# Properties

 Label 320.6.a.i.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 40) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} +25.0000 q^{5} -62.0000 q^{7} -239.000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} +25.0000 q^{5} -62.0000 q^{7} -239.000 q^{9} +144.000 q^{11} +654.000 q^{13} +50.0000 q^{15} -1190.00 q^{17} -556.000 q^{19} -124.000 q^{21} +2182.00 q^{23} +625.000 q^{25} -964.000 q^{27} +1578.00 q^{29} +9660.00 q^{31} +288.000 q^{33} -1550.00 q^{35} +3534.00 q^{37} +1308.00 q^{39} +7462.00 q^{41} +7114.00 q^{43} -5975.00 q^{45} -28294.0 q^{47} -12963.0 q^{49} -2380.00 q^{51} +13046.0 q^{53} +3600.00 q^{55} -1112.00 q^{57} +37092.0 q^{59} -39570.0 q^{61} +14818.0 q^{63} +16350.0 q^{65} +56734.0 q^{67} +4364.00 q^{69} +45588.0 q^{71} +11842.0 q^{73} +1250.00 q^{75} -8928.00 q^{77} +94216.0 q^{79} +56149.0 q^{81} +31482.0 q^{83} -29750.0 q^{85} +3156.00 q^{87} -94054.0 q^{89} -40548.0 q^{91} +19320.0 q^{93} -13900.0 q^{95} +23714.0 q^{97} -34416.0 q^{99} +O(q^{100})$$

## 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
$$3$$ 2.00000 0.128300 0.0641500 0.997940i $$-0.479566\pi$$
0.0641500 + 0.997940i $$0.479566\pi$$
$$4$$ 0 0
$$5$$ 25.0000 0.447214
$$6$$ 0 0
$$7$$ −62.0000 −0.478241 −0.239120 0.970990i $$-0.576859\pi$$
−0.239120 + 0.970990i $$0.576859\pi$$
$$8$$ 0 0
$$9$$ −239.000 −0.983539
$$10$$ 0 0
$$11$$ 144.000 0.358823 0.179412 0.983774i $$-0.442581\pi$$
0.179412 + 0.983774i $$0.442581\pi$$
$$12$$ 0 0
$$13$$ 654.000 1.07330 0.536648 0.843806i $$-0.319690\pi$$
0.536648 + 0.843806i $$0.319690\pi$$
$$14$$ 0 0
$$15$$ 50.0000 0.0573775
$$16$$ 0 0
$$17$$ −1190.00 −0.998676 −0.499338 0.866407i $$-0.666423\pi$$
−0.499338 + 0.866407i $$0.666423\pi$$
$$18$$ 0 0
$$19$$ −556.000 −0.353338 −0.176669 0.984270i $$-0.556532\pi$$
−0.176669 + 0.984270i $$0.556532\pi$$
$$20$$ 0 0
$$21$$ −124.000 −0.0613583
$$22$$ 0 0
$$23$$ 2182.00 0.860073 0.430036 0.902812i $$-0.358501\pi$$
0.430036 + 0.902812i $$0.358501\pi$$
$$24$$ 0 0
$$25$$ 625.000 0.200000
$$26$$ 0 0
$$27$$ −964.000 −0.254488
$$28$$ 0 0
$$29$$ 1578.00 0.348427 0.174214 0.984708i $$-0.444262\pi$$
0.174214 + 0.984708i $$0.444262\pi$$
$$30$$ 0 0
$$31$$ 9660.00 1.80540 0.902699 0.430273i $$-0.141583\pi$$
0.902699 + 0.430273i $$0.141583\pi$$
$$32$$ 0 0
$$33$$ 288.000 0.0460371
$$34$$ 0 0
$$35$$ −1550.00 −0.213876
$$36$$ 0 0
$$37$$ 3534.00 0.424387 0.212194 0.977228i $$-0.431939\pi$$
0.212194 + 0.977228i $$0.431939\pi$$
$$38$$ 0 0
$$39$$ 1308.00 0.137704
$$40$$ 0 0
$$41$$ 7462.00 0.693259 0.346630 0.938002i $$-0.387326\pi$$
0.346630 + 0.938002i $$0.387326\pi$$
$$42$$ 0 0
$$43$$ 7114.00 0.586736 0.293368 0.956000i $$-0.405224\pi$$
0.293368 + 0.956000i $$0.405224\pi$$
$$44$$ 0 0
$$45$$ −5975.00 −0.439852
$$46$$ 0 0
$$47$$ −28294.0 −1.86831 −0.934157 0.356863i $$-0.883846\pi$$
−0.934157 + 0.356863i $$0.883846\pi$$
$$48$$ 0 0
$$49$$ −12963.0 −0.771286
$$50$$ 0 0
$$51$$ −2380.00 −0.128130
$$52$$ 0 0
$$53$$ 13046.0 0.637952 0.318976 0.947763i $$-0.396661\pi$$
0.318976 + 0.947763i $$0.396661\pi$$
$$54$$ 0 0
$$55$$ 3600.00 0.160471
$$56$$ 0 0
$$57$$ −1112.00 −0.0453333
$$58$$ 0 0
$$59$$ 37092.0 1.38724 0.693618 0.720343i $$-0.256016\pi$$
0.693618 + 0.720343i $$0.256016\pi$$
$$60$$ 0 0
$$61$$ −39570.0 −1.36157 −0.680787 0.732481i $$-0.738362\pi$$
−0.680787 + 0.732481i $$0.738362\pi$$
$$62$$ 0 0
$$63$$ 14818.0 0.470368
$$64$$ 0 0
$$65$$ 16350.0 0.479992
$$66$$ 0 0
$$67$$ 56734.0 1.54403 0.772016 0.635603i $$-0.219248\pi$$
0.772016 + 0.635603i $$0.219248\pi$$
$$68$$ 0 0
$$69$$ 4364.00 0.110347
$$70$$ 0 0
$$71$$ 45588.0 1.07326 0.536630 0.843818i $$-0.319697\pi$$
0.536630 + 0.843818i $$0.319697\pi$$
$$72$$ 0 0
$$73$$ 11842.0 0.260087 0.130043 0.991508i $$-0.458488\pi$$
0.130043 + 0.991508i $$0.458488\pi$$
$$74$$ 0 0
$$75$$ 1250.00 0.0256600
$$76$$ 0 0
$$77$$ −8928.00 −0.171604
$$78$$ 0 0
$$79$$ 94216.0 1.69847 0.849233 0.528018i $$-0.177065\pi$$
0.849233 + 0.528018i $$0.177065\pi$$
$$80$$ 0 0
$$81$$ 56149.0 0.950888
$$82$$ 0 0
$$83$$ 31482.0 0.501611 0.250806 0.968037i $$-0.419305\pi$$
0.250806 + 0.968037i $$0.419305\pi$$
$$84$$ 0 0
$$85$$ −29750.0 −0.446622
$$86$$ 0 0
$$87$$ 3156.00 0.0447032
$$88$$ 0 0
$$89$$ −94054.0 −1.25864 −0.629321 0.777145i $$-0.716667\pi$$
−0.629321 + 0.777145i $$0.716667\pi$$
$$90$$ 0 0
$$91$$ −40548.0 −0.513294
$$92$$ 0 0
$$93$$ 19320.0 0.231633
$$94$$ 0 0
$$95$$ −13900.0 −0.158018
$$96$$ 0 0
$$97$$ 23714.0 0.255903 0.127952 0.991780i $$-0.459160\pi$$
0.127952 + 0.991780i $$0.459160\pi$$
$$98$$ 0 0
$$99$$ −34416.0 −0.352917
$$100$$ 0 0
$$101$$ 129674. 1.26488 0.632440 0.774609i $$-0.282053\pi$$
0.632440 + 0.774609i $$0.282053\pi$$
$$102$$ 0 0
$$103$$ 136846. 1.27098 0.635490 0.772109i $$-0.280798\pi$$
0.635490 + 0.772109i $$0.280798\pi$$
$$104$$ 0 0
$$105$$ −3100.00 −0.0274403
$$106$$ 0 0
$$107$$ 193190. 1.63127 0.815634 0.578569i $$-0.196388\pi$$
0.815634 + 0.578569i $$0.196388\pi$$
$$108$$ 0 0
$$109$$ 120046. 0.967791 0.483895 0.875126i $$-0.339222\pi$$
0.483895 + 0.875126i $$0.339222\pi$$
$$110$$ 0 0
$$111$$ 7068.00 0.0544489
$$112$$ 0 0
$$113$$ −152646. −1.12458 −0.562289 0.826941i $$-0.690079\pi$$
−0.562289 + 0.826941i $$0.690079\pi$$
$$114$$ 0 0
$$115$$ 54550.0 0.384636
$$116$$ 0 0
$$117$$ −156306. −1.05563
$$118$$ 0 0
$$119$$ 73780.0 0.477608
$$120$$ 0 0
$$121$$ −140315. −0.871246
$$122$$ 0 0
$$123$$ 14924.0 0.0889452
$$124$$ 0 0
$$125$$ 15625.0 0.0894427
$$126$$ 0 0
$$127$$ 107906. 0.593658 0.296829 0.954931i $$-0.404071\pi$$
0.296829 + 0.954931i $$0.404071\pi$$
$$128$$ 0 0
$$129$$ 14228.0 0.0752783
$$130$$ 0 0
$$131$$ 233072. 1.18662 0.593310 0.804974i $$-0.297821\pi$$
0.593310 + 0.804974i $$0.297821\pi$$
$$132$$ 0 0
$$133$$ 34472.0 0.168981
$$134$$ 0 0
$$135$$ −24100.0 −0.113811
$$136$$ 0 0
$$137$$ 356082. 1.62087 0.810436 0.585827i $$-0.199230\pi$$
0.810436 + 0.585827i $$0.199230\pi$$
$$138$$ 0 0
$$139$$ −312204. −1.37057 −0.685285 0.728275i $$-0.740323\pi$$
−0.685285 + 0.728275i $$0.740323\pi$$
$$140$$ 0 0
$$141$$ −56588.0 −0.239705
$$142$$ 0 0
$$143$$ 94176.0 0.385124
$$144$$ 0 0
$$145$$ 39450.0 0.155821
$$146$$ 0 0
$$147$$ −25926.0 −0.0989560
$$148$$ 0 0
$$149$$ −27498.0 −0.101469 −0.0507347 0.998712i $$-0.516156\pi$$
−0.0507347 + 0.998712i $$0.516156\pi$$
$$150$$ 0 0
$$151$$ −136908. −0.488637 −0.244319 0.969695i $$-0.578564\pi$$
−0.244319 + 0.969695i $$0.578564\pi$$
$$152$$ 0 0
$$153$$ 284410. 0.982237
$$154$$ 0 0
$$155$$ 241500. 0.807398
$$156$$ 0 0
$$157$$ −406714. −1.31686 −0.658431 0.752641i $$-0.728779\pi$$
−0.658431 + 0.752641i $$0.728779\pi$$
$$158$$ 0 0
$$159$$ 26092.0 0.0818492
$$160$$ 0 0
$$161$$ −135284. −0.411322
$$162$$ 0 0
$$163$$ 13642.0 0.0402169 0.0201085 0.999798i $$-0.493599\pi$$
0.0201085 + 0.999798i $$0.493599\pi$$
$$164$$ 0 0
$$165$$ 7200.00 0.0205884
$$166$$ 0 0
$$167$$ −203438. −0.564470 −0.282235 0.959345i $$-0.591076\pi$$
−0.282235 + 0.959345i $$0.591076\pi$$
$$168$$ 0 0
$$169$$ 56423.0 0.151964
$$170$$ 0 0
$$171$$ 132884. 0.347522
$$172$$ 0 0
$$173$$ −127242. −0.323233 −0.161616 0.986854i $$-0.551671\pi$$
−0.161616 + 0.986854i $$0.551671\pi$$
$$174$$ 0 0
$$175$$ −38750.0 −0.0956482
$$176$$ 0 0
$$177$$ 74184.0 0.177982
$$178$$ 0 0
$$179$$ 94684.0 0.220874 0.110437 0.993883i $$-0.464775\pi$$
0.110437 + 0.993883i $$0.464775\pi$$
$$180$$ 0 0
$$181$$ 517018. 1.17303 0.586515 0.809938i $$-0.300499\pi$$
0.586515 + 0.809938i $$0.300499\pi$$
$$182$$ 0 0
$$183$$ −79140.0 −0.174690
$$184$$ 0 0
$$185$$ 88350.0 0.189792
$$186$$ 0 0
$$187$$ −171360. −0.358348
$$188$$ 0 0
$$189$$ 59768.0 0.121707
$$190$$ 0 0
$$191$$ −412300. −0.817768 −0.408884 0.912586i $$-0.634082\pi$$
−0.408884 + 0.912586i $$0.634082\pi$$
$$192$$ 0 0
$$193$$ −771654. −1.49118 −0.745589 0.666406i $$-0.767832\pi$$
−0.745589 + 0.666406i $$0.767832\pi$$
$$194$$ 0 0
$$195$$ 32700.0 0.0615831
$$196$$ 0 0
$$197$$ 190238. 0.349246 0.174623 0.984635i $$-0.444129\pi$$
0.174623 + 0.984635i $$0.444129\pi$$
$$198$$ 0 0
$$199$$ 132072. 0.236417 0.118208 0.992989i $$-0.462285\pi$$
0.118208 + 0.992989i $$0.462285\pi$$
$$200$$ 0 0
$$201$$ 113468. 0.198099
$$202$$ 0 0
$$203$$ −97836.0 −0.166632
$$204$$ 0 0
$$205$$ 186550. 0.310035
$$206$$ 0 0
$$207$$ −521498. −0.845915
$$208$$ 0 0
$$209$$ −80064.0 −0.126786
$$210$$ 0 0
$$211$$ −928704. −1.43606 −0.718028 0.696015i $$-0.754955\pi$$
−0.718028 + 0.696015i $$0.754955\pi$$
$$212$$ 0 0
$$213$$ 91176.0 0.137699
$$214$$ 0 0
$$215$$ 177850. 0.262396
$$216$$ 0 0
$$217$$ −598920. −0.863415
$$218$$ 0 0
$$219$$ 23684.0 0.0333691
$$220$$ 0 0
$$221$$ −778260. −1.07187
$$222$$ 0 0
$$223$$ 421494. 0.567583 0.283791 0.958886i $$-0.408408\pi$$
0.283791 + 0.958886i $$0.408408\pi$$
$$224$$ 0 0
$$225$$ −149375. −0.196708
$$226$$ 0 0
$$227$$ −991962. −1.27770 −0.638852 0.769329i $$-0.720590\pi$$
−0.638852 + 0.769329i $$0.720590\pi$$
$$228$$ 0 0
$$229$$ 266946. 0.336384 0.168192 0.985754i $$-0.446207\pi$$
0.168192 + 0.985754i $$0.446207\pi$$
$$230$$ 0 0
$$231$$ −17856.0 −0.0220168
$$232$$ 0 0
$$233$$ 960314. 1.15884 0.579420 0.815029i $$-0.303279\pi$$
0.579420 + 0.815029i $$0.303279\pi$$
$$234$$ 0 0
$$235$$ −707350. −0.835535
$$236$$ 0 0
$$237$$ 188432. 0.217913
$$238$$ 0 0
$$239$$ −492696. −0.557936 −0.278968 0.960300i $$-0.589992\pi$$
−0.278968 + 0.960300i $$0.589992\pi$$
$$240$$ 0 0
$$241$$ 56078.0 0.0621942 0.0310971 0.999516i $$-0.490100\pi$$
0.0310971 + 0.999516i $$0.490100\pi$$
$$242$$ 0 0
$$243$$ 346550. 0.376487
$$244$$ 0 0
$$245$$ −324075. −0.344929
$$246$$ 0 0
$$247$$ −363624. −0.379237
$$248$$ 0 0
$$249$$ 62964.0 0.0643567
$$250$$ 0 0
$$251$$ −1.96792e6 −1.97162 −0.985810 0.167866i $$-0.946312\pi$$
−0.985810 + 0.167866i $$0.946312\pi$$
$$252$$ 0 0
$$253$$ 314208. 0.308614
$$254$$ 0 0
$$255$$ −59500.0 −0.0573016
$$256$$ 0 0
$$257$$ −971910. −0.917896 −0.458948 0.888463i $$-0.651773\pi$$
−0.458948 + 0.888463i $$0.651773\pi$$
$$258$$ 0 0
$$259$$ −219108. −0.202959
$$260$$ 0 0
$$261$$ −377142. −0.342692
$$262$$ 0 0
$$263$$ −154770. −0.137974 −0.0689870 0.997618i $$-0.521977\pi$$
−0.0689870 + 0.997618i $$0.521977\pi$$
$$264$$ 0 0
$$265$$ 326150. 0.285301
$$266$$ 0 0
$$267$$ −188108. −0.161484
$$268$$ 0 0
$$269$$ −1.02371e6 −0.862577 −0.431289 0.902214i $$-0.641941\pi$$
−0.431289 + 0.902214i $$0.641941\pi$$
$$270$$ 0 0
$$271$$ −1.14776e6 −0.949350 −0.474675 0.880161i $$-0.657434\pi$$
−0.474675 + 0.880161i $$0.657434\pi$$
$$272$$ 0 0
$$273$$ −81096.0 −0.0658556
$$274$$ 0 0
$$275$$ 90000.0 0.0717647
$$276$$ 0 0
$$277$$ 2.49676e6 1.95514 0.977568 0.210619i $$-0.0675481\pi$$
0.977568 + 0.210619i $$0.0675481\pi$$
$$278$$ 0 0
$$279$$ −2.30874e6 −1.77568
$$280$$ 0 0
$$281$$ 1.69540e6 1.28087 0.640436 0.768011i $$-0.278754\pi$$
0.640436 + 0.768011i $$0.278754\pi$$
$$282$$ 0 0
$$283$$ 2.12395e6 1.57645 0.788223 0.615390i $$-0.211001\pi$$
0.788223 + 0.615390i $$0.211001\pi$$
$$284$$ 0 0
$$285$$ −27800.0 −0.0202737
$$286$$ 0 0
$$287$$ −462644. −0.331545
$$288$$ 0 0
$$289$$ −3757.00 −0.00264604
$$290$$ 0 0
$$291$$ 47428.0 0.0328324
$$292$$ 0 0
$$293$$ −992722. −0.675552 −0.337776 0.941227i $$-0.609675\pi$$
−0.337776 + 0.941227i $$0.609675\pi$$
$$294$$ 0 0
$$295$$ 927300. 0.620391
$$296$$ 0 0
$$297$$ −138816. −0.0913163
$$298$$ 0 0
$$299$$ 1.42703e6 0.923112
$$300$$ 0 0
$$301$$ −441068. −0.280601
$$302$$ 0 0
$$303$$ 259348. 0.162284
$$304$$ 0 0
$$305$$ −989250. −0.608915
$$306$$ 0 0
$$307$$ −487522. −0.295222 −0.147611 0.989046i $$-0.547158\pi$$
−0.147611 + 0.989046i $$0.547158\pi$$
$$308$$ 0 0
$$309$$ 273692. 0.163067
$$310$$ 0 0
$$311$$ −444116. −0.260373 −0.130186 0.991490i $$-0.541558\pi$$
−0.130186 + 0.991490i $$0.541558\pi$$
$$312$$ 0 0
$$313$$ 47242.0 0.0272563 0.0136282 0.999907i $$-0.495662\pi$$
0.0136282 + 0.999907i $$0.495662\pi$$
$$314$$ 0 0
$$315$$ 370450. 0.210355
$$316$$ 0 0
$$317$$ −694058. −0.387925 −0.193962 0.981009i $$-0.562134\pi$$
−0.193962 + 0.981009i $$0.562134\pi$$
$$318$$ 0 0
$$319$$ 227232. 0.125024
$$320$$ 0 0
$$321$$ 386380. 0.209292
$$322$$ 0 0
$$323$$ 661640. 0.352871
$$324$$ 0 0
$$325$$ 408750. 0.214659
$$326$$ 0 0
$$327$$ 240092. 0.124168
$$328$$ 0 0
$$329$$ 1.75423e6 0.893504
$$330$$ 0 0
$$331$$ −82168.0 −0.0412223 −0.0206112 0.999788i $$-0.506561\pi$$
−0.0206112 + 0.999788i $$0.506561\pi$$
$$332$$ 0 0
$$333$$ −844626. −0.417401
$$334$$ 0 0
$$335$$ 1.41835e6 0.690512
$$336$$ 0 0
$$337$$ −727934. −0.349154 −0.174577 0.984644i $$-0.555856\pi$$
−0.174577 + 0.984644i $$0.555856\pi$$
$$338$$ 0 0
$$339$$ −305292. −0.144283
$$340$$ 0 0
$$341$$ 1.39104e6 0.647819
$$342$$ 0 0
$$343$$ 1.84574e6 0.847101
$$344$$ 0 0
$$345$$ 109100. 0.0493488
$$346$$ 0 0
$$347$$ −2.02298e6 −0.901919 −0.450959 0.892544i $$-0.648918\pi$$
−0.450959 + 0.892544i $$0.648918\pi$$
$$348$$ 0 0
$$349$$ −4.40858e6 −1.93747 −0.968736 0.248095i $$-0.920196\pi$$
−0.968736 + 0.248095i $$0.920196\pi$$
$$350$$ 0 0
$$351$$ −630456. −0.273141
$$352$$ 0 0
$$353$$ 1.06965e6 0.456883 0.228441 0.973558i $$-0.426637\pi$$
0.228441 + 0.973558i $$0.426637\pi$$
$$354$$ 0 0
$$355$$ 1.13970e6 0.479976
$$356$$ 0 0
$$357$$ 147560. 0.0612771
$$358$$ 0 0
$$359$$ −32968.0 −0.0135007 −0.00675035 0.999977i $$-0.502149\pi$$
−0.00675035 + 0.999977i $$0.502149\pi$$
$$360$$ 0 0
$$361$$ −2.16696e6 −0.875152
$$362$$ 0 0
$$363$$ −280630. −0.111781
$$364$$ 0 0
$$365$$ 296050. 0.116314
$$366$$ 0 0
$$367$$ 3.64081e6 1.41102 0.705509 0.708700i $$-0.250718\pi$$
0.705509 + 0.708700i $$0.250718\pi$$
$$368$$ 0 0
$$369$$ −1.78342e6 −0.681847
$$370$$ 0 0
$$371$$ −808852. −0.305094
$$372$$ 0 0
$$373$$ 3.17311e6 1.18090 0.590450 0.807074i $$-0.298950\pi$$
0.590450 + 0.807074i $$0.298950\pi$$
$$374$$ 0 0
$$375$$ 31250.0 0.0114755
$$376$$ 0 0
$$377$$ 1.03201e6 0.373965
$$378$$ 0 0
$$379$$ −1.60498e6 −0.573947 −0.286973 0.957939i $$-0.592649\pi$$
−0.286973 + 0.957939i $$0.592649\pi$$
$$380$$ 0 0
$$381$$ 215812. 0.0761664
$$382$$ 0 0
$$383$$ 1.98925e6 0.692936 0.346468 0.938062i $$-0.387381\pi$$
0.346468 + 0.938062i $$0.387381\pi$$
$$384$$ 0 0
$$385$$ −223200. −0.0767436
$$386$$ 0 0
$$387$$ −1.70025e6 −0.577078
$$388$$ 0 0
$$389$$ 5.16495e6 1.73058 0.865291 0.501270i $$-0.167134\pi$$
0.865291 + 0.501270i $$0.167134\pi$$
$$390$$ 0 0
$$391$$ −2.59658e6 −0.858934
$$392$$ 0 0
$$393$$ 466144. 0.152243
$$394$$ 0 0
$$395$$ 2.35540e6 0.759577
$$396$$ 0 0
$$397$$ −937586. −0.298562 −0.149281 0.988795i $$-0.547696\pi$$
−0.149281 + 0.988795i $$0.547696\pi$$
$$398$$ 0 0
$$399$$ 68944.0 0.0216802
$$400$$ 0 0
$$401$$ −5.63657e6 −1.75047 −0.875234 0.483699i $$-0.839293\pi$$
−0.875234 + 0.483699i $$0.839293\pi$$
$$402$$ 0 0
$$403$$ 6.31764e6 1.93773
$$404$$ 0 0
$$405$$ 1.40373e6 0.425250
$$406$$ 0 0
$$407$$ 508896. 0.152280
$$408$$ 0 0
$$409$$ 4.06137e6 1.20051 0.600254 0.799810i $$-0.295066\pi$$
0.600254 + 0.799810i $$0.295066\pi$$
$$410$$ 0 0
$$411$$ 712164. 0.207958
$$412$$ 0 0
$$413$$ −2.29970e6 −0.663433
$$414$$ 0 0
$$415$$ 787050. 0.224327
$$416$$ 0 0
$$417$$ −624408. −0.175844
$$418$$ 0 0
$$419$$ 976108. 0.271621 0.135810 0.990735i $$-0.456636\pi$$
0.135810 + 0.990735i $$0.456636\pi$$
$$420$$ 0 0
$$421$$ 1.62706e6 0.447403 0.223701 0.974658i $$-0.428186\pi$$
0.223701 + 0.974658i $$0.428186\pi$$
$$422$$ 0 0
$$423$$ 6.76227e6 1.83756
$$424$$ 0 0
$$425$$ −743750. −0.199735
$$426$$ 0 0
$$427$$ 2.45334e6 0.651161
$$428$$ 0 0
$$429$$ 188352. 0.0494114
$$430$$ 0 0
$$431$$ −4.27900e6 −1.10956 −0.554778 0.831998i $$-0.687197\pi$$
−0.554778 + 0.831998i $$0.687197\pi$$
$$432$$ 0 0
$$433$$ −3.20195e6 −0.820720 −0.410360 0.911924i $$-0.634597\pi$$
−0.410360 + 0.911924i $$0.634597\pi$$
$$434$$ 0 0
$$435$$ 78900.0 0.0199919
$$436$$ 0 0
$$437$$ −1.21319e6 −0.303897
$$438$$ 0 0
$$439$$ 5.09246e6 1.26115 0.630574 0.776129i $$-0.282820\pi$$
0.630574 + 0.776129i $$0.282820\pi$$
$$440$$ 0 0
$$441$$ 3.09816e6 0.758590
$$442$$ 0 0
$$443$$ 5.43551e6 1.31593 0.657963 0.753050i $$-0.271418\pi$$
0.657963 + 0.753050i $$0.271418\pi$$
$$444$$ 0 0
$$445$$ −2.35135e6 −0.562882
$$446$$ 0 0
$$447$$ −54996.0 −0.0130185
$$448$$ 0 0
$$449$$ −2.99007e6 −0.699948 −0.349974 0.936759i $$-0.613810\pi$$
−0.349974 + 0.936759i $$0.613810\pi$$
$$450$$ 0 0
$$451$$ 1.07453e6 0.248758
$$452$$ 0 0
$$453$$ −273816. −0.0626922
$$454$$ 0 0
$$455$$ −1.01370e6 −0.229552
$$456$$ 0 0
$$457$$ 8.01759e6 1.79578 0.897891 0.440218i $$-0.145099\pi$$
0.897891 + 0.440218i $$0.145099\pi$$
$$458$$ 0 0
$$459$$ 1.14716e6 0.254151
$$460$$ 0 0
$$461$$ −2.58462e6 −0.566428 −0.283214 0.959057i $$-0.591401\pi$$
−0.283214 + 0.959057i $$0.591401\pi$$
$$462$$ 0 0
$$463$$ 6.14261e6 1.33168 0.665840 0.746094i $$-0.268073\pi$$
0.665840 + 0.746094i $$0.268073\pi$$
$$464$$ 0 0
$$465$$ 483000. 0.103589
$$466$$ 0 0
$$467$$ 1.59270e6 0.337942 0.168971 0.985621i $$-0.445956\pi$$
0.168971 + 0.985621i $$0.445956\pi$$
$$468$$ 0 0
$$469$$ −3.51751e6 −0.738419
$$470$$ 0 0
$$471$$ −813428. −0.168953
$$472$$ 0 0
$$473$$ 1.02442e6 0.210535
$$474$$ 0 0
$$475$$ −347500. −0.0706677
$$476$$ 0 0
$$477$$ −3.11799e6 −0.627450
$$478$$ 0 0
$$479$$ 863592. 0.171977 0.0859884 0.996296i $$-0.472595\pi$$
0.0859884 + 0.996296i $$0.472595\pi$$
$$480$$ 0 0
$$481$$ 2.31124e6 0.455493
$$482$$ 0 0
$$483$$ −270568. −0.0527726
$$484$$ 0 0
$$485$$ 592850. 0.114443
$$486$$ 0 0
$$487$$ −8.20714e6 −1.56808 −0.784042 0.620707i $$-0.786846\pi$$
−0.784042 + 0.620707i $$0.786846\pi$$
$$488$$ 0 0
$$489$$ 27284.0 0.00515984
$$490$$ 0 0
$$491$$ −8.93394e6 −1.67240 −0.836198 0.548428i $$-0.815227\pi$$
−0.836198 + 0.548428i $$0.815227\pi$$
$$492$$ 0 0
$$493$$ −1.87782e6 −0.347966
$$494$$ 0 0
$$495$$ −860400. −0.157829
$$496$$ 0 0
$$497$$ −2.82646e6 −0.513276
$$498$$ 0 0
$$499$$ −1.11960e6 −0.201284 −0.100642 0.994923i $$-0.532090\pi$$
−0.100642 + 0.994923i $$0.532090\pi$$
$$500$$ 0 0
$$501$$ −406876. −0.0724215
$$502$$ 0 0
$$503$$ 3.68177e6 0.648839 0.324420 0.945913i $$-0.394831\pi$$
0.324420 + 0.945913i $$0.394831\pi$$
$$504$$ 0 0
$$505$$ 3.24185e6 0.565672
$$506$$ 0 0
$$507$$ 112846. 0.0194969
$$508$$ 0 0
$$509$$ 6.73483e6 1.15221 0.576105 0.817375i $$-0.304572\pi$$
0.576105 + 0.817375i $$0.304572\pi$$
$$510$$ 0 0
$$511$$ −734204. −0.124384
$$512$$ 0 0
$$513$$ 535984. 0.0899204
$$514$$ 0 0
$$515$$ 3.42115e6 0.568400
$$516$$ 0 0
$$517$$ −4.07434e6 −0.670395
$$518$$ 0 0
$$519$$ −254484. −0.0414708
$$520$$ 0 0
$$521$$ 441370. 0.0712375 0.0356187 0.999365i $$-0.488660\pi$$
0.0356187 + 0.999365i $$0.488660\pi$$
$$522$$ 0 0
$$523$$ 1.17300e7 1.87518 0.937589 0.347744i $$-0.113052\pi$$
0.937589 + 0.347744i $$0.113052\pi$$
$$524$$ 0 0
$$525$$ −77500.0 −0.0122717
$$526$$ 0 0
$$527$$ −1.14954e7 −1.80301
$$528$$ 0 0
$$529$$ −1.67522e6 −0.260275
$$530$$ 0 0
$$531$$ −8.86499e6 −1.36440
$$532$$ 0 0
$$533$$ 4.88015e6 0.744072
$$534$$ 0 0
$$535$$ 4.82975e6 0.729525
$$536$$ 0 0
$$537$$ 189368. 0.0283381
$$538$$ 0 0
$$539$$ −1.86667e6 −0.276755
$$540$$ 0 0
$$541$$ −744158. −0.109313 −0.0546565 0.998505i $$-0.517406\pi$$
−0.0546565 + 0.998505i $$0.517406\pi$$
$$542$$ 0 0
$$543$$ 1.03404e6 0.150500
$$544$$ 0 0
$$545$$ 3.00115e6 0.432809
$$546$$ 0 0
$$547$$ 3.24801e6 0.464139 0.232070 0.972699i $$-0.425450\pi$$
0.232070 + 0.972699i $$0.425450\pi$$
$$548$$ 0 0
$$549$$ 9.45723e6 1.33916
$$550$$ 0 0
$$551$$ −877368. −0.123113
$$552$$ 0 0
$$553$$ −5.84139e6 −0.812276
$$554$$ 0 0
$$555$$ 176700. 0.0243503
$$556$$ 0 0
$$557$$ 9.94446e6 1.35814 0.679068 0.734075i $$-0.262384\pi$$
0.679068 + 0.734075i $$0.262384\pi$$
$$558$$ 0 0
$$559$$ 4.65256e6 0.629741
$$560$$ 0 0
$$561$$ −342720. −0.0459761
$$562$$ 0 0
$$563$$ −3.89374e6 −0.517721 −0.258861 0.965915i $$-0.583347\pi$$
−0.258861 + 0.965915i $$0.583347\pi$$
$$564$$ 0 0
$$565$$ −3.81615e6 −0.502926
$$566$$ 0 0
$$567$$ −3.48124e6 −0.454754
$$568$$ 0 0
$$569$$ −1.11951e7 −1.44960 −0.724801 0.688958i $$-0.758068\pi$$
−0.724801 + 0.688958i $$0.758068\pi$$
$$570$$ 0 0
$$571$$ 844040. 0.108336 0.0541680 0.998532i $$-0.482749\pi$$
0.0541680 + 0.998532i $$0.482749\pi$$
$$572$$ 0 0
$$573$$ −824600. −0.104920
$$574$$ 0 0
$$575$$ 1.36375e6 0.172015
$$576$$ 0 0
$$577$$ −5.13378e6 −0.641945 −0.320973 0.947088i $$-0.604010\pi$$
−0.320973 + 0.947088i $$0.604010\pi$$
$$578$$ 0 0
$$579$$ −1.54331e6 −0.191318
$$580$$ 0 0
$$581$$ −1.95188e6 −0.239891
$$582$$ 0 0
$$583$$ 1.87862e6 0.228912
$$584$$ 0 0
$$585$$ −3.90765e6 −0.472091
$$586$$ 0 0
$$587$$ −9.76156e6 −1.16929 −0.584647 0.811287i $$-0.698767\pi$$
−0.584647 + 0.811287i $$0.698767\pi$$
$$588$$ 0 0
$$589$$ −5.37096e6 −0.637916
$$590$$ 0 0
$$591$$ 380476. 0.0448083
$$592$$ 0 0
$$593$$ 966226. 0.112835 0.0564173 0.998407i $$-0.482032\pi$$
0.0564173 + 0.998407i $$0.482032\pi$$
$$594$$ 0 0
$$595$$ 1.84450e6 0.213593
$$596$$ 0 0
$$597$$ 264144. 0.0303323
$$598$$ 0 0
$$599$$ −7.90000e6 −0.899622 −0.449811 0.893124i $$-0.648509\pi$$
−0.449811 + 0.893124i $$0.648509\pi$$
$$600$$ 0 0
$$601$$ 1.03126e7 1.16461 0.582307 0.812969i $$-0.302150\pi$$
0.582307 + 0.812969i $$0.302150\pi$$
$$602$$ 0 0
$$603$$ −1.35594e7 −1.51862
$$604$$ 0 0
$$605$$ −3.50788e6 −0.389633
$$606$$ 0 0
$$607$$ −9.70767e6 −1.06941 −0.534704 0.845040i $$-0.679577\pi$$
−0.534704 + 0.845040i $$0.679577\pi$$
$$608$$ 0 0
$$609$$ −195672. −0.0213789
$$610$$ 0 0
$$611$$ −1.85043e7 −2.00525
$$612$$ 0 0
$$613$$ 1.10568e7 1.18844 0.594219 0.804304i $$-0.297461\pi$$
0.594219 + 0.804304i $$0.297461\pi$$
$$614$$ 0 0
$$615$$ 373100. 0.0397775
$$616$$ 0 0
$$617$$ 8.31174e6 0.878980 0.439490 0.898248i $$-0.355159\pi$$
0.439490 + 0.898248i $$0.355159\pi$$
$$618$$ 0 0
$$619$$ −1.15451e7 −1.21108 −0.605539 0.795816i $$-0.707042\pi$$
−0.605539 + 0.795816i $$0.707042\pi$$
$$620$$ 0 0
$$621$$ −2.10345e6 −0.218878
$$622$$ 0 0
$$623$$ 5.83135e6 0.601934
$$624$$ 0 0
$$625$$ 390625. 0.0400000
$$626$$ 0 0
$$627$$ −160128. −0.0162667
$$628$$ 0 0
$$629$$ −4.20546e6 −0.423825
$$630$$ 0 0
$$631$$ −8.20262e6 −0.820123 −0.410062 0.912058i $$-0.634493\pi$$
−0.410062 + 0.912058i $$0.634493\pi$$
$$632$$ 0 0
$$633$$ −1.85741e6 −0.184246
$$634$$ 0 0
$$635$$ 2.69765e6 0.265492
$$636$$ 0 0
$$637$$ −8.47780e6 −0.827818
$$638$$ 0 0
$$639$$ −1.08955e7 −1.05559
$$640$$ 0 0
$$641$$ −5.39695e6 −0.518804 −0.259402 0.965769i $$-0.583525\pi$$
−0.259402 + 0.965769i $$0.583525\pi$$
$$642$$ 0 0
$$643$$ 1.33896e7 1.27715 0.638573 0.769561i $$-0.279525\pi$$
0.638573 + 0.769561i $$0.279525\pi$$
$$644$$ 0 0
$$645$$ 355700. 0.0336655
$$646$$ 0 0
$$647$$ 6.48254e6 0.608814 0.304407 0.952542i $$-0.401542\pi$$
0.304407 + 0.952542i $$0.401542\pi$$
$$648$$ 0 0
$$649$$ 5.34125e6 0.497773
$$650$$ 0 0
$$651$$ −1.19784e6 −0.110776
$$652$$ 0 0
$$653$$ −1.44907e7 −1.32986 −0.664931 0.746904i $$-0.731539\pi$$
−0.664931 + 0.746904i $$0.731539\pi$$
$$654$$ 0 0
$$655$$ 5.82680e6 0.530673
$$656$$ 0 0
$$657$$ −2.83024e6 −0.255805
$$658$$ 0 0
$$659$$ −6.59080e6 −0.591187 −0.295593 0.955314i $$-0.595517\pi$$
−0.295593 + 0.955314i $$0.595517\pi$$
$$660$$ 0 0
$$661$$ 3.25233e6 0.289528 0.144764 0.989466i $$-0.453758\pi$$
0.144764 + 0.989466i $$0.453758\pi$$
$$662$$ 0 0
$$663$$ −1.55652e6 −0.137522
$$664$$ 0 0
$$665$$ 861800. 0.0755705
$$666$$ 0 0
$$667$$ 3.44320e6 0.299673
$$668$$ 0 0
$$669$$ 842988. 0.0728209
$$670$$ 0 0
$$671$$ −5.69808e6 −0.488565
$$672$$ 0 0
$$673$$ 3.86655e6 0.329068 0.164534 0.986371i $$-0.447388\pi$$
0.164534 + 0.986371i $$0.447388\pi$$
$$674$$ 0 0
$$675$$ −602500. −0.0508976
$$676$$ 0 0
$$677$$ −1.23856e6 −0.103859 −0.0519297 0.998651i $$-0.516537\pi$$
−0.0519297 + 0.998651i $$0.516537\pi$$
$$678$$ 0 0
$$679$$ −1.47027e6 −0.122383
$$680$$ 0 0
$$681$$ −1.98392e6 −0.163930
$$682$$ 0 0
$$683$$ 1.31376e7 1.07762 0.538810 0.842427i $$-0.318874\pi$$
0.538810 + 0.842427i $$0.318874\pi$$
$$684$$ 0 0
$$685$$ 8.90205e6 0.724876
$$686$$ 0 0
$$687$$ 533892. 0.0431580
$$688$$ 0 0
$$689$$ 8.53208e6 0.684711
$$690$$ 0 0
$$691$$ 1.23841e7 0.986664 0.493332 0.869841i $$-0.335779\pi$$
0.493332 + 0.869841i $$0.335779\pi$$
$$692$$ 0 0
$$693$$ 2.13379e6 0.168779
$$694$$ 0 0
$$695$$ −7.80510e6 −0.612938
$$696$$ 0 0
$$697$$ −8.87978e6 −0.692341
$$698$$ 0 0
$$699$$ 1.92063e6 0.148679
$$700$$ 0 0
$$701$$ 9.78952e6 0.752430 0.376215 0.926532i $$-0.377225\pi$$
0.376215 + 0.926532i $$0.377225\pi$$
$$702$$ 0 0
$$703$$ −1.96490e6 −0.149952
$$704$$ 0 0
$$705$$ −1.41470e6 −0.107199
$$706$$ 0 0
$$707$$ −8.03979e6 −0.604917
$$708$$ 0 0
$$709$$ −1.22257e7 −0.913397 −0.456699 0.889622i $$-0.650968\pi$$
−0.456699 + 0.889622i $$0.650968\pi$$
$$710$$ 0 0
$$711$$ −2.25176e7 −1.67051
$$712$$ 0 0
$$713$$ 2.10781e7 1.55277
$$714$$ 0 0
$$715$$ 2.35440e6 0.172233
$$716$$ 0 0
$$717$$ −985392. −0.0715832
$$718$$ 0 0
$$719$$ −1.35053e7 −0.974276 −0.487138 0.873325i $$-0.661959\pi$$
−0.487138 + 0.873325i $$0.661959\pi$$
$$720$$ 0 0
$$721$$ −8.48445e6 −0.607835
$$722$$ 0 0
$$723$$ 112156. 0.00797952
$$724$$ 0 0
$$725$$ 986250. 0.0696854
$$726$$ 0 0
$$727$$ 1.17271e7 0.822916 0.411458 0.911429i $$-0.365020\pi$$
0.411458 + 0.911429i $$0.365020\pi$$
$$728$$ 0 0
$$729$$ −1.29511e7 −0.902585
$$730$$ 0 0
$$731$$ −8.46566e6 −0.585959
$$732$$ 0 0
$$733$$ 1.16512e7 0.800960 0.400480 0.916305i $$-0.368843\pi$$
0.400480 + 0.916305i $$0.368843\pi$$
$$734$$ 0 0
$$735$$ −648150. −0.0442545
$$736$$ 0 0
$$737$$ 8.16970e6 0.554035
$$738$$ 0 0
$$739$$ 1.26808e7 0.854155 0.427077 0.904215i $$-0.359543\pi$$
0.427077 + 0.904215i $$0.359543\pi$$
$$740$$ 0 0
$$741$$ −727248. −0.0486561
$$742$$ 0 0
$$743$$ −197370. −0.0131162 −0.00655812 0.999978i $$-0.502088\pi$$
−0.00655812 + 0.999978i $$0.502088\pi$$
$$744$$ 0 0
$$745$$ −687450. −0.0453785
$$746$$ 0 0
$$747$$ −7.52420e6 −0.493354
$$748$$ 0 0
$$749$$ −1.19778e7 −0.780139
$$750$$ 0 0
$$751$$ −1.33282e7 −0.862326 −0.431163 0.902274i $$-0.641897\pi$$
−0.431163 + 0.902274i $$0.641897\pi$$
$$752$$ 0 0
$$753$$ −3.93584e6 −0.252959
$$754$$ 0 0
$$755$$ −3.42270e6 −0.218525
$$756$$ 0 0
$$757$$ 3.86122e6 0.244898 0.122449 0.992475i $$-0.460925\pi$$
0.122449 + 0.992475i $$0.460925\pi$$
$$758$$ 0 0
$$759$$ 628416. 0.0395952
$$760$$ 0 0
$$761$$ −8.31756e6 −0.520636 −0.260318 0.965523i $$-0.583827\pi$$
−0.260318 + 0.965523i $$0.583827\pi$$
$$762$$ 0 0
$$763$$ −7.44285e6 −0.462837
$$764$$ 0 0
$$765$$ 7.11025e6 0.439270
$$766$$ 0 0
$$767$$ 2.42582e7 1.48891
$$768$$ 0 0
$$769$$ 2.76358e7 1.68522 0.842609 0.538527i $$-0.181019\pi$$
0.842609 + 0.538527i $$0.181019\pi$$
$$770$$ 0 0
$$771$$ −1.94382e6 −0.117766
$$772$$ 0 0
$$773$$ −1.78842e7 −1.07652 −0.538259 0.842780i $$-0.680918\pi$$
−0.538259 + 0.842780i $$0.680918\pi$$
$$774$$ 0 0
$$775$$ 6.03750e6 0.361080
$$776$$ 0 0
$$777$$ −438216. −0.0260397
$$778$$ 0 0
$$779$$ −4.14887e6 −0.244955
$$780$$ 0 0
$$781$$ 6.56467e6 0.385111
$$782$$ 0 0
$$783$$ −1.52119e6 −0.0886706
$$784$$ 0 0
$$785$$ −1.01679e7 −0.588918
$$786$$ 0 0
$$787$$ −2.15691e7 −1.24135 −0.620676 0.784067i $$-0.713142\pi$$
−0.620676 + 0.784067i $$0.713142\pi$$
$$788$$ 0 0
$$789$$ −309540. −0.0177021
$$790$$ 0 0
$$791$$ 9.46405e6 0.537819
$$792$$ 0 0
$$793$$ −2.58788e7 −1.46137
$$794$$ 0 0
$$795$$ 652300. 0.0366041
$$796$$ 0 0
$$797$$ 1.03060e7 0.574705 0.287353 0.957825i $$-0.407225\pi$$
0.287353 + 0.957825i $$0.407225\pi$$
$$798$$ 0 0
$$799$$ 3.36699e7 1.86584
$$800$$ 0 0
$$801$$ 2.24789e7 1.23792
$$802$$ 0 0
$$803$$ 1.70525e6 0.0933251
$$804$$ 0 0
$$805$$ −3.38210e6 −0.183949
$$806$$ 0 0
$$807$$ −2.04743e6 −0.110669
$$808$$ 0 0
$$809$$ 372378. 0.0200038 0.0100019 0.999950i $$-0.496816\pi$$
0.0100019 + 0.999950i $$0.496816\pi$$
$$810$$ 0 0
$$811$$ 1.94795e7 1.03998 0.519990 0.854173i $$-0.325936\pi$$
0.519990 + 0.854173i $$0.325936\pi$$
$$812$$ 0 0
$$813$$ −2.29551e6 −0.121802
$$814$$ 0 0
$$815$$ 341050. 0.0179856
$$816$$ 0 0
$$817$$ −3.95538e6 −0.207316
$$818$$ 0 0
$$819$$ 9.69097e6 0.504844
$$820$$ 0 0
$$821$$ 469318. 0.0243002 0.0121501 0.999926i $$-0.496132\pi$$
0.0121501 + 0.999926i $$0.496132\pi$$
$$822$$ 0 0
$$823$$ 1.78622e7 0.919253 0.459626 0.888112i $$-0.347983\pi$$
0.459626 + 0.888112i $$0.347983\pi$$
$$824$$ 0 0
$$825$$ 180000. 0.00920741
$$826$$ 0 0
$$827$$ −9.42560e6 −0.479231 −0.239616 0.970868i $$-0.577021\pi$$
−0.239616 + 0.970868i $$0.577021\pi$$
$$828$$ 0 0
$$829$$ 1.48622e7 0.751098 0.375549 0.926803i $$-0.377454\pi$$
0.375549 + 0.926803i $$0.377454\pi$$
$$830$$ 0 0
$$831$$ 4.99352e6 0.250844
$$832$$ 0 0
$$833$$ 1.54260e7 0.770265
$$834$$ 0 0
$$835$$ −5.08595e6 −0.252439
$$836$$ 0 0
$$837$$ −9.31224e6 −0.459452
$$838$$ 0 0
$$839$$ −4.71170e6 −0.231085 −0.115543 0.993303i $$-0.536861\pi$$
−0.115543 + 0.993303i $$0.536861\pi$$
$$840$$ 0 0
$$841$$ −1.80211e7 −0.878599
$$842$$ 0 0
$$843$$ 3.39080e6 0.164336
$$844$$ 0 0
$$845$$ 1.41058e6 0.0679602
$$846$$ 0 0
$$847$$ 8.69953e6 0.416665
$$848$$ 0 0
$$849$$ 4.24791e6 0.202258
$$850$$ 0 0
$$851$$ 7.71119e6 0.365004
$$852$$ 0 0
$$853$$ −1.62685e7 −0.765552 −0.382776 0.923841i $$-0.625032\pi$$
−0.382776 + 0.923841i $$0.625032\pi$$
$$854$$ 0 0
$$855$$ 3.32210e6 0.155417
$$856$$ 0 0
$$857$$ −2.92667e7 −1.36120 −0.680600 0.732656i $$-0.738281\pi$$
−0.680600 + 0.732656i $$0.738281\pi$$
$$858$$ 0 0
$$859$$ 3.31062e7 1.53083 0.765413 0.643539i $$-0.222535\pi$$
0.765413 + 0.643539i $$0.222535\pi$$
$$860$$ 0 0
$$861$$ −925288. −0.0425372
$$862$$ 0 0
$$863$$ −1.58052e7 −0.722391 −0.361196 0.932490i $$-0.617631\pi$$
−0.361196 + 0.932490i $$0.617631\pi$$
$$864$$ 0 0
$$865$$ −3.18105e6 −0.144554
$$866$$ 0 0
$$867$$ −7514.00 −0.000339487 0
$$868$$ 0 0
$$869$$ 1.35671e7 0.609449
$$870$$ 0 0
$$871$$ 3.71040e7 1.65720
$$872$$ 0 0
$$873$$ −5.66765e6 −0.251691
$$874$$ 0 0
$$875$$ −968750. −0.0427752
$$876$$ 0 0
$$877$$ 4.26834e7 1.87396 0.936980 0.349384i $$-0.113609\pi$$
0.936980 + 0.349384i $$0.113609\pi$$
$$878$$ 0 0
$$879$$ −1.98544e6 −0.0866733
$$880$$ 0 0
$$881$$ −3.57397e6 −0.155135 −0.0775677 0.996987i $$-0.524715\pi$$
−0.0775677 + 0.996987i $$0.524715\pi$$
$$882$$ 0 0
$$883$$ 1.68471e7 0.727149 0.363574 0.931565i $$-0.381556\pi$$
0.363574 + 0.931565i $$0.381556\pi$$
$$884$$ 0 0
$$885$$ 1.85460e6 0.0795962
$$886$$ 0 0
$$887$$ −8.36792e6 −0.357115 −0.178558 0.983929i $$-0.557143\pi$$
−0.178558 + 0.983929i $$0.557143\pi$$
$$888$$ 0 0
$$889$$ −6.69017e6 −0.283911
$$890$$ 0 0
$$891$$ 8.08546e6 0.341201
$$892$$ 0 0
$$893$$ 1.57315e7 0.660147
$$894$$ 0 0
$$895$$ 2.36710e6 0.0987777
$$896$$ 0 0
$$897$$ 2.85406e6 0.118435
$$898$$ 0 0
$$899$$ 1.52435e7 0.629050
$$900$$ 0 0
$$901$$ −1.55247e7 −0.637107
$$902$$ 0 0
$$903$$ −882136. −0.0360011
$$904$$ 0 0
$$905$$ 1.29255e7 0.524595
$$906$$ 0 0
$$907$$ 2.57230e7 1.03825 0.519127 0.854697i $$-0.326257\pi$$
0.519127 + 0.854697i $$0.326257\pi$$
$$908$$ 0 0
$$909$$ −3.09921e7 −1.24406
$$910$$ 0 0
$$911$$ 3.42108e7 1.36574 0.682869 0.730540i $$-0.260732\pi$$
0.682869 + 0.730540i $$0.260732\pi$$
$$912$$ 0 0
$$913$$ 4.53341e6 0.179990
$$914$$ 0 0
$$915$$ −1.97850e6 −0.0781238
$$916$$ 0 0
$$917$$ −1.44505e7 −0.567490
$$918$$ 0 0
$$919$$ 2.44034e6 0.0953149 0.0476575 0.998864i $$-0.484824\pi$$
0.0476575 + 0.998864i $$0.484824\pi$$
$$920$$ 0 0
$$921$$ −975044. −0.0378770
$$922$$ 0 0
$$923$$ 2.98146e7 1.15192
$$924$$ 0 0
$$925$$ 2.20875e6 0.0848774
$$926$$ 0 0
$$927$$ −3.27062e7 −1.25006
$$928$$ 0 0
$$929$$ 1.34361e7 0.510781 0.255390 0.966838i $$-0.417796\pi$$
0.255390 + 0.966838i $$0.417796\pi$$
$$930$$ 0 0
$$931$$ 7.20743e6 0.272525
$$932$$ 0 0
$$933$$ −888232. −0.0334058
$$934$$ 0 0
$$935$$ −4.28400e6 −0.160258
$$936$$ 0 0
$$937$$ 7.96529e6 0.296383 0.148191 0.988959i $$-0.452655\pi$$
0.148191 + 0.988959i $$0.452655\pi$$
$$938$$ 0 0
$$939$$ 94484.0 0.00349699
$$940$$ 0 0
$$941$$ −9.08025e6 −0.334290 −0.167145 0.985932i $$-0.553455\pi$$
−0.167145 + 0.985932i $$0.553455\pi$$
$$942$$ 0 0
$$943$$ 1.62821e7 0.596253
$$944$$ 0 0
$$945$$ 1.49420e6 0.0544289
$$946$$ 0 0
$$947$$ 3.21769e7 1.16592 0.582961 0.812500i $$-0.301894\pi$$
0.582961 + 0.812500i $$0.301894\pi$$
$$948$$ 0 0
$$949$$ 7.74467e6 0.279150
$$950$$ 0 0
$$951$$ −1.38812e6 −0.0497708
$$952$$ 0 0
$$953$$ 5.33807e6 0.190394 0.0951968 0.995458i $$-0.469652\pi$$
0.0951968 + 0.995458i $$0.469652\pi$$
$$954$$ 0 0
$$955$$ −1.03075e7 −0.365717
$$956$$ 0 0
$$957$$ 454464. 0.0160406
$$958$$ 0 0
$$959$$ −2.20771e7 −0.775167
$$960$$ 0 0
$$961$$ 6.46864e7 2.25946
$$962$$ 0 0
$$963$$ −4.61724e7 −1.60442
$$964$$ 0 0
$$965$$ −1.92914e7 −0.666875
$$966$$ 0 0
$$967$$ 3.71522e7 1.27767 0.638834 0.769345i $$-0.279417\pi$$
0.638834 + 0.769345i $$0.279417\pi$$
$$968$$ 0 0
$$969$$ 1.32328e6 0.0452733
$$970$$ 0 0
$$971$$ 1.09865e7 0.373949 0.186975 0.982365i $$-0.440132\pi$$
0.186975 + 0.982365i $$0.440132\pi$$
$$972$$ 0 0
$$973$$ 1.93566e7 0.655463
$$974$$ 0 0
$$975$$ 817500. 0.0275408
$$976$$ 0 0
$$977$$ −2.65054e7 −0.888379 −0.444190 0.895933i $$-0.646508\pi$$
−0.444190 + 0.895933i $$0.646508\pi$$
$$978$$ 0 0
$$979$$ −1.35438e7 −0.451630
$$980$$ 0 0
$$981$$ −2.86910e7 −0.951860
$$982$$ 0 0
$$983$$ −4.75726e7 −1.57027 −0.785133 0.619327i $$-0.787406\pi$$
−0.785133 + 0.619327i $$0.787406\pi$$
$$984$$ 0 0
$$985$$ 4.75595e6 0.156188
$$986$$ 0 0
$$987$$ 3.50846e6 0.114637
$$988$$ 0 0
$$989$$ 1.55227e7 0.504636
$$990$$ 0 0
$$991$$ 3.22149e7 1.04201 0.521006 0.853553i $$-0.325557\pi$$
0.521006 + 0.853553i $$0.325557\pi$$
$$992$$ 0 0
$$993$$ −164336. −0.00528883
$$994$$ 0 0
$$995$$ 3.30180e6 0.105729
$$996$$ 0 0
$$997$$ −3.87072e7 −1.23326 −0.616630 0.787253i $$-0.711502\pi$$
−0.616630 + 0.787253i $$0.711502\pi$$
$$998$$ 0 0
$$999$$ −3.40678e6 −0.108002
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.i.1.1 1
4.3 odd 2 320.6.a.h.1.1 1
8.3 odd 2 80.6.a.d.1.1 1
8.5 even 2 40.6.a.c.1.1 1
24.5 odd 2 360.6.a.f.1.1 1
24.11 even 2 720.6.a.t.1.1 1
40.3 even 4 400.6.c.k.49.2 2
40.13 odd 4 200.6.c.d.49.1 2
40.19 odd 2 400.6.a.h.1.1 1
40.27 even 4 400.6.c.k.49.1 2
40.29 even 2 200.6.a.b.1.1 1
40.37 odd 4 200.6.c.d.49.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.c.1.1 1 8.5 even 2
80.6.a.d.1.1 1 8.3 odd 2
200.6.a.b.1.1 1 40.29 even 2
200.6.c.d.49.1 2 40.13 odd 4
200.6.c.d.49.2 2 40.37 odd 4
320.6.a.h.1.1 1 4.3 odd 2
320.6.a.i.1.1 1 1.1 even 1 trivial
360.6.a.f.1.1 1 24.5 odd 2
400.6.a.h.1.1 1 40.19 odd 2
400.6.c.k.49.1 2 40.27 even 4
400.6.c.k.49.2 2 40.3 even 4
720.6.a.t.1.1 1 24.11 even 2