# Properties

 Label 1764.4.a.bc.1.3 Level $1764$ Weight $4$ Character 1764.1 Self dual yes Analytic conductor $104.079$ Analytic rank $0$ Dimension $4$ 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: $$0$$ Dimension: $$4$$ Coefficient field: 4.4.136768.1 Defining polynomial: $$x^{4} - 2 x^{3} - 23 x^{2} + 18 x + 119$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{4}\cdot 7$$ Twist minimal: no (minimal twist has level 588) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$2.89590$$ of defining polynomial Character $$\chi$$ $$=$$ 1764.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+8.16940 q^{5} +O(q^{10})$$ $$q+8.16940 q^{5} -37.8189 q^{11} -39.9319 q^{13} +9.93596 q^{17} +90.4458 q^{19} -118.595 q^{23} -58.2608 q^{25} +78.4061 q^{29} -92.0110 q^{31} +332.435 q^{37} +71.7451 q^{41} -115.947 q^{43} +307.927 q^{47} +403.150 q^{53} -308.958 q^{55} +593.710 q^{59} -333.170 q^{61} -326.220 q^{65} -743.511 q^{67} +728.272 q^{71} +801.749 q^{73} +1067.91 q^{79} +906.756 q^{83} +81.1709 q^{85} +1113.27 q^{89} +738.889 q^{95} -1480.94 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + O(q^{10})$$ $$4q + 48q^{17} - 192q^{19} - 192q^{23} + 324q^{25} - 96q^{29} - 48q^{31} + 256q^{37} + 1008q^{41} - 112q^{43} + 864q^{47} + 648q^{53} - 2352q^{55} + 336q^{59} - 960q^{61} + 360q^{65} + 720q^{67} + 1344q^{71} - 672q^{73} - 1984q^{79} + 3120q^{83} + 680q^{85} + 2160q^{89} + 3744q^{95} - 2016q^{97} + O(q^{100})$$

## 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
$$5$$ 8.16940 0.730694 0.365347 0.930871i $$-0.380950\pi$$
0.365347 + 0.930871i $$0.380950\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −37.8189 −1.03662 −0.518310 0.855193i $$-0.673439\pi$$
−0.518310 + 0.855193i $$0.673439\pi$$
$$12$$ 0 0
$$13$$ −39.9319 −0.851933 −0.425966 0.904739i $$-0.640066\pi$$
−0.425966 + 0.904739i $$0.640066\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 9.93596 0.141754 0.0708772 0.997485i $$-0.477420\pi$$
0.0708772 + 0.997485i $$0.477420\pi$$
$$18$$ 0 0
$$19$$ 90.4458 1.09209 0.546045 0.837756i $$-0.316133\pi$$
0.546045 + 0.837756i $$0.316133\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −118.595 −1.07516 −0.537580 0.843213i $$-0.680661\pi$$
−0.537580 + 0.843213i $$0.680661\pi$$
$$24$$ 0 0
$$25$$ −58.2608 −0.466087
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 78.4061 0.502057 0.251028 0.967980i $$-0.419231\pi$$
0.251028 + 0.967980i $$0.419231\pi$$
$$30$$ 0 0
$$31$$ −92.0110 −0.533086 −0.266543 0.963823i $$-0.585881\pi$$
−0.266543 + 0.963823i $$0.585881\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 332.435 1.47708 0.738541 0.674209i $$-0.235515\pi$$
0.738541 + 0.674209i $$0.235515\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 71.7451 0.273285 0.136643 0.990620i $$-0.456369\pi$$
0.136643 + 0.990620i $$0.456369\pi$$
$$42$$ 0 0
$$43$$ −115.947 −0.411202 −0.205601 0.978636i $$-0.565915\pi$$
−0.205601 + 0.978636i $$0.565915\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 307.927 0.955656 0.477828 0.878453i $$-0.341424\pi$$
0.477828 + 0.878453i $$0.341424\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 403.150 1.04485 0.522424 0.852686i $$-0.325028\pi$$
0.522424 + 0.852686i $$0.325028\pi$$
$$54$$ 0 0
$$55$$ −308.958 −0.757451
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 593.710 1.31008 0.655038 0.755596i $$-0.272653\pi$$
0.655038 + 0.755596i $$0.272653\pi$$
$$60$$ 0 0
$$61$$ −333.170 −0.699313 −0.349657 0.936878i $$-0.613702\pi$$
−0.349657 + 0.936878i $$0.613702\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −326.220 −0.622502
$$66$$ 0 0
$$67$$ −743.511 −1.35574 −0.677869 0.735183i $$-0.737096\pi$$
−0.677869 + 0.735183i $$0.737096\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 728.272 1.21732 0.608662 0.793429i $$-0.291706\pi$$
0.608662 + 0.793429i $$0.291706\pi$$
$$72$$ 0 0
$$73$$ 801.749 1.28545 0.642723 0.766098i $$-0.277804\pi$$
0.642723 + 0.766098i $$0.277804\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1067.91 1.52087 0.760435 0.649414i $$-0.224986\pi$$
0.760435 + 0.649414i $$0.224986\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 906.756 1.19915 0.599575 0.800319i $$-0.295336\pi$$
0.599575 + 0.800319i $$0.295336\pi$$
$$84$$ 0 0
$$85$$ 81.1709 0.103579
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1113.27 1.32591 0.662957 0.748658i $$-0.269301\pi$$
0.662957 + 0.748658i $$0.269301\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 738.889 0.797983
$$96$$ 0 0
$$97$$ −1480.94 −1.55017 −0.775084 0.631858i $$-0.782293\pi$$
−0.775084 + 0.631858i $$0.782293\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −556.316 −0.548075 −0.274037 0.961719i $$-0.588359\pi$$
−0.274037 + 0.961719i $$0.588359\pi$$
$$102$$ 0 0
$$103$$ −552.435 −0.528476 −0.264238 0.964458i $$-0.585120\pi$$
−0.264238 + 0.964458i $$0.585120\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −533.804 −0.482288 −0.241144 0.970489i $$-0.577523\pi$$
−0.241144 + 0.970489i $$0.577523\pi$$
$$108$$ 0 0
$$109$$ 1094.63 0.961894 0.480947 0.876750i $$-0.340293\pi$$
0.480947 + 0.876750i $$0.340293\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1425.18 1.18646 0.593228 0.805035i $$-0.297853\pi$$
0.593228 + 0.805035i $$0.297853\pi$$
$$114$$ 0 0
$$115$$ −968.847 −0.785612
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 99.2659 0.0745800
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1497.13 −1.07126
$$126$$ 0 0
$$127$$ −786.485 −0.549522 −0.274761 0.961513i $$-0.588599\pi$$
−0.274761 + 0.961513i $$0.588599\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −27.7303 −0.0184947 −0.00924735 0.999957i $$-0.502944\pi$$
−0.00924735 + 0.999957i $$0.502944\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2362.98 1.47360 0.736798 0.676113i $$-0.236337\pi$$
0.736798 + 0.676113i $$0.236337\pi$$
$$138$$ 0 0
$$139$$ −2513.28 −1.53362 −0.766811 0.641873i $$-0.778158\pi$$
−0.766811 + 0.641873i $$0.778158\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 1510.18 0.883130
$$144$$ 0 0
$$145$$ 640.531 0.366850
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2265.83 −1.24580 −0.622900 0.782302i $$-0.714045\pi$$
−0.622900 + 0.782302i $$0.714045\pi$$
$$150$$ 0 0
$$151$$ 283.146 0.152597 0.0762984 0.997085i $$-0.475690\pi$$
0.0762984 + 0.997085i $$0.475690\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −751.675 −0.389522
$$156$$ 0 0
$$157$$ −192.581 −0.0978956 −0.0489478 0.998801i $$-0.515587\pi$$
−0.0489478 + 0.998801i $$0.515587\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −842.833 −0.405005 −0.202502 0.979282i $$-0.564907\pi$$
−0.202502 + 0.979282i $$0.564907\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −3859.21 −1.78823 −0.894116 0.447836i $$-0.852195\pi$$
−0.894116 + 0.447836i $$0.852195\pi$$
$$168$$ 0 0
$$169$$ −602.441 −0.274211
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1510.66 0.663891 0.331946 0.943298i $$-0.392295\pi$$
0.331946 + 0.943298i $$0.392295\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 2464.63 1.02913 0.514566 0.857451i $$-0.327953\pi$$
0.514566 + 0.857451i $$0.327953\pi$$
$$180$$ 0 0
$$181$$ 3297.36 1.35409 0.677047 0.735940i $$-0.263259\pi$$
0.677047 + 0.735940i $$0.263259\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2715.80 1.07929
$$186$$ 0 0
$$187$$ −375.767 −0.146945
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 4729.71 1.79178 0.895889 0.444278i $$-0.146540\pi$$
0.895889 + 0.444278i $$0.146540\pi$$
$$192$$ 0 0
$$193$$ 4553.18 1.69816 0.849080 0.528264i $$-0.177157\pi$$
0.849080 + 0.528264i $$0.177157\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 3109.06 1.12442 0.562212 0.826993i $$-0.309950\pi$$
0.562212 + 0.826993i $$0.309950\pi$$
$$198$$ 0 0
$$199$$ 443.512 0.157989 0.0789943 0.996875i $$-0.474829\pi$$
0.0789943 + 0.996875i $$0.474829\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 586.114 0.199688
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −3420.56 −1.13208
$$210$$ 0 0
$$211$$ 4653.28 1.51822 0.759112 0.650960i $$-0.225633\pi$$
0.759112 + 0.650960i $$0.225633\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −947.214 −0.300463
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −396.762 −0.120765
$$222$$ 0 0
$$223$$ −2778.90 −0.834481 −0.417240 0.908796i $$-0.637003\pi$$
−0.417240 + 0.908796i $$0.637003\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 3217.22 0.940681 0.470340 0.882485i $$-0.344131\pi$$
0.470340 + 0.882485i $$0.344131\pi$$
$$228$$ 0 0
$$229$$ 3728.01 1.07578 0.537891 0.843014i $$-0.319221\pi$$
0.537891 + 0.843014i $$0.319221\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 3603.51 1.01319 0.506596 0.862183i $$-0.330903\pi$$
0.506596 + 0.862183i $$0.330903\pi$$
$$234$$ 0 0
$$235$$ 2515.58 0.698292
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −2348.76 −0.635684 −0.317842 0.948144i $$-0.602958\pi$$
−0.317842 + 0.948144i $$0.602958\pi$$
$$240$$ 0 0
$$241$$ 5093.39 1.36139 0.680693 0.732569i $$-0.261679\pi$$
0.680693 + 0.732569i $$0.261679\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −3611.68 −0.930386
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −5939.02 −1.49350 −0.746749 0.665106i $$-0.768386\pi$$
−0.746749 + 0.665106i $$0.768386\pi$$
$$252$$ 0 0
$$253$$ 4485.11 1.11453
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1515.89 −0.367932 −0.183966 0.982933i $$-0.558894\pi$$
−0.183966 + 0.982933i $$0.558894\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6433.92 1.50849 0.754244 0.656594i $$-0.228003\pi$$
0.754244 + 0.656594i $$0.228003\pi$$
$$264$$ 0 0
$$265$$ 3293.50 0.763464
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −6949.79 −1.57523 −0.787614 0.616169i $$-0.788684\pi$$
−0.787614 + 0.616169i $$0.788684\pi$$
$$270$$ 0 0
$$271$$ 961.994 0.215635 0.107817 0.994171i $$-0.465614\pi$$
0.107817 + 0.994171i $$0.465614\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 2203.36 0.483154
$$276$$ 0 0
$$277$$ 760.010 0.164854 0.0824271 0.996597i $$-0.473733\pi$$
0.0824271 + 0.996597i $$0.473733\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 4412.07 0.936662 0.468331 0.883553i $$-0.344855\pi$$
0.468331 + 0.883553i $$0.344855\pi$$
$$282$$ 0 0
$$283$$ 2602.15 0.546578 0.273289 0.961932i $$-0.411888\pi$$
0.273289 + 0.961932i $$0.411888\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4814.28 −0.979906
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −9332.18 −1.86072 −0.930361 0.366644i $$-0.880507\pi$$
−0.930361 + 0.366644i $$0.880507\pi$$
$$294$$ 0 0
$$295$$ 4850.26 0.957264
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 4735.71 0.915964
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −2721.80 −0.510984
$$306$$ 0 0
$$307$$ −4895.51 −0.910103 −0.455051 0.890465i $$-0.650379\pi$$
−0.455051 + 0.890465i $$0.650379\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 7505.28 1.36844 0.684221 0.729275i $$-0.260142\pi$$
0.684221 + 0.729275i $$0.260142\pi$$
$$312$$ 0 0
$$313$$ 6349.27 1.14659 0.573294 0.819350i $$-0.305665\pi$$
0.573294 + 0.819350i $$0.305665\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 7999.60 1.41736 0.708679 0.705531i $$-0.249292\pi$$
0.708679 + 0.705531i $$0.249292\pi$$
$$318$$ 0 0
$$319$$ −2965.23 −0.520442
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 898.666 0.154808
$$324$$ 0 0
$$325$$ 2326.47 0.397074
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −2121.56 −0.352300 −0.176150 0.984363i $$-0.556364\pi$$
−0.176150 + 0.984363i $$0.556364\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −6074.05 −0.990629
$$336$$ 0 0
$$337$$ −9114.19 −1.47324 −0.736620 0.676307i $$-0.763579\pi$$
−0.736620 + 0.676307i $$0.763579\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 3479.75 0.552607
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1673.07 0.258833 0.129416 0.991590i $$-0.458690\pi$$
0.129416 + 0.991590i $$0.458690\pi$$
$$348$$ 0 0
$$349$$ 3467.56 0.531845 0.265923 0.963994i $$-0.414323\pi$$
0.265923 + 0.963994i $$0.414323\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 3984.24 0.600736 0.300368 0.953823i $$-0.402891\pi$$
0.300368 + 0.953823i $$0.402891\pi$$
$$354$$ 0 0
$$355$$ 5949.55 0.889491
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −2170.93 −0.319157 −0.159579 0.987185i $$-0.551014\pi$$
−0.159579 + 0.987185i $$0.551014\pi$$
$$360$$ 0 0
$$361$$ 1321.45 0.192659
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 6549.81 0.939268
$$366$$ 0 0
$$367$$ −3592.12 −0.510918 −0.255459 0.966820i $$-0.582227\pi$$
−0.255459 + 0.966820i $$0.582227\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 7439.80 1.03276 0.516378 0.856361i $$-0.327280\pi$$
0.516378 + 0.856361i $$0.327280\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −3130.91 −0.427719
$$378$$ 0 0
$$379$$ 11243.9 1.52390 0.761951 0.647635i $$-0.224242\pi$$
0.761951 + 0.647635i $$0.224242\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 3541.25 0.472452 0.236226 0.971698i $$-0.424089\pi$$
0.236226 + 0.971698i $$0.424089\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 10558.2 1.37615 0.688074 0.725640i $$-0.258456\pi$$
0.688074 + 0.725640i $$0.258456\pi$$
$$390$$ 0 0
$$391$$ −1178.35 −0.152409
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 8724.15 1.11129
$$396$$ 0 0
$$397$$ 540.574 0.0683391 0.0341696 0.999416i $$-0.489121\pi$$
0.0341696 + 0.999416i $$0.489121\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −2167.03 −0.269866 −0.134933 0.990855i $$-0.543082\pi$$
−0.134933 + 0.990855i $$0.543082\pi$$
$$402$$ 0 0
$$403$$ 3674.17 0.454153
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −12572.3 −1.53117
$$408$$ 0 0
$$409$$ 957.690 0.115782 0.0578908 0.998323i $$-0.481562\pi$$
0.0578908 + 0.998323i $$0.481562\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 7407.66 0.876211
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 6464.42 0.753718 0.376859 0.926271i $$-0.377004\pi$$
0.376859 + 0.926271i $$0.377004\pi$$
$$420$$ 0 0
$$421$$ −6201.23 −0.717885 −0.358943 0.933360i $$-0.616863\pi$$
−0.358943 + 0.933360i $$0.616863\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −578.877 −0.0660698
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1415.59 −0.158206 −0.0791029 0.996866i $$-0.525206\pi$$
−0.0791029 + 0.996866i $$0.525206\pi$$
$$432$$ 0 0
$$433$$ −8905.73 −0.988411 −0.494206 0.869345i $$-0.664541\pi$$
−0.494206 + 0.869345i $$0.664541\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −10726.4 −1.17417
$$438$$ 0 0
$$439$$ −10876.5 −1.18248 −0.591238 0.806497i $$-0.701361\pi$$
−0.591238 + 0.806497i $$0.701361\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −11403.0 −1.22296 −0.611479 0.791260i $$-0.709425\pi$$
−0.611479 + 0.791260i $$0.709425\pi$$
$$444$$ 0 0
$$445$$ 9094.74 0.968837
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 12689.0 1.33370 0.666852 0.745190i $$-0.267641\pi$$
0.666852 + 0.745190i $$0.267641\pi$$
$$450$$ 0 0
$$451$$ −2713.32 −0.283293
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2270.05 0.232360 0.116180 0.993228i $$-0.462935\pi$$
0.116180 + 0.993228i $$0.462935\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 10731.2 1.08417 0.542085 0.840324i $$-0.317635\pi$$
0.542085 + 0.840324i $$0.317635\pi$$
$$462$$ 0 0
$$463$$ −3307.74 −0.332017 −0.166008 0.986124i $$-0.553088\pi$$
−0.166008 + 0.986124i $$0.553088\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −9246.69 −0.916244 −0.458122 0.888889i $$-0.651478\pi$$
−0.458122 + 0.888889i $$0.651478\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 4384.96 0.426260
$$474$$ 0 0
$$475$$ −5269.45 −0.509008
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 15223.3 1.45213 0.726066 0.687625i $$-0.241347\pi$$
0.726066 + 0.687625i $$0.241347\pi$$
$$480$$ 0 0
$$481$$ −13274.8 −1.25837
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −12098.4 −1.13270
$$486$$ 0 0
$$487$$ −7758.72 −0.721933 −0.360966 0.932579i $$-0.617553\pi$$
−0.360966 + 0.932579i $$0.617553\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 8342.30 0.766767 0.383384 0.923589i $$-0.374759\pi$$
0.383384 + 0.923589i $$0.374759\pi$$
$$492$$ 0 0
$$493$$ 779.040 0.0711688
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −2586.95 −0.232079 −0.116040 0.993245i $$-0.537020\pi$$
−0.116040 + 0.993245i $$0.537020\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 409.682 0.0363157 0.0181578 0.999835i $$-0.494220\pi$$
0.0181578 + 0.999835i $$0.494220\pi$$
$$504$$ 0 0
$$505$$ −4544.77 −0.400475
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 4390.51 0.382330 0.191165 0.981558i $$-0.438774\pi$$
0.191165 + 0.981558i $$0.438774\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −4513.06 −0.386154
$$516$$ 0 0
$$517$$ −11645.5 −0.990652
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −19429.5 −1.63382 −0.816912 0.576762i $$-0.804316\pi$$
−0.816912 + 0.576762i $$0.804316\pi$$
$$522$$ 0 0
$$523$$ −17948.7 −1.50065 −0.750326 0.661067i $$-0.770104\pi$$
−0.750326 + 0.661067i $$0.770104\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −914.217 −0.0755672
$$528$$ 0 0
$$529$$ 1897.67 0.155968
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −2864.92 −0.232821
$$534$$ 0 0
$$535$$ −4360.86 −0.352405
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 23094.0 1.83528 0.917641 0.397411i $$-0.130091\pi$$
0.917641 + 0.397411i $$0.130091\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 8942.47 0.702850
$$546$$ 0 0
$$547$$ −2266.68 −0.177178 −0.0885889 0.996068i $$-0.528236\pi$$
−0.0885889 + 0.996068i $$0.528236\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 7091.50 0.548291
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 11038.5 0.839709 0.419854 0.907592i $$-0.362081\pi$$
0.419854 + 0.907592i $$0.362081\pi$$
$$558$$ 0 0
$$559$$ 4629.97 0.350316
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −7059.36 −0.528448 −0.264224 0.964461i $$-0.585116\pi$$
−0.264224 + 0.964461i $$0.585116\pi$$
$$564$$ 0 0
$$565$$ 11642.9 0.866936
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1352.81 0.0996706 0.0498353 0.998757i $$-0.484130\pi$$
0.0498353 + 0.998757i $$0.484130\pi$$
$$570$$ 0 0
$$571$$ −20839.2 −1.52731 −0.763655 0.645625i $$-0.776597\pi$$
−0.763655 + 0.645625i $$0.776597\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 6909.42 0.501117
$$576$$ 0 0
$$577$$ −10014.6 −0.722556 −0.361278 0.932458i $$-0.617659\pi$$
−0.361278 + 0.932458i $$0.617659\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −15246.7 −1.08311
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 20864.8 1.46709 0.733546 0.679640i $$-0.237864\pi$$
0.733546 + 0.679640i $$0.237864\pi$$
$$588$$ 0 0
$$589$$ −8322.01 −0.582177
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 17547.7 1.21517 0.607586 0.794254i $$-0.292138\pi$$
0.607586 + 0.794254i $$0.292138\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 130.682 0.00891405 0.00445703 0.999990i $$-0.498581\pi$$
0.00445703 + 0.999990i $$0.498581\pi$$
$$600$$ 0 0
$$601$$ 5964.47 0.404818 0.202409 0.979301i $$-0.435123\pi$$
0.202409 + 0.979301i $$0.435123\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 810.944 0.0544951
$$606$$ 0 0
$$607$$ 9911.63 0.662769 0.331384 0.943496i $$-0.392484\pi$$
0.331384 + 0.943496i $$0.392484\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −12296.1 −0.814155
$$612$$ 0 0
$$613$$ −6482.53 −0.427124 −0.213562 0.976930i $$-0.568506\pi$$
−0.213562 + 0.976930i $$0.568506\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −7189.36 −0.469097 −0.234548 0.972104i $$-0.575361\pi$$
−0.234548 + 0.972104i $$0.575361\pi$$
$$618$$ 0 0
$$619$$ −1861.39 −0.120865 −0.0604327 0.998172i $$-0.519248\pi$$
−0.0604327 + 0.998172i $$0.519248\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −4948.07 −0.316677
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 3303.06 0.209383
$$630$$ 0 0
$$631$$ −29032.0 −1.83161 −0.915803 0.401627i $$-0.868445\pi$$
−0.915803 + 0.401627i $$0.868445\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −6425.12 −0.401532
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −24457.7 −1.50705 −0.753527 0.657417i $$-0.771649\pi$$
−0.753527 + 0.657417i $$0.771649\pi$$
$$642$$ 0 0
$$643$$ −10968.2 −0.672695 −0.336348 0.941738i $$-0.609192\pi$$
−0.336348 + 0.941738i $$0.609192\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 5484.74 0.333272 0.166636 0.986018i $$-0.446709\pi$$
0.166636 + 0.986018i $$0.446709\pi$$
$$648$$ 0 0
$$649$$ −22453.4 −1.35805
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 10330.0 0.619055 0.309527 0.950891i $$-0.399829\pi$$
0.309527 + 0.950891i $$0.399829\pi$$
$$654$$ 0 0
$$655$$ −226.540 −0.0135140
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −26822.2 −1.58550 −0.792751 0.609546i $$-0.791352\pi$$
−0.792751 + 0.609546i $$0.791352\pi$$
$$660$$ 0 0
$$661$$ −2498.76 −0.147035 −0.0735177 0.997294i $$-0.523423\pi$$
−0.0735177 + 0.997294i $$0.523423\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −9298.54 −0.539791
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 12600.1 0.724922
$$672$$ 0 0
$$673$$ 10092.1 0.578044 0.289022 0.957322i $$-0.406670\pi$$
0.289022 + 0.957322i $$0.406670\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −26366.4 −1.49681 −0.748406 0.663241i $$-0.769180\pi$$
−0.748406 + 0.663241i $$0.769180\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −22570.8 −1.26449 −0.632245 0.774769i $$-0.717866\pi$$
−0.632245 + 0.774769i $$0.717866\pi$$
$$684$$ 0 0
$$685$$ 19304.1 1.07675
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −16098.6 −0.890140
$$690$$ 0 0
$$691$$ 11931.5 0.656867 0.328434 0.944527i $$-0.393479\pi$$
0.328434 + 0.944527i $$0.393479\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −20532.0 −1.12061
$$696$$ 0 0
$$697$$ 712.856 0.0387394
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −16592.6 −0.893997 −0.446999 0.894535i $$-0.647507\pi$$
−0.446999 + 0.894535i $$0.647507\pi$$
$$702$$ 0 0
$$703$$ 30067.4 1.61311
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 18714.0 0.991283 0.495641 0.868527i $$-0.334933\pi$$
0.495641 + 0.868527i $$0.334933\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 10912.0 0.573152
$$714$$ 0 0
$$715$$ 12337.3 0.645298
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −24854.8 −1.28919 −0.644594 0.764525i $$-0.722974\pi$$
−0.644594 + 0.764525i $$0.722974\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −4568.00 −0.234002
$$726$$ 0 0
$$727$$ 22506.0 1.14814 0.574071 0.818805i $$-0.305363\pi$$
0.574071 + 0.818805i $$0.305363\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1152.04 −0.0582897
$$732$$ 0 0
$$733$$ 23792.0 1.19888 0.599440 0.800420i $$-0.295390\pi$$
0.599440 + 0.800420i $$0.295390\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 28118.8 1.40538
$$738$$ 0 0
$$739$$ 4803.24 0.239093 0.119547 0.992829i $$-0.461856\pi$$
0.119547 + 0.992829i $$0.461856\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −5076.10 −0.250638 −0.125319 0.992116i $$-0.539995\pi$$
−0.125319 + 0.992116i $$0.539995\pi$$
$$744$$ 0 0
$$745$$ −18510.5 −0.910298
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −9158.72 −0.445015 −0.222508 0.974931i $$-0.571424\pi$$
−0.222508 + 0.974931i $$0.571424\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 2313.14 0.111502
$$756$$ 0 0
$$757$$ 33682.2 1.61717 0.808587 0.588377i $$-0.200233\pi$$
0.808587 + 0.588377i $$0.200233\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 13346.3 0.635745 0.317873 0.948133i $$-0.397032\pi$$
0.317873 + 0.948133i $$0.397032\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −23708.0 −1.11610
$$768$$ 0 0
$$769$$ 15530.6 0.728281 0.364140 0.931344i $$-0.381363\pi$$
0.364140 + 0.931344i $$0.381363\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −11015.2 −0.512536 −0.256268 0.966606i $$-0.582493\pi$$
−0.256268 + 0.966606i $$0.582493\pi$$
$$774$$ 0 0
$$775$$ 5360.63 0.248464
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 6489.04 0.298452
$$780$$ 0 0
$$781$$ −27542.4 −1.26190
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −1573.27 −0.0715317
$$786$$ 0 0
$$787$$ −21192.6 −0.959892 −0.479946 0.877298i $$-0.659344\pi$$
−0.479946 + 0.877298i $$0.659344\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 13304.1 0.595768
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 18189.9 0.808432 0.404216 0.914663i $$-0.367544\pi$$
0.404216 + 0.914663i $$0.367544\pi$$
$$798$$ 0 0
$$799$$ 3059.56 0.135468
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −30321.2 −1.33252
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −45516.5 −1.97809 −0.989045 0.147611i $$-0.952842\pi$$
−0.989045 + 0.147611i $$0.952842\pi$$
$$810$$ 0 0
$$811$$ 42099.9 1.82285 0.911423 0.411472i $$-0.134985\pi$$
0.911423 + 0.411472i $$0.134985\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −6885.45 −0.295935
$$816$$ 0 0
$$817$$ −10486.9 −0.449069
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 26555.9 1.12888 0.564439 0.825475i $$-0.309093\pi$$
0.564439 + 0.825475i $$0.309093\pi$$
$$822$$ 0 0
$$823$$ −1554.25 −0.0658295 −0.0329147 0.999458i $$-0.510479\pi$$
−0.0329147 + 0.999458i $$0.510479\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 10548.3 0.443531 0.221766 0.975100i $$-0.428818\pi$$
0.221766 + 0.975100i $$0.428818\pi$$
$$828$$ 0 0
$$829$$ −4331.26 −0.181461 −0.0907303 0.995875i $$-0.528920\pi$$
−0.0907303 + 0.995875i $$0.528920\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −31527.5 −1.30665
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −23557.7 −0.969369 −0.484685 0.874689i $$-0.661066\pi$$
−0.484685 + 0.874689i $$0.661066\pi$$
$$840$$ 0 0
$$841$$ −18241.5 −0.747939
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −4921.59 −0.200364
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −39425.0 −1.58810
$$852$$ 0 0
$$853$$ 11493.6 0.461350 0.230675 0.973031i $$-0.425907\pi$$
0.230675 + 0.973031i $$0.425907\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −2534.23 −0.101012 −0.0505062 0.998724i $$-0.516083\pi$$
−0.0505062 + 0.998724i $$0.516083\pi$$
$$858$$ 0 0
$$859$$ −3127.09 −0.124208 −0.0621041 0.998070i $$-0.519781\pi$$
−0.0621041 + 0.998070i $$0.519781\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −15309.9 −0.603887 −0.301943 0.953326i $$-0.597635\pi$$
−0.301943 + 0.953326i $$0.597635\pi$$
$$864$$ 0 0
$$865$$ 12341.2 0.485101
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −40387.0 −1.57656
$$870$$ 0 0
$$871$$ 29689.8 1.15500
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −42420.7 −1.63335 −0.816673 0.577100i $$-0.804184\pi$$
−0.816673 + 0.577100i $$0.804184\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 10060.8 0.384740 0.192370 0.981322i $$-0.438383\pi$$
0.192370 + 0.981322i $$0.438383\pi$$
$$882$$ 0 0
$$883$$ 17437.8 0.664585 0.332293 0.943176i $$-0.392178\pi$$
0.332293 + 0.943176i $$0.392178\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −16016.7 −0.606299 −0.303149 0.952943i $$-0.598038\pi$$
−0.303149 + 0.952943i $$0.598038\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 27850.8 1.04366
$$894$$ 0 0
$$895$$ 20134.5 0.751981
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −7214.22 −0.267639
$$900$$ 0 0
$$901$$ 4005.69 0.148112
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 26937.5 0.989428
$$906$$ 0 0
$$907$$ −10131.0 −0.370887 −0.185443 0.982655i $$-0.559372\pi$$
−0.185443 + 0.982655i $$0.559372\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −1320.58 −0.0480273 −0.0240137 0.999712i $$-0.507645\pi$$
−0.0240137 + 0.999712i $$0.507645\pi$$
$$912$$ 0 0
$$913$$ −34292.5 −1.24306
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −7285.76 −0.261518 −0.130759 0.991414i $$-0.541741\pi$$
−0.130759 + 0.991414i $$0.541741\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −29081.3 −1.03708
$$924$$ 0 0
$$925$$ −19368.0 −0.688448
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 23708.0 0.837280 0.418640 0.908152i $$-0.362507\pi$$
0.418640 + 0.908152i $$0.362507\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −3069.79 −0.107372
$$936$$ 0 0
$$937$$ 8853.60 0.308682 0.154341 0.988018i $$-0.450675\pi$$
0.154341 + 0.988018i $$0.450675\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −53971.6 −1.86974 −0.934869 0.354994i $$-0.884483\pi$$
−0.934869 + 0.354994i $$0.884483\pi$$
$$942$$ 0 0
$$943$$ −8508.57 −0.293825
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −8019.80 −0.275194 −0.137597 0.990488i $$-0.543938\pi$$
−0.137597 + 0.990488i $$0.543938\pi$$
$$948$$ 0 0
$$949$$ −32015.4 −1.09511
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −42628.0 −1.44896 −0.724479 0.689297i $$-0.757920\pi$$
−0.724479 + 0.689297i $$0.757920\pi$$
$$954$$ 0 0
$$955$$ 38638.9 1.30924
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −21325.0 −0.715820
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 37196.8 1.24084
$$966$$ 0 0
$$967$$ −43161.7 −1.43535 −0.717676 0.696377i $$-0.754794\pi$$
−0.717676 + 0.696377i $$0.754794\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −39775.4 −1.31458 −0.657288 0.753640i $$-0.728296\pi$$
−0.657288 + 0.753640i $$0.728296\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 26658.1 0.872945 0.436472 0.899718i $$-0.356228\pi$$
0.436472 + 0.899718i $$0.356228\pi$$
$$978$$ 0 0
$$979$$ −42102.6 −1.37447
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −2942.43 −0.0954719 −0.0477359 0.998860i $$-0.515201\pi$$
−0.0477359 + 0.998860i $$0.515201\pi$$
$$984$$ 0 0
$$985$$ 25399.2 0.821610
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 13750.6 0.442108
$$990$$ 0 0
$$991$$ 44969.8 1.44149 0.720743 0.693203i $$-0.243801\pi$$
0.720743 + 0.693203i $$0.243801\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 3623.23 0.115441
$$996$$ 0 0
$$997$$ −27116.4 −0.861370 −0.430685 0.902502i $$-0.641728\pi$$
−0.430685 + 0.902502i $$0.641728\pi$$
$$998$$ 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.bc.1.3 4
3.2 odd 2 588.4.a.j.1.2 4
7.2 even 3 1764.4.k.bb.361.2 8
7.3 odd 6 1764.4.k.bd.1549.3 8
7.4 even 3 1764.4.k.bb.1549.2 8
7.5 odd 6 1764.4.k.bd.361.3 8
7.6 odd 2 1764.4.a.ba.1.2 4
12.11 even 2 2352.4.a.cq.1.2 4
21.2 odd 6 588.4.i.l.361.3 8
21.5 even 6 588.4.i.k.361.2 8
21.11 odd 6 588.4.i.l.373.3 8
21.17 even 6 588.4.i.k.373.2 8
21.20 even 2 588.4.a.k.1.3 yes 4
84.83 odd 2 2352.4.a.cl.1.3 4

By twisted newform
Twist Min Dim Char Parity Ord Type
588.4.a.j.1.2 4 3.2 odd 2
588.4.a.k.1.3 yes 4 21.20 even 2
588.4.i.k.361.2 8 21.5 even 6
588.4.i.k.373.2 8 21.17 even 6
588.4.i.l.361.3 8 21.2 odd 6
588.4.i.l.373.3 8 21.11 odd 6
1764.4.a.ba.1.2 4 7.6 odd 2
1764.4.a.bc.1.3 4 1.1 even 1 trivial
1764.4.k.bb.361.2 8 7.2 even 3
1764.4.k.bb.1549.2 8 7.4 even 3
1764.4.k.bd.361.3 8 7.5 odd 6
1764.4.k.bd.1549.3 8 7.3 odd 6
2352.4.a.cl.1.3 4 84.83 odd 2
2352.4.a.cq.1.2 4 12.11 even 2