# Properties

 Label 9408.2.a.c.1.1 Level $9408$ Weight $2$ Character 9408.1 Self dual yes Analytic conductor $75.123$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9408 = 2^{6} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9408.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$75.1232582216$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 672) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 9408.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} -4.00000 q^{5} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} -4.00000 q^{5} +1.00000 q^{9} -2.00000 q^{11} -2.00000 q^{13} +4.00000 q^{15} +4.00000 q^{19} +6.00000 q^{23} +11.0000 q^{25} -1.00000 q^{27} +10.0000 q^{29} -8.00000 q^{31} +2.00000 q^{33} -10.0000 q^{37} +2.00000 q^{39} +4.00000 q^{41} -8.00000 q^{43} -4.00000 q^{45} -4.00000 q^{47} -10.0000 q^{53} +8.00000 q^{55} -4.00000 q^{57} -8.00000 q^{59} -6.00000 q^{61} +8.00000 q^{65} +4.00000 q^{67} -6.00000 q^{69} -14.0000 q^{71} -6.00000 q^{73} -11.0000 q^{75} -4.00000 q^{79} +1.00000 q^{81} +12.0000 q^{83} -10.0000 q^{87} -4.00000 q^{89} +8.00000 q^{93} -16.0000 q^{95} +2.00000 q^{97} -2.00000 q^{99} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.00000 −0.577350
$$4$$ 0 0
$$5$$ −4.00000 −1.78885 −0.894427 0.447214i $$-0.852416\pi$$
−0.894427 + 0.447214i $$0.852416\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 4.00000 1.03280
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 4.00000 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
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ 0 0
$$25$$ 11.0000 2.20000
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 10.0000 1.85695 0.928477 0.371391i $$-0.121119\pi$$
0.928477 + 0.371391i $$0.121119\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 0 0
$$33$$ 2.00000 0.348155
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 0 0
$$39$$ 2.00000 0.320256
$$40$$ 0 0
$$41$$ 4.00000 0.624695 0.312348 0.949968i $$-0.398885\pi$$
0.312348 + 0.949968i $$0.398885\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ −4.00000 −0.596285
$$46$$ 0 0
$$47$$ −4.00000 −0.583460 −0.291730 0.956501i $$-0.594231\pi$$
−0.291730 + 0.956501i $$0.594231\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −10.0000 −1.37361 −0.686803 0.726844i $$-0.740986\pi$$
−0.686803 + 0.726844i $$0.740986\pi$$
$$54$$ 0 0
$$55$$ 8.00000 1.07872
$$56$$ 0 0
$$57$$ −4.00000 −0.529813
$$58$$ 0 0
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 0 0
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 8.00000 0.992278
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 0 0
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ −14.0000 −1.66149 −0.830747 0.556650i $$-0.812086\pi$$
−0.830747 + 0.556650i $$0.812086\pi$$
$$72$$ 0 0
$$73$$ −6.00000 −0.702247 −0.351123 0.936329i $$-0.614200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ 0 0
$$75$$ −11.0000 −1.27017
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −10.0000 −1.07211
$$88$$ 0 0
$$89$$ −4.00000 −0.423999 −0.212000 0.977270i $$-0.567998\pi$$
−0.212000 + 0.977270i $$0.567998\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 8.00000 0.829561
$$94$$ 0 0
$$95$$ −16.0000 −1.64157
$$96$$ 0 0
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −10.0000 −0.966736 −0.483368 0.875417i $$-0.660587\pi$$
−0.483368 + 0.875417i $$0.660587\pi$$
$$108$$ 0 0
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ −24.0000 −2.23801
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ −4.00000 −0.360668
$$124$$ 0 0
$$125$$ −24.0000 −2.14663
$$126$$ 0 0
$$127$$ 20.0000 1.77471 0.887357 0.461084i $$-0.152539\pi$$
0.887357 + 0.461084i $$0.152539\pi$$
$$128$$ 0 0
$$129$$ 8.00000 0.704361
$$130$$ 0 0
$$131$$ 20.0000 1.74741 0.873704 0.486458i $$-0.161711\pi$$
0.873704 + 0.486458i $$0.161711\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 4.00000 0.344265
$$136$$ 0 0
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ 4.00000 0.336861
$$142$$ 0 0
$$143$$ 4.00000 0.334497
$$144$$ 0 0
$$145$$ −40.0000 −3.32182
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 32.0000 2.57030
$$156$$ 0 0
$$157$$ −22.0000 −1.75579 −0.877896 0.478852i $$-0.841053\pi$$
−0.877896 + 0.478852i $$0.841053\pi$$
$$158$$ 0 0
$$159$$ 10.0000 0.793052
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ 0 0
$$165$$ −8.00000 −0.622799
$$166$$ 0 0
$$167$$ 20.0000 1.54765 0.773823 0.633402i $$-0.218342\pi$$
0.773823 + 0.633402i $$0.218342\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ 0 0
$$173$$ 24.0000 1.82469 0.912343 0.409426i $$-0.134271\pi$$
0.912343 + 0.409426i $$0.134271\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 8.00000 0.601317
$$178$$ 0 0
$$179$$ −6.00000 −0.448461 −0.224231 0.974536i $$-0.571987\pi$$
−0.224231 + 0.974536i $$0.571987\pi$$
$$180$$ 0 0
$$181$$ 14.0000 1.04061 0.520306 0.853980i $$-0.325818\pi$$
0.520306 + 0.853980i $$0.325818\pi$$
$$182$$ 0 0
$$183$$ 6.00000 0.443533
$$184$$ 0 0
$$185$$ 40.0000 2.94086
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −6.00000 −0.434145 −0.217072 0.976156i $$-0.569651\pi$$
−0.217072 + 0.976156i $$0.569651\pi$$
$$192$$ 0 0
$$193$$ 6.00000 0.431889 0.215945 0.976406i $$-0.430717\pi$$
0.215945 + 0.976406i $$0.430717\pi$$
$$194$$ 0 0
$$195$$ −8.00000 −0.572892
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −16.0000 −1.11749
$$206$$ 0 0
$$207$$ 6.00000 0.417029
$$208$$ 0 0
$$209$$ −8.00000 −0.553372
$$210$$ 0 0
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ 0 0
$$213$$ 14.0000 0.959264
$$214$$ 0 0
$$215$$ 32.0000 2.18238
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 6.00000 0.405442
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ 0 0
$$225$$ 11.0000 0.733333
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −18.0000 −1.17922 −0.589610 0.807688i $$-0.700718\pi$$
−0.589610 + 0.807688i $$0.700718\pi$$
$$234$$ 0 0
$$235$$ 16.0000 1.04372
$$236$$ 0 0
$$237$$ 4.00000 0.259828
$$238$$ 0 0
$$239$$ 6.00000 0.388108 0.194054 0.980991i $$-0.437836\pi$$
0.194054 + 0.980991i $$0.437836\pi$$
$$240$$ 0 0
$$241$$ 2.00000 0.128831 0.0644157 0.997923i $$-0.479482\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −8.00000 −0.509028
$$248$$ 0 0
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4.00000 0.249513 0.124757 0.992187i $$-0.460185\pi$$
0.124757 + 0.992187i $$0.460185\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 10.0000 0.618984
$$262$$ 0 0
$$263$$ 30.0000 1.84988 0.924940 0.380114i $$-0.124115\pi$$
0.924940 + 0.380114i $$0.124115\pi$$
$$264$$ 0 0
$$265$$ 40.0000 2.45718
$$266$$ 0 0
$$267$$ 4.00000 0.244796
$$268$$ 0 0
$$269$$ 12.0000 0.731653 0.365826 0.930683i $$-0.380786\pi$$
0.365826 + 0.930683i $$0.380786\pi$$
$$270$$ 0 0
$$271$$ −24.0000 −1.45790 −0.728948 0.684569i $$-0.759990\pi$$
−0.728948 + 0.684569i $$0.759990\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −22.0000 −1.32665
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 0 0
$$279$$ −8.00000 −0.478947
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 20.0000 1.18888 0.594438 0.804141i $$-0.297374\pi$$
0.594438 + 0.804141i $$0.297374\pi$$
$$284$$ 0 0
$$285$$ 16.0000 0.947758
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ −2.00000 −0.117242
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 32.0000 1.86311
$$296$$ 0 0
$$297$$ 2.00000 0.116052
$$298$$ 0 0
$$299$$ −12.0000 −0.693978
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 24.0000 1.37424
$$306$$ 0 0
$$307$$ 12.0000 0.684876 0.342438 0.939540i $$-0.388747\pi$$
0.342438 + 0.939540i $$0.388747\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ 14.0000 0.791327 0.395663 0.918396i $$-0.370515\pi$$
0.395663 + 0.918396i $$0.370515\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ −20.0000 −1.11979
$$320$$ 0 0
$$321$$ 10.0000 0.558146
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −22.0000 −1.22034
$$326$$ 0 0
$$327$$ 14.0000 0.774202
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −32.0000 −1.75888 −0.879440 0.476011i $$-0.842082\pi$$
−0.879440 + 0.476011i $$0.842082\pi$$
$$332$$ 0 0
$$333$$ −10.0000 −0.547997
$$334$$ 0 0
$$335$$ −16.0000 −0.874173
$$336$$ 0 0
$$337$$ −22.0000 −1.19842 −0.599208 0.800593i $$-0.704518\pi$$
−0.599208 + 0.800593i $$0.704518\pi$$
$$338$$ 0 0
$$339$$ −2.00000 −0.108625
$$340$$ 0 0
$$341$$ 16.0000 0.866449
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 24.0000 1.29212
$$346$$ 0 0
$$347$$ 2.00000 0.107366 0.0536828 0.998558i $$-0.482904\pi$$
0.0536828 + 0.998558i $$0.482904\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ 0 0
$$353$$ 8.00000 0.425797 0.212899 0.977074i $$-0.431710\pi$$
0.212899 + 0.977074i $$0.431710\pi$$
$$354$$ 0 0
$$355$$ 56.0000 2.97217
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −22.0000 −1.16112 −0.580558 0.814219i $$-0.697165\pi$$
−0.580558 + 0.814219i $$0.697165\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 24.0000 1.25622
$$366$$ 0 0
$$367$$ 24.0000 1.25279 0.626395 0.779506i $$-0.284530\pi$$
0.626395 + 0.779506i $$0.284530\pi$$
$$368$$ 0 0
$$369$$ 4.00000 0.208232
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −14.0000 −0.724893 −0.362446 0.932005i $$-0.618058\pi$$
−0.362446 + 0.932005i $$0.618058\pi$$
$$374$$ 0 0
$$375$$ 24.0000 1.23935
$$376$$ 0 0
$$377$$ −20.0000 −1.03005
$$378$$ 0 0
$$379$$ 32.0000 1.64373 0.821865 0.569683i $$-0.192934\pi$$
0.821865 + 0.569683i $$0.192934\pi$$
$$380$$ 0 0
$$381$$ −20.0000 −1.02463
$$382$$ 0 0
$$383$$ 8.00000 0.408781 0.204390 0.978889i $$-0.434479\pi$$
0.204390 + 0.978889i $$0.434479\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −8.00000 −0.406663
$$388$$ 0 0
$$389$$ −30.0000 −1.52106 −0.760530 0.649303i $$-0.775061\pi$$
−0.760530 + 0.649303i $$0.775061\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −20.0000 −1.00887
$$394$$ 0 0
$$395$$ 16.0000 0.805047
$$396$$ 0 0
$$397$$ −38.0000 −1.90717 −0.953583 0.301131i $$-0.902636\pi$$
−0.953583 + 0.301131i $$0.902636\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 22.0000 1.09863 0.549314 0.835616i $$-0.314889\pi$$
0.549314 + 0.835616i $$0.314889\pi$$
$$402$$ 0 0
$$403$$ 16.0000 0.797017
$$404$$ 0 0
$$405$$ −4.00000 −0.198762
$$406$$ 0 0
$$407$$ 20.0000 0.991363
$$408$$ 0 0
$$409$$ −22.0000 −1.08783 −0.543915 0.839140i $$-0.683059\pi$$
−0.543915 + 0.839140i $$0.683059\pi$$
$$410$$ 0 0
$$411$$ −6.00000 −0.295958
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −48.0000 −2.35623
$$416$$ 0 0
$$417$$ 4.00000 0.195881
$$418$$ 0 0
$$419$$ −16.0000 −0.781651 −0.390826 0.920465i $$-0.627810\pi$$
−0.390826 + 0.920465i $$0.627810\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ 0 0
$$423$$ −4.00000 −0.194487
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −4.00000 −0.193122
$$430$$ 0 0
$$431$$ 18.0000 0.867029 0.433515 0.901146i $$-0.357273\pi$$
0.433515 + 0.901146i $$0.357273\pi$$
$$432$$ 0 0
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 0 0
$$435$$ 40.0000 1.91785
$$436$$ 0 0
$$437$$ 24.0000 1.14808
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ 0 0
$$445$$ 16.0000 0.758473
$$446$$ 0 0
$$447$$ −6.00000 −0.283790
$$448$$ 0 0
$$449$$ 10.0000 0.471929 0.235965 0.971762i $$-0.424175\pi$$
0.235965 + 0.971762i $$0.424175\pi$$
$$450$$ 0 0
$$451$$ −8.00000 −0.376705
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −22.0000 −1.02912 −0.514558 0.857455i $$-0.672044\pi$$
−0.514558 + 0.857455i $$0.672044\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 20.0000 0.929479 0.464739 0.885448i $$-0.346148\pi$$
0.464739 + 0.885448i $$0.346148\pi$$
$$464$$ 0 0
$$465$$ −32.0000 −1.48396
$$466$$ 0 0
$$467$$ 8.00000 0.370196 0.185098 0.982720i $$-0.440740\pi$$
0.185098 + 0.982720i $$0.440740\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 22.0000 1.01371
$$472$$ 0 0
$$473$$ 16.0000 0.735681
$$474$$ 0 0
$$475$$ 44.0000 2.01886
$$476$$ 0 0
$$477$$ −10.0000 −0.457869
$$478$$ 0 0
$$479$$ −12.0000 −0.548294 −0.274147 0.961688i $$-0.588395\pi$$
−0.274147 + 0.961688i $$0.588395\pi$$
$$480$$ 0 0
$$481$$ 20.0000 0.911922
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −8.00000 −0.363261
$$486$$ 0 0
$$487$$ 40.0000 1.81257 0.906287 0.422664i $$-0.138905\pi$$
0.906287 + 0.422664i $$0.138905\pi$$
$$488$$ 0 0
$$489$$ −20.0000 −0.904431
$$490$$ 0 0
$$491$$ 10.0000 0.451294 0.225647 0.974209i $$-0.427550\pi$$
0.225647 + 0.974209i $$0.427550\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 8.00000 0.359573
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 24.0000 1.07439 0.537194 0.843459i $$-0.319484\pi$$
0.537194 + 0.843459i $$0.319484\pi$$
$$500$$ 0 0
$$501$$ −20.0000 −0.893534
$$502$$ 0 0
$$503$$ 24.0000 1.07011 0.535054 0.844818i $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 9.00000 0.399704
$$508$$ 0 0
$$509$$ −36.0000 −1.59567 −0.797836 0.602875i $$-0.794022\pi$$
−0.797836 + 0.602875i $$0.794022\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −4.00000 −0.176604
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 8.00000 0.351840
$$518$$ 0 0
$$519$$ −24.0000 −1.05348
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 36.0000 1.57417 0.787085 0.616844i $$-0.211589\pi$$
0.787085 + 0.616844i $$0.211589\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ −8.00000 −0.347170
$$532$$ 0 0
$$533$$ −8.00000 −0.346518
$$534$$ 0 0
$$535$$ 40.0000 1.72935
$$536$$ 0 0
$$537$$ 6.00000 0.258919
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 14.0000 0.601907 0.300954 0.953639i $$-0.402695\pi$$
0.300954 + 0.953639i $$0.402695\pi$$
$$542$$ 0 0
$$543$$ −14.0000 −0.600798
$$544$$ 0 0
$$545$$ 56.0000 2.39878
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ 0 0
$$549$$ −6.00000 −0.256074
$$550$$ 0 0
$$551$$ 40.0000 1.70406
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −40.0000 −1.69791
$$556$$ 0 0
$$557$$ 22.0000 0.932170 0.466085 0.884740i $$-0.345664\pi$$
0.466085 + 0.884740i $$0.345664\pi$$
$$558$$ 0 0
$$559$$ 16.0000 0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ 0 0
$$565$$ −8.00000 −0.336563
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 14.0000 0.586911 0.293455 0.955973i $$-0.405195\pi$$
0.293455 + 0.955973i $$0.405195\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 0 0
$$573$$ 6.00000 0.250654
$$574$$ 0 0
$$575$$ 66.0000 2.75239
$$576$$ 0 0
$$577$$ 6.00000 0.249783 0.124892 0.992170i $$-0.460142\pi$$
0.124892 + 0.992170i $$0.460142\pi$$
$$578$$ 0 0
$$579$$ −6.00000 −0.249351
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 20.0000 0.828315
$$584$$ 0 0
$$585$$ 8.00000 0.330759
$$586$$ 0 0
$$587$$ −48.0000 −1.98117 −0.990586 0.136892i $$-0.956289\pi$$
−0.990586 + 0.136892i $$0.956289\pi$$
$$588$$ 0 0
$$589$$ −32.0000 −1.31854
$$590$$ 0 0
$$591$$ 2.00000 0.0822690
$$592$$ 0 0
$$593$$ 24.0000 0.985562 0.492781 0.870153i $$-0.335980\pi$$
0.492781 + 0.870153i $$0.335980\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 8.00000 0.327418
$$598$$ 0 0
$$599$$ 10.0000 0.408589 0.204294 0.978909i $$-0.434510\pi$$
0.204294 + 0.978909i $$0.434510\pi$$
$$600$$ 0 0
$$601$$ −34.0000 −1.38689 −0.693444 0.720510i $$-0.743908\pi$$
−0.693444 + 0.720510i $$0.743908\pi$$
$$602$$ 0 0
$$603$$ 4.00000 0.162893
$$604$$ 0 0
$$605$$ 28.0000 1.13836
$$606$$ 0 0
$$607$$ −8.00000 −0.324710 −0.162355 0.986732i $$-0.551909\pi$$
−0.162355 + 0.986732i $$0.551909\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 8.00000 0.323645
$$612$$ 0 0
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ 0 0
$$615$$ 16.0000 0.645182
$$616$$ 0 0
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ 0 0
$$619$$ −36.0000 −1.44696 −0.723481 0.690344i $$-0.757459\pi$$
−0.723481 + 0.690344i $$0.757459\pi$$
$$620$$ 0 0
$$621$$ −6.00000 −0.240772
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 41.0000 1.64000
$$626$$ 0 0
$$627$$ 8.00000 0.319489
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −4.00000 −0.159237 −0.0796187 0.996825i $$-0.525370\pi$$
−0.0796187 + 0.996825i $$0.525370\pi$$
$$632$$ 0 0
$$633$$ −8.00000 −0.317971
$$634$$ 0 0
$$635$$ −80.0000 −3.17470
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −14.0000 −0.553831
$$640$$ 0 0
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 0 0
$$643$$ 12.0000 0.473234 0.236617 0.971603i $$-0.423961\pi$$
0.236617 + 0.971603i $$0.423961\pi$$
$$644$$ 0 0
$$645$$ −32.0000 −1.26000
$$646$$ 0 0
$$647$$ 12.0000 0.471769 0.235884 0.971781i $$-0.424201\pi$$
0.235884 + 0.971781i $$0.424201\pi$$
$$648$$ 0 0
$$649$$ 16.0000 0.628055
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 26.0000 1.01746 0.508729 0.860927i $$-0.330115\pi$$
0.508729 + 0.860927i $$0.330115\pi$$
$$654$$ 0 0
$$655$$ −80.0000 −3.12586
$$656$$ 0 0
$$657$$ −6.00000 −0.234082
$$658$$ 0 0
$$659$$ 6.00000 0.233727 0.116863 0.993148i $$-0.462716\pi$$
0.116863 + 0.993148i $$0.462716\pi$$
$$660$$ 0 0
$$661$$ −22.0000 −0.855701 −0.427850 0.903850i $$-0.640729\pi$$
−0.427850 + 0.903850i $$0.640729\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 60.0000 2.32321
$$668$$ 0 0
$$669$$ 16.0000 0.618596
$$670$$ 0 0
$$671$$ 12.0000 0.463255
$$672$$ 0 0
$$673$$ −34.0000 −1.31060 −0.655302 0.755367i $$-0.727459\pi$$
−0.655302 + 0.755367i $$0.727459\pi$$
$$674$$ 0 0
$$675$$ −11.0000 −0.423390
$$676$$ 0 0
$$677$$ 16.0000 0.614930 0.307465 0.951559i $$-0.400519\pi$$
0.307465 + 0.951559i $$0.400519\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 18.0000 0.688751 0.344375 0.938832i $$-0.388091\pi$$
0.344375 + 0.938832i $$0.388091\pi$$
$$684$$ 0 0
$$685$$ −24.0000 −0.916993
$$686$$ 0 0
$$687$$ −14.0000 −0.534133
$$688$$ 0 0
$$689$$ 20.0000 0.761939
$$690$$ 0 0
$$691$$ 28.0000 1.06517 0.532585 0.846376i $$-0.321221\pi$$
0.532585 + 0.846376i $$0.321221\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 16.0000 0.606915
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 18.0000 0.680823
$$700$$ 0 0
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 0 0
$$703$$ −40.0000 −1.50863
$$704$$ 0 0
$$705$$ −16.0000 −0.602595
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 0 0
$$711$$ −4.00000 −0.150012
$$712$$ 0 0
$$713$$ −48.0000 −1.79761
$$714$$ 0 0
$$715$$ −16.0000 −0.598366
$$716$$ 0 0
$$717$$ −6.00000 −0.224074
$$718$$ 0 0
$$719$$ 32.0000 1.19340 0.596699 0.802465i $$-0.296479\pi$$
0.596699 + 0.802465i $$0.296479\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −2.00000 −0.0743808
$$724$$ 0 0
$$725$$ 110.000 4.08530
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 38.0000 1.40356 0.701781 0.712393i $$-0.252388\pi$$
0.701781 + 0.712393i $$0.252388\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −8.00000 −0.294684
$$738$$ 0 0
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 0 0
$$741$$ 8.00000 0.293887
$$742$$ 0 0
$$743$$ −6.00000 −0.220119 −0.110059 0.993925i $$-0.535104\pi$$
−0.110059 + 0.993925i $$0.535104\pi$$
$$744$$ 0 0
$$745$$ −24.0000 −0.879292
$$746$$ 0 0
$$747$$ 12.0000 0.439057
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −16.0000 −0.583848 −0.291924 0.956441i $$-0.594295\pi$$
−0.291924 + 0.956441i $$0.594295\pi$$
$$752$$ 0 0
$$753$$ −24.0000 −0.874609
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 42.0000 1.52652 0.763258 0.646094i $$-0.223599\pi$$
0.763258 + 0.646094i $$0.223599\pi$$
$$758$$ 0 0
$$759$$ 12.0000 0.435572
$$760$$ 0 0
$$761$$ −12.0000 −0.435000 −0.217500 0.976060i $$-0.569790\pi$$
−0.217500 + 0.976060i $$0.569790\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 16.0000 0.577727
$$768$$ 0 0
$$769$$ −34.0000 −1.22607 −0.613036 0.790055i $$-0.710052\pi$$
−0.613036 + 0.790055i $$0.710052\pi$$
$$770$$ 0 0
$$771$$ −4.00000 −0.144056
$$772$$ 0 0
$$773$$ 24.0000 0.863220 0.431610 0.902060i $$-0.357946\pi$$
0.431610 + 0.902060i $$0.357946\pi$$
$$774$$ 0 0
$$775$$ −88.0000 −3.16105
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 16.0000 0.573259
$$780$$ 0 0
$$781$$ 28.0000 1.00192
$$782$$ 0 0
$$783$$ −10.0000 −0.357371
$$784$$ 0 0
$$785$$ 88.0000 3.14085
$$786$$ 0 0
$$787$$ −36.0000 −1.28326 −0.641631 0.767014i $$-0.721742\pi$$
−0.641631 + 0.767014i $$0.721742\pi$$
$$788$$ 0 0
$$789$$ −30.0000 −1.06803
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 12.0000 0.426132
$$794$$ 0 0
$$795$$ −40.0000 −1.41865
$$796$$ 0 0
$$797$$ 24.0000 0.850124 0.425062 0.905164i $$-0.360252\pi$$
0.425062 + 0.905164i $$0.360252\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −4.00000 −0.141333
$$802$$ 0 0
$$803$$ 12.0000 0.423471
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −12.0000 −0.422420
$$808$$ 0 0
$$809$$ −14.0000 −0.492214 −0.246107 0.969243i $$-0.579151\pi$$
−0.246107 + 0.969243i $$0.579151\pi$$
$$810$$ 0 0
$$811$$ −20.0000 −0.702295 −0.351147 0.936320i $$-0.614208\pi$$
−0.351147 + 0.936320i $$0.614208\pi$$
$$812$$ 0 0
$$813$$ 24.0000 0.841717
$$814$$ 0 0
$$815$$ −80.0000 −2.80228
$$816$$ 0 0
$$817$$ −32.0000 −1.11954
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −2.00000 −0.0698005 −0.0349002 0.999391i $$-0.511111\pi$$
−0.0349002 + 0.999391i $$0.511111\pi$$
$$822$$ 0 0
$$823$$ 4.00000 0.139431 0.0697156 0.997567i $$-0.477791\pi$$
0.0697156 + 0.997567i $$0.477791\pi$$
$$824$$ 0 0
$$825$$ 22.0000 0.765942
$$826$$ 0 0
$$827$$ −26.0000 −0.904109 −0.452054 0.891990i $$-0.649309\pi$$
−0.452054 + 0.891990i $$0.649309\pi$$
$$828$$ 0 0
$$829$$ 14.0000 0.486240 0.243120 0.969996i $$-0.421829\pi$$
0.243120 + 0.969996i $$0.421829\pi$$
$$830$$ 0 0
$$831$$ 10.0000 0.346896
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −80.0000 −2.76851
$$836$$ 0 0
$$837$$ 8.00000 0.276520
$$838$$ 0 0
$$839$$ 44.0000 1.51905 0.759524 0.650479i $$-0.225432\pi$$
0.759524 + 0.650479i $$0.225432\pi$$
$$840$$ 0 0
$$841$$ 71.0000 2.44828
$$842$$ 0 0
$$843$$ −6.00000 −0.206651
$$844$$ 0 0
$$845$$ 36.0000 1.23844
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ −20.0000 −0.686398
$$850$$ 0 0
$$851$$ −60.0000 −2.05677
$$852$$ 0 0
$$853$$ 42.0000 1.43805 0.719026 0.694983i $$-0.244588\pi$$
0.719026 + 0.694983i $$0.244588\pi$$
$$854$$ 0 0
$$855$$ −16.0000 −0.547188
$$856$$ 0 0
$$857$$ −28.0000 −0.956462 −0.478231 0.878234i $$-0.658722\pi$$
−0.478231 + 0.878234i $$0.658722\pi$$
$$858$$ 0 0
$$859$$ 20.0000 0.682391 0.341196 0.939992i $$-0.389168\pi$$
0.341196 + 0.939992i $$0.389168\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 22.0000 0.748889 0.374444 0.927249i $$-0.377833\pi$$
0.374444 + 0.927249i $$0.377833\pi$$
$$864$$ 0 0
$$865$$ −96.0000 −3.26410
$$866$$ 0 0
$$867$$ 17.0000 0.577350
$$868$$ 0 0
$$869$$ 8.00000 0.271381
$$870$$ 0 0
$$871$$ −8.00000 −0.271070
$$872$$ 0 0
$$873$$ 2.00000 0.0676897
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 50.0000 1.68838 0.844190 0.536044i $$-0.180082\pi$$
0.844190 + 0.536044i $$0.180082\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −48.0000 −1.61716 −0.808581 0.588386i $$-0.799764\pi$$
−0.808581 + 0.588386i $$0.799764\pi$$
$$882$$ 0 0
$$883$$ −8.00000 −0.269221 −0.134611 0.990899i $$-0.542978\pi$$
−0.134611 + 0.990899i $$0.542978\pi$$
$$884$$ 0 0
$$885$$ −32.0000 −1.07567
$$886$$ 0 0
$$887$$ −12.0000 −0.402921 −0.201460 0.979497i $$-0.564569\pi$$
−0.201460 + 0.979497i $$0.564569\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −2.00000 −0.0670025
$$892$$ 0 0
$$893$$ −16.0000 −0.535420
$$894$$ 0 0
$$895$$ 24.0000 0.802232
$$896$$ 0 0
$$897$$ 12.0000 0.400668
$$898$$ 0 0
$$899$$ −80.0000 −2.66815
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −56.0000 −1.86150
$$906$$ 0 0
$$907$$ 32.0000 1.06254 0.531271 0.847202i $$-0.321714\pi$$
0.531271 + 0.847202i $$0.321714\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 18.0000 0.596367 0.298183 0.954509i $$-0.403619\pi$$
0.298183 + 0.954509i $$0.403619\pi$$
$$912$$ 0 0
$$913$$ −24.0000 −0.794284
$$914$$ 0 0
$$915$$ −24.0000 −0.793416
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ −12.0000 −0.395413
$$922$$ 0 0
$$923$$ 28.0000 0.921631
$$924$$ 0 0
$$925$$ −110.000 −3.61678
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 36.0000 1.18112 0.590561 0.806993i $$-0.298907\pi$$
0.590561 + 0.806993i $$0.298907\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 12.0000 0.392862
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −2.00000 −0.0653372 −0.0326686 0.999466i $$-0.510401\pi$$
−0.0326686 + 0.999466i $$0.510401\pi$$
$$938$$ 0 0
$$939$$ −14.0000 −0.456873
$$940$$ 0 0
$$941$$ 4.00000 0.130396 0.0651981 0.997872i $$-0.479232\pi$$
0.0651981 + 0.997872i $$0.479232\pi$$
$$942$$ 0 0
$$943$$ 24.0000 0.781548
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −18.0000 −0.584921 −0.292461 0.956278i $$-0.594474\pi$$
−0.292461 + 0.956278i $$0.594474\pi$$
$$948$$ 0 0
$$949$$ 12.0000 0.389536
$$950$$ 0 0
$$951$$ 18.0000 0.583690
$$952$$ 0 0
$$953$$ −6.00000 −0.194359 −0.0971795 0.995267i $$-0.530982\pi$$
−0.0971795 + 0.995267i $$0.530982\pi$$
$$954$$ 0 0
$$955$$ 24.0000 0.776622
$$956$$ 0 0
$$957$$ 20.0000 0.646508
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 0 0
$$963$$ −10.0000 −0.322245
$$964$$ 0 0
$$965$$ −24.0000 −0.772587
$$966$$ 0 0
$$967$$ −12.0000 −0.385894 −0.192947 0.981209i $$-0.561805\pi$$
−0.192947 + 0.981209i $$0.561805\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 20.0000 0.641831 0.320915 0.947108i $$-0.396010\pi$$
0.320915 + 0.947108i $$0.396010\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 22.0000 0.704564
$$976$$ 0 0
$$977$$ 14.0000 0.447900 0.223950 0.974601i $$-0.428105\pi$$
0.223950 + 0.974601i $$0.428105\pi$$
$$978$$ 0 0
$$979$$ 8.00000 0.255681
$$980$$ 0 0
$$981$$ −14.0000 −0.446986
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 8.00000 0.254901
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −48.0000 −1.52631
$$990$$ 0 0
$$991$$ −16.0000 −0.508257 −0.254128 0.967170i $$-0.581789\pi$$
−0.254128 + 0.967170i $$0.581789\pi$$
$$992$$ 0 0
$$993$$ 32.0000 1.01549
$$994$$ 0 0
$$995$$ 32.0000 1.01447
$$996$$ 0 0
$$997$$ −6.00000 −0.190022 −0.0950110 0.995476i $$-0.530289\pi$$
−0.0950110 + 0.995476i $$0.530289\pi$$
$$998$$ 0 0
$$999$$ 10.0000 0.316386
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 9408.2.a.c.1.1 1
4.3 odd 2 9408.2.a.bq.1.1 1
7.6 odd 2 1344.2.a.t.1.1 1
8.3 odd 2 4704.2.a.q.1.1 1
8.5 even 2 4704.2.a.bg.1.1 1
21.20 even 2 4032.2.a.b.1.1 1
28.27 even 2 1344.2.a.j.1.1 1
56.13 odd 2 672.2.a.a.1.1 1
56.27 even 2 672.2.a.e.1.1 yes 1
84.83 odd 2 4032.2.a.c.1.1 1
112.13 odd 4 5376.2.c.bf.2689.2 2
112.27 even 4 5376.2.c.b.2689.2 2
112.69 odd 4 5376.2.c.bf.2689.1 2
112.83 even 4 5376.2.c.b.2689.1 2
168.83 odd 2 2016.2.a.n.1.1 1
168.125 even 2 2016.2.a.m.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
672.2.a.a.1.1 1 56.13 odd 2
672.2.a.e.1.1 yes 1 56.27 even 2
1344.2.a.j.1.1 1 28.27 even 2
1344.2.a.t.1.1 1 7.6 odd 2
2016.2.a.m.1.1 1 168.125 even 2
2016.2.a.n.1.1 1 168.83 odd 2
4032.2.a.b.1.1 1 21.20 even 2
4032.2.a.c.1.1 1 84.83 odd 2
4704.2.a.q.1.1 1 8.3 odd 2
4704.2.a.bg.1.1 1 8.5 even 2
5376.2.c.b.2689.1 2 112.83 even 4
5376.2.c.b.2689.2 2 112.27 even 4
5376.2.c.bf.2689.1 2 112.69 odd 4
5376.2.c.bf.2689.2 2 112.13 odd 4
9408.2.a.c.1.1 1 1.1 even 1 trivial
9408.2.a.bq.1.1 1 4.3 odd 2