# Properties

 Label 1232.4.a.f.1.1 Level $1232$ Weight $4$ Character 1232.1 Self dual yes Analytic conductor $72.690$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1232 = 2^{4} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1232.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$72.6903531271$$ Analytic rank: $$0$$ 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 $$\chi$$ $$=$$ 1232.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} +18.0000 q^{5} -7.00000 q^{7} -23.0000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} +18.0000 q^{5} -7.00000 q^{7} -23.0000 q^{9} +11.0000 q^{11} +56.0000 q^{13} +36.0000 q^{15} +36.0000 q^{17} +28.0000 q^{19} -14.0000 q^{21} -180.000 q^{23} +199.000 q^{25} -100.000 q^{27} -54.0000 q^{29} +334.000 q^{31} +22.0000 q^{33} -126.000 q^{35} +386.000 q^{37} +112.000 q^{39} -444.000 q^{41} +316.000 q^{43} -414.000 q^{45} +402.000 q^{47} +49.0000 q^{49} +72.0000 q^{51} -486.000 q^{53} +198.000 q^{55} +56.0000 q^{57} +282.000 q^{59} +380.000 q^{61} +161.000 q^{63} +1008.00 q^{65} -176.000 q^{67} -360.000 q^{69} +324.000 q^{71} +800.000 q^{73} +398.000 q^{75} -77.0000 q^{77} +1144.00 q^{79} +421.000 q^{81} -468.000 q^{83} +648.000 q^{85} -108.000 q^{87} -870.000 q^{89} -392.000 q^{91} +668.000 q^{93} +504.000 q^{95} -1330.00 q^{97} -253.000 q^{99} +O(q^{100})$$

## 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
$$5$$ 18.0000 1.60997 0.804984 0.593296i $$-0.202174\pi$$
0.804984 + 0.593296i $$0.202174\pi$$
$$6$$ 0 0
$$7$$ −7.00000 −0.377964
$$8$$ 0 0
$$9$$ −23.0000 −0.851852
$$10$$ 0 0
$$11$$ 11.0000 0.301511
$$12$$ 0 0
$$13$$ 56.0000 1.19474 0.597369 0.801966i $$-0.296213\pi$$
0.597369 + 0.801966i $$0.296213\pi$$
$$14$$ 0 0
$$15$$ 36.0000 0.619677
$$16$$ 0 0
$$17$$ 36.0000 0.513605 0.256802 0.966464i $$-0.417331\pi$$
0.256802 + 0.966464i $$0.417331\pi$$
$$18$$ 0 0
$$19$$ 28.0000 0.338086 0.169043 0.985609i $$-0.445932\pi$$
0.169043 + 0.985609i $$0.445932\pi$$
$$20$$ 0 0
$$21$$ −14.0000 −0.145479
$$22$$ 0 0
$$23$$ −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
$$26$$ 0 0
$$27$$ −100.000 −0.712778
$$28$$ 0 0
$$29$$ −54.0000 −0.345778 −0.172889 0.984941i $$-0.555310\pi$$
−0.172889 + 0.984941i $$0.555310\pi$$
$$30$$ 0 0
$$31$$ 334.000 1.93510 0.967551 0.252675i $$-0.0813104\pi$$
0.967551 + 0.252675i $$0.0813104\pi$$
$$32$$ 0 0
$$33$$ 22.0000 0.116052
$$34$$ 0 0
$$35$$ −126.000 −0.608511
$$36$$ 0 0
$$37$$ 386.000 1.71508 0.857541 0.514416i $$-0.171991\pi$$
0.857541 + 0.514416i $$0.171991\pi$$
$$38$$ 0 0
$$39$$ 112.000 0.459855
$$40$$ 0 0
$$41$$ −444.000 −1.69125 −0.845624 0.533779i $$-0.820771\pi$$
−0.845624 + 0.533779i $$0.820771\pi$$
$$42$$ 0 0
$$43$$ 316.000 1.12069 0.560344 0.828260i $$-0.310669\pi$$
0.560344 + 0.828260i $$0.310669\pi$$
$$44$$ 0 0
$$45$$ −414.000 −1.37146
$$46$$ 0 0
$$47$$ 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
$$50$$ 0 0
$$51$$ 72.0000 0.197687
$$52$$ 0 0
$$53$$ −486.000 −1.25957 −0.629785 0.776769i $$-0.716857\pi$$
−0.629785 + 0.776769i $$0.716857\pi$$
$$54$$ 0 0
$$55$$ 198.000 0.485424
$$56$$ 0 0
$$57$$ 56.0000 0.130129
$$58$$ 0 0
$$59$$ 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 $$0.369426\pi$$
$$62$$ 0 0
$$63$$ 161.000 0.321970
$$64$$ 0 0
$$65$$ 1008.00 1.92349
$$66$$ 0 0
$$67$$ −176.000 −0.320923 −0.160461 0.987042i $$-0.551298\pi$$
−0.160461 + 0.987042i $$0.551298\pi$$
$$68$$ 0 0
$$69$$ −360.000 −0.628100
$$70$$ 0 0
$$71$$ 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 $$0.278387\pi$$
$$74$$ 0 0
$$75$$ 398.000 0.612761
$$76$$ 0 0
$$77$$ −77.0000 −0.113961
$$78$$ 0 0
$$79$$ 1144.00 1.62924 0.814621 0.579994i $$-0.196945\pi$$
0.814621 + 0.579994i $$0.196945\pi$$
$$80$$ 0 0
$$81$$ 421.000 0.577503
$$82$$ 0 0
$$83$$ −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
$$86$$ 0 0
$$87$$ −108.000 −0.133090
$$88$$ 0 0
$$89$$ −870.000 −1.03618 −0.518089 0.855327i $$-0.673356\pi$$
−0.518089 + 0.855327i $$0.673356\pi$$
$$90$$ 0 0
$$91$$ −392.000 −0.451569
$$92$$ 0 0
$$93$$ 668.000 0.744821
$$94$$ 0 0
$$95$$ 504.000 0.544309
$$96$$ 0 0
$$97$$ −1330.00 −1.39218 −0.696088 0.717957i $$-0.745078\pi$$
−0.696088 + 0.717957i $$0.745078\pi$$
$$98$$ 0 0
$$99$$ −253.000 −0.256843
$$100$$ 0 0
$$101$$ −120.000 −0.118222 −0.0591111 0.998251i $$-0.518827\pi$$
−0.0591111 + 0.998251i $$0.518827\pi$$
$$102$$ 0 0
$$103$$ 1210.00 1.15752 0.578761 0.815497i $$-0.303536\pi$$
0.578761 + 0.815497i $$0.303536\pi$$
$$104$$ 0 0
$$105$$ −252.000 −0.234216
$$106$$ 0 0
$$107$$ −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 $$0.598631\pi$$
$$110$$ 0 0
$$111$$ 772.000 0.660135
$$112$$ 0 0
$$113$$ 978.000 0.814181 0.407091 0.913388i $$-0.366543\pi$$
0.407091 + 0.913388i $$0.366543\pi$$
$$114$$ 0 0
$$115$$ −3240.00 −2.62723
$$116$$ 0 0
$$117$$ −1288.00 −1.01774
$$118$$ 0 0
$$119$$ −252.000 −0.194124
$$120$$ 0 0
$$121$$ 121.000 0.0909091
$$122$$ 0 0
$$123$$ −888.000 −0.650961
$$124$$ 0 0
$$125$$ 1332.00 0.953102
$$126$$ 0 0
$$127$$ 1216.00 0.849626 0.424813 0.905281i $$-0.360340\pi$$
0.424813 + 0.905281i $$0.360340\pi$$
$$128$$ 0 0
$$129$$ 632.000 0.431353
$$130$$ 0 0
$$131$$ −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
$$134$$ 0 0
$$135$$ −1800.00 −1.14755
$$136$$ 0 0
$$137$$ 1062.00 0.662283 0.331142 0.943581i $$-0.392566\pi$$
0.331142 + 0.943581i $$0.392566\pi$$
$$138$$ 0 0
$$139$$ 508.000 0.309986 0.154993 0.987916i $$-0.450465\pi$$
0.154993 + 0.987916i $$0.450465\pi$$
$$140$$ 0 0
$$141$$ 804.000 0.480206
$$142$$ 0 0
$$143$$ 616.000 0.360227
$$144$$ 0 0
$$145$$ −972.000 −0.556691
$$146$$ 0 0
$$147$$ 98.0000 0.0549857
$$148$$ 0 0
$$149$$ 2598.00 1.42843 0.714216 0.699925i $$-0.246783\pi$$
0.714216 + 0.699925i $$0.246783\pi$$
$$150$$ 0 0
$$151$$ −2648.00 −1.42709 −0.713547 0.700607i $$-0.752912\pi$$
−0.713547 + 0.700607i $$0.752912\pi$$
$$152$$ 0 0
$$153$$ −828.000 −0.437515
$$154$$ 0 0
$$155$$ 6012.00 3.11545
$$156$$ 0 0
$$157$$ −790.000 −0.401585 −0.200793 0.979634i $$-0.564352\pi$$
−0.200793 + 0.979634i $$0.564352\pi$$
$$158$$ 0 0
$$159$$ −972.000 −0.484809
$$160$$ 0 0
$$161$$ 1260.00 0.616782
$$162$$ 0 0
$$163$$ 160.000 0.0768845 0.0384422 0.999261i $$-0.487760\pi$$
0.0384422 + 0.999261i $$0.487760\pi$$
$$164$$ 0 0
$$165$$ 396.000 0.186840
$$166$$ 0 0
$$167$$ −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
$$170$$ 0 0
$$171$$ −644.000 −0.287999
$$172$$ 0 0
$$173$$ 1632.00 0.717218 0.358609 0.933488i $$-0.383251\pi$$
0.358609 + 0.933488i $$0.383251\pi$$
$$174$$ 0 0
$$175$$ −1393.00 −0.601719
$$176$$ 0 0
$$177$$ 564.000 0.239508
$$178$$ 0 0
$$179$$ 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 $$0.440704\pi$$
$$182$$ 0 0
$$183$$ 760.000 0.306999
$$184$$ 0 0
$$185$$ 6948.00 2.76123
$$186$$ 0 0
$$187$$ 396.000 0.154858
$$188$$ 0 0
$$189$$ 700.000 0.269405
$$190$$ 0 0
$$191$$ −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 $$0.372563\pi$$
$$194$$ 0 0
$$195$$ 2016.00 0.740353
$$196$$ 0 0
$$197$$ −1602.00 −0.579380 −0.289690 0.957121i $$-0.593552\pi$$
−0.289690 + 0.957121i $$0.593552\pi$$
$$198$$ 0 0
$$199$$ 3274.00 1.16627 0.583135 0.812375i $$-0.301826\pi$$
0.583135 + 0.812375i $$0.301826\pi$$
$$200$$ 0 0
$$201$$ −352.000 −0.123523
$$202$$ 0 0
$$203$$ 378.000 0.130692
$$204$$ 0 0
$$205$$ −7992.00 −2.72286
$$206$$ 0 0
$$207$$ 4140.00 1.39010
$$208$$ 0 0
$$209$$ 308.000 0.101937
$$210$$ 0 0
$$211$$ 4948.00 1.61438 0.807190 0.590291i $$-0.200987\pi$$
0.807190 + 0.590291i $$0.200987\pi$$
$$212$$ 0 0
$$213$$ 648.000 0.208452
$$214$$ 0 0
$$215$$ 5688.00 1.80427
$$216$$ 0 0
$$217$$ −2338.00 −0.731400
$$218$$ 0 0
$$219$$ 1600.00 0.493689
$$220$$ 0 0
$$221$$ 2016.00 0.613624
$$222$$ 0 0
$$223$$ −2342.00 −0.703282 −0.351641 0.936135i $$-0.614376\pi$$
−0.351641 + 0.936135i $$0.614376\pi$$
$$224$$ 0 0
$$225$$ −4577.00 −1.35615
$$226$$ 0 0
$$227$$ −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 $$0.577271\pi$$
$$230$$ 0 0
$$231$$ −154.000 −0.0438634
$$232$$ 0 0
$$233$$ 4158.00 1.16910 0.584549 0.811359i $$-0.301272\pi$$
0.584549 + 0.811359i $$0.301272\pi$$
$$234$$ 0 0
$$235$$ 7236.00 2.00862
$$236$$ 0 0
$$237$$ 2288.00 0.627095
$$238$$ 0 0
$$239$$ −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 $$0.130773\pi$$
$$242$$ 0 0
$$243$$ 3542.00 0.935059
$$244$$ 0 0
$$245$$ 882.000 0.229996
$$246$$ 0 0
$$247$$ 1568.00 0.403925
$$248$$ 0 0
$$249$$ −936.000 −0.238219
$$250$$ 0 0
$$251$$ 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
$$254$$ 0 0
$$255$$ 1296.00 0.318269
$$256$$ 0 0
$$257$$ −2430.00 −0.589802 −0.294901 0.955528i $$-0.595287\pi$$
−0.294901 + 0.955528i $$0.595287\pi$$
$$258$$ 0 0
$$259$$ −2702.00 −0.648240
$$260$$ 0 0
$$261$$ 1242.00 0.294551
$$262$$ 0 0
$$263$$ −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
$$266$$ 0 0
$$267$$ −1740.00 −0.398825
$$268$$ 0 0
$$269$$ −3834.00 −0.869008 −0.434504 0.900670i $$-0.643076\pi$$
−0.434504 + 0.900670i $$0.643076\pi$$
$$270$$ 0 0
$$271$$ 3508.00 0.786331 0.393166 0.919468i $$-0.371380\pi$$
0.393166 + 0.919468i $$0.371380\pi$$
$$272$$ 0 0
$$273$$ −784.000 −0.173809
$$274$$ 0 0
$$275$$ 2189.00 0.480006
$$276$$ 0 0
$$277$$ 8294.00 1.79905 0.899527 0.436864i $$-0.143911\pi$$
0.899527 + 0.436864i $$0.143911\pi$$
$$278$$ 0 0
$$279$$ −7682.00 −1.64842
$$280$$ 0 0
$$281$$ 8022.00 1.70303 0.851517 0.524327i $$-0.175683\pi$$
0.851517 + 0.524327i $$0.175683\pi$$
$$282$$ 0 0
$$283$$ −392.000 −0.0823392 −0.0411696 0.999152i $$-0.513108\pi$$
−0.0411696 + 0.999152i $$0.513108\pi$$
$$284$$ 0 0
$$285$$ 1008.00 0.209504
$$286$$ 0 0
$$287$$ 3108.00 0.639231
$$288$$ 0 0
$$289$$ −3617.00 −0.736210
$$290$$ 0 0
$$291$$ −2660.00 −0.535849
$$292$$ 0 0
$$293$$ −2748.00 −0.547918 −0.273959 0.961741i $$-0.588333\pi$$
−0.273959 + 0.961741i $$0.588333\pi$$
$$294$$ 0 0
$$295$$ 5076.00 1.00182
$$296$$ 0 0
$$297$$ −1100.00 −0.214911
$$298$$ 0 0
$$299$$ −10080.0 −1.94964
$$300$$ 0 0
$$301$$ −2212.00 −0.423580
$$302$$ 0 0
$$303$$ −240.000 −0.0455038
$$304$$ 0 0
$$305$$ 6840.00 1.28412
$$306$$ 0 0
$$307$$ 3064.00 0.569615 0.284807 0.958585i $$-0.408070\pi$$
0.284807 + 0.958585i $$0.408070\pi$$
$$308$$ 0 0
$$309$$ 2420.00 0.445531
$$310$$ 0 0
$$311$$ −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 $$0.644925\pi$$
$$314$$ 0 0
$$315$$ 2898.00 0.518361
$$316$$ 0 0
$$317$$ 4806.00 0.851520 0.425760 0.904836i $$-0.360007\pi$$
0.425760 + 0.904836i $$0.360007\pi$$
$$318$$ 0 0
$$319$$ −594.000 −0.104256
$$320$$ 0 0
$$321$$ −2472.00 −0.429824
$$322$$ 0 0
$$323$$ 1008.00 0.173643
$$324$$ 0 0
$$325$$ 11144.0 1.90202
$$326$$ 0 0
$$327$$ −1388.00 −0.234730
$$328$$ 0 0
$$329$$ −2814.00 −0.471553
$$330$$ 0 0
$$331$$ −6620.00 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ 0 0
$$333$$ −8878.00 −1.46100
$$334$$ 0 0
$$335$$ −3168.00 −0.516676
$$336$$ 0 0
$$337$$ 1094.00 0.176837 0.0884184 0.996083i $$-0.471819\pi$$
0.0884184 + 0.996083i $$0.471819\pi$$
$$338$$ 0 0
$$339$$ 1956.00 0.313379
$$340$$ 0 0
$$341$$ 3674.00 0.583455
$$342$$ 0 0
$$343$$ −343.000 −0.0539949
$$344$$ 0 0
$$345$$ −6480.00 −1.01122
$$346$$ 0 0
$$347$$ −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 $$0.716097\pi$$
$$350$$ 0 0
$$351$$ −5600.00 −0.851584
$$352$$ 0 0
$$353$$ −5070.00 −0.764444 −0.382222 0.924070i $$-0.624841\pi$$
−0.382222 + 0.924070i $$0.624841\pi$$
$$354$$ 0 0
$$355$$ 5832.00 0.871917
$$356$$ 0 0
$$357$$ −504.000 −0.0747185
$$358$$ 0 0
$$359$$ −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
$$362$$ 0 0
$$363$$ 242.000 0.0349909
$$364$$ 0 0
$$365$$ 14400.0 2.06501
$$366$$ 0 0
$$367$$ −10166.0 −1.44594 −0.722971 0.690878i $$-0.757224\pi$$
−0.722971 + 0.690878i $$0.757224\pi$$
$$368$$ 0 0
$$369$$ 10212.0 1.44069
$$370$$ 0 0
$$371$$ 3402.00 0.476073
$$372$$ 0 0
$$373$$ −2722.00 −0.377855 −0.188927 0.981991i $$-0.560501\pi$$
−0.188927 + 0.981991i $$0.560501\pi$$
$$374$$ 0 0
$$375$$ 2664.00 0.366849
$$376$$ 0 0
$$377$$ −3024.00 −0.413114
$$378$$ 0 0
$$379$$ 5872.00 0.795843 0.397921 0.917420i $$-0.369732\pi$$
0.397921 + 0.917420i $$0.369732\pi$$
$$380$$ 0 0
$$381$$ 2432.00 0.327021
$$382$$ 0 0
$$383$$ −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
$$386$$ 0 0
$$387$$ −7268.00 −0.954659
$$388$$ 0 0
$$389$$ −14586.0 −1.90113 −0.950565 0.310526i $$-0.899495\pi$$
−0.950565 + 0.310526i $$0.899495\pi$$
$$390$$ 0 0
$$391$$ −6480.00 −0.838127
$$392$$ 0 0
$$393$$ −3360.00 −0.431271
$$394$$ 0 0
$$395$$ 20592.0 2.62303
$$396$$ 0 0
$$397$$ 1874.00 0.236910 0.118455 0.992959i $$-0.462206\pi$$
0.118455 + 0.992959i $$0.462206\pi$$
$$398$$ 0 0
$$399$$ −392.000 −0.0491843
$$400$$ 0 0
$$401$$ 13338.0 1.66102 0.830509 0.557006i $$-0.188050\pi$$
0.830509 + 0.557006i $$0.188050\pi$$
$$402$$ 0 0
$$403$$ 18704.0 2.31194
$$404$$ 0 0
$$405$$ 7578.00 0.929763
$$406$$ 0 0
$$407$$ 4246.00 0.517116
$$408$$ 0 0
$$409$$ −8200.00 −0.991354 −0.495677 0.868507i $$-0.665080\pi$$
−0.495677 + 0.868507i $$0.665080\pi$$
$$410$$ 0 0
$$411$$ 2124.00 0.254913
$$412$$ 0 0
$$413$$ −1974.00 −0.235192
$$414$$ 0 0
$$415$$ −8424.00 −0.996429
$$416$$ 0 0
$$417$$ 1016.00 0.119314
$$418$$ 0 0
$$419$$ 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 $$0.737068\pi$$
$$422$$ 0 0
$$423$$ −9246.00 −1.06278
$$424$$ 0 0
$$425$$ 7164.00 0.817659
$$426$$ 0 0
$$427$$ −2660.00 −0.301467
$$428$$ 0 0
$$429$$ 1232.00 0.138652
$$430$$ 0 0
$$431$$ 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 $$0.332765\pi$$
$$434$$ 0 0
$$435$$ −1944.00 −0.214270
$$436$$ 0 0
$$437$$ −5040.00 −0.551707
$$438$$ 0 0
$$439$$ −1964.00 −0.213523 −0.106762 0.994285i $$-0.534048\pi$$
−0.106762 + 0.994285i $$0.534048\pi$$
$$440$$ 0 0
$$441$$ −1127.00 −0.121693
$$442$$ 0 0
$$443$$ −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
$$446$$ 0 0
$$447$$ 5196.00 0.549804
$$448$$ 0 0
$$449$$ 3270.00 0.343699 0.171849 0.985123i $$-0.445026\pi$$
0.171849 + 0.985123i $$0.445026\pi$$
$$450$$ 0 0
$$451$$ −4884.00 −0.509930
$$452$$ 0 0
$$453$$ −5296.00 −0.549289
$$454$$ 0 0
$$455$$ −7056.00 −0.727012
$$456$$ 0 0
$$457$$ −15526.0 −1.58922 −0.794612 0.607117i $$-0.792326\pi$$
−0.794612 + 0.607117i $$0.792326\pi$$
$$458$$ 0 0
$$459$$ −3600.00 −0.366086
$$460$$ 0 0
$$461$$ 10548.0 1.06566 0.532830 0.846222i $$-0.321128\pi$$
0.532830 + 0.846222i $$0.321128\pi$$
$$462$$ 0 0
$$463$$ 3796.00 0.381026 0.190513 0.981685i $$-0.438985\pi$$
0.190513 + 0.981685i $$0.438985\pi$$
$$464$$ 0 0
$$465$$ 12024.0 1.19914
$$466$$ 0 0
$$467$$ −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
$$470$$ 0 0
$$471$$ −1580.00 −0.154570
$$472$$ 0 0
$$473$$ 3476.00 0.337900
$$474$$ 0 0
$$475$$ 5572.00 0.538233
$$476$$ 0 0
$$477$$ 11178.0 1.07297
$$478$$ 0 0
$$479$$ −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
$$482$$ 0 0
$$483$$ 2520.00 0.237400
$$484$$ 0 0
$$485$$ −23940.0 −2.24136
$$486$$ 0 0
$$487$$ −5132.00 −0.477522 −0.238761 0.971078i $$-0.576741\pi$$
−0.238761 + 0.971078i $$0.576741\pi$$
$$488$$ 0 0
$$489$$ 320.000 0.0295928
$$490$$ 0 0
$$491$$ −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
$$494$$ 0 0
$$495$$ −4554.00 −0.413509
$$496$$ 0 0
$$497$$ −2268.00 −0.204696
$$498$$ 0 0
$$499$$ −3848.00 −0.345211 −0.172605 0.984991i $$-0.555219\pi$$
−0.172605 + 0.984991i $$0.555219\pi$$
$$500$$ 0 0
$$501$$ −528.000 −0.0470844
$$502$$ 0 0
$$503$$ 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
$$506$$ 0 0
$$507$$ 1878.00 0.164507
$$508$$ 0 0
$$509$$ −6162.00 −0.536593 −0.268297 0.963336i $$-0.586461\pi$$
−0.268297 + 0.963336i $$0.586461\pi$$
$$510$$ 0 0
$$511$$ −5600.00 −0.484793
$$512$$ 0 0
$$513$$ −2800.00 −0.240981
$$514$$ 0 0
$$515$$ 21780.0 1.86358
$$516$$ 0 0
$$517$$ 4422.00 0.376169
$$518$$ 0 0
$$519$$ 3264.00 0.276057
$$520$$ 0 0
$$521$$ −20946.0 −1.76135 −0.880673 0.473725i $$-0.842909\pi$$
−0.880673 + 0.473725i $$0.842909\pi$$
$$522$$ 0 0
$$523$$ 4696.00 0.392623 0.196311 0.980542i $$-0.437104\pi$$
0.196311 + 0.980542i $$0.437104\pi$$
$$524$$ 0 0
$$525$$ −2786.00 −0.231602
$$526$$ 0 0
$$527$$ 12024.0 0.993878
$$528$$ 0 0
$$529$$ 20233.0 1.66294
$$530$$ 0 0
$$531$$ −6486.00 −0.530072
$$532$$ 0 0
$$533$$ −24864.0 −2.02060
$$534$$ 0 0
$$535$$ −22248.0 −1.79788
$$536$$ 0 0
$$537$$ 1416.00 0.113789
$$538$$ 0 0
$$539$$ 539.000 0.0430730
$$540$$ 0 0
$$541$$ 19358.0 1.53838 0.769192 0.639018i $$-0.220659\pi$$
0.769192 + 0.639018i $$0.220659\pi$$
$$542$$ 0 0
$$543$$ 1804.00 0.142573
$$544$$ 0 0
$$545$$ −12492.0 −0.981832
$$546$$ 0 0
$$547$$ −18020.0 −1.40855 −0.704277 0.709925i $$-0.748729\pi$$
−0.704277 + 0.709925i $$0.748729\pi$$
$$548$$ 0 0
$$549$$ −8740.00 −0.679443
$$550$$ 0 0
$$551$$ −1512.00 −0.116903
$$552$$ 0 0
$$553$$ −8008.00 −0.615795
$$554$$ 0 0
$$555$$ 13896.0 1.06280
$$556$$ 0 0
$$557$$ 14622.0 1.11231 0.556153 0.831080i $$-0.312277\pi$$
0.556153 + 0.831080i $$0.312277\pi$$
$$558$$ 0 0
$$559$$ 17696.0 1.33893
$$560$$ 0 0
$$561$$ 792.000 0.0596048
$$562$$ 0 0
$$563$$ 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
$$566$$ 0 0
$$567$$ −2947.00 −0.218276
$$568$$ 0 0
$$569$$ −3258.00 −0.240039 −0.120020 0.992772i $$-0.538296\pi$$
−0.120020 + 0.992772i $$0.538296\pi$$
$$570$$ 0 0
$$571$$ 6604.00 0.484008 0.242004 0.970275i $$-0.422195\pi$$
0.242004 + 0.970275i $$0.422195\pi$$
$$572$$ 0 0
$$573$$ −3648.00 −0.265964
$$574$$ 0 0
$$575$$ −35820.0 −2.59791
$$576$$ 0 0
$$577$$ −16594.0 −1.19726 −0.598628 0.801027i $$-0.704287\pi$$
−0.598628 + 0.801027i $$0.704287\pi$$
$$578$$ 0 0
$$579$$ 4180.00 0.300026
$$580$$ 0 0
$$581$$ 3276.00 0.233927
$$582$$ 0 0
$$583$$ −5346.00 −0.379775
$$584$$ 0 0
$$585$$ −23184.0 −1.63853
$$586$$ 0 0
$$587$$ 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
$$590$$ 0 0
$$591$$ −3204.00 −0.223003
$$592$$ 0 0
$$593$$ −4776.00 −0.330737 −0.165368 0.986232i $$-0.552881\pi$$
−0.165368 + 0.986232i $$0.552881\pi$$
$$594$$ 0 0
$$595$$ −4536.00 −0.312534
$$596$$ 0 0
$$597$$ 6548.00 0.448897
$$598$$ 0 0
$$599$$ −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 $$0.338124\pi$$
$$602$$ 0 0
$$603$$ 4048.00 0.273379
$$604$$ 0 0
$$605$$ 2178.00 0.146361
$$606$$ 0 0
$$607$$ −24488.0 −1.63746 −0.818729 0.574180i $$-0.805321\pi$$
−0.818729 + 0.574180i $$0.805321\pi$$
$$608$$ 0 0
$$609$$ 756.000 0.0503032
$$610$$ 0 0
$$611$$ 22512.0 1.49057
$$612$$ 0 0
$$613$$ −19654.0 −1.29497 −0.647486 0.762078i $$-0.724179\pi$$
−0.647486 + 0.762078i $$0.724179\pi$$
$$614$$ 0 0
$$615$$ −15984.0 −1.04803
$$616$$ 0 0
$$617$$ 2694.00 0.175780 0.0878901 0.996130i $$-0.471988\pi$$
0.0878901 + 0.996130i $$0.471988\pi$$
$$618$$ 0 0
$$619$$ −10178.0 −0.660886 −0.330443 0.943826i $$-0.607198\pi$$
−0.330443 + 0.943826i $$0.607198\pi$$
$$620$$ 0 0
$$621$$ 18000.0 1.16315
$$622$$ 0 0
$$623$$ 6090.00 0.391638
$$624$$ 0 0
$$625$$ −899.000 −0.0575360
$$626$$ 0 0
$$627$$ 616.000 0.0392355
$$628$$ 0 0
$$629$$ 13896.0 0.880874
$$630$$ 0 0
$$631$$ 7648.00 0.482507 0.241254 0.970462i $$-0.422441\pi$$
0.241254 + 0.970462i $$0.422441\pi$$
$$632$$ 0 0
$$633$$ 9896.00 0.621375
$$634$$ 0 0
$$635$$ 21888.0 1.36787
$$636$$ 0 0
$$637$$ 2744.00 0.170677
$$638$$ 0 0
$$639$$ −7452.00 −0.461340
$$640$$ 0 0
$$641$$ 270.000 0.0166371 0.00831853 0.999965i $$-0.497352\pi$$
0.00831853 + 0.999965i $$0.497352\pi$$
$$642$$ 0 0
$$643$$ −16250.0 −0.996637 −0.498318 0.866994i $$-0.666049\pi$$
−0.498318 + 0.866994i $$0.666049\pi$$
$$644$$ 0 0
$$645$$ 11376.0 0.694464
$$646$$ 0 0
$$647$$ −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
$$650$$ 0 0
$$651$$ −4676.00 −0.281516
$$652$$ 0 0
$$653$$ −17322.0 −1.03807 −0.519037 0.854752i $$-0.673709\pi$$
−0.519037 + 0.854752i $$0.673709\pi$$
$$654$$ 0 0
$$655$$ −30240.0 −1.80393
$$656$$ 0 0
$$657$$ −18400.0 −1.09262
$$658$$ 0 0
$$659$$ −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 $$0.708559\pi$$
$$662$$ 0 0
$$663$$ 4032.00 0.236184
$$664$$ 0 0
$$665$$ −3528.00 −0.205729
$$666$$ 0 0
$$667$$ 9720.00 0.564258
$$668$$ 0 0
$$669$$ −4684.00 −0.270693
$$670$$ 0 0
$$671$$ 4180.00 0.240487
$$672$$ 0 0
$$673$$ −10354.0 −0.593042 −0.296521 0.955026i $$-0.595827\pi$$
−0.296521 + 0.955026i $$0.595827\pi$$
$$674$$ 0 0
$$675$$ −19900.0 −1.13474
$$676$$ 0 0
$$677$$ −10920.0 −0.619926 −0.309963 0.950749i $$-0.600317\pi$$
−0.309963 + 0.950749i $$0.600317\pi$$
$$678$$ 0 0
$$679$$ 9310.00 0.526193
$$680$$ 0 0
$$681$$ −4128.00 −0.232284
$$682$$ 0 0
$$683$$ −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
$$686$$ 0 0
$$687$$ −3332.00 −0.185042
$$688$$ 0 0
$$689$$ −27216.0 −1.50486
$$690$$ 0 0
$$691$$ 25834.0 1.42225 0.711123 0.703068i $$-0.248187\pi$$
0.711123 + 0.703068i $$0.248187\pi$$
$$692$$ 0 0
$$693$$ 1771.00 0.0970775
$$694$$ 0 0
$$695$$ 9144.00 0.499067
$$696$$ 0 0
$$697$$ −15984.0 −0.868633
$$698$$ 0 0
$$699$$ 8316.00 0.449986
$$700$$ 0 0
$$701$$ −10590.0 −0.570583 −0.285292 0.958441i $$-0.592090\pi$$
−0.285292 + 0.958441i $$0.592090\pi$$
$$702$$ 0 0
$$703$$ 10808.0 0.579846
$$704$$ 0 0
$$705$$ 14472.0 0.773116
$$706$$ 0 0
$$707$$ 840.000 0.0446838
$$708$$ 0 0
$$709$$ −6802.00 −0.360302 −0.180151 0.983639i $$-0.557659\pi$$
−0.180151 + 0.983639i $$0.557659\pi$$
$$710$$ 0 0
$$711$$ −26312.0 −1.38787
$$712$$ 0 0
$$713$$ −60120.0 −3.15780
$$714$$ 0 0
$$715$$ 11088.0 0.579955
$$716$$ 0 0
$$717$$ −144.000 −0.00750039
$$718$$ 0 0
$$719$$ −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
$$722$$ 0 0
$$723$$ 13720.0 0.705743
$$724$$ 0 0
$$725$$ −10746.0 −0.550478
$$726$$ 0 0
$$727$$ −4682.00 −0.238853 −0.119426 0.992843i $$-0.538106\pi$$
−0.119426 + 0.992843i $$0.538106\pi$$
$$728$$ 0 0
$$729$$ −4283.00 −0.217599
$$730$$ 0 0
$$731$$ 11376.0 0.575590
$$732$$ 0 0
$$733$$ −17860.0 −0.899965 −0.449982 0.893037i $$-0.648570\pi$$
−0.449982 + 0.893037i $$0.648570\pi$$
$$734$$ 0 0
$$735$$ 1764.00 0.0885253
$$736$$ 0 0
$$737$$ −1936.00 −0.0967618
$$738$$ 0 0
$$739$$ −6860.00 −0.341474 −0.170737 0.985317i $$-0.554615\pi$$
−0.170737 + 0.985317i $$0.554615\pi$$
$$740$$ 0 0
$$741$$ 3136.00 0.155471
$$742$$ 0 0
$$743$$ 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
$$746$$ 0 0
$$747$$ 10764.0 0.527221
$$748$$ 0 0
$$749$$ 8652.00 0.422079
$$750$$ 0 0
$$751$$ −7364.00 −0.357811 −0.178906 0.983866i $$-0.557256\pi$$
−0.178906 + 0.983866i $$0.557256\pi$$
$$752$$ 0 0
$$753$$ 300.000 0.0145187
$$754$$ 0 0
$$755$$ −47664.0 −2.29758
$$756$$ 0 0
$$757$$ −34378.0 −1.65058 −0.825290 0.564709i $$-0.808989\pi$$
−0.825290 + 0.564709i $$0.808989\pi$$
$$758$$ 0 0
$$759$$ −3960.00 −0.189379
$$760$$ 0 0
$$761$$ 27456.0 1.30786 0.653929 0.756556i $$-0.273120\pi$$
0.653929 + 0.756556i $$0.273120\pi$$
$$762$$ 0 0
$$763$$ 4858.00 0.230500
$$764$$ 0 0
$$765$$ −14904.0 −0.704386
$$766$$ 0 0
$$767$$ 15792.0 0.743437
$$768$$ 0 0
$$769$$ 7952.00 0.372895 0.186448 0.982465i $$-0.440303\pi$$
0.186448 + 0.982465i $$0.440303\pi$$
$$770$$ 0 0
$$771$$ −4860.00 −0.227015
$$772$$ 0 0
$$773$$ −4986.00 −0.231997 −0.115999 0.993249i $$-0.537007\pi$$
−0.115999 + 0.993249i $$0.537007\pi$$
$$774$$ 0 0
$$775$$ 66466.0 3.08068
$$776$$ 0 0
$$777$$ −5404.00 −0.249508
$$778$$ 0 0
$$779$$ −12432.0 −0.571788
$$780$$ 0 0
$$781$$ 3564.00 0.163291
$$782$$ 0 0
$$783$$ 5400.00 0.246463
$$784$$ 0 0
$$785$$ −14220.0 −0.646540
$$786$$ 0 0
$$787$$ 42748.0 1.93622 0.968108 0.250534i $$-0.0806062\pi$$
0.968108 + 0.250534i $$0.0806062\pi$$
$$788$$ 0 0
$$789$$ −6096.00 −0.275061
$$790$$ 0 0
$$791$$ −6846.00 −0.307732
$$792$$ 0 0
$$793$$ 21280.0 0.952932
$$794$$ 0 0
$$795$$ −17496.0 −0.780527
$$796$$ 0 0
$$797$$ 35610.0 1.58265 0.791324 0.611397i $$-0.209392\pi$$
0.791324 + 0.611397i $$0.209392\pi$$
$$798$$ 0 0
$$799$$ 14472.0 0.640779
$$800$$ 0 0
$$801$$ 20010.0 0.882670
$$802$$ 0 0
$$803$$ 8800.00 0.386731
$$804$$ 0 0
$$805$$ 22680.0 0.993000
$$806$$ 0 0
$$807$$ −7668.00 −0.334481
$$808$$ 0 0
$$809$$ −17046.0 −0.740798 −0.370399 0.928873i $$-0.620779\pi$$
−0.370399 + 0.928873i $$0.620779\pi$$
$$810$$ 0 0
$$811$$ 2176.00 0.0942166 0.0471083 0.998890i $$-0.484999\pi$$
0.0471083 + 0.998890i $$0.484999\pi$$
$$812$$ 0 0
$$813$$ 7016.00 0.302659
$$814$$ 0 0
$$815$$ 2880.00 0.123782
$$816$$ 0 0
$$817$$ 8848.00 0.378889
$$818$$ 0 0
$$819$$ 9016.00 0.384670
$$820$$ 0 0
$$821$$ 2094.00 0.0890147 0.0445074 0.999009i $$-0.485828\pi$$
0.0445074 + 0.999009i $$0.485828\pi$$
$$822$$ 0 0
$$823$$ −7328.00 −0.310374 −0.155187 0.987885i $$-0.549598\pi$$
−0.155187 + 0.987885i $$0.549598\pi$$
$$824$$ 0 0
$$825$$ 4378.00 0.184754
$$826$$ 0 0
$$827$$ 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 $$0.787465\pi$$
$$830$$ 0 0
$$831$$ 16588.0 0.692456
$$832$$ 0 0
$$833$$ 1764.00 0.0733721
$$834$$ 0 0
$$835$$ −4752.00 −0.196946
$$836$$ 0 0
$$837$$ −33400.0 −1.37930
$$838$$ 0 0
$$839$$ 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
$$842$$ 0 0
$$843$$ 16044.0 0.655498
$$844$$ 0 0
$$845$$ 16902.0 0.688102
$$846$$ 0 0
$$847$$ −847.000 −0.0343604
$$848$$ 0 0
$$849$$ −784.000 −0.0316924
$$850$$ 0 0
$$851$$ −69480.0 −2.79876
$$852$$ 0 0
$$853$$ 9440.00 0.378921 0.189460 0.981888i $$-0.439326\pi$$
0.189460 + 0.981888i $$0.439326\pi$$
$$854$$ 0 0
$$855$$ −11592.0 −0.463670
$$856$$ 0 0
$$857$$ −28440.0 −1.13360 −0.566798 0.823857i $$-0.691818\pi$$
−0.566798 + 0.823857i $$0.691818\pi$$
$$858$$ 0 0
$$859$$ 24334.0 0.966549 0.483274 0.875469i $$-0.339447\pi$$
0.483274 + 0.875469i $$0.339447\pi$$
$$860$$ 0 0
$$861$$ 6216.00 0.246040
$$862$$ 0 0
$$863$$ −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
$$866$$ 0 0
$$867$$ −7234.00 −0.283367
$$868$$ 0 0
$$869$$ 12584.0 0.491235
$$870$$ 0 0
$$871$$ −9856.00 −0.383419
$$872$$ 0 0
$$873$$ 30590.0 1.18593
$$874$$ 0 0
$$875$$ −9324.00 −0.360239
$$876$$ 0 0
$$877$$ 32114.0 1.23650 0.618251 0.785981i $$-0.287841\pi$$
0.618251 + 0.785981i $$0.287841\pi$$
$$878$$ 0 0
$$879$$ −5496.00 −0.210894
$$880$$ 0 0
$$881$$ 41454.0 1.58527 0.792634 0.609698i $$-0.208709\pi$$
0.792634 + 0.609698i $$0.208709\pi$$
$$882$$ 0 0
$$883$$ −2876.00 −0.109609 −0.0548047 0.998497i $$-0.517454\pi$$
−0.0548047 + 0.998497i $$0.517454\pi$$
$$884$$ 0 0
$$885$$ 10152.0 0.385600
$$886$$ 0 0
$$887$$ −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
$$890$$ 0 0
$$891$$ 4631.00 0.174124
$$892$$ 0 0
$$893$$ 11256.0 0.421800
$$894$$ 0 0
$$895$$ 12744.0 0.475961
$$896$$ 0 0
$$897$$ −20160.0 −0.750416
$$898$$ 0 0
$$899$$ −18036.0 −0.669115
$$900$$ 0 0
$$901$$ −17496.0 −0.646921
$$902$$ 0 0
$$903$$ −4424.00 −0.163036
$$904$$ 0 0
$$905$$ 16236.0 0.596357
$$906$$ 0 0
$$907$$ 19768.0 0.723689 0.361844 0.932239i $$-0.382147\pi$$
0.361844 + 0.932239i $$0.382147\pi$$
$$908$$ 0 0
$$909$$ 2760.00 0.100708
$$910$$ 0 0
$$911$$ −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
$$914$$ 0 0
$$915$$ 13680.0 0.494259
$$916$$ 0 0
$$917$$ 11760.0 0.423500
$$918$$ 0 0
$$919$$ −31544.0 −1.13225 −0.566127 0.824318i $$-0.691559\pi$$
−0.566127 + 0.824318i $$0.691559\pi$$
$$920$$ 0 0
$$921$$ 6128.00 0.219245
$$922$$ 0 0
$$923$$ 18144.0 0.647039
$$924$$ 0 0
$$925$$ 76814.0 2.73041
$$926$$ 0 0
$$927$$ −27830.0 −0.986038
$$928$$ 0 0
$$929$$ 11118.0 0.392648 0.196324 0.980539i $$-0.437100\pi$$
0.196324 + 0.980539i $$0.437100\pi$$
$$930$$ 0 0
$$931$$ 1372.00 0.0482980
$$932$$ 0 0
$$933$$ −8124.00 −0.285067
$$934$$ 0 0
$$935$$ 7128.00 0.249316
$$936$$ 0 0
$$937$$ 10568.0 0.368454 0.184227 0.982884i $$-0.441022\pi$$
0.184227 + 0.982884i $$0.441022\pi$$
$$938$$ 0 0
$$939$$ −9740.00 −0.338501
$$940$$ 0 0
$$941$$ 14964.0 0.518398 0.259199 0.965824i $$-0.416541\pi$$
0.259199 + 0.965824i $$0.416541\pi$$
$$942$$ 0 0
$$943$$ 79920.0 2.75987
$$944$$ 0 0
$$945$$ 12600.0 0.433733
$$946$$ 0 0
$$947$$ −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
$$950$$ 0 0
$$951$$ 9612.00 0.327750
$$952$$ 0 0
$$953$$ 3906.00 0.132768 0.0663839 0.997794i $$-0.478854\pi$$
0.0663839 + 0.997794i $$0.478854\pi$$
$$954$$ 0 0
$$955$$ −32832.0 −1.11248
$$956$$ 0 0
$$957$$ −1188.00 −0.0401281
$$958$$ 0 0
$$959$$ −7434.00 −0.250319
$$960$$ 0 0
$$961$$ 81765.0 2.74462
$$962$$ 0 0
$$963$$ 28428.0 0.951277
$$964$$ 0 0
$$965$$ 37620.0 1.25495
$$966$$ 0 0
$$967$$ 36448.0 1.21209 0.606044 0.795431i $$-0.292756\pi$$
0.606044 + 0.795431i $$0.292756\pi$$
$$968$$ 0 0
$$969$$ 2016.00 0.0668351
$$970$$ 0 0
$$971$$ 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
$$974$$ 0 0
$$975$$ 22288.0 0.732089
$$976$$ 0 0
$$977$$ 37434.0 1.22581 0.612907 0.790155i $$-0.290000\pi$$
0.612907 + 0.790155i $$0.290000\pi$$
$$978$$ 0 0
$$979$$ −9570.00 −0.312419
$$980$$ 0 0
$$981$$ 15962.0 0.519498
$$982$$ 0 0
$$983$$ 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
$$986$$ 0 0
$$987$$ −5628.00 −0.181501
$$988$$ 0 0
$$989$$ −56880.0 −1.82880
$$990$$ 0 0
$$991$$ 15220.0 0.487870 0.243935 0.969792i $$-0.421562\pi$$
0.243935 + 0.969792i $$0.421562\pi$$
$$992$$ 0 0
$$993$$ −13240.0 −0.423121
$$994$$ 0 0
$$995$$ 58932.0 1.87766
$$996$$ 0 0
$$997$$ 37664.0 1.19642 0.598210 0.801339i $$-0.295879\pi$$
0.598210 + 0.801339i $$0.295879\pi$$
$$998$$ 0 0
$$999$$ −38600.0 −1.22247
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 1232.4.a.f.1.1 1
4.3 odd 2 154.4.a.d.1.1 1
12.11 even 2 1386.4.a.a.1.1 1
28.27 even 2 1078.4.a.g.1.1 1
44.43 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 4.3 odd 2
1078.4.a.g.1.1 1 28.27 even 2
1232.4.a.f.1.1 1 1.1 even 1 trivial
1386.4.a.a.1.1 1 12.11 even 2
1694.4.a.c.1.1 1 44.43 even 2