# Properties

 Label 320.6.a.f.1.1 Level $320$ Weight $6$ Character 320.1 Self dual yes Analytic conductor $51.323$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 320.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$51.3228223402$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 10) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 320.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-6.00000 q^{3} +25.0000 q^{5} -118.000 q^{7} -207.000 q^{9} +O(q^{10})$$ $$q-6.00000 q^{3} +25.0000 q^{5} -118.000 q^{7} -207.000 q^{9} -192.000 q^{11} -1106.00 q^{13} -150.000 q^{15} +762.000 q^{17} +2740.00 q^{19} +708.000 q^{21} +1566.00 q^{23} +625.000 q^{25} +2700.00 q^{27} -5910.00 q^{29} -6868.00 q^{31} +1152.00 q^{33} -2950.00 q^{35} +5518.00 q^{37} +6636.00 q^{39} -378.000 q^{41} +2434.00 q^{43} -5175.00 q^{45} +13122.0 q^{47} -2883.00 q^{49} -4572.00 q^{51} +9174.00 q^{53} -4800.00 q^{55} -16440.0 q^{57} +34980.0 q^{59} +9838.00 q^{61} +24426.0 q^{63} -27650.0 q^{65} -33722.0 q^{67} -9396.00 q^{69} +70212.0 q^{71} +21986.0 q^{73} -3750.00 q^{75} +22656.0 q^{77} +4520.00 q^{79} +34101.0 q^{81} +109074. q^{83} +19050.0 q^{85} +35460.0 q^{87} +38490.0 q^{89} +130508. q^{91} +41208.0 q^{93} +68500.0 q^{95} -1918.00 q^{97} +39744.0 q^{99} +O(q^{100})$$

## 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
$$3$$ −6.00000 −0.384900 −0.192450 0.981307i $$-0.561643\pi$$
−0.192450 + 0.981307i $$0.561643\pi$$
$$4$$ 0 0
$$5$$ 25.0000 0.447214
$$6$$ 0 0
$$7$$ −118.000 −0.910200 −0.455100 0.890440i $$-0.650397\pi$$
−0.455100 + 0.890440i $$0.650397\pi$$
$$8$$ 0 0
$$9$$ −207.000 −0.851852
$$10$$ 0 0
$$11$$ −192.000 −0.478431 −0.239216 0.970966i $$-0.576890\pi$$
−0.239216 + 0.970966i $$0.576890\pi$$
$$12$$ 0 0
$$13$$ −1106.00 −1.81508 −0.907542 0.419961i $$-0.862044\pi$$
−0.907542 + 0.419961i $$0.862044\pi$$
$$14$$ 0 0
$$15$$ −150.000 −0.172133
$$16$$ 0 0
$$17$$ 762.000 0.639488 0.319744 0.947504i $$-0.396403\pi$$
0.319744 + 0.947504i $$0.396403\pi$$
$$18$$ 0 0
$$19$$ 2740.00 1.74127 0.870636 0.491928i $$-0.163708\pi$$
0.870636 + 0.491928i $$0.163708\pi$$
$$20$$ 0 0
$$21$$ 708.000 0.350336
$$22$$ 0 0
$$23$$ 1566.00 0.617266 0.308633 0.951181i $$-0.400129\pi$$
0.308633 + 0.951181i $$0.400129\pi$$
$$24$$ 0 0
$$25$$ 625.000 0.200000
$$26$$ 0 0
$$27$$ 2700.00 0.712778
$$28$$ 0 0
$$29$$ −5910.00 −1.30495 −0.652473 0.757812i $$-0.726268\pi$$
−0.652473 + 0.757812i $$0.726268\pi$$
$$30$$ 0 0
$$31$$ −6868.00 −1.28359 −0.641795 0.766877i $$-0.721810\pi$$
−0.641795 + 0.766877i $$0.721810\pi$$
$$32$$ 0 0
$$33$$ 1152.00 0.184148
$$34$$ 0 0
$$35$$ −2950.00 −0.407054
$$36$$ 0 0
$$37$$ 5518.00 0.662640 0.331320 0.943519i $$-0.392506\pi$$
0.331320 + 0.943519i $$0.392506\pi$$
$$38$$ 0 0
$$39$$ 6636.00 0.698626
$$40$$ 0 0
$$41$$ −378.000 −0.0351182 −0.0175591 0.999846i $$-0.505590\pi$$
−0.0175591 + 0.999846i $$0.505590\pi$$
$$42$$ 0 0
$$43$$ 2434.00 0.200747 0.100374 0.994950i $$-0.467996\pi$$
0.100374 + 0.994950i $$0.467996\pi$$
$$44$$ 0 0
$$45$$ −5175.00 −0.380960
$$46$$ 0 0
$$47$$ 13122.0 0.866474 0.433237 0.901280i $$-0.357371\pi$$
0.433237 + 0.901280i $$0.357371\pi$$
$$48$$ 0 0
$$49$$ −2883.00 −0.171536
$$50$$ 0 0
$$51$$ −4572.00 −0.246139
$$52$$ 0 0
$$53$$ 9174.00 0.448610 0.224305 0.974519i $$-0.427989\pi$$
0.224305 + 0.974519i $$0.427989\pi$$
$$54$$ 0 0
$$55$$ −4800.00 −0.213961
$$56$$ 0 0
$$57$$ −16440.0 −0.670216
$$58$$ 0 0
$$59$$ 34980.0 1.30825 0.654124 0.756388i $$-0.273038\pi$$
0.654124 + 0.756388i $$0.273038\pi$$
$$60$$ 0 0
$$61$$ 9838.00 0.338518 0.169259 0.985572i $$-0.445863\pi$$
0.169259 + 0.985572i $$0.445863\pi$$
$$62$$ 0 0
$$63$$ 24426.0 0.775356
$$64$$ 0 0
$$65$$ −27650.0 −0.811730
$$66$$ 0 0
$$67$$ −33722.0 −0.917754 −0.458877 0.888500i $$-0.651748\pi$$
−0.458877 + 0.888500i $$0.651748\pi$$
$$68$$ 0 0
$$69$$ −9396.00 −0.237586
$$70$$ 0 0
$$71$$ 70212.0 1.65297 0.826486 0.562957i $$-0.190336\pi$$
0.826486 + 0.562957i $$0.190336\pi$$
$$72$$ 0 0
$$73$$ 21986.0 0.482880 0.241440 0.970416i $$-0.422380\pi$$
0.241440 + 0.970416i $$0.422380\pi$$
$$74$$ 0 0
$$75$$ −3750.00 −0.0769800
$$76$$ 0 0
$$77$$ 22656.0 0.435468
$$78$$ 0 0
$$79$$ 4520.00 0.0814837 0.0407418 0.999170i $$-0.487028\pi$$
0.0407418 + 0.999170i $$0.487028\pi$$
$$80$$ 0 0
$$81$$ 34101.0 0.577503
$$82$$ 0 0
$$83$$ 109074. 1.73790 0.868952 0.494896i $$-0.164794\pi$$
0.868952 + 0.494896i $$0.164794\pi$$
$$84$$ 0 0
$$85$$ 19050.0 0.285988
$$86$$ 0 0
$$87$$ 35460.0 0.502274
$$88$$ 0 0
$$89$$ 38490.0 0.515078 0.257539 0.966268i $$-0.417088\pi$$
0.257539 + 0.966268i $$0.417088\pi$$
$$90$$ 0 0
$$91$$ 130508. 1.65209
$$92$$ 0 0
$$93$$ 41208.0 0.494054
$$94$$ 0 0
$$95$$ 68500.0 0.778720
$$96$$ 0 0
$$97$$ −1918.00 −0.0206976 −0.0103488 0.999946i $$-0.503294\pi$$
−0.0103488 + 0.999946i $$0.503294\pi$$
$$98$$ 0 0
$$99$$ 39744.0 0.407553
$$100$$ 0 0
$$101$$ −77622.0 −0.757149 −0.378575 0.925571i $$-0.623586\pi$$
−0.378575 + 0.925571i $$0.623586\pi$$
$$102$$ 0 0
$$103$$ −46714.0 −0.433864 −0.216932 0.976187i $$-0.569605\pi$$
−0.216932 + 0.976187i $$0.569605\pi$$
$$104$$ 0 0
$$105$$ 17700.0 0.156675
$$106$$ 0 0
$$107$$ 1038.00 0.00876472 0.00438236 0.999990i $$-0.498605\pi$$
0.00438236 + 0.999990i $$0.498605\pi$$
$$108$$ 0 0
$$109$$ −206930. −1.66823 −0.834117 0.551587i $$-0.814023\pi$$
−0.834117 + 0.551587i $$0.814023\pi$$
$$110$$ 0 0
$$111$$ −33108.0 −0.255050
$$112$$ 0 0
$$113$$ 139386. 1.02689 0.513444 0.858123i $$-0.328369\pi$$
0.513444 + 0.858123i $$0.328369\pi$$
$$114$$ 0 0
$$115$$ 39150.0 0.276050
$$116$$ 0 0
$$117$$ 228942. 1.54618
$$118$$ 0 0
$$119$$ −89916.0 −0.582062
$$120$$ 0 0
$$121$$ −124187. −0.771104
$$122$$ 0 0
$$123$$ 2268.00 0.0135170
$$124$$ 0 0
$$125$$ 15625.0 0.0894427
$$126$$ 0 0
$$127$$ 299882. 1.64984 0.824919 0.565252i $$-0.191221\pi$$
0.824919 + 0.565252i $$0.191221\pi$$
$$128$$ 0 0
$$129$$ −14604.0 −0.0772676
$$130$$ 0 0
$$131$$ −7872.00 −0.0400781 −0.0200390 0.999799i $$-0.506379\pi$$
−0.0200390 + 0.999799i $$0.506379\pi$$
$$132$$ 0 0
$$133$$ −323320. −1.58491
$$134$$ 0 0
$$135$$ 67500.0 0.318764
$$136$$ 0 0
$$137$$ −164238. −0.747605 −0.373803 0.927508i $$-0.621946\pi$$
−0.373803 + 0.927508i $$0.621946\pi$$
$$138$$ 0 0
$$139$$ 282100. 1.23841 0.619207 0.785228i $$-0.287454\pi$$
0.619207 + 0.785228i $$0.287454\pi$$
$$140$$ 0 0
$$141$$ −78732.0 −0.333506
$$142$$ 0 0
$$143$$ 212352. 0.868393
$$144$$ 0 0
$$145$$ −147750. −0.583590
$$146$$ 0 0
$$147$$ 17298.0 0.0660241
$$148$$ 0 0
$$149$$ 388950. 1.43525 0.717626 0.696429i $$-0.245229\pi$$
0.717626 + 0.696429i $$0.245229\pi$$
$$150$$ 0 0
$$151$$ −97948.0 −0.349585 −0.174793 0.984605i $$-0.555926\pi$$
−0.174793 + 0.984605i $$0.555926\pi$$
$$152$$ 0 0
$$153$$ −157734. −0.544749
$$154$$ 0 0
$$155$$ −171700. −0.574039
$$156$$ 0 0
$$157$$ 3718.00 0.0120382 0.00601908 0.999982i $$-0.498084\pi$$
0.00601908 + 0.999982i $$0.498084\pi$$
$$158$$ 0 0
$$159$$ −55044.0 −0.172670
$$160$$ 0 0
$$161$$ −184788. −0.561835
$$162$$ 0 0
$$163$$ 43234.0 0.127455 0.0637274 0.997967i $$-0.479701\pi$$
0.0637274 + 0.997967i $$0.479701\pi$$
$$164$$ 0 0
$$165$$ 28800.0 0.0823536
$$166$$ 0 0
$$167$$ 186522. 0.517534 0.258767 0.965940i $$-0.416684\pi$$
0.258767 + 0.965940i $$0.416684\pi$$
$$168$$ 0 0
$$169$$ 851943. 2.29453
$$170$$ 0 0
$$171$$ −567180. −1.48331
$$172$$ 0 0
$$173$$ 374454. 0.951225 0.475612 0.879655i $$-0.342226\pi$$
0.475612 + 0.879655i $$0.342226\pi$$
$$174$$ 0 0
$$175$$ −73750.0 −0.182040
$$176$$ 0 0
$$177$$ −209880. −0.503545
$$178$$ 0 0
$$179$$ −272100. −0.634740 −0.317370 0.948302i $$-0.602800\pi$$
−0.317370 + 0.948302i $$0.602800\pi$$
$$180$$ 0 0
$$181$$ 75418.0 0.171111 0.0855556 0.996333i $$-0.472733\pi$$
0.0855556 + 0.996333i $$0.472733\pi$$
$$182$$ 0 0
$$183$$ −59028.0 −0.130296
$$184$$ 0 0
$$185$$ 137950. 0.296341
$$186$$ 0 0
$$187$$ −146304. −0.305951
$$188$$ 0 0
$$189$$ −318600. −0.648771
$$190$$ 0 0
$$191$$ −356988. −0.708060 −0.354030 0.935234i $$-0.615189\pi$$
−0.354030 + 0.935234i $$0.615189\pi$$
$$192$$ 0 0
$$193$$ −438694. −0.847751 −0.423876 0.905720i $$-0.639331\pi$$
−0.423876 + 0.905720i $$0.639331\pi$$
$$194$$ 0 0
$$195$$ 165900. 0.312435
$$196$$ 0 0
$$197$$ 156798. 0.287856 0.143928 0.989588i $$-0.454027\pi$$
0.143928 + 0.989588i $$0.454027\pi$$
$$198$$ 0 0
$$199$$ −162520. −0.290920 −0.145460 0.989364i $$-0.546466\pi$$
−0.145460 + 0.989364i $$0.546466\pi$$
$$200$$ 0 0
$$201$$ 202332. 0.353244
$$202$$ 0 0
$$203$$ 697380. 1.18776
$$204$$ 0 0
$$205$$ −9450.00 −0.0157053
$$206$$ 0 0
$$207$$ −324162. −0.525819
$$208$$ 0 0
$$209$$ −526080. −0.833079
$$210$$ 0 0
$$211$$ 181648. 0.280882 0.140441 0.990089i $$-0.455148\pi$$
0.140441 + 0.990089i $$0.455148\pi$$
$$212$$ 0 0
$$213$$ −421272. −0.636229
$$214$$ 0 0
$$215$$ 60850.0 0.0897769
$$216$$ 0 0
$$217$$ 810424. 1.16832
$$218$$ 0 0
$$219$$ −131916. −0.185861
$$220$$ 0 0
$$221$$ −842772. −1.16073
$$222$$ 0 0
$$223$$ −288274. −0.388189 −0.194095 0.980983i $$-0.562177\pi$$
−0.194095 + 0.980983i $$0.562177\pi$$
$$224$$ 0 0
$$225$$ −129375. −0.170370
$$226$$ 0 0
$$227$$ −1.12552e6 −1.44974 −0.724869 0.688887i $$-0.758100\pi$$
−0.724869 + 0.688887i $$0.758100\pi$$
$$228$$ 0 0
$$229$$ 415810. 0.523970 0.261985 0.965072i $$-0.415623\pi$$
0.261985 + 0.965072i $$0.415623\pi$$
$$230$$ 0 0
$$231$$ −135936. −0.167612
$$232$$ 0 0
$$233$$ 770586. 0.929889 0.464945 0.885340i $$-0.346074\pi$$
0.464945 + 0.885340i $$0.346074\pi$$
$$234$$ 0 0
$$235$$ 328050. 0.387499
$$236$$ 0 0
$$237$$ −27120.0 −0.0313631
$$238$$ 0 0
$$239$$ −595320. −0.674149 −0.337074 0.941478i $$-0.609437\pi$$
−0.337074 + 0.941478i $$0.609437\pi$$
$$240$$ 0 0
$$241$$ 273902. 0.303775 0.151888 0.988398i $$-0.451465\pi$$
0.151888 + 0.988398i $$0.451465\pi$$
$$242$$ 0 0
$$243$$ −860706. −0.935059
$$244$$ 0 0
$$245$$ −72075.0 −0.0767131
$$246$$ 0 0
$$247$$ −3.03044e6 −3.16055
$$248$$ 0 0
$$249$$ −654444. −0.668920
$$250$$ 0 0
$$251$$ −850752. −0.852351 −0.426176 0.904640i $$-0.640139\pi$$
−0.426176 + 0.904640i $$0.640139\pi$$
$$252$$ 0 0
$$253$$ −300672. −0.295319
$$254$$ 0 0
$$255$$ −114300. −0.110077
$$256$$ 0 0
$$257$$ 825402. 0.779530 0.389765 0.920914i $$-0.372556\pi$$
0.389765 + 0.920914i $$0.372556\pi$$
$$258$$ 0 0
$$259$$ −651124. −0.603135
$$260$$ 0 0
$$261$$ 1.22337e6 1.11162
$$262$$ 0 0
$$263$$ 1.36465e6 1.21655 0.608276 0.793726i $$-0.291861\pi$$
0.608276 + 0.793726i $$0.291861\pi$$
$$264$$ 0 0
$$265$$ 229350. 0.200625
$$266$$ 0 0
$$267$$ −230940. −0.198254
$$268$$ 0 0
$$269$$ 113310. 0.0954745 0.0477373 0.998860i $$-0.484799\pi$$
0.0477373 + 0.998860i $$0.484799\pi$$
$$270$$ 0 0
$$271$$ −849628. −0.702758 −0.351379 0.936233i $$-0.614287\pi$$
−0.351379 + 0.936233i $$0.614287\pi$$
$$272$$ 0 0
$$273$$ −783048. −0.635890
$$274$$ 0 0
$$275$$ −120000. −0.0956862
$$276$$ 0 0
$$277$$ −438602. −0.343456 −0.171728 0.985144i $$-0.554935\pi$$
−0.171728 + 0.985144i $$0.554935\pi$$
$$278$$ 0 0
$$279$$ 1.42168e6 1.09343
$$280$$ 0 0
$$281$$ −1.45670e6 −1.10053 −0.550267 0.834989i $$-0.685474\pi$$
−0.550267 + 0.834989i $$0.685474\pi$$
$$282$$ 0 0
$$283$$ 120394. 0.0893591 0.0446795 0.999001i $$-0.485773\pi$$
0.0446795 + 0.999001i $$0.485773\pi$$
$$284$$ 0 0
$$285$$ −411000. −0.299730
$$286$$ 0 0
$$287$$ 44604.0 0.0319646
$$288$$ 0 0
$$289$$ −839213. −0.591055
$$290$$ 0 0
$$291$$ 11508.0 0.00796650
$$292$$ 0 0
$$293$$ 2.64209e6 1.79796 0.898978 0.437993i $$-0.144311\pi$$
0.898978 + 0.437993i $$0.144311\pi$$
$$294$$ 0 0
$$295$$ 874500. 0.585066
$$296$$ 0 0
$$297$$ −518400. −0.341015
$$298$$ 0 0
$$299$$ −1.73200e6 −1.12039
$$300$$ 0 0
$$301$$ −287212. −0.182720
$$302$$ 0 0
$$303$$ 465732. 0.291427
$$304$$ 0 0
$$305$$ 245950. 0.151390
$$306$$ 0 0
$$307$$ 1.44756e6 0.876577 0.438288 0.898834i $$-0.355585\pi$$
0.438288 + 0.898834i $$0.355585\pi$$
$$308$$ 0 0
$$309$$ 280284. 0.166994
$$310$$ 0 0
$$311$$ −928068. −0.544100 −0.272050 0.962283i $$-0.587702\pi$$
−0.272050 + 0.962283i $$0.587702\pi$$
$$312$$ 0 0
$$313$$ 2.29563e6 1.32446 0.662232 0.749299i $$-0.269609\pi$$
0.662232 + 0.749299i $$0.269609\pi$$
$$314$$ 0 0
$$315$$ 610650. 0.346750
$$316$$ 0 0
$$317$$ −2.73652e6 −1.52950 −0.764752 0.644324i $$-0.777139\pi$$
−0.764752 + 0.644324i $$0.777139\pi$$
$$318$$ 0 0
$$319$$ 1.13472e6 0.624327
$$320$$ 0 0
$$321$$ −6228.00 −0.00337354
$$322$$ 0 0
$$323$$ 2.08788e6 1.11352
$$324$$ 0 0
$$325$$ −691250. −0.363017
$$326$$ 0 0
$$327$$ 1.24158e6 0.642104
$$328$$ 0 0
$$329$$ −1.54840e6 −0.788665
$$330$$ 0 0
$$331$$ −3.81879e6 −1.91583 −0.957913 0.287059i $$-0.907322\pi$$
−0.957913 + 0.287059i $$0.907322\pi$$
$$332$$ 0 0
$$333$$ −1.14223e6 −0.564471
$$334$$ 0 0
$$335$$ −843050. −0.410432
$$336$$ 0 0
$$337$$ −2.21088e6 −1.06045 −0.530225 0.847857i $$-0.677892\pi$$
−0.530225 + 0.847857i $$0.677892\pi$$
$$338$$ 0 0
$$339$$ −836316. −0.395249
$$340$$ 0 0
$$341$$ 1.31866e6 0.614109
$$342$$ 0 0
$$343$$ 2.32342e6 1.06633
$$344$$ 0 0
$$345$$ −234900. −0.106252
$$346$$ 0 0
$$347$$ 2.32724e6 1.03757 0.518785 0.854905i $$-0.326385\pi$$
0.518785 + 0.854905i $$0.326385\pi$$
$$348$$ 0 0
$$349$$ 311290. 0.136805 0.0684024 0.997658i $$-0.478210\pi$$
0.0684024 + 0.997658i $$0.478210\pi$$
$$350$$ 0 0
$$351$$ −2.98620e6 −1.29375
$$352$$ 0 0
$$353$$ −3.08657e6 −1.31838 −0.659189 0.751977i $$-0.729100\pi$$
−0.659189 + 0.751977i $$0.729100\pi$$
$$354$$ 0 0
$$355$$ 1.75530e6 0.739232
$$356$$ 0 0
$$357$$ 539496. 0.224036
$$358$$ 0 0
$$359$$ −3.53076e6 −1.44588 −0.722940 0.690911i $$-0.757210\pi$$
−0.722940 + 0.690911i $$0.757210\pi$$
$$360$$ 0 0
$$361$$ 5.03150e6 2.03203
$$362$$ 0 0
$$363$$ 745122. 0.296798
$$364$$ 0 0
$$365$$ 549650. 0.215950
$$366$$ 0 0
$$367$$ 35762.0 0.0138598 0.00692989 0.999976i $$-0.497794\pi$$
0.00692989 + 0.999976i $$0.497794\pi$$
$$368$$ 0 0
$$369$$ 78246.0 0.0299155
$$370$$ 0 0
$$371$$ −1.08253e6 −0.408325
$$372$$ 0 0
$$373$$ 1.71525e6 0.638346 0.319173 0.947696i $$-0.396595\pi$$
0.319173 + 0.947696i $$0.396595\pi$$
$$374$$ 0 0
$$375$$ −93750.0 −0.0344265
$$376$$ 0 0
$$377$$ 6.53646e6 2.36859
$$378$$ 0 0
$$379$$ 3.10174e6 1.10919 0.554597 0.832119i $$-0.312873\pi$$
0.554597 + 0.832119i $$0.312873\pi$$
$$380$$ 0 0
$$381$$ −1.79929e6 −0.635023
$$382$$ 0 0
$$383$$ 5.31949e6 1.85299 0.926494 0.376309i $$-0.122807\pi$$
0.926494 + 0.376309i $$0.122807\pi$$
$$384$$ 0 0
$$385$$ 566400. 0.194747
$$386$$ 0 0
$$387$$ −503838. −0.171007
$$388$$ 0 0
$$389$$ −1.16145e6 −0.389158 −0.194579 0.980887i $$-0.562334\pi$$
−0.194579 + 0.980887i $$0.562334\pi$$
$$390$$ 0 0
$$391$$ 1.19329e6 0.394734
$$392$$ 0 0
$$393$$ 47232.0 0.0154261
$$394$$ 0 0
$$395$$ 113000. 0.0364406
$$396$$ 0 0
$$397$$ −628562. −0.200157 −0.100079 0.994980i $$-0.531909\pi$$
−0.100079 + 0.994980i $$0.531909\pi$$
$$398$$ 0 0
$$399$$ 1.93992e6 0.610031
$$400$$ 0 0
$$401$$ −2.72432e6 −0.846052 −0.423026 0.906118i $$-0.639032\pi$$
−0.423026 + 0.906118i $$0.639032\pi$$
$$402$$ 0 0
$$403$$ 7.59601e6 2.32982
$$404$$ 0 0
$$405$$ 852525. 0.258267
$$406$$ 0 0
$$407$$ −1.05946e6 −0.317027
$$408$$ 0 0
$$409$$ 1.78019e6 0.526209 0.263104 0.964767i $$-0.415254\pi$$
0.263104 + 0.964767i $$0.415254\pi$$
$$410$$ 0 0
$$411$$ 985428. 0.287753
$$412$$ 0 0
$$413$$ −4.12764e6 −1.19077
$$414$$ 0 0
$$415$$ 2.72685e6 0.777215
$$416$$ 0 0
$$417$$ −1.69260e6 −0.476666
$$418$$ 0 0
$$419$$ −650580. −0.181036 −0.0905181 0.995895i $$-0.528852\pi$$
−0.0905181 + 0.995895i $$0.528852\pi$$
$$420$$ 0 0
$$421$$ 3.54060e6 0.973579 0.486790 0.873519i $$-0.338168\pi$$
0.486790 + 0.873519i $$0.338168\pi$$
$$422$$ 0 0
$$423$$ −2.71625e6 −0.738107
$$424$$ 0 0
$$425$$ 476250. 0.127898
$$426$$ 0 0
$$427$$ −1.16088e6 −0.308119
$$428$$ 0 0
$$429$$ −1.27411e6 −0.334245
$$430$$ 0 0
$$431$$ −548748. −0.142292 −0.0711459 0.997466i $$-0.522666\pi$$
−0.0711459 + 0.997466i $$0.522666\pi$$
$$432$$ 0 0
$$433$$ −1.49241e6 −0.382534 −0.191267 0.981538i $$-0.561260\pi$$
−0.191267 + 0.981538i $$0.561260\pi$$
$$434$$ 0 0
$$435$$ 886500. 0.224624
$$436$$ 0 0
$$437$$ 4.29084e6 1.07483
$$438$$ 0 0
$$439$$ 4.86212e6 1.20411 0.602053 0.798456i $$-0.294350\pi$$
0.602053 + 0.798456i $$0.294350\pi$$
$$440$$ 0 0
$$441$$ 596781. 0.146123
$$442$$ 0 0
$$443$$ 1.86155e6 0.450678 0.225339 0.974280i $$-0.427651\pi$$
0.225339 + 0.974280i $$0.427651\pi$$
$$444$$ 0 0
$$445$$ 962250. 0.230350
$$446$$ 0 0
$$447$$ −2.33370e6 −0.552429
$$448$$ 0 0
$$449$$ 3.73719e6 0.874841 0.437421 0.899257i $$-0.355892\pi$$
0.437421 + 0.899257i $$0.355892\pi$$
$$450$$ 0 0
$$451$$ 72576.0 0.0168016
$$452$$ 0 0
$$453$$ 587688. 0.134555
$$454$$ 0 0
$$455$$ 3.26270e6 0.738837
$$456$$ 0 0
$$457$$ −6.48276e6 −1.45201 −0.726005 0.687690i $$-0.758625\pi$$
−0.726005 + 0.687690i $$0.758625\pi$$
$$458$$ 0 0
$$459$$ 2.05740e6 0.455813
$$460$$ 0 0
$$461$$ −1.50910e6 −0.330724 −0.165362 0.986233i $$-0.552879\pi$$
−0.165362 + 0.986233i $$0.552879\pi$$
$$462$$ 0 0
$$463$$ 8.68401e6 1.88264 0.941321 0.337513i $$-0.109586\pi$$
0.941321 + 0.337513i $$0.109586\pi$$
$$464$$ 0 0
$$465$$ 1.03020e6 0.220948
$$466$$ 0 0
$$467$$ −6.96412e6 −1.47766 −0.738829 0.673893i $$-0.764621\pi$$
−0.738829 + 0.673893i $$0.764621\pi$$
$$468$$ 0 0
$$469$$ 3.97920e6 0.835340
$$470$$ 0 0
$$471$$ −22308.0 −0.00463349
$$472$$ 0 0
$$473$$ −467328. −0.0960437
$$474$$ 0 0
$$475$$ 1.71250e6 0.348254
$$476$$ 0 0
$$477$$ −1.89902e6 −0.382149
$$478$$ 0 0
$$479$$ −5.51052e6 −1.09737 −0.548686 0.836029i $$-0.684872\pi$$
−0.548686 + 0.836029i $$0.684872\pi$$
$$480$$ 0 0
$$481$$ −6.10291e6 −1.20275
$$482$$ 0 0
$$483$$ 1.10873e6 0.216251
$$484$$ 0 0
$$485$$ −47950.0 −0.00925623
$$486$$ 0 0
$$487$$ 5.51808e6 1.05430 0.527152 0.849771i $$-0.323260\pi$$
0.527152 + 0.849771i $$0.323260\pi$$
$$488$$ 0 0
$$489$$ −259404. −0.0490574
$$490$$ 0 0
$$491$$ 1.51277e6 0.283184 0.141592 0.989925i $$-0.454778\pi$$
0.141592 + 0.989925i $$0.454778\pi$$
$$492$$ 0 0
$$493$$ −4.50342e6 −0.834498
$$494$$ 0 0
$$495$$ 993600. 0.182263
$$496$$ 0 0
$$497$$ −8.28502e6 −1.50454
$$498$$ 0 0
$$499$$ 1.93042e6 0.347057 0.173528 0.984829i $$-0.444483\pi$$
0.173528 + 0.984829i $$0.444483\pi$$
$$500$$ 0 0
$$501$$ −1.11913e6 −0.199199
$$502$$ 0 0
$$503$$ 6.73105e6 1.18621 0.593106 0.805124i $$-0.297901\pi$$
0.593106 + 0.805124i $$0.297901\pi$$
$$504$$ 0 0
$$505$$ −1.94055e6 −0.338607
$$506$$ 0 0
$$507$$ −5.11166e6 −0.883165
$$508$$ 0 0
$$509$$ 556650. 0.0952331 0.0476165 0.998866i $$-0.484837\pi$$
0.0476165 + 0.998866i $$0.484837\pi$$
$$510$$ 0 0
$$511$$ −2.59435e6 −0.439517
$$512$$ 0 0
$$513$$ 7.39800e6 1.24114
$$514$$ 0 0
$$515$$ −1.16785e6 −0.194030
$$516$$ 0 0
$$517$$ −2.51942e6 −0.414548
$$518$$ 0 0
$$519$$ −2.24672e6 −0.366127
$$520$$ 0 0
$$521$$ 1.01110e7 1.63192 0.815962 0.578106i $$-0.196208\pi$$
0.815962 + 0.578106i $$0.196208\pi$$
$$522$$ 0 0
$$523$$ 7.03719e6 1.12498 0.562491 0.826804i $$-0.309843\pi$$
0.562491 + 0.826804i $$0.309843\pi$$
$$524$$ 0 0
$$525$$ 442500. 0.0700672
$$526$$ 0 0
$$527$$ −5.23342e6 −0.820840
$$528$$ 0 0
$$529$$ −3.98399e6 −0.618983
$$530$$ 0 0
$$531$$ −7.24086e6 −1.11443
$$532$$ 0 0
$$533$$ 418068. 0.0637425
$$534$$ 0 0
$$535$$ 25950.0 0.00391970
$$536$$ 0 0
$$537$$ 1.63260e6 0.244312
$$538$$ 0 0
$$539$$ 553536. 0.0820680
$$540$$ 0 0
$$541$$ 4.23114e6 0.621533 0.310766 0.950486i $$-0.399414\pi$$
0.310766 + 0.950486i $$0.399414\pi$$
$$542$$ 0 0
$$543$$ −452508. −0.0658608
$$544$$ 0 0
$$545$$ −5.17325e6 −0.746057
$$546$$ 0 0
$$547$$ −4.44024e6 −0.634510 −0.317255 0.948340i $$-0.602761\pi$$
−0.317255 + 0.948340i $$0.602761\pi$$
$$548$$ 0 0
$$549$$ −2.03647e6 −0.288367
$$550$$ 0 0
$$551$$ −1.61934e7 −2.27227
$$552$$ 0 0
$$553$$ −533360. −0.0741665
$$554$$ 0 0
$$555$$ −827700. −0.114062
$$556$$ 0 0
$$557$$ 9.01448e6 1.23113 0.615563 0.788088i $$-0.288929\pi$$
0.615563 + 0.788088i $$0.288929\pi$$
$$558$$ 0 0
$$559$$ −2.69200e6 −0.364373
$$560$$ 0 0
$$561$$ 877824. 0.117761
$$562$$ 0 0
$$563$$ 9.81287e6 1.30474 0.652372 0.757899i $$-0.273774\pi$$
0.652372 + 0.757899i $$0.273774\pi$$
$$564$$ 0 0
$$565$$ 3.48465e6 0.459238
$$566$$ 0 0
$$567$$ −4.02392e6 −0.525644
$$568$$ 0 0
$$569$$ 1.33152e7 1.72412 0.862061 0.506804i $$-0.169173\pi$$
0.862061 + 0.506804i $$0.169173\pi$$
$$570$$ 0 0
$$571$$ −9.95895e6 −1.27827 −0.639136 0.769094i $$-0.720708\pi$$
−0.639136 + 0.769094i $$0.720708\pi$$
$$572$$ 0 0
$$573$$ 2.14193e6 0.272533
$$574$$ 0 0
$$575$$ 978750. 0.123453
$$576$$ 0 0
$$577$$ 4.50372e6 0.563160 0.281580 0.959538i $$-0.409141\pi$$
0.281580 + 0.959538i $$0.409141\pi$$
$$578$$ 0 0
$$579$$ 2.63216e6 0.326300
$$580$$ 0 0
$$581$$ −1.28707e7 −1.58184
$$582$$ 0 0
$$583$$ −1.76141e6 −0.214629
$$584$$ 0 0
$$585$$ 5.72355e6 0.691474
$$586$$ 0 0
$$587$$ −625842. −0.0749669 −0.0374834 0.999297i $$-0.511934\pi$$
−0.0374834 + 0.999297i $$0.511934\pi$$
$$588$$ 0 0
$$589$$ −1.88183e7 −2.23508
$$590$$ 0 0
$$591$$ −940788. −0.110796
$$592$$ 0 0
$$593$$ −2.50385e6 −0.292397 −0.146198 0.989255i $$-0.546704\pi$$
−0.146198 + 0.989255i $$0.546704\pi$$
$$594$$ 0 0
$$595$$ −2.24790e6 −0.260306
$$596$$ 0 0
$$597$$ 975120. 0.111975
$$598$$ 0 0
$$599$$ −756480. −0.0861451 −0.0430725 0.999072i $$-0.513715\pi$$
−0.0430725 + 0.999072i $$0.513715\pi$$
$$600$$ 0 0
$$601$$ −1.38565e7 −1.56483 −0.782413 0.622760i $$-0.786011\pi$$
−0.782413 + 0.622760i $$0.786011\pi$$
$$602$$ 0 0
$$603$$ 6.98045e6 0.781791
$$604$$ 0 0
$$605$$ −3.10468e6 −0.344848
$$606$$ 0 0
$$607$$ 1.13772e7 1.25333 0.626663 0.779291i $$-0.284420\pi$$
0.626663 + 0.779291i $$0.284420\pi$$
$$608$$ 0 0
$$609$$ −4.18428e6 −0.457170
$$610$$ 0 0
$$611$$ −1.45129e7 −1.57272
$$612$$ 0 0
$$613$$ 7.00161e6 0.752570 0.376285 0.926504i $$-0.377201\pi$$
0.376285 + 0.926504i $$0.377201\pi$$
$$614$$ 0 0
$$615$$ 56700.0 0.00604499
$$616$$ 0 0
$$617$$ 7.90300e6 0.835755 0.417878 0.908503i $$-0.362774\pi$$
0.417878 + 0.908503i $$0.362774\pi$$
$$618$$ 0 0
$$619$$ −4.02362e6 −0.422076 −0.211038 0.977478i $$-0.567684\pi$$
−0.211038 + 0.977478i $$0.567684\pi$$
$$620$$ 0 0
$$621$$ 4.22820e6 0.439974
$$622$$ 0 0
$$623$$ −4.54182e6 −0.468824
$$624$$ 0 0
$$625$$ 390625. 0.0400000
$$626$$ 0 0
$$627$$ 3.15648e6 0.320652
$$628$$ 0 0
$$629$$ 4.20472e6 0.423750
$$630$$ 0 0
$$631$$ −1.00227e7 −1.00210 −0.501049 0.865419i $$-0.667052\pi$$
−0.501049 + 0.865419i $$0.667052\pi$$
$$632$$ 0 0
$$633$$ −1.08989e6 −0.108112
$$634$$ 0 0
$$635$$ 7.49705e6 0.737830
$$636$$ 0 0
$$637$$ 3.18860e6 0.311352
$$638$$ 0 0
$$639$$ −1.45339e7 −1.40809
$$640$$ 0 0
$$641$$ 6.37390e6 0.612718 0.306359 0.951916i $$-0.400889\pi$$
0.306359 + 0.951916i $$0.400889\pi$$
$$642$$ 0 0
$$643$$ −5.00457e6 −0.477352 −0.238676 0.971099i $$-0.576713\pi$$
−0.238676 + 0.971099i $$0.576713\pi$$
$$644$$ 0 0
$$645$$ −365100. −0.0345551
$$646$$ 0 0
$$647$$ −8.71928e6 −0.818879 −0.409440 0.912337i $$-0.634276\pi$$
−0.409440 + 0.912337i $$0.634276\pi$$
$$648$$ 0 0
$$649$$ −6.71616e6 −0.625906
$$650$$ 0 0
$$651$$ −4.86254e6 −0.449688
$$652$$ 0 0
$$653$$ 1.58477e6 0.145440 0.0727201 0.997352i $$-0.476832\pi$$
0.0727201 + 0.997352i $$0.476832\pi$$
$$654$$ 0 0
$$655$$ −196800. −0.0179235
$$656$$ 0 0
$$657$$ −4.55110e6 −0.411342
$$658$$ 0 0
$$659$$ −1.26410e7 −1.13388 −0.566940 0.823759i $$-0.691873\pi$$
−0.566940 + 0.823759i $$0.691873\pi$$
$$660$$ 0 0
$$661$$ 3.61572e6 0.321878 0.160939 0.986964i $$-0.448548\pi$$
0.160939 + 0.986964i $$0.448548\pi$$
$$662$$ 0 0
$$663$$ 5.05663e6 0.446763
$$664$$ 0 0
$$665$$ −8.08300e6 −0.708791
$$666$$ 0 0
$$667$$ −9.25506e6 −0.805498
$$668$$ 0 0
$$669$$ 1.72964e6 0.149414
$$670$$ 0 0
$$671$$ −1.88890e6 −0.161958
$$672$$ 0 0
$$673$$ 1.11313e7 0.947349 0.473675 0.880700i $$-0.342927\pi$$
0.473675 + 0.880700i $$0.342927\pi$$
$$674$$ 0 0
$$675$$ 1.68750e6 0.142556
$$676$$ 0 0
$$677$$ 235518. 0.0197493 0.00987467 0.999951i $$-0.496857\pi$$
0.00987467 + 0.999951i $$0.496857\pi$$
$$678$$ 0 0
$$679$$ 226324. 0.0188389
$$680$$ 0 0
$$681$$ 6.75313e6 0.558004
$$682$$ 0 0
$$683$$ −2.05830e7 −1.68833 −0.844164 0.536084i $$-0.819903\pi$$
−0.844164 + 0.536084i $$0.819903\pi$$
$$684$$ 0 0
$$685$$ −4.10595e6 −0.334339
$$686$$ 0 0
$$687$$ −2.49486e6 −0.201676
$$688$$ 0 0
$$689$$ −1.01464e7 −0.814265
$$690$$ 0 0
$$691$$ 9.54825e6 0.760727 0.380363 0.924837i $$-0.375799\pi$$
0.380363 + 0.924837i $$0.375799\pi$$
$$692$$ 0 0
$$693$$ −4.68979e6 −0.370954
$$694$$ 0 0
$$695$$ 7.05250e6 0.553836
$$696$$ 0 0
$$697$$ −288036. −0.0224577
$$698$$ 0 0
$$699$$ −4.62352e6 −0.357915
$$700$$ 0 0
$$701$$ −1.29304e6 −0.0993843 −0.0496921 0.998765i $$-0.515824\pi$$
−0.0496921 + 0.998765i $$0.515824\pi$$
$$702$$ 0 0
$$703$$ 1.51193e7 1.15384
$$704$$ 0 0
$$705$$ −1.96830e6 −0.149148
$$706$$ 0 0
$$707$$ 9.15940e6 0.689157
$$708$$ 0 0
$$709$$ 2.12720e7 1.58926 0.794628 0.607097i $$-0.207666\pi$$
0.794628 + 0.607097i $$0.207666\pi$$
$$710$$ 0 0
$$711$$ −935640. −0.0694120
$$712$$ 0 0
$$713$$ −1.07553e7 −0.792316
$$714$$ 0 0
$$715$$ 5.30880e6 0.388357
$$716$$ 0 0
$$717$$ 3.57192e6 0.259480
$$718$$ 0 0
$$719$$ 8.31732e6 0.600014 0.300007 0.953937i $$-0.403011\pi$$
0.300007 + 0.953937i $$0.403011\pi$$
$$720$$ 0 0
$$721$$ 5.51225e6 0.394903
$$722$$ 0 0
$$723$$ −1.64341e6 −0.116923
$$724$$ 0 0
$$725$$ −3.69375e6 −0.260989
$$726$$ 0 0
$$727$$ −4.36740e6 −0.306469 −0.153235 0.988190i $$-0.548969\pi$$
−0.153235 + 0.988190i $$0.548969\pi$$
$$728$$ 0 0
$$729$$ −3.12231e6 −0.217599
$$730$$ 0 0
$$731$$ 1.85471e6 0.128375
$$732$$ 0 0
$$733$$ 4.05645e6 0.278860 0.139430 0.990232i $$-0.455473\pi$$
0.139430 + 0.990232i $$0.455473\pi$$
$$734$$ 0 0
$$735$$ 432450. 0.0295269
$$736$$ 0 0
$$737$$ 6.47462e6 0.439082
$$738$$ 0 0
$$739$$ −768260. −0.0517484 −0.0258742 0.999665i $$-0.508237\pi$$
−0.0258742 + 0.999665i $$0.508237\pi$$
$$740$$ 0 0
$$741$$ 1.81826e7 1.21650
$$742$$ 0 0
$$743$$ 6.18781e6 0.411211 0.205605 0.978635i $$-0.434084\pi$$
0.205605 + 0.978635i $$0.434084\pi$$
$$744$$ 0 0
$$745$$ 9.72375e6 0.641864
$$746$$ 0 0
$$747$$ −2.25783e7 −1.48044
$$748$$ 0 0
$$749$$ −122484. −0.00797765
$$750$$ 0 0
$$751$$ 1.81698e7 1.17557 0.587787 0.809016i $$-0.299999\pi$$
0.587787 + 0.809016i $$0.299999\pi$$
$$752$$ 0 0
$$753$$ 5.10451e6 0.328070
$$754$$ 0 0
$$755$$ −2.44870e6 −0.156339
$$756$$ 0 0
$$757$$ −1.93494e7 −1.22724 −0.613618 0.789603i $$-0.710286\pi$$
−0.613618 + 0.789603i $$0.710286\pi$$
$$758$$ 0 0
$$759$$ 1.80403e6 0.113668
$$760$$ 0 0
$$761$$ −3.01992e7 −1.89031 −0.945155 0.326621i $$-0.894090\pi$$
−0.945155 + 0.326621i $$0.894090\pi$$
$$762$$ 0 0
$$763$$ 2.44177e7 1.51843
$$764$$ 0 0
$$765$$ −3.94335e6 −0.243619
$$766$$ 0 0
$$767$$ −3.86879e7 −2.37458
$$768$$ 0 0
$$769$$ 2.15854e7 1.31627 0.658134 0.752901i $$-0.271346\pi$$
0.658134 + 0.752901i $$0.271346\pi$$
$$770$$ 0 0
$$771$$ −4.95241e6 −0.300041
$$772$$ 0 0
$$773$$ −3.90895e6 −0.235294 −0.117647 0.993055i $$-0.537535\pi$$
−0.117647 + 0.993055i $$0.537535\pi$$
$$774$$ 0 0
$$775$$ −4.29250e6 −0.256718
$$776$$ 0 0
$$777$$ 3.90674e6 0.232147
$$778$$ 0 0
$$779$$ −1.03572e6 −0.0611503
$$780$$ 0 0
$$781$$ −1.34807e7 −0.790833
$$782$$ 0 0
$$783$$ −1.59570e7 −0.930137
$$784$$ 0 0
$$785$$ 92950.0 0.00538363
$$786$$ 0 0
$$787$$ 2.65082e7 1.52561 0.762806 0.646628i $$-0.223821\pi$$
0.762806 + 0.646628i $$0.223821\pi$$
$$788$$ 0 0
$$789$$ −8.18788e6 −0.468251
$$790$$ 0 0
$$791$$ −1.64475e7 −0.934674
$$792$$ 0 0
$$793$$ −1.08808e7 −0.614439
$$794$$ 0 0
$$795$$ −1.37610e6 −0.0772204
$$796$$ 0 0
$$797$$ −1.07940e7 −0.601919 −0.300960 0.953637i $$-0.597307\pi$$
−0.300960 + 0.953637i $$0.597307\pi$$
$$798$$ 0 0
$$799$$ 9.99896e6 0.554100
$$800$$ 0 0
$$801$$ −7.96743e6 −0.438770
$$802$$ 0 0
$$803$$ −4.22131e6 −0.231025
$$804$$ 0 0
$$805$$ −4.61970e6 −0.251260
$$806$$ 0 0
$$807$$ −679860. −0.0367482
$$808$$ 0 0
$$809$$ −1.11446e7 −0.598675 −0.299338 0.954147i $$-0.596766\pi$$
−0.299338 + 0.954147i $$0.596766\pi$$
$$810$$ 0 0
$$811$$ 1.14866e7 0.613253 0.306626 0.951830i $$-0.400800\pi$$
0.306626 + 0.951830i $$0.400800\pi$$
$$812$$ 0 0
$$813$$ 5.09777e6 0.270492
$$814$$ 0 0
$$815$$ 1.08085e6 0.0569995
$$816$$ 0 0
$$817$$ 6.66916e6 0.349555
$$818$$ 0 0
$$819$$ −2.70152e7 −1.40734
$$820$$ 0 0
$$821$$ −3.04347e7 −1.57584 −0.787918 0.615781i $$-0.788841\pi$$
−0.787918 + 0.615781i $$0.788841\pi$$
$$822$$ 0 0
$$823$$ 4.09773e6 0.210884 0.105442 0.994425i $$-0.466374\pi$$
0.105442 + 0.994425i $$0.466374\pi$$
$$824$$ 0 0
$$825$$ 720000. 0.0368297
$$826$$ 0 0
$$827$$ 1.70652e7 0.867654 0.433827 0.900996i $$-0.357163\pi$$
0.433827 + 0.900996i $$0.357163\pi$$
$$828$$ 0 0
$$829$$ 2.47617e7 1.25139 0.625697 0.780066i $$-0.284815\pi$$
0.625697 + 0.780066i $$0.284815\pi$$
$$830$$ 0 0
$$831$$ 2.63161e6 0.132196
$$832$$ 0 0
$$833$$ −2.19685e6 −0.109695
$$834$$ 0 0
$$835$$ 4.66305e6 0.231448
$$836$$ 0 0
$$837$$ −1.85436e7 −0.914914
$$838$$ 0 0
$$839$$ 3.16529e7 1.55242 0.776208 0.630476i $$-0.217140\pi$$
0.776208 + 0.630476i $$0.217140\pi$$
$$840$$ 0 0
$$841$$ 1.44170e7 0.702884
$$842$$ 0 0
$$843$$ 8.74019e6 0.423596
$$844$$ 0 0
$$845$$ 2.12986e7 1.02615
$$846$$ 0 0
$$847$$ 1.46541e7 0.701859
$$848$$ 0 0
$$849$$ −722364. −0.0343943
$$850$$ 0 0
$$851$$ 8.64119e6 0.409025
$$852$$ 0 0
$$853$$ −2.82671e7 −1.33017 −0.665087 0.746765i $$-0.731606\pi$$
−0.665087 + 0.746765i $$0.731606\pi$$
$$854$$ 0 0
$$855$$ −1.41795e7 −0.663354
$$856$$ 0 0
$$857$$ 2.60870e7 1.21331 0.606655 0.794966i $$-0.292511\pi$$
0.606655 + 0.794966i $$0.292511\pi$$
$$858$$ 0 0
$$859$$ 3.38111e7 1.56342 0.781710 0.623642i $$-0.214348\pi$$
0.781710 + 0.623642i $$0.214348\pi$$
$$860$$ 0 0
$$861$$ −267624. −0.0123032
$$862$$ 0 0
$$863$$ 2.22817e7 1.01841 0.509204 0.860646i $$-0.329940\pi$$
0.509204 + 0.860646i $$0.329940\pi$$
$$864$$ 0 0
$$865$$ 9.36135e6 0.425401
$$866$$ 0 0
$$867$$ 5.03528e6 0.227497
$$868$$ 0 0
$$869$$ −867840. −0.0389843
$$870$$ 0 0
$$871$$ 3.72965e7 1.66580
$$872$$ 0 0
$$873$$ 397026. 0.0176313
$$874$$ 0 0
$$875$$ −1.84375e6 −0.0814108
$$876$$ 0 0
$$877$$ 3.46748e7 1.52235 0.761177 0.648545i $$-0.224622\pi$$
0.761177 + 0.648545i $$0.224622\pi$$
$$878$$ 0 0
$$879$$ −1.58526e7 −0.692034
$$880$$ 0 0
$$881$$ 1.42603e7 0.618998 0.309499 0.950900i $$-0.399839\pi$$
0.309499 + 0.950900i $$0.399839\pi$$
$$882$$ 0 0
$$883$$ 3.75177e7 1.61933 0.809663 0.586895i $$-0.199650\pi$$
0.809663 + 0.586895i $$0.199650\pi$$
$$884$$ 0 0
$$885$$ −5.24700e6 −0.225192
$$886$$ 0 0
$$887$$ 4.07657e7 1.73975 0.869873 0.493275i $$-0.164200\pi$$
0.869873 + 0.493275i $$0.164200\pi$$
$$888$$ 0 0
$$889$$ −3.53861e7 −1.50168
$$890$$ 0 0
$$891$$ −6.54739e6 −0.276296
$$892$$ 0 0
$$893$$ 3.59543e7 1.50877
$$894$$ 0 0
$$895$$ −6.80250e6 −0.283864
$$896$$ 0 0
$$897$$ 1.03920e7 0.431238
$$898$$ 0 0
$$899$$ 4.05899e7 1.67501
$$900$$ 0 0
$$901$$ 6.99059e6 0.286881
$$902$$ 0 0
$$903$$ 1.72327e6 0.0703290
$$904$$ 0 0
$$905$$ 1.88545e6 0.0765233
$$906$$ 0 0
$$907$$ 3.57116e7 1.44142 0.720712 0.693235i $$-0.243815\pi$$
0.720712 + 0.693235i $$0.243815\pi$$
$$908$$ 0 0
$$909$$ 1.60678e7 0.644979
$$910$$ 0 0
$$911$$ −2.11389e7 −0.843893 −0.421947 0.906621i $$-0.638653\pi$$
−0.421947 + 0.906621i $$0.638653\pi$$
$$912$$ 0 0
$$913$$ −2.09422e7 −0.831468
$$914$$ 0 0
$$915$$ −1.47570e6 −0.0582700
$$916$$ 0 0
$$917$$ 928896. 0.0364791
$$918$$ 0 0
$$919$$ 1.85996e7 0.726465 0.363233 0.931698i $$-0.381673\pi$$
0.363233 + 0.931698i $$0.381673\pi$$
$$920$$ 0 0
$$921$$ −8.68535e6 −0.337395
$$922$$ 0 0
$$923$$ −7.76545e7 −3.00028
$$924$$ 0 0
$$925$$ 3.44875e6 0.132528
$$926$$ 0 0
$$927$$ 9.66980e6 0.369588
$$928$$ 0 0
$$929$$ 4.45110e7 1.69211 0.846055 0.533096i $$-0.178972\pi$$
0.846055 + 0.533096i $$0.178972\pi$$
$$930$$ 0 0
$$931$$ −7.89942e6 −0.298690
$$932$$ 0 0
$$933$$ 5.56841e6 0.209424
$$934$$ 0 0
$$935$$ −3.65760e6 −0.136826
$$936$$ 0 0
$$937$$ −2.19419e7 −0.816441 −0.408221 0.912883i $$-0.633851\pi$$
−0.408221 + 0.912883i $$0.633851\pi$$
$$938$$ 0 0
$$939$$ −1.37738e7 −0.509787
$$940$$ 0 0
$$941$$ 7.77722e6 0.286319 0.143160 0.989700i $$-0.454274\pi$$
0.143160 + 0.989700i $$0.454274\pi$$
$$942$$ 0 0
$$943$$ −591948. −0.0216773
$$944$$ 0 0
$$945$$ −7.96500e6 −0.290139
$$946$$ 0 0
$$947$$ −3.17199e7 −1.14936 −0.574681 0.818378i $$-0.694874\pi$$
−0.574681 + 0.818378i $$0.694874\pi$$
$$948$$ 0 0
$$949$$ −2.43165e7 −0.876468
$$950$$ 0 0
$$951$$ 1.64191e7 0.588707
$$952$$ 0 0
$$953$$ −5.60285e6 −0.199838 −0.0999188 0.994996i $$-0.531858\pi$$
−0.0999188 + 0.994996i $$0.531858\pi$$
$$954$$ 0 0
$$955$$ −8.92470e6 −0.316654
$$956$$ 0 0
$$957$$ −6.80832e6 −0.240304
$$958$$ 0 0
$$959$$ 1.93801e7 0.680470
$$960$$ 0 0
$$961$$ 1.85403e7 0.647601
$$962$$ 0 0
$$963$$ −214866. −0.00746624
$$964$$ 0 0
$$965$$ −1.09673e7 −0.379126
$$966$$ 0 0
$$967$$ −2.03532e7 −0.699949 −0.349975 0.936759i $$-0.613810\pi$$
−0.349975 + 0.936759i $$0.613810\pi$$
$$968$$ 0 0
$$969$$ −1.25273e7 −0.428595
$$970$$ 0 0
$$971$$ 2.34306e7 0.797510 0.398755 0.917057i $$-0.369442\pi$$
0.398755 + 0.917057i $$0.369442\pi$$
$$972$$ 0 0
$$973$$ −3.32878e7 −1.12721
$$974$$ 0 0
$$975$$ 4.14750e6 0.139725
$$976$$ 0 0
$$977$$ −4.30412e7 −1.44261 −0.721303 0.692619i $$-0.756457\pi$$
−0.721303 + 0.692619i $$0.756457\pi$$
$$978$$ 0 0
$$979$$ −7.39008e6 −0.246429
$$980$$ 0 0
$$981$$ 4.28345e7 1.42109
$$982$$ 0 0
$$983$$ −4.75003e7 −1.56788 −0.783940 0.620837i $$-0.786793\pi$$
−0.783940 + 0.620837i $$0.786793\pi$$
$$984$$ 0 0
$$985$$ 3.91995e6 0.128733
$$986$$ 0 0
$$987$$ 9.29038e6 0.303557
$$988$$ 0 0
$$989$$ 3.81164e6 0.123914
$$990$$ 0 0
$$991$$ 2.09231e7 0.676770 0.338385 0.941008i $$-0.390119\pi$$
0.338385 + 0.941008i $$0.390119\pi$$
$$992$$ 0 0
$$993$$ 2.29128e7 0.737402
$$994$$ 0 0
$$995$$ −4.06300e6 −0.130104
$$996$$ 0 0
$$997$$ −2.96332e7 −0.944148 −0.472074 0.881559i $$-0.656495\pi$$
−0.472074 + 0.881559i $$0.656495\pi$$
$$998$$ 0 0
$$999$$ 1.48986e7 0.472315
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 320.6.a.f.1.1 1
4.3 odd 2 320.6.a.k.1.1 1
8.3 odd 2 80.6.a.c.1.1 1
8.5 even 2 10.6.a.c.1.1 1
24.5 odd 2 90.6.a.b.1.1 1
24.11 even 2 720.6.a.v.1.1 1
40.3 even 4 400.6.c.i.49.1 2
40.13 odd 4 50.6.b.b.49.1 2
40.19 odd 2 400.6.a.i.1.1 1
40.27 even 4 400.6.c.i.49.2 2
40.29 even 2 50.6.a.b.1.1 1
40.37 odd 4 50.6.b.b.49.2 2
56.13 odd 2 490.6.a.k.1.1 1
120.29 odd 2 450.6.a.u.1.1 1
120.53 even 4 450.6.c.f.199.2 2
120.77 even 4 450.6.c.f.199.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.a.c.1.1 1 8.5 even 2
50.6.a.b.1.1 1 40.29 even 2
50.6.b.b.49.1 2 40.13 odd 4
50.6.b.b.49.2 2 40.37 odd 4
80.6.a.c.1.1 1 8.3 odd 2
90.6.a.b.1.1 1 24.5 odd 2
320.6.a.f.1.1 1 1.1 even 1 trivial
320.6.a.k.1.1 1 4.3 odd 2
400.6.a.i.1.1 1 40.19 odd 2
400.6.c.i.49.1 2 40.3 even 4
400.6.c.i.49.2 2 40.27 even 4
450.6.a.u.1.1 1 120.29 odd 2
450.6.c.f.199.1 2 120.77 even 4
450.6.c.f.199.2 2 120.53 even 4
490.6.a.k.1.1 1 56.13 odd 2
720.6.a.v.1.1 1 24.11 even 2