LMFDB - Embedded newform 312.4.m.a.181.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.39
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.457367 - 2.79120i) q^{2} -3.00000i q^{3} +(-7.58163 + 2.55321i) q^{4} +4.56929 q^{5} +(-8.37361 + 1.37210i) q^{6} -23.0002i q^{7} +(10.5941 + 19.9941i) q^{8} -9.00000 q^{9} +(-2.08984 - 12.7538i) q^{10} -9.02801 q^{11} +(7.65962 + 22.7449i) q^{12} +(3.63901 - 46.7307i) q^{13} +(-64.1982 + 10.5195i) q^{14} -13.7079i q^{15} +(50.9623 - 38.7150i) q^{16} -59.4245 q^{17} +(4.11630 + 25.1208i) q^{18} -27.0061 q^{19} +(-34.6427 + 11.6664i) q^{20} -69.0006 q^{21} +(4.12911 + 25.1990i) q^{22} +35.7672 q^{23} +(59.9824 - 31.7823i) q^{24} -104.122 q^{25} +(-132.099 + 11.2158i) q^{26} +27.0000i q^{27} +(58.7243 + 174.379i) q^{28} -142.184i q^{29} +(-38.2615 + 6.26953i) q^{30} +303.839i q^{31} +(-131.370 - 124.539i) q^{32} +27.0840i q^{33} +(27.1788 + 165.866i) q^{34} -105.095i q^{35} +(68.2347 - 22.9789i) q^{36} -241.300 q^{37} +(12.3517 + 75.3795i) q^{38} +(-140.192 - 10.9170i) q^{39} +(48.4076 + 91.3590i) q^{40} +280.464i q^{41} +(31.5586 + 192.595i) q^{42} -198.269i q^{43} +(68.4470 - 23.0504i) q^{44} -41.1236 q^{45} +(-16.3587 - 99.8335i) q^{46} +319.409i q^{47} +(-116.145 - 152.887i) q^{48} -186.009 q^{49} +(47.6217 + 290.624i) q^{50} +178.273i q^{51} +(91.7235 + 363.586i) q^{52} -531.123i q^{53} +(75.3625 - 12.3489i) q^{54} -41.2516 q^{55} +(459.869 - 243.666i) q^{56} +81.0182i q^{57} +(-396.863 + 65.0301i) q^{58} +378.115 q^{59} +(34.9991 + 103.928i) q^{60} +878.946i q^{61} +(848.076 - 138.966i) q^{62} +207.002i q^{63} +(-287.530 + 423.640i) q^{64} +(16.6277 - 213.526i) q^{65} +(75.5970 - 12.3873i) q^{66} +247.600 q^{67} +(450.534 - 151.723i) q^{68} -107.302i q^{69} +(-293.340 + 48.0668i) q^{70} +182.156i q^{71} +(-95.3470 - 179.947i) q^{72} -815.886i q^{73} +(110.363 + 673.517i) q^{74} +312.365i q^{75} +(204.750 - 68.9521i) q^{76} +207.646i q^{77} +(33.6475 + 396.298i) q^{78} -817.462 q^{79} +(232.862 - 176.900i) q^{80} +81.0000 q^{81} +(782.832 - 128.275i) q^{82} -246.607 q^{83} +(523.137 - 176.173i) q^{84} -271.528 q^{85} +(-553.408 + 90.6816i) q^{86} -426.551 q^{87} +(-95.6437 - 180.507i) q^{88} -355.903i q^{89} +(18.8086 + 114.784i) q^{90} +(-1074.81 - 83.6980i) q^{91} +(-271.174 + 91.3211i) q^{92} +911.517 q^{93} +(891.534 - 146.087i) q^{94} -123.399 q^{95} +(-373.617 + 394.109i) q^{96} -506.709i q^{97} +(85.0742 + 519.188i) q^{98} +81.2521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.457367	−	2.79120i	−0.161704	−	0.986839i
$2$	−0.457367	−	2.79120i	−0.161704	−	0.986839i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−7.58163	+	2.55321i	−0.947704	+	0.319151i
$5$	4.56929			0.408690			0.204345	−	0.978899i	$-0.434494\pi$
$5$	4.56929			0.408690			0.204345	+	0.978899i	$0.434494\pi$
$6$	−8.37361	+	1.37210i	−0.569752	+	0.0933596i
$7$		−	23.0002i		−	1.24189i	−0.783853	−	0.620947i	$-0.786748\pi$
$7$		−	23.0002i		−	1.24189i	0.783853	−	0.620947i	$-0.213252\pi$
$8$	10.5941	+	19.9941i	0.468198	+	0.883624i
$9$	−9.00000			−0.333333
$10$	−2.08984	−	12.7538i	−0.0660866	−	0.403311i
$11$	−9.02801			−0.247459			−0.123729	−	0.992316i	$-0.539485\pi$
$11$	−9.02801			−0.247459			−0.123729	+	0.992316i	$0.539485\pi$
$12$	7.65962	+	22.7449i	0.184262	+	0.547157i
$13$	3.63901	−	46.7307i	0.0776370	−	0.996982i
$13$	3.63901	−	46.7307i	0.0776370	−	0.996982i
$14$	−64.1982	+	10.5195i	−1.22555	+	0.200819i
$15$		−	13.7079i		−	0.235957i
$16$	50.9623	−	38.7150i	0.796285	−	0.604921i
$17$	−59.4245			−0.847797			−0.423899	−	0.905710i	$-0.639339\pi$
$17$	−59.4245			−0.847797			−0.423899	+	0.905710i	$0.639339\pi$
$18$	4.11630	+	25.1208i	0.0539012	+	0.328946i
$19$	−27.0061			−0.326085			−0.163043	−	0.986619i	$-0.552131\pi$
$19$	−27.0061			−0.326085			−0.163043	+	0.986619i	$0.552131\pi$
$20$	−34.6427	+	11.6664i	−0.387317	+	0.130434i
$21$	−69.0006			−0.717008
$22$	4.12911	+	25.1990i	0.0400150	+	0.244202i
$23$	35.7672			0.324260			0.162130	−	0.986769i	$-0.448164\pi$
$23$	35.7672			0.324260			0.162130	+	0.986769i	$0.448164\pi$
$24$	59.9824	−	31.7823i	0.510160	−	0.270314i
$25$	−104.122			−0.832972
$26$	−132.099	+	11.2158i	−0.996415	+	0.0846003i
$27$			27.0000i			0.192450i
$28$	58.7243	+	174.379i	0.396351	+	1.17695i
$29$		−	142.184i		−	0.910442i	−0.890378	−	0.455221i	$-0.849560\pi$
$29$		−	142.184i		−	0.910442i	0.890378	−	0.455221i	$-0.150440\pi$
$30$	−38.2615	+	6.26953i	−0.232852	+	0.0381551i
$31$			303.839i			1.76036i	0.474643	+	0.880179i	$0.342577\pi$
$31$			303.839i			1.76036i	−0.474643	+	0.880179i	$0.657423\pi$
$32$	−131.370	−	124.539i	−0.725722	−	0.687988i
$33$			27.0840i			0.142870i
$34$	27.1788	+	165.866i	0.137092	+	0.836640i
$35$		−	105.095i		−	0.507550i
$36$	68.2347	−	22.9789i	0.315901	−	0.106384i
$37$	−241.300			−1.07215			−0.536074	−	0.844171i	$-0.680093\pi$
$37$	−241.300			−1.07215			−0.536074	+	0.844171i	$0.680093\pi$
$38$	12.3517	+	75.3795i	0.0527292	+	0.321794i
$39$	−140.192	−	10.9170i	−0.575608	−	0.0448237i
$40$	48.4076	+	91.3590i	0.191348	+	0.361128i
$41$			280.464i			1.06832i	0.845383	+	0.534160i	$0.179372\pi$
$41$			280.464i			1.06832i	−0.845383	+	0.534160i	$0.820628\pi$
$42$	31.5586	+	192.595i	0.115943	+	0.707571i
$43$		−	198.269i		−	0.703156i	−0.936159	−	0.351578i	$-0.885645\pi$
$43$		−	198.269i		−	0.703156i	0.936159	−	0.351578i	$-0.114355\pi$
$44$	68.4470	−	23.0504i	0.234518	−	0.0789767i
$45$	−41.1236			−0.136230
$46$	−16.3587	−	99.8335i	−0.0524340	−	0.319992i
$47$			319.409i			0.991288i	0.868526	+	0.495644i	$0.165068\pi$
$47$			319.409i			0.991288i	−0.868526	+	0.495644i	$0.834932\pi$
$48$	−116.145	−	152.887i	−0.349251	−	0.459736i
$49$	−186.009			−0.542300
$50$	47.6217	+	290.624i	0.134695	+	0.822010i
$51$			178.273i			0.489476i
$52$	91.7235	+	363.586i	0.244611	+	0.969621i
$53$		−	531.123i		−	1.37652i	−0.725466	−	0.688258i	$-0.758376\pi$
$53$		−	531.123i		−	1.37652i	0.725466	−	0.688258i	$-0.241624\pi$
$54$	75.3625	−	12.3489i	0.189917	−	0.0311199i
$55$	−41.2516			−0.101134
$56$	459.869	−	243.666i	1.09737	−	0.581452i
$57$			81.0182i			0.188265i
$58$	−396.863	+	65.0301i	−0.898460	+	0.147222i
$59$	378.115			0.834345			0.417172	−	0.908827i	$-0.363021\pi$
$59$	378.115			0.834345			0.417172	+	0.908827i	$0.363021\pi$
$60$	34.9991	+	103.928i	0.0753060	+	0.223618i
$61$			878.946i			1.84488i	0.386145	+	0.922438i	$0.373807\pi$
$61$			878.946i			1.84488i	−0.386145	+	0.922438i	$0.626193\pi$
$62$	848.076	−	138.966i	1.73719	−	0.284656i
$63$			207.002i			0.413965i
$64$	−287.530	+	423.640i	−0.561582	+	0.827421i
$65$	16.6277	−	213.526i	0.0317295	−	0.407457i
$66$	75.5970	−	12.3873i	0.140990	−	0.0231027i
$67$	247.600			0.451480			0.225740	−	0.974188i	$-0.427520\pi$
$67$	247.600			0.451480			0.225740	+	0.974188i	$0.427520\pi$
$68$	450.534	−	151.723i	0.803461	−	0.270575i
$69$		−	107.302i		−	0.187211i
$70$	−293.340	+	48.0668i	−0.500870	+	0.0820726i
$71$			182.156i			0.304478i	0.988344	+	0.152239i	$0.0486483\pi$
$71$			182.156i			0.304478i	−0.988344	+	0.152239i	$0.951352\pi$
$72$	−95.3470	−	179.947i	−0.156066	−	0.294541i
$73$		−	815.886i		−	1.30811i	−0.756446	−	0.654057i	$-0.773066\pi$
$73$		−	815.886i		−	1.30811i	0.756446	−	0.654057i	$-0.226934\pi$
$74$	110.363	+	673.517i	0.173370	+	1.05804i
$75$			312.365i			0.480917i
$76$	204.750	−	68.9521i	0.309032	−	0.104070i
$77$			207.646i			0.307317i
$78$	33.6475	+	396.298i	0.0488440	+	0.575280i
$79$	−817.462			−1.16420			−0.582099	−	0.813118i	$-0.697769\pi$
$79$	−817.462			−1.16420			−0.582099	+	0.813118i	$0.697769\pi$
$80$	232.862	−	176.900i	0.325434	−	0.247225i
$81$	81.0000			0.111111
$82$	782.832	−	128.275i	1.05426	−	0.172751i
$83$	−246.607			−0.326128			−0.163064	−	0.986616i	$-0.552138\pi$
$83$	−246.607			−0.326128			−0.163064	+	0.986616i	$0.552138\pi$
$84$	523.137	−	176.173i	0.679511	−	0.228834i
$85$	−271.528			−0.346486
$86$	−553.408	+	90.6816i	−0.693902	+	0.113703i
$87$	−426.551			−0.525644
$88$	−95.6437	−	180.507i	−0.115860	−	0.218660i
$89$		−	355.903i		−	0.423883i	−0.977282	−	0.211942i	$-0.932021\pi$
$89$		−	355.903i		−	0.423883i	0.977282	−	0.211942i	$-0.0679787\pi$
$90$	18.8086	+	114.784i	0.0220289	+	0.134437i
$91$	−1074.81	−	83.6980i	−1.23815	−	0.0964168i
$92$	−271.174	+	91.3211i	−0.307302	+	0.103488i
$93$	911.517			1.01634
$94$	891.534	−	146.087i	0.978242	−	0.160295i
$95$	−123.399			−0.133268
$96$	−373.617	+	394.109i	−0.397210	+	0.418996i
$97$		−	506.709i		−	0.530397i	−0.964194	−	0.265199i	$-0.914563\pi$
$97$		−	506.709i		−	0.530397i	0.964194	−	0.265199i	$-0.0854375\pi$
$98$	85.0742	+	519.188i	0.0876918	+	0.535163i
$99$	81.2521			0.0824863
$100$	789.411	−	265.844i	0.789411	−	0.265844i
$101$		−	877.066i		−	0.864073i	−0.901856	−	0.432036i	$-0.857795\pi$
$101$		−	877.066i		−	0.864073i	0.901856	−	0.432036i	$-0.142205\pi$
$102$	497.597	−	81.5363i	0.483034	−	0.0791500i
$103$	−1177.42			−1.12636			−0.563179	−	0.826335i	$-0.690422\pi$
$103$	−1177.42			−1.12636			−0.563179	+	0.826335i	$0.690422\pi$
$104$	972.891	−	422.311i	0.917306	−	0.398183i
$105$	−315.284			−0.293034
$106$	−1482.47	+	242.918i	−1.35840	+	0.222587i
$107$		−	1125.19i		−	1.01660i	−0.861179	−	0.508301i	$-0.830274\pi$
$107$		−	1125.19i		−	1.01660i	0.861179	−	0.508301i	$-0.169726\pi$
$108$	−68.9366	−	204.704i	−0.0614206	−	0.182386i
$109$	−788.108			−0.692542			−0.346271	−	0.938135i	$-0.612552\pi$
$109$	−788.108			−0.692542			−0.346271	+	0.938135i	$0.612552\pi$
$110$	18.8671	+	115.142i	0.0163537	+	0.0998029i
$111$			723.900i			0.619005i
$112$	−890.451	−	1172.14i	−0.751248	−	0.988902i
$113$	−1182.33			−0.984284			−0.492142	−	0.870515i	$-0.663786\pi$
$113$	−1182.33			−0.984284			−0.492142	+	0.870515i	$0.663786\pi$
$114$	226.138	−	37.0551i	0.185788	−	0.0304432i
$115$	163.431			0.132522
$116$	363.024	+	1077.98i	0.290569	+	0.862830i
$117$	−32.7511	+	420.576i	−0.0258790	+	0.332327i
$118$	−172.937	−	1055.39i	−0.134917	−	0.823364i
$119$			1366.77i			1.05287i
$120$	274.077	−	145.223i	0.208497	−	0.110475i
$121$	−1249.50			−0.938764
$122$	2453.32	−	402.001i	1.82060	−	0.298323i
$123$	841.392			0.616795
$124$	−775.764	−	2303.59i	−0.561820	−	1.66830i
$125$	−1046.92			−0.749118
$126$	577.784	−	94.6757i	0.408516	−	0.0669395i
$127$	1038.87			0.725864			0.362932	−	0.931816i	$-0.381776\pi$
$127$	1038.87			0.725864			0.362932	+	0.931816i	$0.381776\pi$
$128$	1313.97	+	608.795i	0.907342	+	0.420394i
$129$	−594.806			−0.405967
$130$	−603.600	+	51.2485i	−0.407225	+	0.0345753i
$131$		−	142.564i		−	0.0950833i	−0.998869	−	0.0475417i	$-0.984861\pi$
$131$		−	142.564i		−	0.0950833i	0.998869	−	0.0475417i	$-0.0151387\pi$
$132$	−69.1511	−	205.341i	−0.0455972	−	0.135399i
$133$			621.145i			0.404963i
$134$	−113.244	−	691.102i	−0.0730059	−	0.445538i
$135$			123.371i			0.0786524i
$136$	−629.549	−	1188.14i	−0.396937	−	0.749134i
$137$		−	2413.02i		−	1.50481i	−0.658703	−	0.752403i	$-0.728895\pi$
$137$		−	2413.02i		−	1.50481i	0.658703	−	0.752403i	$-0.271105\pi$
$138$	−299.500	+	49.0762i	−0.184748	+	0.0302728i
$139$		−	827.007i		−	0.504646i	−0.967643	−	0.252323i	$-0.918805\pi$
$139$		−	827.007i		−	0.504646i	0.967643	−	0.252323i	$-0.0811946\pi$
$140$	268.328	+	796.789i	0.161985	+	0.481007i
$141$	958.226			0.572320
$142$	508.434	−	83.3120i	0.300471	−	0.0492351i
$143$	−32.8530	+	421.885i	−0.0192119	+	0.246712i
$144$	−458.660	+	348.435i	−0.265428	+	0.201640i
$145$		−	649.679i		−	0.372089i
$146$	−2277.30	+	373.159i	−1.29090	+	0.211527i
$147$			558.026i			0.313097i
$148$	1829.45	−	616.089i	1.01608	−	0.342177i
$149$	3151.97			1.73302			0.866509	−	0.499162i	$-0.166359\pi$
$149$	3151.97			1.73302			0.866509	+	0.499162i	$0.166359\pi$
$150$	871.873	−	142.865i	0.474588	−	0.0777660i
$151$		−	934.341i		−	0.503547i	−0.967786	−	0.251774i	$-0.918986\pi$
$151$		−	934.341i		−	0.503547i	0.967786	−	0.251774i	$-0.0810138\pi$
$152$	−286.105	−	539.963i	−0.152672	−	0.288137i
$153$	534.820			0.282599
$154$	579.582	−	94.9703i	0.303273	−	0.0496943i
$155$			1388.33i			0.719441i
$156$	1090.76	−	275.171i	0.559811	−	0.141226i
$157$		−	307.214i		−	0.156168i	−0.996947	−	0.0780840i	$-0.975120\pi$
$157$		−	307.214i		−	0.156168i	0.996947	−	0.0780840i	$-0.0248802\pi$
$158$	373.880	+	2281.70i	0.188255	+	1.14888i
$159$	−1593.37			−0.794732
$160$	−600.267	−	569.056i	−0.296595	−	0.281174i
$161$		−	822.652i		−	0.402696i
$162$	−37.0467	−	226.087i	−0.0179671	−	0.109649i
$163$	−368.699			−0.177170			−0.0885851	−	0.996069i	$-0.528235\pi$
$163$	−368.699			−0.177170			−0.0885851	+	0.996069i	$0.528235\pi$
$164$	−716.083	−	2126.37i	−0.340955	−	1.01245i
$165$			123.755i			0.0583897i
$166$	112.790	+	688.329i	0.0527360	+	0.321836i
$167$		−	402.412i		−	0.186464i	−0.995644	−	0.0932322i	$-0.970280\pi$
$167$		−	402.412i		−	0.186464i	0.995644	−	0.0932322i	$-0.0297199\pi$
$168$	−730.999	−	1379.61i	−0.335701	−	0.633565i
$169$	−2170.52	−	340.107i	−0.987945	−	0.154805i
$170$	124.188	+	757.890i	0.0560281	+	0.341926i
$171$	243.055			0.108695
$172$	506.221	+	1503.20i	0.224413	+	0.666384i
$173$		−	3541.26i		−	1.55629i	−0.628088	−	0.778143i	$-0.716162\pi$
$173$		−	3541.26i		−	1.55629i	0.628088	−	0.778143i	$-0.283838\pi$
$174$	195.090	+	1190.59i	0.0849986	+	0.518726i
$175$			2394.82i			1.03446i
$176$	−460.088	+	349.519i	−0.197048	+	0.149693i
$177$		−	1134.34i		−	0.481709i
$178$	−993.397	+	162.778i	−0.418305	+	0.0685434i
$179$		−	3755.60i		−	1.56819i	−0.620640	−	0.784096i	$-0.713127\pi$
$179$		−	3755.60i		−	1.56819i	0.620640	−	0.784096i	$-0.286873\pi$
$180$	311.784	−	104.997i	0.129106	−	0.0434779i
$181$		−	1146.21i		−	0.470701i	−0.971911	−	0.235350i	$-0.924376\pi$
$181$		−	1146.21i		−	0.470701i	0.971911	−	0.235350i	$-0.0756238\pi$
$182$	257.967	+	3038.31i	0.105065	+	1.23744i
$183$	2636.84			1.06514
$184$	378.921	+	715.134i	0.151818	+	0.286524i
$185$	−1102.57			−0.438176
$186$	−416.897	−	2544.23i	−0.164346	−	1.00297i
$187$	536.485			0.209795
$188$	−815.517	−	2421.64i	−0.316371	−	0.939448i
$189$	621.005			0.239003
$190$	56.4385	+	344.431i	0.0215499	+	0.131514i
$191$	2181.45			0.826410			0.413205	−	0.910638i	$-0.364409\pi$
$191$	2181.45			0.826410			0.413205	+	0.910638i	$0.364409\pi$
$192$	1270.92	+	862.589i	0.477712	+	0.324229i
$193$		−	4438.58i		−	1.65542i	−0.561158	−	0.827709i	$-0.689644\pi$
$193$		−	4438.58i		−	1.65542i	0.561158	−	0.827709i	$-0.310356\pi$
$194$	−1414.33	+	231.752i	−0.523417	+	0.0857671i
$195$	−640.579	−	49.8831i	−0.235245	−	0.0183190i
$196$	1410.25	−	474.919i	0.513939	−	0.173075i
$197$	3788.49			1.37014			0.685072	−	0.728475i	$-0.259771\pi$
$197$	3788.49			1.37014			0.685072	+	0.728475i	$0.259771\pi$
$198$	−37.1620	−	226.791i	−0.0133383	−	0.0814007i
$199$	1535.85			0.547102			0.273551	−	0.961858i	$-0.411802\pi$
$199$	1535.85			0.547102			0.273551	+	0.961858i	$0.411802\pi$
$200$	−1103.07	−	2081.82i	−0.389996	−	0.736034i
$201$		−	742.800i		−	0.260662i
$202$	−2448.07	+	401.141i	−0.852701	+	0.139724i
$203$	−3270.25			−1.13067
$204$	−455.169	−	1351.60i	−0.156217	−	0.463878i
$205$			1281.52i			0.436612i
$206$	538.514	+	3286.42i	0.182136	+	1.11153i
$207$	−321.905			−0.108087
$208$	−1623.72	−	2522.39i	−0.541274	−	0.840846i
$209$	243.811			0.0806927
$210$	144.200	+	880.021i	0.0473846	+	0.289177i
$211$			5166.95i			1.68582i	0.538055	+	0.842909i	$0.319159\pi$
$211$			5166.95i			1.68582i	−0.538055	+	0.842909i	$0.680841\pi$
$212$	1356.07	+	4026.78i	0.439316	+	1.30453i
$213$	546.467			0.175790
$214$	−3140.64	+	514.626i	−1.00322	+	0.164388i
$215$		−	905.948i		−	0.287373i
$216$	−539.841	+	286.041i	−0.170053	+	0.0901047i
$217$	6988.35			2.18618
$218$	360.454	+	2199.77i	0.111986	+	0.683428i
$219$	−2447.66			−0.755240
$220$	312.755	−	105.324i	0.0958450	−	0.0322770i
$221$	−216.246	+	2776.95i	−0.0658204	+	0.845238i
$222$	2020.55	−	331.088i	0.610858	−	0.100095i
$223$			4812.46i			1.44514i	0.691297	+	0.722570i	$0.257039\pi$
$223$			4812.46i			1.44514i	−0.691297	+	0.722570i	$0.742961\pi$
$224$	−2864.42	+	3021.53i	−0.854408	+	0.901270i
$225$	937.094			0.277657
$226$	540.758	+	3300.12i	0.159162	+	0.971330i
$227$	−584.946			−0.171032			−0.0855159	−	0.996337i	$-0.527254\pi$
$227$	−584.946			−0.171032			−0.0855159	+	0.996337i	$0.527254\pi$
$228$	−206.856	−	614.250i	−0.0600851	−	0.178420i
$229$	−4584.28			−1.32287			−0.661436	−	0.750001i	$-0.730053\pi$
$229$	−4584.28			−1.32287			−0.661436	+	0.750001i	$0.730053\pi$
$230$	−74.7478	−	456.169i	−0.0214292	−	0.130778i
$231$	622.938			0.177430
$232$	2842.84	−	1506.31i	0.804489	−	0.426267i
$233$	4302.16			1.20963			0.604815	−	0.796366i	$-0.293247\pi$
$233$	4302.16			1.20963			0.604815	+	0.796366i	$0.293247\pi$
$234$	1188.89	−	100.943i	0.332138	−	0.0282001i
$235$			1459.47i			0.405130i
$236$	−2866.73	+	965.405i	−0.790712	+	0.266282i
$237$			2452.39i			0.672150i
$238$	3814.94	−	625.117i	1.03902	−	0.170253i
$239$			7132.42i			1.93037i	0.261573	+	0.965184i	$0.415759\pi$
$239$			7132.42i			1.93037i	−0.261573	+	0.965184i	$0.584241\pi$
$240$	−530.700	−	698.585i	−0.142736	−	0.187889i
$241$			813.188i			0.217353i	0.994077	+	0.108676i	$0.0346612\pi$
$241$			813.188i			0.217353i	−0.994077	+	0.108676i	$0.965339\pi$
$242$	571.478	+	3487.59i	0.151802	+	0.926409i
$243$		−	243.000i		−	0.0641500i
$244$	−2244.13	−	6663.84i	−0.588794	−	1.74840i
$245$	−849.929			−0.221632
$246$	−384.825	−	2348.50i	−0.0997379	−	0.608677i
$247$	−98.2755	+	1262.01i	−0.0253163	+	0.325101i
$248$	−6074.99	+	3218.90i	−1.55549	+	0.824195i
$249$			739.820i			0.188290i
$250$	478.828	+	2922.18i	0.121135	+	0.739259i
$251$		−	98.3380i		−	0.0247292i	−0.999924	−	0.0123646i	$-0.996064\pi$
$251$		−	98.3380i		−	0.0247292i	0.999924	−	0.0123646i	$-0.00393588\pi$
$252$	−528.518	−	1569.41i	−0.132117	−	0.392316i
$253$	−322.906			−0.0802409
$254$	−475.144	−	2899.69i	−0.117375	−	0.716311i
$255$			814.584i			0.200044i
$256$	1098.30	−	3946.00i	0.268141	−	0.963380i
$257$	2348.27			0.569966			0.284983	−	0.958533i	$-0.408012\pi$
$257$	2348.27			0.569966			0.284983	+	0.958533i	$0.408012\pi$
$258$	272.045	+	1660.23i	0.0656464	+	0.400624i
$259$			5549.94i			1.33149i
$260$	419.112	+	1661.33i	0.0999700	+	0.396275i
$261$			1279.65i			0.303481i
$262$	−397.926	+	65.2043i	−0.0938320	+	0.0153753i
$263$	−3653.13			−0.856507			−0.428254	−	0.903659i	$-0.640871\pi$
$263$	−3653.13			−0.856507			−0.428254	+	0.903659i	$0.640871\pi$
$264$	−541.521	+	286.931i	−0.126244	+	0.0668916i
$265$		−	2426.86i		−	0.562568i
$266$	1733.74	−	284.091i	0.399634	−	0.0654840i
$267$	−1067.71			−0.244729
$268$	−1877.21	+	632.174i	−0.427869	+	0.144090i
$269$		−	496.183i		−	0.112464i	−0.998418	−	0.0562320i	$-0.982091\pi$
$269$		−	496.183i		−	0.112464i	0.998418	−	0.0562320i	$-0.0179086\pi$
$270$	344.353	−	56.4258i	0.0776173	−	0.0127184i
$271$			1164.70i			0.261072i	0.991444	+	0.130536i	$0.0416698\pi$
$271$			1164.70i			0.261072i	−0.991444	+	0.130536i	$0.958330\pi$
$272$	−3028.41	+	2300.62i	−0.675089	+	0.512850i
$273$	−251.094	+	3224.44i	−0.0556663	+	0.714843i
$274$	−6735.23	+	1103.64i	−1.48500	+	0.243332i
$275$	940.010			0.206126
$276$	273.963	+	813.521i	0.0597487	+	0.177421i
$277$		−	3541.96i		−	0.768289i	−0.923273	−	0.384144i	$-0.874496\pi$
$277$		−	3541.96i		−	0.768289i	0.923273	−	0.384144i	$-0.125504\pi$
$278$	−2308.35	+	378.246i	−0.498005	+	0.0816031i
$279$		−	2734.55i		−	0.586786i
$280$	2101.27	−	1113.38i	0.448483	−	0.237634i
$281$		−	1001.92i		−	0.212703i	−0.994329	−	0.106352i	$-0.966083\pi$
$281$		−	1001.92i		−	0.212703i	0.994329	−	0.106352i	$-0.0339169\pi$
$282$	−438.261	−	2674.60i	−0.0925463	−	0.564788i
$283$		−	4471.46i		−	0.939226i	−0.882872	−	0.469613i	$-0.844393\pi$
$283$		−	4471.46i		−	0.939226i	0.882872	−	0.469613i	$-0.155607\pi$
$284$	−465.081	−	1381.04i	−0.0971743	−	0.288555i
$285$			370.196i			0.0769422i
$286$	1192.59	−	101.257i	0.246572	−	0.0209351i
$287$	6450.73			1.32674
$288$	1182.33	+	1120.85i	0.241907	+	0.229329i
$289$	−1381.73			−0.281240
$290$	−1813.39	+	297.141i	−0.367192	+	0.0601681i
$291$	−1520.13			−0.306225
$292$	2083.13	+	6185.75i	0.417486	+	1.23970i
$293$	3292.99			0.656582			0.328291	−	0.944577i	$-0.393527\pi$
$293$	3292.99			0.656582			0.328291	+	0.944577i	$0.393527\pi$
$294$	1557.56	−	255.223i	0.308976	−	0.0506289i
$295$	1727.72			0.340988
$296$	−2556.36	−	4824.58i	−0.501977	−	0.947375i
$297$		−	243.756i		−	0.0476235i
$298$	−1441.61	−	8797.79i	−0.280235	−	1.71021i
$299$	130.157	−	1671.43i	0.0251745	−	0.323281i
$300$	−797.532	−	2368.23i	−0.153485	−	0.455767i
$301$	−4560.22			−0.873245
$302$	−2607.94	+	427.337i	−0.496920	+	0.0814254i
$303$	−2631.20			−0.498873
$304$	−1376.29	+	1045.54i	−0.259657	+	0.197256i
$305$			4016.16i			0.753983i
$306$	−244.609	−	1492.79i	−0.0456973	−	0.278880i
$307$	3274.18			0.608688			0.304344	−	0.952562i	$-0.401563\pi$
$307$	3274.18			0.608688			0.304344	+	0.952562i	$0.401563\pi$
$308$	−530.163	−	1574.29i	−0.0980806	−	0.291246i
$309$			3532.27i			0.650303i
$310$	3875.11	−	634.976i	0.709972	−	0.116336i
$311$	3191.33			0.581876			0.290938	−	0.956742i	$-0.406033\pi$
$311$	3191.33			0.581876			0.290938	+	0.956742i	$0.406033\pi$
$312$	−1266.93	−	2918.67i	−0.229891	−	0.529607i
$313$	5529.90			0.998621			0.499311	−	0.866423i	$-0.333587\pi$
$313$	5529.90			0.998621			0.499311	+	0.866423i	$0.333587\pi$
$314$	−857.498	+	140.510i	−0.154113	+	0.0252529i
$315$			945.852i			0.169183i
$316$	6197.70	−	2087.15i	1.10332	−	0.371555i
$317$	−6475.59			−1.14734			−0.573668	−	0.819088i	$-0.694480\pi$
$317$	−6475.59			−1.14734			−0.573668	+	0.819088i	$0.694480\pi$
$318$	728.754	+	4447.41i	0.128511	+	0.784272i
$319$			1283.63i			0.225297i
$320$	−1313.81	+	1935.73i	−0.229513	+	0.338159i
$321$	−3375.58			−0.586936
$322$	−2296.19	+	376.254i	−0.397396	+	0.0651174i
$323$	1604.82			0.276454
$324$	−614.112	+	206.810i	−0.105300	+	0.0354612i
$325$	−378.900	+	4865.67i	−0.0646694	+	0.830458i
$326$	168.631	+	1029.11i	0.0286491	+	0.174839i
$327$			2364.32i			0.399839i
$328$	−5607.63	+	2971.27i	−0.943993	+	0.500185i
$329$	7346.46			1.23107
$330$	345.425	−	56.6014i	0.0576213	−	0.00944182i
$331$	10016.3			1.66327			0.831637	−	0.555319i	$-0.187404\pi$
$331$	10016.3			1.66327			0.831637	+	0.555319i	$0.187404\pi$
$332$	1869.68	−	629.638i	0.309072	−	0.104084i
$333$	2171.70			0.357382
$334$	−1123.21	+	184.050i	−0.184010	+	0.0301519i
$335$	1131.36			0.184515
$336$	−3516.43	+	2671.35i	−0.570943	+	0.433733i
$337$	−6602.82			−1.06730			−0.533648	−	0.845707i	$-0.679179\pi$
$337$	−6602.82			−1.06730			−0.533648	+	0.845707i	$0.679179\pi$
$338$	43.4135	+	6213.90i	0.00698634	+	0.999976i
$339$			3546.99i			0.568277i
$340$	2058.62	−	693.267i	0.328366	−	0.110581i
$341$		−	2743.06i		−	0.435616i
$342$	−111.165	−	678.415i	−0.0175764	−	0.107265i
$343$		−	3610.83i		−	0.568415i
$344$	3964.21	−	2100.48i	0.621325	−	0.329216i
$345$		−	490.292i		−	0.0765115i
$346$	−9884.39	+	1619.66i	−1.53580	+	0.251657i
$347$		−	8226.15i		−	1.27263i	−0.771429	−	0.636315i	$-0.780458\pi$
$347$		−	8226.15i		−	1.27263i	0.771429	−	0.636315i	$-0.219542\pi$
$348$	3233.95	−	1089.07i	0.498155	−	0.167760i
$349$	5987.66			0.918373			0.459187	−	0.888340i	$-0.348141\pi$
$349$	5987.66			0.918373			0.459187	+	0.888340i	$0.348141\pi$
$350$	6684.42	−	1095.31i	1.02085	−	0.167276i
$351$	1261.73	+	98.2533i	0.191869	+	0.0149412i
$352$	1186.01	+	1124.34i	0.179586	+	0.170249i
$353$		−	8372.28i		−	1.26236i	−0.775638	−	0.631178i	$-0.782572\pi$
$353$		−	8372.28i		−	1.26236i	0.775638	−	0.631178i	$-0.217428\pi$
$354$	−3166.18	+	518.811i	−0.475369	+	0.0778941i
$355$			832.323i			0.124437i
$356$	908.693	+	2698.32i	0.135283	+	0.401716i
$357$	4100.32			0.607877
$358$	−10482.6	+	1717.68i	−1.54755	+	0.253582i
$359$		−	5365.50i		−	0.788803i	−0.918938	−	0.394401i	$-0.870952\pi$
$359$		−	5365.50i		−	0.788803i	0.918938	−	0.394401i	$-0.129048\pi$
$360$	−435.668	−	822.231i	−0.0637826	−	0.120376i
$361$	−6129.67			−0.893668
$362$	−3199.29	+	524.237i	−0.464506	+	0.0761140i
$363$			3748.49i			0.541996i
$364$	8362.55	−	2109.66i	1.20417	−	0.303781i
$365$		−	3728.02i		−	0.534613i
$366$	−1206.00	−	7359.95i	−0.172237	−	1.05112i
$367$	2032.50			0.289089			0.144545	−	0.989498i	$-0.453828\pi$
$367$	2032.50			0.289089			0.144545	+	0.989498i	$0.453828\pi$
$368$	1822.78	−	1384.73i	0.258203	−	0.196152i
$369$		−	2524.18i		−	0.356107i
$370$	504.279	+	3077.50i	0.0708546	+	0.432409i
$371$	−12215.9			−1.70949
$372$	−6910.78	+	2327.29i	−0.963192	+	0.324367i
$373$			13867.4i			1.92500i	0.271282	+	0.962500i	$0.412552\pi$
$373$			13867.4i			1.92500i	−0.271282	+	0.962500i	$0.587448\pi$
$374$	−245.370	−	1497.44i	−0.0339246	−	0.207034i
$375$			3140.77i			0.432503i
$376$	−6386.30	+	3383.85i	−0.875926	+	0.464119i
$377$	−6644.34	−	517.408i	−0.907694	−	0.0706840i
$378$	−284.027	−	1733.35i	−0.0386476	−	0.235857i
$379$	−4445.76			−0.602542			−0.301271	−	0.953539i	$-0.597411\pi$
$379$	−4445.76			−0.602542			−0.301271	+	0.953539i	$0.597411\pi$
$380$	935.564	−	315.063i	0.126298	−	0.0425325i
$381$		−	3116.61i		−	0.419078i
$382$	−997.724	−	6088.87i	−0.133633	−	0.815534i
$383$			1882.41i			0.251141i	0.992085	+	0.125570i	$0.0400761\pi$
$383$			1882.41i			0.251141i	−0.992085	+	0.125570i	$0.959924\pi$
$384$	1826.39	−	3941.91i	0.242714	−	0.523854i
$385$			948.795i			0.125598i
$386$	−12389.0	+	2030.06i	−1.63363	+	0.267687i
$387$			1784.42i			0.234385i
$388$	1293.73	+	3841.68i	0.169277	+	0.502659i
$389$		−	4490.10i		−	0.585237i	−0.956229	−	0.292619i	$-0.905473\pi$
$389$		−	4490.10i		−	0.585237i	0.956229	−	0.292619i	$-0.0945266\pi$
$390$	153.745	+	1810.80i	0.0199621	+	0.235111i
$391$	−2125.45			−0.274907
$392$	−1970.60	−	3719.08i	−0.253903	−	0.479189i
$393$	−427.693			−0.0548964
$394$	−1732.73	−	10574.4i	−0.221557	−	1.35211i
$395$	−3735.23			−0.475796
$396$	−616.023	+	207.453i	−0.0781725	+	0.0263256i
$397$	−9505.67			−1.20170			−0.600852	−	0.799361i	$-0.705172\pi$
$397$	−9505.67			−1.20170			−0.600852	+	0.799361i	$0.705172\pi$
$398$	−702.445	−	4286.86i	−0.0884683	−	0.539902i
$399$	1863.44			0.233806
$400$	−5306.27	+	4031.06i	−0.663284	+	0.503883i
$401$			9181.79i			1.14343i	0.820451	+	0.571716i	$0.193722\pi$
$401$			9181.79i			1.14343i	−0.820451	+	0.571716i	$0.806278\pi$
$402$	−2073.31	+	339.732i	−0.257232	+	0.0421500i
$403$	14198.6	+	1105.67i	1.75504	+	0.136669i
$404$	2239.33	+	6649.59i	0.275770	+	0.818885i
$405$	370.113			0.0454100
$406$	1495.70	+	9127.93i	0.182834	+	1.11579i
$407$	2178.46			0.265312
$408$	−3564.42	+	1888.65i	−0.432513	+	0.229172i
$409$			3469.65i			0.419470i	0.977758	+	0.209735i	$0.0672601\pi$
$409$			3469.65i			0.419470i	−0.977758	+	0.209735i	$0.932740\pi$
$410$	3576.99	−	586.126i	0.430866	−	0.0706017i
$411$	−7239.07			−0.868800
$412$	8926.78	−	3006.20i	1.06745	−	0.359478i
$413$		−	8696.71i		−	1.03617i
$414$	147.229	+	898.501i	0.0174780	+	0.106664i
$415$	−1126.82			−0.133285
$416$	−6297.85	+	5685.80i	−0.742254	+	0.670118i
$417$	−2481.02			−0.291358
$418$	−111.511	−	680.526i	−0.0130483	−	0.0796307i
$419$		−	12868.1i		−	1.50035i	−0.661241	−	0.750174i	$-0.729970\pi$
$419$		−	12868.1i		−	1.50035i	0.661241	−	0.750174i	$-0.270030\pi$
$420$	2390.37	−	804.985i	0.277709	−	0.0935220i
$421$	−4414.39			−0.511031			−0.255516	−	0.966805i	$-0.582245\pi$
$421$	−4414.39			−0.511031			−0.255516	+	0.966805i	$0.582245\pi$
$422$	14422.0	−	2363.19i	1.66363	−	0.272603i
$423$		−	2874.68i		−	0.330429i
$424$	10619.3	−	5626.77i	1.21632	−	0.644482i
$425$	6187.37			0.706192
$426$	−249.936	−	1525.30i	−0.0284259	−	0.173477i
$427$	20215.9			2.29114
$428$	2872.85	+	8530.79i	0.324450	+	0.963438i
$429$	1265.65	+	98.5591i	0.142439	+	0.0110920i
$430$	−2528.69	+	414.351i	−0.283591	+	0.0464692i
$431$		−	11981.4i		−	1.33903i	−0.742797	−	0.669517i	$-0.766501\pi$
$431$		−	11981.4i		−	1.33903i	0.742797	−	0.669517i	$-0.233499\pi$
$432$	1045.30	+	1375.98i	0.116417	+	0.153245i
$433$	4268.40			0.473733			0.236866	−	0.971542i	$-0.423880\pi$
$433$	4268.40			0.473733			0.236866	+	0.971542i	$0.423880\pi$
$434$	−3196.24	−	19505.9i	−0.353513	−	2.15740i
$435$	−1949.04			−0.214826
$436$	5975.14	−	2012.20i	0.656325	−	0.221025i
$437$	−965.932			−0.105736
$438$	1119.48	+	6831.91i	0.122125	+	0.745300i
$439$	7424.25			0.807152			0.403576	−	0.914946i	$-0.367767\pi$
$439$	7424.25			0.807152			0.403576	+	0.914946i	$0.367767\pi$
$440$	−437.024	−	824.790i	−0.0473507	−	0.0893643i
$441$	1674.08			0.180767
$442$	7849.93	−	666.496i	0.844758	−	0.0717239i
$443$			3110.29i			0.333576i	0.985993	+	0.166788i	$0.0533395\pi$
$443$			3110.29i			0.333576i	−0.985993	+	0.166788i	$0.946660\pi$
$444$	−1848.27	−	5488.34i	−0.197556	−	0.586633i
$445$		−	1626.22i		−	0.173237i
$446$	13432.6	−	2201.06i	1.42612	−	0.233684i
$447$		−	9455.91i		−	1.00056i
$448$	9743.79	+	6613.24i	1.02757	+	0.697425i
$449$		−	5412.37i		−	0.568876i	−0.958694	−	0.284438i	$-0.908193\pi$
$449$		−	5412.37i		−	0.568876i	0.958694	−	0.284438i	$-0.0918071\pi$
$450$	−428.596	−	2615.62i	−0.0448982	−	0.274003i
$451$		−	2532.03i		−	0.264365i
$452$	8963.98	−	3018.73i	0.932810	−	0.314135i
$453$	−2803.02			−0.290723
$454$	267.535	+	1632.70i	0.0276565	+	0.168781i
$455$	−4911.14	−	382.441i	−0.506018	−	0.0394046i
$456$	−1619.89	+	858.316i	−0.166356	+	0.0881455i
$457$			3771.11i			0.386007i	0.981198	+	0.193003i	$0.0618228\pi$
$457$			3771.11i			0.386007i	−0.981198	+	0.193003i	$0.938177\pi$
$458$	2096.70	+	12795.7i	0.213913	+	1.30546i
$459$		−	1604.46i		−	0.163159i
$460$	−1239.07	+	417.273i	−0.125591	+	0.0422944i
$461$	1276.30			0.128944			0.0644722	−	0.997920i	$-0.479464\pi$
$461$	1276.30			0.128944			0.0644722	+	0.997920i	$0.479464\pi$
$462$	−284.911	−	1738.75i	−0.0286910	−	0.175095i
$463$		−	10359.5i		−	1.03984i	−0.854216	−	0.519919i	$-0.825962\pi$
$463$		−	10359.5i		−	1.03984i	0.854216	−	0.519919i	$-0.174038\pi$
$464$	−5504.63	−	7246.00i	−0.550746	−	0.724972i
$465$	4164.99			0.415369
$466$	−1967.66	−	12008.2i	−0.195602	−	1.19371i
$467$			18643.9i			1.84740i	0.383112	+	0.923702i	$0.374852\pi$
$467$			18643.9i			1.84740i	−0.383112	+	0.923702i	$0.625148\pi$
$468$	−825.512	−	3272.27i	−0.0815369	−	0.323207i
$469$		−	5694.85i		−	0.560690i
$470$	4073.68	−	667.514i	0.399798	−	0.0655109i
$471$	−921.643			−0.0901636
$472$	4005.79	+	7560.07i	0.390638	+	0.737247i
$473$			1789.97i			0.174002i
$474$	6845.11	−	1121.64i	0.663304	−	0.108689i
$475$	2811.92			0.271620
$476$	−3489.66	−	10362.4i	−0.336026	−	0.997813i
$477$			4780.10i			0.458838i
$478$	19908.0	−	3262.13i	1.90496	−	0.312147i
$479$		−	4124.15i		−	0.393397i	−0.980464	−	0.196699i	$-0.936978\pi$
$479$		−	4124.15i		−	0.393397i	0.980464	−	0.196699i	$-0.0630221\pi$
$480$	−1707.17	+	1800.80i	−0.162336	+	0.171239i
$481$	−878.093	+	11276.1i	−0.0832383	+	1.06891i
$482$	2269.77	−	371.925i	0.214492	−	0.0351467i
$483$	−2467.96			−0.232497
$484$	9473.21	−	3190.22i	0.889670	−	0.299607i
$485$		−	2315.30i		−	0.216768i
$486$	−678.262	+	111.140i	−0.0633058	+	0.0103733i
$487$			3948.63i			0.367412i	0.982981	+	0.183706i	$0.0588095\pi$
$487$			3948.63i			0.367412i	−0.982981	+	0.183706i	$0.941191\pi$
$488$	−17573.7	+	9311.65i	−1.63018	+	0.863767i
$489$			1106.10i			0.102289i
$490$	388.729	+	2372.32i	0.0358388	+	0.218716i
$491$		−	9699.68i		−	0.891528i	−0.895150	−	0.445764i	$-0.852932\pi$
$491$		−	9699.68i		−	0.891528i	0.895150	−	0.445764i	$-0.147068\pi$
$492$	−6379.12	+	2148.25i	−0.584539	+	0.196851i
$493$			8449.19i			0.771871i
$494$	3567.48	−	302.896i	0.324916	−	0.0275869i
$495$	371.265			0.0337113
$496$	11763.1	+	15484.3i	1.06488	+	1.40175i
$497$	4189.62			0.378129
$498$	2064.99	−	338.369i	0.185812	−	0.0304472i
$499$	10351.2			0.928620			0.464310	−	0.885673i	$-0.346302\pi$
$499$	10351.2			0.928620			0.464310	+	0.885673i	$0.346302\pi$
$500$	7937.39	−	2673.01i	0.709942	−	0.239082i
$501$	−1207.23			−0.107655
$502$	−274.481	+	44.9765i	−0.0244038	+	0.00399881i
$503$	−14291.2			−1.26682			−0.633412	−	0.773815i	$-0.718346\pi$
$503$	−14291.2			−1.26682			−0.633412	+	0.773815i	$0.718346\pi$
$504$	−4138.82	+	2193.00i	−0.365789	+	0.193817i
$505$		−	4007.57i		−	0.353138i
$506$	147.687	+	901.297i	0.0129752	+	0.0791849i
$507$	−1020.32	+	6511.55i	−0.0893769	+	0.570390i
$508$	−7876.32	+	2652.45i	−0.687904	+	0.231660i
$509$	6030.07			0.525104			0.262552	−	0.964918i	$-0.415436\pi$
$509$	6030.07			0.525104			0.262552	+	0.964918i	$0.415436\pi$
$510$	2273.67	−	372.564i	0.197411	−	0.0323478i
$511$	−18765.5			−1.62454
$512$	−11516.4	−	1260.82i	−0.994060	−	0.108830i
$513$		−	729.164i		−	0.0627551i
$514$	−1074.02	−	6554.51i	−0.0921655	−	0.562465i
$515$	−5379.99			−0.460331
$516$	4509.60	−	1518.66i	0.384737	−	0.129565i
$517$		−	2883.62i		−	0.245303i
$518$	15491.0	−	2538.36i	1.31397	−	0.215307i
$519$	−10623.8			−0.898522
$520$	4445.43	−	1929.66i	0.374894	−	0.162733i
$521$	−2617.24			−0.220083			−0.110042	−	0.993927i	$-0.535098\pi$
$521$	−2617.24			−0.220083			−0.110042	+	0.993927i	$0.535098\pi$
$522$	3571.77	−	585.271i	0.299487	−	0.0490739i
$523$		−	21188.4i		−	1.77152i	−0.464144	−	0.885760i	$-0.653638\pi$
$523$		−	21188.4i		−	1.77152i	0.464144	−	0.885760i	$-0.346362\pi$
$524$	363.997	+	1080.87i	0.0303459	+	0.0901108i
$525$	7184.45			0.597248
$526$	1670.82	+	10196.6i	0.138500	+	0.845235i
$527$		−	18055.5i		−	1.49243i
$528$	1048.56	+	1380.26i	0.0864253	+	0.113766i
$529$	−10887.7			−0.894856
$530$	−6773.85	+	1109.96i	−0.555164	+	0.0909693i
$531$	−3403.03			−0.278115
$532$	−1585.91	−	4709.29i	−0.129244	−	0.383785i
$533$	13106.3	+	1020.61i	1.06510	+	0.0829411i
$534$	488.334	+	2980.19i	0.0395736	+	0.241508i
$535$		−	5141.33i		−	0.415475i
$536$	2623.10	+	4950.54i	0.211382	+	0.398938i
$537$	−11266.8			−0.905396
$538$	−1384.95	+	226.938i	−0.110984	+	0.0181858i
$539$	1679.29			0.134197
$540$	−314.992	−	935.353i	−0.0251020	−	0.0745392i
$541$	−5104.29			−0.405639			−0.202819	−	0.979216i	$-0.565010\pi$
$541$	−5104.29			−0.405639			−0.202819	+	0.979216i	$0.565010\pi$
$542$	3250.92	−	532.695i	0.257636	−	0.0422163i
$543$	−3438.62			−0.271759
$544$	7806.58	+	7400.67i	0.615265	+	0.583274i
$545$	−3601.10			−0.283035
$546$	9114.92	−	773.900i	0.714437	−	0.0606591i
$547$		−	10142.1i		−	0.792770i	−0.918084	−	0.396385i	$-0.870265\pi$
$547$		−	10142.1i		−	0.792770i	0.918084	−	0.396385i	$-0.129735\pi$
$548$	6160.95	+	18294.6i	0.480260	+	1.42611i
$549$		−	7910.51i		−	0.614959i
$550$	−429.929	−	2623.76i	−0.0333314	−	0.203414i
$551$			3839.82i			0.296882i
$552$	2145.40	−	1136.76i	0.165424	−	0.0876520i
$553$			18801.8i			1.44581i
$554$	−9886.34	+	1619.98i	−0.758178	+	0.124235i
$555$			3307.71i			0.252981i
$556$	2111.52	+	6270.07i	0.161058	+	0.478255i
$557$	1339.31			0.101882			0.0509409	−	0.998702i	$-0.483778\pi$
$557$	1339.31			0.101882			0.0509409	+	0.998702i	$0.483778\pi$
$558$	−7632.68	+	1250.69i	−0.579063	+	0.0948854i
$559$	−9265.24	−	721.503i	−0.701034	−	0.0545909i
$560$	−4068.73	−	5355.86i	−0.307027	−	0.404154i
$561$		−	1609.45i		−	0.121125i
$562$	−2796.57	+	458.245i	−0.209904	+	0.0343949i
$563$			7894.26i			0.590947i	0.955351	+	0.295474i	$0.0954775\pi$
$563$			7894.26i			0.590947i	−0.955351	+	0.295474i	$0.904523\pi$
$564$	−7264.92	+	2446.55i	−0.542390	+	0.182657i
$565$	−5402.41			−0.402267
$566$	−12480.8	+	2045.10i	−0.926865	+	0.151876i
$567$		−	1863.02i		−	0.137988i
$568$	−3642.04	+	1929.78i	−0.269044	+	0.142556i
$569$	−5150.43			−0.379468			−0.189734	−	0.981836i	$-0.560763\pi$
$569$	−5150.43			−0.379468			−0.189734	+	0.981836i	$0.560763\pi$
$570$	1033.29	−	169.315i	0.0759296	−	0.0124418i
$571$			9653.04i			0.707473i	0.935345	+	0.353737i	$0.115089\pi$
$571$			9653.04i			0.707473i	−0.935345	+	0.353737i	$0.884911\pi$
$572$	−828.080	−	3282.46i	−0.0605311	−	0.239941i
$573$		−	6544.35i		−	0.477128i
$574$	−2950.35	−	18005.3i	−0.214539	−	1.30928i
$575$	−3724.14			−0.270099
$576$	2587.77	−	3812.76i	0.187194	−	0.275807i
$577$		−	6097.68i		−	0.439948i	−0.975506	−	0.219974i	$-0.929403\pi$
$577$		−	6097.68i		−	0.439948i	0.975506	−	0.219974i	$-0.0705972\pi$
$578$	631.958	+	3856.69i	0.0454775	+	0.277539i
$579$	−13315.7			−0.955756
$580$	1658.76	+	4925.62i	0.118752	+	0.352630i
$581$			5672.00i			0.405016i
$582$	695.256	+	4242.98i	0.0495177	+	0.302195i
$583$			4794.98i			0.340631i
$584$	16312.9	−	8643.59i	1.15588	−	0.612456i
$585$	−149.649	+	1921.74i	−0.0105765	+	0.135819i
$586$	−1506.10	−	9191.41i	−0.106172	−	0.647941i
$587$	−18721.5			−1.31639			−0.658195	−	0.752847i	$-0.728680\pi$
$587$	−18721.5			−1.31639			−0.658195	+	0.752847i	$0.728680\pi$
$588$	−1424.76	−	4230.75i	−0.0999251	−	0.296723i
$589$		−	8205.50i		−	0.574027i
$590$	−790.200	−	4822.41i	−0.0551390	−	0.336501i
$591$		−	11365.5i		−	0.791053i
$592$	−12297.2	+	9341.91i	−0.853735	+	0.648565i
$593$			27503.7i			1.90462i	0.305127	+	0.952312i	$0.401301\pi$
$593$			27503.7i			1.90462i	−0.305127	+	0.952312i	$0.598699\pi$
$594$	−680.373	+	111.486i	−0.0469967	+	0.00770088i
$595$			6245.19i			0.430299i
$596$	−23897.1	+	8047.64i	−1.64239	+	0.553094i
$597$		−	4607.54i		−	0.315869i
$598$	−4724.82	+	401.159i	−0.323097	+	0.0274325i
$599$	6924.86			0.472357			0.236179	−	0.971710i	$-0.424105\pi$
$599$	6924.86			0.472357			0.236179	+	0.971710i	$0.424105\pi$
$600$	−6245.46	+	3309.22i	−0.424950	+	0.225164i
$601$	−438.105			−0.0297349			−0.0148674	−	0.999889i	$-0.504733\pi$
$601$	−438.105			−0.0297349			−0.0148674	+	0.999889i	$0.504733\pi$
$602$	2085.69	+	12728.5i	0.141207	+	0.861752i
$603$	−2228.40			−0.150493
$604$	2385.57	+	7083.83i	0.160708	+	0.477214i
$605$	−5709.31			−0.383664
$606$	1203.42	+	7344.21i	0.0806695	+	0.492307i
$607$	−130.867			−0.00875076			−0.00437538	−	0.999990i	$-0.501393\pi$
$607$	−130.867			−0.00875076			−0.00437538	+	0.999990i	$0.501393\pi$
$608$	3547.78	+	3363.31i	0.236647	+	0.224343i
$609$			9810.75i			0.652794i
$610$	11209.9	−	1836.86i	0.744060	−	0.121922i
$611$	14926.2	+	1162.33i	0.988296	+	0.0769606i
$612$	−4054.81	+	1365.51i	−0.267820	+	0.0901918i
$613$	−14591.0			−0.961382			−0.480691	−	0.876890i	$-0.659614\pi$
$613$	−14591.0			−0.961382			−0.480691	+	0.876890i	$0.659614\pi$
$614$	−1497.50	−	9138.89i	−0.0984270	−	0.600677i
$615$	3844.57			0.252078
$616$	−4151.70	+	2199.82i	−0.271553	+	0.143885i
$617$			26154.6i			1.70656i	0.521457	+	0.853278i	$0.325389\pi$
$617$			26154.6i			1.70656i	−0.521457	+	0.853278i	$0.674611\pi$
$618$	9859.27	−	1615.54i	0.641745	−	0.105156i
$619$	−5541.38			−0.359817			−0.179909	−	0.983683i	$-0.557580\pi$
$619$	−5541.38			−0.359817			−0.179909	+	0.983683i	$0.557580\pi$
$620$	−3544.69	−	10525.8i	−0.229610	−	0.681817i
$621$			965.714i			0.0624038i
$622$	−1459.61	−	8907.64i	−0.0940915	−	0.574218i
$623$	−8185.83			−0.526418
$624$	−7567.16	+	4871.17i	−0.485463	+	0.312505i
$625$	8231.49			0.526815
$626$	−2529.19	−	15435.1i	−0.161481	−	0.985479i
$627$		−	731.433i		−	0.0465879i
$628$	784.382	+	2329.19i	0.0498412	+	0.148001i
$629$	14339.1			0.908963
$630$	2640.06	−	432.601i	0.166957	−	0.0273575i
$631$			3022.53i			0.190689i	0.995444	+	0.0953447i	$0.0303953\pi$
$631$			3022.53i			0.190689i	−0.995444	+	0.0953447i	$0.969605\pi$
$632$	−8660.28	−	16344.4i	−0.545075	−	1.02871i
$633$	15500.9			0.973308
$634$	2961.72	+	18074.7i	0.185528	+	1.13224i
$635$	4746.90			0.296653
$636$	12080.3	−	4068.20i	0.753170	−	0.253639i
$637$	−676.888	+	8692.32i	−0.0421025	+	0.540663i
$638$	3582.88	−	587.092i	0.222332	−	0.0364313i
$639$		−	1639.40i		−	0.101493i
$640$	6003.92	+	2781.76i	0.370822	+	0.171811i
$641$	−24068.8			−1.48309			−0.741545	−	0.670904i	$-0.765906\pi$
$641$	−24068.8			−1.48309			−0.741545	+	0.670904i	$0.765906\pi$
$642$	1543.88	+	9421.92i	0.0949096	+	0.579211i
$643$	−10923.5			−0.669952			−0.334976	−	0.942227i	$-0.608728\pi$
$643$	−10923.5			−0.669952			−0.334976	+	0.942227i	$0.608728\pi$
$644$	2100.40	+	6237.05i	0.128521	+	0.381637i
$645$	−2717.84			−0.165915
$646$	−733.992	−	4479.39i	−0.0447036	−	0.272816i
$647$	−6403.53			−0.389102			−0.194551	−	0.980892i	$-0.562325\pi$
$647$	−6403.53			−0.389102			−0.194551	+	0.980892i	$0.562325\pi$
$648$	858.123	+	1619.52i	0.0520220	+	0.0981804i
$649$	−3413.62			−0.206466
$650$	13754.4	−	1167.81i	0.829986	−	0.0704697i
$651$		−	20965.1i		−	1.26219i
$652$	2795.34	−	941.365i	0.167905	−	0.0565440i
$653$			3560.37i			0.213366i	0.994293	+	0.106683i	$0.0340230\pi$
$653$			3560.37i			0.213366i	−0.994293	+	0.106683i	$0.965977\pi$
$654$	6599.31	−	1081.36i	0.394577	−	0.0646554i
$655$		−	651.419i		−	0.0388596i
$656$	10858.2	+	14293.1i	0.646249	+	0.850688i
$657$			7342.98i			0.436038i
$658$	−3360.03	−	20505.5i	−0.199069	−	1.21487i
$659$			18983.0i			1.12212i	0.827776	+	0.561058i	$0.189606\pi$
$659$			18983.0i			1.12212i	−0.827776	+	0.561058i	$0.810394\pi$
$660$	−315.972	−	938.264i	−0.0186351	−	0.0553362i
$661$	−6588.80			−0.387707			−0.193854	−	0.981030i	$-0.562099\pi$
$661$	−6588.80			−0.387707			−0.193854	+	0.981030i	$0.562099\pi$
$662$	−4581.11	−	27957.4i	−0.268957	−	1.64138i
$663$	8330.84	+	648.739i	0.487999	+	0.0380014i
$664$	−2612.58	−	4930.68i	−0.152692	−	0.288174i
$665$			2838.19i			0.165504i
$666$	−993.263	−	6061.65i	−0.0577900	−	0.352679i
$667$		−	5085.51i		−	0.295220i
$668$	1027.44	+	3050.94i	0.0595103	+	0.176713i
$669$	14437.4			0.834352
$670$	−517.445	−	3157.85i	−0.0298368	−	0.182087i
$671$		−	7935.13i		−	0.456531i
$672$	9064.59	+	8593.27i	0.520348	+	0.493292i
$673$	−11113.6			−0.636547			−0.318273	−	0.947999i	$-0.603103\pi$
$673$	−11113.6			−0.636547			−0.318273	+	0.947999i	$0.603103\pi$
$674$	3019.91	+	18429.8i	0.172586	+	1.05325i
$675$		−	2811.28i		−	0.160306i
$676$	17324.4	−	2963.21i	0.985686	−	0.168594i
$677$		−	7932.48i		−	0.450325i	−0.974321	−	0.225162i	$-0.927709\pi$
$677$		−	7932.48i		−	0.450325i	0.974321	−	0.225162i	$-0.0722913\pi$
$678$	9900.36	−	1622.27i	0.560798	−	0.0918924i
$679$	−11654.4			−0.658697
$680$	−2876.60	−	5428.96i	−0.162224	−	0.306163i
$681$			1754.84i			0.0987453i
$682$	−7656.44	+	1254.58i	−0.429883	+	0.0704406i
$683$	3650.03			0.204487			0.102244	−	0.994759i	$-0.467398\pi$
$683$	3650.03			0.204487			0.102244	+	0.994759i	$0.467398\pi$
$684$	−1842.75	+	620.569i	−0.103011	+	0.0346901i
$685$		−	11025.8i		−	0.614999i
$686$	−10078.6	+	1651.47i	−0.560934	+	0.0919148i
$687$			13752.8i			0.763761i
$688$	−7675.97	−	10104.2i	−0.425354	−	0.559913i
$689$	−24819.7	−	1932.76i	−1.37236	−	0.106868i
$690$	−1368.51	+	224.243i	−0.0755045	+	0.0123722i
$691$	7823.65			0.430717			0.215359	−	0.976535i	$-0.430908\pi$
$691$	7823.65			0.430717			0.215359	+	0.976535i	$0.430908\pi$
$692$	9041.58	+	26848.6i	0.496690	+	1.47490i
$693$		−	1868.81i		−	0.102439i
$694$	−22960.9	+	3762.37i	−1.25588	+	0.205789i
$695$		−	3778.84i		−	0.206244i
$696$	−4518.93	−	8528.51i	−0.246105	−	0.464472i
$697$		−	16666.4i		−	0.905719i
$698$	−2738.56	−	16712.8i	−0.148504	−	0.906287i
$699$		−	12906.5i		−	0.698380i
$700$	−6114.46	−	18156.6i	−0.330150	−	0.980365i
$701$			30382.7i			1.63700i	0.574507	+	0.818500i	$0.305194\pi$
$701$			30382.7i			1.63700i	−0.574507	+	0.818500i	$0.694806\pi$
$702$	−302.828	−	3566.68i	−0.0162813	−	0.191760i
$703$	6516.56			0.349611
$704$	2595.82	−	3824.62i	0.138968	−	0.204753i
$705$	4378.42			0.233902
$706$	−23368.7	+	3829.20i	−1.24574	+	0.204127i
$707$	−20172.7			−1.07309
$708$	2896.21	+	8600.18i	0.153738	+	0.456518i
$709$	−19960.9			−1.05733			−0.528665	−	0.848830i	$-0.677307\pi$
$709$	−19960.9			−1.05733			−0.528665	+	0.848830i	$0.677307\pi$
$710$	2323.18	−	380.677i	0.122799	−	0.0201219i
$711$	7357.16			0.388066
$712$	7115.96	−	3770.47i	0.374553	−	0.198461i
$713$			10867.5i			0.570813i
$714$	−1875.35	−	11444.8i	−0.0982959	−	0.599877i
$715$	−150.115	+	1927.72i	−0.00785173	+	0.100829i
$716$	9588.81	+	28473.5i	0.500490	+	1.48618i
$717$	21397.3			1.11450
$718$	−14976.2	+	2454.00i	−0.778422	+	0.127552i
$719$	10658.4			0.552838			0.276419	−	0.961037i	$-0.410852\pi$
$719$	10658.4			0.552838			0.276419	+	0.961037i	$0.410852\pi$
$720$	−2095.75	+	1592.10i	−0.108478	+	0.0824084i
$721$			27080.9i			1.39882i
$722$	2803.51	+	17109.2i	0.144509	+	0.881907i
$723$	2439.56			0.125489
$724$	2926.50	+	8690.11i	0.150225	+	0.446085i
$725$			14804.4i			0.758373i
$726$	10462.8	−	1714.43i	0.534863	−	0.0876427i
$727$	20458.2			1.04368			0.521838	−	0.853045i	$-0.325247\pi$
$727$	20458.2			1.04368			0.521838	+	0.853045i	$0.325247\pi$
$728$	−9713.24	−	22376.7i	−0.494501	−	1.13920i
$729$	−729.000			−0.0370370
$730$	−10405.7	+	1705.07i	−0.527577	+	0.0864488i
$731$			11782.0i			0.596134i
$732$	−19991.5	+	6732.39i	−1.00944	+	0.339940i
$733$	−31681.2			−1.59642			−0.798208	−	0.602382i	$-0.794218\pi$
$733$	−31681.2			−1.59642			−0.798208	+	0.602382i	$0.794218\pi$
$734$	−929.598	−	5673.12i	−0.0467467	−	0.285284i
$735$			2549.79i			0.127960i
$736$	−4698.73	−	4454.41i	−0.235323	−	0.223087i
$737$	−2235.33			−0.111723
$738$	−7045.49	+	1154.47i	−0.351420	+	0.0575837i
$739$	33577.7			1.67142			0.835709	−	0.549173i	$-0.185057\pi$
$739$	33577.7			1.67142			0.835709	+	0.549173i	$0.185057\pi$
$740$	8359.28	−	2815.09i	0.415261	−	0.139844i
$741$	3786.04	+	294.826i	0.187697	+	0.0146164i
$742$	5587.16	+	34097.1i	0.276430	+	1.68699i
$743$			19963.9i			0.985740i	0.870103	+	0.492870i	$0.164052\pi$
$743$			19963.9i			0.985740i	−0.870103	+	0.492870i	$0.835948\pi$
$744$	9656.70	+	18225.0i	0.475849	+	0.898064i
$745$	14402.3			0.708267
$746$	38706.6	−	6342.47i	1.89967	−	0.311279i
$747$	2219.46			0.108709
$748$	−4067.43	+	1369.76i	−0.198823	+	0.0669562i
$749$	−25879.6			−1.26251
$750$	8766.53	−	1436.48i	0.426811	−	0.0699373i
$751$	34167.4			1.66017			0.830083	−	0.557640i	$-0.188293\pi$
$751$	34167.4			1.66017			0.830083	+	0.557640i	$0.188293\pi$
$752$	12365.9	+	16277.8i	0.599651	+	0.789348i
$753$	−295.014			−0.0142774
$754$	1594.71	+	18782.3i	0.0770237	+	0.907179i
$755$		−	4269.28i		−	0.205795i
$756$	−4708.23	+	1585.55i	−0.226504	+	0.0762779i
$757$		−	35511.1i		−	1.70498i	−0.522741	−	0.852492i	$-0.675090\pi$
$757$		−	35511.1i		−	1.70498i	0.522741	−	0.852492i	$-0.324910\pi$
$758$	2033.34	+	12409.0i	0.0974332	+	0.594612i
$759$			968.719i			0.0463271i
$760$	−1307.30	−	2467.25i	−0.0623957	−	0.117759i
$761$		−	29278.7i		−	1.39468i	−0.716741	−	0.697340i	$-0.754367\pi$
$761$		−	29278.7i		−	1.39468i	0.716741	−	0.697340i	$-0.245633\pi$
$762$	−8699.08	+	1425.43i	−0.413562	+	0.0677663i
$763$			18126.6i			0.860063i
$764$	−16539.0	+	5569.70i	−0.783192	+	0.263749i
$765$	2443.75			0.115495
$766$	5254.20	−	860.954i	0.247835	−	0.0406103i
$767$	1375.96	−	17669.6i	0.0647760	−	0.831826i
$768$	−11838.0	−	3294.91i	−0.556208	−	0.154811i
$769$		−	26102.0i		−	1.22401i	−0.790855	−	0.612003i	$-0.790364\pi$
$769$		−	26102.0i		−	1.22401i	0.790855	−	0.612003i	$-0.209636\pi$
$770$	2648.28	−	433.947i	0.123945	−	0.0203096i
$771$		−	7044.82i		−	0.329070i
$772$	11332.6	+	33651.6i	0.528328	+	1.56885i
$773$	29899.4			1.39121			0.695605	−	0.718424i	$-0.255136\pi$
$773$	29899.4			1.39121			0.695605	+	0.718424i	$0.255136\pi$
$774$	4980.68	−	816.134i	0.231301	−	0.0379009i
$775$		−	31636.2i		−	1.46633i
$776$	10131.2	−	5368.13i	0.468671	−	0.248331i
$777$	16649.8			0.768738
$778$	−12532.8	+	2053.62i	−0.577535	+	0.0946350i
$779$		−	7574.23i		−	0.348363i
$780$	4983.99	−	1257.33i	0.228789	−	0.0577177i
$781$		−	1644.50i		−	0.0753457i
$782$	972.109	+	5932.55i	0.0444534	+	0.271289i
$783$	3838.96			0.175215
$784$	−9479.43	+	7201.32i	−0.431825	+	0.328049i
$785$		−	1403.75i		−	0.0638243i
$786$	195.613	+	1193.78i	0.00887694	+	0.0541739i
$787$	−12011.5			−0.544047			−0.272024	−	0.962291i	$-0.587693\pi$
$787$	−12011.5			−0.544047			−0.272024	+	0.962291i	$0.587693\pi$
$788$	−28722.9	+	9672.79i	−1.29849	+	0.437283i
$789$			10959.4i			0.494505i
$790$	1708.37	+	10425.8i	0.0769380	+	0.469535i
$791$			27193.8i			1.22238i
$792$	860.793	+	1624.56i	0.0386199	+	0.0728868i
$793$	41073.7	+	3198.49i	1.83931	+	0.143231i
$794$	4347.58	+	26532.3i	0.194320	+	1.18589i
$795$	−7280.57			−0.324799
$796$	−11644.2	+	3921.34i	−0.518491	+	0.174608i
$797$			41415.5i			1.84067i	0.391132	+	0.920335i	$0.372084\pi$
$797$			41415.5i			1.84067i	−0.391132	+	0.920335i	$0.627916\pi$
$798$	−852.273	−	5201.23i	−0.0378072	−	0.230729i
$799$		−	18980.7i		−	0.840411i
$800$	13678.4	+	12967.2i	0.604507	+	0.573075i
$801$			3203.12i			0.141294i
$802$	25628.2	−	4199.44i	1.12838	−	0.184897i
$803$			7365.83i			0.323704i
$804$	1896.52	+	5631.64i	0.0831905	+	0.247030i
$805$		−	3758.94i		−	0.164578i
$806$	−3407.81	−	40136.9i	−0.148927	−	1.75405i
$807$	−1488.55			−0.0649311
$808$	17536.2	−	9291.74i	0.763515	−	0.404557i
$809$	31305.7			1.36051			0.680254	−	0.732977i	$-0.261869\pi$
$809$	31305.7			1.36051			0.680254	+	0.732977i	$0.261869\pi$
$810$	−169.277	−	1033.06i	−0.00734296	−	0.0448124i
$811$	13622.4			0.589822			0.294911	−	0.955525i	$-0.404710\pi$
$811$	13622.4			0.589822			0.294911	+	0.955525i	$0.404710\pi$
$812$	24793.8	−	8349.63i	1.07154	−	0.360855i
$813$	3494.10			0.150730
$814$	−996.354	−	6080.51i	−0.0429019	−	0.261821i
$815$	−1684.69			−0.0724077
$816$	6901.85	+	9085.22i	0.296094	+	0.389763i
$817$			5354.46i			0.229289i
$818$	9684.49	−	1586.90i	0.413949	−	0.0678297i
$819$	9673.33	+	753.282i	0.412715	+	0.0321389i
$820$	−3271.99	−	9716.03i	−0.139345	−	0.413779i
$821$	21506.4			0.914226			0.457113	−	0.889409i	$-0.348883\pi$
$821$	21506.4			0.914226			0.457113	+	0.889409i	$0.348883\pi$
$822$	3310.91	+	20205.7i	0.140488	+	0.857366i
$823$	−23500.9			−0.995369			−0.497684	−	0.867358i	$-0.665816\pi$
$823$	−23500.9			−0.995369			−0.497684	+	0.867358i	$0.665816\pi$
$824$	−12473.7	−	23541.5i	−0.527358	−	0.995277i
$825$		−	2820.03i		−	0.119007i
$826$	−24274.3	+	3977.59i	−1.02253	+	0.167552i
$827$	−11952.1			−0.502559			−0.251279	−	0.967915i	$-0.580851\pi$
$827$	−11952.1			−0.502559			−0.251279	+	0.967915i	$0.580851\pi$
$828$	2440.56	−	821.889i	0.102434	−	0.0344959i
$829$		−	11126.3i		−	0.466144i	−0.972459	−	0.233072i	$-0.925122\pi$
$829$		−	11126.3i		−	0.466144i	0.972459	−	0.233072i	$-0.0748778\pi$
$830$	515.369	+	3145.18i	0.0215527	+	0.131531i
$831$	−10625.9			−0.443572
$832$	18750.7	+	14978.1i	0.781324	+	0.624125i
$833$	11053.5			0.459760
$834$	1134.74	+	6925.04i	0.0471136	+	0.287523i
$835$		−	1838.74i		−	0.0762061i
$836$	−1848.49	+	622.500i	−0.0764727	+	0.0257531i
$837$	−8203.65			−0.338781
$838$	−35917.3	+	5885.42i	−1.48060	+	0.242612i
$839$		−	13125.0i		−	0.540077i	−0.962850	−	0.270039i	$-0.912964\pi$
$839$		−	13125.0i		−	0.540077i	0.962850	−	0.270039i	$-0.0870364\pi$
$840$	−3340.15	−	6303.82i	−0.137198	−	0.258932i
$841$	4172.82			0.171094
$842$	2018.99	+	12321.5i	0.0826356	+	0.504306i
$843$	−3005.76			−0.122804
$844$	−13192.3	−	39173.9i	−0.538031	−	1.59766i
$845$	−9917.72	−	1554.05i	−0.403763	−	0.0632674i
$846$	−8023.81	+	1314.78i	−0.326081	+	0.0534316i
$847$			28738.6i			1.16585i
$848$	−20562.4	−	27067.2i	−0.832683	−	1.09610i
$849$	−13414.4			−0.542262
$850$	−2829.90	−	17270.2i	−0.114194	−	0.696898i
$851$	−8630.62			−0.347654
$852$	−4143.11	+	1395.24i	−0.166597	+	0.0561036i
$853$	−40716.0			−1.63434			−0.817169	−	0.576398i	$-0.804458\pi$
$853$	−40716.0			−1.63434			−0.817169	+	0.576398i	$0.804458\pi$
$854$	−9246.09	−	56426.7i	−0.370486	−	2.26099i
$855$	1110.59			0.0444226
$856$	22497.2	−	11920.4i	0.898294	−	0.475971i
$857$	34628.7			1.38027			0.690136	−	0.723680i	$-0.257551\pi$
$857$	34628.7			1.38027			0.690136	+	0.723680i	$0.257551\pi$
$858$	−303.770	−	3577.78i	−0.0120869	−	0.142358i
$859$		−	22608.8i		−	0.898024i	−0.893526	−	0.449012i	$-0.851776\pi$
$859$		−	22608.8i		−	0.898024i	0.893526	−	0.449012i	$-0.148224\pi$
$860$	2313.07	+	6868.57i	0.0917153	+	0.272344i
$861$		−	19352.2i		−	0.765994i
$862$	−33442.5	+	5479.89i	−1.32141	+	0.216526i
$863$			4002.67i			0.157882i	0.996879	+	0.0789412i	$0.0251539\pi$
$863$			4002.67i			0.157882i	−0.996879	+	0.0789412i	$0.974846\pi$
$864$	3362.56	−	3546.98i	0.132403	−	0.139665i
$865$		−	16181.1i		−	0.636038i
$866$	−1952.23	−	11914.0i	−0.0766043	−	0.467498i
$867$			4145.19i			0.162374i
$868$	−52983.1	+	17842.7i	−2.07185	+	0.697720i
$869$	7380.05			0.288091
$870$	891.424	+	5440.16i	0.0347381	+	0.211998i
$871$	901.020	−	11570.5i	0.0350515	−	0.450117i
$872$	−8349.30	−	15757.5i	−0.324247	−	0.611946i
$873$			4560.38i			0.176799i
$874$	441.785	+	2696.11i	0.0170979	+	0.104345i
$875$			24079.4i			0.930324i
$876$	18557.2	−	6249.38i	0.715743	−	0.241035i
$877$	39433.0			1.51831			0.759154	−	0.650911i	$-0.225613\pi$
$877$	39433.0			1.51831			0.759154	+	0.650911i	$0.225613\pi$
$878$	−3395.60	−	20722.6i	−0.130519	−	0.796530i
$879$		−	9878.97i		−	0.379078i
$880$	−2102.28	+	1597.05i	−0.0805315	+	0.0611781i
$881$	−31588.5			−1.20799			−0.603997	−	0.796987i	$-0.706426\pi$
$881$	−31588.5			−1.20799			−0.603997	+	0.796987i	$0.706426\pi$
$882$	−765.668	−	4672.69i	−0.0292306	−	0.178388i
$883$		−	21145.2i		−	0.805879i	−0.915227	−	0.402939i	$-0.867989\pi$
$883$		−	21145.2i		−	0.805879i	0.915227	−	0.402939i	$-0.132011\pi$
$884$	−5450.62	−	21605.9i	−0.207380	−	0.822042i
$885$		−	5183.15i		−	0.196870i
$886$	8681.44	−	1422.54i	0.329186	−	0.0539404i
$887$	47339.2			1.79199			0.895996	−	0.444063i	$-0.146463\pi$
$887$	47339.2			1.79199			0.895996	+	0.444063i	$0.146463\pi$
$888$	−14473.7	+	7669.07i	−0.546967	+	0.289817i
$889$		−	23894.2i		−	0.901445i
$890$	−4539.12	+	743.781i	−0.170957	+	0.0280130i
$891$	−731.269			−0.0274954
$892$	−12287.2	−	36486.3i	−0.461218	−	1.36957i
$893$		−	8625.98i		−	0.323244i
$894$	−26393.4	+	4324.82i	−0.987390	+	0.161794i
$895$		−	17160.4i		−	0.640904i
$896$	14002.4	−	30221.6i	0.522084	−	1.12682i
$897$	−5014.28	−	390.472i	−0.186646	−	0.0145345i
$898$	−15107.0	+	2475.44i	−0.561390	+	0.0919893i
$899$	43200.9			1.60270
$900$	−7104.70	+	2392.60i	−0.263137	+	0.0886146i
$901$			31561.7i			1.16701i
$902$	−7067.41	+	1158.07i	−0.260886	+	0.0427488i
$903$			13680.7i			0.504168i
$904$	−12525.7	−	23639.6i	−0.460840	−	0.869737i
$905$		−	5237.35i		−	0.192371i
$906$	1282.01	+	7823.81i	0.0470110	+	0.286897i
$907$			13454.8i			0.492568i	0.969198	+	0.246284i	$0.0792097\pi$
$907$			13454.8i			0.492568i	−0.969198	+	0.246284i	$0.920790\pi$
$908$	4434.84	−	1493.49i	0.162088	−	0.0545850i
$909$			7893.60i			0.288024i
$910$	1178.73	+	13882.9i	0.0429389	+	0.505730i
$911$	−2696.73			−0.0980753			−0.0490376	−	0.998797i	$-0.515615\pi$
$911$	−2696.73			−0.0980753			−0.0490376	+	0.998797i	$0.515615\pi$
$912$	3136.62	+	4128.87i	0.113886	+	0.149913i
$913$	2226.37			0.0807031
$914$	10525.9	−	1724.78i	0.380927	−	0.0624187i
$915$	12048.5			0.435312
$916$	34756.3	−	11704.6i	1.25369	−	0.422196i
$917$	−3279.01			−0.118083
$918$	−4478.38	+	733.827i	−0.161011	+	0.0263833i
$919$	−20653.8			−0.741355			−0.370678	−	0.928762i	$-0.620875\pi$
$919$	−20653.8			−0.741355			−0.370678	+	0.928762i	$0.620875\pi$
$920$	1731.40	+	3267.66i	0.0620464	+	0.117099i
$921$		−	9822.53i		−	0.351426i
$922$	−583.739	−	3562.42i	−0.0208508	−	0.127247i
$923$	8512.26	+	662.867i	0.303559	+	0.0236387i
$924$	−4722.88	+	1590.49i	−0.168151	+	0.0566269i
$925$	25124.5			0.893069
$926$	−28915.4	+	4738.07i	−1.02615	+	0.168145i
$927$	10596.8			0.375453
$928$	−17707.4	+	18678.6i	−0.626373	+	0.660728i
$929$		−	29376.6i		−	1.03748i	−0.854933	−	0.518738i	$-0.826402\pi$
$929$		−	29376.6i		−	1.03748i	0.854933	−	0.518738i	$-0.173598\pi$
$930$	−1904.93	−	11625.3i	−0.0671667	−	0.409903i
$931$	5023.37			0.176836
$932$	−32617.4	+	10984.3i	−1.14637	+	0.386055i
$933$		−	9573.98i		−	0.335946i
$934$	52039.0	−	8527.11i	1.82309	−	0.298732i
$935$	2451.36			0.0857411
$936$	−8756.02	+	3800.80i	−0.305769	+	0.132728i
$937$	26554.0			0.925808			0.462904	−	0.886408i	$-0.346807\pi$
$937$	26554.0			0.925808			0.462904	+	0.886408i	$0.346807\pi$
$938$	−15895.5	+	2604.63i	−0.553311	+	0.0906656i
$939$		−	16589.7i		−	0.576554i
$940$	−3726.33	−	11065.2i	−0.129297	−	0.383943i
$941$	2991.18			0.103623			0.0518117	−	0.998657i	$-0.483500\pi$
$941$	2991.18			0.103623			0.0518117	+	0.998657i	$0.483500\pi$
$942$	421.529	+	2572.49i	0.0145798	+	0.0889770i
$943$			10031.4i			0.346413i
$944$	19269.6	−	14638.7i	0.664376	−	0.504713i
$945$	2837.56			0.0976780
$946$	4996.18	−	818.674i	0.171712	−	0.0281368i
$947$	−26370.3			−0.904878			−0.452439	−	0.891795i	$-0.649446\pi$
$947$	−26370.3			−0.904878			−0.452439	+	0.891795i	$0.649446\pi$
$948$	−6261.45	−	18593.1i	−0.214517	−	0.637000i
$949$	−38126.9	−	2969.02i	−1.30417	−	0.101558i
$950$	−1286.08	−	7848.63i	−0.0439219	−	0.268045i
$951$			19426.8i			0.662415i
$952$	−27327.5	+	14479.8i	−0.930344	+	0.492953i
$953$	37295.1			1.26769			0.633845	−	0.773460i	$-0.281476\pi$
$953$	37295.1			1.26769			0.633845	+	0.773460i	$0.281476\pi$
$954$	13342.2	−	2186.26i	0.452800	−	0.0741958i
$955$	9967.69			0.337746
$956$	−18210.5	−	54075.4i	−0.616079	−	1.82942i
$957$	3850.90			0.130075
$958$	−11511.4	+	1886.25i	−0.388220	+	0.0636138i
$959$	−55500.0			−1.86881
$960$	5807.20	+	3941.42i	0.195236	+	0.132509i
$961$	−62527.1			−2.09886
$962$	31875.5	−	2706.38i	1.06830	−	0.0907040i
$963$			10126.7i			0.338867i
$964$	−2076.24	−	6165.29i	−0.0693683	−	0.205986i
$965$		−	20281.2i		−	0.676553i
$966$	1128.76	+	6888.57i	0.0375956	+	0.229437i
$967$			55463.6i			1.84446i	0.386647	+	0.922228i	$0.373633\pi$
$967$			55463.6i			1.84446i	−0.386647	+	0.922228i	$0.626367\pi$
$968$	−13237.3	−	24982.6i	−0.439527	−	0.829514i
$969$		−	4814.47i		−	0.159611i
$970$	−6462.48	+	1058.94i	−0.213915	+	0.0350522i
$971$			41859.8i			1.38347i	0.722153	+	0.691733i	$0.243153\pi$
$971$			41859.8i			1.38347i	−0.722153	+	0.691733i	$0.756847\pi$
$972$	620.429	+	1842.34i	0.0204735	+	0.0607952i
$973$	−19021.3			−0.626717
$974$	11021.4	−	1805.97i	0.362577	−	0.0594119i
$975$	14597.0	+	1136.70i	0.479465	+	0.0373369i
$976$	34028.3	+	44793.1i	1.11600	+	1.46905i
$977$		−	5960.78i		−	0.195192i	−0.995226	−	0.0975958i	$-0.968885\pi$
$977$		−	5960.78i		−	0.195192i	0.995226	−	0.0975958i	$-0.0311152\pi$
$978$	3087.34	−	505.892i	0.100943	−	0.0165405i
$979$			3213.09i			0.104894i
$980$	6443.85	−	2170.04i	0.210042	−	0.0707342i
$981$	7092.97			0.230847
$982$	−27073.8	+	4436.31i	−0.879795	+	0.144163i
$983$		−	6517.91i		−	0.211484i	−0.994394	−	0.105742i	$-0.966278\pi$
$983$		−	6517.91i		−	0.211484i	0.994394	−	0.105742i	$-0.0337218\pi$
$984$	8913.80	+	16822.9i	0.288782	+	0.545015i
$985$	17310.7			0.559964
$986$	23583.4	−	3864.38i	0.761712	−	0.124814i
$987$		−	22039.4i		−	0.710761i
$988$	−2477.09	−	9819.03i	−0.0797640	−	0.316179i
$989$		−	7091.52i		−	0.228005i
$990$	−169.804	−	1036.27i	−0.00545124	−	0.0332676i
$991$	34170.6			1.09532			0.547661	−	0.836701i	$-0.315518\pi$
$991$	34170.6			1.09532			0.547661	+	0.836701i	$0.315518\pi$
$992$	37839.8	−	39915.2i	1.21110	−	1.27753i
$993$		−	30048.8i		−	0.960292i
$994$	−1916.19	−	11694.1i	−0.0611448	−	0.373152i
$995$	7017.73			0.223595
$996$	−1888.91	−	5609.04i	−0.0600929	−	0.178443i
$997$			29232.1i			0.928577i	0.885684	+	0.464289i	$0.153690\pi$
$997$			29232.1i			0.928577i	−0.885684	+	0.464289i	$0.846310\pi$
$998$	−4734.27	−	28892.2i	−0.150161	−	0.916398i
$999$		−	6515.10i		−	0.206335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.4.m.a.181.39	✓	84
4.3	odd	2		1248.4.m.a.337.12		84
8.3	odd	2		1248.4.m.a.337.9		84
8.5	even	2	inner	312.4.m.a.181.45	yes	84
13.12	even	2	inner	312.4.m.a.181.46	yes	84
52.51	odd	2		1248.4.m.a.337.11		84
104.51	odd	2		1248.4.m.a.337.10		84
104.77	even	2	inner	312.4.m.a.181.40	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.4.m.a.181.39	✓	84	1.1	even	1	trivial
312.4.m.a.181.40	yes	84	104.77	even	2	inner
312.4.m.a.181.45	yes	84	8.5	even	2	inner
312.4.m.a.181.46	yes	84	13.12	even	2	inner
1248.4.m.a.337.9		84	8.3	odd	2
1248.4.m.a.337.10		84	104.51	odd	2
1248.4.m.a.337.11		84	52.51	odd	2
1248.4.m.a.337.12		84	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.457367 - 2.79120i) q^{2} -3.00000i q^{3} +(-7.58163 + 2.55321i) q^{4} +4.56929 q^{5} +(-8.37361 + 1.37210i) q^{6} -23.0002i q^{7} +(10.5941 + 19.9941i) q^{8} -9.00000 q^{9} +(-2.08984 - 12.7538i) q^{10} -9.02801 q^{11} +(7.65962 + 22.7449i) q^{12} +(3.63901 - 46.7307i) q^{13} +(-64.1982 + 10.5195i) q^{14} -13.7079i q^{15} +(50.9623 - 38.7150i) q^{16} -59.4245 q^{17} +(4.11630 + 25.1208i) q^{18} -27.0061 q^{19} +(-34.6427 + 11.6664i) q^{20} -69.0006 q^{21} +(4.12911 + 25.1990i) q^{22} +35.7672 q^{23} +(59.9824 - 31.7823i) q^{24} -104.122 q^{25} +(-132.099 + 11.2158i) q^{26} +27.0000i q^{27} +(58.7243 + 174.379i) q^{28} -142.184i q^{29} +(-38.2615 + 6.26953i) q^{30} +303.839i q^{31} +(-131.370 - 124.539i) q^{32} +27.0840i q^{33} +(27.1788 + 165.866i) q^{34} -105.095i q^{35} +(68.2347 - 22.9789i) q^{36} -241.300 q^{37} +(12.3517 + 75.3795i) q^{38} +(-140.192 - 10.9170i) q^{39} +(48.4076 + 91.3590i) q^{40} +280.464i q^{41} +(31.5586 + 192.595i) q^{42} -198.269i q^{43} +(68.4470 - 23.0504i) q^{44} -41.1236 q^{45} +(-16.3587 - 99.8335i) q^{46} +319.409i q^{47} +(-116.145 - 152.887i) q^{48} -186.009 q^{49} +(47.6217 + 290.624i) q^{50} +178.273i q^{51} +(91.7235 + 363.586i) q^{52} -531.123i q^{53} +(75.3625 - 12.3489i) q^{54} -41.2516 q^{55} +(459.869 - 243.666i) q^{56} +81.0182i q^{57} +(-396.863 + 65.0301i) q^{58} +378.115 q^{59} +(34.9991 + 103.928i) q^{60} +878.946i q^{61} +(848.076 - 138.966i) q^{62} +207.002i q^{63} +(-287.530 + 423.640i) q^{64} +(16.6277 - 213.526i) q^{65} +(75.5970 - 12.3873i) q^{66} +247.600 q^{67} +(450.534 - 151.723i) q^{68} -107.302i q^{69} +(-293.340 + 48.0668i) q^{70} +182.156i q^{71} +(-95.3470 - 179.947i) q^{72} -815.886i q^{73} +(110.363 + 673.517i) q^{74} +312.365i q^{75} +(204.750 - 68.9521i) q^{76} +207.646i q^{77} +(33.6475 + 396.298i) q^{78} -817.462 q^{79} +(232.862 - 176.900i) q^{80} +81.0000 q^{81} +(782.832 - 128.275i) q^{82} -246.607 q^{83} +(523.137 - 176.173i) q^{84} -271.528 q^{85} +(-553.408 + 90.6816i) q^{86} -426.551 q^{87} +(-95.6437 - 180.507i) q^{88} -355.903i q^{89} +(18.8086 + 114.784i) q^{90} +(-1074.81 - 83.6980i) q^{91} +(-271.174 + 91.3211i) q^{92} +911.517 q^{93} +(891.534 - 146.087i) q^{94} -123.399 q^{95} +(-373.617 + 394.109i) q^{96} -506.709i q^{97} +(85.0742 + 519.188i) q^{98} +81.2521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Introduction

L-functions

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