# Properties

 Label 720.4.a.t.1.1 Level $720$ Weight $4$ Character 720.1 Self dual yes Analytic conductor $42.481$ Analytic rank $0$ 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: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 90) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+5.00000 q^{5} -14.0000 q^{7} +O(q^{10})$$ $$q+5.00000 q^{5} -14.0000 q^{7} +6.00000 q^{11} +68.0000 q^{13} -78.0000 q^{17} -44.0000 q^{19} +120.000 q^{23} +25.0000 q^{25} -126.000 q^{29} +244.000 q^{31} -70.0000 q^{35} -304.000 q^{37} +480.000 q^{41} -104.000 q^{43} +600.000 q^{47} -147.000 q^{49} +258.000 q^{53} +30.0000 q^{55} +534.000 q^{59} +362.000 q^{61} +340.000 q^{65} +268.000 q^{67} -972.000 q^{71} +470.000 q^{73} -84.0000 q^{77} -1244.00 q^{79} +396.000 q^{83} -390.000 q^{85} +972.000 q^{89} -952.000 q^{91} -220.000 q^{95} -46.0000 q^{97} +O(q^{100})$$

## 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
$$11$$ 6.00000 0.164461 0.0822304 0.996613i $$-0.473796\pi$$
0.0822304 + 0.996613i $$0.473796\pi$$
$$12$$ 0 0
$$13$$ 68.0000 1.45075 0.725377 0.688352i $$-0.241665\pi$$
0.725377 + 0.688352i $$0.241665\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −78.0000 −1.11281 −0.556405 0.830911i $$-0.687820\pi$$
−0.556405 + 0.830911i $$0.687820\pi$$
$$18$$ 0 0
$$19$$ −44.0000 −0.531279 −0.265639 0.964072i $$-0.585583\pi$$
−0.265639 + 0.964072i $$0.585583\pi$$
$$20$$ 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
$$29$$ −126.000 −0.806814 −0.403407 0.915021i $$-0.632174\pi$$
−0.403407 + 0.915021i $$0.632174\pi$$
$$30$$ 0 0
$$31$$ 244.000 1.41367 0.706834 0.707380i $$-0.250123\pi$$
0.706834 + 0.707380i $$0.250123\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −70.0000 −0.338062
$$36$$ 0 0
$$37$$ −304.000 −1.35074 −0.675369 0.737480i $$-0.736016\pi$$
−0.675369 + 0.737480i $$0.736016\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 480.000 1.82838 0.914188 0.405291i $$-0.132830\pi$$
0.914188 + 0.405291i $$0.132830\pi$$
$$42$$ 0 0
$$43$$ −104.000 −0.368834 −0.184417 0.982848i $$-0.559040\pi$$
−0.184417 + 0.982848i $$0.559040\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 600.000 1.86211 0.931053 0.364884i $$-0.118891\pi$$
0.931053 + 0.364884i $$0.118891\pi$$
$$48$$ 0 0
$$49$$ −147.000 −0.428571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 258.000 0.668661 0.334330 0.942456i $$-0.391490\pi$$
0.334330 + 0.942456i $$0.391490\pi$$
$$54$$ 0 0
$$55$$ 30.0000 0.0735491
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 534.000 1.17832 0.589160 0.808016i $$-0.299459\pi$$
0.589160 + 0.808016i $$0.299459\pi$$
$$60$$ 0 0
$$61$$ 362.000 0.759825 0.379913 0.925022i $$-0.375954\pi$$
0.379913 + 0.925022i $$0.375954\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 340.000 0.648797
$$66$$ 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
$$71$$ −972.000 −1.62472 −0.812360 0.583156i $$-0.801818\pi$$
−0.812360 + 0.583156i $$0.801818\pi$$
$$72$$ 0 0
$$73$$ 470.000 0.753553 0.376776 0.926304i $$-0.377033\pi$$
0.376776 + 0.926304i $$0.377033\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −84.0000 −0.124321
$$78$$ 0 0
$$79$$ −1244.00 −1.77166 −0.885829 0.464012i $$-0.846409\pi$$
−0.885829 + 0.464012i $$0.846409\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 396.000 0.523695 0.261847 0.965109i $$-0.415668\pi$$
0.261847 + 0.965109i $$0.415668\pi$$
$$84$$ 0 0
$$85$$ −390.000 −0.497664
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 972.000 1.15766 0.578830 0.815448i $$-0.303509\pi$$
0.578830 + 0.815448i $$0.303509\pi$$
$$90$$ 0 0
$$91$$ −952.000 −1.09667
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −220.000 −0.237595
$$96$$ 0 0
$$97$$ −46.0000 −0.0481504 −0.0240752 0.999710i $$-0.507664\pi$$
−0.0240752 + 0.999710i $$0.507664\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1506.00 1.48369 0.741845 0.670572i $$-0.233951\pi$$
0.741845 + 0.670572i $$0.233951\pi$$
$$102$$ 0 0
$$103$$ 1474.00 1.41007 0.705037 0.709171i $$-0.250931\pi$$
0.705037 + 0.709171i $$0.250931\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 924.000 0.834827 0.417413 0.908717i $$-0.362937\pi$$
0.417413 + 0.908717i $$0.362937\pi$$
$$108$$ 0 0
$$109$$ 698.000 0.613360 0.306680 0.951813i $$-0.400782\pi$$
0.306680 + 0.951813i $$0.400782\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 222.000 0.184814 0.0924071 0.995721i $$-0.470544\pi$$
0.0924071 + 0.995721i $$0.470544\pi$$
$$114$$ 0 0
$$115$$ 600.000 0.486524
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 1092.00 0.841206
$$120$$ 0 0
$$121$$ −1295.00 −0.972953
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ 1906.00 1.33173 0.665867 0.746071i $$-0.268062\pi$$
0.665867 + 0.746071i $$0.268062\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2874.00 1.91681 0.958407 0.285406i $$-0.0921285\pi$$
0.958407 + 0.285406i $$0.0921285\pi$$
$$132$$ 0 0
$$133$$ 616.000 0.401609
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 798.000 0.497648 0.248824 0.968549i $$-0.419956\pi$$
0.248824 + 0.968549i $$0.419956\pi$$
$$138$$ 0 0
$$139$$ 700.000 0.427146 0.213573 0.976927i $$-0.431490\pi$$
0.213573 + 0.976927i $$0.431490\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 408.000 0.238592
$$144$$ 0 0
$$145$$ −630.000 −0.360818
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −114.000 −0.0626795 −0.0313397 0.999509i $$-0.509977\pi$$
−0.0313397 + 0.999509i $$0.509977\pi$$
$$150$$ 0 0
$$151$$ −1064.00 −0.573424 −0.286712 0.958017i $$-0.592562\pi$$
−0.286712 + 0.958017i $$0.592562\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1220.00 0.632211
$$156$$ 0 0
$$157$$ −1948.00 −0.990238 −0.495119 0.868825i $$-0.664875\pi$$
−0.495119 + 0.868825i $$0.664875\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −1680.00 −0.822376
$$162$$ 0 0
$$163$$ −2060.00 −0.989887 −0.494944 0.868925i $$-0.664811\pi$$
−0.494944 + 0.868925i $$0.664811\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1248.00 −0.578282 −0.289141 0.957286i $$-0.593370\pi$$
−0.289141 + 0.957286i $$0.593370\pi$$
$$168$$ 0 0
$$169$$ 2427.00 1.10469
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1146.00 0.503634 0.251817 0.967775i $$-0.418972\pi$$
0.251817 + 0.967775i $$0.418972\pi$$
$$174$$ 0 0
$$175$$ −350.000 −0.151186
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1146.00 −0.478525 −0.239263 0.970955i $$-0.576906\pi$$
−0.239263 + 0.970955i $$0.576906\pi$$
$$180$$ 0 0
$$181$$ −118.000 −0.0484579 −0.0242289 0.999706i $$-0.507713\pi$$
−0.0242289 + 0.999706i $$0.507713\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1520.00 −0.604068
$$186$$ 0 0
$$187$$ −468.000 −0.183014
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1692.00 0.640989 0.320494 0.947250i $$-0.396151\pi$$
0.320494 + 0.947250i $$0.396151\pi$$
$$192$$ 0 0
$$193$$ 3350.00 1.24942 0.624711 0.780856i $$-0.285217\pi$$
0.624711 + 0.780856i $$0.285217\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 3606.00 1.30415 0.652073 0.758156i $$-0.273899\pi$$
0.652073 + 0.758156i $$0.273899\pi$$
$$198$$ 0 0
$$199$$ −2696.00 −0.960374 −0.480187 0.877166i $$-0.659431\pi$$
−0.480187 + 0.877166i $$0.659431\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 1764.00 0.609894
$$204$$ 0 0
$$205$$ 2400.00 0.817674
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −264.000 −0.0873745
$$210$$ 0 0
$$211$$ 4.00000 0.00130508 0.000652539 1.00000i $$-0.499792\pi$$
0.000652539 1.00000i $$0.499792\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −520.000 −0.164947
$$216$$ 0 0
$$217$$ −3416.00 −1.06863
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −5304.00 −1.61441
$$222$$ 0 0
$$223$$ 1162.00 0.348938 0.174469 0.984663i $$-0.444179\pi$$
0.174469 + 0.984663i $$0.444179\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −2400.00 −0.701734 −0.350867 0.936425i $$-0.614113\pi$$
−0.350867 + 0.936425i $$0.614113\pi$$
$$228$$ 0 0
$$229$$ −2314.00 −0.667744 −0.333872 0.942618i $$-0.608355\pi$$
−0.333872 + 0.942618i $$0.608355\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 18.0000 0.00506103 0.00253051 0.999997i $$-0.499195\pi$$
0.00253051 + 0.999997i $$0.499195\pi$$
$$234$$ 0 0
$$235$$ 3000.00 0.832759
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −5868.00 −1.58816 −0.794078 0.607816i $$-0.792046\pi$$
−0.794078 + 0.607816i $$0.792046\pi$$
$$240$$ 0 0
$$241$$ −4330.00 −1.15734 −0.578672 0.815560i $$-0.696429\pi$$
−0.578672 + 0.815560i $$0.696429\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −735.000 −0.191663
$$246$$ 0 0
$$247$$ −2992.00 −0.770755
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 498.000 0.125233 0.0626165 0.998038i $$-0.480056\pi$$
0.0626165 + 0.998038i $$0.480056\pi$$
$$252$$ 0 0
$$253$$ 720.000 0.178917
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −642.000 −0.155824 −0.0779122 0.996960i $$-0.524825\pi$$
−0.0779122 + 0.996960i $$0.524825\pi$$
$$258$$ 0 0
$$259$$ 4256.00 1.02106
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −7968.00 −1.86817 −0.934084 0.357055i $$-0.883781\pi$$
−0.934084 + 0.357055i $$0.883781\pi$$
$$264$$ 0 0
$$265$$ 1290.00 0.299034
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 4218.00 0.956045 0.478022 0.878348i $$-0.341354\pi$$
0.478022 + 0.878348i $$0.341354\pi$$
$$270$$ 0 0
$$271$$ −848.000 −0.190082 −0.0950412 0.995473i $$-0.530298\pi$$
−0.0950412 + 0.995473i $$0.530298\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 150.000 0.0328921
$$276$$ 0 0
$$277$$ −1504.00 −0.326233 −0.163117 0.986607i $$-0.552155\pi$$
−0.163117 + 0.986607i $$0.552155\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1308.00 0.277682 0.138841 0.990315i $$-0.455662\pi$$
0.138841 + 0.990315i $$0.455662\pi$$
$$282$$ 0 0
$$283$$ 5932.00 1.24601 0.623005 0.782218i $$-0.285912\pi$$
0.623005 + 0.782218i $$0.285912\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −6720.00 −1.38212
$$288$$ 0 0
$$289$$ 1171.00 0.238347
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −5226.00 −1.04200 −0.521000 0.853556i $$-0.674441\pi$$
−0.521000 + 0.853556i $$0.674441\pi$$
$$294$$ 0 0
$$295$$ 2670.00 0.526961
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 8160.00 1.57828
$$300$$ 0 0
$$301$$ 1456.00 0.278812
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 1810.00 0.339804
$$306$$ 0 0
$$307$$ −4448.00 −0.826908 −0.413454 0.910525i $$-0.635678\pi$$
−0.413454 + 0.910525i $$0.635678\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −9132.00 −1.66504 −0.832521 0.553993i $$-0.813103\pi$$
−0.832521 + 0.553993i $$0.813103\pi$$
$$312$$ 0 0
$$313$$ −2170.00 −0.391871 −0.195936 0.980617i $$-0.562774\pi$$
−0.195936 + 0.980617i $$0.562774\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −7674.00 −1.35967 −0.679834 0.733366i $$-0.737948\pi$$
−0.679834 + 0.733366i $$0.737948\pi$$
$$318$$ 0 0
$$319$$ −756.000 −0.132689
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 3432.00 0.591212
$$324$$ 0 0
$$325$$ 1700.00 0.290151
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −8400.00 −1.40762
$$330$$ 0 0
$$331$$ −9596.00 −1.59349 −0.796743 0.604318i $$-0.793446\pi$$
−0.796743 + 0.604318i $$0.793446\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1340.00 0.218543
$$336$$ 0 0
$$337$$ 12158.0 1.96525 0.982624 0.185608i $$-0.0594255\pi$$
0.982624 + 0.185608i $$0.0594255\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1464.00 0.232493
$$342$$ 0 0
$$343$$ 6860.00 1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 10320.0 1.59656 0.798280 0.602286i $$-0.205743\pi$$
0.798280 + 0.602286i $$0.205743\pi$$
$$348$$ 0 0
$$349$$ −2158.00 −0.330989 −0.165494 0.986211i $$-0.552922\pi$$
−0.165494 + 0.986211i $$0.552922\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 330.000 0.0497567 0.0248784 0.999690i $$-0.492080\pi$$
0.0248784 + 0.999690i $$0.492080\pi$$
$$354$$ 0 0
$$355$$ −4860.00 −0.726597
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −8664.00 −1.27373 −0.636864 0.770976i $$-0.719769\pi$$
−0.636864 + 0.770976i $$0.719769\pi$$
$$360$$ 0 0
$$361$$ −4923.00 −0.717743
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2350.00 0.336999
$$366$$ 0 0
$$367$$ −3782.00 −0.537926 −0.268963 0.963151i $$-0.586681\pi$$
−0.268963 + 0.963151i $$0.586681\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −3612.00 −0.505460
$$372$$ 0 0
$$373$$ 11276.0 1.56528 0.782640 0.622475i $$-0.213873\pi$$
0.782640 + 0.622475i $$0.213873\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −8568.00 −1.17049
$$378$$ 0 0
$$379$$ −980.000 −0.132821 −0.0664106 0.997792i $$-0.521155\pi$$
−0.0664106 + 0.997792i $$0.521155\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −4200.00 −0.560339 −0.280170 0.959950i $$-0.590391\pi$$
−0.280170 + 0.959950i $$0.590391\pi$$
$$384$$ 0 0
$$385$$ −420.000 −0.0555979
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −13338.0 −1.73847 −0.869233 0.494402i $$-0.835387\pi$$
−0.869233 + 0.494402i $$0.835387\pi$$
$$390$$ 0 0
$$391$$ −9360.00 −1.21063
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −6220.00 −0.792309
$$396$$ 0 0
$$397$$ −7192.00 −0.909209 −0.454605 0.890693i $$-0.650219\pi$$
−0.454605 + 0.890693i $$0.650219\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 2316.00 0.288418 0.144209 0.989547i $$-0.453936\pi$$
0.144209 + 0.989547i $$0.453936\pi$$
$$402$$ 0 0
$$403$$ 16592.0 2.05088
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −1824.00 −0.222143
$$408$$ 0 0
$$409$$ −12358.0 −1.49404 −0.747022 0.664800i $$-0.768517\pi$$
−0.747022 + 0.664800i $$0.768517\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −7476.00 −0.890726
$$414$$ 0 0
$$415$$ 1980.00 0.234203
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 3306.00 0.385462 0.192731 0.981252i $$-0.438265\pi$$
0.192731 + 0.981252i $$0.438265\pi$$
$$420$$ 0 0
$$421$$ −14506.0 −1.67929 −0.839643 0.543139i $$-0.817236\pi$$
−0.839643 + 0.543139i $$0.817236\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −1950.00 −0.222562
$$426$$ 0 0
$$427$$ −5068.00 −0.574374
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −6480.00 −0.724201 −0.362100 0.932139i $$-0.617940\pi$$
−0.362100 + 0.932139i $$0.617940\pi$$
$$432$$ 0 0
$$433$$ 11894.0 1.32007 0.660034 0.751236i $$-0.270542\pi$$
0.660034 + 0.751236i $$0.270542\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −5280.00 −0.577979
$$438$$ 0 0
$$439$$ 12688.0 1.37942 0.689710 0.724086i $$-0.257738\pi$$
0.689710 + 0.724086i $$0.257738\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 4968.00 0.532814 0.266407 0.963861i $$-0.414163\pi$$
0.266407 + 0.963861i $$0.414163\pi$$
$$444$$ 0 0
$$445$$ 4860.00 0.517722
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 11508.0 1.20957 0.604784 0.796389i $$-0.293259\pi$$
0.604784 + 0.796389i $$0.293259\pi$$
$$450$$ 0 0
$$451$$ 2880.00 0.300696
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −4760.00 −0.490444
$$456$$ 0 0
$$457$$ 1082.00 0.110752 0.0553762 0.998466i $$-0.482364\pi$$
0.0553762 + 0.998466i $$0.482364\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 11238.0 1.13537 0.567685 0.823246i $$-0.307839\pi$$
0.567685 + 0.823246i $$0.307839\pi$$
$$462$$ 0 0
$$463$$ 2302.00 0.231065 0.115532 0.993304i $$-0.463143\pi$$
0.115532 + 0.993304i $$0.463143\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 15876.0 1.57313 0.786567 0.617505i $$-0.211856\pi$$
0.786567 + 0.617505i $$0.211856\pi$$
$$468$$ 0 0
$$469$$ −3752.00 −0.369406
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −624.000 −0.0606587
$$474$$ 0 0
$$475$$ −1100.00 −0.106256
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 4644.00 0.442985 0.221492 0.975162i $$-0.428907\pi$$
0.221492 + 0.975162i $$0.428907\pi$$
$$480$$ 0 0
$$481$$ −20672.0 −1.95959
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −230.000 −0.0215335
$$486$$ 0 0
$$487$$ −2426.00 −0.225734 −0.112867 0.993610i $$-0.536003\pi$$
−0.112867 + 0.993610i $$0.536003\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 234.000 0.0215077 0.0107538 0.999942i $$-0.496577\pi$$
0.0107538 + 0.999942i $$0.496577\pi$$
$$492$$ 0 0
$$493$$ 9828.00 0.897831
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 13608.0 1.22817
$$498$$ 0 0
$$499$$ −14204.0 −1.27427 −0.637133 0.770754i $$-0.719880\pi$$
−0.637133 + 0.770754i $$0.719880\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4920.00 0.436127 0.218064 0.975935i $$-0.430026\pi$$
0.218064 + 0.975935i $$0.430026\pi$$
$$504$$ 0 0
$$505$$ 7530.00 0.663526
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 4458.00 0.388207 0.194104 0.980981i $$-0.437820\pi$$
0.194104 + 0.980981i $$0.437820\pi$$
$$510$$ 0 0
$$511$$ −6580.00 −0.569632
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 7370.00 0.630604
$$516$$ 0 0
$$517$$ 3600.00 0.306243
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −4212.00 −0.354186 −0.177093 0.984194i $$-0.556669\pi$$
−0.177093 + 0.984194i $$0.556669\pi$$
$$522$$ 0 0
$$523$$ 11212.0 0.937412 0.468706 0.883354i $$-0.344720\pi$$
0.468706 + 0.883354i $$0.344720\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −19032.0 −1.57314
$$528$$ 0 0
$$529$$ 2233.00 0.183529
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 32640.0 2.65252
$$534$$ 0 0
$$535$$ 4620.00 0.373346
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −882.000 −0.0704832
$$540$$ 0 0
$$541$$ 14018.0 1.11401 0.557006 0.830508i $$-0.311950\pi$$
0.557006 + 0.830508i $$0.311950\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 3490.00 0.274303
$$546$$ 0 0
$$547$$ −18200.0 −1.42262 −0.711312 0.702876i $$-0.751899\pi$$
−0.711312 + 0.702876i $$0.751899\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 5544.00 0.428643
$$552$$ 0 0
$$553$$ 17416.0 1.33925
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 11826.0 0.899612 0.449806 0.893126i $$-0.351493\pi$$
0.449806 + 0.893126i $$0.351493\pi$$
$$558$$ 0 0
$$559$$ −7072.00 −0.535087
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −2952.00 −0.220980 −0.110490 0.993877i $$-0.535242\pi$$
−0.110490 + 0.993877i $$0.535242\pi$$
$$564$$ 0 0
$$565$$ 1110.00 0.0826514
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −3084.00 −0.227220 −0.113610 0.993525i $$-0.536241\pi$$
−0.113610 + 0.993525i $$0.536241\pi$$
$$570$$ 0 0
$$571$$ 4756.00 0.348568 0.174284 0.984695i $$-0.444239\pi$$
0.174284 + 0.984695i $$0.444239\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 3000.00 0.217580
$$576$$ 0 0
$$577$$ −11014.0 −0.794660 −0.397330 0.917676i $$-0.630063\pi$$
−0.397330 + 0.917676i $$0.630063\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −5544.00 −0.395876
$$582$$ 0 0
$$583$$ 1548.00 0.109968
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −852.000 −0.0599077 −0.0299538 0.999551i $$-0.509536\pi$$
−0.0299538 + 0.999551i $$0.509536\pi$$
$$588$$ 0 0
$$589$$ −10736.0 −0.751051
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −15546.0 −1.07656 −0.538278 0.842767i $$-0.680925\pi$$
−0.538278 + 0.842767i $$0.680925\pi$$
$$594$$ 0 0
$$595$$ 5460.00 0.376199
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −8616.00 −0.587713 −0.293857 0.955850i $$-0.594939\pi$$
−0.293857 + 0.955850i $$0.594939\pi$$
$$600$$ 0 0
$$601$$ 17510.0 1.18843 0.594216 0.804305i $$-0.297462\pi$$
0.594216 + 0.804305i $$0.297462\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −6475.00 −0.435118
$$606$$ 0 0
$$607$$ 13894.0 0.929061 0.464531 0.885557i $$-0.346223\pi$$
0.464531 + 0.885557i $$0.346223\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 40800.0 2.70146
$$612$$ 0 0
$$613$$ −6496.00 −0.428011 −0.214006 0.976832i $$-0.568651\pi$$
−0.214006 + 0.976832i $$0.568651\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 570.000 0.0371918 0.0185959 0.999827i $$-0.494080\pi$$
0.0185959 + 0.999827i $$0.494080\pi$$
$$618$$ 0 0
$$619$$ 2140.00 0.138956 0.0694781 0.997583i $$-0.477867\pi$$
0.0694781 + 0.997583i $$0.477867\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −13608.0 −0.875109
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 23712.0 1.50312
$$630$$ 0 0
$$631$$ −14660.0 −0.924890 −0.462445 0.886648i $$-0.653028\pi$$
−0.462445 + 0.886648i $$0.653028\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 9530.00 0.595569
$$636$$ 0 0
$$637$$ −9996.00 −0.621752
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 456.000 0.0280982 0.0140491 0.999901i $$-0.495528\pi$$
0.0140491 + 0.999901i $$0.495528\pi$$
$$642$$ 0 0
$$643$$ 23452.0 1.43835 0.719173 0.694831i $$-0.244521\pi$$
0.719173 + 0.694831i $$0.244521\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 7224.00 0.438956 0.219478 0.975617i $$-0.429565\pi$$
0.219478 + 0.975617i $$0.429565\pi$$
$$648$$ 0 0
$$649$$ 3204.00 0.193787
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −19146.0 −1.14738 −0.573691 0.819072i $$-0.694489\pi$$
−0.573691 + 0.819072i $$0.694489\pi$$
$$654$$ 0 0
$$655$$ 14370.0 0.857225
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 27810.0 1.64389 0.821945 0.569567i $$-0.192889\pi$$
0.821945 + 0.569567i $$0.192889\pi$$
$$660$$ 0 0
$$661$$ −30598.0 −1.80049 −0.900245 0.435383i $$-0.856613\pi$$
−0.900245 + 0.435383i $$0.856613\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 3080.00 0.179605
$$666$$ 0 0
$$667$$ −15120.0 −0.877734
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 2172.00 0.124961
$$672$$ 0 0
$$673$$ −3778.00 −0.216391 −0.108196 0.994130i $$-0.534507\pi$$
−0.108196 + 0.994130i $$0.534507\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 27198.0 1.54402 0.772012 0.635608i $$-0.219251\pi$$
0.772012 + 0.635608i $$0.219251\pi$$
$$678$$ 0 0
$$679$$ 644.000 0.0363983
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 32316.0 1.81045 0.905225 0.424933i $$-0.139702\pi$$
0.905225 + 0.424933i $$0.139702\pi$$
$$684$$ 0 0
$$685$$ 3990.00 0.222555
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 17544.0 0.970063
$$690$$ 0 0
$$691$$ −29324.0 −1.61438 −0.807191 0.590291i $$-0.799013\pi$$
−0.807191 + 0.590291i $$0.799013\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 3500.00 0.191025
$$696$$ 0 0
$$697$$ −37440.0 −2.03464
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −22782.0 −1.22748 −0.613741 0.789508i $$-0.710336\pi$$
−0.613741 + 0.789508i $$0.710336\pi$$
$$702$$ 0 0
$$703$$ 13376.0 0.717618
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −21084.0 −1.12156
$$708$$ 0 0
$$709$$ 26054.0 1.38008 0.690041 0.723770i $$-0.257592\pi$$
0.690041 + 0.723770i $$0.257592\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 29280.0 1.53793
$$714$$ 0 0
$$715$$ 2040.00 0.106702
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −5976.00 −0.309968 −0.154984 0.987917i $$-0.549533\pi$$
−0.154984 + 0.987917i $$0.549533\pi$$
$$720$$ 0 0
$$721$$ −20636.0 −1.06592
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −3150.00 −0.161363
$$726$$ 0 0
$$727$$ 5110.00 0.260687 0.130343 0.991469i $$-0.458392\pi$$
0.130343 + 0.991469i $$0.458392\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 8112.00 0.410442
$$732$$ 0 0
$$733$$ 17336.0 0.873560 0.436780 0.899568i $$-0.356119\pi$$
0.436780 + 0.899568i $$0.356119\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 1608.00 0.0803683
$$738$$ 0 0
$$739$$ 13660.0 0.679961 0.339981 0.940432i $$-0.389580\pi$$
0.339981 + 0.940432i $$0.389580\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 1320.00 0.0651765 0.0325882 0.999469i $$-0.489625\pi$$
0.0325882 + 0.999469i $$0.489625\pi$$
$$744$$ 0 0
$$745$$ −570.000 −0.0280311
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −12936.0 −0.631070
$$750$$ 0 0
$$751$$ −15860.0 −0.770625 −0.385313 0.922786i $$-0.625906\pi$$
−0.385313 + 0.922786i $$0.625906\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −5320.00 −0.256443
$$756$$ 0 0
$$757$$ 22160.0 1.06396 0.531981 0.846756i $$-0.321448\pi$$
0.531981 + 0.846756i $$0.321448\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −13116.0 −0.624776 −0.312388 0.949955i $$-0.601129\pi$$
−0.312388 + 0.949955i $$0.601129\pi$$
$$762$$ 0 0
$$763$$ −9772.00 −0.463657
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 36312.0 1.70945
$$768$$ 0 0
$$769$$ 32846.0 1.54026 0.770128 0.637889i $$-0.220192\pi$$
0.770128 + 0.637889i $$0.220192\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 11982.0 0.557520 0.278760 0.960361i $$-0.410077\pi$$
0.278760 + 0.960361i $$0.410077\pi$$
$$774$$ 0 0
$$775$$ 6100.00 0.282734
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −21120.0 −0.971377
$$780$$ 0 0
$$781$$ −5832.00 −0.267203
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −9740.00 −0.442848
$$786$$ 0 0
$$787$$ 21076.0 0.954610 0.477305 0.878738i $$-0.341614\pi$$
0.477305 + 0.878738i $$0.341614\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −3108.00 −0.139706
$$792$$ 0 0
$$793$$ 24616.0 1.10232
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −22086.0 −0.981589 −0.490794 0.871275i $$-0.663293\pi$$
−0.490794 + 0.871275i $$0.663293\pi$$
$$798$$ 0 0
$$799$$ −46800.0 −2.07217
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 2820.00 0.123930
$$804$$ 0 0
$$805$$ −8400.00 −0.367778
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −21384.0 −0.929322 −0.464661 0.885489i $$-0.653824\pi$$
−0.464661 + 0.885489i $$0.653824\pi$$
$$810$$ 0 0
$$811$$ −5228.00 −0.226362 −0.113181 0.993574i $$-0.536104\pi$$
−0.113181 + 0.993574i $$0.536104\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −10300.0 −0.442691
$$816$$ 0 0
$$817$$ 4576.00 0.195953
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 38010.0 1.61578 0.807892 0.589331i $$-0.200609\pi$$
0.807892 + 0.589331i $$0.200609\pi$$
$$822$$ 0 0
$$823$$ −38642.0 −1.63667 −0.818333 0.574745i $$-0.805101\pi$$
−0.818333 + 0.574745i $$0.805101\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −15432.0 −0.648879 −0.324440 0.945906i $$-0.605176\pi$$
−0.324440 + 0.945906i $$0.605176\pi$$
$$828$$ 0 0
$$829$$ −3886.00 −0.162806 −0.0814031 0.996681i $$-0.525940\pi$$
−0.0814031 + 0.996681i $$0.525940\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 11466.0 0.476919
$$834$$ 0 0
$$835$$ −6240.00 −0.258616
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 27552.0 1.13373 0.566866 0.823810i $$-0.308156\pi$$
0.566866 + 0.823810i $$0.308156\pi$$
$$840$$ 0 0
$$841$$ −8513.00 −0.349051
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 12135.0 0.494032
$$846$$ 0 0
$$847$$ 18130.0 0.735483
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −36480.0 −1.46947
$$852$$ 0 0
$$853$$ 15104.0 0.606273 0.303137 0.952947i $$-0.401966\pi$$
0.303137 + 0.952947i $$0.401966\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 12306.0 0.490508 0.245254 0.969459i $$-0.421129\pi$$
0.245254 + 0.969459i $$0.421129\pi$$
$$858$$ 0 0
$$859$$ 47500.0 1.88670 0.943352 0.331793i $$-0.107654\pi$$
0.943352 + 0.331793i $$0.107654\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 4272.00 0.168506 0.0842529 0.996444i $$-0.473150\pi$$
0.0842529 + 0.996444i $$0.473150\pi$$
$$864$$ 0 0
$$865$$ 5730.00 0.225232
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −7464.00 −0.291368
$$870$$ 0 0
$$871$$ 18224.0 0.708951
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −1750.00 −0.0676123
$$876$$ 0 0
$$877$$ −27796.0 −1.07024 −0.535122 0.844775i $$-0.679734\pi$$
−0.535122 + 0.844775i $$0.679734\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 39996.0 1.52951 0.764756 0.644320i $$-0.222860\pi$$
0.764756 + 0.644320i $$0.222860\pi$$
$$882$$ 0 0
$$883$$ 3772.00 0.143758 0.0718788 0.997413i $$-0.477101\pi$$
0.0718788 + 0.997413i $$0.477101\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −5784.00 −0.218949 −0.109474 0.993990i $$-0.534917\pi$$
−0.109474 + 0.993990i $$0.534917\pi$$
$$888$$ 0 0
$$889$$ −26684.0 −1.00670
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −26400.0 −0.989297
$$894$$ 0 0
$$895$$ −5730.00 −0.214003
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −30744.0 −1.14057
$$900$$ 0 0
$$901$$ −20124.0 −0.744093
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −590.000 −0.0216710
$$906$$ 0 0
$$907$$ 8440.00 0.308981 0.154490 0.987994i $$-0.450626\pi$$
0.154490 + 0.987994i $$0.450626\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −31920.0 −1.16087 −0.580437 0.814305i $$-0.697118\pi$$
−0.580437 + 0.814305i $$0.697118\pi$$
$$912$$ 0 0
$$913$$ 2376.00 0.0861272
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −40236.0 −1.44897
$$918$$ 0 0
$$919$$ −34652.0 −1.24381 −0.621906 0.783092i $$-0.713642\pi$$
−0.621906 + 0.783092i $$0.713642\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −66096.0 −2.35707
$$924$$ 0 0
$$925$$ −7600.00 −0.270148
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −1404.00 −0.0495842 −0.0247921 0.999693i $$-0.507892\pi$$
−0.0247921 + 0.999693i $$0.507892\pi$$
$$930$$ 0 0
$$931$$ 6468.00 0.227691
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −2340.00 −0.0818462
$$936$$ 0 0
$$937$$ −7654.00 −0.266857 −0.133429 0.991058i $$-0.542599\pi$$
−0.133429 + 0.991058i $$0.542599\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −11298.0 −0.391397 −0.195698 0.980664i $$-0.562697\pi$$
−0.195698 + 0.980664i $$0.562697\pi$$
$$942$$ 0 0
$$943$$ 57600.0 1.98909
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 28968.0 0.994016 0.497008 0.867746i $$-0.334432\pi$$
0.497008 + 0.867746i $$0.334432\pi$$
$$948$$ 0 0
$$949$$ 31960.0 1.09322
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −46410.0 −1.57751 −0.788755 0.614707i $$-0.789274\pi$$
−0.788755 + 0.614707i $$0.789274\pi$$
$$954$$ 0 0
$$955$$ 8460.00 0.286659
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −11172.0 −0.376186
$$960$$ 0 0
$$961$$ 29745.0 0.998456
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 16750.0 0.558758
$$966$$ 0 0
$$967$$ 41506.0 1.38029 0.690146 0.723670i $$-0.257546\pi$$
0.690146 + 0.723670i $$0.257546\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −18246.0 −0.603030 −0.301515 0.953461i $$-0.597492\pi$$
−0.301515 + 0.953461i $$0.597492\pi$$
$$972$$ 0 0
$$973$$ −9800.00 −0.322892
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −25998.0 −0.851330 −0.425665 0.904881i $$-0.639960\pi$$
−0.425665 + 0.904881i $$0.639960\pi$$
$$978$$ 0 0
$$979$$ 5832.00 0.190390
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 14616.0 0.474240 0.237120 0.971480i $$-0.423797\pi$$
0.237120 + 0.971480i $$0.423797\pi$$
$$984$$ 0 0
$$985$$ 18030.0 0.583232
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −12480.0 −0.401255
$$990$$ 0 0
$$991$$ 2968.00 0.0951379 0.0475689 0.998868i $$-0.484853\pi$$
0.0475689 + 0.998868i $$0.484853\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −13480.0 −0.429492
$$996$$ 0 0
$$997$$ −9052.00 −0.287542 −0.143771 0.989611i $$-0.545923\pi$$
−0.143771 + 0.989611i $$0.545923\pi$$
$$998$$ 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.t.1.1 1
3.2 odd 2 720.4.a.e.1.1 1
4.3 odd 2 90.4.a.e.1.1 yes 1
12.11 even 2 90.4.a.b.1.1 1
20.3 even 4 450.4.c.f.199.1 2
20.7 even 4 450.4.c.f.199.2 2
20.19 odd 2 450.4.a.c.1.1 1
36.7 odd 6 810.4.e.a.271.1 2
36.11 even 6 810.4.e.u.271.1 2
36.23 even 6 810.4.e.u.541.1 2
36.31 odd 6 810.4.e.a.541.1 2
60.23 odd 4 450.4.c.g.199.2 2
60.47 odd 4 450.4.c.g.199.1 2
60.59 even 2 450.4.a.m.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
90.4.a.b.1.1 1 12.11 even 2
90.4.a.e.1.1 yes 1 4.3 odd 2
450.4.a.c.1.1 1 20.19 odd 2
450.4.a.m.1.1 1 60.59 even 2
450.4.c.f.199.1 2 20.3 even 4
450.4.c.f.199.2 2 20.7 even 4
450.4.c.g.199.1 2 60.47 odd 4
450.4.c.g.199.2 2 60.23 odd 4
720.4.a.e.1.1 1 3.2 odd 2
720.4.a.t.1.1 1 1.1 even 1 trivial
810.4.e.a.271.1 2 36.7 odd 6
810.4.e.a.541.1 2 36.31 odd 6
810.4.e.u.271.1 2 36.11 even 6
810.4.e.u.541.1 2 36.23 even 6