LMFDB - Embedded newform 180.3.f.h.19.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,3,Mod(19,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$180 = 2^{2} \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	180.f (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.389136420864.4
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256$ x^8 + 5x^6 + 24x^4 + 80*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{8}$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.6
Root			$0.656712 + 1.88911i$ of defining polynomial
Character	$\chi$	$=$	180.19
Dual form			180.3.f.h.19.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.656712 + 1.88911i) q^{2} +(-3.13746 + 2.48120i) q^{4} +(3.27492 + 3.77822i) q^{5} -9.55505 q^{7} +(-6.74766 - 4.29756i) q^{8} +(-4.98678 + 8.66787i) q^{10} +9.92480i q^{11} +7.55643i q^{13} +(-6.27492 - 18.0505i) q^{14} +(3.68729 - 15.5693i) q^{16} +17.1903i q^{17} -26.1762i q^{19} +(-19.6494 - 3.72827i) q^{20} +(-18.7490 + 6.51774i) q^{22} -1.67451 q^{23} +(-3.54983 + 24.7467i) q^{25} +(-14.2749 + 4.96240i) q^{26} +(29.9786 - 23.7080i) q^{28} +0.350497 q^{29} +46.0258i q^{31} +(31.8336 - 3.25887i) q^{32} +(-32.4743 + 11.2890i) q^{34} +(-31.2920 - 36.1010i) q^{35} -22.6693i q^{37} +(49.4498 - 17.1903i) q^{38} +(-5.86091 - 39.5683i) q^{40} +77.2990 q^{41} +41.7994 q^{43} +(-24.6254 - 31.1386i) q^{44} +(-1.09967 - 3.16332i) q^{46} +14.0866 q^{47} +42.2990 q^{49} +(-49.0804 + 9.54543i) q^{50} +(-18.7490 - 23.7080i) q^{52} +22.6693i q^{53} +(-37.4980 + 32.5029i) q^{55} +(64.4743 + 41.0634i) q^{56} +(0.230175 + 0.662126i) q^{58} +94.7802i q^{59} +38.0000 q^{61} +(-86.9478 + 30.2257i) q^{62} +(27.0619 + 57.9970i) q^{64} +(-28.5498 + 24.7467i) q^{65} +29.8477 q^{67} +(-42.6525 - 53.9337i) q^{68} +(47.6489 - 82.8220i) q^{70} +7.19630i q^{71} -34.3805i q^{73} +(42.8248 - 14.8872i) q^{74} +(64.9485 + 82.1269i) q^{76} -94.8320i q^{77} -46.0258i q^{79} +(70.8999 - 37.0569i) q^{80} +(50.7632 + 146.026i) q^{82} +24.1336 q^{83} +(-64.9485 + 56.2967i) q^{85} +(27.4502 + 78.9636i) q^{86} +(42.6525 - 66.9692i) q^{88} -100.199 q^{89} -72.2021i q^{91} +(5.25370 - 4.15479i) q^{92} +(9.25083 + 26.6111i) q^{94} +(98.8995 - 85.7250i) q^{95} -131.861i q^{97} +(27.7783 + 79.9074i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 10 q^{4} - 4 q^{5} - 42 q^{10} - 20 q^{14} - 46 q^{16} - 52 q^{20} + 32 q^{25} - 84 q^{26} + 184 q^{29} + 12 q^{34} - 6 q^{40} + 256 q^{41} - 348 q^{44} + 112 q^{46} - 24 q^{49} - 72 q^{50} + 244 q^{56}+ \cdots + 376 q^{94}+O(q^{100})$ 8 * q - 10 * q^4 - 4 * q^5 - 42 * q^10 - 20 * q^14 - 46 * q^16 - 52 * q^20 + 32 * q^25 - 84 * q^26 + 184 * q^29 + 12 * q^34 - 6 * q^40 + 256 * q^41 - 348 * q^44 + 112 * q^46 - 24 * q^49 - 72 * q^50 + 244 * q^56 + 304 * q^61 - 10 * q^64 - 168 * q^65 - 104 * q^70 + 252 * q^74 - 24 * q^76 + 308 * q^80 + 24 * q^85 + 280 * q^86 - 560 * q^89 + 376 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$ .

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$1$

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

)

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

$2$	0.656712	+	1.88911i	0.328356	+	0.944554i
$2$	0.656712	+	1.88911i	0.328356	+	0.944554i
$3$		0			0
$3$		0			0
$4$	−3.13746	+	2.48120i	−0.784365	+	0.620300i
$5$	3.27492	+	3.77822i	0.654983	+	0.755643i
$5$	3.27492	+	3.77822i	0.654983	+	0.755643i
$6$		0			0
$7$	−9.55505			−1.36501			−0.682504	−	0.730882i	$-0.739109\pi$
$7$	−9.55505			−1.36501			−0.682504	+	0.730882i	$0.739109\pi$
$8$	−6.74766	−	4.29756i	−0.843458	−	0.537196i
$9$		0			0
$10$	−4.98678	+	8.66787i	−0.498678	+	0.866787i
$11$			9.92480i			0.902255i	0.892460	+	0.451127i	$0.148978\pi$
$11$			9.92480i			0.902255i	−0.892460	+	0.451127i	$0.851022\pi$
$12$		0			0
$13$			7.55643i			0.581264i	0.956835	+	0.290632i	$0.0938655\pi$
$13$			7.55643i			0.581264i	−0.956835	+	0.290632i	$0.906134\pi$
$14$	−6.27492	−	18.0505i	−0.448208	−	1.28932i
$15$		0			0
$16$	3.68729	−	15.5693i	0.230456	−	0.973083i
$17$			17.1903i			1.01119i	0.862770	+	0.505596i	$0.168727\pi$
$17$			17.1903i			1.01119i	−0.862770	+	0.505596i	$0.831273\pi$
$18$		0			0
$19$		−	26.1762i		−	1.37770i	−0.724905	−	0.688849i	$-0.758116\pi$
$19$		−	26.1762i		−	1.37770i	0.724905	−	0.688849i	$-0.241884\pi$
$20$	−19.6494	−	3.72827i	−0.982471	−	0.186414i
$21$		0			0
$22$	−18.7490	+	6.51774i	−0.852228	+	0.296261i
$23$	−1.67451			−0.0728047			−0.0364023	−	0.999337i	$-0.511590\pi$
$23$	−1.67451			−0.0728047			−0.0364023	+	0.999337i	$0.511590\pi$
$24$		0			0
$25$	−3.54983	+	24.7467i	−0.141993	+	0.989868i
$26$	−14.2749	+	4.96240i	−0.549035	+	0.190862i
$27$		0			0
$28$	29.9786	−	23.7080i	1.07066	−	0.846714i
$29$	0.350497			0.0120861			0.00604305	−	0.999982i	$-0.498076\pi$
$29$	0.350497			0.0120861			0.00604305	+	0.999982i	$0.498076\pi$
$30$		0			0
$31$			46.0258i			1.48470i	0.670010	+	0.742352i	$0.266290\pi$
$31$			46.0258i			1.48470i	−0.670010	+	0.742352i	$0.733710\pi$
$32$	31.8336	−	3.25887i	0.994801	−	0.101840i
$33$		0			0
$34$	−32.4743	+	11.2890i	−0.955125	+	0.332031i
$35$	−31.2920	−	36.1010i	−0.894057	−	1.03146i
$36$		0			0
$37$		−	22.6693i		−	0.612684i	−0.951922	−	0.306342i	$-0.900895\pi$
$37$		−	22.6693i		−	0.612684i	0.951922	−	0.306342i	$-0.0991051\pi$
$38$	49.4498	−	17.1903i	1.30131	−	0.452375i
$39$		0			0
$40$	−5.86091	−	39.5683i	−0.146523	−	0.989207i
$41$	77.2990			1.88534			0.942671	−	0.333724i	$-0.108305\pi$
$41$	77.2990			1.88534			0.942671	+	0.333724i	$0.108305\pi$
$42$		0			0
$43$	41.7994			0.972079			0.486039	−	0.873937i	$-0.338441\pi$
$43$	41.7994			0.972079			0.486039	+	0.873937i	$0.338441\pi$
$44$	−24.6254	−	31.1386i	−0.559668	−	0.707697i
$45$		0			0
$46$	−1.09967	−	3.16332i	−0.0239058	−	0.0687679i
$47$	14.0866			0.299715			0.149857	−	0.988708i	$-0.452119\pi$
$47$	14.0866			0.299715			0.149857	+	0.988708i	$0.452119\pi$
$48$		0			0
$49$	42.2990			0.863245
$50$	−49.0804	+	9.54543i	−0.981608	+	0.190909i
$51$		0			0
$52$	−18.7490	−	23.7080i	−0.360558	−	0.455923i
$53$			22.6693i			0.427723i	0.976864	+	0.213861i	$0.0686041\pi$
$53$			22.6693i			0.427723i	−0.976864	+	0.213861i	$0.931396\pi$
$54$		0			0
$55$	−37.4980	+	32.5029i	−0.681783	+	0.590962i
$56$	64.4743	+	41.0634i	1.15133	+	0.733276i
$57$		0			0
$58$	0.230175	+	0.662126i	0.00396854	+	0.0114160i
$59$			94.7802i			1.60644i	0.595680	+	0.803222i	$0.296883\pi$
$59$			94.7802i			1.60644i	−0.595680	+	0.803222i	$0.703117\pi$
$60$		0			0
$61$	38.0000			0.622951			0.311475	−	0.950254i	$-0.399177\pi$
$61$	38.0000			0.622951			0.311475	+	0.950254i	$0.399177\pi$
$62$	−86.9478	+	30.2257i	−1.40238	+	0.487512i
$63$		0			0
$64$	27.0619	+	57.9970i	0.422842	+	0.906203i
$65$	−28.5498	+	24.7467i	−0.439228	+	0.380718i
$66$		0			0
$67$	29.8477			0.445488			0.222744	−	0.974877i	$-0.428499\pi$
$67$	29.8477			0.445488			0.222744	+	0.974877i	$0.428499\pi$
$68$	−42.6525	−	53.9337i	−0.627242	−	0.793143i
$69$		0			0
$70$	47.6489	−	82.8220i	0.680699	−	1.18317i
$71$			7.19630i			0.101356i	0.998715	+	0.0506782i	$0.0161383\pi$
$71$			7.19630i			0.101356i	−0.998715	+	0.0506782i	$0.983862\pi$
$72$		0			0
$73$		−	34.3805i		−	0.470966i	−0.971878	−	0.235483i	$-0.924333\pi$
$73$		−	34.3805i		−	0.470966i	0.971878	−	0.235483i	$-0.0756672\pi$
$74$	42.8248	−	14.8872i	0.578713	−	0.201178i
$75$		0			0
$76$	64.9485	+	82.1269i	0.854586	+	1.08062i
$77$		−	94.8320i		−	1.23158i
$78$		0			0
$79$		−	46.0258i		−	0.582606i	−0.956631	−	0.291303i	$-0.905911\pi$
$79$		−	46.0258i		−	0.582606i	0.956631	−	0.291303i	$-0.0940887\pi$
$80$	70.8999	−	37.0569i	0.886248	−	0.463211i
$81$		0			0
$82$	50.7632	+	146.026i	0.619063	+	1.78081i
$83$	24.1336			0.290767			0.145383	−	0.989375i	$-0.453558\pi$
$83$	24.1336			0.290767			0.145383	+	0.989375i	$0.453558\pi$
$84$		0			0
$85$	−64.9485	+	56.2967i	−0.764100	+	0.662314i
$86$	27.4502	+	78.9636i	0.319188	+	0.918181i
$87$		0			0
$88$	42.6525	−	66.9692i	0.484687	−	0.761014i
$89$	−100.199			−1.12584			−0.562918	−	0.826513i	$-0.690321\pi$
$89$	−100.199			−1.12584			−0.562918	+	0.826513i	$0.690321\pi$
$90$		0			0
$91$		−	72.2021i		−	0.793430i
$92$	5.25370	−	4.15479i	0.0571054	−	0.0451607i
$93$		0			0
$94$	9.25083	+	26.6111i	0.0984131	+	0.283097i
$95$	98.8995	−	85.7250i	1.04105	−	0.902369i
$96$		0			0
$97$		−	131.861i		−	1.35939i	−0.733494	−	0.679696i	$-0.762112\pi$
$97$		−	131.861i		−	1.35939i	0.733494	−	0.679696i	$-0.237888\pi$
$98$	27.7783	+	79.9074i	0.283452	+	0.815382i
$99$		0			0
$100$	−50.2640	−	86.4496i	−0.502640	−	0.864496i
$101$	−29.4502			−0.291586			−0.145793	−	0.989315i	$-0.546573\pi$
$101$	−29.4502			−0.291586			−0.145793	+	0.989315i	$0.546573\pi$
$102$		0			0
$103$	−143.786			−1.39598			−0.697991	−	0.716107i	$-0.745922\pi$
$103$	−143.786			−1.39598			−0.697991	+	0.716107i	$0.745922\pi$
$104$	32.4743	−	50.9882i	0.312252	−	0.490272i
$105$		0			0
$106$	−42.8248	+	14.8872i	−0.404007	+	0.140445i
$107$	−35.1014			−0.328050			−0.164025	−	0.986456i	$-0.552448\pi$
$107$	−35.1014			−0.328050			−0.164025	+	0.986456i	$0.552448\pi$
$108$		0			0
$109$	−151.498			−1.38989			−0.694947	−	0.719061i	$-0.744572\pi$
$109$	−151.498			−1.38989			−0.694947	+	0.719061i	$0.744572\pi$
$110$	−86.0269	−	49.4928i	−0.782063	−	0.449935i
$111$		0			0
$112$	−35.2323	+	148.766i	−0.314574	+	1.32827i
$113$		−	32.3031i		−	0.285868i	−0.989732	−	0.142934i	$-0.954346\pi$
$113$		−	32.3031i		−	0.285868i	0.989732	−	0.142934i	$-0.0456537\pi$
$114$		0			0
$115$	−5.48387	−	6.32665i	−0.0476858	−	0.0550143i
$116$	−1.09967	+	0.869652i	−0.00947990	+	0.00749700i
$117$		0			0
$118$	−179.050	+	62.2433i	−1.51737	+	0.527486i
$119$		−	164.254i		−	1.38028i
$120$		0			0
$121$	22.4983			0.185937
$122$	24.9551	+	71.7861i	0.204550	+	0.588411i
$123$		0			0
$124$	−114.199	−	144.404i	−0.920962	−	1.16455i
$125$	−105.124	+	67.6313i	−0.840990	+	0.541051i
$126$		0			0
$127$	192.053			1.51223			0.756116	−	0.654438i	$-0.227095\pi$
$127$	192.053			1.51223			0.756116	+	0.654438i	$0.227095\pi$
$128$	−91.7908	+	89.2102i	−0.717115	+	0.696954i
$129$		0			0
$130$	−65.4982	−	37.6823i	−0.503832	−	0.289864i
$131$			42.4277i			0.323876i	0.986801	+	0.161938i	$0.0517744\pi$
$131$			42.4277i			0.323876i	−0.986801	+	0.161938i	$0.948226\pi$
$132$		0			0
$133$			250.115i			1.88057i
$134$	19.6013	+	56.3855i	0.146279	+	0.420787i
$135$		0			0
$136$	73.8762	−	115.994i	0.543208	−	0.852897i
$137$		−	206.854i		−	1.50988i	−0.655791	−	0.754942i	$-0.727665\pi$
$137$		−	206.854i		−	1.50988i	0.655791	−	0.754942i	$-0.272335\pi$
$138$		0			0
$139$			46.0258i			0.331121i	0.986200	+	0.165561i	$0.0529433\pi$
$139$			46.0258i			0.331121i	−0.986200	+	0.165561i	$0.947057\pi$
$140$	187.751	+	35.6238i	1.34108	+	0.254456i
$141$		0			0
$142$	−13.5946	+	4.72590i	−0.0957366	+	0.0332810i
$143$	−74.9961			−0.524448
$144$		0			0
$145$	1.14785	+	1.32425i	0.00791619	+	0.00913277i
$146$	64.9485	−	22.5781i	0.444853	−	0.154645i
$147$		0			0
$148$	56.2471	+	71.1240i	0.380048	+	0.480567i
$149$	−11.6495			−0.0781846			−0.0390923	−	0.999236i	$-0.512447\pi$
$149$	−11.6495			−0.0781846			−0.0390923	+	0.999236i	$0.512447\pi$
$150$		0			0
$151$			125.424i			0.830624i	0.909679	+	0.415312i	$0.136328\pi$
$151$			125.424i			0.830624i	−0.909679	+	0.415312i	$0.863672\pi$
$152$	−112.494	+	176.628i	−0.740093	+	1.16203i
$153$		0			0
$154$	179.148	−	62.2773i	1.16330	−	0.404398i
$155$	−173.896	+	150.731i	−1.12191	+	0.972457i
$156$		0			0
$157$		−	197.220i		−	1.25618i	−0.778140	−	0.628090i	$-0.783837\pi$
$157$		−	197.220i		−	1.25618i	0.778140	−	0.628090i	$-0.216163\pi$
$158$	86.9478	−	30.2257i	0.550303	−	0.191302i
$159$		0			0
$160$	116.565	+	109.602i	0.728532	+	0.685011i
$161$	16.0000			0.0993789
$162$		0			0
$163$	18.4196			0.113004			0.0565018	−	0.998402i	$-0.482005\pi$
$163$	18.4196			0.113004			0.0565018	+	0.998402i	$0.482005\pi$
$164$	−242.522	+	191.794i	−1.47880	+	1.16948i
$165$		0			0
$166$	15.8488	+	45.5910i	0.0954749	+	0.274645i
$167$	92.8920			0.556240			0.278120	−	0.960546i	$-0.410289\pi$
$167$	92.8920			0.556240			0.278120	+	0.960546i	$0.410289\pi$
$168$		0			0
$169$	111.900			0.662132
$170$	−149.003	−	85.7241i	−0.876488	−	0.504259i
$171$		0			0
$172$	−131.144	+	103.713i	−0.762464	+	0.602981i
$173$			117.501i			0.679198i	0.940570	+	0.339599i	$0.110291\pi$
$173$			117.501i			0.679198i	−0.940570	+	0.339599i	$0.889709\pi$
$174$		0			0
$175$	33.9189	−	236.456i	0.193822	−	1.35118i
$176$	154.522	+	36.5956i	0.877968	+	0.207930i
$177$		0			0
$178$	−65.8021	−	189.287i	−0.369675	−	1.06341i
$179$		−	231.988i		−	1.29602i	−0.761631	−	0.648011i	$-0.775601\pi$
$179$		−	231.988i		−	1.29602i	0.761631	−	0.648011i	$-0.224399\pi$
$180$		0			0
$181$	−218.096			−1.20495			−0.602476	−	0.798137i	$-0.705819\pi$
$181$	−218.096			−1.20495			−0.602476	+	0.798137i	$0.705819\pi$
$182$	136.398	−	47.4160i	0.749437	−	0.260527i
$183$		0			0
$184$	11.2990	+	7.19630i	0.0614076	+	0.0391103i
$185$	85.6495	−	74.2401i	0.462970	−	0.401298i
$186$		0			0
$187$	−170.610			−0.912352
$188$	−44.1961	+	34.9516i	−0.235085	+	0.185913i
$189$		0			0
$190$	226.892	+	130.535i	1.19417	+	0.687027i
$191$			137.208i			0.718366i	0.933267	+	0.359183i	$0.116945\pi$
$191$			137.208i			0.718366i	−0.933267	+	0.359183i	$0.883055\pi$
$192$		0			0
$193$		−	37.0290i		−	0.191860i	−0.995388	−	0.0959301i	$-0.969417\pi$
$193$		−	37.0290i		−	0.191860i	0.995388	−	0.0959301i	$-0.0305825\pi$
$194$	249.100	−	86.5947i	1.28402	−	0.446364i
$195$		0			0
$196$	−132.711	+	104.952i	−0.677099	+	0.535471i
$197$			194.572i			0.987674i	0.869554	+	0.493837i	$0.164406\pi$
$197$			194.572i			0.987674i	−0.869554	+	0.493837i	$0.835594\pi$
$198$		0			0
$199$			176.037i			0.884610i	0.896865	+	0.442305i	$0.145839\pi$
$199$			176.037i			0.884610i	−0.896865	+	0.442305i	$0.854161\pi$
$200$	130.304	−	151.727i	0.651518	−	0.758633i
$201$		0			0
$202$	−19.3403	−	55.6345i	−0.0957440	−	0.275419i
$203$	−3.34901			−0.0164976
$204$		0			0
$205$	253.148	+	292.052i	1.23487	+	1.42465i
$206$	−94.4261	−	271.628i	−0.458379	−	1.31858i
$207$		0			0
$208$	117.649	+	27.8628i	0.565618	+	0.133956i
$209$	259.794			1.24303
$210$		0			0
$211$		−	20.7193i		−	0.0981955i	−0.998794	−	0.0490978i	$-0.984365\pi$
$211$		−	20.7193i		−	0.0981955i	0.998794	−	0.0490978i	$-0.0156346\pi$
$212$	−56.2471	−	71.1240i	−0.265316	−	0.335490i
$213$		0			0
$214$	−23.0515	−	66.3103i	−0.107717	−	0.309861i
$215$	136.890	+	157.927i	0.636696	+	0.734545i
$216$		0			0
$217$		−	439.779i		−	2.02663i
$218$	−99.4908	−	286.197i	−0.456380	−	1.31283i
$219$		0			0
$220$	37.0024	−	195.017i	0.168193	−	0.886439i
$221$	−129.897			−0.587769
$222$		0			0
$223$	−97.0265			−0.435096			−0.217548	−	0.976050i	$-0.569806\pi$
$223$	−97.0265			−0.435096			−0.217548	+	0.976050i	$0.569806\pi$
$224$	−304.172	+	31.1386i	−1.35791	+	0.139012i
$225$		0			0
$226$	61.0241	−	21.2138i	0.270018	−	0.0938666i
$227$	407.256			1.79408			0.897040	−	0.441948i	$-0.145713\pi$
$227$	407.256			1.79408			0.897040	+	0.441948i	$0.145713\pi$
$228$		0			0
$229$	−7.89702			−0.0344848			−0.0172424	−	0.999851i	$-0.505489\pi$
$229$	−7.89702			−0.0344848			−0.0172424	+	0.999851i	$0.505489\pi$
$230$	8.35040	−	14.5144i	0.0363061	−	0.0631061i
$231$		0			0
$232$	−2.36503	−	1.50628i	−0.0101941	−	0.00649260i
$233$		−	28.1483i		−	0.120808i	−0.998174	−	0.0604042i	$-0.980761\pi$
$233$		−	28.1483i		−	0.120808i	0.998174	−	0.0604042i	$-0.0192390\pi$
$234$		0			0
$235$	46.1324	+	53.2222i	0.196308	+	0.226477i
$236$	−235.169	−	297.369i	−0.996477	−	1.26004i
$237$		0			0
$238$	310.293	−	107.867i	1.30375	−	0.453225i
$239$			296.005i			1.23851i	0.785189	+	0.619257i	$0.212566\pi$
$239$			296.005i			1.23851i	−0.785189	+	0.619257i	$0.787434\pi$
$240$		0			0
$241$	465.794			1.93276			0.966378	−	0.257127i	$-0.0827758\pi$
$241$	465.794			1.93276			0.966378	+	0.257127i	$0.0827758\pi$
$242$	14.7749	+	42.5018i	0.0610534	+	0.175627i
$243$		0			0
$244$	−119.223	+	94.2856i	−0.488621	+	0.386416i
$245$	138.526	+	159.815i	0.565411	+	0.652305i
$246$		0			0
$247$	197.799			0.800806
$248$	197.799	−	310.567i	0.797577	−	1.25229i
$249$		0			0
$250$	−196.799	−	154.176i	−0.787196	−	0.616703i
$251$		−	141.676i		−	0.564445i	−0.959349	−	0.282223i	$-0.908928\pi$
$251$		−	141.676i		−	0.564445i	0.959349	−	0.282223i	$-0.0910716\pi$
$252$		0			0
$253$		−	16.6191i		−	0.0656883i
$254$	126.124	+	362.810i	0.496550	+	1.42838i
$255$		0			0
$256$	−228.808	−	114.817i	−0.893780	−	0.448505i
$257$		−	41.7549i		−	0.162470i	−0.996695	−	0.0812352i	$-0.974113\pi$
$257$		−	41.7549i		−	0.162470i	0.996695	−	0.0812352i	$-0.0258865\pi$
$258$		0			0
$259$			216.606i			0.836318i
$260$	28.1724	−	148.480i	0.108356	−	0.571075i
$261$		0			0
$262$	−80.1505	+	27.8628i	−0.305918	+	0.106346i
$263$	−203.283			−0.772939			−0.386469	−	0.922302i	$-0.626306\pi$
$263$	−203.283			−0.772939			−0.386469	+	0.922302i	$0.626306\pi$
$264$		0			0
$265$	−85.6495	+	74.2401i	−0.323206	+	0.280151i
$266$	−472.495	+	164.254i	−1.77630	+	0.617495i
$267$		0			0
$268$	−93.6458	+	74.0580i	−0.349425	+	0.276336i
$269$	244.048			0.907242			0.453621	−	0.891195i	$-0.350132\pi$
$269$	244.048			0.907242			0.453621	+	0.891195i	$0.350132\pi$
$270$		0			0
$271$		−	466.585i		−	1.72172i	−0.508845	−	0.860858i	$-0.669927\pi$
$271$		−	466.585i		−	1.72172i	0.508845	−	0.860858i	$-0.330073\pi$
$272$	267.641	+	63.3855i	0.983973	+	0.233035i
$273$		0			0
$274$	390.770	−	135.844i	1.42617	−	0.495780i
$275$	−245.606	−	35.2314i	−0.893113	−	0.128114i
$276$		0			0
$277$			494.181i			1.78405i	0.451990	+	0.892023i	$0.350714\pi$
$277$			494.181i			1.78405i	−0.451990	+	0.892023i	$0.649286\pi$
$278$	−86.9478	+	30.2257i	−0.312762	+	0.108726i
$279$		0			0
$280$	56.0013	+	378.077i	0.200005	+	1.35028i
$281$	43.4020			0.154455			0.0772277	−	0.997013i	$-0.475393\pi$
$281$	43.4020			0.154455			0.0772277	+	0.997013i	$0.475393\pi$
$282$		0			0
$283$	310.785			1.09818			0.549090	−	0.835763i	$-0.314974\pi$
$283$	310.785			1.09818			0.549090	+	0.835763i	$0.314974\pi$
$284$	−17.8555	−	22.5781i	−0.0628714	−	0.0795003i
$285$		0			0
$286$	−49.2508	−	141.676i	−0.172206	−	0.495370i
$287$	−738.596			−2.57351
$288$		0			0
$289$	−6.50497			−0.0225085
$290$	−1.74785	+	3.03806i	−0.00602707	+	0.0104761i
$291$		0			0
$292$	85.3049	+	107.867i	0.292140	+	0.369409i
$293$			245.207i			0.836886i	0.908243	+	0.418443i	$0.137424\pi$
$293$			245.207i			0.836886i	−0.908243	+	0.418443i	$0.862576\pi$
$294$		0			0
$295$	−358.100	+	310.397i	−1.21390	+	1.05219i
$296$	−97.4228	+	152.965i	−0.329131	+	0.516773i
$297$		0			0
$298$	−7.65037	−	22.0072i	−0.0256724	−	0.0738496i
$299$		−	12.6533i		−	0.0423187i
$300$		0			0
$301$	−399.395			−1.32689
$302$	−236.940	+	82.3676i	−0.784569	+	0.272740i
$303$		0			0
$304$	−407.547	−	96.5195i	−1.34061	−	0.317498i
$305$	124.447	+	143.572i	0.408022	+	0.470729i
$306$		0			0
$307$	−337.514			−1.09939			−0.549697	−	0.835364i	$-0.685257\pi$
$307$	−337.514			−1.09939			−0.549697	+	0.835364i	$0.685257\pi$
$308$	235.297	+	297.531i	0.763952	+	0.966011i
$309$		0			0
$310$	−398.946	−	229.521i	−1.28692	−	0.740390i
$311$		−	427.756i		−	1.37542i	−0.725986	−	0.687710i	$-0.758616\pi$
$311$		−	427.756i		−	1.37542i	0.725986	−	0.687710i	$-0.241384\pi$
$312$		0			0
$313$			83.8739i			0.267968i	0.990984	+	0.133984i	$0.0427770\pi$
$313$			83.8739i			0.267968i	−0.990984	+	0.133984i	$0.957223\pi$
$314$	372.571	−	129.517i	1.18653	−	0.412475i
$315$		0			0
$316$	114.199	+	144.404i	0.361390	+	0.456975i
$317$		−	112.204i		−	0.353957i	−0.984215	−	0.176978i	$-0.943368\pi$
$317$		−	112.204i		−	0.353957i	0.984215	−	0.176978i	$-0.0566323\pi$
$318$		0			0
$319$			3.47861i			0.0109047i
$320$	−130.500	+	292.181i	−0.407812	+	0.913066i
$321$		0			0
$322$	10.5074	+	30.2257i	0.0326317	+	0.0938687i
$323$	449.976			1.39312
$324$		0			0
$325$	−186.997	−	26.8241i	−0.575374	−	0.0825356i
$326$	12.0964	+	34.7966i	0.0371054	+	0.106738i
$327$		0			0
$328$	−521.588	−	332.197i	−1.59021	−	1.01280i
$329$	−134.598			−0.409113
$330$		0			0
$331$			132.621i			0.400666i	0.979728	+	0.200333i	$0.0642025\pi$
$331$			132.621i			0.400666i	−0.979728	+	0.200333i	$0.935798\pi$
$332$	−75.7182	+	59.8803i	−0.228067	+	0.180362i
$333$		0			0
$334$	61.0033	+	175.483i	0.182645	+	0.525398i
$335$	97.7487	+	112.771i	0.291787	+	0.336630i
$336$		0			0
$337$			20.7739i			0.0616437i	0.999525	+	0.0308219i	$0.00981246\pi$
$337$			20.7739i			0.0616437i	−0.999525	+	0.0308219i	$0.990188\pi$
$338$	73.4863	+	211.392i	0.217415	+	0.625420i
$339$		0			0
$340$	64.0900	−	337.779i	0.188500	−	0.993467i
$341$	−456.797			−1.33958
$342$		0			0
$343$	64.0283			0.186672
$344$	−282.048	−	179.636i	−0.819907	−	0.522196i
$345$		0			0
$346$	−221.973	+	77.1645i	−0.641539	+	0.223019i
$347$	8.89616			0.0256374			0.0128187	−	0.999918i	$-0.495920\pi$
$347$	8.89616			0.0256374			0.0128187	+	0.999918i	$0.495920\pi$
$348$		0			0
$349$	19.4020			0.0555931			0.0277965	−	0.999614i	$-0.491151\pi$
$349$	19.4020			0.0555931			0.0277965	+	0.999614i	$0.491151\pi$
$350$	468.966	−	91.2071i	1.33990	−	0.260592i
$351$		0			0
$352$	32.3436	+	315.942i	0.0918853	+	0.897564i
$353$		−	80.2902i		−	0.227451i	−0.993512	−	0.113726i	$-0.963722\pi$
$353$		−	80.2902i		−	0.227451i	0.993512	−	0.113726i	$-0.0362784\pi$
$354$		0			0
$355$	−27.1892	+	23.5673i	−0.0765892	+	0.0663867i
$356$	314.371	−	248.615i	0.883065	−	0.698356i
$357$		0			0
$358$	438.251	−	152.349i	1.22416	−	0.425557i
$359$			314.115i			0.874972i	0.899225	+	0.437486i	$0.144131\pi$
$359$			314.115i			0.874972i	−0.899225	+	0.437486i	$0.855869\pi$
$360$		0			0
$361$	−324.196			−0.898050
$362$	−143.227	−	412.008i	−0.395653	−	1.13814i
$363$		0			0
$364$	179.148	+	226.531i	0.492164	+	0.622338i
$365$	129.897	−	112.593i	0.355882	−	0.308475i
$366$		0			0
$367$	476.800			1.29918			0.649592	−	0.760283i	$-0.274940\pi$
$367$	476.800			1.29918			0.649592	+	0.760283i	$0.274940\pi$
$368$	−6.17440	+	26.0709i	−0.0167783	+	0.0708450i
$369$		0			0
$370$	196.495	+	113.047i	0.531066	+	0.305532i
$371$		−	216.606i		−	0.583844i
$372$		0			0
$373$		−	86.1333i		−	0.230920i	−0.993312	−	0.115460i	$-0.963166\pi$
$373$		−	86.1333i		−	0.230920i	0.993312	−	0.115460i	$-0.0368343\pi$
$374$	−112.042	−	322.300i	−0.299576	−	0.861766i
$375$		0			0
$376$	−95.0515	−	60.5380i	−0.252797	−	0.161005i
$377$			2.64850i			0.00702521i
$378$		0			0
$379$		−	638.035i		−	1.68347i	−0.539891	−	0.841735i	$-0.681534\pi$
$379$		−	638.035i		−	1.68347i	0.539891	−	0.841735i	$-0.318466\pi$
$380$	−97.5922	+	514.348i	−0.256822	+	1.35355i
$381$		0			0
$382$	−259.201	+	90.1061i	−0.678535	+	0.235880i
$383$	216.742			0.565907			0.282953	−	0.959134i	$-0.408686\pi$
$383$	216.742			0.565907			0.282953	+	0.959134i	$0.408686\pi$
$384$		0			0
$385$	358.296	−	310.567i	0.930638	−	0.806667i
$386$	69.9518	−	24.3174i	0.181222	−	0.0629985i
$387$		0			0
$388$	327.174	+	413.708i	0.843231	+	1.06626i
$389$	−476.640			−1.22529			−0.612647	−	0.790356i	$-0.709895\pi$
$389$	−476.640			−1.22529			−0.612647	+	0.790356i	$0.709895\pi$
$390$		0			0
$391$		−	28.7852i		−	0.0736195i
$392$	−285.419	−	181.783i	−0.728111	−	0.463731i
$393$		0			0
$394$	−367.567	+	127.778i	−0.932912	+	0.324309i
$395$	173.896	−	150.731i	0.440242	−	0.381597i
$396$		0			0
$397$			43.0792i			0.108512i	0.998527	+	0.0542559i	$0.0172787\pi$
$397$			43.0792i			0.108512i	−0.998527	+	0.0542559i	$0.982721\pi$
$398$	−332.554	+	115.606i	−0.835562	+	0.290467i
$399$		0			0
$400$	372.200	+	146.517i	0.930500	+	0.366292i
$401$	168.694			0.420684			0.210342	−	0.977628i	$-0.432542\pi$
$401$	168.694			0.420684			0.210342	+	0.977628i	$0.432542\pi$
$402$		0			0
$403$	−347.791			−0.863005
$404$	92.3987	−	73.0718i	0.228710	−	0.180871i
$405$		0			0
$406$	−2.19934	−	6.32665i	−0.00541709	−	0.0155829i
$407$	224.988			0.552797
$408$		0			0
$409$	373.890			0.914157			0.457079	−	0.889426i	$-0.348896\pi$
$409$	373.890			0.914157			0.457079	+	0.889426i	$0.348896\pi$
$410$	−385.473	+	670.018i	−0.940179	+	1.63419i
$411$		0			0
$412$	451.123	−	356.762i	1.09496	−	0.865927i
$413$		−	905.630i		−	2.19281i
$414$		0			0
$415$	79.0356	+	91.1820i	0.190447	+	0.219716i
$416$	24.6254	+	240.549i	0.0591957	+	0.578242i
$417$		0			0
$418$	170.610	+	490.779i	0.408158	+	1.17411i
$419$			87.5839i			0.209031i	0.994523	+	0.104515i	$0.0333291\pi$
$419$			87.5839i			0.209031i	−0.994523	+	0.104515i	$0.966671\pi$
$420$		0			0
$421$	70.3023			0.166989			0.0834944	−	0.996508i	$-0.473392\pi$
$421$	70.3023			0.166989			0.0834944	+	0.996508i	$0.473392\pi$
$422$	39.1409	−	13.6066i	0.0927510	−	0.0322431i
$423$		0			0
$424$	97.4228	−	152.965i	0.229771	−	0.360766i
$425$	−425.402	−	61.0226i	−1.00095	−	0.143583i
$426$		0			0
$427$	−363.092			−0.850332
$428$	110.129	−	87.0935i	0.257311	−	0.203490i
$429$		0			0
$430$	−208.444	+	362.312i	−0.484754	+	0.842586i
$431$			247.370i			0.573944i	0.957939	+	0.286972i	$0.0926487\pi$
$431$			247.370i			0.573944i	−0.957939	+	0.286972i	$0.907351\pi$
$432$		0			0
$433$		−	636.247i		−	1.46939i	−0.678397	−	0.734696i	$-0.737325\pi$
$433$		−	636.247i		−	1.46939i	0.678397	−	0.734696i	$-0.262675\pi$
$434$	830.791	−	288.808i	1.91426	−	0.665457i
$435$		0			0
$436$	475.320	−	375.898i	1.09018	−	0.862151i
$437$			43.8323i			0.100303i
$438$		0			0
$439$		−	769.786i		−	1.75350i	−0.480947	−	0.876750i	$-0.659707\pi$
$439$		−	769.786i		−	1.75350i	0.480947	−	0.876750i	$-0.340293\pi$
$440$	392.707	−	58.1683i	0.892517	−	0.132201i
$441$		0			0
$442$	−85.3049	−	245.390i	−0.192998	−	0.555180i
$443$	−612.214			−1.38197			−0.690986	−	0.722868i	$-0.742823\pi$
$443$	−612.214			−1.38197			−0.690986	+	0.722868i	$0.742823\pi$
$444$		0			0
$445$	−328.145	−	378.575i	−0.737403	−	0.850730i
$446$	−63.7185	−	183.294i	−0.142867	−	0.410972i
$447$		0			0
$448$	−258.578	−	554.165i	−0.577182	−	1.23697i
$449$	−175.897			−0.391753			−0.195876	−	0.980629i	$-0.562755\pi$
$449$	−175.897			−0.391753			−0.195876	+	0.980629i	$0.562755\pi$
$450$		0			0
$451$			767.177i			1.70106i
$452$	80.1505	+	101.350i	0.177324	+	0.224225i
$453$		0			0
$454$	267.450	+	769.351i	0.589097	+	1.69461i
$455$	272.795	−	236.456i	0.599550	−	0.519683i
$456$		0			0
$457$			365.357i			0.799469i	0.916631	+	0.399734i	$0.130898\pi$
$457$			365.357i			0.799469i	−0.916631	+	0.399734i	$0.869102\pi$
$458$	−5.18607	−	14.9183i	−0.0113233	−	0.0325728i
$459$		0			0
$460$	32.9031	+	6.24302i	0.0715285	+	0.0135718i
$461$	−308.350			−0.668873			−0.334437	−	0.942418i	$-0.608546\pi$
$461$	−308.350			−0.668873			−0.334437	+	0.942418i	$0.608546\pi$
$462$		0			0
$463$	92.6302			0.200065			0.100033	−	0.994984i	$-0.468105\pi$
$463$	92.6302			0.200065			0.100033	+	0.994984i	$0.468105\pi$
$464$	1.29238	−	5.45700i	0.00278531	−	0.0117608i
$465$		0			0
$466$	53.1752	−	18.4854i	0.114110	−	0.0396681i
$467$	606.103			1.29786			0.648932	−	0.760846i	$-0.275216\pi$
$467$	606.103			1.29786			0.648932	+	0.760846i	$0.275216\pi$
$468$		0			0
$469$	−285.196			−0.608094
$470$	−70.2467	+	122.101i	−0.149461	+	0.259789i
$471$		0			0
$472$	407.324	−	639.545i	0.862975	−	1.35497i
$473$			414.851i			0.877063i
$474$		0			0
$475$	647.776	+	92.9214i	1.36374	+	0.195624i
$476$	407.547	+	515.339i	0.856190	+	1.08265i
$477$		0			0
$478$	−559.185	+	194.390i	−1.16984	+	0.406673i
$479$		−	138.947i		−	0.290078i	−0.989426	−	0.145039i	$-0.953669\pi$
$479$		−	138.947i		−	0.290078i	0.989426	−	0.145039i	$-0.0463307\pi$
$480$		0			0
$481$	171.299			0.356131
$482$	305.893	+	879.935i	0.634632	+	1.82559i
$483$		0			0
$484$	−70.5876	+	55.8229i	−0.145842	+	0.115337i
$485$	498.199	−	431.834i	1.02722	−	0.890379i
$486$		0			0
$487$	201.243			0.413230			0.206615	−	0.978422i	$-0.433755\pi$
$487$	201.243			0.413230			0.206615	+	0.978422i	$0.433755\pi$
$488$	−256.411	−	163.307i	−0.525433	−	0.334646i
$489$		0			0
$490$	−210.936	+	366.642i	−0.430481	+	0.748250i
$491$			347.368i			0.707470i	0.935346	+	0.353735i	$0.115089\pi$
$491$			347.368i			0.707470i	−0.935346	+	0.353735i	$0.884911\pi$
$492$		0			0
$493$			6.02513i			0.0122214i
$494$	129.897	+	373.664i	0.262949	+	0.756404i
$495$		0			0
$496$	716.591	+	169.711i	1.44474	+	0.342159i
$497$		−	68.7610i		−	0.138352i
$498$		0			0
$499$			672.277i			1.34725i	0.739074	+	0.673625i	$0.235264\pi$
$499$			672.277i			1.34725i	−0.739074	+	0.673625i	$0.764736\pi$
$500$	162.015	−	473.024i	0.324029	−	0.946047i
$501$		0			0
$502$	267.641	−	93.0401i	0.533149	−	0.185339i
$503$	436.350			0.867496			0.433748	−	0.901034i	$-0.357191\pi$
$503$	436.350			0.867496			0.433748	+	0.901034i	$0.357191\pi$
$504$		0			0
$505$	−96.4469	−	111.269i	−0.190984	−	0.220335i
$506$	31.3954	−	10.9140i	0.0620462	−	0.0215692i
$507$		0			0
$508$	−602.559	+	476.523i	−1.18614	+	0.938037i
$509$	109.547			0.215219			0.107610	−	0.994193i	$-0.465680\pi$
$509$	109.547			0.215219			0.107610	+	0.994193i	$0.465680\pi$
$510$		0			0
$511$			328.508i			0.642872i
$512$	66.6415	−	507.644i	0.130159	−	0.991493i
$513$		0			0
$514$	78.8796	−	27.4210i	0.153462	−	0.0533482i
$515$	−470.888	−	543.255i	−0.914345	−	1.05486i
$516$		0			0
$517$			139.807i			0.270419i
$518$	−409.193	+	142.248i	−0.789947	+	0.274610i
$519$		0			0
$520$	298.995	−	44.2875i	0.574991	−	0.0851683i
$521$	743.100			1.42629			0.713147	−	0.701014i	$-0.247269\pi$
$521$	743.100			1.42629			0.713147	+	0.701014i	$0.247269\pi$
$522$		0			0
$523$	366.211			0.700212			0.350106	−	0.936710i	$-0.386146\pi$
$523$	366.211			0.700212			0.350106	+	0.936710i	$0.386146\pi$
$524$	−105.272	−	133.115i	−0.200900	−	0.254037i
$525$		0			0
$526$	−133.498	−	384.023i	−0.253799	−	0.730083i
$527$	−791.196			−1.50132
$528$		0			0
$529$	−526.196			−0.994699
$530$	−196.495	−	113.047i	−0.370744	−	0.213296i
$531$		0			0
$532$	−620.586	−	784.727i	−1.16652	−	1.47505i
$533$			584.105i			1.09588i
$534$		0			0
$535$	−114.954	−	132.621i	−0.214867	−	0.247889i
$536$	−201.402	−	128.272i	−0.375750	−	0.239314i
$537$		0			0
$538$	160.269	+	461.033i	0.297898	+	0.856939i
$539$			419.809i			0.778867i
$540$		0			0
$541$	170.688			0.315504			0.157752	−	0.987479i	$-0.449575\pi$
$541$	170.688			0.315504			0.157752	+	0.987479i	$0.449575\pi$
$542$	881.430	−	306.412i	1.62625	−	0.565336i
$543$		0			0
$544$	56.0208	+	547.228i	0.102979	+	1.00593i
$545$	−496.145	−	572.393i	−0.910357	−	1.05026i
$546$		0			0
$547$	−507.600			−0.927971			−0.463986	−	0.885843i	$-0.653581\pi$
$547$	−507.600			−0.927971			−0.463986	+	0.885843i	$0.653581\pi$
$548$	513.247	+	648.997i	0.936581	+	1.18430i
$549$		0			0
$550$	−94.7365	−	487.113i	−0.172248	−	0.885660i
$551$		−	9.17469i		−	0.0166510i
$552$		0			0
$553$			439.779i			0.795261i
$554$	−933.561	+	324.534i	−1.68513	+	0.585802i
$555$		0			0
$556$	−114.199	−	144.404i	−0.205394	−	0.259720i
$557$			788.492i			1.41561i	0.706410	+	0.707803i	$0.250314\pi$
$557$			788.492i			1.41561i	−0.706410	+	0.707803i	$0.749686\pi$
$558$		0			0
$559$			315.854i			0.565035i
$560$	−677.452	+	354.080i	−1.20974	+	0.632286i
$561$		0			0
$562$	28.5026	+	81.9910i	0.0507164	+	0.145892i
$563$	−936.102			−1.66270			−0.831351	−	0.555747i	$-0.812432\pi$
$563$	−936.102			−1.66270			−0.831351	+	0.555747i	$0.812432\pi$
$564$		0			0
$565$	122.048	−	105.790i	0.216014	−	0.187239i
$566$	204.096	+	587.107i	0.360594	+	1.03729i
$567$		0			0
$568$	30.9266	−	48.5582i	0.0544482	−	0.0854898i
$569$	95.4983			0.167835			0.0839177	−	0.996473i	$-0.473257\pi$
$569$	95.4983			0.167835			0.0839177	+	0.996473i	$0.473257\pi$
$570$		0			0
$571$		−	889.123i		−	1.55713i	−0.627562	−	0.778566i	$-0.715947\pi$
$571$		−	889.123i		−	1.55713i	0.627562	−	0.778566i	$-0.284053\pi$
$572$	235.297	−	186.080i	0.411359	−	0.325315i
$573$		0			0
$574$	−485.045	−	1395.29i	−0.845026	−	2.43081i
$575$	5.94422	−	41.4385i	0.0103378	−	0.0720670i
$576$		0			0
$577$			522.147i			0.904934i	0.891781	+	0.452467i	$0.149456\pi$
$577$			522.147i			0.904934i	−0.891781	+	0.452467i	$0.850544\pi$
$578$	−4.27189	−	12.2886i	−0.00739081	−	0.0212605i
$579$		0			0
$580$	−6.88706	−	1.30675i	−0.0118742	−	0.00225301i
$581$	−230.598			−0.396898
$582$		0			0
$583$	−224.988			−0.385915
$584$	−147.752	+	231.988i	−0.253001	+	0.397240i
$585$		0			0
$586$	−463.223	+	161.031i	−0.790484	+	0.274796i
$587$	95.8440			0.163278			0.0816388	−	0.996662i	$-0.473985\pi$
$587$	95.8440			0.163278			0.0816388	+	0.996662i	$0.473985\pi$
$588$		0			0
$589$	1204.78			2.04547
$590$	−821.543	−	472.648i	−1.39245	−	0.801098i
$591$		0			0
$592$	−352.946	−	83.5883i	−0.596192	−	0.141197i
$593$		−	878.624i		−	1.48166i	−0.671693	−	0.740829i	$-0.734433\pi$
$593$		−	878.624i		−	1.48166i	0.671693	−	0.740829i	$-0.265567\pi$
$594$		0			0
$595$	620.586	−	537.918i	1.04300	−	0.904063i
$596$	36.5498	−	28.9047i	0.0613252	−	0.0484979i
$597$		0			0
$598$	23.9034	−	8.30957i	0.0399723	−	0.0138956i
$599$		−	967.652i		−	1.61545i	−0.589563	−	0.807723i	$-0.700700\pi$
$599$		−	967.652i		−	1.61545i	0.589563	−	0.807723i	$-0.299300\pi$
$600$		0			0
$601$	279.704			0.465398			0.232699	−	0.972549i	$-0.425244\pi$
$601$	279.704			0.465398			0.232699	+	0.972549i	$0.425244\pi$
$602$	−262.288	−	754.501i	−0.435694	−	1.25332i
$603$		0			0
$604$	−311.203	−	393.513i	−0.515236	−	0.651512i
$605$	73.6802	+	85.0036i	0.121785	+	0.140502i
$606$		0			0
$607$	−747.564			−1.23157			−0.615786	−	0.787914i	$-0.711161\pi$
$607$	−747.564			−1.23157			−0.615786	+	0.787914i	$0.711161\pi$
$608$	−85.3049	−	833.285i	−0.140304	−	1.37053i
$609$		0			0
$610$	−189.498	+	329.379i	−0.310652	+	0.539966i
$611$			106.444i			0.174213i
$612$		0			0
$613$			457.152i			0.745761i	0.927879	+	0.372881i	$0.121630\pi$
$613$			457.152i			0.745761i	−0.927879	+	0.372881i	$0.878370\pi$
$614$	−221.650	−	637.600i	−0.360993	−	1.03844i
$615$		0			0
$616$	−407.547	+	639.894i	−0.661601	+	1.03879i
$617$			764.888i			1.23969i	0.784725	+	0.619844i	$0.212804\pi$
$617$			764.888i			1.23969i	−0.784725	+	0.619844i	$0.787196\pi$
$618$		0			0
$619$		−	365.359i		−	0.590240i	−0.955460	−	0.295120i	$-0.904640\pi$
$619$		−	365.359i		−	0.590240i	0.955460	−	0.295120i	$-0.0953597\pi$
$620$	171.597	−	904.382i	0.276769	−	1.45868i
$621$		0			0
$622$	808.077	−	280.912i	1.29916	−	0.451627i
$623$	957.410			1.53677
$624$		0			0
$625$	−599.797	−	175.693i	−0.959676	−	0.281109i
$626$	−158.447	+	55.0810i	−0.253110	+	0.0879888i
$627$		0			0
$628$	489.343	+	618.771i	0.779209	+	0.985304i
$629$	389.691			0.619541
$630$		0			0
$631$			62.1578i			0.0985067i	0.998786	+	0.0492534i	$0.0156842\pi$
$631$			62.1578i			0.0985067i	−0.998786	+	0.0492534i	$0.984316\pi$
$632$	−197.799	+	310.567i	−0.312973	+	0.491403i
$633$		0			0
$634$	211.966	−	73.6859i	0.334331	−	0.116224i
$635$	628.959	+	725.619i	0.990486	+	1.14271i
$636$		0			0
$637$			319.630i			0.501773i
$638$	−6.57147	+	2.28444i	−0.0103001	+	0.00358063i
$639$		0			0
$640$	−637.662	−	54.6495i	−0.996348	−	0.0853899i
$641$	1111.69			1.73431			0.867154	−	0.498041i	$-0.165947\pi$
$641$	1111.69			1.73431			0.867154	+	0.498041i	$0.165947\pi$
$642$		0			0
$643$	−468.983			−0.729367			−0.364683	−	0.931132i	$-0.618823\pi$
$643$	−468.983			−0.729367			−0.364683	+	0.931132i	$0.618823\pi$
$644$	−50.1993	+	39.6992i	−0.0779493	+	0.0616447i
$645$		0			0
$646$	295.505	+	850.054i	0.457438	+	1.31587i
$647$	−96.7647			−0.149559			−0.0747795	−	0.997200i	$-0.523825\pi$
$647$	−96.7647			−0.149559			−0.0747795	+	0.997200i	$0.523825\pi$
$648$		0			0
$649$	−940.675			−1.44942
$650$	−72.1294	−	370.873i	−0.110968	−	0.570573i
$651$		0			0
$652$	−57.7907	+	45.7027i	−0.0886360	+	0.0700961i
$653$			920.353i			1.40942i	0.709494	+	0.704712i	$0.248924\pi$
$653$			920.353i			1.40942i	−0.709494	+	0.704712i	$0.751076\pi$
$654$		0			0
$655$	−160.301	+	138.947i	−0.244734	+	0.212133i
$656$	285.024	−	1203.49i	0.434488	−	1.83459i
$657$		0			0
$658$	−88.3921	−	254.270i	−0.134335	−	0.386429i
$659$			591.020i			0.896844i	0.893822	+	0.448422i	$0.148014\pi$
$659$			591.020i			0.896844i	−0.893822	+	0.448422i	$0.851986\pi$
$660$		0			0
$661$	−306.193			−0.463226			−0.231613	−	0.972808i	$-0.574400\pi$
$661$	−306.193			−0.463226			−0.231613	+	0.972808i	$0.574400\pi$
$662$	−250.535	+	87.0935i	−0.378451	+	0.131561i
$663$		0			0
$664$	−162.846	−	103.716i	−0.245249	−	0.156198i
$665$	−944.990	+	819.107i	−1.42104	+	1.23174i
$666$		0			0
$667$	−0.586909			−0.000879924
$668$	−291.445	+	230.484i	−0.436295	+	0.345035i
$669$		0			0
$670$	−148.844	+	258.716i	−0.222155	+	0.386143i
$671$			377.142i			0.562060i
$672$		0			0
$673$		−	556.892i		−	0.827476i	−0.910396	−	0.413738i	$-0.864223\pi$
$673$		−	556.892i		−	0.827476i	0.910396	−	0.413738i	$-0.135777\pi$
$674$	−39.2442	+	13.6425i	−0.0582258	+	0.0202411i
$675$		0			0
$676$	−351.083	+	277.647i	−0.519353	+	0.410721i
$677$			58.1920i			0.0859557i	0.999076	+	0.0429779i	$0.0136845\pi$
$677$			58.1920i			0.0859557i	−0.999076	+	0.0429779i	$0.986316\pi$
$678$		0			0
$679$			1259.94i			1.85558i
$680$	680.189	−	100.750i	1.00028	−	0.148162i
$681$		0			0
$682$	−299.984	−	862.940i	−0.439860	−	1.26531i
$683$	−357.274			−0.523096			−0.261548	−	0.965191i	$-0.584233\pi$
$683$	−357.274			−0.523096			−0.261548	+	0.965191i	$0.584233\pi$
$684$		0			0
$685$	781.540	−	677.430i	1.14093	−	0.988949i
$686$	42.0482	+	120.956i	0.0612947	+	0.176321i
$687$		0			0
$688$	154.127	−	650.788i	0.224021	−	0.945913i
$689$	−171.299			−0.248620
$690$		0			0
$691$		−	614.707i		−	0.889590i	−0.895632	−	0.444795i	$-0.853276\pi$
$691$		−	614.707i		−	0.889590i	0.895632	−	0.444795i	$-0.146724\pi$
$692$	−291.544	−	368.655i	−0.421307	−	0.532739i
$693$		0			0
$694$	5.84222	+	16.8058i	0.00841818	+	0.0242159i
$695$	−173.896	+	150.731i	−0.250210	+	0.216879i
$696$		0			0
$697$			1328.79i			1.90644i
$698$	12.7415	+	36.6524i	0.0182543	+	0.0525107i
$699$		0			0
$700$	480.275	+	826.030i	0.686108	+	1.18004i
$701$	886.028			1.26395			0.631975	−	0.774989i	$-0.282245\pi$
$701$	886.028			1.26395			0.631975	+	0.774989i	$0.282245\pi$
$702$		0			0
$703$	−593.397			−0.844093
$704$	−575.609	+	268.584i	−0.817626	+	0.381511i
$705$		0			0
$706$	151.677	−	52.7276i	0.214840	−	0.0746849i
$707$	281.398			0.398017
$708$		0			0
$709$	−760.887			−1.07318			−0.536592	−	0.843842i	$-0.680288\pi$
$709$	−760.887			−1.07318			−0.536592	+	0.843842i	$0.680288\pi$
$710$	−62.3766	−	35.8864i	−0.0878544	−	0.0505442i
$711$		0			0
$712$	676.111	+	430.613i	0.949594	+	0.604794i
$713$		−	77.0706i		−	0.108093i
$714$		0			0
$715$	−245.606	−	283.351i	−0.343505	−	0.396296i
$716$	575.609	+	727.853i	0.803923	+	1.01655i
$717$		0			0
$718$	−593.397	+	206.283i	−0.826458	+	0.287302i
$719$		−	575.877i		−	0.800942i	−0.916309	−	0.400471i	$-0.868846\pi$
$719$		−	575.877i		−	0.800942i	0.916309	−	0.400471i	$-0.131154\pi$
$720$		0			0
$721$	1373.88			1.90553
$722$	−212.903	−	612.441i	−0.294880	−	0.848257i
$723$		0			0
$724$	684.268	−	541.141i	0.945122	−	0.747432i
$725$	−1.24421	+	8.67363i	−0.00171615	+	0.0119636i
$726$		0			0
$727$	327.332			0.450250			0.225125	−	0.974330i	$-0.427721\pi$
$727$	327.332			0.450250			0.225125	+	0.974330i	$0.427721\pi$
$728$	−310.293	+	487.195i	−0.426227	+	0.669224i
$729$		0			0
$730$	298.006	+	171.448i	0.408227	+	0.234860i
$731$			718.542i			0.982958i
$732$		0			0
$733$		−	947.567i		−	1.29272i	−0.763031	−	0.646362i	$-0.776290\pi$
$733$		−	947.567i		−	1.29272i	0.763031	−	0.646362i	$-0.223710\pi$
$734$	313.120	+	900.727i	0.426595	+	1.22715i
$735$		0			0
$736$	−53.3056	+	5.45700i	−0.0724261	+	0.00741440i
$737$			296.232i			0.401943i
$738$		0			0
$739$		−	183.234i		−	0.247948i	−0.992285	−	0.123974i	$-0.960436\pi$
$739$		−	183.234i		−	0.247948i	0.992285	−	0.123974i	$-0.0395640\pi$
$740$	−84.5173	+	445.439i	−0.114213	+	0.601944i
$741$		0			0
$742$	409.193	−	142.248i	0.551473	−	0.191709i
$743$	−183.712			−0.247258			−0.123629	−	0.992329i	$-0.539453\pi$
$743$	−183.712			−0.247258			−0.123629	+	0.992329i	$0.539453\pi$
$744$		0			0
$745$	−38.1512	−	44.0143i	−0.0512096	−	0.0590797i
$746$	162.715	−	56.5648i	0.218117	−	0.0758241i
$747$		0			0
$748$	535.281	−	423.317i	0.715617	−	0.565932i
$749$	335.395			0.447791
$750$		0			0
$751$			345.748i			0.460384i	0.973145	+	0.230192i	$0.0739354\pi$
$751$			345.748i			0.460384i	−0.973145	+	0.230192i	$0.926065\pi$
$752$	51.9414	−	219.319i	0.0690710	−	0.291647i
$753$		0			0
$754$	−5.00331	+	1.73930i	−0.00663569	+	0.00230677i
$755$	−473.880	+	410.754i	−0.627656	+	0.544045i
$756$		0			0
$757$			549.335i			0.725674i	0.931853	+	0.362837i	$0.118192\pi$
$757$			549.335i			0.725674i	−0.931853	+	0.362837i	$0.881808\pi$
$758$	1205.32	−	419.005i	1.59013	−	0.552778i
$759$		0			0
$760$	−1035.75	+	153.417i	−1.36283	+	0.201864i
$761$	−251.485			−0.330467			−0.165233	−	0.986255i	$-0.552838\pi$
$761$	−251.485			−0.330467			−0.165233	+	0.986255i	$0.552838\pi$
$762$		0			0
$763$	1447.57			1.89721
$764$	−340.440	−	430.484i	−0.445602	−	0.563461i
$765$		0			0
$766$	142.337	+	409.450i	0.185819	+	0.534529i
$767$	−716.200			−0.933768
$768$		0			0
$769$	583.691			0.759026			0.379513	−	0.925186i	$-0.376092\pi$
$769$	583.691			0.759026			0.379513	+	0.925186i	$0.376092\pi$
$770$	821.991	+	472.906i	1.06752	+	0.614164i
$771$		0			0
$772$	91.8764	+	116.177i	0.119011	+	0.150488i
$773$		−	1328.04i		−	1.71803i	−0.511951	−	0.859015i	$-0.671077\pi$
$773$		−	1328.04i		−	1.71803i	0.511951	−	0.859015i	$-0.328923\pi$
$774$		0			0
$775$	−1138.99	−	163.384i	−1.46966	−	0.210818i
$776$	−566.681	+	889.753i	−0.730259	+	1.14659i
$777$		0			0
$778$	−313.015	−	900.424i	−0.402333	−	1.15736i
$779$		−	2023.40i		−	2.59743i
$780$		0			0
$781$	−71.4219			−0.0914492
$782$	54.3784	−	18.9036i	0.0695376	−	0.0241734i
$783$		0			0
$784$	155.969	−	658.567i	0.198940	−	0.840009i
$785$	745.141	−	645.880i	0.949224	−	0.822778i
$786$		0			0
$787$	1318.83			1.67577			0.837883	−	0.545850i	$-0.183793\pi$
$787$	1318.83			1.67577			0.837883	+	0.545850i	$0.183793\pi$
$788$	−482.772	−	610.461i	−0.612654	−	0.774697i
$789$		0			0
$790$	398.946	+	229.521i	0.504995	+	0.290533i
$791$			308.658i			0.390212i
$792$		0			0
$793$			287.144i			0.362099i
$794$	−81.3812	+	28.2906i	−0.102495	+	0.0356305i
$795$		0			0
$796$	−436.784	−	552.310i	−0.548724	−	0.693857i
$797$		−	1277.40i		−	1.60276i	−0.598154	−	0.801381i	$-0.704099\pi$
$797$		−	1277.40i		−	1.60276i	0.598154	−	0.801381i	$-0.295901\pi$
$798$		0			0
$799$			242.152i			0.303069i
$800$	−32.3579	+	799.345i	−0.0404474	+	0.999182i
$801$		0			0
$802$	110.784	+	318.682i	0.138134	+	0.397359i
$803$	341.220			0.424931
$804$		0			0
$805$	52.3987	+	60.4515i	0.0650915	+	0.0750950i
$806$	−228.399	−	657.015i	−0.283373	−	0.815155i
$807$		0			0
$808$	198.720	+	126.564i	0.245940	+	0.156639i
$809$	−321.093			−0.396901			−0.198451	−	0.980111i	$-0.563591\pi$
$809$	−321.093			−0.396901			−0.198451	+	0.980111i	$0.563591\pi$
$810$		0			0
$811$			946.932i			1.16761i	0.811894	+	0.583805i	$0.198437\pi$
$811$			946.932i			1.16761i	−0.811894	+	0.583805i	$0.801563\pi$
$812$	10.5074	−	8.30957i	0.0129401	−	0.0102335i
$813$		0			0
$814$	147.752	+	425.027i	0.181514	+	0.522146i
$815$	60.3226	+	69.5931i	0.0740154	+	0.0853904i
$816$		0			0
$817$		−	1094.15i		−	1.33923i
$818$	245.538	+	706.319i	0.300169	+	0.863471i
$819$		0			0
$820$	−1518.88	−	288.192i	−1.85229	−	0.351453i
$821$	−1169.34			−1.42429			−0.712144	−	0.702033i	$-0.752276\pi$
$821$	−1169.34			−1.42429			−0.712144	+	0.702033i	$0.752276\pi$
$822$		0			0
$823$	1251.71			1.52091			0.760457	−	0.649389i	$-0.224975\pi$
$823$	1251.71			1.52091			0.760457	+	0.649389i	$0.224975\pi$
$824$	970.220	+	617.930i	1.17745	+	0.749915i
$825$		0			0
$826$	1710.83	−	594.738i	2.07123	−	0.720022i
$827$	−892.104			−1.07872			−0.539362	−	0.842074i	$-0.681334\pi$
$827$	−892.104			−1.07872			−0.539362	+	0.842074i	$0.681334\pi$
$828$		0			0
$829$	998.688			1.20469			0.602345	−	0.798236i	$-0.294233\pi$
$829$	998.688			1.20469			0.602345	+	0.798236i	$0.294233\pi$
$830$	−120.349	+	209.187i	−0.144999	+	0.252033i
$831$		0			0
$832$	−438.251	+	204.491i	−0.526743	+	0.245783i
$833$			727.131i			0.872906i
$834$		0			0
$835$	304.214	+	350.966i	0.364328	+	0.420319i
$836$	−815.093	+	644.601i	−0.974992	+	0.771054i
$837$		0			0
$838$	−165.455	+	57.5174i	−0.197441	+	0.0686365i
$839$			610.359i			0.727484i	0.931500	+	0.363742i	$0.118501\pi$
$839$			610.359i			0.727484i	−0.931500	+	0.363742i	$0.881499\pi$
$840$		0			0
$841$	−840.877			−0.999854
$842$	46.1684	+	132.809i	0.0548318	+	0.157730i
$843$		0			0
$844$	51.4086	+	65.0058i	0.0609107	+	0.0770211i
$845$	366.464	+	422.784i	0.433686	+	0.500336i
$846$		0			0
$847$	−214.973			−0.253805
$848$	352.946	+	83.5883i	0.416209	+	0.0985712i
$849$		0			0
$850$	−164.088	−	843.705i	−0.193045	−	0.992594i
$851$			37.9599i			0.0446062i
$852$		0			0
$853$		−	832.689i		−	0.976189i	−0.872791	−	0.488094i	$-0.837692\pi$
$853$		−	832.689i		−	0.976189i	0.872791	−	0.488094i	$-0.162308\pi$
$854$	−238.447	−	685.920i	−0.279212	−	0.803185i
$855$		0			0
$856$	236.852	+	150.850i	0.276696	+	0.176227i
$857$			149.415i			0.174347i	0.996193	+	0.0871735i	$0.0277834\pi$
$857$			149.415i			0.174347i	−0.996193	+	0.0871735i	$0.972217\pi$
$858$		0			0
$859$			394.144i			0.458840i	0.973327	+	0.229420i	$0.0736830\pi$
$859$			394.144i			0.458840i	−0.973327	+	0.229420i	$0.926317\pi$
$860$	−821.334	−	155.840i	−0.955040	−	0.181209i
$861$		0			0
$862$	−467.308	+	162.451i	−0.542121	+	0.188458i
$863$	1409.58			1.63335			0.816677	−	0.577095i	$-0.195814\pi$
$863$	1409.58			1.63335			0.816677	+	0.577095i	$0.195814\pi$
$864$		0			0
$865$	−443.945	+	384.807i	−0.513231	+	0.444864i
$866$	1201.94	−	417.831i	1.38792	−	0.482484i
$867$		0			0
$868$	1091.18	+	1379.79i	1.25712	+	1.58962i
$869$	456.797			0.525659
$870$		0			0
$871$			225.542i			0.258946i
$872$	1022.26	+	651.074i	1.17232	+	0.746644i
$873$		0			0
$874$	−82.8040	+	28.7852i	−0.0947414	+	0.0329350i
$875$	1004.46	−	646.221i	1.14796	−	0.738538i
$876$		0			0
$877$		−	872.780i		−	0.995189i	−0.867410	−	0.497594i	$-0.834217\pi$
$877$		−	872.780i		−	0.995189i	0.867410	−	0.497594i	$-0.165783\pi$
$878$	1454.21	−	505.528i	1.65627	−	0.575772i
$879$		0			0
$880$	367.782	+	703.667i	0.417934	+	0.799621i
$881$	−1103.38			−1.25241			−0.626206	−	0.779657i	$-0.715393\pi$
$881$	−1103.38			−1.25241			−0.626206	+	0.779657i	$0.715393\pi$
$882$		0			0
$883$	−536.884			−0.608023			−0.304011	−	0.952668i	$-0.598326\pi$
$883$	−536.884			−0.608023			−0.304011	+	0.952668i	$0.598326\pi$
$884$	407.547	−	322.300i	0.461025	−	0.364593i
$885$		0			0
$886$	−402.048	−	1156.54i	−0.453779	−	1.30535i
$887$	888.945			1.00219			0.501096	−	0.865392i	$-0.332930\pi$
$887$	888.945			1.00219			0.501096	+	0.865392i	$0.332930\pi$
$888$		0			0
$889$	−1835.08			−2.06421
$890$	499.672	−	868.515i	0.561429	−	0.975860i
$891$		0			0
$892$	304.417	−	240.742i	0.341274	−	0.269890i
$893$		−	368.734i		−	0.412916i
$894$		0			0
$895$	876.501	−	759.742i	0.979331	−	0.848874i
$896$	877.066	−	852.408i	0.978868	−	0.951348i
$897$		0			0
$898$	−115.514	−	332.288i	−0.128634	−	0.370032i
$899$			16.1319i			0.0179443i
$900$		0			0
$901$	−389.691			−0.432510
$902$	−1449.28	+	503.814i	−1.60674	+	0.558553i
$903$		0			0
$904$	−138.825	+	217.971i	−0.153567	+	0.241118i
$905$	−714.248	−	824.015i	−0.789224	−	0.910514i
$906$		0			0
$907$	−1668.40			−1.83947			−0.919734	−	0.392543i	$-0.871595\pi$
$907$	−1668.40			−1.83947			−0.919734	+	0.392543i	$0.871595\pi$
$908$	−1277.75	+	1010.48i	−1.40721	+	1.11287i
$909$		0			0
$910$	625.839	+	360.056i	0.687735	+	0.395666i
$911$		−	1498.13i		−	1.64449i	−0.569131	−	0.822247i	$-0.692720\pi$
$911$		−	1498.13i		−	1.64449i	0.569131	−	0.822247i	$-0.307280\pi$
$912$		0			0
$913$			239.521i			0.262345i
$914$	−690.199	+	239.935i	−0.755142	+	0.262510i
$915$		0			0
$916$	24.7766	−	19.5941i	0.0270487	−	0.0213909i
$917$		−	405.399i		−	0.442093i
$918$		0			0
$919$		−	1094.82i		−	1.19131i	−0.803240	−	0.595656i	$-0.796892\pi$
$919$		−	1094.82i		−	1.19131i	0.803240	−	0.595656i	$-0.203108\pi$
$920$	9.81413	+	66.2574i	0.0106675	+	0.0720189i
$921$		0			0
$922$	−202.497	−	582.507i	−0.219629	−	0.631787i
$923$	−54.3784			−0.0589148
$924$		0			0
$925$	560.990	+	80.4723i	0.606476	+	0.0869970i
$926$	60.8314	+	174.988i	0.0656926	+	0.188972i
$927$		0			0
$928$	11.1576	−	1.14222i	0.0120233	−	0.00123084i
$929$	−1145.90			−1.23348			−0.616740	−	0.787167i	$-0.711547\pi$
$929$	−1145.90			−1.23348			−0.616740	+	0.787167i	$0.711547\pi$
$930$		0			0
$931$		−	1107.23i		−	1.18929i
$932$	69.8417	+	88.3142i	0.0749374	+	0.0947578i
$933$		0			0
$934$	398.035	+	1144.99i	0.426162	+	1.22590i
$935$	−558.733	−	644.601i	−0.597576	−	0.689413i
$936$		0			0
$937$			1272.49i			1.35805i	0.734115	+	0.679025i	$0.237597\pi$
$937$			1272.49i			1.35805i	−0.734115	+	0.679025i	$0.762403\pi$
$938$	−187.292	−	538.766i	−0.199671	−	0.574378i
$939$		0			0
$940$	−276.793	−	52.5186i	−0.294461	−	0.0558709i
$941$	−707.360			−0.751711			−0.375856	−	0.926678i	$-0.622651\pi$
$941$	−707.360			−0.751711			−0.375856	+	0.926678i	$0.622651\pi$
$942$		0			0
$943$	−129.438			−0.137262
$944$	1475.66	+	349.482i	1.56320	+	0.370214i
$945$		0			0
$946$	−783.698	+	272.437i	−0.828433	+	0.287989i
$947$	284.977			0.300926			0.150463	−	0.988616i	$-0.451924\pi$
$947$	284.977			0.300926			0.150463	+	0.988616i	$0.451924\pi$
$948$		0			0
$949$	259.794			0.273756
$950$	249.864	+	1284.74i	0.263014	+	1.35236i
$951$		0			0
$952$	−705.891	+	1108.33i	−0.741482	+	1.16421i
$953$			295.247i			0.309808i	0.987930	+	0.154904i	$0.0495068\pi$
$953$			295.247i			0.309808i	−0.987930	+	0.154904i	$0.950493\pi$
$954$		0			0
$955$	−518.401	+	449.344i	−0.542828	+	0.470518i
$956$	−734.447	−	928.702i	−0.768250	−	0.971446i
$957$		0			0
$958$	262.486	−	91.2483i	0.273994	−	0.0952487i
$959$			1976.50i			2.06100i
$960$		0			0
$961$	−1157.38			−1.20435
$962$	112.494	+	323.602i	0.116938	+	0.336385i
$963$		0			0
$964$	−1461.41	+	1155.73i	−1.51598	+	1.19889i
$965$	139.904	−	121.267i	0.144978	−	0.125665i
$966$		0			0
$967$	−348.013			−0.359889			−0.179945	−	0.983677i	$-0.557592\pi$
$967$	−348.013			−0.359889			−0.179945	+	0.983677i	$0.557592\pi$
$968$	−151.811	−	96.6881i	−0.156830	−	0.0998844i
$969$		0			0
$970$	1142.95	+	657.562i	1.17830	+	0.677899i
$971$		−	798.691i		−	0.822545i	−0.911513	−	0.411272i	$-0.865085\pi$
$971$		−	798.691i		−	0.822545i	0.911513	−	0.411272i	$-0.134915\pi$
$972$		0			0
$973$		−	439.779i		−	0.451983i
$974$	132.159	+	380.170i	0.135687	+	0.390318i
$975$		0			0
$976$	140.117	−	591.634i	0.143563	−	0.606183i
$977$		−	721.834i		−	0.738827i	−0.929265	−	0.369413i	$-0.879559\pi$
$977$		−	721.834i		−	0.738827i	0.929265	−	0.369413i	$-0.120441\pi$
$978$		0			0
$979$		−	994.458i		−	1.01579i
$980$	−831.151	−	157.702i	−0.848114	−	0.160921i
$981$		0			0
$982$	−656.216	+	228.121i	−0.668244	+	0.232302i
$983$	−1717.25			−1.74695			−0.873474	−	0.486870i	$-0.838139\pi$
$983$	−1717.25			−1.74695			−0.873474	+	0.486870i	$0.838139\pi$
$984$		0			0
$985$	−735.135	+	637.207i	−0.746330	+	0.646910i
$986$	−11.3821	+	3.95677i	−0.0115437	+	0.00401296i
$987$		0			0
$988$	−620.586	+	490.779i	−0.628124	+	0.496740i
$989$	−69.9934			−0.0707719
$990$		0			0
$991$		−	342.270i		−	0.345378i	−0.984976	−	0.172689i	$-0.944754\pi$
$991$		−	342.270i		−	0.345378i	0.984976	−	0.172689i	$-0.0552456\pi$
$992$	149.992	+	1465.17i	0.151202	+	1.47699i
$993$		0			0
$994$	129.897	−	45.1562i	0.130681	−	0.0454288i
$995$	−665.108	+	576.508i	−0.668450	+	0.579405i
$996$		0			0
$997$		−	1586.05i		−	1.59082i	−0.606072	−	0.795410i	$-0.707256\pi$
$997$		−	1586.05i		−	1.59082i	0.606072	−	0.795410i	$-0.292744\pi$
$998$	−1270.00	+	441.493i	−1.27255	+	0.442377i
$999$		0			0

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

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a_p

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.f.h.19.6		8
3.2	odd	2		60.3.f.b.19.3	✓	8
4.3	odd	2	inner	180.3.f.h.19.4		8
5.2	odd	4		900.3.c.r.451.2		8
5.3	odd	4		900.3.c.r.451.7		8
5.4	even	2	inner	180.3.f.h.19.3		8
12.11	even	2		60.3.f.b.19.5	yes	8
15.2	even	4		300.3.c.f.151.7		8
15.8	even	4		300.3.c.f.151.2		8
15.14	odd	2		60.3.f.b.19.6	yes	8
20.3	even	4		900.3.c.r.451.8		8
20.7	even	4		900.3.c.r.451.1		8
20.19	odd	2	inner	180.3.f.h.19.5		8
24.5	odd	2		960.3.j.e.319.8		8
24.11	even	2		960.3.j.e.319.4		8
60.23	odd	4		300.3.c.f.151.1		8
60.47	odd	4		300.3.c.f.151.8		8
60.59	even	2		60.3.f.b.19.4	yes	8
120.29	odd	2		960.3.j.e.319.3		8
120.59	even	2		960.3.j.e.319.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.b.19.3	✓	8	3.2	odd	2
60.3.f.b.19.4	yes	8	60.59	even	2
60.3.f.b.19.5	yes	8	12.11	even	2
60.3.f.b.19.6	yes	8	15.14	odd	2
180.3.f.h.19.3		8	5.4	even	2	inner
180.3.f.h.19.4		8	4.3	odd	2	inner
180.3.f.h.19.5		8	20.19	odd	2	inner
180.3.f.h.19.6		8	1.1	even	1	trivial
300.3.c.f.151.1		8	60.23	odd	4
300.3.c.f.151.2		8	15.8	even	4
300.3.c.f.151.7		8	15.2	even	4
300.3.c.f.151.8		8	60.47	odd	4
900.3.c.r.451.1		8	20.7	even	4
900.3.c.r.451.2		8	5.2	odd	4
900.3.c.r.451.7		8	5.3	odd	4
900.3.c.r.451.8		8	20.3	even	4
960.3.j.e.319.3		8	120.29	odd	2
960.3.j.e.319.4		8	24.11	even	2
960.3.j.e.319.7		8	120.59	even	2
960.3.j.e.319.8		8	24.5	odd	2

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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

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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	180.3.f.h.19.6

Level	$180$
Weight	$3$
Character	180.19
Analytic conductor	$4.905$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$