LMFDB - Embedded newform 208.3.bd.b.193.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,3,Mod(33,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.33"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	208.bd (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,0,6,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.66758949869$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.193
Dual form			208.3.bd.b.97.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.73205 - 4.73205i) q^{3} +(4.09808 + 4.09808i) q^{5} +(2.92820 + 10.9282i) q^{7} +(-10.4282 + 18.0622i) q^{9} +(8.92820 + 2.39230i) q^{11} +(11.2583 - 6.50000i) q^{13} +(8.19615 - 30.5885i) q^{15} +(-0.866025 - 0.500000i) q^{17} +(-16.1962 + 4.33975i) q^{19} +(43.7128 - 43.7128i) q^{21} +(5.66025 - 3.26795i) q^{23} +8.58846i q^{25} +64.7846 q^{27} +(16.3301 + 28.2846i) q^{29} +(12.9282 + 12.9282i) q^{31} +(-13.0718 - 48.7846i) q^{33} +(-32.7846 + 56.7846i) q^{35} +(-6.50000 - 1.74167i) q^{37} +(-61.5167 - 35.5167i) q^{39} +(6.50704 - 24.2846i) q^{41} +(48.9282 + 28.2487i) q^{43} +(-116.756 + 31.2846i) q^{45} +(-30.3923 + 30.3923i) q^{47} +(-68.4160 + 39.5000i) q^{49} +5.46410i q^{51} +25.2872 q^{53} +(26.7846 + 46.3923i) q^{55} +(64.7846 + 64.7846i) q^{57} +(-9.96152 - 37.1769i) q^{59} +(19.3564 - 33.5263i) q^{61} +(-227.923 - 61.0718i) q^{63} +(72.7750 + 19.5000i) q^{65} +(29.6603 - 110.694i) q^{67} +(-30.9282 - 17.8564i) q^{69} +(-16.7321 + 4.48334i) q^{71} +(-23.0596 + 23.0596i) q^{73} +(40.6410 - 23.4641i) q^{75} +104.574i q^{77} +65.2820 q^{79} +(-83.1410 - 144.004i) q^{81} +(-3.60770 - 3.60770i) q^{83} +(-1.50000 - 5.59808i) q^{85} +(89.2295 - 154.550i) q^{87} +(-108.988 - 29.2032i) q^{89} +(104.000 + 104.000i) q^{91} +(25.8564 - 96.4974i) q^{93} +(-84.1577 - 48.5885i) q^{95} +(75.4186 - 20.2083i) q^{97} +(-136.315 + 136.315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 6 q^{5} - 16 q^{7} - 14 q^{9} + 8 q^{11} + 12 q^{15} - 44 q^{19} + 64 q^{21} - 12 q^{23} + 176 q^{27} + 48 q^{29} + 24 q^{31} - 80 q^{33} - 48 q^{35} - 26 q^{37} - 156 q^{39} - 116 q^{41}+ \cdots - 88 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 6 * q^5 - 16 * q^7 - 14 * q^9 + 8 * q^11 + 12 * q^15 - 44 * q^19 + 64 * q^21 - 12 * q^23 + 176 * q^27 + 48 * q^29 + 24 * q^31 - 80 * q^33 - 48 * q^35 - 26 * q^37 - 156 * q^39 - 116 * q^41 + 168 * q^43 - 228 * q^45 - 80 * q^47 + 212 * q^53 + 24 * q^55 + 176 * q^57 + 168 * q^59 + 22 * q^61 - 496 * q^63 + 156 * q^65 + 84 * q^67 - 96 * q^69 - 60 * q^71 + 126 * q^73 + 24 * q^75 - 16 * q^79 - 194 * q^81 - 56 * q^83 - 6 * q^85 + 156 * q^87 - 190 * q^89 + 416 * q^91 + 48 * q^93 - 108 * q^95 + 222 * q^97 - 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.73205	−	4.73205i	−0.910684	−	1.57735i	−0.813101	−	0.582123i	$-0.802222\pi$
$3$	−2.73205	−	4.73205i	−0.910684	−	1.57735i	−0.0975828	−	0.995227i	$-0.531111\pi$
$4$		0			0
$5$	4.09808	+	4.09808i	0.819615	+	0.819615i	0.986052	−	0.166437i	$-0.0532262\pi$
$5$	4.09808	+	4.09808i	0.819615	+	0.819615i	−0.166437	+	0.986052i	$0.553226\pi$
$6$		0			0
$7$	2.92820	+	10.9282i	0.418315	+	1.56117i	0.778102	+	0.628138i	$0.216183\pi$
$7$	2.92820	+	10.9282i	0.418315	+	1.56117i	−0.359788	+	0.933034i	$0.617151\pi$
$8$		0			0
$9$	−10.4282	+	18.0622i	−1.15869	+	2.00691i
$10$		0			0
$11$	8.92820	+	2.39230i	0.811655	+	0.217482i	0.640695	−	0.767796i	$-0.278646\pi$
$11$	8.92820	+	2.39230i	0.811655	+	0.217482i	0.170960	+	0.985278i	$0.445313\pi$
$12$		0			0
$13$	11.2583	−	6.50000i	0.866025	−	0.500000i
$13$	11.2583	−	6.50000i	0.866025	−	0.500000i
$14$		0			0
$15$	8.19615	−	30.5885i	0.546410	−	2.03923i
$16$		0			0
$17$	−0.866025	−	0.500000i	−0.0509427	−	0.0294118i	0.474312	−	0.880357i	$-0.342697\pi$
$17$	−0.866025	−	0.500000i	−0.0509427	−	0.0294118i	−0.525255	+	0.850945i	$0.676030\pi$
$18$		0			0
$19$	−16.1962	+	4.33975i	−0.852429	+	0.228408i	−0.658475	−	0.752603i	$-0.728798\pi$
$19$	−16.1962	+	4.33975i	−0.852429	+	0.228408i	−0.193954	+	0.981011i	$0.562131\pi$
$20$		0			0
$21$	43.7128	−	43.7128i	2.08156	−	2.08156i
$22$		0			0
$23$	5.66025	−	3.26795i	0.246098	−	0.142085i	−0.371878	−	0.928282i	$-0.621286\pi$
$23$	5.66025	−	3.26795i	0.246098	−	0.142085i	0.617976	+	0.786197i	$0.287953\pi$
$24$		0			0
$25$			8.58846i			0.343538i
$26$		0			0
$27$	64.7846			2.39943
$28$		0			0
$29$	16.3301	+	28.2846i	0.563108	+	0.975331i	0.997223	+	0.0744740i	$0.0237278\pi$
$29$	16.3301	+	28.2846i	0.563108	+	0.975331i	−0.434115	+	0.900857i	$0.642939\pi$
$30$		0			0
$31$	12.9282	+	12.9282i	0.417039	+	0.417039i	0.884182	−	0.467143i	$-0.154717\pi$
$31$	12.9282	+	12.9282i	0.417039	+	0.417039i	−0.467143	+	0.884182i	$0.654717\pi$
$32$		0			0
$33$	−13.0718	−	48.7846i	−0.396115	−	1.47832i
$34$		0			0
$35$	−32.7846	+	56.7846i	−0.936703	+	1.62242i
$36$		0			0
$37$	−6.50000	−	1.74167i	−0.175676	−	0.0470722i	0.169909	−	0.985460i	$-0.445653\pi$
$37$	−6.50000	−	1.74167i	−0.175676	−	0.0470722i	−0.345585	+	0.938388i	$0.612319\pi$
$38$		0			0
$39$	−61.5167	−	35.5167i	−1.57735	−	0.910684i
$40$		0			0
$41$	6.50704	−	24.2846i	0.158708	−	0.592308i	−0.840051	−	0.542508i	$-0.817475\pi$
$41$	6.50704	−	24.2846i	0.158708	−	0.592308i	0.998759	−	0.0497999i	$-0.0158584\pi$
$42$		0			0
$43$	48.9282	+	28.2487i	1.13787	+	0.656947i	0.945901	−	0.324455i	$-0.105181\pi$
$43$	48.9282	+	28.2487i	1.13787	+	0.656947i	0.191964	+	0.981402i	$0.438514\pi$
$44$		0			0
$45$	−116.756	+	31.2846i	−2.59457	+	0.695214i
$46$		0			0
$47$	−30.3923	+	30.3923i	−0.646645	+	0.646645i	−0.952181	−	0.305536i	$-0.901164\pi$
$47$	−30.3923	+	30.3923i	−0.646645	+	0.646645i	0.305536	+	0.952181i	$0.401164\pi$
$48$		0			0
$49$	−68.4160	+	39.5000i	−1.39625	+	0.806122i
$50$		0			0
$51$			5.46410i			0.107139i
$52$		0			0
$53$	25.2872			0.477117			0.238558	−	0.971128i	$-0.423325\pi$
$53$	25.2872			0.477117			0.238558	+	0.971128i	$0.423325\pi$
$54$		0			0
$55$	26.7846	+	46.3923i	0.486993	+	0.843496i
$56$		0			0
$57$	64.7846	+	64.7846i	1.13657	+	1.13657i
$58$		0			0
$59$	−9.96152	−	37.1769i	−0.168839	−	0.630117i	−0.997519	−	0.0703943i	$-0.977574\pi$
$59$	−9.96152	−	37.1769i	−0.168839	−	0.630117i	0.828680	−	0.559723i	$-0.189092\pi$
$60$		0			0
$61$	19.3564	−	33.5263i	0.317318	−	0.549611i	−0.662609	−	0.748965i	$-0.730551\pi$
$61$	19.3564	−	33.5263i	0.317318	−	0.549611i	0.979928	+	0.199354i	$0.0638844\pi$
$62$		0			0
$63$	−227.923	−	61.0718i	−3.61783	−	0.969394i
$64$		0			0
$65$	72.7750	+	19.5000i	1.11962	+	0.300000i
$66$		0			0
$67$	29.6603	−	110.694i	0.442690	−	1.65214i	−0.279273	−	0.960212i	$-0.590093\pi$
$67$	29.6603	−	110.694i	0.442690	−	1.65214i	0.721963	−	0.691931i	$-0.243240\pi$
$68$		0			0
$69$	−30.9282	−	17.8564i	−0.448235	−	0.258788i
$70$		0			0
$71$	−16.7321	+	4.48334i	−0.235663	+	0.0631456i	−0.374717	−	0.927139i	$-0.622260\pi$
$71$	−16.7321	+	4.48334i	−0.235663	+	0.0631456i	0.139055	+	0.990285i	$0.455594\pi$
$72$		0			0
$73$	−23.0596	+	23.0596i	−0.315885	+	0.315885i	−0.847184	−	0.531299i	$-0.821704\pi$
$73$	−23.0596	+	23.0596i	−0.315885	+	0.315885i	0.531299	+	0.847184i	$0.321704\pi$
$74$		0			0
$75$	40.6410	−	23.4641i	0.541880	−	0.312855i
$76$		0			0
$77$			104.574i			1.35811i
$78$		0			0
$79$	65.2820			0.826355			0.413177	−	0.910651i	$-0.364419\pi$
$79$	65.2820			0.826355			0.413177	+	0.910651i	$0.364419\pi$
$80$		0			0
$81$	−83.1410	−	144.004i	−1.02643	−	1.77783i
$82$		0			0
$83$	−3.60770	−	3.60770i	−0.0434662	−	0.0434662i	0.685040	−	0.728506i	$-0.259785\pi$
$83$	−3.60770	−	3.60770i	−0.0434662	−	0.0434662i	−0.728506	+	0.685040i	$0.759785\pi$
$84$		0			0
$85$	−1.50000	−	5.59808i	−0.0176471	−	0.0658597i
$86$		0			0
$87$	89.2295	−	154.550i	1.02563	−	1.77644i
$88$		0			0
$89$	−108.988	−	29.2032i	−1.22458	−	0.328126i	−0.412114	−	0.911132i	$-0.635210\pi$
$89$	−108.988	−	29.2032i	−1.22458	−	0.328126i	−0.812468	+	0.583006i	$0.801876\pi$
$90$		0			0
$91$	104.000	+	104.000i	1.14286	+	1.14286i
$92$		0			0
$93$	25.8564	−	96.4974i	0.278026	−	1.03761i
$94$		0			0
$95$	−84.1577	−	48.5885i	−0.885870	−	0.511457i
$96$		0			0
$97$	75.4186	−	20.2083i	0.777511	−	0.208333i	0.151824	−	0.988408i	$-0.451485\pi$
$97$	75.4186	−	20.2083i	0.777511	−	0.208333i	0.625687	+	0.780074i	$0.284819\pi$
$98$		0			0
$99$	−136.315	+	136.315i	−1.37692	+	1.37692i
$100$		0			0
$101$	−142.567	+	82.3109i	−1.41155	+	0.814959i	−0.995535	−	0.0943978i	$-0.969907\pi$
$101$	−142.567	+	82.3109i	−1.41155	+	0.814959i	−0.416016	+	0.909357i	$0.636574\pi$
$102$		0			0
$103$		−	40.8897i		−	0.396988i	−0.980102	−	0.198494i	$-0.936395\pi$
$103$		−	40.8897i		−	0.396988i	0.980102	−	0.198494i	$-0.0636050\pi$
$104$		0			0
$105$	358.277			3.41216
$106$		0			0
$107$	74.8372	+	129.622i	0.699413	+	1.21142i	0.968670	+	0.248350i	$0.0798884\pi$
$107$	74.8372	+	129.622i	0.699413	+	1.21142i	−0.269258	+	0.963068i	$0.586778\pi$
$108$		0			0
$109$	−82.2154	−	82.2154i	−0.754270	−	0.754270i	0.221003	−	0.975273i	$-0.429067\pi$
$109$	−82.2154	−	82.2154i	−0.754270	−	0.754270i	−0.975273	+	0.221003i	$0.929067\pi$
$110$		0			0
$111$	9.51666	+	35.5167i	0.0857357	+	0.319970i
$112$		0			0
$113$	−73.6506	+	127.567i	−0.651776	+	1.12891i	0.330916	+	0.943660i	$0.392642\pi$
$113$	−73.6506	+	127.567i	−0.651776	+	1.12891i	−0.982692	+	0.185248i	$0.940691\pi$
$114$		0			0
$115$	36.5885	+	9.80385i	0.318160	+	0.0852508i
$116$		0			0
$117$			271.133i			2.31738i
$118$		0			0
$119$	2.92820	−	10.9282i	0.0246067	−	0.0918336i
$120$		0			0
$121$	−30.7994	−	17.7820i	−0.254540	−	0.146959i
$122$		0			0
$123$	−132.694	+	35.5551i	−1.07881	+	0.289066i
$124$		0			0
$125$	67.2558	−	67.2558i	0.538046	−	0.538046i
$126$		0			0
$127$	−158.196	+	91.3346i	−1.24564	+	0.719170i	−0.970237	−	0.242159i	$-0.922144\pi$
$127$	−158.196	+	91.3346i	−1.24564	+	0.719170i	−0.275402	+	0.961329i	$0.588811\pi$
$128$		0			0
$129$		−	308.708i		−	2.39308i
$130$		0			0
$131$	−170.459			−1.30121			−0.650607	−	0.759415i	$-0.725485\pi$
$131$	−170.459			−1.30121			−0.650607	+	0.759415i	$0.725485\pi$
$132$		0			0
$133$	−94.8513	−	164.287i	−0.713167	−	1.23524i
$134$		0			0
$135$	265.492	+	265.492i	1.96661	+	1.96661i
$136$		0			0
$137$	19.1359	+	71.4160i	0.139678	+	0.521285i	0.999935	+	0.0114239i	$0.00363643\pi$
$137$	19.1359	+	71.4160i	0.139678	+	0.521285i	−0.860257	+	0.509861i	$0.829697\pi$
$138$		0			0
$139$	132.459	−	229.426i	0.952942	−	1.65054i	0.213933	−	0.976848i	$-0.431372\pi$
$139$	132.459	−	229.426i	0.952942	−	1.65054i	0.739009	−	0.673696i	$-0.235294\pi$
$140$		0			0
$141$	226.851	+	60.7846i	1.60887	+	0.431097i
$142$		0			0
$143$	116.067	−	31.1000i	0.811655	−	0.217482i
$144$		0			0
$145$	−48.9904	+	182.835i	−0.337865	+	1.26093i
$146$		0			0
$147$	373.832	+	215.832i	2.54307	+	1.46824i
$148$		0			0
$149$	−43.2846	+	11.5981i	−0.290501	+	0.0778394i	−0.401126	−	0.916023i	$-0.631381\pi$
$149$	−43.2846	+	11.5981i	−0.290501	+	0.0778394i	0.110626	+	0.993862i	$0.464715\pi$
$150$		0			0
$151$	100.431	−	100.431i	0.665105	−	0.665105i	−0.291474	−	0.956579i	$-0.594146\pi$
$151$	100.431	−	100.431i	0.665105	−	0.665105i	0.956579	+	0.291474i	$0.0941457\pi$
$152$		0			0
$153$	18.0622	−	10.4282i	0.118053	−	0.0681582i
$154$		0			0
$155$			105.962i			0.683623i
$156$		0			0
$157$	−68.3731			−0.435497			−0.217749	−	0.976005i	$-0.569871\pi$
$157$	−68.3731			−0.435497			−0.217749	+	0.976005i	$0.569871\pi$
$158$		0			0
$159$	−69.0859	−	119.660i	−0.434502	−	0.752580i
$160$		0			0
$161$	52.2872	+	52.2872i	0.324765	+	0.324765i
$162$		0			0
$163$	−63.6462	−	237.531i	−0.390467	−	1.45724i	−0.829365	−	0.558707i	$-0.811298\pi$
$163$	−63.6462	−	237.531i	−0.390467	−	1.45724i	0.438898	−	0.898537i	$-0.355369\pi$
$164$		0			0
$165$	146.354	−	253.492i	0.886993	−	1.53632i
$166$		0			0
$167$	28.2487	+	7.56922i	0.169154	+	0.0453247i	0.342402	−	0.939554i	$-0.388760\pi$
$167$	28.2487	+	7.56922i	0.169154	+	0.0453247i	−0.173248	+	0.984878i	$0.555426\pi$
$168$		0			0
$169$	84.5000	−	146.358i	0.500000	−	0.866025i
$170$		0			0
$171$	90.5115	−	337.794i	0.529307	−	1.97540i
$172$		0			0
$173$	163.426	+	94.3538i	0.944657	+	0.545398i	0.891417	−	0.453184i	$-0.149712\pi$
$173$	163.426	+	94.3538i	0.944657	+	0.545398i	0.0532398	+	0.998582i	$0.483045\pi$
$174$		0			0
$175$	−93.8564	+	25.1487i	−0.536322	+	0.143707i
$176$		0			0
$177$	−148.708	+	148.708i	−0.840156	+	0.840156i
$178$		0			0
$179$	−66.9282	+	38.6410i	−0.373901	+	0.215872i	−0.675161	−	0.737670i	$-0.735926\pi$
$179$	−66.9282	+	38.6410i	−0.373901	+	0.215872i	0.301261	+	0.953542i	$0.402593\pi$
$180$		0			0
$181$		−	240.559i		−	1.32905i	−0.747264	−	0.664527i	$-0.768633\pi$
$181$		−	240.559i		−	1.32905i	0.747264	−	0.664527i	$-0.231367\pi$
$182$		0			0
$183$	−211.531			−1.15591
$184$		0			0
$185$	−19.5000	−	33.7750i	−0.105405	−	0.182568i
$186$		0			0
$187$	−6.53590	−	6.53590i	−0.0349513	−	0.0349513i
$188$		0			0
$189$	189.703	+	707.979i	1.00372	+	3.74592i
$190$		0			0
$191$	58.6936	−	101.660i	0.307296	−	0.532253i	−0.670474	−	0.741933i	$-0.733909\pi$
$191$	58.6936	−	101.660i	0.307296	−	0.532253i	0.977770	+	0.209681i	$0.0672424\pi$
$192$		0			0
$193$	197.789	+	52.9974i	1.02481	+	0.274598i	0.731807	−	0.681512i	$-0.238677\pi$
$193$	197.789	+	52.9974i	1.02481	+	0.274598i	0.293007	+	0.956110i	$0.405344\pi$
$194$		0			0
$195$	−106.550	−	397.650i	−0.546410	−	2.03923i
$196$		0			0
$197$	89.8057	−	335.160i	0.455867	−	1.70132i	−0.229661	−	0.973271i	$-0.573762\pi$
$197$	89.8057	−	335.160i	0.455867	−	1.70132i	0.685527	−	0.728047i	$-0.259572\pi$
$198$		0			0
$199$	−99.1910	−	57.2679i	−0.498447	−	0.287779i	0.229625	−	0.973279i	$-0.426250\pi$
$199$	−99.1910	−	57.2679i	−0.498447	−	0.287779i	−0.728072	+	0.685501i	$0.759583\pi$
$200$		0			0
$201$	−604.841	+	162.067i	−3.00916	+	0.806302i
$202$		0			0
$203$	−261.282	+	261.282i	−1.28710	+	1.28710i
$204$		0			0
$205$	126.187	−	72.8538i	0.615544	−	0.355385i
$206$		0			0
$207$			136.315i			0.658528i
$208$		0			0
$209$	−154.985			−0.741553
$210$		0			0
$211$	26.0526	+	45.1244i	0.123472	+	0.213860i	0.921135	−	0.389244i	$-0.127264\pi$
$211$	26.0526	+	45.1244i	0.123472	+	0.213860i	−0.797663	+	0.603104i	$0.793930\pi$
$212$		0			0
$213$	66.9282	+	66.9282i	0.314217	+	0.314217i
$214$		0			0
$215$	84.7461	+	316.277i	0.394168	+	1.47106i
$216$		0			0
$217$	−103.426	+	179.138i	−0.476616	+	0.825523i
$218$		0			0
$219$	172.119	+	46.1192i	0.785932	+	0.210590i
$220$		0			0
$221$	−13.0000			−0.0588235
$222$		0			0
$223$	−40.6166	+	151.583i	−0.182137	+	0.679746i	0.813088	+	0.582141i	$0.197785\pi$
$223$	−40.6166	+	151.583i	−0.182137	+	0.679746i	−0.995225	+	0.0976048i	$0.968882\pi$
$224$		0			0
$225$	−155.126	−	89.5622i	−0.689450	−	0.398054i
$226$		0			0
$227$	4.73205	−	1.26795i	0.0208460	−	0.00558568i	−0.248381	−	0.968662i	$-0.579898\pi$
$227$	4.73205	−	1.26795i	0.0208460	−	0.00558568i	0.269227	+	0.963077i	$0.413232\pi$
$228$		0			0
$229$	148.359	−	148.359i	0.647856	−	0.647856i	−0.304619	−	0.952474i	$-0.598529\pi$
$229$	148.359	−	148.359i	0.647856	−	0.647856i	0.952474	+	0.304619i	$0.0985290\pi$
$230$		0			0
$231$	494.851	−	285.703i	2.14221	−	1.23681i
$232$		0			0
$233$			427.138i			1.83321i	0.399792	+	0.916606i	$0.369083\pi$
$233$			427.138i			1.83321i	−0.399792	+	0.916606i	$0.630917\pi$
$234$		0			0
$235$	−249.100			−1.06000
$236$		0			0
$237$	−178.354	−	308.918i	−0.752548	−	1.30345i
$238$		0			0
$239$	−38.2769	−	38.2769i	−0.160154	−	0.160154i	0.622481	−	0.782635i	$-0.286125\pi$
$239$	−38.2769	−	38.2769i	−0.160154	−	0.160154i	−0.782635	+	0.622481i	$0.786125\pi$
$240$		0			0
$241$	−60.0744	−	224.201i	−0.249271	−	0.930293i	−0.971188	−	0.238313i	$-0.923405\pi$
$241$	−60.0744	−	224.201i	−0.249271	−	0.930293i	0.721917	−	0.691980i	$-0.243261\pi$
$242$		0			0
$243$	−162.760	+	281.909i	−0.669795	+	1.16012i
$244$		0			0
$245$	−442.248	−	118.500i	−1.80509	−	0.483673i
$246$		0			0
$247$	−154.133	+	154.133i	−0.624021	+	0.624021i
$248$		0			0
$249$	−7.21539	+	26.9282i	−0.0289775	+	0.108145i
$250$		0			0
$251$	−408.291	−	235.727i	−1.62666	−	0.939151i	−0.985081	−	0.172092i	$-0.944947\pi$
$251$	−408.291	−	235.727i	−1.62666	−	0.939151i	−0.641576	−	0.767059i	$-0.721719\pi$
$252$		0			0
$253$	58.3538	−	15.6359i	0.230648	−	0.0618018i
$254$		0			0
$255$	−22.3923	+	22.3923i	−0.0878130	+	0.0878130i
$256$		0			0
$257$	107.495	−	62.0622i	0.418268	−	0.241487i	−0.276068	−	0.961138i	$-0.589032\pi$
$257$	107.495	−	62.0622i	0.418268	−	0.241487i	0.694336	+	0.719651i	$0.255698\pi$
$258$		0			0
$259$		−	76.1333i		−	0.293951i
$260$		0			0
$261$	−681.176			−2.60987
$262$		0			0
$263$	−53.1103	−	91.9897i	−0.201940	−	0.349771i	0.747213	−	0.664584i	$-0.231391\pi$
$263$	−53.1103	−	91.9897i	−0.201940	−	0.349771i	−0.949154	+	0.314814i	$0.898058\pi$
$264$		0			0
$265$	103.629	+	103.629i	0.391052	+	0.391052i
$266$		0			0
$267$	159.569	+	595.520i	0.597638	+	2.23041i
$268$		0			0
$269$	45.7795	−	79.2923i	0.170184	−	0.294767i	−0.768300	−	0.640090i	$-0.778897\pi$
$269$	45.7795	−	79.2923i	0.170184	−	0.294767i	0.938484	+	0.345323i	$0.112231\pi$
$270$		0			0
$271$	91.4256	+	24.4974i	0.337364	+	0.0903964i	0.423524	−	0.905885i	$-0.360793\pi$
$271$	91.4256	+	24.4974i	0.337364	+	0.0903964i	−0.0861600	+	0.996281i	$0.527460\pi$
$272$		0			0
$273$	208.000	−	776.267i	0.761905	−	2.84347i
$274$		0			0
$275$	−20.5462	+	76.6795i	−0.0747135	+	0.278835i
$276$		0			0
$277$	388.500	+	224.301i	1.40253	+	0.809749i	0.994651	−	0.103288i	$-0.0329364\pi$
$277$	388.500	+	224.301i	1.40253	+	0.809749i	0.407876	+	0.913038i	$0.366270\pi$
$278$		0			0
$279$	−368.329	+	98.6936i	−1.32018	+	0.353740i
$280$		0			0
$281$	−162.725	+	162.725i	−0.579093	+	0.579093i	−0.934653	−	0.355561i	$-0.884290\pi$
$281$	−162.725	+	162.725i	−0.579093	+	0.579093i	0.355561	+	0.934653i	$0.384290\pi$
$282$		0			0
$283$	−216.679	+	125.100i	−0.765652	+	0.442049i	−0.831321	−	0.555792i	$-0.812415\pi$
$283$	−216.679	+	125.100i	−0.765652	+	0.442049i	0.0656694	+	0.997841i	$0.479082\pi$
$284$		0			0
$285$			530.985i			1.86310i
$286$		0			0
$287$	284.441			0.991084
$288$		0			0
$289$	−144.000	−	249.415i	−0.498270	−	0.863029i
$290$		0			0
$291$	−301.674	−	301.674i	−1.03668	−	1.03668i
$292$		0			0
$293$	−91.7314	−	342.346i	−0.313076	−	1.16842i	−0.925767	−	0.378094i	$-0.876580\pi$
$293$	−91.7314	−	342.346i	−0.313076	−	1.16842i	0.612691	−	0.790323i	$-0.290087\pi$
$294$		0			0
$295$	111.531	−	193.177i	0.378070	−	0.654837i
$296$		0			0
$297$	578.410	+	154.985i	1.94751	+	0.521833i
$298$		0			0
$299$	42.4833	−	73.5833i	0.142085	−	0.246098i
$300$		0			0
$301$	−165.436	+	617.415i	−0.549621	+	2.05121i
$302$		0			0
$303$	778.999	+	449.755i	2.57095	+	1.48434i
$304$		0			0
$305$	216.717	−	58.0692i	0.710548	−	0.190391i
$306$		0			0
$307$	222.497	−	222.497i	0.724747	−	0.724747i	−0.244821	−	0.969568i	$-0.578729\pi$
$307$	222.497	−	222.497i	0.724747	−	0.724747i	0.969568	+	0.244821i	$0.0787292\pi$
$308$		0			0
$309$	−193.492	+	111.713i	−0.626189	+	0.361530i
$310$		0			0
$311$		−	70.5922i		−	0.226985i	−0.993539	−	0.113492i	$-0.963796\pi$
$311$		−	70.5922i		−	0.226985i	0.993539	−	0.113492i	$-0.0362037\pi$
$312$		0			0
$313$	550.123			1.75758			0.878791	−	0.477207i	$-0.158351\pi$
$313$	550.123			1.75758			0.878791	+	0.477207i	$0.158351\pi$
$314$		0			0
$315$	−683.769	−	1184.32i	−2.17070	−	3.75976i
$316$		0			0
$317$	−287.011	−	287.011i	−0.905397	−	0.905397i	0.0904996	−	0.995896i	$-0.471154\pi$
$317$	−287.011	−	287.011i	−0.905397	−	0.905397i	−0.995896	+	0.0904996i	$0.971154\pi$
$318$		0			0
$319$	78.1333	+	291.597i	0.244932	+	0.914098i
$320$		0			0
$321$	408.918	−	708.267i	1.27389	−	2.20644i
$322$		0			0
$323$	16.1962	+	4.33975i	0.0501429	+	0.0134357i
$324$		0			0
$325$	55.8250	+	96.6917i	0.171769	+	0.297513i
$326$		0			0
$327$	−164.431	+	613.664i	−0.502846	+	1.87665i
$328$		0			0
$329$	−421.128	−	243.138i	−1.28002	−	0.739023i
$330$		0			0
$331$	−32.6025	+	8.73582i	−0.0984971	+	0.0263922i	−0.307731	−	0.951473i	$-0.599570\pi$
$331$	−32.6025	+	8.73582i	−0.0984971	+	0.0263922i	0.209234	+	0.977866i	$0.432903\pi$
$332$		0			0
$333$	99.2417	−	99.2417i	0.298023	−	0.298023i
$334$		0			0
$335$	575.181	−	332.081i	1.71696	−	0.991286i
$336$		0			0
$337$			289.420i			0.858814i	0.903111	+	0.429407i	$0.141277\pi$
$337$			289.420i			0.858814i	−0.903111	+	0.429407i	$0.858723\pi$
$338$		0			0
$339$	804.869			2.37425
$340$		0			0
$341$	84.4974	+	146.354i	0.247793	+	0.429190i
$342$		0			0
$343$	−240.000	−	240.000i	−0.699708	−	0.699708i
$344$		0			0
$345$	−53.5692	−	199.923i	−0.155273	−	0.579487i
$346$		0			0
$347$	206.970	−	358.483i	0.596457	−	1.03309i	−0.396883	−	0.917869i	$-0.629908\pi$
$347$	206.970	−	358.483i	0.596457	−	1.03309i	0.993340	−	0.115224i	$-0.0367586\pi$
$348$		0			0
$349$	−151.538	−	40.6044i	−0.434206	−	0.116345i	0.0350940	−	0.999384i	$-0.488827\pi$
$349$	−151.538	−	40.6044i	−0.434206	−	0.116345i	−0.469300	+	0.883039i	$0.655494\pi$
$350$		0			0
$351$	729.367	−	421.100i	2.07797	−	1.19971i
$352$		0			0
$353$	−100.556	+	375.281i	−0.284862	+	1.06312i	0.664078	+	0.747663i	$0.268824\pi$
$353$	−100.556	+	375.281i	−0.284862	+	1.06312i	−0.948940	+	0.315457i	$0.897842\pi$
$354$		0			0
$355$	−86.9423	−	50.1962i	−0.244908	−	0.141398i
$356$		0			0
$357$	−59.7128	+	16.0000i	−0.167263	+	0.0448179i
$358$		0			0
$359$	−326.985	+	326.985i	−0.910820	+	0.910820i	−0.996337	−	0.0855163i	$-0.972746\pi$
$359$	−326.985	+	326.985i	−0.910820	+	0.910820i	0.0855163	+	0.996337i	$0.472746\pi$
$360$		0			0
$361$	−69.1532	+	39.9256i	−0.191560	+	0.110597i
$362$		0			0
$363$			194.326i			0.535332i
$364$		0			0
$365$	−189.000			−0.517808
$366$		0			0
$367$	−240.435	−	416.445i	−0.655135	−	1.13473i	−0.981860	−	0.189608i	$-0.939278\pi$
$367$	−240.435	−	416.445i	−0.655135	−	1.13473i	0.326725	−	0.945119i	$-0.394055\pi$
$368$		0			0
$369$	370.776	+	370.776i	1.00481	+	1.00481i
$370$		0			0
$371$	74.0460	+	276.344i	0.199585	+	0.744861i
$372$		0			0
$373$	81.3250	−	140.859i	0.218029	−	0.377638i	−0.736176	−	0.676790i	$-0.763370\pi$
$373$	81.3250	−	140.859i	0.218029	−	0.377638i	0.954205	+	0.299152i	$0.0967038\pi$
$374$		0			0
$375$	−502.004	−	134.512i	−1.33868	−	0.358697i
$376$		0			0
$377$	367.700	+	212.292i	0.975331	+	0.563108i
$378$		0			0
$379$	−135.019	+	503.899i	−0.356251	+	1.32955i	0.522651	+	0.852547i	$0.324943\pi$
$379$	−135.019	+	503.899i	−0.356251	+	1.32955i	−0.878903	+	0.477001i	$0.841724\pi$
$380$		0			0
$381$	864.400	+	499.061i	2.26877	+	1.30987i
$382$		0			0
$383$	183.923	−	49.2820i	0.480217	−	0.128674i	−0.0105867	−	0.999944i	$-0.503370\pi$
$383$	183.923	−	49.2820i	0.480217	−	0.128674i	0.490804	+	0.871270i	$0.336703\pi$
$384$		0			0
$385$	−428.554	+	428.554i	−1.11313	+	1.11313i
$386$		0			0
$387$	−1020.47	+	589.167i	−2.63686	+	1.52239i
$388$		0			0
$389$			615.256i			1.58164i	0.612052	+	0.790818i	$0.290344\pi$
$389$			615.256i			1.58164i	−0.612052	+	0.790818i	$0.709656\pi$
$390$		0			0
$391$	−6.53590			−0.0167159
$392$		0			0
$393$	465.703	+	806.620i	1.18499	+	2.05247i
$394$		0			0
$395$	267.531	+	267.531i	0.677293	+	0.677293i
$396$		0			0
$397$	91.1647	+	340.231i	0.229634	+	0.857006i	0.980495	+	0.196545i	$0.0629723\pi$
$397$	91.1647	+	340.231i	0.229634	+	0.857006i	−0.750861	+	0.660461i	$0.770361\pi$
$398$		0			0
$399$	−518.277	+	897.682i	−1.29894	+	2.24983i
$400$		0			0
$401$	−189.279	−	50.7173i	−0.472019	−	0.126477i	0.0149652	−	0.999888i	$-0.495236\pi$
$401$	−189.279	−	50.7173i	−0.472019	−	0.126477i	−0.486984	+	0.873411i	$0.661903\pi$
$402$		0			0
$403$	229.583	+	61.5167i	0.569686	+	0.152647i
$404$		0			0
$405$	249.423	−	930.859i	0.615859	−	2.29842i
$406$		0			0
$407$	−53.8667	−	31.1000i	−0.132351	−	0.0764127i
$408$		0			0
$409$	465.635	−	124.767i	1.13847	−	0.305053i	0.360136	−	0.932900i	$-0.382730\pi$
$409$	465.635	−	124.767i	1.13847	−	0.305053i	0.778337	+	0.627847i	$0.216064\pi$
$410$		0			0
$411$	285.664	−	285.664i	0.695046	−	0.695046i
$412$		0			0
$413$	377.108	−	217.723i	0.913093	−	0.527175i
$414$		0			0
$415$		−	29.5692i		−	0.0712511i
$416$		0			0
$417$	−1447.54			−3.47131
$418$		0			0
$419$	130.273	+	225.640i	0.310914	+	0.538519i	0.978561	−	0.205959i	$-0.0660314\pi$
$419$	130.273	+	225.640i	0.310914	+	0.538519i	−0.667646	+	0.744479i	$0.732698\pi$
$420$		0			0
$421$	−240.107	−	240.107i	−0.570325	−	0.570325i	0.361894	−	0.932219i	$-0.382130\pi$
$421$	−240.107	−	240.107i	−0.570325	−	0.570325i	−0.932219	+	0.361894i	$0.882130\pi$
$422$		0			0
$423$	−232.014	−	865.888i	−0.548497	−	2.04702i
$424$		0			0
$425$	4.29423	−	7.43782i	0.0101041	−	0.0175008i
$426$		0			0
$427$	423.061	+	113.359i	0.990776	+	0.265478i
$428$		0			0
$429$	−464.267	−	464.267i	−1.08221	−	1.08221i
$430$		0			0
$431$	198.613	−	741.233i	0.460819	−	1.71980i	−0.209575	−	0.977793i	$-0.567208\pi$
$431$	198.613	−	741.233i	0.460819	−	1.71980i	0.670393	−	0.742006i	$-0.266125\pi$
$432$		0			0
$433$	−146.264	−	84.4456i	−0.337792	−	0.195024i	0.321503	−	0.946909i	$-0.395812\pi$
$433$	−146.264	−	84.4456i	−0.337792	−	0.195024i	−0.659295	+	0.751884i	$0.729145\pi$
$434$		0			0
$435$	999.027	−	267.688i	2.29661	−	0.615376i
$436$		0			0
$437$	−77.4923	+	77.4923i	−0.177328	+	0.177328i
$438$		0			0
$439$	106.259	−	61.3487i	0.242048	−	0.139746i	−0.374070	−	0.927401i	$-0.622038\pi$
$439$	106.259	−	61.3487i	0.242048	−	0.139746i	0.616118	+	0.787654i	$0.288705\pi$
$440$		0			0
$441$		−	1647.66i		−	3.73618i
$442$		0			0
$443$	−71.4256			−0.161232			−0.0806158	−	0.996745i	$-0.525689\pi$
$443$	−71.4256			−0.161232			−0.0806158	+	0.996745i	$0.525689\pi$
$444$		0			0
$445$	−326.963	−	566.317i	−0.734749	−	1.27262i
$446$		0			0
$447$	173.138	+	173.138i	0.387334	+	0.387334i
$448$		0			0
$449$	40.1314	+	149.772i	0.0893795	+	0.333569i	0.996107	−	0.0881472i	$-0.0280946\pi$
$449$	40.1314	+	149.772i	0.0893795	+	0.333569i	−0.906728	+	0.421716i	$0.861428\pi$
$450$		0			0
$451$	116.192	−	201.251i	0.257633	−	0.446233i
$452$		0			0
$453$	−749.626	−	200.862i	−1.65480	−	0.443403i
$454$		0			0
$455$			852.400i			1.87341i
$456$		0			0
$457$	98.5648	−	367.849i	0.215678	−	0.804921i	−0.770249	−	0.637743i	$-0.779868\pi$
$457$	98.5648	−	367.849i	0.215678	−	0.804921i	0.985927	−	0.167177i	$-0.0534652\pi$
$458$		0			0
$459$	−56.1051	−	32.3923i	−0.122233	−	0.0705715i
$460$		0			0
$461$	635.054	−	170.162i	1.37756	−	0.369115i	0.507324	−	0.861755i	$-0.330635\pi$
$461$	635.054	−	170.162i	1.37756	−	0.369115i	0.870233	+	0.492640i	$0.163968\pi$
$462$		0			0
$463$	11.3205	−	11.3205i	0.0244503	−	0.0244503i	−0.694776	−	0.719226i	$-0.744496\pi$
$463$	11.3205	−	11.3205i	0.0244503	−	0.0244503i	0.719226	+	0.694776i	$0.244496\pi$
$464$		0			0
$465$	501.415	−	289.492i	1.07831	−	0.622564i
$466$		0			0
$467$			251.482i			0.538505i	0.963070	+	0.269253i	$0.0867767\pi$
$467$			251.482i			0.538505i	−0.963070	+	0.269253i	$0.913223\pi$
$468$		0			0
$469$	1296.53			2.76446
$470$		0			0
$471$	186.799	+	323.545i	0.396600	+	0.686932i
$472$		0			0
$473$	369.261	+	369.261i	0.780680	+	0.780680i
$474$		0			0
$475$	−37.2717	−	139.100i	−0.0784668	−	0.292842i
$476$		0			0
$477$	−263.700	+	456.742i	−0.552830	+	0.957530i
$478$		0			0
$479$	235.517	+	63.1065i	0.491684	+	0.131746i	0.496138	−	0.868244i	$-0.334751\pi$
$479$	235.517	+	63.1065i	0.491684	+	0.131746i	−0.00445385	+	0.999990i	$0.501418\pi$
$480$		0			0
$481$	−84.5000	+	22.6417i	−0.175676	+	0.0470722i
$482$		0			0
$483$	104.574	−	390.277i	0.216510	−	0.808027i
$484$		0			0
$485$	391.886	+	226.256i	0.808013	+	0.466507i
$486$		0			0
$487$	−408.669	+	109.503i	−0.839156	+	0.224851i	−0.652704	−	0.757613i	$-0.726366\pi$
$487$	−408.669	+	109.503i	−0.839156	+	0.224851i	−0.186452	+	0.982464i	$0.559699\pi$
$488$		0			0
$489$	−950.123	+	950.123i	−1.94299	+	1.94299i
$490$		0			0
$491$	−167.885	+	96.9282i	−0.341924	+	0.197410i	−0.661122	−	0.750278i	$-0.729920\pi$
$491$	−167.885	+	96.9282i	−0.341924	+	0.197410i	0.319199	+	0.947688i	$0.396586\pi$
$492$		0			0
$493$		−	32.6603i		−	0.0662480i
$494$		0			0
$495$	−1117.26			−2.25709
$496$		0			0
$497$	−97.9897	−	169.723i	−0.197162	−	0.341495i
$498$		0			0
$499$	209.636	+	209.636i	0.420112	+	0.420112i	0.885242	−	0.465130i	$-0.153993\pi$
$499$	209.636	+	209.636i	0.420112	+	0.420112i	−0.465130	+	0.885242i	$0.653993\pi$
$500$		0			0
$501$	−41.3590	−	154.354i	−0.0825529	−	0.308091i
$502$		0			0
$503$	18.6692	−	32.3360i	0.0371157	−	0.0642862i	−0.846871	−	0.531799i	$-0.821516\pi$
$503$	18.6692	−	32.3360i	0.0371157	−	0.0642862i	0.883987	+	0.467512i	$0.154850\pi$
$504$		0			0
$505$	−921.565	−	246.933i	−1.82488	−	0.488976i
$506$		0			0
$507$	−923.433			−1.82137
$508$		0			0
$509$	95.4648	−	356.279i	0.187554	−	0.699960i	−0.806516	−	0.591213i	$-0.798649\pi$
$509$	95.4648	−	356.279i	0.187554	−	0.699960i	0.994069	−	0.108747i	$-0.0346839\pi$
$510$		0			0
$511$	−319.523	−	184.477i	−0.625290	−	0.361011i
$512$		0			0
$513$	−1049.26	+	281.149i	−2.04534	+	0.548048i
$514$		0			0
$515$	167.569	−	167.569i	0.325377	−	0.325377i
$516$		0			0
$517$	−344.056	+	198.641i	−0.665486	+	0.384219i
$518$		0			0
$519$		−	1031.12i		−	1.98674i
$520$		0			0
$521$	772.717			1.48314			0.741571	−	0.670875i	$-0.234081\pi$
$521$	772.717			1.48314			0.741571	+	0.670875i	$0.234081\pi$
$522$		0			0
$523$	−54.2487	−	93.9615i	−0.103726	−	0.179659i	0.809491	−	0.587132i	$-0.199743\pi$
$523$	−54.2487	−	93.9615i	−0.103726	−	0.179659i	−0.913217	+	0.407474i	$0.866410\pi$
$524$		0			0
$525$	375.426	+	375.426i	0.715096	+	0.715096i
$526$		0			0
$527$	−4.73205	−	17.6603i	−0.00897922	−	0.0335109i
$528$		0			0
$529$	−243.141	+	421.133i	−0.459624	+	0.796092i
$530$		0			0
$531$	775.377	+	207.762i	1.46022	+	0.391265i
$532$		0			0
$533$	−84.5915	−	315.700i	−0.158708	−	0.592308i
$534$		0			0
$535$	−224.512	+	837.888i	−0.419648	+	1.56615i
$536$		0			0
$537$	365.703	+	211.138i	0.681010	+	0.393181i
$538$		0			0
$539$	−705.328	+	188.992i	−1.30859	+	0.350635i
$540$		0			0
$541$	30.4519	−	30.4519i	0.0562882	−	0.0562882i	−0.678402	−	0.734691i	$-0.737327\pi$
$541$	30.4519	−	30.4519i	0.0562882	−	0.0562882i	0.734691	+	0.678402i	$0.237327\pi$
$542$		0			0
$543$	−1138.34	+	657.219i	−2.09638	+	1.21035i
$544$		0			0
$545$		−	673.850i		−	1.23642i
$546$		0			0
$547$	−422.438			−0.772282			−0.386141	−	0.922440i	$-0.626192\pi$
$547$	−422.438			−0.772282			−0.386141	+	0.922440i	$0.626192\pi$
$548$		0			0
$549$	403.705	+	699.238i	0.735346	+	1.27366i
$550$		0			0
$551$	−387.233	−	387.233i	−0.702783	−	0.702783i
$552$		0			0
$553$	191.159	+	713.415i	0.345676	+	1.29008i
$554$		0			0
$555$	−106.550	+	184.550i	−0.191982	+	0.332522i
$556$		0			0
$557$	−409.234	−	109.654i	−0.734711	−	0.196865i	−0.127985	−	0.991776i	$-0.540851\pi$
$557$	−409.234	−	109.654i	−0.734711	−	0.196865i	−0.606726	+	0.794911i	$0.707518\pi$
$558$		0			0
$559$	734.466			1.31389
$560$		0			0
$561$	−13.0718	+	48.7846i	−0.0233009	+	0.0869601i
$562$		0			0
$563$	−367.510	−	212.182i	−0.652771	−	0.376878i	0.136746	−	0.990606i	$-0.456336\pi$
$563$	−367.510	−	212.182i	−0.652771	−	0.376878i	−0.789517	+	0.613729i	$0.789669\pi$
$564$		0			0
$565$	−824.604	+	220.952i	−1.45948	+	0.391065i
$566$		0			0
$567$	1330.26	−	1330.26i	2.34613	−	2.34613i
$568$		0			0
$569$	−267.482	+	154.431i	−0.470091	+	0.271407i	−0.716278	−	0.697815i	$-0.754156\pi$
$569$	−267.482	+	154.431i	−0.470091	+	0.271407i	0.246187	+	0.969222i	$0.420822\pi$
$570$		0			0
$571$			971.272i			1.70100i	0.525974	+	0.850501i	$0.323701\pi$
$571$			971.272i			1.70100i	−0.525974	+	0.850501i	$0.676299\pi$
$572$		0			0
$573$	−641.415			−1.11940
$574$		0			0
$575$	28.0666	+	48.6128i	0.0488116	+	0.0845441i
$576$		0			0
$577$	−413.542	−	413.542i	−0.716710	−	0.716710i	0.251220	−	0.967930i	$-0.419168\pi$
$577$	−413.542	−	413.542i	−0.716710	−	0.716710i	−0.967930	+	0.251220i	$0.919168\pi$
$578$		0			0
$579$	−289.583	−	1080.74i	−0.500144	−	1.86656i
$580$		0			0
$581$	28.8616	−	49.9897i	0.0496757	−	0.0860408i
$582$		0			0
$583$	225.769	+	60.4947i	0.387254	+	0.103764i
$584$		0			0
$585$	−1111.12	+	1111.12i	−1.89936	+	1.89936i
$586$		0			0
$587$	238.582	−	890.400i	0.406443	−	1.51687i	−0.394936	−	0.918708i	$-0.629233\pi$
$587$	238.582	−	890.400i	0.406443	−	1.51687i	0.801379	−	0.598157i	$-0.204100\pi$
$588$		0			0
$589$	−265.492	−	153.282i	−0.450751	−	0.260241i
$590$		0			0
$591$	−1831.35	+	490.708i	−3.09872	+	0.830301i
$592$		0			0
$593$	439.901	−	439.901i	0.741822	−	0.741822i	−0.231106	−	0.972928i	$-0.574235\pi$
$593$	439.901	−	439.901i	0.741822	−	0.741822i	0.972928	+	0.231106i	$0.0742345\pi$
$594$		0			0
$595$	56.7846	−	32.7846i	0.0954363	−	0.0551002i
$596$		0			0
$597$			625.836i			1.04830i
$598$		0			0
$599$	1081.06			1.80477			0.902386	−	0.430928i	$-0.141814\pi$
$599$	1081.06			1.80477			0.902386	+	0.430928i	$0.141814\pi$
$600$		0			0
$601$	24.3391	+	42.1565i	0.0404976	+	0.0701439i	0.885564	−	0.464518i	$-0.153772\pi$
$601$	24.3391	+	42.1565i	0.0404976	+	0.0701439i	−0.845066	+	0.534662i	$0.820439\pi$
$602$		0			0
$603$	1690.06	+	1690.06i	2.80276	+	2.80276i
$604$		0			0
$605$	−53.3461	−	199.090i	−0.0881754	−	0.329075i
$606$		0			0
$607$	134.550	−	233.047i	0.221664	−	0.383933i	−0.733649	−	0.679528i	$-0.762185\pi$
$607$	134.550	−	233.047i	0.221664	−	0.383933i	0.955313	+	0.295595i	$0.0955179\pi$
$608$		0			0
$609$	1950.24	+	522.564i	3.20236	+	0.858069i
$610$		0			0
$611$	−144.617	+	539.717i	−0.236688	+	0.883333i
$612$		0			0
$613$	25.9256	−	96.7558i	0.0422930	−	0.157840i	−0.941550	−	0.336874i	$-0.890630\pi$
$613$	25.9256	−	96.7558i	0.0422930	−	0.157840i	0.983843	+	0.179034i	$0.0572972\pi$
$614$		0			0
$615$	−689.496	−	398.081i	−1.12113	−	0.647286i
$616$		0			0
$617$	258.141	−	69.1687i	0.418381	−	0.112105i	−0.0434861	−	0.999054i	$-0.513846\pi$
$617$	258.141	−	69.1687i	0.418381	−	0.112105i	0.461867	+	0.886949i	$0.347180\pi$
$618$		0			0
$619$	−192.862	+	192.862i	−0.311570	+	0.311570i	−0.845517	−	0.533948i	$-0.820708\pi$
$619$	−192.862	+	192.862i	−0.311570	+	0.311570i	0.533948	+	0.845517i	$0.320708\pi$
$620$		0			0
$621$	366.697	−	211.713i	0.590495	−	0.340922i
$622$		0			0
$623$		−	1276.55i		−	2.04904i
$624$		0			0
$625$	765.950			1.22552
$626$		0			0
$627$	423.426	+	733.395i	0.675320	+	1.16969i
$628$		0			0
$629$	4.75833	+	4.75833i	0.00756491	+	0.00756491i
$630$		0			0
$631$	7.08211	+	26.4308i	0.0112236	+	0.0418871i	0.971311	−	0.237815i	$-0.0764311\pi$
$631$	7.08211	+	26.4308i	0.0112236	+	0.0418871i	−0.960087	+	0.279702i	$0.909764\pi$
$632$		0			0
$633$	142.354	−	246.564i	0.224888	−	0.389517i
$634$		0			0
$635$	−1022.60	−	274.004i	−1.61039	−	0.431502i
$636$		0			0
$637$	−513.500	+	889.408i	−0.806122	+	1.39625i
$638$		0			0
$639$	93.5064	−	348.970i	0.146332	−	0.546120i
$640$		0			0
$641$	−924.395	−	533.700i	−1.44211	−	0.832605i	−0.444124	−	0.895965i	$-0.646485\pi$
$641$	−924.395	−	533.700i	−1.44211	−	0.832605i	−0.997991	+	0.0633603i	$0.979818\pi$
$642$		0			0
$643$	530.161	−	142.056i	0.824512	−	0.220927i	0.178194	−	0.983995i	$-0.442975\pi$
$643$	530.161	−	142.056i	0.824512	−	0.220927i	0.646318	+	0.763068i	$0.276308\pi$
$644$		0			0
$645$	1265.11	−	1265.11i	1.96141	−	1.96141i
$646$		0			0
$647$	−71.9756	+	41.5551i	−0.111245	+	0.0642274i	−0.554590	−	0.832124i	$-0.687125\pi$
$647$	−71.9756	+	41.5551i	−0.111245	+	0.0642274i	0.443345	+	0.896351i	$0.353792\pi$
$648$		0			0
$649$		−	355.754i		−	0.548157i
$650$		0			0
$651$	1130.26			1.73618
$652$		0			0
$653$	480.400	+	832.077i	0.735681	+	1.27424i	0.954424	+	0.298455i	$0.0964712\pi$
$653$	480.400	+	832.077i	0.735681	+	1.27424i	−0.218743	+	0.975783i	$0.570195\pi$
$654$		0			0
$655$	−698.554	−	698.554i	−1.06649	−	1.06649i
$656$		0			0
$657$	−176.036	−	656.977i	−0.267940	−	0.999965i
$658$		0			0
$659$	−30.3538	+	52.5744i	−0.0460604	+	0.0797790i	−0.888136	−	0.459580i	$-0.848000\pi$
$659$	−30.3538	+	52.5744i	−0.0460604	+	0.0797790i	0.842076	+	0.539359i	$0.181333\pi$
$660$		0			0
$661$	79.7820	+	21.3775i	0.120699	+	0.0323412i	0.318663	−	0.947868i	$-0.396766\pi$
$661$	79.7820	+	21.3775i	0.120699	+	0.0323412i	−0.197964	+	0.980209i	$0.563433\pi$
$662$		0			0
$663$	35.5167	+	61.5167i	0.0535696	+	0.0927853i
$664$		0			0
$665$	284.554	−	1061.97i	0.427900	−	1.59695i
$666$		0			0
$667$	184.865	+	106.732i	0.277159	+	0.160018i
$668$		0			0
$669$	828.267	−	221.933i	1.23807	−	0.331739i
$670$		0			0
$671$	253.023	−	253.023i	0.377083	−	0.377083i
$672$		0			0
$673$	140.789	−	81.2846i	0.209196	−	0.120780i	−0.391742	−	0.920075i	$-0.628127\pi$
$673$	140.789	−	81.2846i	0.209196	−	0.120780i	0.600938	+	0.799296i	$0.294794\pi$
$674$		0			0
$675$			556.400i			0.824296i
$676$		0			0
$677$	354.554			0.523713			0.261857	−	0.965107i	$-0.415665\pi$
$677$	354.554			0.523713			0.261857	+	0.965107i	$0.415665\pi$
$678$		0			0
$679$	441.682	+	765.015i	0.650489	+	1.12668i
$680$		0			0
$681$	−18.9282	−	18.9282i	−0.0277947	−	0.0277947i
$682$		0			0
$683$	−61.6781	−	230.186i	−0.0903047	−	0.337022i	0.905961	−	0.423361i	$-0.139150\pi$
$683$	−61.6781	−	230.186i	−0.0903047	−	0.337022i	−0.996266	+	0.0863392i	$0.972483\pi$
$684$		0			0
$685$	−214.248	+	371.088i	−0.312771	+	0.541735i
$686$		0			0
$687$	−1107.37	−	296.718i	−1.61189	−	0.431904i
$688$		0			0
$689$	284.692	−	164.367i	0.413195	−	0.238558i
$690$		0			0
$691$	−121.397	+	453.061i	−0.175684	+	0.655661i	0.820750	+	0.571287i	$0.193556\pi$
$691$	−121.397	+	453.061i	−0.175684	+	0.655661i	−0.996434	+	0.0843737i	$0.973111\pi$
$692$		0			0
$693$	−1888.84	−	1090.52i	−2.72560	−	1.57363i
$694$		0			0
$695$	1483.03	−	397.377i	2.13386	−	0.571765i
$696$		0			0
$697$	−17.7776	+	17.7776i	−0.0255058	+	0.0255058i
$698$		0			0
$699$	2021.24	−	1166.96i	2.89162	−	1.66948i
$700$		0			0
$701$		−	657.692i		−	0.938220i	−0.883140	−	0.469110i	$-0.844575\pi$
$701$		−	657.692i		−	0.938220i	0.883140	−	0.469110i	$-0.155425\pi$
$702$		0			0
$703$	112.833			0.160503
$704$		0			0
$705$	680.554	+	1178.75i	0.965324	+	1.67199i
$706$		0			0
$707$	−1316.97	−	1316.97i	−1.86276	−	1.86276i
$708$		0			0
$709$	−160.279	−	598.171i	−0.226064	−	0.843683i	−0.981975	−	0.189009i	$-0.939473\pi$
$709$	−160.279	−	598.171i	−0.226064	−	0.843683i	0.755911	−	0.654674i	$-0.227194\pi$
$710$		0			0
$711$	−680.774	+	1179.14i	−0.957488	+	1.65842i
$712$		0			0
$713$	115.426	+	30.9282i	0.161887	+	0.0433776i
$714$		0			0
$715$	603.100	+	348.200i	0.843496	+	0.486993i
$716$		0			0
$717$	−76.5538	+	285.703i	−0.106770	+	0.398469i
$718$		0			0
$719$	487.923	+	281.703i	0.678613	+	0.391798i	0.799332	−	0.600889i	$-0.205187\pi$
$719$	487.923	+	281.703i	0.678613	+	0.391798i	−0.120719	+	0.992687i	$0.538520\pi$
$720$		0			0
$721$	446.851	−	119.733i	0.619766	−	0.166066i
$722$		0			0
$723$	−896.802	+	896.802i	−1.24039	+	1.24039i
$724$		0			0
$725$	−242.921	+	140.251i	−0.335064	+	0.193449i
$726$		0			0
$727$			877.779i			1.20740i	0.797212	+	0.603700i	$0.206307\pi$
$727$			877.779i			1.20740i	−0.797212	+	0.603700i	$0.793693\pi$
$728$		0			0
$729$	282.138			0.387021
$730$		0			0
$731$	−28.2487	−	48.9282i	−0.0386439	−	0.0669332i
$732$		0			0
$733$	−629.878	−	629.878i	−0.859315	−	0.859315i	0.131943	−	0.991257i	$-0.457878\pi$
$733$	−629.878	−	629.878i	−0.859315	−	0.859315i	−0.991257	+	0.131943i	$0.957878\pi$
$734$		0			0
$735$	647.496	+	2416.49i	0.880947	+	3.28774i
$736$		0			0
$737$	529.626	−	917.338i	0.718624	−	1.24469i
$738$		0			0
$739$	1064.61	+	285.261i	1.44061	+	0.386010i	0.892747	−	0.450559i	$-0.148775\pi$
$739$	1064.61	+	285.261i	1.44061	+	0.386010i	0.547862	+	0.836569i	$0.315442\pi$
$740$		0			0
$741$	1150.47	+	308.267i	1.55259	+	0.416014i
$742$		0			0
$743$	10.3848	−	38.7564i	0.0139768	−	0.0521621i	−0.958585	−	0.284806i	$-0.908071\pi$
$743$	10.3848	−	38.7564i	0.0139768	−	0.0521621i	0.972562	+	0.232644i	$0.0747376\pi$
$744$		0			0
$745$	−224.913	−	129.854i	−0.301897	−	0.174300i
$746$		0			0
$747$	102.785	−	27.5411i	0.137597	−	0.0368689i
$748$		0			0
$749$	−1197.39	+	1197.39i	−1.59866	+	1.59866i
$750$		0			0
$751$	−234.413	+	135.338i	−0.312134	+	0.180211i	−0.647881	−	0.761741i	$-0.724345\pi$
$751$	−234.413	+	135.338i	−0.312134	+	0.180211i	0.335747	+	0.941952i	$0.391011\pi$
$752$		0			0
$753$			2576.07i			3.42108i
$754$		0			0
$755$	823.146			1.09026
$756$		0			0
$757$	211.354	+	366.076i	0.279199	+	0.483587i	0.971186	−	0.238323i	$-0.0765977\pi$
$757$	211.354	+	366.076i	0.279199	+	0.483587i	−0.691987	+	0.721910i	$0.743264\pi$
$758$		0			0
$759$	−233.415	−	233.415i	−0.307530	−	0.307530i
$760$		0			0
$761$	−252.362	−	941.829i	−0.331619	−	1.23762i	−0.907488	−	0.420078i	$-0.862003\pi$
$761$	−252.362	−	941.829i	−0.331619	−	1.23762i	0.575869	−	0.817542i	$-0.304664\pi$
$762$		0			0
$763$	657.723	−	1139.21i	0.862022	−	1.49307i
$764$		0			0
$765$	116.756	+	31.2846i	0.152622	+	0.0408949i
$766$		0			0
$767$	−353.800	−	353.800i	−0.461278	−	0.461278i
$768$		0			0
$769$	−41.1149	+	153.443i	−0.0534654	+	0.199536i	−0.987492	−	0.157667i	$-0.949603\pi$
$769$	−41.1149	+	153.443i	−0.0534654	+	0.199536i	0.934027	+	0.357203i	$0.116269\pi$
$770$		0			0
$771$	−587.363	−	339.114i	−0.761819	−	0.439837i
$772$		0			0
$773$	−698.599	+	187.189i	−0.903751	+	0.242159i	−0.680626	−	0.732631i	$-0.738292\pi$
$773$	−698.599	+	187.189i	−0.903751	+	0.242159i	−0.223124	+	0.974790i	$0.571626\pi$
$774$		0			0
$775$	−111.033	+	111.033i	−0.143269	+	0.143269i
$776$		0			0
$777$	−360.267	+	208.000i	−0.463664	+	0.267696i
$778$		0			0
$779$			421.556i			0.541150i
$780$		0			0
$781$	−160.113			−0.205010
$782$		0			0
$783$	1057.94	+	1832.41i	1.35114	+	2.34024i
$784$		0			0
$785$	−280.198	−	280.198i	−0.356940	−	0.356940i
$786$		0			0
$787$	−268.750	−	1002.99i	−0.341487	−	1.27445i	−0.896663	−	0.442713i	$-0.854016\pi$
$787$	−268.750	−	1002.99i	−0.341487	−	1.27445i	0.555177	−	0.831732i	$-0.312651\pi$
$788$		0			0
$789$	−290.200	+	502.641i	−0.367807	+	0.637061i
$790$		0			0
$791$	−1609.74	−	431.328i	−2.03507	−	0.545295i
$792$		0			0
$793$		−	503.267i		−	0.634636i
$794$		0			0
$795$	207.258	−	773.496i	0.260701	−	0.972951i
$796$		0			0
$797$	1033.00	+	596.405i	1.29612	+	0.748312i	0.979731	−	0.200319i	$-0.0641977\pi$
$797$	1033.00	+	596.405i	1.29612	+	0.748312i	0.316384	+	0.948631i	$0.397531\pi$
$798$		0			0
$799$	41.5167	−	11.1244i	0.0519608	−	0.0139228i
$800$		0			0
$801$	1664.02	−	1664.02i	2.07743	−	2.07743i
$802$		0			0
$803$	−261.046	+	150.715i	−0.325089	+	0.187690i
$804$		0			0
$805$			428.554i			0.532365i
$806$		0			0
$807$	−500.287			−0.619935
$808$		0			0
$809$	−192.845	−	334.018i	−0.238375	−	0.412878i	0.721873	−	0.692025i	$-0.243281\pi$
$809$	−192.845	−	334.018i	−0.238375	−	0.412878i	−0.960248	+	0.279148i	$0.909948\pi$
$810$		0			0
$811$	−496.823	−	496.823i	−0.612606	−	0.612606i	0.331019	−	0.943624i	$-0.392608\pi$
$811$	−496.823	−	496.823i	−0.612606	−	0.612606i	−0.943624	+	0.331019i	$0.892608\pi$
$812$		0			0
$813$	−133.856	−	499.559i	−0.164645	−	0.614464i
$814$		0			0
$815$	712.592	−	1234.25i	0.874346	−	1.51441i
$816$		0			0
$817$	−915.041	−	245.184i	−1.12000	−	0.300103i
$818$		0			0
$819$	−2963.00	+	793.933i	−3.61783	+	0.969394i
$820$		0			0
$821$	−414.570	+	1547.20i	−0.504957	+	1.88453i	−0.0399843	+	0.999200i	$0.512731\pi$
$821$	−414.570	+	1547.20i	−0.504957	+	1.88453i	−0.464973	+	0.885325i	$0.653936\pi$
$822$		0			0
$823$	−525.282	−	303.272i	−0.638253	−	0.368495i	0.145688	−	0.989331i	$-0.453460\pi$
$823$	−525.282	−	303.272i	−0.638253	−	0.368495i	−0.783941	+	0.620835i	$0.786794\pi$
$824$		0			0
$825$	418.985	−	112.267i	0.507860	−	0.136081i
$826$		0			0
$827$	−815.167	+	815.167i	−0.985691	+	0.985691i	−0.999899	−	0.0142079i	$-0.995477\pi$
$827$	−815.167	+	815.167i	−0.985691	+	0.985691i	0.0142079	+	0.999899i	$0.495477\pi$
$828$		0			0
$829$	−547.172	+	315.910i	−0.660038	+	0.381073i	−0.792291	−	0.610143i	$-0.791112\pi$
$829$	−547.172	+	315.910i	−0.660038	+	0.381073i	0.132253	+	0.991216i	$0.457779\pi$
$830$		0			0
$831$		−	2451.20i		−	2.94970i
$832$		0			0
$833$	79.0000			0.0948379
$834$		0			0
$835$	84.7461	+	146.785i	0.101492	+	0.175790i
$836$		0			0
$837$	837.549	+	837.549i	1.00066	+	1.00066i
$838$		0			0
$839$	−29.4473	−	109.899i	−0.0350980	−	0.130988i	0.946154	−	0.323717i	$-0.104933\pi$
$839$	−29.4473	−	109.899i	−0.0350980	−	0.130988i	−0.981252	+	0.192730i	$0.938266\pi$
$840$		0			0
$841$	−112.846	+	195.455i	−0.134181	+	0.232408i
$842$		0			0
$843$	1214.60	+	325.450i	1.44080	+	0.386062i
$844$		0			0
$845$	946.075	−	253.500i	1.11962	−	0.300000i
$846$		0			0
$847$	104.139	−	388.651i	0.122950	−	0.458856i
$848$		0			0
$849$	1183.96	+	683.559i	1.39453	+	0.805134i
$850$		0			0
$851$	−42.4833	+	11.3834i	−0.0499217	+	0.0133765i
$852$		0			0
$853$	−265.826	+	265.826i	−0.311637	+	0.311637i	−0.845544	−	0.533907i	$-0.820723\pi$
$853$	−265.826	+	265.826i	−0.311637	+	0.311637i	0.533907	+	0.845544i	$0.320723\pi$
$854$		0			0
$855$	1755.23	−	1013.38i	2.05290	−	1.18524i
$856$		0			0
$857$			670.268i			0.782110i	0.920367	+	0.391055i	$0.127890\pi$
$857$			670.268i			0.782110i	−0.920367	+	0.391055i	$0.872110\pi$
$858$		0			0
$859$	−36.8334			−0.0428794			−0.0214397	−	0.999770i	$-0.506825\pi$
$859$	−36.8334			−0.0428794			−0.0214397	+	0.999770i	$0.506825\pi$
$860$		0			0
$861$	−777.108	−	1345.99i	−0.902564	−	1.56329i
$862$		0			0
$863$	124.939	+	124.939i	0.144772	+	0.144772i	0.775778	−	0.631006i	$-0.217358\pi$
$863$	124.939	+	124.939i	0.144772	+	0.144772i	−0.631006	+	0.775778i	$0.717358\pi$
$864$		0			0
$865$	283.061	+	1056.40i	0.327239	+	1.22127i
$866$		0			0
$867$	−786.831	+	1362.83i	−0.907532	+	1.57189i
$868$		0			0
$869$	582.851	+	156.175i	0.670715	+	0.179718i
$870$		0			0
$871$	−385.583	−	1439.02i	−0.442690	−	1.65214i
$872$		0			0
$873$	−421.474	+	1572.96i	−0.482788	+	1.80179i
$874$		0			0
$875$	931.923	+	538.046i	1.06505	+	0.614910i
$876$		0			0
$877$	502.038	−	134.521i	0.572449	−	0.153387i	0.0390295	−	0.999238i	$-0.487573\pi$
$877$	502.038	−	134.521i	0.572449	−	0.153387i	0.533420	+	0.845851i	$0.320907\pi$
$878$		0			0
$879$	−1369.38	+	1369.38i	−1.55789	+	1.55789i
$880$		0			0
$881$	−1146.46	+	661.908i	−1.30132	+	0.751315i	−0.980630	−	0.195871i	$-0.937247\pi$
$881$	−1146.46	+	661.908i	−1.30132	+	0.751315i	−0.320686	+	0.947186i	$0.603913\pi$
$882$		0			0
$883$		−	789.464i		−	0.894070i	−0.894516	−	0.447035i	$-0.852480\pi$
$883$		−	789.464i		−	0.894070i	0.894516	−	0.447035i	$-0.147520\pi$
$884$		0			0
$885$	−1218.83			−1.37721
$886$		0			0
$887$	632.410	+	1095.37i	0.712977	+	1.23491i	0.963735	+	0.266862i	$0.0859867\pi$
$887$	632.410	+	1095.37i	0.712977	+	1.23491i	−0.250758	+	0.968050i	$0.580680\pi$
$888$		0			0
$889$	−1461.35	−	1461.35i	−1.64382	−	1.64382i
$890$		0			0
$891$	−397.797	−	1484.60i	−0.446462	−	1.66622i
$892$		0			0
$893$	360.344	−	624.133i	0.403520	−	0.698917i
$894$		0			0
$895$	−432.631	−	115.923i	−0.483386	−	0.129523i
$896$		0			0
$897$	−464.267			−0.517577
$898$		0			0
$899$	−154.550	+	576.788i	−0.171913	+	0.641589i
$900$		0			0
$901$	−21.8993	−	12.6436i	−0.0243056	−	0.0140328i
$902$		0			0
$903$	3373.62	−	903.959i	3.73601	−	1.00106i
$904$		0			0
$905$	985.829	−	985.829i	1.08931	−	1.08931i
$906$		0			0
$907$	−1122.13	+	647.864i	−1.23719	+	0.714293i	−0.968519	−	0.248938i	$-0.919918\pi$
$907$	−1122.13	+	647.864i	−1.23719	+	0.714293i	−0.268673	+	0.963232i	$0.586585\pi$
$908$		0			0
$909$		−	3433.42i		−	3.77714i
$910$		0			0
$911$	458.733			0.503549			0.251774	−	0.967786i	$-0.418986\pi$
$911$	458.733			0.503549			0.251774	+	0.967786i	$0.418986\pi$
$912$		0			0
$913$	−23.5795	−	40.8409i	−0.0258264	−	0.0447327i
$914$		0			0
$915$	−866.869	−	866.869i	−0.947398	−	0.947398i
$916$		0			0
$917$	−499.138	−	1862.81i	−0.544317	−	2.03142i
$918$		0			0
$919$	−637.804	+	1104.71i	−0.694019	+	1.20208i	0.276491	+	0.961017i	$0.410828\pi$
$919$	−637.804	+	1104.71i	−0.694019	+	1.20208i	−0.970510	+	0.241060i	$0.922505\pi$
$920$		0			0
$921$	−1660.74	−	444.995i	−1.80320	−	0.483165i
$922$		0			0
$923$	−159.233	+	159.233i	−0.172517	+	0.172517i
$924$		0			0
$925$	14.9583	−	55.8250i	0.0161711	−	0.0603513i
$926$		0			0
$927$	738.558	+	426.406i	0.796718	+	0.459985i
$928$		0			0
$929$	−742.056	+	198.833i	−0.798768	+	0.214029i	−0.635043	−	0.772477i	$-0.719018\pi$
$929$	−742.056	+	198.833i	−0.798768	+	0.214029i	−0.163725	+	0.986506i	$0.552351\pi$
$930$		0			0
$931$	936.656	−	936.656i	1.00608	−	1.00608i
$932$		0			0
$933$	−334.046	+	192.862i	−0.358034	+	0.206711i
$934$		0			0
$935$		−	53.5692i		−	0.0572933i
$936$		0			0
$937$	−969.985			−1.03520			−0.517601	−	0.855622i	$-0.673175\pi$
$937$	−969.985			−1.03520			−0.517601	+	0.855622i	$0.673175\pi$
$938$		0			0
$939$	−1502.96	−	2603.21i	−1.60060	−	2.77232i
$940$		0			0
$941$	880.815	+	880.815i	0.936042	+	0.936042i	0.998074	−	0.0620325i	$-0.0197582\pi$
$941$	880.815	+	880.815i	0.936042	+	0.936042i	−0.0620325	+	0.998074i	$0.519758\pi$
$942$		0			0
$943$	−42.5294	−	158.722i	−0.0451001	−	0.168316i
$944$		0			0
$945$	−2123.94	+	3678.77i	−2.24755	+	3.89288i
$946$		0			0
$947$	708.865	+	189.940i	0.748538	+	0.200570i	0.612869	−	0.790184i	$-0.290015\pi$
$947$	708.865	+	189.940i	0.748538	+	0.200570i	0.135668	+	0.990754i	$0.456682\pi$
$948$		0			0
$949$	−109.725	+	409.500i	−0.115622	+	0.431507i
$950$		0			0
$951$	−574.022	+	2142.28i	−0.603598	+	2.25266i
$952$		0			0
$953$	−846.431	−	488.687i	−0.888175	−	0.512788i	−0.0148299	−	0.999890i	$-0.504721\pi$
$953$	−846.431	−	488.687i	−0.888175	−	0.512788i	−0.873345	+	0.487102i	$0.838054\pi$
$954$		0			0
$955$	657.142	−	176.081i	0.688107	−	0.184378i
$956$		0			0
$957$	1166.39	−	1166.39i	1.21880	−	1.21880i
$958$		0			0
$959$	−724.415	+	418.241i	−0.755386	+	0.436122i
$960$		0			0
$961$		−	626.723i		−	0.652157i
$962$		0			0
$963$	−3121.67			−3.24161
$964$		0			0
$965$	593.367	+	1027.74i	0.614888	+	1.06502i
$966$		0			0
$967$	931.492	+	931.492i	0.963281	+	0.963281i	0.999349	−	0.0360688i	$-0.0114835\pi$
$967$	931.492	+	931.492i	0.963281	+	0.963281i	−0.0360688	+	0.999349i	$0.511484\pi$
$968$		0			0
$969$	−23.7128	−	88.4974i	−0.0244714	−	0.0913286i
$970$		0			0
$971$	−665.678	+	1152.99i	−0.685559	+	1.18742i	0.287701	+	0.957720i	$0.407109\pi$
$971$	−665.678	+	1152.99i	−0.685559	+	1.18742i	−0.973261	+	0.229703i	$0.926224\pi$
$972$		0			0
$973$	2895.08	+	775.733i	2.97541	+	0.797259i
$974$		0			0
$975$	305.033	−	528.333i	0.312855	−	0.541880i
$976$		0			0
$977$	−185.625	+	692.761i	−0.189995	+	0.709070i	0.803511	+	0.595290i	$0.202963\pi$
$977$	−185.625	+	692.761i	−0.189995	+	0.709070i	−0.993506	+	0.113780i	$0.963704\pi$
$978$		0			0
$979$	−903.202	−	521.464i	−0.922576	−	0.532650i
$980$		0			0
$981$	2342.35	−	627.630i	2.38771	−	0.639786i
$982$		0			0
$983$	788.487	−	788.487i	0.802123	−	0.802123i	−0.181304	−	0.983427i	$-0.558032\pi$
$983$	788.487	−	788.487i	0.802123	−	0.802123i	0.983427	+	0.181304i	$0.0580318\pi$
$984$		0			0
$985$	1741.54	−	1005.48i	1.76806	−	1.02079i
$986$		0			0
$987$			2657.07i			2.69206i
$988$		0			0
$989$	369.261			0.373368
$990$		0			0
$991$	340.627	+	589.983i	0.343720	+	0.595341i	0.985120	−	0.171865i	$-0.0549794\pi$
$991$	340.627	+	589.983i	0.343720	+	0.595341i	−0.641400	+	0.767207i	$0.721646\pi$
$992$		0			0
$993$	130.410	+	130.410i	0.131329	+	0.131329i
$994$		0			0
$995$	−171.804	−	641.181i	−0.172667	−	0.644403i
$996$		0			0
$997$	247.761	−	429.135i	0.248507	−	0.430427i	−0.714605	−	0.699528i	$-0.753393\pi$
$997$	247.761	−	429.135i	0.248507	−	0.430427i	0.963112	+	0.269102i	$0.0867268\pi$
$998$		0			0
$999$	−421.100	−	112.833i	−0.421521	−	0.112946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.3.bd.b.193.1		4
4.3	odd	2		104.3.v.b.89.1	✓	4
13.6	odd	12	inner	208.3.bd.b.97.1		4
52.19	even	12		104.3.v.b.97.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.3.v.b.89.1	✓	4	4.3	odd	2
104.3.v.b.97.1	yes	4	52.19	even	12
208.3.bd.b.97.1		4	13.6	odd	12	inner
208.3.bd.b.193.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	208.bd (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.73205 - 4.73205i) q^{3} +(4.09808 + 4.09808i) q^{5} +(2.92820 + 10.9282i) q^{7} +(-10.4282 + 18.0622i) q^{9} +(8.92820 + 2.39230i) q^{11} +(11.2583 - 6.50000i) q^{13} +(8.19615 - 30.5885i) q^{15} +(-0.866025 - 0.500000i) q^{17} +(-16.1962 + 4.33975i) q^{19} +(43.7128 - 43.7128i) q^{21} +(5.66025 - 3.26795i) q^{23} +8.58846i q^{25} +64.7846 q^{27} +(16.3301 + 28.2846i) q^{29} +(12.9282 + 12.9282i) q^{31} +(-13.0718 - 48.7846i) q^{33} +(-32.7846 + 56.7846i) q^{35} +(-6.50000 - 1.74167i) q^{37} +(-61.5167 - 35.5167i) q^{39} +(6.50704 - 24.2846i) q^{41} +(48.9282 + 28.2487i) q^{43} +(-116.756 + 31.2846i) q^{45} +(-30.3923 + 30.3923i) q^{47} +(-68.4160 + 39.5000i) q^{49} +5.46410i q^{51} +25.2872 q^{53} +(26.7846 + 46.3923i) q^{55} +(64.7846 + 64.7846i) q^{57} +(-9.96152 - 37.1769i) q^{59} +(19.3564 - 33.5263i) q^{61} +(-227.923 - 61.0718i) q^{63} +(72.7750 + 19.5000i) q^{65} +(29.6603 - 110.694i) q^{67} +(-30.9282 - 17.8564i) q^{69} +(-16.7321 + 4.48334i) q^{71} +(-23.0596 + 23.0596i) q^{73} +(40.6410 - 23.4641i) q^{75} +104.574i q^{77} +65.2820 q^{79} +(-83.1410 - 144.004i) q^{81} +(-3.60770 - 3.60770i) q^{83} +(-1.50000 - 5.59808i) q^{85} +(89.2295 - 154.550i) q^{87} +(-108.988 - 29.2032i) q^{89} +(104.000 + 104.000i) q^{91} +(25.8564 - 96.4974i) q^{93} +(-84.1577 - 48.5885i) q^{95} +(75.4186 - 20.2083i) q^{97} +(-136.315 + 136.315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 6 q^{5} - 16 q^{7} - 14 q^{9} + 8 q^{11} + 12 q^{15} - 44 q^{19} + 64 q^{21} - 12 q^{23} + 176 q^{27} + 48 q^{29} + 24 q^{31} - 80 q^{33} - 48 q^{35} - 26 q^{37} - 156 q^{39} - 116 q^{41}+ \cdots - 88 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^5 - 16 * q^7 - 14 * q^9 + 8 * q^11 + 12 * q^15 - 44 * q^19 + 64 * q^21 - 12 * q^23 + 176 * q^27 + 48 * q^29 + 24 * q^31 - 80 * q^33 - 48 * q^35 - 26 * q^37 - 156 * q^39 - 116 * q^41 + 168 * q^43 - 228 * q^45 - 80 * q^47 + 212 * q^53 + 24 * q^55 + 176 * q^57 + 168 * q^59 + 22 * q^61 - 496 * q^63 + 156 * q^65 + 84 * q^67 - 96 * q^69 - 60 * q^71 + 126 * q^73 + 24 * q^75 - 16 * q^79 - 194 * q^81 - 56 * q^83 - 6 * q^85 + 156 * q^87 - 190 * q^89 + 416 * q^91 + 48 * q^93 - 108 * q^95 + 222 * q^97 - 88 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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