# Properties

 Label 1600.4.a.bj.1.1 Level $1600$ Weight $4$ Character 1600.1 Self dual yes Analytic conductor $94.403$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1600 = 2^{6} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1600.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$94.4030560092$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 160) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1600.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} +6.00000 q^{7} -23.0000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} +6.00000 q^{7} -23.0000 q^{9} +60.0000 q^{11} +50.0000 q^{13} +30.0000 q^{17} +40.0000 q^{19} +12.0000 q^{21} +178.000 q^{23} -100.000 q^{27} -166.000 q^{29} -20.0000 q^{31} +120.000 q^{33} +10.0000 q^{37} +100.000 q^{39} -250.000 q^{41} -142.000 q^{43} +214.000 q^{47} -307.000 q^{49} +60.0000 q^{51} +490.000 q^{53} +80.0000 q^{57} -800.000 q^{59} -250.000 q^{61} -138.000 q^{63} +774.000 q^{67} +356.000 q^{69} -100.000 q^{71} +230.000 q^{73} +360.000 q^{77} +1320.00 q^{79} +421.000 q^{81} -982.000 q^{83} -332.000 q^{87} +874.000 q^{89} +300.000 q^{91} -40.0000 q^{93} +310.000 q^{97} -1380.00 q^{99} +O(q^{100})$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 2.00000 0.384900 0.192450 0.981307i $$-0.438357\pi$$
0.192450 + 0.981307i $$0.438357\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 6.00000 0.323970 0.161985 0.986793i $$-0.448210\pi$$
0.161985 + 0.986793i $$0.448210\pi$$
$$8$$ 0 0
$$9$$ −23.0000 −0.851852
$$10$$ 0 0
$$11$$ 60.0000 1.64461 0.822304 0.569049i $$-0.192689\pi$$
0.822304 + 0.569049i $$0.192689\pi$$
$$12$$ 0 0
$$13$$ 50.0000 1.06673 0.533366 0.845885i $$-0.320927\pi$$
0.533366 + 0.845885i $$0.320927\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 30.0000 0.428004 0.214002 0.976833i $$-0.431350\pi$$
0.214002 + 0.976833i $$0.431350\pi$$
$$18$$ 0 0
$$19$$ 40.0000 0.482980 0.241490 0.970403i $$-0.422364\pi$$
0.241490 + 0.970403i $$0.422364\pi$$
$$20$$ 0 0
$$21$$ 12.0000 0.124696
$$22$$ 0 0
$$23$$ 178.000 1.61372 0.806860 0.590743i $$-0.201165\pi$$
0.806860 + 0.590743i $$0.201165\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −100.000 −0.712778
$$28$$ 0 0
$$29$$ −166.000 −1.06295 −0.531473 0.847075i $$-0.678361\pi$$
−0.531473 + 0.847075i $$0.678361\pi$$
$$30$$ 0 0
$$31$$ −20.0000 −0.115874 −0.0579372 0.998320i $$-0.518452\pi$$
−0.0579372 + 0.998320i $$0.518452\pi$$
$$32$$ 0 0
$$33$$ 120.000 0.633010
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 10.0000 0.0444322 0.0222161 0.999753i $$-0.492928\pi$$
0.0222161 + 0.999753i $$0.492928\pi$$
$$38$$ 0 0
$$39$$ 100.000 0.410585
$$40$$ 0 0
$$41$$ −250.000 −0.952279 −0.476140 0.879370i $$-0.657964\pi$$
−0.476140 + 0.879370i $$0.657964\pi$$
$$42$$ 0 0
$$43$$ −142.000 −0.503600 −0.251800 0.967779i $$-0.581023\pi$$
−0.251800 + 0.967779i $$0.581023\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 214.000 0.664151 0.332076 0.943253i $$-0.392251\pi$$
0.332076 + 0.943253i $$0.392251\pi$$
$$48$$ 0 0
$$49$$ −307.000 −0.895044
$$50$$ 0 0
$$51$$ 60.0000 0.164739
$$52$$ 0 0
$$53$$ 490.000 1.26994 0.634969 0.772538i $$-0.281013\pi$$
0.634969 + 0.772538i $$0.281013\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 80.0000 0.185899
$$58$$ 0 0
$$59$$ −800.000 −1.76527 −0.882637 0.470056i $$-0.844234\pi$$
−0.882637 + 0.470056i $$0.844234\pi$$
$$60$$ 0 0
$$61$$ −250.000 −0.524741 −0.262371 0.964967i $$-0.584504\pi$$
−0.262371 + 0.964967i $$0.584504\pi$$
$$62$$ 0 0
$$63$$ −138.000 −0.275974
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 774.000 1.41133 0.705665 0.708545i $$-0.250648\pi$$
0.705665 + 0.708545i $$0.250648\pi$$
$$68$$ 0 0
$$69$$ 356.000 0.621121
$$70$$ 0 0
$$71$$ −100.000 −0.167152 −0.0835762 0.996501i $$-0.526634\pi$$
−0.0835762 + 0.996501i $$0.526634\pi$$
$$72$$ 0 0
$$73$$ 230.000 0.368760 0.184380 0.982855i $$-0.440972\pi$$
0.184380 + 0.982855i $$0.440972\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 360.000 0.532803
$$78$$ 0 0
$$79$$ 1320.00 1.87989 0.939947 0.341321i $$-0.110874\pi$$
0.939947 + 0.341321i $$0.110874\pi$$
$$80$$ 0 0
$$81$$ 421.000 0.577503
$$82$$ 0 0
$$83$$ −982.000 −1.29866 −0.649328 0.760508i $$-0.724950\pi$$
−0.649328 + 0.760508i $$0.724950\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −332.000 −0.409128
$$88$$ 0 0
$$89$$ 874.000 1.04094 0.520471 0.853879i $$-0.325756\pi$$
0.520471 + 0.853879i $$0.325756\pi$$
$$90$$ 0 0
$$91$$ 300.000 0.345588
$$92$$ 0 0
$$93$$ −40.0000 −0.0446001
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 310.000 0.324492 0.162246 0.986750i $$-0.448126\pi$$
0.162246 + 0.986750i $$0.448126\pi$$
$$98$$ 0 0
$$99$$ −1380.00 −1.40096
$$100$$ 0 0
$$101$$ 1498.00 1.47581 0.737904 0.674906i $$-0.235816\pi$$
0.737904 + 0.674906i $$0.235816\pi$$
$$102$$ 0 0
$$103$$ 1402.00 1.34120 0.670598 0.741821i $$-0.266038\pi$$
0.670598 + 0.741821i $$0.266038\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1194.00 −1.07877 −0.539385 0.842059i $$-0.681343\pi$$
−0.539385 + 0.842059i $$0.681343\pi$$
$$108$$ 0 0
$$109$$ −650.000 −0.571181 −0.285590 0.958352i $$-0.592190\pi$$
−0.285590 + 0.958352i $$0.592190\pi$$
$$110$$ 0 0
$$111$$ 20.0000 0.0171019
$$112$$ 0 0
$$113$$ 1510.00 1.25707 0.628535 0.777782i $$-0.283655\pi$$
0.628535 + 0.777782i $$0.283655\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1150.00 −0.908697
$$118$$ 0 0
$$119$$ 180.000 0.138660
$$120$$ 0 0
$$121$$ 2269.00 1.70473
$$122$$ 0 0
$$123$$ −500.000 −0.366532
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1246.00 0.870588 0.435294 0.900288i $$-0.356645\pi$$
0.435294 + 0.900288i $$0.356645\pi$$
$$128$$ 0 0
$$129$$ −284.000 −0.193836
$$130$$ 0 0
$$131$$ 2660.00 1.77409 0.887043 0.461687i $$-0.152756\pi$$
0.887043 + 0.461687i $$0.152756\pi$$
$$132$$ 0 0
$$133$$ 240.000 0.156471
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2770.00 −1.72742 −0.863712 0.503986i $$-0.831866\pi$$
−0.863712 + 0.503986i $$0.831866\pi$$
$$138$$ 0 0
$$139$$ −560.000 −0.341716 −0.170858 0.985296i $$-0.554654\pi$$
−0.170858 + 0.985296i $$0.554654\pi$$
$$140$$ 0 0
$$141$$ 428.000 0.255632
$$142$$ 0 0
$$143$$ 3000.00 1.75435
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −614.000 −0.344502
$$148$$ 0 0
$$149$$ 2350.00 1.29208 0.646039 0.763305i $$-0.276424\pi$$
0.646039 + 0.763305i $$0.276424\pi$$
$$150$$ 0 0
$$151$$ −580.000 −0.312581 −0.156290 0.987711i $$-0.549954\pi$$
−0.156290 + 0.987711i $$0.549954\pi$$
$$152$$ 0 0
$$153$$ −690.000 −0.364596
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −1310.00 −0.665920 −0.332960 0.942941i $$-0.608047\pi$$
−0.332960 + 0.942941i $$0.608047\pi$$
$$158$$ 0 0
$$159$$ 980.000 0.488799
$$160$$ 0 0
$$161$$ 1068.00 0.522796
$$162$$ 0 0
$$163$$ −1862.00 −0.894743 −0.447371 0.894348i $$-0.647640\pi$$
−0.447371 + 0.894348i $$0.647640\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 726.000 0.336405 0.168202 0.985752i $$-0.446204\pi$$
0.168202 + 0.985752i $$0.446204\pi$$
$$168$$ 0 0
$$169$$ 303.000 0.137915
$$170$$ 0 0
$$171$$ −920.000 −0.411428
$$172$$ 0 0
$$173$$ 3250.00 1.42828 0.714141 0.700001i $$-0.246817\pi$$
0.714141 + 0.700001i $$0.246817\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −1600.00 −0.679454
$$178$$ 0 0
$$179$$ −1120.00 −0.467669 −0.233834 0.972276i $$-0.575127\pi$$
−0.233834 + 0.972276i $$0.575127\pi$$
$$180$$ 0 0
$$181$$ 2842.00 1.16710 0.583548 0.812079i $$-0.301664\pi$$
0.583548 + 0.812079i $$0.301664\pi$$
$$182$$ 0 0
$$183$$ −500.000 −0.201973
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 1800.00 0.703899
$$188$$ 0 0
$$189$$ −600.000 −0.230918
$$190$$ 0 0
$$191$$ −3180.00 −1.20469 −0.602347 0.798234i $$-0.705768\pi$$
−0.602347 + 0.798234i $$0.705768\pi$$
$$192$$ 0 0
$$193$$ 4670.00 1.74173 0.870865 0.491522i $$-0.163559\pi$$
0.870865 + 0.491522i $$0.163559\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2990.00 −1.08136 −0.540682 0.841227i $$-0.681834\pi$$
−0.540682 + 0.841227i $$0.681834\pi$$
$$198$$ 0 0
$$199$$ 4240.00 1.51038 0.755190 0.655506i $$-0.227545\pi$$
0.755190 + 0.655506i $$0.227545\pi$$
$$200$$ 0 0
$$201$$ 1548.00 0.543221
$$202$$ 0 0
$$203$$ −996.000 −0.344362
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −4094.00 −1.37465
$$208$$ 0 0
$$209$$ 2400.00 0.794313
$$210$$ 0 0
$$211$$ −4060.00 −1.32465 −0.662327 0.749215i $$-0.730431\pi$$
−0.662327 + 0.749215i $$0.730431\pi$$
$$212$$ 0 0
$$213$$ −200.000 −0.0643370
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −120.000 −0.0375398
$$218$$ 0 0
$$219$$ 460.000 0.141936
$$220$$ 0 0
$$221$$ 1500.00 0.456565
$$222$$ 0 0
$$223$$ −5622.00 −1.68824 −0.844119 0.536156i $$-0.819876\pi$$
−0.844119 + 0.536156i $$0.819876\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1554.00 −0.454373 −0.227186 0.973851i $$-0.572953\pi$$
−0.227186 + 0.973851i $$0.572953\pi$$
$$228$$ 0 0
$$229$$ −1134.00 −0.327235 −0.163618 0.986524i $$-0.552316\pi$$
−0.163618 + 0.986524i $$0.552316\pi$$
$$230$$ 0 0
$$231$$ 720.000 0.205076
$$232$$ 0 0
$$233$$ 1710.00 0.480798 0.240399 0.970674i $$-0.422722\pi$$
0.240399 + 0.970674i $$0.422722\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 2640.00 0.723571
$$238$$ 0 0
$$239$$ −4440.00 −1.20167 −0.600836 0.799372i $$-0.705166\pi$$
−0.600836 + 0.799372i $$0.705166\pi$$
$$240$$ 0 0
$$241$$ −850.000 −0.227192 −0.113596 0.993527i $$-0.536237\pi$$
−0.113596 + 0.993527i $$0.536237\pi$$
$$242$$ 0 0
$$243$$ 3542.00 0.935059
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 2000.00 0.515210
$$248$$ 0 0
$$249$$ −1964.00 −0.499853
$$250$$ 0 0
$$251$$ −660.000 −0.165971 −0.0829857 0.996551i $$-0.526446\pi$$
−0.0829857 + 0.996551i $$0.526446\pi$$
$$252$$ 0 0
$$253$$ 10680.0 2.65394
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 7590.00 1.84222 0.921111 0.389299i $$-0.127283\pi$$
0.921111 + 0.389299i $$0.127283\pi$$
$$258$$ 0 0
$$259$$ 60.0000 0.0143947
$$260$$ 0 0
$$261$$ 3818.00 0.905472
$$262$$ 0 0
$$263$$ 762.000 0.178658 0.0893288 0.996002i $$-0.471528\pi$$
0.0893288 + 0.996002i $$0.471528\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 1748.00 0.400659
$$268$$ 0 0
$$269$$ 150.000 0.0339987 0.0169994 0.999856i $$-0.494589\pi$$
0.0169994 + 0.999856i $$0.494589\pi$$
$$270$$ 0 0
$$271$$ 6580.00 1.47493 0.737466 0.675384i $$-0.236022\pi$$
0.737466 + 0.675384i $$0.236022\pi$$
$$272$$ 0 0
$$273$$ 600.000 0.133017
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 4530.00 0.982604 0.491302 0.870989i $$-0.336521\pi$$
0.491302 + 0.870989i $$0.336521\pi$$
$$278$$ 0 0
$$279$$ 460.000 0.0987078
$$280$$ 0 0
$$281$$ 6950.00 1.47545 0.737726 0.675100i $$-0.235899\pi$$
0.737726 + 0.675100i $$0.235899\pi$$
$$282$$ 0 0
$$283$$ 3882.00 0.815410 0.407705 0.913114i $$-0.366329\pi$$
0.407705 + 0.913114i $$0.366329\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −1500.00 −0.308509
$$288$$ 0 0
$$289$$ −4013.00 −0.816813
$$290$$ 0 0
$$291$$ 620.000 0.124897
$$292$$ 0 0
$$293$$ 1370.00 0.273161 0.136581 0.990629i $$-0.456389\pi$$
0.136581 + 0.990629i $$0.456389\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −6000.00 −1.17224
$$298$$ 0 0
$$299$$ 8900.00 1.72141
$$300$$ 0 0
$$301$$ −852.000 −0.163151
$$302$$ 0 0
$$303$$ 2996.00 0.568039
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −4106.00 −0.763328 −0.381664 0.924301i $$-0.624649\pi$$
−0.381664 + 0.924301i $$0.624649\pi$$
$$308$$ 0 0
$$309$$ 2804.00 0.516226
$$310$$ 0 0
$$311$$ −2220.00 −0.404774 −0.202387 0.979306i $$-0.564870\pi$$
−0.202387 + 0.979306i $$0.564870\pi$$
$$312$$ 0 0
$$313$$ 9430.00 1.70292 0.851462 0.524417i $$-0.175717\pi$$
0.851462 + 0.524417i $$0.175717\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −6470.00 −1.14635 −0.573173 0.819435i $$-0.694288\pi$$
−0.573173 + 0.819435i $$0.694288\pi$$
$$318$$ 0 0
$$319$$ −9960.00 −1.74813
$$320$$ 0 0
$$321$$ −2388.00 −0.415219
$$322$$ 0 0
$$323$$ 1200.00 0.206718
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −1300.00 −0.219848
$$328$$ 0 0
$$329$$ 1284.00 0.215165
$$330$$ 0 0
$$331$$ 900.000 0.149452 0.0747258 0.997204i $$-0.476192\pi$$
0.0747258 + 0.997204i $$0.476192\pi$$
$$332$$ 0 0
$$333$$ −230.000 −0.0378496
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −530.000 −0.0856704 −0.0428352 0.999082i $$-0.513639\pi$$
−0.0428352 + 0.999082i $$0.513639\pi$$
$$338$$ 0 0
$$339$$ 3020.00 0.483846
$$340$$ 0 0
$$341$$ −1200.00 −0.190568
$$342$$ 0 0
$$343$$ −3900.00 −0.613936
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 414.000 0.0640481 0.0320240 0.999487i $$-0.489805\pi$$
0.0320240 + 0.999487i $$0.489805\pi$$
$$348$$ 0 0
$$349$$ −8614.00 −1.32119 −0.660597 0.750741i $$-0.729697\pi$$
−0.660597 + 0.750741i $$0.729697\pi$$
$$350$$ 0 0
$$351$$ −5000.00 −0.760343
$$352$$ 0 0
$$353$$ 2270.00 0.342266 0.171133 0.985248i $$-0.445257\pi$$
0.171133 + 0.985248i $$0.445257\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 360.000 0.0533704
$$358$$ 0 0
$$359$$ −8080.00 −1.18787 −0.593936 0.804512i $$-0.702427\pi$$
−0.593936 + 0.804512i $$0.702427\pi$$
$$360$$ 0 0
$$361$$ −5259.00 −0.766730
$$362$$ 0 0
$$363$$ 4538.00 0.656152
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 2374.00 0.337662 0.168831 0.985645i $$-0.446001\pi$$
0.168831 + 0.985645i $$0.446001\pi$$
$$368$$ 0 0
$$369$$ 5750.00 0.811201
$$370$$ 0 0
$$371$$ 2940.00 0.411421
$$372$$ 0 0
$$373$$ 1810.00 0.251255 0.125628 0.992077i $$-0.459906\pi$$
0.125628 + 0.992077i $$0.459906\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −8300.00 −1.13388
$$378$$ 0 0
$$379$$ 8120.00 1.10052 0.550259 0.834994i $$-0.314529\pi$$
0.550259 + 0.834994i $$0.314529\pi$$
$$380$$ 0 0
$$381$$ 2492.00 0.335089
$$382$$ 0 0
$$383$$ −11782.0 −1.57189 −0.785943 0.618299i $$-0.787822\pi$$
−0.785943 + 0.618299i $$0.787822\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 3266.00 0.428993
$$388$$ 0 0
$$389$$ 4350.00 0.566976 0.283488 0.958976i $$-0.408508\pi$$
0.283488 + 0.958976i $$0.408508\pi$$
$$390$$ 0 0
$$391$$ 5340.00 0.690679
$$392$$ 0 0
$$393$$ 5320.00 0.682846
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7470.00 −0.944354 −0.472177 0.881504i $$-0.656532\pi$$
−0.472177 + 0.881504i $$0.656532\pi$$
$$398$$ 0 0
$$399$$ 480.000 0.0602257
$$400$$ 0 0
$$401$$ 11698.0 1.45678 0.728392 0.685161i $$-0.240268\pi$$
0.728392 + 0.685161i $$0.240268\pi$$
$$402$$ 0 0
$$403$$ −1000.00 −0.123607
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 600.000 0.0730735
$$408$$ 0 0
$$409$$ −3650.00 −0.441274 −0.220637 0.975356i $$-0.570814\pi$$
−0.220637 + 0.975356i $$0.570814\pi$$
$$410$$ 0 0
$$411$$ −5540.00 −0.664886
$$412$$ 0 0
$$413$$ −4800.00 −0.571895
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −1120.00 −0.131527
$$418$$ 0 0
$$419$$ −1120.00 −0.130586 −0.0652931 0.997866i $$-0.520798\pi$$
−0.0652931 + 0.997866i $$0.520798\pi$$
$$420$$ 0 0
$$421$$ −4850.00 −0.561460 −0.280730 0.959787i $$-0.590576\pi$$
−0.280730 + 0.959787i $$0.590576\pi$$
$$422$$ 0 0
$$423$$ −4922.00 −0.565758
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −1500.00 −0.170000
$$428$$ 0 0
$$429$$ 6000.00 0.675251
$$430$$ 0 0
$$431$$ 12580.0 1.40593 0.702967 0.711223i $$-0.251858\pi$$
0.702967 + 0.711223i $$0.251858\pi$$
$$432$$ 0 0
$$433$$ −13130.0 −1.45725 −0.728623 0.684915i $$-0.759839\pi$$
−0.728623 + 0.684915i $$0.759839\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 7120.00 0.779395
$$438$$ 0 0
$$439$$ −8560.00 −0.930630 −0.465315 0.885145i $$-0.654059\pi$$
−0.465315 + 0.885145i $$0.654059\pi$$
$$440$$ 0 0
$$441$$ 7061.00 0.762445
$$442$$ 0 0
$$443$$ 4258.00 0.456667 0.228334 0.973583i $$-0.426672\pi$$
0.228334 + 0.973583i $$0.426672\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 4700.00 0.497321
$$448$$ 0 0
$$449$$ 2550.00 0.268022 0.134011 0.990980i $$-0.457214\pi$$
0.134011 + 0.990980i $$0.457214\pi$$
$$450$$ 0 0
$$451$$ −15000.0 −1.56613
$$452$$ 0 0
$$453$$ −1160.00 −0.120312
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 6710.00 0.686828 0.343414 0.939184i $$-0.388417\pi$$
0.343414 + 0.939184i $$0.388417\pi$$
$$458$$ 0 0
$$459$$ −3000.00 −0.305072
$$460$$ 0 0
$$461$$ 14482.0 1.46311 0.731555 0.681782i $$-0.238795\pi$$
0.731555 + 0.681782i $$0.238795\pi$$
$$462$$ 0 0
$$463$$ 162.000 0.0162609 0.00813043 0.999967i $$-0.497412\pi$$
0.00813043 + 0.999967i $$0.497412\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 15974.0 1.58284 0.791422 0.611270i $$-0.209341\pi$$
0.791422 + 0.611270i $$0.209341\pi$$
$$468$$ 0 0
$$469$$ 4644.00 0.457228
$$470$$ 0 0
$$471$$ −2620.00 −0.256313
$$472$$ 0 0
$$473$$ −8520.00 −0.828224
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −11270.0 −1.08180
$$478$$ 0 0
$$479$$ 10760.0 1.02638 0.513191 0.858274i $$-0.328463\pi$$
0.513191 + 0.858274i $$0.328463\pi$$
$$480$$ 0 0
$$481$$ 500.000 0.0473972
$$482$$ 0 0
$$483$$ 2136.00 0.201224
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −9266.00 −0.862182 −0.431091 0.902309i $$-0.641871\pi$$
−0.431091 + 0.902309i $$0.641871\pi$$
$$488$$ 0 0
$$489$$ −3724.00 −0.344387
$$490$$ 0 0
$$491$$ 2860.00 0.262872 0.131436 0.991325i $$-0.458041\pi$$
0.131436 + 0.991325i $$0.458041\pi$$
$$492$$ 0 0
$$493$$ −4980.00 −0.454945
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −600.000 −0.0541523
$$498$$ 0 0
$$499$$ 7160.00 0.642336 0.321168 0.947022i $$-0.395925\pi$$
0.321168 + 0.947022i $$0.395925\pi$$
$$500$$ 0 0
$$501$$ 1452.00 0.129482
$$502$$ 0 0
$$503$$ −1398.00 −0.123924 −0.0619620 0.998079i $$-0.519736\pi$$
−0.0619620 + 0.998079i $$0.519736\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 606.000 0.0530836
$$508$$ 0 0
$$509$$ −7446.00 −0.648405 −0.324203 0.945988i $$-0.605096\pi$$
−0.324203 + 0.945988i $$0.605096\pi$$
$$510$$ 0 0
$$511$$ 1380.00 0.119467
$$512$$ 0 0
$$513$$ −4000.00 −0.344258
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 12840.0 1.09227
$$518$$ 0 0
$$519$$ 6500.00 0.549746
$$520$$ 0 0
$$521$$ −16438.0 −1.38227 −0.691134 0.722726i $$-0.742889\pi$$
−0.691134 + 0.722726i $$0.742889\pi$$
$$522$$ 0 0
$$523$$ 7322.00 0.612177 0.306089 0.952003i $$-0.400980\pi$$
0.306089 + 0.952003i $$0.400980\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −600.000 −0.0495947
$$528$$ 0 0
$$529$$ 19517.0 1.60409
$$530$$ 0 0
$$531$$ 18400.0 1.50375
$$532$$ 0 0
$$533$$ −12500.0 −1.01583
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −2240.00 −0.180006
$$538$$ 0 0
$$539$$ −18420.0 −1.47200
$$540$$ 0 0
$$541$$ −10878.0 −0.864476 −0.432238 0.901759i $$-0.642276\pi$$
−0.432238 + 0.901759i $$0.642276\pi$$
$$542$$ 0 0
$$543$$ 5684.00 0.449215
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −16114.0 −1.25957 −0.629785 0.776769i $$-0.716857\pi$$
−0.629785 + 0.776769i $$0.716857\pi$$
$$548$$ 0 0
$$549$$ 5750.00 0.447002
$$550$$ 0 0
$$551$$ −6640.00 −0.513382
$$552$$ 0 0
$$553$$ 7920.00 0.609028
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 3690.00 0.280701 0.140350 0.990102i $$-0.455177\pi$$
0.140350 + 0.990102i $$0.455177\pi$$
$$558$$ 0 0
$$559$$ −7100.00 −0.537206
$$560$$ 0 0
$$561$$ 3600.00 0.270931
$$562$$ 0 0
$$563$$ 2562.00 0.191786 0.0958929 0.995392i $$-0.469429\pi$$
0.0958929 + 0.995392i $$0.469429\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 2526.00 0.187094
$$568$$ 0 0
$$569$$ −6050.00 −0.445746 −0.222873 0.974848i $$-0.571543\pi$$
−0.222873 + 0.974848i $$0.571543\pi$$
$$570$$ 0 0
$$571$$ 8260.00 0.605377 0.302688 0.953090i $$-0.402116\pi$$
0.302688 + 0.953090i $$0.402116\pi$$
$$572$$ 0 0
$$573$$ −6360.00 −0.463687
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 16870.0 1.21717 0.608585 0.793489i $$-0.291737\pi$$
0.608585 + 0.793489i $$0.291737\pi$$
$$578$$ 0 0
$$579$$ 9340.00 0.670392
$$580$$ 0 0
$$581$$ −5892.00 −0.420725
$$582$$ 0 0
$$583$$ 29400.0 2.08855
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 966.000 0.0679235 0.0339617 0.999423i $$-0.489188\pi$$
0.0339617 + 0.999423i $$0.489188\pi$$
$$588$$ 0 0
$$589$$ −800.000 −0.0559651
$$590$$ 0 0
$$591$$ −5980.00 −0.416217
$$592$$ 0 0
$$593$$ −26290.0 −1.82057 −0.910287 0.413977i $$-0.864139\pi$$
−0.910287 + 0.413977i $$0.864139\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 8480.00 0.581346
$$598$$ 0 0
$$599$$ 11640.0 0.793986 0.396993 0.917822i $$-0.370054\pi$$
0.396993 + 0.917822i $$0.370054\pi$$
$$600$$ 0 0
$$601$$ −25450.0 −1.72733 −0.863667 0.504064i $$-0.831838\pi$$
−0.863667 + 0.504064i $$0.831838\pi$$
$$602$$ 0 0
$$603$$ −17802.0 −1.20224
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 16694.0 1.11629 0.558145 0.829743i $$-0.311513\pi$$
0.558145 + 0.829743i $$0.311513\pi$$
$$608$$ 0 0
$$609$$ −1992.00 −0.132545
$$610$$ 0 0
$$611$$ 10700.0 0.708471
$$612$$ 0 0
$$613$$ 15890.0 1.04697 0.523484 0.852036i $$-0.324632\pi$$
0.523484 + 0.852036i $$0.324632\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1230.00 0.0802560 0.0401280 0.999195i $$-0.487223\pi$$
0.0401280 + 0.999195i $$0.487223\pi$$
$$618$$ 0 0
$$619$$ −10840.0 −0.703871 −0.351936 0.936024i $$-0.614476\pi$$
−0.351936 + 0.936024i $$0.614476\pi$$
$$620$$ 0 0
$$621$$ −17800.0 −1.15022
$$622$$ 0 0
$$623$$ 5244.00 0.337233
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 4800.00 0.305731
$$628$$ 0 0
$$629$$ 300.000 0.0190171
$$630$$ 0 0
$$631$$ 14060.0 0.887036 0.443518 0.896265i $$-0.353730\pi$$
0.443518 + 0.896265i $$0.353730\pi$$
$$632$$ 0 0
$$633$$ −8120.00 −0.509859
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −15350.0 −0.954771
$$638$$ 0 0
$$639$$ 2300.00 0.142389
$$640$$ 0 0
$$641$$ −17650.0 −1.08757 −0.543786 0.839224i $$-0.683010\pi$$
−0.543786 + 0.839224i $$0.683010\pi$$
$$642$$ 0 0
$$643$$ −27358.0 −1.67791 −0.838953 0.544203i $$-0.816832\pi$$
−0.838953 + 0.544203i $$0.816832\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −6786.00 −0.412342 −0.206171 0.978516i $$-0.566100\pi$$
−0.206171 + 0.978516i $$0.566100\pi$$
$$648$$ 0 0
$$649$$ −48000.0 −2.90318
$$650$$ 0 0
$$651$$ −240.000 −0.0144491
$$652$$ 0 0
$$653$$ −9030.00 −0.541150 −0.270575 0.962699i $$-0.587214\pi$$
−0.270575 + 0.962699i $$0.587214\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −5290.00 −0.314129
$$658$$ 0 0
$$659$$ −15600.0 −0.922139 −0.461070 0.887364i $$-0.652534\pi$$
−0.461070 + 0.887364i $$0.652534\pi$$
$$660$$ 0 0
$$661$$ −16850.0 −0.991511 −0.495756 0.868462i $$-0.665109\pi$$
−0.495756 + 0.868462i $$0.665109\pi$$
$$662$$ 0 0
$$663$$ 3000.00 0.175732
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −29548.0 −1.71530
$$668$$ 0 0
$$669$$ −11244.0 −0.649803
$$670$$ 0 0
$$671$$ −15000.0 −0.862993
$$672$$ 0 0
$$673$$ 7990.00 0.457640 0.228820 0.973469i $$-0.426513\pi$$
0.228820 + 0.973469i $$0.426513\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 18690.0 1.06103 0.530513 0.847677i $$-0.321999\pi$$
0.530513 + 0.847677i $$0.321999\pi$$
$$678$$ 0 0
$$679$$ 1860.00 0.105126
$$680$$ 0 0
$$681$$ −3108.00 −0.174888
$$682$$ 0 0
$$683$$ −19182.0 −1.07464 −0.537320 0.843379i $$-0.680563\pi$$
−0.537320 + 0.843379i $$0.680563\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −2268.00 −0.125953
$$688$$ 0 0
$$689$$ 24500.0 1.35468
$$690$$ 0 0
$$691$$ −23380.0 −1.28714 −0.643572 0.765385i $$-0.722548\pi$$
−0.643572 + 0.765385i $$0.722548\pi$$
$$692$$ 0 0
$$693$$ −8280.00 −0.453869
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −7500.00 −0.407579
$$698$$ 0 0
$$699$$ 3420.00 0.185059
$$700$$ 0 0
$$701$$ −11850.0 −0.638471 −0.319236 0.947675i $$-0.603426\pi$$
−0.319236 + 0.947675i $$0.603426\pi$$
$$702$$ 0 0
$$703$$ 400.000 0.0214599
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 8988.00 0.478117
$$708$$ 0 0
$$709$$ −25646.0 −1.35847 −0.679235 0.733921i $$-0.737688\pi$$
−0.679235 + 0.733921i $$0.737688\pi$$
$$710$$ 0 0
$$711$$ −30360.0 −1.60139
$$712$$ 0 0
$$713$$ −3560.00 −0.186989
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −8880.00 −0.462524
$$718$$ 0 0
$$719$$ 30280.0 1.57059 0.785294 0.619122i $$-0.212512\pi$$
0.785294 + 0.619122i $$0.212512\pi$$
$$720$$ 0 0
$$721$$ 8412.00 0.434507
$$722$$ 0 0
$$723$$ −1700.00 −0.0874463
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 17446.0 0.890009 0.445004 0.895528i $$-0.353202\pi$$
0.445004 + 0.895528i $$0.353202\pi$$
$$728$$ 0 0
$$729$$ −4283.00 −0.217599
$$730$$ 0 0
$$731$$ −4260.00 −0.215543
$$732$$ 0 0
$$733$$ −16750.0 −0.844032 −0.422016 0.906588i $$-0.638677\pi$$
−0.422016 + 0.906588i $$0.638677\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 46440.0 2.32108
$$738$$ 0 0
$$739$$ −36560.0 −1.81987 −0.909933 0.414755i $$-0.863867\pi$$
−0.909933 + 0.414755i $$0.863867\pi$$
$$740$$ 0 0
$$741$$ 4000.00 0.198305
$$742$$ 0 0
$$743$$ −30142.0 −1.48829 −0.744147 0.668016i $$-0.767144\pi$$
−0.744147 + 0.668016i $$0.767144\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 22586.0 1.10626
$$748$$ 0 0
$$749$$ −7164.00 −0.349488
$$750$$ 0 0
$$751$$ −11860.0 −0.576268 −0.288134 0.957590i $$-0.593035\pi$$
−0.288134 + 0.957590i $$0.593035\pi$$
$$752$$ 0 0
$$753$$ −1320.00 −0.0638824
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 37010.0 1.77695 0.888475 0.458925i $$-0.151765\pi$$
0.888475 + 0.458925i $$0.151765\pi$$
$$758$$ 0 0
$$759$$ 21360.0 1.02150
$$760$$ 0 0
$$761$$ −11718.0 −0.558183 −0.279091 0.960265i $$-0.590033\pi$$
−0.279091 + 0.960265i $$0.590033\pi$$
$$762$$ 0 0
$$763$$ −3900.00 −0.185045
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −40000.0 −1.88307
$$768$$ 0 0
$$769$$ 4706.00 0.220680 0.110340 0.993894i $$-0.464806\pi$$
0.110340 + 0.993894i $$0.464806\pi$$
$$770$$ 0 0
$$771$$ 15180.0 0.709072
$$772$$ 0 0
$$773$$ −28670.0 −1.33401 −0.667004 0.745054i $$-0.732424\pi$$
−0.667004 + 0.745054i $$0.732424\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 120.000 0.00554051
$$778$$ 0 0
$$779$$ −10000.0 −0.459932
$$780$$ 0 0
$$781$$ −6000.00 −0.274900
$$782$$ 0 0
$$783$$ 16600.0 0.757644
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −20434.0 −0.925532 −0.462766 0.886481i $$-0.653143\pi$$
−0.462766 + 0.886481i $$0.653143\pi$$
$$788$$ 0 0
$$789$$ 1524.00 0.0687653
$$790$$ 0 0
$$791$$ 9060.00 0.407252
$$792$$ 0 0
$$793$$ −12500.0 −0.559758
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 3930.00 0.174665 0.0873323 0.996179i $$-0.472166\pi$$
0.0873323 + 0.996179i $$0.472166\pi$$
$$798$$ 0 0
$$799$$ 6420.00 0.284259
$$800$$ 0 0
$$801$$ −20102.0 −0.886728
$$802$$ 0 0
$$803$$ 13800.0 0.606465
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 300.000 0.0130861
$$808$$ 0 0
$$809$$ −4854.00 −0.210949 −0.105474 0.994422i $$-0.533636\pi$$
−0.105474 + 0.994422i $$0.533636\pi$$
$$810$$ 0 0
$$811$$ −13140.0 −0.568937 −0.284468 0.958685i $$-0.591817\pi$$
−0.284468 + 0.958685i $$0.591817\pi$$
$$812$$ 0 0
$$813$$ 13160.0 0.567702
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −5680.00 −0.243229
$$818$$ 0 0
$$819$$ −6900.00 −0.294390
$$820$$ 0 0
$$821$$ −22050.0 −0.937333 −0.468666 0.883375i $$-0.655265\pi$$
−0.468666 + 0.883375i $$0.655265\pi$$
$$822$$ 0 0
$$823$$ 14578.0 0.617445 0.308722 0.951152i $$-0.400099\pi$$
0.308722 + 0.951152i $$0.400099\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 37054.0 1.55803 0.779017 0.627003i $$-0.215719\pi$$
0.779017 + 0.627003i $$0.215719\pi$$
$$828$$ 0 0
$$829$$ 6150.00 0.257658 0.128829 0.991667i $$-0.458878\pi$$
0.128829 + 0.991667i $$0.458878\pi$$
$$830$$ 0 0
$$831$$ 9060.00 0.378204
$$832$$ 0 0
$$833$$ −9210.00 −0.383082
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 2000.00 0.0825927
$$838$$ 0 0
$$839$$ 8200.00 0.337420 0.168710 0.985666i $$-0.446040\pi$$
0.168710 + 0.985666i $$0.446040\pi$$
$$840$$ 0 0
$$841$$ 3167.00 0.129854
$$842$$ 0 0
$$843$$ 13900.0 0.567902
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 13614.0 0.552282
$$848$$ 0 0
$$849$$ 7764.00 0.313851
$$850$$ 0 0
$$851$$ 1780.00 0.0717011
$$852$$ 0 0
$$853$$ −42990.0 −1.72561 −0.862807 0.505533i $$-0.831296\pi$$
−0.862807 + 0.505533i $$0.831296\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −32130.0 −1.28068 −0.640338 0.768093i $$-0.721206\pi$$
−0.640338 + 0.768093i $$0.721206\pi$$
$$858$$ 0 0
$$859$$ 15440.0 0.613278 0.306639 0.951826i $$-0.400796\pi$$
0.306639 + 0.951826i $$0.400796\pi$$
$$860$$ 0 0
$$861$$ −3000.00 −0.118745
$$862$$ 0 0
$$863$$ 46938.0 1.85143 0.925717 0.378216i $$-0.123462\pi$$
0.925717 + 0.378216i $$0.123462\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −8026.00 −0.314391
$$868$$ 0 0
$$869$$ 79200.0 3.09169
$$870$$ 0 0
$$871$$ 38700.0 1.50551
$$872$$ 0 0
$$873$$ −7130.00 −0.276419
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −31230.0 −1.20247 −0.601233 0.799074i $$-0.705324\pi$$
−0.601233 + 0.799074i $$0.705324\pi$$
$$878$$ 0 0
$$879$$ 2740.00 0.105140
$$880$$ 0 0
$$881$$ 25550.0 0.977073 0.488537 0.872543i $$-0.337531\pi$$
0.488537 + 0.872543i $$0.337531\pi$$
$$882$$ 0 0
$$883$$ −4318.00 −0.164567 −0.0822833 0.996609i $$-0.526221\pi$$
−0.0822833 + 0.996609i $$0.526221\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1766.00 0.0668506 0.0334253 0.999441i $$-0.489358\pi$$
0.0334253 + 0.999441i $$0.489358\pi$$
$$888$$ 0 0
$$889$$ 7476.00 0.282044
$$890$$ 0 0
$$891$$ 25260.0 0.949766
$$892$$ 0 0
$$893$$ 8560.00 0.320772
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 17800.0 0.662569
$$898$$ 0 0
$$899$$ 3320.00 0.123168
$$900$$ 0 0
$$901$$ 14700.0 0.543538
$$902$$ 0 0
$$903$$ −1704.00 −0.0627969
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −41906.0 −1.53414 −0.767071 0.641563i $$-0.778286\pi$$
−0.767071 + 0.641563i $$0.778286\pi$$
$$908$$ 0 0
$$909$$ −34454.0 −1.25717
$$910$$ 0 0
$$911$$ −25140.0 −0.914298 −0.457149 0.889390i $$-0.651129\pi$$
−0.457149 + 0.889390i $$0.651129\pi$$
$$912$$ 0 0
$$913$$ −58920.0 −2.13578
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 15960.0 0.574750
$$918$$ 0 0
$$919$$ −32920.0 −1.18164 −0.590822 0.806802i $$-0.701196\pi$$
−0.590822 + 0.806802i $$0.701196\pi$$
$$920$$ 0 0
$$921$$ −8212.00 −0.293805
$$922$$ 0 0
$$923$$ −5000.00 −0.178307
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −32246.0 −1.14250
$$928$$ 0 0
$$929$$ 10150.0 0.358461 0.179231 0.983807i $$-0.442639\pi$$
0.179231 + 0.983807i $$0.442639\pi$$
$$930$$ 0 0
$$931$$ −12280.0 −0.432289
$$932$$ 0 0
$$933$$ −4440.00 −0.155798
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −28530.0 −0.994701 −0.497350 0.867550i $$-0.665694\pi$$
−0.497350 + 0.867550i $$0.665694\pi$$
$$938$$ 0 0
$$939$$ 18860.0 0.655456
$$940$$ 0 0
$$941$$ −9678.00 −0.335275 −0.167638 0.985849i $$-0.553614\pi$$
−0.167638 + 0.985849i $$0.553614\pi$$
$$942$$ 0 0
$$943$$ −44500.0 −1.53671
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −36986.0 −1.26915 −0.634574 0.772862i $$-0.718824\pi$$
−0.634574 + 0.772862i $$0.718824\pi$$
$$948$$ 0 0
$$949$$ 11500.0 0.393368
$$950$$ 0 0
$$951$$ −12940.0 −0.441228
$$952$$ 0 0
$$953$$ 3350.00 0.113869 0.0569345 0.998378i $$-0.481867\pi$$
0.0569345 + 0.998378i $$0.481867\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −19920.0 −0.672855
$$958$$ 0 0
$$959$$ −16620.0 −0.559633
$$960$$ 0 0
$$961$$ −29391.0 −0.986573
$$962$$ 0 0
$$963$$ 27462.0 0.918952
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 43774.0 1.45572 0.727858 0.685728i $$-0.240516\pi$$
0.727858 + 0.685728i $$0.240516\pi$$
$$968$$ 0 0
$$969$$ 2400.00 0.0795656
$$970$$ 0 0
$$971$$ 8740.00 0.288857 0.144428 0.989515i $$-0.453866\pi$$
0.144428 + 0.989515i $$0.453866\pi$$
$$972$$ 0 0
$$973$$ −3360.00 −0.110706
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 48310.0 1.58196 0.790979 0.611843i $$-0.209571\pi$$
0.790979 + 0.611843i $$0.209571\pi$$
$$978$$ 0 0
$$979$$ 52440.0 1.71194
$$980$$ 0 0
$$981$$ 14950.0 0.486561
$$982$$ 0 0
$$983$$ 2282.00 0.0740432 0.0370216 0.999314i $$-0.488213\pi$$
0.0370216 + 0.999314i $$0.488213\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 2568.00 0.0828170
$$988$$ 0 0
$$989$$ −25276.0 −0.812669
$$990$$ 0 0
$$991$$ 31580.0 1.01228 0.506141 0.862451i $$-0.331071\pi$$
0.506141 + 0.862451i $$0.331071\pi$$
$$992$$ 0 0
$$993$$ 1800.00 0.0575239
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −2790.00 −0.0886261 −0.0443130 0.999018i $$-0.514110\pi$$
−0.0443130 + 0.999018i $$0.514110\pi$$
$$998$$ 0 0
$$999$$ −1000.00 −0.0316703
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1600.4.a.bj.1.1 1
4.3 odd 2 1600.4.a.r.1.1 1
5.4 even 2 320.4.a.f.1.1 1
8.3 odd 2 800.4.a.h.1.1 1
8.5 even 2 800.4.a.d.1.1 1
20.19 odd 2 320.4.a.i.1.1 1
40.3 even 4 800.4.c.f.449.2 2
40.13 odd 4 800.4.c.e.449.1 2
40.19 odd 2 160.4.a.a.1.1 1
40.27 even 4 800.4.c.f.449.1 2
40.29 even 2 160.4.a.b.1.1 yes 1
40.37 odd 4 800.4.c.e.449.2 2
80.19 odd 4 1280.4.d.f.641.2 2
80.29 even 4 1280.4.d.k.641.1 2
80.59 odd 4 1280.4.d.f.641.1 2
80.69 even 4 1280.4.d.k.641.2 2
120.29 odd 2 1440.4.a.n.1.1 1
120.59 even 2 1440.4.a.o.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
160.4.a.a.1.1 1 40.19 odd 2
160.4.a.b.1.1 yes 1 40.29 even 2
320.4.a.f.1.1 1 5.4 even 2
320.4.a.i.1.1 1 20.19 odd 2
800.4.a.d.1.1 1 8.5 even 2
800.4.a.h.1.1 1 8.3 odd 2
800.4.c.e.449.1 2 40.13 odd 4
800.4.c.e.449.2 2 40.37 odd 4
800.4.c.f.449.1 2 40.27 even 4
800.4.c.f.449.2 2 40.3 even 4
1280.4.d.f.641.1 2 80.59 odd 4
1280.4.d.f.641.2 2 80.19 odd 4
1280.4.d.k.641.1 2 80.29 even 4
1280.4.d.k.641.2 2 80.69 even 4
1440.4.a.n.1.1 1 120.29 odd 2
1440.4.a.o.1.1 1 120.59 even 2
1600.4.a.r.1.1 1 4.3 odd 2
1600.4.a.bj.1.1 1 1.1 even 1 trivial