Properties

 Label 1575.4.a.e.1.1 Level $1575$ Weight $4$ Character 1575.1 Self dual yes Analytic conductor $92.928$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1575.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$92.9280082590$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 7) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1575.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -7.00000 q^{4} +7.00000 q^{7} +15.0000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} -7.00000 q^{4} +7.00000 q^{7} +15.0000 q^{8} +8.00000 q^{11} -28.0000 q^{13} -7.00000 q^{14} +41.0000 q^{16} +54.0000 q^{17} -110.000 q^{19} -8.00000 q^{22} +48.0000 q^{23} +28.0000 q^{26} -49.0000 q^{28} +110.000 q^{29} +12.0000 q^{31} -161.000 q^{32} -54.0000 q^{34} +246.000 q^{37} +110.000 q^{38} -182.000 q^{41} -128.000 q^{43} -56.0000 q^{44} -48.0000 q^{46} +324.000 q^{47} +49.0000 q^{49} +196.000 q^{52} -162.000 q^{53} +105.000 q^{56} -110.000 q^{58} -810.000 q^{59} -488.000 q^{61} -12.0000 q^{62} -167.000 q^{64} -244.000 q^{67} -378.000 q^{68} +768.000 q^{71} +702.000 q^{73} -246.000 q^{74} +770.000 q^{76} +56.0000 q^{77} +440.000 q^{79} +182.000 q^{82} -1302.00 q^{83} +128.000 q^{86} +120.000 q^{88} -730.000 q^{89} -196.000 q^{91} -336.000 q^{92} -324.000 q^{94} -294.000 q^{97} -49.0000 q^{98} +O(q^{100})$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.353553 −0.176777 0.984251i $$-0.556567\pi$$
−0.176777 + 0.984251i $$0.556567\pi$$
$$3$$ 0 0
$$4$$ −7.00000 −0.875000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 7.00000 0.377964
$$8$$ 15.0000 0.662913
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 8.00000 0.219281 0.109640 0.993971i $$-0.465030\pi$$
0.109640 + 0.993971i $$0.465030\pi$$
$$12$$ 0 0
$$13$$ −28.0000 −0.597369 −0.298685 0.954352i $$-0.596548\pi$$
−0.298685 + 0.954352i $$0.596548\pi$$
$$14$$ −7.00000 −0.133631
$$15$$ 0 0
$$16$$ 41.0000 0.640625
$$17$$ 54.0000 0.770407 0.385204 0.922832i $$-0.374131\pi$$
0.385204 + 0.922832i $$0.374131\pi$$
$$18$$ 0 0
$$19$$ −110.000 −1.32820 −0.664098 0.747645i $$-0.731184\pi$$
−0.664098 + 0.747645i $$0.731184\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −8.00000 −0.0775275
$$23$$ 48.0000 0.435161 0.217580 0.976042i $$-0.430184\pi$$
0.217580 + 0.976042i $$0.430184\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 28.0000 0.211202
$$27$$ 0 0
$$28$$ −49.0000 −0.330719
$$29$$ 110.000 0.704362 0.352181 0.935932i $$-0.385440\pi$$
0.352181 + 0.935932i $$0.385440\pi$$
$$30$$ 0 0
$$31$$ 12.0000 0.0695246 0.0347623 0.999396i $$-0.488933\pi$$
0.0347623 + 0.999396i $$0.488933\pi$$
$$32$$ −161.000 −0.889408
$$33$$ 0 0
$$34$$ −54.0000 −0.272380
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 246.000 1.09303 0.546516 0.837449i $$-0.315954\pi$$
0.546516 + 0.837449i $$0.315954\pi$$
$$38$$ 110.000 0.469588
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −182.000 −0.693259 −0.346630 0.938002i $$-0.612674\pi$$
−0.346630 + 0.938002i $$0.612674\pi$$
$$42$$ 0 0
$$43$$ −128.000 −0.453949 −0.226975 0.973901i $$-0.572883\pi$$
−0.226975 + 0.973901i $$0.572883\pi$$
$$44$$ −56.0000 −0.191871
$$45$$ 0 0
$$46$$ −48.0000 −0.153852
$$47$$ 324.000 1.00554 0.502769 0.864421i $$-0.332315\pi$$
0.502769 + 0.864421i $$0.332315\pi$$
$$48$$ 0 0
$$49$$ 49.0000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 196.000 0.522698
$$53$$ −162.000 −0.419857 −0.209928 0.977717i $$-0.567323\pi$$
−0.209928 + 0.977717i $$0.567323\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 105.000 0.250557
$$57$$ 0 0
$$58$$ −110.000 −0.249029
$$59$$ −810.000 −1.78734 −0.893670 0.448725i $$-0.851878\pi$$
−0.893670 + 0.448725i $$0.851878\pi$$
$$60$$ 0 0
$$61$$ −488.000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ −12.0000 −0.0245807
$$63$$ 0 0
$$64$$ −167.000 −0.326172
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −244.000 −0.444916 −0.222458 0.974942i $$-0.571408\pi$$
−0.222458 + 0.974942i $$0.571408\pi$$
$$68$$ −378.000 −0.674106
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 768.000 1.28373 0.641865 0.766818i $$-0.278161\pi$$
0.641865 + 0.766818i $$0.278161\pi$$
$$72$$ 0 0
$$73$$ 702.000 1.12552 0.562759 0.826621i $$-0.309740\pi$$
0.562759 + 0.826621i $$0.309740\pi$$
$$74$$ −246.000 −0.386445
$$75$$ 0 0
$$76$$ 770.000 1.16217
$$77$$ 56.0000 0.0828804
$$78$$ 0 0
$$79$$ 440.000 0.626631 0.313316 0.949649i $$-0.398560\pi$$
0.313316 + 0.949649i $$0.398560\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 182.000 0.245104
$$83$$ −1302.00 −1.72184 −0.860922 0.508737i $$-0.830113\pi$$
−0.860922 + 0.508737i $$0.830113\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 128.000 0.160495
$$87$$ 0 0
$$88$$ 120.000 0.145364
$$89$$ −730.000 −0.869436 −0.434718 0.900567i $$-0.643152\pi$$
−0.434718 + 0.900567i $$0.643152\pi$$
$$90$$ 0 0
$$91$$ −196.000 −0.225784
$$92$$ −336.000 −0.380765
$$93$$ 0 0
$$94$$ −324.000 −0.355511
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −294.000 −0.307744 −0.153872 0.988091i $$-0.549174\pi$$
−0.153872 + 0.988091i $$0.549174\pi$$
$$98$$ −49.0000 −0.0505076
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 688.000 0.677808 0.338904 0.940821i $$-0.389944\pi$$
0.338904 + 0.940821i $$0.389944\pi$$
$$102$$ 0 0
$$103$$ −1388.00 −1.32780 −0.663901 0.747820i $$-0.731101\pi$$
−0.663901 + 0.747820i $$0.731101\pi$$
$$104$$ −420.000 −0.396004
$$105$$ 0 0
$$106$$ 162.000 0.148442
$$107$$ 244.000 0.220452 0.110226 0.993907i $$-0.464843\pi$$
0.110226 + 0.993907i $$0.464843\pi$$
$$108$$ 0 0
$$109$$ 90.0000 0.0790866 0.0395433 0.999218i $$-0.487410\pi$$
0.0395433 + 0.999218i $$0.487410\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 287.000 0.242133
$$113$$ 1318.00 1.09723 0.548615 0.836075i $$-0.315155\pi$$
0.548615 + 0.836075i $$0.315155\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −770.000 −0.616316
$$117$$ 0 0
$$118$$ 810.000 0.631920
$$119$$ 378.000 0.291187
$$120$$ 0 0
$$121$$ −1267.00 −0.951916
$$122$$ 488.000 0.362143
$$123$$ 0 0
$$124$$ −84.0000 −0.0608341
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1776.00 1.24090 0.620451 0.784245i $$-0.286950\pi$$
0.620451 + 0.784245i $$0.286950\pi$$
$$128$$ 1455.00 1.00473
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1118.00 0.745650 0.372825 0.927902i $$-0.378389\pi$$
0.372825 + 0.927902i $$0.378389\pi$$
$$132$$ 0 0
$$133$$ −770.000 −0.502011
$$134$$ 244.000 0.157301
$$135$$ 0 0
$$136$$ 810.000 0.510713
$$137$$ 2274.00 1.41811 0.709054 0.705154i $$-0.249122\pi$$
0.709054 + 0.705154i $$0.249122\pi$$
$$138$$ 0 0
$$139$$ −210.000 −0.128144 −0.0640718 0.997945i $$-0.520409\pi$$
−0.0640718 + 0.997945i $$0.520409\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −768.000 −0.453867
$$143$$ −224.000 −0.130992
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −702.000 −0.397931
$$147$$ 0 0
$$148$$ −1722.00 −0.956402
$$149$$ 2010.00 1.10514 0.552569 0.833467i $$-0.313648\pi$$
0.552569 + 0.833467i $$0.313648\pi$$
$$150$$ 0 0
$$151$$ 1112.00 0.599293 0.299647 0.954050i $$-0.403131\pi$$
0.299647 + 0.954050i $$0.403131\pi$$
$$152$$ −1650.00 −0.880478
$$153$$ 0 0
$$154$$ −56.0000 −0.0293027
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −124.000 −0.0630336 −0.0315168 0.999503i $$-0.510034\pi$$
−0.0315168 + 0.999503i $$0.510034\pi$$
$$158$$ −440.000 −0.221548
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 336.000 0.164475
$$162$$ 0 0
$$163$$ −2008.00 −0.964900 −0.482450 0.875924i $$-0.660253\pi$$
−0.482450 + 0.875924i $$0.660253\pi$$
$$164$$ 1274.00 0.606602
$$165$$ 0 0
$$166$$ 1302.00 0.608764
$$167$$ 2884.00 1.33635 0.668176 0.744004i $$-0.267076\pi$$
0.668176 + 0.744004i $$0.267076\pi$$
$$168$$ 0 0
$$169$$ −1413.00 −0.643150
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 896.000 0.397206
$$173$$ 2228.00 0.979143 0.489571 0.871963i $$-0.337153\pi$$
0.489571 + 0.871963i $$0.337153\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 328.000 0.140477
$$177$$ 0 0
$$178$$ 730.000 0.307392
$$179$$ 820.000 0.342400 0.171200 0.985236i $$-0.445236\pi$$
0.171200 + 0.985236i $$0.445236\pi$$
$$180$$ 0 0
$$181$$ 3892.00 1.59829 0.799144 0.601140i $$-0.205287\pi$$
0.799144 + 0.601140i $$0.205287\pi$$
$$182$$ 196.000 0.0798268
$$183$$ 0 0
$$184$$ 720.000 0.288473
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 432.000 0.168936
$$188$$ −2268.00 −0.879845
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 5048.00 1.91236 0.956179 0.292782i $$-0.0945810\pi$$
0.956179 + 0.292782i $$0.0945810\pi$$
$$192$$ 0 0
$$193$$ 2962.00 1.10471 0.552356 0.833608i $$-0.313729\pi$$
0.552356 + 0.833608i $$0.313729\pi$$
$$194$$ 294.000 0.108804
$$195$$ 0 0
$$196$$ −343.000 −0.125000
$$197$$ 3334.00 1.20577 0.602887 0.797826i $$-0.294017\pi$$
0.602887 + 0.797826i $$0.294017\pi$$
$$198$$ 0 0
$$199$$ 1860.00 0.662572 0.331286 0.943530i $$-0.392517\pi$$
0.331286 + 0.943530i $$0.392517\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −688.000 −0.239641
$$203$$ 770.000 0.266224
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 1388.00 0.469449
$$207$$ 0 0
$$208$$ −1148.00 −0.382690
$$209$$ −880.000 −0.291248
$$210$$ 0 0
$$211$$ −4268.00 −1.39252 −0.696259 0.717791i $$-0.745153\pi$$
−0.696259 + 0.717791i $$0.745153\pi$$
$$212$$ 1134.00 0.367375
$$213$$ 0 0
$$214$$ −244.000 −0.0779416
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 84.0000 0.0262778
$$218$$ −90.0000 −0.0279613
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1512.00 −0.460218
$$222$$ 0 0
$$223$$ 5432.00 1.63118 0.815591 0.578629i $$-0.196412\pi$$
0.815591 + 0.578629i $$0.196412\pi$$
$$224$$ −1127.00 −0.336165
$$225$$ 0 0
$$226$$ −1318.00 −0.387929
$$227$$ −2046.00 −0.598228 −0.299114 0.954217i $$-0.596691\pi$$
−0.299114 + 0.954217i $$0.596691\pi$$
$$228$$ 0 0
$$229$$ −2980.00 −0.859930 −0.429965 0.902846i $$-0.641474\pi$$
−0.429965 + 0.902846i $$0.641474\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 1650.00 0.466930
$$233$$ 4458.00 1.25345 0.626724 0.779241i $$-0.284395\pi$$
0.626724 + 0.779241i $$0.284395\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 5670.00 1.56392
$$237$$ 0 0
$$238$$ −378.000 −0.102950
$$239$$ −4440.00 −1.20167 −0.600836 0.799372i $$-0.705166\pi$$
−0.600836 + 0.799372i $$0.705166\pi$$
$$240$$ 0 0
$$241$$ 3302.00 0.882575 0.441287 0.897366i $$-0.354522\pi$$
0.441287 + 0.897366i $$0.354522\pi$$
$$242$$ 1267.00 0.336553
$$243$$ 0 0
$$244$$ 3416.00 0.896258
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3080.00 0.793424
$$248$$ 180.000 0.0460888
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1582.00 −0.397829 −0.198914 0.980017i $$-0.563742\pi$$
−0.198914 + 0.980017i $$0.563742\pi$$
$$252$$ 0 0
$$253$$ 384.000 0.0954224
$$254$$ −1776.00 −0.438725
$$255$$ 0 0
$$256$$ −119.000 −0.0290527
$$257$$ 2354.00 0.571356 0.285678 0.958326i $$-0.407781\pi$$
0.285678 + 0.958326i $$0.407781\pi$$
$$258$$ 0 0
$$259$$ 1722.00 0.413127
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −1118.00 −0.263627
$$263$$ −3872.00 −0.907824 −0.453912 0.891046i $$-0.649972\pi$$
−0.453912 + 0.891046i $$0.649972\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 770.000 0.177488
$$267$$ 0 0
$$268$$ 1708.00 0.389301
$$269$$ −180.000 −0.0407985 −0.0203992 0.999792i $$-0.506494\pi$$
−0.0203992 + 0.999792i $$0.506494\pi$$
$$270$$ 0 0
$$271$$ 2032.00 0.455480 0.227740 0.973722i $$-0.426866\pi$$
0.227740 + 0.973722i $$0.426866\pi$$
$$272$$ 2214.00 0.493542
$$273$$ 0 0
$$274$$ −2274.00 −0.501377
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 5426.00 1.17696 0.588478 0.808513i $$-0.299727\pi$$
0.588478 + 0.808513i $$0.299727\pi$$
$$278$$ 210.000 0.0453056
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −842.000 −0.178753 −0.0893764 0.995998i $$-0.528487\pi$$
−0.0893764 + 0.995998i $$0.528487\pi$$
$$282$$ 0 0
$$283$$ 3782.00 0.794405 0.397202 0.917731i $$-0.369981\pi$$
0.397202 + 0.917731i $$0.369981\pi$$
$$284$$ −5376.00 −1.12326
$$285$$ 0 0
$$286$$ 224.000 0.0463126
$$287$$ −1274.00 −0.262027
$$288$$ 0 0
$$289$$ −1997.00 −0.406473
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −4914.00 −0.984829
$$293$$ −4312.00 −0.859760 −0.429880 0.902886i $$-0.641444\pi$$
−0.429880 + 0.902886i $$0.641444\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 3690.00 0.724584
$$297$$ 0 0
$$298$$ −2010.00 −0.390725
$$299$$ −1344.00 −0.259952
$$300$$ 0 0
$$301$$ −896.000 −0.171577
$$302$$ −1112.00 −0.211882
$$303$$ 0 0
$$304$$ −4510.00 −0.850876
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −2674.00 −0.497112 −0.248556 0.968618i $$-0.579956\pi$$
−0.248556 + 0.968618i $$0.579956\pi$$
$$308$$ −392.000 −0.0725204
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 3768.00 0.687021 0.343511 0.939149i $$-0.388384\pi$$
0.343511 + 0.939149i $$0.388384\pi$$
$$312$$ 0 0
$$313$$ −2438.00 −0.440268 −0.220134 0.975470i $$-0.570649\pi$$
−0.220134 + 0.975470i $$0.570649\pi$$
$$314$$ 124.000 0.0222857
$$315$$ 0 0
$$316$$ −3080.00 −0.548302
$$317$$ −3186.00 −0.564491 −0.282245 0.959342i $$-0.591079\pi$$
−0.282245 + 0.959342i $$0.591079\pi$$
$$318$$ 0 0
$$319$$ 880.000 0.154453
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −336.000 −0.0581508
$$323$$ −5940.00 −1.02325
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 2008.00 0.341144
$$327$$ 0 0
$$328$$ −2730.00 −0.459570
$$329$$ 2268.00 0.380057
$$330$$ 0 0
$$331$$ 8672.00 1.44005 0.720025 0.693949i $$-0.244131\pi$$
0.720025 + 0.693949i $$0.244131\pi$$
$$332$$ 9114.00 1.50661
$$333$$ 0 0
$$334$$ −2884.00 −0.472471
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −814.000 −0.131577 −0.0657884 0.997834i $$-0.520956\pi$$
−0.0657884 + 0.997834i $$0.520956\pi$$
$$338$$ 1413.00 0.227388
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 96.0000 0.0152454
$$342$$ 0 0
$$343$$ 343.000 0.0539949
$$344$$ −1920.00 −0.300929
$$345$$ 0 0
$$346$$ −2228.00 −0.346179
$$347$$ 9344.00 1.44557 0.722784 0.691074i $$-0.242862\pi$$
0.722784 + 0.691074i $$0.242862\pi$$
$$348$$ 0 0
$$349$$ −5180.00 −0.794496 −0.397248 0.917711i $$-0.630035\pi$$
−0.397248 + 0.917711i $$0.630035\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −1288.00 −0.195030
$$353$$ 12178.0 1.83617 0.918087 0.396379i $$-0.129733\pi$$
0.918087 + 0.396379i $$0.129733\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 5110.00 0.760757
$$357$$ 0 0
$$358$$ −820.000 −0.121057
$$359$$ −440.000 −0.0646861 −0.0323431 0.999477i $$-0.510297\pi$$
−0.0323431 + 0.999477i $$0.510297\pi$$
$$360$$ 0 0
$$361$$ 5241.00 0.764106
$$362$$ −3892.00 −0.565080
$$363$$ 0 0
$$364$$ 1372.00 0.197561
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 9816.00 1.39616 0.698080 0.716019i $$-0.254038\pi$$
0.698080 + 0.716019i $$0.254038\pi$$
$$368$$ 1968.00 0.278775
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −1134.00 −0.158691
$$372$$ 0 0
$$373$$ 442.000 0.0613563 0.0306781 0.999529i $$-0.490233\pi$$
0.0306781 + 0.999529i $$0.490233\pi$$
$$374$$ −432.000 −0.0597278
$$375$$ 0 0
$$376$$ 4860.00 0.666583
$$377$$ −3080.00 −0.420764
$$378$$ 0 0
$$379$$ −3960.00 −0.536706 −0.268353 0.963321i $$-0.586479\pi$$
−0.268353 + 0.963321i $$0.586479\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −5048.00 −0.676121
$$383$$ 6708.00 0.894942 0.447471 0.894298i $$-0.352325\pi$$
0.447471 + 0.894298i $$0.352325\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2962.00 −0.390575
$$387$$ 0 0
$$388$$ 2058.00 0.269276
$$389$$ 13350.0 1.74003 0.870015 0.493025i $$-0.164109\pi$$
0.870015 + 0.493025i $$0.164109\pi$$
$$390$$ 0 0
$$391$$ 2592.00 0.335251
$$392$$ 735.000 0.0947018
$$393$$ 0 0
$$394$$ −3334.00 −0.426306
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1356.00 0.171425 0.0857125 0.996320i $$-0.472683\pi$$
0.0857125 + 0.996320i $$0.472683\pi$$
$$398$$ −1860.00 −0.234255
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −6222.00 −0.774843 −0.387421 0.921903i $$-0.626634\pi$$
−0.387421 + 0.921903i $$0.626634\pi$$
$$402$$ 0 0
$$403$$ −336.000 −0.0415319
$$404$$ −4816.00 −0.593082
$$405$$ 0 0
$$406$$ −770.000 −0.0941243
$$407$$ 1968.00 0.239681
$$408$$ 0 0
$$409$$ 5150.00 0.622619 0.311309 0.950309i $$-0.399232\pi$$
0.311309 + 0.950309i $$0.399232\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 9716.00 1.16183
$$413$$ −5670.00 −0.675551
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 4508.00 0.531305
$$417$$ 0 0
$$418$$ 880.000 0.102972
$$419$$ −2310.00 −0.269334 −0.134667 0.990891i $$-0.542996\pi$$
−0.134667 + 0.990891i $$0.542996\pi$$
$$420$$ 0 0
$$421$$ 1262.00 0.146095 0.0730476 0.997328i $$-0.476727\pi$$
0.0730476 + 0.997328i $$0.476727\pi$$
$$422$$ 4268.00 0.492329
$$423$$ 0 0
$$424$$ −2430.00 −0.278328
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −3416.00 −0.387147
$$428$$ −1708.00 −0.192896
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 4488.00 0.501576 0.250788 0.968042i $$-0.419310\pi$$
0.250788 + 0.968042i $$0.419310\pi$$
$$432$$ 0 0
$$433$$ −17038.0 −1.89098 −0.945490 0.325652i $$-0.894416\pi$$
−0.945490 + 0.325652i $$0.894416\pi$$
$$434$$ −84.0000 −0.00929062
$$435$$ 0 0
$$436$$ −630.000 −0.0692008
$$437$$ −5280.00 −0.577979
$$438$$ 0 0
$$439$$ 16200.0 1.76124 0.880619 0.473824i $$-0.157127\pi$$
0.880619 + 0.473824i $$0.157127\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 1512.00 0.162712
$$443$$ −8772.00 −0.940791 −0.470395 0.882456i $$-0.655889\pi$$
−0.470395 + 0.882456i $$0.655889\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −5432.00 −0.576710
$$447$$ 0 0
$$448$$ −1169.00 −0.123281
$$449$$ −2130.00 −0.223877 −0.111939 0.993715i $$-0.535706\pi$$
−0.111939 + 0.993715i $$0.535706\pi$$
$$450$$ 0 0
$$451$$ −1456.00 −0.152019
$$452$$ −9226.00 −0.960076
$$453$$ 0 0
$$454$$ 2046.00 0.211506
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −10534.0 −1.07825 −0.539124 0.842226i $$-0.681245\pi$$
−0.539124 + 0.842226i $$0.681245\pi$$
$$458$$ 2980.00 0.304031
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 9268.00 0.936342 0.468171 0.883638i $$-0.344913\pi$$
0.468171 + 0.883638i $$0.344913\pi$$
$$462$$ 0 0
$$463$$ 9392.00 0.942728 0.471364 0.881939i $$-0.343762\pi$$
0.471364 + 0.881939i $$0.343762\pi$$
$$464$$ 4510.00 0.451232
$$465$$ 0 0
$$466$$ −4458.00 −0.443161
$$467$$ −10806.0 −1.07075 −0.535377 0.844613i $$-0.679830\pi$$
−0.535377 + 0.844613i $$0.679830\pi$$
$$468$$ 0 0
$$469$$ −1708.00 −0.168162
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −12150.0 −1.18485
$$473$$ −1024.00 −0.0995424
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −2646.00 −0.254788
$$477$$ 0 0
$$478$$ 4440.00 0.424855
$$479$$ −4940.00 −0.471220 −0.235610 0.971848i $$-0.575709\pi$$
−0.235610 + 0.971848i $$0.575709\pi$$
$$480$$ 0 0
$$481$$ −6888.00 −0.652943
$$482$$ −3302.00 −0.312037
$$483$$ 0 0
$$484$$ 8869.00 0.832926
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 5216.00 0.485338 0.242669 0.970109i $$-0.421977\pi$$
0.242669 + 0.970109i $$0.421977\pi$$
$$488$$ −7320.00 −0.679018
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −4412.00 −0.405521 −0.202760 0.979228i $$-0.564991\pi$$
−0.202760 + 0.979228i $$0.564991\pi$$
$$492$$ 0 0
$$493$$ 5940.00 0.542645
$$494$$ −3080.00 −0.280518
$$495$$ 0 0
$$496$$ 492.000 0.0445392
$$497$$ 5376.00 0.485204
$$498$$ 0 0
$$499$$ 19060.0 1.70991 0.854953 0.518706i $$-0.173586\pi$$
0.854953 + 0.518706i $$0.173586\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 1582.00 0.140654
$$503$$ 12768.0 1.13180 0.565902 0.824473i $$-0.308528\pi$$
0.565902 + 0.824473i $$0.308528\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −384.000 −0.0337369
$$507$$ 0 0
$$508$$ −12432.0 −1.08579
$$509$$ 5500.00 0.478945 0.239473 0.970903i $$-0.423025\pi$$
0.239473 + 0.970903i $$0.423025\pi$$
$$510$$ 0 0
$$511$$ 4914.00 0.425406
$$512$$ −11521.0 −0.994455
$$513$$ 0 0
$$514$$ −2354.00 −0.202005
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 2592.00 0.220495
$$518$$ −1722.00 −0.146062
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 7338.00 0.617051 0.308526 0.951216i $$-0.400164\pi$$
0.308526 + 0.951216i $$0.400164\pi$$
$$522$$ 0 0
$$523$$ 17582.0 1.46999 0.734997 0.678070i $$-0.237183\pi$$
0.734997 + 0.678070i $$0.237183\pi$$
$$524$$ −7826.00 −0.652444
$$525$$ 0 0
$$526$$ 3872.00 0.320964
$$527$$ 648.000 0.0535623
$$528$$ 0 0
$$529$$ −9863.00 −0.810635
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 5390.00 0.439260
$$533$$ 5096.00 0.414132
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −3660.00 −0.294940
$$537$$ 0 0
$$538$$ 180.000 0.0144244
$$539$$ 392.000 0.0313259
$$540$$ 0 0
$$541$$ −1618.00 −0.128583 −0.0642914 0.997931i $$-0.520479\pi$$
−0.0642914 + 0.997931i $$0.520479\pi$$
$$542$$ −2032.00 −0.161037
$$543$$ 0 0
$$544$$ −8694.00 −0.685206
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −16144.0 −1.26192 −0.630958 0.775817i $$-0.717338\pi$$
−0.630958 + 0.775817i $$0.717338\pi$$
$$548$$ −15918.0 −1.24085
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −12100.0 −0.935531
$$552$$ 0 0
$$553$$ 3080.00 0.236844
$$554$$ −5426.00 −0.416117
$$555$$ 0 0
$$556$$ 1470.00 0.112126
$$557$$ 4654.00 0.354033 0.177016 0.984208i $$-0.443355\pi$$
0.177016 + 0.984208i $$0.443355\pi$$
$$558$$ 0 0
$$559$$ 3584.00 0.271175
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 842.000 0.0631986
$$563$$ 10078.0 0.754418 0.377209 0.926128i $$-0.376884\pi$$
0.377209 + 0.926128i $$0.376884\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −3782.00 −0.280865
$$567$$ 0 0
$$568$$ 11520.0 0.851001
$$569$$ 5930.00 0.436904 0.218452 0.975848i $$-0.429899\pi$$
0.218452 + 0.975848i $$0.429899\pi$$
$$570$$ 0 0
$$571$$ −19048.0 −1.39603 −0.698016 0.716082i $$-0.745933\pi$$
−0.698016 + 0.716082i $$0.745933\pi$$
$$572$$ 1568.00 0.114618
$$573$$ 0 0
$$574$$ 1274.00 0.0926406
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 14366.0 1.03651 0.518253 0.855227i $$-0.326582\pi$$
0.518253 + 0.855227i $$0.326582\pi$$
$$578$$ 1997.00 0.143710
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −9114.00 −0.650796
$$582$$ 0 0
$$583$$ −1296.00 −0.0920666
$$584$$ 10530.0 0.746121
$$585$$ 0 0
$$586$$ 4312.00 0.303971
$$587$$ −3626.00 −0.254959 −0.127480 0.991841i $$-0.540689\pi$$
−0.127480 + 0.991841i $$0.540689\pi$$
$$588$$ 0 0
$$589$$ −1320.00 −0.0923424
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 10086.0 0.700223
$$593$$ −1062.00 −0.0735432 −0.0367716 0.999324i $$-0.511707\pi$$
−0.0367716 + 0.999324i $$0.511707\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −14070.0 −0.966996
$$597$$ 0 0
$$598$$ 1344.00 0.0919068
$$599$$ 10200.0 0.695761 0.347880 0.937539i $$-0.386902\pi$$
0.347880 + 0.937539i $$0.386902\pi$$
$$600$$ 0 0
$$601$$ −25158.0 −1.70751 −0.853757 0.520671i $$-0.825682\pi$$
−0.853757 + 0.520671i $$0.825682\pi$$
$$602$$ 896.000 0.0606615
$$603$$ 0 0
$$604$$ −7784.00 −0.524382
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −25664.0 −1.71609 −0.858047 0.513570i $$-0.828323\pi$$
−0.858047 + 0.513570i $$0.828323\pi$$
$$608$$ 17710.0 1.18131
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −9072.00 −0.600677
$$612$$ 0 0
$$613$$ −19018.0 −1.25307 −0.626533 0.779395i $$-0.715527\pi$$
−0.626533 + 0.779395i $$0.715527\pi$$
$$614$$ 2674.00 0.175755
$$615$$ 0 0
$$616$$ 840.000 0.0549425
$$617$$ 17334.0 1.13102 0.565511 0.824741i $$-0.308679\pi$$
0.565511 + 0.824741i $$0.308679\pi$$
$$618$$ 0 0
$$619$$ 18730.0 1.21619 0.608096 0.793864i $$-0.291934\pi$$
0.608096 + 0.793864i $$0.291934\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −3768.00 −0.242899
$$623$$ −5110.00 −0.328616
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 2438.00 0.155658
$$627$$ 0 0
$$628$$ 868.000 0.0551544
$$629$$ 13284.0 0.842079
$$630$$ 0 0
$$631$$ −6928.00 −0.437083 −0.218541 0.975828i $$-0.570130\pi$$
−0.218541 + 0.975828i $$0.570130\pi$$
$$632$$ 6600.00 0.415402
$$633$$ 0 0
$$634$$ 3186.00 0.199578
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −1372.00 −0.0853385
$$638$$ −880.000 −0.0546074
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −16302.0 −1.00451 −0.502255 0.864720i $$-0.667496\pi$$
−0.502255 + 0.864720i $$0.667496\pi$$
$$642$$ 0 0
$$643$$ −4718.00 −0.289362 −0.144681 0.989478i $$-0.546216\pi$$
−0.144681 + 0.989478i $$0.546216\pi$$
$$644$$ −2352.00 −0.143916
$$645$$ 0 0
$$646$$ 5940.00 0.361774
$$647$$ −21436.0 −1.30253 −0.651264 0.758851i $$-0.725761\pi$$
−0.651264 + 0.758851i $$0.725761\pi$$
$$648$$ 0 0
$$649$$ −6480.00 −0.391930
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 14056.0 0.844287
$$653$$ 4458.00 0.267159 0.133580 0.991038i $$-0.457353\pi$$
0.133580 + 0.991038i $$0.457353\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −7462.00 −0.444119
$$657$$ 0 0
$$658$$ −2268.00 −0.134371
$$659$$ 26640.0 1.57473 0.787365 0.616487i $$-0.211445\pi$$
0.787365 + 0.616487i $$0.211445\pi$$
$$660$$ 0 0
$$661$$ 7432.00 0.437324 0.218662 0.975801i $$-0.429831\pi$$
0.218662 + 0.975801i $$0.429831\pi$$
$$662$$ −8672.00 −0.509134
$$663$$ 0 0
$$664$$ −19530.0 −1.14143
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 5280.00 0.306510
$$668$$ −20188.0 −1.16931
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −3904.00 −0.224608
$$672$$ 0 0
$$673$$ −58.0000 −0.00332204 −0.00166102 0.999999i $$-0.500529\pi$$
−0.00166102 + 0.999999i $$0.500529\pi$$
$$674$$ 814.000 0.0465194
$$675$$ 0 0
$$676$$ 9891.00 0.562756
$$677$$ −21516.0 −1.22146 −0.610729 0.791840i $$-0.709124\pi$$
−0.610729 + 0.791840i $$0.709124\pi$$
$$678$$ 0 0
$$679$$ −2058.00 −0.116316
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −96.0000 −0.00539007
$$683$$ 18108.0 1.01447 0.507235 0.861808i $$-0.330668\pi$$
0.507235 + 0.861808i $$0.330668\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −343.000 −0.0190901
$$687$$ 0 0
$$688$$ −5248.00 −0.290811
$$689$$ 4536.00 0.250810
$$690$$ 0 0
$$691$$ −10078.0 −0.554827 −0.277413 0.960751i $$-0.589477\pi$$
−0.277413 + 0.960751i $$0.589477\pi$$
$$692$$ −15596.0 −0.856750
$$693$$ 0 0
$$694$$ −9344.00 −0.511086
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −9828.00 −0.534092
$$698$$ 5180.00 0.280897
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −18762.0 −1.01089 −0.505443 0.862860i $$-0.668671\pi$$
−0.505443 + 0.862860i $$0.668671\pi$$
$$702$$ 0 0
$$703$$ −27060.0 −1.45176
$$704$$ −1336.00 −0.0715233
$$705$$ 0 0
$$706$$ −12178.0 −0.649186
$$707$$ 4816.00 0.256187
$$708$$ 0 0
$$709$$ 6810.00 0.360726 0.180363 0.983600i $$-0.442273\pi$$
0.180363 + 0.983600i $$0.442273\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −10950.0 −0.576360
$$713$$ 576.000 0.0302544
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −5740.00 −0.299600
$$717$$ 0 0
$$718$$ 440.000 0.0228700
$$719$$ −4860.00 −0.252083 −0.126041 0.992025i $$-0.540227\pi$$
−0.126041 + 0.992025i $$0.540227\pi$$
$$720$$ 0 0
$$721$$ −9716.00 −0.501862
$$722$$ −5241.00 −0.270152
$$723$$ 0 0
$$724$$ −27244.0 −1.39850
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 13636.0 0.695641 0.347821 0.937561i $$-0.386922\pi$$
0.347821 + 0.937561i $$0.386922\pi$$
$$728$$ −2940.00 −0.149675
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −6912.00 −0.349726
$$732$$ 0 0
$$733$$ −2088.00 −0.105214 −0.0526071 0.998615i $$-0.516753\pi$$
−0.0526071 + 0.998615i $$0.516753\pi$$
$$734$$ −9816.00 −0.493617
$$735$$ 0 0
$$736$$ −7728.00 −0.387035
$$737$$ −1952.00 −0.0975615
$$738$$ 0 0
$$739$$ −5160.00 −0.256852 −0.128426 0.991719i $$-0.540992\pi$$
−0.128426 + 0.991719i $$0.540992\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 1134.00 0.0561057
$$743$$ −28152.0 −1.39004 −0.695018 0.718992i $$-0.744604\pi$$
−0.695018 + 0.718992i $$0.744604\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −442.000 −0.0216927
$$747$$ 0 0
$$748$$ −3024.00 −0.147819
$$749$$ 1708.00 0.0833230
$$750$$ 0 0
$$751$$ −16808.0 −0.816688 −0.408344 0.912828i $$-0.633894\pi$$
−0.408344 + 0.912828i $$0.633894\pi$$
$$752$$ 13284.0 0.644172
$$753$$ 0 0
$$754$$ 3080.00 0.148763
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −21674.0 −1.04063 −0.520314 0.853975i $$-0.674185\pi$$
−0.520314 + 0.853975i $$0.674185\pi$$
$$758$$ 3960.00 0.189754
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −7422.00 −0.353544 −0.176772 0.984252i $$-0.556566\pi$$
−0.176772 + 0.984252i $$0.556566\pi$$
$$762$$ 0 0
$$763$$ 630.000 0.0298919
$$764$$ −35336.0 −1.67331
$$765$$ 0 0
$$766$$ −6708.00 −0.316410
$$767$$ 22680.0 1.06770
$$768$$ 0 0
$$769$$ 13790.0 0.646658 0.323329 0.946287i $$-0.395198\pi$$
0.323329 + 0.946287i $$0.395198\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −20734.0 −0.966623
$$773$$ −6232.00 −0.289973 −0.144987 0.989434i $$-0.546314\pi$$
−0.144987 + 0.989434i $$0.546314\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −4410.00 −0.204007
$$777$$ 0 0
$$778$$ −13350.0 −0.615194
$$779$$ 20020.0 0.920784
$$780$$ 0 0
$$781$$ 6144.00 0.281498
$$782$$ −2592.00 −0.118529
$$783$$ 0 0
$$784$$ 2009.00 0.0915179
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 1766.00 0.0799887 0.0399943 0.999200i $$-0.487266\pi$$
0.0399943 + 0.999200i $$0.487266\pi$$
$$788$$ −23338.0 −1.05505
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 9226.00 0.414714
$$792$$ 0 0
$$793$$ 13664.0 0.611883
$$794$$ −1356.00 −0.0606079
$$795$$ 0 0
$$796$$ −13020.0 −0.579751
$$797$$ 1204.00 0.0535105 0.0267552 0.999642i $$-0.491483\pi$$
0.0267552 + 0.999642i $$0.491483\pi$$
$$798$$ 0 0
$$799$$ 17496.0 0.774673
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 6222.00 0.273948
$$803$$ 5616.00 0.246805
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 336.000 0.0146837
$$807$$ 0 0
$$808$$ 10320.0 0.449327
$$809$$ 7050.00 0.306384 0.153192 0.988196i $$-0.451045\pi$$
0.153192 + 0.988196i $$0.451045\pi$$
$$810$$ 0 0
$$811$$ 23282.0 1.00807 0.504033 0.863684i $$-0.331849\pi$$
0.504033 + 0.863684i $$0.331849\pi$$
$$812$$ −5390.00 −0.232946
$$813$$ 0 0
$$814$$ −1968.00 −0.0847400
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 14080.0 0.602934
$$818$$ −5150.00 −0.220129
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −10142.0 −0.431131 −0.215565 0.976489i $$-0.569159\pi$$
−0.215565 + 0.976489i $$0.569159\pi$$
$$822$$ 0 0
$$823$$ 9192.00 0.389323 0.194662 0.980870i $$-0.437639\pi$$
0.194662 + 0.980870i $$0.437639\pi$$
$$824$$ −20820.0 −0.880217
$$825$$ 0 0
$$826$$ 5670.00 0.238843
$$827$$ −46716.0 −1.96430 −0.982149 0.188104i $$-0.939766\pi$$
−0.982149 + 0.188104i $$0.939766\pi$$
$$828$$ 0 0
$$829$$ 11240.0 0.470906 0.235453 0.971886i $$-0.424343\pi$$
0.235453 + 0.971886i $$0.424343\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 4676.00 0.194845
$$833$$ 2646.00 0.110058
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 6160.00 0.254842
$$837$$ 0 0
$$838$$ 2310.00 0.0952239
$$839$$ −700.000 −0.0288042 −0.0144021 0.999896i $$-0.504584\pi$$
−0.0144021 + 0.999896i $$0.504584\pi$$
$$840$$ 0 0
$$841$$ −12289.0 −0.503875
$$842$$ −1262.00 −0.0516525
$$843$$ 0 0
$$844$$ 29876.0 1.21845
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −8869.00 −0.359790
$$848$$ −6642.00 −0.268971
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 11808.0 0.475644
$$852$$ 0 0
$$853$$ 37492.0 1.50493 0.752463 0.658635i $$-0.228866\pi$$
0.752463 + 0.658635i $$0.228866\pi$$
$$854$$ 3416.00 0.136877
$$855$$ 0 0
$$856$$ 3660.00 0.146140
$$857$$ 28894.0 1.15169 0.575846 0.817558i $$-0.304673\pi$$
0.575846 + 0.817558i $$0.304673\pi$$
$$858$$ 0 0
$$859$$ −2770.00 −0.110025 −0.0550123 0.998486i $$-0.517520\pi$$
−0.0550123 + 0.998486i $$0.517520\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −4488.00 −0.177334
$$863$$ 17688.0 0.697690 0.348845 0.937180i $$-0.386574\pi$$
0.348845 + 0.937180i $$0.386574\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 17038.0 0.668562
$$867$$ 0 0
$$868$$ −588.000 −0.0229931
$$869$$ 3520.00 0.137408
$$870$$ 0 0
$$871$$ 6832.00 0.265779
$$872$$ 1350.00 0.0524275
$$873$$ 0 0
$$874$$ 5280.00 0.204346
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 33566.0 1.29241 0.646205 0.763164i $$-0.276355\pi$$
0.646205 + 0.763164i $$0.276355\pi$$
$$878$$ −16200.0 −0.622692
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 16758.0 0.640853 0.320426 0.947273i $$-0.396174\pi$$
0.320426 + 0.947273i $$0.396174\pi$$
$$882$$ 0 0
$$883$$ −11468.0 −0.437066 −0.218533 0.975830i $$-0.570127\pi$$
−0.218533 + 0.975830i $$0.570127\pi$$
$$884$$ 10584.0 0.402691
$$885$$ 0 0
$$886$$ 8772.00 0.332620
$$887$$ −50356.0 −1.90619 −0.953094 0.302674i $$-0.902121\pi$$
−0.953094 + 0.302674i $$0.902121\pi$$
$$888$$ 0 0
$$889$$ 12432.0 0.469017
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −38024.0 −1.42728
$$893$$ −35640.0 −1.33555
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 10185.0 0.379751
$$897$$ 0 0
$$898$$ 2130.00 0.0791526
$$899$$ 1320.00 0.0489705
$$900$$ 0 0
$$901$$ −8748.00 −0.323461
$$902$$ 1456.00 0.0537467
$$903$$ 0 0
$$904$$ 19770.0 0.727368
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 8716.00 0.319085 0.159542 0.987191i $$-0.448998\pi$$
0.159542 + 0.987191i $$0.448998\pi$$
$$908$$ 14322.0 0.523450
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −7632.00 −0.277563 −0.138781 0.990323i $$-0.544318\pi$$
−0.138781 + 0.990323i $$0.544318\pi$$
$$912$$ 0 0
$$913$$ −10416.0 −0.377568
$$914$$ 10534.0 0.381219
$$915$$ 0 0
$$916$$ 20860.0 0.752439
$$917$$ 7826.00 0.281829
$$918$$ 0 0
$$919$$ −23080.0 −0.828443 −0.414221 0.910176i $$-0.635946\pi$$
−0.414221 + 0.910176i $$0.635946\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −9268.00 −0.331047
$$923$$ −21504.0 −0.766861
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −9392.00 −0.333305
$$927$$ 0 0
$$928$$ −17710.0 −0.626465
$$929$$ −45110.0 −1.59312 −0.796561 0.604558i $$-0.793350\pi$$
−0.796561 + 0.604558i $$0.793350\pi$$
$$930$$ 0 0
$$931$$ −5390.00 −0.189742
$$932$$ −31206.0 −1.09677
$$933$$ 0 0
$$934$$ 10806.0 0.378569
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −16674.0 −0.581340 −0.290670 0.956823i $$-0.593878\pi$$
−0.290670 + 0.956823i $$0.593878\pi$$
$$938$$ 1708.00 0.0594543
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −43832.0 −1.51847 −0.759236 0.650815i $$-0.774427\pi$$
−0.759236 + 0.650815i $$0.774427\pi$$
$$942$$ 0 0
$$943$$ −8736.00 −0.301679
$$944$$ −33210.0 −1.14501
$$945$$ 0 0
$$946$$ 1024.00 0.0351936
$$947$$ −736.000 −0.0252553 −0.0126277 0.999920i $$-0.504020\pi$$
−0.0126277 + 0.999920i $$0.504020\pi$$
$$948$$ 0 0
$$949$$ −19656.0 −0.672351
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 5670.00 0.193031
$$953$$ 38138.0 1.29634 0.648169 0.761496i $$-0.275535\pi$$
0.648169 + 0.761496i $$0.275535\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 31080.0 1.05146
$$957$$ 0 0
$$958$$ 4940.00 0.166601
$$959$$ 15918.0 0.535995
$$960$$ 0 0
$$961$$ −29647.0 −0.995166
$$962$$ 6888.00 0.230850
$$963$$ 0 0
$$964$$ −23114.0 −0.772253
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −26224.0 −0.872086 −0.436043 0.899926i $$-0.643620\pi$$
−0.436043 + 0.899926i $$0.643620\pi$$
$$968$$ −19005.0 −0.631037
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −18762.0 −0.620084 −0.310042 0.950723i $$-0.600343\pi$$
−0.310042 + 0.950723i $$0.600343\pi$$
$$972$$ 0 0
$$973$$ −1470.00 −0.0484337
$$974$$ −5216.00 −0.171593
$$975$$ 0 0
$$976$$ −20008.0 −0.656189
$$977$$ 38394.0 1.25725 0.628625 0.777709i $$-0.283618\pi$$
0.628625 + 0.777709i $$0.283618\pi$$
$$978$$ 0 0
$$979$$ −5840.00 −0.190651
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 4412.00 0.143373
$$983$$ 5388.00 0.174822 0.0874112 0.996172i $$-0.472141\pi$$
0.0874112 + 0.996172i $$0.472141\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −5940.00 −0.191854
$$987$$ 0 0
$$988$$ −21560.0 −0.694246
$$989$$ −6144.00 −0.197541
$$990$$ 0 0
$$991$$ 25472.0 0.816493 0.408247 0.912872i $$-0.366140\pi$$
0.408247 + 0.912872i $$0.366140\pi$$
$$992$$ −1932.00 −0.0618357
$$993$$ 0 0
$$994$$ −5376.00 −0.171546
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 17096.0 0.543065 0.271532 0.962429i $$-0.412470\pi$$
0.271532 + 0.962429i $$0.412470\pi$$
$$998$$ −19060.0 −0.604543
$$999$$ 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 1575.4.a.e.1.1 1
3.2 odd 2 175.4.a.b.1.1 1
5.4 even 2 63.4.a.b.1.1 1
15.2 even 4 175.4.b.b.99.2 2
15.8 even 4 175.4.b.b.99.1 2
15.14 odd 2 7.4.a.a.1.1 1
20.19 odd 2 1008.4.a.c.1.1 1
21.20 even 2 1225.4.a.j.1.1 1
35.4 even 6 441.4.e.h.226.1 2
35.9 even 6 441.4.e.h.361.1 2
35.19 odd 6 441.4.e.e.361.1 2
35.24 odd 6 441.4.e.e.226.1 2
35.34 odd 2 441.4.a.i.1.1 1
60.59 even 2 112.4.a.f.1.1 1
105.44 odd 6 49.4.c.c.18.1 2
105.59 even 6 49.4.c.b.30.1 2
105.74 odd 6 49.4.c.c.30.1 2
105.89 even 6 49.4.c.b.18.1 2
105.104 even 2 49.4.a.b.1.1 1
120.29 odd 2 448.4.a.i.1.1 1
120.59 even 2 448.4.a.e.1.1 1
165.164 even 2 847.4.a.b.1.1 1
195.194 odd 2 1183.4.a.b.1.1 1
255.254 odd 2 2023.4.a.a.1.1 1
420.419 odd 2 784.4.a.g.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
7.4.a.a.1.1 1 15.14 odd 2
49.4.a.b.1.1 1 105.104 even 2
49.4.c.b.18.1 2 105.89 even 6
49.4.c.b.30.1 2 105.59 even 6
49.4.c.c.18.1 2 105.44 odd 6
49.4.c.c.30.1 2 105.74 odd 6
63.4.a.b.1.1 1 5.4 even 2
112.4.a.f.1.1 1 60.59 even 2
175.4.a.b.1.1 1 3.2 odd 2
175.4.b.b.99.1 2 15.8 even 4
175.4.b.b.99.2 2 15.2 even 4
441.4.a.i.1.1 1 35.34 odd 2
441.4.e.e.226.1 2 35.24 odd 6
441.4.e.e.361.1 2 35.19 odd 6
441.4.e.h.226.1 2 35.4 even 6
441.4.e.h.361.1 2 35.9 even 6
448.4.a.e.1.1 1 120.59 even 2
448.4.a.i.1.1 1 120.29 odd 2
784.4.a.g.1.1 1 420.419 odd 2
847.4.a.b.1.1 1 165.164 even 2
1008.4.a.c.1.1 1 20.19 odd 2
1183.4.a.b.1.1 1 195.194 odd 2
1225.4.a.j.1.1 1 21.20 even 2
1575.4.a.e.1.1 1 1.1 even 1 trivial
2023.4.a.a.1.1 1 255.254 odd 2