# Properties

 Label 1386.2.a.i.1.1 Level $1386$ Weight $2$ Character 1386.1 Self dual yes Analytic conductor $11.067$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$11.0672657201$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 462) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1386.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{11} -2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +6.00000 q^{19} +1.00000 q^{22} +4.00000 q^{23} -5.00000 q^{25} -2.00000 q^{26} -1.00000 q^{28} +10.0000 q^{29} +6.00000 q^{31} +1.00000 q^{32} +4.00000 q^{34} -6.00000 q^{37} +6.00000 q^{38} +12.0000 q^{41} -8.00000 q^{43} +1.00000 q^{44} +4.00000 q^{46} -2.00000 q^{47} +1.00000 q^{49} -5.00000 q^{50} -2.00000 q^{52} -6.00000 q^{53} -1.00000 q^{56} +10.0000 q^{58} +8.00000 q^{59} +6.00000 q^{61} +6.00000 q^{62} +1.00000 q^{64} -4.00000 q^{67} +4.00000 q^{68} -12.0000 q^{73} -6.00000 q^{74} +6.00000 q^{76} -1.00000 q^{77} +12.0000 q^{82} -14.0000 q^{83} -8.00000 q^{86} +1.00000 q^{88} -10.0000 q^{89} +2.00000 q^{91} +4.00000 q^{92} -2.00000 q^{94} +10.0000 q^{97} +1.00000 q^{98} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.00000 0.301511
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ 0 0
$$19$$ 6.00000 1.37649 0.688247 0.725476i $$-0.258380\pi$$
0.688247 + 0.725476i $$0.258380\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ −2.00000 −0.392232
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ 10.0000 1.85695 0.928477 0.371391i $$-0.121119\pi$$
0.928477 + 0.371391i $$0.121119\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 4.00000 0.685994
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −6.00000 −0.986394 −0.493197 0.869918i $$-0.664172\pi$$
−0.493197 + 0.869918i $$0.664172\pi$$
$$38$$ 6.00000 0.973329
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 12.0000 1.87409 0.937043 0.349215i $$-0.113552\pi$$
0.937043 + 0.349215i $$0.113552\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 1.00000 0.150756
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ −2.00000 −0.291730 −0.145865 0.989305i $$-0.546597\pi$$
−0.145865 + 0.989305i $$0.546597\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ −5.00000 −0.707107
$$51$$ 0 0
$$52$$ −2.00000 −0.277350
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −1.00000 −0.133631
$$57$$ 0 0
$$58$$ 10.0000 1.31306
$$59$$ 8.00000 1.04151 0.520756 0.853706i $$-0.325650\pi$$
0.520756 + 0.853706i $$0.325650\pi$$
$$60$$ 0 0
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 6.00000 0.762001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −4.00000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ 4.00000 0.485071
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −12.0000 −1.40449 −0.702247 0.711934i $$-0.747820\pi$$
−0.702247 + 0.711934i $$0.747820\pi$$
$$74$$ −6.00000 −0.697486
$$75$$ 0 0
$$76$$ 6.00000 0.688247
$$77$$ −1.00000 −0.113961
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 12.0000 1.32518
$$83$$ −14.0000 −1.53670 −0.768350 0.640030i $$-0.778922\pi$$
−0.768350 + 0.640030i $$0.778922\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −8.00000 −0.862662
$$87$$ 0 0
$$88$$ 1.00000 0.106600
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 4.00000 0.417029
$$93$$ 0 0
$$94$$ −2.00000 −0.206284
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ −5.00000 −0.500000
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 0 0
$$103$$ 10.0000 0.985329 0.492665 0.870219i $$-0.336023\pi$$
0.492665 + 0.870219i $$0.336023\pi$$
$$104$$ −2.00000 −0.196116
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ −8.00000 −0.773389 −0.386695 0.922208i $$-0.626383\pi$$
−0.386695 + 0.922208i $$0.626383\pi$$
$$108$$ 0 0
$$109$$ 18.0000 1.72409 0.862044 0.506834i $$-0.169184\pi$$
0.862044 + 0.506834i $$0.169184\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −1.00000 −0.0944911
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 10.0000 0.928477
$$117$$ 0 0
$$118$$ 8.00000 0.736460
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ 1.00000 0.0909091
$$122$$ 6.00000 0.543214
$$123$$ 0 0
$$124$$ 6.00000 0.538816
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −16.0000 −1.41977 −0.709885 0.704317i $$-0.751253\pi$$
−0.709885 + 0.704317i $$0.751253\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −10.0000 −0.873704 −0.436852 0.899533i $$-0.643907\pi$$
−0.436852 + 0.899533i $$0.643907\pi$$
$$132$$ 0 0
$$133$$ −6.00000 −0.520266
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ 4.00000 0.342997
$$137$$ 10.0000 0.854358 0.427179 0.904167i $$-0.359507\pi$$
0.427179 + 0.904167i $$0.359507\pi$$
$$138$$ 0 0
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −2.00000 −0.167248
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −12.0000 −0.993127
$$147$$ 0 0
$$148$$ −6.00000 −0.493197
$$149$$ −10.0000 −0.819232 −0.409616 0.912258i $$-0.634337\pi$$
−0.409616 + 0.912258i $$0.634337\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 6.00000 0.486664
$$153$$ 0 0
$$154$$ −1.00000 −0.0805823
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 12.0000 0.957704 0.478852 0.877896i $$-0.341053\pi$$
0.478852 + 0.877896i $$0.341053\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −4.00000 −0.315244
$$162$$ 0 0
$$163$$ 12.0000 0.939913 0.469956 0.882690i $$-0.344270\pi$$
0.469956 + 0.882690i $$0.344270\pi$$
$$164$$ 12.0000 0.937043
$$165$$ 0 0
$$166$$ −14.0000 −1.08661
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −8.00000 −0.609994
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ 0 0
$$175$$ 5.00000 0.377964
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ −10.0000 −0.749532
$$179$$ −20.0000 −1.49487 −0.747435 0.664335i $$-0.768715\pi$$
−0.747435 + 0.664335i $$0.768715\pi$$
$$180$$ 0 0
$$181$$ −8.00000 −0.594635 −0.297318 0.954779i $$-0.596092\pi$$
−0.297318 + 0.954779i $$0.596092\pi$$
$$182$$ 2.00000 0.148250
$$183$$ 0 0
$$184$$ 4.00000 0.294884
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 4.00000 0.292509
$$188$$ −2.00000 −0.145865
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ −22.0000 −1.58359 −0.791797 0.610784i $$-0.790854\pi$$
−0.791797 + 0.610784i $$0.790854\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ 10.0000 0.708881 0.354441 0.935079i $$-0.384671\pi$$
0.354441 + 0.935079i $$0.384671\pi$$
$$200$$ −5.00000 −0.353553
$$201$$ 0 0
$$202$$ 6.00000 0.422159
$$203$$ −10.0000 −0.701862
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 10.0000 0.696733
$$207$$ 0 0
$$208$$ −2.00000 −0.138675
$$209$$ 6.00000 0.415029
$$210$$ 0 0
$$211$$ −8.00000 −0.550743 −0.275371 0.961338i $$-0.588801\pi$$
−0.275371 + 0.961338i $$0.588801\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 0 0
$$214$$ −8.00000 −0.546869
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −6.00000 −0.407307
$$218$$ 18.0000 1.21911
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −8.00000 −0.538138
$$222$$ 0 0
$$223$$ −2.00000 −0.133930 −0.0669650 0.997755i $$-0.521332\pi$$
−0.0669650 + 0.997755i $$0.521332\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 0 0
$$226$$ 2.00000 0.133038
$$227$$ 14.0000 0.929213 0.464606 0.885517i $$-0.346196\pi$$
0.464606 + 0.885517i $$0.346196\pi$$
$$228$$ 0 0
$$229$$ 24.0000 1.58596 0.792982 0.609245i $$-0.208527\pi$$
0.792982 + 0.609245i $$0.208527\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 10.0000 0.656532
$$233$$ 26.0000 1.70332 0.851658 0.524097i $$-0.175597\pi$$
0.851658 + 0.524097i $$0.175597\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 8.00000 0.520756
$$237$$ 0 0
$$238$$ −4.00000 −0.259281
$$239$$ 8.00000 0.517477 0.258738 0.965947i $$-0.416693\pi$$
0.258738 + 0.965947i $$0.416693\pi$$
$$240$$ 0 0
$$241$$ −28.0000 −1.80364 −0.901819 0.432113i $$-0.857768\pi$$
−0.901819 + 0.432113i $$0.857768\pi$$
$$242$$ 1.00000 0.0642824
$$243$$ 0 0
$$244$$ 6.00000 0.384111
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −12.0000 −0.763542
$$248$$ 6.00000 0.381000
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −8.00000 −0.504956 −0.252478 0.967603i $$-0.581245\pi$$
−0.252478 + 0.967603i $$0.581245\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ −16.0000 −1.00393
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 0 0
$$259$$ 6.00000 0.372822
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −10.0000 −0.617802
$$263$$ −16.0000 −0.986602 −0.493301 0.869859i $$-0.664210\pi$$
−0.493301 + 0.869859i $$0.664210\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −6.00000 −0.367884
$$267$$ 0 0
$$268$$ −4.00000 −0.244339
$$269$$ −24.0000 −1.46331 −0.731653 0.681677i $$-0.761251\pi$$
−0.731653 + 0.681677i $$0.761251\pi$$
$$270$$ 0 0
$$271$$ −4.00000 −0.242983 −0.121491 0.992592i $$-0.538768\pi$$
−0.121491 + 0.992592i $$0.538768\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ 10.0000 0.604122
$$275$$ −5.00000 −0.301511
$$276$$ 0 0
$$277$$ −22.0000 −1.32185 −0.660926 0.750451i $$-0.729836\pi$$
−0.660926 + 0.750451i $$0.729836\pi$$
$$278$$ −14.0000 −0.839664
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −30.0000 −1.78965 −0.894825 0.446417i $$-0.852700\pi$$
−0.894825 + 0.446417i $$0.852700\pi$$
$$282$$ 0 0
$$283$$ 2.00000 0.118888 0.0594438 0.998232i $$-0.481067\pi$$
0.0594438 + 0.998232i $$0.481067\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −2.00000 −0.118262
$$287$$ −12.0000 −0.708338
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −12.0000 −0.702247
$$293$$ −6.00000 −0.350524 −0.175262 0.984522i $$-0.556077\pi$$
−0.175262 + 0.984522i $$0.556077\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −6.00000 −0.348743
$$297$$ 0 0
$$298$$ −10.0000 −0.579284
$$299$$ −8.00000 −0.462652
$$300$$ 0 0
$$301$$ 8.00000 0.461112
$$302$$ −16.0000 −0.920697
$$303$$ 0 0
$$304$$ 6.00000 0.344124
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −14.0000 −0.799022 −0.399511 0.916728i $$-0.630820\pi$$
−0.399511 + 0.916728i $$0.630820\pi$$
$$308$$ −1.00000 −0.0569803
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 10.0000 0.567048 0.283524 0.958965i $$-0.408496\pi$$
0.283524 + 0.958965i $$0.408496\pi$$
$$312$$ 0 0
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 12.0000 0.677199
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ 10.0000 0.559893
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −4.00000 −0.222911
$$323$$ 24.0000 1.33540
$$324$$ 0 0
$$325$$ 10.0000 0.554700
$$326$$ 12.0000 0.664619
$$327$$ 0 0
$$328$$ 12.0000 0.662589
$$329$$ 2.00000 0.110264
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ −14.0000 −0.768350
$$333$$ 0 0
$$334$$ −12.0000 −0.656611
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 22.0000 1.19842 0.599208 0.800593i $$-0.295482\pi$$
0.599208 + 0.800593i $$0.295482\pi$$
$$338$$ −9.00000 −0.489535
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 6.00000 0.324918
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ −8.00000 −0.431331
$$345$$ 0 0
$$346$$ 18.0000 0.967686
$$347$$ −16.0000 −0.858925 −0.429463 0.903085i $$-0.641297\pi$$
−0.429463 + 0.903085i $$0.641297\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 5.00000 0.267261
$$351$$ 0 0
$$352$$ 1.00000 0.0533002
$$353$$ −10.0000 −0.532246 −0.266123 0.963939i $$-0.585743\pi$$
−0.266123 + 0.963939i $$0.585743\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −10.0000 −0.529999
$$357$$ 0 0
$$358$$ −20.0000 −1.05703
$$359$$ −8.00000 −0.422224 −0.211112 0.977462i $$-0.567708\pi$$
−0.211112 + 0.977462i $$0.567708\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ −8.00000 −0.420471
$$363$$ 0 0
$$364$$ 2.00000 0.104828
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −10.0000 −0.521996 −0.260998 0.965339i $$-0.584052\pi$$
−0.260998 + 0.965339i $$0.584052\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 6.00000 0.311504
$$372$$ 0 0
$$373$$ 22.0000 1.13912 0.569558 0.821951i $$-0.307114\pi$$
0.569558 + 0.821951i $$0.307114\pi$$
$$374$$ 4.00000 0.206835
$$375$$ 0 0
$$376$$ −2.00000 −0.103142
$$377$$ −20.0000 −1.03005
$$378$$ 0 0
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 12.0000 0.613973
$$383$$ 10.0000 0.510976 0.255488 0.966812i $$-0.417764\pi$$
0.255488 + 0.966812i $$0.417764\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −22.0000 −1.11977
$$387$$ 0 0
$$388$$ 10.0000 0.507673
$$389$$ −2.00000 −0.101404 −0.0507020 0.998714i $$-0.516146\pi$$
−0.0507020 + 0.998714i $$0.516146\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ −6.00000 −0.302276
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −4.00000 −0.200754 −0.100377 0.994949i $$-0.532005\pi$$
−0.100377 + 0.994949i $$0.532005\pi$$
$$398$$ 10.0000 0.501255
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ 34.0000 1.69788 0.848939 0.528490i $$-0.177242\pi$$
0.848939 + 0.528490i $$0.177242\pi$$
$$402$$ 0 0
$$403$$ −12.0000 −0.597763
$$404$$ 6.00000 0.298511
$$405$$ 0 0
$$406$$ −10.0000 −0.496292
$$407$$ −6.00000 −0.297409
$$408$$ 0 0
$$409$$ 24.0000 1.18672 0.593362 0.804936i $$-0.297800\pi$$
0.593362 + 0.804936i $$0.297800\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 10.0000 0.492665
$$413$$ −8.00000 −0.393654
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −2.00000 −0.0980581
$$417$$ 0 0
$$418$$ 6.00000 0.293470
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ 0 0
$$421$$ 6.00000 0.292422 0.146211 0.989253i $$-0.453292\pi$$
0.146211 + 0.989253i $$0.453292\pi$$
$$422$$ −8.00000 −0.389434
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ −20.0000 −0.970143
$$426$$ 0 0
$$427$$ −6.00000 −0.290360
$$428$$ −8.00000 −0.386695
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −8.00000 −0.385346 −0.192673 0.981263i $$-0.561716\pi$$
−0.192673 + 0.981263i $$0.561716\pi$$
$$432$$ 0 0
$$433$$ −22.0000 −1.05725 −0.528626 0.848855i $$-0.677293\pi$$
−0.528626 + 0.848855i $$0.677293\pi$$
$$434$$ −6.00000 −0.288009
$$435$$ 0 0
$$436$$ 18.0000 0.862044
$$437$$ 24.0000 1.14808
$$438$$ 0 0
$$439$$ 28.0000 1.33637 0.668184 0.743996i $$-0.267072\pi$$
0.668184 + 0.743996i $$0.267072\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −8.00000 −0.380521
$$443$$ −12.0000 −0.570137 −0.285069 0.958507i $$-0.592016\pi$$
−0.285069 + 0.958507i $$0.592016\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −2.00000 −0.0947027
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ 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
$$452$$ 2.00000 0.0940721
$$453$$ 0 0
$$454$$ 14.0000 0.657053
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −6.00000 −0.280668 −0.140334 0.990104i $$-0.544818\pi$$
−0.140334 + 0.990104i $$0.544818\pi$$
$$458$$ 24.0000 1.12145
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ 10.0000 0.464238
$$465$$ 0 0
$$466$$ 26.0000 1.20443
$$467$$ −4.00000 −0.185098 −0.0925490 0.995708i $$-0.529501\pi$$
−0.0925490 + 0.995708i $$0.529501\pi$$
$$468$$ 0 0
$$469$$ 4.00000 0.184703
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 8.00000 0.368230
$$473$$ −8.00000 −0.367840
$$474$$ 0 0
$$475$$ −30.0000 −1.37649
$$476$$ −4.00000 −0.183340
$$477$$ 0 0
$$478$$ 8.00000 0.365911
$$479$$ 8.00000 0.365529 0.182765 0.983157i $$-0.441495\pi$$
0.182765 + 0.983157i $$0.441495\pi$$
$$480$$ 0 0
$$481$$ 12.0000 0.547153
$$482$$ −28.0000 −1.27537
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −28.0000 −1.26880 −0.634401 0.773004i $$-0.718753\pi$$
−0.634401 + 0.773004i $$0.718753\pi$$
$$488$$ 6.00000 0.271607
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ 0 0
$$493$$ 40.0000 1.80151
$$494$$ −12.0000 −0.539906
$$495$$ 0 0
$$496$$ 6.00000 0.269408
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −8.00000 −0.357057
$$503$$ 4.00000 0.178351 0.0891756 0.996016i $$-0.471577\pi$$
0.0891756 + 0.996016i $$0.471577\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 4.00000 0.177822
$$507$$ 0 0
$$508$$ −16.0000 −0.709885
$$509$$ 32.0000 1.41838 0.709188 0.705020i $$-0.249062\pi$$
0.709188 + 0.705020i $$0.249062\pi$$
$$510$$ 0 0
$$511$$ 12.0000 0.530849
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 6.00000 0.264649
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −2.00000 −0.0879599
$$518$$ 6.00000 0.263625
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 30.0000 1.31432 0.657162 0.753749i $$-0.271757\pi$$
0.657162 + 0.753749i $$0.271757\pi$$
$$522$$ 0 0
$$523$$ −22.0000 −0.961993 −0.480996 0.876723i $$-0.659725\pi$$
−0.480996 + 0.876723i $$0.659725\pi$$
$$524$$ −10.0000 −0.436852
$$525$$ 0 0
$$526$$ −16.0000 −0.697633
$$527$$ 24.0000 1.04546
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −6.00000 −0.260133
$$533$$ −24.0000 −1.03956
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −4.00000 −0.172774
$$537$$ 0 0
$$538$$ −24.0000 −1.03471
$$539$$ 1.00000 0.0430730
$$540$$ 0 0
$$541$$ −34.0000 −1.46177 −0.730887 0.682498i $$-0.760893\pi$$
−0.730887 + 0.682498i $$0.760893\pi$$
$$542$$ −4.00000 −0.171815
$$543$$ 0 0
$$544$$ 4.00000 0.171499
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 28.0000 1.19719 0.598597 0.801050i $$-0.295725\pi$$
0.598597 + 0.801050i $$0.295725\pi$$
$$548$$ 10.0000 0.427179
$$549$$ 0 0
$$550$$ −5.00000 −0.213201
$$551$$ 60.0000 2.55609
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −22.0000 −0.934690
$$555$$ 0 0
$$556$$ −14.0000 −0.593732
$$557$$ −30.0000 −1.27114 −0.635570 0.772043i $$-0.719235\pi$$
−0.635570 + 0.772043i $$0.719235\pi$$
$$558$$ 0 0
$$559$$ 16.0000 0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −30.0000 −1.26547
$$563$$ 6.00000 0.252870 0.126435 0.991975i $$-0.459647\pi$$
0.126435 + 0.991975i $$0.459647\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 2.00000 0.0840663
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 42.0000 1.76073 0.880366 0.474295i $$-0.157297\pi$$
0.880366 + 0.474295i $$0.157297\pi$$
$$570$$ 0 0
$$571$$ −44.0000 −1.84134 −0.920671 0.390339i $$-0.872358\pi$$
−0.920671 + 0.390339i $$0.872358\pi$$
$$572$$ −2.00000 −0.0836242
$$573$$ 0 0
$$574$$ −12.0000 −0.500870
$$575$$ −20.0000 −0.834058
$$576$$ 0 0
$$577$$ 14.0000 0.582828 0.291414 0.956597i $$-0.405874\pi$$
0.291414 + 0.956597i $$0.405874\pi$$
$$578$$ −1.00000 −0.0415945
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 14.0000 0.580818
$$582$$ 0 0
$$583$$ −6.00000 −0.248495
$$584$$ −12.0000 −0.496564
$$585$$ 0 0
$$586$$ −6.00000 −0.247858
$$587$$ 32.0000 1.32078 0.660391 0.750922i $$-0.270391\pi$$
0.660391 + 0.750922i $$0.270391\pi$$
$$588$$ 0 0
$$589$$ 36.0000 1.48335
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −6.00000 −0.246598
$$593$$ 4.00000 0.164260 0.0821302 0.996622i $$-0.473828\pi$$
0.0821302 + 0.996622i $$0.473828\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −10.0000 −0.409616
$$597$$ 0 0
$$598$$ −8.00000 −0.327144
$$599$$ 16.0000 0.653742 0.326871 0.945069i $$-0.394006\pi$$
0.326871 + 0.945069i $$0.394006\pi$$
$$600$$ 0 0
$$601$$ −8.00000 −0.326327 −0.163163 0.986599i $$-0.552170\pi$$
−0.163163 + 0.986599i $$0.552170\pi$$
$$602$$ 8.00000 0.326056
$$603$$ 0 0
$$604$$ −16.0000 −0.651031
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 24.0000 0.974130 0.487065 0.873366i $$-0.338067\pi$$
0.487065 + 0.873366i $$0.338067\pi$$
$$608$$ 6.00000 0.243332
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 4.00000 0.161823
$$612$$ 0 0
$$613$$ 22.0000 0.888572 0.444286 0.895885i $$-0.353457\pi$$
0.444286 + 0.895885i $$0.353457\pi$$
$$614$$ −14.0000 −0.564994
$$615$$ 0 0
$$616$$ −1.00000 −0.0402911
$$617$$ −2.00000 −0.0805170 −0.0402585 0.999189i $$-0.512818\pi$$
−0.0402585 + 0.999189i $$0.512818\pi$$
$$618$$ 0 0
$$619$$ 12.0000 0.482321 0.241160 0.970485i $$-0.422472\pi$$
0.241160 + 0.970485i $$0.422472\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 10.0000 0.400963
$$623$$ 10.0000 0.400642
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 6.00000 0.239808
$$627$$ 0 0
$$628$$ 12.0000 0.478852
$$629$$ −24.0000 −0.956943
$$630$$ 0 0
$$631$$ −44.0000 −1.75161 −0.875806 0.482663i $$-0.839670\pi$$
−0.875806 + 0.482663i $$0.839670\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 18.0000 0.714871
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −2.00000 −0.0792429
$$638$$ 10.0000 0.395904
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 38.0000 1.50091 0.750455 0.660922i $$-0.229834\pi$$
0.750455 + 0.660922i $$0.229834\pi$$
$$642$$ 0 0
$$643$$ −16.0000 −0.630978 −0.315489 0.948929i $$-0.602169\pi$$
−0.315489 + 0.948929i $$0.602169\pi$$
$$644$$ −4.00000 −0.157622
$$645$$ 0 0
$$646$$ 24.0000 0.944267
$$647$$ 10.0000 0.393141 0.196570 0.980490i $$-0.437020\pi$$
0.196570 + 0.980490i $$0.437020\pi$$
$$648$$ 0 0
$$649$$ 8.00000 0.314027
$$650$$ 10.0000 0.392232
$$651$$ 0 0
$$652$$ 12.0000 0.469956
$$653$$ 6.00000 0.234798 0.117399 0.993085i $$-0.462544\pi$$
0.117399 + 0.993085i $$0.462544\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 12.0000 0.468521
$$657$$ 0 0
$$658$$ 2.00000 0.0779681
$$659$$ 16.0000 0.623272 0.311636 0.950202i $$-0.399123\pi$$
0.311636 + 0.950202i $$0.399123\pi$$
$$660$$ 0 0
$$661$$ −32.0000 −1.24466 −0.622328 0.782757i $$-0.713813\pi$$
−0.622328 + 0.782757i $$0.713813\pi$$
$$662$$ −20.0000 −0.777322
$$663$$ 0 0
$$664$$ −14.0000 −0.543305
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 40.0000 1.54881
$$668$$ −12.0000 −0.464294
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 6.00000 0.231627
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ 22.0000 0.847408
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −6.00000 −0.230599 −0.115299 0.993331i $$-0.536783\pi$$
−0.115299 + 0.993331i $$0.536783\pi$$
$$678$$ 0 0
$$679$$ −10.0000 −0.383765
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 6.00000 0.229752
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −1.00000 −0.0381802
$$687$$ 0 0
$$688$$ −8.00000 −0.304997
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ −40.0000 −1.52167 −0.760836 0.648944i $$-0.775211\pi$$
−0.760836 + 0.648944i $$0.775211\pi$$
$$692$$ 18.0000 0.684257
$$693$$ 0 0
$$694$$ −16.0000 −0.607352
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 48.0000 1.81813
$$698$$ 2.00000 0.0757011
$$699$$ 0 0
$$700$$ 5.00000 0.188982
$$701$$ −50.0000 −1.88847 −0.944237 0.329267i $$-0.893198\pi$$
−0.944237 + 0.329267i $$0.893198\pi$$
$$702$$ 0 0
$$703$$ −36.0000 −1.35777
$$704$$ 1.00000 0.0376889
$$705$$ 0 0
$$706$$ −10.0000 −0.376355
$$707$$ −6.00000 −0.225653
$$708$$ 0 0
$$709$$ −6.00000 −0.225335 −0.112667 0.993633i $$-0.535939\pi$$
−0.112667 + 0.993633i $$0.535939\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −10.0000 −0.374766
$$713$$ 24.0000 0.898807
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −20.0000 −0.747435
$$717$$ 0 0
$$718$$ −8.00000 −0.298557
$$719$$ −38.0000 −1.41716 −0.708580 0.705630i $$-0.750664\pi$$
−0.708580 + 0.705630i $$0.750664\pi$$
$$720$$ 0 0
$$721$$ −10.0000 −0.372419
$$722$$ 17.0000 0.632674
$$723$$ 0 0
$$724$$ −8.00000 −0.297318
$$725$$ −50.0000 −1.85695
$$726$$ 0 0
$$727$$ −34.0000 −1.26099 −0.630495 0.776193i $$-0.717148\pi$$
−0.630495 + 0.776193i $$0.717148\pi$$
$$728$$ 2.00000 0.0741249
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −32.0000 −1.18356
$$732$$ 0 0
$$733$$ 14.0000 0.517102 0.258551 0.965998i $$-0.416755\pi$$
0.258551 + 0.965998i $$0.416755\pi$$
$$734$$ −10.0000 −0.369107
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ −4.00000 −0.147342
$$738$$ 0 0
$$739$$ 28.0000 1.03000 0.514998 0.857191i $$-0.327793\pi$$
0.514998 + 0.857191i $$0.327793\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 6.00000 0.220267
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 22.0000 0.805477
$$747$$ 0 0
$$748$$ 4.00000 0.146254
$$749$$ 8.00000 0.292314
$$750$$ 0 0
$$751$$ 44.0000 1.60558 0.802791 0.596260i $$-0.203347\pi$$
0.802791 + 0.596260i $$0.203347\pi$$
$$752$$ −2.00000 −0.0729325
$$753$$ 0 0
$$754$$ −20.0000 −0.728357
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 50.0000 1.81728 0.908640 0.417579i $$-0.137121\pi$$
0.908640 + 0.417579i $$0.137121\pi$$
$$758$$ −4.00000 −0.145287
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 48.0000 1.74000 0.869999 0.493053i $$-0.164119\pi$$
0.869999 + 0.493053i $$0.164119\pi$$
$$762$$ 0 0
$$763$$ −18.0000 −0.651644
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ 10.0000 0.361315
$$767$$ −16.0000 −0.577727
$$768$$ 0 0
$$769$$ −40.0000 −1.44244 −0.721218 0.692708i $$-0.756418\pi$$
−0.721218 + 0.692708i $$0.756418\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −22.0000 −0.791797
$$773$$ 28.0000 1.00709 0.503545 0.863969i $$-0.332029\pi$$
0.503545 + 0.863969i $$0.332029\pi$$
$$774$$ 0 0
$$775$$ −30.0000 −1.07763
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ −2.00000 −0.0717035
$$779$$ 72.0000 2.57967
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 16.0000 0.572159
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 22.0000 0.784215 0.392108 0.919919i $$-0.371746\pi$$
0.392108 + 0.919919i $$0.371746\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −2.00000 −0.0711118
$$792$$ 0 0
$$793$$ −12.0000 −0.426132
$$794$$ −4.00000 −0.141955
$$795$$ 0 0
$$796$$ 10.0000 0.354441
$$797$$ −12.0000 −0.425062 −0.212531 0.977154i $$-0.568171\pi$$
−0.212531 + 0.977154i $$0.568171\pi$$
$$798$$ 0 0
$$799$$ −8.00000 −0.283020
$$800$$ −5.00000 −0.176777
$$801$$ 0 0
$$802$$ 34.0000 1.20058
$$803$$ −12.0000 −0.423471
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −12.0000 −0.422682
$$807$$ 0 0
$$808$$ 6.00000 0.211079
$$809$$ 30.0000 1.05474 0.527372 0.849635i $$-0.323177\pi$$
0.527372 + 0.849635i $$0.323177\pi$$
$$810$$ 0 0
$$811$$ 2.00000 0.0702295 0.0351147 0.999383i $$-0.488820\pi$$
0.0351147 + 0.999383i $$0.488820\pi$$
$$812$$ −10.0000 −0.350931
$$813$$ 0 0
$$814$$ −6.00000 −0.210300
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −48.0000 −1.67931
$$818$$ 24.0000 0.839140
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −10.0000 −0.349002 −0.174501 0.984657i $$-0.555831\pi$$
−0.174501 + 0.984657i $$0.555831\pi$$
$$822$$ 0 0
$$823$$ 44.0000 1.53374 0.766872 0.641800i $$-0.221812\pi$$
0.766872 + 0.641800i $$0.221812\pi$$
$$824$$ 10.0000 0.348367
$$825$$ 0 0
$$826$$ −8.00000 −0.278356
$$827$$ 12.0000 0.417281 0.208640 0.977992i $$-0.433096\pi$$
0.208640 + 0.977992i $$0.433096\pi$$
$$828$$ 0 0
$$829$$ 56.0000 1.94496 0.972480 0.232986i $$-0.0748495\pi$$
0.972480 + 0.232986i $$0.0748495\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −2.00000 −0.0693375
$$833$$ 4.00000 0.138592
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 6.00000 0.207514
$$837$$ 0 0
$$838$$ −28.0000 −0.967244
$$839$$ −14.0000 −0.483334 −0.241667 0.970359i $$-0.577694\pi$$
−0.241667 + 0.970359i $$0.577694\pi$$
$$840$$ 0 0
$$841$$ 71.0000 2.44828
$$842$$ 6.00000 0.206774
$$843$$ 0 0
$$844$$ −8.00000 −0.275371
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −1.00000 −0.0343604
$$848$$ −6.00000 −0.206041
$$849$$ 0 0
$$850$$ −20.0000 −0.685994
$$851$$ −24.0000 −0.822709
$$852$$ 0 0
$$853$$ −18.0000 −0.616308 −0.308154 0.951336i $$-0.599711\pi$$
−0.308154 + 0.951336i $$0.599711\pi$$
$$854$$ −6.00000 −0.205316
$$855$$ 0 0
$$856$$ −8.00000 −0.273434
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 8.00000 0.272956 0.136478 0.990643i $$-0.456422\pi$$
0.136478 + 0.990643i $$0.456422\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −8.00000 −0.272481
$$863$$ −12.0000 −0.408485 −0.204242 0.978920i $$-0.565473\pi$$
−0.204242 + 0.978920i $$0.565473\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ −22.0000 −0.747590
$$867$$ 0 0
$$868$$ −6.00000 −0.203653
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 8.00000 0.271070
$$872$$ 18.0000 0.609557
$$873$$ 0 0
$$874$$ 24.0000 0.811812
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 50.0000 1.68838 0.844190 0.536044i $$-0.180082\pi$$
0.844190 + 0.536044i $$0.180082\pi$$
$$878$$ 28.0000 0.944954
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ −28.0000 −0.942275 −0.471138 0.882060i $$-0.656156\pi$$
−0.471138 + 0.882060i $$0.656156\pi$$
$$884$$ −8.00000 −0.269069
$$885$$ 0 0
$$886$$ −12.0000 −0.403148
$$887$$ −8.00000 −0.268614 −0.134307 0.990940i $$-0.542881\pi$$
−0.134307 + 0.990940i $$0.542881\pi$$
$$888$$ 0 0
$$889$$ 16.0000 0.536623
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −2.00000 −0.0669650
$$893$$ −12.0000 −0.401565
$$894$$ 0 0
$$895$$ 0 0
$$896$$ −1.00000 −0.0334077
$$897$$ 0 0
$$898$$ 2.00000 0.0667409
$$899$$ 60.0000 2.00111
$$900$$ 0 0
$$901$$ −24.0000 −0.799556
$$902$$ 12.0000 0.399556
$$903$$ 0 0
$$904$$ 2.00000 0.0665190
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −44.0000 −1.46100 −0.730498 0.682915i $$-0.760712\pi$$
−0.730498 + 0.682915i $$0.760712\pi$$
$$908$$ 14.0000 0.464606
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ −14.0000 −0.463332
$$914$$ −6.00000 −0.198462
$$915$$ 0 0
$$916$$ 24.0000 0.792982
$$917$$ 10.0000 0.330229
$$918$$ 0 0
$$919$$ 24.0000 0.791687 0.395843 0.918318i $$-0.370452\pi$$
0.395843 + 0.918318i $$0.370452\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 6.00000 0.197599
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 30.0000 0.986394
$$926$$ 16.0000 0.525793
$$927$$ 0 0
$$928$$ 10.0000 0.328266
$$929$$ −42.0000 −1.37798 −0.688988 0.724773i $$-0.741945\pi$$
−0.688988 + 0.724773i $$0.741945\pi$$
$$930$$ 0 0
$$931$$ 6.00000 0.196642
$$932$$ 26.0000 0.851658
$$933$$ 0 0
$$934$$ −4.00000 −0.130884
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −4.00000 −0.130674 −0.0653372 0.997863i $$-0.520812\pi$$
−0.0653372 + 0.997863i $$0.520812\pi$$
$$938$$ 4.00000 0.130605
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −6.00000 −0.195594 −0.0977972 0.995206i $$-0.531180\pi$$
−0.0977972 + 0.995206i $$0.531180\pi$$
$$942$$ 0 0
$$943$$ 48.0000 1.56310
$$944$$ 8.00000 0.260378
$$945$$ 0 0
$$946$$ −8.00000 −0.260102
$$947$$ −12.0000 −0.389948 −0.194974 0.980808i $$-0.562462\pi$$
−0.194974 + 0.980808i $$0.562462\pi$$
$$948$$ 0 0
$$949$$ 24.0000 0.779073
$$950$$ −30.0000 −0.973329
$$951$$ 0 0
$$952$$ −4.00000 −0.129641
$$953$$ −50.0000 −1.61966 −0.809829 0.586665i $$-0.800440\pi$$
−0.809829 + 0.586665i $$0.800440\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 8.00000 0.258738
$$957$$ 0 0
$$958$$ 8.00000 0.258468
$$959$$ −10.0000 −0.322917
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ 12.0000 0.386896
$$963$$ 0 0
$$964$$ −28.0000 −0.901819
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −56.0000 −1.80084 −0.900419 0.435023i $$-0.856740\pi$$
−0.900419 + 0.435023i $$0.856740\pi$$
$$968$$ 1.00000 0.0321412
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ 0 0
$$973$$ 14.0000 0.448819
$$974$$ −28.0000 −0.897178
$$975$$ 0 0
$$976$$ 6.00000 0.192055
$$977$$ −18.0000 −0.575871 −0.287936 0.957650i $$-0.592969\pi$$
−0.287936 + 0.957650i $$0.592969\pi$$
$$978$$ 0 0
$$979$$ −10.0000 −0.319601
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −12.0000 −0.382935
$$983$$ 14.0000 0.446531 0.223265 0.974758i $$-0.428328\pi$$
0.223265 + 0.974758i $$0.428328\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 40.0000 1.27386
$$987$$ 0 0
$$988$$ −12.0000 −0.381771
$$989$$ −32.0000 −1.01754
$$990$$ 0 0
$$991$$ −48.0000 −1.52477 −0.762385 0.647124i $$-0.775972\pi$$
−0.762385 + 0.647124i $$0.775972\pi$$
$$992$$ 6.00000 0.190500
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 10.0000 0.316703 0.158352 0.987383i $$-0.449382\pi$$
0.158352 + 0.987383i $$0.449382\pi$$
$$998$$ 4.00000 0.126618
$$999$$ 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 1386.2.a.i.1.1 1
3.2 odd 2 462.2.a.b.1.1 1
7.6 odd 2 9702.2.a.bt.1.1 1
12.11 even 2 3696.2.a.y.1.1 1
21.20 even 2 3234.2.a.k.1.1 1
33.32 even 2 5082.2.a.s.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.a.b.1.1 1 3.2 odd 2
1386.2.a.i.1.1 1 1.1 even 1 trivial
3234.2.a.k.1.1 1 21.20 even 2
3696.2.a.y.1.1 1 12.11 even 2
5082.2.a.s.1.1 1 33.32 even 2
9702.2.a.bt.1.1 1 7.6 odd 2