# Properties

 Label 1764.4.a.j.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 84) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+6.00000 q^{5} +O(q^{10})$$ $$q+6.00000 q^{5} -36.0000 q^{11} -62.0000 q^{13} +114.000 q^{17} +76.0000 q^{19} +24.0000 q^{23} -89.0000 q^{25} -54.0000 q^{29} +112.000 q^{31} -178.000 q^{37} +378.000 q^{41} -172.000 q^{43} -192.000 q^{47} +402.000 q^{53} -216.000 q^{55} +396.000 q^{59} -254.000 q^{61} -372.000 q^{65} -1012.00 q^{67} -840.000 q^{71} -890.000 q^{73} +80.0000 q^{79} -108.000 q^{83} +684.000 q^{85} -1638.00 q^{89} +456.000 q^{95} -1010.00 q^{97} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 6.00000 0.536656 0.268328 0.963328i $$-0.413529\pi$$
0.268328 + 0.963328i $$0.413529\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −36.0000 −0.986764 −0.493382 0.869813i $$-0.664240\pi$$
−0.493382 + 0.869813i $$0.664240\pi$$
$$12$$ 0 0
$$13$$ −62.0000 −1.32275 −0.661373 0.750057i $$-0.730026\pi$$
−0.661373 + 0.750057i $$0.730026\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 114.000 1.62642 0.813208 0.581974i $$-0.197719\pi$$
0.813208 + 0.581974i $$0.197719\pi$$
$$18$$ 0 0
$$19$$ 76.0000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 24.0000 0.217580 0.108790 0.994065i $$-0.465302\pi$$
0.108790 + 0.994065i $$0.465302\pi$$
$$24$$ 0 0
$$25$$ −89.0000 −0.712000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −54.0000 −0.345778 −0.172889 0.984941i $$-0.555310\pi$$
−0.172889 + 0.984941i $$0.555310\pi$$
$$30$$ 0 0
$$31$$ 112.000 0.648897 0.324448 0.945903i $$-0.394821\pi$$
0.324448 + 0.945903i $$0.394821\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −178.000 −0.790892 −0.395446 0.918489i $$-0.629410\pi$$
−0.395446 + 0.918489i $$0.629410\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 378.000 1.43985 0.719923 0.694054i $$-0.244177\pi$$
0.719923 + 0.694054i $$0.244177\pi$$
$$42$$ 0 0
$$43$$ −172.000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −192.000 −0.595874 −0.297937 0.954586i $$-0.596299\pi$$
−0.297937 + 0.954586i $$0.596299\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 402.000 1.04187 0.520933 0.853597i $$-0.325584\pi$$
0.520933 + 0.853597i $$0.325584\pi$$
$$54$$ 0 0
$$55$$ −216.000 −0.529553
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 396.000 0.873810 0.436905 0.899508i $$-0.356075\pi$$
0.436905 + 0.899508i $$0.356075\pi$$
$$60$$ 0 0
$$61$$ −254.000 −0.533137 −0.266569 0.963816i $$-0.585890\pi$$
−0.266569 + 0.963816i $$0.585890\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −372.000 −0.709860
$$66$$ 0 0
$$67$$ −1012.00 −1.84531 −0.922653 0.385632i $$-0.873984\pi$$
−0.922653 + 0.385632i $$0.873984\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −840.000 −1.40408 −0.702040 0.712138i $$-0.747727\pi$$
−0.702040 + 0.712138i $$0.747727\pi$$
$$72$$ 0 0
$$73$$ −890.000 −1.42694 −0.713470 0.700686i $$-0.752878\pi$$
−0.713470 + 0.700686i $$0.752878\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 80.0000 0.113933 0.0569665 0.998376i $$-0.481857\pi$$
0.0569665 + 0.998376i $$0.481857\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −108.000 −0.142826 −0.0714129 0.997447i $$-0.522751\pi$$
−0.0714129 + 0.997447i $$0.522751\pi$$
$$84$$ 0 0
$$85$$ 684.000 0.872826
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −1638.00 −1.95087 −0.975436 0.220282i $$-0.929302\pi$$
−0.975436 + 0.220282i $$0.929302\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 456.000 0.492470
$$96$$ 0 0
$$97$$ −1010.00 −1.05722 −0.528608 0.848866i $$-0.677286\pi$$
−0.528608 + 0.848866i $$0.677286\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 6.00000 0.00591111 0.00295556 0.999996i $$-0.499059\pi$$
0.00295556 + 0.999996i $$0.499059\pi$$
$$102$$ 0 0
$$103$$ 472.000 0.451530 0.225765 0.974182i $$-0.427512\pi$$
0.225765 + 0.974182i $$0.427512\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 972.000 0.878194 0.439097 0.898440i $$-0.355298\pi$$
0.439097 + 0.898440i $$0.355298\pi$$
$$108$$ 0 0
$$109$$ −1786.00 −1.56943 −0.784715 0.619857i $$-0.787190\pi$$
−0.784715 + 0.619857i $$0.787190\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2286.00 1.90309 0.951543 0.307515i $$-0.0994973\pi$$
0.951543 + 0.307515i $$0.0994973\pi$$
$$114$$ 0 0
$$115$$ 144.000 0.116766
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −35.0000 −0.0262960
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1284.00 −0.918756
$$126$$ 0 0
$$127$$ 1328.00 0.927881 0.463941 0.885866i $$-0.346435\pi$$
0.463941 + 0.885866i $$0.346435\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1212.00 −0.808343 −0.404171 0.914683i $$-0.632440\pi$$
−0.404171 + 0.914683i $$0.632440\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1254.00 0.782018 0.391009 0.920387i $$-0.372126\pi$$
0.391009 + 0.920387i $$0.372126\pi$$
$$138$$ 0 0
$$139$$ 340.000 0.207471 0.103735 0.994605i $$-0.466921\pi$$
0.103735 + 0.994605i $$0.466921\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2232.00 1.30524
$$144$$ 0 0
$$145$$ −324.000 −0.185564
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1038.00 −0.570713 −0.285357 0.958421i $$-0.592112\pi$$
−0.285357 + 0.958421i $$0.592112\pi$$
$$150$$ 0 0
$$151$$ 2936.00 1.58231 0.791153 0.611618i $$-0.209481\pi$$
0.791153 + 0.611618i $$0.209481\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 672.000 0.348234
$$156$$ 0 0
$$157$$ 1330.00 0.676086 0.338043 0.941131i $$-0.390235\pi$$
0.338043 + 0.941131i $$0.390235\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −3364.00 −1.61650 −0.808248 0.588842i $$-0.799584\pi$$
−0.808248 + 0.588842i $$0.799584\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 3048.00 1.41234 0.706172 0.708041i $$-0.250421\pi$$
0.706172 + 0.708041i $$0.250421\pi$$
$$168$$ 0 0
$$169$$ 1647.00 0.749659
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −2706.00 −1.18921 −0.594605 0.804018i $$-0.702692\pi$$
−0.594605 + 0.804018i $$0.702692\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −4716.00 −1.96922 −0.984610 0.174766i $$-0.944083\pi$$
−0.984610 + 0.174766i $$0.944083\pi$$
$$180$$ 0 0
$$181$$ −1910.00 −0.784360 −0.392180 0.919888i $$-0.628279\pi$$
−0.392180 + 0.919888i $$0.628279\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1068.00 −0.424437
$$186$$ 0 0
$$187$$ −4104.00 −1.60489
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4080.00 −1.54565 −0.772823 0.634621i $$-0.781156\pi$$
−0.772823 + 0.634621i $$0.781156\pi$$
$$192$$ 0 0
$$193$$ −2686.00 −1.00177 −0.500887 0.865512i $$-0.666993\pi$$
−0.500887 + 0.865512i $$0.666993\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −510.000 −0.184447 −0.0922233 0.995738i $$-0.529397\pi$$
−0.0922233 + 0.995738i $$0.529397\pi$$
$$198$$ 0 0
$$199$$ −1352.00 −0.481612 −0.240806 0.970573i $$-0.577412\pi$$
−0.240806 + 0.970573i $$0.577412\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 2268.00 0.772702
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −2736.00 −0.905517
$$210$$ 0 0
$$211$$ −3364.00 −1.09757 −0.548785 0.835963i $$-0.684909\pi$$
−0.548785 + 0.835963i $$0.684909\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −1032.00 −0.327357
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −7068.00 −2.15134
$$222$$ 0 0
$$223$$ 4768.00 1.43179 0.715894 0.698209i $$-0.246019\pi$$
0.715894 + 0.698209i $$0.246019\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 420.000 0.122803 0.0614017 0.998113i $$-0.480443\pi$$
0.0614017 + 0.998113i $$0.480443\pi$$
$$228$$ 0 0
$$229$$ 1882.00 0.543083 0.271542 0.962427i $$-0.412467\pi$$
0.271542 + 0.962427i $$0.412467\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −5082.00 −1.42890 −0.714448 0.699688i $$-0.753322\pi$$
−0.714448 + 0.699688i $$0.753322\pi$$
$$234$$ 0 0
$$235$$ −1152.00 −0.319780
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 5424.00 1.46799 0.733995 0.679155i $$-0.237654\pi$$
0.733995 + 0.679155i $$0.237654\pi$$
$$240$$ 0 0
$$241$$ 2590.00 0.692268 0.346134 0.938185i $$-0.387494\pi$$
0.346134 + 0.938185i $$0.387494\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −4712.00 −1.21384
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −4932.00 −1.24026 −0.620130 0.784499i $$-0.712920\pi$$
−0.620130 + 0.784499i $$0.712920\pi$$
$$252$$ 0 0
$$253$$ −864.000 −0.214700
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −3438.00 −0.834461 −0.417231 0.908801i $$-0.636999\pi$$
−0.417231 + 0.908801i $$0.636999\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −6120.00 −1.43489 −0.717444 0.696617i $$-0.754688\pi$$
−0.717444 + 0.696617i $$0.754688\pi$$
$$264$$ 0 0
$$265$$ 2412.00 0.559124
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −18.0000 −0.00407985 −0.00203992 0.999998i $$-0.500649\pi$$
−0.00203992 + 0.999998i $$0.500649\pi$$
$$270$$ 0 0
$$271$$ −6896.00 −1.54576 −0.772882 0.634549i $$-0.781186\pi$$
−0.772882 + 0.634549i $$0.781186\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 3204.00 0.702576
$$276$$ 0 0
$$277$$ 6254.00 1.35656 0.678279 0.734805i $$-0.262726\pi$$
0.678279 + 0.734805i $$0.262726\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1194.00 −0.253481 −0.126740 0.991936i $$-0.540451\pi$$
−0.126740 + 0.991936i $$0.540451\pi$$
$$282$$ 0 0
$$283$$ 7156.00 1.50311 0.751555 0.659671i $$-0.229304\pi$$
0.751555 + 0.659671i $$0.229304\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8083.00 1.64523
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −3738.00 −0.745312 −0.372656 0.927970i $$-0.621553\pi$$
−0.372656 + 0.927970i $$0.621553\pi$$
$$294$$ 0 0
$$295$$ 2376.00 0.468936
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −1488.00 −0.287804
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −1524.00 −0.286111
$$306$$ 0 0
$$307$$ 844.000 0.156904 0.0784522 0.996918i $$-0.475002\pi$$
0.0784522 + 0.996918i $$0.475002\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 6312.00 1.15087 0.575435 0.817847i $$-0.304833\pi$$
0.575435 + 0.817847i $$0.304833\pi$$
$$312$$ 0 0
$$313$$ −8282.00 −1.49561 −0.747806 0.663918i $$-0.768892\pi$$
−0.747806 + 0.663918i $$0.768892\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −9318.00 −1.65095 −0.825475 0.564439i $$-0.809093\pi$$
−0.825475 + 0.564439i $$0.809093\pi$$
$$318$$ 0 0
$$319$$ 1944.00 0.341201
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8664.00 1.49250
$$324$$ 0 0
$$325$$ 5518.00 0.941796
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1652.00 0.274327 0.137163 0.990548i $$-0.456201\pi$$
0.137163 + 0.990548i $$0.456201\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −6072.00 −0.990295
$$336$$ 0 0
$$337$$ −1294.00 −0.209165 −0.104583 0.994516i $$-0.533351\pi$$
−0.104583 + 0.994516i $$0.533351\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −4032.00 −0.640308
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −3636.00 −0.562509 −0.281255 0.959633i $$-0.590751\pi$$
−0.281255 + 0.959633i $$0.590751\pi$$
$$348$$ 0 0
$$349$$ −10478.0 −1.60709 −0.803545 0.595244i $$-0.797055\pi$$
−0.803545 + 0.595244i $$0.797055\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −7566.00 −1.14079 −0.570393 0.821372i $$-0.693209\pi$$
−0.570393 + 0.821372i $$0.693209\pi$$
$$354$$ 0 0
$$355$$ −5040.00 −0.753508
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 8040.00 1.18199 0.590996 0.806675i $$-0.298735\pi$$
0.590996 + 0.806675i $$0.298735\pi$$
$$360$$ 0 0
$$361$$ −1083.00 −0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −5340.00 −0.765776
$$366$$ 0 0
$$367$$ −7568.00 −1.07642 −0.538210 0.842811i $$-0.680899\pi$$
−0.538210 + 0.842811i $$0.680899\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −13522.0 −1.87706 −0.938529 0.345200i $$-0.887811\pi$$
−0.938529 + 0.345200i $$0.887811\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 3348.00 0.457376
$$378$$ 0 0
$$379$$ 2468.00 0.334492 0.167246 0.985915i $$-0.446513\pi$$
0.167246 + 0.985915i $$0.446513\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −12336.0 −1.64580 −0.822898 0.568189i $$-0.807644\pi$$
−0.822898 + 0.568189i $$0.807644\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 3762.00 0.490337 0.245168 0.969481i $$-0.421157\pi$$
0.245168 + 0.969481i $$0.421157\pi$$
$$390$$ 0 0
$$391$$ 2736.00 0.353876
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 480.000 0.0611428
$$396$$ 0 0
$$397$$ 8770.00 1.10870 0.554350 0.832284i $$-0.312967\pi$$
0.554350 + 0.832284i $$0.312967\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6642.00 −0.827146 −0.413573 0.910471i $$-0.635719\pi$$
−0.413573 + 0.910471i $$0.635719\pi$$
$$402$$ 0 0
$$403$$ −6944.00 −0.858326
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 6408.00 0.780424
$$408$$ 0 0
$$409$$ 1510.00 0.182554 0.0912771 0.995826i $$-0.470905\pi$$
0.0912771 + 0.995826i $$0.470905\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −648.000 −0.0766484
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −1260.00 −0.146909 −0.0734547 0.997299i $$-0.523402\pi$$
−0.0734547 + 0.997299i $$0.523402\pi$$
$$420$$ 0 0
$$421$$ 3998.00 0.462828 0.231414 0.972855i $$-0.425665\pi$$
0.231414 + 0.972855i $$0.425665\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −10146.0 −1.15801
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 2736.00 0.305774 0.152887 0.988244i $$-0.451143\pi$$
0.152887 + 0.988244i $$0.451143\pi$$
$$432$$ 0 0
$$433$$ −2690.00 −0.298552 −0.149276 0.988796i $$-0.547694\pi$$
−0.149276 + 0.988796i $$0.547694\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 1824.00 0.199665
$$438$$ 0 0
$$439$$ 1240.00 0.134811 0.0674054 0.997726i $$-0.478528\pi$$
0.0674054 + 0.997726i $$0.478528\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 3900.00 0.418272 0.209136 0.977887i $$-0.432935\pi$$
0.209136 + 0.977887i $$0.432935\pi$$
$$444$$ 0 0
$$445$$ −9828.00 −1.04695
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 10878.0 1.14335 0.571675 0.820480i $$-0.306294\pi$$
0.571675 + 0.820480i $$0.306294\pi$$
$$450$$ 0 0
$$451$$ −13608.0 −1.42079
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2330.00 0.238496 0.119248 0.992864i $$-0.461952\pi$$
0.119248 + 0.992864i $$0.461952\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 15150.0 1.53060 0.765299 0.643675i $$-0.222591\pi$$
0.765299 + 0.643675i $$0.222591\pi$$
$$462$$ 0 0
$$463$$ −2992.00 −0.300324 −0.150162 0.988661i $$-0.547980\pi$$
−0.150162 + 0.988661i $$0.547980\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 8724.00 0.864451 0.432225 0.901766i $$-0.357728\pi$$
0.432225 + 0.901766i $$0.357728\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 6192.00 0.601921
$$474$$ 0 0
$$475$$ −6764.00 −0.653376
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 9744.00 0.929467 0.464734 0.885451i $$-0.346150\pi$$
0.464734 + 0.885451i $$0.346150\pi$$
$$480$$ 0 0
$$481$$ 11036.0 1.04615
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −6060.00 −0.567362
$$486$$ 0 0
$$487$$ 4136.00 0.384846 0.192423 0.981312i $$-0.438365\pi$$
0.192423 + 0.981312i $$0.438365\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −16212.0 −1.49010 −0.745048 0.667011i $$-0.767574\pi$$
−0.745048 + 0.667011i $$0.767574\pi$$
$$492$$ 0 0
$$493$$ −6156.00 −0.562378
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 2396.00 0.214949 0.107475 0.994208i $$-0.465724\pi$$
0.107475 + 0.994208i $$0.465724\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 13128.0 1.16371 0.581857 0.813291i $$-0.302326\pi$$
0.581857 + 0.813291i $$0.302326\pi$$
$$504$$ 0 0
$$505$$ 36.0000 0.00317224
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 12798.0 1.11446 0.557231 0.830357i $$-0.311864\pi$$
0.557231 + 0.830357i $$0.311864\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 2832.00 0.242316
$$516$$ 0 0
$$517$$ 6912.00 0.587987
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 7386.00 0.621087 0.310544 0.950559i $$-0.399489\pi$$
0.310544 + 0.950559i $$0.399489\pi$$
$$522$$ 0 0
$$523$$ −5180.00 −0.433089 −0.216545 0.976273i $$-0.569479\pi$$
−0.216545 + 0.976273i $$0.569479\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 12768.0 1.05538
$$528$$ 0 0
$$529$$ −11591.0 −0.952659
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −23436.0 −1.90455
$$534$$ 0 0
$$535$$ 5832.00 0.471288
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 4070.00 0.323444 0.161722 0.986836i $$-0.448295\pi$$
0.161722 + 0.986836i $$0.448295\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −10716.0 −0.842244
$$546$$ 0 0
$$547$$ 14780.0 1.15530 0.577648 0.816286i $$-0.303971\pi$$
0.577648 + 0.816286i $$0.303971\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −4104.00 −0.317307
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 6858.00 0.521693 0.260846 0.965380i $$-0.415998\pi$$
0.260846 + 0.965380i $$0.415998\pi$$
$$558$$ 0 0
$$559$$ 10664.0 0.806868
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 6660.00 0.498553 0.249277 0.968432i $$-0.419807\pi$$
0.249277 + 0.968432i $$0.419807\pi$$
$$564$$ 0 0
$$565$$ 13716.0 1.02130
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 150.000 0.0110515 0.00552577 0.999985i $$-0.498241\pi$$
0.00552577 + 0.999985i $$0.498241\pi$$
$$570$$ 0 0
$$571$$ −8188.00 −0.600100 −0.300050 0.953923i $$-0.597003\pi$$
−0.300050 + 0.953923i $$0.597003\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −2136.00 −0.154917
$$576$$ 0 0
$$577$$ 5854.00 0.422366 0.211183 0.977447i $$-0.432268\pi$$
0.211183 + 0.977447i $$0.432268\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −14472.0 −1.02808
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 17580.0 1.23612 0.618062 0.786130i $$-0.287918\pi$$
0.618062 + 0.786130i $$0.287918\pi$$
$$588$$ 0 0
$$589$$ 8512.00 0.595468
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 17154.0 1.18791 0.593955 0.804498i $$-0.297566\pi$$
0.593955 + 0.804498i $$0.297566\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 18120.0 1.23600 0.617999 0.786179i $$-0.287943\pi$$
0.617999 + 0.786179i $$0.287943\pi$$
$$600$$ 0 0
$$601$$ −17546.0 −1.19088 −0.595438 0.803401i $$-0.703021\pi$$
−0.595438 + 0.803401i $$0.703021\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −210.000 −0.0141119
$$606$$ 0 0
$$607$$ 14560.0 0.973595 0.486798 0.873515i $$-0.338165\pi$$
0.486798 + 0.873515i $$0.338165\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 11904.0 0.788190
$$612$$ 0 0
$$613$$ −4498.00 −0.296366 −0.148183 0.988960i $$-0.547343\pi$$
−0.148183 + 0.988960i $$0.547343\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 5478.00 0.357433 0.178716 0.983901i $$-0.442806\pi$$
0.178716 + 0.983901i $$0.442806\pi$$
$$618$$ 0 0
$$619$$ −6044.00 −0.392454 −0.196227 0.980559i $$-0.562869\pi$$
−0.196227 + 0.980559i $$0.562869\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 3421.00 0.218944
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −20292.0 −1.28632
$$630$$ 0 0
$$631$$ −15352.0 −0.968547 −0.484274 0.874917i $$-0.660916\pi$$
−0.484274 + 0.874917i $$0.660916\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 7968.00 0.497953
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 22398.0 1.38014 0.690068 0.723744i $$-0.257580\pi$$
0.690068 + 0.723744i $$0.257580\pi$$
$$642$$ 0 0
$$643$$ −3764.00 −0.230852 −0.115426 0.993316i $$-0.536823\pi$$
−0.115426 + 0.993316i $$0.536823\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −17688.0 −1.07479 −0.537393 0.843332i $$-0.680591\pi$$
−0.537393 + 0.843332i $$0.680591\pi$$
$$648$$ 0 0
$$649$$ −14256.0 −0.862245
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −19878.0 −1.19125 −0.595625 0.803263i $$-0.703096\pi$$
−0.595625 + 0.803263i $$0.703096\pi$$
$$654$$ 0 0
$$655$$ −7272.00 −0.433802
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 20004.0 1.18247 0.591233 0.806501i $$-0.298641\pi$$
0.591233 + 0.806501i $$0.298641\pi$$
$$660$$ 0 0
$$661$$ 1306.00 0.0768495 0.0384247 0.999261i $$-0.487766\pi$$
0.0384247 + 0.999261i $$0.487766\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −1296.00 −0.0752344
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 9144.00 0.526081
$$672$$ 0 0
$$673$$ −13054.0 −0.747689 −0.373845 0.927491i $$-0.621961\pi$$
−0.373845 + 0.927491i $$0.621961\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 5046.00 0.286460 0.143230 0.989689i $$-0.454251\pi$$
0.143230 + 0.989689i $$0.454251\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12468.0 −0.698499 −0.349249 0.937030i $$-0.613563\pi$$
−0.349249 + 0.937030i $$0.613563\pi$$
$$684$$ 0 0
$$685$$ 7524.00 0.419675
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −24924.0 −1.37813
$$690$$ 0 0
$$691$$ 23212.0 1.27790 0.638948 0.769250i $$-0.279370\pi$$
0.638948 + 0.769250i $$0.279370\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 2040.00 0.111340
$$696$$ 0 0
$$697$$ 43092.0 2.34179
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −35958.0 −1.93740 −0.968698 0.248241i $$-0.920147\pi$$
−0.968698 + 0.248241i $$0.920147\pi$$
$$702$$ 0 0
$$703$$ −13528.0 −0.725773
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 6446.00 0.341445 0.170723 0.985319i $$-0.445390\pi$$
0.170723 + 0.985319i $$0.445390\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 2688.00 0.141187
$$714$$ 0 0
$$715$$ 13392.0 0.700465
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −4704.00 −0.243991 −0.121996 0.992531i $$-0.538929\pi$$
−0.121996 + 0.992531i $$0.538929\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 4806.00 0.246194
$$726$$ 0 0
$$727$$ 10600.0 0.540760 0.270380 0.962754i $$-0.412851\pi$$
0.270380 + 0.962754i $$0.412851\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −19608.0 −0.992104
$$732$$ 0 0
$$733$$ −12542.0 −0.631991 −0.315995 0.948761i $$-0.602338\pi$$
−0.315995 + 0.948761i $$0.602338\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 36432.0 1.82088
$$738$$ 0 0
$$739$$ 23324.0 1.16101 0.580506 0.814256i $$-0.302855\pi$$
0.580506 + 0.814256i $$0.302855\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 6312.00 0.311662 0.155831 0.987784i $$-0.450194\pi$$
0.155831 + 0.987784i $$0.450194\pi$$
$$744$$ 0 0
$$745$$ −6228.00 −0.306277
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 35840.0 1.74144 0.870719 0.491781i $$-0.163654\pi$$
0.870719 + 0.491781i $$0.163654\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 17616.0 0.849155
$$756$$ 0 0
$$757$$ −34594.0 −1.66095 −0.830476 0.557055i $$-0.811931\pi$$
−0.830476 + 0.557055i $$0.811931\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 23946.0 1.14066 0.570330 0.821416i $$-0.306815\pi$$
0.570330 + 0.821416i $$0.306815\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −24552.0 −1.15583
$$768$$ 0 0
$$769$$ −18770.0 −0.880187 −0.440093 0.897952i $$-0.645055\pi$$
−0.440093 + 0.897952i $$0.645055\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 30342.0 1.41181 0.705903 0.708309i $$-0.250541\pi$$
0.705903 + 0.708309i $$0.250541\pi$$
$$774$$ 0 0
$$775$$ −9968.00 −0.462014
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 28728.0 1.32129
$$780$$ 0 0
$$781$$ 30240.0 1.38550
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 7980.00 0.362826
$$786$$ 0 0
$$787$$ 26188.0 1.18615 0.593076 0.805147i $$-0.297913\pi$$
0.593076 + 0.805147i $$0.297913\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 15748.0 0.705205
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −34818.0 −1.54745 −0.773724 0.633522i $$-0.781609\pi$$
−0.773724 + 0.633522i $$0.781609\pi$$
$$798$$ 0 0
$$799$$ −21888.0 −0.969139
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 32040.0 1.40805
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 21702.0 0.943142 0.471571 0.881828i $$-0.343687\pi$$
0.471571 + 0.881828i $$0.343687\pi$$
$$810$$ 0 0
$$811$$ 20356.0 0.881376 0.440688 0.897660i $$-0.354735\pi$$
0.440688 + 0.897660i $$0.354735\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −20184.0 −0.867503
$$816$$ 0 0
$$817$$ −13072.0 −0.559769
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 19890.0 0.845513 0.422756 0.906243i $$-0.361063\pi$$
0.422756 + 0.906243i $$0.361063\pi$$
$$822$$ 0 0
$$823$$ 4232.00 0.179245 0.0896223 0.995976i $$-0.471434\pi$$
0.0896223 + 0.995976i $$0.471434\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −9636.00 −0.405171 −0.202586 0.979265i $$-0.564934\pi$$
−0.202586 + 0.979265i $$0.564934\pi$$
$$828$$ 0 0
$$829$$ −35294.0 −1.47866 −0.739331 0.673342i $$-0.764858\pi$$
−0.739331 + 0.673342i $$0.764858\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 18288.0 0.757943
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −3768.00 −0.155049 −0.0775243 0.996990i $$-0.524702\pi$$
−0.0775243 + 0.996990i $$0.524702\pi$$
$$840$$ 0 0
$$841$$ −21473.0 −0.880438
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 9882.00 0.402309
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −4272.00 −0.172083
$$852$$ 0 0
$$853$$ 39466.0 1.58416 0.792081 0.610416i $$-0.208998\pi$$
0.792081 + 0.610416i $$0.208998\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −34038.0 −1.35673 −0.678364 0.734726i $$-0.737311\pi$$
−0.678364 + 0.734726i $$0.737311\pi$$
$$858$$ 0 0
$$859$$ 3364.00 0.133618 0.0668092 0.997766i $$-0.478718\pi$$
0.0668092 + 0.997766i $$0.478718\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −13104.0 −0.516878 −0.258439 0.966028i $$-0.583208\pi$$
−0.258439 + 0.966028i $$0.583208\pi$$
$$864$$ 0 0
$$865$$ −16236.0 −0.638197
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −2880.00 −0.112425
$$870$$ 0 0
$$871$$ 62744.0 2.44087
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −40858.0 −1.57318 −0.786589 0.617477i $$-0.788155\pi$$
−0.786589 + 0.617477i $$0.788155\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −37374.0 −1.42924 −0.714621 0.699512i $$-0.753401\pi$$
−0.714621 + 0.699512i $$0.753401\pi$$
$$882$$ 0 0
$$883$$ 9788.00 0.373038 0.186519 0.982451i $$-0.440279\pi$$
0.186519 + 0.982451i $$0.440279\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 50424.0 1.90876 0.954381 0.298591i $$-0.0965166\pi$$
0.954381 + 0.298591i $$0.0965166\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −14592.0 −0.546811
$$894$$ 0 0
$$895$$ −28296.0 −1.05679
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −6048.00 −0.224374
$$900$$ 0 0
$$901$$ 45828.0 1.69451
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −11460.0 −0.420932
$$906$$ 0 0
$$907$$ −12412.0 −0.454392 −0.227196 0.973849i $$-0.572956\pi$$
−0.227196 + 0.973849i $$0.572956\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −6576.00 −0.239158 −0.119579 0.992825i $$-0.538154\pi$$
−0.119579 + 0.992825i $$0.538154\pi$$
$$912$$ 0 0
$$913$$ 3888.00 0.140935
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 8264.00 0.296631 0.148316 0.988940i $$-0.452615\pi$$
0.148316 + 0.988940i $$0.452615\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 52080.0 1.85724
$$924$$ 0 0
$$925$$ 15842.0 0.563115
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 39426.0 1.39238 0.696192 0.717855i $$-0.254876\pi$$
0.696192 + 0.717855i $$0.254876\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −24624.0 −0.861274
$$936$$ 0 0
$$937$$ 4678.00 0.163099 0.0815494 0.996669i $$-0.474013\pi$$
0.0815494 + 0.996669i $$0.474013\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −17346.0 −0.600918 −0.300459 0.953795i $$-0.597140\pi$$
−0.300459 + 0.953795i $$0.597140\pi$$
$$942$$ 0 0
$$943$$ 9072.00 0.313282
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −19452.0 −0.667482 −0.333741 0.942665i $$-0.608311\pi$$
−0.333741 + 0.942665i $$0.608311\pi$$
$$948$$ 0 0
$$949$$ 55180.0 1.88748
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −4458.00 −0.151531 −0.0757654 0.997126i $$-0.524140\pi$$
−0.0757654 + 0.997126i $$0.524140\pi$$
$$954$$ 0 0
$$955$$ −24480.0 −0.829481
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −17247.0 −0.578933
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −16116.0 −0.537609
$$966$$ 0 0
$$967$$ 52520.0 1.74657 0.873283 0.487213i $$-0.161987\pi$$
0.873283 + 0.487213i $$0.161987\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −10404.0 −0.343852 −0.171926 0.985110i $$-0.554999\pi$$
−0.171926 + 0.985110i $$0.554999\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 7566.00 0.247756 0.123878 0.992297i $$-0.460467\pi$$
0.123878 + 0.992297i $$0.460467\pi$$
$$978$$ 0 0
$$979$$ 58968.0 1.92505
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 44376.0 1.43985 0.719926 0.694051i $$-0.244176\pi$$
0.719926 + 0.694051i $$0.244176\pi$$
$$984$$ 0 0
$$985$$ −3060.00 −0.0989845
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −4128.00 −0.132723
$$990$$ 0 0
$$991$$ −27328.0 −0.875986 −0.437993 0.898978i $$-0.644311\pi$$
−0.437993 + 0.898978i $$0.644311\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −8112.00 −0.258460
$$996$$ 0 0
$$997$$ −2774.00 −0.0881178 −0.0440589 0.999029i $$-0.514029\pi$$
−0.0440589 + 0.999029i $$0.514029\pi$$
$$998$$ 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.j.1.1 1
3.2 odd 2 588.4.a.d.1.1 1
7.2 even 3 1764.4.k.f.361.1 2
7.3 odd 6 1764.4.k.l.1549.1 2
7.4 even 3 1764.4.k.f.1549.1 2
7.5 odd 6 1764.4.k.l.361.1 2
7.6 odd 2 252.4.a.b.1.1 1
12.11 even 2 2352.4.a.d.1.1 1
21.2 odd 6 588.4.i.c.361.1 2
21.5 even 6 588.4.i.f.361.1 2
21.11 odd 6 588.4.i.c.373.1 2
21.17 even 6 588.4.i.f.373.1 2
21.20 even 2 84.4.a.a.1.1 1
28.27 even 2 1008.4.a.h.1.1 1
84.83 odd 2 336.4.a.k.1.1 1
105.62 odd 4 2100.4.k.j.1849.2 2
105.83 odd 4 2100.4.k.j.1849.1 2
105.104 even 2 2100.4.a.l.1.1 1
168.83 odd 2 1344.4.a.d.1.1 1
168.125 even 2 1344.4.a.q.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
84.4.a.a.1.1 1 21.20 even 2
252.4.a.b.1.1 1 7.6 odd 2
336.4.a.k.1.1 1 84.83 odd 2
588.4.a.d.1.1 1 3.2 odd 2
588.4.i.c.361.1 2 21.2 odd 6
588.4.i.c.373.1 2 21.11 odd 6
588.4.i.f.361.1 2 21.5 even 6
588.4.i.f.373.1 2 21.17 even 6
1008.4.a.h.1.1 1 28.27 even 2
1344.4.a.d.1.1 1 168.83 odd 2
1344.4.a.q.1.1 1 168.125 even 2
1764.4.a.j.1.1 1 1.1 even 1 trivial
1764.4.k.f.361.1 2 7.2 even 3
1764.4.k.f.1549.1 2 7.4 even 3
1764.4.k.l.361.1 2 7.5 odd 6
1764.4.k.l.1549.1 2 7.3 odd 6
2100.4.a.l.1.1 1 105.104 even 2
2100.4.k.j.1849.1 2 105.83 odd 4
2100.4.k.j.1849.2 2 105.62 odd 4
2352.4.a.d.1.1 1 12.11 even 2