LMFDB - Embedded newform 228.3.b.e.227.58

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			227.58
Character	$\chi$	$=$	228.227
Dual form			228.3.b.e.227.60

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56001 - 1.25155i) q^{2} +(2.94611 - 0.566091i) q^{3} +(0.867237 - 3.90486i) q^{4} +9.23717i q^{5} +(3.88745 - 4.57031i) q^{6} +4.75673i q^{7} +(-3.53423 - 7.17699i) q^{8} +(8.35908 - 3.33553i) q^{9} +O(q^{10})$	\(q+(1.56001 - 1.25155i) q^{2} +(2.94611 - 0.566091i) q^{3} +(0.867237 - 3.90486i) q^{4} +9.23717i q^{5} +(3.88745 - 4.57031i) 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} +(0.344470 - 11.9951i) 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} +(8.86564 - 15.6653i) 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} +(-14.4751 - 19.1435i) 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} +(42.2167 + 35.9090i) 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} +(-5.77544 - 35.5337i) 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} +(21.7397 + 18.4916i) 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} +(-46.5402 - 11.7477i) 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} +(17.2511 - 51.1703i) q^{54} +100.212i q^{55} +(34.1390 - 16.8114i) q^{56} +(10.1215 - 56.0942i) q^{57} +(-46.2882 + 37.1358i) q^{58} -41.8200i q^{59} +(110.800 + 3.18193i) 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} +(42.1742 - 49.5824i) 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} +(-53.4820 - 48.2045i) 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} +(-77.4619 - 65.8882i) 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} +(57.0573 + 1.63855i) 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} +(144.703 + 81.8934i) 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} +(-87.3058 + 39.9211i) 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	$0.374865\pi$
$5$			9.23717i			1.84743i	−0.383077	+	0.923717i	$0.625135\pi$
$6$	3.88745	−	4.57031i	0.647909	−	0.761718i
$7$			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	$-0.335854\pi$
$11$	10.8488			0.986255			0.493128	+	0.869957i	$0.335854\pi$
$12$	0.344470	−	11.9951i	0.0287058	−	0.999588i
$13$		−	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	$0.140276\pi$
$17$			14.5032i			0.853130i	−0.904457	+	0.426565i	$0.859724\pi$
$18$	8.86564	−	15.6653i	0.492535	−	0.870292i
$19$	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	$-0.731506\pi$
$23$	−30.5832			−1.32971			−0.664853	+	0.746974i	$0.731506\pi$
$24$	−14.4751	−	19.1435i	−0.603127	−	0.797645i
$25$	−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	$-0.670941\pi$
$29$	−29.6718			−1.02317			−0.511583	+	0.859234i	$0.670941\pi$
$30$	42.2167	+	35.9090i	1.40722	+	1.19697i
$31$	−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
$36$	−5.77544	−	35.5337i	−0.160429	−	0.987047i
$37$			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	$-0.265549\pi$
$41$	55.0823			1.34347			0.671735	+	0.740791i	$0.265549\pi$
$42$	21.7397	+	18.4916i	0.517613	+	0.440275i
$43$		−	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	$-0.562783\pi$
$47$	−18.4203			−0.391922			−0.195961	+	0.980612i	$0.562783\pi$
$48$	−46.5402	−	11.7477i	−0.969588	−	0.244743i
$49$	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	$-0.598391\pi$
$53$	−32.2458			−0.608412			−0.304206	+	0.952606i	$0.598391\pi$
$54$	17.2511	−	51.1703i	0.319466	−	0.947598i
$55$			100.212i			1.82204i
$56$	34.1390	−	16.8114i	0.609625	−	0.300204i
$57$	10.1215	−	56.0942i	0.177570	−	0.984108i
$58$	−46.2882	+	37.1358i	−0.798073	+	0.640273i
$59$		−	41.8200i		−	0.708814i	−0.935091	−	0.354407i	$-0.884683\pi$
$59$		−	41.8200i		−	0.708814i	0.935091	−	0.354407i	$-0.115317\pi$
$60$	110.800	+	3.18193i	1.84667	+	0.0530321i
$61$	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
$66$	42.1742	−	49.5824i	0.639003	−	0.751248i
$67$	−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	$-0.781192\pi$
$71$		−	90.1038i		−	1.26907i	0.772895	−	0.634534i	$-0.218808\pi$
$72$	−53.4820	−	48.2045i	−0.742805	−	0.669507i
$73$	−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
$78$	−77.4619	−	65.8882i	−0.993101	−	0.844720i
$79$	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	$-0.571500\pi$
$83$	−36.9746			−0.445477			−0.222738	+	0.974878i	$0.571500\pi$
$84$	57.0573	+	1.63855i	0.679253	+	0.0195066i
$85$	−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	$-0.629944\pi$
$89$	−70.6634			−0.793971			−0.396985	+	0.917825i	$0.629944\pi$
$90$	144.703	+	81.8934i	1.60781	+	0.909926i
$91$	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
$96$	−87.3058	+	39.9211i	−0.909436	+	0.415845i
$97$			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	$0.0367330\pi$
$101$			23.2591i			0.230288i	−0.993349	+	0.115144i	$0.963267\pi$
$102$	66.2841	+	56.3805i	0.649844	+	0.552750i
$103$	−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	$0.0453028\pi$
$107$			30.3544i			0.283686i	−0.989889	+	0.141843i	$0.954697\pi$
$108$	−37.1304	−	101.417i	−0.343800	−	0.939043i
$109$			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	$-0.365360\pi$
$113$	92.7692			0.820966			0.410483	+	0.911868i	$0.365360\pi$
$114$	−54.4152	−	100.175i	−0.477326	−	0.878726i
$115$		−	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
$120$	176.831	−	133.708i	1.47360	−	1.11424i
$121$	−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
$126$	74.5155	+	42.1715i	0.591393	+	0.334694i
$127$	−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	$-0.531159\pi$
$131$	−25.6062			−0.195468			−0.0977338	+	0.995213i	$0.531159\pi$
$132$	3.73709	−	130.132i	0.0283113	−	0.985849i
$133$	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	$-0.940946\pi$
$137$		−	50.5421i		−	0.368920i	0.982840	−	0.184460i	$-0.0590537\pi$
$138$	−118.891	+	139.775i	−0.861528	+	1.01286i
$139$			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
$144$	−143.763	−	8.26387i	−0.998352	−	0.0573880i
$145$		−	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	$-0.984441\pi$
$149$		−	14.5602i		−	0.0977196i	0.998806	−	0.0488598i	$-0.0155588\pi$
$150$	−234.511	+	275.705i	−1.56341	+	1.83803i
$151$	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
$156$	−203.303	−	5.83840i	−1.30323	−	0.0374256i
$157$	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
$162$	21.8567	−	160.519i	0.134918	−	0.990857i
$163$			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	$-0.902484\pi$
$167$		−	100.730i		−	0.603174i	0.953439	−	0.301587i	$-0.0975164\pi$
$168$	91.0604	−	68.8540i	0.542026	−	0.409845i
$169$	−118.266			−0.699801
$170$	−208.992	+	167.669i	−1.22936	+	0.986285i
$171$	−1.93542	−	170.989i	−0.0113182	−	0.999936i
$172$	−88.3102	−	19.6130i	−0.513431	−	0.114029i
$173$	224.024			1.29494			0.647470	−	0.762091i	$-0.275827\pi$
$173$	224.024			1.29494			0.647470	+	0.762091i	$0.275827\pi$
$174$	−115.348	+	135.609i	−0.662918	+	0.779364i
$175$		−	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	$0.157020\pi$
$179$			169.523i			0.947055i	−0.880779	+	0.473528i	$0.842980\pi$
$180$	328.231	−	53.3487i	1.82350	−	0.296382i
$181$		−	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
$186$	−77.7907	+	91.4551i	−0.418229	+	0.491694i
$187$			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	$-0.416609\pi$
$191$	98.9361			0.517990			0.258995	+	0.965879i	$0.416609\pi$
$192$	−86.2343	+	171.545i	−0.449137	+	0.893463i
$193$		−	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	$0.133111\pi$
$197$			160.003i			0.812198i	−0.913829	+	0.406099i	$0.866889\pi$
$198$	96.1816	−	169.949i	0.485766	−	0.858330i
$199$			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
$204$	173.967	+	4.99592i	0.852778	+	0.0244898i
$205$			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
$210$	−170.810	+	200.814i	−0.813379	+	0.956255i
$211$	−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
$216$	−184.852	−	111.740i	−0.855795	−	0.517315i
$217$		−	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
$222$	175.696	+	149.445i	0.791424	+	0.673176i
$223$	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	$-0.986004\pi$
$227$		−	19.9560i		−	0.0879121i	0.999033	−	0.0439560i	$-0.0139961\pi$
$228$	−210.262	−	88.1699i	−0.922201	−	0.386710i
$229$	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	$0.222086\pi$
$233$			299.386i			1.28492i	−0.766320	+	0.642459i	$0.777914\pi$
$234$	−265.510	−	150.263i	−1.13466	−	0.642150i
$235$		−	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	$-0.402905\pi$
$239$	143.556			0.600651			0.300326	+	0.953837i	$0.402905\pi$
$240$	108.515	−	429.900i	0.452146	−	1.79125i
$241$		−	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
$246$	214.130	−	251.743i	0.870446	−	1.02335i
$247$	−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	$-0.718922\pi$
$251$	−318.675			−1.26962			−0.634811	+	0.772667i	$0.718922\pi$
$252$	169.024	−	27.4722i	0.670731	−	0.109017i
$253$	−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	$-0.489398\pi$
$257$	17.1171			0.0666035			0.0333017	+	0.999445i	$0.489398\pi$
$258$	−103.360	−	87.9165i	−0.400619	−	0.340762i
$259$	−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	$-0.455218\pi$
$263$	73.7567			0.280444			0.140222	+	0.990120i	$0.455218\pi$
$264$	−157.037	−	207.684i	−0.594837	−	0.786681i
$265$		−	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	$-0.722497\pi$
$269$	−346.176			−1.28690			−0.643449	+	0.765489i	$0.722497\pi$
$270$	472.668	+	159.352i	1.75062	+	0.590192i
$271$		−	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
$276$	−10.5350	+	366.848i	−0.0381703	+	1.32916i
$277$	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	$-0.565695\pi$
$281$	−115.168			−0.409849			−0.204925	+	0.978778i	$0.565695\pi$
$282$	−71.6081	+	84.1865i	−0.253929	+	0.298534i
$283$			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
$285$	518.151	+	93.4938i	1.81807	+	0.328048i
$286$	−230.130	−	286.847i	−0.804650	−	1.00296i
$287$			262.012i			0.912933i
$288$	−234.613	+	167.035i	−0.814629	+	0.579982i
$289$	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	$-0.631768\pi$
$293$	−235.712			−0.804477			−0.402239	+	0.915535i	$0.631768\pi$
$294$	102.526	−	120.535i	0.348727	−	0.409983i
$295$	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
$300$	−20.7802	+	723.605i	−0.0692674	+	2.41202i
$301$	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
$306$	227.197	+	128.580i	0.742472	+	0.420197i
$307$	−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	$-0.624281\pi$
$311$	−236.730			−0.761190			−0.380595	+	0.924742i	$0.624281\pi$
$312$	−324.462	+	245.337i	−1.03994	+	0.786336i
$313$	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	$-0.237379\pi$
$317$	465.724			1.46916			0.734581	+	0.678521i	$0.237379\pi$
$318$	−125.354	+	147.373i	−0.394195	+	0.463438i
$319$	−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
$324$	−166.801	−	277.765i	−0.514818	−	0.857300i
$325$			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
$330$	458.001	+	389.570i	1.38788	+	1.18052i
$331$	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
$336$	55.8805	−	221.379i	0.166311	−	0.658867i
$337$			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
$342$	−217.021	−	264.322i	−0.634564	−	0.772870i
$343$			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	$-0.529826\pi$
$347$	−64.9325			−0.187125			−0.0935626	+	0.995613i	$0.529826\pi$
$348$	−10.2210	+	355.915i	−0.0293708	+	1.02274i
$349$	−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	$-0.975290\pi$
$353$		−	54.7512i		−	0.155103i	0.996988	−	0.0775513i	$-0.0247102\pi$
$354$	−191.130	−	162.573i	−0.539916	−	0.459247i
$355$	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	$-0.414382\pi$
$359$	190.804			0.531488			0.265744	+	0.964044i	$0.414382\pi$
$360$	445.273	−	494.022i	1.23687	−	1.37228i
$361$	−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
$366$	171.955	−	202.160i	0.469823	−	0.552351i
$367$		−	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
$372$	−6.89309	+	240.030i	−0.0185298	+	0.645241i
$373$			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
$378$	243.403	+	82.0591i	0.643924	+	0.217088i
$379$	−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	$-0.731812\pi$
$383$		−	571.692i		−	1.49267i	0.665572	−	0.746334i	$-0.268188\pi$
$384$	80.1712	+	375.538i	0.208779	+	0.977963i
$385$	−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	$0.0904515\pi$
$389$			218.115i			0.560706i	−0.959897	+	0.280353i	$0.909548\pi$
$390$	608.620	−	715.528i	1.56056	−	1.83469i
$391$		−	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
$396$	−62.6567	−	385.498i	−0.158224	−	0.973481i
$397$	−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
$399$	266.825	+	48.1452i	0.668734	+	0.120665i
$400$	874.463	+	408.575i	2.18616	+	1.02144i
$401$	457.051			1.13978			0.569889	−	0.821722i	$-0.306986\pi$
$401$	457.051			1.13978			0.569889	+	0.821722i	$0.306986\pi$
$402$	−91.5895	+	107.678i	−0.227835	+	0.267855i
$403$			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
$408$	277.642	−	209.935i	0.680495	−	0.514546i
$409$		−	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
$414$	−271.140	+	479.094i	−0.654927	+	1.15723i
$415$		−	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	$-0.328354\pi$
$419$	430.301			1.02697			0.513486	+	0.858098i	$0.328354\pi$
$420$	−15.1356	+	527.047i	−0.0360371	+	1.25487i
$421$			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
$426$	−411.802	−	350.274i	−0.966671	−	0.822240i
$427$			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	$0.161209\pi$
$431$			418.139i			0.970160i	−0.874470	+	0.485080i	$0.838791\pi$
$432$	−428.218	+	57.0365i	−0.991246	+	0.132029i
$433$			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
$438$	−116.850	+	137.376i	−0.266781	+	0.313643i
$439$	−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	$-0.180809\pi$
$443$	746.866			1.68593			0.842964	+	0.537970i	$0.180809\pi$
$444$	461.125	+	13.2424i	1.03857	+	0.0298253i
$445$		−	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	$-0.610603\pi$
$449$	−305.787			−0.681041			−0.340521	+	0.940237i	$0.610603\pi$
$450$	−534.822	+	945.011i	−1.18849	+	2.10002i
$451$	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
$456$	−438.359	+	125.608i	−0.961314	+	0.275457i
$457$	−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	$0.0105882\pi$
$461$			30.6637i			0.0665156i	−0.999447	+	0.0332578i	$0.989412\pi$
$462$	235.850	+	200.611i	0.510498	+	0.434224i
$463$		−	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	$-0.651100\pi$
$467$	−426.900			−0.914134			−0.457067	+	0.889432i	$0.651100\pi$
$468$	−602.259	+	97.8876i	−1.28688	+	0.209162i
$469$		−	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
$474$	196.844	−	231.421i	0.415282	−	0.488229i
$475$	−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	$-0.666501\pi$
$479$	−478.569			−0.999100			−0.499550	+	0.866285i	$0.666501\pi$
$480$	−368.758	−	806.458i	−0.768245	−	1.68012i
$481$	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
$486$	−26.4760	−	485.278i	−0.0544773	−	0.998515i
$487$	−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	$-0.400033\pi$
$491$	303.358			0.617837			0.308918	+	0.951089i	$0.400033\pi$
$492$	18.9742	−	660.715i	0.0385654	−	1.34292i
$493$		−	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
$498$	−143.737	+	168.985i	−0.288628	+	0.339328i
$499$			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	$-0.536768\pi$
$503$	−115.945			−0.230507			−0.115253	+	0.993336i	$0.536768\pi$
$504$	229.296	−	254.400i	0.454952	−	0.504761i
$505$	−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	$-0.842762\pi$
$509$	−896.301			−1.76091			−0.880453	+	0.474133i	$0.842762\pi$
$510$	−520.796	+	612.278i	−1.02117	+	1.20054i
$511$		−	142.979i		−	0.279803i
$512$	501.991	+	100.742i	0.980451	+	0.196761i
$513$	−102.497	−	502.656i	−0.199800	−	0.979837i
$514$	26.7028	−	21.4229i	0.0519509	−	0.0416788i
$515$		−	858.925i		−	1.66782i
$516$	−271.274	−	7.79035i	−0.525724	−	0.0150976i
$517$	−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	$-0.297745\pi$
$521$	618.428			1.18700			0.593501	+	0.804833i	$0.297745\pi$
$522$	−263.060	+	464.817i	−0.503946	+	0.890454i
$523$	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
$528$	−504.906	−	127.448i	−0.956261	−	0.241379i
$529$	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
$534$	−274.701	+	322.954i	−0.514421	+	0.604782i
$535$	−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
$540$	936.802	−	342.979i	1.73482	−	0.635147i
$541$	−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
$546$	313.412	−	368.465i	0.574015	−	0.674845i
$547$	−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
$552$	442.694	+	585.469i	0.801982	+	1.06063i
$553$			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	$0.260548\pi$
$557$			813.383i			1.46029i	−0.683291	+	0.730146i	$0.739452\pi$
$558$	−177.408	+	313.473i	−0.317935	+	0.561780i
$559$	−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	$0.406917\pi$
$563$			1078.20i			1.91509i	−0.288278	+	0.957547i	$0.593083\pi$
$564$	−6.34524	+	220.953i	−0.0112504	+	0.391760i
$565$			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	$-0.562365\pi$
$569$	−221.539			−0.389348			−0.194674	+	0.980868i	$0.562365\pi$
$570$	925.331	−	502.642i	1.62339	−	0.881828i
$571$			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
$576$	−156.946	+	554.206i	−0.272475	+	0.962163i
$577$	−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
$582$	384.540	+	327.086i	0.660722	+	0.562003i
$583$	−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	$-0.445786\pi$
$587$	198.987			0.338990			0.169495	+	0.985531i	$0.445786\pi$
$588$	9.08488	−	316.352i	0.0154505	−	0.538013i
$589$	−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	$-0.807648\pi$
$593$		−	673.859i		−	1.13636i	0.822906	−	0.568178i	$-0.192352\pi$
$594$	187.154	−	555.137i	0.315075	−	0.934573i
$595$		−	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	$-0.864844\pi$
$599$		−	493.529i		−	0.823922i	0.911202	−	0.411961i	$-0.135156\pi$
$600$	873.211	+	1154.83i	1.45535	+	1.92472i
$601$		−	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
$606$	106.301	+	90.4187i	0.175415	+	0.149206i
$607$	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
$612$	515.353	−	83.7624i	0.842080	−	0.136867i
$613$	−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	$-0.826635\pi$
$617$		−	639.350i		−	1.03622i	0.855313	−	0.518112i	$-0.173365\pi$
$618$	−361.478	+	424.974i	−0.584915	+	0.687660i
$619$			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
$624$	−199.110	+	788.807i	−0.319087	+	1.26411i
$625$	1506.00			2.40961
$626$	257.703	−	206.748i	0.411666	−	0.330269i
$627$	109.806	−	608.555i	0.175129	−	0.970582i
$628$	247.174	−	1112.93i	0.393588	−	1.77219i
$629$	−557.546			−0.886400
$630$	−389.545	+	688.312i	−0.618325	+	1.09256i
$631$		−	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
$636$	−11.1077	+	386.791i	−0.0174650	+	0.608161i
$637$		−	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	$-0.480919\pi$
$641$	76.8048			0.119820			0.0599101	+	0.998204i	$0.480919\pi$
$642$	138.729	+	118.001i	0.216089	+	0.183802i
$643$		−	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	$-0.805048\pi$
$647$	−1058.80			−1.63647			−0.818236	+	0.574882i	$0.805048\pi$
$648$	−607.848	−	224.555i	−0.938037	−	0.346536i
$649$		−	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	$0.157250\pi$
$653$			619.260i			0.948331i	−0.880436	+	0.474166i	$0.842750\pi$
$654$	363.967	+	309.586i	0.556524	+	0.473373i
$655$		−	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	$-0.760337\pi$
$659$		−	901.216i		−	1.36755i	0.729693	−	0.683775i	$-0.239663\pi$
$660$	1202.05	+	34.5201i	1.82129	+	0.0523032i
$661$			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
$666$	602.219	+	340.821i	0.904232	+	0.511743i
$667$	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
$672$	−189.894	−	415.290i	−0.282580	−	0.617992i
$673$		−	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	$-0.530783\pi$
$677$	−130.737			−0.193112			−0.0965560	+	0.995328i	$0.530783\pi$
$678$	360.636	−	423.984i	0.531911	−	0.625345i
$679$	−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	$-0.687611\pi$
$683$		−	1135.52i		−	1.66255i	0.555861	−	0.831275i	$-0.312389\pi$
$684$	−669.366	−	140.730i	−0.978605	−	0.205746i
$685$	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
$690$	−1291.12	−	1098.21i	−1.87119	−	1.59161i
$691$		−	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
$696$	429.501	+	568.022i	0.617100	+	0.816123i
$697$			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	$-0.758492\pi$
$701$		−	964.565i		−	1.37598i	0.725718	−	0.687992i	$-0.241508\pi$
$702$	−867.282	−	292.389i	−1.23544	−	0.416508i
$703$	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
$708$	−501.633	−	14.4057i	−0.708522	−	0.0203471i
$709$	−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
$714$	−268.187	+	315.296i	−0.375612	+	0.441591i
$715$	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	$-0.350623\pi$
$719$	650.329			0.904491			0.452245	+	0.891894i	$0.350623\pi$
$720$	76.3347	−	1327.96i	0.106020	−	1.84439i
$721$		−	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
$726$	−12.8417	+	15.0974i	−0.0176883	+	0.0207954i
$727$			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
$732$	15.2371	−	530.582i	0.0208157	−	0.724839i
$733$	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
$738$	488.340	−	862.879i	0.661707	−	1.16921i
$739$			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
$741$	−950.736	−	171.548i	−1.28305	−	0.231509i
$742$	−191.969	−	239.281i	−0.258718	−	0.322481i
$743$			591.155i			0.795633i	0.917465	+	0.397816i	$0.130232\pi$
$743$			591.155i			0.795633i	−0.917465	+	0.397816i	$0.869768\pi$
$744$	289.656	+	383.075i	0.389323	+	0.514885i
$745$	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
$750$	−1491.31	−	1268.50i	−1.98842	−	1.69133i
$751$	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
$756$	482.412	−	176.619i	0.638111	−	0.233623i
$757$	−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	$0.0642294\pi$
$761$			305.033i			0.400832i	−0.979711	+	0.200416i	$0.935771\pi$
$762$	−336.774	+	395.931i	−0.441961	+	0.519594i
$763$	−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
$768$	595.072	+	485.503i	0.774834	+	0.632165i
$769$	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	$-0.321421\pi$
$773$	822.552			1.06410			0.532052	+	0.846712i	$0.321421\pi$
$774$	−354.277	−	200.501i	−0.457723	−	0.259045i
$775$	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
$780$	53.9302	−	1877.95i	0.0691413	−	2.40762i
$781$		−	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
$786$	−99.5430	+	117.028i	−0.126645	+	0.148891i
$787$	−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
$792$	−580.216	−	522.962i	−0.732596	−	0.660305i
$793$		−	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	$-0.478996\pi$
$797$	105.103			0.131874			0.0659368	+	0.997824i	$0.478996\pi$
$798$	476.505	−	258.838i	0.597124	−	0.324359i
$799$		−	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
$804$	−8.11581	+	282.607i	−0.0100943	+	0.351501i
$805$	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	$-0.870167\pi$
$809$		−	641.806i		−	0.793333i	0.917963	−	0.396666i	$-0.129833\pi$
$810$	1482.74	+	201.894i	1.83054	+	0.249252i
$811$	−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
$816$	170.379	−	674.982i	0.208797	−	0.827184i
$817$	−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	$-0.983847\pi$
$821$		−	83.2903i		−	0.101450i	0.998713	−	0.0507249i	$-0.0161532\pi$
$822$	−230.993	−	196.480i	−0.281013	−	0.239027i
$823$		−	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	$0.261442\pi$
$827$			1210.83i			1.46413i	−0.681237	+	0.732063i	$0.738558\pi$
$828$	176.632	+	1086.74i	0.213323	+	1.31248i
$829$			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
$834$	1231.37	+	1047.39i	1.47647	+	1.25586i
$835$	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	$-0.896190\pi$
$839$		−	537.597i		−	0.640759i	0.947289	−	0.320380i	$-0.103810\pi$
$840$	636.015	+	841.140i	0.757161	+	1.00136i
$841$	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
$846$	−163.308	+	288.559i	−0.193035	+	0.341086i
$847$		−	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
$852$	−1080.80	−	31.0380i	−1.26854	−	0.0364296i
$853$	−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
$855$	1579.45	−	17.8778i	1.84731	−	0.0209097i
$856$	217.853	−	107.279i	0.254501	−	0.125326i
$857$	−577.913			−0.674344			−0.337172	−	0.941443i	$-0.609470\pi$
$857$	−577.913			−0.674344			−0.337172	+	0.941443i	$0.609470\pi$
$858$	−840.369	−	714.808i	−0.979451	−	0.833110i
$859$		−	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	$0.252455\pi$
$863$			1229.84i			1.42508i	−0.701632	+	0.712539i	$0.747545\pi$
$864$	−596.639	+	624.914i	−0.690554	+	0.723281i
$865$			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
$870$	−1252.65	−	1065.49i	−1.43982	−	1.22470i
$871$			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
$876$	−10.3542	+	360.551i	−0.0118198	+	0.411588i
$877$		−	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	$-0.937951\pi$
$881$		−	341.298i		−	0.387399i	0.981061	−	0.193699i	$-0.0620486\pi$
$882$	233.818	−	413.148i	0.265100	−	0.468422i
$883$			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	$-0.729328\pi$
$887$		−	1333.17i		−	1.50301i	0.659727	−	0.751506i	$-0.270672\pi$
$888$	735.931	−	556.464i	0.828752	−	0.626648i
$889$		−	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
$894$	−66.5447	−	56.6022i	−0.0744348	−	0.0633134i
$895$	−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
$900$	348.405	+	2143.58i	0.387117	+	2.38175i
$901$		−	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
$906$	1001.95	−	1177.95i	1.10591	−	1.30017i
$907$	−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	$-0.969117\pi$
$911$		−	176.494i		−	0.193736i	0.995297	−	0.0968681i	$-0.0308825\pi$
$912$	−526.637	+	744.578i	−0.577453	+	0.816424i
$913$	−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
$918$	742.133	+	250.197i	0.808424	+	0.272546i
$919$		−	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
$924$	619.003	+	17.7763i	0.669917	+	0.0192384i
$925$		−	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	$-0.908122\pi$
$929$		−	528.885i		−	0.569306i	0.958631	−	0.284653i	$-0.0918784\pi$
$930$	−844.786	−	718.565i	−0.908372	−	0.772651i
$931$	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
$936$	−817.015	+	906.463i	−0.872880	+	0.968443i
$937$	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	$-0.297783\pi$
$941$	1116.79			1.18681			0.593405	+	0.804904i	$0.297783\pi$
$942$	1107.97	−	1302.60i	1.17619	−	1.38280i
$943$	−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	$-0.316255\pi$
$947$	1033.60			1.09144			0.545722	+	0.837966i	$0.316255\pi$
$948$	17.4425	−	607.378i	0.0183992	−	0.640694i
$949$			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	$-0.783492\pi$
$953$	−1481.84			−1.55492			−0.777459	+	0.628933i	$0.783492\pi$
$954$	−285.880	+	505.139i	−0.299664	+	0.529496i
$955$			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
$960$	−1584.59	−	796.561i	−1.65061	−	0.829751i
$961$	−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
$966$	−664.871	−	565.532i	−0.688273	−	0.585437i
$967$			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
$969$	813.545	+	146.794i	0.839572	+	0.151490i
$970$	−1212.44	+	972.711i	−1.24994	+	1.00279i
$971$		−	1520.53i		−	1.56594i	−0.622058	−	0.782971i	$-0.713703\pi$
$971$		−	1520.53i		−	1.56594i	0.622058	−	0.782971i	$-0.286297\pi$
$972$	−648.654	−	723.901i	−0.667339	−	0.744754i
$973$	−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	$-0.559824\pi$
$977$	−365.082			−0.373676			−0.186838	+	0.982391i	$0.559824\pi$
$978$	417.199	+	354.864i	0.426584	+	0.362847i
$979$	−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	$-0.869198\pi$
$983$		−	785.338i		−	0.798920i	0.916751	−	0.399460i	$-0.130802\pi$
$984$	−797.320	−	1054.47i	−0.810284	−	1.07161i
$985$	−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
$990$	1569.85	+	888.445i	1.58571	+	0.897419i
$991$	−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
$996$	−12.7366	+	443.512i	−0.0127878	+	0.445293i
$997$	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.227.58	yes	72
3.2	odd	2	inner	228.3.b.e.227.16	yes	72
4.3	odd	2	inner	228.3.b.e.227.59	yes	72
12.11	even	2	inner	228.3.b.e.227.13	✓	72
19.18	odd	2	inner	228.3.b.e.227.15	yes	72
57.56	even	2	inner	228.3.b.e.227.57	yes	72
76.75	even	2	inner	228.3.b.e.227.14	yes	72
228.227	odd	2	inner	228.3.b.e.227.60	yes	72

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

\(f(q)\)	\(=\)	\(q+(1.56001 - 1.25155i) q^{2} +(2.94611 - 0.566091i) q^{3} +(0.867237 - 3.90486i) q^{4} +9.23717i q^{5} +(3.88745 - 4.57031i) q^{6} +4.75673i q^{7} +(-3.53423 - 7.17699i) q^{8} +(8.35908 - 3.33553i) q^{9} +O(q^{10})\)	\(q+(1.56001 - 1.25155i) q^{2} +(2.94611 - 0.566091i) q^{3} +(0.867237 - 3.90486i) q^{4} +9.23717i q^{5} +(3.88745 - 4.57031i) 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} +(0.344470 - 11.9951i) 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} +(8.86564 - 15.6653i) 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} +(-14.4751 - 19.1435i) 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} +(42.2167 + 35.9090i) 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} +(-5.77544 - 35.5337i) 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} +(21.7397 + 18.4916i) 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} +(-46.5402 - 11.7477i) 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} +(17.2511 - 51.1703i) q^{54} +100.212i q^{55} +(34.1390 - 16.8114i) q^{56} +(10.1215 - 56.0942i) q^{57} +(-46.2882 + 37.1358i) q^{58} -41.8200i q^{59} +(110.800 + 3.18193i) 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} +(42.1742 - 49.5824i) 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} +(-53.4820 - 48.2045i) 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} +(-77.4619 - 65.8882i) 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} +(57.0573 + 1.63855i) 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} +(144.703 + 81.8934i) 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} +(-87.3058 + 39.9211i) 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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