# Properties

 Label 1764.4.a.d.1.1 Level $1764$ Weight $4$ Character 1764.1 Self dual yes Analytic conductor $104.079$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1764.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$104.079369250$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 588) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1764.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-4.00000 q^{5} +O(q^{10})$$ $$q-4.00000 q^{5} +20.0000 q^{11} -4.00000 q^{13} -24.0000 q^{17} +44.0000 q^{19} -72.0000 q^{23} -109.000 q^{25} +38.0000 q^{29} +184.000 q^{31} -30.0000 q^{37} +216.000 q^{41} -164.000 q^{43} -520.000 q^{47} +146.000 q^{53} -80.0000 q^{55} -460.000 q^{59} +628.000 q^{61} +16.0000 q^{65} +556.000 q^{67} -592.000 q^{71} +1024.00 q^{73} -104.000 q^{79} +324.000 q^{83} +96.0000 q^{85} -896.000 q^{89} -176.000 q^{95} -920.000 q^{97} +O(q^{100})$$

## 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
$$5$$ −4.00000 −0.357771 −0.178885 0.983870i $$-0.557249\pi$$
−0.178885 + 0.983870i $$0.557249\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 20.0000 0.548202 0.274101 0.961701i $$-0.411620\pi$$
0.274101 + 0.961701i $$0.411620\pi$$
$$12$$ 0 0
$$13$$ −4.00000 −0.0853385 −0.0426692 0.999089i $$-0.513586\pi$$
−0.0426692 + 0.999089i $$0.513586\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −24.0000 −0.342403 −0.171202 0.985236i $$-0.554765\pi$$
−0.171202 + 0.985236i $$0.554765\pi$$
$$18$$ 0 0
$$19$$ 44.0000 0.531279 0.265639 0.964072i $$-0.414417\pi$$
0.265639 + 0.964072i $$0.414417\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −72.0000 −0.652741 −0.326370 0.945242i $$-0.605826\pi$$
−0.326370 + 0.945242i $$0.605826\pi$$
$$24$$ 0 0
$$25$$ −109.000 −0.872000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 38.0000 0.243325 0.121662 0.992572i $$-0.461177\pi$$
0.121662 + 0.992572i $$0.461177\pi$$
$$30$$ 0 0
$$31$$ 184.000 1.06604 0.533022 0.846101i $$-0.321056\pi$$
0.533022 + 0.846101i $$0.321056\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −30.0000 −0.133296 −0.0666482 0.997777i $$-0.521231\pi$$
−0.0666482 + 0.997777i $$0.521231\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 216.000 0.822769 0.411385 0.911462i $$-0.365045\pi$$
0.411385 + 0.911462i $$0.365045\pi$$
$$42$$ 0 0
$$43$$ −164.000 −0.581622 −0.290811 0.956780i $$-0.593925\pi$$
−0.290811 + 0.956780i $$0.593925\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −520.000 −1.61383 −0.806913 0.590671i $$-0.798863\pi$$
−0.806913 + 0.590671i $$0.798863\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 146.000 0.378389 0.189195 0.981940i $$-0.439412\pi$$
0.189195 + 0.981940i $$0.439412\pi$$
$$54$$ 0 0
$$55$$ −80.0000 −0.196131
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −460.000 −1.01503 −0.507516 0.861642i $$-0.669436\pi$$
−0.507516 + 0.861642i $$0.669436\pi$$
$$60$$ 0 0
$$61$$ 628.000 1.31815 0.659075 0.752077i $$-0.270948\pi$$
0.659075 + 0.752077i $$0.270948\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 16.0000 0.0305316
$$66$$ 0 0
$$67$$ 556.000 1.01382 0.506912 0.861998i $$-0.330787\pi$$
0.506912 + 0.861998i $$0.330787\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −592.000 −0.989542 −0.494771 0.869023i $$-0.664748\pi$$
−0.494771 + 0.869023i $$0.664748\pi$$
$$72$$ 0 0
$$73$$ 1024.00 1.64178 0.820891 0.571084i $$-0.193477\pi$$
0.820891 + 0.571084i $$0.193477\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −104.000 −0.148113 −0.0740564 0.997254i $$-0.523594\pi$$
−0.0740564 + 0.997254i $$0.523594\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 324.000 0.428477 0.214239 0.976781i $$-0.431273\pi$$
0.214239 + 0.976781i $$0.431273\pi$$
$$84$$ 0 0
$$85$$ 96.0000 0.122502
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −896.000 −1.06714 −0.533572 0.845755i $$-0.679151\pi$$
−0.533572 + 0.845755i $$0.679151\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −176.000 −0.190076
$$96$$ 0 0
$$97$$ −920.000 −0.963009 −0.481504 0.876444i $$-0.659909\pi$$
−0.481504 + 0.876444i $$0.659909\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1108.00 −1.09159 −0.545793 0.837920i $$-0.683771\pi$$
−0.545793 + 0.837920i $$0.683771\pi$$
$$102$$ 0 0
$$103$$ 1448.00 1.38520 0.692600 0.721321i $$-0.256465\pi$$
0.692600 + 0.721321i $$0.256465\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1316.00 −1.18900 −0.594498 0.804097i $$-0.702649\pi$$
−0.594498 + 0.804097i $$0.702649\pi$$
$$108$$ 0 0
$$109$$ −86.0000 −0.0755716 −0.0377858 0.999286i $$-0.512030\pi$$
−0.0377858 + 0.999286i $$0.512030\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1778.00 −1.48018 −0.740089 0.672509i $$-0.765217\pi$$
−0.740089 + 0.672509i $$0.765217\pi$$
$$114$$ 0 0
$$115$$ 288.000 0.233532
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −931.000 −0.699474
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 936.000 0.669747
$$126$$ 0 0
$$127$$ −928.000 −0.648399 −0.324200 0.945989i $$-0.605095\pi$$
−0.324200 + 0.945989i $$0.605095\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1404.00 −0.936397 −0.468199 0.883623i $$-0.655097\pi$$
−0.468199 + 0.883623i $$0.655097\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1370.00 0.854358 0.427179 0.904167i $$-0.359507\pi$$
0.427179 + 0.904167i $$0.359507\pi$$
$$138$$ 0 0
$$139$$ 516.000 0.314867 0.157434 0.987530i $$-0.449678\pi$$
0.157434 + 0.987530i $$0.449678\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −80.0000 −0.0467828
$$144$$ 0 0
$$145$$ −152.000 −0.0870546
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1390.00 −0.764250 −0.382125 0.924111i $$-0.624808\pi$$
−0.382125 + 0.924111i $$0.624808\pi$$
$$150$$ 0 0
$$151$$ 136.000 0.0732949 0.0366474 0.999328i $$-0.488332\pi$$
0.0366474 + 0.999328i $$0.488332\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −736.000 −0.381400
$$156$$ 0 0
$$157$$ −148.000 −0.0752337 −0.0376168 0.999292i $$-0.511977\pi$$
−0.0376168 + 0.999292i $$0.511977\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −1212.00 −0.582400 −0.291200 0.956662i $$-0.594054\pi$$
−0.291200 + 0.956662i $$0.594054\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1976.00 −0.915614 −0.457807 0.889052i $$-0.651365\pi$$
−0.457807 + 0.889052i $$0.651365\pi$$
$$168$$ 0 0
$$169$$ −2181.00 −0.992717
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 2692.00 1.18306 0.591529 0.806284i $$-0.298525\pi$$
0.591529 + 0.806284i $$0.298525\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 2580.00 1.07731 0.538654 0.842527i $$-0.318933\pi$$
0.538654 + 0.842527i $$0.318933\pi$$
$$180$$ 0 0
$$181$$ −2036.00 −0.836103 −0.418052 0.908423i $$-0.637287\pi$$
−0.418052 + 0.908423i $$0.637287\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 120.000 0.0476896
$$186$$ 0 0
$$187$$ −480.000 −0.187706
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3960.00 −1.50019 −0.750093 0.661332i $$-0.769991\pi$$
−0.750093 + 0.661332i $$0.769991\pi$$
$$192$$ 0 0
$$193$$ 2.00000 0.000745923 0 0.000372962 1.00000i $$-0.499881\pi$$
0.000372962 1.00000i $$0.499881\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −3774.00 −1.36491 −0.682453 0.730930i $$-0.739087\pi$$
−0.682453 + 0.730930i $$0.739087\pi$$
$$198$$ 0 0
$$199$$ −3560.00 −1.26815 −0.634075 0.773272i $$-0.718619\pi$$
−0.634075 + 0.773272i $$0.718619\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −864.000 −0.294363
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 880.000 0.291248
$$210$$ 0 0
$$211$$ −2692.00 −0.878317 −0.439159 0.898410i $$-0.644723\pi$$
−0.439159 + 0.898410i $$0.644723\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 656.000 0.208088
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 96.0000 0.0292202
$$222$$ 0 0
$$223$$ 4528.00 1.35972 0.679859 0.733342i $$-0.262041\pi$$
0.679859 + 0.733342i $$0.262041\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 3652.00 1.06781 0.533903 0.845546i $$-0.320725\pi$$
0.533903 + 0.845546i $$0.320725\pi$$
$$228$$ 0 0
$$229$$ −4804.00 −1.38628 −0.693138 0.720805i $$-0.743772\pi$$
−0.693138 + 0.720805i $$0.743772\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −2758.00 −0.775462 −0.387731 0.921773i $$-0.626741\pi$$
−0.387731 + 0.921773i $$0.626741\pi$$
$$234$$ 0 0
$$235$$ 2080.00 0.577380
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −6528.00 −1.76678 −0.883392 0.468635i $$-0.844746\pi$$
−0.883392 + 0.468635i $$0.844746\pi$$
$$240$$ 0 0
$$241$$ −56.0000 −0.0149680 −0.00748398 0.999972i $$-0.502382\pi$$
−0.00748398 + 0.999972i $$0.502382\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −176.000 −0.0453385
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −4900.00 −1.23221 −0.616106 0.787663i $$-0.711291\pi$$
−0.616106 + 0.787663i $$0.711291\pi$$
$$252$$ 0 0
$$253$$ −1440.00 −0.357834
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 6784.00 1.64659 0.823296 0.567612i $$-0.192133\pi$$
0.823296 + 0.567612i $$0.192133\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 4544.00 1.06538 0.532690 0.846310i $$-0.321181\pi$$
0.532690 + 0.846310i $$0.321181\pi$$
$$264$$ 0 0
$$265$$ −584.000 −0.135377
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 4052.00 0.918419 0.459210 0.888328i $$-0.348133\pi$$
0.459210 + 0.888328i $$0.348133\pi$$
$$270$$ 0 0
$$271$$ −2752.00 −0.616871 −0.308436 0.951245i $$-0.599805\pi$$
−0.308436 + 0.951245i $$0.599805\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −2180.00 −0.478033
$$276$$ 0 0
$$277$$ 4366.00 0.947031 0.473515 0.880786i $$-0.342985\pi$$
0.473515 + 0.880786i $$0.342985\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −7734.00 −1.64189 −0.820946 0.571006i $$-0.806553\pi$$
−0.820946 + 0.571006i $$0.806553\pi$$
$$282$$ 0 0
$$283$$ −4052.00 −0.851118 −0.425559 0.904931i $$-0.639923\pi$$
−0.425559 + 0.904931i $$0.639923\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4337.00 −0.882760
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 3420.00 0.681906 0.340953 0.940080i $$-0.389250\pi$$
0.340953 + 0.940080i $$0.389250\pi$$
$$294$$ 0 0
$$295$$ 1840.00 0.363149
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 288.000 0.0557039
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −2512.00 −0.471596
$$306$$ 0 0
$$307$$ 7324.00 1.36157 0.680786 0.732482i $$-0.261638\pi$$
0.680786 + 0.732482i $$0.261638\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 4192.00 0.764330 0.382165 0.924094i $$-0.375179\pi$$
0.382165 + 0.924094i $$0.375179\pi$$
$$312$$ 0 0
$$313$$ −6840.00 −1.23521 −0.617603 0.786490i $$-0.711896\pi$$
−0.617603 + 0.786490i $$0.711896\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −6630.00 −1.17469 −0.587347 0.809335i $$-0.699828\pi$$
−0.587347 + 0.809335i $$0.699828\pi$$
$$318$$ 0 0
$$319$$ 760.000 0.133391
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1056.00 −0.181911
$$324$$ 0 0
$$325$$ 436.000 0.0744152
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −6868.00 −1.14048 −0.570241 0.821478i $$-0.693150\pi$$
−0.570241 + 0.821478i $$0.693150\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −2224.00 −0.362717
$$336$$ 0 0
$$337$$ −7378.00 −1.19260 −0.596299 0.802763i $$-0.703363\pi$$
−0.596299 + 0.802763i $$0.703363\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 3680.00 0.584408
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 2676.00 0.413992 0.206996 0.978342i $$-0.433631\pi$$
0.206996 + 0.978342i $$0.433631\pi$$
$$348$$ 0 0
$$349$$ −5124.00 −0.785907 −0.392953 0.919558i $$-0.628547\pi$$
−0.392953 + 0.919558i $$0.628547\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −4560.00 −0.687548 −0.343774 0.939052i $$-0.611705\pi$$
−0.343774 + 0.939052i $$0.611705\pi$$
$$354$$ 0 0
$$355$$ 2368.00 0.354029
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −3656.00 −0.537483 −0.268741 0.963212i $$-0.586608\pi$$
−0.268741 + 0.963212i $$0.586608\pi$$
$$360$$ 0 0
$$361$$ −4923.00 −0.717743
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −4096.00 −0.587382
$$366$$ 0 0
$$367$$ −1616.00 −0.229849 −0.114924 0.993374i $$-0.536663\pi$$
−0.114924 + 0.993374i $$0.536663\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 2734.00 0.379521 0.189760 0.981830i $$-0.439229\pi$$
0.189760 + 0.981830i $$0.439229\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −152.000 −0.0207650
$$378$$ 0 0
$$379$$ −1380.00 −0.187034 −0.0935169 0.995618i $$-0.529811\pi$$
−0.0935169 + 0.995618i $$0.529811\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −6888.00 −0.918957 −0.459478 0.888189i $$-0.651964\pi$$
−0.459478 + 0.888189i $$0.651964\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 2046.00 0.266674 0.133337 0.991071i $$-0.457431\pi$$
0.133337 + 0.991071i $$0.457431\pi$$
$$390$$ 0 0
$$391$$ 1728.00 0.223501
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 416.000 0.0529905
$$396$$ 0 0
$$397$$ 3116.00 0.393923 0.196962 0.980411i $$-0.436893\pi$$
0.196962 + 0.980411i $$0.436893\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −2958.00 −0.368368 −0.184184 0.982892i $$-0.558964\pi$$
−0.184184 + 0.982892i $$0.558964\pi$$
$$402$$ 0 0
$$403$$ −736.000 −0.0909746
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −600.000 −0.0730735
$$408$$ 0 0
$$409$$ 7944.00 0.960405 0.480202 0.877158i $$-0.340563\pi$$
0.480202 + 0.877158i $$0.340563\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −1296.00 −0.153297
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −4084.00 −0.476173 −0.238086 0.971244i $$-0.576520\pi$$
−0.238086 + 0.971244i $$0.576520\pi$$
$$420$$ 0 0
$$421$$ −6306.00 −0.730013 −0.365007 0.931005i $$-0.618933\pi$$
−0.365007 + 0.931005i $$0.618933\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2616.00 0.298576
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 11824.0 1.32144 0.660722 0.750631i $$-0.270250\pi$$
0.660722 + 0.750631i $$0.270250\pi$$
$$432$$ 0 0
$$433$$ −4504.00 −0.499881 −0.249940 0.968261i $$-0.580411\pi$$
−0.249940 + 0.968261i $$0.580411\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3168.00 −0.346787
$$438$$ 0 0
$$439$$ 13056.0 1.41943 0.709714 0.704490i $$-0.248824\pi$$
0.709714 + 0.704490i $$0.248824\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −132.000 −0.0141569 −0.00707845 0.999975i $$-0.502253\pi$$
−0.00707845 + 0.999975i $$0.502253\pi$$
$$444$$ 0 0
$$445$$ 3584.00 0.381793
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −4866.00 −0.511449 −0.255725 0.966750i $$-0.582314\pi$$
−0.255725 + 0.966750i $$0.582314\pi$$
$$450$$ 0 0
$$451$$ 4320.00 0.451044
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 10106.0 1.03444 0.517220 0.855853i $$-0.326967\pi$$
0.517220 + 0.855853i $$0.326967\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 18036.0 1.82217 0.911085 0.412219i $$-0.135246\pi$$
0.911085 + 0.412219i $$0.135246\pi$$
$$462$$ 0 0
$$463$$ 5288.00 0.530787 0.265393 0.964140i $$-0.414498\pi$$
0.265393 + 0.964140i $$0.414498\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −15164.0 −1.50258 −0.751291 0.659971i $$-0.770569\pi$$
−0.751291 + 0.659971i $$0.770569\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −3280.00 −0.318847
$$474$$ 0 0
$$475$$ −4796.00 −0.463275
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −7896.00 −0.753189 −0.376594 0.926378i $$-0.622905\pi$$
−0.376594 + 0.926378i $$0.622905\pi$$
$$480$$ 0 0
$$481$$ 120.000 0.0113753
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 3680.00 0.344536
$$486$$ 0 0
$$487$$ 2920.00 0.271700 0.135850 0.990729i $$-0.456624\pi$$
0.135850 + 0.990729i $$0.456624\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 7932.00 0.729055 0.364528 0.931193i $$-0.381230\pi$$
0.364528 + 0.931193i $$0.381230\pi$$
$$492$$ 0 0
$$493$$ −912.000 −0.0833152
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −2004.00 −0.179782 −0.0898911 0.995952i $$-0.528652\pi$$
−0.0898911 + 0.995952i $$0.528652\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −4496.00 −0.398542 −0.199271 0.979944i $$-0.563857\pi$$
−0.199271 + 0.979944i $$0.563857\pi$$
$$504$$ 0 0
$$505$$ 4432.00 0.390537
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −12620.0 −1.09896 −0.549481 0.835506i $$-0.685175\pi$$
−0.549481 + 0.835506i $$0.685175\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −5792.00 −0.495584
$$516$$ 0 0
$$517$$ −10400.0 −0.884703
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −18008.0 −1.51429 −0.757145 0.653247i $$-0.773406\pi$$
−0.757145 + 0.653247i $$0.773406\pi$$
$$522$$ 0 0
$$523$$ 13292.0 1.11132 0.555658 0.831411i $$-0.312466\pi$$
0.555658 + 0.831411i $$0.312466\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −4416.00 −0.365017
$$528$$ 0 0
$$529$$ −6983.00 −0.573929
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −864.000 −0.0702139
$$534$$ 0 0
$$535$$ 5264.00 0.425388
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −8570.00 −0.681059 −0.340530 0.940234i $$-0.610606\pi$$
−0.340530 + 0.940234i $$0.610606\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 344.000 0.0270373
$$546$$ 0 0
$$547$$ −1916.00 −0.149766 −0.0748832 0.997192i $$-0.523858\pi$$
−0.0748832 + 0.997192i $$0.523858\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 1672.00 0.129273
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −19926.0 −1.51578 −0.757892 0.652380i $$-0.773771\pi$$
−0.757892 + 0.652380i $$0.773771\pi$$
$$558$$ 0 0
$$559$$ 656.000 0.0496348
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −4244.00 −0.317697 −0.158848 0.987303i $$-0.550778\pi$$
−0.158848 + 0.987303i $$0.550778\pi$$
$$564$$ 0 0
$$565$$ 7112.00 0.529565
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 22794.0 1.67939 0.839696 0.543057i $$-0.182733\pi$$
0.839696 + 0.543057i $$0.182733\pi$$
$$570$$ 0 0
$$571$$ 14028.0 1.02811 0.514057 0.857756i $$-0.328142\pi$$
0.514057 + 0.857756i $$0.328142\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 7848.00 0.569190
$$576$$ 0 0
$$577$$ 8368.00 0.603751 0.301876 0.953347i $$-0.402387\pi$$
0.301876 + 0.953347i $$0.402387\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 2920.00 0.207434
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −52.0000 −0.00365634 −0.00182817 0.999998i $$-0.500582\pi$$
−0.00182817 + 0.999998i $$0.500582\pi$$
$$588$$ 0 0
$$589$$ 8096.00 0.566366
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −5808.00 −0.402202 −0.201101 0.979570i $$-0.564452\pi$$
−0.201101 + 0.979570i $$0.564452\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 10464.0 0.713769 0.356884 0.934149i $$-0.383839\pi$$
0.356884 + 0.934149i $$0.383839\pi$$
$$600$$ 0 0
$$601$$ 1184.00 0.0803600 0.0401800 0.999192i $$-0.487207\pi$$
0.0401800 + 0.999192i $$0.487207\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 3724.00 0.250251
$$606$$ 0 0
$$607$$ 13152.0 0.879445 0.439723 0.898134i $$-0.355077\pi$$
0.439723 + 0.898134i $$0.355077\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 2080.00 0.137721
$$612$$ 0 0
$$613$$ −18334.0 −1.20800 −0.603999 0.796985i $$-0.706427\pi$$
−0.603999 + 0.796985i $$0.706427\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 8122.00 0.529950 0.264975 0.964255i $$-0.414636\pi$$
0.264975 + 0.964255i $$0.414636\pi$$
$$618$$ 0 0
$$619$$ 5980.00 0.388298 0.194149 0.980972i $$-0.437805\pi$$
0.194149 + 0.980972i $$0.437805\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9881.00 0.632384
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 720.000 0.0456411
$$630$$ 0 0
$$631$$ 12528.0 0.790383 0.395192 0.918599i $$-0.370678\pi$$
0.395192 + 0.918599i $$0.370678\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 3712.00 0.231978
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −20798.0 −1.28155 −0.640773 0.767730i $$-0.721386\pi$$
−0.640773 + 0.767730i $$0.721386\pi$$
$$642$$ 0 0
$$643$$ −1932.00 −0.118492 −0.0592462 0.998243i $$-0.518870\pi$$
−0.0592462 + 0.998243i $$0.518870\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 8424.00 0.511873 0.255936 0.966694i $$-0.417616\pi$$
0.255936 + 0.966694i $$0.417616\pi$$
$$648$$ 0 0
$$649$$ −9200.00 −0.556443
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 17750.0 1.06372 0.531862 0.846831i $$-0.321493\pi$$
0.531862 + 0.846831i $$0.321493\pi$$
$$654$$ 0 0
$$655$$ 5616.00 0.335016
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 27580.0 1.63029 0.815147 0.579254i $$-0.196656\pi$$
0.815147 + 0.579254i $$0.196656\pi$$
$$660$$ 0 0
$$661$$ −9292.00 −0.546773 −0.273386 0.961904i $$-0.588144\pi$$
−0.273386 + 0.961904i $$0.588144\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −2736.00 −0.158828
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 12560.0 0.722613
$$672$$ 0 0
$$673$$ 11486.0 0.657879 0.328940 0.944351i $$-0.393309\pi$$
0.328940 + 0.944351i $$0.393309\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −7116.00 −0.403974 −0.201987 0.979388i $$-0.564740\pi$$
−0.201987 + 0.979388i $$0.564740\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 7612.00 0.426450 0.213225 0.977003i $$-0.431603\pi$$
0.213225 + 0.977003i $$0.431603\pi$$
$$684$$ 0 0
$$685$$ −5480.00 −0.305664
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −584.000 −0.0322912
$$690$$ 0 0
$$691$$ −21572.0 −1.18761 −0.593804 0.804609i $$-0.702375\pi$$
−0.593804 + 0.804609i $$0.702375\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −2064.00 −0.112650
$$696$$ 0 0
$$697$$ −5184.00 −0.281719
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1702.00 0.0917028 0.0458514 0.998948i $$-0.485400\pi$$
0.0458514 + 0.998948i $$0.485400\pi$$
$$702$$ 0 0
$$703$$ −1320.00 −0.0708176
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 6370.00 0.337419 0.168710 0.985666i $$-0.446040\pi$$
0.168710 + 0.985666i $$0.446040\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −13248.0 −0.695851
$$714$$ 0 0
$$715$$ 320.000 0.0167375
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 8808.00 0.456861 0.228430 0.973560i $$-0.426641\pi$$
0.228430 + 0.973560i $$0.426641\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −4142.00 −0.212179
$$726$$ 0 0
$$727$$ 17768.0 0.906436 0.453218 0.891400i $$-0.350276\pi$$
0.453218 + 0.891400i $$0.350276\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 3936.00 0.199149
$$732$$ 0 0
$$733$$ −5564.00 −0.280370 −0.140185 0.990125i $$-0.544770\pi$$
−0.140185 + 0.990125i $$0.544770\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 11120.0 0.555781
$$738$$ 0 0
$$739$$ −17564.0 −0.874293 −0.437146 0.899390i $$-0.644011\pi$$
−0.437146 + 0.899390i $$0.644011\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 38280.0 1.89012 0.945059 0.326901i $$-0.106004\pi$$
0.945059 + 0.326901i $$0.106004\pi$$
$$744$$ 0 0
$$745$$ 5560.00 0.273426
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 36192.0 1.75854 0.879271 0.476322i $$-0.158030\pi$$
0.879271 + 0.476322i $$0.158030\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −544.000 −0.0262228
$$756$$ 0 0
$$757$$ −14.0000 −0.000672178 0 −0.000336089 1.00000i $$-0.500107\pi$$
−0.000336089 1.00000i $$0.500107\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 26504.0 1.26251 0.631254 0.775576i $$-0.282540\pi$$
0.631254 + 0.775576i $$0.282540\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1840.00 0.0866213
$$768$$ 0 0
$$769$$ 40184.0 1.88436 0.942180 0.335109i $$-0.108773\pi$$
0.942180 + 0.335109i $$0.108773\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 35340.0 1.64436 0.822181 0.569226i $$-0.192757\pi$$
0.822181 + 0.569226i $$0.192757\pi$$
$$774$$ 0 0
$$775$$ −20056.0 −0.929591
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 9504.00 0.437120
$$780$$ 0 0
$$781$$ −11840.0 −0.542469
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 592.000 0.0269164
$$786$$ 0 0
$$787$$ −14852.0 −0.672702 −0.336351 0.941737i $$-0.609193\pi$$
−0.336351 + 0.941737i $$0.609193\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −2512.00 −0.112489
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −19788.0 −0.879457 −0.439728 0.898131i $$-0.644925\pi$$
−0.439728 + 0.898131i $$0.644925\pi$$
$$798$$ 0 0
$$799$$ 12480.0 0.552579
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 20480.0 0.900029
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −16986.0 −0.738190 −0.369095 0.929392i $$-0.620332\pi$$
−0.369095 + 0.929392i $$0.620332\pi$$
$$810$$ 0 0
$$811$$ −26596.0 −1.15156 −0.575778 0.817606i $$-0.695301\pi$$
−0.575778 + 0.817606i $$0.695301\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 4848.00 0.208366
$$816$$ 0 0
$$817$$ −7216.00 −0.309004
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 34898.0 1.48349 0.741747 0.670680i $$-0.233998\pi$$
0.741747 + 0.670680i $$0.233998\pi$$
$$822$$ 0 0
$$823$$ 12928.0 0.547560 0.273780 0.961792i $$-0.411726\pi$$
0.273780 + 0.961792i $$0.411726\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 43164.0 1.81494 0.907472 0.420112i $$-0.138009\pi$$
0.907472 + 0.420112i $$0.138009\pi$$
$$828$$ 0 0
$$829$$ −41228.0 −1.72727 −0.863635 0.504117i $$-0.831818\pi$$
−0.863635 + 0.504117i $$0.831818\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 7904.00 0.327580
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 1368.00 0.0562915 0.0281458 0.999604i $$-0.491040\pi$$
0.0281458 + 0.999604i $$0.491040\pi$$
$$840$$ 0 0
$$841$$ −22945.0 −0.940793
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 8724.00 0.355165
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 2160.00 0.0870080
$$852$$ 0 0
$$853$$ 5276.00 0.211778 0.105889 0.994378i $$-0.466231\pi$$
0.105889 + 0.994378i $$0.466231\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −840.000 −0.0334817 −0.0167409 0.999860i $$-0.505329\pi$$
−0.0167409 + 0.999860i $$0.505329\pi$$
$$858$$ 0 0
$$859$$ −26028.0 −1.03383 −0.516917 0.856035i $$-0.672921\pi$$
−0.516917 + 0.856035i $$0.672921\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 29448.0 1.16155 0.580777 0.814063i $$-0.302749\pi$$
0.580777 + 0.814063i $$0.302749\pi$$
$$864$$ 0 0
$$865$$ −10768.0 −0.423264
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −2080.00 −0.0811958
$$870$$ 0 0
$$871$$ −2224.00 −0.0865182
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 25866.0 0.995932 0.497966 0.867196i $$-0.334080\pi$$
0.497966 + 0.867196i $$0.334080\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −9472.00 −0.362225 −0.181112 0.983462i $$-0.557970\pi$$
−0.181112 + 0.983462i $$0.557970\pi$$
$$882$$ 0 0
$$883$$ 49372.0 1.88165 0.940827 0.338888i $$-0.110051\pi$$
0.940827 + 0.338888i $$0.110051\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 11160.0 0.422453 0.211227 0.977437i $$-0.432254\pi$$
0.211227 + 0.977437i $$0.432254\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −22880.0 −0.857391
$$894$$ 0 0
$$895$$ −10320.0 −0.385430
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 6992.00 0.259395
$$900$$ 0 0
$$901$$ −3504.00 −0.129562
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 8144.00 0.299133
$$906$$ 0 0
$$907$$ 22708.0 0.831319 0.415660 0.909520i $$-0.363551\pi$$
0.415660 + 0.909520i $$0.363551\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 16192.0 0.588875 0.294437 0.955671i $$-0.404868\pi$$
0.294437 + 0.955671i $$0.404868\pi$$
$$912$$ 0 0
$$913$$ 6480.00 0.234892
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −46320.0 −1.66263 −0.831314 0.555802i $$-0.812411\pi$$
−0.831314 + 0.555802i $$0.812411\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 2368.00 0.0844460
$$924$$ 0 0
$$925$$ 3270.00 0.116235
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 2280.00 0.0805214 0.0402607 0.999189i $$-0.487181\pi$$
0.0402607 + 0.999189i $$0.487181\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 1920.00 0.0671558
$$936$$ 0 0
$$937$$ 49056.0 1.71034 0.855171 0.518347i $$-0.173452\pi$$
0.855171 + 0.518347i $$0.173452\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 24876.0 0.861779 0.430890 0.902405i $$-0.358200\pi$$
0.430890 + 0.902405i $$0.358200\pi$$
$$942$$ 0 0
$$943$$ −15552.0 −0.537055
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −23428.0 −0.803915 −0.401958 0.915658i $$-0.631670\pi$$
−0.401958 + 0.915658i $$0.631670\pi$$
$$948$$ 0 0
$$949$$ −4096.00 −0.140107
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 6678.00 0.226990 0.113495 0.993539i $$-0.463795\pi$$
0.113495 + 0.993539i $$0.463795\pi$$
$$954$$ 0 0
$$955$$ 15840.0 0.536723
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 4065.00 0.136451
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −8.00000 −0.000266870 0
$$966$$ 0 0
$$967$$ 15544.0 0.516920 0.258460 0.966022i $$-0.416785\pi$$
0.258460 + 0.966022i $$0.416785\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 31124.0 1.02865 0.514324 0.857596i $$-0.328043\pi$$
0.514324 + 0.857596i $$0.328043\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −50062.0 −1.63933 −0.819665 0.572843i $$-0.805840\pi$$
−0.819665 + 0.572843i $$0.805840\pi$$
$$978$$ 0 0
$$979$$ −17920.0 −0.585011
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −328.000 −0.0106425 −0.00532125 0.999986i $$-0.501694\pi$$
−0.00532125 + 0.999986i $$0.501694\pi$$
$$984$$ 0 0
$$985$$ 15096.0 0.488323
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 11808.0 0.379649
$$990$$ 0 0
$$991$$ −20872.0 −0.669042 −0.334521 0.942388i $$-0.608575\pi$$
−0.334521 + 0.942388i $$0.608575\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 14240.0 0.453707
$$996$$ 0 0
$$997$$ −46924.0 −1.49057 −0.745285 0.666746i $$-0.767687\pi$$
−0.745285 + 0.666746i $$0.767687\pi$$
$$998$$ 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 1764.4.a.d.1.1 1
3.2 odd 2 588.4.a.b.1.1 1
7.2 even 3 1764.4.k.j.361.1 2
7.3 odd 6 1764.4.k.g.1549.1 2
7.4 even 3 1764.4.k.j.1549.1 2
7.5 odd 6 1764.4.k.g.361.1 2
7.6 odd 2 1764.4.a.i.1.1 1
12.11 even 2 2352.4.a.be.1.1 1
21.2 odd 6 588.4.i.g.361.1 2
21.5 even 6 588.4.i.b.361.1 2
21.11 odd 6 588.4.i.g.373.1 2
21.17 even 6 588.4.i.b.373.1 2
21.20 even 2 588.4.a.e.1.1 yes 1
84.83 odd 2 2352.4.a.g.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
588.4.a.b.1.1 1 3.2 odd 2
588.4.a.e.1.1 yes 1 21.20 even 2
588.4.i.b.361.1 2 21.5 even 6
588.4.i.b.373.1 2 21.17 even 6
588.4.i.g.361.1 2 21.2 odd 6
588.4.i.g.373.1 2 21.11 odd 6
1764.4.a.d.1.1 1 1.1 even 1 trivial
1764.4.a.i.1.1 1 7.6 odd 2
1764.4.k.g.361.1 2 7.5 odd 6
1764.4.k.g.1549.1 2 7.3 odd 6
1764.4.k.j.361.1 2 7.2 even 3
1764.4.k.j.1549.1 2 7.4 even 3
2352.4.a.g.1.1 1 84.83 odd 2
2352.4.a.be.1.1 1 12.11 even 2