.925886	+	0.865809i
$95$		0			0
$96$	32.1051	−	45.1803i	0.334428	−	0.470628i
$97$			97.1384i			1.00143i	0.865613	+	0.500714i	$0.166929\pi$
$97$			97.1384i			1.00143i	−0.865613	+	0.500714i	$0.833071\pi$
$98$	−64.8975	−	60.6865i	−0.662220	−	0.619250i
$99$	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	$0.900471\pi$
$102$	−29.9991	−	28.0526i	−0.294109	−	0.275025i
$103$	27.8041			0.269943			0.134971	−	0.990849i	$-0.456906\pi$
$103$	27.8041			0.269943			0.134971	+	0.990849i	$0.456906\pi$
$104$	59.1384	−	72.4114i	0.568639	−	0.696263i
$105$		0			0
$106$	−45.8038	−	42.8318i	−0.432112	−	0.404073i
$107$			37.7795i			0.353079i	0.984294	+	0.176540i	$0.0564903\pi$
$107$			37.7795i			0.353079i	−0.984294	+	0.176540i	$0.943510\pi$
$108$	20.7379	−	1.39230i	0.192018	−	0.0128917i
$109$			141.691i			1.29992i	0.759968	+	0.649960i	$0.225214\pi$
$109$			141.691i			1.29992i	−0.759968	+	0.649960i	$0.774786\pi$
$110$		0			0
$111$			47.8922i			0.431461i
$112$	−33.9133	+	4.57437i	−0.302798	+	0.0408426i
$113$			58.2872i			0.515816i	0.966170	+	0.257908i	$0.0830331\pi$
$113$			58.2872i			0.515816i	−0.966170	+	0.257908i	$0.916967\pi$
$114$	35.3205	−	37.7714i	0.309829	−	0.331328i
$115$		0			0
$116$	−2.28719	+	0.153557i	−0.0197171	+	0.00132377i
$117$	35.0595			0.299654
$118$	77.1084	+	72.1051i	0.653461	+	0.611060i
$119$			25.3582i			0.213094i
$120$		0			0
$121$	−57.0000			−0.471074
$122$	−81.3860	+	87.0333i	−0.667098	+	0.713388i
$123$		−	54.6795i		−	0.444549i
$124$	−229.244	+	15.3910i	−1.84874	+	0.124121i
$125$		0			0
$126$	−9.37307	−	8.76488i	−0.0743894	−	0.0695625i
$127$	185.152			1.45789			0.728946	−	0.684571i	$-0.240010\pi$
$127$	185.152			1.45789			0.728946	+	0.684571i	$0.240010\pi$
$128$	66.9876	−	109.072i	0.523341	−	0.852123i
$129$	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	$0.341192\pi$
$132$	55.3011	−	3.71281i	0.418948	−	0.0281274i
$133$	−31.9281			−0.240061
$134$	115.818	−	123.854i	0.864313	−	0.924287i
$135$		0			0
$136$	−73.4641	−	59.9982i	−0.540177	−	0.441163i
$137$			99.5692i			0.726783i	0.931637	+	0.363391i	$0.118381\pi$
$137$			99.5692i			0.726783i	−0.931637	+	0.363391i	$0.881619\pi$
$138$	−10.1208	+	10.8231i	−0.0733392	+	0.0784282i
$139$	−177.492			−1.27692			−0.638461	−	0.769654i	$-0.720429\pi$
$139$	−177.492			−1.27692			−0.638461	+	0.769654i	$0.720429\pi$
$140$		0			0
$141$			103.193i			0.731867i
$142$	−58.0130	+	62.0385i	−0.408542	+	0.436891i
$143$	93.4920			0.653790
$144$	47.5692	−	6.41634i	0.330342	−	0.0445579i
$145$		0			0
$146$	−7.41154	+	7.92582i	−0.0507640	+	0.0542865i
$147$		−	76.9474i		−	0.523452i
$148$	7.40895	+	110.354i	0.0500605	+	0.745634i
$149$			87.8023i			0.589277i	0.955609	+	0.294639i	$0.0951993\pi$
$149$			87.8023i			0.589277i	−0.955609	+	0.294639i	$0.904801\pi$
$150$		0			0
$151$			219.066i			1.45077i	0.688345	+	0.725383i	$0.258337\pi$
$151$			219.066i			1.45077i	−0.688345	+	0.725383i	$0.741663\pi$
$152$	75.5427	−	92.4974i	0.496992	−	0.608536i
$153$		−	35.5692i		−	0.232479i
$154$	−24.9948	−	23.3730i	−0.162304	−	0.151773i
$155$		0			0
$156$	80.7846	−	5.42373i	0.517850	−	0.0347675i
$157$	−253.440			−1.61427			−0.807133	−	0.590370i	$-0.798982\pi$
$157$	−253.440			−1.61427			−0.807133	+	0.590370i	$0.798982\pi$
$158$	−60.9346	+	65.1628i	−0.385662	+	0.412423i
$159$		−	54.3085i		−	0.341563i
$160$		0			0
$161$	9.14875			0.0568245
$162$	13.1473	+	12.2942i	0.0811563	+	0.0758903i
$163$			102.354i			0.627938i	0.949433	+	0.313969i	$0.101659\pi$
$163$			102.354i			0.627938i	−0.949433	+	0.313969i	$0.898341\pi$
$164$	−8.45895	−	125.993i	−0.0515789	−	0.768251i
$165$		0			0
$166$	92.4974	−	98.9158i	0.557213	−	0.595878i
$167$	281.090			1.68318			0.841588	−	0.540120i	$-0.181621\pi$
$167$	281.090			1.68318			0.841588	+	0.540120i	$0.181621\pi$
$168$	−22.9535	−	18.7461i	−0.136628	−	0.111584i
$169$	−32.4256			−0.191868
$170$		0			0
$171$	44.7846			0.261898
$172$	114.880	−	7.71281i	0.667906	−	0.0448419i
$173$	242.858			1.40381			0.701903	−	0.712273i	$-0.252334\pi$
$173$	242.858			1.40381			0.701903	+	0.712273i	$0.252334\pi$
$174$	−1.45002	−	1.35593i	−0.00833344	−	0.00779271i
$175$		0			0
$176$	126.851	−	17.1102i	0.720746	−	0.0972172i
$177$			91.4256i			0.516529i
$178$	194.490	+	181.870i	1.09264	+	1.02174i
$179$	−318.354			−1.77851			−0.889257	−	0.457409i	$-0.848778\pi$
$179$	−318.354			−1.77851			−0.889257	+	0.457409i	$0.848778\pi$
$180$		0			0
$181$		−	79.5132i		−	0.439299i	−0.975579	−	0.219650i	$-0.929509\pi$
$181$		−	79.5132i		−	0.439299i	0.975579	−	0.219650i	$-0.0704914\pi$
$182$	−36.5128	−	34.1436i	−0.200620	−	0.187602i
$183$	−103.193			−0.563898
$184$	−21.6462	+	26.5044i	−0.117642	+	0.144046i
$185$		0			0
$186$	−145.335	−	135.904i	−0.781369	−	0.730668i
$187$		−	94.8513i		−	0.507226i
$188$	15.9641	+	237.779i	0.0849152	+	1.26478i
$189$		−	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	$-0.374925\pi$
$192$	108.617	−	22.1436i	0.565714	−	0.115331i
$193$			284.277i			1.47294i	0.676472	+	0.736469i	$0.263508\pi$
$193$			284.277i			1.47294i	−0.676472	+	0.736469i	$0.736492\pi$
$194$	−132.694	+	141.901i	−0.683988	+	0.731449i
$195$		0			0
$196$	−11.9038	−	177.303i	−0.0607337	−	0.904609i
$197$	75.8087			0.384816			0.192408	−	0.981315i	$-0.438370\pi$
$197$	75.8087			0.384816			0.192408	+	0.981315i	$0.438370\pi$
$198$	35.0595	+	32.7846i	0.177068	+	0.165579i
$199$		−	104.186i		−	0.523547i	−0.965129	−	0.261774i	$-0.915693\pi$
$199$		−	104.186i		−	0.523547i	0.965129	−	0.261774i	$-0.0843074\pi$
$200$		0			0
$201$	146.851			0.730603
$202$	−84.8807	+	90.7705i	−0.420202	+	0.449359i
$203$			1.22570i			0.00603793i
$204$	−5.50258	−	81.9591i	−0.0269734	−	0.401760i
$205$		0			0
$206$	40.6166	+	37.9811i	0.197168	+	0.184374i
$207$	−12.8327			−0.0619936
$208$	185.306	−	24.9948i	0.890894	−	0.120168i
$209$	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	$0.394821\pi$
$212$	−8.40156	−	125.138i	−0.0396300	−	0.590276i
$213$	−73.5575			−0.345341
$214$	−51.6077	+	55.1887i	−0.241157	+	0.257891i
$215$		0			0
$216$	32.1962	+	26.2946i	0.149056	+	0.121734i
$217$			122.851i			0.566135i
$218$	−193.554	+	206.985i	−0.887862	+	0.949470i
$219$	−9.39746			−0.0429108
$220$		0			0
$221$		−	138.560i		−	0.626968i
$222$	−65.4219	+	69.9615i	−0.294693	+	0.315142i
$223$	53.1624			0.238396			0.119198	−	0.992870i	$-0.461968\pi$
$223$	53.1624			0.238396			0.119198	+	0.992870i	$0.461968\pi$
$224$	−55.7898	−	39.6442i	−0.249061	−	0.176983i
$225$		0			0
$226$	−79.6218	+	85.1467i	−0.352309	+	0.376755i
$227$		−	119.846i		−	0.527956i	−0.964529	−	0.263978i	$-0.914965\pi$
$227$		−	119.846i		−	0.527956i	0.964529	−	0.263978i	$-0.0850347\pi$
$228$	103.193	−	6.92820i	0.452602	−	0.0303869i
$229$			214.103i			0.934946i	0.884007	+	0.467473i	$0.154836\pi$
$229$			214.103i			0.934946i	−0.884007	+	0.467473i	$0.845164\pi$
$230$		0			0
$231$		−	29.6358i		−	0.128293i
$232$	−3.55092	−	2.90004i	−0.0153057	−	0.0125002i
$233$			127.436i			0.546935i	0.961881	+	0.273468i	$0.0881707\pi$
$233$			127.436i			0.546935i	−0.961881	+	0.273468i	$0.911829\pi$
$234$	51.2154	+	47.8922i	0.218869	+	0.204667i
$235$		0			0
$236$	14.1436	+	210.664i	0.0599305	+	0.892645i
$237$	−77.2620			−0.326000
$238$	−34.6400	+	37.0436i	−0.145546	+	0.155646i
$239$		−	319.281i		−	1.33590i	−0.744204	−	0.667952i	$-0.767171\pi$
$239$		−	319.281i		−	1.33590i	0.744204	−	0.667952i	$-0.232829\pi$
$240$		0			0
$241$	−247.415			−1.02662			−0.513310	−	0.858203i	$-0.671581\pi$
$241$	−247.415			−1.02662			−0.513310	+	0.858203i	$0.671581\pi$
$242$	−83.2663	−	77.8634i	−0.344076	−	0.321750i
$243$			15.5885i			0.0641500i
$244$	−237.779	+	15.9641i	−0.974506	+	0.0654265i
$245$		0			0
$246$	74.6936	−	79.8765i	0.303632	−	0.324701i
$247$	174.459			0.706310
$248$	−355.906	−	290.669i	−1.43511	−	1.17205i
$249$	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	$0.640778\pi$
$252$	−1.71925	−	25.6077i	−0.00682243	−	0.101618i
$253$	−34.2205			−0.135259
$254$	270.473	+	252.923i	1.06485	+	0.995759i
$255$		0			0
$256$	246.851	−	67.8267i	0.964263	−	0.264948i
$257$		−	84.2769i		−	0.327926i	−0.986467	−	0.163963i	$-0.947572\pi$
$257$		−	84.2769i		−	0.327926i	0.986467	−	0.163963i	$-0.0524277\pi$
$258$	72.8309	+	68.1051i	0.282290	+	0.263973i
$259$	59.1384			0.228334
$260$		0			0
$261$		−	1.71925i		−	0.00658717i
$262$	183.126	+	171.244i	0.698954	+	0.653601i
$263$	277.120			1.05369			0.526844	−	0.849962i	$-0.323375\pi$
$263$	277.120			1.05369			0.526844	+	0.849962i	$0.323375\pi$
$264$	85.8564	+	70.1190i	0.325214	+	0.265602i
$265$		0			0
$266$	−46.6410	−	43.6146i	−0.175342	−	0.163965i
$267$			230.603i			0.863680i
$268$	338.377	−	22.7180i	1.26260	−	0.0847685i
$269$			123.701i			0.459855i	0.973208	+	0.229927i	$0.0738489\pi$
$269$			123.701i			0.459855i	−0.973208	+	0.229927i	$0.926151\pi$
$270$		0			0
$271$			197.985i			0.730572i	0.930895	+	0.365286i	$0.119029\pi$
$271$			197.985i			0.730572i	−0.930895	+	0.365286i	$0.880971\pi$
$272$	−25.3582	−	188.000i	−0.0932288	−	0.691176i
$273$		−	43.2923i		−	0.158580i
$274$	−136.014	+	145.452i	−0.496402	+	0.530847i
$275$		0			0
$276$	−29.5692	+	1.98522i	−0.107135	+	0.00719283i
$277$	−247.709			−0.894256			−0.447128	−	0.894470i	$-0.647553\pi$
$277$	−247.709			−0.894256			−0.447128	+	0.894470i	$0.647553\pi$
$278$	−259.283	−	242.459i	−0.932673	−	0.872154i
$279$		−	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	$0.210866\pi$
$282$	−140.965	+	150.746i	−0.499875	+	0.534561i
$283$			294.620i			1.04106i	0.853843	+	0.520531i	$0.174266\pi$
$283$			294.620i			1.04106i	−0.853843	+	0.520531i	$0.825734\pi$
$284$	−169.492	+	11.3794i	−0.596804	+	0.0400683i
$285$		0			0
$286$	136.574	+	127.712i	0.477533	+	0.446547i
$287$	−67.5196			−0.235260
$288$	78.2546	+	55.6077i	0.271717	+	0.193082i
$289$	148.426			0.513583
$290$		0			0
$291$	−168.249			−0.578174
$292$	−21.6538	+	1.45379i	−0.0741567	+	0.00497874i
$293$	66.7217			0.227719			0.113859	−	0.993497i	$-0.463679\pi$
$293$	66.7217			0.227719			0.113859	+	0.993497i	$0.463679\pi$
$294$	105.112	−	112.406i	0.357524	−	0.382333i
$295$		0			0
$296$	−139.923	+	171.327i	−0.472713	+	0.578808i
$297$			41.5692i			0.139964i
$298$	−119.940	+	128.263i	−0.402484	+	0.430412i
$299$	−49.9897			−0.167190
$300$		0			0
$301$		−	61.5639i		−	0.204531i
$302$	−299.249	+	320.014i	−0.990892	+	1.05965i
$303$	−107.624			−0.355196
$304$	236.708	−	31.9281i	0.778644	−	0.105027i
$305$		0			0
$306$	48.5885	−	51.9600i	0.158786	−	0.169804i
$307$		−	524.210i		−	1.70753i	−0.520662	−	0.853763i	$-0.674315\pi$
$307$		−	524.210i		−	1.70753i	0.520662	−	0.853763i	$-0.325685\pi$
$308$	−4.58467	−	68.2872i	−0.0148853	−	0.221712i
$309$			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	$-0.197763\pi$
$312$	125.420	+	102.431i	0.401988	+	0.328304i
$313$		−	252.277i		−	0.805996i	−0.915201	−	0.402998i	$-0.867968\pi$
$313$		−	252.277i		−	0.805996i	0.915201	−	0.402998i	$-0.132032\pi$
$314$	−370.228	−	346.205i	−1.17907	−	1.10256i
$315$		0			0
$316$	−178.028	+	11.9525i	−0.563380	+	0.0378243i
$317$	−80.3934			−0.253607			−0.126803	−	0.991928i	$-0.540472\pi$
$317$	−80.3934			−0.253607			−0.126803	+	0.991928i	$0.540472\pi$
$318$	74.1868	−	79.3346i	0.233292	−	0.249480i
$319$		−	4.58467i		−	0.0143720i
$320$		0			0
$321$	−65.4359			−0.203850
$322$	13.3646	+	12.4974i	0.0415050	+	0.0388119i
$323$		−	176.995i		−	0.547972i
$324$	2.41154	+	35.9191i	0.00744303	+	0.110862i
$325$		0			0
$326$	−139.818	+	149.520i	−0.428889	+	0.458650i
$327$	−245.417			−0.750509
$328$	159.753	−	195.608i	0.487052	−	0.596365i
$329$	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	$0.416309\pi$
$332$	270.243	−	18.1436i	0.813985	−	0.0546494i
$333$	−82.9517			−0.249104
$334$	410.620	+	383.977i	1.22940	+	1.14963i
$335$		0			0
$336$	−7.92305	−	58.7396i	−0.0235805	−	0.174820i
$337$			564.277i			1.67441i	0.546888	+	0.837206i	$0.315813\pi$
$337$			564.277i			1.67441i	−0.546888	+	0.837206i	$0.684187\pi$
$338$	−47.3678	−	44.2942i	−0.140141	−	0.131048i
$339$	−100.956			−0.297806
$340$		0			0
$341$		−	459.519i		−	1.34756i
$342$	65.4219	+	61.1769i	0.191292	+	0.178880i
$343$	−199.817			−0.582556
$344$	178.354	+	145.662i	0.518470	+	0.423435i
$345$		0			0
$346$	354.771	+	331.751i	1.02535	+	0.958817i
$347$		−	286.123i		−	0.824562i	−0.911057	−	0.412281i	$-0.864732\pi$
$347$		−	286.123i		−	0.824562i	0.911057	−	0.412281i	$-0.135268\pi$
$348$	−0.265969	−	3.96152i	−0.000764279	−	0.0113837i
$349$		−	421.021i		−	1.20636i	−0.797603	−	0.603182i	$-0.793899\pi$
$349$		−	421.021i		−	1.20636i	0.797603	−	0.603182i	$-0.206101\pi$
$350$		0			0
$351$			60.7249i			0.173005i
$352$	208.679	+	148.287i	0.592838	+	0.421270i
$353$		−	429.138i		−	1.21569i	−0.794056	−	0.607845i	$-0.792034\pi$
$353$		−	429.138i		−	1.21569i	0.794056	−	0.607845i	$-0.207966\pi$
$354$	−124.890	+	133.556i	−0.352796	+	0.377276i
$355$		0			0
$356$	35.6743	+	531.358i	0.100209	+	1.49258i
$357$	−43.9217			−0.123030
$358$	−465.055	−	434.879i	−1.29904	−	1.21475i
$359$		−	263.673i		−	0.734465i	−0.930129	−	0.367233i	$-0.880305\pi$
$359$		−	263.673i		−	0.734465i	0.930129	−	0.367233i	$-0.119695\pi$
$360$		0			0
$361$	−138.149			−0.382684
$362$	108.617	−	116.154i	0.300047	−	0.320867i
$363$		−	98.7269i		−	0.271975i
$364$	−6.69735	−	99.7548i	−0.0183993	−	0.274052i
$365$		0			0
$366$	−150.746	−	140.965i	−0.411875	−	0.385149i
$367$	129.544			0.352981			0.176491	−	0.984302i	$-0.443525\pi$
$367$	129.544			0.352981			0.176491	+	0.984302i	$0.443525\pi$
$368$	−67.8267	+	9.14875i	−0.184312	+	0.0248607i
$369$	94.7077			0.256660
$370$		0			0
$371$	−67.0615			−0.180759
$372$	−26.6580	−	397.061i	−0.0716612	−	1.06737i
$373$	−302.478			−0.810933			−0.405467	−	0.914110i	$-0.632891\pi$
$373$	−302.478			−0.810933			−0.405467	+	0.914110i	$0.632891\pi$
$374$	129.569	−	138.560i	0.346442	−	0.370481i
$375$		0			0
$376$	−301.492	+	369.159i	−0.801841	+	0.981805i
$377$		−	6.69735i		−	0.0177649i
$378$	15.1812	−	16.2346i	0.0401619	−	0.0429488i
$379$	116.210			0.306623			0.153312	−	0.988178i	$-0.451006\pi$
$379$	116.210			0.306623			0.153312	+	0.988178i	$0.451006\pi$
$380$		0			0
$381$			320.693i			0.841715i
$382$	482.053	−	515.503i	1.26192	−	1.34948i
$383$	566.151			1.47820			0.739101	−	0.673595i	$-0.235251\pi$
$383$	566.151			1.47820			0.739101	+	0.673595i	$0.235251\pi$
$384$	188.918	+	116.026i	0.491974	+	0.302151i
$385$		0			0
$386$	−388.329	+	415.275i	−1.00603	+	1.07584i
$387$			86.3538i			0.223137i
$388$	−387.681	+	26.0282i	−0.999178	+	0.0670829i
$389$			350.104i			0.900011i	0.893026	+	0.450006i	$0.148578\pi$
$389$			350.104i			0.900011i	−0.893026	+	0.450006i	$0.851422\pi$
$390$		0			0
$391$			50.7165i			0.129710i
$392$	224.812	−	275.268i	0.573499	−	0.702214i
$393$			217.128i			0.552489i
$394$	110.742	+	103.557i	0.281072	+	0.262834i
$395$		0			0
$396$	6.43078	+	95.7844i	0.0162393	+	0.241880i
$397$	−544.149			−1.37065			−0.685326	−	0.728236i	$-0.740340\pi$
$397$	−544.149			−1.37065			−0.685326	+	0.728236i	$0.740340\pi$
$398$	142.321	−	152.196i	0.357589	−	0.382402i
$399$		−	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	$0.620510\pi$
$402$	214.522	+	200.603i	0.533637	+	0.499011i
$403$		−	671.272i		−	1.66569i
$404$	−247.990	+	16.6496i	−0.613836	+	0.0412118i
$405$		0			0
$406$	−1.67434	+	1.79052i	−0.00412398	+	0.00441014i
$407$	−221.205			−0.543500
$408$	103.920	−	127.244i	0.254706	−	0.311871i
$409$	247.415			0.604927			0.302464	−	0.953161i	$-0.402191\pi$
$409$	247.415			0.604927			0.302464	+	0.953161i	$0.402191\pi$
$410$		0			0
$411$	−172.459			−0.419608
$412$	7.45009	+	110.967i	0.0180827	+	0.269337i
$413$	112.895			0.273353
$414$	−18.7461	−	17.5298i	−0.0452805	−	0.0423424i
$415$		0			0
$416$	304.841	+	216.620i	0.732791	+	0.520721i
$417$		−	307.426i		−	0.737232i
$418$	174.459	+	163.138i	0.417365	+	0.390283i
$419$	92.1333			0.219889			0.109944	−	0.993938i	$-0.464933\pi$
$419$	92.1333			0.219889			0.109944	+	0.993938i	$0.464933\pi$
$420$		0			0
$421$		−	445.540i		−	1.05829i	−0.848531	−	0.529145i	$-0.822513\pi$
$421$		−	445.540i		−	1.05829i	0.848531	−	0.529145i	$-0.177487\pi$
$422$	200.011	+	187.033i	0.473961	+	0.443207i
$423$	−178.736			−0.422544
$424$	158.669	−	194.281i	0.374220	−	0.458209i
$425$		0			0
$426$	−107.454	−	100.481i	−0.252239	−	0.235872i
$427$			127.426i			0.298421i
$428$	−150.778	+	10.1230i	−0.352286	+	0.0236518i
$429$			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	$-0.0694845\pi$
$432$	11.1134	+	82.3923i	0.0257255	+	0.190723i
$433$		−	291.128i		−	0.672351i	−0.941799	−	0.336176i	$-0.890866\pi$
$433$		−	291.128i		−	0.672351i	0.941799	−	0.336176i	$-0.109134\pi$
$434$	−167.818	+	179.463i	−0.386677	+	0.413509i
$435$		0			0
$436$	−565.492	+	37.9661i	−1.29700	+	0.0870782i
$437$	−63.8562			−0.146124
$438$	−13.7279	−	12.8372i	−0.0313423	−	0.0293086i
$439$		−	87.6899i		−	0.199749i	−0.995000	−	0.0998746i	$-0.968156\pi$
$439$		−	87.6899i		−	0.199749i	0.995000	−	0.0998746i	$-0.0318442\pi$
$440$		0			0
$441$	133.277			0.302215
$442$	189.276	−	202.410i	0.428227	−	0.457942i
$443$		−	20.7077i		−	0.0467441i	−0.999727	−	0.0233721i	$-0.992560\pi$
$443$		−	20.7077i		−	0.0467441i	0.999727	−	0.0233721i	$-0.00744024\pi$
$444$	−191.138	+	12.8327i	−0.430492	+	0.0289024i
$445$		0			0
$446$	77.6603	+	72.6211i	0.174126	+	0.162828i
$447$	−152.078			−0.340219
$448$	−27.3435	−	134.123i	−0.0610345	−	0.299382i
$449$	−584.410			−1.30158			−0.650791	−	0.759257i	$-0.725563\pi$
$449$	−584.410			−1.30158			−0.650791	+	0.759257i	$0.725563\pi$
$450$		0			0
$451$	252.554			0.559986
$452$	−232.625	+	15.6180i	−0.514657	+	0.0345531i
$453$	−379.433			−0.837600
$454$	163.713	−	175.073i	0.360601	−	0.385623i
$455$		0			0
$456$	160.210	+	130.844i	0.351338	+	0.286938i
$457$		−	269.692i		−	0.590136i	−0.955476	−	0.295068i	$-0.904658\pi$
$457$		−	269.692i		−	0.590136i	0.955476	−	0.295068i	$-0.0953423\pi$
$458$	−292.470	+	312.764i	−0.638580	+	0.682891i
$459$	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	$-0.0153673\pi$
$462$	40.4832	−	43.2923i	0.0876261	−	0.0937064i
$463$	−611.065			−1.31980			−0.659898	−	0.751355i	$-0.729400\pi$
$463$	−611.065			−1.31980			−0.659898	+	0.751355i	$0.729400\pi$
$464$	−1.22570	−	9.08705i	−0.00264159	−	0.0195842i
$465$		0			0
$466$	−174.081	+	186.160i	−0.373564	+	0.399485i
$467$			146.410i			0.313512i	0.987637	+	0.156756i	$0.0501036\pi$
$467$			146.410i			0.313512i	−0.987637	+	0.156756i	$0.949896\pi$
$468$	9.39417	+	139.923i	0.0200730	+	0.298981i
$469$		−	181.336i		−	0.386643i
$470$		0			0
$471$		−	438.971i		−	0.931997i
$472$	−267.111	+	327.061i	−0.565914	+	0.692927i
$473$			230.277i			0.486843i
$474$	−112.865	−	105.542i	−0.238113	−	0.222662i
$475$		0			0
$476$	−101.205	+	6.79472i	−0.212616	+	0.0142746i
$477$	94.0651			0.197201
$478$	436.146	−	466.410i	0.912440	−	0.975753i
$479$			191.876i			0.400576i	0.979737	+	0.200288i	$0.0641878\pi$
$479$			191.876i			0.400576i	−0.979737	+	0.200288i	$0.935812\pi$
$480$		0			0
$481$	−323.138			−0.671805
$482$	−361.428	−	337.976i	−0.749850	−	0.701194i
$483$			15.8461i			0.0328077i
$484$	−15.2731	−	227.488i	−0.0315560	−	0.470016i
$485$		0			0
$486$	−21.2942	+	22.7718i	−0.0438153	+	0.0468556i
$487$	−610.758			−1.25412			−0.627062	−	0.778969i	$-0.715743\pi$
$487$	−610.758			−1.25412			−0.627062	+	0.778969i	$0.715743\pi$
$488$	−369.159	−	301.492i	−0.756473	−	0.617812i
$489$	−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	$0.546306\pi$
$492$	218.227	−	14.6513i	0.443550	−	0.0297791i
$493$	−6.79472			−0.0137824
$494$	254.851	+	238.315i	0.515893	+	0.482419i
$495$		0			0
$496$	−122.851	−	910.791i	−0.247684	−	1.83627i
$497$			90.8306i			0.182758i
$498$	171.327	+	160.210i	0.344030	+	0.321707i
$499$	−91.3693			−0.183105			−0.0915524	−	0.995800i	$-0.529183\pi$
$499$	−91.3693			−0.183105			−0.0915524	+	0.995800i	$0.529183\pi$
$500$		0			0
$501$			486.863i			0.971782i
$502$	−313.857	−	293.492i	−0.625214	−	0.584646i
$503$	−230.067			−0.457389			−0.228695	−	0.973498i	$-0.573446\pi$
$503$	−230.067			−0.457389			−0.228695	+	0.973498i	$0.573446\pi$
$504$	32.4693	−	39.7566i	0.0644231	−	0.0788821i
$505$		0			0
$506$	−49.9897	−	46.7460i	−0.0987939	−	0.0923834i
$507$		−	56.1628i		−	0.110775i
$508$	49.6114	+	738.946i	0.0976603	+	1.45462i
$509$		−	527.387i		−	1.03612i	−0.855343	−	0.518062i	$-0.826654\pi$
$509$		−	527.387i		−	1.03612i	0.855343	−	0.518062i	$-0.173346\pi$
$510$		0			0
$511$			11.6042i			0.0227088i
$512$	453.256	+	238.123i	0.885267	+	0.465084i
$513$			77.5692i			0.151207i
$514$	115.124	−	123.113i	0.223977	−	0.239519i
$515$		0			0
$516$	13.3590	+	198.978i	0.0258895	+	0.385616i
$517$	−476.630			−0.921914
$518$	86.3902	+	80.7846i	0.166776	+	0.155955i
$519$			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	$0.441055\pi$
$522$	2.34854	−	2.51151i	0.00449912	−	0.00481131i
$523$		−	105.492i		−	0.201706i	−0.994901	−	0.100853i	$-0.967843\pi$
$523$		−	105.492i		−	0.201706i	0.994901	−	0.100853i	$-0.0321572\pi$
$524$	33.5898	+	500.310i	0.0641027	+	0.954789i
$525$		0			0
$526$	404.820	+	378.553i	0.769620	+	0.719682i
$527$	−681.031			−1.29228
$528$	29.6358	+	219.713i	0.0561284	+	0.416123i
$529$	−510.703			−0.965411
$530$		0			0
$531$	−158.354			−0.298218
$532$	−8.55511	−	127.426i	−0.0160810	−	0.239522i
$533$	368.934			0.692184
$534$	−315.009	+	336.867i	−0.589904	+	0.630837i
$535$		0			0
$536$	525.338	+	429.044i	0.980109	+	0.800456i
$537$		−	551.405i		−	1.02682i
$538$	−168.979	+	180.704i	−0.314087	+	0.335881i
$539$	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	$-0.139691\pi$
$542$	−270.453	+	289.219i	−0.498990	+	0.533615i
$543$	137.721			0.253630
$544$	219.769	−	309.273i	0.403987	−	0.568516i
$545$		0			0
$546$	59.1384	−	63.2420i	0.108312	−	0.115828i
$547$			67.3693i			0.123161i	0.998102	+	0.0615807i	$0.0196142\pi$
$547$			67.3693i			0.123161i	−0.998102	+	0.0615807i	$0.980386\pi$
$548$	−397.382	+	26.6795i	−0.725150	+	0.0486852i
$549$		−	178.736i		−	0.325567i
$550$		0			0
$551$		−	8.55511i		−	0.0155265i
$552$	−45.9070	−	37.4923i	−0.0831648	−	0.0679208i
$553$			95.4050i			0.172523i
$554$	−361.856	−	338.377i	−0.653170	−	0.610788i
$555$		0			0
$556$	−47.5589	−	708.374i	−0.0855376	−	1.27405i
$557$	476.671			0.855782			0.427891	−	0.903830i	$-0.359257\pi$
$557$	476.671			0.855782			0.427891	+	0.903830i	$0.359257\pi$
$558$	235.393	−	251.727i	0.421851	−	0.451123i
$559$			336.391i			0.601774i
$560$		0			0
$561$	164.287			0.292847
$562$	647.327	+	605.324i	1.15183	+	1.07709i
$563$			910.123i			1.61656i	0.588799	+	0.808280i	$0.299601\pi$
$563$			910.123i			1.61656i	−0.588799	+	0.808280i	$0.700399\pi$
$564$	−411.846	+	27.6506i	−0.730224	+	0.0490258i
$565$		0			0
$566$	−402.459	+	430.385i	−0.711058	+	0.760398i
$567$	19.2490			0.0339489
$568$	−263.141	−	214.908i	−0.463276	−	0.378358i
$569$	124.123			0.218142			0.109071	−	0.994034i	$-0.465212\pi$
$569$	124.123			0.218142			0.109071	+	0.994034i	$0.465212\pi$
$570$		0			0
$571$	945.031			1.65504			0.827522	−	0.561433i	$-0.189750\pi$
$571$	945.031			1.65504			0.827522	+	0.561433i	$0.189750\pi$
$572$	25.0511	+	373.128i	0.0437957	+	0.652322i
$573$	611.219			1.06670
$574$	−98.6335	−	92.2335i	−0.171835	−	0.160685i
$575$		0			0
$576$	38.3538	+	188.130i	0.0665865	+	0.326615i
$577$			215.682i			0.373799i	0.982379	+	0.186899i	$0.0598438\pi$
$577$			215.682i			0.373799i	−0.982379	+	0.186899i	$0.940156\pi$
$578$	216.822	+	202.753i	0.375125	+	0.350784i
$579$	−492.382			−0.850401
$580$		0			0
$581$		−	144.823i		−	0.249265i
$582$	−245.780	−	229.832i	−0.422302	−	0.394900i
$583$	250.840			0.430258
$584$	−33.6180	−	27.4559i	−0.0575651	−	0.0470135i
$585$		0			0
$586$	97.4679	+	91.1435i	0.166327	+	0.155535i
$587$			900.785i			1.53456i	0.641314	+	0.767278i	$0.278389\pi$
$587$			900.785i			1.53456i	−0.641314	+	0.767278i	$0.721611\pi$
$588$	307.098	−	20.6180i	0.522276	−	0.0350646i
$589$		−	857.475i		−	1.45581i
$590$		0			0
$591$			131.305i			0.222174i
$592$	−438.439	+	59.1384i	−0.740606	+	0.0998960i
$593$			508.585i			0.857647i	0.903388	+	0.428824i	$0.141072\pi$
$593$			508.585i			0.857647i	−0.903388	+	0.428824i	$0.858928\pi$
$594$	−56.7846	+	60.7249i	−0.0955970	+	0.102230i
$595$		0			0
$596$	−350.420	+	23.5266i	−0.587954	+	0.0394741i
$597$	180.455			0.302270
$598$	−73.0256	−	68.2872i	−0.122116	−	0.114193i
$599$			846.934i			1.41391i	0.707257	+	0.706957i	$0.249933\pi$
$599$			846.934i			1.41391i	−0.707257	+	0.706957i	$0.750067\pi$
$600$		0			0
$601$	−406.000			−0.675541			−0.337770	−	0.941229i	$-0.609673\pi$
$601$	−406.000			−0.675541			−0.337770	+	0.941229i	$0.609673\pi$
$602$	84.0979	−	89.9334i	0.139697	−	0.149391i
$603$			254.354i			0.421814i
$604$	−874.295	+	58.6985i	−1.44751	+	0.0971829i
$605$		0			0
$606$	−157.219	−	147.018i	−0.259438	−	0.242603i
$607$	771.156			1.27044			0.635219	−	0.772332i	$-0.280910\pi$
$607$	771.156			1.27044			0.635219	+	0.772332i	$0.280910\pi$
$608$	389.400	+	276.708i	0.640461	+	0.455111i
$609$	−2.12297			−0.00348600
$610$		0			0
$611$	−696.267			−1.13955
$612$	141.957	−	9.53074i	0.231956	−	0.0155731i
$613$	−336.699			−0.549264			−0.274632	−	0.961549i	$-0.588556\pi$
$613$	−336.699			−0.549264			−0.274632	+	0.961549i	$0.588556\pi$
$614$	716.084	−	765.773i	1.16626	−	1.24719i
$615$		0			0
$616$	86.5847	−	106.018i	0.140560	−	0.172106i
$617$		−	908.831i		−	1.47298i	−0.676447	−	0.736492i	$-0.736481\pi$
$617$		−	908.831i		−	1.47298i	0.676447	−	0.736492i	$-0.263519\pi$
$618$	−65.7853	+	70.3501i	−0.106449	+	0.113835i
$619$	1047.77			1.69268			0.846340	−	0.532643i	$-0.178801\pi$
$619$	1047.77			1.69268			0.846340	+	0.532643i	$0.178801\pi$
$620$		0			0
$621$		−	22.2268i		−	0.0357920i
$622$	494.579	−	528.897i	0.795143	−	0.850317i
$623$	284.754			0.457068
$624$	43.2923	+	320.959i	0.0693788	+	0.514358i
$625$		0			0
$626$	344.617	−	368.529i	0.550506	−	0.588705i
$627$			206.851i			0.329906i
$628$	−67.9090	−	1011.48i	−0.108135	−	1.61064i
$629$			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	$0.839198\pi$
$632$	−276.393	−	225.731i	−0.437331	−	0.357169i
$633$			237.149i			0.374643i
$634$	−117.440	−	109.819i	−0.185236	−	0.173217i
$635$		0			0
$636$	216.746	−	14.5519i	0.340796	−	0.0228804i
$637$	519.180			0.815040
$638$	6.26278	−	6.69735i	0.00981627	−	0.0104974i
$639$		−	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	$0.497616\pi$
$642$	−95.5897	−	89.3872i	−0.148894	−	0.139232i
$643$		−	86.1999i		−	0.134059i	−0.997751	−	0.0670295i	$-0.978648\pi$
$643$		−	86.1999i		−	0.134059i	0.997751	−	0.0670295i	$-0.0213522\pi$
$644$	2.45140	+	36.5128i	0.00380652	+	0.0566969i
$645$		0			0
$646$	241.779	−	258.556i	0.374272	−	0.400242i
$647$	352.580			0.544946			0.272473	−	0.962163i	$-0.412158\pi$
$647$	352.580			0.544946			0.272473	+	0.962163i	$0.412158\pi$
$648$	−45.5436	+	55.7654i	−0.0702834	+	0.0860577i
$649$	−422.277			−0.650658
$650$		0			0
$651$	−212.785			−0.326858
$652$	−408.496	+	27.4256i	−0.626527	+	0.0420638i
$653$	−319.322			−0.489008			−0.244504	−	0.969648i	$-0.578625\pi$
$653$	−319.322			−0.489008			−0.244504	+	0.969648i	$0.578625\pi$
$654$	−358.508	−	335.245i	−0.548177	−	0.512607i
$655$		0			0
$656$	500.574	−	67.5196i	0.763071	−	0.102926i
$657$		−	16.2769i		−	0.0247745i
$658$	186.145	+	174.067i	0.282895	+	0.264539i
$659$	−275.328			−0.417797			−0.208898	−	0.977937i	$-0.566988\pi$
$659$	−275.328			−0.417797			−0.208898	+	0.977937i	$0.566988\pi$
$660$		0			0
$661$		−	133.668i		−	0.202221i	−0.994875	−	0.101111i	$-0.967760\pi$
$661$		−	133.668i		−	0.202221i	0.994875	−	0.101111i	$-0.0322396\pi$
$662$	251.342	+	235.033i	0.379671	+	0.355035i
$663$	239.993			0.361980
$664$	419.559	+	342.654i	0.631866	+	0.516046i
$665$		0			0
$666$	−121.177	−	113.314i	−0.181947	−	0.170141i
$667$			2.45140i			0.00367526i
$668$	75.3179	+	1121.84i	0.112751	+	1.67939i
$669$			92.0799i			0.137638i
$670$		0			0
$671$		−	476.630i		−	0.710327i
$672$	68.6657	−	96.6307i	0.102181	−	0.143796i
$673$		−	187.703i		−	0.278904i	−0.990229	−	0.139452i	$-0.955466\pi$
$673$		−	187.703i		−	0.278904i	0.990229	−	0.139452i	$-0.0445341\pi$
$674$	−770.817	+	824.303i	−1.14364	+	1.22300i
$675$		0			0
$676$	−8.68842	−	129.411i	−0.0128527	−	0.191437i
$677$	1169.84			1.72797			0.863986	−	0.503515i	$-0.167960\pi$
$677$	1169.84			1.72797			0.863986	+	0.503515i	$0.167960\pi$
$678$	−147.478	−	137.909i	−0.217520	−	0.203406i
$679$			207.758i			0.305976i
$680$		0			0
$681$	207.580			0.304816
$682$	627.715	−	671.272i	0.920403	−	0.984269i
$683$		−	89.4566i		−	0.130976i	−0.997853	−	0.0654880i	$-0.979140\pi$
$683$		−	89.4566i		−	0.130976i	0.997853	−	0.0654880i	$-0.0208604\pi$
$684$	12.0000	+	178.736i	0.0175439	+	0.261310i
$685$		0			0
$686$	−291.895	−	272.955i	−0.425503	−	0.397893i
$687$	−370.837			−0.539791
$688$	61.5639	+	456.420i	0.0894824	+	0.663402i
$689$	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	$0.467907\pi$
$692$	65.0737	+	969.251i	0.0940371	+	1.40065i
$693$	51.3307			0.0740703
$694$	390.851	−	417.972i	0.563186	−	0.602265i
$695$		0			0
$696$	5.02301	−	6.15037i	0.00721697	−	0.00883673i
$697$		−	374.297i		−	0.537012i
$698$	575.126	−	615.033i	0.823962	−	0.881137i
$699$	−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	$0.664760\pi$
$702$	−82.9517	+	88.7077i	−0.118165	+	0.126364i
$703$	−412.773			−0.587160
$704$	102.277	+	501.681i	0.145280	+	0.712615i
$705$		0			0
$706$	586.214	−	626.891i	0.830331	−	0.887948i
$707$			132.897i			0.187974i
$708$	−364.881	+	24.4974i	−0.515369	+	0.0346009i
$709$		−	1080.13i		−	1.52346i	−0.647895	−	0.761730i	$-0.724351\pi$
$709$		−	1080.13i		−	1.52346i	0.647895	−	0.761730i	$-0.275649\pi$
$710$		0			0
$711$		−	133.822i		−	0.188216i
$712$	−673.734	+	824.946i	−0.946256	+	1.15863i
$713$			245.703i			0.344604i
$714$	−64.1615	−	59.9982i	−0.0898620	−	0.0840311i
$715$		0			0
$716$	−85.3027	−	1270.56i	−0.119138	−	1.77452i
$717$	553.011			0.771285
$718$	360.184	−	385.177i	0.501649	−	0.536458i
$719$		−	20.7736i		−	0.0288923i	−0.999896	−	0.0144461i	$-0.995401\pi$
$719$		−	20.7736i		−	0.0288923i	0.999896	−	0.0144461i	$-0.00459851\pi$
$720$		0			0
$721$	59.4669			0.0824783
$722$	−201.809	−	188.715i	−0.279515	−	0.261378i
$723$		−	428.536i		−	0.592719i
$724$	317.338	−	21.3055i	0.438313	−	0.0294275i
$725$		0			0
$726$	134.863	−	144.222i	0.185762	−	0.198652i
$727$	1031.17			1.41838			0.709192	−	0.705015i	$-0.249060\pi$
$727$	1031.17			1.41838			0.709192	+	0.705015i	$0.249060\pi$
$728$	126.484	−	154.872i	0.173742	−	0.212736i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	341.282			0.466870
$732$	−27.6506	−	411.846i	−0.0377740	−	0.562631i
$733$	881.072			1.20201			0.601004	−	0.799246i	$-0.294767\pi$
$733$	881.072			1.20201			0.601004	+	0.799246i	$0.294767\pi$
$734$	189.240	+	176.961i	0.257820	+	0.241091i
$735$		0			0
$736$	−111.580	−	79.2884i	−0.151603	−	0.107729i
$737$			678.277i			0.920321i
$738$	138.350	+	129.373i	0.187466	+	0.175302i
$739$	671.195			0.908247			0.454124	−	0.890939i	$-0.349952\pi$
$739$	671.195			0.908247			0.454124	+	0.890939i	$0.349952\pi$
$740$		0			0
$741$			302.171i			0.407788i
$742$	−97.9643	−	91.6077i	−0.132027	−	0.123461i
$743$	254.197			0.342122			0.171061	−	0.985260i	$-0.445281\pi$
$743$	254.197			0.342122			0.171061	+	0.985260i	$0.445281\pi$
$744$	503.454	−	616.448i	0.676685	−	0.828559i
$745$		0			0
$746$	−441.864	−	413.193i	−0.592311	−	0.553878i
$747$			203.138i			0.271939i
$748$	378.553	−	25.4153i	0.506087	−	0.0339777i
$749$			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	$0.838693\pi$
$752$	−944.704	+	127.426i	−1.25626	+	0.169449i
$753$		−	372.133i		−	0.494201i
$754$	9.14875	−	9.78357i	0.0121336	−	0.0129756i
$755$		0			0
$756$	44.3538	−	2.97783i	0.0586691	−	0.00393893i
$757$	372.679			0.492311			0.246155	−	0.969230i	$-0.420833\pi$
$757$	372.679			0.492311			0.246155	+	0.969230i	$0.420833\pi$
$758$	169.761	+	158.746i	0.223960	+	0.209428i
$759$		−	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	$0.190376\pi$
$762$	−438.075	+	468.473i	−0.574902	+	0.614794i
$763$			303.046i			0.397177i
$764$	1408.38	−	94.5559i	1.84343	−	0.123764i
$765$		0			0
$766$	827.041	+	773.377i	1.07969	+	1.00963i
$767$	−616.868			−0.804260
$768$	117.479	+	427.559i	0.152968	+	0.556717i
$769$	−247.703			−0.322110			−0.161055	−	0.986945i	$-0.551490\pi$
$769$	−247.703			−0.322110			−0.161055	+	0.986945i	$0.551490\pi$
$770$		0			0
$771$	145.972			0.189328
$772$	−1134.55	+	76.1718i	−1.46963	+	0.0986681i
$773$	587.805			0.760420			0.380210	−	0.924900i	$-0.375852\pi$
$773$	587.805			0.760420			0.380210	+	0.924900i	$0.375852\pi$
$774$	−117.962	+	126.147i	−0.152405	+	0.162980i
$775$		0			0
$776$	−601.885	−	491.560i	−0.775624	−	0.633453i
$777$			102.431i			0.131829i
$778$	−478.251	+	511.437i	−0.614719	+	0.657374i
$779$	471.272			0.604970
$780$		0			0
$781$		−	339.748i		−	0.435016i
$782$	−69.2800	+	74.0873i	−0.0885933	+	0.0947407i
$783$	2.97783			0.00380311
$784$	704.431	−	95.0166i	0.898509	−	0.121195i
$785$		0			0
$786$	−296.603	+	317.184i	−0.377357	+	0.403541i
$787$		−	31.0821i		−	0.0394944i	−0.999805	−	0.0197472i	$-0.993714\pi$
$787$		−	31.0821i		−	0.0394944i	0.999805	−	0.0197472i	$-0.00628614\pi$
$788$	20.3129	+	302.554i	0.0257778	+	0.383951i
$789$			479.986i			0.608347i
$790$		0			0
$791$			124.663i			0.157602i
$792$	−121.450	+	148.708i	−0.153346	+	0.187762i
$793$		−	696.267i		−	0.878016i
$794$	−794.900	−	743.321i	−1.00113	−	0.936173i
$795$		0			0
$796$	415.808	−	27.9165i	0.522371	−	0.0350710i
$797$	490.260			0.615132			0.307566	−	0.951527i	$-0.400486\pi$
$797$	490.260			0.615132			0.307566	+	0.951527i	$0.400486\pi$
$798$	75.5427	−	80.7846i	0.0946651	−	0.101234i
$799$			706.389i			0.884092i
$800$		0			0
$801$	−399.415			−0.498646
$802$	−433.030	−	404.932i	−0.539938	−	0.504903i
$803$		−	43.4050i		−	0.0540536i
$804$	39.3487	+	586.086i	0.0489411	+	0.728962i
$805$		0			0
$806$	916.974	−	980.602i	1.13769	−	1.21663i
$807$	−214.256			−0.265497
$808$	−385.010	−	314.438i	−0.476498	−	0.389156i
$809$	−676.102			−0.835726			−0.417863	−	0.908510i	$-0.637221\pi$
$809$	−676.102			−0.835726			−0.417863	+	0.908510i	$0.637221\pi$
$810$		0			0
$811$	−74.1793			−0.0914665			−0.0457332	−	0.998954i	$-0.514562\pi$
$811$	−74.1793			−0.0914665			−0.0457332	+	0.998954i	$0.514562\pi$
$812$	−4.89179	+	0.328425i	−0.00602437	+	0.000404465i
$813$	−342.920			−0.421796
$814$	−323.138	−	302.171i	−0.396976	−	0.371217i
$815$		0			0
$816$	325.626	−	43.9217i	0.399051	−	0.0538257i
$817$			429.703i			0.525952i
$818$	361.428	+	337.976i	0.441843	+	0.413173i
$819$	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	$0.758252\pi$
$822$	−251.930	−	235.583i	−0.306485	−	0.286598i
$823$	82.1839			0.0998589			0.0499295	−	0.998753i	$-0.484100\pi$
$823$	82.1839			0.0998589			0.0499295	+	0.998753i	$0.484100\pi$
$824$	−140.700	+	172.279i	−0.170753	+	0.209076i
$825$		0			0
$826$	164.918	+	154.217i	0.199658	+	0.186703i
$827$			1504.57i			1.81931i	0.415365	+	0.909655i	$0.363654\pi$
$827$			1504.57i			1.81931i	−0.415365	+	0.909655i	$0.636346\pi$
$828$	−3.43850	−	51.2154i	−0.00415278	−	0.0618543i
$829$			1409.65i			1.70042i	0.526445	+	0.850209i	$0.323525\pi$
$829$			1409.65i			1.70042i	−0.526445	+	0.850209i	$0.676475\pi$
$830$		0			0
$831$		−	429.044i		−	0.516299i
$832$	149.407	+	732.862i	0.179576	+	0.880843i
$833$		−	526.728i		−	0.632327i
$834$	419.951	−	449.091i	0.503539	−	0.538479i
$835$		0			0
$836$	32.0000	+	476.630i	0.0382775	+	0.570131i
$837$	298.467			0.356591
$838$	134.589	+	125.856i	0.160608	+	0.150187i
$839$		−	288.110i		−	0.343397i	−0.985150	−	0.171698i	$-0.945075\pi$
$839$		−	288.110i		−	0.343397i	0.985150	−	0.171698i	$-0.0549254\pi$
$840$		0			0
$841$	840.672			0.999609
$842$	608.620	−	650.851i	0.722826	−	0.772982i
$843$			767.520i			0.910463i
$844$	36.6870	+	546.441i	0.0434681	+	0.647442i
$845$		0			0
$846$	−261.100	−	244.158i	−0.308629	−	0.288603i
$847$	−121.910			−0.143932
$848$	497.178	−	67.0615i	0.586295	−	0.0790819i
$849$	−510.297			−0.601057
$850$		0			0
$851$	118.277			0.138986
$852$	−19.7097	−	293.569i	−0.0231334	−	0.344565i
$853$	645.132			0.756310			0.378155	−	0.925742i	$-0.376559\pi$
$853$	645.132			0.756310			0.378155	+	0.925742i	$0.376559\pi$
$854$	−174.067	+	186.145i	−0.203825	+	0.217968i
$855$		0			0
$856$	−234.087	−	191.179i	−0.273466	−	0.223340i
$857$		−	995.549i		−	1.16167i	−0.814022	−	0.580833i	$-0.802727\pi$
$857$		−	995.549i		−	1.16167i	0.814022	−	0.580833i	$-0.197273\pi$
$858$	−221.205	+	236.554i	−0.257814	+	0.275704i
$859$	774.354			0.901460			0.450730	−	0.892660i	$-0.351164\pi$
$859$	774.354			0.901460			0.450730	+	0.892660i	$0.351164\pi$
$860$		0			0
$861$		−	116.947i		−	0.135827i
$862$	255.005	−	272.700i	0.295830	−	0.316357i
$863$	−1007.33			−1.16724			−0.583622	−	0.812025i	$-0.698365\pi$
$863$	−1007.33			−1.16724			−0.583622	+	0.812025i	$0.698365\pi$
$864$	−96.3154	+	135.541i	−0.111476	+	0.156876i
$865$		0			0
$866$	397.688	−	425.284i	0.459225	−	0.491090i
$867$			257.081i			0.296518i
$868$	−490.301	+	32.9179i	−0.564863	+	0.0379238i
$869$		−	356.858i		−	0.410654i
$870$		0			0
$871$			990.836i			1.13758i
$872$	−877.941	−	717.015i	−1.00681	−	0.822265i
$873$		−	291.415i		−	0.333809i
$874$	−93.2820	−	87.2293i	−0.106730	−	0.0998046i
$875$		0			0
$876$	−2.51804	−	37.5054i	−0.00287448	−	0.0428144i
$877$	681.645			0.777246			0.388623	−	0.921397i	$-0.372951\pi$
$877$	681.645			0.777246			0.388623	+	0.921397i	$0.372951\pi$
$878$	119.787	−	128.099i	0.136431	−	0.145898i
$879$			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	$0.625943\pi$
$882$	194.693	+	182.060i	0.220740	+	0.206417i
$883$			1059.44i			1.19982i	0.800068	+	0.599910i	$0.204797\pi$
$883$			1059.44i			1.19982i	−0.800068	+	0.599910i	$0.795203\pi$
$884$	552.995	−	37.1270i	0.625560	−	0.0419989i
$885$		0			0
$886$	28.2872	−	30.2500i	0.0319268	−	0.0341422i
$887$	−856.411			−0.965514			−0.482757	−	0.875754i	$-0.660365\pi$
$887$	−856.411			−0.965514			−0.482757	+	0.875754i	$0.660365\pi$
$888$	−296.747	−	242.354i	−0.334175	−	0.272921i
$889$	396.000			0.445444
$890$		0			0
$891$	−72.0000			−0.0808081
$892$	14.2448	+	212.172i	0.0159695	+	0.237861i
$893$	−889.403			−0.995972
$894$	−222.158	−	207.743i	−0.248499	−	0.232374i
$895$		0			0
$896$	143.272	−	233.280i	0.159901	−	0.260358i
$897$		−	86.5847i		−	0.0965270i
$898$	−853.714	−	798.319i	−0.950684	−	0.888997i
$899$	−32.9179			−0.0366161
$900$		0			0
$901$		−	371.758i		−	0.412606i
$902$	368.934	+	344.995i	0.409018	+	0.382478i
$903$	106.632			0.118086
$904$	−361.156	−	294.957i	−0.399509	−	0.326280i
$905$		0			0
$906$	−554.281	−	518.315i	−0.611789	−	0.572092i
$907$		−	761.492i		−	0.839573i	−0.907623	−	0.419786i	$-0.862105\pi$
$907$		−	761.492i		−	0.839573i	0.907623	−	0.419786i	$-0.137895\pi$
$908$	478.308	−	32.1127i	0.526770	−	0.0353664i
$909$		−	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	$0.836081\pi$
$912$	55.3011	+	409.990i	0.0606372	+	0.449550i
$913$			541.703i			0.593321i
$914$	368.406	−	393.970i	0.403070	−	0.431039i
$915$		0			0
$916$	−854.487	+	57.3686i	−0.932846	+	0.0626295i
$917$	268.115			0.292383
$918$	89.9973	+	84.1577i	0.0980363	+	0.0916750i
$919$			62.6388i			0.0681598i	0.999419	+	0.0340799i	$0.0108501\pi$
$919$			62.6388i			0.0681598i	−0.999419	+	0.0340799i	$0.989150\pi$
$920$		0			0
$921$	907.959			0.985840
$922$	60.7811	−	64.9986i	0.0659231	−	0.0704974i
$923$		−	496.308i		−	0.537712i
$924$	118.277	−	7.94089i	0.128005	−	0.00859403i
$925$		0			0
$926$	−892.652	−	834.731i	−0.963987	−	0.901437i
$927$	−83.4124			−0.0899810
$928$	10.6226	−	14.9488i	0.0114468	−	0.0161086i
$929$	−253.313			−0.272673			−0.136336	−	0.990663i	$-0.543533\pi$
$929$	−253.313			−0.272673			−0.136336	+	0.990663i	$0.543533\pi$
$930$		0			0
$931$	663.195			0.712347
$932$	−508.599	+	34.1464i	−0.545707	+	0.0366377i
$933$	627.101			0.672134
$934$	−200.000	+	213.878i	−0.214133	+	0.228991i
$935$		0			0
$936$	−177.415	+	217.234i	−0.189546	+	0.232088i
$937$		−	30.5538i		−	0.0326081i	−0.999867	−	0.0163040i	$-0.994810\pi$
$937$		−	30.5538i		−	0.0326081i	0.999867	−	0.0163040i	$-0.00518996\pi$
$938$	247.709	−	264.897i	0.264082	−	0.282406i
$939$	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	$0.933773\pi$
$942$	599.645	−	641.254i	0.636566	−	0.680737i
$943$	−135.039			−0.143202
$944$	−836.974	+	112.895i	−0.886625	+	0.119592i
$945$		0			0
$946$	−314.564	+	336.391i	−0.332520	+	0.355594i
$947$		−	263.615i		−	0.278369i	−0.990266	−	0.139184i	$-0.955552\pi$
$947$		−	263.615i		−	0.278369i	0.990266	−	0.139184i	$-0.0444481\pi$
$948$	−20.7023	−	308.354i	−0.0218379	−	0.325268i
$949$		−	63.4066i		−	0.0668141i
$950$		0			0
$951$		−	139.245i		−	0.146420i
$952$	−157.123	−	128.323i	−0.165046	−	0.134793i
$953$		−	1292.41i		−	1.35615i	−0.734993	−	0.678075i	$-0.762815\pi$
$953$		−	1292.41i		−	1.35615i	0.734993	−	0.678075i	$-0.237185\pi$
$954$	137.412	+	128.495i	0.144037	+	0.134691i
$955$		0			0
$956$	1274.26	−	85.5511i	1.33290	−	0.0894886i
$957$	7.94089			0.00829769
$958$	−262.107	+	280.295i	−0.273598	+	0.292583i
$959$			212.957i			0.222061i
$960$		0			0
$961$	−2338.34			−2.43324
$962$	−472.045	−	441.415i	−0.490691	−	0.458852i
$963$		−	113.338i		−	0.117693i
$964$	−66.2947	−	987.438i	−0.0687705	−	1.02431i
$965$		0			0
$966$	−21.6462	+	23.1482i	−0.0224080	+	0.0239629i
$967$	−1110.00			−1.14788			−0.573942	−	0.818896i	$-0.694587\pi$
$967$	−1110.00			−1.14788			−0.573942	+	0.818896i	$0.694587\pi$
$968$	288.443	−	353.181i	0.297978	−	0.364856i
$969$	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	$0.742770\pi$
$972$	−62.2138	+	4.17691i	−0.0640059	+	0.00429724i
$973$	−379.617			−0.390151
$974$	−892.204	−	834.311i	−0.916020	−	0.856583i
$975$		0			0
$976$	−127.426	−	944.704i	−0.130559	−	0.967934i
$977$		−	920.431i		−	0.942099i	−0.882107	−	0.471050i	$-0.843875\pi$
$977$		−	920.431i		−	0.942099i	0.882107	−	0.471050i	$-0.156125\pi$
$978$	−258.976	−	242.172i	−0.264802	−	0.247619i
$979$	−1065.11			−1.08795
$980$		0			0
$981$		−	425.074i		−	0.433307i
$982$	−207.952	−	194.459i	−0.211764	−	0.198023i
$983$	−1697.84			−1.72720			−0.863601	−	0.504176i	$-0.831796\pi$
$983$	−1697.84			−1.72720			−0.863601	+	0.504176i	$0.831796\pi$
$984$	338.802	+	276.700i	0.344311	+	0.281200i
$985$		0			0
$986$	−9.92581	−	9.28176i	−0.0100667	−	0.00941355i
$987$			220.708i			0.223615i
$988$	46.7460	+	696.267i	0.0473138	+	0.704723i
$989$		−	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	$-0.0458921\pi$
$992$	1064.70	−	1498.31i	1.07329	−	1.51040i
$993$			298.010i			0.300111i
$994$	−124.077	+	132.687i	−0.124826	+	0.133487i
$995$		0			0
$996$	31.4256	+	468.074i	0.0315518	+	0.469954i
$997$	1093.80			1.09710			0.548548	−	0.836119i	$-0.315181\pi$
$997$	1093.80			1.09710			0.548548	+	0.836119i	$0.315181\pi$
$998$	−133.473	−	124.813i	−0.133741	−	0.125063i
$999$		−	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.p.a.499.6		8
4.3	odd	2		2400.3.p.a.1999.2		8
5.2	odd	4		600.3.g.a.451.2		4
5.3	odd	4		24.3.b.a.19.3	✓	4
5.4	even	2	inner	600.3.p.a.499.3		8
8.3	odd	2	inner	600.3.p.a.499.4		8
8.5	even	2		2400.3.p.a.1999.3		8
15.8	even	4		72.3.b.b.19.2		4
20.3	even	4		96.3.b.a.79.4		4
20.7	even	4		2400.3.g.a.751.1		4
20.19	odd	2		2400.3.p.a.1999.7		8
40.3	even	4		24.3.b.a.19.4	yes	4
40.13	odd	4		96.3.b.a.79.3		4
40.19	odd	2	inner	600.3.p.a.499.5		8
40.27	even	4		600.3.g.a.451.1		4
40.29	even	2		2400.3.p.a.1999.6		8
40.37	odd	4		2400.3.g.a.751.2		4
60.23	odd	4		288.3.b.b.271.1		4
80.3	even	4		768.3.g.h.511.8		8
80.13	odd	4		768.3.g.h.511.4		8
80.43	even	4		768.3.g.h.511.1		8
80.53	odd	4		768.3.g.h.511.5		8
120.53	even	4		288.3.b.b.271.4		4
120.83	odd	4		72.3.b.b.19.1		4
240.53	even	4		2304.3.g.z.1279.8		8
240.83	odd	4		2304.3.g.z.1279.1		8
240.173	even	4		2304.3.g.z.1279.2		8
240.203	odd	4		2304.3.g.z.1279.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.3.b.a.19.3	✓	4	5.3	odd	4
24.3.b.a.19.4	yes	4	40.3	even	4
72.3.b.b.19.1		4	120.83	odd	4
72.3.b.b.19.2		4	15.8	even	4
96.3.b.a.79.3		4	40.13	odd	4
96.3.b.a.79.4		4	20.3	even	4
288.3.b.b.271.1		4	60.23	odd	4
288.3.b.b.271.4		4	120.53	even	4
600.3.g.a.451.1		4	40.27	even	4
600.3.g.a.451.2		4	5.2	odd	4
600.3.p.a.499.3		8	5.4	even	2	inner
600.3.p.a.499.4		8	8.3	odd	2	inner
600.3.p.a.499.5		8	40.19	odd	2	inner
600.3.p.a.499.6		8	1.1	even	1	trivial
768.3.g.h.511.1		8	80.43	even	4
768.3.g.h.511.4		8	80.13	odd	4
768.3.g.h.511.5		8	80.53	odd	4
768.3.g.h.511.8		8	80.3	even	4
2304.3.g.z.1279.1		8	240.83	odd	4
2304.3.g.z.1279.2		8	240.173	even	4
2304.3.g.z.1279.7		8	240.203	odd	4
2304.3.g.z.1279.8		8	240.53	even	4
2400.3.g.a.751.1		4	20.7	even	4
2400.3.g.a.751.2		4	40.37	odd	4
2400.3.p.a.1999.2		8	4.3	odd	2
2400.3.p.a.1999.3		8	8.5	even	2
2400.3.p.a.1999.6		8	40.29	even	2
2400.3.p.a.1999.7		8	20.19	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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.p.a.499.6

Level	$600$
Weight	$3$
Character	600.499
Analytic conductor	$16.349$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$