Properties

 Label 7440.2.a.v.1.1 Level $7440$ Weight $2$ Character 7440.1 Self dual yes Analytic conductor $59.409$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7440.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$59.4086991038$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 930) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7440.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} -1.00000 q^{5} +3.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} -1.00000 q^{5} +3.00000 q^{7} +1.00000 q^{9} -3.00000 q^{11} -2.00000 q^{13} -1.00000 q^{15} -4.00000 q^{17} +3.00000 q^{19} +3.00000 q^{21} -5.00000 q^{23} +1.00000 q^{25} +1.00000 q^{27} +4.00000 q^{29} -1.00000 q^{31} -3.00000 q^{33} -3.00000 q^{35} -2.00000 q^{39} +4.00000 q^{41} -1.00000 q^{43} -1.00000 q^{45} -10.0000 q^{47} +2.00000 q^{49} -4.00000 q^{51} +3.00000 q^{53} +3.00000 q^{55} +3.00000 q^{57} -6.00000 q^{59} -2.00000 q^{61} +3.00000 q^{63} +2.00000 q^{65} -2.00000 q^{67} -5.00000 q^{69} -7.00000 q^{71} +5.00000 q^{73} +1.00000 q^{75} -9.00000 q^{77} +1.00000 q^{79} +1.00000 q^{81} -12.0000 q^{83} +4.00000 q^{85} +4.00000 q^{87} +1.00000 q^{89} -6.00000 q^{91} -1.00000 q^{93} -3.00000 q^{95} -10.0000 q^{97} -3.00000 q^{99} +O(q^{100})$$

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
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −3.00000 −0.904534 −0.452267 0.891883i $$-0.649385\pi$$
−0.452267 + 0.891883i $$0.649385\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −0.258199
$$16$$ 0 0
$$17$$ −4.00000 −0.970143 −0.485071 0.874475i $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ 0 0
$$19$$ 3.00000 0.688247 0.344124 0.938924i $$-0.388176\pi$$
0.344124 + 0.938924i $$0.388176\pi$$
$$20$$ 0 0
$$21$$ 3.00000 0.654654
$$22$$ 0 0
$$23$$ −5.00000 −1.04257 −0.521286 0.853382i $$-0.674548\pi$$
−0.521286 + 0.853382i $$0.674548\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −0.179605
$$32$$ 0 0
$$33$$ −3.00000 −0.522233
$$34$$ 0 0
$$35$$ −3.00000 −0.507093
$$36$$ 0 0
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 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
$$43$$ −1.00000 −0.152499 −0.0762493 0.997089i $$-0.524294\pi$$
−0.0762493 + 0.997089i $$0.524294\pi$$
$$44$$ 0 0
$$45$$ −1.00000 −0.149071
$$46$$ 0 0
$$47$$ −10.0000 −1.45865 −0.729325 0.684167i $$-0.760166\pi$$
−0.729325 + 0.684167i $$0.760166\pi$$
$$48$$ 0 0
$$49$$ 2.00000 0.285714
$$50$$ 0 0
$$51$$ −4.00000 −0.560112
$$52$$ 0 0
$$53$$ 3.00000 0.412082 0.206041 0.978543i $$-0.433942\pi$$
0.206041 + 0.978543i $$0.433942\pi$$
$$54$$ 0 0
$$55$$ 3.00000 0.404520
$$56$$ 0 0
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ −6.00000 −0.781133 −0.390567 0.920575i $$-0.627721\pi$$
−0.390567 + 0.920575i $$0.627721\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 0 0
$$63$$ 3.00000 0.377964
$$64$$ 0 0
$$65$$ 2.00000 0.248069
$$66$$ 0 0
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 0 0
$$69$$ −5.00000 −0.601929
$$70$$ 0 0
$$71$$ −7.00000 −0.830747 −0.415374 0.909651i $$-0.636349\pi$$
−0.415374 + 0.909651i $$0.636349\pi$$
$$72$$ 0 0
$$73$$ 5.00000 0.585206 0.292603 0.956234i $$-0.405479\pi$$
0.292603 + 0.956234i $$0.405479\pi$$
$$74$$ 0 0
$$75$$ 1.00000 0.115470
$$76$$ 0 0
$$77$$ −9.00000 −1.02565
$$78$$ 0 0
$$79$$ 1.00000 0.112509 0.0562544 0.998416i $$-0.482084\pi$$
0.0562544 + 0.998416i $$0.482084\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 4.00000 0.433861
$$86$$ 0 0
$$87$$ 4.00000 0.428845
$$88$$ 0 0
$$89$$ 1.00000 0.106000 0.0529999 0.998595i $$-0.483122\pi$$
0.0529999 + 0.998595i $$0.483122\pi$$
$$90$$ 0 0
$$91$$ −6.00000 −0.628971
$$92$$ 0 0
$$93$$ −1.00000 −0.103695
$$94$$ 0 0
$$95$$ −3.00000 −0.307794
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ −3.00000 −0.301511
$$100$$ 0 0
$$101$$ −1.00000 −0.0995037 −0.0497519 0.998762i $$-0.515843\pi$$
−0.0497519 + 0.998762i $$0.515843\pi$$
$$102$$ 0 0
$$103$$ −16.0000 −1.57653 −0.788263 0.615338i $$-0.789020\pi$$
−0.788263 + 0.615338i $$0.789020\pi$$
$$104$$ 0 0
$$105$$ −3.00000 −0.292770
$$106$$ 0 0
$$107$$ −9.00000 −0.870063 −0.435031 0.900415i $$-0.643263\pi$$
−0.435031 + 0.900415i $$0.643263\pi$$
$$108$$ 0 0
$$109$$ 20.0000 1.91565 0.957826 0.287348i $$-0.0927736\pi$$
0.957826 + 0.287348i $$0.0927736\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 9.00000 0.846649 0.423324 0.905978i $$-0.360863\pi$$
0.423324 + 0.905978i $$0.360863\pi$$
$$114$$ 0 0
$$115$$ 5.00000 0.466252
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ −12.0000 −1.10004
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ 4.00000 0.360668
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ −1.00000 −0.0880451
$$130$$ 0 0
$$131$$ −6.00000 −0.524222 −0.262111 0.965038i $$-0.584419\pi$$
−0.262111 + 0.965038i $$0.584419\pi$$
$$132$$ 0 0
$$133$$ 9.00000 0.780399
$$134$$ 0 0
$$135$$ −1.00000 −0.0860663
$$136$$ 0 0
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 0 0
$$139$$ 14.0000 1.18746 0.593732 0.804663i $$-0.297654\pi$$
0.593732 + 0.804663i $$0.297654\pi$$
$$140$$ 0 0
$$141$$ −10.0000 −0.842152
$$142$$ 0 0
$$143$$ 6.00000 0.501745
$$144$$ 0 0
$$145$$ −4.00000 −0.332182
$$146$$ 0 0
$$147$$ 2.00000 0.164957
$$148$$ 0 0
$$149$$ −11.0000 −0.901155 −0.450578 0.892737i $$-0.648782\pi$$
−0.450578 + 0.892737i $$0.648782\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ −4.00000 −0.323381
$$154$$ 0 0
$$155$$ 1.00000 0.0803219
$$156$$ 0 0
$$157$$ −5.00000 −0.399043 −0.199522 0.979893i $$-0.563939\pi$$
−0.199522 + 0.979893i $$0.563939\pi$$
$$158$$ 0 0
$$159$$ 3.00000 0.237915
$$160$$ 0 0
$$161$$ −15.0000 −1.18217
$$162$$ 0 0
$$163$$ −14.0000 −1.09656 −0.548282 0.836293i $$-0.684718\pi$$
−0.548282 + 0.836293i $$0.684718\pi$$
$$164$$ 0 0
$$165$$ 3.00000 0.233550
$$166$$ 0 0
$$167$$ 19.0000 1.47026 0.735132 0.677924i $$-0.237120\pi$$
0.735132 + 0.677924i $$0.237120\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 3.00000 0.229416
$$172$$ 0 0
$$173$$ −22.0000 −1.67263 −0.836315 0.548250i $$-0.815294\pi$$
−0.836315 + 0.548250i $$0.815294\pi$$
$$174$$ 0 0
$$175$$ 3.00000 0.226779
$$176$$ 0 0
$$177$$ −6.00000 −0.450988
$$178$$ 0 0
$$179$$ −4.00000 −0.298974 −0.149487 0.988764i $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 0 0
$$181$$ 5.00000 0.371647 0.185824 0.982583i $$-0.440505\pi$$
0.185824 + 0.982583i $$0.440505\pi$$
$$182$$ 0 0
$$183$$ −2.00000 −0.147844
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 12.0000 0.877527
$$188$$ 0 0
$$189$$ 3.00000 0.218218
$$190$$ 0 0
$$191$$ −16.0000 −1.15772 −0.578860 0.815427i $$-0.696502\pi$$
−0.578860 + 0.815427i $$0.696502\pi$$
$$192$$ 0 0
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ 0 0
$$195$$ 2.00000 0.143223
$$196$$ 0 0
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ −7.00000 −0.496217 −0.248108 0.968732i $$-0.579809\pi$$
−0.248108 + 0.968732i $$0.579809\pi$$
$$200$$ 0 0
$$201$$ −2.00000 −0.141069
$$202$$ 0 0
$$203$$ 12.0000 0.842235
$$204$$ 0 0
$$205$$ −4.00000 −0.279372
$$206$$ 0 0
$$207$$ −5.00000 −0.347524
$$208$$ 0 0
$$209$$ −9.00000 −0.622543
$$210$$ 0 0
$$211$$ 19.0000 1.30801 0.654007 0.756489i $$-0.273087\pi$$
0.654007 + 0.756489i $$0.273087\pi$$
$$212$$ 0 0
$$213$$ −7.00000 −0.479632
$$214$$ 0 0
$$215$$ 1.00000 0.0681994
$$216$$ 0 0
$$217$$ −3.00000 −0.203653
$$218$$ 0 0
$$219$$ 5.00000 0.337869
$$220$$ 0 0
$$221$$ 8.00000 0.538138
$$222$$ 0 0
$$223$$ 6.00000 0.401790 0.200895 0.979613i $$-0.435615\pi$$
0.200895 + 0.979613i $$0.435615\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ 27.0000 1.79205 0.896026 0.444001i $$-0.146441\pi$$
0.896026 + 0.444001i $$0.146441\pi$$
$$228$$ 0 0
$$229$$ 13.0000 0.859064 0.429532 0.903052i $$-0.358679\pi$$
0.429532 + 0.903052i $$0.358679\pi$$
$$230$$ 0 0
$$231$$ −9.00000 −0.592157
$$232$$ 0 0
$$233$$ 15.0000 0.982683 0.491341 0.870967i $$-0.336507\pi$$
0.491341 + 0.870967i $$0.336507\pi$$
$$234$$ 0 0
$$235$$ 10.0000 0.652328
$$236$$ 0 0
$$237$$ 1.00000 0.0649570
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ 1.00000 0.0641500
$$244$$ 0 0
$$245$$ −2.00000 −0.127775
$$246$$ 0 0
$$247$$ −6.00000 −0.381771
$$248$$ 0 0
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 15.0000 0.943042
$$254$$ 0 0
$$255$$ 4.00000 0.250490
$$256$$ 0 0
$$257$$ −23.0000 −1.43470 −0.717350 0.696713i $$-0.754645\pi$$
−0.717350 + 0.696713i $$0.754645\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 4.00000 0.247594
$$262$$ 0 0
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ 0 0
$$265$$ −3.00000 −0.184289
$$266$$ 0 0
$$267$$ 1.00000 0.0611990
$$268$$ 0 0
$$269$$ 2.00000 0.121942 0.0609711 0.998140i $$-0.480580\pi$$
0.0609711 + 0.998140i $$0.480580\pi$$
$$270$$ 0 0
$$271$$ −13.0000 −0.789694 −0.394847 0.918747i $$-0.629202\pi$$
−0.394847 + 0.918747i $$0.629202\pi$$
$$272$$ 0 0
$$273$$ −6.00000 −0.363137
$$274$$ 0 0
$$275$$ −3.00000 −0.180907
$$276$$ 0 0
$$277$$ 12.0000 0.721010 0.360505 0.932757i $$-0.382604\pi$$
0.360505 + 0.932757i $$0.382604\pi$$
$$278$$ 0 0
$$279$$ −1.00000 −0.0598684
$$280$$ 0 0
$$281$$ 16.0000 0.954480 0.477240 0.878773i $$-0.341637\pi$$
0.477240 + 0.878773i $$0.341637\pi$$
$$282$$ 0 0
$$283$$ 24.0000 1.42665 0.713326 0.700832i $$-0.247188\pi$$
0.713326 + 0.700832i $$0.247188\pi$$
$$284$$ 0 0
$$285$$ −3.00000 −0.177705
$$286$$ 0 0
$$287$$ 12.0000 0.708338
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ −10.0000 −0.586210
$$292$$ 0 0
$$293$$ 30.0000 1.75262 0.876309 0.481749i $$-0.159998\pi$$
0.876309 + 0.481749i $$0.159998\pi$$
$$294$$ 0 0
$$295$$ 6.00000 0.349334
$$296$$ 0 0
$$297$$ −3.00000 −0.174078
$$298$$ 0 0
$$299$$ 10.0000 0.578315
$$300$$ 0 0
$$301$$ −3.00000 −0.172917
$$302$$ 0 0
$$303$$ −1.00000 −0.0574485
$$304$$ 0 0
$$305$$ 2.00000 0.114520
$$306$$ 0 0
$$307$$ −16.0000 −0.913168 −0.456584 0.889680i $$-0.650927\pi$$
−0.456584 + 0.889680i $$0.650927\pi$$
$$308$$ 0 0
$$309$$ −16.0000 −0.910208
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 30.0000 1.69570 0.847850 0.530236i $$-0.177897\pi$$
0.847850 + 0.530236i $$0.177897\pi$$
$$314$$ 0 0
$$315$$ −3.00000 −0.169031
$$316$$ 0 0
$$317$$ −8.00000 −0.449325 −0.224662 0.974437i $$-0.572128\pi$$
−0.224662 + 0.974437i $$0.572128\pi$$
$$318$$ 0 0
$$319$$ −12.0000 −0.671871
$$320$$ 0 0
$$321$$ −9.00000 −0.502331
$$322$$ 0 0
$$323$$ −12.0000 −0.667698
$$324$$ 0 0
$$325$$ −2.00000 −0.110940
$$326$$ 0 0
$$327$$ 20.0000 1.10600
$$328$$ 0 0
$$329$$ −30.0000 −1.65395
$$330$$ 0 0
$$331$$ −12.0000 −0.659580 −0.329790 0.944054i $$-0.606978\pi$$
−0.329790 + 0.944054i $$0.606978\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 2.00000 0.109272
$$336$$ 0 0
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ 0 0
$$339$$ 9.00000 0.488813
$$340$$ 0 0
$$341$$ 3.00000 0.162459
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ 0 0
$$345$$ 5.00000 0.269191
$$346$$ 0 0
$$347$$ 32.0000 1.71785 0.858925 0.512101i $$-0.171133\pi$$
0.858925 + 0.512101i $$0.171133\pi$$
$$348$$ 0 0
$$349$$ −24.0000 −1.28469 −0.642345 0.766415i $$-0.722038\pi$$
−0.642345 + 0.766415i $$0.722038\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −0.106752
$$352$$ 0 0
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 0 0
$$355$$ 7.00000 0.371521
$$356$$ 0 0
$$357$$ −12.0000 −0.635107
$$358$$ 0 0
$$359$$ −15.0000 −0.791670 −0.395835 0.918322i $$-0.629545\pi$$
−0.395835 + 0.918322i $$0.629545\pi$$
$$360$$ 0 0
$$361$$ −10.0000 −0.526316
$$362$$ 0 0
$$363$$ −2.00000 −0.104973
$$364$$ 0 0
$$365$$ −5.00000 −0.261712
$$366$$ 0 0
$$367$$ −2.00000 −0.104399 −0.0521996 0.998637i $$-0.516623\pi$$
−0.0521996 + 0.998637i $$0.516623\pi$$
$$368$$ 0 0
$$369$$ 4.00000 0.208232
$$370$$ 0 0
$$371$$ 9.00000 0.467257
$$372$$ 0 0
$$373$$ −9.00000 −0.466002 −0.233001 0.972476i $$-0.574855\pi$$
−0.233001 + 0.972476i $$0.574855\pi$$
$$374$$ 0 0
$$375$$ −1.00000 −0.0516398
$$376$$ 0 0
$$377$$ −8.00000 −0.412021
$$378$$ 0 0
$$379$$ −15.0000 −0.770498 −0.385249 0.922813i $$-0.625884\pi$$
−0.385249 + 0.922813i $$0.625884\pi$$
$$380$$ 0 0
$$381$$ −8.00000 −0.409852
$$382$$ 0 0
$$383$$ −12.0000 −0.613171 −0.306586 0.951843i $$-0.599187\pi$$
−0.306586 + 0.951843i $$0.599187\pi$$
$$384$$ 0 0
$$385$$ 9.00000 0.458682
$$386$$ 0 0
$$387$$ −1.00000 −0.0508329
$$388$$ 0 0
$$389$$ −26.0000 −1.31825 −0.659126 0.752032i $$-0.729074\pi$$
−0.659126 + 0.752032i $$0.729074\pi$$
$$390$$ 0 0
$$391$$ 20.0000 1.01144
$$392$$ 0 0
$$393$$ −6.00000 −0.302660
$$394$$ 0 0
$$395$$ −1.00000 −0.0503155
$$396$$ 0 0
$$397$$ 35.0000 1.75660 0.878300 0.478110i $$-0.158678\pi$$
0.878300 + 0.478110i $$0.158678\pi$$
$$398$$ 0 0
$$399$$ 9.00000 0.450564
$$400$$ 0 0
$$401$$ 25.0000 1.24844 0.624220 0.781248i $$-0.285417\pi$$
0.624220 + 0.781248i $$0.285417\pi$$
$$402$$ 0 0
$$403$$ 2.00000 0.0996271
$$404$$ 0 0
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 8.00000 0.395575 0.197787 0.980245i $$-0.436624\pi$$
0.197787 + 0.980245i $$0.436624\pi$$
$$410$$ 0 0
$$411$$ −10.0000 −0.493264
$$412$$ 0 0
$$413$$ −18.0000 −0.885722
$$414$$ 0 0
$$415$$ 12.0000 0.589057
$$416$$ 0 0
$$417$$ 14.0000 0.685583
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 0 0
$$423$$ −10.0000 −0.486217
$$424$$ 0 0
$$425$$ −4.00000 −0.194029
$$426$$ 0 0
$$427$$ −6.00000 −0.290360
$$428$$ 0 0
$$429$$ 6.00000 0.289683
$$430$$ 0 0
$$431$$ −16.0000 −0.770693 −0.385346 0.922772i $$-0.625918\pi$$
−0.385346 + 0.922772i $$0.625918\pi$$
$$432$$ 0 0
$$433$$ −1.00000 −0.0480569 −0.0240285 0.999711i $$-0.507649\pi$$
−0.0240285 + 0.999711i $$0.507649\pi$$
$$434$$ 0 0
$$435$$ −4.00000 −0.191785
$$436$$ 0 0
$$437$$ −15.0000 −0.717547
$$438$$ 0 0
$$439$$ −18.0000 −0.859093 −0.429547 0.903045i $$-0.641327\pi$$
−0.429547 + 0.903045i $$0.641327\pi$$
$$440$$ 0 0
$$441$$ 2.00000 0.0952381
$$442$$ 0 0
$$443$$ −15.0000 −0.712672 −0.356336 0.934358i $$-0.615974\pi$$
−0.356336 + 0.934358i $$0.615974\pi$$
$$444$$ 0 0
$$445$$ −1.00000 −0.0474045
$$446$$ 0 0
$$447$$ −11.0000 −0.520282
$$448$$ 0 0
$$449$$ 2.00000 0.0943858 0.0471929 0.998886i $$-0.484972\pi$$
0.0471929 + 0.998886i $$0.484972\pi$$
$$450$$ 0 0
$$451$$ −12.0000 −0.565058
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 6.00000 0.281284
$$456$$ 0 0
$$457$$ 10.0000 0.467780 0.233890 0.972263i $$-0.424854\pi$$
0.233890 + 0.972263i $$0.424854\pi$$
$$458$$ 0 0
$$459$$ −4.00000 −0.186704
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ 0 0
$$465$$ 1.00000 0.0463739
$$466$$ 0 0
$$467$$ −24.0000 −1.11059 −0.555294 0.831654i $$-0.687394\pi$$
−0.555294 + 0.831654i $$0.687394\pi$$
$$468$$ 0 0
$$469$$ −6.00000 −0.277054
$$470$$ 0 0
$$471$$ −5.00000 −0.230388
$$472$$ 0 0
$$473$$ 3.00000 0.137940
$$474$$ 0 0
$$475$$ 3.00000 0.137649
$$476$$ 0 0
$$477$$ 3.00000 0.137361
$$478$$ 0 0
$$479$$ −3.00000 −0.137073 −0.0685367 0.997649i $$-0.521833\pi$$
−0.0685367 + 0.997649i $$0.521833\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ −15.0000 −0.682524
$$484$$ 0 0
$$485$$ 10.0000 0.454077
$$486$$ 0 0
$$487$$ −32.0000 −1.45006 −0.725029 0.688718i $$-0.758174\pi$$
−0.725029 + 0.688718i $$0.758174\pi$$
$$488$$ 0 0
$$489$$ −14.0000 −0.633102
$$490$$ 0 0
$$491$$ 37.0000 1.66979 0.834893 0.550412i $$-0.185529\pi$$
0.834893 + 0.550412i $$0.185529\pi$$
$$492$$ 0 0
$$493$$ −16.0000 −0.720604
$$494$$ 0 0
$$495$$ 3.00000 0.134840
$$496$$ 0 0
$$497$$ −21.0000 −0.941979
$$498$$ 0 0
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ 0 0
$$501$$ 19.0000 0.848857
$$502$$ 0 0
$$503$$ −20.0000 −0.891756 −0.445878 0.895094i $$-0.647108\pi$$
−0.445878 + 0.895094i $$0.647108\pi$$
$$504$$ 0 0
$$505$$ 1.00000 0.0444994
$$506$$ 0 0
$$507$$ −9.00000 −0.399704
$$508$$ 0 0
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 15.0000 0.663561
$$512$$ 0 0
$$513$$ 3.00000 0.132453
$$514$$ 0 0
$$515$$ 16.0000 0.705044
$$516$$ 0 0
$$517$$ 30.0000 1.31940
$$518$$ 0 0
$$519$$ −22.0000 −0.965693
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 0 0
$$523$$ 43.0000 1.88026 0.940129 0.340818i $$-0.110704\pi$$
0.940129 + 0.340818i $$0.110704\pi$$
$$524$$ 0 0
$$525$$ 3.00000 0.130931
$$526$$ 0 0
$$527$$ 4.00000 0.174243
$$528$$ 0 0
$$529$$ 2.00000 0.0869565
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 0 0
$$533$$ −8.00000 −0.346518
$$534$$ 0 0
$$535$$ 9.00000 0.389104
$$536$$ 0 0
$$537$$ −4.00000 −0.172613
$$538$$ 0 0
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ 0 0
$$543$$ 5.00000 0.214571
$$544$$ 0 0
$$545$$ −20.0000 −0.856706
$$546$$ 0 0
$$547$$ −22.0000 −0.940652 −0.470326 0.882493i $$-0.655864\pi$$
−0.470326 + 0.882493i $$0.655864\pi$$
$$548$$ 0 0
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ 12.0000 0.511217
$$552$$ 0 0
$$553$$ 3.00000 0.127573
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −1.00000 −0.0423714 −0.0211857 0.999776i $$-0.506744\pi$$
−0.0211857 + 0.999776i $$0.506744\pi$$
$$558$$ 0 0
$$559$$ 2.00000 0.0845910
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ 0 0
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ 0 0
$$565$$ −9.00000 −0.378633
$$566$$ 0 0
$$567$$ 3.00000 0.125988
$$568$$ 0 0
$$569$$ −23.0000 −0.964210 −0.482105 0.876113i $$-0.660128\pi$$
−0.482105 + 0.876113i $$0.660128\pi$$
$$570$$ 0 0
$$571$$ −22.0000 −0.920671 −0.460336 0.887745i $$-0.652271\pi$$
−0.460336 + 0.887745i $$0.652271\pi$$
$$572$$ 0 0
$$573$$ −16.0000 −0.668410
$$574$$ 0 0
$$575$$ −5.00000 −0.208514
$$576$$ 0 0
$$577$$ 4.00000 0.166522 0.0832611 0.996528i $$-0.473466\pi$$
0.0832611 + 0.996528i $$0.473466\pi$$
$$578$$ 0 0
$$579$$ −6.00000 −0.249351
$$580$$ 0 0
$$581$$ −36.0000 −1.49353
$$582$$ 0 0
$$583$$ −9.00000 −0.372742
$$584$$ 0 0
$$585$$ 2.00000 0.0826898
$$586$$ 0 0
$$587$$ −44.0000 −1.81607 −0.908037 0.418890i $$-0.862419\pi$$
−0.908037 + 0.418890i $$0.862419\pi$$
$$588$$ 0 0
$$589$$ −3.00000 −0.123613
$$590$$ 0 0
$$591$$ −6.00000 −0.246807
$$592$$ 0 0
$$593$$ 22.0000 0.903432 0.451716 0.892162i $$-0.350812\pi$$
0.451716 + 0.892162i $$0.350812\pi$$
$$594$$ 0 0
$$595$$ 12.0000 0.491952
$$596$$ 0 0
$$597$$ −7.00000 −0.286491
$$598$$ 0 0
$$599$$ 27.0000 1.10319 0.551595 0.834112i $$-0.314019\pi$$
0.551595 + 0.834112i $$0.314019\pi$$
$$600$$ 0 0
$$601$$ 42.0000 1.71322 0.856608 0.515968i $$-0.172568\pi$$
0.856608 + 0.515968i $$0.172568\pi$$
$$602$$ 0 0
$$603$$ −2.00000 −0.0814463
$$604$$ 0 0
$$605$$ 2.00000 0.0813116
$$606$$ 0 0
$$607$$ −29.0000 −1.17707 −0.588537 0.808470i $$-0.700296\pi$$
−0.588537 + 0.808470i $$0.700296\pi$$
$$608$$ 0 0
$$609$$ 12.0000 0.486265
$$610$$ 0 0
$$611$$ 20.0000 0.809113
$$612$$ 0 0
$$613$$ −22.0000 −0.888572 −0.444286 0.895885i $$-0.646543\pi$$
−0.444286 + 0.895885i $$0.646543\pi$$
$$614$$ 0 0
$$615$$ −4.00000 −0.161296
$$616$$ 0 0
$$617$$ −27.0000 −1.08698 −0.543490 0.839416i $$-0.682897\pi$$
−0.543490 + 0.839416i $$0.682897\pi$$
$$618$$ 0 0
$$619$$ 38.0000 1.52735 0.763674 0.645601i $$-0.223393\pi$$
0.763674 + 0.645601i $$0.223393\pi$$
$$620$$ 0 0
$$621$$ −5.00000 −0.200643
$$622$$ 0 0
$$623$$ 3.00000 0.120192
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ −9.00000 −0.359425
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −17.0000 −0.676759 −0.338380 0.941010i $$-0.609879\pi$$
−0.338380 + 0.941010i $$0.609879\pi$$
$$632$$ 0 0
$$633$$ 19.0000 0.755182
$$634$$ 0 0
$$635$$ 8.00000 0.317470
$$636$$ 0 0
$$637$$ −4.00000 −0.158486
$$638$$ 0 0
$$639$$ −7.00000 −0.276916
$$640$$ 0 0
$$641$$ 26.0000 1.02694 0.513469 0.858108i $$-0.328360\pi$$
0.513469 + 0.858108i $$0.328360\pi$$
$$642$$ 0 0
$$643$$ −19.0000 −0.749287 −0.374643 0.927169i $$-0.622235\pi$$
−0.374643 + 0.927169i $$0.622235\pi$$
$$644$$ 0 0
$$645$$ 1.00000 0.0393750
$$646$$ 0 0
$$647$$ −3.00000 −0.117942 −0.0589711 0.998260i $$-0.518782\pi$$
−0.0589711 + 0.998260i $$0.518782\pi$$
$$648$$ 0 0
$$649$$ 18.0000 0.706562
$$650$$ 0 0
$$651$$ −3.00000 −0.117579
$$652$$ 0 0
$$653$$ −26.0000 −1.01746 −0.508729 0.860927i $$-0.669885\pi$$
−0.508729 + 0.860927i $$0.669885\pi$$
$$654$$ 0 0
$$655$$ 6.00000 0.234439
$$656$$ 0 0
$$657$$ 5.00000 0.195069
$$658$$ 0 0
$$659$$ 4.00000 0.155818 0.0779089 0.996960i $$-0.475176\pi$$
0.0779089 + 0.996960i $$0.475176\pi$$
$$660$$ 0 0
$$661$$ −14.0000 −0.544537 −0.272268 0.962221i $$-0.587774\pi$$
−0.272268 + 0.962221i $$0.587774\pi$$
$$662$$ 0 0
$$663$$ 8.00000 0.310694
$$664$$ 0 0
$$665$$ −9.00000 −0.349005
$$666$$ 0 0
$$667$$ −20.0000 −0.774403
$$668$$ 0 0
$$669$$ 6.00000 0.231973
$$670$$ 0 0
$$671$$ 6.00000 0.231627
$$672$$ 0 0
$$673$$ 26.0000 1.00223 0.501113 0.865382i $$-0.332924\pi$$
0.501113 + 0.865382i $$0.332924\pi$$
$$674$$ 0 0
$$675$$ 1.00000 0.0384900
$$676$$ 0 0
$$677$$ 27.0000 1.03769 0.518847 0.854867i $$-0.326361\pi$$
0.518847 + 0.854867i $$0.326361\pi$$
$$678$$ 0 0
$$679$$ −30.0000 −1.15129
$$680$$ 0 0
$$681$$ 27.0000 1.03464
$$682$$ 0 0
$$683$$ 19.0000 0.727015 0.363507 0.931591i $$-0.381579\pi$$
0.363507 + 0.931591i $$0.381579\pi$$
$$684$$ 0 0
$$685$$ 10.0000 0.382080
$$686$$ 0 0
$$687$$ 13.0000 0.495981
$$688$$ 0 0
$$689$$ −6.00000 −0.228582
$$690$$ 0 0
$$691$$ 31.0000 1.17930 0.589648 0.807661i $$-0.299267\pi$$
0.589648 + 0.807661i $$0.299267\pi$$
$$692$$ 0 0
$$693$$ −9.00000 −0.341882
$$694$$ 0 0
$$695$$ −14.0000 −0.531050
$$696$$ 0 0
$$697$$ −16.0000 −0.606043
$$698$$ 0 0
$$699$$ 15.0000 0.567352
$$700$$ 0 0
$$701$$ −21.0000 −0.793159 −0.396580 0.918000i $$-0.629803\pi$$
−0.396580 + 0.918000i $$0.629803\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 10.0000 0.376622
$$706$$ 0 0
$$707$$ −3.00000 −0.112827
$$708$$ 0 0
$$709$$ −25.0000 −0.938895 −0.469447 0.882960i $$-0.655547\pi$$
−0.469447 + 0.882960i $$0.655547\pi$$
$$710$$ 0 0
$$711$$ 1.00000 0.0375029
$$712$$ 0 0
$$713$$ 5.00000 0.187251
$$714$$ 0 0
$$715$$ −6.00000 −0.224387
$$716$$ 0 0
$$717$$ −12.0000 −0.448148
$$718$$ 0 0
$$719$$ −26.0000 −0.969636 −0.484818 0.874615i $$-0.661114\pi$$
−0.484818 + 0.874615i $$0.661114\pi$$
$$720$$ 0 0
$$721$$ −48.0000 −1.78761
$$722$$ 0 0
$$723$$ −18.0000 −0.669427
$$724$$ 0 0
$$725$$ 4.00000 0.148556
$$726$$ 0 0
$$727$$ −45.0000 −1.66896 −0.834479 0.551040i $$-0.814231\pi$$
−0.834479 + 0.551040i $$0.814231\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 4.00000 0.147945
$$732$$ 0 0
$$733$$ −18.0000 −0.664845 −0.332423 0.943131i $$-0.607866\pi$$
−0.332423 + 0.943131i $$0.607866\pi$$
$$734$$ 0 0
$$735$$ −2.00000 −0.0737711
$$736$$ 0 0
$$737$$ 6.00000 0.221013
$$738$$ 0 0
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 0 0
$$741$$ −6.00000 −0.220416
$$742$$ 0 0
$$743$$ 37.0000 1.35740 0.678699 0.734416i $$-0.262544\pi$$
0.678699 + 0.734416i $$0.262544\pi$$
$$744$$ 0 0
$$745$$ 11.0000 0.403009
$$746$$ 0 0
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ −27.0000 −0.986559
$$750$$ 0 0
$$751$$ 50.0000 1.82453 0.912263 0.409605i $$-0.134333\pi$$
0.912263 + 0.409605i $$0.134333\pi$$
$$752$$ 0 0
$$753$$ 12.0000 0.437304
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 50.0000 1.81728 0.908640 0.417579i $$-0.137121\pi$$
0.908640 + 0.417579i $$0.137121\pi$$
$$758$$ 0 0
$$759$$ 15.0000 0.544466
$$760$$ 0 0
$$761$$ 45.0000 1.63125 0.815624 0.578582i $$-0.196394\pi$$
0.815624 + 0.578582i $$0.196394\pi$$
$$762$$ 0 0
$$763$$ 60.0000 2.17215
$$764$$ 0 0
$$765$$ 4.00000 0.144620
$$766$$ 0 0
$$767$$ 12.0000 0.433295
$$768$$ 0 0
$$769$$ 9.00000 0.324548 0.162274 0.986746i $$-0.448117\pi$$
0.162274 + 0.986746i $$0.448117\pi$$
$$770$$ 0 0
$$771$$ −23.0000 −0.828325
$$772$$ 0 0
$$773$$ −31.0000 −1.11499 −0.557496 0.830179i $$-0.688238\pi$$
−0.557496 + 0.830179i $$0.688238\pi$$
$$774$$ 0 0
$$775$$ −1.00000 −0.0359211
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 12.0000 0.429945
$$780$$ 0 0
$$781$$ 21.0000 0.751439
$$782$$ 0 0
$$783$$ 4.00000 0.142948
$$784$$ 0 0
$$785$$ 5.00000 0.178458
$$786$$ 0 0
$$787$$ 35.0000 1.24762 0.623808 0.781578i $$-0.285585\pi$$
0.623808 + 0.781578i $$0.285585\pi$$
$$788$$ 0 0
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 27.0000 0.960009
$$792$$ 0 0
$$793$$ 4.00000 0.142044
$$794$$ 0 0
$$795$$ −3.00000 −0.106399
$$796$$ 0 0
$$797$$ 2.00000 0.0708436 0.0354218 0.999372i $$-0.488723\pi$$
0.0354218 + 0.999372i $$0.488723\pi$$
$$798$$ 0 0
$$799$$ 40.0000 1.41510
$$800$$ 0 0
$$801$$ 1.00000 0.0353333
$$802$$ 0 0
$$803$$ −15.0000 −0.529339
$$804$$ 0 0
$$805$$ 15.0000 0.528681
$$806$$ 0 0
$$807$$ 2.00000 0.0704033
$$808$$ 0 0
$$809$$ 17.0000 0.597688 0.298844 0.954302i $$-0.403399\pi$$
0.298844 + 0.954302i $$0.403399\pi$$
$$810$$ 0 0
$$811$$ 27.0000 0.948098 0.474049 0.880498i $$-0.342792\pi$$
0.474049 + 0.880498i $$0.342792\pi$$
$$812$$ 0 0
$$813$$ −13.0000 −0.455930
$$814$$ 0 0
$$815$$ 14.0000 0.490399
$$816$$ 0 0
$$817$$ −3.00000 −0.104957
$$818$$ 0 0
$$819$$ −6.00000 −0.209657
$$820$$ 0 0
$$821$$ 40.0000 1.39601 0.698005 0.716093i $$-0.254071\pi$$
0.698005 + 0.716093i $$0.254071\pi$$
$$822$$ 0 0
$$823$$ 18.0000 0.627441 0.313720 0.949515i $$-0.398425\pi$$
0.313720 + 0.949515i $$0.398425\pi$$
$$824$$ 0 0
$$825$$ −3.00000 −0.104447
$$826$$ 0 0
$$827$$ −20.0000 −0.695468 −0.347734 0.937593i $$-0.613049\pi$$
−0.347734 + 0.937593i $$0.613049\pi$$
$$828$$ 0 0
$$829$$ −35.0000 −1.21560 −0.607800 0.794090i $$-0.707948\pi$$
−0.607800 + 0.794090i $$0.707948\pi$$
$$830$$ 0 0
$$831$$ 12.0000 0.416275
$$832$$ 0 0
$$833$$ −8.00000 −0.277184
$$834$$ 0 0
$$835$$ −19.0000 −0.657522
$$836$$ 0 0
$$837$$ −1.00000 −0.0345651
$$838$$ 0 0
$$839$$ −51.0000 −1.76072 −0.880358 0.474310i $$-0.842698\pi$$
−0.880358 + 0.474310i $$0.842698\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ 0 0
$$843$$ 16.0000 0.551069
$$844$$ 0 0
$$845$$ 9.00000 0.309609
$$846$$ 0 0
$$847$$ −6.00000 −0.206162
$$848$$ 0 0
$$849$$ 24.0000 0.823678
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −41.0000 −1.40381 −0.701907 0.712269i $$-0.747668\pi$$
−0.701907 + 0.712269i $$0.747668\pi$$
$$854$$ 0 0
$$855$$ −3.00000 −0.102598
$$856$$ 0 0
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ −32.0000 −1.09183 −0.545913 0.837842i $$-0.683817\pi$$
−0.545913 + 0.837842i $$0.683817\pi$$
$$860$$ 0 0
$$861$$ 12.0000 0.408959
$$862$$ 0 0
$$863$$ −43.0000 −1.46374 −0.731869 0.681446i $$-0.761351\pi$$
−0.731869 + 0.681446i $$0.761351\pi$$
$$864$$ 0 0
$$865$$ 22.0000 0.748022
$$866$$ 0 0
$$867$$ −1.00000 −0.0339618
$$868$$ 0 0
$$869$$ −3.00000 −0.101768
$$870$$ 0 0
$$871$$ 4.00000 0.135535
$$872$$ 0 0
$$873$$ −10.0000 −0.338449
$$874$$ 0 0
$$875$$ −3.00000 −0.101419
$$876$$ 0 0
$$877$$ 46.0000 1.55331 0.776655 0.629926i $$-0.216915\pi$$
0.776655 + 0.629926i $$0.216915\pi$$
$$878$$ 0 0
$$879$$ 30.0000 1.01187
$$880$$ 0 0
$$881$$ 26.0000 0.875962 0.437981 0.898984i $$-0.355694\pi$$
0.437981 + 0.898984i $$0.355694\pi$$
$$882$$ 0 0
$$883$$ −11.0000 −0.370179 −0.185090 0.982722i $$-0.559258\pi$$
−0.185090 + 0.982722i $$0.559258\pi$$
$$884$$ 0 0
$$885$$ 6.00000 0.201688
$$886$$ 0 0
$$887$$ 46.0000 1.54453 0.772264 0.635301i $$-0.219124\pi$$
0.772264 + 0.635301i $$0.219124\pi$$
$$888$$ 0 0
$$889$$ −24.0000 −0.804934
$$890$$ 0 0
$$891$$ −3.00000 −0.100504
$$892$$ 0 0
$$893$$ −30.0000 −1.00391
$$894$$ 0 0
$$895$$ 4.00000 0.133705
$$896$$ 0 0
$$897$$ 10.0000 0.333890
$$898$$ 0 0
$$899$$ −4.00000 −0.133407
$$900$$ 0 0
$$901$$ −12.0000 −0.399778
$$902$$ 0 0
$$903$$ −3.00000 −0.0998337
$$904$$ 0 0
$$905$$ −5.00000 −0.166206
$$906$$ 0 0
$$907$$ 52.0000 1.72663 0.863316 0.504664i $$-0.168384\pi$$
0.863316 + 0.504664i $$0.168384\pi$$
$$908$$ 0 0
$$909$$ −1.00000 −0.0331679
$$910$$ 0 0
$$911$$ −20.0000 −0.662630 −0.331315 0.943520i $$-0.607492\pi$$
−0.331315 + 0.943520i $$0.607492\pi$$
$$912$$ 0 0
$$913$$ 36.0000 1.19143
$$914$$ 0 0
$$915$$ 2.00000 0.0661180
$$916$$ 0 0
$$917$$ −18.0000 −0.594412
$$918$$ 0 0
$$919$$ 38.0000 1.25350 0.626752 0.779219i $$-0.284384\pi$$
0.626752 + 0.779219i $$0.284384\pi$$
$$920$$ 0 0
$$921$$ −16.0000 −0.527218
$$922$$ 0 0
$$923$$ 14.0000 0.460816
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −16.0000 −0.525509
$$928$$ 0 0
$$929$$ −41.0000 −1.34517 −0.672583 0.740022i $$-0.734815\pi$$
−0.672583 + 0.740022i $$0.734815\pi$$
$$930$$ 0 0
$$931$$ 6.00000 0.196642
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −12.0000 −0.392442
$$936$$ 0 0
$$937$$ −52.0000 −1.69877 −0.849383 0.527777i $$-0.823026\pi$$
−0.849383 + 0.527777i $$0.823026\pi$$
$$938$$ 0 0
$$939$$ 30.0000 0.979013
$$940$$ 0 0
$$941$$ 40.0000 1.30396 0.651981 0.758235i $$-0.273938\pi$$
0.651981 + 0.758235i $$0.273938\pi$$
$$942$$ 0 0
$$943$$ −20.0000 −0.651290
$$944$$ 0 0
$$945$$ −3.00000 −0.0975900
$$946$$ 0 0
$$947$$ −30.0000 −0.974869 −0.487435 0.873160i $$-0.662067\pi$$
−0.487435 + 0.873160i $$0.662067\pi$$
$$948$$ 0 0
$$949$$ −10.0000 −0.324614
$$950$$ 0 0
$$951$$ −8.00000 −0.259418
$$952$$ 0 0
$$953$$ −52.0000 −1.68445 −0.842223 0.539130i $$-0.818753\pi$$
−0.842223 + 0.539130i $$0.818753\pi$$
$$954$$ 0 0
$$955$$ 16.0000 0.517748
$$956$$ 0 0
$$957$$ −12.0000 −0.387905
$$958$$ 0 0
$$959$$ −30.0000 −0.968751
$$960$$ 0 0
$$961$$ 1.00000 0.0322581
$$962$$ 0 0
$$963$$ −9.00000 −0.290021
$$964$$ 0 0
$$965$$ 6.00000 0.193147
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ 0 0
$$969$$ −12.0000 −0.385496
$$970$$ 0 0
$$971$$ 54.0000 1.73294 0.866471 0.499227i $$-0.166383\pi$$
0.866471 + 0.499227i $$0.166383\pi$$
$$972$$ 0 0
$$973$$ 42.0000 1.34646
$$974$$ 0 0
$$975$$ −2.00000 −0.0640513
$$976$$ 0 0
$$977$$ 38.0000 1.21573 0.607864 0.794041i $$-0.292027\pi$$
0.607864 + 0.794041i $$0.292027\pi$$
$$978$$ 0 0
$$979$$ −3.00000 −0.0958804
$$980$$ 0 0
$$981$$ 20.0000 0.638551
$$982$$ 0 0
$$983$$ 56.0000 1.78612 0.893061 0.449935i $$-0.148553\pi$$
0.893061 + 0.449935i $$0.148553\pi$$
$$984$$ 0 0
$$985$$ 6.00000 0.191176
$$986$$ 0 0
$$987$$ −30.0000 −0.954911
$$988$$ 0 0
$$989$$ 5.00000 0.158991
$$990$$ 0 0
$$991$$ 25.0000 0.794151 0.397076 0.917786i $$-0.370025\pi$$
0.397076 + 0.917786i $$0.370025\pi$$
$$992$$ 0 0
$$993$$ −12.0000 −0.380808
$$994$$ 0 0
$$995$$ 7.00000 0.221915
$$996$$ 0 0
$$997$$ −42.0000 −1.33015 −0.665077 0.746775i $$-0.731601\pi$$
−0.665077 + 0.746775i $$0.731601\pi$$
$$998$$ 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 7440.2.a.v.1.1 1
4.3 odd 2 930.2.a.a.1.1 1
12.11 even 2 2790.2.a.y.1.1 1
20.3 even 4 4650.2.d.y.3349.2 2
20.7 even 4 4650.2.d.y.3349.1 2
20.19 odd 2 4650.2.a.bv.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.a.1.1 1 4.3 odd 2
2790.2.a.y.1.1 1 12.11 even 2
4650.2.a.bv.1.1 1 20.19 odd 2
4650.2.d.y.3349.1 2 20.7 even 4
4650.2.d.y.3349.2 2 20.3 even 4
7440.2.a.v.1.1 1 1.1 even 1 trivial