# Properties

 Label 2160.4.a.b.1.1 Level $2160$ Weight $4$ Character 2160.1 Self dual yes Analytic conductor $127.444$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2160 = 2^{4} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 2160.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$127.444125612$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 270) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2160.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-5.00000 q^{5} -14.0000 q^{7} +O(q^{10})$$ $$q-5.00000 q^{5} -14.0000 q^{7} +3.00000 q^{11} +47.0000 q^{13} +39.0000 q^{17} -32.0000 q^{19} -99.0000 q^{23} +25.0000 q^{25} -51.0000 q^{29} -83.0000 q^{31} +70.0000 q^{35} +314.000 q^{37} +108.000 q^{41} -299.000 q^{43} +531.000 q^{47} -147.000 q^{49} -564.000 q^{53} -15.0000 q^{55} +12.0000 q^{59} +230.000 q^{61} -235.000 q^{65} +268.000 q^{67} +120.000 q^{71} +1106.00 q^{73} -42.0000 q^{77} +739.000 q^{79} +1086.00 q^{83} -195.000 q^{85} +120.000 q^{89} -658.000 q^{91} +160.000 q^{95} -1642.00 q^{97} +O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −5.00000 −0.447214
$$6$$ 0 0
$$7$$ −14.0000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.00000 0.0822304 0.0411152 0.999154i $$-0.486909\pi$$
0.0411152 + 0.999154i $$0.486909\pi$$
$$12$$ 0 0
$$13$$ 47.0000 1.00273 0.501364 0.865237i $$-0.332832\pi$$
0.501364 + 0.865237i $$0.332832\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 39.0000 0.556405 0.278203 0.960522i $$-0.410261\pi$$
0.278203 + 0.960522i $$0.410261\pi$$
$$18$$ 0 0
$$19$$ −32.0000 −0.386384 −0.193192 0.981161i $$-0.561884\pi$$
−0.193192 + 0.981161i $$0.561884\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −99.0000 −0.897519 −0.448759 0.893653i $$-0.648134\pi$$
−0.448759 + 0.893653i $$0.648134\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −51.0000 −0.326568 −0.163284 0.986579i $$-0.552209\pi$$
−0.163284 + 0.986579i $$0.552209\pi$$
$$30$$ 0 0
$$31$$ −83.0000 −0.480879 −0.240439 0.970664i $$-0.577292\pi$$
−0.240439 + 0.970664i $$0.577292\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 70.0000 0.338062
$$36$$ 0 0
$$37$$ 314.000 1.39517 0.697585 0.716502i $$-0.254258\pi$$
0.697585 + 0.716502i $$0.254258\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 108.000 0.411385 0.205692 0.978617i $$-0.434055\pi$$
0.205692 + 0.978617i $$0.434055\pi$$
$$42$$ 0 0
$$43$$ −299.000 −1.06040 −0.530199 0.847874i $$-0.677883\pi$$
−0.530199 + 0.847874i $$0.677883\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 531.000 1.64796 0.823982 0.566616i $$-0.191748\pi$$
0.823982 + 0.566616i $$0.191748\pi$$
$$48$$ 0 0
$$49$$ −147.000 −0.428571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −564.000 −1.46172 −0.730862 0.682525i $$-0.760882\pi$$
−0.730862 + 0.682525i $$0.760882\pi$$
$$54$$ 0 0
$$55$$ −15.0000 −0.0367745
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 12.0000 0.0264791 0.0132396 0.999912i $$-0.495786\pi$$
0.0132396 + 0.999912i $$0.495786\pi$$
$$60$$ 0 0
$$61$$ 230.000 0.482762 0.241381 0.970430i $$-0.422400\pi$$
0.241381 + 0.970430i $$0.422400\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −235.000 −0.448433
$$66$$ 0 0
$$67$$ 268.000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 120.000 0.200583 0.100291 0.994958i $$-0.468022\pi$$
0.100291 + 0.994958i $$0.468022\pi$$
$$72$$ 0 0
$$73$$ 1106.00 1.77325 0.886627 0.462486i $$-0.153042\pi$$
0.886627 + 0.462486i $$0.153042\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −42.0000 −0.0621603
$$78$$ 0 0
$$79$$ 739.000 1.05246 0.526228 0.850344i $$-0.323606\pi$$
0.526228 + 0.850344i $$0.323606\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 1086.00 1.43619 0.718096 0.695944i $$-0.245014\pi$$
0.718096 + 0.695944i $$0.245014\pi$$
$$84$$ 0 0
$$85$$ −195.000 −0.248832
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 120.000 0.142921 0.0714605 0.997443i $$-0.477234\pi$$
0.0714605 + 0.997443i $$0.477234\pi$$
$$90$$ 0 0
$$91$$ −658.000 −0.757991
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 160.000 0.172796
$$96$$ 0 0
$$97$$ −1642.00 −1.71876 −0.859381 0.511336i $$-0.829151\pi$$
−0.859381 + 0.511336i $$0.829151\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −33.0000 −0.0325111 −0.0162556 0.999868i $$-0.505175\pi$$
−0.0162556 + 0.999868i $$0.505175\pi$$
$$102$$ 0 0
$$103$$ 1198.00 1.14604 0.573022 0.819540i $$-0.305771\pi$$
0.573022 + 0.819540i $$0.305771\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1542.00 −1.39318 −0.696592 0.717467i $$-0.745301\pi$$
−0.696592 + 0.717467i $$0.745301\pi$$
$$108$$ 0 0
$$109$$ −556.000 −0.488579 −0.244290 0.969702i $$-0.578555\pi$$
−0.244290 + 0.969702i $$0.578555\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1605.00 −1.33616 −0.668078 0.744091i $$-0.732883\pi$$
−0.668078 + 0.744091i $$0.732883\pi$$
$$114$$ 0 0
$$115$$ 495.000 0.401383
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −546.000 −0.420603
$$120$$ 0 0
$$121$$ −1322.00 −0.993238
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −125.000 −0.0894427
$$126$$ 0 0
$$127$$ −1334.00 −0.932074 −0.466037 0.884765i $$-0.654319\pi$$
−0.466037 + 0.884765i $$0.654319\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −2883.00 −1.92282 −0.961408 0.275127i $$-0.911280\pi$$
−0.961408 + 0.275127i $$0.911280\pi$$
$$132$$ 0 0
$$133$$ 448.000 0.292079
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −282.000 −0.175860 −0.0879302 0.996127i $$-0.528025\pi$$
−0.0879302 + 0.996127i $$0.528025\pi$$
$$138$$ 0 0
$$139$$ 2494.00 1.52186 0.760929 0.648835i $$-0.224743\pi$$
0.760929 + 0.648835i $$0.224743\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 141.000 0.0824546
$$144$$ 0 0
$$145$$ 255.000 0.146045
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2595.00 −1.42678 −0.713392 0.700766i $$-0.752842\pi$$
−0.713392 + 0.700766i $$0.752842\pi$$
$$150$$ 0 0
$$151$$ −1229.00 −0.662348 −0.331174 0.943570i $$-0.607445\pi$$
−0.331174 + 0.943570i $$0.607445\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 415.000 0.215055
$$156$$ 0 0
$$157$$ −1591.00 −0.808762 −0.404381 0.914591i $$-0.632513\pi$$
−0.404381 + 0.914591i $$0.632513\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1386.00 0.678460
$$162$$ 0 0
$$163$$ 457.000 0.219601 0.109801 0.993954i $$-0.464979\pi$$
0.109801 + 0.993954i $$0.464979\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1164.00 −0.539359 −0.269680 0.962950i $$-0.586918\pi$$
−0.269680 + 0.962950i $$0.586918\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.00546199
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −3942.00 −1.73240 −0.866199 0.499700i $$-0.833444\pi$$
−0.866199 + 0.499700i $$0.833444\pi$$
$$174$$ 0 0
$$175$$ −350.000 −0.151186
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1212.00 −0.506085 −0.253042 0.967455i $$-0.581431\pi$$
−0.253042 + 0.967455i $$0.581431\pi$$
$$180$$ 0 0
$$181$$ 2288.00 0.939590 0.469795 0.882776i $$-0.344328\pi$$
0.469795 + 0.882776i $$0.344328\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1570.00 −0.623939
$$186$$ 0 0
$$187$$ 117.000 0.0457534
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1938.00 −0.734182 −0.367091 0.930185i $$-0.619646\pi$$
−0.367091 + 0.930185i $$0.619646\pi$$
$$192$$ 0 0
$$193$$ −1498.00 −0.558696 −0.279348 0.960190i $$-0.590118\pi$$
−0.279348 + 0.960190i $$0.590118\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2124.00 0.768166 0.384083 0.923299i $$-0.374518\pi$$
0.384083 + 0.923299i $$0.374518\pi$$
$$198$$ 0 0
$$199$$ 385.000 0.137145 0.0685727 0.997646i $$-0.478155\pi$$
0.0685727 + 0.997646i $$0.478155\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 714.000 0.246862
$$204$$ 0 0
$$205$$ −540.000 −0.183977
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −96.0000 −0.0317725
$$210$$ 0 0
$$211$$ −3170.00 −1.03427 −0.517137 0.855903i $$-0.673002\pi$$
−0.517137 + 0.855903i $$0.673002\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1495.00 0.474224
$$216$$ 0 0
$$217$$ 1162.00 0.363510
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1833.00 0.557923
$$222$$ 0 0
$$223$$ −1388.00 −0.416804 −0.208402 0.978043i $$-0.566826\pi$$
−0.208402 + 0.978043i $$0.566826\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −4644.00 −1.35786 −0.678928 0.734205i $$-0.737555\pi$$
−0.678928 + 0.734205i $$0.737555\pi$$
$$228$$ 0 0
$$229$$ 4736.00 1.36665 0.683327 0.730113i $$-0.260532\pi$$
0.683327 + 0.730113i $$0.260532\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −2814.00 −0.791207 −0.395604 0.918421i $$-0.629465\pi$$
−0.395604 + 0.918421i $$0.629465\pi$$
$$234$$ 0 0
$$235$$ −2655.00 −0.736992
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −2202.00 −0.595965 −0.297982 0.954571i $$-0.596314\pi$$
−0.297982 + 0.954571i $$0.596314\pi$$
$$240$$ 0 0
$$241$$ 3485.00 0.931488 0.465744 0.884920i $$-0.345787\pi$$
0.465744 + 0.884920i $$0.345787\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 735.000 0.191663
$$246$$ 0 0
$$247$$ −1504.00 −0.387438
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −6345.00 −1.59559 −0.797795 0.602929i $$-0.794000\pi$$
−0.797795 + 0.602929i $$0.794000\pi$$
$$252$$ 0 0
$$253$$ −297.000 −0.0738033
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −525.000 −0.127426 −0.0637132 0.997968i $$-0.520294\pi$$
−0.0637132 + 0.997968i $$0.520294\pi$$
$$258$$ 0 0
$$259$$ −4396.00 −1.05465
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 5196.00 1.21825 0.609124 0.793075i $$-0.291521\pi$$
0.609124 + 0.793075i $$0.291521\pi$$
$$264$$ 0 0
$$265$$ 2820.00 0.653703
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 7479.00 1.69518 0.847589 0.530654i $$-0.178054\pi$$
0.847589 + 0.530654i $$0.178054\pi$$
$$270$$ 0 0
$$271$$ 856.000 0.191876 0.0959378 0.995387i $$-0.469415\pi$$
0.0959378 + 0.995387i $$0.469415\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 75.0000 0.0164461
$$276$$ 0 0
$$277$$ −7054.00 −1.53009 −0.765043 0.643979i $$-0.777282\pi$$
−0.765043 + 0.643979i $$0.777282\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1014.00 −0.215268 −0.107634 0.994191i $$-0.534327\pi$$
−0.107634 + 0.994191i $$0.534327\pi$$
$$282$$ 0 0
$$283$$ −992.000 −0.208368 −0.104184 0.994558i $$-0.533223\pi$$
−0.104184 + 0.994558i $$0.533223\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −1512.00 −0.310977
$$288$$ 0 0
$$289$$ −3392.00 −0.690413
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 4950.00 0.986970 0.493485 0.869754i $$-0.335723\pi$$
0.493485 + 0.869754i $$0.335723\pi$$
$$294$$ 0 0
$$295$$ −60.0000 −0.0118418
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −4653.00 −0.899966
$$300$$ 0 0
$$301$$ 4186.00 0.801585
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −1150.00 −0.215898
$$306$$ 0 0
$$307$$ 4777.00 0.888071 0.444035 0.896009i $$-0.353546\pi$$
0.444035 + 0.896009i $$0.353546\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −7692.00 −1.40249 −0.701243 0.712922i $$-0.747371\pi$$
−0.701243 + 0.712922i $$0.747371\pi$$
$$312$$ 0 0
$$313$$ −2932.00 −0.529477 −0.264739 0.964320i $$-0.585286\pi$$
−0.264739 + 0.964320i $$0.585286\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −8352.00 −1.47980 −0.739898 0.672720i $$-0.765126\pi$$
−0.739898 + 0.672720i $$0.765126\pi$$
$$318$$ 0 0
$$319$$ −153.000 −0.0268538
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1248.00 −0.214986
$$324$$ 0 0
$$325$$ 1175.00 0.200545
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −7434.00 −1.24574
$$330$$ 0 0
$$331$$ 3070.00 0.509796 0.254898 0.966968i $$-0.417958\pi$$
0.254898 + 0.966968i $$0.417958\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −1340.00 −0.218543
$$336$$ 0 0
$$337$$ −1672.00 −0.270266 −0.135133 0.990827i $$-0.543146\pi$$
−0.135133 + 0.990827i $$0.543146\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −249.000 −0.0395428
$$342$$ 0 0
$$343$$ 6860.00 1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −5076.00 −0.785285 −0.392643 0.919691i $$-0.628439\pi$$
−0.392643 + 0.919691i $$0.628439\pi$$
$$348$$ 0 0
$$349$$ 8594.00 1.31813 0.659063 0.752087i $$-0.270953\pi$$
0.659063 + 0.752087i $$0.270953\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −12711.0 −1.91654 −0.958269 0.285866i $$-0.907719\pi$$
−0.958269 + 0.285866i $$0.907719\pi$$
$$354$$ 0 0
$$355$$ −600.000 −0.0897034
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1464.00 −0.215228 −0.107614 0.994193i $$-0.534321\pi$$
−0.107614 + 0.994193i $$0.534321\pi$$
$$360$$ 0 0
$$361$$ −5835.00 −0.850707
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −5530.00 −0.793023
$$366$$ 0 0
$$367$$ 7630.00 1.08524 0.542620 0.839979i $$-0.317433\pi$$
0.542620 + 0.839979i $$0.317433\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 7896.00 1.10496
$$372$$ 0 0
$$373$$ −3883.00 −0.539019 −0.269510 0.962998i $$-0.586862\pi$$
−0.269510 + 0.962998i $$0.586862\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −2397.00 −0.327458
$$378$$ 0 0
$$379$$ 13768.0 1.86600 0.933001 0.359874i $$-0.117180\pi$$
0.933001 + 0.359874i $$0.117180\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −14139.0 −1.88634 −0.943171 0.332307i $$-0.892173\pi$$
−0.943171 + 0.332307i $$0.892173\pi$$
$$384$$ 0 0
$$385$$ 210.000 0.0277989
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −567.000 −0.0739024 −0.0369512 0.999317i $$-0.511765\pi$$
−0.0369512 + 0.999317i $$0.511765\pi$$
$$390$$ 0 0
$$391$$ −3861.00 −0.499384
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −3695.00 −0.470672
$$396$$ 0 0
$$397$$ −6685.00 −0.845115 −0.422557 0.906336i $$-0.638867\pi$$
−0.422557 + 0.906336i $$0.638867\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −4572.00 −0.569364 −0.284682 0.958622i $$-0.591888\pi$$
−0.284682 + 0.958622i $$0.591888\pi$$
$$402$$ 0 0
$$403$$ −3901.00 −0.482190
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 942.000 0.114725
$$408$$ 0 0
$$409$$ −25.0000 −0.00302242 −0.00151121 0.999999i $$-0.500481\pi$$
−0.00151121 + 0.999999i $$0.500481\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −168.000 −0.0200163
$$414$$ 0 0
$$415$$ −5430.00 −0.642285
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 12453.0 1.45195 0.725977 0.687719i $$-0.241388\pi$$
0.725977 + 0.687719i $$0.241388\pi$$
$$420$$ 0 0
$$421$$ 5048.00 0.584381 0.292191 0.956360i $$-0.405616\pi$$
0.292191 + 0.956360i $$0.405616\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 975.000 0.111281
$$426$$ 0 0
$$427$$ −3220.00 −0.364934
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 5400.00 0.603501 0.301750 0.953387i $$-0.402429\pi$$
0.301750 + 0.953387i $$0.402429\pi$$
$$432$$ 0 0
$$433$$ −6298.00 −0.698990 −0.349495 0.936938i $$-0.613647\pi$$
−0.349495 + 0.936938i $$0.613647\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 3168.00 0.346787
$$438$$ 0 0
$$439$$ 6208.00 0.674924 0.337462 0.941339i $$-0.390432\pi$$
0.337462 + 0.941339i $$0.390432\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −3360.00 −0.360358 −0.180179 0.983634i $$-0.557668\pi$$
−0.180179 + 0.983634i $$0.557668\pi$$
$$444$$ 0 0
$$445$$ −600.000 −0.0639162
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −14394.0 −1.51291 −0.756453 0.654048i $$-0.773069\pi$$
−0.756453 + 0.654048i $$0.773069\pi$$
$$450$$ 0 0
$$451$$ 324.000 0.0338283
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 3290.00 0.338984
$$456$$ 0 0
$$457$$ −916.000 −0.0937608 −0.0468804 0.998901i $$-0.514928\pi$$
−0.0468804 + 0.998901i $$0.514928\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −8550.00 −0.863803 −0.431902 0.901921i $$-0.642157\pi$$
−0.431902 + 0.901921i $$0.642157\pi$$
$$462$$ 0 0
$$463$$ −3734.00 −0.374803 −0.187401 0.982283i $$-0.560007\pi$$
−0.187401 + 0.982283i $$0.560007\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 9840.00 0.975034 0.487517 0.873113i $$-0.337903\pi$$
0.487517 + 0.873113i $$0.337903\pi$$
$$468$$ 0 0
$$469$$ −3752.00 −0.369406
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −897.000 −0.0871968
$$474$$ 0 0
$$475$$ −800.000 −0.0772769
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −17280.0 −1.64832 −0.824158 0.566360i $$-0.808351\pi$$
−0.824158 + 0.566360i $$0.808351\pi$$
$$480$$ 0 0
$$481$$ 14758.0 1.39897
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 8210.00 0.768653
$$486$$ 0 0
$$487$$ 4588.00 0.426904 0.213452 0.976954i $$-0.431529\pi$$
0.213452 + 0.976954i $$0.431529\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 636.000 0.0584568 0.0292284 0.999573i $$-0.490695\pi$$
0.0292284 + 0.999573i $$0.490695\pi$$
$$492$$ 0 0
$$493$$ −1989.00 −0.181704
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −1680.00 −0.151626
$$498$$ 0 0
$$499$$ 11716.0 1.05106 0.525531 0.850774i $$-0.323867\pi$$
0.525531 + 0.850774i $$0.323867\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4653.00 0.412459 0.206230 0.978504i $$-0.433881\pi$$
0.206230 + 0.978504i $$0.433881\pi$$
$$504$$ 0 0
$$505$$ 165.000 0.0145394
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −16479.0 −1.43501 −0.717504 0.696555i $$-0.754715\pi$$
−0.717504 + 0.696555i $$0.754715\pi$$
$$510$$ 0 0
$$511$$ −15484.0 −1.34045
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −5990.00 −0.512526
$$516$$ 0 0
$$517$$ 1593.00 0.135513
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −3120.00 −0.262360 −0.131180 0.991359i $$-0.541877\pi$$
−0.131180 + 0.991359i $$0.541877\pi$$
$$522$$ 0 0
$$523$$ −17645.0 −1.47526 −0.737631 0.675204i $$-0.764056\pi$$
−0.737631 + 0.675204i $$0.764056\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −3237.00 −0.267563
$$528$$ 0 0
$$529$$ −2366.00 −0.194460
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 5076.00 0.412507
$$534$$ 0 0
$$535$$ 7710.00 0.623051
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −441.000 −0.0352416
$$540$$ 0 0
$$541$$ −2182.00 −0.173404 −0.0867019 0.996234i $$-0.527633\pi$$
−0.0867019 + 0.996234i $$0.527633\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 2780.00 0.218499
$$546$$ 0 0
$$547$$ 4033.00 0.315244 0.157622 0.987499i $$-0.449617\pi$$
0.157622 + 0.987499i $$0.449617\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1632.00 0.126181
$$552$$ 0 0
$$553$$ −10346.0 −0.795582
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 960.000 0.0730278 0.0365139 0.999333i $$-0.488375\pi$$
0.0365139 + 0.999333i $$0.488375\pi$$
$$558$$ 0 0
$$559$$ −14053.0 −1.06329
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −23754.0 −1.77817 −0.889087 0.457739i $$-0.848660\pi$$
−0.889087 + 0.457739i $$0.848660\pi$$
$$564$$ 0 0
$$565$$ 8025.00 0.597547
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 22536.0 1.66038 0.830192 0.557478i $$-0.188231\pi$$
0.830192 + 0.557478i $$0.188231\pi$$
$$570$$ 0 0
$$571$$ −17726.0 −1.29914 −0.649571 0.760301i $$-0.725051\pi$$
−0.649571 + 0.760301i $$0.725051\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −2475.00 −0.179504
$$576$$ 0 0
$$577$$ 17168.0 1.23867 0.619336 0.785126i $$-0.287402\pi$$
0.619336 + 0.785126i $$0.287402\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −15204.0 −1.08566
$$582$$ 0 0
$$583$$ −1692.00 −0.120198
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7542.00 0.530309 0.265155 0.964206i $$-0.414577\pi$$
0.265155 + 0.964206i $$0.414577\pi$$
$$588$$ 0 0
$$589$$ 2656.00 0.185804
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 15543.0 1.07635 0.538174 0.842834i $$-0.319114\pi$$
0.538174 + 0.842834i $$0.319114\pi$$
$$594$$ 0 0
$$595$$ 2730.00 0.188099
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 16026.0 1.09316 0.546581 0.837406i $$-0.315929\pi$$
0.546581 + 0.837406i $$0.315929\pi$$
$$600$$ 0 0
$$601$$ 10469.0 0.710548 0.355274 0.934762i $$-0.384388\pi$$
0.355274 + 0.934762i $$0.384388\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 6610.00 0.444190
$$606$$ 0 0
$$607$$ 8074.00 0.539891 0.269945 0.962876i $$-0.412994\pi$$
0.269945 + 0.962876i $$0.412994\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 24957.0 1.65246
$$612$$ 0 0
$$613$$ 26855.0 1.76943 0.884717 0.466128i $$-0.154351\pi$$
0.884717 + 0.466128i $$0.154351\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −24447.0 −1.59514 −0.797568 0.603229i $$-0.793881\pi$$
−0.797568 + 0.603229i $$0.793881\pi$$
$$618$$ 0 0
$$619$$ −1850.00 −0.120126 −0.0600628 0.998195i $$-0.519130\pi$$
−0.0600628 + 0.998195i $$0.519130\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −1680.00 −0.108038
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 12246.0 0.776280
$$630$$ 0 0
$$631$$ −21728.0 −1.37081 −0.685403 0.728164i $$-0.740374\pi$$
−0.685403 + 0.728164i $$0.740374\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 6670.00 0.416836
$$636$$ 0 0
$$637$$ −6909.00 −0.429740
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −23862.0 −1.47035 −0.735173 0.677879i $$-0.762899\pi$$
−0.735173 + 0.677879i $$0.762899\pi$$
$$642$$ 0 0
$$643$$ −10523.0 −0.645391 −0.322696 0.946503i $$-0.604589\pi$$
−0.322696 + 0.946503i $$0.604589\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 5484.00 0.333228 0.166614 0.986022i $$-0.446717\pi$$
0.166614 + 0.986022i $$0.446717\pi$$
$$648$$ 0 0
$$649$$ 36.0000 0.00217739
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 26784.0 1.60511 0.802557 0.596576i $$-0.203473\pi$$
0.802557 + 0.596576i $$0.203473\pi$$
$$654$$ 0 0
$$655$$ 14415.0 0.859909
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −12120.0 −0.716431 −0.358216 0.933639i $$-0.616615\pi$$
−0.358216 + 0.933639i $$0.616615\pi$$
$$660$$ 0 0
$$661$$ −18226.0 −1.07248 −0.536240 0.844066i $$-0.680156\pi$$
−0.536240 + 0.844066i $$0.680156\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −2240.00 −0.130622
$$666$$ 0 0
$$667$$ 5049.00 0.293101
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 690.000 0.0396977
$$672$$ 0 0
$$673$$ −11062.0 −0.633594 −0.316797 0.948493i $$-0.602607\pi$$
−0.316797 + 0.948493i $$0.602607\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 9348.00 0.530684 0.265342 0.964154i $$-0.414515\pi$$
0.265342 + 0.964154i $$0.414515\pi$$
$$678$$ 0 0
$$679$$ 22988.0 1.29926
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 19248.0 1.07834 0.539169 0.842198i $$-0.318739\pi$$
0.539169 + 0.842198i $$0.318739\pi$$
$$684$$ 0 0
$$685$$ 1410.00 0.0786472
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −26508.0 −1.46571
$$690$$ 0 0
$$691$$ 17710.0 0.974993 0.487496 0.873125i $$-0.337910\pi$$
0.487496 + 0.873125i $$0.337910\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −12470.0 −0.680596
$$696$$ 0 0
$$697$$ 4212.00 0.228897
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 19437.0 1.04725 0.523627 0.851947i $$-0.324578\pi$$
0.523627 + 0.851947i $$0.324578\pi$$
$$702$$ 0 0
$$703$$ −10048.0 −0.539072
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 462.000 0.0245761
$$708$$ 0 0
$$709$$ −19516.0 −1.03376 −0.516882 0.856057i $$-0.672907\pi$$
−0.516882 + 0.856057i $$0.672907\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 8217.00 0.431598
$$714$$ 0 0
$$715$$ −705.000 −0.0368748
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 17358.0 0.900340 0.450170 0.892943i $$-0.351363\pi$$
0.450170 + 0.892943i $$0.351363\pi$$
$$720$$ 0 0
$$721$$ −16772.0 −0.866327
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1275.00 −0.0653135
$$726$$ 0 0
$$727$$ −24428.0 −1.24620 −0.623098 0.782144i $$-0.714126\pi$$
−0.623098 + 0.782144i $$0.714126\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −11661.0 −0.590010
$$732$$ 0 0
$$733$$ −21418.0 −1.07925 −0.539626 0.841905i $$-0.681434\pi$$
−0.539626 + 0.841905i $$0.681434\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 804.000 0.0401842
$$738$$ 0 0
$$739$$ 664.000 0.0330523 0.0165261 0.999863i $$-0.494739\pi$$
0.0165261 + 0.999863i $$0.494739\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −34209.0 −1.68911 −0.844553 0.535471i $$-0.820134\pi$$
−0.844553 + 0.535471i $$0.820134\pi$$
$$744$$ 0 0
$$745$$ 12975.0 0.638077
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 21588.0 1.05315
$$750$$ 0 0
$$751$$ −6857.00 −0.333176 −0.166588 0.986027i $$-0.553275\pi$$
−0.166588 + 0.986027i $$0.553275\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 6145.00 0.296211
$$756$$ 0 0
$$757$$ −23719.0 −1.13881 −0.569407 0.822056i $$-0.692827\pi$$
−0.569407 + 0.822056i $$0.692827\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 14418.0 0.686796 0.343398 0.939190i $$-0.388422\pi$$
0.343398 + 0.939190i $$0.388422\pi$$
$$762$$ 0 0
$$763$$ 7784.00 0.369331
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 564.000 0.0265513
$$768$$ 0 0
$$769$$ −4849.00 −0.227385 −0.113693 0.993516i $$-0.536268\pi$$
−0.113693 + 0.993516i $$0.536268\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 36258.0 1.68708 0.843538 0.537070i $$-0.180469\pi$$
0.843538 + 0.537070i $$0.180469\pi$$
$$774$$ 0 0
$$775$$ −2075.00 −0.0961757
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −3456.00 −0.158953
$$780$$ 0 0
$$781$$ 360.000 0.0164940
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 7955.00 0.361689
$$786$$ 0 0
$$787$$ 18877.0 0.855009 0.427505 0.904013i $$-0.359393\pi$$
0.427505 + 0.904013i $$0.359393\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 22470.0 1.01004
$$792$$ 0 0
$$793$$ 10810.0 0.484079
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 16200.0 0.719992 0.359996 0.932954i $$-0.382778\pi$$
0.359996 + 0.932954i $$0.382778\pi$$
$$798$$ 0 0
$$799$$ 20709.0 0.916936
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 3318.00 0.145815
$$804$$ 0 0
$$805$$ −6930.00 −0.303417
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 26760.0 1.16296 0.581478 0.813562i $$-0.302475\pi$$
0.581478 + 0.813562i $$0.302475\pi$$
$$810$$ 0 0
$$811$$ 10510.0 0.455063 0.227531 0.973771i $$-0.426935\pi$$
0.227531 + 0.973771i $$0.426935\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −2285.00 −0.0982087
$$816$$ 0 0
$$817$$ 9568.00 0.409721
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 28230.0 1.20004 0.600021 0.799985i $$-0.295159\pi$$
0.600021 + 0.799985i $$0.295159\pi$$
$$822$$ 0 0
$$823$$ 39868.0 1.68859 0.844296 0.535877i $$-0.180019\pi$$
0.844296 + 0.535877i $$0.180019\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 32394.0 1.36209 0.681046 0.732241i $$-0.261525\pi$$
0.681046 + 0.732241i $$0.261525\pi$$
$$828$$ 0 0
$$829$$ 34820.0 1.45880 0.729402 0.684085i $$-0.239798\pi$$
0.729402 + 0.684085i $$0.239798\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −5733.00 −0.238459
$$834$$ 0 0
$$835$$ 5820.00 0.241209
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −1146.00 −0.0471565 −0.0235783 0.999722i $$-0.507506\pi$$
−0.0235783 + 0.999722i $$0.507506\pi$$
$$840$$ 0 0
$$841$$ −21788.0 −0.893354
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −60.0000 −0.00244268
$$846$$ 0 0
$$847$$ 18508.0 0.750817
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −31086.0 −1.25219
$$852$$ 0 0
$$853$$ −19393.0 −0.778433 −0.389217 0.921146i $$-0.627254\pi$$
−0.389217 + 0.921146i $$0.627254\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 8430.00 0.336013 0.168007 0.985786i $$-0.446267\pi$$
0.168007 + 0.985786i $$0.446267\pi$$
$$858$$ 0 0
$$859$$ −15470.0 −0.614470 −0.307235 0.951634i $$-0.599404\pi$$
−0.307235 + 0.951634i $$0.599404\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 5871.00 0.231577 0.115789 0.993274i $$-0.463060\pi$$
0.115789 + 0.993274i $$0.463060\pi$$
$$864$$ 0 0
$$865$$ 19710.0 0.774752
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 2217.00 0.0865438
$$870$$ 0 0
$$871$$ 12596.0 0.490011
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 1750.00 0.0676123
$$876$$ 0 0
$$877$$ −11299.0 −0.435051 −0.217526 0.976055i $$-0.569799\pi$$
−0.217526 + 0.976055i $$0.569799\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −29682.0 −1.13509 −0.567544 0.823343i $$-0.692106\pi$$
−0.567544 + 0.823343i $$0.692106\pi$$
$$882$$ 0 0
$$883$$ −40316.0 −1.53651 −0.768257 0.640142i $$-0.778876\pi$$
−0.768257 + 0.640142i $$0.778876\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −21945.0 −0.830711 −0.415356 0.909659i $$-0.636343\pi$$
−0.415356 + 0.909659i $$0.636343\pi$$
$$888$$ 0 0
$$889$$ 18676.0 0.704581
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −16992.0 −0.636748
$$894$$ 0 0
$$895$$ 6060.00 0.226328
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 4233.00 0.157039
$$900$$ 0 0
$$901$$ −21996.0 −0.813311
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −11440.0 −0.420197
$$906$$ 0 0
$$907$$ −24911.0 −0.911969 −0.455985 0.889988i $$-0.650713\pi$$
−0.455985 + 0.889988i $$0.650713\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 33264.0 1.20975 0.604877 0.796319i $$-0.293222\pi$$
0.604877 + 0.796319i $$0.293222\pi$$
$$912$$ 0 0
$$913$$ 3258.00 0.118099
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 40362.0 1.45351
$$918$$ 0 0
$$919$$ 23191.0 0.832427 0.416214 0.909267i $$-0.363357\pi$$
0.416214 + 0.909267i $$0.363357\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 5640.00 0.201130
$$924$$ 0 0
$$925$$ 7850.00 0.279034
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −2160.00 −0.0762834 −0.0381417 0.999272i $$-0.512144\pi$$
−0.0381417 + 0.999272i $$0.512144\pi$$
$$930$$ 0 0
$$931$$ 4704.00 0.165593
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −585.000 −0.0204615
$$936$$ 0 0
$$937$$ 2066.00 0.0720312 0.0360156 0.999351i $$-0.488533\pi$$
0.0360156 + 0.999351i $$0.488533\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 22233.0 0.770218 0.385109 0.922871i $$-0.374164\pi$$
0.385109 + 0.922871i $$0.374164\pi$$
$$942$$ 0 0
$$943$$ −10692.0 −0.369225
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −17754.0 −0.609216 −0.304608 0.952478i $$-0.598525\pi$$
−0.304608 + 0.952478i $$0.598525\pi$$
$$948$$ 0 0
$$949$$ 51982.0 1.77809
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −33891.0 −1.15198 −0.575990 0.817457i $$-0.695383\pi$$
−0.575990 + 0.817457i $$0.695383\pi$$
$$954$$ 0 0
$$955$$ 9690.00 0.328336
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 3948.00 0.132938
$$960$$ 0 0
$$961$$ −22902.0 −0.768756
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 7490.00 0.249857
$$966$$ 0 0
$$967$$ −51074.0 −1.69848 −0.849239 0.528008i $$-0.822939\pi$$
−0.849239 + 0.528008i $$0.822939\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 20967.0 0.692959 0.346479 0.938058i $$-0.387377\pi$$
0.346479 + 0.938058i $$0.387377\pi$$
$$972$$ 0 0
$$973$$ −34916.0 −1.15042
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −31749.0 −1.03965 −0.519826 0.854272i $$-0.674003\pi$$
−0.519826 + 0.854272i $$0.674003\pi$$
$$978$$ 0 0
$$979$$ 360.000 0.0117525
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 47325.0 1.53554 0.767769 0.640727i $$-0.221367\pi$$
0.767769 + 0.640727i $$0.221367\pi$$
$$984$$ 0 0
$$985$$ −10620.0 −0.343534
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 29601.0 0.951726
$$990$$ 0 0
$$991$$ −2363.00 −0.0757449 −0.0378724 0.999283i $$-0.512058\pi$$
−0.0378724 + 0.999283i $$0.512058\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −1925.00 −0.0613333
$$996$$ 0 0
$$997$$ 45569.0 1.44753 0.723764 0.690048i $$-0.242411\pi$$
0.723764 + 0.690048i $$0.242411\pi$$
$$998$$ 0 0
$$999$$ 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 2160.4.a.b.1.1 1
3.2 odd 2 2160.4.a.l.1.1 1
4.3 odd 2 270.4.a.j.1.1 yes 1
12.11 even 2 270.4.a.f.1.1 1
20.3 even 4 1350.4.c.j.649.1 2
20.7 even 4 1350.4.c.j.649.2 2
20.19 odd 2 1350.4.a.e.1.1 1
36.7 odd 6 810.4.e.f.271.1 2
36.11 even 6 810.4.e.n.271.1 2
36.23 even 6 810.4.e.n.541.1 2
36.31 odd 6 810.4.e.f.541.1 2
60.23 odd 4 1350.4.c.k.649.2 2
60.47 odd 4 1350.4.c.k.649.1 2
60.59 even 2 1350.4.a.r.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.f.1.1 1 12.11 even 2
270.4.a.j.1.1 yes 1 4.3 odd 2
810.4.e.f.271.1 2 36.7 odd 6
810.4.e.f.541.1 2 36.31 odd 6
810.4.e.n.271.1 2 36.11 even 6
810.4.e.n.541.1 2 36.23 even 6
1350.4.a.e.1.1 1 20.19 odd 2
1350.4.a.r.1.1 1 60.59 even 2
1350.4.c.j.649.1 2 20.3 even 4
1350.4.c.j.649.2 2 20.7 even 4
1350.4.c.k.649.1 2 60.47 odd 4
1350.4.c.k.649.2 2 60.23 odd 4
2160.4.a.b.1.1 1 1.1 even 1 trivial
2160.4.a.l.1.1 1 3.2 odd 2