# Properties

 Label 720.4.a.h.1.1 Level $720$ Weight $4$ Character 720.1 Self dual yes Analytic conductor $42.481$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 720.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$42.4813752041$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 180) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 720.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-5.00000 q^{5} -2.00000 q^{7} +O(q^{10})$$ $$q-5.00000 q^{5} -2.00000 q^{7} +30.0000 q^{11} -4.00000 q^{13} -90.0000 q^{17} +28.0000 q^{19} +120.000 q^{23} +25.0000 q^{25} -210.000 q^{29} +4.00000 q^{31} +10.0000 q^{35} +200.000 q^{37} -240.000 q^{41} +136.000 q^{43} -120.000 q^{47} -339.000 q^{49} +30.0000 q^{53} -150.000 q^{55} -450.000 q^{59} -166.000 q^{61} +20.0000 q^{65} -908.000 q^{67} -1020.00 q^{71} -250.000 q^{73} -60.0000 q^{77} +916.000 q^{79} -1140.00 q^{83} +450.000 q^{85} +420.000 q^{89} +8.00000 q^{91} -140.000 q^{95} +1538.00 q^{97} +O(q^{100})$$

## 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
$$7$$ −2.00000 −0.107990 −0.0539949 0.998541i $$-0.517195\pi$$
−0.0539949 + 0.998541i $$0.517195\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 30.0000 0.822304 0.411152 0.911567i $$-0.365127\pi$$
0.411152 + 0.911567i $$0.365127\pi$$
$$12$$ 0 0
$$13$$ −4.00000 −0.0853385 −0.0426692 0.999089i $$-0.513586\pi$$
−0.0426692 + 0.999089i $$0.513586\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −90.0000 −1.28401 −0.642006 0.766700i $$-0.721898\pi$$
−0.642006 + 0.766700i $$0.721898\pi$$
$$18$$ 0 0
$$19$$ 28.0000 0.338086 0.169043 0.985609i $$-0.445932\pi$$
0.169043 + 0.985609i $$0.445932\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 120.000 1.08790 0.543951 0.839117i $$-0.316928\pi$$
0.543951 + 0.839117i $$0.316928\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −210.000 −1.34469 −0.672345 0.740238i $$-0.734713\pi$$
−0.672345 + 0.740238i $$0.734713\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.0231749 0.0115874 0.999933i $$-0.496312\pi$$
0.0115874 + 0.999933i $$0.496312\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 10.0000 0.0482945
$$36$$ 0 0
$$37$$ 200.000 0.888643 0.444322 0.895867i $$-0.353445\pi$$
0.444322 + 0.895867i $$0.353445\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −240.000 −0.914188 −0.457094 0.889418i $$-0.651110\pi$$
−0.457094 + 0.889418i $$0.651110\pi$$
$$42$$ 0 0
$$43$$ 136.000 0.482321 0.241161 0.970485i $$-0.422472\pi$$
0.241161 + 0.970485i $$0.422472\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −120.000 −0.372421 −0.186211 0.982510i $$-0.559621\pi$$
−0.186211 + 0.982510i $$0.559621\pi$$
$$48$$ 0 0
$$49$$ −339.000 −0.988338
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 30.0000 0.0777513 0.0388756 0.999244i $$-0.487622\pi$$
0.0388756 + 0.999244i $$0.487622\pi$$
$$54$$ 0 0
$$55$$ −150.000 −0.367745
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −450.000 −0.992966 −0.496483 0.868046i $$-0.665376\pi$$
−0.496483 + 0.868046i $$0.665376\pi$$
$$60$$ 0 0
$$61$$ −166.000 −0.348428 −0.174214 0.984708i $$-0.555738\pi$$
−0.174214 + 0.984708i $$0.555738\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 20.0000 0.0381645
$$66$$ 0 0
$$67$$ −908.000 −1.65567 −0.827835 0.560972i $$-0.810428\pi$$
−0.827835 + 0.560972i $$0.810428\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −1020.00 −1.70495 −0.852477 0.522765i $$-0.824901\pi$$
−0.852477 + 0.522765i $$0.824901\pi$$
$$72$$ 0 0
$$73$$ −250.000 −0.400826 −0.200413 0.979712i $$-0.564228\pi$$
−0.200413 + 0.979712i $$0.564228\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −60.0000 −0.0888004
$$78$$ 0 0
$$79$$ 916.000 1.30453 0.652266 0.757990i $$-0.273818\pi$$
0.652266 + 0.757990i $$0.273818\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1140.00 −1.50761 −0.753803 0.657101i $$-0.771783\pi$$
−0.753803 + 0.657101i $$0.771783\pi$$
$$84$$ 0 0
$$85$$ 450.000 0.574228
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 420.000 0.500224 0.250112 0.968217i $$-0.419533\pi$$
0.250112 + 0.968217i $$0.419533\pi$$
$$90$$ 0 0
$$91$$ 8.00000 0.00921569
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −140.000 −0.151197
$$96$$ 0 0
$$97$$ 1538.00 1.60990 0.804950 0.593343i $$-0.202192\pi$$
0.804950 + 0.593343i $$0.202192\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −450.000 −0.443333 −0.221667 0.975122i $$-0.571150\pi$$
−0.221667 + 0.975122i $$0.571150\pi$$
$$102$$ 0 0
$$103$$ 1150.00 1.10012 0.550062 0.835124i $$-0.314604\pi$$
0.550062 + 0.835124i $$0.314604\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1620.00 −1.46366 −0.731829 0.681489i $$-0.761333\pi$$
−0.731829 + 0.681489i $$0.761333\pi$$
$$108$$ 0 0
$$109$$ −1702.00 −1.49561 −0.747807 0.663916i $$-0.768893\pi$$
−0.747807 + 0.663916i $$0.768893\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1350.00 −1.12387 −0.561935 0.827181i $$-0.689943\pi$$
−0.561935 + 0.827181i $$0.689943\pi$$
$$114$$ 0 0
$$115$$ −600.000 −0.486524
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 180.000 0.138660
$$120$$ 0 0
$$121$$ −431.000 −0.323817
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −125.000 −0.0894427
$$126$$ 0 0
$$127$$ −2450.00 −1.71183 −0.855915 0.517117i $$-0.827005\pi$$
−0.855915 + 0.517117i $$0.827005\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 690.000 0.460195 0.230098 0.973168i $$-0.426095\pi$$
0.230098 + 0.973168i $$0.426095\pi$$
$$132$$ 0 0
$$133$$ −56.0000 −0.0365099
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2070.00 −1.29089 −0.645445 0.763806i $$-0.723328\pi$$
−0.645445 + 0.763806i $$0.723328\pi$$
$$138$$ 0 0
$$139$$ 1924.00 1.17404 0.587020 0.809572i $$-0.300301\pi$$
0.587020 + 0.809572i $$0.300301\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −120.000 −0.0701742
$$144$$ 0 0
$$145$$ 1050.00 0.601364
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2910.00 −1.59998 −0.799988 0.600016i $$-0.795161\pi$$
−0.799988 + 0.600016i $$0.795161\pi$$
$$150$$ 0 0
$$151$$ −176.000 −0.0948522 −0.0474261 0.998875i $$-0.515102\pi$$
−0.0474261 + 0.998875i $$0.515102\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −20.0000 −0.0103641
$$156$$ 0 0
$$157$$ 2348.00 1.19357 0.596786 0.802400i $$-0.296444\pi$$
0.596786 + 0.802400i $$0.296444\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −240.000 −0.117482
$$162$$ 0 0
$$163$$ 1996.00 0.959134 0.479567 0.877505i $$-0.340794\pi$$
0.479567 + 0.877505i $$0.340794\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 3120.00 1.44571 0.722853 0.691002i $$-0.242830\pi$$
0.722853 + 0.691002i $$0.242830\pi$$
$$168$$ 0 0
$$169$$ −2181.00 −0.992717
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1770.00 −0.777865 −0.388932 0.921266i $$-0.627156\pi$$
−0.388932 + 0.921266i $$0.627156\pi$$
$$174$$ 0 0
$$175$$ −50.0000 −0.0215980
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −2130.00 −0.889406 −0.444703 0.895678i $$-0.646691\pi$$
−0.444703 + 0.895678i $$0.646691\pi$$
$$180$$ 0 0
$$181$$ −1654.00 −0.679231 −0.339616 0.940564i $$-0.610297\pi$$
−0.339616 + 0.940564i $$0.610297\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1000.00 −0.397413
$$186$$ 0 0
$$187$$ −2700.00 −1.05585
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1740.00 0.659173 0.329586 0.944125i $$-0.393091\pi$$
0.329586 + 0.944125i $$0.393091\pi$$
$$192$$ 0 0
$$193$$ 86.0000 0.0320747 0.0160373 0.999871i $$-0.494895\pi$$
0.0160373 + 0.999871i $$0.494895\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2490.00 0.900534 0.450267 0.892894i $$-0.351329\pi$$
0.450267 + 0.892894i $$0.351329\pi$$
$$198$$ 0 0
$$199$$ 832.000 0.296376 0.148188 0.988959i $$-0.452656\pi$$
0.148188 + 0.988959i $$0.452656\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 420.000 0.145213
$$204$$ 0 0
$$205$$ 1200.00 0.408837
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 840.000 0.278010
$$210$$ 0 0
$$211$$ −2084.00 −0.679945 −0.339973 0.940435i $$-0.610418\pi$$
−0.339973 + 0.940435i $$0.610418\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −680.000 −0.215701
$$216$$ 0 0
$$217$$ −8.00000 −0.00250265
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 360.000 0.109576
$$222$$ 0 0
$$223$$ 1174.00 0.352542 0.176271 0.984342i $$-0.443597\pi$$
0.176271 + 0.984342i $$0.443597\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −3120.00 −0.912254 −0.456127 0.889915i $$-0.650764\pi$$
−0.456127 + 0.889915i $$0.650764\pi$$
$$228$$ 0 0
$$229$$ −58.0000 −0.0167369 −0.00836845 0.999965i $$-0.502664\pi$$
−0.00836845 + 0.999965i $$0.502664\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5910.00 1.66170 0.830852 0.556494i $$-0.187854\pi$$
0.830852 + 0.556494i $$0.187854\pi$$
$$234$$ 0 0
$$235$$ 600.000 0.166552
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3300.00 0.893135 0.446567 0.894750i $$-0.352646\pi$$
0.446567 + 0.894750i $$0.352646\pi$$
$$240$$ 0 0
$$241$$ −2986.00 −0.798113 −0.399056 0.916926i $$-0.630662\pi$$
−0.399056 + 0.916926i $$0.630662\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 1695.00 0.441998
$$246$$ 0 0
$$247$$ −112.000 −0.0288518
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −6630.00 −1.66726 −0.833629 0.552324i $$-0.813741\pi$$
−0.833629 + 0.552324i $$0.813741\pi$$
$$252$$ 0 0
$$253$$ 3600.00 0.894585
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1530.00 0.371357 0.185679 0.982611i $$-0.440552\pi$$
0.185679 + 0.982611i $$0.440552\pi$$
$$258$$ 0 0
$$259$$ −400.000 −0.0959644
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 2640.00 0.618971 0.309486 0.950904i $$-0.399843\pi$$
0.309486 + 0.950904i $$0.399843\pi$$
$$264$$ 0 0
$$265$$ −150.000 −0.0347714
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 7350.00 1.66594 0.832969 0.553319i $$-0.186639\pi$$
0.832969 + 0.553319i $$0.186639\pi$$
$$270$$ 0 0
$$271$$ −3512.00 −0.787228 −0.393614 0.919276i $$-0.628775\pi$$
−0.393614 + 0.919276i $$0.628775\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 750.000 0.164461
$$276$$ 0 0
$$277$$ −5368.00 −1.16437 −0.582187 0.813055i $$-0.697803\pi$$
−0.582187 + 0.813055i $$0.697803\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 3060.00 0.649624 0.324812 0.945779i $$-0.394699\pi$$
0.324812 + 0.945779i $$0.394699\pi$$
$$282$$ 0 0
$$283$$ 5044.00 1.05949 0.529743 0.848158i $$-0.322288\pi$$
0.529743 + 0.848158i $$0.322288\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 480.000 0.0987230
$$288$$ 0 0
$$289$$ 3187.00 0.648687
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 2010.00 0.400769 0.200385 0.979717i $$-0.435781\pi$$
0.200385 + 0.979717i $$0.435781\pi$$
$$294$$ 0 0
$$295$$ 2250.00 0.444068
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −480.000 −0.0928399
$$300$$ 0 0
$$301$$ −272.000 −0.0520858
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 830.000 0.155822
$$306$$ 0 0
$$307$$ 2752.00 0.511612 0.255806 0.966728i $$-0.417659\pi$$
0.255806 + 0.966728i $$0.417659\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 9540.00 1.73943 0.869717 0.493551i $$-0.164301\pi$$
0.869717 + 0.493551i $$0.164301\pi$$
$$312$$ 0 0
$$313$$ 9254.00 1.67114 0.835570 0.549384i $$-0.185137\pi$$
0.835570 + 0.549384i $$0.185137\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −150.000 −0.0265768 −0.0132884 0.999912i $$-0.504230\pi$$
−0.0132884 + 0.999912i $$0.504230\pi$$
$$318$$ 0 0
$$319$$ −6300.00 −1.10574
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −2520.00 −0.434107
$$324$$ 0 0
$$325$$ −100.000 −0.0170677
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 240.000 0.0402177
$$330$$ 0 0
$$331$$ −1892.00 −0.314180 −0.157090 0.987584i $$-0.550211\pi$$
−0.157090 + 0.987584i $$0.550211\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 4540.00 0.740438
$$336$$ 0 0
$$337$$ −7378.00 −1.19260 −0.596299 0.802763i $$-0.703363\pi$$
−0.596299 + 0.802763i $$0.703363\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 120.000 0.0190568
$$342$$ 0 0
$$343$$ 1364.00 0.214720
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6720.00 1.03962 0.519811 0.854282i $$-0.326003\pi$$
0.519811 + 0.854282i $$0.326003\pi$$
$$348$$ 0 0
$$349$$ 5186.00 0.795416 0.397708 0.917512i $$-0.369806\pi$$
0.397708 + 0.917512i $$0.369806\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −3330.00 −0.502091 −0.251045 0.967975i $$-0.580774\pi$$
−0.251045 + 0.967975i $$0.580774\pi$$
$$354$$ 0 0
$$355$$ 5100.00 0.762479
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 9000.00 1.32312 0.661562 0.749890i $$-0.269894\pi$$
0.661562 + 0.749890i $$0.269894\pi$$
$$360$$ 0 0
$$361$$ −6075.00 −0.885698
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1250.00 0.179255
$$366$$ 0 0
$$367$$ 8758.00 1.24568 0.622839 0.782350i $$-0.285979\pi$$
0.622839 + 0.782350i $$0.285979\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −60.0000 −0.00839635
$$372$$ 0 0
$$373$$ 4724.00 0.655763 0.327881 0.944719i $$-0.393665\pi$$
0.327881 + 0.944719i $$0.393665\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 840.000 0.114754
$$378$$ 0 0
$$379$$ −7292.00 −0.988298 −0.494149 0.869377i $$-0.664520\pi$$
−0.494149 + 0.869377i $$0.664520\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 14520.0 1.93717 0.968587 0.248676i $$-0.0799956\pi$$
0.968587 + 0.248676i $$0.0799956\pi$$
$$384$$ 0 0
$$385$$ 300.000 0.0397128
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −7110.00 −0.926713 −0.463356 0.886172i $$-0.653355\pi$$
−0.463356 + 0.886172i $$0.653355\pi$$
$$390$$ 0 0
$$391$$ −10800.0 −1.39688
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −4580.00 −0.583405
$$396$$ 0 0
$$397$$ −11488.0 −1.45231 −0.726154 0.687532i $$-0.758694\pi$$
−0.726154 + 0.687532i $$0.758694\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −780.000 −0.0971355 −0.0485678 0.998820i $$-0.515466\pi$$
−0.0485678 + 0.998820i $$0.515466\pi$$
$$402$$ 0 0
$$403$$ −16.0000 −0.00197771
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 6000.00 0.730735
$$408$$ 0 0
$$409$$ 5402.00 0.653085 0.326542 0.945183i $$-0.394116\pi$$
0.326542 + 0.945183i $$0.394116\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 900.000 0.107230
$$414$$ 0 0
$$415$$ 5700.00 0.674222
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −2190.00 −0.255342 −0.127671 0.991817i $$-0.540750\pi$$
−0.127671 + 0.991817i $$0.540750\pi$$
$$420$$ 0 0
$$421$$ −7162.00 −0.829108 −0.414554 0.910025i $$-0.636062\pi$$
−0.414554 + 0.910025i $$0.636062\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −2250.00 −0.256802
$$426$$ 0 0
$$427$$ 332.000 0.0376267
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 9360.00 1.04607 0.523034 0.852312i $$-0.324800\pi$$
0.523034 + 0.852312i $$0.324800\pi$$
$$432$$ 0 0
$$433$$ 12806.0 1.42129 0.710643 0.703552i $$-0.248404\pi$$
0.710643 + 0.703552i $$0.248404\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 3360.00 0.367805
$$438$$ 0 0
$$439$$ −11288.0 −1.22721 −0.613607 0.789612i $$-0.710282\pi$$
−0.613607 + 0.789612i $$0.710282\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −8520.00 −0.913764 −0.456882 0.889527i $$-0.651034\pi$$
−0.456882 + 0.889527i $$0.651034\pi$$
$$444$$ 0 0
$$445$$ −2100.00 −0.223707
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 1260.00 0.132434 0.0662172 0.997805i $$-0.478907\pi$$
0.0662172 + 0.997805i $$0.478907\pi$$
$$450$$ 0 0
$$451$$ −7200.00 −0.751740
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −40.0000 −0.00412138
$$456$$ 0 0
$$457$$ −13750.0 −1.40744 −0.703718 0.710480i $$-0.748478\pi$$
−0.703718 + 0.710480i $$0.748478\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 3210.00 0.324305 0.162152 0.986766i $$-0.448156\pi$$
0.162152 + 0.986766i $$0.448156\pi$$
$$462$$ 0 0
$$463$$ 12850.0 1.28983 0.644914 0.764255i $$-0.276893\pi$$
0.644914 + 0.764255i $$0.276893\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −8220.00 −0.814510 −0.407255 0.913314i $$-0.633514\pi$$
−0.407255 + 0.913314i $$0.633514\pi$$
$$468$$ 0 0
$$469$$ 1816.00 0.178795
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 4080.00 0.396614
$$474$$ 0 0
$$475$$ 700.000 0.0676173
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −7020.00 −0.669628 −0.334814 0.942284i $$-0.608674\pi$$
−0.334814 + 0.942284i $$0.608674\pi$$
$$480$$ 0 0
$$481$$ −800.000 −0.0758355
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −7690.00 −0.719969
$$486$$ 0 0
$$487$$ 8122.00 0.755735 0.377868 0.925860i $$-0.376657\pi$$
0.377868 + 0.925860i $$0.376657\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −13470.0 −1.23807 −0.619035 0.785363i $$-0.712476\pi$$
−0.619035 + 0.785363i $$0.712476\pi$$
$$492$$ 0 0
$$493$$ 18900.0 1.72660
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 2040.00 0.184118
$$498$$ 0 0
$$499$$ −2468.00 −0.221409 −0.110704 0.993853i $$-0.535311\pi$$
−0.110704 + 0.993853i $$0.535311\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −4440.00 −0.393578 −0.196789 0.980446i $$-0.563051\pi$$
−0.196789 + 0.980446i $$0.563051\pi$$
$$504$$ 0 0
$$505$$ 2250.00 0.198265
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 11190.0 0.974436 0.487218 0.873280i $$-0.338012\pi$$
0.487218 + 0.873280i $$0.338012\pi$$
$$510$$ 0 0
$$511$$ 500.000 0.0432851
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −5750.00 −0.491991
$$516$$ 0 0
$$517$$ −3600.00 −0.306243
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 4020.00 0.338041 0.169021 0.985613i $$-0.445940\pi$$
0.169021 + 0.985613i $$0.445940\pi$$
$$522$$ 0 0
$$523$$ 9076.00 0.758826 0.379413 0.925228i $$-0.376126\pi$$
0.379413 + 0.925228i $$0.376126\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −360.000 −0.0297568
$$528$$ 0 0
$$529$$ 2233.00 0.183529
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 960.000 0.0780154
$$534$$ 0 0
$$535$$ 8100.00 0.654567
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −10170.0 −0.812714
$$540$$ 0 0
$$541$$ −7486.00 −0.594914 −0.297457 0.954735i $$-0.596138\pi$$
−0.297457 + 0.954735i $$0.596138\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 8510.00 0.668859
$$546$$ 0 0
$$547$$ −7400.00 −0.578430 −0.289215 0.957264i $$-0.593394\pi$$
−0.289215 + 0.957264i $$0.593394\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −5880.00 −0.454621
$$552$$ 0 0
$$553$$ −1832.00 −0.140876
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −11490.0 −0.874052 −0.437026 0.899449i $$-0.643968\pi$$
−0.437026 + 0.899449i $$0.643968\pi$$
$$558$$ 0 0
$$559$$ −544.000 −0.0411606
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −19320.0 −1.44625 −0.723127 0.690715i $$-0.757296\pi$$
−0.723127 + 0.690715i $$0.757296\pi$$
$$564$$ 0 0
$$565$$ 6750.00 0.502610
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −8340.00 −0.614466 −0.307233 0.951634i $$-0.599403\pi$$
−0.307233 + 0.951634i $$0.599403\pi$$
$$570$$ 0 0
$$571$$ −21044.0 −1.54232 −0.771159 0.636642i $$-0.780323\pi$$
−0.771159 + 0.636642i $$0.780323\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 3000.00 0.217580
$$576$$ 0 0
$$577$$ 1418.00 0.102309 0.0511543 0.998691i $$-0.483710\pi$$
0.0511543 + 0.998691i $$0.483710\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 2280.00 0.162806
$$582$$ 0 0
$$583$$ 900.000 0.0639351
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −22020.0 −1.54832 −0.774159 0.632991i $$-0.781827\pi$$
−0.774159 + 0.632991i $$0.781827\pi$$
$$588$$ 0 0
$$589$$ 112.000 0.00783511
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −25230.0 −1.74717 −0.873585 0.486671i $$-0.838211\pi$$
−0.873585 + 0.486671i $$0.838211\pi$$
$$594$$ 0 0
$$595$$ −900.000 −0.0620108
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 8280.00 0.564794 0.282397 0.959298i $$-0.408870\pi$$
0.282397 + 0.959298i $$0.408870\pi$$
$$600$$ 0 0
$$601$$ −18874.0 −1.28101 −0.640505 0.767954i $$-0.721275\pi$$
−0.640505 + 0.767954i $$0.721275\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2155.00 0.144815
$$606$$ 0 0
$$607$$ −10550.0 −0.705455 −0.352728 0.935726i $$-0.614746\pi$$
−0.352728 + 0.935726i $$0.614746\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 480.000 0.0317819
$$612$$ 0 0
$$613$$ 11000.0 0.724773 0.362386 0.932028i $$-0.381962\pi$$
0.362386 + 0.932028i $$0.381962\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 11310.0 0.737963 0.368982 0.929437i $$-0.379706\pi$$
0.368982 + 0.929437i $$0.379706\pi$$
$$618$$ 0 0
$$619$$ 17572.0 1.14100 0.570499 0.821298i $$-0.306750\pi$$
0.570499 + 0.821298i $$0.306750\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −840.000 −0.0540191
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −18000.0 −1.14103
$$630$$ 0 0
$$631$$ −1604.00 −0.101195 −0.0505976 0.998719i $$-0.516113\pi$$
−0.0505976 + 0.998719i $$0.516113\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 12250.0 0.765553
$$636$$ 0 0
$$637$$ 1356.00 0.0843433
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −31320.0 −1.92990 −0.964950 0.262435i $$-0.915475\pi$$
−0.964950 + 0.262435i $$0.915475\pi$$
$$642$$ 0 0
$$643$$ 31300.0 1.91968 0.959838 0.280555i $$-0.0905186\pi$$
0.959838 + 0.280555i $$0.0905186\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 10920.0 0.663539 0.331769 0.943361i $$-0.392354\pi$$
0.331769 + 0.943361i $$0.392354\pi$$
$$648$$ 0 0
$$649$$ −13500.0 −0.816520
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 3210.00 0.192369 0.0961845 0.995364i $$-0.469336\pi$$
0.0961845 + 0.995364i $$0.469336\pi$$
$$654$$ 0 0
$$655$$ −3450.00 −0.205806
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −11910.0 −0.704018 −0.352009 0.935997i $$-0.614501\pi$$
−0.352009 + 0.935997i $$0.614501\pi$$
$$660$$ 0 0
$$661$$ −3382.00 −0.199008 −0.0995042 0.995037i $$-0.531726\pi$$
−0.0995042 + 0.995037i $$0.531726\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 280.000 0.0163277
$$666$$ 0 0
$$667$$ −25200.0 −1.46289
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −4980.00 −0.286514
$$672$$ 0 0
$$673$$ 15950.0 0.913562 0.456781 0.889579i $$-0.349002\pi$$
0.456781 + 0.889579i $$0.349002\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −32190.0 −1.82742 −0.913709 0.406369i $$-0.866795\pi$$
−0.913709 + 0.406369i $$0.866795\pi$$
$$678$$ 0 0
$$679$$ −3076.00 −0.173853
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 22140.0 1.24036 0.620178 0.784461i $$-0.287060\pi$$
0.620178 + 0.784461i $$0.287060\pi$$
$$684$$ 0 0
$$685$$ 10350.0 0.577304
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −120.000 −0.00663518
$$690$$ 0 0
$$691$$ 6172.00 0.339789 0.169894 0.985462i $$-0.445657\pi$$
0.169894 + 0.985462i $$0.445657\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −9620.00 −0.525047
$$696$$ 0 0
$$697$$ 21600.0 1.17383
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −19170.0 −1.03287 −0.516434 0.856327i $$-0.672741\pi$$
−0.516434 + 0.856327i $$0.672741\pi$$
$$702$$ 0 0
$$703$$ 5600.00 0.300438
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 900.000 0.0478755
$$708$$ 0 0
$$709$$ −21898.0 −1.15994 −0.579969 0.814638i $$-0.696936\pi$$
−0.579969 + 0.814638i $$0.696936\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 480.000 0.0252120
$$714$$ 0 0
$$715$$ 600.000 0.0313828
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 16680.0 0.865173 0.432586 0.901593i $$-0.357601\pi$$
0.432586 + 0.901593i $$0.357601\pi$$
$$720$$ 0 0
$$721$$ −2300.00 −0.118802
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −5250.00 −0.268938
$$726$$ 0 0
$$727$$ −6518.00 −0.332516 −0.166258 0.986082i $$-0.553168\pi$$
−0.166258 + 0.986082i $$0.553168\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −12240.0 −0.619306
$$732$$ 0 0
$$733$$ −23200.0 −1.16905 −0.584524 0.811377i $$-0.698719\pi$$
−0.584524 + 0.811377i $$0.698719\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −27240.0 −1.36146
$$738$$ 0 0
$$739$$ 16324.0 0.812568 0.406284 0.913747i $$-0.366824\pi$$
0.406284 + 0.913747i $$0.366824\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −120.000 −0.00592513 −0.00296257 0.999996i $$-0.500943\pi$$
−0.00296257 + 0.999996i $$0.500943\pi$$
$$744$$ 0 0
$$745$$ 14550.0 0.715531
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 3240.00 0.158060
$$750$$ 0 0
$$751$$ −30548.0 −1.48430 −0.742152 0.670232i $$-0.766195\pi$$
−0.742152 + 0.670232i $$0.766195\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 880.000 0.0424192
$$756$$ 0 0
$$757$$ 16952.0 0.813911 0.406956 0.913448i $$-0.366590\pi$$
0.406956 + 0.913448i $$0.366590\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 20220.0 0.963173 0.481586 0.876399i $$-0.340061\pi$$
0.481586 + 0.876399i $$0.340061\pi$$
$$762$$ 0 0
$$763$$ 3404.00 0.161511
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1800.00 0.0847382
$$768$$ 0 0
$$769$$ −20722.0 −0.971722 −0.485861 0.874036i $$-0.661494\pi$$
−0.485861 + 0.874036i $$0.661494\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −4350.00 −0.202404 −0.101202 0.994866i $$-0.532269\pi$$
−0.101202 + 0.994866i $$0.532269\pi$$
$$774$$ 0 0
$$775$$ 100.000 0.00463498
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −6720.00 −0.309074
$$780$$ 0 0
$$781$$ −30600.0 −1.40199
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −11740.0 −0.533782
$$786$$ 0 0
$$787$$ −41972.0 −1.90107 −0.950534 0.310621i $$-0.899463\pi$$
−0.950534 + 0.310621i $$0.899463\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2700.00 0.121367
$$792$$ 0 0
$$793$$ 664.000 0.0297343
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 39510.0 1.75598 0.877990 0.478679i $$-0.158884\pi$$
0.877990 + 0.478679i $$0.158884\pi$$
$$798$$ 0 0
$$799$$ 10800.0 0.478193
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −7500.00 −0.329601
$$804$$ 0 0
$$805$$ 1200.00 0.0525397
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −16680.0 −0.724892 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$810$$ 0 0
$$811$$ 15484.0 0.670428 0.335214 0.942142i $$-0.391191\pi$$
0.335214 + 0.942142i $$0.391191\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −9980.00 −0.428938
$$816$$ 0 0
$$817$$ 3808.00 0.163066
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −4170.00 −0.177264 −0.0886322 0.996064i $$-0.528250\pi$$
−0.0886322 + 0.996064i $$0.528250\pi$$
$$822$$ 0 0
$$823$$ 30226.0 1.28021 0.640105 0.768288i $$-0.278891\pi$$
0.640105 + 0.768288i $$0.278891\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −14760.0 −0.620623 −0.310312 0.950635i $$-0.600433\pi$$
−0.310312 + 0.950635i $$0.600433\pi$$
$$828$$ 0 0
$$829$$ −9934.00 −0.416191 −0.208095 0.978109i $$-0.566726\pi$$
−0.208095 + 0.978109i $$0.566726\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 30510.0 1.26904
$$834$$ 0 0
$$835$$ −15600.0 −0.646539
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −23520.0 −0.967820 −0.483910 0.875118i $$-0.660784\pi$$
−0.483910 + 0.875118i $$0.660784\pi$$
$$840$$ 0 0
$$841$$ 19711.0 0.808192
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 10905.0 0.443957
$$846$$ 0 0
$$847$$ 862.000 0.0349689
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 24000.0 0.966756
$$852$$ 0 0
$$853$$ 29816.0 1.19681 0.598406 0.801193i $$-0.295801\pi$$
0.598406 + 0.801193i $$0.295801\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 35430.0 1.41221 0.706106 0.708106i $$-0.250450\pi$$
0.706106 + 0.708106i $$0.250450\pi$$
$$858$$ 0 0
$$859$$ 36196.0 1.43771 0.718854 0.695161i $$-0.244667\pi$$
0.718854 + 0.695161i $$0.244667\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 480.000 0.0189332 0.00946662 0.999955i $$-0.496987\pi$$
0.00946662 + 0.999955i $$0.496987\pi$$
$$864$$ 0 0
$$865$$ 8850.00 0.347872
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 27480.0 1.07272
$$870$$ 0 0
$$871$$ 3632.00 0.141292
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 250.000 0.00965891
$$876$$ 0 0
$$877$$ 28532.0 1.09858 0.549291 0.835631i $$-0.314898\pi$$
0.549291 + 0.835631i $$0.314898\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 20340.0 0.777834 0.388917 0.921273i $$-0.372849\pi$$
0.388917 + 0.921273i $$0.372849\pi$$
$$882$$ 0 0
$$883$$ 10756.0 0.409930 0.204965 0.978769i $$-0.434292\pi$$
0.204965 + 0.978769i $$0.434292\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 600.000 0.0227125 0.0113563 0.999936i $$-0.496385\pi$$
0.0113563 + 0.999936i $$0.496385\pi$$
$$888$$ 0 0
$$889$$ 4900.00 0.184860
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −3360.00 −0.125911
$$894$$ 0 0
$$895$$ 10650.0 0.397754
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −840.000 −0.0311630
$$900$$ 0 0
$$901$$ −2700.00 −0.0998336
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 8270.00 0.303761
$$906$$ 0 0
$$907$$ −25400.0 −0.929871 −0.464936 0.885345i $$-0.653923\pi$$
−0.464936 + 0.885345i $$0.653923\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −36240.0 −1.31799 −0.658993 0.752149i $$-0.729017\pi$$
−0.658993 + 0.752149i $$0.729017\pi$$
$$912$$ 0 0
$$913$$ −34200.0 −1.23971
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −1380.00 −0.0496964
$$918$$ 0 0
$$919$$ −6572.00 −0.235898 −0.117949 0.993020i $$-0.537632\pi$$
−0.117949 + 0.993020i $$0.537632\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 4080.00 0.145498
$$924$$ 0 0
$$925$$ 5000.00 0.177729
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −2340.00 −0.0826404 −0.0413202 0.999146i $$-0.513156\pi$$
−0.0413202 + 0.999146i $$0.513156\pi$$
$$930$$ 0 0
$$931$$ −9492.00 −0.334144
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 13500.0 0.472190
$$936$$ 0 0
$$937$$ 2522.00 0.0879297 0.0439649 0.999033i $$-0.486001\pi$$
0.0439649 + 0.999033i $$0.486001\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 52770.0 1.82811 0.914056 0.405589i $$-0.132933\pi$$
0.914056 + 0.405589i $$0.132933\pi$$
$$942$$ 0 0
$$943$$ −28800.0 −0.994546
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 28200.0 0.967663 0.483832 0.875161i $$-0.339245\pi$$
0.483832 + 0.875161i $$0.339245\pi$$
$$948$$ 0 0
$$949$$ 1000.00 0.0342059
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 15570.0 0.529236 0.264618 0.964353i $$-0.414754\pi$$
0.264618 + 0.964353i $$0.414754\pi$$
$$954$$ 0 0
$$955$$ −8700.00 −0.294791
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 4140.00 0.139403
$$960$$ 0 0
$$961$$ −29775.0 −0.999463
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −430.000 −0.0143442
$$966$$ 0 0
$$967$$ 8350.00 0.277681 0.138841 0.990315i $$-0.455662\pi$$
0.138841 + 0.990315i $$0.455662\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 43650.0 1.44263 0.721316 0.692606i $$-0.243538\pi$$
0.721316 + 0.692606i $$0.243538\pi$$
$$972$$ 0 0
$$973$$ −3848.00 −0.126784
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −18810.0 −0.615952 −0.307976 0.951394i $$-0.599652\pi$$
−0.307976 + 0.951394i $$0.599652\pi$$
$$978$$ 0 0
$$979$$ 12600.0 0.411336
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −25320.0 −0.821549 −0.410774 0.911737i $$-0.634742\pi$$
−0.410774 + 0.911737i $$0.634742\pi$$
$$984$$ 0 0
$$985$$ −12450.0 −0.402731
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 16320.0 0.524718
$$990$$ 0 0
$$991$$ 6736.00 0.215919 0.107960 0.994155i $$-0.465568\pi$$
0.107960 + 0.994155i $$0.465568\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −4160.00 −0.132544
$$996$$ 0 0
$$997$$ −20500.0 −0.651195 −0.325598 0.945508i $$-0.605565\pi$$
−0.325598 + 0.945508i $$0.605565\pi$$
$$998$$ 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 720.4.a.h.1.1 1
3.2 odd 2 720.4.a.w.1.1 1
4.3 odd 2 180.4.a.b.1.1 1
12.11 even 2 180.4.a.e.1.1 yes 1
20.3 even 4 900.4.d.d.649.1 2
20.7 even 4 900.4.d.d.649.2 2
20.19 odd 2 900.4.a.i.1.1 1
36.7 odd 6 1620.4.i.i.1081.1 2
36.11 even 6 1620.4.i.c.1081.1 2
36.23 even 6 1620.4.i.c.541.1 2
36.31 odd 6 1620.4.i.i.541.1 2
60.23 odd 4 900.4.d.i.649.1 2
60.47 odd 4 900.4.d.i.649.2 2
60.59 even 2 900.4.a.j.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
180.4.a.b.1.1 1 4.3 odd 2
180.4.a.e.1.1 yes 1 12.11 even 2
720.4.a.h.1.1 1 1.1 even 1 trivial
720.4.a.w.1.1 1 3.2 odd 2
900.4.a.i.1.1 1 20.19 odd 2
900.4.a.j.1.1 1 60.59 even 2
900.4.d.d.649.1 2 20.3 even 4
900.4.d.d.649.2 2 20.7 even 4
900.4.d.i.649.1 2 60.23 odd 4
900.4.d.i.649.2 2 60.47 odd 4
1620.4.i.c.541.1 2 36.23 even 6
1620.4.i.c.1081.1 2 36.11 even 6
1620.4.i.i.541.1 2 36.31 odd 6
1620.4.i.i.1081.1 2 36.7 odd 6