# Properties

 Label 1386.4.a.a.1.1 Level $1386$ Weight $4$ Character 1386.1 Self dual yes Analytic conductor $81.777$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1386.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$81.7766472680$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1386.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{2} +4.00000 q^{4} -18.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})$$ $$q-2.00000 q^{2} +4.00000 q^{4} -18.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +36.0000 q^{10} +11.0000 q^{11} +56.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -36.0000 q^{17} -28.0000 q^{19} -72.0000 q^{20} -22.0000 q^{22} -180.000 q^{23} +199.000 q^{25} -112.000 q^{26} +28.0000 q^{28} +54.0000 q^{29} -334.000 q^{31} -32.0000 q^{32} +72.0000 q^{34} -126.000 q^{35} +386.000 q^{37} +56.0000 q^{38} +144.000 q^{40} +444.000 q^{41} -316.000 q^{43} +44.0000 q^{44} +360.000 q^{46} +402.000 q^{47} +49.0000 q^{49} -398.000 q^{50} +224.000 q^{52} +486.000 q^{53} -198.000 q^{55} -56.0000 q^{56} -108.000 q^{58} +282.000 q^{59} +380.000 q^{61} +668.000 q^{62} +64.0000 q^{64} -1008.00 q^{65} +176.000 q^{67} -144.000 q^{68} +252.000 q^{70} +324.000 q^{71} +800.000 q^{73} -772.000 q^{74} -112.000 q^{76} +77.0000 q^{77} -1144.00 q^{79} -288.000 q^{80} -888.000 q^{82} -468.000 q^{83} +648.000 q^{85} +632.000 q^{86} -88.0000 q^{88} +870.000 q^{89} +392.000 q^{91} -720.000 q^{92} -804.000 q^{94} +504.000 q^{95} -1330.00 q^{97} -98.0000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.00000 −0.707107
$$3$$ 0 0
$$4$$ 4.00000 0.500000
$$5$$ −18.0000 −1.60997 −0.804984 0.593296i $$-0.797826\pi$$
−0.804984 + 0.593296i $$0.797826\pi$$
$$6$$ 0 0
$$7$$ 7.00000 0.377964
$$8$$ −8.00000 −0.353553
$$9$$ 0 0
$$10$$ 36.0000 1.13842
$$11$$ 11.0000 0.301511
$$12$$ 0 0
$$13$$ 56.0000 1.19474 0.597369 0.801966i $$-0.296213\pi$$
0.597369 + 0.801966i $$0.296213\pi$$
$$14$$ −14.0000 −0.267261
$$15$$ 0 0
$$16$$ 16.0000 0.250000
$$17$$ −36.0000 −0.513605 −0.256802 0.966464i $$-0.582669\pi$$
−0.256802 + 0.966464i $$0.582669\pi$$
$$18$$ 0 0
$$19$$ −28.0000 −0.338086 −0.169043 0.985609i $$-0.554068\pi$$
−0.169043 + 0.985609i $$0.554068\pi$$
$$20$$ −72.0000 −0.804984
$$21$$ 0 0
$$22$$ −22.0000 −0.213201
$$23$$ −180.000 −1.63185 −0.815926 0.578156i $$-0.803772\pi$$
−0.815926 + 0.578156i $$0.803772\pi$$
$$24$$ 0 0
$$25$$ 199.000 1.59200
$$26$$ −112.000 −0.844808
$$27$$ 0 0
$$28$$ 28.0000 0.188982
$$29$$ 54.0000 0.345778 0.172889 0.984941i $$-0.444690\pi$$
0.172889 + 0.984941i $$0.444690\pi$$
$$30$$ 0 0
$$31$$ −334.000 −1.93510 −0.967551 0.252675i $$-0.918690\pi$$
−0.967551 + 0.252675i $$0.918690\pi$$
$$32$$ −32.0000 −0.176777
$$33$$ 0 0
$$34$$ 72.0000 0.363173
$$35$$ −126.000 −0.608511
$$36$$ 0 0
$$37$$ 386.000 1.71508 0.857541 0.514416i $$-0.171991\pi$$
0.857541 + 0.514416i $$0.171991\pi$$
$$38$$ 56.0000 0.239063
$$39$$ 0 0
$$40$$ 144.000 0.569210
$$41$$ 444.000 1.69125 0.845624 0.533779i $$-0.179229\pi$$
0.845624 + 0.533779i $$0.179229\pi$$
$$42$$ 0 0
$$43$$ −316.000 −1.12069 −0.560344 0.828260i $$-0.689331\pi$$
−0.560344 + 0.828260i $$0.689331\pi$$
$$44$$ 44.0000 0.150756
$$45$$ 0 0
$$46$$ 360.000 1.15389
$$47$$ 402.000 1.24761 0.623806 0.781580i $$-0.285586\pi$$
0.623806 + 0.781580i $$0.285586\pi$$
$$48$$ 0 0
$$49$$ 49.0000 0.142857
$$50$$ −398.000 −1.12571
$$51$$ 0 0
$$52$$ 224.000 0.597369
$$53$$ 486.000 1.25957 0.629785 0.776769i $$-0.283143\pi$$
0.629785 + 0.776769i $$0.283143\pi$$
$$54$$ 0 0
$$55$$ −198.000 −0.485424
$$56$$ −56.0000 −0.133631
$$57$$ 0 0
$$58$$ −108.000 −0.244502
$$59$$ 282.000 0.622259 0.311129 0.950368i $$-0.399293\pi$$
0.311129 + 0.950368i $$0.399293\pi$$
$$60$$ 0 0
$$61$$ 380.000 0.797607 0.398803 0.917036i $$-0.369426\pi$$
0.398803 + 0.917036i $$0.369426\pi$$
$$62$$ 668.000 1.36832
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −1008.00 −1.92349
$$66$$ 0 0
$$67$$ 176.000 0.320923 0.160461 0.987042i $$-0.448702\pi$$
0.160461 + 0.987042i $$0.448702\pi$$
$$68$$ −144.000 −0.256802
$$69$$ 0 0
$$70$$ 252.000 0.430282
$$71$$ 324.000 0.541574 0.270787 0.962639i $$-0.412716\pi$$
0.270787 + 0.962639i $$0.412716\pi$$
$$72$$ 0 0
$$73$$ 800.000 1.28264 0.641321 0.767272i $$-0.278387\pi$$
0.641321 + 0.767272i $$0.278387\pi$$
$$74$$ −772.000 −1.21275
$$75$$ 0 0
$$76$$ −112.000 −0.169043
$$77$$ 77.0000 0.113961
$$78$$ 0 0
$$79$$ −1144.00 −1.62924 −0.814621 0.579994i $$-0.803055\pi$$
−0.814621 + 0.579994i $$0.803055\pi$$
$$80$$ −288.000 −0.402492
$$81$$ 0 0
$$82$$ −888.000 −1.19589
$$83$$ −468.000 −0.618912 −0.309456 0.950914i $$-0.600147\pi$$
−0.309456 + 0.950914i $$0.600147\pi$$
$$84$$ 0 0
$$85$$ 648.000 0.826888
$$86$$ 632.000 0.792445
$$87$$ 0 0
$$88$$ −88.0000 −0.106600
$$89$$ 870.000 1.03618 0.518089 0.855327i $$-0.326644\pi$$
0.518089 + 0.855327i $$0.326644\pi$$
$$90$$ 0 0
$$91$$ 392.000 0.451569
$$92$$ −720.000 −0.815926
$$93$$ 0 0
$$94$$ −804.000 −0.882194
$$95$$ 504.000 0.544309
$$96$$ 0 0
$$97$$ −1330.00 −1.39218 −0.696088 0.717957i $$-0.745078\pi$$
−0.696088 + 0.717957i $$0.745078\pi$$
$$98$$ −98.0000 −0.101015
$$99$$ 0 0
$$100$$ 796.000 0.796000
$$101$$ 120.000 0.118222 0.0591111 0.998251i $$-0.481173\pi$$
0.0591111 + 0.998251i $$0.481173\pi$$
$$102$$ 0 0
$$103$$ −1210.00 −1.15752 −0.578761 0.815497i $$-0.696464\pi$$
−0.578761 + 0.815497i $$0.696464\pi$$
$$104$$ −448.000 −0.422404
$$105$$ 0 0
$$106$$ −972.000 −0.890651
$$107$$ −1236.00 −1.11672 −0.558358 0.829600i $$-0.688568\pi$$
−0.558358 + 0.829600i $$0.688568\pi$$
$$108$$ 0 0
$$109$$ −694.000 −0.609845 −0.304923 0.952377i $$-0.598631\pi$$
−0.304923 + 0.952377i $$0.598631\pi$$
$$110$$ 396.000 0.343247
$$111$$ 0 0
$$112$$ 112.000 0.0944911
$$113$$ −978.000 −0.814181 −0.407091 0.913388i $$-0.633457\pi$$
−0.407091 + 0.913388i $$0.633457\pi$$
$$114$$ 0 0
$$115$$ 3240.00 2.62723
$$116$$ 216.000 0.172889
$$117$$ 0 0
$$118$$ −564.000 −0.440003
$$119$$ −252.000 −0.194124
$$120$$ 0 0
$$121$$ 121.000 0.0909091
$$122$$ −760.000 −0.563993
$$123$$ 0 0
$$124$$ −1336.00 −0.967551
$$125$$ −1332.00 −0.953102
$$126$$ 0 0
$$127$$ −1216.00 −0.849626 −0.424813 0.905281i $$-0.639660\pi$$
−0.424813 + 0.905281i $$0.639660\pi$$
$$128$$ −128.000 −0.0883883
$$129$$ 0 0
$$130$$ 2016.00 1.36011
$$131$$ −1680.00 −1.12048 −0.560238 0.828332i $$-0.689290\pi$$
−0.560238 + 0.828332i $$0.689290\pi$$
$$132$$ 0 0
$$133$$ −196.000 −0.127785
$$134$$ −352.000 −0.226927
$$135$$ 0 0
$$136$$ 288.000 0.181587
$$137$$ −1062.00 −0.662283 −0.331142 0.943581i $$-0.607434\pi$$
−0.331142 + 0.943581i $$0.607434\pi$$
$$138$$ 0 0
$$139$$ −508.000 −0.309986 −0.154993 0.987916i $$-0.549535\pi$$
−0.154993 + 0.987916i $$0.549535\pi$$
$$140$$ −504.000 −0.304256
$$141$$ 0 0
$$142$$ −648.000 −0.382950
$$143$$ 616.000 0.360227
$$144$$ 0 0
$$145$$ −972.000 −0.556691
$$146$$ −1600.00 −0.906965
$$147$$ 0 0
$$148$$ 1544.00 0.857541
$$149$$ −2598.00 −1.42843 −0.714216 0.699925i $$-0.753217\pi$$
−0.714216 + 0.699925i $$0.753217\pi$$
$$150$$ 0 0
$$151$$ 2648.00 1.42709 0.713547 0.700607i $$-0.247088\pi$$
0.713547 + 0.700607i $$0.247088\pi$$
$$152$$ 224.000 0.119532
$$153$$ 0 0
$$154$$ −154.000 −0.0805823
$$155$$ 6012.00 3.11545
$$156$$ 0 0
$$157$$ −790.000 −0.401585 −0.200793 0.979634i $$-0.564352\pi$$
−0.200793 + 0.979634i $$0.564352\pi$$
$$158$$ 2288.00 1.15205
$$159$$ 0 0
$$160$$ 576.000 0.284605
$$161$$ −1260.00 −0.616782
$$162$$ 0 0
$$163$$ −160.000 −0.0768845 −0.0384422 0.999261i $$-0.512240\pi$$
−0.0384422 + 0.999261i $$0.512240\pi$$
$$164$$ 1776.00 0.845624
$$165$$ 0 0
$$166$$ 936.000 0.437637
$$167$$ −264.000 −0.122329 −0.0611645 0.998128i $$-0.519481\pi$$
−0.0611645 + 0.998128i $$0.519481\pi$$
$$168$$ 0 0
$$169$$ 939.000 0.427401
$$170$$ −1296.00 −0.584698
$$171$$ 0 0
$$172$$ −1264.00 −0.560344
$$173$$ −1632.00 −0.717218 −0.358609 0.933488i $$-0.616749\pi$$
−0.358609 + 0.933488i $$0.616749\pi$$
$$174$$ 0 0
$$175$$ 1393.00 0.601719
$$176$$ 176.000 0.0753778
$$177$$ 0 0
$$178$$ −1740.00 −0.732688
$$179$$ 708.000 0.295634 0.147817 0.989015i $$-0.452775\pi$$
0.147817 + 0.989015i $$0.452775\pi$$
$$180$$ 0 0
$$181$$ 902.000 0.370415 0.185208 0.982699i $$-0.440704\pi$$
0.185208 + 0.982699i $$0.440704\pi$$
$$182$$ −784.000 −0.319307
$$183$$ 0 0
$$184$$ 1440.00 0.576947
$$185$$ −6948.00 −2.76123
$$186$$ 0 0
$$187$$ −396.000 −0.154858
$$188$$ 1608.00 0.623806
$$189$$ 0 0
$$190$$ −1008.00 −0.384884
$$191$$ −1824.00 −0.690995 −0.345497 0.938420i $$-0.612290\pi$$
−0.345497 + 0.938420i $$0.612290\pi$$
$$192$$ 0 0
$$193$$ 2090.00 0.779490 0.389745 0.920923i $$-0.372563\pi$$
0.389745 + 0.920923i $$0.372563\pi$$
$$194$$ 2660.00 0.984417
$$195$$ 0 0
$$196$$ 196.000 0.0714286
$$197$$ 1602.00 0.579380 0.289690 0.957121i $$-0.406448\pi$$
0.289690 + 0.957121i $$0.406448\pi$$
$$198$$ 0 0
$$199$$ −3274.00 −1.16627 −0.583135 0.812375i $$-0.698174\pi$$
−0.583135 + 0.812375i $$0.698174\pi$$
$$200$$ −1592.00 −0.562857
$$201$$ 0 0
$$202$$ −240.000 −0.0835957
$$203$$ 378.000 0.130692
$$204$$ 0 0
$$205$$ −7992.00 −2.72286
$$206$$ 2420.00 0.818492
$$207$$ 0 0
$$208$$ 896.000 0.298685
$$209$$ −308.000 −0.101937
$$210$$ 0 0
$$211$$ −4948.00 −1.61438 −0.807190 0.590291i $$-0.799013\pi$$
−0.807190 + 0.590291i $$0.799013\pi$$
$$212$$ 1944.00 0.629785
$$213$$ 0 0
$$214$$ 2472.00 0.789638
$$215$$ 5688.00 1.80427
$$216$$ 0 0
$$217$$ −2338.00 −0.731400
$$218$$ 1388.00 0.431226
$$219$$ 0 0
$$220$$ −792.000 −0.242712
$$221$$ −2016.00 −0.613624
$$222$$ 0 0
$$223$$ 2342.00 0.703282 0.351641 0.936135i $$-0.385624\pi$$
0.351641 + 0.936135i $$0.385624\pi$$
$$224$$ −224.000 −0.0668153
$$225$$ 0 0
$$226$$ 1956.00 0.575713
$$227$$ −2064.00 −0.603491 −0.301746 0.953388i $$-0.597569\pi$$
−0.301746 + 0.953388i $$0.597569\pi$$
$$228$$ 0 0
$$229$$ −1666.00 −0.480753 −0.240376 0.970680i $$-0.577271\pi$$
−0.240376 + 0.970680i $$0.577271\pi$$
$$230$$ −6480.00 −1.85773
$$231$$ 0 0
$$232$$ −432.000 −0.122251
$$233$$ −4158.00 −1.16910 −0.584549 0.811359i $$-0.698728\pi$$
−0.584549 + 0.811359i $$0.698728\pi$$
$$234$$ 0 0
$$235$$ −7236.00 −2.00862
$$236$$ 1128.00 0.311129
$$237$$ 0 0
$$238$$ 504.000 0.137267
$$239$$ −72.0000 −0.0194866 −0.00974329 0.999953i $$-0.503101\pi$$
−0.00974329 + 0.999953i $$0.503101\pi$$
$$240$$ 0 0
$$241$$ 6860.00 1.83357 0.916787 0.399376i $$-0.130773\pi$$
0.916787 + 0.399376i $$0.130773\pi$$
$$242$$ −242.000 −0.0642824
$$243$$ 0 0
$$244$$ 1520.00 0.398803
$$245$$ −882.000 −0.229996
$$246$$ 0 0
$$247$$ −1568.00 −0.403925
$$248$$ 2672.00 0.684162
$$249$$ 0 0
$$250$$ 2664.00 0.673945
$$251$$ 150.000 0.0377208 0.0188604 0.999822i $$-0.493996\pi$$
0.0188604 + 0.999822i $$0.493996\pi$$
$$252$$ 0 0
$$253$$ −1980.00 −0.492022
$$254$$ 2432.00 0.600777
$$255$$ 0 0
$$256$$ 256.000 0.0625000
$$257$$ 2430.00 0.589802 0.294901 0.955528i $$-0.404713\pi$$
0.294901 + 0.955528i $$0.404713\pi$$
$$258$$ 0 0
$$259$$ 2702.00 0.648240
$$260$$ −4032.00 −0.961746
$$261$$ 0 0
$$262$$ 3360.00 0.792296
$$263$$ −3048.00 −0.714630 −0.357315 0.933984i $$-0.616308\pi$$
−0.357315 + 0.933984i $$0.616308\pi$$
$$264$$ 0 0
$$265$$ −8748.00 −2.02787
$$266$$ 392.000 0.0903574
$$267$$ 0 0
$$268$$ 704.000 0.160461
$$269$$ 3834.00 0.869008 0.434504 0.900670i $$-0.356924\pi$$
0.434504 + 0.900670i $$0.356924\pi$$
$$270$$ 0 0
$$271$$ −3508.00 −0.786331 −0.393166 0.919468i $$-0.628620\pi$$
−0.393166 + 0.919468i $$0.628620\pi$$
$$272$$ −576.000 −0.128401
$$273$$ 0 0
$$274$$ 2124.00 0.468305
$$275$$ 2189.00 0.480006
$$276$$ 0 0
$$277$$ 8294.00 1.79905 0.899527 0.436864i $$-0.143911\pi$$
0.899527 + 0.436864i $$0.143911\pi$$
$$278$$ 1016.00 0.219193
$$279$$ 0 0
$$280$$ 1008.00 0.215141
$$281$$ −8022.00 −1.70303 −0.851517 0.524327i $$-0.824317\pi$$
−0.851517 + 0.524327i $$0.824317\pi$$
$$282$$ 0 0
$$283$$ 392.000 0.0823392 0.0411696 0.999152i $$-0.486892\pi$$
0.0411696 + 0.999152i $$0.486892\pi$$
$$284$$ 1296.00 0.270787
$$285$$ 0 0
$$286$$ −1232.00 −0.254719
$$287$$ 3108.00 0.639231
$$288$$ 0 0
$$289$$ −3617.00 −0.736210
$$290$$ 1944.00 0.393640
$$291$$ 0 0
$$292$$ 3200.00 0.641321
$$293$$ 2748.00 0.547918 0.273959 0.961741i $$-0.411667\pi$$
0.273959 + 0.961741i $$0.411667\pi$$
$$294$$ 0 0
$$295$$ −5076.00 −1.00182
$$296$$ −3088.00 −0.606373
$$297$$ 0 0
$$298$$ 5196.00 1.01005
$$299$$ −10080.0 −1.94964
$$300$$ 0 0
$$301$$ −2212.00 −0.423580
$$302$$ −5296.00 −1.00911
$$303$$ 0 0
$$304$$ −448.000 −0.0845216
$$305$$ −6840.00 −1.28412
$$306$$ 0 0
$$307$$ −3064.00 −0.569615 −0.284807 0.958585i $$-0.591930\pi$$
−0.284807 + 0.958585i $$0.591930\pi$$
$$308$$ 308.000 0.0569803
$$309$$ 0 0
$$310$$ −12024.0 −2.20296
$$311$$ −4062.00 −0.740627 −0.370313 0.928907i $$-0.620750\pi$$
−0.370313 + 0.928907i $$0.620750\pi$$
$$312$$ 0 0
$$313$$ −4870.00 −0.879453 −0.439726 0.898132i $$-0.644925\pi$$
−0.439726 + 0.898132i $$0.644925\pi$$
$$314$$ 1580.00 0.283964
$$315$$ 0 0
$$316$$ −4576.00 −0.814621
$$317$$ −4806.00 −0.851520 −0.425760 0.904836i $$-0.639993\pi$$
−0.425760 + 0.904836i $$0.639993\pi$$
$$318$$ 0 0
$$319$$ 594.000 0.104256
$$320$$ −1152.00 −0.201246
$$321$$ 0 0
$$322$$ 2520.00 0.436131
$$323$$ 1008.00 0.173643
$$324$$ 0 0
$$325$$ 11144.0 1.90202
$$326$$ 320.000 0.0543655
$$327$$ 0 0
$$328$$ −3552.00 −0.597946
$$329$$ 2814.00 0.471553
$$330$$ 0 0
$$331$$ 6620.00 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ −1872.00 −0.309456
$$333$$ 0 0
$$334$$ 528.000 0.0864996
$$335$$ −3168.00 −0.516676
$$336$$ 0 0
$$337$$ 1094.00 0.176837 0.0884184 0.996083i $$-0.471819\pi$$
0.0884184 + 0.996083i $$0.471819\pi$$
$$338$$ −1878.00 −0.302218
$$339$$ 0 0
$$340$$ 2592.00 0.413444
$$341$$ −3674.00 −0.583455
$$342$$ 0 0
$$343$$ 343.000 0.0539949
$$344$$ 2528.00 0.396223
$$345$$ 0 0
$$346$$ 3264.00 0.507150
$$347$$ −3468.00 −0.536519 −0.268259 0.963347i $$-0.586448\pi$$
−0.268259 + 0.963347i $$0.586448\pi$$
$$348$$ 0 0
$$349$$ −8188.00 −1.25586 −0.627928 0.778272i $$-0.716097\pi$$
−0.627928 + 0.778272i $$0.716097\pi$$
$$350$$ −2786.00 −0.425480
$$351$$ 0 0
$$352$$ −352.000 −0.0533002
$$353$$ 5070.00 0.764444 0.382222 0.924070i $$-0.375159\pi$$
0.382222 + 0.924070i $$0.375159\pi$$
$$354$$ 0 0
$$355$$ −5832.00 −0.871917
$$356$$ 3480.00 0.518089
$$357$$ 0 0
$$358$$ −1416.00 −0.209044
$$359$$ −1656.00 −0.243455 −0.121727 0.992564i $$-0.538843\pi$$
−0.121727 + 0.992564i $$0.538843\pi$$
$$360$$ 0 0
$$361$$ −6075.00 −0.885698
$$362$$ −1804.00 −0.261923
$$363$$ 0 0
$$364$$ 1568.00 0.225784
$$365$$ −14400.0 −2.06501
$$366$$ 0 0
$$367$$ 10166.0 1.44594 0.722971 0.690878i $$-0.242776\pi$$
0.722971 + 0.690878i $$0.242776\pi$$
$$368$$ −2880.00 −0.407963
$$369$$ 0 0
$$370$$ 13896.0 1.95248
$$371$$ 3402.00 0.476073
$$372$$ 0 0
$$373$$ −2722.00 −0.377855 −0.188927 0.981991i $$-0.560501\pi$$
−0.188927 + 0.981991i $$0.560501\pi$$
$$374$$ 792.000 0.109501
$$375$$ 0 0
$$376$$ −3216.00 −0.441097
$$377$$ 3024.00 0.413114
$$378$$ 0 0
$$379$$ −5872.00 −0.795843 −0.397921 0.917420i $$-0.630268\pi$$
−0.397921 + 0.917420i $$0.630268\pi$$
$$380$$ 2016.00 0.272154
$$381$$ 0 0
$$382$$ 3648.00 0.488607
$$383$$ −12330.0 −1.64500 −0.822498 0.568768i $$-0.807420\pi$$
−0.822498 + 0.568768i $$0.807420\pi$$
$$384$$ 0 0
$$385$$ −1386.00 −0.183473
$$386$$ −4180.00 −0.551182
$$387$$ 0 0
$$388$$ −5320.00 −0.696088
$$389$$ 14586.0 1.90113 0.950565 0.310526i $$-0.100505\pi$$
0.950565 + 0.310526i $$0.100505\pi$$
$$390$$ 0 0
$$391$$ 6480.00 0.838127
$$392$$ −392.000 −0.0505076
$$393$$ 0 0
$$394$$ −3204.00 −0.409683
$$395$$ 20592.0 2.62303
$$396$$ 0 0
$$397$$ 1874.00 0.236910 0.118455 0.992959i $$-0.462206\pi$$
0.118455 + 0.992959i $$0.462206\pi$$
$$398$$ 6548.00 0.824677
$$399$$ 0 0
$$400$$ 3184.00 0.398000
$$401$$ −13338.0 −1.66102 −0.830509 0.557006i $$-0.811950\pi$$
−0.830509 + 0.557006i $$0.811950\pi$$
$$402$$ 0 0
$$403$$ −18704.0 −2.31194
$$404$$ 480.000 0.0591111
$$405$$ 0 0
$$406$$ −756.000 −0.0924129
$$407$$ 4246.00 0.517116
$$408$$ 0 0
$$409$$ −8200.00 −0.991354 −0.495677 0.868507i $$-0.665080\pi$$
−0.495677 + 0.868507i $$0.665080\pi$$
$$410$$ 15984.0 1.92535
$$411$$ 0 0
$$412$$ −4840.00 −0.578761
$$413$$ 1974.00 0.235192
$$414$$ 0 0
$$415$$ 8424.00 0.996429
$$416$$ −1792.00 −0.211202
$$417$$ 0 0
$$418$$ 616.000 0.0720803
$$419$$ 7362.00 0.858370 0.429185 0.903216i $$-0.358801\pi$$
0.429185 + 0.903216i $$0.358801\pi$$
$$420$$ 0 0
$$421$$ −11710.0 −1.35561 −0.677803 0.735243i $$-0.737068\pi$$
−0.677803 + 0.735243i $$0.737068\pi$$
$$422$$ 9896.00 1.14154
$$423$$ 0 0
$$424$$ −3888.00 −0.445325
$$425$$ −7164.00 −0.817659
$$426$$ 0 0
$$427$$ 2660.00 0.301467
$$428$$ −4944.00 −0.558358
$$429$$ 0 0
$$430$$ −11376.0 −1.27581
$$431$$ 936.000 0.104607 0.0523034 0.998631i $$-0.483344\pi$$
0.0523034 + 0.998631i $$0.483344\pi$$
$$432$$ 0 0
$$433$$ 9038.00 1.00309 0.501546 0.865131i $$-0.332765\pi$$
0.501546 + 0.865131i $$0.332765\pi$$
$$434$$ 4676.00 0.517178
$$435$$ 0 0
$$436$$ −2776.00 −0.304923
$$437$$ 5040.00 0.551707
$$438$$ 0 0
$$439$$ 1964.00 0.213523 0.106762 0.994285i $$-0.465952\pi$$
0.106762 + 0.994285i $$0.465952\pi$$
$$440$$ 1584.00 0.171623
$$441$$ 0 0
$$442$$ 4032.00 0.433897
$$443$$ −10068.0 −1.07979 −0.539893 0.841734i $$-0.681535\pi$$
−0.539893 + 0.841734i $$0.681535\pi$$
$$444$$ 0 0
$$445$$ −15660.0 −1.66821
$$446$$ −4684.00 −0.497296
$$447$$ 0 0
$$448$$ 448.000 0.0472456
$$449$$ −3270.00 −0.343699 −0.171849 0.985123i $$-0.554974\pi$$
−0.171849 + 0.985123i $$0.554974\pi$$
$$450$$ 0 0
$$451$$ 4884.00 0.509930
$$452$$ −3912.00 −0.407091
$$453$$ 0 0
$$454$$ 4128.00 0.426733
$$455$$ −7056.00 −0.727012
$$456$$ 0 0
$$457$$ −15526.0 −1.58922 −0.794612 0.607117i $$-0.792326\pi$$
−0.794612 + 0.607117i $$0.792326\pi$$
$$458$$ 3332.00 0.339944
$$459$$ 0 0
$$460$$ 12960.0 1.31362
$$461$$ −10548.0 −1.06566 −0.532830 0.846222i $$-0.678872\pi$$
−0.532830 + 0.846222i $$0.678872\pi$$
$$462$$ 0 0
$$463$$ −3796.00 −0.381026 −0.190513 0.981685i $$-0.561015\pi$$
−0.190513 + 0.981685i $$0.561015\pi$$
$$464$$ 864.000 0.0864444
$$465$$ 0 0
$$466$$ 8316.00 0.826677
$$467$$ −7122.00 −0.705711 −0.352855 0.935678i $$-0.614789\pi$$
−0.352855 + 0.935678i $$0.614789\pi$$
$$468$$ 0 0
$$469$$ 1232.00 0.121297
$$470$$ 14472.0 1.42031
$$471$$ 0 0
$$472$$ −2256.00 −0.220002
$$473$$ −3476.00 −0.337900
$$474$$ 0 0
$$475$$ −5572.00 −0.538233
$$476$$ −1008.00 −0.0970622
$$477$$ 0 0
$$478$$ 144.000 0.0137791
$$479$$ −2292.00 −0.218631 −0.109315 0.994007i $$-0.534866\pi$$
−0.109315 + 0.994007i $$0.534866\pi$$
$$480$$ 0 0
$$481$$ 21616.0 2.04907
$$482$$ −13720.0 −1.29653
$$483$$ 0 0
$$484$$ 484.000 0.0454545
$$485$$ 23940.0 2.24136
$$486$$ 0 0
$$487$$ 5132.00 0.477522 0.238761 0.971078i $$-0.423259\pi$$
0.238761 + 0.971078i $$0.423259\pi$$
$$488$$ −3040.00 −0.281997
$$489$$ 0 0
$$490$$ 1764.00 0.162631
$$491$$ −4188.00 −0.384932 −0.192466 0.981304i $$-0.561649\pi$$
−0.192466 + 0.981304i $$0.561649\pi$$
$$492$$ 0 0
$$493$$ −1944.00 −0.177593
$$494$$ 3136.00 0.285618
$$495$$ 0 0
$$496$$ −5344.00 −0.483776
$$497$$ 2268.00 0.204696
$$498$$ 0 0
$$499$$ 3848.00 0.345211 0.172605 0.984991i $$-0.444781\pi$$
0.172605 + 0.984991i $$0.444781\pi$$
$$500$$ −5328.00 −0.476551
$$501$$ 0 0
$$502$$ −300.000 −0.0266726
$$503$$ 1068.00 0.0946715 0.0473358 0.998879i $$-0.484927\pi$$
0.0473358 + 0.998879i $$0.484927\pi$$
$$504$$ 0 0
$$505$$ −2160.00 −0.190334
$$506$$ 3960.00 0.347912
$$507$$ 0 0
$$508$$ −4864.00 −0.424813
$$509$$ 6162.00 0.536593 0.268297 0.963336i $$-0.413539\pi$$
0.268297 + 0.963336i $$0.413539\pi$$
$$510$$ 0 0
$$511$$ 5600.00 0.484793
$$512$$ −512.000 −0.0441942
$$513$$ 0 0
$$514$$ −4860.00 −0.417053
$$515$$ 21780.0 1.86358
$$516$$ 0 0
$$517$$ 4422.00 0.376169
$$518$$ −5404.00 −0.458375
$$519$$ 0 0
$$520$$ 8064.00 0.680057
$$521$$ 20946.0 1.76135 0.880673 0.473725i $$-0.157091\pi$$
0.880673 + 0.473725i $$0.157091\pi$$
$$522$$ 0 0
$$523$$ −4696.00 −0.392623 −0.196311 0.980542i $$-0.562896\pi$$
−0.196311 + 0.980542i $$0.562896\pi$$
$$524$$ −6720.00 −0.560238
$$525$$ 0 0
$$526$$ 6096.00 0.505320
$$527$$ 12024.0 0.993878
$$528$$ 0 0
$$529$$ 20233.0 1.66294
$$530$$ 17496.0 1.43392
$$531$$ 0 0
$$532$$ −784.000 −0.0638923
$$533$$ 24864.0 2.02060
$$534$$ 0 0
$$535$$ 22248.0 1.79788
$$536$$ −1408.00 −0.113463
$$537$$ 0 0
$$538$$ −7668.00 −0.614481
$$539$$ 539.000 0.0430730
$$540$$ 0 0
$$541$$ 19358.0 1.53838 0.769192 0.639018i $$-0.220659\pi$$
0.769192 + 0.639018i $$0.220659\pi$$
$$542$$ 7016.00 0.556020
$$543$$ 0 0
$$544$$ 1152.00 0.0907934
$$545$$ 12492.0 0.981832
$$546$$ 0 0
$$547$$ 18020.0 1.40855 0.704277 0.709925i $$-0.251271\pi$$
0.704277 + 0.709925i $$0.251271\pi$$
$$548$$ −4248.00 −0.331142
$$549$$ 0 0
$$550$$ −4378.00 −0.339416
$$551$$ −1512.00 −0.116903
$$552$$ 0 0
$$553$$ −8008.00 −0.615795
$$554$$ −16588.0 −1.27212
$$555$$ 0 0
$$556$$ −2032.00 −0.154993
$$557$$ −14622.0 −1.11231 −0.556153 0.831080i $$-0.687723\pi$$
−0.556153 + 0.831080i $$0.687723\pi$$
$$558$$ 0 0
$$559$$ −17696.0 −1.33893
$$560$$ −2016.00 −0.152128
$$561$$ 0 0
$$562$$ 16044.0 1.20423
$$563$$ 2244.00 0.167981 0.0839905 0.996467i $$-0.473233\pi$$
0.0839905 + 0.996467i $$0.473233\pi$$
$$564$$ 0 0
$$565$$ 17604.0 1.31081
$$566$$ −784.000 −0.0582226
$$567$$ 0 0
$$568$$ −2592.00 −0.191475
$$569$$ 3258.00 0.240039 0.120020 0.992772i $$-0.461704\pi$$
0.120020 + 0.992772i $$0.461704\pi$$
$$570$$ 0 0
$$571$$ −6604.00 −0.484008 −0.242004 0.970275i $$-0.577805\pi$$
−0.242004 + 0.970275i $$0.577805\pi$$
$$572$$ 2464.00 0.180114
$$573$$ 0 0
$$574$$ −6216.00 −0.452005
$$575$$ −35820.0 −2.59791
$$576$$ 0 0
$$577$$ −16594.0 −1.19726 −0.598628 0.801027i $$-0.704287\pi$$
−0.598628 + 0.801027i $$0.704287\pi$$
$$578$$ 7234.00 0.520579
$$579$$ 0 0
$$580$$ −3888.00 −0.278346
$$581$$ −3276.00 −0.233927
$$582$$ 0 0
$$583$$ 5346.00 0.379775
$$584$$ −6400.00 −0.453483
$$585$$ 0 0
$$586$$ −5496.00 −0.387436
$$587$$ 19062.0 1.34033 0.670164 0.742213i $$-0.266224\pi$$
0.670164 + 0.742213i $$0.266224\pi$$
$$588$$ 0 0
$$589$$ 9352.00 0.654232
$$590$$ 10152.0 0.708392
$$591$$ 0 0
$$592$$ 6176.00 0.428770
$$593$$ 4776.00 0.330737 0.165368 0.986232i $$-0.447119\pi$$
0.165368 + 0.986232i $$0.447119\pi$$
$$594$$ 0 0
$$595$$ 4536.00 0.312534
$$596$$ −10392.0 −0.714216
$$597$$ 0 0
$$598$$ 20160.0 1.37860
$$599$$ −7956.00 −0.542693 −0.271347 0.962482i $$-0.587469\pi$$
−0.271347 + 0.962482i $$0.587469\pi$$
$$600$$ 0 0
$$601$$ 14348.0 0.973822 0.486911 0.873452i $$-0.338124\pi$$
0.486911 + 0.873452i $$0.338124\pi$$
$$602$$ 4424.00 0.299516
$$603$$ 0 0
$$604$$ 10592.0 0.713547
$$605$$ −2178.00 −0.146361
$$606$$ 0 0
$$607$$ 24488.0 1.63746 0.818729 0.574180i $$-0.194679\pi$$
0.818729 + 0.574180i $$0.194679\pi$$
$$608$$ 896.000 0.0597658
$$609$$ 0 0
$$610$$ 13680.0 0.908011
$$611$$ 22512.0 1.49057
$$612$$ 0 0
$$613$$ −19654.0 −1.29497 −0.647486 0.762078i $$-0.724179\pi$$
−0.647486 + 0.762078i $$0.724179\pi$$
$$614$$ 6128.00 0.402778
$$615$$ 0 0
$$616$$ −616.000 −0.0402911
$$617$$ −2694.00 −0.175780 −0.0878901 0.996130i $$-0.528012\pi$$
−0.0878901 + 0.996130i $$0.528012\pi$$
$$618$$ 0 0
$$619$$ 10178.0 0.660886 0.330443 0.943826i $$-0.392802\pi$$
0.330443 + 0.943826i $$0.392802\pi$$
$$620$$ 24048.0 1.55773
$$621$$ 0 0
$$622$$ 8124.00 0.523702
$$623$$ 6090.00 0.391638
$$624$$ 0 0
$$625$$ −899.000 −0.0575360
$$626$$ 9740.00 0.621867
$$627$$ 0 0
$$628$$ −3160.00 −0.200793
$$629$$ −13896.0 −0.880874
$$630$$ 0 0
$$631$$ −7648.00 −0.482507 −0.241254 0.970462i $$-0.577559\pi$$
−0.241254 + 0.970462i $$0.577559\pi$$
$$632$$ 9152.00 0.576024
$$633$$ 0 0
$$634$$ 9612.00 0.602116
$$635$$ 21888.0 1.36787
$$636$$ 0 0
$$637$$ 2744.00 0.170677
$$638$$ −1188.00 −0.0737200
$$639$$ 0 0
$$640$$ 2304.00 0.142302
$$641$$ −270.000 −0.0166371 −0.00831853 0.999965i $$-0.502648\pi$$
−0.00831853 + 0.999965i $$0.502648\pi$$
$$642$$ 0 0
$$643$$ 16250.0 0.996637 0.498318 0.866994i $$-0.333951\pi$$
0.498318 + 0.866994i $$0.333951\pi$$
$$644$$ −5040.00 −0.308391
$$645$$ 0 0
$$646$$ −2016.00 −0.122784
$$647$$ −10242.0 −0.622341 −0.311170 0.950354i $$-0.600721\pi$$
−0.311170 + 0.950354i $$0.600721\pi$$
$$648$$ 0 0
$$649$$ 3102.00 0.187618
$$650$$ −22288.0 −1.34493
$$651$$ 0 0
$$652$$ −640.000 −0.0384422
$$653$$ 17322.0 1.03807 0.519037 0.854752i $$-0.326291\pi$$
0.519037 + 0.854752i $$0.326291\pi$$
$$654$$ 0 0
$$655$$ 30240.0 1.80393
$$656$$ 7104.00 0.422812
$$657$$ 0 0
$$658$$ −5628.00 −0.333438
$$659$$ −11676.0 −0.690186 −0.345093 0.938569i $$-0.612153\pi$$
−0.345093 + 0.938569i $$0.612153\pi$$
$$660$$ 0 0
$$661$$ −20710.0 −1.21865 −0.609323 0.792922i $$-0.708559\pi$$
−0.609323 + 0.792922i $$0.708559\pi$$
$$662$$ −13240.0 −0.777322
$$663$$ 0 0
$$664$$ 3744.00 0.218818
$$665$$ 3528.00 0.205729
$$666$$ 0 0
$$667$$ −9720.00 −0.564258
$$668$$ −1056.00 −0.0611645
$$669$$ 0 0
$$670$$ 6336.00 0.365345
$$671$$ 4180.00 0.240487
$$672$$ 0 0
$$673$$ −10354.0 −0.593042 −0.296521 0.955026i $$-0.595827\pi$$
−0.296521 + 0.955026i $$0.595827\pi$$
$$674$$ −2188.00 −0.125042
$$675$$ 0 0
$$676$$ 3756.00 0.213701
$$677$$ 10920.0 0.619926 0.309963 0.950749i $$-0.399683\pi$$
0.309963 + 0.950749i $$0.399683\pi$$
$$678$$ 0 0
$$679$$ −9310.00 −0.526193
$$680$$ −5184.00 −0.292349
$$681$$ 0 0
$$682$$ 7348.00 0.412565
$$683$$ −27804.0 −1.55767 −0.778836 0.627227i $$-0.784190\pi$$
−0.778836 + 0.627227i $$0.784190\pi$$
$$684$$ 0 0
$$685$$ 19116.0 1.06626
$$686$$ −686.000 −0.0381802
$$687$$ 0 0
$$688$$ −5056.00 −0.280172
$$689$$ 27216.0 1.50486
$$690$$ 0 0
$$691$$ −25834.0 −1.42225 −0.711123 0.703068i $$-0.751813\pi$$
−0.711123 + 0.703068i $$0.751813\pi$$
$$692$$ −6528.00 −0.358609
$$693$$ 0 0
$$694$$ 6936.00 0.379376
$$695$$ 9144.00 0.499067
$$696$$ 0 0
$$697$$ −15984.0 −0.868633
$$698$$ 16376.0 0.888024
$$699$$ 0 0
$$700$$ 5572.00 0.300860
$$701$$ 10590.0 0.570583 0.285292 0.958441i $$-0.407910\pi$$
0.285292 + 0.958441i $$0.407910\pi$$
$$702$$ 0 0
$$703$$ −10808.0 −0.579846
$$704$$ 704.000 0.0376889
$$705$$ 0 0
$$706$$ −10140.0 −0.540544
$$707$$ 840.000 0.0446838
$$708$$ 0 0
$$709$$ −6802.00 −0.360302 −0.180151 0.983639i $$-0.557659\pi$$
−0.180151 + 0.983639i $$0.557659\pi$$
$$710$$ 11664.0 0.616538
$$711$$ 0 0
$$712$$ −6960.00 −0.366344
$$713$$ 60120.0 3.15780
$$714$$ 0 0
$$715$$ −11088.0 −0.579955
$$716$$ 2832.00 0.147817
$$717$$ 0 0
$$718$$ 3312.00 0.172149
$$719$$ −23010.0 −1.19350 −0.596751 0.802426i $$-0.703542\pi$$
−0.596751 + 0.802426i $$0.703542\pi$$
$$720$$ 0 0
$$721$$ −8470.00 −0.437502
$$722$$ 12150.0 0.626283
$$723$$ 0 0
$$724$$ 3608.00 0.185208
$$725$$ 10746.0 0.550478
$$726$$ 0 0
$$727$$ 4682.00 0.238853 0.119426 0.992843i $$-0.461894\pi$$
0.119426 + 0.992843i $$0.461894\pi$$
$$728$$ −3136.00 −0.159654
$$729$$ 0 0
$$730$$ 28800.0 1.46019
$$731$$ 11376.0 0.575590
$$732$$ 0 0
$$733$$ −17860.0 −0.899965 −0.449982 0.893037i $$-0.648570\pi$$
−0.449982 + 0.893037i $$0.648570\pi$$
$$734$$ −20332.0 −1.02244
$$735$$ 0 0
$$736$$ 5760.00 0.288473
$$737$$ 1936.00 0.0967618
$$738$$ 0 0
$$739$$ 6860.00 0.341474 0.170737 0.985317i $$-0.445385\pi$$
0.170737 + 0.985317i $$0.445385\pi$$
$$740$$ −27792.0 −1.38061
$$741$$ 0 0
$$742$$ −6804.00 −0.336634
$$743$$ 22752.0 1.12341 0.561703 0.827339i $$-0.310147\pi$$
0.561703 + 0.827339i $$0.310147\pi$$
$$744$$ 0 0
$$745$$ 46764.0 2.29973
$$746$$ 5444.00 0.267184
$$747$$ 0 0
$$748$$ −1584.00 −0.0774288
$$749$$ −8652.00 −0.422079
$$750$$ 0 0
$$751$$ 7364.00 0.357811 0.178906 0.983866i $$-0.442744\pi$$
0.178906 + 0.983866i $$0.442744\pi$$
$$752$$ 6432.00 0.311903
$$753$$ 0 0
$$754$$ −6048.00 −0.292116
$$755$$ −47664.0 −2.29758
$$756$$ 0 0
$$757$$ −34378.0 −1.65058 −0.825290 0.564709i $$-0.808989\pi$$
−0.825290 + 0.564709i $$0.808989\pi$$
$$758$$ 11744.0 0.562746
$$759$$ 0 0
$$760$$ −4032.00 −0.192442
$$761$$ −27456.0 −1.30786 −0.653929 0.756556i $$-0.726880\pi$$
−0.653929 + 0.756556i $$0.726880\pi$$
$$762$$ 0 0
$$763$$ −4858.00 −0.230500
$$764$$ −7296.00 −0.345497
$$765$$ 0 0
$$766$$ 24660.0 1.16319
$$767$$ 15792.0 0.743437
$$768$$ 0 0
$$769$$ 7952.00 0.372895 0.186448 0.982465i $$-0.440303\pi$$
0.186448 + 0.982465i $$0.440303\pi$$
$$770$$ 2772.00 0.129735
$$771$$ 0 0
$$772$$ 8360.00 0.389745
$$773$$ 4986.00 0.231997 0.115999 0.993249i $$-0.462993\pi$$
0.115999 + 0.993249i $$0.462993\pi$$
$$774$$ 0 0
$$775$$ −66466.0 −3.08068
$$776$$ 10640.0 0.492208
$$777$$ 0 0
$$778$$ −29172.0 −1.34430
$$779$$ −12432.0 −0.571788
$$780$$ 0 0
$$781$$ 3564.00 0.163291
$$782$$ −12960.0 −0.592645
$$783$$ 0 0
$$784$$ 784.000 0.0357143
$$785$$ 14220.0 0.646540
$$786$$ 0 0
$$787$$ −42748.0 −1.93622 −0.968108 0.250534i $$-0.919394\pi$$
−0.968108 + 0.250534i $$0.919394\pi$$
$$788$$ 6408.00 0.289690
$$789$$ 0 0
$$790$$ −41184.0 −1.85476
$$791$$ −6846.00 −0.307732
$$792$$ 0 0
$$793$$ 21280.0 0.952932
$$794$$ −3748.00 −0.167521
$$795$$ 0 0
$$796$$ −13096.0 −0.583135
$$797$$ −35610.0 −1.58265 −0.791324 0.611397i $$-0.790608\pi$$
−0.791324 + 0.611397i $$0.790608\pi$$
$$798$$ 0 0
$$799$$ −14472.0 −0.640779
$$800$$ −6368.00 −0.281428
$$801$$ 0 0
$$802$$ 26676.0 1.17452
$$803$$ 8800.00 0.386731
$$804$$ 0 0
$$805$$ 22680.0 0.993000
$$806$$ 37408.0 1.63479
$$807$$ 0 0
$$808$$ −960.000 −0.0417979
$$809$$ 17046.0 0.740798 0.370399 0.928873i $$-0.379221\pi$$
0.370399 + 0.928873i $$0.379221\pi$$
$$810$$ 0 0
$$811$$ −2176.00 −0.0942166 −0.0471083 0.998890i $$-0.515001\pi$$
−0.0471083 + 0.998890i $$0.515001\pi$$
$$812$$ 1512.00 0.0653458
$$813$$ 0 0
$$814$$ −8492.00 −0.365657
$$815$$ 2880.00 0.123782
$$816$$ 0 0
$$817$$ 8848.00 0.378889
$$818$$ 16400.0 0.700993
$$819$$ 0 0
$$820$$ −31968.0 −1.36143
$$821$$ −2094.00 −0.0890147 −0.0445074 0.999009i $$-0.514172\pi$$
−0.0445074 + 0.999009i $$0.514172\pi$$
$$822$$ 0 0
$$823$$ 7328.00 0.310374 0.155187 0.987885i $$-0.450402\pi$$
0.155187 + 0.987885i $$0.450402\pi$$
$$824$$ 9680.00 0.409246
$$825$$ 0 0
$$826$$ −3948.00 −0.166306
$$827$$ 12492.0 0.525259 0.262630 0.964897i $$-0.415410\pi$$
0.262630 + 0.964897i $$0.415410\pi$$
$$828$$ 0 0
$$829$$ −37486.0 −1.57050 −0.785249 0.619180i $$-0.787465\pi$$
−0.785249 + 0.619180i $$0.787465\pi$$
$$830$$ −16848.0 −0.704581
$$831$$ 0 0
$$832$$ 3584.00 0.149342
$$833$$ −1764.00 −0.0733721
$$834$$ 0 0
$$835$$ 4752.00 0.196946
$$836$$ −1232.00 −0.0509684
$$837$$ 0 0
$$838$$ −14724.0 −0.606960
$$839$$ 17574.0 0.723149 0.361574 0.932343i $$-0.382239\pi$$
0.361574 + 0.932343i $$0.382239\pi$$
$$840$$ 0 0
$$841$$ −21473.0 −0.880438
$$842$$ 23420.0 0.958559
$$843$$ 0 0
$$844$$ −19792.0 −0.807190
$$845$$ −16902.0 −0.688102
$$846$$ 0 0
$$847$$ 847.000 0.0343604
$$848$$ 7776.00 0.314893
$$849$$ 0 0
$$850$$ 14328.0 0.578172
$$851$$ −69480.0 −2.79876
$$852$$ 0 0
$$853$$ 9440.00 0.378921 0.189460 0.981888i $$-0.439326\pi$$
0.189460 + 0.981888i $$0.439326\pi$$
$$854$$ −5320.00 −0.213169
$$855$$ 0 0
$$856$$ 9888.00 0.394819
$$857$$ 28440.0 1.13360 0.566798 0.823857i $$-0.308182\pi$$
0.566798 + 0.823857i $$0.308182\pi$$
$$858$$ 0 0
$$859$$ −24334.0 −0.966549 −0.483274 0.875469i $$-0.660553\pi$$
−0.483274 + 0.875469i $$0.660553\pi$$
$$860$$ 22752.0 0.902136
$$861$$ 0 0
$$862$$ −1872.00 −0.0739682
$$863$$ −39264.0 −1.54874 −0.774370 0.632733i $$-0.781933\pi$$
−0.774370 + 0.632733i $$0.781933\pi$$
$$864$$ 0 0
$$865$$ 29376.0 1.15470
$$866$$ −18076.0 −0.709293
$$867$$ 0 0
$$868$$ −9352.00 −0.365700
$$869$$ −12584.0 −0.491235
$$870$$ 0 0
$$871$$ 9856.00 0.383419
$$872$$ 5552.00 0.215613
$$873$$ 0 0
$$874$$ −10080.0 −0.390116
$$875$$ −9324.00 −0.360239
$$876$$ 0 0
$$877$$ 32114.0 1.23650 0.618251 0.785981i $$-0.287841\pi$$
0.618251 + 0.785981i $$0.287841\pi$$
$$878$$ −3928.00 −0.150984
$$879$$ 0 0
$$880$$ −3168.00 −0.121356
$$881$$ −41454.0 −1.58527 −0.792634 0.609698i $$-0.791291\pi$$
−0.792634 + 0.609698i $$0.791291\pi$$
$$882$$ 0 0
$$883$$ 2876.00 0.109609 0.0548047 0.998497i $$-0.482546\pi$$
0.0548047 + 0.998497i $$0.482546\pi$$
$$884$$ −8064.00 −0.306812
$$885$$ 0 0
$$886$$ 20136.0 0.763524
$$887$$ −13932.0 −0.527385 −0.263693 0.964607i $$-0.584940\pi$$
−0.263693 + 0.964607i $$0.584940\pi$$
$$888$$ 0 0
$$889$$ −8512.00 −0.321129
$$890$$ 31320.0 1.17961
$$891$$ 0 0
$$892$$ 9368.00 0.351641
$$893$$ −11256.0 −0.421800
$$894$$ 0 0
$$895$$ −12744.0 −0.475961
$$896$$ −896.000 −0.0334077
$$897$$ 0 0
$$898$$ 6540.00 0.243032
$$899$$ −18036.0 −0.669115
$$900$$ 0 0
$$901$$ −17496.0 −0.646921
$$902$$ −9768.00 −0.360575
$$903$$ 0 0
$$904$$ 7824.00 0.287857
$$905$$ −16236.0 −0.596357
$$906$$ 0 0
$$907$$ −19768.0 −0.723689 −0.361844 0.932239i $$-0.617853\pi$$
−0.361844 + 0.932239i $$0.617853\pi$$
$$908$$ −8256.00 −0.301746
$$909$$ 0 0
$$910$$ 14112.0 0.514075
$$911$$ −43836.0 −1.59424 −0.797119 0.603822i $$-0.793644\pi$$
−0.797119 + 0.603822i $$0.793644\pi$$
$$912$$ 0 0
$$913$$ −5148.00 −0.186609
$$914$$ 31052.0 1.12375
$$915$$ 0 0
$$916$$ −6664.00 −0.240376
$$917$$ −11760.0 −0.423500
$$918$$ 0 0
$$919$$ 31544.0 1.13225 0.566127 0.824318i $$-0.308441\pi$$
0.566127 + 0.824318i $$0.308441\pi$$
$$920$$ −25920.0 −0.928866
$$921$$ 0 0
$$922$$ 21096.0 0.753536
$$923$$ 18144.0 0.647039
$$924$$ 0 0
$$925$$ 76814.0 2.73041
$$926$$ 7592.00 0.269426
$$927$$ 0 0
$$928$$ −1728.00 −0.0611254
$$929$$ −11118.0 −0.392648 −0.196324 0.980539i $$-0.562900\pi$$
−0.196324 + 0.980539i $$0.562900\pi$$
$$930$$ 0 0
$$931$$ −1372.00 −0.0482980
$$932$$ −16632.0 −0.584549
$$933$$ 0 0
$$934$$ 14244.0 0.499013
$$935$$ 7128.00 0.249316
$$936$$ 0 0
$$937$$ 10568.0 0.368454 0.184227 0.982884i $$-0.441022\pi$$
0.184227 + 0.982884i $$0.441022\pi$$
$$938$$ −2464.00 −0.0857702
$$939$$ 0 0
$$940$$ −28944.0 −1.00431
$$941$$ −14964.0 −0.518398 −0.259199 0.965824i $$-0.583459\pi$$
−0.259199 + 0.965824i $$0.583459\pi$$
$$942$$ 0 0
$$943$$ −79920.0 −2.75987
$$944$$ 4512.00 0.155565
$$945$$ 0 0
$$946$$ 6952.00 0.238931
$$947$$ −3324.00 −0.114061 −0.0570304 0.998372i $$-0.518163\pi$$
−0.0570304 + 0.998372i $$0.518163\pi$$
$$948$$ 0 0
$$949$$ 44800.0 1.53242
$$950$$ 11144.0 0.380589
$$951$$ 0 0
$$952$$ 2016.00 0.0686333
$$953$$ −3906.00 −0.132768 −0.0663839 0.997794i $$-0.521146\pi$$
−0.0663839 + 0.997794i $$0.521146\pi$$
$$954$$ 0 0
$$955$$ 32832.0 1.11248
$$956$$ −288.000 −0.00974329
$$957$$ 0 0
$$958$$ 4584.00 0.154595
$$959$$ −7434.00 −0.250319
$$960$$ 0 0
$$961$$ 81765.0 2.74462
$$962$$ −43232.0 −1.44891
$$963$$ 0 0
$$964$$ 27440.0 0.916787
$$965$$ −37620.0 −1.25495
$$966$$ 0 0
$$967$$ −36448.0 −1.21209 −0.606044 0.795431i $$-0.707244\pi$$
−0.606044 + 0.795431i $$0.707244\pi$$
$$968$$ −968.000 −0.0321412
$$969$$ 0 0
$$970$$ −47880.0 −1.58488
$$971$$ 20526.0 0.678384 0.339192 0.940717i $$-0.389846\pi$$
0.339192 + 0.940717i $$0.389846\pi$$
$$972$$ 0 0
$$973$$ −3556.00 −0.117164
$$974$$ −10264.0 −0.337659
$$975$$ 0 0
$$976$$ 6080.00 0.199402
$$977$$ −37434.0 −1.22581 −0.612907 0.790155i $$-0.710000\pi$$
−0.612907 + 0.790155i $$0.710000\pi$$
$$978$$ 0 0
$$979$$ 9570.00 0.312419
$$980$$ −3528.00 −0.114998
$$981$$ 0 0
$$982$$ 8376.00 0.272188
$$983$$ 52194.0 1.69352 0.846760 0.531975i $$-0.178550\pi$$
0.846760 + 0.531975i $$0.178550\pi$$
$$984$$ 0 0
$$985$$ −28836.0 −0.932783
$$986$$ 3888.00 0.125577
$$987$$ 0 0
$$988$$ −6272.00 −0.201962
$$989$$ 56880.0 1.82880
$$990$$ 0 0
$$991$$ −15220.0 −0.487870 −0.243935 0.969792i $$-0.578438\pi$$
−0.243935 + 0.969792i $$0.578438\pi$$
$$992$$ 10688.0 0.342081
$$993$$ 0 0
$$994$$ −4536.00 −0.144742
$$995$$ 58932.0 1.87766
$$996$$ 0 0
$$997$$ 37664.0 1.19642 0.598210 0.801339i $$-0.295879\pi$$
0.598210 + 0.801339i $$0.295879\pi$$
$$998$$ −7696.00 −0.244101
$$999$$ 0 0
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 1386.4.a.a.1.1 1
3.2 odd 2 154.4.a.d.1.1 1
12.11 even 2 1232.4.a.f.1.1 1
21.20 even 2 1078.4.a.g.1.1 1
33.32 even 2 1694.4.a.c.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.d.1.1 1 3.2 odd 2
1078.4.a.g.1.1 1 21.20 even 2
1232.4.a.f.1.1 1 12.11 even 2
1386.4.a.a.1.1 1 1.1 even 1 trivial
1694.4.a.c.1.1 1 33.32 even 2