# Properties

 Label 8280.2.a.bq.1.2 Level $8280$ Weight $2$ Character 8280.1 Self dual yes Analytic conductor $66.116$ Analytic rank $1$ Dimension $4$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 8280.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$66.1161328736$$ Analytic rank: $$1$$ Dimension: $$4$$ Coefficient field: 4.4.54764.1 Defining polynomial: $$x^{4} - x^{3} - 9x^{2} + 3x + 2$$ x^4 - x^3 - 9*x^2 + 3*x + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 2760) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$-0.339102$$ of defining polynomial Character $$\chi$$ $$=$$ 8280.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{5} -0.845563 q^{7} +O(q^{10})$$ $$q+1.00000 q^{5} -0.845563 q^{7} +4.55883 q^{11} +5.23704 q^{13} -4.72619 q^{17} -5.54591 q^{19} -1.00000 q^{23} +1.00000 q^{25} -7.06968 q^{29} -1.83264 q^{31} -0.845563 q^{35} -9.93738 q^{37} -5.71327 q^{41} +4.78294 q^{43} -5.54591 q^{47} -6.28502 q^{49} +14.4962 q^{53} +4.55883 q^{55} -5.06968 q^{59} -6.22411 q^{61} +5.23704 q^{65} -7.85849 q^{67} -3.71327 q^{71} +1.23704 q^{73} -3.85478 q^{77} -13.7700 q^{79} -7.50913 q^{83} -4.72619 q^{85} -2.98708 q^{89} -4.42825 q^{91} -5.54591 q^{95} -2.33472 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{5}+O(q^{10})$$ 4 * q + 4 * q^5 $$4 q + 4 q^{5} - 2 q^{13} - 2 q^{17} - 6 q^{19} - 4 q^{23} + 4 q^{25} - 4 q^{29} - 6 q^{31} - 4 q^{37} - 8 q^{41} - 20 q^{43} - 6 q^{47} + 10 q^{49} + 4 q^{53} + 4 q^{59} - 4 q^{61} - 2 q^{65} - 26 q^{67} - 18 q^{73} - 6 q^{77} - 18 q^{79} + 26 q^{83} - 2 q^{85} - 14 q^{89} - 38 q^{91} - 6 q^{95} - 12 q^{97}+O(q^{100})$$ 4 * q + 4 * q^5 - 2 * q^13 - 2 * q^17 - 6 * q^19 - 4 * q^23 + 4 * q^25 - 4 * q^29 - 6 * q^31 - 4 * q^37 - 8 * q^41 - 20 * q^43 - 6 * q^47 + 10 * q^49 + 4 * q^53 + 4 * q^59 - 4 * q^61 - 2 * q^65 - 26 * q^67 - 18 * q^73 - 6 * q^77 - 18 * q^79 + 26 * q^83 - 2 * q^85 - 14 * q^89 - 38 * q^91 - 6 * q^95 - 12 * q^97

## 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
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ −0.845563 −0.319593 −0.159796 0.987150i $$-0.551084\pi$$
−0.159796 + 0.987150i $$0.551084\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 4.55883 1.37454 0.687270 0.726402i $$-0.258809\pi$$
0.687270 + 0.726402i $$0.258809\pi$$
$$12$$ 0 0
$$13$$ 5.23704 1.45249 0.726246 0.687435i $$-0.241263\pi$$
0.726246 + 0.687435i $$0.241263\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −4.72619 −1.14627 −0.573135 0.819461i $$-0.694273\pi$$
−0.573135 + 0.819461i $$0.694273\pi$$
$$18$$ 0 0
$$19$$ −5.54591 −1.27232 −0.636159 0.771558i $$-0.719478\pi$$
−0.636159 + 0.771558i $$0.719478\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −7.06968 −1.31281 −0.656403 0.754411i $$-0.727923\pi$$
−0.656403 + 0.754411i $$0.727923\pi$$
$$30$$ 0 0
$$31$$ −1.83264 −0.329152 −0.164576 0.986364i $$-0.552626\pi$$
−0.164576 + 0.986364i $$0.552626\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −0.845563 −0.142926
$$36$$ 0 0
$$37$$ −9.93738 −1.63370 −0.816848 0.576854i $$-0.804280\pi$$
−0.816848 + 0.576854i $$0.804280\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −5.71327 −0.892263 −0.446131 0.894968i $$-0.647199\pi$$
−0.446131 + 0.894968i $$0.647199\pi$$
$$42$$ 0 0
$$43$$ 4.78294 0.729392 0.364696 0.931127i $$-0.381173\pi$$
0.364696 + 0.931127i $$0.381173\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −5.54591 −0.808954 −0.404477 0.914548i $$-0.632546\pi$$
−0.404477 + 0.914548i $$0.632546\pi$$
$$48$$ 0 0
$$49$$ −6.28502 −0.897860
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 14.4962 1.99121 0.995604 0.0936641i $$-0.0298580\pi$$
0.995604 + 0.0936641i $$0.0298580\pi$$
$$54$$ 0 0
$$55$$ 4.55883 0.614713
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −5.06968 −0.660015 −0.330008 0.943978i $$-0.607051\pi$$
−0.330008 + 0.943978i $$0.607051\pi$$
$$60$$ 0 0
$$61$$ −6.22411 −0.796916 −0.398458 0.917187i $$-0.630455\pi$$
−0.398458 + 0.917187i $$0.630455\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 5.23704 0.649574
$$66$$ 0 0
$$67$$ −7.85849 −0.960067 −0.480033 0.877250i $$-0.659375\pi$$
−0.480033 + 0.877250i $$0.659375\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −3.71327 −0.440684 −0.220342 0.975423i $$-0.570717\pi$$
−0.220342 + 0.975423i $$0.570717\pi$$
$$72$$ 0 0
$$73$$ 1.23704 0.144784 0.0723920 0.997376i $$-0.476937\pi$$
0.0723920 + 0.997376i $$0.476937\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −3.85478 −0.439293
$$78$$ 0 0
$$79$$ −13.7700 −1.54925 −0.774624 0.632422i $$-0.782061\pi$$
−0.774624 + 0.632422i $$0.782061\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −7.50913 −0.824235 −0.412117 0.911131i $$-0.635211\pi$$
−0.412117 + 0.911131i $$0.635211\pi$$
$$84$$ 0 0
$$85$$ −4.72619 −0.512627
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −2.98708 −0.316630 −0.158315 0.987389i $$-0.550606\pi$$
−0.158315 + 0.987389i $$0.550606\pi$$
$$90$$ 0 0
$$91$$ −4.42825 −0.464206
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −5.54591 −0.568998
$$96$$ 0 0
$$97$$ −2.33472 −0.237055 −0.118527 0.992951i $$-0.537817\pi$$
−0.118527 + 0.992951i $$0.537817\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 12.1873 1.21269 0.606343 0.795203i $$-0.292636\pi$$
0.606343 + 0.795203i $$0.292636\pi$$
$$102$$ 0 0
$$103$$ −18.1047 −1.78391 −0.891956 0.452121i $$-0.850667\pi$$
−0.891956 + 0.452121i $$0.850667\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 6.39147 0.617887 0.308943 0.951080i $$-0.400025\pi$$
0.308943 + 0.951080i $$0.400025\pi$$
$$108$$ 0 0
$$109$$ 6.55883 0.628222 0.314111 0.949386i $$-0.398294\pi$$
0.314111 + 0.949386i $$0.398294\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 14.0826 1.32478 0.662390 0.749159i $$-0.269542\pi$$
0.662390 + 0.749159i $$0.269542\pi$$
$$114$$ 0 0
$$115$$ −1.00000 −0.0932505
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 3.99629 0.366340
$$120$$ 0 0
$$121$$ 9.78294 0.889358
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −13.2629 −1.17689 −0.588445 0.808537i $$-0.700260\pi$$
−0.588445 + 0.808537i $$0.700260\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 7.38225 0.644991 0.322495 0.946571i $$-0.395478\pi$$
0.322495 + 0.946571i $$0.395478\pi$$
$$132$$ 0 0
$$133$$ 4.68942 0.406624
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −10.1306 −0.865514 −0.432757 0.901511i $$-0.642459\pi$$
−0.432757 + 0.901511i $$0.642459\pi$$
$$138$$ 0 0
$$139$$ 11.7332 0.995201 0.497600 0.867406i $$-0.334215\pi$$
0.497600 + 0.867406i $$0.334215\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 23.8748 1.99651
$$144$$ 0 0
$$145$$ −7.06968 −0.587105
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 10.5934 0.867849 0.433924 0.900949i $$-0.357129\pi$$
0.433924 + 0.900949i $$0.357129\pi$$
$$150$$ 0 0
$$151$$ 8.16520 0.664474 0.332237 0.943196i $$-0.392197\pi$$
0.332237 + 0.943196i $$0.392197\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1.83264 −0.147201
$$156$$ 0 0
$$157$$ −10.6068 −0.846516 −0.423258 0.906009i $$-0.639114\pi$$
−0.423258 + 0.906009i $$0.639114\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0.845563 0.0666397
$$162$$ 0 0
$$163$$ −15.6653 −1.22700 −0.613500 0.789695i $$-0.710239\pi$$
−0.613500 + 0.789695i $$0.710239\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.16365 0.167429 0.0837143 0.996490i $$-0.473322\pi$$
0.0837143 + 0.996490i $$0.473322\pi$$
$$168$$ 0 0
$$169$$ 14.4265 1.10973
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 8.30887 0.631712 0.315856 0.948807i $$-0.397708\pi$$
0.315856 + 0.948807i $$0.397708\pi$$
$$174$$ 0 0
$$175$$ −0.845563 −0.0639186
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 10.7571 0.804023 0.402012 0.915635i $$-0.368311\pi$$
0.402012 + 0.915635i $$0.368311\pi$$
$$180$$ 0 0
$$181$$ 19.2482 1.43071 0.715356 0.698761i $$-0.246265\pi$$
0.715356 + 0.698761i $$0.246265\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −9.93738 −0.730611
$$186$$ 0 0
$$187$$ −21.5459 −1.57559
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.78465 −0.129133 −0.0645665 0.997913i $$-0.520566\pi$$
−0.0645665 + 0.997913i $$0.520566\pi$$
$$192$$ 0 0
$$193$$ −11.4524 −0.824361 −0.412180 0.911102i $$-0.635233\pi$$
−0.412180 + 0.911102i $$0.635233\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2.23874 −0.159504 −0.0797520 0.996815i $$-0.525413\pi$$
−0.0797520 + 0.996815i $$0.525413\pi$$
$$198$$ 0 0
$$199$$ 18.5530 1.31518 0.657592 0.753374i $$-0.271575\pi$$
0.657592 + 0.753374i $$0.271575\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 5.97786 0.419563
$$204$$ 0 0
$$205$$ −5.71327 −0.399032
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −25.2829 −1.74885
$$210$$ 0 0
$$211$$ −25.0204 −1.72248 −0.861239 0.508201i $$-0.830311\pi$$
−0.861239 + 0.508201i $$0.830311\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 4.78294 0.326194
$$216$$ 0 0
$$217$$ 1.54961 0.105195
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −24.7512 −1.66495
$$222$$ 0 0
$$223$$ −7.71697 −0.516767 −0.258383 0.966042i $$-0.583190\pi$$
−0.258383 + 0.966042i $$0.583190\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 14.4395 0.958381 0.479190 0.877711i $$-0.340930\pi$$
0.479190 + 0.877711i $$0.340930\pi$$
$$228$$ 0 0
$$229$$ 15.8660 1.04845 0.524227 0.851578i $$-0.324354\pi$$
0.524227 + 0.851578i $$0.324354\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 8.36057 0.547719 0.273859 0.961770i $$-0.411700\pi$$
0.273859 + 0.961770i $$0.411700\pi$$
$$234$$ 0 0
$$235$$ −5.54591 −0.361775
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −11.6173 −0.751460 −0.375730 0.926729i $$-0.622608\pi$$
−0.375730 + 0.926729i $$0.622608\pi$$
$$240$$ 0 0
$$241$$ −25.0675 −1.61474 −0.807370 0.590045i $$-0.799110\pi$$
−0.807370 + 0.590045i $$0.799110\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −6.28502 −0.401535
$$246$$ 0 0
$$247$$ −29.0441 −1.84803
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 13.4870 0.851291 0.425646 0.904890i $$-0.360047\pi$$
0.425646 + 0.904890i $$0.360047\pi$$
$$252$$ 0 0
$$253$$ −4.55883 −0.286611
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1.85478 0.115698 0.0578490 0.998325i $$-0.481576\pi$$
0.0578490 + 0.998325i $$0.481576\pi$$
$$258$$ 0 0
$$259$$ 8.40269 0.522117
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −16.2132 −0.999748 −0.499874 0.866098i $$-0.666620\pi$$
−0.499874 + 0.866098i $$0.666620\pi$$
$$264$$ 0 0
$$265$$ 14.4962 0.890495
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 8.80508 0.536855 0.268428 0.963300i $$-0.413496\pi$$
0.268428 + 0.963300i $$0.413496\pi$$
$$270$$ 0 0
$$271$$ 3.23333 0.196411 0.0982054 0.995166i $$-0.468690\pi$$
0.0982054 + 0.995166i $$0.468690\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 4.55883 0.274908
$$276$$ 0 0
$$277$$ 2.61775 0.157285 0.0786426 0.996903i $$-0.474941\pi$$
0.0786426 + 0.996903i $$0.474941\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 14.6031 0.871149 0.435574 0.900153i $$-0.356545\pi$$
0.435574 + 0.900153i $$0.356545\pi$$
$$282$$ 0 0
$$283$$ −22.7808 −1.35418 −0.677088 0.735902i $$-0.736759\pi$$
−0.677088 + 0.735902i $$0.736759\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 4.83093 0.285161
$$288$$ 0 0
$$289$$ 5.33688 0.313934
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 25.5880 1.49487 0.747434 0.664336i $$-0.231285\pi$$
0.747434 + 0.664336i $$0.231285\pi$$
$$294$$ 0 0
$$295$$ −5.06968 −0.295168
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −5.23704 −0.302866
$$300$$ 0 0
$$301$$ −4.04428 −0.233109
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −6.22411 −0.356392
$$306$$ 0 0
$$307$$ 12.4507 0.710597 0.355299 0.934753i $$-0.384379\pi$$
0.355299 + 0.934753i $$0.384379\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −10.9048 −0.618352 −0.309176 0.951005i $$-0.600053\pi$$
−0.309176 + 0.951005i $$0.600053\pi$$
$$312$$ 0 0
$$313$$ −30.7549 −1.73837 −0.869186 0.494486i $$-0.835356\pi$$
−0.869186 + 0.494486i $$0.835356\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −24.9983 −1.40404 −0.702022 0.712155i $$-0.747719\pi$$
−0.702022 + 0.712155i $$0.747719\pi$$
$$318$$ 0 0
$$319$$ −32.2295 −1.80450
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 26.2110 1.45842
$$324$$ 0 0
$$325$$ 5.23704 0.290498
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 4.68942 0.258536
$$330$$ 0 0
$$331$$ −9.59390 −0.527328 −0.263664 0.964615i $$-0.584931\pi$$
−0.263664 + 0.964615i $$0.584931\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −7.85849 −0.429355
$$336$$ 0 0
$$337$$ 3.97415 0.216486 0.108243 0.994124i $$-0.465478\pi$$
0.108243 + 0.994124i $$0.465478\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −8.35470 −0.452432
$$342$$ 0 0
$$343$$ 11.2333 0.606543
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −13.1177 −0.704193 −0.352097 0.935964i $$-0.614531\pi$$
−0.352097 + 0.935964i $$0.614531\pi$$
$$348$$ 0 0
$$349$$ 9.80679 0.524946 0.262473 0.964939i $$-0.415462\pi$$
0.262473 + 0.964939i $$0.415462\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 8.55007 0.455074 0.227537 0.973769i $$-0.426933\pi$$
0.227537 + 0.973769i $$0.426933\pi$$
$$354$$ 0 0
$$355$$ −3.71327 −0.197080
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −28.3990 −1.49884 −0.749420 0.662094i $$-0.769668\pi$$
−0.749420 + 0.662094i $$0.769668\pi$$
$$360$$ 0 0
$$361$$ 11.7571 0.618795
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1.23704 0.0647494
$$366$$ 0 0
$$367$$ 24.3121 1.26908 0.634539 0.772890i $$-0.281190\pi$$
0.634539 + 0.772890i $$0.281190\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −12.2575 −0.636376
$$372$$ 0 0
$$373$$ −20.3435 −1.05335 −0.526673 0.850068i $$-0.676561\pi$$
−0.526673 + 0.850068i $$0.676561\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −37.0241 −1.90684
$$378$$ 0 0
$$379$$ 7.33056 0.376546 0.188273 0.982117i $$-0.439711\pi$$
0.188273 + 0.982117i $$0.439711\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −28.2575 −1.44389 −0.721945 0.691951i $$-0.756751\pi$$
−0.721945 + 0.691951i $$0.756751\pi$$
$$384$$ 0 0
$$385$$ −3.85478 −0.196458
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −23.9966 −1.21667 −0.608337 0.793678i $$-0.708163\pi$$
−0.608337 + 0.793678i $$0.708163\pi$$
$$390$$ 0 0
$$391$$ 4.72619 0.239014
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −13.7700 −0.692845
$$396$$ 0 0
$$397$$ −3.02169 −0.151654 −0.0758271 0.997121i $$-0.524160\pi$$
−0.0758271 + 0.997121i $$0.524160\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 29.6263 1.47947 0.739735 0.672899i $$-0.234951\pi$$
0.739735 + 0.672899i $$0.234951\pi$$
$$402$$ 0 0
$$403$$ −9.59760 −0.478091
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −45.3028 −2.24558
$$408$$ 0 0
$$409$$ −7.42437 −0.367112 −0.183556 0.983009i $$-0.558761\pi$$
−0.183556 + 0.983009i $$0.558761\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 4.28673 0.210936
$$414$$ 0 0
$$415$$ −7.50913 −0.368609
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 2.20568 0.107754 0.0538772 0.998548i $$-0.482842\pi$$
0.0538772 + 0.998548i $$0.482842\pi$$
$$420$$ 0 0
$$421$$ 34.0989 1.66188 0.830939 0.556364i $$-0.187804\pi$$
0.830939 + 0.556364i $$0.187804\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −4.72619 −0.229254
$$426$$ 0 0
$$427$$ 5.26288 0.254689
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −4.16952 −0.200839 −0.100419 0.994945i $$-0.532018\pi$$
−0.100419 + 0.994945i $$0.532018\pi$$
$$432$$ 0 0
$$433$$ 7.08965 0.340707 0.170353 0.985383i $$-0.445509\pi$$
0.170353 + 0.985383i $$0.445509\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 5.54591 0.265297
$$438$$ 0 0
$$439$$ −36.7537 −1.75416 −0.877079 0.480347i $$-0.840511\pi$$
−0.877079 + 0.480347i $$0.840511\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −23.3505 −1.10942 −0.554709 0.832045i $$-0.687170\pi$$
−0.554709 + 0.832045i $$0.687170\pi$$
$$444$$ 0 0
$$445$$ −2.98708 −0.141601
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −30.0437 −1.41785 −0.708924 0.705285i $$-0.750819\pi$$
−0.708924 + 0.705285i $$0.750819\pi$$
$$450$$ 0 0
$$451$$ −26.0458 −1.22645
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −4.42825 −0.207599
$$456$$ 0 0
$$457$$ 19.5496 0.914492 0.457246 0.889340i $$-0.348836\pi$$
0.457246 + 0.889340i $$0.348836\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 22.6577 1.05527 0.527637 0.849470i $$-0.323078\pi$$
0.527637 + 0.849470i $$0.323078\pi$$
$$462$$ 0 0
$$463$$ −21.7037 −1.00866 −0.504328 0.863512i $$-0.668260\pi$$
−0.504328 + 0.863512i $$0.668260\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −25.2003 −1.16613 −0.583065 0.812426i $$-0.698147\pi$$
−0.583065 + 0.812426i $$0.698147\pi$$
$$468$$ 0 0
$$469$$ 6.64485 0.306831
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 21.8046 1.00258
$$474$$ 0 0
$$475$$ −5.54591 −0.254464
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 19.1635 0.875602 0.437801 0.899072i $$-0.355757\pi$$
0.437801 + 0.899072i $$0.355757\pi$$
$$480$$ 0 0
$$481$$ −52.0424 −2.37293
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −2.33472 −0.106014
$$486$$ 0 0
$$487$$ 14.3805 0.651645 0.325822 0.945431i $$-0.394359\pi$$
0.325822 + 0.945431i $$0.394359\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 16.3267 0.736813 0.368407 0.929665i $$-0.379903\pi$$
0.368407 + 0.929665i $$0.379903\pi$$
$$492$$ 0 0
$$493$$ 33.4126 1.50483
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 3.13980 0.140839
$$498$$ 0 0
$$499$$ 29.8726 1.33728 0.668641 0.743586i $$-0.266877\pi$$
0.668641 + 0.743586i $$0.266877\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −33.6831 −1.50186 −0.750928 0.660385i $$-0.770393\pi$$
−0.750928 + 0.660385i $$0.770393\pi$$
$$504$$ 0 0
$$505$$ 12.1873 0.542329
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 29.9265 1.32647 0.663233 0.748413i $$-0.269184\pi$$
0.663233 + 0.748413i $$0.269184\pi$$
$$510$$ 0 0
$$511$$ −1.04599 −0.0462719
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −18.1047 −0.797790
$$516$$ 0 0
$$517$$ −25.2829 −1.11194
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 8.19827 0.359173 0.179586 0.983742i $$-0.442524\pi$$
0.179586 + 0.983742i $$0.442524\pi$$
$$522$$ 0 0
$$523$$ −8.15779 −0.356715 −0.178358 0.983966i $$-0.557078\pi$$
−0.178358 + 0.983966i $$0.557078\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 8.66141 0.377297
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −29.9206 −1.29600
$$534$$ 0 0
$$535$$ 6.39147 0.276327
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −28.6524 −1.23414
$$540$$ 0 0
$$541$$ −43.4406 −1.86766 −0.933830 0.357718i $$-0.883555\pi$$
−0.933830 + 0.357718i $$0.883555\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 6.55883 0.280949
$$546$$ 0 0
$$547$$ −37.5659 −1.60620 −0.803101 0.595843i $$-0.796818\pi$$
−0.803101 + 0.595843i $$0.796818\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 39.2078 1.67031
$$552$$ 0 0
$$553$$ 11.6434 0.495129
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −13.0438 −0.552685 −0.276342 0.961059i $$-0.589122\pi$$
−0.276342 + 0.961059i $$0.589122\pi$$
$$558$$ 0 0
$$559$$ 25.0484 1.05944
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 4.25212 0.179206 0.0896028 0.995978i $$-0.471440\pi$$
0.0896028 + 0.995978i $$0.471440\pi$$
$$564$$ 0 0
$$565$$ 14.0826 0.592459
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −45.8358 −1.92154 −0.960769 0.277350i $$-0.910544\pi$$
−0.960769 + 0.277350i $$0.910544\pi$$
$$570$$ 0 0
$$571$$ 22.7595 0.952457 0.476229 0.879321i $$-0.342003\pi$$
0.476229 + 0.879321i $$0.342003\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ 40.2310 1.67484 0.837419 0.546561i $$-0.184063\pi$$
0.837419 + 0.546561i $$0.184063\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 6.34945 0.263420
$$582$$ 0 0
$$583$$ 66.0858 2.73699
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 42.7278 1.76357 0.881783 0.471655i $$-0.156343\pi$$
0.881783 + 0.471655i $$0.156343\pi$$
$$588$$ 0 0
$$589$$ 10.1637 0.418786
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −22.1852 −0.911036 −0.455518 0.890227i $$-0.650546\pi$$
−0.455518 + 0.890227i $$0.650546\pi$$
$$594$$ 0 0
$$595$$ 3.99629 0.163832
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 9.85632 0.402718 0.201359 0.979517i $$-0.435464\pi$$
0.201359 + 0.979517i $$0.435464\pi$$
$$600$$ 0 0
$$601$$ 12.1157 0.494208 0.247104 0.968989i $$-0.420521\pi$$
0.247104 + 0.968989i $$0.420521\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 9.78294 0.397733
$$606$$ 0 0
$$607$$ 14.4984 0.588471 0.294235 0.955733i $$-0.404935\pi$$
0.294235 + 0.955733i $$0.404935\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −29.0441 −1.17500
$$612$$ 0 0
$$613$$ −36.0312 −1.45529 −0.727643 0.685956i $$-0.759384\pi$$
−0.727643 + 0.685956i $$0.759384\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 44.0792 1.77456 0.887280 0.461230i $$-0.152592\pi$$
0.887280 + 0.461230i $$0.152592\pi$$
$$618$$ 0 0
$$619$$ 32.9998 1.32638 0.663188 0.748453i $$-0.269203\pi$$
0.663188 + 0.748453i $$0.269203\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 2.52576 0.101193
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 46.9660 1.87266
$$630$$ 0 0
$$631$$ −12.8200 −0.510356 −0.255178 0.966894i $$-0.582134\pi$$
−0.255178 + 0.966894i $$0.582134\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −13.2629 −0.526321
$$636$$ 0 0
$$637$$ −32.9149 −1.30414
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −38.8126 −1.53301 −0.766503 0.642241i $$-0.778005\pi$$
−0.766503 + 0.642241i $$0.778005\pi$$
$$642$$ 0 0
$$643$$ −33.1339 −1.30667 −0.653337 0.757067i $$-0.726632\pi$$
−0.653337 + 0.757067i $$0.726632\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −24.3547 −0.957482 −0.478741 0.877956i $$-0.658907\pi$$
−0.478741 + 0.877956i $$0.658907\pi$$
$$648$$ 0 0
$$649$$ −23.1118 −0.907217
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −12.5943 −0.492855 −0.246427 0.969161i $$-0.579257\pi$$
−0.246427 + 0.969161i $$0.579257\pi$$
$$654$$ 0 0
$$655$$ 7.38225 0.288449
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 41.9259 1.63320 0.816601 0.577202i $$-0.195856\pi$$
0.816601 + 0.577202i $$0.195856\pi$$
$$660$$ 0 0
$$661$$ 45.1664 1.75677 0.878384 0.477955i $$-0.158622\pi$$
0.878384 + 0.477955i $$0.158622\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 4.68942 0.181848
$$666$$ 0 0
$$667$$ 7.06968 0.273739
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −28.3747 −1.09539
$$672$$ 0 0
$$673$$ −13.4022 −0.516618 −0.258309 0.966062i $$-0.583165\pi$$
−0.258309 + 0.966062i $$0.583165\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 41.5662 1.59752 0.798759 0.601651i $$-0.205490\pi$$
0.798759 + 0.601651i $$0.205490\pi$$
$$678$$ 0 0
$$679$$ 1.97415 0.0757611
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 24.1778 0.925136 0.462568 0.886584i $$-0.346928\pi$$
0.462568 + 0.886584i $$0.346928\pi$$
$$684$$ 0 0
$$685$$ −10.1306 −0.387070
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 75.9172 2.89221
$$690$$ 0 0
$$691$$ 4.99242 0.189921 0.0949603 0.995481i $$-0.469728\pi$$
0.0949603 + 0.995481i $$0.469728\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 11.7332 0.445067
$$696$$ 0 0
$$697$$ 27.0020 1.02277
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −28.0384 −1.05900 −0.529498 0.848311i $$-0.677620\pi$$
−0.529498 + 0.848311i $$0.677620\pi$$
$$702$$ 0 0
$$703$$ 55.1118 2.07858
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −10.3052 −0.387566
$$708$$ 0 0
$$709$$ 40.9594 1.53826 0.769130 0.639092i $$-0.220690\pi$$
0.769130 + 0.639092i $$0.220690\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.83264 0.0686329
$$714$$ 0 0
$$715$$ 23.8748 0.892865
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −26.8568 −1.00159 −0.500794 0.865566i $$-0.666959\pi$$
−0.500794 + 0.865566i $$0.666959\pi$$
$$720$$ 0 0
$$721$$ 15.3087 0.570126
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −7.06968 −0.262561
$$726$$ 0 0
$$727$$ −34.9849 −1.29752 −0.648759 0.760994i $$-0.724712\pi$$
−0.648759 + 0.760994i $$0.724712\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −22.6051 −0.836080
$$732$$ 0 0
$$733$$ 28.2170 1.04222 0.521109 0.853490i $$-0.325518\pi$$
0.521109 + 0.853490i $$0.325518\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −35.8255 −1.31965
$$738$$ 0 0
$$739$$ 30.8251 1.13392 0.566959 0.823746i $$-0.308120\pi$$
0.566959 + 0.823746i $$0.308120\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −53.2093 −1.95206 −0.976030 0.217635i $$-0.930166\pi$$
−0.976030 + 0.217635i $$0.930166\pi$$
$$744$$ 0 0
$$745$$ 10.5934 0.388114
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −5.40439 −0.197472
$$750$$ 0 0
$$751$$ 25.0513 0.914136 0.457068 0.889432i $$-0.348900\pi$$
0.457068 + 0.889432i $$0.348900\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 8.16520 0.297162
$$756$$ 0 0
$$757$$ 2.72032 0.0988718 0.0494359 0.998777i $$-0.484258\pi$$
0.0494359 + 0.998777i $$0.484258\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 11.9779 0.434197 0.217099 0.976150i $$-0.430341\pi$$
0.217099 + 0.976150i $$0.430341\pi$$
$$762$$ 0 0
$$763$$ −5.54591 −0.200775
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −26.5501 −0.958667
$$768$$ 0 0
$$769$$ 14.2412 0.513551 0.256775 0.966471i $$-0.417340\pi$$
0.256775 + 0.966471i $$0.417340\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −15.0660 −0.541885 −0.270943 0.962595i $$-0.587335\pi$$
−0.270943 + 0.962595i $$0.587335\pi$$
$$774$$ 0 0
$$775$$ −1.83264 −0.0658304
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 31.6853 1.13524
$$780$$ 0 0
$$781$$ −16.9282 −0.605737
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −10.6068 −0.378574
$$786$$ 0 0
$$787$$ 4.79922 0.171074 0.0855368 0.996335i $$-0.472739\pi$$
0.0855368 + 0.996335i $$0.472739\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −11.9077 −0.423390
$$792$$ 0 0
$$793$$ −32.5959 −1.15751
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −51.6538 −1.82967 −0.914836 0.403825i $$-0.867680\pi$$
−0.914836 + 0.403825i $$0.867680\pi$$
$$798$$ 0 0
$$799$$ 26.2110 0.927279
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 5.63943 0.199011
$$804$$ 0 0
$$805$$ 0.845563 0.0298022
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 9.30500 0.327146 0.163573 0.986531i $$-0.447698\pi$$
0.163573 + 0.986531i $$0.447698\pi$$
$$810$$ 0 0
$$811$$ −39.2041 −1.37664 −0.688320 0.725407i $$-0.741652\pi$$
−0.688320 + 0.725407i $$0.741652\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −15.6653 −0.548731
$$816$$ 0 0
$$817$$ −26.5258 −0.928019
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 9.23948 0.322460 0.161230 0.986917i $$-0.448454\pi$$
0.161230 + 0.986917i $$0.448454\pi$$
$$822$$ 0 0
$$823$$ −26.3931 −0.920006 −0.460003 0.887917i $$-0.652152\pi$$
−0.460003 + 0.887917i $$0.652152\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 16.7520 0.582525 0.291263 0.956643i $$-0.405925\pi$$
0.291263 + 0.956643i $$0.405925\pi$$
$$828$$ 0 0
$$829$$ −32.1381 −1.11620 −0.558101 0.829773i $$-0.688470\pi$$
−0.558101 + 0.829773i $$0.688470\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 29.7042 1.02919
$$834$$ 0 0
$$835$$ 2.16365 0.0748763
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −15.8748 −0.548058 −0.274029 0.961721i $$-0.588356\pi$$
−0.274029 + 0.961721i $$0.588356\pi$$
$$840$$ 0 0
$$841$$ 20.9803 0.723459
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 14.4265 0.496288
$$846$$ 0 0
$$847$$ −8.27210 −0.284233
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 9.93738 0.340649
$$852$$ 0 0
$$853$$ −27.4481 −0.939804 −0.469902 0.882719i $$-0.655711\pi$$
−0.469902 + 0.882719i $$0.655711\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 49.3929 1.68723 0.843615 0.536948i $$-0.180423\pi$$
0.843615 + 0.536948i $$0.180423\pi$$
$$858$$ 0 0
$$859$$ −18.5863 −0.634157 −0.317078 0.948399i $$-0.602702\pi$$
−0.317078 + 0.948399i $$0.602702\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 33.6619 1.14586 0.572932 0.819603i $$-0.305806\pi$$
0.572932 + 0.819603i $$0.305806\pi$$
$$864$$ 0 0
$$865$$ 8.30887 0.282510
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −62.7752 −2.12950
$$870$$ 0 0
$$871$$ −41.1552 −1.39449
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −0.845563 −0.0285853
$$876$$ 0 0
$$877$$ 29.2321 0.987097 0.493548 0.869718i $$-0.335700\pi$$
0.493548 + 0.869718i $$0.335700\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −1.20242 −0.0405107 −0.0202553 0.999795i $$-0.506448\pi$$
−0.0202553 + 0.999795i $$0.506448\pi$$
$$882$$ 0 0
$$883$$ −2.82877 −0.0951956 −0.0475978 0.998867i $$-0.515157\pi$$
−0.0475978 + 0.998867i $$0.515157\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 6.86048 0.230352 0.115176 0.993345i $$-0.463257\pi$$
0.115176 + 0.993345i $$0.463257\pi$$
$$888$$ 0 0
$$889$$ 11.2146 0.376126
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 30.7571 1.02925
$$894$$ 0 0
$$895$$ 10.7571 0.359570
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 12.9562 0.432113
$$900$$ 0 0
$$901$$ −68.5119 −2.28246
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 19.2482 0.639833
$$906$$ 0 0
$$907$$ −15.1198 −0.502046 −0.251023 0.967981i $$-0.580767\pi$$
−0.251023 + 0.967981i $$0.580767\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 50.3931 1.66960 0.834799 0.550555i $$-0.185584\pi$$
0.834799 + 0.550555i $$0.185584\pi$$
$$912$$ 0 0
$$913$$ −34.2329 −1.13294
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −6.24216 −0.206134
$$918$$ 0 0
$$919$$ −40.0053 −1.31965 −0.659827 0.751417i $$-0.729371\pi$$
−0.659827 + 0.751417i $$0.729371\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −19.4465 −0.640090
$$924$$ 0 0
$$925$$ −9.93738 −0.326739
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −39.0921 −1.28257 −0.641285 0.767303i $$-0.721598\pi$$
−0.641285 + 0.767303i $$0.721598\pi$$
$$930$$ 0 0
$$931$$ 34.8562 1.14236
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −21.5459 −0.704627
$$936$$ 0 0
$$937$$ 48.2310 1.57564 0.787819 0.615907i $$-0.211210\pi$$
0.787819 + 0.615907i $$0.211210\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −10.7337 −0.349909 −0.174954 0.984577i $$-0.555978\pi$$
−0.174954 + 0.984577i $$0.555978\pi$$
$$942$$ 0 0
$$943$$ 5.71327 0.186050
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 12.9257 0.420029 0.210015 0.977698i $$-0.432649\pi$$
0.210015 + 0.977698i $$0.432649\pi$$
$$948$$ 0 0
$$949$$ 6.47840 0.210298
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 53.4051 1.72996 0.864981 0.501805i $$-0.167330\pi$$
0.864981 + 0.501805i $$0.167330\pi$$
$$954$$ 0 0
$$955$$ −1.78465 −0.0577500
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 8.56605 0.276612
$$960$$ 0 0
$$961$$ −27.6414 −0.891659
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −11.4524 −0.368665
$$966$$ 0 0
$$967$$ −28.1852 −0.906374 −0.453187 0.891415i $$-0.649713\pi$$
−0.453187 + 0.891415i $$0.649713\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −33.1922 −1.06519 −0.532595 0.846370i $$-0.678783\pi$$
−0.532595 + 0.846370i $$0.678783\pi$$
$$972$$ 0 0
$$973$$ −9.92120 −0.318059
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −11.0750 −0.354321 −0.177161 0.984182i $$-0.556691\pi$$
−0.177161 + 0.984182i $$0.556691\pi$$
$$978$$ 0 0
$$979$$ −13.6176 −0.435220
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 11.8785 0.378864 0.189432 0.981894i $$-0.439335\pi$$
0.189432 + 0.981894i $$0.439335\pi$$
$$984$$ 0 0
$$985$$ −2.23874 −0.0713323
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −4.78294 −0.152089
$$990$$ 0 0
$$991$$ −33.8800 −1.07623 −0.538117 0.842870i $$-0.680864\pi$$
−0.538117 + 0.842870i $$0.680864\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 18.5530 0.588168
$$996$$ 0 0
$$997$$ −9.33797 −0.295737 −0.147868 0.989007i $$-0.547241\pi$$
−0.147868 + 0.989007i $$0.547241\pi$$
$$998$$ 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 8280.2.a.bq.1.2 4
3.2 odd 2 2760.2.a.v.1.2 4
12.11 even 2 5520.2.a.cb.1.3 4

By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.v.1.2 4 3.2 odd 2
5520.2.a.cb.1.3 4 12.11 even 2
8280.2.a.bq.1.2 4 1.1 even 1 trivial