# Properties

 Label 720.4.a.s.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 120) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+5.00000 q^{5} -20.0000 q^{7} +O(q^{10})$$ $$q+5.00000 q^{5} -20.0000 q^{7} +16.0000 q^{11} +58.0000 q^{13} -38.0000 q^{17} -4.00000 q^{19} -80.0000 q^{23} +25.0000 q^{25} -82.0000 q^{29} +8.00000 q^{31} -100.000 q^{35} +426.000 q^{37} +246.000 q^{41} +524.000 q^{43} -464.000 q^{47} +57.0000 q^{49} +702.000 q^{53} +80.0000 q^{55} -592.000 q^{59} +574.000 q^{61} +290.000 q^{65} +172.000 q^{67} +768.000 q^{71} -558.000 q^{73} -320.000 q^{77} -408.000 q^{79} +164.000 q^{83} -190.000 q^{85} +510.000 q^{89} -1160.00 q^{91} -20.0000 q^{95} +514.000 q^{97} +O(q^{100})$$

## 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
$$7$$ −20.0000 −1.07990 −0.539949 0.841698i $$-0.681557\pi$$
−0.539949 + 0.841698i $$0.681557\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 16.0000 0.438562 0.219281 0.975662i $$-0.429629\pi$$
0.219281 + 0.975662i $$0.429629\pi$$
$$12$$ 0 0
$$13$$ 58.0000 1.23741 0.618704 0.785624i $$-0.287658\pi$$
0.618704 + 0.785624i $$0.287658\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −38.0000 −0.542138 −0.271069 0.962560i $$-0.587377\pi$$
−0.271069 + 0.962560i $$0.587377\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.0482980 −0.0241490 0.999708i $$-0.507688\pi$$
−0.0241490 + 0.999708i $$0.507688\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −80.0000 −0.725268 −0.362634 0.931932i $$-0.618122\pi$$
−0.362634 + 0.931932i $$0.618122\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −82.0000 −0.525070 −0.262535 0.964923i $$-0.584558\pi$$
−0.262535 + 0.964923i $$0.584558\pi$$
$$30$$ 0 0
$$31$$ 8.00000 0.0463498 0.0231749 0.999731i $$-0.492623\pi$$
0.0231749 + 0.999731i $$0.492623\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −100.000 −0.482945
$$36$$ 0 0
$$37$$ 426.000 1.89281 0.946405 0.322982i $$-0.104685\pi$$
0.946405 + 0.322982i $$0.104685\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 246.000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 524.000 1.85835 0.929177 0.369634i $$-0.120517\pi$$
0.929177 + 0.369634i $$0.120517\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −464.000 −1.44003 −0.720014 0.693959i $$-0.755865\pi$$
−0.720014 + 0.693959i $$0.755865\pi$$
$$48$$ 0 0
$$49$$ 57.0000 0.166181
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 702.000 1.81938 0.909690 0.415288i $$-0.136319\pi$$
0.909690 + 0.415288i $$0.136319\pi$$
$$54$$ 0 0
$$55$$ 80.0000 0.196131
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −592.000 −1.30630 −0.653151 0.757228i $$-0.726553\pi$$
−0.653151 + 0.757228i $$0.726553\pi$$
$$60$$ 0 0
$$61$$ 574.000 1.20481 0.602403 0.798192i $$-0.294210\pi$$
0.602403 + 0.798192i $$0.294210\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 290.000 0.553386
$$66$$ 0 0
$$67$$ 172.000 0.313629 0.156815 0.987628i $$-0.449878\pi$$
0.156815 + 0.987628i $$0.449878\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 768.000 1.28373 0.641865 0.766818i $$-0.278161\pi$$
0.641865 + 0.766818i $$0.278161\pi$$
$$72$$ 0 0
$$73$$ −558.000 −0.894643 −0.447322 0.894373i $$-0.647622\pi$$
−0.447322 + 0.894373i $$0.647622\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −320.000 −0.473602
$$78$$ 0 0
$$79$$ −408.000 −0.581058 −0.290529 0.956866i $$-0.593831\pi$$
−0.290529 + 0.956866i $$0.593831\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 164.000 0.216884 0.108442 0.994103i $$-0.465414\pi$$
0.108442 + 0.994103i $$0.465414\pi$$
$$84$$ 0 0
$$85$$ −190.000 −0.242452
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 510.000 0.607415 0.303707 0.952765i $$-0.401776\pi$$
0.303707 + 0.952765i $$0.401776\pi$$
$$90$$ 0 0
$$91$$ −1160.00 −1.33628
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −20.0000 −0.0215995
$$96$$ 0 0
$$97$$ 514.000 0.538029 0.269014 0.963136i $$-0.413302\pi$$
0.269014 + 0.963136i $$0.413302\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −666.000 −0.656133 −0.328067 0.944655i $$-0.606397\pi$$
−0.328067 + 0.944655i $$0.606397\pi$$
$$102$$ 0 0
$$103$$ 1100.00 1.05229 0.526147 0.850394i $$-0.323636\pi$$
0.526147 + 0.850394i $$0.323636\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 1212.00 1.09503 0.547516 0.836795i $$-0.315573\pi$$
0.547516 + 0.836795i $$0.315573\pi$$
$$108$$ 0 0
$$109$$ 2078.00 1.82602 0.913011 0.407936i $$-0.133751\pi$$
0.913011 + 0.407936i $$0.133751\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1458.00 1.21378 0.606890 0.794786i $$-0.292417\pi$$
0.606890 + 0.794786i $$0.292417\pi$$
$$114$$ 0 0
$$115$$ −400.000 −0.324349
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 760.000 0.585455
$$120$$ 0 0
$$121$$ −1075.00 −0.807663
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ 2436.00 1.70205 0.851024 0.525127i $$-0.175982\pi$$
0.851024 + 0.525127i $$0.175982\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2544.00 1.69672 0.848360 0.529420i $$-0.177590\pi$$
0.848360 + 0.529420i $$0.177590\pi$$
$$132$$ 0 0
$$133$$ 80.0000 0.0521570
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −694.000 −0.432791 −0.216396 0.976306i $$-0.569430\pi$$
−0.216396 + 0.976306i $$0.569430\pi$$
$$138$$ 0 0
$$139$$ −516.000 −0.314867 −0.157434 0.987530i $$-0.550322\pi$$
−0.157434 + 0.987530i $$0.550322\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 928.000 0.542680
$$144$$ 0 0
$$145$$ −410.000 −0.234818
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −770.000 −0.423361 −0.211681 0.977339i $$-0.567894\pi$$
−0.211681 + 0.977339i $$0.567894\pi$$
$$150$$ 0 0
$$151$$ 424.000 0.228507 0.114254 0.993452i $$-0.463552\pi$$
0.114254 + 0.993452i $$0.463552\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 40.0000 0.0207282
$$156$$ 0 0
$$157$$ 922.000 0.468685 0.234343 0.972154i $$-0.424706\pi$$
0.234343 + 0.972154i $$0.424706\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1600.00 0.783215
$$162$$ 0 0
$$163$$ 3788.00 1.82024 0.910120 0.414345i $$-0.135989\pi$$
0.910120 + 0.414345i $$0.135989\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −48.0000 −0.0222416 −0.0111208 0.999938i $$-0.503540\pi$$
−0.0111208 + 0.999938i $$0.503540\pi$$
$$168$$ 0 0
$$169$$ 1167.00 0.531179
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −3242.00 −1.42477 −0.712384 0.701790i $$-0.752384\pi$$
−0.712384 + 0.701790i $$0.752384\pi$$
$$174$$ 0 0
$$175$$ −500.000 −0.215980
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −2728.00 −1.13911 −0.569554 0.821954i $$-0.692884\pi$$
−0.569554 + 0.821954i $$0.692884\pi$$
$$180$$ 0 0
$$181$$ −4090.00 −1.67960 −0.839799 0.542897i $$-0.817327\pi$$
−0.839799 + 0.542897i $$0.817327\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2130.00 0.846490
$$186$$ 0 0
$$187$$ −608.000 −0.237761
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1480.00 −0.560676 −0.280338 0.959901i $$-0.590446\pi$$
−0.280338 + 0.959901i $$0.590446\pi$$
$$192$$ 0 0
$$193$$ −1622.00 −0.604944 −0.302472 0.953158i $$-0.597812\pi$$
−0.302472 + 0.953158i $$0.597812\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2530.00 −0.915000 −0.457500 0.889210i $$-0.651255\pi$$
−0.457500 + 0.889210i $$0.651255\pi$$
$$198$$ 0 0
$$199$$ 2440.00 0.869181 0.434590 0.900628i $$-0.356893\pi$$
0.434590 + 0.900628i $$0.356893\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 1640.00 0.567022
$$204$$ 0 0
$$205$$ 1230.00 0.419058
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −64.0000 −0.0211817
$$210$$ 0 0
$$211$$ 148.000 0.0482879 0.0241439 0.999708i $$-0.492314\pi$$
0.0241439 + 0.999708i $$0.492314\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 2620.00 0.831081
$$216$$ 0 0
$$217$$ −160.000 −0.0500530
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −2204.00 −0.670847
$$222$$ 0 0
$$223$$ 676.000 0.202997 0.101498 0.994836i $$-0.467636\pi$$
0.101498 + 0.994836i $$0.467636\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −6276.00 −1.83503 −0.917517 0.397696i $$-0.869810\pi$$
−0.917517 + 0.397696i $$0.869810\pi$$
$$228$$ 0 0
$$229$$ 6190.00 1.78623 0.893115 0.449828i $$-0.148515\pi$$
0.893115 + 0.449828i $$0.148515\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −5406.00 −1.52000 −0.759998 0.649926i $$-0.774800\pi$$
−0.759998 + 0.649926i $$0.774800\pi$$
$$234$$ 0 0
$$235$$ −2320.00 −0.644000
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −600.000 −0.162388 −0.0811941 0.996698i $$-0.525873\pi$$
−0.0811941 + 0.996698i $$0.525873\pi$$
$$240$$ 0 0
$$241$$ −1054.00 −0.281718 −0.140859 0.990030i $$-0.544986\pi$$
−0.140859 + 0.990030i $$0.544986\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 285.000 0.0743183
$$246$$ 0 0
$$247$$ −232.000 −0.0597644
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −2232.00 −0.561285 −0.280643 0.959812i $$-0.590548\pi$$
−0.280643 + 0.959812i $$0.590548\pi$$
$$252$$ 0 0
$$253$$ −1280.00 −0.318075
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −3630.00 −0.881063 −0.440531 0.897737i $$-0.645210\pi$$
−0.440531 + 0.897737i $$0.645210\pi$$
$$258$$ 0 0
$$259$$ −8520.00 −2.04404
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6960.00 1.63183 0.815916 0.578170i $$-0.196233\pi$$
0.815916 + 0.578170i $$0.196233\pi$$
$$264$$ 0 0
$$265$$ 3510.00 0.813651
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 2062.00 0.467369 0.233685 0.972312i $$-0.424922\pi$$
0.233685 + 0.972312i $$0.424922\pi$$
$$270$$ 0 0
$$271$$ 2544.00 0.570247 0.285124 0.958491i $$-0.407965\pi$$
0.285124 + 0.958491i $$0.407965\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 400.000 0.0877124
$$276$$ 0 0
$$277$$ −694.000 −0.150536 −0.0752679 0.997163i $$-0.523981\pi$$
−0.0752679 + 0.997163i $$0.523981\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1982.00 0.420769 0.210385 0.977619i $$-0.432528\pi$$
0.210385 + 0.977619i $$0.432528\pi$$
$$282$$ 0 0
$$283$$ −5228.00 −1.09814 −0.549068 0.835778i $$-0.685017\pi$$
−0.549068 + 0.835778i $$0.685017\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −4920.00 −1.01191
$$288$$ 0 0
$$289$$ −3469.00 −0.706086
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 7454.00 1.48624 0.743118 0.669160i $$-0.233346\pi$$
0.743118 + 0.669160i $$0.233346\pi$$
$$294$$ 0 0
$$295$$ −2960.00 −0.584196
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −4640.00 −0.897452
$$300$$ 0 0
$$301$$ −10480.0 −2.00683
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 2870.00 0.538806
$$306$$ 0 0
$$307$$ 1316.00 0.244652 0.122326 0.992490i $$-0.460965\pi$$
0.122326 + 0.992490i $$0.460965\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −832.000 −0.151699 −0.0758495 0.997119i $$-0.524167\pi$$
−0.0758495 + 0.997119i $$0.524167\pi$$
$$312$$ 0 0
$$313$$ 6770.00 1.22257 0.611283 0.791412i $$-0.290654\pi$$
0.611283 + 0.791412i $$0.290654\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 6582.00 1.16619 0.583095 0.812404i $$-0.301842\pi$$
0.583095 + 0.812404i $$0.301842\pi$$
$$318$$ 0 0
$$319$$ −1312.00 −0.230276
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 152.000 0.0261842
$$324$$ 0 0
$$325$$ 1450.00 0.247482
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 9280.00 1.55508
$$330$$ 0 0
$$331$$ −11292.0 −1.87512 −0.937560 0.347825i $$-0.886920\pi$$
−0.937560 + 0.347825i $$0.886920\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 860.000 0.140259
$$336$$ 0 0
$$337$$ −8006.00 −1.29411 −0.647054 0.762444i $$-0.723999\pi$$
−0.647054 + 0.762444i $$0.723999\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 128.000 0.0203272
$$342$$ 0 0
$$343$$ 5720.00 0.900440
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −316.000 −0.0488869 −0.0244435 0.999701i $$-0.507781\pi$$
−0.0244435 + 0.999701i $$0.507781\pi$$
$$348$$ 0 0
$$349$$ 4926.00 0.755538 0.377769 0.925900i $$-0.376691\pi$$
0.377769 + 0.925900i $$0.376691\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −2438.00 −0.367597 −0.183798 0.982964i $$-0.558839\pi$$
−0.183798 + 0.982964i $$0.558839\pi$$
$$354$$ 0 0
$$355$$ 3840.00 0.574102
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −3336.00 −0.490438 −0.245219 0.969468i $$-0.578860\pi$$
−0.245219 + 0.969468i $$0.578860\pi$$
$$360$$ 0 0
$$361$$ −6843.00 −0.997667
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2790.00 −0.400097
$$366$$ 0 0
$$367$$ −44.0000 −0.00625826 −0.00312913 0.999995i $$-0.500996\pi$$
−0.00312913 + 0.999995i $$0.500996\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −14040.0 −1.96475
$$372$$ 0 0
$$373$$ −11966.0 −1.66106 −0.830531 0.556973i $$-0.811963\pi$$
−0.830531 + 0.556973i $$0.811963\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4756.00 −0.649725
$$378$$ 0 0
$$379$$ −12676.0 −1.71800 −0.859001 0.511975i $$-0.828914\pi$$
−0.859001 + 0.511975i $$0.828914\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 6672.00 0.890139 0.445070 0.895496i $$-0.353179\pi$$
0.445070 + 0.895496i $$0.353179\pi$$
$$384$$ 0 0
$$385$$ −1600.00 −0.211801
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −354.000 −0.0461401 −0.0230701 0.999734i $$-0.507344\pi$$
−0.0230701 + 0.999734i $$0.507344\pi$$
$$390$$ 0 0
$$391$$ 3040.00 0.393195
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −2040.00 −0.259857
$$396$$ 0 0
$$397$$ −5054.00 −0.638924 −0.319462 0.947599i $$-0.603502\pi$$
−0.319462 + 0.947599i $$0.603502\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −10266.0 −1.27845 −0.639226 0.769019i $$-0.720745\pi$$
−0.639226 + 0.769019i $$0.720745\pi$$
$$402$$ 0 0
$$403$$ 464.000 0.0573536
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 6816.00 0.830114
$$408$$ 0 0
$$409$$ −1526.00 −0.184489 −0.0922443 0.995736i $$-0.529404\pi$$
−0.0922443 + 0.995736i $$0.529404\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 11840.0 1.41067
$$414$$ 0 0
$$415$$ 820.000 0.0969933
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 2064.00 0.240652 0.120326 0.992734i $$-0.461606\pi$$
0.120326 + 0.992734i $$0.461606\pi$$
$$420$$ 0 0
$$421$$ 4590.00 0.531361 0.265680 0.964061i $$-0.414403\pi$$
0.265680 + 0.964061i $$0.414403\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −950.000 −0.108428
$$426$$ 0 0
$$427$$ −11480.0 −1.30107
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −5536.00 −0.618700 −0.309350 0.950948i $$-0.600111\pi$$
−0.309350 + 0.950948i $$0.600111\pi$$
$$432$$ 0 0
$$433$$ 1850.00 0.205324 0.102662 0.994716i $$-0.467264\pi$$
0.102662 + 0.994716i $$0.467264\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 320.000 0.0350290
$$438$$ 0 0
$$439$$ −11704.0 −1.27244 −0.636220 0.771507i $$-0.719503\pi$$
−0.636220 + 0.771507i $$0.719503\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 6948.00 0.745168 0.372584 0.927998i $$-0.378472\pi$$
0.372584 + 0.927998i $$0.378472\pi$$
$$444$$ 0 0
$$445$$ 2550.00 0.271644
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −12090.0 −1.27074 −0.635370 0.772208i $$-0.719152\pi$$
−0.635370 + 0.772208i $$0.719152\pi$$
$$450$$ 0 0
$$451$$ 3936.00 0.410951
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −5800.00 −0.597600
$$456$$ 0 0
$$457$$ 11626.0 1.19002 0.595012 0.803717i $$-0.297147\pi$$
0.595012 + 0.803717i $$0.297147\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −16314.0 −1.64820 −0.824098 0.566447i $$-0.808318\pi$$
−0.824098 + 0.566447i $$0.808318\pi$$
$$462$$ 0 0
$$463$$ 15756.0 1.58152 0.790760 0.612127i $$-0.209686\pi$$
0.790760 + 0.612127i $$0.209686\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 5684.00 0.563221 0.281610 0.959529i $$-0.409131\pi$$
0.281610 + 0.959529i $$0.409131\pi$$
$$468$$ 0 0
$$469$$ −3440.00 −0.338688
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 8384.00 0.815004
$$474$$ 0 0
$$475$$ −100.000 −0.00965961
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −3368.00 −0.321269 −0.160634 0.987014i $$-0.551354\pi$$
−0.160634 + 0.987014i $$0.551354\pi$$
$$480$$ 0 0
$$481$$ 24708.0 2.34218
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 2570.00 0.240614
$$486$$ 0 0
$$487$$ 5588.00 0.519952 0.259976 0.965615i $$-0.416285\pi$$
0.259976 + 0.965615i $$0.416285\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 10584.0 0.972809 0.486405 0.873734i $$-0.338308\pi$$
0.486405 + 0.873734i $$0.338308\pi$$
$$492$$ 0 0
$$493$$ 3116.00 0.284660
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −15360.0 −1.38630
$$498$$ 0 0
$$499$$ 12220.0 1.09628 0.548139 0.836388i $$-0.315337\pi$$
0.548139 + 0.836388i $$0.315337\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 16152.0 1.43177 0.715887 0.698216i $$-0.246023\pi$$
0.715887 + 0.698216i $$0.246023\pi$$
$$504$$ 0 0
$$505$$ −3330.00 −0.293432
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −10642.0 −0.926716 −0.463358 0.886171i $$-0.653356\pi$$
−0.463358 + 0.886171i $$0.653356\pi$$
$$510$$ 0 0
$$511$$ 11160.0 0.966124
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 5500.00 0.470600
$$516$$ 0 0
$$517$$ −7424.00 −0.631542
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −22882.0 −1.92414 −0.962072 0.272797i $$-0.912051\pi$$
−0.962072 + 0.272797i $$0.912051\pi$$
$$522$$ 0 0
$$523$$ 10052.0 0.840427 0.420213 0.907425i $$-0.361955\pi$$
0.420213 + 0.907425i $$0.361955\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −304.000 −0.0251280
$$528$$ 0 0
$$529$$ −5767.00 −0.473987
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 14268.0 1.15950
$$534$$ 0 0
$$535$$ 6060.00 0.489713
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 912.000 0.0728806
$$540$$ 0 0
$$541$$ −6530.00 −0.518940 −0.259470 0.965751i $$-0.583548\pi$$
−0.259470 + 0.965751i $$0.583548\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 10390.0 0.816621
$$546$$ 0 0
$$547$$ −16652.0 −1.30162 −0.650812 0.759239i $$-0.725571\pi$$
−0.650812 + 0.759239i $$0.725571\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 328.000 0.0253598
$$552$$ 0 0
$$553$$ 8160.00 0.627484
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 12886.0 0.980247 0.490123 0.871653i $$-0.336952\pi$$
0.490123 + 0.871653i $$0.336952\pi$$
$$558$$ 0 0
$$559$$ 30392.0 2.29954
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −11108.0 −0.831521 −0.415761 0.909474i $$-0.636485\pi$$
−0.415761 + 0.909474i $$0.636485\pi$$
$$564$$ 0 0
$$565$$ 7290.00 0.542819
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 9214.00 0.678859 0.339430 0.940631i $$-0.389766\pi$$
0.339430 + 0.940631i $$0.389766\pi$$
$$570$$ 0 0
$$571$$ 4052.00 0.296972 0.148486 0.988915i $$-0.452560\pi$$
0.148486 + 0.988915i $$0.452560\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −2000.00 −0.145054
$$576$$ 0 0
$$577$$ −8446.00 −0.609379 −0.304689 0.952452i $$-0.598553\pi$$
−0.304689 + 0.952452i $$0.598553\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3280.00 −0.234212
$$582$$ 0 0
$$583$$ 11232.0 0.797911
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 2172.00 0.152722 0.0763612 0.997080i $$-0.475670\pi$$
0.0763612 + 0.997080i $$0.475670\pi$$
$$588$$ 0 0
$$589$$ −32.0000 −0.00223860
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1218.00 0.0843461 0.0421731 0.999110i $$-0.486572\pi$$
0.0421731 + 0.999110i $$0.486572\pi$$
$$594$$ 0 0
$$595$$ 3800.00 0.261823
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 21240.0 1.44882 0.724410 0.689370i $$-0.242112\pi$$
0.724410 + 0.689370i $$0.242112\pi$$
$$600$$ 0 0
$$601$$ 17626.0 1.19631 0.598153 0.801382i $$-0.295902\pi$$
0.598153 + 0.801382i $$0.295902\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −5375.00 −0.361198
$$606$$ 0 0
$$607$$ −2580.00 −0.172519 −0.0862594 0.996273i $$-0.527491\pi$$
−0.0862594 + 0.996273i $$0.527491\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −26912.0 −1.78190
$$612$$ 0 0
$$613$$ −14166.0 −0.933376 −0.466688 0.884422i $$-0.654553\pi$$
−0.466688 + 0.884422i $$0.654553\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 21426.0 1.39802 0.699010 0.715112i $$-0.253624\pi$$
0.699010 + 0.715112i $$0.253624\pi$$
$$618$$ 0 0
$$619$$ −3668.00 −0.238173 −0.119087 0.992884i $$-0.537997\pi$$
−0.119087 + 0.992884i $$0.537997\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −10200.0 −0.655946
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −16188.0 −1.02617
$$630$$ 0 0
$$631$$ −20032.0 −1.26381 −0.631903 0.775048i $$-0.717726\pi$$
−0.631903 + 0.775048i $$0.717726\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 12180.0 0.761179
$$636$$ 0 0
$$637$$ 3306.00 0.205633
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −7458.00 −0.459553 −0.229776 0.973243i $$-0.573799\pi$$
−0.229776 + 0.973243i $$0.573799\pi$$
$$642$$ 0 0
$$643$$ −7092.00 −0.434963 −0.217481 0.976064i $$-0.569784\pi$$
−0.217481 + 0.976064i $$0.569784\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 3384.00 0.205624 0.102812 0.994701i $$-0.467216\pi$$
0.102812 + 0.994701i $$0.467216\pi$$
$$648$$ 0 0
$$649$$ −9472.00 −0.572894
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 29398.0 1.76177 0.880883 0.473335i $$-0.156950\pi$$
0.880883 + 0.473335i $$0.156950\pi$$
$$654$$ 0 0
$$655$$ 12720.0 0.758796
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −6624.00 −0.391554 −0.195777 0.980648i $$-0.562723\pi$$
−0.195777 + 0.980648i $$0.562723\pi$$
$$660$$ 0 0
$$661$$ 8646.00 0.508760 0.254380 0.967104i $$-0.418129\pi$$
0.254380 + 0.967104i $$0.418129\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 400.000 0.0233253
$$666$$ 0 0
$$667$$ 6560.00 0.380816
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 9184.00 0.528382
$$672$$ 0 0
$$673$$ 28698.0 1.64372 0.821862 0.569686i $$-0.192935\pi$$
0.821862 + 0.569686i $$0.192935\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −19426.0 −1.10281 −0.551405 0.834238i $$-0.685908\pi$$
−0.551405 + 0.834238i $$0.685908\pi$$
$$678$$ 0 0
$$679$$ −10280.0 −0.581016
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 8604.00 0.482025 0.241012 0.970522i $$-0.422521\pi$$
0.241012 + 0.970522i $$0.422521\pi$$
$$684$$ 0 0
$$685$$ −3470.00 −0.193550
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 40716.0 2.25132
$$690$$ 0 0
$$691$$ −12980.0 −0.714591 −0.357296 0.933991i $$-0.616301\pi$$
−0.357296 + 0.933991i $$0.616301\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −2580.00 −0.140813
$$696$$ 0 0
$$697$$ −9348.00 −0.508007
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 19630.0 1.05765 0.528827 0.848730i $$-0.322632\pi$$
0.528827 + 0.848730i $$0.322632\pi$$
$$702$$ 0 0
$$703$$ −1704.00 −0.0914190
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 13320.0 0.708558
$$708$$ 0 0
$$709$$ 8030.00 0.425350 0.212675 0.977123i $$-0.431782\pi$$
0.212675 + 0.977123i $$0.431782\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −640.000 −0.0336160
$$714$$ 0 0
$$715$$ 4640.00 0.242694
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 22720.0 1.17846 0.589230 0.807965i $$-0.299431\pi$$
0.589230 + 0.807965i $$0.299431\pi$$
$$720$$ 0 0
$$721$$ −22000.0 −1.13637
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2050.00 −0.105014
$$726$$ 0 0
$$727$$ −27116.0 −1.38332 −0.691662 0.722221i $$-0.743121\pi$$
−0.691662 + 0.722221i $$0.743121\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −19912.0 −1.00749
$$732$$ 0 0
$$733$$ 30882.0 1.55614 0.778071 0.628176i $$-0.216198\pi$$
0.778071 + 0.628176i $$0.216198\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 2752.00 0.137546
$$738$$ 0 0
$$739$$ 13836.0 0.688722 0.344361 0.938837i $$-0.388096\pi$$
0.344361 + 0.938837i $$0.388096\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 32712.0 1.61519 0.807595 0.589737i $$-0.200769\pi$$
0.807595 + 0.589737i $$0.200769\pi$$
$$744$$ 0 0
$$745$$ −3850.00 −0.189333
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −24240.0 −1.18252
$$750$$ 0 0
$$751$$ 8472.00 0.411648 0.205824 0.978589i $$-0.434013\pi$$
0.205824 + 0.978589i $$0.434013\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 2120.00 0.102192
$$756$$ 0 0
$$757$$ 9866.00 0.473693 0.236847 0.971547i $$-0.423886\pi$$
0.236847 + 0.971547i $$0.423886\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 3774.00 0.179773 0.0898866 0.995952i $$-0.471350\pi$$
0.0898866 + 0.995952i $$0.471350\pi$$
$$762$$ 0 0
$$763$$ −41560.0 −1.97192
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −34336.0 −1.61643
$$768$$ 0 0
$$769$$ −28670.0 −1.34443 −0.672215 0.740356i $$-0.734657\pi$$
−0.672215 + 0.740356i $$0.734657\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 3246.00 0.151036 0.0755178 0.997144i $$-0.475939\pi$$
0.0755178 + 0.997144i $$0.475939\pi$$
$$774$$ 0 0
$$775$$ 200.000 0.00926995
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −984.000 −0.0452573
$$780$$ 0 0
$$781$$ 12288.0 0.562995
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 4610.00 0.209602
$$786$$ 0 0
$$787$$ 19372.0 0.877430 0.438715 0.898626i $$-0.355434\pi$$
0.438715 + 0.898626i $$0.355434\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −29160.0 −1.31076
$$792$$ 0 0
$$793$$ 33292.0 1.49084
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 11814.0 0.525061 0.262530 0.964924i $$-0.415443\pi$$
0.262530 + 0.964924i $$0.415443\pi$$
$$798$$ 0 0
$$799$$ 17632.0 0.780695
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −8928.00 −0.392357
$$804$$ 0 0
$$805$$ 8000.00 0.350265
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 30054.0 1.30611 0.653055 0.757311i $$-0.273487\pi$$
0.653055 + 0.757311i $$0.273487\pi$$
$$810$$ 0 0
$$811$$ −2852.00 −0.123486 −0.0617431 0.998092i $$-0.519666\pi$$
−0.0617431 + 0.998092i $$0.519666\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 18940.0 0.814036
$$816$$ 0 0
$$817$$ −2096.00 −0.0897549
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −2170.00 −0.0922455 −0.0461227 0.998936i $$-0.514687\pi$$
−0.0461227 + 0.998936i $$0.514687\pi$$
$$822$$ 0 0
$$823$$ −19804.0 −0.838790 −0.419395 0.907804i $$-0.637758\pi$$
−0.419395 + 0.907804i $$0.637758\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 5508.00 0.231598 0.115799 0.993273i $$-0.463057\pi$$
0.115799 + 0.993273i $$0.463057\pi$$
$$828$$ 0 0
$$829$$ 33262.0 1.39353 0.696765 0.717299i $$-0.254622\pi$$
0.696765 + 0.717299i $$0.254622\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −2166.00 −0.0900930
$$834$$ 0 0
$$835$$ −240.000 −0.00994676
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −4600.00 −0.189284 −0.0946422 0.995511i $$-0.530171\pi$$
−0.0946422 + 0.995511i $$0.530171\pi$$
$$840$$ 0 0
$$841$$ −17665.0 −0.724302
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 5835.00 0.237550
$$846$$ 0 0
$$847$$ 21500.0 0.872195
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −34080.0 −1.37279
$$852$$ 0 0
$$853$$ −4198.00 −0.168507 −0.0842537 0.996444i $$-0.526851\pi$$
−0.0842537 + 0.996444i $$0.526851\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 5826.00 0.232220 0.116110 0.993236i $$-0.462958\pi$$
0.116110 + 0.993236i $$0.462958\pi$$
$$858$$ 0 0
$$859$$ 3004.00 0.119319 0.0596596 0.998219i $$-0.480998\pi$$
0.0596596 + 0.998219i $$0.480998\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −36936.0 −1.45691 −0.728457 0.685092i $$-0.759762\pi$$
−0.728457 + 0.685092i $$0.759762\pi$$
$$864$$ 0 0
$$865$$ −16210.0 −0.637175
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −6528.00 −0.254830
$$870$$ 0 0
$$871$$ 9976.00 0.388087
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −2500.00 −0.0965891
$$876$$ 0 0
$$877$$ 5434.00 0.209228 0.104614 0.994513i $$-0.466639\pi$$
0.104614 + 0.994513i $$0.466639\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 4758.00 0.181954 0.0909768 0.995853i $$-0.471001\pi$$
0.0909768 + 0.995853i $$0.471001\pi$$
$$882$$ 0 0
$$883$$ −15476.0 −0.589818 −0.294909 0.955525i $$-0.595289\pi$$
−0.294909 + 0.955525i $$0.595289\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −27440.0 −1.03872 −0.519360 0.854555i $$-0.673830\pi$$
−0.519360 + 0.854555i $$0.673830\pi$$
$$888$$ 0 0
$$889$$ −48720.0 −1.83804
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 1856.00 0.0695506
$$894$$ 0 0
$$895$$ −13640.0 −0.509424
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −656.000 −0.0243368
$$900$$ 0 0
$$901$$ −26676.0 −0.986356
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −20450.0 −0.751139
$$906$$ 0 0
$$907$$ 48924.0 1.79106 0.895532 0.444997i $$-0.146795\pi$$
0.895532 + 0.444997i $$0.146795\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −3440.00 −0.125107 −0.0625534 0.998042i $$-0.519924\pi$$
−0.0625534 + 0.998042i $$0.519924\pi$$
$$912$$ 0 0
$$913$$ 2624.00 0.0951169
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −50880.0 −1.83229
$$918$$ 0 0
$$919$$ 27184.0 0.975753 0.487877 0.872913i $$-0.337772\pi$$
0.487877 + 0.872913i $$0.337772\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 44544.0 1.58850
$$924$$ 0 0
$$925$$ 10650.0 0.378562
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −42490.0 −1.50059 −0.750297 0.661101i $$-0.770089\pi$$
−0.750297 + 0.661101i $$0.770089\pi$$
$$930$$ 0 0
$$931$$ −228.000 −0.00802621
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −3040.00 −0.106330
$$936$$ 0 0
$$937$$ 37354.0 1.30235 0.651175 0.758928i $$-0.274276\pi$$
0.651175 + 0.758928i $$0.274276\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 24470.0 0.847714 0.423857 0.905729i $$-0.360676\pi$$
0.423857 + 0.905729i $$0.360676\pi$$
$$942$$ 0 0
$$943$$ −19680.0 −0.679607
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −34100.0 −1.17012 −0.585059 0.810991i $$-0.698929\pi$$
−0.585059 + 0.810991i $$0.698929\pi$$
$$948$$ 0 0
$$949$$ −32364.0 −1.10704
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −1878.00 −0.0638346 −0.0319173 0.999491i $$-0.510161\pi$$
−0.0319173 + 0.999491i $$0.510161\pi$$
$$954$$ 0 0
$$955$$ −7400.00 −0.250742
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 13880.0 0.467371
$$960$$ 0 0
$$961$$ −29727.0 −0.997852
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −8110.00 −0.270539
$$966$$ 0 0
$$967$$ −38484.0 −1.27980 −0.639898 0.768460i $$-0.721023\pi$$
−0.639898 + 0.768460i $$0.721023\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 45272.0 1.49624 0.748119 0.663564i $$-0.230957\pi$$
0.748119 + 0.663564i $$0.230957\pi$$
$$972$$ 0 0
$$973$$ 10320.0 0.340025
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 25354.0 0.830242 0.415121 0.909766i $$-0.363739\pi$$
0.415121 + 0.909766i $$0.363739\pi$$
$$978$$ 0 0
$$979$$ 8160.00 0.266389
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −18744.0 −0.608180 −0.304090 0.952643i $$-0.598352\pi$$
−0.304090 + 0.952643i $$0.598352\pi$$
$$984$$ 0 0
$$985$$ −12650.0 −0.409201
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −41920.0 −1.34780
$$990$$ 0 0
$$991$$ −59600.0 −1.91045 −0.955225 0.295880i $$-0.904387\pi$$
−0.955225 + 0.295880i $$0.904387\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 12200.0 0.388710
$$996$$ 0 0
$$997$$ −17886.0 −0.568160 −0.284080 0.958801i $$-0.591688\pi$$
−0.284080 + 0.958801i $$0.591688\pi$$
$$998$$ 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.s.1.1 1
3.2 odd 2 240.4.a.a.1.1 1
4.3 odd 2 360.4.a.m.1.1 1
12.11 even 2 120.4.a.e.1.1 1
15.2 even 4 1200.4.f.h.49.2 2
15.8 even 4 1200.4.f.h.49.1 2
15.14 odd 2 1200.4.a.bj.1.1 1
20.3 even 4 1800.4.f.k.649.1 2
20.7 even 4 1800.4.f.k.649.2 2
20.19 odd 2 1800.4.a.e.1.1 1
24.5 odd 2 960.4.a.bd.1.1 1
24.11 even 2 960.4.a.q.1.1 1
60.23 odd 4 600.4.f.f.49.2 2
60.47 odd 4 600.4.f.f.49.1 2
60.59 even 2 600.4.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.a.e.1.1 1 12.11 even 2
240.4.a.a.1.1 1 3.2 odd 2
360.4.a.m.1.1 1 4.3 odd 2
600.4.a.a.1.1 1 60.59 even 2
600.4.f.f.49.1 2 60.47 odd 4
600.4.f.f.49.2 2 60.23 odd 4
720.4.a.s.1.1 1 1.1 even 1 trivial
960.4.a.q.1.1 1 24.11 even 2
960.4.a.bd.1.1 1 24.5 odd 2
1200.4.a.bj.1.1 1 15.14 odd 2
1200.4.f.h.49.1 2 15.8 even 4
1200.4.f.h.49.2 2 15.2 even 4
1800.4.a.e.1.1 1 20.19 odd 2
1800.4.f.k.649.1 2 20.3 even 4
1800.4.f.k.649.2 2 20.7 even 4