LMFDB - Embedded newform 228.3.b.e.227.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(227,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("228.227");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.21255002741$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			227.16
Character	$\chi$	$=$	228.227
Dual form			228.3.b.e.227.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56001 + 1.25155i) q^{2} +(2.94611 + 0.566091i) q^{3} +(0.867237 - 3.90486i) q^{4} -9.23717i q^{5} +(-5.30443 + 2.80410i) q^{6} +4.75673i q^{7} +(3.53423 + 7.17699i) q^{8} +(8.35908 + 3.33553i) q^{9} +O(q^{10})$	\(q+(-1.56001 + 1.25155i) q^{2} +(2.94611 + 0.566091i) q^{3} +(0.867237 - 3.90486i) q^{4} -9.23717i q^{5} +(-5.30443 + 2.80410i) q^{6} +4.75673i q^{7} +(3.53423 + 7.17699i) q^{8} +(8.35908 + 3.33553i) q^{9} +(11.5608 + 14.4100i) q^{10} -10.8488 q^{11} +(4.76547 - 11.0132i) q^{12} -16.9489i q^{13} +(-5.95330 - 7.42053i) q^{14} +(5.22907 - 27.2137i) q^{15} +(-14.4958 - 6.77287i) q^{16} -14.5032i q^{17} +(-17.2148 + 5.25839i) q^{18} +(6.84148 - 17.7255i) q^{19} +(-36.0698 - 8.01081i) q^{20} +(-2.69274 + 14.0138i) q^{21} +(16.9242 - 13.5778i) q^{22} +30.5832 q^{23} +(6.34940 + 23.1449i) q^{24} -60.3252 q^{25} +(21.2125 + 26.4404i) q^{26} +(22.7385 + 14.5588i) q^{27} +(18.5744 + 4.12521i) q^{28} +29.6718 q^{29} +(25.9019 + 48.9979i) q^{30} -20.0107 q^{31} +(31.0901 - 7.57653i) q^{32} +(-31.9617 - 6.14141i) q^{33} +(18.1515 + 22.6251i) q^{34} +43.9387 q^{35} +(20.2741 - 29.7483i) q^{36} +38.4429i q^{37} +(11.5117 + 36.2144i) q^{38} +(9.59463 - 49.9334i) q^{39} +(66.2950 - 32.6463i) q^{40} -55.0823 q^{41} +(-13.3384 - 25.2318i) q^{42} -22.6155i q^{43} +(-9.40849 + 42.3630i) q^{44} +(30.8108 - 77.2142i) q^{45} +(-47.7100 + 38.2765i) q^{46} +18.4203 q^{47} +(-38.8721 - 28.1595i) q^{48} +26.3735 q^{49} +(94.1077 - 75.5002i) q^{50} +(8.21013 - 42.7280i) q^{51} +(-66.1832 - 14.6987i) q^{52} +32.2458 q^{53} +(-53.6934 + 5.74663i) q^{54} +100.212i q^{55} +(-34.1390 + 16.8114i) q^{56} +(30.1900 - 48.3484i) q^{57} +(-46.2882 + 37.1358i) q^{58} +41.8200i q^{59} +(-101.731 - 44.0195i) q^{60} +44.2334 q^{61} +(31.2168 - 25.0444i) q^{62} +(-15.8662 + 39.7619i) q^{63} +(-39.0184 + 50.7303i) q^{64} -156.560 q^{65} +(57.5468 - 30.4211i) q^{66} -23.5603 q^{67} +(-56.6329 - 12.5777i) q^{68} +(90.1014 + 17.3129i) q^{69} +(-68.5447 + 54.9916i) q^{70} +90.1038i q^{71} +(5.60393 + 71.7816i) q^{72} -30.0583 q^{73} +(-48.1133 - 59.9712i) q^{74} +(-177.725 - 34.1495i) q^{75} +(-63.2824 - 42.0872i) q^{76} -51.6049i q^{77} +(47.5265 + 89.9045i) q^{78} +50.6357 q^{79} +(-62.5621 + 133.900i) q^{80} +(58.7485 + 55.7639i) q^{81} +(85.9287 - 68.9384i) q^{82} +36.9746 q^{83} +(52.3868 + 22.6681i) q^{84} -133.969 q^{85} +(28.3044 + 35.2803i) q^{86} +(87.4163 + 16.7969i) q^{87} +(-38.3422 - 77.8618i) q^{88} +70.6634 q^{89} +(48.5726 + 159.016i) q^{90} +80.6215 q^{91} +(26.5229 - 119.423i) q^{92} +(-58.9537 - 11.3279i) q^{93} +(-28.7358 + 23.0540i) q^{94} +(-163.734 - 63.1959i) q^{95} +(95.8838 - 4.72142i) q^{96} +84.1388i q^{97} +(-41.1428 + 33.0078i) q^{98} +(-90.6861 - 36.1865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9}+O(q^{10}) $ 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9	$ 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9} - 40 q^{16} + 94 q^{24} - 408 q^{25} + 60 q^{28} + 176 q^{30} - 214 q^{36} + 2 q^{42} + 96 q^{45} - 616 q^{49} + 72 q^{54} + 320 q^{57} + 564 q^{58} + 592 q^{61} - 424 q^{64} + 608 q^{66} + 128 q^{73} - 292 q^{76} - 208 q^{81} + 472 q^{82} - 160 q^{85} + 128 q^{93} + 166 q^{96}+O(q^{100}) $ 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9 - 40 * q^16 + 94 * q^24 - 408 * q^25 + 60 * q^28 + 176 * q^30 - 214 * q^36 + 2 * q^42 + 96 * q^45 - 616 * q^49 + 72 * q^54 + 320 * q^57 + 564 * q^58 + 592 * q^61 - 424 * q^64 + 608 * q^66 + 128 * q^73 - 292 * q^76 - 208 * q^81 + 472 * q^82 - 160 * q^85 + 128 * q^93 + 166 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.56001	+	1.25155i	−0.780003	+	0.625776i
$2$	−1.56001	+	1.25155i	−0.780003	+	0.625776i
$3$	2.94611	+	0.566091i	0.982035	+	0.188697i
$3$	2.94611	+	0.566091i	0.982035	+	0.188697i
$4$	0.867237	−	3.90486i	0.216809	−	0.976214i
$5$		−	9.23717i		−	1.84743i	−0.383077	−	0.923717i	$-0.625135\pi$
$5$		−	9.23717i		−	1.84743i	0.383077	−	0.923717i	$-0.374865\pi$
$6$	−5.30443	+	2.80410i	−0.884072	+	0.467350i
$7$			4.75673i			0.679533i	0.940510	+	0.339767i	$0.110348\pi$
$7$			4.75673i			0.679533i	−0.940510	+	0.339767i	$0.889652\pi$
$8$	3.53423	+	7.17699i	0.441779	+	0.897124i
$9$	8.35908	+	3.33553i	0.928787	+	0.370614i
$10$	11.5608	+	14.4100i	1.15608	+	1.44100i
$11$	−10.8488			−0.986255			−0.493128	−	0.869957i	$-0.664146\pi$
$11$	−10.8488			−0.986255			−0.493128	+	0.869957i	$0.664146\pi$
$12$	4.76547	−	11.0132i	0.397123	−	0.917765i
$13$		−	16.9489i		−	1.30376i	−0.758320	−	0.651882i	$-0.773980\pi$
$13$		−	16.9489i		−	1.30376i	0.758320	−	0.651882i	$-0.226020\pi$
$14$	−5.95330	−	7.42053i	−0.425235	−	0.530038i
$15$	5.22907	−	27.2137i	0.348605	−	1.81424i
$16$	−14.4958	−	6.77287i	−0.905988	−	0.423304i
$17$		−	14.5032i		−	0.853130i	−0.904457	−	0.426565i	$-0.859724\pi$
$17$		−	14.5032i		−	0.853130i	0.904457	−	0.426565i	$-0.140276\pi$
$18$	−17.2148	+	5.25839i	−0.956378	+	0.292133i
$19$	6.84148	−	17.7255i	0.360078	−	0.932922i
$19$	6.84148	−	17.7255i	0.360078	−	0.932922i
$20$	−36.0698	−	8.01081i	−1.80349	−	0.400541i
$21$	−2.69274	+	14.0138i	−0.128226	+	0.667326i
$22$	16.9242	−	13.5778i	0.769282	−	0.617175i
$23$	30.5832			1.32971			0.664853	−	0.746974i	$-0.268494\pi$
$23$	30.5832			1.32971			0.664853	+	0.746974i	$0.268494\pi$
$24$	6.34940	+	23.1449i	0.264559	+	0.964370i
$25$	−60.3252			−2.41301
$26$	21.2125	+	26.4404i	0.815864	+	1.01694i
$27$	22.7385	+	14.5588i	0.842168	+	0.539215i
$28$	18.5744	+	4.12521i	0.663370	+	0.147329i
$29$	29.6718			1.02317			0.511583	−	0.859234i	$-0.329059\pi$
$29$	29.6718			1.02317			0.511583	+	0.859234i	$0.329059\pi$
$30$	25.9019	+	48.9979i	0.863398	+	1.63326i
$31$	−20.0107			−0.645507			−0.322753	−	0.946483i	$-0.604608\pi$
$31$	−20.0107			−0.645507			−0.322753	+	0.946483i	$0.604608\pi$
$32$	31.0901	−	7.57653i	0.971567	−	0.236766i
$33$	−31.9617	−	6.14141i	−0.968538	−	0.186103i
$34$	18.1515	+	22.6251i	0.533868	+	0.665444i
$35$	43.9387			1.25539
$36$	20.2741	−	29.7483i	0.563168	−	0.826342i
$37$			38.4429i			1.03900i	0.854471	+	0.519499i	$0.173881\pi$
$37$			38.4429i			1.03900i	−0.854471	+	0.519499i	$0.826119\pi$
$38$	11.5117	+	36.2144i	0.302938	+	0.953010i
$39$	9.59463	−	49.9334i	0.246016	−	1.28034i
$40$	66.2950	−	32.6463i	1.65738	−	0.816158i
$41$	−55.0823			−1.34347			−0.671735	−	0.740791i	$-0.734451\pi$
$41$	−55.0823			−1.34347			−0.671735	+	0.740791i	$0.734451\pi$
$42$	−13.3384	−	25.2318i	−0.317580	−	0.600757i
$43$		−	22.6155i		−	0.525941i	−0.964804	−	0.262971i	$-0.915298\pi$
$43$		−	22.6155i		−	0.525941i	0.964804	−	0.262971i	$-0.0847022\pi$
$44$	−9.40849	+	42.3630i	−0.213829	+	0.962796i
$45$	30.8108	−	77.2142i	0.684684	−	1.71587i
$46$	−47.7100	+	38.2765i	−1.03717	+	0.832098i
$47$	18.4203			0.391922			0.195961	−	0.980612i	$-0.437217\pi$
$47$	18.4203			0.391922			0.195961	+	0.980612i	$0.437217\pi$
$48$	−38.8721	−	28.1595i	−0.809836	−	0.586657i
$49$	26.3735			0.538235
$50$	94.1077	−	75.5002i	1.88215	−	1.51000i
$51$	8.21013	−	42.7280i	0.160983	−	0.837804i
$52$	−66.1832	−	14.6987i	−1.27275	−	0.282668i
$53$	32.2458			0.608412			0.304206	−	0.952606i	$-0.401609\pi$
$53$	32.2458			0.608412			0.304206	+	0.952606i	$0.401609\pi$
$54$	−53.6934	+	5.74663i	−0.994321	+	0.106419i
$55$			100.212i			1.82204i
$56$	−34.1390	+	16.8114i	−0.609625	+	0.300204i
$57$	30.1900	−	48.3484i	0.529649	−	0.848217i
$58$	−46.2882	+	37.1358i	−0.798073	+	0.640273i
$59$			41.8200i			0.708814i	0.935091	+	0.354407i	$0.115317\pi$
$59$			41.8200i			0.708814i	−0.935091	+	0.354407i	$0.884683\pi$
$60$	−101.731	−	44.0195i	−1.69551	−	0.733658i
$61$	44.2334			0.725138			0.362569	−	0.931957i	$-0.381900\pi$
$61$	44.2334			0.725138			0.362569	+	0.931957i	$0.381900\pi$
$62$	31.2168	−	25.0444i	0.503497	−	0.403943i
$63$	−15.8662	+	39.7619i	−0.251844	+	0.631142i
$64$	−39.0184	+	50.7303i	−0.609662	+	0.792661i
$65$	−156.560			−2.40862
$66$	57.5468	−	30.4211i	0.871921	−	0.460926i
$67$	−23.5603			−0.351646			−0.175823	−	0.984422i	$-0.556259\pi$
$67$	−23.5603			−0.351646			−0.175823	+	0.984422i	$0.556259\pi$
$68$	−56.6329	−	12.5777i	−0.832837	−	0.184966i
$69$	90.1014	+	17.3129i	1.30582	+	0.250911i
$70$	−68.5447	+	54.9916i	−0.979210	+	0.785594i
$71$			90.1038i			1.26907i	0.772895	+	0.634534i	$0.218808\pi$
$71$			90.1038i			1.26907i	−0.772895	+	0.634534i	$0.781192\pi$
$72$	5.60393	+	71.7816i	0.0778323	+	0.996966i
$73$	−30.0583			−0.411758			−0.205879	−	0.978577i	$-0.566005\pi$
$73$	−30.0583			−0.411758			−0.205879	+	0.978577i	$0.566005\pi$
$74$	−48.1133	−	59.9712i	−0.650180	−	0.810422i
$75$	−177.725	−	34.1495i	−2.36966	−	0.455327i
$76$	−63.2824	−	42.0872i	−0.832664	−	0.553779i
$77$		−	51.6049i		−	0.670193i
$78$	47.5265	+	89.9045i	0.609314	+	1.15262i
$79$	50.6357			0.640958			0.320479	−	0.947256i	$-0.396156\pi$
$79$	50.6357			0.640958			0.320479	+	0.947256i	$0.396156\pi$
$80$	−62.5621	+	133.900i	−0.782027	+	1.67375i
$81$	58.7485	+	55.7639i	0.725291	+	0.688443i
$82$	85.9287	−	68.9384i	1.04791	−	0.840712i
$83$	36.9746			0.445477			0.222738	−	0.974878i	$-0.428500\pi$
$83$	36.9746			0.445477			0.222738	+	0.974878i	$0.428500\pi$
$84$	52.3868	+	22.6681i	0.623652	+	0.269858i
$85$	−133.969			−1.57610
$86$	28.3044	+	35.2803i	0.329121	+	0.410236i
$87$	87.4163	+	16.7969i	1.00479	+	0.193068i
$88$	−38.3422	−	77.8618i	−0.435707	−	0.884793i
$89$	70.6634			0.793971			0.396985	−	0.917825i	$-0.370056\pi$
$89$	70.6634			0.793971			0.396985	+	0.917825i	$0.370056\pi$
$90$	48.5726	+	159.016i	0.539695	+	1.76684i
$91$	80.6215			0.885951
$92$	26.5229	−	119.423i	0.288292	−	1.29808i
$93$	−58.9537	−	11.3279i	−0.633911	−	0.121805i
$94$	−28.7358	+	23.0540i	−0.305700	+	0.245255i
$95$	−163.734	−	63.1959i	−1.72351	−	0.665220i
$96$	95.8838	−	4.72142i	0.998790	−	0.0491815i
$97$			84.1388i			0.867410i	0.901055	+	0.433705i	$0.142794\pi$
$97$			84.1388i			0.867410i	−0.901055	+	0.433705i	$0.857206\pi$
$98$	−41.1428	+	33.0078i	−0.419825	+	0.336814i
$99$	−90.6861	−	36.1865i	−0.916021	−	0.365520i
$100$	−52.3163	+	235.561i	−0.523163	+	2.35561i
$101$		−	23.2591i		−	0.230288i	−0.993349	−	0.115144i	$-0.963267\pi$
$101$		−	23.2591i		−	0.230288i	0.993349	−	0.115144i	$-0.0367330\pi$
$102$	40.6684	+	76.9313i	0.398710	+	0.754229i
$103$	−92.9858			−0.902774			−0.451387	−	0.892328i	$-0.649071\pi$
$103$	−92.9858			−0.902774			−0.451387	+	0.892328i	$0.649071\pi$
$104$	121.642	−	59.9015i	1.16964	−	0.575976i
$105$	129.448	+	24.8733i	1.23284	+	0.236889i
$106$	−50.3037	+	40.3573i	−0.474563	+	0.380729i
$107$		−	30.3544i		−	0.283686i	−0.989889	−	0.141843i	$-0.954697\pi$
$107$		−	30.3544i		−	0.283686i	0.989889	−	0.141843i	$-0.0453028\pi$
$108$	76.5698	−	76.1648i	0.708979	−	0.705229i
$109$			79.6372i			0.730616i	0.930887	+	0.365308i	$0.119036\pi$
$109$			79.6372i			0.730616i	−0.930887	+	0.365308i	$0.880964\pi$
$110$	−125.421	−	156.332i	−1.14019	−	1.42120i
$111$	−21.7622	+	113.257i	−0.196056	+	1.02033i
$112$	32.2167	−	68.9526i	0.287649	−	0.615649i
$113$	−92.7692			−0.820966			−0.410483	−	0.911868i	$-0.634640\pi$
$113$	−92.7692			−0.820966			−0.410483	+	0.911868i	$0.634640\pi$
$114$	13.4139	+	113.208i	0.117666	+	0.993053i
$115$		−	282.502i		−	2.45654i
$116$	25.7325	−	115.864i	0.221832	−	0.998829i
$117$	56.5336	−	141.678i	0.483193	−	1.21092i
$118$	−52.3399	−	65.2395i	−0.443559	−	0.552877i
$119$	68.9879			0.579730
$120$	213.793	−	58.6505i	1.78161	−	0.488754i
$121$	−3.30337			−0.0273006
$122$	−69.0044	+	55.3604i	−0.565610	+	0.453774i
$123$	−162.278	−	31.1816i	−1.31934	−	0.253509i
$124$	−17.3540	+	78.1390i	−0.139952	+	0.630153i
$125$			326.305i			2.61044i
$126$	−25.0127	−	81.8862i	−0.198514	−	0.649890i
$127$	−86.6311			−0.682135			−0.341067	−	0.940039i	$-0.610788\pi$
$127$	−86.6311			−0.682135			−0.341067	+	0.940039i	$0.610788\pi$
$128$	−2.62274	−	127.973i	−0.0204901	−	0.999790i
$129$	12.8024	−	66.6276i	0.0992434	−	0.516493i
$130$	244.235	−	195.943i	1.87873	−	1.50725i
$131$	25.6062			0.195468			0.0977338	−	0.995213i	$-0.468841\pi$
$131$	25.6062			0.195468			0.0977338	+	0.995213i	$0.468841\pi$
$132$	−51.6997	+	119.480i	−0.391664	+	0.905151i
$133$	84.3156	+	32.5431i	0.633952	+	0.244685i
$134$	36.7542	−	29.4869i	0.274285	−	0.220052i
$135$	134.482	−	210.040i	0.996164	−	1.55585i
$136$	104.089	−	51.2577i	0.765363	−	0.376895i
$137$			50.5421i			0.368920i	0.982840	+	0.184460i	$0.0590537\pi$
$137$			50.5421i			0.368920i	−0.982840	+	0.184460i	$0.940946\pi$
$138$	−162.227	+	85.7584i	−1.17556	+	0.621438i
$139$			269.429i			1.93834i	0.246402	+	0.969168i	$0.420752\pi$
$139$			269.429i			1.93834i	−0.246402	+	0.969168i	$0.579248\pi$
$140$	38.1053	−	171.574i	0.272181	−	1.22553i
$141$	54.2682	+	10.4276i	0.384881	+	0.0739544i
$142$	−112.770	−	140.562i	−0.794152	−	0.989876i
$143$			183.876i			1.28584i
$144$	−98.5805	−	104.966i	−0.684587	−	0.728931i
$145$		−	274.084i		−	1.89023i
$146$	46.8912	−	37.6195i	0.321172	−	0.257668i
$147$	77.6991	+	14.9298i	0.528566	+	0.101563i
$148$	150.114	+	33.3391i	1.01428	+	0.225264i
$149$			14.5602i			0.0977196i	0.998806	+	0.0488598i	$0.0155588\pi$
$149$			14.5602i			0.0977196i	−0.998806	+	0.0488598i	$0.984441\pi$
$150$	319.991	−	169.158i	2.13328	−	1.12772i
$151$	257.740			1.70689			0.853445	−	0.521184i	$-0.174509\pi$
$151$	257.740			1.70689			0.853445	+	0.521184i	$0.174509\pi$
$152$	151.395	−	13.5449i	0.996022	−	0.0891112i
$153$	48.3758	−	121.234i	0.316182	−	0.792376i
$154$	64.5862	+	80.5039i	0.419391	+	0.522753i
$155$			184.842i			1.19253i
$156$	−186.662	−	80.7697i	−1.19655	−	0.517755i
$157$	285.013			1.81537			0.907684	−	0.419655i	$-0.137849\pi$
$157$	285.013			1.81537			0.907684	+	0.419655i	$0.137849\pi$
$158$	−78.9920	+	63.3732i	−0.499949	+	0.401096i
$159$	94.9996	+	18.2541i	0.597482	+	0.114805i
$160$	−69.9856	−	287.185i	−0.437410	−	1.79490i
$161$			145.476i			0.903579i
$162$	−161.439	−	13.4651i	−0.996540	−	0.0831181i
$163$			91.2846i			0.560028i	0.959996	+	0.280014i	$0.0903391\pi$
$163$			91.2846i			0.560028i	−0.959996	+	0.280014i	$0.909661\pi$
$164$	−47.7694	+	215.088i	−0.291277	+	1.31152i
$165$	−56.7292	+	295.236i	−0.343813	+	1.78931i
$166$	−57.6805	+	46.2756i	−0.347473	+	0.278769i
$167$			100.730i			0.603174i	0.953439	+	0.301587i	$0.0975164\pi$
$167$			100.730i			0.603174i	−0.953439	+	0.301587i	$0.902484\pi$
$168$	−110.094	+	30.2024i	−0.655321	+	0.179776i
$169$	−118.266			−0.699801
$170$	208.992	−	167.669i	1.22936	−	0.986285i
$171$	116.312	−	125.349i	0.680190	−	0.733036i
$172$	−88.3102	−	19.6130i	−0.513431	−	0.114029i
$173$	−224.024			−1.29494			−0.647470	−	0.762091i	$-0.724173\pi$
$173$	−224.024			−1.29494			−0.647470	+	0.762091i	$0.724173\pi$
$174$	−157.392	+	83.2027i	−0.904553	+	0.478177i
$175$		−	286.951i		−	1.63972i
$176$	157.262	+	73.4776i	0.893535	+	0.417486i
$177$	−23.6739	+	123.206i	−0.133751	+	0.696080i
$178$	−110.235	+	88.4389i	−0.619300	+	0.496848i
$179$		−	169.523i		−	0.947055i	−0.880779	−	0.473528i	$-0.842980\pi$
$179$		−	169.523i		−	0.947055i	0.880779	−	0.473528i	$-0.157020\pi$
$180$	−274.790	−	187.275i	−1.52661	−	1.04042i
$181$		−	262.117i		−	1.44816i	−0.689716	−	0.724080i	$-0.742265\pi$
$181$		−	262.117i		−	1.44816i	0.689716	−	0.724080i	$-0.257735\pi$
$182$	−125.770	+	100.902i	−0.691044	+	0.554407i
$183$	130.316	+	25.0401i	0.712111	+	0.136831i
$184$	108.088	+	219.496i	0.587436	+	1.19291i
$185$	355.104			1.91948
$186$	106.146	−	56.1120i	0.570675	−	0.301678i
$187$			157.342i			0.841404i
$188$	15.9748	−	71.9287i	0.0849722	−	0.382599i
$189$	−69.2524	+	108.161i	−0.366415	+	0.572281i
$190$	334.518	−	106.335i	1.76062	−	0.559658i
$191$	−98.9361			−0.517990			−0.258995	−	0.965879i	$-0.583391\pi$
$191$	−98.9361			−0.517990			−0.258995	+	0.965879i	$0.583391\pi$
$192$	−143.670	+	127.369i	−0.748282	+	0.663380i
$193$		−	155.628i		−	0.806362i	−0.915120	−	0.403181i	$-0.867904\pi$
$193$		−	155.628i		−	0.806362i	0.915120	−	0.403181i	$-0.132096\pi$
$194$	−105.304	−	131.257i	−0.542804	−	0.676583i
$195$	−461.243	−	88.6272i	−2.36535	−	0.454498i
$196$	22.8721	−	102.985i	0.116694	−	0.525432i
$197$		−	160.003i		−	0.812198i	−0.913829	−	0.406099i	$-0.866889\pi$
$197$		−	160.003i		−	0.812198i	0.913829	−	0.406099i	$-0.133111\pi$
$198$	186.760	−	57.0472i	0.943233	−	0.288117i
$199$			185.073i			0.930017i	0.885306	+	0.465009i	$0.153949\pi$
$199$			185.073i			0.930017i	−0.885306	+	0.465009i	$0.846051\pi$
$200$	−213.204	−	432.954i	−1.06602	−	2.16477i
$201$	−69.4111	−	13.3373i	−0.345329	−	0.0663545i
$202$	29.1100	+	36.2844i	0.144109	+	0.179626i
$203$			141.141i			0.695275i
$204$	−159.727	−	69.1146i	−0.782973	−	0.338797i
$205$			508.804i			2.48197i
$206$	145.058	−	116.376i	0.704167	−	0.564934i
$207$	255.648	+	102.011i	1.23501	+	0.492807i
$208$	−114.793	+	245.688i	−0.551889	+	1.18119i
$209$	−74.2219	+	192.301i	−0.355129	+	0.920099i
$210$	−233.070	+	123.209i	−1.10986	+	0.586707i
$211$	−216.029			−1.02383			−0.511917	−	0.859035i	$-0.671065\pi$
$211$	−216.029			−1.02383			−0.511917	+	0.859035i	$0.671065\pi$
$212$	27.9648	−	125.915i	0.131909	−	0.593940i
$213$	−51.0069	+	265.455i	−0.239469	+	1.24627i
$214$	37.9901	+	47.3530i	0.177524	+	0.221276i
$215$	−208.903			−0.971641
$216$	−24.1251	+	214.649i	−0.111690	+	0.993743i
$217$		−	95.1856i		−	0.438643i
$218$	−99.6701	−	124.234i	−0.457202	−	0.569883i
$219$	−88.5550	−	17.0157i	−0.404361	−	0.0776974i
$220$	391.314	+	86.9077i	1.77870	+	0.395035i
$221$	−245.814			−1.11228
$222$	−107.798	−	203.918i	−0.485576	−	0.918550i
$223$	66.2752			0.297198			0.148599	−	0.988898i	$-0.452524\pi$
$223$	66.2752			0.297198			0.148599	+	0.988898i	$0.452524\pi$
$224$	36.0395	+	147.887i	0.160891	+	0.660212i
$225$	−504.264	−	201.216i	−2.24117	−	0.894295i
$226$	144.720	−	116.105i	0.640356	−	0.513741i
$227$			19.9560i			0.0879121i	0.999033	+	0.0439560i	$0.0139961\pi$
$227$			19.9560i			0.0879121i	−0.999033	+	0.0439560i	$0.986004\pi$
$228$	−162.612	−	159.817i	−0.713209	−	0.700952i
$229$	232.209			1.01401			0.507007	−	0.861942i	$-0.330752\pi$
$229$	232.209			1.01401			0.507007	+	0.861942i	$0.330752\pi$
$230$	353.566	+	440.705i	1.53724	+	1.91611i
$231$	29.2130	−	152.033i	0.126463	−	0.658153i
$232$	104.867	+	212.954i	0.452014	+	0.917907i
$233$		−	299.386i		−	1.28492i	−0.766320	−	0.642459i	$-0.777914\pi$
$233$		−	299.386i		−	1.28492i	0.766320	−	0.642459i	$-0.222086\pi$
$234$	89.1240	+	291.773i	0.380872	+	1.24689i
$235$		−	170.152i		−	0.724049i
$236$	163.301	+	36.2679i	0.691954	+	0.153677i
$237$	149.178	+	28.6644i	0.629443	+	0.120947i
$238$	−107.621	+	86.3419i	−0.452191	+	0.362781i
$239$	−143.556			−0.600651			−0.300326	−	0.953837i	$-0.597095\pi$
$239$	−143.556			−0.600651			−0.300326	+	0.953837i	$0.597095\pi$
$240$	−260.114	+	359.068i	−1.08381	+	1.49612i
$241$		−	60.2680i		−	0.250075i	−0.992152	−	0.125037i	$-0.960095\pi$
$241$		−	60.2680i		−	0.250075i	0.992152	−	0.125037i	$-0.0399051\pi$
$242$	5.15328	−	4.13434i	0.0212946	−	0.0170841i
$243$	141.512	+	197.543i	0.582354	+	0.812935i
$244$	38.3608	−	172.725i	0.157217	−	0.707890i
$245$		−	243.616i		−	0.994353i
$246$	292.181	−	154.456i	1.18773	−	0.627871i
$247$	−300.429	−	115.956i	−1.21631	−	0.469457i
$248$	−70.7226	−	143.617i	−0.285172	−	0.579100i
$249$	108.931	+	20.9310i	0.437474	+	0.0840601i
$250$	−408.388	−	509.038i	−1.63355	−	2.03615i
$251$	318.675			1.26962			0.634811	−	0.772667i	$-0.281078\pi$
$251$	318.675			1.26962			0.634811	+	0.772667i	$0.281078\pi$
$252$	141.505	+	96.4382i	0.561527	+	0.382691i
$253$	−331.792			−1.31143
$254$	135.145	−	108.423i	0.532067	−	0.426863i
$255$	−394.686	−	75.8383i	−1.54779	−	0.297405i
$256$	164.256	+	196.356i	0.641627	+	0.767017i
$257$	−17.1171			−0.0666035			−0.0333017	−	0.999445i	$-0.510602\pi$
$257$	−17.1171			−0.0666035			−0.0333017	+	0.999445i	$0.510602\pi$
$258$	63.4160	+	119.962i	0.245799	+	0.464970i
$259$	−182.863			−0.706034
$260$	−135.775	+	611.345i	−0.522210	+	2.35133i
$261$	248.029	+	98.9711i	0.950304	+	0.379200i
$262$	−39.9459	+	32.0475i	−0.152465	+	0.122319i
$263$	−73.7567			−0.280444			−0.140222	−	0.990120i	$-0.544782\pi$
$263$	−73.7567			−0.280444			−0.140222	+	0.990120i	$0.544782\pi$
$264$	−68.8835	−	251.094i	−0.260922	−	0.951115i
$265$		−	297.860i		−	1.12400i
$266$	−172.262	+	54.7579i	−0.647602	+	0.205857i
$267$	208.182	+	40.0019i	0.779708	+	0.149820i
$268$	−20.4324	+	91.9996i	−0.0762401	+	0.343282i
$269$	346.176			1.28690			0.643449	−	0.765489i	$-0.277503\pi$
$269$	346.176			1.28690			0.643449	+	0.765489i	$0.277503\pi$
$270$	53.0825	+	495.974i	0.196602	+	1.83694i
$271$		−	74.9215i		−	0.276463i	−0.990400	−	0.138232i	$-0.955858\pi$
$271$		−	74.9215i		−	0.276463i	0.990400	−	0.138232i	$-0.0441418\pi$
$272$	−98.2283	+	210.236i	−0.361134	+	0.772925i
$273$	237.520	+	45.6391i	0.870035	+	0.167176i
$274$	−63.2560	−	78.8459i	−0.230861	−	0.287759i
$275$	654.457			2.37984
$276$	145.744	−	336.819i	0.528056	−	1.22036i
$277$	274.809			0.992091			0.496045	−	0.868297i	$-0.334785\pi$
$277$	274.809			0.992091			0.496045	+	0.868297i	$0.334785\pi$
$278$	−337.204	−	420.310i	−1.21296	−	1.51191i
$279$	−167.271	−	66.7462i	−0.599538	−	0.239234i
$280$	155.290	+	315.348i	0.554606	+	1.12624i
$281$	115.168			0.409849			0.204925	−	0.978778i	$-0.434305\pi$
$281$	115.168			0.409849			0.204925	+	0.978778i	$0.434305\pi$
$282$	−97.7094	+	51.6524i	−0.346487	+	0.183165i
$283$			68.8062i			0.243132i	0.992583	+	0.121566i	$0.0387915\pi$
$283$			68.8062i			0.243132i	−0.992583	+	0.121566i	$0.961208\pi$
$284$	351.842	+	78.1413i	1.23888	+	0.275145i
$285$	−446.602	−	278.870i	−1.56702	−	0.978491i
$286$	−230.130	−	286.847i	−0.804650	−	1.00296i
$287$		−	262.012i		−	0.912933i
$288$	285.157	+	40.3691i	0.990127	+	0.140171i
$289$	78.6570			0.272170
$290$	343.030	+	427.572i	1.18286	+	1.47439i
$291$	−47.6302	+	247.882i	−0.163678	+	0.851828i
$292$	−26.0677	+	117.373i	−0.0892729	+	0.401964i
$293$	235.712			0.804477			0.402239	−	0.915535i	$-0.368232\pi$
$293$	235.712			0.804477			0.402239	+	0.915535i	$0.368232\pi$
$294$	−139.897	+	73.9539i	−0.475838	+	0.251544i
$295$	386.299			1.30949
$296$	−275.905	+	135.866i	−0.932110	+	0.459008i
$297$	−246.686	−	157.946i	−0.830593	−	0.531804i
$298$	−18.2229	−	22.7140i	−0.0611506	−	0.0762216i
$299$		−	518.353i		−	1.73362i
$300$	−287.478	+	664.373i	−0.958261	+	2.21458i
$301$	107.576			0.357394
$302$	−402.076	+	322.575i	−1.33138	+	1.06813i
$303$	13.1668	−	68.5238i	0.0434547	−	0.226151i
$304$	−219.225	+	210.609i	−0.721136	+	0.692793i
$305$		−	408.591i		−	1.33964i
$306$	76.2634	+	249.670i	0.249227	+	0.815914i
$307$	−399.054			−1.29985			−0.649925	−	0.759998i	$-0.725200\pi$
$307$	−399.054			−1.29985			−0.649925	+	0.759998i	$0.725200\pi$
$308$	−201.510	−	44.7536i	−0.654252	−	0.145304i
$309$	−273.946	−	52.6384i	−0.886556	−	0.170351i
$310$	−231.340	−	288.355i	−0.746257	−	0.930178i
$311$	236.730			0.761190			0.380595	−	0.924742i	$-0.375719\pi$
$311$	236.730			0.761190			0.380595	+	0.924742i	$0.375719\pi$
$312$	392.281	−	107.616i	1.25731	−	0.344922i
$313$	165.194			0.527775			0.263888	−	0.964553i	$-0.414995\pi$
$313$	165.194			0.527775			0.263888	+	0.964553i	$0.414995\pi$
$314$	−444.622	+	356.708i	−1.41599	+	1.13601i
$315$	367.287	+	146.559i	1.16599	+	0.465266i
$316$	43.9131	−	197.725i	0.138966	−	0.625712i
$317$	−465.724			−1.46916			−0.734581	−	0.678521i	$-0.762621\pi$
$317$	−465.724			−1.46916			−0.734581	+	0.678521i	$0.762621\pi$
$318$	−171.046	+	90.4205i	−0.537880	+	0.284341i
$319$	−321.904			−1.00910
$320$	468.604	+	360.419i	1.46439	+	1.12631i
$321$	17.1833	−	89.4272i	0.0535306	−	0.278589i
$322$	−182.071	−	226.944i	−0.565438	−	0.704794i
$323$	−257.077	−	99.2234i	−0.795904	−	0.307193i
$324$	268.699	−	181.044i	0.829317	−	0.558778i
$325$			1022.45i			3.14600i
$326$	−114.247	−	142.404i	−0.350452	−	0.436824i
$327$	−45.0819	+	234.620i	−0.137865	+	0.717491i
$328$	−194.674	−	395.325i	−0.593518	−	1.20526i
$329$			87.6205i			0.266324i
$330$	−281.005	−	531.569i	−0.851531	−	1.61082i
$331$	585.474			1.76880			0.884401	−	0.466728i	$-0.154567\pi$
$331$	585.474			1.76880			0.884401	+	0.466728i	$0.154567\pi$
$332$	32.0657	−	144.380i	0.0965835	−	0.434881i
$333$	−128.227	+	321.348i	−0.385067	+	0.965008i
$334$	−126.069	−	157.140i	−0.377452	−	0.470478i
$335$			217.630i			0.649643i
$336$	133.947	−	184.904i	0.398653	−	0.550310i
$337$			27.4673i			0.0815054i	0.999169	+	0.0407527i	$0.0129756\pi$
$337$			27.4673i			0.0815054i	−0.999169	+	0.0407527i	$0.987024\pi$
$338$	184.496	−	148.017i	0.545847	−	0.437919i
$339$	−273.308	−	52.5157i	−0.806218	−	0.154914i
$340$	−116.182	+	523.128i	−0.341713	+	1.53861i
$341$	217.092			0.636635
$342$	−24.5671	+	341.116i	−0.0718337	+	0.997417i
$343$			358.532i			1.04528i
$344$	162.311	−	79.9284i	0.471834	−	0.232350i
$345$	159.922	−	832.282i	0.463542	−	2.41241i
$346$	349.479	−	280.378i	1.01006	−	0.810342i
$347$	64.9325			0.187125			0.0935626	−	0.995613i	$-0.470174\pi$
$347$	64.9325			0.187125			0.0935626	+	0.995613i	$0.470174\pi$
$348$	141.400	−	326.781i	0.406323	−	0.939027i
$349$	−85.2370			−0.244232			−0.122116	−	0.992516i	$-0.538968\pi$
$349$	−85.2370			−0.244232			−0.122116	+	0.992516i	$0.538968\pi$
$350$	359.134	+	447.645i	1.02610	+	1.27899i
$351$	246.756	−	385.394i	0.703009	−	1.09799i
$352$	−337.291	+	82.1963i	−0.958213	+	0.233512i
$353$			54.7512i			0.155103i	0.996988	+	0.0775513i	$0.0247102\pi$
$353$			54.7512i			0.155103i	−0.996988	+	0.0775513i	$0.975290\pi$
$354$	−117.268	−	221.832i	−0.331264	−	0.626643i
$355$	832.303			2.34452
$356$	61.2819	−	275.930i	0.172140	−	0.775086i
$357$	203.246	+	39.0534i	0.569315	+	0.109393i
$358$	212.167	+	264.457i	0.592644	+	0.738706i
$359$	−190.804			−0.531488			−0.265744	−	0.964044i	$-0.585618\pi$
$359$	−190.804			−0.531488			−0.265744	+	0.964044i	$0.585618\pi$
$360$	663.058	−	51.7644i	1.84183	−	0.143790i
$361$	−267.388	−	242.538i	−0.740688	−	0.671849i
$362$	328.053	+	408.904i	0.906224	+	1.12957i
$363$	−9.73209	−	1.87001i	−0.0268102	−	0.00515154i
$364$	69.9180	−	314.816i	0.192082	−	0.864878i
$365$			277.654i			0.760695i
$366$	−234.633	+	124.035i	−0.641074	+	0.338893i
$367$		−	538.449i		−	1.46716i	−0.679601	−	0.733582i	$-0.737847\pi$
$367$		−	538.449i		−	1.46716i	0.679601	−	0.733582i	$-0.262153\pi$
$368$	−443.328	−	207.136i	−1.20470	−	0.562870i
$369$	−460.438	−	183.728i	−1.24780	−	0.497909i
$370$	−553.964	+	444.431i	−1.49720	+	1.20116i
$371$			153.385i			0.413436i
$372$	−95.3605	+	220.382i	−0.256346	+	0.592424i
$373$			103.249i			0.276807i	0.990376	+	0.138403i	$0.0441970\pi$
$373$			103.249i			0.276807i	−0.990376	+	0.138403i	$0.955803\pi$
$374$	−196.922	−	245.455i	−0.526530	−	0.656297i
$375$	−184.718	+	961.329i	−0.492582	+	2.56355i
$376$	65.1017	+	132.202i	0.173143	+	0.351602i
$377$		−	502.906i		−	1.33397i
$378$	−27.3352	−	255.405i	−0.0723152	−	0.675674i
$379$	−175.759			−0.463743			−0.231872	−	0.972746i	$-0.574485\pi$
$379$	−175.759			−0.463743			−0.231872	+	0.972746i	$0.574485\pi$
$380$	−388.767	+	584.550i	−1.02307	+	1.53829i
$381$	−255.224	−	49.0411i	−0.669880	−	0.128717i
$382$	154.341	−	123.824i	0.404034	−	0.324146i
$383$			571.692i			1.49267i	0.665572	+	0.746334i	$0.268188\pi$
$383$			571.692i			1.49267i	−0.665572	+	0.746334i	$0.731812\pi$
$384$	64.7175	−	378.507i	0.168535	−	0.985696i
$385$	−476.683			−1.23814
$386$	194.776	+	242.780i	0.504602	+	0.628965i
$387$	75.4345	−	189.045i	0.194921	−	0.488487i
$388$	328.550	+	72.9683i	0.846778	+	0.188063i
$389$		−	218.115i		−	0.560706i	−0.959897	−	0.280353i	$-0.909548\pi$
$389$		−	218.115i		−	0.560706i	0.959897	−	0.280353i	$-0.0904515\pi$
$390$	830.463	−	439.010i	2.12939	−	1.12567i
$391$		−	443.555i		−	1.13441i
$392$	93.2101	+	189.282i	0.237781	+	0.482863i
$393$	75.4387	+	14.4955i	0.191956	+	0.0368841i
$394$	200.252	+	249.606i	0.508254	+	0.633517i
$395$		−	467.730i		−	1.18413i
$396$	−219.949	+	322.734i	−0.555427	+	0.814984i
$397$	−114.053			−0.287288			−0.143644	−	0.989629i	$-0.545882\pi$
$397$	−114.053			−0.287288			−0.143644	+	0.989629i	$0.545882\pi$
$398$	−231.629	−	288.716i	−0.581982	−	0.725416i
$399$	229.980	+	143.606i	0.576392	+	0.359914i
$400$	874.463	+	408.575i	2.18616	+	1.02144i
$401$	−457.051			−1.13978			−0.569889	−	0.821722i	$-0.693014\pi$
$401$	−457.051			−1.13978			−0.569889	+	0.821722i	$0.693014\pi$
$402$	124.974	−	66.0654i	0.310881	−	0.164342i
$403$			339.160i			0.841589i
$404$	−90.8235	−	20.1712i	−0.224811	−	0.0499286i
$405$	515.100	−	542.670i	1.27185	−	1.33993i
$406$	−176.645	−	220.181i	−0.435087	−	0.542317i
$407$		−	417.060i		−	1.02472i
$408$	335.675	−	92.0867i	0.822732	−	0.225703i
$409$		−	810.654i		−	1.98204i	−0.133715	−	0.991020i	$-0.542691\pi$
$409$		−	810.654i		−	1.98204i	0.133715	−	0.991020i	$-0.457309\pi$
$410$	−636.795	−	793.738i	−1.55316	−	1.93595i
$411$	−28.6114	+	148.902i	−0.0696141	+	0.362293i
$412$	−80.6407	+	363.096i	−0.195730	+	0.881301i
$413$	−198.927			−0.481663
$414$	−526.484	+	160.818i	−1.27170	+	0.388450i
$415$		−	341.540i		−	0.822989i
$416$	−128.414	−	526.945i	−0.308688	−	1.26669i
$417$	−152.521	+	793.765i	−0.365758	+	1.90351i
$418$	−124.888	−	392.883i	−0.298774	−	0.939911i
$419$	−430.301			−1.02697			−0.513486	−	0.858098i	$-0.671646\pi$
$419$	−430.301			−1.02697			−0.513486	+	0.858098i	$0.671646\pi$
$420$	209.389	−	483.905i	0.498545	−	1.15216i
$421$			196.962i			0.467844i	0.972255	+	0.233922i	$0.0751560\pi$
$421$			196.962i			0.467844i	−0.972255	+	0.233922i	$0.924844\pi$
$422$	337.007	−	270.372i	0.798594	−	0.640691i
$423$	153.977	+	61.4414i	0.364012	+	0.145252i
$424$	113.964	+	231.428i	0.268784	+	0.545821i
$425$			874.909i			2.05861i
$426$	−252.660	−	477.950i	−0.593098	−	1.12195i
$427$			210.406i			0.492755i
$428$	−118.529	−	26.3244i	−0.276938	−	0.0615057i
$429$	−104.090	+	541.717i	−0.242635	+	1.26274i
$430$	325.890	−	261.453i	0.757883	−	0.608030i
$431$		−	418.139i		−	0.970160i	−0.874470	−	0.485080i	$-0.838791\pi$
$431$		−	418.139i		−	0.970160i	0.874470	−	0.485080i	$-0.161209\pi$
$432$	−231.008	−	365.047i	−0.534742	−	0.845016i
$433$			728.486i			1.68242i	0.540712	+	0.841208i	$0.318155\pi$
$433$			728.486i			1.68242i	−0.540712	+	0.841208i	$0.681845\pi$
$434$	119.130	+	148.490i	0.274492	+	0.342143i
$435$	155.156	−	807.479i	0.356681	−	1.85627i
$436$	310.972	+	69.0643i	0.713238	+	0.158404i
$437$	209.235	−	542.104i	0.478798	−	1.24051i
$438$	159.442	−	84.2865i	0.364024	−	0.192435i
$439$	−51.8932			−0.118208			−0.0591039	−	0.998252i	$-0.518824\pi$
$439$	−51.8932			−0.118208			−0.0591039	+	0.998252i	$0.518824\pi$
$440$	−719.222	+	354.174i	−1.63460	+	0.804940i
$441$	220.458	+	87.9695i	0.499905	+	0.199477i
$442$	383.471	−	307.649i	0.867582	−	0.696038i
$443$	−746.866			−1.68593			−0.842964	−	0.537970i	$-0.819191\pi$
$443$	−746.866			−1.68593			−0.842964	+	0.537970i	$0.819191\pi$
$444$	423.379	+	183.199i	0.953557	+	0.412610i
$445$		−	652.730i		−	1.46681i
$446$	−103.390	+	82.9469i	−0.231816	+	0.185980i
$447$	−8.24240	+	42.8960i	−0.0184394	+	0.0959641i
$448$	−241.311	−	185.600i	−0.538640	−	0.414286i
$449$	305.787			0.681041			0.340521	−	0.940237i	$-0.389397\pi$
$449$	305.787			0.681041			0.340521	+	0.940237i	$0.389397\pi$
$450$	1038.49	−	317.213i	2.30775	−	0.704918i
$451$	597.577			1.32501
$452$	−80.4528	+	362.250i	−0.177993	+	0.801439i
$453$	759.330	+	145.904i	1.67623	+	0.322085i
$454$	−24.9760	−	31.1315i	−0.0550132	−	0.0685717i
$455$		−	744.715i		−	1.63674i
$456$	453.694	+	45.7987i	0.994944	+	0.100436i
$457$	−569.448			−1.24606			−0.623028	−	0.782200i	$-0.714098\pi$
$457$	−569.448			−1.24606			−0.623028	+	0.782200i	$0.714098\pi$
$458$	−362.248	+	290.622i	−0.790934	+	0.634545i
$459$	211.149	−	329.782i	0.460021	−	0.718479i
$460$	−1103.13	−	244.996i	−2.39811	−	0.532601i
$461$		−	30.6637i		−	0.0665156i	−0.999447	−	0.0332578i	$-0.989412\pi$
$461$		−	30.6637i		−	0.0665156i	0.999447	−	0.0332578i	$-0.0105882\pi$
$462$	144.705	+	273.735i	0.313215	+	0.592499i
$463$		−	244.855i		−	0.528846i	−0.964407	−	0.264423i	$-0.914819\pi$
$463$		−	244.855i		−	0.528846i	0.964407	−	0.264423i	$-0.0851814\pi$
$464$	−430.117	−	200.963i	−0.926976	−	0.433111i
$465$	−104.637	+	544.565i	−0.225027	+	1.17111i
$466$	374.697	+	467.044i	0.804071	+	1.00224i
$467$	426.900			0.914134			0.457067	−	0.889432i	$-0.348900\pi$
$467$	426.900			0.914134			0.457067	+	0.889432i	$0.348900\pi$
$468$	−504.202	−	343.624i	−1.07736	−	0.734238i
$469$		−	112.070i		−	0.238955i
$470$	212.953	+	265.437i	0.453092	+	0.564760i
$471$	839.678	+	161.343i	1.78276	+	0.342554i
$472$	−300.142	+	147.802i	−0.635894	+	0.313139i
$473$			245.351i			0.518712i
$474$	−268.594	+	141.987i	−0.566653	+	0.299552i
$475$	−412.714	+	1069.30i	−0.868872	+	2.25115i
$476$	59.8288	−	269.388i	0.125691	−	0.565941i
$477$	269.546	+	107.557i	0.565085	+	0.225486i
$478$	223.948	−	179.667i	0.468510	−	0.375873i
$479$	478.569			0.999100			0.499550	−	0.866285i	$-0.333499\pi$
$479$	478.569			0.999100			0.499550	+	0.866285i	$0.333499\pi$
$480$	−43.6126	−	885.695i	−0.0908595	−	1.84520i
$481$	651.567			1.35461
$482$	75.4285	+	94.0185i	0.156491	+	0.195059i
$483$	−82.3527	+	428.588i	−0.170503	+	0.887347i
$484$	−2.86481	+	12.8992i	−0.00591902	+	0.0266512i
$485$	777.204			1.60248
$486$	−467.995	−	131.059i	−0.962953	−	0.269669i
$487$	−526.464			−1.08103			−0.540517	−	0.841333i	$-0.681772\pi$
$487$	−526.464			−1.08103			−0.540517	+	0.841333i	$0.681772\pi$
$488$	156.331	+	317.463i	0.320351	+	0.650538i
$489$	−51.6753	+	268.934i	−0.105676	+	0.549967i
$490$	304.899	+	380.043i	0.622242	+	0.775598i
$491$	−303.358			−0.617837			−0.308918	−	0.951089i	$-0.599967\pi$
$491$	−303.358			−0.617837			−0.308918	+	0.951089i	$0.599967\pi$
$492$	−262.493	+	606.632i	−0.533523	+	1.23299i
$493$		−	430.337i		−	0.872894i
$494$	613.795	−	195.110i	1.24250	−	0.394960i
$495$	−334.260	+	837.682i	−0.675274	+	1.69229i
$496$	290.071	+	135.530i	0.584821	+	0.273246i
$497$	−428.599			−0.862373
$498$	−196.129	+	103.680i	−0.393834	+	0.208194i
$499$			689.492i			1.38175i	0.722976	+	0.690873i	$0.242774\pi$
$499$			689.492i			1.38175i	−0.722976	+	0.690873i	$0.757226\pi$
$500$	1274.17	+	282.984i	2.54835	+	0.565968i
$501$	−57.0224	+	296.762i	−0.113817	+	0.592339i
$502$	−497.135	+	398.839i	−0.990310	+	0.794499i
$503$	115.945			0.230507			0.115253	−	0.993336i	$-0.463232\pi$
$503$	115.945			0.230507			0.115253	+	0.993336i	$0.463232\pi$
$504$	−341.446	+	26.6564i	−0.677472	+	0.0528896i
$505$	−214.848			−0.425442
$506$	517.597	−	415.254i	1.02292	−	0.820661i
$507$	−348.425	−	66.9495i	−0.687230	−	0.132050i
$508$	−75.1297	+	338.282i	−0.147893	+	0.665909i
$509$	896.301			1.76091			0.880453	−	0.474133i	$-0.157238\pi$
$509$	896.301			1.76091			0.880453	+	0.474133i	$0.157238\pi$
$510$	710.627	−	375.661i	1.39339	−	0.736590i
$511$		−	142.979i		−	0.279803i
$512$	−501.991	−	100.742i	−0.980451	−	0.196761i
$513$	413.628	−	303.449i	0.806292	−	0.591518i
$514$	26.7028	−	21.4229i	0.0519509	−	0.0416788i
$515$			858.925i			1.66782i
$516$	−249.068	−	107.773i	−0.482691	−	0.208863i
$517$	−199.838			−0.386535
$518$	285.267	−	228.862i	0.550708	−	0.441819i
$519$	−660.000	−	126.818i	−1.27168	−	0.244351i
$520$	−553.320	−	1123.63i	−1.06408	−	2.16083i
$521$	−618.428			−1.18700			−0.593501	−	0.804833i	$-0.702255\pi$
$521$	−618.428			−1.18700			−0.593501	+	0.804833i	$0.702255\pi$
$522$	−510.795	+	156.026i	−0.978534	+	0.298900i
$523$	271.445			0.519015			0.259508	−	0.965741i	$-0.416440\pi$
$523$	271.445			0.519015			0.259508	+	0.965741i	$0.416440\pi$
$524$	22.2067	−	99.9887i	0.0423792	−	0.190818i
$525$	162.440	−	845.388i	0.309410	−	1.61026i
$526$	115.061	−	92.3104i	0.218747	−	0.175495i
$527$			290.220i			0.550701i
$528$	421.716	+	305.497i	0.798705	+	0.578593i
$529$	406.334			0.768117
$530$	372.787	+	464.664i	0.703372	+	0.876724i
$531$	−139.492	+	349.577i	−0.262696	+	0.658337i
$532$	200.198	−	301.018i	0.376311	−	0.565822i
$533$			933.587i			1.75157i
$534$	−374.829	+	198.147i	−0.701928	+	0.371062i
$535$	−280.388			−0.524090
$536$	−83.2676	−	169.092i	−0.155350	−	0.315470i
$537$	95.9653	−	499.432i	0.178706	−	0.930042i
$538$	−540.036	+	433.257i	−1.00378	+	0.805310i
$539$	−286.121			−0.530837
$540$	−703.547	−	707.288i	−1.30286	−	1.30979i
$541$	−44.4572			−0.0821761			−0.0410880	−	0.999156i	$-0.513082\pi$
$541$	−44.4572			−0.0821761			−0.0410880	+	0.999156i	$0.513082\pi$
$542$	93.7682	+	116.878i	0.173004	+	0.215642i
$543$	148.382	−	772.225i	0.273263	−	1.42214i
$544$	−109.884	−	450.907i	−0.201993	−	0.828872i
$545$	735.622			1.34977
$546$	−427.652	+	226.071i	−0.783245	+	0.414049i
$547$	−909.767			−1.66319			−0.831597	−	0.555379i	$-0.812573\pi$
$547$	−909.767			−1.66319			−0.831597	+	0.555379i	$0.812573\pi$
$548$	197.360	+	43.8319i	0.360145	+	0.0799853i
$549$	369.751	+	147.542i	0.673499	+	0.268746i
$550$	−1020.96	+	819.087i	−1.85628	+	1.48925i
$551$	202.999	−	525.949i	0.368420	−	0.954535i
$552$	194.185	+	707.845i	0.351785	+	1.28233i
$553$			240.860i			0.435552i
$554$	−428.704	+	343.938i	−0.773834	+	0.620826i
$555$	1046.17	+	201.021i	1.88500	+	0.362200i
$556$	1052.08	+	233.658i	1.89223	+	0.420249i
$557$		−	813.383i		−	1.46029i	−0.683291	−	0.730146i	$-0.739452\pi$
$557$		−	813.383i		−	1.46029i	0.683291	−	0.730146i	$-0.260548\pi$
$558$	344.480	−	105.224i	0.617348	−	0.188574i
$559$	−383.308			−0.685703
$560$	−636.927	−	297.591i	−1.13737	−	0.531413i
$561$	−89.0701	+	463.548i	−0.158770	+	0.826288i
$562$	−179.662	+	144.138i	−0.319684	+	0.256474i
$563$		−	1078.20i		−	1.91509i	−0.288278	−	0.957547i	$-0.593083\pi$
$563$		−	1078.20i		−	1.91509i	0.288278	−	0.957547i	$-0.406917\pi$
$564$	87.7815	−	202.866i	0.155641	−	0.359692i
$565$			856.924i			1.51668i
$566$	−86.1146	−	107.338i	−0.152146	−	0.189643i
$567$	−265.254	+	279.451i	−0.467820	+	0.492859i
$568$	−646.674	+	318.448i	−1.13851	+	0.560648i
$569$	221.539			0.389348			0.194674	−	0.980868i	$-0.437635\pi$
$569$	221.539			0.389348			0.194674	+	0.980868i	$0.437635\pi$
$570$	1045.72	−	123.907i	1.83460	−	0.217380i
$571$			270.879i			0.474394i	0.971462	+	0.237197i	$0.0762288\pi$
$571$			270.879i			0.474394i	−0.971462	+	0.237197i	$0.923771\pi$
$572$	718.008	+	159.464i	1.25526	+	0.278783i
$573$	−291.476	−	56.0068i	−0.508685	−	0.0977431i
$574$	327.921	+	408.740i	0.571291	+	0.712090i
$575$	−1844.94			−3.20859
$576$	−495.370	+	293.912i	−0.860018	+	0.510264i
$577$	−1060.67			−1.83825			−0.919123	−	0.393971i	$-0.871101\pi$
$577$	−1060.67			−1.83825			−0.919123	+	0.393971i	$0.871101\pi$
$578$	−122.705	+	98.4433i	−0.212293	+	0.170317i
$579$	88.0995	−	458.496i	0.152158	−	0.791876i
$580$	−1070.26	−	237.695i	−1.84527	−	0.409820i
$581$			175.878i			0.302716i
$582$	−235.934	−	446.309i	−0.405384	−	0.766854i
$583$	−349.829			−0.600049
$584$	−106.233	−	215.728i	−0.181906	−	0.369398i
$585$	−1308.70	−	522.210i	−2.23709	−	0.892667i
$586$	−367.712	+	295.006i	−0.627495	+	0.503422i
$587$	−198.987			−0.338990			−0.169495	−	0.985531i	$-0.554214\pi$
$587$	−198.987			−0.338990			−0.169495	+	0.985531i	$0.554214\pi$
$588$	125.682	−	290.456i	0.213745	−	0.493973i
$589$	−136.903	+	354.700i	−0.232433	+	0.602208i
$590$	−602.628	+	483.473i	−1.02140	+	0.819445i
$591$	90.5762	−	471.386i	0.153259	−	0.797607i
$592$	260.369	−	557.261i	0.439812	−	0.941319i
$593$			673.859i			1.13636i	0.822906	+	0.568178i	$0.192352\pi$
$593$			673.859i			1.13636i	−0.822906	+	0.568178i	$0.807648\pi$
$594$	582.509	−	62.3440i	0.980655	−	0.104956i
$595$		−	637.252i		−	1.07101i
$596$	56.8556	+	12.6272i	0.0953953	+	0.0211865i
$597$	−104.768	+	545.246i	−0.175491	+	0.913310i
$598$	648.746	+	808.634i	1.08486	+	1.35223i
$599$			493.529i			0.823922i	0.911202	+	0.411961i	$0.135156\pi$
$599$			493.529i			0.823922i	−0.911202	+	0.411961i	$0.864844\pi$
$600$	−383.029	−	1396.22i	−0.638382	−	2.32703i
$601$		−	457.954i		−	0.761986i	−0.924578	−	0.380993i	$-0.875582\pi$
$601$		−	457.954i		−	0.761986i	0.924578	−	0.380993i	$-0.124418\pi$
$602$	−167.819	+	134.637i	−0.278769	+	0.223649i
$603$	−196.942	−	78.5860i	−0.326604	−	0.130325i
$604$	223.522	−	1006.44i	0.370069	−	1.66629i
$605$			30.5138i			0.0504361i
$606$	65.2209	+	123.376i	0.107625	+	0.203592i
$607$	541.209			0.891613			0.445806	−	0.895129i	$-0.352917\pi$
$607$	541.209			0.891613			0.445806	+	0.895129i	$0.352917\pi$
$608$	78.4047	−	602.923i	0.128955	−	0.991650i
$609$	−79.8985	+	415.816i	−0.131196	+	0.682785i
$610$	511.373	+	637.405i	0.838317	+	1.04493i
$611$		−	312.205i		−	0.510973i
$612$	−431.446	−	294.039i	−0.704977	−	0.480455i
$613$	−383.693			−0.625927			−0.312963	−	0.949765i	$-0.601322\pi$
$613$	−383.693			−0.625927			−0.312963	+	0.949765i	$0.601322\pi$
$614$	622.526	−	499.437i	1.01389	−	0.813415i
$615$	−288.029	+	1498.99i	−0.468340	+	2.43739i
$616$	370.368	−	182.384i	0.601246	−	0.296077i
$617$			639.350i			1.03622i	0.855313	+	0.518112i	$0.173365\pi$
$617$			639.350i			1.03622i	−0.855313	+	0.518112i	$0.826635\pi$
$618$	493.237	−	260.741i	0.798118	−	0.421912i
$619$			28.0531i			0.0453200i	0.999743	+	0.0226600i	$0.00721351\pi$
$619$			28.0531i			0.0453200i	−0.999743	+	0.0226600i	$0.992786\pi$
$620$	721.782	+	160.302i	1.16417	+	0.258552i
$621$	695.418	+	445.255i	1.11984	+	0.716997i
$622$	−369.300	+	296.280i	−0.593731	+	0.476334i
$623$			336.127i			0.539530i
$624$	−477.274	+	658.841i	−0.764862	+	1.05583i
$625$	1506.00			2.40961
$626$	−257.703	+	206.748i	−0.411666	+	0.330269i
$627$	−327.525	+	524.522i	−0.522369	+	0.836559i
$628$	247.174	−	1112.93i	0.393588	−	1.77219i
$629$	557.546			0.886400
$630$	−756.396	+	231.047i	−1.20063	+	0.366741i
$631$		−	312.635i		−	0.495460i	−0.968829	−	0.247730i	$-0.920315\pi$
$631$		−	312.635i		−	0.495460i	0.968829	−	0.247730i	$-0.0796846\pi$
$632$	178.958	+	363.412i	0.283162	+	0.575019i
$633$	−636.445	−	122.292i	−1.00544	−	0.193194i
$634$	726.532	−	582.878i	1.14595	−	0.919366i
$635$			800.226i			1.26020i
$636$	153.667	−	355.129i	0.241614	−	0.558379i
$637$		−	447.003i		−	0.701731i
$638$	502.172	−	402.879i	0.787103	−	0.631472i
$639$	−300.543	+	753.185i	−0.470334	+	1.17869i
$640$	−1182.11	+	24.2267i	−1.84705	+	0.0378542i
$641$	−76.8048			−0.119820			−0.0599101	−	0.998204i	$-0.519081\pi$
$641$	−76.8048			−0.119820			−0.0599101	+	0.998204i	$0.519081\pi$
$642$	85.1167	+	161.013i	0.132580	+	0.250799i
$643$		−	515.334i		−	0.801453i	−0.916198	−	0.400727i	$-0.868758\pi$
$643$		−	515.334i		−	0.801453i	0.916198	−	0.400727i	$-0.131242\pi$
$644$	568.064	+	126.162i	0.882087	+	0.195904i
$645$	−615.450	−	118.258i	−0.954186	−	0.183346i
$646$	525.225	−	166.956i	0.813041	−	0.258446i
$647$	1058.80			1.63647			0.818236	−	0.574882i	$-0.194952\pi$
$647$	1058.80			1.63647			0.818236	+	0.574882i	$0.194952\pi$
$648$	−192.586	+	618.720i	−0.297200	+	0.954815i
$649$		−	453.697i		−	0.699071i
$650$	−1279.65	−	1595.03i	−1.96869	−	2.45389i
$651$	53.8837	−	280.427i	0.0827706	−	0.430763i
$652$	356.453	+	79.1654i	0.546707	+	0.121419i
$653$		−	619.260i		−	0.948331i	−0.880436	−	0.474166i	$-0.842750\pi$
$653$		−	619.260i		−	0.948331i	0.880436	−	0.474166i	$-0.157250\pi$
$654$	−223.311	−	422.430i	−0.341454	−	0.645918i
$655$		−	236.529i		−	0.361113i
$656$	798.462	+	373.065i	1.21717	+	0.568697i
$657$	−251.260	−	100.260i	−0.382435	−	0.152603i
$658$	−109.662	−	136.688i	−0.166659	−	0.207733i
$659$			901.216i			1.36755i	0.729693	+	0.683775i	$0.239663\pi$
$659$			901.216i			1.36755i	−0.729693	+	0.683775i	$0.760337\pi$
$660$	1103.66	+	477.559i	1.67221	+	0.723574i
$661$			882.766i			1.33550i	0.744386	+	0.667750i	$0.232742\pi$
$661$			882.766i			1.33550i	−0.744386	+	0.667750i	$0.767258\pi$
$662$	−913.342	+	732.750i	−1.37967	+	1.10687i
$663$	−724.194	−	139.153i	−1.09230	−	0.209884i
$664$	130.677	+	265.366i	0.196802	+	0.399648i
$665$	300.606	−	778.837i	0.452039	−	1.17118i
$666$	−202.148	−	661.787i	−0.303525	−	0.993675i
$667$	907.460			1.36051
$668$	393.337	+	87.3569i	0.588827	+	0.130774i
$669$	195.254	+	37.5178i	0.291859	+	0.0560804i
$670$	−272.376	−	339.505i	−0.406531	−	0.506723i
$671$	−479.880			−0.715171
$672$	22.4585	+	456.094i	0.0334205	+	0.678711i
$673$		−	0.631755i		−	0.000938715i	−1.00000		0.000469357i	$-0.999851\pi$
$673$		−	0.631755i		−	0.000938715i	1.00000		0.000469357i	$-0.000149401\pi$
$674$	−34.3768	−	42.8492i	−0.0510041	−	0.0635744i
$675$	−1371.71	−	878.264i	−2.03216	−	1.30113i
$676$	−102.565	+	461.813i	−0.151723	+	0.683156i
$677$	130.737			0.193112			0.0965560	−	0.995328i	$-0.469217\pi$
$677$	130.737			0.193112			0.0965560	+	0.995328i	$0.469217\pi$
$678$	492.088	−	260.134i	0.725793	−	0.383678i
$679$	−400.226			−0.589434
$680$	−473.476	−	961.491i	−0.696289	−	1.41396i
$681$	−11.2969	+	58.7926i	−0.0165887	+	0.0863328i
$682$	−338.665	+	271.702i	−0.496577	+	0.398391i
$683$			1135.52i			1.66255i	0.555861	+	0.831275i	$0.312389\pi$
$683$			1135.52i			1.66255i	−0.555861	+	0.831275i	$0.687611\pi$
$684$	−388.600	−	562.891i	−0.568129	−	0.822940i
$685$	466.865			0.681555
$686$	−448.721	−	559.311i	−0.654112	−	0.815323i
$687$	684.113	+	131.451i	0.995797	+	0.191341i
$688$	−153.172	+	327.829i	−0.222633	+	0.476496i
$689$		−	546.533i		−	0.793226i
$690$	792.165	+	1498.52i	1.14806	+	2.17176i
$691$		−	241.304i		−	0.349209i	−0.984639	−	0.174605i	$-0.944135\pi$
$691$		−	241.304i		−	0.349209i	0.984639	−	0.174605i	$-0.0558648\pi$
$692$	−194.282	+	874.783i	−0.280755	+	1.26414i
$693$	172.129	−	431.369i	0.248383	−	0.622467i
$694$	−101.295	+	81.2664i	−0.145958	+	0.117098i
$695$	2488.76			3.58095
$696$	188.398	+	686.751i	0.270687	+	0.986710i
$697$			798.870i			1.14616i
$698$	132.970	−	106.678i	0.190502	−	0.152834i
$699$	169.480	−	882.023i	0.242460	−	1.26184i
$700$	−1120.50	−	248.854i	−1.60072	−	0.355506i
$701$			964.565i			1.37598i	0.725718	+	0.687992i	$0.241508\pi$
$701$			964.565i			1.37598i	−0.725718	+	0.687992i	$0.758492\pi$
$702$	97.3992	+	910.045i	0.138745	+	1.29636i
$703$	681.421	+	263.007i	0.969305	+	0.374120i
$704$	423.303	−	550.364i	0.601282	−	0.781766i
$705$	96.3212	−	501.284i	0.136626	−	0.711042i
$706$	−68.5240	−	85.4123i	−0.0970595	−	0.120981i
$707$	110.637			0.156489
$708$	460.572	+	199.292i	0.650525	+	0.281486i
$709$	−603.054			−0.850570			−0.425285	−	0.905059i	$-0.639826\pi$
$709$	−603.054			−0.850570			−0.425285	+	0.905059i	$0.639826\pi$
$710$	−1298.40	+	1041.67i	−1.82873	+	1.46714i
$711$	423.268	+	168.897i	0.595313	+	0.237548i
$712$	249.741	+	507.151i	0.350760	+	0.712290i
$713$	−611.992			−0.858334
$714$	−365.942	+	193.449i	−0.512523	+	0.270937i
$715$	1698.49			2.37551
$716$	−661.962	−	147.016i	−0.924529	−	0.205330i
$717$	−422.930	−	81.2655i	−0.589861	−	0.113341i
$718$	297.656	−	238.801i	0.414562	−	0.332592i
$719$	−650.329			−0.904491			−0.452245	−	0.891894i	$-0.649377\pi$
$719$	−650.329			−0.904491			−0.452245	+	0.891894i	$0.649377\pi$
$720$	−969.589	+	910.605i	−1.34665	+	1.26473i
$721$		−	442.308i		−	0.613465i
$722$	720.676	+	43.7099i	0.998166	+	0.0605401i
$723$	34.1172	−	177.556i	0.0471883	−	0.245582i
$724$	−1023.53	−	227.318i	−1.41371	−	0.313975i
$725$	−1789.96			−2.46891
$726$	17.5225	−	9.26299i	0.0241357	−	0.0127589i
$727$			630.184i			0.866828i	0.901195	+	0.433414i	$0.142691\pi$
$727$			630.184i			0.866828i	−0.901195	+	0.433414i	$0.857309\pi$
$728$	284.935	+	578.620i	0.391395	+	0.794808i
$729$	305.082	+	662.092i	0.418494	+	0.908220i
$730$	−347.498	−	433.141i	−0.476025	−	0.593345i
$731$	−327.997			−0.448696
$732$	210.793	−	487.151i	0.287969	−	0.665506i
$733$	748.687			1.02140			0.510700	−	0.859759i	$-0.329386\pi$
$733$	748.687			1.02140			0.510700	+	0.859759i	$0.329386\pi$
$734$	673.897	+	839.983i	0.918115	+	1.14439i
$735$	137.909	−	717.720i	0.187631	−	0.976489i
$736$	950.837	−	231.715i	1.29190	−	0.314830i
$737$	255.601			0.346813
$738$	948.231	−	289.644i	1.28487	−	0.392472i
$739$			356.653i			0.482616i	0.970449	+	0.241308i	$0.0775764\pi$
$739$			356.653i			0.482616i	−0.970449	+	0.241308i	$0.922424\pi$
$740$	307.959	−	1386.63i	0.416161	−	1.87382i
$741$	−819.453	−	511.688i	−1.10588	−	0.690537i
$742$	−191.969	−	239.281i	−0.258718	−	0.322481i
$743$		−	591.155i		−	0.795633i	−0.917465	−	0.397816i	$-0.869768\pi$
$743$		−	591.155i		−	0.795633i	0.917465	−	0.397816i	$-0.130232\pi$
$744$	−127.056	−	463.145i	−0.170774	−	0.622507i
$745$	134.495			0.180530
$746$	−129.221	−	161.069i	−0.173219	−	0.215910i
$747$	309.074	+	123.330i	0.413753	+	0.165100i
$748$	614.400	+	136.453i	0.821390	+	0.182424i
$749$	144.388			0.192774
$750$	−914.992	−	1730.86i	−1.21999	−	2.30782i
$751$	95.6870			0.127413			0.0637064	−	0.997969i	$-0.479708\pi$
$751$	95.6870			0.127413			0.0637064	+	0.997969i	$0.479708\pi$
$752$	−267.017	−	124.758i	−0.355076	−	0.165902i
$753$	938.851	+	180.399i	1.24681	+	0.239574i
$754$	629.413	+	784.536i	0.834765	+	1.04050i
$755$		−	2380.79i		−	3.15336i
$756$	362.295	+	364.222i	0.479227	+	0.481775i
$757$	−62.9465			−0.0831526			−0.0415763	−	0.999135i	$-0.513238\pi$
$757$	−62.9465			−0.0831526			−0.0415763	+	0.999135i	$0.513238\pi$
$758$	274.185	−	219.971i	0.361721	−	0.290199i
$759$	−977.493	−	187.824i	−1.28787	−	0.247463i
$760$	−125.117	−	1398.46i	−0.164627	−	1.84008i
$761$		−	305.033i		−	0.400832i	−0.979711	−	0.200416i	$-0.935771\pi$
$761$		−	305.033i		−	0.400832i	0.979711	−	0.200416i	$-0.0642294\pi$
$762$	459.529	−	242.922i	0.603057	−	0.318796i
$763$	−378.813			−0.496478
$764$	−85.8010	+	386.331i	−0.112305	+	0.505669i
$765$	−1119.85	−	446.855i	−1.46386	−	0.584125i
$766$	−715.502	−	891.842i	−0.934075	−	1.16429i
$767$	708.805			0.924126
$768$	372.762	+	671.471i	0.485367	+	0.874311i
$769$	826.446			1.07470			0.537351	−	0.843359i	$-0.319425\pi$
$769$	826.446			1.07470			0.537351	+	0.843359i	$0.319425\pi$
$770$	743.628	−	596.593i	0.965751	−	0.774796i
$771$	−50.4288	−	9.68982i	−0.0654070	−	0.0125679i
$772$	−607.704	−	134.966i	−0.787182	−	0.174827i
$773$	−822.552			−1.06410			−0.532052	−	0.846712i	$-0.678579\pi$
$773$	−822.552			−1.06410			−0.532052	+	0.846712i	$0.678579\pi$
$774$	118.921	+	389.321i	0.153645	+	0.502998i
$775$	1207.15			1.55761
$776$	−603.863	+	297.366i	−0.778174	+	0.383204i
$777$	−538.733	−	103.517i	−0.693350	−	0.133226i
$778$	272.982	+	340.260i	0.350876	+	0.437352i
$779$	−376.845	+	976.363i	−0.483754	+	1.25335i
$780$	−746.083	+	1724.23i	−0.956517	+	2.21055i
$781$		−	977.518i		−	1.25162i
$782$	555.132	+	691.948i	0.709887	+	0.884844i
$783$	674.694	+	431.986i	0.861678	+	0.551707i
$784$	−382.305	−	178.624i	−0.487634	−	0.227837i
$785$		−	2632.71i		−	3.35377i
$786$	−135.827	+	71.8025i	−0.172807	+	0.0913517i
$787$	−1052.47			−1.33732			−0.668661	−	0.743568i	$-0.733132\pi$
$787$	−1052.47			−1.33732			−0.668661	+	0.743568i	$0.733132\pi$
$788$	−624.789	−	138.761i	−0.792879	−	0.176092i
$789$	−217.295	−	41.7530i	−0.275406	−	0.0529189i
$790$	585.389	+	729.662i	0.740998	+	0.923623i
$791$		−	441.278i		−	0.557874i
$792$	−60.7959	−	778.745i	−0.0767625	−	0.983263i
$793$		−	749.709i		−	0.945409i
$794$	177.924	−	142.744i	0.224085	−	0.179778i
$795$	168.616	−	877.527i	0.212095	−	1.10381i
$796$	722.685	+	160.503i	0.907896	+	0.201636i
$797$	−105.103			−0.131874			−0.0659368	−	0.997824i	$-0.521004\pi$
$797$	−105.103			−0.131874			−0.0659368	+	0.997824i	$0.521004\pi$
$798$	−538.500	+	63.8065i	−0.674813	+	0.0799580i
$799$		−	267.154i		−	0.334360i
$800$	−1875.52	+	457.056i	−2.34440	+	0.571320i
$801$	590.681	+	235.700i	0.737430	+	0.294257i
$802$	713.002	−	572.023i	0.889030	−	0.713245i
$803$	326.097			0.406098
$804$	−112.276	+	259.474i	−0.139647	+	0.322729i
$805$	1343.79			1.66930
$806$	−424.477	−	529.092i	−0.526646	−	0.656442i
$807$	1019.87	+	195.967i	1.26378	+	0.242834i
$808$	166.930	−	82.2032i	0.206597	−	0.101737i
$809$			641.806i			0.793333i	0.917963	+	0.396666i	$0.129833\pi$
$809$			641.806i			0.793333i	−0.917963	+	0.396666i	$0.870167\pi$
$810$	−124.380	+	1491.24i	−0.153555	+	1.84104i
$811$	−968.547			−1.19426			−0.597131	−	0.802143i	$-0.703693\pi$
$811$	−968.547			−1.19426			−0.597131	+	0.802143i	$0.703693\pi$
$812$	551.135	+	122.403i	0.678738	+	0.150742i
$813$	42.4124	−	220.727i	0.0521677	−	0.271497i
$814$	521.972	+	650.616i	0.641243	+	0.799283i
$815$	843.211			1.03461
$816$	−408.403	+	563.770i	−0.500494	+	0.690895i
$817$	−400.871	−	154.723i	−0.490662	−	0.189380i
$818$	1014.58	+	1264.63i	1.24031	+	1.54600i
$819$	673.922	+	268.915i	0.822860	+	0.328346i
$820$	1986.81	+	441.254i	2.42294	+	0.538115i
$821$			83.2903i			0.101450i	0.998713	+	0.0507249i	$0.0161532\pi$
$821$			83.2903i			0.101450i	−0.998713	+	0.0507249i	$0.983847\pi$
$822$	−141.725	−	268.097i	−0.172415	−	0.326152i
$823$		−	942.771i		−	1.14553i	−0.819720	−	0.572765i	$-0.805871\pi$
$823$		−	942.771i		−	1.14553i	0.819720	−	0.572765i	$-0.194129\pi$
$824$	−328.633	−	667.358i	−0.398827	−	0.809900i
$825$	1928.10	+	370.482i	2.33709	+	0.449069i
$826$	310.327	−	248.967i	0.375698	−	0.301413i
$827$		−	1210.83i		−	1.46413i	−0.681237	−	0.732063i	$-0.738558\pi$
$827$		−	1210.83i		−	1.46413i	0.681237	−	0.732063i	$-0.261442\pi$
$828$	620.046	−	909.800i	0.748848	−	1.09879i
$829$			404.774i			0.488268i	0.969742	+	0.244134i	$0.0785036\pi$
$829$			404.774i			0.488268i	−0.969742	+	0.244134i	$0.921496\pi$
$830$	427.455	+	532.805i	0.515006	+	0.641933i
$831$	809.617	+	155.567i	0.974268	+	0.187204i
$832$	859.825	+	661.320i	1.03344	+	0.794856i
$833$		−	382.500i		−	0.459184i
$834$	−755.505	−	1429.17i	−0.905881	−	1.71363i
$835$	930.461			1.11432
$836$	686.539	+	456.596i	0.821219	+	0.546168i
$837$	−455.014	−	291.332i	−0.543625	−	0.348067i
$838$	671.272	−	538.544i	0.801041	−	0.642654i
$839$			537.597i			0.640759i	0.947289	+	0.320380i	$0.103810\pi$
$839$			537.597i			0.640759i	−0.947289	+	0.320380i	$0.896190\pi$
$840$	278.985	+	1016.96i	0.332125	+	1.21066i
$841$	39.4170			0.0468692
$842$	−246.508	−	307.262i	−0.292765	−	0.364920i
$843$	339.296	+	65.1953i	0.402487	+	0.0773373i
$844$	−187.348	+	843.563i	−0.221977	+	0.999482i
$845$			1092.45i			1.29284i
$846$	−317.102	+	96.8611i	−0.374825	+	0.114493i
$847$		−	15.7133i		−	0.0185517i
$848$	−467.429	−	218.397i	−0.551214	−	0.257543i
$849$	−38.9506	+	202.710i	−0.0458782	+	0.238764i
$850$	−1094.99	−	1364.86i	−1.28823	−	1.60572i
$851$			1175.71i			1.38156i
$852$	992.330	+	429.387i	1.16471	+	0.503976i
$853$	−1376.23			−1.61340			−0.806700	−	0.590961i	$-0.798749\pi$
$853$	−1376.23			−1.61340			−0.806700	+	0.590961i	$0.798749\pi$
$854$	−263.335	−	328.235i	−0.308354	−	0.384350i
$855$	−1157.87	−	1074.40i	−1.35424	−	1.25661i
$856$	217.853	−	107.279i	0.254501	−	0.125326i
$857$	577.913			0.674344			0.337172	−	0.941443i	$-0.390530\pi$
$857$	577.913			0.674344			0.337172	+	0.941443i	$0.390530\pi$
$858$	−515.606	−	975.357i	−0.600939	−	1.13678i
$859$		−	1311.37i		−	1.52663i	−0.646028	−	0.763313i	$-0.723571\pi$
$859$		−	1311.37i		−	1.52663i	0.646028	−	0.763313i	$-0.276429\pi$
$860$	−181.168	+	815.736i	−0.210661	+	0.948530i
$861$	148.322	−	771.915i	0.172268	−	0.896533i
$862$	523.322	+	652.299i	0.607102	+	0.756727i
$863$		−	1229.84i		−	1.42508i	−0.701632	−	0.712539i	$-0.747545\pi$
$863$		−	1229.84i		−	1.42508i	0.701632	−	0.712539i	$-0.252455\pi$
$864$	817.249	+	280.356i	0.945890	+	0.324486i
$865$			2069.35i			2.39231i
$866$	−911.738	−	1136.44i	−1.05282	−	1.31229i
$867$	231.732	+	44.5270i	0.267280	+	0.0513575i
$868$	−371.686	−	82.5485i	−0.428210	−	0.0951019i
$869$	−549.337			−0.632148
$870$	768.558	+	1453.86i	0.883399	+	1.67110i
$871$			399.322i			0.458464i
$872$	−571.555	+	281.457i	−0.655453	+	0.322771i
$873$	−280.647	+	703.323i	−0.321474	+	0.805639i
$874$	352.064	+	1107.55i	0.402819	+	1.26722i
$875$	−1552.15			−1.77388
$876$	−143.242	+	331.038i	−0.163518	+	0.377897i
$877$		−	256.683i		−	0.292683i	−0.989234	−	0.146342i	$-0.953250\pi$
$877$		−	256.683i		−	0.292683i	0.989234	−	0.146342i	$-0.0467499\pi$
$878$	80.9537	−	64.9470i	0.0922024	−	0.0739716i
$879$	694.432	+	133.434i	0.790025	+	0.151802i
$880$	678.724	−	1452.66i	0.771278	−	1.65075i
$881$			341.298i			0.387399i	0.981061	+	0.193699i	$0.0620486\pi$
$881$			341.298i			0.387399i	−0.981061	+	0.193699i	$0.937951\pi$
$882$	−454.015	+	138.682i	−0.514756	+	0.157236i
$883$			1079.99i			1.22310i	0.791208	+	0.611548i	$0.209453\pi$
$883$			1079.99i			1.22310i	−0.791208	+	0.611548i	$0.790547\pi$
$884$	−213.179	+	959.868i	−0.241153	+	1.08582i
$885$	1138.08	+	218.680i	1.28596	+	0.247096i
$886$	1165.12	−	934.741i	1.31503	−	1.05501i
$887$			1333.17i			1.50301i	0.659727	+	0.751506i	$0.270672\pi$
$887$			1333.17i			1.50301i	−0.659727	+	0.751506i	$0.729328\pi$
$888$	−889.757	+	244.090i	−1.00198	+	0.274876i
$889$		−	412.081i		−	0.463533i
$890$	816.925	+	1018.26i	0.917893	+	1.14411i
$891$	−637.352	−	604.971i	−0.715322	−	0.678980i
$892$	57.4763	−	258.795i	0.0644353	−	0.290129i
$893$	126.022	−	326.510i	0.141122	−	0.365632i
$894$	−40.8283	−	77.2337i	−0.0456693	−	0.0863912i
$895$	−1565.91			−1.74962
$896$	608.734	−	12.4757i	0.679390	−	0.0139237i
$897$	293.435	−	1527.12i	0.327129	−	1.70248i
$898$	−477.030	+	382.709i	−0.531214	+	0.426179i
$899$	−593.754			−0.660461
$900$	−1223.04	+	1794.57i	−1.35893	+	1.99397i
$901$		−	467.668i		−	0.519054i
$902$	−932.224	+	747.899i	−1.03351	+	0.829156i
$903$	316.930	+	60.8976i	0.350974	+	0.0674392i
$904$	−327.868	−	665.803i	−0.362686	−	0.736508i
$905$	−2421.22			−2.67538
$906$	−1367.17	+	722.729i	−1.50901	+	0.797715i
$907$	−1334.40			−1.47122			−0.735611	−	0.677404i	$-0.763105\pi$
$907$	−1334.40			−1.47122			−0.735611	+	0.677404i	$0.763105\pi$
$908$	77.9254	+	17.3066i	0.0858210	+	0.0190601i
$909$	77.5814	−	194.425i	0.0853481	−	0.213889i
$910$	932.049	+	1161.76i	1.02423	+	1.27666i
$911$			176.494i			0.193736i	0.995297	+	0.0968681i	$0.0308825\pi$
$911$			176.494i			0.193736i	−0.995297	+	0.0968681i	$0.969117\pi$
$912$	−765.085	+	496.376i	−0.838909	+	0.544271i
$913$	−401.130			−0.439354
$914$	888.342	−	712.693i	0.971927	−	0.779752i
$915$	231.300	−	1203.75i	0.252787	−	1.31558i
$916$	201.380	−	906.743i	0.219848	−	0.989894i
$917$			121.802i			0.132827i
$918$	83.3445	+	778.726i	0.0907892	+	0.848285i
$919$		−	979.013i		−	1.06530i	−0.846335	−	0.532651i	$-0.821196\pi$
$919$		−	979.013i		−	1.06530i	0.846335	−	0.532651i	$-0.178804\pi$
$920$	2027.52	−	998.430i	2.20382	−	1.08525i
$921$	−1175.66	−	225.901i	−1.27650	−	0.245278i
$922$	38.3772	+	47.8355i	0.0416239	+	0.0518824i
$923$	1527.16			1.65456
$924$	−568.334	−	245.922i	−0.615080	−	0.266149i
$925$		−	2319.08i		−	2.50711i
$926$	306.449	+	381.976i	0.330939	+	0.412501i
$927$	−777.276	−	310.156i	−0.838485	−	0.334581i
$928$	922.501	−	224.809i	0.994074	−	0.242251i
$929$			528.885i			0.569306i	0.958631	+	0.284653i	$0.0918784\pi$
$929$			528.885i			0.569306i	−0.958631	+	0.284653i	$0.908122\pi$
$930$	−518.316	−	980.484i	−0.557329	−	1.05428i
$931$	180.434	−	467.484i	0.193806	−	0.502131i
$932$	−1169.06	−	259.639i	−1.25436	−	0.278582i
$933$	697.432	+	134.011i	0.747516	+	0.143634i
$934$	−665.967	+	534.288i	−0.713027	+	0.572043i
$935$	1453.40			1.55444
$936$	1216.62	−	94.9806i	1.29981	−	0.101475i
$937$	858.303			0.916012			0.458006	−	0.888949i	$-0.348564\pi$
$937$	858.303			0.916012			0.458006	+	0.888949i	$0.348564\pi$
$938$	140.261	+	174.830i	0.149532	+	0.186386i
$939$	486.678	+	93.5146i	0.518294	+	0.0995895i
$940$	−664.417	−	147.562i	−0.706827	−	0.156980i
$941$	−1116.79			−1.18681			−0.593405	−	0.804904i	$-0.702217\pi$
$941$	−1116.79			−1.18681			−0.593405	+	0.804904i	$0.702217\pi$
$942$	−1511.83	+	799.204i	−1.60492	+	0.848412i
$943$	−1684.59			−1.78642
$944$	283.242	−	606.215i	0.300044	−	0.642177i
$945$	999.102	+	639.696i	1.05725	+	0.676926i
$946$	−307.069	−	382.749i	−0.324598	−	0.404597i
$947$	−1033.60			−1.09144			−0.545722	−	0.837966i	$-0.683745\pi$
$947$	−1033.60			−1.09144			−0.545722	+	0.837966i	$0.683745\pi$
$948$	241.303	−	557.660i	0.254539	−	0.588249i
$949$			509.457i			0.536835i
$950$	−694.443	−	2184.64i	−0.730993	−	2.29962i
$951$	−1372.07	−	263.642i	−1.44277	−	0.277226i
$952$	243.819	+	495.125i	0.256113	+	0.520090i
$953$	1481.84			1.55492			0.777459	−	0.628933i	$-0.216508\pi$
$953$	1481.84			1.55492			0.777459	+	0.628933i	$0.216508\pi$
$954$	−555.106	+	169.561i	−0.581872	+	0.177737i
$955$			913.889i			0.956952i
$956$	−124.497	+	560.564i	−0.130227	+	0.586364i
$957$	−948.363	−	182.227i	−0.990975	−	0.190415i
$958$	−746.570	+	598.953i	−0.779301	+	0.625212i
$959$	−240.415			−0.250694
$960$	1176.53	+	1327.11i	1.22555	+	1.38240i
$961$	−560.571			−0.583321
$962$	−1016.45	+	815.470i	−1.05660	+	0.847681i
$963$	101.248	−	253.735i	0.105138	−	0.263484i
$964$	−235.338	−	52.2666i	−0.244126	−	0.0542185i
$965$	−1437.56			−1.48970
$966$	−407.930	−	771.669i	−0.422288	−	0.798829i
$967$			1395.05i			1.44265i	0.692595	+	0.721327i	$0.256468\pi$
$967$			1395.05i			1.44265i	−0.692595	+	0.721327i	$0.743532\pi$
$968$	−11.6749	−	23.7083i	−0.0120608	−	0.0244920i
$969$	−701.206	−	437.852i	−0.723639	−	0.451859i
$970$	−1212.44	+	972.711i	−1.24994	+	1.00279i
$971$			1520.53i			1.56594i	0.622058	+	0.782971i	$0.286297\pi$
$971$			1520.53i			1.56594i	−0.622058	+	0.782971i	$0.713703\pi$
$972$	894.102	−	381.267i	0.919859	−	0.392250i
$973$	−1281.60			−1.31716
$974$	821.287	−	658.897i	0.843210	−	0.676486i
$975$	−578.798	+	3012.24i	−0.593639	+	3.08948i
$976$	−641.199	−	299.587i	−0.656966	−	0.306954i
$977$	365.082			0.373676			0.186838	−	0.982391i	$-0.440176\pi$
$977$	365.082			0.373676			0.186838	+	0.982391i	$0.440176\pi$
$978$	−255.971	−	484.213i	−0.261729	−	0.495105i
$979$	−766.614			−0.783058
$980$	−951.287	−	211.273i	−0.970701	−	0.215585i
$981$	−265.632	+	665.694i	−0.270777	+	0.678587i
$982$	473.240	−	379.668i	0.481914	−	0.386627i
$983$			785.338i			0.798920i	0.916751	+	0.399460i	$0.130802\pi$
$983$			785.338i			0.798920i	−0.916751	+	0.399460i	$0.869198\pi$
$984$	−349.740	−	1274.87i	−0.355427	−	1.29560i
$985$	−1477.97			−1.50048
$986$	538.588	+	671.328i	0.546236	+	0.680860i
$987$	−49.6011	+	258.139i	−0.0502544	+	0.261539i
$988$	−713.334	+	1072.57i	−0.721998	+	1.08560i
$989$		−	691.654i		−	0.699347i
$990$	−526.955	−	1725.13i	−0.532277	−	1.74256i
$991$	−292.757			−0.295415			−0.147708	−	0.989031i	$-0.547189\pi$
$991$	−292.757			−0.295415			−0.147708	+	0.989031i	$0.547189\pi$
$992$	−622.136	+	151.612i	−0.627153	+	0.152834i
$993$	1724.87	+	331.431i	1.73703	+	0.333767i
$994$	668.618	−	536.414i	0.672654	−	0.539652i
$995$	1709.55			1.71815
$996$	176.201	−	407.208i	0.176909	−	0.408843i
$997$	1286.04			1.28991			0.644955	−	0.764220i	$-0.276876\pi$
$997$	1286.04			1.28991			0.644955	+	0.764220i	$0.276876\pi$
$998$	−862.934	−	1075.61i	−0.864664	−	1.07777i
$999$	−559.683	+	874.136i	−0.560244	+	0.875011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.b.e.227.16	yes	72
3.2	odd	2	inner	228.3.b.e.227.58	yes	72
4.3	odd	2	inner	228.3.b.e.227.13	✓	72
12.11	even	2	inner	228.3.b.e.227.59	yes	72
19.18	odd	2	inner	228.3.b.e.227.57	yes	72
57.56	even	2	inner	228.3.b.e.227.15	yes	72
76.75	even	2	inner	228.3.b.e.227.60	yes	72
228.227	odd	2	inner	228.3.b.e.227.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.b.e.227.13	✓	72	4.3	odd	2	inner
228.3.b.e.227.14	yes	72	228.227	odd	2	inner
228.3.b.e.227.15	yes	72	57.56	even	2	inner
228.3.b.e.227.16	yes	72	1.1	even	1	trivial
228.3.b.e.227.57	yes	72	19.18	odd	2	inner
228.3.b.e.227.58	yes	72	3.2	odd	2	inner
228.3.b.e.227.59	yes	72	12.11	even	2	inner
228.3.b.e.227.60	yes	72	76.75	even	2	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56001 + 1.25155i) q^{2} +(2.94611 + 0.566091i) q^{3} +(0.867237 - 3.90486i) q^{4} -9.23717i q^{5} +(-5.30443 + 2.80410i) q^{6} +4.75673i q^{7} +(3.53423 + 7.17699i) q^{8} +(8.35908 + 3.33553i) q^{9} +O(q^{10})\)	\(q+(-1.56001 + 1.25155i) q^{2} +(2.94611 + 0.566091i) q^{3} +(0.867237 - 3.90486i) q^{4} -9.23717i q^{5} +(-5.30443 + 2.80410i) q^{6} +4.75673i q^{7} +(3.53423 + 7.17699i) q^{8} +(8.35908 + 3.33553i) q^{9} +(11.5608 + 14.4100i) q^{10} -10.8488 q^{11} +(4.76547 - 11.0132i) q^{12} -16.9489i q^{13} +(-5.95330 - 7.42053i) q^{14} +(5.22907 - 27.2137i) q^{15} +(-14.4958 - 6.77287i) q^{16} -14.5032i q^{17} +(-17.2148 + 5.25839i) q^{18} +(6.84148 - 17.7255i) q^{19} +(-36.0698 - 8.01081i) q^{20} +(-2.69274 + 14.0138i) q^{21} +(16.9242 - 13.5778i) q^{22} +30.5832 q^{23} +(6.34940 + 23.1449i) q^{24} -60.3252 q^{25} +(21.2125 + 26.4404i) q^{26} +(22.7385 + 14.5588i) q^{27} +(18.5744 + 4.12521i) q^{28} +29.6718 q^{29} +(25.9019 + 48.9979i) q^{30} -20.0107 q^{31} +(31.0901 - 7.57653i) q^{32} +(-31.9617 - 6.14141i) q^{33} +(18.1515 + 22.6251i) q^{34} +43.9387 q^{35} +(20.2741 - 29.7483i) q^{36} +38.4429i q^{37} +(11.5117 + 36.2144i) q^{38} +(9.59463 - 49.9334i) q^{39} +(66.2950 - 32.6463i) q^{40} -55.0823 q^{41} +(-13.3384 - 25.2318i) q^{42} -22.6155i q^{43} +(-9.40849 + 42.3630i) q^{44} +(30.8108 - 77.2142i) q^{45} +(-47.7100 + 38.2765i) q^{46} +18.4203 q^{47} +(-38.8721 - 28.1595i) q^{48} +26.3735 q^{49} +(94.1077 - 75.5002i) q^{50} +(8.21013 - 42.7280i) q^{51} +(-66.1832 - 14.6987i) q^{52} +32.2458 q^{53} +(-53.6934 + 5.74663i) q^{54} +100.212i q^{55} +(-34.1390 + 16.8114i) q^{56} +(30.1900 - 48.3484i) q^{57} +(-46.2882 + 37.1358i) q^{58} +41.8200i q^{59} +(-101.731 - 44.0195i) q^{60} +44.2334 q^{61} +(31.2168 - 25.0444i) q^{62} +(-15.8662 + 39.7619i) q^{63} +(-39.0184 + 50.7303i) q^{64} -156.560 q^{65} +(57.5468 - 30.4211i) q^{66} -23.5603 q^{67} +(-56.6329 - 12.5777i) q^{68} +(90.1014 + 17.3129i) q^{69} +(-68.5447 + 54.9916i) q^{70} +90.1038i q^{71} +(5.60393 + 71.7816i) q^{72} -30.0583 q^{73} +(-48.1133 - 59.9712i) q^{74} +(-177.725 - 34.1495i) q^{75} +(-63.2824 - 42.0872i) q^{76} -51.6049i q^{77} +(47.5265 + 89.9045i) q^{78} +50.6357 q^{79} +(-62.5621 + 133.900i) q^{80} +(58.7485 + 55.7639i) q^{81} +(85.9287 - 68.9384i) q^{82} +36.9746 q^{83} +(52.3868 + 22.6681i) q^{84} -133.969 q^{85} +(28.3044 + 35.2803i) q^{86} +(87.4163 + 16.7969i) q^{87} +(-38.3422 - 77.8618i) q^{88} +70.6634 q^{89} +(48.5726 + 159.016i) q^{90} +80.6215 q^{91} +(26.5229 - 119.423i) q^{92} +(-58.9537 - 11.3279i) q^{93} +(-28.7358 + 23.0540i) q^{94} +(-163.734 - 63.1959i) q^{95} +(95.8838 - 4.72142i) q^{96} +84.1388i q^{97} +(-41.1428 + 33.0078i) q^{98} +(-90.6861 - 36.1865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9}+O(q^{10}) \) 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9	\( 72 q - 16 q^{4} + 6 q^{6} - 48 q^{9} - 40 q^{16} + 94 q^{24} - 408 q^{25} + 60 q^{28} + 176 q^{30} - 214 q^{36} + 2 q^{42} + 96 q^{45} - 616 q^{49} + 72 q^{54} + 320 q^{57} + 564 q^{58} + 592 q^{61} - 424 q^{64} + 608 q^{66} + 128 q^{73} - 292 q^{76} - 208 q^{81} + 472 q^{82} - 160 q^{85} + 128 q^{93} + 166 q^{96}+O(q^{100}) \) 72 * q - 16 * q^4 + 6 * q^6 - 48 * q^9 - 40 * q^16 + 94 * q^24 - 408 * q^25 + 60 * q^28 + 176 * q^30 - 214 * q^36 + 2 * q^42 + 96 * q^45 - 616 * q^49 + 72 * q^54 + 320 * q^57 + 564 * q^58 + 592 * q^61 - 424 * q^64 + 608 * q^66 + 128 * q^73 - 292 * q^76 - 208 * q^81 + 472 * q^82 - 160 * q^85 + 128 * q^93 + 166 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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