# Properties

 Label 392.2.a.f.1.1 Level $392$ Weight $2$ Character 392.1 Self dual yes Analytic conductor $3.130$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$392 = 2^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 392.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$3.13013575923$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 56) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 392.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.00000 q^{3} -1.00000 q^{5} +6.00000 q^{9} +O(q^{10})$$ $$q+3.00000 q^{3} -1.00000 q^{5} +6.00000 q^{9} -1.00000 q^{11} +2.00000 q^{13} -3.00000 q^{15} +3.00000 q^{17} +5.00000 q^{19} -3.00000 q^{23} -4.00000 q^{25} +9.00000 q^{27} -6.00000 q^{29} -1.00000 q^{31} -3.00000 q^{33} -5.00000 q^{37} +6.00000 q^{39} -10.0000 q^{41} -4.00000 q^{43} -6.00000 q^{45} +1.00000 q^{47} +9.00000 q^{51} -9.00000 q^{53} +1.00000 q^{55} +15.0000 q^{57} +3.00000 q^{59} +3.00000 q^{61} -2.00000 q^{65} +11.0000 q^{67} -9.00000 q^{69} +16.0000 q^{71} +7.00000 q^{73} -12.0000 q^{75} -11.0000 q^{79} +9.00000 q^{81} -4.00000 q^{83} -3.00000 q^{85} -18.0000 q^{87} -9.00000 q^{89} -3.00000 q^{93} -5.00000 q^{95} +6.00000 q^{97} -6.00000 q^{99} +O(q^{100})$$

## 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
$$3$$ 3.00000 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 0 0
$$5$$ −1.00000 −0.447214 −0.223607 0.974679i $$-0.571783\pi$$
−0.223607 + 0.974679i $$0.571783\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 6.00000 2.00000
$$10$$ 0 0
$$11$$ −1.00000 −0.301511 −0.150756 0.988571i $$-0.548171\pi$$
−0.150756 + 0.988571i $$0.548171\pi$$
$$12$$ 0 0
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 0 0
$$15$$ −3.00000 −0.774597
$$16$$ 0 0
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 0 0
$$19$$ 5.00000 1.14708 0.573539 0.819178i $$-0.305570\pi$$
0.573539 + 0.819178i $$0.305570\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.00000 −0.625543 −0.312772 0.949828i $$-0.601257\pi$$
−0.312772 + 0.949828i $$0.601257\pi$$
$$24$$ 0 0
$$25$$ −4.00000 −0.800000
$$26$$ 0 0
$$27$$ 9.00000 1.73205
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −0.179605 −0.0898027 0.995960i $$-0.528624\pi$$
−0.0898027 + 0.995960i $$0.528624\pi$$
$$32$$ 0 0
$$33$$ −3.00000 −0.522233
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ 0 0
$$39$$ 6.00000 0.960769
$$40$$ 0 0
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ −6.00000 −0.894427
$$46$$ 0 0
$$47$$ 1.00000 0.145865 0.0729325 0.997337i $$-0.476764\pi$$
0.0729325 + 0.997337i $$0.476764\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 9.00000 1.26025
$$52$$ 0 0
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ 0 0
$$55$$ 1.00000 0.134840
$$56$$ 0 0
$$57$$ 15.0000 1.98680
$$58$$ 0 0
$$59$$ 3.00000 0.390567 0.195283 0.980747i $$-0.437437\pi$$
0.195283 + 0.980747i $$0.437437\pi$$
$$60$$ 0 0
$$61$$ 3.00000 0.384111 0.192055 0.981384i $$-0.438485\pi$$
0.192055 + 0.981384i $$0.438485\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −2.00000 −0.248069
$$66$$ 0 0
$$67$$ 11.0000 1.34386 0.671932 0.740613i $$-0.265465\pi$$
0.671932 + 0.740613i $$0.265465\pi$$
$$68$$ 0 0
$$69$$ −9.00000 −1.08347
$$70$$ 0 0
$$71$$ 16.0000 1.89885 0.949425 0.313993i $$-0.101667\pi$$
0.949425 + 0.313993i $$0.101667\pi$$
$$72$$ 0 0
$$73$$ 7.00000 0.819288 0.409644 0.912245i $$-0.365653\pi$$
0.409644 + 0.912245i $$0.365653\pi$$
$$74$$ 0 0
$$75$$ −12.0000 −1.38564
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −11.0000 −1.23760 −0.618798 0.785550i $$-0.712380\pi$$
−0.618798 + 0.785550i $$0.712380\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ −3.00000 −0.325396
$$86$$ 0 0
$$87$$ −18.0000 −1.92980
$$88$$ 0 0
$$89$$ −9.00000 −0.953998 −0.476999 0.878904i $$-0.658275\pi$$
−0.476999 + 0.878904i $$0.658275\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −3.00000 −0.311086
$$94$$ 0 0
$$95$$ −5.00000 −0.512989
$$96$$ 0 0
$$97$$ 6.00000 0.609208 0.304604 0.952479i $$-0.401476\pi$$
0.304604 + 0.952479i $$0.401476\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ −13.0000 −1.29355 −0.646774 0.762682i $$-0.723882\pi$$
−0.646774 + 0.762682i $$0.723882\pi$$
$$102$$ 0 0
$$103$$ 5.00000 0.492665 0.246332 0.969185i $$-0.420775\pi$$
0.246332 + 0.969185i $$0.420775\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −3.00000 −0.290021 −0.145010 0.989430i $$-0.546322\pi$$
−0.145010 + 0.989430i $$0.546322\pi$$
$$108$$ 0 0
$$109$$ 11.0000 1.05361 0.526804 0.849987i $$-0.323390\pi$$
0.526804 + 0.849987i $$0.323390\pi$$
$$110$$ 0 0
$$111$$ −15.0000 −1.42374
$$112$$ 0 0
$$113$$ −10.0000 −0.940721 −0.470360 0.882474i $$-0.655876\pi$$
−0.470360 + 0.882474i $$0.655876\pi$$
$$114$$ 0 0
$$115$$ 3.00000 0.279751
$$116$$ 0 0
$$117$$ 12.0000 1.10940
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ 0 0
$$123$$ −30.0000 −2.70501
$$124$$ 0 0
$$125$$ 9.00000 0.804984
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ −12.0000 −1.05654
$$130$$ 0 0
$$131$$ 17.0000 1.48530 0.742648 0.669681i $$-0.233569\pi$$
0.742648 + 0.669681i $$0.233569\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −9.00000 −0.774597
$$136$$ 0 0
$$137$$ 3.00000 0.256307 0.128154 0.991754i $$-0.459095\pi$$
0.128154 + 0.991754i $$0.459095\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 3.00000 0.252646
$$142$$ 0 0
$$143$$ −2.00000 −0.167248
$$144$$ 0 0
$$145$$ 6.00000 0.498273
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 15.0000 1.22885 0.614424 0.788976i $$-0.289388\pi$$
0.614424 + 0.788976i $$0.289388\pi$$
$$150$$ 0 0
$$151$$ 15.0000 1.22068 0.610341 0.792139i $$-0.291032\pi$$
0.610341 + 0.792139i $$0.291032\pi$$
$$152$$ 0 0
$$153$$ 18.0000 1.45521
$$154$$ 0 0
$$155$$ 1.00000 0.0803219
$$156$$ 0 0
$$157$$ 15.0000 1.19713 0.598565 0.801074i $$-0.295738\pi$$
0.598565 + 0.801074i $$0.295738\pi$$
$$158$$ 0 0
$$159$$ −27.0000 −2.14124
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 9.00000 0.704934 0.352467 0.935824i $$-0.385343\pi$$
0.352467 + 0.935824i $$0.385343\pi$$
$$164$$ 0 0
$$165$$ 3.00000 0.233550
$$166$$ 0 0
$$167$$ −20.0000 −1.54765 −0.773823 0.633402i $$-0.781658\pi$$
−0.773823 + 0.633402i $$0.781658\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 30.0000 2.29416
$$172$$ 0 0
$$173$$ −21.0000 −1.59660 −0.798300 0.602260i $$-0.794267\pi$$
−0.798300 + 0.602260i $$0.794267\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 9.00000 0.676481
$$178$$ 0 0
$$179$$ −1.00000 −0.0747435 −0.0373718 0.999301i $$-0.511899\pi$$
−0.0373718 + 0.999301i $$0.511899\pi$$
$$180$$ 0 0
$$181$$ 22.0000 1.63525 0.817624 0.575753i $$-0.195291\pi$$
0.817624 + 0.575753i $$0.195291\pi$$
$$182$$ 0 0
$$183$$ 9.00000 0.665299
$$184$$ 0 0
$$185$$ 5.00000 0.367607
$$186$$ 0 0
$$187$$ −3.00000 −0.219382
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 17.0000 1.23008 0.615038 0.788497i $$-0.289140\pi$$
0.615038 + 0.788497i $$0.289140\pi$$
$$192$$ 0 0
$$193$$ −5.00000 −0.359908 −0.179954 0.983675i $$-0.557595\pi$$
−0.179954 + 0.983675i $$0.557595\pi$$
$$194$$ 0 0
$$195$$ −6.00000 −0.429669
$$196$$ 0 0
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ −9.00000 −0.637993 −0.318997 0.947756i $$-0.603346\pi$$
−0.318997 + 0.947756i $$0.603346\pi$$
$$200$$ 0 0
$$201$$ 33.0000 2.32764
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 10.0000 0.698430
$$206$$ 0 0
$$207$$ −18.0000 −1.25109
$$208$$ 0 0
$$209$$ −5.00000 −0.345857
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 0 0
$$213$$ 48.0000 3.28891
$$214$$ 0 0
$$215$$ 4.00000 0.272798
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 21.0000 1.41905
$$220$$ 0 0
$$221$$ 6.00000 0.403604
$$222$$ 0 0
$$223$$ 24.0000 1.60716 0.803579 0.595198i $$-0.202926\pi$$
0.803579 + 0.595198i $$0.202926\pi$$
$$224$$ 0 0
$$225$$ −24.0000 −1.60000
$$226$$ 0 0
$$227$$ 7.00000 0.464606 0.232303 0.972643i $$-0.425374\pi$$
0.232303 + 0.972643i $$0.425374\pi$$
$$228$$ 0 0
$$229$$ 7.00000 0.462573 0.231287 0.972886i $$-0.425707\pi$$
0.231287 + 0.972886i $$0.425707\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −13.0000 −0.851658 −0.425829 0.904804i $$-0.640018\pi$$
−0.425829 + 0.904804i $$0.640018\pi$$
$$234$$ 0 0
$$235$$ −1.00000 −0.0652328
$$236$$ 0 0
$$237$$ −33.0000 −2.14358
$$238$$ 0 0
$$239$$ −4.00000 −0.258738 −0.129369 0.991596i $$-0.541295\pi$$
−0.129369 + 0.991596i $$0.541295\pi$$
$$240$$ 0 0
$$241$$ −17.0000 −1.09507 −0.547533 0.836784i $$-0.684433\pi$$
−0.547533 + 0.836784i $$0.684433\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 10.0000 0.636285
$$248$$ 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
$$253$$ 3.00000 0.188608
$$254$$ 0 0
$$255$$ −9.00000 −0.563602
$$256$$ 0 0
$$257$$ −13.0000 −0.810918 −0.405459 0.914113i $$-0.632888\pi$$
−0.405459 + 0.914113i $$0.632888\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −36.0000 −2.22834
$$262$$ 0 0
$$263$$ 3.00000 0.184988 0.0924940 0.995713i $$-0.470516\pi$$
0.0924940 + 0.995713i $$0.470516\pi$$
$$264$$ 0 0
$$265$$ 9.00000 0.552866
$$266$$ 0 0
$$267$$ −27.0000 −1.65237
$$268$$ 0 0
$$269$$ −17.0000 −1.03651 −0.518254 0.855227i $$-0.673418\pi$$
−0.518254 + 0.855227i $$0.673418\pi$$
$$270$$ 0 0
$$271$$ −3.00000 −0.182237 −0.0911185 0.995840i $$-0.529044\pi$$
−0.0911185 + 0.995840i $$0.529044\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 4.00000 0.241209
$$276$$ 0 0
$$277$$ 7.00000 0.420589 0.210295 0.977638i $$-0.432558\pi$$
0.210295 + 0.977638i $$0.432558\pi$$
$$278$$ 0 0
$$279$$ −6.00000 −0.359211
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ −17.0000 −1.01055 −0.505273 0.862960i $$-0.668608\pi$$
−0.505273 + 0.862960i $$0.668608\pi$$
$$284$$ 0 0
$$285$$ −15.0000 −0.888523
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 18.0000 1.05518
$$292$$ 0 0
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 0 0
$$295$$ −3.00000 −0.174667
$$296$$ 0 0
$$297$$ −9.00000 −0.522233
$$298$$ 0 0
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −39.0000 −2.24049
$$304$$ 0 0
$$305$$ −3.00000 −0.171780
$$306$$ 0 0
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 0 0
$$309$$ 15.0000 0.853320
$$310$$ 0 0
$$311$$ 11.0000 0.623753 0.311876 0.950123i $$-0.399043\pi$$
0.311876 + 0.950123i $$0.399043\pi$$
$$312$$ 0 0
$$313$$ 31.0000 1.75222 0.876112 0.482108i $$-0.160129\pi$$
0.876112 + 0.482108i $$0.160129\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 27.0000 1.51647 0.758236 0.651981i $$-0.226062\pi$$
0.758236 + 0.651981i $$0.226062\pi$$
$$318$$ 0 0
$$319$$ 6.00000 0.335936
$$320$$ 0 0
$$321$$ −9.00000 −0.502331
$$322$$ 0 0
$$323$$ 15.0000 0.834622
$$324$$ 0 0
$$325$$ −8.00000 −0.443760
$$326$$ 0 0
$$327$$ 33.0000 1.82490
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −7.00000 −0.384755 −0.192377 0.981321i $$-0.561620\pi$$
−0.192377 + 0.981321i $$0.561620\pi$$
$$332$$ 0 0
$$333$$ −30.0000 −1.64399
$$334$$ 0 0
$$335$$ −11.0000 −0.600994
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 0 0
$$339$$ −30.0000 −1.62938
$$340$$ 0 0
$$341$$ 1.00000 0.0541530
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 9.00000 0.484544
$$346$$ 0 0
$$347$$ 3.00000 0.161048 0.0805242 0.996753i $$-0.474341\pi$$
0.0805242 + 0.996753i $$0.474341\pi$$
$$348$$ 0 0
$$349$$ −6.00000 −0.321173 −0.160586 0.987022i $$-0.551338\pi$$
−0.160586 + 0.987022i $$0.551338\pi$$
$$350$$ 0 0
$$351$$ 18.0000 0.960769
$$352$$ 0 0
$$353$$ −5.00000 −0.266123 −0.133062 0.991108i $$-0.542481\pi$$
−0.133062 + 0.991108i $$0.542481\pi$$
$$354$$ 0 0
$$355$$ −16.0000 −0.849192
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −15.0000 −0.791670 −0.395835 0.918322i $$-0.629545\pi$$
−0.395835 + 0.918322i $$0.629545\pi$$
$$360$$ 0 0
$$361$$ 6.00000 0.315789
$$362$$ 0 0
$$363$$ −30.0000 −1.57459
$$364$$ 0 0
$$365$$ −7.00000 −0.366397
$$366$$ 0 0
$$367$$ 19.0000 0.991792 0.495896 0.868382i $$-0.334840\pi$$
0.495896 + 0.868382i $$0.334840\pi$$
$$368$$ 0 0
$$369$$ −60.0000 −3.12348
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 19.0000 0.983783 0.491891 0.870657i $$-0.336306\pi$$
0.491891 + 0.870657i $$0.336306\pi$$
$$374$$ 0 0
$$375$$ 27.0000 1.39427
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ −16.0000 −0.821865 −0.410932 0.911666i $$-0.634797\pi$$
−0.410932 + 0.911666i $$0.634797\pi$$
$$380$$ 0 0
$$381$$ −24.0000 −1.22956
$$382$$ 0 0
$$383$$ 9.00000 0.459879 0.229939 0.973205i $$-0.426147\pi$$
0.229939 + 0.973205i $$0.426147\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −24.0000 −1.21999
$$388$$ 0 0
$$389$$ 19.0000 0.963338 0.481669 0.876353i $$-0.340031\pi$$
0.481669 + 0.876353i $$0.340031\pi$$
$$390$$ 0 0
$$391$$ −9.00000 −0.455150
$$392$$ 0 0
$$393$$ 51.0000 2.57261
$$394$$ 0 0
$$395$$ 11.0000 0.553470
$$396$$ 0 0
$$397$$ −17.0000 −0.853206 −0.426603 0.904439i $$-0.640290\pi$$
−0.426603 + 0.904439i $$0.640290\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 3.00000 0.149813 0.0749064 0.997191i $$-0.476134\pi$$
0.0749064 + 0.997191i $$0.476134\pi$$
$$402$$ 0 0
$$403$$ −2.00000 −0.0996271
$$404$$ 0 0
$$405$$ −9.00000 −0.447214
$$406$$ 0 0
$$407$$ 5.00000 0.247841
$$408$$ 0 0
$$409$$ 19.0000 0.939490 0.469745 0.882802i $$-0.344346\pi$$
0.469745 + 0.882802i $$0.344346\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 4.00000 0.196352
$$416$$ 0 0
$$417$$ 12.0000 0.587643
$$418$$ 0 0
$$419$$ 20.0000 0.977064 0.488532 0.872546i $$-0.337533\pi$$
0.488532 + 0.872546i $$0.337533\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ 0 0
$$423$$ 6.00000 0.291730
$$424$$ 0 0
$$425$$ −12.0000 −0.582086
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ −41.0000 −1.97490 −0.987450 0.157930i $$-0.949518\pi$$
−0.987450 + 0.157930i $$0.949518\pi$$
$$432$$ 0 0
$$433$$ −26.0000 −1.24948 −0.624740 0.780833i $$-0.714795\pi$$
−0.624740 + 0.780833i $$0.714795\pi$$
$$434$$ 0 0
$$435$$ 18.0000 0.863034
$$436$$ 0 0
$$437$$ −15.0000 −0.717547
$$438$$ 0 0
$$439$$ −15.0000 −0.715911 −0.357955 0.933739i $$-0.616526\pi$$
−0.357955 + 0.933739i $$0.616526\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −27.0000 −1.28281 −0.641404 0.767203i $$-0.721648\pi$$
−0.641404 + 0.767203i $$0.721648\pi$$
$$444$$ 0 0
$$445$$ 9.00000 0.426641
$$446$$ 0 0
$$447$$ 45.0000 2.12843
$$448$$ 0 0
$$449$$ −2.00000 −0.0943858 −0.0471929 0.998886i $$-0.515028\pi$$
−0.0471929 + 0.998886i $$0.515028\pi$$
$$450$$ 0 0
$$451$$ 10.0000 0.470882
$$452$$ 0 0
$$453$$ 45.0000 2.11428
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −17.0000 −0.795226 −0.397613 0.917553i $$-0.630161\pi$$
−0.397613 + 0.917553i $$0.630161\pi$$
$$458$$ 0 0
$$459$$ 27.0000 1.26025
$$460$$ 0 0
$$461$$ −6.00000 −0.279448 −0.139724 0.990190i $$-0.544622\pi$$
−0.139724 + 0.990190i $$0.544622\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 3.00000 0.139122
$$466$$ 0 0
$$467$$ 25.0000 1.15686 0.578431 0.815731i $$-0.303665\pi$$
0.578431 + 0.815731i $$0.303665\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 45.0000 2.07349
$$472$$ 0 0
$$473$$ 4.00000 0.183920
$$474$$ 0 0
$$475$$ −20.0000 −0.917663
$$476$$ 0 0
$$477$$ −54.0000 −2.47249
$$478$$ 0 0
$$479$$ −21.0000 −0.959514 −0.479757 0.877401i $$-0.659275\pi$$
−0.479757 + 0.877401i $$0.659275\pi$$
$$480$$ 0 0
$$481$$ −10.0000 −0.455961
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −6.00000 −0.272446
$$486$$ 0 0
$$487$$ −13.0000 −0.589086 −0.294543 0.955638i $$-0.595167\pi$$
−0.294543 + 0.955638i $$0.595167\pi$$
$$488$$ 0 0
$$489$$ 27.0000 1.22098
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ −18.0000 −0.810679
$$494$$ 0 0
$$495$$ 6.00000 0.269680
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −7.00000 −0.313363 −0.156682 0.987649i $$-0.550080\pi$$
−0.156682 + 0.987649i $$0.550080\pi$$
$$500$$ 0 0
$$501$$ −60.0000 −2.68060
$$502$$ 0 0
$$503$$ 16.0000 0.713405 0.356702 0.934218i $$-0.383901\pi$$
0.356702 + 0.934218i $$0.383901\pi$$
$$504$$ 0 0
$$505$$ 13.0000 0.578492
$$506$$ 0 0
$$507$$ −27.0000 −1.19911
$$508$$ 0 0
$$509$$ 7.00000 0.310270 0.155135 0.987893i $$-0.450419\pi$$
0.155135 + 0.987893i $$0.450419\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 45.0000 1.98680
$$514$$ 0 0
$$515$$ −5.00000 −0.220326
$$516$$ 0 0
$$517$$ −1.00000 −0.0439799
$$518$$ 0 0
$$519$$ −63.0000 −2.76539
$$520$$ 0 0
$$521$$ 15.0000 0.657162 0.328581 0.944476i $$-0.393430\pi$$
0.328581 + 0.944476i $$0.393430\pi$$
$$522$$ 0 0
$$523$$ 13.0000 0.568450 0.284225 0.958758i $$-0.408264\pi$$
0.284225 + 0.958758i $$0.408264\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −3.00000 −0.130682
$$528$$ 0 0
$$529$$ −14.0000 −0.608696
$$530$$ 0 0
$$531$$ 18.0000 0.781133
$$532$$ 0 0
$$533$$ −20.0000 −0.866296
$$534$$ 0 0
$$535$$ 3.00000 0.129701
$$536$$ 0 0
$$537$$ −3.00000 −0.129460
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −25.0000 −1.07483 −0.537417 0.843317i $$-0.680600\pi$$
−0.537417 + 0.843317i $$0.680600\pi$$
$$542$$ 0 0
$$543$$ 66.0000 2.83233
$$544$$ 0 0
$$545$$ −11.0000 −0.471188
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 0 0
$$549$$ 18.0000 0.768221
$$550$$ 0 0
$$551$$ −30.0000 −1.27804
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 15.0000 0.636715
$$556$$ 0 0
$$557$$ 11.0000 0.466085 0.233042 0.972467i $$-0.425132\pi$$
0.233042 + 0.972467i $$0.425132\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ −9.00000 −0.379980
$$562$$ 0 0
$$563$$ 11.0000 0.463595 0.231797 0.972764i $$-0.425539\pi$$
0.231797 + 0.972764i $$0.425539\pi$$
$$564$$ 0 0
$$565$$ 10.0000 0.420703
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.00000 −0.0419222 −0.0209611 0.999780i $$-0.506673\pi$$
−0.0209611 + 0.999780i $$0.506673\pi$$
$$570$$ 0 0
$$571$$ −17.0000 −0.711428 −0.355714 0.934595i $$-0.615762\pi$$
−0.355714 + 0.934595i $$0.615762\pi$$
$$572$$ 0 0
$$573$$ 51.0000 2.13056
$$574$$ 0 0
$$575$$ 12.0000 0.500435
$$576$$ 0 0
$$577$$ 31.0000 1.29055 0.645273 0.763952i $$-0.276743\pi$$
0.645273 + 0.763952i $$0.276743\pi$$
$$578$$ 0 0
$$579$$ −15.0000 −0.623379
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 9.00000 0.372742
$$584$$ 0 0
$$585$$ −12.0000 −0.496139
$$586$$ 0 0
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ −5.00000 −0.206021
$$590$$ 0 0
$$591$$ 54.0000 2.22126
$$592$$ 0 0
$$593$$ 43.0000 1.76580 0.882899 0.469563i $$-0.155588\pi$$
0.882899 + 0.469563i $$0.155588\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −27.0000 −1.10504
$$598$$ 0 0
$$599$$ −21.0000 −0.858037 −0.429018 0.903296i $$-0.641140\pi$$
−0.429018 + 0.903296i $$0.641140\pi$$
$$600$$ 0 0
$$601$$ −34.0000 −1.38689 −0.693444 0.720510i $$-0.743908\pi$$
−0.693444 + 0.720510i $$0.743908\pi$$
$$602$$ 0 0
$$603$$ 66.0000 2.68773
$$604$$ 0 0
$$605$$ 10.0000 0.406558
$$606$$ 0 0
$$607$$ −7.00000 −0.284121 −0.142061 0.989858i $$-0.545373\pi$$
−0.142061 + 0.989858i $$0.545373\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 2.00000 0.0809113
$$612$$ 0 0
$$613$$ −21.0000 −0.848182 −0.424091 0.905620i $$-0.639406\pi$$
−0.424091 + 0.905620i $$0.639406\pi$$
$$614$$ 0 0
$$615$$ 30.0000 1.20972
$$616$$ 0 0
$$617$$ 22.0000 0.885687 0.442843 0.896599i $$-0.353970\pi$$
0.442843 + 0.896599i $$0.353970\pi$$
$$618$$ 0 0
$$619$$ −5.00000 −0.200967 −0.100483 0.994939i $$-0.532039\pi$$
−0.100483 + 0.994939i $$0.532039\pi$$
$$620$$ 0 0
$$621$$ −27.0000 −1.08347
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ 0 0
$$627$$ −15.0000 −0.599042
$$628$$ 0 0
$$629$$ −15.0000 −0.598089
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 36.0000 1.43087
$$634$$ 0 0
$$635$$ 8.00000 0.317470
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 96.0000 3.79770
$$640$$ 0 0
$$641$$ 15.0000 0.592464 0.296232 0.955116i $$-0.404270\pi$$
0.296232 + 0.955116i $$0.404270\pi$$
$$642$$ 0 0
$$643$$ −44.0000 −1.73519 −0.867595 0.497271i $$-0.834335\pi$$
−0.867595 + 0.497271i $$0.834335\pi$$
$$644$$ 0 0
$$645$$ 12.0000 0.472500
$$646$$ 0 0
$$647$$ 43.0000 1.69050 0.845252 0.534368i $$-0.179450\pi$$
0.845252 + 0.534368i $$0.179450\pi$$
$$648$$ 0 0
$$649$$ −3.00000 −0.117760
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −5.00000 −0.195665 −0.0978326 0.995203i $$-0.531191\pi$$
−0.0978326 + 0.995203i $$0.531191\pi$$
$$654$$ 0 0
$$655$$ −17.0000 −0.664245
$$656$$ 0 0
$$657$$ 42.0000 1.63858
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −1.00000 −0.0388955 −0.0194477 0.999811i $$-0.506191\pi$$
−0.0194477 + 0.999811i $$0.506191\pi$$
$$662$$ 0 0
$$663$$ 18.0000 0.699062
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 18.0000 0.696963
$$668$$ 0 0
$$669$$ 72.0000 2.78368
$$670$$ 0 0
$$671$$ −3.00000 −0.115814
$$672$$ 0 0
$$673$$ −2.00000 −0.0770943 −0.0385472 0.999257i $$-0.512273\pi$$
−0.0385472 + 0.999257i $$0.512273\pi$$
$$674$$ 0 0
$$675$$ −36.0000 −1.38564
$$676$$ 0 0
$$677$$ −9.00000 −0.345898 −0.172949 0.984931i $$-0.555330\pi$$
−0.172949 + 0.984931i $$0.555330\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 21.0000 0.804722
$$682$$ 0 0
$$683$$ 39.0000 1.49229 0.746147 0.665782i $$-0.231902\pi$$
0.746147 + 0.665782i $$0.231902\pi$$
$$684$$ 0 0
$$685$$ −3.00000 −0.114624
$$686$$ 0 0
$$687$$ 21.0000 0.801200
$$688$$ 0 0
$$689$$ −18.0000 −0.685745
$$690$$ 0 0
$$691$$ −47.0000 −1.78796 −0.893982 0.448103i $$-0.852100\pi$$
−0.893982 + 0.448103i $$0.852100\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −4.00000 −0.151729
$$696$$ 0 0
$$697$$ −30.0000 −1.13633
$$698$$ 0 0
$$699$$ −39.0000 −1.47512
$$700$$ 0 0
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ 0 0
$$703$$ −25.0000 −0.942893
$$704$$ 0 0
$$705$$ −3.00000 −0.112987
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 27.0000 1.01401 0.507003 0.861944i $$-0.330753\pi$$
0.507003 + 0.861944i $$0.330753\pi$$
$$710$$ 0 0
$$711$$ −66.0000 −2.47519
$$712$$ 0 0
$$713$$ 3.00000 0.112351
$$714$$ 0 0
$$715$$ 2.00000 0.0747958
$$716$$ 0 0
$$717$$ −12.0000 −0.448148
$$718$$ 0 0
$$719$$ 29.0000 1.08152 0.540759 0.841178i $$-0.318137\pi$$
0.540759 + 0.841178i $$0.318137\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −51.0000 −1.89671
$$724$$ 0 0
$$725$$ 24.0000 0.891338
$$726$$ 0 0
$$727$$ 16.0000 0.593407 0.296704 0.954970i $$-0.404113\pi$$
0.296704 + 0.954970i $$0.404113\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ 11.0000 0.406294 0.203147 0.979148i $$-0.434883\pi$$
0.203147 + 0.979148i $$0.434883\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −11.0000 −0.405190
$$738$$ 0 0
$$739$$ −41.0000 −1.50821 −0.754105 0.656754i $$-0.771929\pi$$
−0.754105 + 0.656754i $$0.771929\pi$$
$$740$$ 0 0
$$741$$ 30.0000 1.10208
$$742$$ 0 0
$$743$$ 32.0000 1.17397 0.586983 0.809599i $$-0.300316\pi$$
0.586983 + 0.809599i $$0.300316\pi$$
$$744$$ 0 0
$$745$$ −15.0000 −0.549557
$$746$$ 0 0
$$747$$ −24.0000 −0.878114
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −47.0000 −1.71505 −0.857527 0.514439i $$-0.828000\pi$$
−0.857527 + 0.514439i $$0.828000\pi$$
$$752$$ 0 0
$$753$$ 72.0000 2.62383
$$754$$ 0 0
$$755$$ −15.0000 −0.545906
$$756$$ 0 0
$$757$$ 34.0000 1.23575 0.617876 0.786276i $$-0.287994\pi$$
0.617876 + 0.786276i $$0.287994\pi$$
$$758$$ 0 0
$$759$$ 9.00000 0.326679
$$760$$ 0 0
$$761$$ 27.0000 0.978749 0.489375 0.872074i $$-0.337225\pi$$
0.489375 + 0.872074i $$0.337225\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −18.0000 −0.650791
$$766$$ 0 0
$$767$$ 6.00000 0.216647
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ −39.0000 −1.40455
$$772$$ 0 0
$$773$$ 35.0000 1.25886 0.629431 0.777056i $$-0.283288\pi$$
0.629431 + 0.777056i $$0.283288\pi$$
$$774$$ 0 0
$$775$$ 4.00000 0.143684
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −50.0000 −1.79144
$$780$$ 0 0
$$781$$ −16.0000 −0.572525
$$782$$ 0 0
$$783$$ −54.0000 −1.92980
$$784$$ 0 0
$$785$$ −15.0000 −0.535373
$$786$$ 0 0
$$787$$ −13.0000 −0.463400 −0.231700 0.972787i $$-0.574429\pi$$
−0.231700 + 0.972787i $$0.574429\pi$$
$$788$$ 0 0
$$789$$ 9.00000 0.320408
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 6.00000 0.213066
$$794$$ 0 0
$$795$$ 27.0000 0.957591
$$796$$ 0 0
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ 0 0
$$799$$ 3.00000 0.106132
$$800$$ 0 0
$$801$$ −54.0000 −1.90800
$$802$$ 0 0
$$803$$ −7.00000 −0.247025
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −51.0000 −1.79529
$$808$$ 0 0
$$809$$ −25.0000 −0.878953 −0.439477 0.898254i $$-0.644836\pi$$
−0.439477 + 0.898254i $$0.644836\pi$$
$$810$$ 0 0
$$811$$ −20.0000 −0.702295 −0.351147 0.936320i $$-0.614208\pi$$
−0.351147 + 0.936320i $$0.614208\pi$$
$$812$$ 0 0
$$813$$ −9.00000 −0.315644
$$814$$ 0 0
$$815$$ −9.00000 −0.315256
$$816$$ 0 0
$$817$$ −20.0000 −0.699711
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −25.0000 −0.872506 −0.436253 0.899824i $$-0.643695\pi$$
−0.436253 + 0.899824i $$0.643695\pi$$
$$822$$ 0 0
$$823$$ −21.0000 −0.732014 −0.366007 0.930612i $$-0.619275\pi$$
−0.366007 + 0.930612i $$0.619275\pi$$
$$824$$ 0 0
$$825$$ 12.0000 0.417786
$$826$$ 0 0
$$827$$ −4.00000 −0.139094 −0.0695468 0.997579i $$-0.522155\pi$$
−0.0695468 + 0.997579i $$0.522155\pi$$
$$828$$ 0 0
$$829$$ −37.0000 −1.28506 −0.642532 0.766259i $$-0.722116\pi$$
−0.642532 + 0.766259i $$0.722116\pi$$
$$830$$ 0 0
$$831$$ 21.0000 0.728482
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 20.0000 0.692129
$$836$$ 0 0
$$837$$ −9.00000 −0.311086
$$838$$ 0 0
$$839$$ −24.0000 −0.828572 −0.414286 0.910147i $$-0.635969\pi$$
−0.414286 + 0.910147i $$0.635969\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ −54.0000 −1.85986
$$844$$ 0 0
$$845$$ 9.00000 0.309609
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ −51.0000 −1.75032
$$850$$ 0 0
$$851$$ 15.0000 0.514193
$$852$$ 0 0
$$853$$ −22.0000 −0.753266 −0.376633 0.926363i $$-0.622918\pi$$
−0.376633 + 0.926363i $$0.622918\pi$$
$$854$$ 0 0
$$855$$ −30.0000 −1.02598
$$856$$ 0 0
$$857$$ −57.0000 −1.94708 −0.973541 0.228510i $$-0.926614\pi$$
−0.973541 + 0.228510i $$0.926614\pi$$
$$858$$ 0 0
$$859$$ 5.00000 0.170598 0.0852989 0.996355i $$-0.472815\pi$$
0.0852989 + 0.996355i $$0.472815\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 37.0000 1.25949 0.629747 0.776800i $$-0.283158\pi$$
0.629747 + 0.776800i $$0.283158\pi$$
$$864$$ 0 0
$$865$$ 21.0000 0.714021
$$866$$ 0 0
$$867$$ −24.0000 −0.815083
$$868$$ 0 0
$$869$$ 11.0000 0.373149
$$870$$ 0 0
$$871$$ 22.0000 0.745442
$$872$$ 0 0
$$873$$ 36.0000 1.21842
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 39.0000 1.31694 0.658468 0.752609i $$-0.271205\pi$$
0.658468 + 0.752609i $$0.271205\pi$$
$$878$$ 0 0
$$879$$ 18.0000 0.607125
$$880$$ 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 $$-0.343844\pi$$
0.471138 + 0.882060i $$0.343844\pi$$
$$884$$ 0 0
$$885$$ −9.00000 −0.302532
$$886$$ 0 0
$$887$$ −55.0000 −1.84672 −0.923360 0.383936i $$-0.874568\pi$$
−0.923360 + 0.383936i $$0.874568\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −9.00000 −0.301511
$$892$$ 0 0
$$893$$ 5.00000 0.167319
$$894$$ 0 0
$$895$$ 1.00000 0.0334263
$$896$$ 0 0
$$897$$ −18.0000 −0.601003
$$898$$ 0 0
$$899$$ 6.00000 0.200111
$$900$$ 0 0
$$901$$ −27.0000 −0.899500
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −22.0000 −0.731305
$$906$$ 0 0
$$907$$ −13.0000 −0.431658 −0.215829 0.976431i $$-0.569245\pi$$
−0.215829 + 0.976431i $$0.569245\pi$$
$$908$$ 0 0
$$909$$ −78.0000 −2.58710
$$910$$ 0 0
$$911$$ −48.0000 −1.59031 −0.795155 0.606406i $$-0.792611\pi$$
−0.795155 + 0.606406i $$0.792611\pi$$
$$912$$ 0 0
$$913$$ 4.00000 0.132381
$$914$$ 0 0
$$915$$ −9.00000 −0.297531
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 17.0000 0.560778 0.280389 0.959886i $$-0.409536\pi$$
0.280389 + 0.959886i $$0.409536\pi$$
$$920$$ 0 0
$$921$$ 12.0000 0.395413
$$922$$ 0 0
$$923$$ 32.0000 1.05329
$$924$$ 0 0
$$925$$ 20.0000 0.657596
$$926$$ 0 0
$$927$$ 30.0000 0.985329
$$928$$ 0 0
$$929$$ −41.0000 −1.34517 −0.672583 0.740022i $$-0.734815\pi$$
−0.672583 + 0.740022i $$0.734815\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 33.0000 1.08037
$$934$$ 0 0
$$935$$ 3.00000 0.0981105
$$936$$ 0 0
$$937$$ −38.0000 −1.24141 −0.620703 0.784046i $$-0.713153\pi$$
−0.620703 + 0.784046i $$0.713153\pi$$
$$938$$ 0 0
$$939$$ 93.0000 3.03494
$$940$$ 0 0
$$941$$ 39.0000 1.27136 0.635682 0.771951i $$-0.280719\pi$$
0.635682 + 0.771951i $$0.280719\pi$$
$$942$$ 0 0
$$943$$ 30.0000 0.976934
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 49.0000 1.59229 0.796143 0.605108i $$-0.206870\pi$$
0.796143 + 0.605108i $$0.206870\pi$$
$$948$$ 0 0
$$949$$ 14.0000 0.454459
$$950$$ 0 0
$$951$$ 81.0000 2.62660
$$952$$ 0 0
$$953$$ 30.0000 0.971795 0.485898 0.874016i $$-0.338493\pi$$
0.485898 + 0.874016i $$0.338493\pi$$
$$954$$ 0 0
$$955$$ −17.0000 −0.550107
$$956$$ 0 0
$$957$$ 18.0000 0.581857
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −30.0000 −0.967742
$$962$$ 0 0
$$963$$ −18.0000 −0.580042
$$964$$ 0 0
$$965$$ 5.00000 0.160956
$$966$$ 0 0
$$967$$ 32.0000 1.02905 0.514525 0.857475i $$-0.327968\pi$$
0.514525 + 0.857475i $$0.327968\pi$$
$$968$$ 0 0
$$969$$ 45.0000 1.44561
$$970$$ 0 0
$$971$$ 57.0000 1.82922 0.914609 0.404341i $$-0.132499\pi$$
0.914609 + 0.404341i $$0.132499\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ −24.0000 −0.768615
$$976$$ 0 0
$$977$$ −37.0000 −1.18373 −0.591867 0.806035i $$-0.701609\pi$$
−0.591867 + 0.806035i $$0.701609\pi$$
$$978$$ 0 0
$$979$$ 9.00000 0.287641
$$980$$ 0 0
$$981$$ 66.0000 2.10722
$$982$$ 0 0
$$983$$ −33.0000 −1.05254 −0.526268 0.850319i $$-0.676409\pi$$
−0.526268 + 0.850319i $$0.676409\pi$$
$$984$$ 0 0
$$985$$ −18.0000 −0.573528
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 12.0000 0.381578
$$990$$ 0 0
$$991$$ 59.0000 1.87420 0.937098 0.349065i $$-0.113501\pi$$
0.937098 + 0.349065i $$0.113501\pi$$
$$992$$ 0 0
$$993$$ −21.0000 −0.666415
$$994$$ 0 0
$$995$$ 9.00000 0.285319
$$996$$ 0 0
$$997$$ 31.0000 0.981780 0.490890 0.871222i $$-0.336672\pi$$
0.490890 + 0.871222i $$0.336672\pi$$
$$998$$ 0 0
$$999$$ −45.0000 −1.42374
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 392.2.a.f.1.1 1
3.2 odd 2 3528.2.a.r.1.1 1
4.3 odd 2 784.2.a.a.1.1 1
5.4 even 2 9800.2.a.b.1.1 1
7.2 even 3 56.2.i.a.25.1 yes 2
7.3 odd 6 392.2.i.f.177.1 2
7.4 even 3 56.2.i.a.9.1 2
7.5 odd 6 392.2.i.f.361.1 2
7.6 odd 2 392.2.a.a.1.1 1
8.3 odd 2 3136.2.a.bc.1.1 1
8.5 even 2 3136.2.a.b.1.1 1
12.11 even 2 7056.2.a.bi.1.1 1
21.2 odd 6 504.2.s.e.361.1 2
21.5 even 6 3528.2.s.o.361.1 2
21.11 odd 6 504.2.s.e.289.1 2
21.17 even 6 3528.2.s.o.3313.1 2
21.20 even 2 3528.2.a.k.1.1 1
28.3 even 6 784.2.i.a.177.1 2
28.11 odd 6 112.2.i.c.65.1 2
28.19 even 6 784.2.i.a.753.1 2
28.23 odd 6 112.2.i.c.81.1 2
28.27 even 2 784.2.a.j.1.1 1
35.2 odd 12 1400.2.bh.f.249.2 4
35.4 even 6 1400.2.q.g.401.1 2
35.9 even 6 1400.2.q.g.1201.1 2
35.18 odd 12 1400.2.bh.f.849.2 4
35.23 odd 12 1400.2.bh.f.249.1 4
35.32 odd 12 1400.2.bh.f.849.1 4
35.34 odd 2 9800.2.a.bp.1.1 1
56.11 odd 6 448.2.i.a.65.1 2
56.13 odd 2 3136.2.a.bb.1.1 1
56.27 even 2 3136.2.a.a.1.1 1
56.37 even 6 448.2.i.f.193.1 2
56.51 odd 6 448.2.i.a.193.1 2
56.53 even 6 448.2.i.f.65.1 2
84.11 even 6 1008.2.s.e.289.1 2
84.23 even 6 1008.2.s.e.865.1 2
84.83 odd 2 7056.2.a.s.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.i.a.9.1 2 7.4 even 3
56.2.i.a.25.1 yes 2 7.2 even 3
112.2.i.c.65.1 2 28.11 odd 6
112.2.i.c.81.1 2 28.23 odd 6
392.2.a.a.1.1 1 7.6 odd 2
392.2.a.f.1.1 1 1.1 even 1 trivial
392.2.i.f.177.1 2 7.3 odd 6
392.2.i.f.361.1 2 7.5 odd 6
448.2.i.a.65.1 2 56.11 odd 6
448.2.i.a.193.1 2 56.51 odd 6
448.2.i.f.65.1 2 56.53 even 6
448.2.i.f.193.1 2 56.37 even 6
504.2.s.e.289.1 2 21.11 odd 6
504.2.s.e.361.1 2 21.2 odd 6
784.2.a.a.1.1 1 4.3 odd 2
784.2.a.j.1.1 1 28.27 even 2
784.2.i.a.177.1 2 28.3 even 6
784.2.i.a.753.1 2 28.19 even 6
1008.2.s.e.289.1 2 84.11 even 6
1008.2.s.e.865.1 2 84.23 even 6
1400.2.q.g.401.1 2 35.4 even 6
1400.2.q.g.1201.1 2 35.9 even 6
1400.2.bh.f.249.1 4 35.23 odd 12
1400.2.bh.f.249.2 4 35.2 odd 12
1400.2.bh.f.849.1 4 35.32 odd 12
1400.2.bh.f.849.2 4 35.18 odd 12
3136.2.a.a.1.1 1 56.27 even 2
3136.2.a.b.1.1 1 8.5 even 2
3136.2.a.bb.1.1 1 56.13 odd 2
3136.2.a.bc.1.1 1 8.3 odd 2
3528.2.a.k.1.1 1 21.20 even 2
3528.2.a.r.1.1 1 3.2 odd 2
3528.2.s.o.361.1 2 21.5 even 6
3528.2.s.o.3313.1 2 21.17 even 6
7056.2.a.s.1.1 1 84.83 odd 2
7056.2.a.bi.1.1 1 12.11 even 2
9800.2.a.b.1.1 1 5.4 even 2
9800.2.a.bp.1.1 1 35.34 odd 2