Properties

 Label 270.4.a.f.1.1 Level $270$ Weight $4$ Character 270.1 Self dual yes Analytic conductor $15.931$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$270 = 2 \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 270.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$15.9305157015$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 270.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} +14.0000 q^{7} -8.00000 q^{8} +O(q^{10})$$ $$q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} +14.0000 q^{7} -8.00000 q^{8} -10.0000 q^{10} +3.00000 q^{11} +47.0000 q^{13} -28.0000 q^{14} +16.0000 q^{16} -39.0000 q^{17} +32.0000 q^{19} +20.0000 q^{20} -6.00000 q^{22} -99.0000 q^{23} +25.0000 q^{25} -94.0000 q^{26} +56.0000 q^{28} +51.0000 q^{29} +83.0000 q^{31} -32.0000 q^{32} +78.0000 q^{34} +70.0000 q^{35} +314.000 q^{37} -64.0000 q^{38} -40.0000 q^{40} -108.000 q^{41} +299.000 q^{43} +12.0000 q^{44} +198.000 q^{46} +531.000 q^{47} -147.000 q^{49} -50.0000 q^{50} +188.000 q^{52} +564.000 q^{53} +15.0000 q^{55} -112.000 q^{56} -102.000 q^{58} +12.0000 q^{59} +230.000 q^{61} -166.000 q^{62} +64.0000 q^{64} +235.000 q^{65} -268.000 q^{67} -156.000 q^{68} -140.000 q^{70} +120.000 q^{71} +1106.00 q^{73} -628.000 q^{74} +128.000 q^{76} +42.0000 q^{77} -739.000 q^{79} +80.0000 q^{80} +216.000 q^{82} +1086.00 q^{83} -195.000 q^{85} -598.000 q^{86} -24.0000 q^{88} -120.000 q^{89} +658.000 q^{91} -396.000 q^{92} -1062.00 q^{94} +160.000 q^{95} -1642.00 q^{97} +294.000 q^{98} +O(q^{100})$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.00000 −0.707107
$$3$$ 0 0
$$4$$ 4.00000 0.500000
$$5$$ 5.00000 0.447214
$$6$$ 0 0
$$7$$ 14.0000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ −8.00000 −0.353553
$$9$$ 0 0
$$10$$ −10.0000 −0.316228
$$11$$ 3.00000 0.0822304 0.0411152 0.999154i $$-0.486909\pi$$
0.0411152 + 0.999154i $$0.486909\pi$$
$$12$$ 0 0
$$13$$ 47.0000 1.00273 0.501364 0.865237i $$-0.332832\pi$$
0.501364 + 0.865237i $$0.332832\pi$$
$$14$$ −28.0000 −0.534522
$$15$$ 0 0
$$16$$ 16.0000 0.250000
$$17$$ −39.0000 −0.556405 −0.278203 0.960522i $$-0.589739\pi$$
−0.278203 + 0.960522i $$0.589739\pi$$
$$18$$ 0 0
$$19$$ 32.0000 0.386384 0.193192 0.981161i $$-0.438116\pi$$
0.193192 + 0.981161i $$0.438116\pi$$
$$20$$ 20.0000 0.223607
$$21$$ 0 0
$$22$$ −6.00000 −0.0581456
$$23$$ −99.0000 −0.897519 −0.448759 0.893653i $$-0.648134\pi$$
−0.448759 + 0.893653i $$0.648134\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ −94.0000 −0.709035
$$27$$ 0 0
$$28$$ 56.0000 0.377964
$$29$$ 51.0000 0.326568 0.163284 0.986579i $$-0.447791\pi$$
0.163284 + 0.986579i $$0.447791\pi$$
$$30$$ 0 0
$$31$$ 83.0000 0.480879 0.240439 0.970664i $$-0.422708\pi$$
0.240439 + 0.970664i $$0.422708\pi$$
$$32$$ −32.0000 −0.176777
$$33$$ 0 0
$$34$$ 78.0000 0.393438
$$35$$ 70.0000 0.338062
$$36$$ 0 0
$$37$$ 314.000 1.39517 0.697585 0.716502i $$-0.254258\pi$$
0.697585 + 0.716502i $$0.254258\pi$$
$$38$$ −64.0000 −0.273215
$$39$$ 0 0
$$40$$ −40.0000 −0.158114
$$41$$ −108.000 −0.411385 −0.205692 0.978617i $$-0.565945\pi$$
−0.205692 + 0.978617i $$0.565945\pi$$
$$42$$ 0 0
$$43$$ 299.000 1.06040 0.530199 0.847874i $$-0.322117\pi$$
0.530199 + 0.847874i $$0.322117\pi$$
$$44$$ 12.0000 0.0411152
$$45$$ 0 0
$$46$$ 198.000 0.634641
$$47$$ 531.000 1.64796 0.823982 0.566616i $$-0.191748\pi$$
0.823982 + 0.566616i $$0.191748\pi$$
$$48$$ 0 0
$$49$$ −147.000 −0.428571
$$50$$ −50.0000 −0.141421
$$51$$ 0 0
$$52$$ 188.000 0.501364
$$53$$ 564.000 1.46172 0.730862 0.682525i $$-0.239118\pi$$
0.730862 + 0.682525i $$0.239118\pi$$
$$54$$ 0 0
$$55$$ 15.0000 0.0367745
$$56$$ −112.000 −0.267261
$$57$$ 0 0
$$58$$ −102.000 −0.230918
$$59$$ 12.0000 0.0264791 0.0132396 0.999912i $$-0.495786\pi$$
0.0132396 + 0.999912i $$0.495786\pi$$
$$60$$ 0 0
$$61$$ 230.000 0.482762 0.241381 0.970430i $$-0.422400\pi$$
0.241381 + 0.970430i $$0.422400\pi$$
$$62$$ −166.000 −0.340033
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ 235.000 0.448433
$$66$$ 0 0
$$67$$ −268.000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ −156.000 −0.278203
$$69$$ 0 0
$$70$$ −140.000 −0.239046
$$71$$ 120.000 0.200583 0.100291 0.994958i $$-0.468022\pi$$
0.100291 + 0.994958i $$0.468022\pi$$
$$72$$ 0 0
$$73$$ 1106.00 1.77325 0.886627 0.462486i $$-0.153042\pi$$
0.886627 + 0.462486i $$0.153042\pi$$
$$74$$ −628.000 −0.986534
$$75$$ 0 0
$$76$$ 128.000 0.193192
$$77$$ 42.0000 0.0621603
$$78$$ 0 0
$$79$$ −739.000 −1.05246 −0.526228 0.850344i $$-0.676394\pi$$
−0.526228 + 0.850344i $$0.676394\pi$$
$$80$$ 80.0000 0.111803
$$81$$ 0 0
$$82$$ 216.000 0.290893
$$83$$ 1086.00 1.43619 0.718096 0.695944i $$-0.245014\pi$$
0.718096 + 0.695944i $$0.245014\pi$$
$$84$$ 0 0
$$85$$ −195.000 −0.248832
$$86$$ −598.000 −0.749814
$$87$$ 0 0
$$88$$ −24.0000 −0.0290728
$$89$$ −120.000 −0.142921 −0.0714605 0.997443i $$-0.522766\pi$$
−0.0714605 + 0.997443i $$0.522766\pi$$
$$90$$ 0 0
$$91$$ 658.000 0.757991
$$92$$ −396.000 −0.448759
$$93$$ 0 0
$$94$$ −1062.00 −1.16529
$$95$$ 160.000 0.172796
$$96$$ 0 0
$$97$$ −1642.00 −1.71876 −0.859381 0.511336i $$-0.829151\pi$$
−0.859381 + 0.511336i $$0.829151\pi$$
$$98$$ 294.000 0.303046
$$99$$ 0 0
$$100$$ 100.000 0.100000
$$101$$ 33.0000 0.0325111 0.0162556 0.999868i $$-0.494825\pi$$
0.0162556 + 0.999868i $$0.494825\pi$$
$$102$$ 0 0
$$103$$ −1198.00 −1.14604 −0.573022 0.819540i $$-0.694229\pi$$
−0.573022 + 0.819540i $$0.694229\pi$$
$$104$$ −376.000 −0.354518
$$105$$ 0 0
$$106$$ −1128.00 −1.03359
$$107$$ −1542.00 −1.39318 −0.696592 0.717467i $$-0.745301\pi$$
−0.696592 + 0.717467i $$0.745301\pi$$
$$108$$ 0 0
$$109$$ −556.000 −0.488579 −0.244290 0.969702i $$-0.578555\pi$$
−0.244290 + 0.969702i $$0.578555\pi$$
$$110$$ −30.0000 −0.0260035
$$111$$ 0 0
$$112$$ 224.000 0.188982
$$113$$ 1605.00 1.33616 0.668078 0.744091i $$-0.267117\pi$$
0.668078 + 0.744091i $$0.267117\pi$$
$$114$$ 0 0
$$115$$ −495.000 −0.401383
$$116$$ 204.000 0.163284
$$117$$ 0 0
$$118$$ −24.0000 −0.0187236
$$119$$ −546.000 −0.420603
$$120$$ 0 0
$$121$$ −1322.00 −0.993238
$$122$$ −460.000 −0.341364
$$123$$ 0 0
$$124$$ 332.000 0.240439
$$125$$ 125.000 0.0894427
$$126$$ 0 0
$$127$$ 1334.00 0.932074 0.466037 0.884765i $$-0.345681\pi$$
0.466037 + 0.884765i $$0.345681\pi$$
$$128$$ −128.000 −0.0883883
$$129$$ 0 0
$$130$$ −470.000 −0.317090
$$131$$ −2883.00 −1.92282 −0.961408 0.275127i $$-0.911280\pi$$
−0.961408 + 0.275127i $$0.911280\pi$$
$$132$$ 0 0
$$133$$ 448.000 0.292079
$$134$$ 536.000 0.345547
$$135$$ 0 0
$$136$$ 312.000 0.196719
$$137$$ 282.000 0.175860 0.0879302 0.996127i $$-0.471975\pi$$
0.0879302 + 0.996127i $$0.471975\pi$$
$$138$$ 0 0
$$139$$ −2494.00 −1.52186 −0.760929 0.648835i $$-0.775257\pi$$
−0.760929 + 0.648835i $$0.775257\pi$$
$$140$$ 280.000 0.169031
$$141$$ 0 0
$$142$$ −240.000 −0.141833
$$143$$ 141.000 0.0824546
$$144$$ 0 0
$$145$$ 255.000 0.146045
$$146$$ −2212.00 −1.25388
$$147$$ 0 0
$$148$$ 1256.00 0.697585
$$149$$ 2595.00 1.42678 0.713392 0.700766i $$-0.247158\pi$$
0.713392 + 0.700766i $$0.247158\pi$$
$$150$$ 0 0
$$151$$ 1229.00 0.662348 0.331174 0.943570i $$-0.392555\pi$$
0.331174 + 0.943570i $$0.392555\pi$$
$$152$$ −256.000 −0.136608
$$153$$ 0 0
$$154$$ −84.0000 −0.0439540
$$155$$ 415.000 0.215055
$$156$$ 0 0
$$157$$ −1591.00 −0.808762 −0.404381 0.914591i $$-0.632513\pi$$
−0.404381 + 0.914591i $$0.632513\pi$$
$$158$$ 1478.00 0.744199
$$159$$ 0 0
$$160$$ −160.000 −0.0790569
$$161$$ −1386.00 −0.678460
$$162$$ 0 0
$$163$$ −457.000 −0.219601 −0.109801 0.993954i $$-0.535021\pi$$
−0.109801 + 0.993954i $$0.535021\pi$$
$$164$$ −432.000 −0.205692
$$165$$ 0 0
$$166$$ −2172.00 −1.01554
$$167$$ −1164.00 −0.539359 −0.269680 0.962950i $$-0.586918\pi$$
−0.269680 + 0.962950i $$0.586918\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.00546199
$$170$$ 390.000 0.175951
$$171$$ 0 0
$$172$$ 1196.00 0.530199
$$173$$ 3942.00 1.73240 0.866199 0.499700i $$-0.166556\pi$$
0.866199 + 0.499700i $$0.166556\pi$$
$$174$$ 0 0
$$175$$ 350.000 0.151186
$$176$$ 48.0000 0.0205576
$$177$$ 0 0
$$178$$ 240.000 0.101060
$$179$$ −1212.00 −0.506085 −0.253042 0.967455i $$-0.581431\pi$$
−0.253042 + 0.967455i $$0.581431\pi$$
$$180$$ 0 0
$$181$$ 2288.00 0.939590 0.469795 0.882776i $$-0.344328\pi$$
0.469795 + 0.882776i $$0.344328\pi$$
$$182$$ −1316.00 −0.535980
$$183$$ 0 0
$$184$$ 792.000 0.317321
$$185$$ 1570.00 0.623939
$$186$$ 0 0
$$187$$ −117.000 −0.0457534
$$188$$ 2124.00 0.823982
$$189$$ 0 0
$$190$$ −320.000 −0.122185
$$191$$ −1938.00 −0.734182 −0.367091 0.930185i $$-0.619646\pi$$
−0.367091 + 0.930185i $$0.619646\pi$$
$$192$$ 0 0
$$193$$ −1498.00 −0.558696 −0.279348 0.960190i $$-0.590118\pi$$
−0.279348 + 0.960190i $$0.590118\pi$$
$$194$$ 3284.00 1.21535
$$195$$ 0 0
$$196$$ −588.000 −0.214286
$$197$$ −2124.00 −0.768166 −0.384083 0.923299i $$-0.625482\pi$$
−0.384083 + 0.923299i $$0.625482\pi$$
$$198$$ 0 0
$$199$$ −385.000 −0.137145 −0.0685727 0.997646i $$-0.521845\pi$$
−0.0685727 + 0.997646i $$0.521845\pi$$
$$200$$ −200.000 −0.0707107
$$201$$ 0 0
$$202$$ −66.0000 −0.0229888
$$203$$ 714.000 0.246862
$$204$$ 0 0
$$205$$ −540.000 −0.183977
$$206$$ 2396.00 0.810375
$$207$$ 0 0
$$208$$ 752.000 0.250682
$$209$$ 96.0000 0.0317725
$$210$$ 0 0
$$211$$ 3170.00 1.03427 0.517137 0.855903i $$-0.326998\pi$$
0.517137 + 0.855903i $$0.326998\pi$$
$$212$$ 2256.00 0.730862
$$213$$ 0 0
$$214$$ 3084.00 0.985130
$$215$$ 1495.00 0.474224
$$216$$ 0 0
$$217$$ 1162.00 0.363510
$$218$$ 1112.00 0.345478
$$219$$ 0 0
$$220$$ 60.0000 0.0183873
$$221$$ −1833.00 −0.557923
$$222$$ 0 0
$$223$$ 1388.00 0.416804 0.208402 0.978043i $$-0.433174\pi$$
0.208402 + 0.978043i $$0.433174\pi$$
$$224$$ −448.000 −0.133631
$$225$$ 0 0
$$226$$ −3210.00 −0.944805
$$227$$ −4644.00 −1.35786 −0.678928 0.734205i $$-0.737555\pi$$
−0.678928 + 0.734205i $$0.737555\pi$$
$$228$$ 0 0
$$229$$ 4736.00 1.36665 0.683327 0.730113i $$-0.260532\pi$$
0.683327 + 0.730113i $$0.260532\pi$$
$$230$$ 990.000 0.283820
$$231$$ 0 0
$$232$$ −408.000 −0.115459
$$233$$ 2814.00 0.791207 0.395604 0.918421i $$-0.370535\pi$$
0.395604 + 0.918421i $$0.370535\pi$$
$$234$$ 0 0
$$235$$ 2655.00 0.736992
$$236$$ 48.0000 0.0132396
$$237$$ 0 0
$$238$$ 1092.00 0.297411
$$239$$ −2202.00 −0.595965 −0.297982 0.954571i $$-0.596314\pi$$
−0.297982 + 0.954571i $$0.596314\pi$$
$$240$$ 0 0
$$241$$ 3485.00 0.931488 0.465744 0.884920i $$-0.345787\pi$$
0.465744 + 0.884920i $$0.345787\pi$$
$$242$$ 2644.00 0.702325
$$243$$ 0 0
$$244$$ 920.000 0.241381
$$245$$ −735.000 −0.191663
$$246$$ 0 0
$$247$$ 1504.00 0.387438
$$248$$ −664.000 −0.170016
$$249$$ 0 0
$$250$$ −250.000 −0.0632456
$$251$$ −6345.00 −1.59559 −0.797795 0.602929i $$-0.794000\pi$$
−0.797795 + 0.602929i $$0.794000\pi$$
$$252$$ 0 0
$$253$$ −297.000 −0.0738033
$$254$$ −2668.00 −0.659076
$$255$$ 0 0
$$256$$ 256.000 0.0625000
$$257$$ 525.000 0.127426 0.0637132 0.997968i $$-0.479706\pi$$
0.0637132 + 0.997968i $$0.479706\pi$$
$$258$$ 0 0
$$259$$ 4396.00 1.05465
$$260$$ 940.000 0.224217
$$261$$ 0 0
$$262$$ 5766.00 1.35964
$$263$$ 5196.00 1.21825 0.609124 0.793075i $$-0.291521\pi$$
0.609124 + 0.793075i $$0.291521\pi$$
$$264$$ 0 0
$$265$$ 2820.00 0.653703
$$266$$ −896.000 −0.206531
$$267$$ 0 0
$$268$$ −1072.00 −0.244339
$$269$$ −7479.00 −1.69518 −0.847589 0.530654i $$-0.821946\pi$$
−0.847589 + 0.530654i $$0.821946\pi$$
$$270$$ 0 0
$$271$$ −856.000 −0.191876 −0.0959378 0.995387i $$-0.530585\pi$$
−0.0959378 + 0.995387i $$0.530585\pi$$
$$272$$ −624.000 −0.139101
$$273$$ 0 0
$$274$$ −564.000 −0.124352
$$275$$ 75.0000 0.0164461
$$276$$ 0 0
$$277$$ −7054.00 −1.53009 −0.765043 0.643979i $$-0.777282\pi$$
−0.765043 + 0.643979i $$0.777282\pi$$
$$278$$ 4988.00 1.07612
$$279$$ 0 0
$$280$$ −560.000 −0.119523
$$281$$ 1014.00 0.215268 0.107634 0.994191i $$-0.465673\pi$$
0.107634 + 0.994191i $$0.465673\pi$$
$$282$$ 0 0
$$283$$ 992.000 0.208368 0.104184 0.994558i $$-0.466777\pi$$
0.104184 + 0.994558i $$0.466777\pi$$
$$284$$ 480.000 0.100291
$$285$$ 0 0
$$286$$ −282.000 −0.0583042
$$287$$ −1512.00 −0.310977
$$288$$ 0 0
$$289$$ −3392.00 −0.690413
$$290$$ −510.000 −0.103270
$$291$$ 0 0
$$292$$ 4424.00 0.886627
$$293$$ −4950.00 −0.986970 −0.493485 0.869754i $$-0.664277\pi$$
−0.493485 + 0.869754i $$0.664277\pi$$
$$294$$ 0 0
$$295$$ 60.0000 0.0118418
$$296$$ −2512.00 −0.493267
$$297$$ 0 0
$$298$$ −5190.00 −1.00889
$$299$$ −4653.00 −0.899966
$$300$$ 0 0
$$301$$ 4186.00 0.801585
$$302$$ −2458.00 −0.468351
$$303$$ 0 0
$$304$$ 512.000 0.0965961
$$305$$ 1150.00 0.215898
$$306$$ 0 0
$$307$$ −4777.00 −0.888071 −0.444035 0.896009i $$-0.646454\pi$$
−0.444035 + 0.896009i $$0.646454\pi$$
$$308$$ 168.000 0.0310802
$$309$$ 0 0
$$310$$ −830.000 −0.152067
$$311$$ −7692.00 −1.40249 −0.701243 0.712922i $$-0.747371\pi$$
−0.701243 + 0.712922i $$0.747371\pi$$
$$312$$ 0 0
$$313$$ −2932.00 −0.529477 −0.264739 0.964320i $$-0.585286\pi$$
−0.264739 + 0.964320i $$0.585286\pi$$
$$314$$ 3182.00 0.571881
$$315$$ 0 0
$$316$$ −2956.00 −0.526228
$$317$$ 8352.00 1.47980 0.739898 0.672720i $$-0.234874\pi$$
0.739898 + 0.672720i $$0.234874\pi$$
$$318$$ 0 0
$$319$$ 153.000 0.0268538
$$320$$ 320.000 0.0559017
$$321$$ 0 0
$$322$$ 2772.00 0.479744
$$323$$ −1248.00 −0.214986
$$324$$ 0 0
$$325$$ 1175.00 0.200545
$$326$$ 914.000 0.155282
$$327$$ 0 0
$$328$$ 864.000 0.145446
$$329$$ 7434.00 1.24574
$$330$$ 0 0
$$331$$ −3070.00 −0.509796 −0.254898 0.966968i $$-0.582042\pi$$
−0.254898 + 0.966968i $$0.582042\pi$$
$$332$$ 4344.00 0.718096
$$333$$ 0 0
$$334$$ 2328.00 0.381385
$$335$$ −1340.00 −0.218543
$$336$$ 0 0
$$337$$ −1672.00 −0.270266 −0.135133 0.990827i $$-0.543146\pi$$
−0.135133 + 0.990827i $$0.543146\pi$$
$$338$$ −24.0000 −0.00386221
$$339$$ 0 0
$$340$$ −780.000 −0.124416
$$341$$ 249.000 0.0395428
$$342$$ 0 0
$$343$$ −6860.00 −1.07990
$$344$$ −2392.00 −0.374907
$$345$$ 0 0
$$346$$ −7884.00 −1.22499
$$347$$ −5076.00 −0.785285 −0.392643 0.919691i $$-0.628439\pi$$
−0.392643 + 0.919691i $$0.628439\pi$$
$$348$$ 0 0
$$349$$ 8594.00 1.31813 0.659063 0.752087i $$-0.270953\pi$$
0.659063 + 0.752087i $$0.270953\pi$$
$$350$$ −700.000 −0.106904
$$351$$ 0 0
$$352$$ −96.0000 −0.0145364
$$353$$ 12711.0 1.91654 0.958269 0.285866i $$-0.0922813\pi$$
0.958269 + 0.285866i $$0.0922813\pi$$
$$354$$ 0 0
$$355$$ 600.000 0.0897034
$$356$$ −480.000 −0.0714605
$$357$$ 0 0
$$358$$ 2424.00 0.357856
$$359$$ −1464.00 −0.215228 −0.107614 0.994193i $$-0.534321\pi$$
−0.107614 + 0.994193i $$0.534321\pi$$
$$360$$ 0 0
$$361$$ −5835.00 −0.850707
$$362$$ −4576.00 −0.664390
$$363$$ 0 0
$$364$$ 2632.00 0.378995
$$365$$ 5530.00 0.793023
$$366$$ 0 0
$$367$$ −7630.00 −1.08524 −0.542620 0.839979i $$-0.682567\pi$$
−0.542620 + 0.839979i $$0.682567\pi$$
$$368$$ −1584.00 −0.224380
$$369$$ 0 0
$$370$$ −3140.00 −0.441191
$$371$$ 7896.00 1.10496
$$372$$ 0 0
$$373$$ −3883.00 −0.539019 −0.269510 0.962998i $$-0.586862\pi$$
−0.269510 + 0.962998i $$0.586862\pi$$
$$374$$ 234.000 0.0323525
$$375$$ 0 0
$$376$$ −4248.00 −0.582643
$$377$$ 2397.00 0.327458
$$378$$ 0 0
$$379$$ −13768.0 −1.86600 −0.933001 0.359874i $$-0.882820\pi$$
−0.933001 + 0.359874i $$0.882820\pi$$
$$380$$ 640.000 0.0863982
$$381$$ 0 0
$$382$$ 3876.00 0.519145
$$383$$ −14139.0 −1.88634 −0.943171 0.332307i $$-0.892173\pi$$
−0.943171 + 0.332307i $$0.892173\pi$$
$$384$$ 0 0
$$385$$ 210.000 0.0277989
$$386$$ 2996.00 0.395058
$$387$$ 0 0
$$388$$ −6568.00 −0.859381
$$389$$ 567.000 0.0739024 0.0369512 0.999317i $$-0.488235\pi$$
0.0369512 + 0.999317i $$0.488235\pi$$
$$390$$ 0 0
$$391$$ 3861.00 0.499384
$$392$$ 1176.00 0.151523
$$393$$ 0 0
$$394$$ 4248.00 0.543176
$$395$$ −3695.00 −0.470672
$$396$$ 0 0
$$397$$ −6685.00 −0.845115 −0.422557 0.906336i $$-0.638867\pi$$
−0.422557 + 0.906336i $$0.638867\pi$$
$$398$$ 770.000 0.0969764
$$399$$ 0 0
$$400$$ 400.000 0.0500000
$$401$$ 4572.00 0.569364 0.284682 0.958622i $$-0.408112\pi$$
0.284682 + 0.958622i $$0.408112\pi$$
$$402$$ 0 0
$$403$$ 3901.00 0.482190
$$404$$ 132.000 0.0162556
$$405$$ 0 0
$$406$$ −1428.00 −0.174558
$$407$$ 942.000 0.114725
$$408$$ 0 0
$$409$$ −25.0000 −0.00302242 −0.00151121 0.999999i $$-0.500481\pi$$
−0.00151121 + 0.999999i $$0.500481\pi$$
$$410$$ 1080.00 0.130091
$$411$$ 0 0
$$412$$ −4792.00 −0.573022
$$413$$ 168.000 0.0200163
$$414$$ 0 0
$$415$$ 5430.00 0.642285
$$416$$ −1504.00 −0.177259
$$417$$ 0 0
$$418$$ −192.000 −0.0224666
$$419$$ 12453.0 1.45195 0.725977 0.687719i $$-0.241388\pi$$
0.725977 + 0.687719i $$0.241388\pi$$
$$420$$ 0 0
$$421$$ 5048.00 0.584381 0.292191 0.956360i $$-0.405616\pi$$
0.292191 + 0.956360i $$0.405616\pi$$
$$422$$ −6340.00 −0.731342
$$423$$ 0 0
$$424$$ −4512.00 −0.516797
$$425$$ −975.000 −0.111281
$$426$$ 0 0
$$427$$ 3220.00 0.364934
$$428$$ −6168.00 −0.696592
$$429$$ 0 0
$$430$$ −2990.00 −0.335327
$$431$$ 5400.00 0.603501 0.301750 0.953387i $$-0.402429\pi$$
0.301750 + 0.953387i $$0.402429\pi$$
$$432$$ 0 0
$$433$$ −6298.00 −0.698990 −0.349495 0.936938i $$-0.613647\pi$$
−0.349495 + 0.936938i $$0.613647\pi$$
$$434$$ −2324.00 −0.257040
$$435$$ 0 0
$$436$$ −2224.00 −0.244290
$$437$$ −3168.00 −0.346787
$$438$$ 0 0
$$439$$ −6208.00 −0.674924 −0.337462 0.941339i $$-0.609568\pi$$
−0.337462 + 0.941339i $$0.609568\pi$$
$$440$$ −120.000 −0.0130018
$$441$$ 0 0
$$442$$ 3666.00 0.394511
$$443$$ −3360.00 −0.360358 −0.180179 0.983634i $$-0.557668\pi$$
−0.180179 + 0.983634i $$0.557668\pi$$
$$444$$ 0 0
$$445$$ −600.000 −0.0639162
$$446$$ −2776.00 −0.294725
$$447$$ 0 0
$$448$$ 896.000 0.0944911
$$449$$ 14394.0 1.51291 0.756453 0.654048i $$-0.226931\pi$$
0.756453 + 0.654048i $$0.226931\pi$$
$$450$$ 0 0
$$451$$ −324.000 −0.0338283
$$452$$ 6420.00 0.668078
$$453$$ 0 0
$$454$$ 9288.00 0.960149
$$455$$ 3290.00 0.338984
$$456$$ 0 0
$$457$$ −916.000 −0.0937608 −0.0468804 0.998901i $$-0.514928\pi$$
−0.0468804 + 0.998901i $$0.514928\pi$$
$$458$$ −9472.00 −0.966370
$$459$$ 0 0
$$460$$ −1980.00 −0.200691
$$461$$ 8550.00 0.863803 0.431902 0.901921i $$-0.357843\pi$$
0.431902 + 0.901921i $$0.357843\pi$$
$$462$$ 0 0
$$463$$ 3734.00 0.374803 0.187401 0.982283i $$-0.439993\pi$$
0.187401 + 0.982283i $$0.439993\pi$$
$$464$$ 816.000 0.0816419
$$465$$ 0 0
$$466$$ −5628.00 −0.559468
$$467$$ 9840.00 0.975034 0.487517 0.873113i $$-0.337903\pi$$
0.487517 + 0.873113i $$0.337903\pi$$
$$468$$ 0 0
$$469$$ −3752.00 −0.369406
$$470$$ −5310.00 −0.521132
$$471$$ 0 0
$$472$$ −96.0000 −0.00936178
$$473$$ 897.000 0.0871968
$$474$$ 0 0
$$475$$ 800.000 0.0772769
$$476$$ −2184.00 −0.210301
$$477$$ 0 0
$$478$$ 4404.00 0.421411
$$479$$ −17280.0 −1.64832 −0.824158 0.566360i $$-0.808351\pi$$
−0.824158 + 0.566360i $$0.808351\pi$$
$$480$$ 0 0
$$481$$ 14758.0 1.39897
$$482$$ −6970.00 −0.658661
$$483$$ 0 0
$$484$$ −5288.00 −0.496619
$$485$$ −8210.00 −0.768653
$$486$$ 0 0
$$487$$ −4588.00 −0.426904 −0.213452 0.976954i $$-0.568471\pi$$
−0.213452 + 0.976954i $$0.568471\pi$$
$$488$$ −1840.00 −0.170682
$$489$$ 0 0
$$490$$ 1470.00 0.135526
$$491$$ 636.000 0.0584568 0.0292284 0.999573i $$-0.490695\pi$$
0.0292284 + 0.999573i $$0.490695\pi$$
$$492$$ 0 0
$$493$$ −1989.00 −0.181704
$$494$$ −3008.00 −0.273960
$$495$$ 0 0
$$496$$ 1328.00 0.120220
$$497$$ 1680.00 0.151626
$$498$$ 0 0
$$499$$ −11716.0 −1.05106 −0.525531 0.850774i $$-0.676133\pi$$
−0.525531 + 0.850774i $$0.676133\pi$$
$$500$$ 500.000 0.0447214
$$501$$ 0 0
$$502$$ 12690.0 1.12825
$$503$$ 4653.00 0.412459 0.206230 0.978504i $$-0.433881\pi$$
0.206230 + 0.978504i $$0.433881\pi$$
$$504$$ 0 0
$$505$$ 165.000 0.0145394
$$506$$ 594.000 0.0521868
$$507$$ 0 0
$$508$$ 5336.00 0.466037
$$509$$ 16479.0 1.43501 0.717504 0.696555i $$-0.245285\pi$$
0.717504 + 0.696555i $$0.245285\pi$$
$$510$$ 0 0
$$511$$ 15484.0 1.34045
$$512$$ −512.000 −0.0441942
$$513$$ 0 0
$$514$$ −1050.00 −0.0901041
$$515$$ −5990.00 −0.512526
$$516$$ 0 0
$$517$$ 1593.00 0.135513
$$518$$ −8792.00 −0.745750
$$519$$ 0 0
$$520$$ −1880.00 −0.158545
$$521$$ 3120.00 0.262360 0.131180 0.991359i $$-0.458123\pi$$
0.131180 + 0.991359i $$0.458123\pi$$
$$522$$ 0 0
$$523$$ 17645.0 1.47526 0.737631 0.675204i $$-0.235944\pi$$
0.737631 + 0.675204i $$0.235944\pi$$
$$524$$ −11532.0 −0.961408
$$525$$ 0 0
$$526$$ −10392.0 −0.861431
$$527$$ −3237.00 −0.267563
$$528$$ 0 0
$$529$$ −2366.00 −0.194460
$$530$$ −5640.00 −0.462238
$$531$$ 0 0
$$532$$ 1792.00 0.146040
$$533$$ −5076.00 −0.412507
$$534$$ 0 0
$$535$$ −7710.00 −0.623051
$$536$$ 2144.00 0.172774
$$537$$ 0 0
$$538$$ 14958.0 1.19867
$$539$$ −441.000 −0.0352416
$$540$$ 0 0
$$541$$ −2182.00 −0.173404 −0.0867019 0.996234i $$-0.527633\pi$$
−0.0867019 + 0.996234i $$0.527633\pi$$
$$542$$ 1712.00 0.135677
$$543$$ 0 0
$$544$$ 1248.00 0.0983595
$$545$$ −2780.00 −0.218499
$$546$$ 0 0
$$547$$ −4033.00 −0.315244 −0.157622 0.987499i $$-0.550383\pi$$
−0.157622 + 0.987499i $$0.550383\pi$$
$$548$$ 1128.00 0.0879302
$$549$$ 0 0
$$550$$ −150.000 −0.0116291
$$551$$ 1632.00 0.126181
$$552$$ 0 0
$$553$$ −10346.0 −0.795582
$$554$$ 14108.0 1.08193
$$555$$ 0 0
$$556$$ −9976.00 −0.760929
$$557$$ −960.000 −0.0730278 −0.0365139 0.999333i $$-0.511625\pi$$
−0.0365139 + 0.999333i $$0.511625\pi$$
$$558$$ 0 0
$$559$$ 14053.0 1.06329
$$560$$ 1120.00 0.0845154
$$561$$ 0 0
$$562$$ −2028.00 −0.152217
$$563$$ −23754.0 −1.77817 −0.889087 0.457739i $$-0.848660\pi$$
−0.889087 + 0.457739i $$0.848660\pi$$
$$564$$ 0 0
$$565$$ 8025.00 0.597547
$$566$$ −1984.00 −0.147339
$$567$$ 0 0
$$568$$ −960.000 −0.0709167
$$569$$ −22536.0 −1.66038 −0.830192 0.557478i $$-0.811769\pi$$
−0.830192 + 0.557478i $$0.811769\pi$$
$$570$$ 0 0
$$571$$ 17726.0 1.29914 0.649571 0.760301i $$-0.274949\pi$$
0.649571 + 0.760301i $$0.274949\pi$$
$$572$$ 564.000 0.0412273
$$573$$ 0 0
$$574$$ 3024.00 0.219894
$$575$$ −2475.00 −0.179504
$$576$$ 0 0
$$577$$ 17168.0 1.23867 0.619336 0.785126i $$-0.287402\pi$$
0.619336 + 0.785126i $$0.287402\pi$$
$$578$$ 6784.00 0.488196
$$579$$ 0 0
$$580$$ 1020.00 0.0730227
$$581$$ 15204.0 1.08566
$$582$$ 0 0
$$583$$ 1692.00 0.120198
$$584$$ −8848.00 −0.626940
$$585$$ 0 0
$$586$$ 9900.00 0.697893
$$587$$ 7542.00 0.530309 0.265155 0.964206i $$-0.414577\pi$$
0.265155 + 0.964206i $$0.414577\pi$$
$$588$$ 0 0
$$589$$ 2656.00 0.185804
$$590$$ −120.000 −0.00837343
$$591$$ 0 0
$$592$$ 5024.00 0.348792
$$593$$ −15543.0 −1.07635 −0.538174 0.842834i $$-0.680886\pi$$
−0.538174 + 0.842834i $$0.680886\pi$$
$$594$$ 0 0
$$595$$ −2730.00 −0.188099
$$596$$ 10380.0 0.713392
$$597$$ 0 0
$$598$$ 9306.00 0.636372
$$599$$ 16026.0 1.09316 0.546581 0.837406i $$-0.315929\pi$$
0.546581 + 0.837406i $$0.315929\pi$$
$$600$$ 0 0
$$601$$ 10469.0 0.710548 0.355274 0.934762i $$-0.384388\pi$$
0.355274 + 0.934762i $$0.384388\pi$$
$$602$$ −8372.00 −0.566806
$$603$$ 0 0
$$604$$ 4916.00 0.331174
$$605$$ −6610.00 −0.444190
$$606$$ 0 0
$$607$$ −8074.00 −0.539891 −0.269945 0.962876i $$-0.587006\pi$$
−0.269945 + 0.962876i $$0.587006\pi$$
$$608$$ −1024.00 −0.0683038
$$609$$ 0 0
$$610$$ −2300.00 −0.152663
$$611$$ 24957.0 1.65246
$$612$$ 0 0
$$613$$ 26855.0 1.76943 0.884717 0.466128i $$-0.154351\pi$$
0.884717 + 0.466128i $$0.154351\pi$$
$$614$$ 9554.00 0.627961
$$615$$ 0 0
$$616$$ −336.000 −0.0219770
$$617$$ 24447.0 1.59514 0.797568 0.603229i $$-0.206119\pi$$
0.797568 + 0.603229i $$0.206119\pi$$
$$618$$ 0 0
$$619$$ 1850.00 0.120126 0.0600628 0.998195i $$-0.480870\pi$$
0.0600628 + 0.998195i $$0.480870\pi$$
$$620$$ 1660.00 0.107528
$$621$$ 0 0
$$622$$ 15384.0 0.991708
$$623$$ −1680.00 −0.108038
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 5864.00 0.374397
$$627$$ 0 0
$$628$$ −6364.00 −0.404381
$$629$$ −12246.0 −0.776280
$$630$$ 0 0
$$631$$ 21728.0 1.37081 0.685403 0.728164i $$-0.259626\pi$$
0.685403 + 0.728164i $$0.259626\pi$$
$$632$$ 5912.00 0.372099
$$633$$ 0 0
$$634$$ −16704.0 −1.04637
$$635$$ 6670.00 0.416836
$$636$$ 0 0
$$637$$ −6909.00 −0.429740
$$638$$ −306.000 −0.0189885
$$639$$ 0 0
$$640$$ −640.000 −0.0395285
$$641$$ 23862.0 1.47035 0.735173 0.677879i $$-0.237101\pi$$
0.735173 + 0.677879i $$0.237101\pi$$
$$642$$ 0 0
$$643$$ 10523.0 0.645391 0.322696 0.946503i $$-0.395411\pi$$
0.322696 + 0.946503i $$0.395411\pi$$
$$644$$ −5544.00 −0.339230
$$645$$ 0 0
$$646$$ 2496.00 0.152018
$$647$$ 5484.00 0.333228 0.166614 0.986022i $$-0.446717\pi$$
0.166614 + 0.986022i $$0.446717\pi$$
$$648$$ 0 0
$$649$$ 36.0000 0.00217739
$$650$$ −2350.00 −0.141807
$$651$$ 0 0
$$652$$ −1828.00 −0.109801
$$653$$ −26784.0 −1.60511 −0.802557 0.596576i $$-0.796527\pi$$
−0.802557 + 0.596576i $$0.796527\pi$$
$$654$$ 0 0
$$655$$ −14415.0 −0.859909
$$656$$ −1728.00 −0.102846
$$657$$ 0 0
$$658$$ −14868.0 −0.880874
$$659$$ −12120.0 −0.716431 −0.358216 0.933639i $$-0.616615\pi$$
−0.358216 + 0.933639i $$0.616615\pi$$
$$660$$ 0 0
$$661$$ −18226.0 −1.07248 −0.536240 0.844066i $$-0.680156\pi$$
−0.536240 + 0.844066i $$0.680156\pi$$
$$662$$ 6140.00 0.360480
$$663$$ 0 0
$$664$$ −8688.00 −0.507771
$$665$$ 2240.00 0.130622
$$666$$ 0 0
$$667$$ −5049.00 −0.293101
$$668$$ −4656.00 −0.269680
$$669$$ 0 0
$$670$$ 2680.00 0.154533
$$671$$ 690.000 0.0396977
$$672$$ 0 0
$$673$$ −11062.0 −0.633594 −0.316797 0.948493i $$-0.602607\pi$$
−0.316797 + 0.948493i $$0.602607\pi$$
$$674$$ 3344.00 0.191107
$$675$$ 0 0
$$676$$ 48.0000 0.00273100
$$677$$ −9348.00 −0.530684 −0.265342 0.964154i $$-0.585485\pi$$
−0.265342 + 0.964154i $$0.585485\pi$$
$$678$$ 0 0
$$679$$ −22988.0 −1.29926
$$680$$ 1560.00 0.0879754
$$681$$ 0 0
$$682$$ −498.000 −0.0279610
$$683$$ 19248.0 1.07834 0.539169 0.842198i $$-0.318739\pi$$
0.539169 + 0.842198i $$0.318739\pi$$
$$684$$ 0 0
$$685$$ 1410.00 0.0786472
$$686$$ 13720.0 0.763604
$$687$$ 0 0
$$688$$ 4784.00 0.265099
$$689$$ 26508.0 1.46571
$$690$$ 0 0
$$691$$ −17710.0 −0.974993 −0.487496 0.873125i $$-0.662090\pi$$
−0.487496 + 0.873125i $$0.662090\pi$$
$$692$$ 15768.0 0.866199
$$693$$ 0 0
$$694$$ 10152.0 0.555280
$$695$$ −12470.0 −0.680596
$$696$$ 0 0
$$697$$ 4212.00 0.228897
$$698$$ −17188.0 −0.932056
$$699$$ 0 0
$$700$$ 1400.00 0.0755929
$$701$$ −19437.0 −1.04725 −0.523627 0.851947i $$-0.675422\pi$$
−0.523627 + 0.851947i $$0.675422\pi$$
$$702$$ 0 0
$$703$$ 10048.0 0.539072
$$704$$ 192.000 0.0102788
$$705$$ 0 0
$$706$$ −25422.0 −1.35520
$$707$$ 462.000 0.0245761
$$708$$ 0 0
$$709$$ −19516.0 −1.03376 −0.516882 0.856057i $$-0.672907\pi$$
−0.516882 + 0.856057i $$0.672907\pi$$
$$710$$ −1200.00 −0.0634299
$$711$$ 0 0
$$712$$ 960.000 0.0505302
$$713$$ −8217.00 −0.431598
$$714$$ 0 0
$$715$$ 705.000 0.0368748
$$716$$ −4848.00 −0.253042
$$717$$ 0 0
$$718$$ 2928.00 0.152189
$$719$$ 17358.0 0.900340 0.450170 0.892943i $$-0.351363\pi$$
0.450170 + 0.892943i $$0.351363\pi$$
$$720$$ 0 0
$$721$$ −16772.0 −0.866327
$$722$$ 11670.0 0.601541
$$723$$ 0 0
$$724$$ 9152.00 0.469795
$$725$$ 1275.00 0.0653135
$$726$$ 0 0
$$727$$ 24428.0 1.24620 0.623098 0.782144i $$-0.285874\pi$$
0.623098 + 0.782144i $$0.285874\pi$$
$$728$$ −5264.00 −0.267990
$$729$$ 0 0
$$730$$ −11060.0 −0.560752
$$731$$ −11661.0 −0.590010
$$732$$ 0 0
$$733$$ −21418.0 −1.07925 −0.539626 0.841905i $$-0.681434\pi$$
−0.539626 + 0.841905i $$0.681434\pi$$
$$734$$ 15260.0 0.767380
$$735$$ 0 0
$$736$$ 3168.00 0.158660
$$737$$ −804.000 −0.0401842
$$738$$ 0 0
$$739$$ −664.000 −0.0330523 −0.0165261 0.999863i $$-0.505261\pi$$
−0.0165261 + 0.999863i $$0.505261\pi$$
$$740$$ 6280.00 0.311969
$$741$$ 0 0
$$742$$ −15792.0 −0.781324
$$743$$ −34209.0 −1.68911 −0.844553 0.535471i $$-0.820134\pi$$
−0.844553 + 0.535471i $$0.820134\pi$$
$$744$$ 0 0
$$745$$ 12975.0 0.638077
$$746$$ 7766.00 0.381144
$$747$$ 0 0
$$748$$ −468.000 −0.0228767
$$749$$ −21588.0 −1.05315
$$750$$ 0 0
$$751$$ 6857.00 0.333176 0.166588 0.986027i $$-0.446725\pi$$
0.166588 + 0.986027i $$0.446725\pi$$
$$752$$ 8496.00 0.411991
$$753$$ 0 0
$$754$$ −4794.00 −0.231548
$$755$$ 6145.00 0.296211
$$756$$ 0 0
$$757$$ −23719.0 −1.13881 −0.569407 0.822056i $$-0.692827\pi$$
−0.569407 + 0.822056i $$0.692827\pi$$
$$758$$ 27536.0 1.31946
$$759$$ 0 0
$$760$$ −1280.00 −0.0610927
$$761$$ −14418.0 −0.686796 −0.343398 0.939190i $$-0.611578\pi$$
−0.343398 + 0.939190i $$0.611578\pi$$
$$762$$ 0 0
$$763$$ −7784.00 −0.369331
$$764$$ −7752.00 −0.367091
$$765$$ 0 0
$$766$$ 28278.0 1.33385
$$767$$ 564.000 0.0265513
$$768$$ 0 0
$$769$$ −4849.00 −0.227385 −0.113693 0.993516i $$-0.536268\pi$$
−0.113693 + 0.993516i $$0.536268\pi$$
$$770$$ −420.000 −0.0196568
$$771$$ 0 0
$$772$$ −5992.00 −0.279348
$$773$$ −36258.0 −1.68708 −0.843538 0.537070i $$-0.819531\pi$$
−0.843538 + 0.537070i $$0.819531\pi$$
$$774$$ 0 0
$$775$$ 2075.00 0.0961757
$$776$$ 13136.0 0.607674
$$777$$ 0 0
$$778$$ −1134.00 −0.0522569
$$779$$ −3456.00 −0.158953
$$780$$ 0 0
$$781$$ 360.000 0.0164940
$$782$$ −7722.00 −0.353118
$$783$$ 0 0
$$784$$ −2352.00 −0.107143
$$785$$ −7955.00 −0.361689
$$786$$ 0 0
$$787$$ −18877.0 −0.855009 −0.427505 0.904013i $$-0.640607\pi$$
−0.427505 + 0.904013i $$0.640607\pi$$
$$788$$ −8496.00 −0.384083
$$789$$ 0 0
$$790$$ 7390.00 0.332816
$$791$$ 22470.0 1.01004
$$792$$ 0 0
$$793$$ 10810.0 0.484079
$$794$$ 13370.0 0.597586
$$795$$ 0 0
$$796$$ −1540.00 −0.0685727
$$797$$ −16200.0 −0.719992 −0.359996 0.932954i $$-0.617222\pi$$
−0.359996 + 0.932954i $$0.617222\pi$$
$$798$$ 0 0
$$799$$ −20709.0 −0.916936
$$800$$ −800.000 −0.0353553
$$801$$ 0 0
$$802$$ −9144.00 −0.402601
$$803$$ 3318.00 0.145815
$$804$$ 0 0
$$805$$ −6930.00 −0.303417
$$806$$ −7802.00 −0.340960
$$807$$ 0 0
$$808$$ −264.000 −0.0114944
$$809$$ −26760.0 −1.16296 −0.581478 0.813562i $$-0.697525\pi$$
−0.581478 + 0.813562i $$0.697525\pi$$
$$810$$ 0 0
$$811$$ −10510.0 −0.455063 −0.227531 0.973771i $$-0.573065\pi$$
−0.227531 + 0.973771i $$0.573065\pi$$
$$812$$ 2856.00 0.123431
$$813$$ 0 0
$$814$$ −1884.00 −0.0811231
$$815$$ −2285.00 −0.0982087
$$816$$ 0 0
$$817$$ 9568.00 0.409721
$$818$$ 50.0000 0.00213717
$$819$$ 0 0
$$820$$ −2160.00 −0.0919884
$$821$$ −28230.0 −1.20004 −0.600021 0.799985i $$-0.704841\pi$$
−0.600021 + 0.799985i $$0.704841\pi$$
$$822$$ 0 0
$$823$$ −39868.0 −1.68859 −0.844296 0.535877i $$-0.819981\pi$$
−0.844296 + 0.535877i $$0.819981\pi$$
$$824$$ 9584.00 0.405187
$$825$$ 0 0
$$826$$ −336.000 −0.0141537
$$827$$ 32394.0 1.36209 0.681046 0.732241i $$-0.261525\pi$$
0.681046 + 0.732241i $$0.261525\pi$$
$$828$$ 0 0
$$829$$ 34820.0 1.45880 0.729402 0.684085i $$-0.239798\pi$$
0.729402 + 0.684085i $$0.239798\pi$$
$$830$$ −10860.0 −0.454164
$$831$$ 0 0
$$832$$ 3008.00 0.125341
$$833$$ 5733.00 0.238459
$$834$$ 0 0
$$835$$ −5820.00 −0.241209
$$836$$ 384.000 0.0158863
$$837$$ 0 0
$$838$$ −24906.0 −1.02669
$$839$$ −1146.00 −0.0471565 −0.0235783 0.999722i $$-0.507506\pi$$
−0.0235783 + 0.999722i $$0.507506\pi$$
$$840$$ 0 0
$$841$$ −21788.0 −0.893354
$$842$$ −10096.0 −0.413220
$$843$$ 0 0
$$844$$ 12680.0 0.517137
$$845$$ 60.0000 0.00244268
$$846$$ 0 0
$$847$$ −18508.0 −0.750817
$$848$$ 9024.00 0.365431
$$849$$ 0 0
$$850$$ 1950.00 0.0786876
$$851$$ −31086.0 −1.25219
$$852$$ 0 0
$$853$$ −19393.0 −0.778433 −0.389217 0.921146i $$-0.627254\pi$$
−0.389217 + 0.921146i $$0.627254\pi$$
$$854$$ −6440.00 −0.258047
$$855$$ 0 0
$$856$$ 12336.0 0.492565
$$857$$ −8430.00 −0.336013 −0.168007 0.985786i $$-0.553733\pi$$
−0.168007 + 0.985786i $$0.553733\pi$$
$$858$$ 0 0
$$859$$ 15470.0 0.614470 0.307235 0.951634i $$-0.400596\pi$$
0.307235 + 0.951634i $$0.400596\pi$$
$$860$$ 5980.00 0.237112
$$861$$ 0 0
$$862$$ −10800.0 −0.426740
$$863$$ 5871.00 0.231577 0.115789 0.993274i $$-0.463060\pi$$
0.115789 + 0.993274i $$0.463060\pi$$
$$864$$ 0 0
$$865$$ 19710.0 0.774752
$$866$$ 12596.0 0.494260
$$867$$ 0 0
$$868$$ 4648.00 0.181755
$$869$$ −2217.00 −0.0865438
$$870$$ 0 0
$$871$$ −12596.0 −0.490011
$$872$$ 4448.00 0.172739
$$873$$ 0 0
$$874$$ 6336.00 0.245216
$$875$$ 1750.00 0.0676123
$$876$$ 0 0
$$877$$ −11299.0 −0.435051 −0.217526 0.976055i $$-0.569799\pi$$
−0.217526 + 0.976055i $$0.569799\pi$$
$$878$$ 12416.0 0.477243
$$879$$ 0 0
$$880$$ 240.000 0.00919363
$$881$$ 29682.0 1.13509 0.567544 0.823343i $$-0.307894\pi$$
0.567544 + 0.823343i $$0.307894\pi$$
$$882$$ 0 0
$$883$$ 40316.0 1.53651 0.768257 0.640142i $$-0.221124\pi$$
0.768257 + 0.640142i $$0.221124\pi$$
$$884$$ −7332.00 −0.278961
$$885$$ 0 0
$$886$$ 6720.00 0.254811
$$887$$ −21945.0 −0.830711 −0.415356 0.909659i $$-0.636343\pi$$
−0.415356 + 0.909659i $$0.636343\pi$$
$$888$$ 0 0
$$889$$ 18676.0 0.704581
$$890$$ 1200.00 0.0451956
$$891$$ 0 0
$$892$$ 5552.00 0.208402
$$893$$ 16992.0 0.636748
$$894$$ 0 0
$$895$$ −6060.00 −0.226328
$$896$$ −1792.00 −0.0668153
$$897$$ 0 0
$$898$$ −28788.0 −1.06979
$$899$$ 4233.00 0.157039
$$900$$ 0 0
$$901$$ −21996.0 −0.813311
$$902$$ 648.000 0.0239202
$$903$$ 0 0
$$904$$ −12840.0 −0.472403
$$905$$ 11440.0 0.420197
$$906$$ 0 0
$$907$$ 24911.0 0.911969 0.455985 0.889988i $$-0.349287\pi$$
0.455985 + 0.889988i $$0.349287\pi$$
$$908$$ −18576.0 −0.678928
$$909$$ 0 0
$$910$$ −6580.00 −0.239698
$$911$$ 33264.0 1.20975 0.604877 0.796319i $$-0.293222\pi$$
0.604877 + 0.796319i $$0.293222\pi$$
$$912$$ 0 0
$$913$$ 3258.00 0.118099
$$914$$ 1832.00 0.0662989
$$915$$ 0 0
$$916$$ 18944.0 0.683327
$$917$$ −40362.0 −1.45351
$$918$$ 0 0
$$919$$ −23191.0 −0.832427 −0.416214 0.909267i $$-0.636643\pi$$
−0.416214 + 0.909267i $$0.636643\pi$$
$$920$$ 3960.00 0.141910
$$921$$ 0 0
$$922$$ −17100.0 −0.610801
$$923$$ 5640.00 0.201130
$$924$$ 0 0
$$925$$ 7850.00 0.279034
$$926$$ −7468.00 −0.265026
$$927$$ 0 0
$$928$$ −1632.00 −0.0577296
$$929$$ 2160.00 0.0762834 0.0381417 0.999272i $$-0.487856\pi$$
0.0381417 + 0.999272i $$0.487856\pi$$
$$930$$ 0 0
$$931$$ −4704.00 −0.165593
$$932$$ 11256.0 0.395604
$$933$$ 0 0
$$934$$ −19680.0 −0.689453
$$935$$ −585.000 −0.0204615
$$936$$ 0 0
$$937$$ 2066.00 0.0720312 0.0360156 0.999351i $$-0.488533\pi$$
0.0360156 + 0.999351i $$0.488533\pi$$
$$938$$ 7504.00 0.261209
$$939$$ 0 0
$$940$$ 10620.0 0.368496
$$941$$ −22233.0 −0.770218 −0.385109 0.922871i $$-0.625836\pi$$
−0.385109 + 0.922871i $$0.625836\pi$$
$$942$$ 0 0
$$943$$ 10692.0 0.369225
$$944$$ 192.000 0.00661978
$$945$$ 0 0
$$946$$ −1794.00 −0.0616575
$$947$$ −17754.0 −0.609216 −0.304608 0.952478i $$-0.598525\pi$$
−0.304608 + 0.952478i $$0.598525\pi$$
$$948$$ 0 0
$$949$$ 51982.0 1.77809
$$950$$ −1600.00 −0.0546430
$$951$$ 0 0
$$952$$ 4368.00 0.148706
$$953$$ 33891.0 1.15198 0.575990 0.817457i $$-0.304617\pi$$
0.575990 + 0.817457i $$0.304617\pi$$
$$954$$ 0 0
$$955$$ −9690.00 −0.328336
$$956$$ −8808.00 −0.297982
$$957$$ 0 0
$$958$$ 34560.0 1.16554
$$959$$ 3948.00 0.132938
$$960$$ 0 0
$$961$$ −22902.0 −0.768756
$$962$$ −29516.0 −0.989225
$$963$$ 0 0
$$964$$ 13940.0 0.465744
$$965$$ −7490.00 −0.249857
$$966$$ 0 0
$$967$$ 51074.0 1.69848 0.849239 0.528008i $$-0.177061\pi$$
0.849239 + 0.528008i $$0.177061\pi$$
$$968$$ 10576.0 0.351163
$$969$$ 0 0
$$970$$ 16420.0 0.543520
$$971$$ 20967.0 0.692959 0.346479 0.938058i $$-0.387377\pi$$
0.346479 + 0.938058i $$0.387377\pi$$
$$972$$ 0 0
$$973$$ −34916.0 −1.15042
$$974$$ 9176.00 0.301867
$$975$$ 0 0
$$976$$ 3680.00 0.120691
$$977$$ 31749.0 1.03965 0.519826 0.854272i $$-0.325997\pi$$
0.519826 + 0.854272i $$0.325997\pi$$
$$978$$ 0 0
$$979$$ −360.000 −0.0117525
$$980$$ −2940.00 −0.0958315
$$981$$ 0 0
$$982$$ −1272.00 −0.0413352
$$983$$ 47325.0 1.53554 0.767769 0.640727i $$-0.221367\pi$$
0.767769 + 0.640727i $$0.221367\pi$$
$$984$$ 0 0
$$985$$ −10620.0 −0.343534
$$986$$ 3978.00 0.128484
$$987$$ 0 0
$$988$$ 6016.00 0.193719
$$989$$ −29601.0 −0.951726
$$990$$ 0 0
$$991$$ 2363.00 0.0757449 0.0378724 0.999283i $$-0.487942\pi$$
0.0378724 + 0.999283i $$0.487942\pi$$
$$992$$ −2656.00 −0.0850081
$$993$$ 0 0
$$994$$ −3360.00 −0.107216
$$995$$ −1925.00 −0.0613333
$$996$$ 0 0
$$997$$ 45569.0 1.44753 0.723764 0.690048i $$-0.242411\pi$$
0.723764 + 0.690048i $$0.242411\pi$$
$$998$$ 23432.0 0.743213
$$999$$ 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 270.4.a.f.1.1 1
3.2 odd 2 270.4.a.j.1.1 yes 1
4.3 odd 2 2160.4.a.l.1.1 1
5.2 odd 4 1350.4.c.k.649.1 2
5.3 odd 4 1350.4.c.k.649.2 2
5.4 even 2 1350.4.a.r.1.1 1
9.2 odd 6 810.4.e.f.271.1 2
9.4 even 3 810.4.e.n.541.1 2
9.5 odd 6 810.4.e.f.541.1 2
9.7 even 3 810.4.e.n.271.1 2
12.11 even 2 2160.4.a.b.1.1 1
15.2 even 4 1350.4.c.j.649.2 2
15.8 even 4 1350.4.c.j.649.1 2
15.14 odd 2 1350.4.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.f.1.1 1 1.1 even 1 trivial
270.4.a.j.1.1 yes 1 3.2 odd 2
810.4.e.f.271.1 2 9.2 odd 6
810.4.e.f.541.1 2 9.5 odd 6
810.4.e.n.271.1 2 9.7 even 3
810.4.e.n.541.1 2 9.4 even 3
1350.4.a.e.1.1 1 15.14 odd 2
1350.4.a.r.1.1 1 5.4 even 2
1350.4.c.j.649.1 2 15.8 even 4
1350.4.c.j.649.2 2 15.2 even 4
1350.4.c.k.649.1 2 5.2 odd 4
1350.4.c.k.649.2 2 5.3 odd 4
2160.4.a.b.1.1 1 12.11 even 2
2160.4.a.l.1.1 1 4.3 odd 2