Properties

 Label 175.4.a.b.1.1 Level $175$ Weight $4$ Character 175.1 Self dual yes Analytic conductor $10.325$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$175 = 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 175.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$10.3253342510$$ Analytic rank: $$1$$ 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 $$\chi$$ $$=$$ 175.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +2.00000 q^{3} -7.00000 q^{4} +2.00000 q^{6} +7.00000 q^{7} -15.0000 q^{8} -23.0000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +2.00000 q^{3} -7.00000 q^{4} +2.00000 q^{6} +7.00000 q^{7} -15.0000 q^{8} -23.0000 q^{9} -8.00000 q^{11} -14.0000 q^{12} -28.0000 q^{13} +7.00000 q^{14} +41.0000 q^{16} -54.0000 q^{17} -23.0000 q^{18} -110.000 q^{19} +14.0000 q^{21} -8.00000 q^{22} -48.0000 q^{23} -30.0000 q^{24} -28.0000 q^{26} -100.000 q^{27} -49.0000 q^{28} -110.000 q^{29} +12.0000 q^{31} +161.000 q^{32} -16.0000 q^{33} -54.0000 q^{34} +161.000 q^{36} +246.000 q^{37} -110.000 q^{38} -56.0000 q^{39} +182.000 q^{41} +14.0000 q^{42} -128.000 q^{43} +56.0000 q^{44} -48.0000 q^{46} -324.000 q^{47} +82.0000 q^{48} +49.0000 q^{49} -108.000 q^{51} +196.000 q^{52} +162.000 q^{53} -100.000 q^{54} -105.000 q^{56} -220.000 q^{57} -110.000 q^{58} +810.000 q^{59} -488.000 q^{61} +12.0000 q^{62} -161.000 q^{63} -167.000 q^{64} -16.0000 q^{66} -244.000 q^{67} +378.000 q^{68} -96.0000 q^{69} -768.000 q^{71} +345.000 q^{72} +702.000 q^{73} +246.000 q^{74} +770.000 q^{76} -56.0000 q^{77} -56.0000 q^{78} +440.000 q^{79} +421.000 q^{81} +182.000 q^{82} +1302.00 q^{83} -98.0000 q^{84} -128.000 q^{86} -220.000 q^{87} +120.000 q^{88} +730.000 q^{89} -196.000 q^{91} +336.000 q^{92} +24.0000 q^{93} -324.000 q^{94} +322.000 q^{96} -294.000 q^{97} +49.0000 q^{98} +184.000 q^{99} +O(q^{100})$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.353553 0.176777 0.984251i $$-0.443433\pi$$
0.176777 + 0.984251i $$0.443433\pi$$
$$3$$ 2.00000 0.384900 0.192450 0.981307i $$-0.438357\pi$$
0.192450 + 0.981307i $$0.438357\pi$$
$$4$$ −7.00000 −0.875000
$$5$$ 0 0
$$6$$ 2.00000 0.136083
$$7$$ 7.00000 0.377964
$$8$$ −15.0000 −0.662913
$$9$$ −23.0000 −0.851852
$$10$$ 0 0
$$11$$ −8.00000 −0.219281 −0.109640 0.993971i $$-0.534970\pi$$
−0.109640 + 0.993971i $$0.534970\pi$$
$$12$$ −14.0000 −0.336788
$$13$$ −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 $$-0.625869\pi$$
−0.385204 + 0.922832i $$0.625869\pi$$
$$18$$ −23.0000 −0.301175
$$19$$ −110.000 −1.32820 −0.664098 0.747645i $$-0.731184\pi$$
−0.664098 + 0.747645i $$0.731184\pi$$
$$20$$ 0 0
$$21$$ 14.0000 0.145479
$$22$$ −8.00000 −0.0775275
$$23$$ −48.0000 −0.435161 −0.217580 0.976042i $$-0.569816\pi$$
−0.217580 + 0.976042i $$0.569816\pi$$
$$24$$ −30.0000 −0.255155
$$25$$ 0 0
$$26$$ −28.0000 −0.211202
$$27$$ −100.000 −0.712778
$$28$$ −49.0000 −0.330719
$$29$$ −110.000 −0.704362 −0.352181 0.935932i $$-0.614560\pi$$
−0.352181 + 0.935932i $$0.614560\pi$$
$$30$$ 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
$$33$$ −16.0000 −0.0844013
$$34$$ −54.0000 −0.272380
$$35$$ 0 0
$$36$$ 161.000 0.745370
$$37$$ 246.000 1.09303 0.546516 0.837449i $$-0.315954\pi$$
0.546516 + 0.837449i $$0.315954\pi$$
$$38$$ −110.000 −0.469588
$$39$$ −56.0000 −0.229928
$$40$$ 0 0
$$41$$ 182.000 0.693259 0.346630 0.938002i $$-0.387326\pi$$
0.346630 + 0.938002i $$0.387326\pi$$
$$42$$ 14.0000 0.0514344
$$43$$ −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 $$-0.667685\pi$$
−0.502769 + 0.864421i $$0.667685\pi$$
$$48$$ 82.0000 0.246577
$$49$$ 49.0000 0.142857
$$50$$ 0 0
$$51$$ −108.000 −0.296530
$$52$$ 196.000 0.522698
$$53$$ 162.000 0.419857 0.209928 0.977717i $$-0.432677\pi$$
0.209928 + 0.977717i $$0.432677\pi$$
$$54$$ −100.000 −0.252005
$$55$$ 0 0
$$56$$ −105.000 −0.250557
$$57$$ −220.000 −0.511223
$$58$$ −110.000 −0.249029
$$59$$ 810.000 1.78734 0.893670 0.448725i $$-0.148122\pi$$
0.893670 + 0.448725i $$0.148122\pi$$
$$60$$ 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
$$63$$ −161.000 −0.321970
$$64$$ −167.000 −0.326172
$$65$$ 0 0
$$66$$ −16.0000 −0.0298404
$$67$$ −244.000 −0.444916 −0.222458 0.974942i $$-0.571408\pi$$
−0.222458 + 0.974942i $$0.571408\pi$$
$$68$$ 378.000 0.674106
$$69$$ −96.0000 −0.167493
$$70$$ 0 0
$$71$$ −768.000 −1.28373 −0.641865 0.766818i $$-0.721839\pi$$
−0.641865 + 0.766818i $$0.721839\pi$$
$$72$$ 345.000 0.564703
$$73$$ 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
$$78$$ −56.0000 −0.0812917
$$79$$ 440.000 0.626631 0.313316 0.949649i $$-0.398560\pi$$
0.313316 + 0.949649i $$0.398560\pi$$
$$80$$ 0 0
$$81$$ 421.000 0.577503
$$82$$ 182.000 0.245104
$$83$$ 1302.00 1.72184 0.860922 0.508737i $$-0.169887\pi$$
0.860922 + 0.508737i $$0.169887\pi$$
$$84$$ −98.0000 −0.127294
$$85$$ 0 0
$$86$$ −128.000 −0.160495
$$87$$ −220.000 −0.271109
$$88$$ 120.000 0.145364
$$89$$ 730.000 0.869436 0.434718 0.900567i $$-0.356848\pi$$
0.434718 + 0.900567i $$0.356848\pi$$
$$90$$ 0 0
$$91$$ −196.000 −0.225784
$$92$$ 336.000 0.380765
$$93$$ 24.0000 0.0267600
$$94$$ −324.000 −0.355511
$$95$$ 0 0
$$96$$ 322.000 0.342333
$$97$$ −294.000 −0.307744 −0.153872 0.988091i $$-0.549174\pi$$
−0.153872 + 0.988091i $$0.549174\pi$$
$$98$$ 49.0000 0.0505076
$$99$$ 184.000 0.186795
$$100$$ 0 0
$$101$$ −688.000 −0.677808 −0.338904 0.940821i $$-0.610056\pi$$
−0.338904 + 0.940821i $$0.610056\pi$$
$$102$$ −108.000 −0.104839
$$103$$ −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 $$-0.535157\pi$$
−0.110226 + 0.993907i $$0.535157\pi$$
$$108$$ 700.000 0.623681
$$109$$ 90.0000 0.0790866 0.0395433 0.999218i $$-0.487410\pi$$
0.0395433 + 0.999218i $$0.487410\pi$$
$$110$$ 0 0
$$111$$ 492.000 0.420708
$$112$$ 287.000 0.242133
$$113$$ −1318.00 −1.09723 −0.548615 0.836075i $$-0.684845\pi$$
−0.548615 + 0.836075i $$0.684845\pi$$
$$114$$ −220.000 −0.180745
$$115$$ 0 0
$$116$$ 770.000 0.616316
$$117$$ 644.000 0.508870
$$118$$ 810.000 0.631920
$$119$$ −378.000 −0.291187
$$120$$ 0 0
$$121$$ −1267.00 −0.951916
$$122$$ −488.000 −0.362143
$$123$$ 364.000 0.266836
$$124$$ −84.0000 −0.0608341
$$125$$ 0 0
$$126$$ −161.000 −0.113833
$$127$$ 1776.00 1.24090 0.620451 0.784245i $$-0.286950\pi$$
0.620451 + 0.784245i $$0.286950\pi$$
$$128$$ −1455.00 −1.00473
$$129$$ −256.000 −0.174725
$$130$$ 0 0
$$131$$ −1118.00 −0.745650 −0.372825 0.927902i $$-0.621611\pi$$
−0.372825 + 0.927902i $$0.621611\pi$$
$$132$$ 112.000 0.0738511
$$133$$ −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 $$-0.750878\pi$$
−0.709054 + 0.705154i $$0.750878\pi$$
$$138$$ −96.0000 −0.0592178
$$139$$ −210.000 −0.128144 −0.0640718 0.997945i $$-0.520409\pi$$
−0.0640718 + 0.997945i $$0.520409\pi$$
$$140$$ 0 0
$$141$$ −648.000 −0.387032
$$142$$ −768.000 −0.453867
$$143$$ 224.000 0.130992
$$144$$ −943.000 −0.545718
$$145$$ 0 0
$$146$$ 702.000 0.397931
$$147$$ 98.0000 0.0549857
$$148$$ −1722.00 −0.956402
$$149$$ −2010.00 −1.10514 −0.552569 0.833467i $$-0.686352\pi$$
−0.552569 + 0.833467i $$0.686352\pi$$
$$150$$ 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
$$153$$ 1242.00 0.656273
$$154$$ −56.0000 −0.0293027
$$155$$ 0 0
$$156$$ 392.000 0.201187
$$157$$ −124.000 −0.0630336 −0.0315168 0.999503i $$-0.510034\pi$$
−0.0315168 + 0.999503i $$0.510034\pi$$
$$158$$ 440.000 0.221548
$$159$$ 324.000 0.161603
$$160$$ 0 0
$$161$$ −336.000 −0.164475
$$162$$ 421.000 0.204178
$$163$$ −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 $$-0.732924\pi$$
−0.668176 + 0.744004i $$0.732924\pi$$
$$168$$ −210.000 −0.0964396
$$169$$ −1413.00 −0.643150
$$170$$ 0 0
$$171$$ 2530.00 1.13143
$$172$$ 896.000 0.397206
$$173$$ −2228.00 −0.979143 −0.489571 0.871963i $$-0.662847\pi$$
−0.489571 + 0.871963i $$0.662847\pi$$
$$174$$ −220.000 −0.0958515
$$175$$ 0 0
$$176$$ −328.000 −0.140477
$$177$$ 1620.00 0.687947
$$178$$ 730.000 0.307392
$$179$$ −820.000 −0.342400 −0.171200 0.985236i $$-0.554764\pi$$
−0.171200 + 0.985236i $$0.554764\pi$$
$$180$$ 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
$$183$$ −976.000 −0.394251
$$184$$ 720.000 0.288473
$$185$$ 0 0
$$186$$ 24.0000 0.00946110
$$187$$ 432.000 0.168936
$$188$$ 2268.00 0.879845
$$189$$ −700.000 −0.269405
$$190$$ 0 0
$$191$$ −5048.00 −1.91236 −0.956179 0.292782i $$-0.905419\pi$$
−0.956179 + 0.292782i $$0.905419\pi$$
$$192$$ −334.000 −0.125544
$$193$$ 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 $$-0.705983\pi$$
−0.602887 + 0.797826i $$0.705983\pi$$
$$198$$ 184.000 0.0660420
$$199$$ 1860.00 0.662572 0.331286 0.943530i $$-0.392517\pi$$
0.331286 + 0.943530i $$0.392517\pi$$
$$200$$ 0 0
$$201$$ −488.000 −0.171248
$$202$$ −688.000 −0.239641
$$203$$ −770.000 −0.266224
$$204$$ 756.000 0.259464
$$205$$ 0 0
$$206$$ −1388.00 −0.469449
$$207$$ 1104.00 0.370692
$$208$$ −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
$$213$$ −1536.00 −0.494108
$$214$$ −244.000 −0.0779416
$$215$$ 0 0
$$216$$ 1500.00 0.472510
$$217$$ 84.0000 0.0262778
$$218$$ 90.0000 0.0279613
$$219$$ 1404.00 0.433212
$$220$$ 0 0
$$221$$ 1512.00 0.460218
$$222$$ 492.000 0.148743
$$223$$ 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 $$-0.403309\pi$$
0.299114 + 0.954217i $$0.403309\pi$$
$$228$$ 1540.00 0.447320
$$229$$ −2980.00 −0.859930 −0.429965 0.902846i $$-0.641474\pi$$
−0.429965 + 0.902846i $$0.641474\pi$$
$$230$$ 0 0
$$231$$ −112.000 −0.0319007
$$232$$ 1650.00 0.466930
$$233$$ −4458.00 −1.25345 −0.626724 0.779241i $$-0.715605\pi$$
−0.626724 + 0.779241i $$0.715605\pi$$
$$234$$ 644.000 0.179913
$$235$$ 0 0
$$236$$ −5670.00 −1.56392
$$237$$ 880.000 0.241190
$$238$$ −378.000 −0.102950
$$239$$ 4440.00 1.20167 0.600836 0.799372i $$-0.294834\pi$$
0.600836 + 0.799372i $$0.294834\pi$$
$$240$$ 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
$$243$$ 3542.00 0.935059
$$244$$ 3416.00 0.896258
$$245$$ 0 0
$$246$$ 364.000 0.0943406
$$247$$ 3080.00 0.793424
$$248$$ −180.000 −0.0460888
$$249$$ 2604.00 0.662738
$$250$$ 0 0
$$251$$ 1582.00 0.397829 0.198914 0.980017i $$-0.436258\pi$$
0.198914 + 0.980017i $$0.436258\pi$$
$$252$$ 1127.00 0.281724
$$253$$ 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 $$-0.592219\pi$$
−0.285678 + 0.958326i $$0.592219\pi$$
$$258$$ −256.000 −0.0617747
$$259$$ 1722.00 0.413127
$$260$$ 0 0
$$261$$ 2530.00 0.600012
$$262$$ −1118.00 −0.263627
$$263$$ 3872.00 0.907824 0.453912 0.891046i $$-0.350028\pi$$
0.453912 + 0.891046i $$0.350028\pi$$
$$264$$ 240.000 0.0559507
$$265$$ 0 0
$$266$$ −770.000 −0.177488
$$267$$ 1460.00 0.334646
$$268$$ 1708.00 0.389301
$$269$$ 180.000 0.0407985 0.0203992 0.999792i $$-0.493506\pi$$
0.0203992 + 0.999792i $$0.493506\pi$$
$$270$$ 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
$$273$$ −392.000 −0.0869045
$$274$$ −2274.00 −0.501377
$$275$$ 0 0
$$276$$ 672.000 0.146557
$$277$$ 5426.00 1.17696 0.588478 0.808513i $$-0.299727\pi$$
0.588478 + 0.808513i $$0.299727\pi$$
$$278$$ −210.000 −0.0453056
$$279$$ −276.000 −0.0592247
$$280$$ 0 0
$$281$$ 842.000 0.178753 0.0893764 0.995998i $$-0.471513\pi$$
0.0893764 + 0.995998i $$0.471513\pi$$
$$282$$ −648.000 −0.136836
$$283$$ 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
$$288$$ −3703.00 −0.757644
$$289$$ −1997.00 −0.406473
$$290$$ 0 0
$$291$$ −588.000 −0.118451
$$292$$ −4914.00 −0.984829
$$293$$ 4312.00 0.859760 0.429880 0.902886i $$-0.358556\pi$$
0.429880 + 0.902886i $$0.358556\pi$$
$$294$$ 98.0000 0.0194404
$$295$$ 0 0
$$296$$ −3690.00 −0.724584
$$297$$ 800.000 0.156299
$$298$$ −2010.00 −0.390725
$$299$$ 1344.00 0.259952
$$300$$ 0 0
$$301$$ −896.000 −0.171577
$$302$$ 1112.00 0.211882
$$303$$ −1376.00 −0.260888
$$304$$ −4510.00 −0.850876
$$305$$ 0 0
$$306$$ 1242.00 0.232027
$$307$$ −2674.00 −0.497112 −0.248556 0.968618i $$-0.579956\pi$$
−0.248556 + 0.968618i $$0.579956\pi$$
$$308$$ 392.000 0.0725204
$$309$$ −2776.00 −0.511072
$$310$$ 0 0
$$311$$ −3768.00 −0.687021 −0.343511 0.939149i $$-0.611616\pi$$
−0.343511 + 0.939149i $$0.611616\pi$$
$$312$$ 840.000 0.152422
$$313$$ −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 $$-0.408921\pi$$
0.282245 + 0.959342i $$0.408921\pi$$
$$318$$ 324.000 0.0571353
$$319$$ 880.000 0.154453
$$320$$ 0 0
$$321$$ −488.000 −0.0848520
$$322$$ −336.000 −0.0581508
$$323$$ 5940.00 1.02325
$$324$$ −2947.00 −0.505316
$$325$$ 0 0
$$326$$ −2008.00 −0.341144
$$327$$ 180.000 0.0304404
$$328$$ −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
$$333$$ −5658.00 −0.931101
$$334$$ −2884.00 −0.472471
$$335$$ 0 0
$$336$$ 574.000 0.0931972
$$337$$ −814.000 −0.131577 −0.0657884 0.997834i $$-0.520956\pi$$
−0.0657884 + 0.997834i $$0.520956\pi$$
$$338$$ −1413.00 −0.227388
$$339$$ −2636.00 −0.422324
$$340$$ 0 0
$$341$$ −96.0000 −0.0152454
$$342$$ 2530.00 0.400020
$$343$$ 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 $$-0.757138\pi$$
−0.722784 + 0.691074i $$0.757138\pi$$
$$348$$ 1540.00 0.237220
$$349$$ −5180.00 −0.794496 −0.397248 0.917711i $$-0.630035\pi$$
−0.397248 + 0.917711i $$0.630035\pi$$
$$350$$ 0 0
$$351$$ 2800.00 0.425792
$$352$$ −1288.00 −0.195030
$$353$$ −12178.0 −1.83617 −0.918087 0.396379i $$-0.870267\pi$$
−0.918087 + 0.396379i $$0.870267\pi$$
$$354$$ 1620.00 0.243226
$$355$$ 0 0
$$356$$ −5110.00 −0.760757
$$357$$ −756.000 −0.112078
$$358$$ −820.000 −0.121057
$$359$$ 440.000 0.0646861 0.0323431 0.999477i $$-0.489703\pi$$
0.0323431 + 0.999477i $$0.489703\pi$$
$$360$$ 0 0
$$361$$ 5241.00 0.764106
$$362$$ 3892.00 0.565080
$$363$$ −2534.00 −0.366393
$$364$$ 1372.00 0.197561
$$365$$ 0 0
$$366$$ −976.000 −0.139389
$$367$$ 9816.00 1.39616 0.698080 0.716019i $$-0.254038\pi$$
0.698080 + 0.716019i $$0.254038\pi$$
$$368$$ −1968.00 −0.278775
$$369$$ −4186.00 −0.590554
$$370$$ 0 0
$$371$$ 1134.00 0.158691
$$372$$ −168.000 −0.0234150
$$373$$ 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
$$378$$ −700.000 −0.0952490
$$379$$ −3960.00 −0.536706 −0.268353 0.963321i $$-0.586479\pi$$
−0.268353 + 0.963321i $$0.586479\pi$$
$$380$$ 0 0
$$381$$ 3552.00 0.477623
$$382$$ −5048.00 −0.676121
$$383$$ −6708.00 −0.894942 −0.447471 0.894298i $$-0.647675\pi$$
−0.447471 + 0.894298i $$0.647675\pi$$
$$384$$ −2910.00 −0.386720
$$385$$ 0 0
$$386$$ 2962.00 0.390575
$$387$$ 2944.00 0.386697
$$388$$ 2058.00 0.269276
$$389$$ −13350.0 −1.74003 −0.870015 0.493025i $$-0.835891\pi$$
−0.870015 + 0.493025i $$0.835891\pi$$
$$390$$ 0 0
$$391$$ 2592.00 0.335251
$$392$$ −735.000 −0.0947018
$$393$$ −2236.00 −0.287001
$$394$$ −3334.00 −0.426306
$$395$$ 0 0
$$396$$ −1288.00 −0.163446
$$397$$ 1356.00 0.171425 0.0857125 0.996320i $$-0.472683\pi$$
0.0857125 + 0.996320i $$0.472683\pi$$
$$398$$ 1860.00 0.234255
$$399$$ −1540.00 −0.193224
$$400$$ 0 0
$$401$$ 6222.00 0.774843 0.387421 0.921903i $$-0.373366\pi$$
0.387421 + 0.921903i $$0.373366\pi$$
$$402$$ −488.000 −0.0605453
$$403$$ −336.000 −0.0415319
$$404$$ 4816.00 0.593082
$$405$$ 0 0
$$406$$ −770.000 −0.0941243
$$407$$ −1968.00 −0.239681
$$408$$ 1620.00 0.196573
$$409$$ 5150.00 0.622619 0.311309 0.950309i $$-0.399232\pi$$
0.311309 + 0.950309i $$0.399232\pi$$
$$410$$ 0 0
$$411$$ −4548.00 −0.545830
$$412$$ 9716.00 1.16183
$$413$$ 5670.00 0.675551
$$414$$ 1104.00 0.131060
$$415$$ 0 0
$$416$$ −4508.00 −0.531305
$$417$$ −420.000 −0.0493225
$$418$$ 880.000 0.102972
$$419$$ 2310.00 0.269334 0.134667 0.990891i $$-0.457004\pi$$
0.134667 + 0.990891i $$0.457004\pi$$
$$420$$ 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
$$423$$ 7452.00 0.856569
$$424$$ −2430.00 −0.278328
$$425$$ 0 0
$$426$$ −1536.00 −0.174694
$$427$$ −3416.00 −0.387147
$$428$$ 1708.00 0.192896
$$429$$ 448.000 0.0504188
$$430$$ 0 0
$$431$$ −4488.00 −0.501576 −0.250788 0.968042i $$-0.580690\pi$$
−0.250788 + 0.968042i $$0.580690\pi$$
$$432$$ −4100.00 −0.456623
$$433$$ −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
$$438$$ 1404.00 0.153164
$$439$$ 16200.0 1.76124 0.880619 0.473824i $$-0.157127\pi$$
0.880619 + 0.473824i $$0.157127\pi$$
$$440$$ 0 0
$$441$$ −1127.00 −0.121693
$$442$$ 1512.00 0.162712
$$443$$ 8772.00 0.940791 0.470395 0.882456i $$-0.344111\pi$$
0.470395 + 0.882456i $$0.344111\pi$$
$$444$$ −3444.00 −0.368119
$$445$$ 0 0
$$446$$ 5432.00 0.576710
$$447$$ −4020.00 −0.425368
$$448$$ −1169.00 −0.123281
$$449$$ 2130.00 0.223877 0.111939 0.993715i $$-0.464294\pi$$
0.111939 + 0.993715i $$0.464294\pi$$
$$450$$ 0 0
$$451$$ −1456.00 −0.152019
$$452$$ 9226.00 0.960076
$$453$$ 2224.00 0.230668
$$454$$ 2046.00 0.211506
$$455$$ 0 0
$$456$$ 3300.00 0.338896
$$457$$ −10534.0 −1.07825 −0.539124 0.842226i $$-0.681245\pi$$
−0.539124 + 0.842226i $$0.681245\pi$$
$$458$$ −2980.00 −0.304031
$$459$$ 5400.00 0.549129
$$460$$ 0 0
$$461$$ −9268.00 −0.936342 −0.468171 0.883638i $$-0.655087\pi$$
−0.468171 + 0.883638i $$0.655087\pi$$
$$462$$ −112.000 −0.0112786
$$463$$ 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 $$-0.320170\pi$$
0.535377 + 0.844613i $$0.320170\pi$$
$$468$$ −4508.00 −0.445261
$$469$$ −1708.00 −0.168162
$$470$$ 0 0
$$471$$ −248.000 −0.0242616
$$472$$ −12150.0 −1.18485
$$473$$ 1024.00 0.0995424
$$474$$ 880.000 0.0852737
$$475$$ 0 0
$$476$$ 2646.00 0.254788
$$477$$ −3726.00 −0.357656
$$478$$ 4440.00 0.424855
$$479$$ 4940.00 0.471220 0.235610 0.971848i $$-0.424291\pi$$
0.235610 + 0.971848i $$0.424291\pi$$
$$480$$ 0 0
$$481$$ −6888.00 −0.652943
$$482$$ 3302.00 0.312037
$$483$$ −672.000 −0.0633065
$$484$$ 8869.00 0.832926
$$485$$ 0 0
$$486$$ 3542.00 0.330593
$$487$$ 5216.00 0.485338 0.242669 0.970109i $$-0.421977\pi$$
0.242669 + 0.970109i $$0.421977\pi$$
$$488$$ 7320.00 0.679018
$$489$$ −4016.00 −0.371390
$$490$$ 0 0
$$491$$ 4412.00 0.405521 0.202760 0.979228i $$-0.435009\pi$$
0.202760 + 0.979228i $$0.435009\pi$$
$$492$$ −2548.00 −0.233481
$$493$$ 5940.00 0.542645
$$494$$ 3080.00 0.280518
$$495$$ 0 0
$$496$$ 492.000 0.0445392
$$497$$ −5376.00 −0.485204
$$498$$ 2604.00 0.234313
$$499$$ 19060.0 1.70991 0.854953 0.518706i $$-0.173586\pi$$
0.854953 + 0.518706i $$0.173586\pi$$
$$500$$ 0 0
$$501$$ −5768.00 −0.514362
$$502$$ 1582.00 0.140654
$$503$$ −12768.0 −1.13180 −0.565902 0.824473i $$-0.691472\pi$$
−0.565902 + 0.824473i $$0.691472\pi$$
$$504$$ 2415.00 0.213438
$$505$$ 0 0
$$506$$ 384.000 0.0337369
$$507$$ −2826.00 −0.247548
$$508$$ −12432.0 −1.08579
$$509$$ −5500.00 −0.478945 −0.239473 0.970903i $$-0.576975\pi$$
−0.239473 + 0.970903i $$0.576975\pi$$
$$510$$ 0 0
$$511$$ 4914.00 0.425406
$$512$$ 11521.0 0.994455
$$513$$ 11000.0 0.946709
$$514$$ −2354.00 −0.202005
$$515$$ 0 0
$$516$$ 1792.00 0.152884
$$517$$ 2592.00 0.220495
$$518$$ 1722.00 0.146062
$$519$$ −4456.00 −0.376872
$$520$$ 0 0
$$521$$ −7338.00 −0.617051 −0.308526 0.951216i $$-0.599836\pi$$
−0.308526 + 0.951216i $$0.599836\pi$$
$$522$$ 2530.00 0.212136
$$523$$ 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
$$528$$ −656.000 −0.0540696
$$529$$ −9863.00 −0.810635
$$530$$ 0 0
$$531$$ −18630.0 −1.52255
$$532$$ 5390.00 0.439260
$$533$$ −5096.00 −0.414132
$$534$$ 1460.00 0.118315
$$535$$ 0 0
$$536$$ 3660.00 0.294940
$$537$$ −1640.00 −0.131790
$$538$$ 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
$$543$$ 7784.00 0.615181
$$544$$ −8694.00 −0.685206
$$545$$ 0 0
$$546$$ −392.000 −0.0307254
$$547$$ −16144.0 −1.26192 −0.630958 0.775817i $$-0.717338\pi$$
−0.630958 + 0.775817i $$0.717338\pi$$
$$548$$ 15918.0 1.24085
$$549$$ 11224.0 0.872548
$$550$$ 0 0
$$551$$ 12100.0 0.935531
$$552$$ 1440.00 0.111033
$$553$$ 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 $$-0.556645\pi$$
−0.177016 + 0.984208i $$0.556645\pi$$
$$558$$ −276.000 −0.0209391
$$559$$ 3584.00 0.271175
$$560$$ 0 0
$$561$$ 864.000 0.0650234
$$562$$ 842.000 0.0631986
$$563$$ −10078.0 −0.754418 −0.377209 0.926128i $$-0.623116\pi$$
−0.377209 + 0.926128i $$0.623116\pi$$
$$564$$ 4536.00 0.338653
$$565$$ 0 0
$$566$$ 3782.00 0.280865
$$567$$ 2947.00 0.218276
$$568$$ 11520.0 0.851001
$$569$$ −5930.00 −0.436904 −0.218452 0.975848i $$-0.570101\pi$$
−0.218452 + 0.975848i $$0.570101\pi$$
$$570$$ 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
$$573$$ −10096.0 −0.736067
$$574$$ 1274.00 0.0926406
$$575$$ 0 0
$$576$$ 3841.00 0.277850
$$577$$ 14366.0 1.03651 0.518253 0.855227i $$-0.326582\pi$$
0.518253 + 0.855227i $$0.326582\pi$$
$$578$$ −1997.00 −0.143710
$$579$$ 5924.00 0.425204
$$580$$ 0 0
$$581$$ 9114.00 0.650796
$$582$$ −588.000 −0.0418787
$$583$$ −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 $$-0.459311\pi$$
0.127480 + 0.991841i $$0.459311\pi$$
$$588$$ −686.000 −0.0481125
$$589$$ −1320.00 −0.0923424
$$590$$ 0 0
$$591$$ −6668.00 −0.464103
$$592$$ 10086.0 0.700223
$$593$$ 1062.00 0.0735432 0.0367716 0.999324i $$-0.488293\pi$$
0.0367716 + 0.999324i $$0.488293\pi$$
$$594$$ 800.000 0.0552599
$$595$$ 0 0
$$596$$ 14070.0 0.966996
$$597$$ 3720.00 0.255024
$$598$$ 1344.00 0.0919068
$$599$$ −10200.0 −0.695761 −0.347880 0.937539i $$-0.613098\pi$$
−0.347880 + 0.937539i $$0.613098\pi$$
$$600$$ 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
$$603$$ 5612.00 0.379002
$$604$$ −7784.00 −0.524382
$$605$$ 0 0
$$606$$ −1376.00 −0.0922379
$$607$$ −25664.0 −1.71609 −0.858047 0.513570i $$-0.828323\pi$$
−0.858047 + 0.513570i $$0.828323\pi$$
$$608$$ −17710.0 −1.18131
$$609$$ −1540.00 −0.102470
$$610$$ 0 0
$$611$$ 9072.00 0.600677
$$612$$ −8694.00 −0.574239
$$613$$ −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 $$-0.691321\pi$$
−0.565511 + 0.824741i $$0.691321\pi$$
$$618$$ −2776.00 −0.180691
$$619$$ 18730.0 1.21619 0.608096 0.793864i $$-0.291934\pi$$
0.608096 + 0.793864i $$0.291934\pi$$
$$620$$ 0 0
$$621$$ 4800.00 0.310173
$$622$$ −3768.00 −0.242899
$$623$$ 5110.00 0.328616
$$624$$ −2296.00 −0.147297
$$625$$ 0 0
$$626$$ −2438.00 −0.155658
$$627$$ 1760.00 0.112101
$$628$$ 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
$$633$$ −8536.00 −0.535980
$$634$$ 3186.00 0.199578
$$635$$ 0 0
$$636$$ −2268.00 −0.141403
$$637$$ −1372.00 −0.0853385
$$638$$ 880.000 0.0546074
$$639$$ 17664.0 1.09355
$$640$$ 0 0
$$641$$ 16302.0 1.00451 0.502255 0.864720i $$-0.332504\pi$$
0.502255 + 0.864720i $$0.332504\pi$$
$$642$$ −488.000 −0.0299997
$$643$$ −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 $$-0.274239\pi$$
0.651264 + 0.758851i $$0.274239\pi$$
$$648$$ −6315.00 −0.382834
$$649$$ −6480.00 −0.391930
$$650$$ 0 0
$$651$$ 168.000 0.0101143
$$652$$ 14056.0 0.844287
$$653$$ −4458.00 −0.267159 −0.133580 0.991038i $$-0.542647\pi$$
−0.133580 + 0.991038i $$0.542647\pi$$
$$654$$ 180.000 0.0107623
$$655$$ 0 0
$$656$$ 7462.00 0.444119
$$657$$ −16146.0 −0.958775
$$658$$ −2268.00 −0.134371
$$659$$ −26640.0 −1.57473 −0.787365 0.616487i $$-0.788555\pi$$
−0.787365 + 0.616487i $$0.788555\pi$$
$$660$$ 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
$$663$$ 3024.00 0.177138
$$664$$ −19530.0 −1.14143
$$665$$ 0 0
$$666$$ −5658.00 −0.329194
$$667$$ 5280.00 0.306510
$$668$$ 20188.0 1.16931
$$669$$ 10864.0 0.627842
$$670$$ 0 0
$$671$$ 3904.00 0.224608
$$672$$ 2254.00 0.129390
$$673$$ −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 $$-0.290876\pi$$
0.610729 + 0.791840i $$0.290876\pi$$
$$678$$ −2636.00 −0.149314
$$679$$ −2058.00 −0.116316
$$680$$ 0 0
$$681$$ 4092.00 0.230258
$$682$$ −96.0000 −0.00539007
$$683$$ −18108.0 −1.01447 −0.507235 0.861808i $$-0.669332\pi$$
−0.507235 + 0.861808i $$0.669332\pi$$
$$684$$ −17710.0 −0.989998
$$685$$ 0 0
$$686$$ 343.000 0.0190901
$$687$$ −5960.00 −0.330987
$$688$$ −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
$$693$$ 1288.00 0.0706018
$$694$$ −9344.00 −0.511086
$$695$$ 0 0
$$696$$ 3300.00 0.179722
$$697$$ −9828.00 −0.534092
$$698$$ −5180.00 −0.280897
$$699$$ −8916.00 −0.482452
$$700$$ 0 0
$$701$$ 18762.0 1.01089 0.505443 0.862860i $$-0.331329\pi$$
0.505443 + 0.862860i $$0.331329\pi$$
$$702$$ 2800.00 0.150540
$$703$$ −27060.0 −1.45176
$$704$$ 1336.00 0.0715233
$$705$$ 0 0
$$706$$ −12178.0 −0.649186
$$707$$ −4816.00 −0.256187
$$708$$ −11340.0 −0.601954
$$709$$ 6810.00 0.360726 0.180363 0.983600i $$-0.442273\pi$$
0.180363 + 0.983600i $$0.442273\pi$$
$$710$$ 0 0
$$711$$ −10120.0 −0.533797
$$712$$ −10950.0 −0.576360
$$713$$ −576.000 −0.0302544
$$714$$ −756.000 −0.0396255
$$715$$ 0 0
$$716$$ 5740.00 0.299600
$$717$$ 8880.00 0.462524
$$718$$ 440.000 0.0228700
$$719$$ 4860.00 0.252083 0.126041 0.992025i $$-0.459773\pi$$
0.126041 + 0.992025i $$0.459773\pi$$
$$720$$ 0 0
$$721$$ −9716.00 −0.501862
$$722$$ 5241.00 0.270152
$$723$$ 6604.00 0.339703
$$724$$ −27244.0 −1.39850
$$725$$ 0 0
$$726$$ −2534.00 −0.129539
$$727$$ 13636.0 0.695641 0.347821 0.937561i $$-0.386922\pi$$
0.347821 + 0.937561i $$0.386922\pi$$
$$728$$ 2940.00 0.149675
$$729$$ −4283.00 −0.217599
$$730$$ 0 0
$$731$$ 6912.00 0.349726
$$732$$ 6832.00 0.344970
$$733$$ −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
$$738$$ −4186.00 −0.208792
$$739$$ −5160.00 −0.256852 −0.128426 0.991719i $$-0.540992\pi$$
−0.128426 + 0.991719i $$0.540992\pi$$
$$740$$ 0 0
$$741$$ 6160.00 0.305389
$$742$$ 1134.00 0.0561057
$$743$$ 28152.0 1.39004 0.695018 0.718992i $$-0.255396\pi$$
0.695018 + 0.718992i $$0.255396\pi$$
$$744$$ −360.000 −0.0177396
$$745$$ 0 0
$$746$$ 442.000 0.0216927
$$747$$ −29946.0 −1.46676
$$748$$ −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
$$753$$ 3164.00 0.153124
$$754$$ 3080.00 0.148763
$$755$$ 0 0
$$756$$ 4900.00 0.235729
$$757$$ −21674.0 −1.04063 −0.520314 0.853975i $$-0.674185\pi$$
−0.520314 + 0.853975i $$0.674185\pi$$
$$758$$ −3960.00 −0.189754
$$759$$ 768.000 0.0367281
$$760$$ 0 0
$$761$$ 7422.00 0.353544 0.176772 0.984252i $$-0.443434\pi$$
0.176772 + 0.984252i $$0.443434\pi$$
$$762$$ 3552.00 0.168865
$$763$$ 630.000 0.0298919
$$764$$ 35336.0 1.67331
$$765$$ 0 0
$$766$$ −6708.00 −0.316410
$$767$$ −22680.0 −1.06770
$$768$$ −238.000 −0.0111824
$$769$$ 13790.0 0.646658 0.323329 0.946287i $$-0.395198\pi$$
0.323329 + 0.946287i $$0.395198\pi$$
$$770$$ 0 0
$$771$$ −4708.00 −0.219915
$$772$$ −20734.0 −0.966623
$$773$$ 6232.00 0.289973 0.144987 0.989434i $$-0.453686\pi$$
0.144987 + 0.989434i $$0.453686\pi$$
$$774$$ 2944.00 0.136718
$$775$$ 0 0
$$776$$ 4410.00 0.204007
$$777$$ 3444.00 0.159013
$$778$$ −13350.0 −0.615194
$$779$$ −20020.0 −0.920784
$$780$$ 0 0
$$781$$ 6144.00 0.281498
$$782$$ 2592.00 0.118529
$$783$$ 11000.0 0.502054
$$784$$ 2009.00 0.0915179
$$785$$ 0 0
$$786$$ −2236.00 −0.101470
$$787$$ 1766.00 0.0799887 0.0399943 0.999200i $$-0.487266\pi$$
0.0399943 + 0.999200i $$0.487266\pi$$
$$788$$ 23338.0 1.05505
$$789$$ 7744.00 0.349422
$$790$$ 0 0
$$791$$ −9226.00 −0.414714
$$792$$ −2760.00 −0.123829
$$793$$ 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 $$-0.508517\pi$$
−0.0267552 + 0.999642i $$0.508517\pi$$
$$798$$ −1540.00 −0.0683150
$$799$$ 17496.0 0.774673
$$800$$ 0 0
$$801$$ −16790.0 −0.740631
$$802$$ 6222.00 0.273948
$$803$$ −5616.00 −0.246805
$$804$$ 3416.00 0.149842
$$805$$ 0 0
$$806$$ −336.000 −0.0146837
$$807$$ 360.000 0.0157033
$$808$$ 10320.0 0.449327
$$809$$ −7050.00 −0.306384 −0.153192 0.988196i $$-0.548955\pi$$
−0.153192 + 0.988196i $$0.548955\pi$$
$$810$$ 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
$$813$$ 4064.00 0.175315
$$814$$ −1968.00 −0.0847400
$$815$$ 0 0
$$816$$ −4428.00 −0.189964
$$817$$ 14080.0 0.602934
$$818$$ 5150.00 0.220129
$$819$$ 4508.00 0.192335
$$820$$ 0 0
$$821$$ 10142.0 0.431131 0.215565 0.976489i $$-0.430841\pi$$
0.215565 + 0.976489i $$0.430841\pi$$
$$822$$ −4548.00 −0.192980
$$823$$ 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 $$-0.0602344\pi$$
0.982149 + 0.188104i $$0.0602344\pi$$
$$828$$ −7728.00 −0.324356
$$829$$ 11240.0 0.470906 0.235453 0.971886i $$-0.424343\pi$$
0.235453 + 0.971886i $$0.424343\pi$$
$$830$$ 0 0
$$831$$ 10852.0 0.453010
$$832$$ 4676.00 0.194845
$$833$$ −2646.00 −0.110058
$$834$$ −420.000 −0.0174381
$$835$$ 0 0
$$836$$ −6160.00 −0.254842
$$837$$ −1200.00 −0.0495556
$$838$$ 2310.00 0.0952239
$$839$$ 700.000 0.0288042 0.0144021 0.999896i $$-0.495416\pi$$
0.0144021 + 0.999896i $$0.495416\pi$$
$$840$$ 0 0
$$841$$ −12289.0 −0.503875
$$842$$ 1262.00 0.0516525
$$843$$ 1684.00 0.0688019
$$844$$ 29876.0 1.21845
$$845$$ 0 0
$$846$$ 7452.00 0.302843
$$847$$ −8869.00 −0.359790
$$848$$ 6642.00 0.268971
$$849$$ 7564.00 0.305767
$$850$$ 0 0
$$851$$ −11808.0 −0.475644
$$852$$ 10752.0 0.432344
$$853$$ 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 $$-0.695327\pi$$
−0.575846 + 0.817558i $$0.695327\pi$$
$$858$$ 448.000 0.0178257
$$859$$ −2770.00 −0.110025 −0.0550123 0.998486i $$-0.517520\pi$$
−0.0550123 + 0.998486i $$0.517520\pi$$
$$860$$ 0 0
$$861$$ 2548.00 0.100854
$$862$$ −4488.00 −0.177334
$$863$$ −17688.0 −0.697690 −0.348845 0.937180i $$-0.613426\pi$$
−0.348845 + 0.937180i $$0.613426\pi$$
$$864$$ −16100.0 −0.633950
$$865$$ 0 0
$$866$$ −17038.0 −0.668562
$$867$$ −3994.00 −0.156451
$$868$$ −588.000 −0.0229931
$$869$$ −3520.00 −0.137408
$$870$$ 0 0
$$871$$ 6832.00 0.265779
$$872$$ −1350.00 −0.0524275
$$873$$ 6762.00 0.262152
$$874$$ 5280.00 0.204346
$$875$$ 0 0
$$876$$ −9828.00 −0.379061
$$877$$ 33566.0 1.29241 0.646205 0.763164i $$-0.276355\pi$$
0.646205 + 0.763164i $$0.276355\pi$$
$$878$$ 16200.0 0.622692
$$879$$ 8624.00 0.330922
$$880$$ 0 0
$$881$$ −16758.0 −0.640853 −0.320426 0.947273i $$-0.603826\pi$$
−0.320426 + 0.947273i $$0.603826\pi$$
$$882$$ −1127.00 −0.0430250
$$883$$ −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 $$-0.0978793\pi$$
0.953094 + 0.302674i $$0.0978793\pi$$
$$888$$ −7380.00 −0.278893
$$889$$ 12432.0 0.469017
$$890$$ 0 0
$$891$$ −3368.00 −0.126636
$$892$$ −38024.0 −1.42728
$$893$$ 35640.0 1.33555
$$894$$ −4020.00 −0.150390
$$895$$ 0 0
$$896$$ −10185.0 −0.379751
$$897$$ 2688.00 0.100055
$$898$$ 2130.00 0.0791526
$$899$$ −1320.00 −0.0489705
$$900$$ 0 0
$$901$$ −8748.00 −0.323461
$$902$$ −1456.00 −0.0537467
$$903$$ −1792.00 −0.0660399
$$904$$ 19770.0 0.727368
$$905$$ 0 0
$$906$$ 2224.00 0.0815535
$$907$$ 8716.00 0.319085 0.159542 0.987191i $$-0.448998\pi$$
0.159542 + 0.987191i $$0.448998\pi$$
$$908$$ −14322.0 −0.523450
$$909$$ 15824.0 0.577392
$$910$$ 0 0
$$911$$ 7632.00 0.277563 0.138781 0.990323i $$-0.455682\pi$$
0.138781 + 0.990323i $$0.455682\pi$$
$$912$$ −9020.00 −0.327502
$$913$$ −10416.0 −0.377568
$$914$$ −10534.0 −0.381219
$$915$$ 0 0
$$916$$ 20860.0 0.752439
$$917$$ −7826.00 −0.281829
$$918$$ 5400.00 0.194147
$$919$$ −23080.0 −0.828443 −0.414221 0.910176i $$-0.635946\pi$$
−0.414221 + 0.910176i $$0.635946\pi$$
$$920$$ 0 0
$$921$$ −5348.00 −0.191338
$$922$$ −9268.00 −0.331047
$$923$$ 21504.0 0.766861
$$924$$ 784.000 0.0279131
$$925$$ 0 0
$$926$$ 9392.00 0.333305
$$927$$ 31924.0 1.13109
$$928$$ −17710.0 −0.626465
$$929$$ 45110.0 1.59312 0.796561 0.604558i $$-0.206650\pi$$
0.796561 + 0.604558i $$0.206650\pi$$
$$930$$ 0 0
$$931$$ −5390.00 −0.189742
$$932$$ 31206.0 1.09677
$$933$$ −7536.00 −0.264435
$$934$$ 10806.0 0.378569
$$935$$ 0 0
$$936$$ −9660.00 −0.337337
$$937$$ −16674.0 −0.581340 −0.290670 0.956823i $$-0.593878\pi$$
−0.290670 + 0.956823i $$0.593878\pi$$
$$938$$ −1708.00 −0.0594543
$$939$$ −4876.00 −0.169459
$$940$$ 0 0
$$941$$ 43832.0 1.51847 0.759236 0.650815i $$-0.225573\pi$$
0.759236 + 0.650815i $$0.225573\pi$$
$$942$$ −248.000 −0.00857779
$$943$$ −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 $$-0.495980\pi$$
0.0126277 + 0.999920i $$0.495980\pi$$
$$948$$ −6160.00 −0.211042
$$949$$ −19656.0 −0.672351
$$950$$ 0 0
$$951$$ 6372.00 0.217273
$$952$$ 5670.00 0.193031
$$953$$ −38138.0 −1.29634 −0.648169 0.761496i $$-0.724465\pi$$
−0.648169 + 0.761496i $$0.724465\pi$$
$$954$$ −3726.00 −0.126450
$$955$$ 0 0
$$956$$ −31080.0 −1.05146
$$957$$ 1760.00 0.0594490
$$958$$ 4940.00 0.166601
$$959$$ −15918.0 −0.535995
$$960$$ 0 0
$$961$$ −29647.0 −0.995166
$$962$$ −6888.00 −0.230850
$$963$$ 5612.00 0.187792
$$964$$ −23114.0 −0.772253
$$965$$ 0 0
$$966$$ −672.000 −0.0223822
$$967$$ −26224.0 −0.872086 −0.436043 0.899926i $$-0.643620\pi$$
−0.436043 + 0.899926i $$0.643620\pi$$
$$968$$ 19005.0 0.631037
$$969$$ 11880.0 0.393850
$$970$$ 0 0
$$971$$ 18762.0 0.620084 0.310042 0.950723i $$-0.399657\pi$$
0.310042 + 0.950723i $$0.399657\pi$$
$$972$$ −24794.0 −0.818177
$$973$$ −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 $$-0.716382\pi$$
−0.628625 + 0.777709i $$0.716382\pi$$
$$978$$ −4016.00 −0.131306
$$979$$ −5840.00 −0.190651
$$980$$ 0 0
$$981$$ −2070.00 −0.0673700
$$982$$ 4412.00 0.143373
$$983$$ −5388.00 −0.174822 −0.0874112 0.996172i $$-0.527859\pi$$
−0.0874112 + 0.996172i $$0.527859\pi$$
$$984$$ −5460.00 −0.176889
$$985$$ 0 0
$$986$$ 5940.00 0.191854
$$987$$ −4536.00 −0.146284
$$988$$ −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
$$993$$ 17344.0 0.554275
$$994$$ −5376.00 −0.171546
$$995$$ 0 0
$$996$$ −18228.0 −0.579896
$$997$$ 17096.0 0.543065 0.271532 0.962429i $$-0.412470\pi$$
0.271532 + 0.962429i $$0.412470\pi$$
$$998$$ 19060.0 0.604543
$$999$$ −24600.0 −0.779089
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 175.4.a.b.1.1 1
3.2 odd 2 1575.4.a.e.1.1 1
5.2 odd 4 175.4.b.b.99.2 2
5.3 odd 4 175.4.b.b.99.1 2
5.4 even 2 7.4.a.a.1.1 1
7.6 odd 2 1225.4.a.j.1.1 1
15.14 odd 2 63.4.a.b.1.1 1
20.19 odd 2 112.4.a.f.1.1 1
35.4 even 6 49.4.c.c.30.1 2
35.9 even 6 49.4.c.c.18.1 2
35.19 odd 6 49.4.c.b.18.1 2
35.24 odd 6 49.4.c.b.30.1 2
35.34 odd 2 49.4.a.b.1.1 1
40.19 odd 2 448.4.a.e.1.1 1
40.29 even 2 448.4.a.i.1.1 1
55.54 odd 2 847.4.a.b.1.1 1
60.59 even 2 1008.4.a.c.1.1 1
65.64 even 2 1183.4.a.b.1.1 1
85.84 even 2 2023.4.a.a.1.1 1
105.44 odd 6 441.4.e.h.361.1 2
105.59 even 6 441.4.e.e.226.1 2
105.74 odd 6 441.4.e.h.226.1 2
105.89 even 6 441.4.e.e.361.1 2
105.104 even 2 441.4.a.i.1.1 1
140.139 even 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 5.4 even 2
49.4.a.b.1.1 1 35.34 odd 2
49.4.c.b.18.1 2 35.19 odd 6
49.4.c.b.30.1 2 35.24 odd 6
49.4.c.c.18.1 2 35.9 even 6
49.4.c.c.30.1 2 35.4 even 6
63.4.a.b.1.1 1 15.14 odd 2
112.4.a.f.1.1 1 20.19 odd 2
175.4.a.b.1.1 1 1.1 even 1 trivial
175.4.b.b.99.1 2 5.3 odd 4
175.4.b.b.99.2 2 5.2 odd 4
441.4.a.i.1.1 1 105.104 even 2
441.4.e.e.226.1 2 105.59 even 6
441.4.e.e.361.1 2 105.89 even 6
441.4.e.h.226.1 2 105.74 odd 6
441.4.e.h.361.1 2 105.44 odd 6
448.4.a.e.1.1 1 40.19 odd 2
448.4.a.i.1.1 1 40.29 even 2
784.4.a.g.1.1 1 140.139 even 2
847.4.a.b.1.1 1 55.54 odd 2
1008.4.a.c.1.1 1 60.59 even 2
1183.4.a.b.1.1 1 65.64 even 2
1225.4.a.j.1.1 1 7.6 odd 2
1575.4.a.e.1.1 1 3.2 odd 2
2023.4.a.a.1.1 1 85.84 even 2