# Properties

 Label 720.6.a.v.1.1 Level $720$ Weight $6$ Character 720.1 Self dual yes Analytic conductor $115.476$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 720.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$115.476350265$$ 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 $$\chi$$ $$=$$ 720.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+25.0000 q^{5} +118.000 q^{7} +O(q^{10})$$ $$q+25.0000 q^{5} +118.000 q^{7} +192.000 q^{11} +1106.00 q^{13} -762.000 q^{17} +2740.00 q^{19} +1566.00 q^{23} +625.000 q^{25} -5910.00 q^{29} +6868.00 q^{31} +2950.00 q^{35} -5518.00 q^{37} +378.000 q^{41} +2434.00 q^{43} +13122.0 q^{47} -2883.00 q^{49} +9174.00 q^{53} +4800.00 q^{55} -34980.0 q^{59} -9838.00 q^{61} +27650.0 q^{65} -33722.0 q^{67} +70212.0 q^{71} +21986.0 q^{73} +22656.0 q^{77} -4520.00 q^{79} -109074. q^{83} -19050.0 q^{85} -38490.0 q^{89} +130508. q^{91} +68500.0 q^{95} -1918.00 q^{97} +O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 25.0000 0.447214
$$6$$ 0 0
$$7$$ 118.000 0.910200 0.455100 0.890440i $$-0.349603\pi$$
0.455100 + 0.890440i $$0.349603\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 192.000 0.478431 0.239216 0.970966i $$-0.423110\pi$$
0.239216 + 0.970966i $$0.423110\pi$$
$$12$$ 0 0
$$13$$ 1106.00 1.81508 0.907542 0.419961i $$-0.137956\pi$$
0.907542 + 0.419961i $$0.137956\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −762.000 −0.639488 −0.319744 0.947504i $$-0.603597\pi$$
−0.319744 + 0.947504i $$0.603597\pi$$
$$18$$ 0 0
$$19$$ 2740.00 1.74127 0.870636 0.491928i $$-0.163708\pi$$
0.870636 + 0.491928i $$0.163708\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 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
$$27$$ 0 0
$$28$$ 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 $$-0.278190\pi$$
0.641795 + 0.766877i $$0.278190\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 2950.00 0.407054
$$36$$ 0 0
$$37$$ −5518.00 −0.662640 −0.331320 0.943519i $$-0.607494\pi$$
−0.331320 + 0.943519i $$0.607494\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 378.000 0.0351182 0.0175591 0.999846i $$-0.494410\pi$$
0.0175591 + 0.999846i $$0.494410\pi$$
$$42$$ 0 0
$$43$$ 2434.00 0.200747 0.100374 0.994950i $$-0.467996\pi$$
0.100374 + 0.994950i $$0.467996\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 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
$$51$$ 0 0
$$52$$ 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
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −34980.0 −1.30825 −0.654124 0.756388i $$-0.726962\pi$$
−0.654124 + 0.756388i $$0.726962\pi$$
$$60$$ 0 0
$$61$$ −9838.00 −0.338518 −0.169259 0.985572i $$-0.554137\pi$$
−0.169259 + 0.985572i $$0.554137\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 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
$$69$$ 0 0
$$70$$ 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
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 22656.0 0.435468
$$78$$ 0 0
$$79$$ −4520.00 −0.0814837 −0.0407418 0.999170i $$-0.512972\pi$$
−0.0407418 + 0.999170i $$0.512972\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −109074. −1.73790 −0.868952 0.494896i $$-0.835206\pi$$
−0.868952 + 0.494896i $$0.835206\pi$$
$$84$$ 0 0
$$85$$ −19050.0 −0.285988
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −38490.0 −0.515078 −0.257539 0.966268i $$-0.582912\pi$$
−0.257539 + 0.966268i $$0.582912\pi$$
$$90$$ 0 0
$$91$$ 130508. 1.65209
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 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
$$99$$ 0 0
$$100$$ 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 $$-0.430395\pi$$
0.216932 + 0.976187i $$0.430395\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1038.00 −0.00876472 −0.00438236 0.999990i $$-0.501395\pi$$
−0.00438236 + 0.999990i $$0.501395\pi$$
$$108$$ 0 0
$$109$$ 206930. 1.66823 0.834117 0.551587i $$-0.185977\pi$$
0.834117 + 0.551587i $$0.185977\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −139386. −1.02689 −0.513444 0.858123i $$-0.671631\pi$$
−0.513444 + 0.858123i $$0.671631\pi$$
$$114$$ 0 0
$$115$$ 39150.0 0.276050
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −89916.0 −0.582062
$$120$$ 0 0
$$121$$ −124187. −0.771104
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 15625.0 0.0894427
$$126$$ 0 0
$$127$$ −299882. −1.64984 −0.824919 0.565252i $$-0.808779\pi$$
−0.824919 + 0.565252i $$0.808779\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 7872.00 0.0400781 0.0200390 0.999799i $$-0.493621\pi$$
0.0200390 + 0.999799i $$0.493621\pi$$
$$132$$ 0 0
$$133$$ 323320. 1.58491
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 164238. 0.747605 0.373803 0.927508i $$-0.378054\pi$$
0.373803 + 0.927508i $$0.378054\pi$$
$$138$$ 0 0
$$139$$ 282100. 1.23841 0.619207 0.785228i $$-0.287454\pi$$
0.619207 + 0.785228i $$0.287454\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 212352. 0.868393
$$144$$ 0 0
$$145$$ −147750. −0.583590
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 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 $$-0.444074\pi$$
0.174793 + 0.984605i $$0.444074\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 171700. 0.574039
$$156$$ 0 0
$$157$$ −3718.00 −0.0120382 −0.00601908 0.999982i $$-0.501916\pi$$
−0.00601908 + 0.999982i $$0.501916\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 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
$$165$$ 0 0
$$166$$ 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
$$171$$ 0 0
$$172$$ 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
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 272100. 0.634740 0.317370 0.948302i $$-0.397200\pi$$
0.317370 + 0.948302i $$0.397200\pi$$
$$180$$ 0 0
$$181$$ −75418.0 −0.171111 −0.0855556 0.996333i $$-0.527267\pi$$
−0.0855556 + 0.996333i $$0.527267\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −137950. −0.296341
$$186$$ 0 0
$$187$$ −146304. −0.305951
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 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
$$195$$ 0 0
$$196$$ 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 $$-0.453534\pi$$
0.145460 + 0.989364i $$0.453534\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −697380. −1.18776
$$204$$ 0 0
$$205$$ 9450.00 0.0157053
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 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
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 60850.0 0.0897769
$$216$$ 0 0
$$217$$ 810424. 1.16832
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −842772. −1.16073
$$222$$ 0 0
$$223$$ 288274. 0.388189 0.194095 0.980983i $$-0.437823\pi$$
0.194095 + 0.980983i $$0.437823\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1.12552e6 1.44974 0.724869 0.688887i $$-0.241900\pi$$
0.724869 + 0.688887i $$0.241900\pi$$
$$228$$ 0 0
$$229$$ −415810. −0.523970 −0.261985 0.965072i $$-0.584377\pi$$
−0.261985 + 0.965072i $$0.584377\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −770586. −0.929889 −0.464945 0.885340i $$-0.653926\pi$$
−0.464945 + 0.885340i $$0.653926\pi$$
$$234$$ 0 0
$$235$$ 328050. 0.387499
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 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
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −72075.0 −0.0767131
$$246$$ 0 0
$$247$$ 3.03044e6 3.16055
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 850752. 0.852351 0.426176 0.904640i $$-0.359861\pi$$
0.426176 + 0.904640i $$0.359861\pi$$
$$252$$ 0 0
$$253$$ 300672. 0.295319
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −825402. −0.779530 −0.389765 0.920914i $$-0.627444\pi$$
−0.389765 + 0.920914i $$0.627444\pi$$
$$258$$ 0 0
$$259$$ −651124. −0.603135
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 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
$$267$$ 0 0
$$268$$ 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 $$-0.385713\pi$$
0.351379 + 0.936233i $$0.385713\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 120000. 0.0956862
$$276$$ 0 0
$$277$$ 438602. 0.343456 0.171728 0.985144i $$-0.445065\pi$$
0.171728 + 0.985144i $$0.445065\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.45670e6 1.10053 0.550267 0.834989i $$-0.314526\pi$$
0.550267 + 0.834989i $$0.314526\pi$$
$$282$$ 0 0
$$283$$ 120394. 0.0893591 0.0446795 0.999001i $$-0.485773\pi$$
0.0446795 + 0.999001i $$0.485773\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 44604.0 0.0319646
$$288$$ 0 0
$$289$$ −839213. −0.591055
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 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
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1.73200e6 1.12039
$$300$$ 0 0
$$301$$ 287212. 0.182720
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 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
$$309$$ 0 0
$$310$$ 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
$$315$$ 0 0
$$316$$ 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
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −2.08788e6 −1.11352
$$324$$ 0 0
$$325$$ 691250. 0.363017
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 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
$$333$$ 0 0
$$334$$ 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
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.31866e6 0.614109
$$342$$ 0 0
$$343$$ −2.32342e6 −1.06633
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −2.32724e6 −1.03757 −0.518785 0.854905i $$-0.673615\pi$$
−0.518785 + 0.854905i $$0.673615\pi$$
$$348$$ 0 0
$$349$$ −311290. −0.136805 −0.0684024 0.997658i $$-0.521790\pi$$
−0.0684024 + 0.997658i $$0.521790\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 3.08657e6 1.31838 0.659189 0.751977i $$-0.270900\pi$$
0.659189 + 0.751977i $$0.270900\pi$$
$$354$$ 0 0
$$355$$ 1.75530e6 0.739232
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 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
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 549650. 0.215950
$$366$$ 0 0
$$367$$ −35762.0 −0.0138598 −0.00692989 0.999976i $$-0.502206\pi$$
−0.00692989 + 0.999976i $$0.502206\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 1.08253e6 0.408325
$$372$$ 0 0
$$373$$ −1.71525e6 −0.638346 −0.319173 0.947696i $$-0.603405\pi$$
−0.319173 + 0.947696i $$0.603405\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 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
$$381$$ 0 0
$$382$$ 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
$$387$$ 0 0
$$388$$ 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
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −113000. −0.0364406
$$396$$ 0 0
$$397$$ 628562. 0.200157 0.100079 0.994980i $$-0.468091\pi$$
0.100079 + 0.994980i $$0.468091\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 2.72432e6 0.846052 0.423026 0.906118i $$-0.360968\pi$$
0.423026 + 0.906118i $$0.360968\pi$$
$$402$$ 0 0
$$403$$ 7.59601e6 2.32982
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 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
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −4.12764e6 −1.19077
$$414$$ 0 0
$$415$$ −2.72685e6 −0.777215
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 650580. 0.181036 0.0905181 0.995895i $$-0.471148\pi$$
0.0905181 + 0.995895i $$0.471148\pi$$
$$420$$ 0 0
$$421$$ −3.54060e6 −0.973579 −0.486790 0.873519i $$-0.661832\pi$$
−0.486790 + 0.873519i $$0.661832\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −476250. −0.127898
$$426$$ 0 0
$$427$$ −1.16088e6 −0.308119
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 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
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 4.29084e6 1.07483
$$438$$ 0 0
$$439$$ −4.86212e6 −1.20411 −0.602053 0.798456i $$-0.705650\pi$$
−0.602053 + 0.798456i $$0.705650\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −1.86155e6 −0.450678 −0.225339 0.974280i $$-0.572349\pi$$
−0.225339 + 0.974280i $$0.572349\pi$$
$$444$$ 0 0
$$445$$ −962250. −0.230350
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −3.73719e6 −0.874841 −0.437421 0.899257i $$-0.644108\pi$$
−0.437421 + 0.899257i $$0.644108\pi$$
$$450$$ 0 0
$$451$$ 72576.0 0.0168016
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 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
$$459$$ 0 0
$$460$$ 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 $$-0.890414\pi$$
−0.941321 + 0.337513i $$0.890414\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 6.96412e6 1.47766 0.738829 0.673893i $$-0.235379\pi$$
0.738829 + 0.673893i $$0.235379\pi$$
$$468$$ 0 0
$$469$$ −3.97920e6 −0.835340
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 467328. 0.0960437
$$474$$ 0 0
$$475$$ 1.71250e6 0.348254
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 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
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −47950.0 −0.00925623
$$486$$ 0 0
$$487$$ −5.51808e6 −1.05430 −0.527152 0.849771i $$-0.676740\pi$$
−0.527152 + 0.849771i $$0.676740\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −1.51277e6 −0.283184 −0.141592 0.989925i $$-0.545222\pi$$
−0.141592 + 0.989925i $$0.545222\pi$$
$$492$$ 0 0
$$493$$ 4.50342e6 0.834498
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 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
$$501$$ 0 0
$$502$$ 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
$$507$$ 0 0
$$508$$ 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
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 1.16785e6 0.194030
$$516$$ 0 0
$$517$$ 2.51942e6 0.414548
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.01110e7 −1.63192 −0.815962 0.578106i $$-0.803792\pi$$
−0.815962 + 0.578106i $$0.803792\pi$$
$$522$$ 0 0
$$523$$ 7.03719e6 1.12498 0.562491 0.826804i $$-0.309843\pi$$
0.562491 + 0.826804i $$0.309843\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −5.23342e6 −0.820840
$$528$$ 0 0
$$529$$ −3.98399e6 −0.618983
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 418068. 0.0637425
$$534$$ 0 0
$$535$$ −25950.0 −0.00391970
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −553536. −0.0820680
$$540$$ 0 0
$$541$$ −4.23114e6 −0.621533 −0.310766 0.950486i $$-0.600586\pi$$
−0.310766 + 0.950486i $$0.600586\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 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
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1.61934e7 −2.27227
$$552$$ 0 0
$$553$$ −533360. −0.0741665
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 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
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −9.81287e6 −1.30474 −0.652372 0.757899i $$-0.726226\pi$$
−0.652372 + 0.757899i $$0.726226\pi$$
$$564$$ 0 0
$$565$$ −3.48465e6 −0.459238
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.33152e7 −1.72412 −0.862061 0.506804i $$-0.830827\pi$$
−0.862061 + 0.506804i $$0.830827\pi$$
$$570$$ 0 0
$$571$$ −9.95895e6 −1.27827 −0.639136 0.769094i $$-0.720708\pi$$
−0.639136 + 0.769094i $$0.720708\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 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
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −1.28707e7 −1.58184
$$582$$ 0 0
$$583$$ 1.76141e6 0.214629
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 625842. 0.0749669 0.0374834 0.999297i $$-0.488066\pi$$
0.0374834 + 0.999297i $$0.488066\pi$$
$$588$$ 0 0
$$589$$ 1.88183e7 2.23508
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 2.50385e6 0.292397 0.146198 0.989255i $$-0.453296\pi$$
0.146198 + 0.989255i $$0.453296\pi$$
$$594$$ 0 0
$$595$$ −2.24790e6 −0.260306
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 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
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −3.10468e6 −0.344848
$$606$$ 0 0
$$607$$ −1.13772e7 −1.25333 −0.626663 0.779291i $$-0.715580\pi$$
−0.626663 + 0.779291i $$0.715580\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 1.45129e7 1.57272
$$612$$ 0 0
$$613$$ −7.00161e6 −0.752570 −0.376285 0.926504i $$-0.622799\pi$$
−0.376285 + 0.926504i $$0.622799\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −7.90300e6 −0.835755 −0.417878 0.908503i $$-0.637226\pi$$
−0.417878 + 0.908503i $$0.637226\pi$$
$$618$$ 0 0
$$619$$ −4.02362e6 −0.422076 −0.211038 0.977478i $$-0.567684\pi$$
−0.211038 + 0.977478i $$0.567684\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −4.54182e6 −0.468824
$$624$$ 0 0
$$625$$ 390625. 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 4.20472e6 0.423750
$$630$$ 0 0
$$631$$ 1.00227e7 1.00210 0.501049 0.865419i $$-0.332948\pi$$
0.501049 + 0.865419i $$0.332948\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −7.49705e6 −0.737830
$$636$$ 0 0
$$637$$ −3.18860e6 −0.311352
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −6.37390e6 −0.612718 −0.306359 0.951916i $$-0.599111\pi$$
−0.306359 + 0.951916i $$0.599111\pi$$
$$642$$ 0 0
$$643$$ −5.00457e6 −0.477352 −0.238676 0.971099i $$-0.576713\pi$$
−0.238676 + 0.971099i $$0.576713\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 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
$$651$$ 0 0
$$652$$ 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
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 1.26410e7 1.13388 0.566940 0.823759i $$-0.308127\pi$$
0.566940 + 0.823759i $$0.308127\pi$$
$$660$$ 0 0
$$661$$ −3.61572e6 −0.321878 −0.160939 0.986964i $$-0.551452\pi$$
−0.160939 + 0.986964i $$0.551452\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 8.08300e6 0.708791
$$666$$ 0 0
$$667$$ −9.25506e6 −0.805498
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 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
$$675$$ 0 0
$$676$$ 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
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 2.05830e7 1.68833 0.844164 0.536084i $$-0.180097\pi$$
0.844164 + 0.536084i $$0.180097\pi$$
$$684$$ 0 0
$$685$$ 4.10595e6 0.334339
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 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
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 7.05250e6 0.553836
$$696$$ 0 0
$$697$$ −288036. −0.0224577
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 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
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −9.15940e6 −0.689157
$$708$$ 0 0
$$709$$ −2.12720e7 −1.58926 −0.794628 0.607097i $$-0.792334\pi$$
−0.794628 + 0.607097i $$0.792334\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.07553e7 0.792316
$$714$$ 0 0
$$715$$ 5.30880e6 0.388357
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 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
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −3.69375e6 −0.260989
$$726$$ 0 0
$$727$$ 4.36740e6 0.306469 0.153235 0.988190i $$-0.451031\pi$$
0.153235 + 0.988190i $$0.451031\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1.85471e6 −0.128375
$$732$$ 0 0
$$733$$ −4.05645e6 −0.278860 −0.139430 0.990232i $$-0.544527\pi$$
−0.139430 + 0.990232i $$0.544527\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 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
$$741$$ 0 0
$$742$$ 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
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −122484. −0.00797765
$$750$$ 0 0
$$751$$ −1.81698e7 −1.17557 −0.587787 0.809016i $$-0.700001\pi$$
−0.587787 + 0.809016i $$0.700001\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 2.44870e6 0.156339
$$756$$ 0 0
$$757$$ 1.93494e7 1.22724 0.613618 0.789603i $$-0.289714\pi$$
0.613618 + 0.789603i $$0.289714\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 3.01992e7 1.89031 0.945155 0.326621i $$-0.105910\pi$$
0.945155 + 0.326621i $$0.105910\pi$$
$$762$$ 0 0
$$763$$ 2.44177e7 1.51843
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 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
$$771$$ 0 0
$$772$$ 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
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 1.03572e6 0.0611503
$$780$$ 0 0
$$781$$ 1.34807e7 0.790833
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 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
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −1.64475e7 −0.934674
$$792$$ 0 0
$$793$$ −1.08808e7 −0.614439
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 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
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 4.22131e6 0.231025
$$804$$ 0 0
$$805$$ 4.61970e6 0.251260
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 1.11446e7 0.598675 0.299338 0.954147i $$-0.403234\pi$$
0.299338 + 0.954147i $$0.403234\pi$$
$$810$$ 0 0
$$811$$ 1.14866e7 0.613253 0.306626 0.951830i $$-0.400800\pi$$
0.306626 + 0.951830i $$0.400800\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 1.08085e6 0.0569995
$$816$$ 0 0
$$817$$ 6.66916e6 0.349555
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 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 $$-0.533626\pi$$
−0.105442 + 0.994425i $$0.533626\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −1.70652e7 −0.867654 −0.433827 0.900996i $$-0.642837\pi$$
−0.433827 + 0.900996i $$0.642837\pi$$
$$828$$ 0 0
$$829$$ −2.47617e7 −1.25139 −0.625697 0.780066i $$-0.715185\pi$$
−0.625697 + 0.780066i $$0.715185\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 2.19685e6 0.109695
$$834$$ 0 0
$$835$$ 4.66305e6 0.231448
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 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
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 2.12986e7 1.02615
$$846$$ 0 0
$$847$$ −1.46541e7 −0.701859
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −8.64119e6 −0.409025
$$852$$ 0 0
$$853$$ 2.82671e7 1.33017 0.665087 0.746765i $$-0.268394\pi$$
0.665087 + 0.746765i $$0.268394\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −2.60870e7 −1.21331 −0.606655 0.794966i $$-0.707489\pi$$
−0.606655 + 0.794966i $$0.707489\pi$$
$$858$$ 0 0
$$859$$ 3.38111e7 1.56342 0.781710 0.623642i $$-0.214348\pi$$
0.781710 + 0.623642i $$0.214348\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 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
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −867840. −0.0389843
$$870$$ 0 0
$$871$$ −3.72965e7 −1.66580
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 1.84375e6 0.0814108
$$876$$ 0 0
$$877$$ −3.46748e7 −1.52235 −0.761177 0.648545i $$-0.775378\pi$$
−0.761177 + 0.648545i $$0.775378\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −1.42603e7 −0.618998 −0.309499 0.950900i $$-0.600161\pi$$
−0.309499 + 0.950900i $$0.600161\pi$$
$$882$$ 0 0
$$883$$ 3.75177e7 1.61933 0.809663 0.586895i $$-0.199650\pi$$
0.809663 + 0.586895i $$0.199650\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 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
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 3.59543e7 1.50877
$$894$$ 0 0
$$895$$ 6.80250e6 0.283864
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −4.05899e7 −1.67501
$$900$$ 0 0
$$901$$ −6.99059e6 −0.286881
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 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
$$909$$ 0 0
$$910$$ 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
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 928896. 0.0364791
$$918$$ 0 0
$$919$$ −1.85996e7 −0.726465 −0.363233 0.931698i $$-0.618327\pi$$
−0.363233 + 0.931698i $$0.618327\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 7.76545e7 3.00028
$$924$$ 0 0
$$925$$ −3.44875e6 −0.132528
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −4.45110e7 −1.69211 −0.846055 0.533096i $$-0.821028\pi$$
−0.846055 + 0.533096i $$0.821028\pi$$
$$930$$ 0 0
$$931$$ −7.89942e6 −0.298690
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 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
$$939$$ 0 0
$$940$$ 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
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 3.17199e7 1.14936 0.574681 0.818378i $$-0.305126\pi$$
0.574681 + 0.818378i $$0.305126\pi$$
$$948$$ 0 0
$$949$$ 2.43165e7 0.876468
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 5.60285e6 0.199838 0.0999188 0.994996i $$-0.468142\pi$$
0.0999188 + 0.994996i $$0.468142\pi$$
$$954$$ 0 0
$$955$$ −8.92470e6 −0.316654
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 1.93801e7 0.680470
$$960$$ 0 0
$$961$$ 1.85403e7 0.647601
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −1.09673e7 −0.379126
$$966$$ 0 0
$$967$$ 2.03532e7 0.699949 0.349975 0.936759i $$-0.386190\pi$$
0.349975 + 0.936759i $$0.386190\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −2.34306e7 −0.797510 −0.398755 0.917057i $$-0.630558\pi$$
−0.398755 + 0.917057i $$0.630558\pi$$
$$972$$ 0 0
$$973$$ 3.32878e7 1.12721
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 4.30412e7 1.44261 0.721303 0.692619i $$-0.243543\pi$$
0.721303 + 0.692619i $$0.243543\pi$$
$$978$$ 0 0
$$979$$ −7.39008e6 −0.246429
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 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
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 3.81164e6 0.123914
$$990$$ 0 0
$$991$$ −2.09231e7 −0.676770 −0.338385 0.941008i $$-0.609881\pi$$
−0.338385 + 0.941008i $$0.609881\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 4.06300e6 0.130104
$$996$$ 0 0
$$997$$ 2.96332e7 0.944148 0.472074 0.881559i $$-0.343505\pi$$
0.472074 + 0.881559i $$0.343505\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 720.6.a.v.1.1 1
3.2 odd 2 80.6.a.c.1.1 1
4.3 odd 2 90.6.a.b.1.1 1
12.11 even 2 10.6.a.c.1.1 1
15.2 even 4 400.6.c.i.49.2 2
15.8 even 4 400.6.c.i.49.1 2
15.14 odd 2 400.6.a.i.1.1 1
20.3 even 4 450.6.c.f.199.2 2
20.7 even 4 450.6.c.f.199.1 2
20.19 odd 2 450.6.a.u.1.1 1
24.5 odd 2 320.6.a.k.1.1 1
24.11 even 2 320.6.a.f.1.1 1
60.23 odd 4 50.6.b.b.49.1 2
60.47 odd 4 50.6.b.b.49.2 2
60.59 even 2 50.6.a.b.1.1 1
84.83 odd 2 490.6.a.k.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.a.c.1.1 1 12.11 even 2
50.6.a.b.1.1 1 60.59 even 2
50.6.b.b.49.1 2 60.23 odd 4
50.6.b.b.49.2 2 60.47 odd 4
80.6.a.c.1.1 1 3.2 odd 2
90.6.a.b.1.1 1 4.3 odd 2
320.6.a.f.1.1 1 24.11 even 2
320.6.a.k.1.1 1 24.5 odd 2
400.6.a.i.1.1 1 15.14 odd 2
400.6.c.i.49.1 2 15.8 even 4
400.6.c.i.49.2 2 15.2 even 4
450.6.a.u.1.1 1 20.19 odd 2
450.6.c.f.199.1 2 20.7 even 4
450.6.c.f.199.2 2 20.3 even 4
490.6.a.k.1.1 1 84.83 odd 2
720.6.a.v.1.1 1 1.1 even 1 trivial