# Properties

 Label 4900.2.a.w.1.1 Level $4900$ Weight $2$ Character 4900.1 Self dual yes Analytic conductor $39.127$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4900 = 2^{2} \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4900.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$39.1266969904$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 140) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 4900.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.00000 q^{3} +6.00000 q^{9} +O(q^{10})$$ $$q+3.00000 q^{3} +6.00000 q^{9} +3.00000 q^{11} +1.00000 q^{13} -5.00000 q^{17} +8.00000 q^{19} -2.00000 q^{23} +9.00000 q^{27} -1.00000 q^{29} +2.00000 q^{31} +9.00000 q^{33} -10.0000 q^{37} +3.00000 q^{39} +6.00000 q^{41} +4.00000 q^{43} +11.0000 q^{47} -15.0000 q^{51} -6.00000 q^{53} +24.0000 q^{57} +10.0000 q^{59} +10.0000 q^{67} -6.00000 q^{69} -10.0000 q^{73} -7.00000 q^{79} +9.00000 q^{81} +12.0000 q^{83} -3.00000 q^{87} -8.00000 q^{89} +6.00000 q^{93} +3.00000 q^{97} +18.0000 q^{99} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 3.00000 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 6.00000 2.00000
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 0 0
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −5.00000 −1.21268 −0.606339 0.795206i $$-0.707363\pi$$
−0.606339 + 0.795206i $$0.707363\pi$$
$$18$$ 0 0
$$19$$ 8.00000 1.83533 0.917663 0.397360i $$-0.130073\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2.00000 −0.417029 −0.208514 0.978019i $$-0.566863\pi$$
−0.208514 + 0.978019i $$0.566863\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 9.00000 1.73205
$$28$$ 0 0
$$29$$ −1.00000 −0.185695 −0.0928477 0.995680i $$-0.529597\pi$$
−0.0928477 + 0.995680i $$0.529597\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 0 0
$$33$$ 9.00000 1.56670
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ 3.00000 0.480384
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 11.0000 1.60451 0.802257 0.596978i $$-0.203632\pi$$
0.802257 + 0.596978i $$0.203632\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −15.0000 −2.10042
$$52$$ 0 0
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 24.0000 3.17888
$$58$$ 0 0
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 10.0000 1.22169 0.610847 0.791748i $$-0.290829\pi$$
0.610847 + 0.791748i $$0.290829\pi$$
$$68$$ 0 0
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −7.00000 −0.787562 −0.393781 0.919204i $$-0.628833\pi$$
−0.393781 + 0.919204i $$0.628833\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −3.00000 −0.321634
$$88$$ 0 0
$$89$$ −8.00000 −0.847998 −0.423999 0.905663i $$-0.639374\pi$$
−0.423999 + 0.905663i $$0.639374\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 6.00000 0.622171
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 3.00000 0.304604 0.152302 0.988334i $$-0.451331\pi$$
0.152302 + 0.988334i $$0.451331\pi$$
$$98$$ 0 0
$$99$$ 18.0000 1.80907
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 0 0
$$103$$ −5.00000 −0.492665 −0.246332 0.969185i $$-0.579225\pi$$
−0.246332 + 0.969185i $$0.579225\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −8.00000 −0.773389 −0.386695 0.922208i $$-0.626383\pi$$
−0.386695 + 0.922208i $$0.626383\pi$$
$$108$$ 0 0
$$109$$ −7.00000 −0.670478 −0.335239 0.942133i $$-0.608817\pi$$
−0.335239 + 0.942133i $$0.608817\pi$$
$$110$$ 0 0
$$111$$ −30.0000 −2.84747
$$112$$ 0 0
$$113$$ 10.0000 0.940721 0.470360 0.882474i $$-0.344124\pi$$
0.470360 + 0.882474i $$0.344124\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 6.00000 0.554700
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ 18.0000 1.62301
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 0 0
$$129$$ 12.0000 1.05654
$$130$$ 0 0
$$131$$ −2.00000 −0.174741 −0.0873704 0.996176i $$-0.527846\pi$$
−0.0873704 + 0.996176i $$0.527846\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −4.00000 −0.341743 −0.170872 0.985293i $$-0.554658\pi$$
−0.170872 + 0.985293i $$0.554658\pi$$
$$138$$ 0 0
$$139$$ −10.0000 −0.848189 −0.424094 0.905618i $$-0.639408\pi$$
−0.424094 + 0.905618i $$0.639408\pi$$
$$140$$ 0 0
$$141$$ 33.0000 2.77910
$$142$$ 0 0
$$143$$ 3.00000 0.250873
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ 9.00000 0.732410 0.366205 0.930534i $$-0.380657\pi$$
0.366205 + 0.930534i $$0.380657\pi$$
$$152$$ 0 0
$$153$$ −30.0000 −2.42536
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −18.0000 −1.43656 −0.718278 0.695756i $$-0.755069\pi$$
−0.718278 + 0.695756i $$0.755069\pi$$
$$158$$ 0 0
$$159$$ −18.0000 −1.42749
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −6.00000 −0.469956 −0.234978 0.972001i $$-0.575502\pi$$
−0.234978 + 0.972001i $$0.575502\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 3.00000 0.232147 0.116073 0.993241i $$-0.462969\pi$$
0.116073 + 0.993241i $$0.462969\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 48.0000 3.67065
$$172$$ 0 0
$$173$$ −9.00000 −0.684257 −0.342129 0.939653i $$-0.611148\pi$$
−0.342129 + 0.939653i $$0.611148\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 30.0000 2.25494
$$178$$ 0 0
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −15.0000 −1.09691
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 7.00000 0.506502 0.253251 0.967401i $$-0.418500\pi$$
0.253251 + 0.967401i $$0.418500\pi$$
$$192$$ 0 0
$$193$$ −8.00000 −0.575853 −0.287926 0.957653i $$-0.592966\pi$$
−0.287926 + 0.957653i $$0.592966\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −10.0000 −0.712470 −0.356235 0.934396i $$-0.615940\pi$$
−0.356235 + 0.934396i $$0.615940\pi$$
$$198$$ 0 0
$$199$$ −18.0000 −1.27599 −0.637993 0.770042i $$-0.720235\pi$$
−0.637993 + 0.770042i $$0.720235\pi$$
$$200$$ 0 0
$$201$$ 30.0000 2.11604
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −12.0000 −0.834058
$$208$$ 0 0
$$209$$ 24.0000 1.66011
$$210$$ 0 0
$$211$$ −3.00000 −0.206529 −0.103264 0.994654i $$-0.532929\pi$$
−0.103264 + 0.994654i $$0.532929\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −30.0000 −2.02721
$$220$$ 0 0
$$221$$ −5.00000 −0.336336
$$222$$ 0 0
$$223$$ 19.0000 1.27233 0.636167 0.771551i $$-0.280519\pi$$
0.636167 + 0.771551i $$0.280519\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 27.0000 1.79205 0.896026 0.444001i $$-0.146441\pi$$
0.896026 + 0.444001i $$0.146441\pi$$
$$228$$ 0 0
$$229$$ 26.0000 1.71813 0.859064 0.511868i $$-0.171046\pi$$
0.859064 + 0.511868i $$0.171046\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −16.0000 −1.04819 −0.524097 0.851658i $$-0.675597\pi$$
−0.524097 + 0.851658i $$0.675597\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −21.0000 −1.36410
$$238$$ 0 0
$$239$$ 5.00000 0.323423 0.161712 0.986838i $$-0.448299\pi$$
0.161712 + 0.986838i $$0.448299\pi$$
$$240$$ 0 0
$$241$$ 18.0000 1.15948 0.579741 0.814801i $$-0.303154\pi$$
0.579741 + 0.814801i $$0.303154\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 8.00000 0.509028
$$248$$ 0 0
$$249$$ 36.0000 2.28141
$$250$$ 0 0
$$251$$ −2.00000 −0.126239 −0.0631194 0.998006i $$-0.520105\pi$$
−0.0631194 + 0.998006i $$0.520105\pi$$
$$252$$ 0 0
$$253$$ −6.00000 −0.377217
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −24.0000 −1.46878
$$268$$ 0 0
$$269$$ −2.00000 −0.121942 −0.0609711 0.998140i $$-0.519420\pi$$
−0.0609711 + 0.998140i $$0.519420\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 14.0000 0.841178 0.420589 0.907251i $$-0.361823\pi$$
0.420589 + 0.907251i $$0.361823\pi$$
$$278$$ 0 0
$$279$$ 12.0000 0.718421
$$280$$ 0 0
$$281$$ 15.0000 0.894825 0.447412 0.894328i $$-0.352346\pi$$
0.447412 + 0.894328i $$0.352346\pi$$
$$282$$ 0 0
$$283$$ −7.00000 −0.416107 −0.208053 0.978117i $$-0.566713\pi$$
−0.208053 + 0.978117i $$0.566713\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8.00000 0.470588
$$290$$ 0 0
$$291$$ 9.00000 0.527589
$$292$$ 0 0
$$293$$ 15.0000 0.876309 0.438155 0.898900i $$-0.355632\pi$$
0.438155 + 0.898900i $$0.355632\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 27.0000 1.56670
$$298$$ 0 0
$$299$$ −2.00000 −0.115663
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 36.0000 2.06815
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −19.0000 −1.08439 −0.542194 0.840254i $$-0.682406\pi$$
−0.542194 + 0.840254i $$0.682406\pi$$
$$308$$ 0 0
$$309$$ −15.0000 −0.853320
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ −7.00000 −0.395663 −0.197832 0.980236i $$-0.563390\pi$$
−0.197832 + 0.980236i $$0.563390\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −28.0000 −1.57264 −0.786318 0.617822i $$-0.788015\pi$$
−0.786318 + 0.617822i $$0.788015\pi$$
$$318$$ 0 0
$$319$$ −3.00000 −0.167968
$$320$$ 0 0
$$321$$ −24.0000 −1.33955
$$322$$ 0 0
$$323$$ −40.0000 −2.22566
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −21.0000 −1.16130
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ 0 0
$$333$$ −60.0000 −3.28798
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −22.0000 −1.19842 −0.599208 0.800593i $$-0.704518\pi$$
−0.599208 + 0.800593i $$0.704518\pi$$
$$338$$ 0 0
$$339$$ 30.0000 1.62938
$$340$$ 0 0
$$341$$ 6.00000 0.324918
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −18.0000 −0.966291 −0.483145 0.875540i $$-0.660506\pi$$
−0.483145 + 0.875540i $$0.660506\pi$$
$$348$$ 0 0
$$349$$ −36.0000 −1.92704 −0.963518 0.267644i $$-0.913755\pi$$
−0.963518 + 0.267644i $$0.913755\pi$$
$$350$$ 0 0
$$351$$ 9.00000 0.480384
$$352$$ 0 0
$$353$$ −9.00000 −0.479022 −0.239511 0.970894i $$-0.576987\pi$$
−0.239511 + 0.970894i $$0.576987\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 28.0000 1.47778 0.738892 0.673824i $$-0.235349\pi$$
0.738892 + 0.673824i $$0.235349\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ 0 0
$$363$$ −6.00000 −0.314918
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 19.0000 0.991792 0.495896 0.868382i $$-0.334840\pi$$
0.495896 + 0.868382i $$0.334840\pi$$
$$368$$ 0 0
$$369$$ 36.0000 1.87409
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −32.0000 −1.65690 −0.828449 0.560065i $$-0.810776\pi$$
−0.828449 + 0.560065i $$0.810776\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −1.00000 −0.0515026
$$378$$ 0 0
$$379$$ 28.0000 1.43826 0.719132 0.694874i $$-0.244540\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$380$$ 0 0
$$381$$ 6.00000 0.307389
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 24.0000 1.21999
$$388$$ 0 0
$$389$$ 9.00000 0.456318 0.228159 0.973624i $$-0.426729\pi$$
0.228159 + 0.973624i $$0.426729\pi$$
$$390$$ 0 0
$$391$$ 10.0000 0.505722
$$392$$ 0 0
$$393$$ −6.00000 −0.302660
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −17.0000 −0.853206 −0.426603 0.904439i $$-0.640290\pi$$
−0.426603 + 0.904439i $$0.640290\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −27.0000 −1.34832 −0.674158 0.738587i $$-0.735493\pi$$
−0.674158 + 0.738587i $$0.735493\pi$$
$$402$$ 0 0
$$403$$ 2.00000 0.0996271
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −30.0000 −1.48704
$$408$$ 0 0
$$409$$ −4.00000 −0.197787 −0.0988936 0.995098i $$-0.531530\pi$$
−0.0988936 + 0.995098i $$0.531530\pi$$
$$410$$ 0 0
$$411$$ −12.0000 −0.591916
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −30.0000 −1.46911
$$418$$ 0 0
$$419$$ −2.00000 −0.0977064 −0.0488532 0.998806i $$-0.515557\pi$$
−0.0488532 + 0.998806i $$0.515557\pi$$
$$420$$ 0 0
$$421$$ −23.0000 −1.12095 −0.560476 0.828171i $$-0.689382\pi$$
−0.560476 + 0.828171i $$0.689382\pi$$
$$422$$ 0 0
$$423$$ 66.0000 3.20903
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 9.00000 0.434524
$$430$$ 0 0
$$431$$ −37.0000 −1.78223 −0.891114 0.453780i $$-0.850075\pi$$
−0.891114 + 0.453780i $$0.850075\pi$$
$$432$$ 0 0
$$433$$ −38.0000 −1.82616 −0.913082 0.407777i $$-0.866304\pi$$
−0.913082 + 0.407777i $$0.866304\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −16.0000 −0.765384
$$438$$ 0 0
$$439$$ −26.0000 −1.24091 −0.620456 0.784241i $$-0.713053\pi$$
−0.620456 + 0.784241i $$0.713053\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −12.0000 −0.570137 −0.285069 0.958507i $$-0.592016\pi$$
−0.285069 + 0.958507i $$0.592016\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −18.0000 −0.851371
$$448$$ 0 0
$$449$$ 11.0000 0.519122 0.259561 0.965727i $$-0.416422\pi$$
0.259561 + 0.965727i $$0.416422\pi$$
$$450$$ 0 0
$$451$$ 18.0000 0.847587
$$452$$ 0 0
$$453$$ 27.0000 1.26857
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 0 0
$$459$$ −45.0000 −2.10042
$$460$$ 0 0
$$461$$ −28.0000 −1.30409 −0.652045 0.758180i $$-0.726089\pi$$
−0.652045 + 0.758180i $$0.726089\pi$$
$$462$$ 0 0
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −23.0000 −1.06431 −0.532157 0.846646i $$-0.678618\pi$$
−0.532157 + 0.846646i $$0.678618\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −54.0000 −2.48819
$$472$$ 0 0
$$473$$ 12.0000 0.551761
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −36.0000 −1.64833
$$478$$ 0 0
$$479$$ 18.0000 0.822441 0.411220 0.911536i $$-0.365103\pi$$
0.411220 + 0.911536i $$0.365103\pi$$
$$480$$ 0 0
$$481$$ −10.0000 −0.455961
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 26.0000 1.17817 0.589086 0.808070i $$-0.299488\pi$$
0.589086 + 0.808070i $$0.299488\pi$$
$$488$$ 0 0
$$489$$ −18.0000 −0.813988
$$490$$ 0 0
$$491$$ 33.0000 1.48927 0.744635 0.667472i $$-0.232624\pi$$
0.744635 + 0.667472i $$0.232624\pi$$
$$492$$ 0 0
$$493$$ 5.00000 0.225189
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −29.0000 −1.29822 −0.649109 0.760695i $$-0.724858\pi$$
−0.649109 + 0.760695i $$0.724858\pi$$
$$500$$ 0 0
$$501$$ 9.00000 0.402090
$$502$$ 0 0
$$503$$ 1.00000 0.0445878 0.0222939 0.999751i $$-0.492903\pi$$
0.0222939 + 0.999751i $$0.492903\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −36.0000 −1.59882
$$508$$ 0 0
$$509$$ −26.0000 −1.15243 −0.576215 0.817298i $$-0.695471\pi$$
−0.576215 + 0.817298i $$0.695471\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 72.0000 3.17888
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 33.0000 1.45134
$$518$$ 0 0
$$519$$ −27.0000 −1.18517
$$520$$ 0 0
$$521$$ −12.0000 −0.525730 −0.262865 0.964833i $$-0.584667\pi$$
−0.262865 + 0.964833i $$0.584667\pi$$
$$522$$ 0 0
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −10.0000 −0.435607
$$528$$ 0 0
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 60.0000 2.60378
$$532$$ 0 0
$$533$$ 6.00000 0.259889
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 12.0000 0.517838
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −25.0000 −1.07483 −0.537417 0.843317i $$-0.680600\pi$$
−0.537417 + 0.843317i $$0.680600\pi$$
$$542$$ 0 0
$$543$$ 30.0000 1.28742
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 8.00000 0.342055 0.171028 0.985266i $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −8.00000 −0.340811
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −20.0000 −0.847427 −0.423714 0.905796i $$-0.639274\pi$$
−0.423714 + 0.905796i $$0.639274\pi$$
$$558$$ 0 0
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ −45.0000 −1.89990
$$562$$ 0 0
$$563$$ −16.0000 −0.674320 −0.337160 0.941447i $$-0.609466\pi$$
−0.337160 + 0.941447i $$0.609466\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 0 0
$$573$$ 21.0000 0.877288
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 17.0000 0.707719 0.353860 0.935299i $$-0.384869\pi$$
0.353860 + 0.935299i $$0.384869\pi$$
$$578$$ 0 0
$$579$$ −24.0000 −0.997406
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −18.0000 −0.745484
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 28.0000 1.15568 0.577842 0.816149i $$-0.303895\pi$$
0.577842 + 0.816149i $$0.303895\pi$$
$$588$$ 0 0
$$589$$ 16.0000 0.659269
$$590$$ 0 0
$$591$$ −30.0000 −1.23404
$$592$$ 0 0
$$593$$ −3.00000 −0.123195 −0.0615976 0.998101i $$-0.519620\pi$$
−0.0615976 + 0.998101i $$0.519620\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −54.0000 −2.21007
$$598$$ 0 0
$$599$$ −21.0000 −0.858037 −0.429018 0.903296i $$-0.641140\pi$$
−0.429018 + 0.903296i $$0.641140\pi$$
$$600$$ 0 0
$$601$$ −8.00000 −0.326327 −0.163163 0.986599i $$-0.552170\pi$$
−0.163163 + 0.986599i $$0.552170\pi$$
$$602$$ 0 0
$$603$$ 60.0000 2.44339
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 5.00000 0.202944 0.101472 0.994838i $$-0.467645\pi$$
0.101472 + 0.994838i $$0.467645\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 11.0000 0.445012
$$612$$ 0 0
$$613$$ 12.0000 0.484675 0.242338 0.970192i $$-0.422086\pi$$
0.242338 + 0.970192i $$0.422086\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 34.0000 1.36879 0.684394 0.729112i $$-0.260067\pi$$
0.684394 + 0.729112i $$0.260067\pi$$
$$618$$ 0 0
$$619$$ 2.00000 0.0803868 0.0401934 0.999192i $$-0.487203\pi$$
0.0401934 + 0.999192i $$0.487203\pi$$
$$620$$ 0 0
$$621$$ −18.0000 −0.722315
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 72.0000 2.87540
$$628$$ 0 0
$$629$$ 50.0000 1.99363
$$630$$ 0 0
$$631$$ 15.0000 0.597141 0.298570 0.954388i $$-0.403490\pi$$
0.298570 + 0.954388i $$0.403490\pi$$
$$632$$ 0 0
$$633$$ −9.00000 −0.357718
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −26.0000 −1.02694 −0.513469 0.858108i $$-0.671640\pi$$
−0.513469 + 0.858108i $$0.671640\pi$$
$$642$$ 0 0
$$643$$ −5.00000 −0.197181 −0.0985904 0.995128i $$-0.531433\pi$$
−0.0985904 + 0.995128i $$0.531433\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 0 0
$$649$$ 30.0000 1.17760
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −36.0000 −1.40879 −0.704394 0.709809i $$-0.748781\pi$$
−0.704394 + 0.709809i $$0.748781\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −60.0000 −2.34082
$$658$$ 0 0
$$659$$ 39.0000 1.51922 0.759612 0.650376i $$-0.225389\pi$$
0.759612 + 0.650376i $$0.225389\pi$$
$$660$$ 0 0
$$661$$ −28.0000 −1.08907 −0.544537 0.838737i $$-0.683295\pi$$
−0.544537 + 0.838737i $$0.683295\pi$$
$$662$$ 0 0
$$663$$ −15.0000 −0.582552
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 2.00000 0.0774403
$$668$$ 0 0
$$669$$ 57.0000 2.20375
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 16.0000 0.616755 0.308377 0.951264i $$-0.400214\pi$$
0.308377 + 0.951264i $$0.400214\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −11.0000 −0.422764 −0.211382 0.977403i $$-0.567796\pi$$
−0.211382 + 0.977403i $$0.567796\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 81.0000 3.10393
$$682$$ 0 0
$$683$$ −40.0000 −1.53056 −0.765279 0.643699i $$-0.777399\pi$$
−0.765279 + 0.643699i $$0.777399\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 78.0000 2.97589
$$688$$ 0 0
$$689$$ −6.00000 −0.228582
$$690$$ 0 0
$$691$$ −40.0000 −1.52167 −0.760836 0.648944i $$-0.775211\pi$$
−0.760836 + 0.648944i $$0.775211\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −30.0000 −1.13633
$$698$$ 0 0
$$699$$ −48.0000 −1.81553
$$700$$ 0 0
$$701$$ −25.0000 −0.944237 −0.472118 0.881535i $$-0.656511\pi$$
−0.472118 + 0.881535i $$0.656511\pi$$
$$702$$ 0 0
$$703$$ −80.0000 −3.01726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 15.0000 0.563337 0.281668 0.959512i $$-0.409112\pi$$
0.281668 + 0.959512i $$0.409112\pi$$
$$710$$ 0 0
$$711$$ −42.0000 −1.57512
$$712$$ 0 0
$$713$$ −4.00000 −0.149801
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 15.0000 0.560185
$$718$$ 0 0
$$719$$ −2.00000 −0.0745874 −0.0372937 0.999304i $$-0.511874\pi$$
−0.0372937 + 0.999304i $$0.511874\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 54.0000 2.00828
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 28.0000 1.03846 0.519231 0.854634i $$-0.326218\pi$$
0.519231 + 0.854634i $$0.326218\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −20.0000 −0.739727
$$732$$ 0 0
$$733$$ 41.0000 1.51437 0.757185 0.653201i $$-0.226574\pi$$
0.757185 + 0.653201i $$0.226574\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 30.0000 1.10506
$$738$$ 0 0
$$739$$ −5.00000 −0.183928 −0.0919640 0.995762i $$-0.529314\pi$$
−0.0919640 + 0.995762i $$0.529314\pi$$
$$740$$ 0 0
$$741$$ 24.0000 0.881662
$$742$$ 0 0
$$743$$ −30.0000 −1.10059 −0.550297 0.834969i $$-0.685485\pi$$
−0.550297 + 0.834969i $$0.685485\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 72.0000 2.63434
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 13.0000 0.474377 0.237188 0.971464i $$-0.423774\pi$$
0.237188 + 0.971464i $$0.423774\pi$$
$$752$$ 0 0
$$753$$ −6.00000 −0.218652
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 48.0000 1.74459 0.872295 0.488980i $$-0.162631\pi$$
0.872295 + 0.488980i $$0.162631\pi$$
$$758$$ 0 0
$$759$$ −18.0000 −0.653359
$$760$$ 0 0
$$761$$ 38.0000 1.37750 0.688749 0.724999i $$-0.258160\pi$$
0.688749 + 0.724999i $$0.258160\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 10.0000 0.361079
$$768$$ 0 0
$$769$$ −16.0000 −0.576975 −0.288487 0.957484i $$-0.593152\pi$$
−0.288487 + 0.957484i $$0.593152\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 0 0
$$773$$ −27.0000 −0.971123 −0.485561 0.874203i $$-0.661385\pi$$
−0.485561 + 0.874203i $$0.661385\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 48.0000 1.71978
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −9.00000 −0.321634
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 3.00000 0.106938 0.0534692 0.998569i $$-0.482972\pi$$
0.0534692 + 0.998569i $$0.482972\pi$$
$$788$$ 0 0
$$789$$ 72.0000 2.56327
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 43.0000 1.52314 0.761569 0.648084i $$-0.224429\pi$$
0.761569 + 0.648084i $$0.224429\pi$$
$$798$$ 0 0
$$799$$ −55.0000 −1.94576
$$800$$ 0 0
$$801$$ −48.0000 −1.69600
$$802$$ 0 0
$$803$$ −30.0000 −1.05868
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −6.00000 −0.211210
$$808$$ 0 0
$$809$$ −11.0000 −0.386739 −0.193370 0.981126i $$-0.561942\pi$$
−0.193370 + 0.981126i $$0.561942\pi$$
$$810$$ 0 0
$$811$$ −6.00000 −0.210688 −0.105344 0.994436i $$-0.533594\pi$$
−0.105344 + 0.994436i $$0.533594\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 32.0000 1.11954
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 45.0000 1.57051 0.785255 0.619172i $$-0.212532\pi$$
0.785255 + 0.619172i $$0.212532\pi$$
$$822$$ 0 0
$$823$$ 18.0000 0.627441 0.313720 0.949515i $$-0.398425\pi$$
0.313720 + 0.949515i $$0.398425\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 22.0000 0.765015 0.382507 0.923952i $$-0.375061\pi$$
0.382507 + 0.923952i $$0.375061\pi$$
$$828$$ 0 0
$$829$$ −34.0000 −1.18087 −0.590434 0.807086i $$-0.701044\pi$$
−0.590434 + 0.807086i $$0.701044\pi$$
$$830$$ 0 0
$$831$$ 42.0000 1.45696
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 18.0000 0.622171
$$838$$ 0 0
$$839$$ 46.0000 1.58810 0.794048 0.607855i $$-0.207970\pi$$
0.794048 + 0.607855i $$0.207970\pi$$
$$840$$ 0 0
$$841$$ −28.0000 −0.965517
$$842$$ 0 0
$$843$$ 45.0000 1.54988
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ −21.0000 −0.720718
$$850$$ 0 0
$$851$$ 20.0000 0.685591
$$852$$ 0 0
$$853$$ 26.0000 0.890223 0.445112 0.895475i $$-0.353164\pi$$
0.445112 + 0.895475i $$0.353164\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −22.0000 −0.751506 −0.375753 0.926720i $$-0.622616\pi$$
−0.375753 + 0.926720i $$0.622616\pi$$
$$858$$ 0 0
$$859$$ −24.0000 −0.818869 −0.409435 0.912339i $$-0.634274\pi$$
−0.409435 + 0.912339i $$0.634274\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −46.0000 −1.56586 −0.782929 0.622111i $$-0.786275\pi$$
−0.782929 + 0.622111i $$0.786275\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 24.0000 0.815083
$$868$$ 0 0
$$869$$ −21.0000 −0.712376
$$870$$ 0 0
$$871$$ 10.0000 0.338837
$$872$$ 0 0
$$873$$ 18.0000 0.609208
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −40.0000 −1.35070 −0.675352 0.737496i $$-0.736008\pi$$
−0.675352 + 0.737496i $$0.736008\pi$$
$$878$$ 0 0
$$879$$ 45.0000 1.51781
$$880$$ 0 0
$$881$$ 48.0000 1.61716 0.808581 0.588386i $$-0.200236\pi$$
0.808581 + 0.588386i $$0.200236\pi$$
$$882$$ 0 0
$$883$$ −4.00000 −0.134611 −0.0673054 0.997732i $$-0.521440\pi$$
−0.0673054 + 0.997732i $$0.521440\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 12.0000 0.402921 0.201460 0.979497i $$-0.435431\pi$$
0.201460 + 0.979497i $$0.435431\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 27.0000 0.904534
$$892$$ 0 0
$$893$$ 88.0000 2.94481
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −6.00000 −0.200334
$$898$$ 0 0
$$899$$ −2.00000 −0.0667037
$$900$$ 0 0
$$901$$ 30.0000 0.999445
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −38.0000 −1.26177 −0.630885 0.775877i $$-0.717308\pi$$
−0.630885 + 0.775877i $$0.717308\pi$$
$$908$$ 0 0
$$909$$ 72.0000 2.38809
$$910$$ 0 0
$$911$$ −52.0000 −1.72284 −0.861418 0.507896i $$-0.830423\pi$$
−0.861418 + 0.507896i $$0.830423\pi$$
$$912$$ 0 0
$$913$$ 36.0000 1.19143
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −55.0000 −1.81428 −0.907141 0.420826i $$-0.861740\pi$$
−0.907141 + 0.420826i $$0.861740\pi$$
$$920$$ 0 0
$$921$$ −57.0000 −1.87821
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −30.0000 −0.985329
$$928$$ 0 0
$$929$$ 18.0000 0.590561 0.295280 0.955411i $$-0.404587\pi$$
0.295280 + 0.955411i $$0.404587\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ −36.0000 −1.17859
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 7.00000 0.228680 0.114340 0.993442i $$-0.463525\pi$$
0.114340 + 0.993442i $$0.463525\pi$$
$$938$$ 0 0
$$939$$ −21.0000 −0.685309
$$940$$ 0 0
$$941$$ 40.0000 1.30396 0.651981 0.758235i $$-0.273938\pi$$
0.651981 + 0.758235i $$0.273938\pi$$
$$942$$ 0 0
$$943$$ −12.0000 −0.390774
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −6.00000 −0.194974 −0.0974869 0.995237i $$-0.531080\pi$$
−0.0974869 + 0.995237i $$0.531080\pi$$
$$948$$ 0 0
$$949$$ −10.0000 −0.324614
$$950$$ 0 0
$$951$$ −84.0000 −2.72389
$$952$$ 0 0
$$953$$ 42.0000 1.36051 0.680257 0.732974i $$-0.261868\pi$$
0.680257 + 0.732974i $$0.261868\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −9.00000 −0.290929
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 0 0
$$963$$ −48.0000 −1.54678
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −8.00000 −0.257263 −0.128631 0.991692i $$-0.541058\pi$$
−0.128631 + 0.991692i $$0.541058\pi$$
$$968$$ 0 0
$$969$$ −120.000 −3.85496
$$970$$ 0 0
$$971$$ −18.0000 −0.577647 −0.288824 0.957382i $$-0.593264\pi$$
−0.288824 + 0.957382i $$0.593264\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 60.0000 1.91957 0.959785 0.280736i $$-0.0905785\pi$$
0.959785 + 0.280736i $$0.0905785\pi$$
$$978$$ 0 0
$$979$$ −24.0000 −0.767043
$$980$$ 0 0
$$981$$ −42.0000 −1.34096
$$982$$ 0 0
$$983$$ 13.0000 0.414636 0.207318 0.978274i $$-0.433527\pi$$
0.207318 + 0.978274i $$0.433527\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −8.00000 −0.254385
$$990$$ 0 0
$$991$$ −32.0000 −1.01651 −0.508257 0.861206i $$-0.669710\pi$$
−0.508257 + 0.861206i $$0.669710\pi$$
$$992$$ 0 0
$$993$$ 60.0000 1.90404
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −53.0000 −1.67853 −0.839263 0.543725i $$-0.817013\pi$$
−0.839263 + 0.543725i $$0.817013\pi$$
$$998$$ 0 0
$$999$$ −90.0000 −2.84747
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 4900.2.a.w.1.1 1
5.2 odd 4 980.2.e.b.589.1 2
5.3 odd 4 980.2.e.b.589.2 2
5.4 even 2 4900.2.a.b.1.1 1
7.6 odd 2 700.2.a.a.1.1 1
21.20 even 2 6300.2.a.c.1.1 1
28.27 even 2 2800.2.a.bf.1.1 1
35.2 odd 12 980.2.q.c.949.2 4
35.3 even 12 980.2.q.f.569.1 4
35.12 even 12 980.2.q.f.949.1 4
35.13 even 4 140.2.e.a.29.1 2
35.17 even 12 980.2.q.f.569.2 4
35.18 odd 12 980.2.q.c.569.2 4
35.23 odd 12 980.2.q.c.949.1 4
35.27 even 4 140.2.e.a.29.2 yes 2
35.32 odd 12 980.2.q.c.569.1 4
35.33 even 12 980.2.q.f.949.2 4
35.34 odd 2 700.2.a.j.1.1 1
105.62 odd 4 1260.2.k.c.1009.1 2
105.83 odd 4 1260.2.k.c.1009.2 2
105.104 even 2 6300.2.a.t.1.1 1
140.27 odd 4 560.2.g.a.449.1 2
140.83 odd 4 560.2.g.a.449.2 2
140.139 even 2 2800.2.a.a.1.1 1
280.13 even 4 2240.2.g.e.449.2 2
280.27 odd 4 2240.2.g.f.449.2 2
280.83 odd 4 2240.2.g.f.449.1 2
280.237 even 4 2240.2.g.e.449.1 2
420.83 even 4 5040.2.t.s.1009.2 2
420.167 even 4 5040.2.t.s.1009.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.e.a.29.1 2 35.13 even 4
140.2.e.a.29.2 yes 2 35.27 even 4
560.2.g.a.449.1 2 140.27 odd 4
560.2.g.a.449.2 2 140.83 odd 4
700.2.a.a.1.1 1 7.6 odd 2
700.2.a.j.1.1 1 35.34 odd 2
980.2.e.b.589.1 2 5.2 odd 4
980.2.e.b.589.2 2 5.3 odd 4
980.2.q.c.569.1 4 35.32 odd 12
980.2.q.c.569.2 4 35.18 odd 12
980.2.q.c.949.1 4 35.23 odd 12
980.2.q.c.949.2 4 35.2 odd 12
980.2.q.f.569.1 4 35.3 even 12
980.2.q.f.569.2 4 35.17 even 12
980.2.q.f.949.1 4 35.12 even 12
980.2.q.f.949.2 4 35.33 even 12
1260.2.k.c.1009.1 2 105.62 odd 4
1260.2.k.c.1009.2 2 105.83 odd 4
2240.2.g.e.449.1 2 280.237 even 4
2240.2.g.e.449.2 2 280.13 even 4
2240.2.g.f.449.1 2 280.83 odd 4
2240.2.g.f.449.2 2 280.27 odd 4
2800.2.a.a.1.1 1 140.139 even 2
2800.2.a.bf.1.1 1 28.27 even 2
4900.2.a.b.1.1 1 5.4 even 2
4900.2.a.w.1.1 1 1.1 even 1 trivial
5040.2.t.s.1009.1 2 420.167 even 4
5040.2.t.s.1009.2 2 420.83 even 4
6300.2.a.c.1.1 1 21.20 even 2
6300.2.a.t.1.1 1 105.104 even 2