Properties

 Label 882.4.a.bg.1.2 Level $882$ Weight $4$ Character 882.1 Self dual yes Analytic conductor $52.040$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 882.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$52.0396846251$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{8})^+$$ Defining polynomial: $$x^{2} - 2$$ x^2 - 2 Coefficient ring: $$\Z[a_1, \ldots, a_{17}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 98) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.2 Root $$1.41421$$ of defining polynomial Character $$\chi$$ $$=$$ 882.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{2} +4.00000 q^{4} +19.7990 q^{5} +8.00000 q^{8} +O(q^{10})$$ $$q+2.00000 q^{2} +4.00000 q^{4} +19.7990 q^{5} +8.00000 q^{8} +39.5980 q^{10} +14.0000 q^{11} +50.9117 q^{13} +16.0000 q^{16} -1.41421 q^{17} -1.41421 q^{19} +79.1960 q^{20} +28.0000 q^{22} -140.000 q^{23} +267.000 q^{25} +101.823 q^{26} +286.000 q^{29} -93.3381 q^{31} +32.0000 q^{32} -2.82843 q^{34} -38.0000 q^{37} -2.82843 q^{38} +158.392 q^{40} +125.865 q^{41} -34.0000 q^{43} +56.0000 q^{44} -280.000 q^{46} -523.259 q^{47} +534.000 q^{50} +203.647 q^{52} +74.0000 q^{53} +277.186 q^{55} +572.000 q^{58} -434.164 q^{59} +14.1421 q^{61} -186.676 q^{62} +64.0000 q^{64} +1008.00 q^{65} +684.000 q^{67} -5.65685 q^{68} -588.000 q^{71} -270.115 q^{73} -76.0000 q^{74} -5.65685 q^{76} +1220.00 q^{79} +316.784 q^{80} +251.730 q^{82} -422.850 q^{83} -28.0000 q^{85} -68.0000 q^{86} +112.000 q^{88} -618.011 q^{89} -560.000 q^{92} -1046.52 q^{94} -28.0000 q^{95} +1483.51 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{2} + 8 q^{4} + 16 q^{8}+O(q^{10})$$ 2 * q + 4 * q^2 + 8 * q^4 + 16 * q^8 $$2 q + 4 q^{2} + 8 q^{4} + 16 q^{8} + 28 q^{11} + 32 q^{16} + 56 q^{22} - 280 q^{23} + 534 q^{25} + 572 q^{29} + 64 q^{32} - 76 q^{37} - 68 q^{43} + 112 q^{44} - 560 q^{46} + 1068 q^{50} + 148 q^{53} + 1144 q^{58} + 128 q^{64} + 2016 q^{65} + 1368 q^{67} - 1176 q^{71} - 152 q^{74} + 2440 q^{79} - 56 q^{85} - 136 q^{86} + 224 q^{88} - 1120 q^{92} - 56 q^{95}+O(q^{100})$$ 2 * q + 4 * q^2 + 8 * q^4 + 16 * q^8 + 28 * q^11 + 32 * q^16 + 56 * q^22 - 280 * q^23 + 534 * q^25 + 572 * q^29 + 64 * q^32 - 76 * q^37 - 68 * q^43 + 112 * q^44 - 560 * q^46 + 1068 * q^50 + 148 * q^53 + 1144 * q^58 + 128 * q^64 + 2016 * q^65 + 1368 * q^67 - 1176 * q^71 - 152 * q^74 + 2440 * q^79 - 56 * q^85 - 136 * q^86 + 224 * q^88 - 1120 * q^92 - 56 * q^95

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
$$5$$ 19.7990 1.77088 0.885438 0.464758i $$-0.153859\pi$$
0.885438 + 0.464758i $$0.153859\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 8.00000 0.353553
$$9$$ 0 0
$$10$$ 39.5980 1.25220
$$11$$ 14.0000 0.383742 0.191871 0.981420i $$-0.438545\pi$$
0.191871 + 0.981420i $$0.438545\pi$$
$$12$$ 0 0
$$13$$ 50.9117 1.08618 0.543091 0.839674i $$-0.317254\pi$$
0.543091 + 0.839674i $$0.317254\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 16.0000 0.250000
$$17$$ −1.41421 −0.0201763 −0.0100882 0.999949i $$-0.503211\pi$$
−0.0100882 + 0.999949i $$0.503211\pi$$
$$18$$ 0 0
$$19$$ −1.41421 −0.0170759 −0.00853797 0.999964i $$-0.502718\pi$$
−0.00853797 + 0.999964i $$0.502718\pi$$
$$20$$ 79.1960 0.885438
$$21$$ 0 0
$$22$$ 28.0000 0.271346
$$23$$ −140.000 −1.26922 −0.634609 0.772833i $$-0.718839\pi$$
−0.634609 + 0.772833i $$0.718839\pi$$
$$24$$ 0 0
$$25$$ 267.000 2.13600
$$26$$ 101.823 0.768046
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 286.000 1.83134 0.915670 0.401931i $$-0.131661\pi$$
0.915670 + 0.401931i $$0.131661\pi$$
$$30$$ 0 0
$$31$$ −93.3381 −0.540775 −0.270387 0.962752i $$-0.587152\pi$$
−0.270387 + 0.962752i $$0.587152\pi$$
$$32$$ 32.0000 0.176777
$$33$$ 0 0
$$34$$ −2.82843 −0.0142668
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −38.0000 −0.168842 −0.0844211 0.996430i $$-0.526904\pi$$
−0.0844211 + 0.996430i $$0.526904\pi$$
$$38$$ −2.82843 −0.0120745
$$39$$ 0 0
$$40$$ 158.392 0.626099
$$41$$ 125.865 0.479434 0.239717 0.970843i $$-0.422945\pi$$
0.239717 + 0.970843i $$0.422945\pi$$
$$42$$ 0 0
$$43$$ −34.0000 −0.120580 −0.0602901 0.998181i $$-0.519203\pi$$
−0.0602901 + 0.998181i $$0.519203\pi$$
$$44$$ 56.0000 0.191871
$$45$$ 0 0
$$46$$ −280.000 −0.897473
$$47$$ −523.259 −1.62394 −0.811970 0.583699i $$-0.801605\pi$$
−0.811970 + 0.583699i $$0.801605\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 534.000 1.51038
$$51$$ 0 0
$$52$$ 203.647 0.543091
$$53$$ 74.0000 0.191786 0.0958932 0.995392i $$-0.469429\pi$$
0.0958932 + 0.995392i $$0.469429\pi$$
$$54$$ 0 0
$$55$$ 277.186 0.679559
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 572.000 1.29495
$$59$$ −434.164 −0.958022 −0.479011 0.877809i $$-0.659005\pi$$
−0.479011 + 0.877809i $$0.659005\pi$$
$$60$$ 0 0
$$61$$ 14.1421 0.0296839 0.0148419 0.999890i $$-0.495275\pi$$
0.0148419 + 0.999890i $$0.495275\pi$$
$$62$$ −186.676 −0.382385
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ 1008.00 1.92349
$$66$$ 0 0
$$67$$ 684.000 1.24722 0.623611 0.781735i $$-0.285665\pi$$
0.623611 + 0.781735i $$0.285665\pi$$
$$68$$ −5.65685 −0.0100882
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −588.000 −0.982856 −0.491428 0.870918i $$-0.663525\pi$$
−0.491428 + 0.870918i $$0.663525\pi$$
$$72$$ 0 0
$$73$$ −270.115 −0.433076 −0.216538 0.976274i $$-0.569477\pi$$
−0.216538 + 0.976274i $$0.569477\pi$$
$$74$$ −76.0000 −0.119389
$$75$$ 0 0
$$76$$ −5.65685 −0.00853797
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 1220.00 1.73748 0.868739 0.495271i $$-0.164931\pi$$
0.868739 + 0.495271i $$0.164931\pi$$
$$80$$ 316.784 0.442719
$$81$$ 0 0
$$82$$ 251.730 0.339011
$$83$$ −422.850 −0.559202 −0.279601 0.960116i $$-0.590202\pi$$
−0.279601 + 0.960116i $$0.590202\pi$$
$$84$$ 0 0
$$85$$ −28.0000 −0.0357297
$$86$$ −68.0000 −0.0852631
$$87$$ 0 0
$$88$$ 112.000 0.135673
$$89$$ −618.011 −0.736057 −0.368028 0.929815i $$-0.619967\pi$$
−0.368028 + 0.929815i $$0.619967\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −560.000 −0.634609
$$93$$ 0 0
$$94$$ −1046.52 −1.14830
$$95$$ −28.0000 −0.0302394
$$96$$ 0 0
$$97$$ 1483.51 1.55286 0.776431 0.630202i $$-0.217028\pi$$
0.776431 + 0.630202i $$0.217028\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1068.00 1.06800
$$101$$ −1128.54 −1.11182 −0.555912 0.831241i $$-0.687631\pi$$
−0.555912 + 0.831241i $$0.687631\pi$$
$$102$$ 0 0
$$103$$ −868.327 −0.830668 −0.415334 0.909669i $$-0.636335\pi$$
−0.415334 + 0.909669i $$0.636335\pi$$
$$104$$ 407.294 0.384023
$$105$$ 0 0
$$106$$ 148.000 0.135613
$$107$$ 1684.00 1.52148 0.760740 0.649056i $$-0.224836\pi$$
0.760740 + 0.649056i $$0.224836\pi$$
$$108$$ 0 0
$$109$$ −818.000 −0.718809 −0.359405 0.933182i $$-0.617020\pi$$
−0.359405 + 0.933182i $$0.617020\pi$$
$$110$$ 554.372 0.480521
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 540.000 0.449548 0.224774 0.974411i $$-0.427836\pi$$
0.224774 + 0.974411i $$0.427836\pi$$
$$114$$ 0 0
$$115$$ −2771.86 −2.24763
$$116$$ 1144.00 0.915670
$$117$$ 0 0
$$118$$ −868.327 −0.677424
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1135.00 −0.852742
$$122$$ 28.2843 0.0209897
$$123$$ 0 0
$$124$$ −373.352 −0.270387
$$125$$ 2811.46 2.01171
$$126$$ 0 0
$$127$$ 1720.00 1.20177 0.600887 0.799334i $$-0.294814\pi$$
0.600887 + 0.799334i $$0.294814\pi$$
$$128$$ 128.000 0.0883883
$$129$$ 0 0
$$130$$ 2016.00 1.36011
$$131$$ 1735.24 1.15732 0.578659 0.815570i $$-0.303576\pi$$
0.578659 + 0.815570i $$0.303576\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 1368.00 0.881919
$$135$$ 0 0
$$136$$ −11.3137 −0.00713340
$$137$$ −828.000 −0.516356 −0.258178 0.966097i $$-0.583122\pi$$
−0.258178 + 0.966097i $$0.583122\pi$$
$$138$$ 0 0
$$139$$ −425.678 −0.259752 −0.129876 0.991530i $$-0.541458\pi$$
−0.129876 + 0.991530i $$0.541458\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −1176.00 −0.694984
$$143$$ 712.764 0.416813
$$144$$ 0 0
$$145$$ 5662.51 3.24308
$$146$$ −540.230 −0.306231
$$147$$ 0 0
$$148$$ −152.000 −0.0844211
$$149$$ −2050.00 −1.12713 −0.563566 0.826071i $$-0.690571\pi$$
−0.563566 + 0.826071i $$0.690571\pi$$
$$150$$ 0 0
$$151$$ −472.000 −0.254376 −0.127188 0.991879i $$-0.540595\pi$$
−0.127188 + 0.991879i $$0.540595\pi$$
$$152$$ −11.3137 −0.00603726
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1848.00 −0.957645
$$156$$ 0 0
$$157$$ −2211.83 −1.12435 −0.562176 0.827018i $$-0.690036\pi$$
−0.562176 + 0.827018i $$0.690036\pi$$
$$158$$ 2440.00 1.22858
$$159$$ 0 0
$$160$$ 633.568 0.313050
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 3286.00 1.57901 0.789507 0.613741i $$-0.210336\pi$$
0.789507 + 0.613741i $$0.210336\pi$$
$$164$$ 503.460 0.239717
$$165$$ 0 0
$$166$$ −845.700 −0.395416
$$167$$ 1490.58 0.690686 0.345343 0.938476i $$-0.387763\pi$$
0.345343 + 0.938476i $$0.387763\pi$$
$$168$$ 0 0
$$169$$ 395.000 0.179791
$$170$$ −56.0000 −0.0252647
$$171$$ 0 0
$$172$$ −136.000 −0.0602901
$$173$$ 2070.41 0.909886 0.454943 0.890521i $$-0.349660\pi$$
0.454943 + 0.890521i $$0.349660\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 224.000 0.0959354
$$177$$ 0 0
$$178$$ −1236.02 −0.520471
$$179$$ −540.000 −0.225483 −0.112742 0.993624i $$-0.535963\pi$$
−0.112742 + 0.993624i $$0.535963\pi$$
$$180$$ 0 0
$$181$$ 3784.44 1.55412 0.777058 0.629429i $$-0.216711\pi$$
0.777058 + 0.629429i $$0.216711\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −1120.00 −0.448736
$$185$$ −752.362 −0.298999
$$186$$ 0 0
$$187$$ −19.7990 −0.00774249
$$188$$ −2093.04 −0.811970
$$189$$ 0 0
$$190$$ −56.0000 −0.0213825
$$191$$ −1028.00 −0.389442 −0.194721 0.980859i $$-0.562380\pi$$
−0.194721 + 0.980859i $$0.562380\pi$$
$$192$$ 0 0
$$193$$ 4592.00 1.71264 0.856320 0.516446i $$-0.172745\pi$$
0.856320 + 0.516446i $$0.172745\pi$$
$$194$$ 2967.02 1.09804
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −794.000 −0.287158 −0.143579 0.989639i $$-0.545861\pi$$
−0.143579 + 0.989639i $$0.545861\pi$$
$$198$$ 0 0
$$199$$ 2486.19 0.885634 0.442817 0.896612i $$-0.353979\pi$$
0.442817 + 0.896612i $$0.353979\pi$$
$$200$$ 2136.00 0.755190
$$201$$ 0 0
$$202$$ −2257.08 −0.786178
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 2492.00 0.849019
$$206$$ −1736.65 −0.587371
$$207$$ 0 0
$$208$$ 814.587 0.271545
$$209$$ −19.7990 −0.00655275
$$210$$ 0 0
$$211$$ −2748.00 −0.896588 −0.448294 0.893886i $$-0.647968\pi$$
−0.448294 + 0.893886i $$0.647968\pi$$
$$212$$ 296.000 0.0958932
$$213$$ 0 0
$$214$$ 3368.00 1.07585
$$215$$ −673.166 −0.213533
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −1636.00 −0.508275
$$219$$ 0 0
$$220$$ 1108.74 0.339779
$$221$$ −72.0000 −0.0219151
$$222$$ 0 0
$$223$$ −3428.05 −1.02941 −0.514707 0.857366i $$-0.672099\pi$$
−0.514707 + 0.857366i $$0.672099\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1080.00 0.317878
$$227$$ −5290.57 −1.54691 −0.773453 0.633854i $$-0.781472\pi$$
−0.773453 + 0.633854i $$0.781472\pi$$
$$228$$ 0 0
$$229$$ −2749.23 −0.793338 −0.396669 0.917962i $$-0.629834\pi$$
−0.396669 + 0.917962i $$0.629834\pi$$
$$230$$ −5543.72 −1.58931
$$231$$ 0 0
$$232$$ 2288.00 0.647477
$$233$$ −72.0000 −0.0202441 −0.0101221 0.999949i $$-0.503222\pi$$
−0.0101221 + 0.999949i $$0.503222\pi$$
$$234$$ 0 0
$$235$$ −10360.0 −2.87580
$$236$$ −1736.65 −0.479011
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −4308.00 −1.16595 −0.582974 0.812491i $$-0.698111\pi$$
−0.582974 + 0.812491i $$0.698111\pi$$
$$240$$ 0 0
$$241$$ −1540.08 −0.411640 −0.205820 0.978590i $$-0.565986\pi$$
−0.205820 + 0.978590i $$0.565986\pi$$
$$242$$ −2270.00 −0.602980
$$243$$ 0 0
$$244$$ 56.5685 0.0148419
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −72.0000 −0.0185476
$$248$$ −746.705 −0.191193
$$249$$ 0 0
$$250$$ 5622.91 1.42250
$$251$$ −931.967 −0.234363 −0.117182 0.993110i $$-0.537386\pi$$
−0.117182 + 0.993110i $$0.537386\pi$$
$$252$$ 0 0
$$253$$ −1960.00 −0.487052
$$254$$ 3440.00 0.849783
$$255$$ 0 0
$$256$$ 256.000 0.0625000
$$257$$ −937.624 −0.227577 −0.113789 0.993505i $$-0.536299\pi$$
−0.113789 + 0.993505i $$0.536299\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 4032.00 0.961746
$$261$$ 0 0
$$262$$ 3470.48 0.818347
$$263$$ −7140.00 −1.67404 −0.837018 0.547176i $$-0.815703\pi$$
−0.837018 + 0.547176i $$0.815703\pi$$
$$264$$ 0 0
$$265$$ 1465.13 0.339630
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 2736.00 0.623611
$$269$$ −4610.34 −1.04497 −0.522485 0.852648i $$-0.674995\pi$$
−0.522485 + 0.852648i $$0.674995\pi$$
$$270$$ 0 0
$$271$$ −2364.57 −0.530026 −0.265013 0.964245i $$-0.585376\pi$$
−0.265013 + 0.964245i $$0.585376\pi$$
$$272$$ −22.6274 −0.00504408
$$273$$ 0 0
$$274$$ −1656.00 −0.365119
$$275$$ 3738.00 0.819672
$$276$$ 0 0
$$277$$ 4006.00 0.868943 0.434472 0.900686i $$-0.356935\pi$$
0.434472 + 0.900686i $$0.356935\pi$$
$$278$$ −851.357 −0.183673
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 5984.00 1.27038 0.635188 0.772358i $$-0.280923\pi$$
0.635188 + 0.772358i $$0.280923\pi$$
$$282$$ 0 0
$$283$$ −4928.53 −1.03523 −0.517617 0.855613i $$-0.673181\pi$$
−0.517617 + 0.855613i $$0.673181\pi$$
$$284$$ −2352.00 −0.491428
$$285$$ 0 0
$$286$$ 1425.53 0.294731
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4911.00 −0.999593
$$290$$ 11325.0 2.29320
$$291$$ 0 0
$$292$$ −1080.46 −0.216538
$$293$$ −1971.41 −0.393076 −0.196538 0.980496i $$-0.562970\pi$$
−0.196538 + 0.980496i $$0.562970\pi$$
$$294$$ 0 0
$$295$$ −8596.00 −1.69654
$$296$$ −304.000 −0.0596947
$$297$$ 0 0
$$298$$ −4100.00 −0.797002
$$299$$ −7127.64 −1.37860
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −944.000 −0.179871
$$303$$ 0 0
$$304$$ −22.6274 −0.00426898
$$305$$ 280.000 0.0525664
$$306$$ 0 0
$$307$$ −4767.31 −0.886270 −0.443135 0.896455i $$-0.646134\pi$$
−0.443135 + 0.896455i $$0.646134\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −3696.00 −0.677157
$$311$$ 6776.91 1.23564 0.617819 0.786320i $$-0.288016\pi$$
0.617819 + 0.786320i $$0.288016\pi$$
$$312$$ 0 0
$$313$$ −6190.01 −1.11783 −0.558914 0.829226i $$-0.688782\pi$$
−0.558914 + 0.829226i $$0.688782\pi$$
$$314$$ −4423.66 −0.795037
$$315$$ 0 0
$$316$$ 4880.00 0.868739
$$317$$ −9826.00 −1.74096 −0.870478 0.492207i $$-0.836190\pi$$
−0.870478 + 0.492207i $$0.836190\pi$$
$$318$$ 0 0
$$319$$ 4004.00 0.702762
$$320$$ 1267.14 0.221359
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2.00000 0.000344529 0
$$324$$ 0 0
$$325$$ 13593.4 2.32008
$$326$$ 6572.00 1.11653
$$327$$ 0 0
$$328$$ 1006.92 0.169506
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −5738.00 −0.952837 −0.476418 0.879219i $$-0.658065\pi$$
−0.476418 + 0.879219i $$0.658065\pi$$
$$332$$ −1691.40 −0.279601
$$333$$ 0 0
$$334$$ 2981.16 0.488389
$$335$$ 13542.5 2.20868
$$336$$ 0 0
$$337$$ −2254.00 −0.364342 −0.182171 0.983267i $$-0.558312\pi$$
−0.182171 + 0.983267i $$0.558312\pi$$
$$338$$ 790.000 0.127131
$$339$$ 0 0
$$340$$ −112.000 −0.0178649
$$341$$ −1306.73 −0.207518
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −272.000 −0.0426316
$$345$$ 0 0
$$346$$ 4140.82 0.643386
$$347$$ 1986.00 0.307245 0.153623 0.988130i $$-0.450906\pi$$
0.153623 + 0.988130i $$0.450906\pi$$
$$348$$ 0 0
$$349$$ 6771.25 1.03856 0.519279 0.854605i $$-0.326200\pi$$
0.519279 + 0.854605i $$0.326200\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 448.000 0.0678366
$$353$$ −6993.29 −1.05443 −0.527217 0.849731i $$-0.676764\pi$$
−0.527217 + 0.849731i $$0.676764\pi$$
$$354$$ 0 0
$$355$$ −11641.8 −1.74052
$$356$$ −2472.05 −0.368028
$$357$$ 0 0
$$358$$ −1080.00 −0.159441
$$359$$ −5944.00 −0.873850 −0.436925 0.899498i $$-0.643933\pi$$
−0.436925 + 0.899498i $$0.643933\pi$$
$$360$$ 0 0
$$361$$ −6857.00 −0.999708
$$362$$ 7568.87 1.09893
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −5348.00 −0.766924
$$366$$ 0 0
$$367$$ −842.871 −0.119884 −0.0599421 0.998202i $$-0.519092\pi$$
−0.0599421 + 0.998202i $$0.519092\pi$$
$$368$$ −2240.00 −0.317305
$$369$$ 0 0
$$370$$ −1504.72 −0.211424
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −5726.00 −0.794855 −0.397428 0.917634i $$-0.630097\pi$$
−0.397428 + 0.917634i $$0.630097\pi$$
$$374$$ −39.5980 −0.00547477
$$375$$ 0 0
$$376$$ −4186.07 −0.574149
$$377$$ 14560.7 1.98917
$$378$$ 0 0
$$379$$ 10330.0 1.40004 0.700022 0.714122i $$-0.253174\pi$$
0.700022 + 0.714122i $$0.253174\pi$$
$$380$$ −112.000 −0.0151197
$$381$$ 0 0
$$382$$ −2056.00 −0.275377
$$383$$ −1004.09 −0.133960 −0.0669800 0.997754i $$-0.521336\pi$$
−0.0669800 + 0.997754i $$0.521336\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 9184.00 1.21102
$$387$$ 0 0
$$388$$ 5934.04 0.776431
$$389$$ −5210.00 −0.679068 −0.339534 0.940594i $$-0.610269\pi$$
−0.339534 + 0.940594i $$0.610269\pi$$
$$390$$ 0 0
$$391$$ 197.990 0.0256081
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −1588.00 −0.203051
$$395$$ 24154.8 3.07686
$$396$$ 0 0
$$397$$ −73.5391 −0.00929678 −0.00464839 0.999989i $$-0.501480\pi$$
−0.00464839 + 0.999989i $$0.501480\pi$$
$$398$$ 4972.37 0.626238
$$399$$ 0 0
$$400$$ 4272.00 0.534000
$$401$$ 498.000 0.0620173 0.0310086 0.999519i $$-0.490128\pi$$
0.0310086 + 0.999519i $$0.490128\pi$$
$$402$$ 0 0
$$403$$ −4752.00 −0.587380
$$404$$ −4514.17 −0.555912
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −532.000 −0.0647918
$$408$$ 0 0
$$409$$ 3355.93 0.405721 0.202861 0.979208i $$-0.434976\pi$$
0.202861 + 0.979208i $$0.434976\pi$$
$$410$$ 4984.00 0.600347
$$411$$ 0 0
$$412$$ −3473.31 −0.415334
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −8372.00 −0.990278
$$416$$ 1629.17 0.192012
$$417$$ 0 0
$$418$$ −39.5980 −0.00463349
$$419$$ −14545.2 −1.69589 −0.847946 0.530082i $$-0.822161\pi$$
−0.847946 + 0.530082i $$0.822161\pi$$
$$420$$ 0 0
$$421$$ 10854.0 1.25651 0.628256 0.778007i $$-0.283769\pi$$
0.628256 + 0.778007i $$0.283769\pi$$
$$422$$ −5496.00 −0.633984
$$423$$ 0 0
$$424$$ 592.000 0.0678067
$$425$$ −377.595 −0.0430966
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 6736.00 0.760740
$$429$$ 0 0
$$430$$ −1346.33 −0.150990
$$431$$ 5364.00 0.599477 0.299739 0.954021i $$-0.403100\pi$$
0.299739 + 0.954021i $$0.403100\pi$$
$$432$$ 0 0
$$433$$ −6487.00 −0.719966 −0.359983 0.932959i $$-0.617217\pi$$
−0.359983 + 0.932959i $$0.617217\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −3272.00 −0.359405
$$437$$ 197.990 0.0216731
$$438$$ 0 0
$$439$$ 13932.8 1.51476 0.757378 0.652977i $$-0.226480\pi$$
0.757378 + 0.652977i $$0.226480\pi$$
$$440$$ 2217.49 0.240260
$$441$$ 0 0
$$442$$ −144.000 −0.0154963
$$443$$ −5996.00 −0.643067 −0.321533 0.946898i $$-0.604198\pi$$
−0.321533 + 0.946898i $$0.604198\pi$$
$$444$$ 0 0
$$445$$ −12236.0 −1.30347
$$446$$ −6856.11 −0.727906
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −2622.00 −0.275590 −0.137795 0.990461i $$-0.544001\pi$$
−0.137795 + 0.990461i $$0.544001\pi$$
$$450$$ 0 0
$$451$$ 1762.11 0.183979
$$452$$ 2160.00 0.224774
$$453$$ 0 0
$$454$$ −10581.1 −1.09383
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11208.0 1.14724 0.573619 0.819122i $$-0.305539\pi$$
0.573619 + 0.819122i $$0.305539\pi$$
$$458$$ −5498.46 −0.560974
$$459$$ 0 0
$$460$$ −11087.4 −1.12381
$$461$$ −9786.36 −0.988712 −0.494356 0.869260i $$-0.664596\pi$$
−0.494356 + 0.869260i $$0.664596\pi$$
$$462$$ 0 0
$$463$$ 3952.00 0.396685 0.198342 0.980133i $$-0.436444\pi$$
0.198342 + 0.980133i $$0.436444\pi$$
$$464$$ 4576.00 0.457835
$$465$$ 0 0
$$466$$ −144.000 −0.0143147
$$467$$ −17506.5 −1.73470 −0.867352 0.497696i $$-0.834180\pi$$
−0.867352 + 0.497696i $$0.834180\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −20720.0 −2.03349
$$471$$ 0 0
$$472$$ −3473.31 −0.338712
$$473$$ −476.000 −0.0462717
$$474$$ 0 0
$$475$$ −377.595 −0.0364742
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −8616.00 −0.824449
$$479$$ −2288.20 −0.218268 −0.109134 0.994027i $$-0.534808\pi$$
−0.109134 + 0.994027i $$0.534808\pi$$
$$480$$ 0 0
$$481$$ −1934.64 −0.183393
$$482$$ −3080.16 −0.291073
$$483$$ 0 0
$$484$$ −4540.00 −0.426371
$$485$$ 29372.0 2.74993
$$486$$ 0 0
$$487$$ 972.000 0.0904426 0.0452213 0.998977i $$-0.485601\pi$$
0.0452213 + 0.998977i $$0.485601\pi$$
$$488$$ 113.137 0.0104948
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 7404.00 0.680525 0.340263 0.940330i $$-0.389484\pi$$
0.340263 + 0.940330i $$0.389484\pi$$
$$492$$ 0 0
$$493$$ −404.465 −0.0369497
$$494$$ −144.000 −0.0131151
$$495$$ 0 0
$$496$$ −1493.41 −0.135194
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −12244.0 −1.09843 −0.549215 0.835681i $$-0.685073\pi$$
−0.549215 + 0.835681i $$0.685073\pi$$
$$500$$ 11245.8 1.00586
$$501$$ 0 0
$$502$$ −1863.93 −0.165720
$$503$$ 2415.48 0.214117 0.107058 0.994253i $$-0.465857\pi$$
0.107058 + 0.994253i $$0.465857\pi$$
$$504$$ 0 0
$$505$$ −22344.0 −1.96890
$$506$$ −3920.00 −0.344398
$$507$$ 0 0
$$508$$ 6880.00 0.600887
$$509$$ 5707.77 0.497038 0.248519 0.968627i $$-0.420056\pi$$
0.248519 + 0.968627i $$0.420056\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 512.000 0.0441942
$$513$$ 0 0
$$514$$ −1875.25 −0.160921
$$515$$ −17192.0 −1.47101
$$516$$ 0 0
$$517$$ −7325.63 −0.623173
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 8064.00 0.680057
$$521$$ −1.41421 −0.000118921 0 −5.94605e−5 1.00000i $$-0.500019\pi$$
−5.94605e−5 1.00000i $$0.500019\pi$$
$$522$$ 0 0
$$523$$ −12257.0 −1.02478 −0.512391 0.858752i $$-0.671240\pi$$
−0.512391 + 0.858752i $$0.671240\pi$$
$$524$$ 6940.96 0.578659
$$525$$ 0 0
$$526$$ −14280.0 −1.18372
$$527$$ 132.000 0.0109108
$$528$$ 0 0
$$529$$ 7433.00 0.610915
$$530$$ 2930.25 0.240155
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 6408.00 0.520753
$$534$$ 0 0
$$535$$ 33341.5 2.69435
$$536$$ 5472.00 0.440960
$$537$$ 0 0
$$538$$ −9220.67 −0.738906
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 2050.00 0.162914 0.0814569 0.996677i $$-0.474043\pi$$
0.0814569 + 0.996677i $$0.474043\pi$$
$$542$$ −4729.13 −0.374785
$$543$$ 0 0
$$544$$ −45.2548 −0.00356670
$$545$$ −16195.6 −1.27292
$$546$$ 0 0
$$547$$ 14554.0 1.13763 0.568815 0.822465i $$-0.307402\pi$$
0.568815 + 0.822465i $$0.307402\pi$$
$$548$$ −3312.00 −0.258178
$$549$$ 0 0
$$550$$ 7476.00 0.579596
$$551$$ −404.465 −0.0312719
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 8012.00 0.614435
$$555$$ 0 0
$$556$$ −1702.71 −0.129876
$$557$$ −6954.00 −0.528995 −0.264498 0.964386i $$-0.585206\pi$$
−0.264498 + 0.964386i $$0.585206\pi$$
$$558$$ 0 0
$$559$$ −1731.00 −0.130972
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 11968.0 0.898291
$$563$$ 1636.25 0.122486 0.0612429 0.998123i $$-0.480494\pi$$
0.0612429 + 0.998123i $$0.480494\pi$$
$$564$$ 0 0
$$565$$ 10691.5 0.796094
$$566$$ −9857.07 −0.732020
$$567$$ 0 0
$$568$$ −4704.00 −0.347492
$$569$$ 7142.00 0.526201 0.263100 0.964768i $$-0.415255\pi$$
0.263100 + 0.964768i $$0.415255\pi$$
$$570$$ 0 0
$$571$$ −20606.0 −1.51022 −0.755109 0.655599i $$-0.772416\pi$$
−0.755109 + 0.655599i $$0.772416\pi$$
$$572$$ 2851.05 0.208407
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −37380.0 −2.71105
$$576$$ 0 0
$$577$$ −8803.48 −0.635171 −0.317585 0.948230i $$-0.602872\pi$$
−0.317585 + 0.948230i $$0.602872\pi$$
$$578$$ −9822.00 −0.706819
$$579$$ 0 0
$$580$$ 22650.0 1.62154
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 1036.00 0.0735965
$$584$$ −2160.92 −0.153115
$$585$$ 0 0
$$586$$ −3942.83 −0.277947
$$587$$ −6503.97 −0.457321 −0.228661 0.973506i $$-0.573435\pi$$
−0.228661 + 0.973506i $$0.573435\pi$$
$$588$$ 0 0
$$589$$ 132.000 0.00923424
$$590$$ −17192.0 −1.19963
$$591$$ 0 0
$$592$$ −608.000 −0.0422106
$$593$$ 23140.8 1.60249 0.801246 0.598335i $$-0.204171\pi$$
0.801246 + 0.598335i $$0.204171\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −8200.00 −0.563566
$$597$$ 0 0
$$598$$ −14255.3 −0.974818
$$599$$ 11296.0 0.770521 0.385260 0.922808i $$-0.374112\pi$$
0.385260 + 0.922808i $$0.374112\pi$$
$$600$$ 0 0
$$601$$ 8727.11 0.592323 0.296162 0.955138i $$-0.404293\pi$$
0.296162 + 0.955138i $$0.404293\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −1888.00 −0.127188
$$605$$ −22471.9 −1.51010
$$606$$ 0 0
$$607$$ 19736.8 1.31975 0.659877 0.751374i $$-0.270608\pi$$
0.659877 + 0.751374i $$0.270608\pi$$
$$608$$ −45.2548 −0.00301863
$$609$$ 0 0
$$610$$ 560.000 0.0371701
$$611$$ −26640.0 −1.76389
$$612$$ 0 0
$$613$$ 16962.0 1.11760 0.558800 0.829302i $$-0.311262\pi$$
0.558800 + 0.829302i $$0.311262\pi$$
$$614$$ −9534.63 −0.626688
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 19034.0 1.24194 0.620972 0.783832i $$-0.286738\pi$$
0.620972 + 0.783832i $$0.286738\pi$$
$$618$$ 0 0
$$619$$ −18677.5 −1.21278 −0.606392 0.795166i $$-0.707384\pi$$
−0.606392 + 0.795166i $$0.707384\pi$$
$$620$$ −7392.00 −0.478822
$$621$$ 0 0
$$622$$ 13553.8 0.873728
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 22289.0 1.42650
$$626$$ −12380.0 −0.790424
$$627$$ 0 0
$$628$$ −8847.32 −0.562176
$$629$$ 53.7401 0.00340661
$$630$$ 0 0
$$631$$ −14716.0 −0.928423 −0.464211 0.885724i $$-0.653662\pi$$
−0.464211 + 0.885724i $$0.653662\pi$$
$$632$$ 9760.00 0.614291
$$633$$ 0 0
$$634$$ −19652.0 −1.23104
$$635$$ 34054.3 2.12819
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 8008.00 0.496928
$$639$$ 0 0
$$640$$ 2534.27 0.156525
$$641$$ −4730.00 −0.291457 −0.145728 0.989325i $$-0.546553\pi$$
−0.145728 + 0.989325i $$0.546553\pi$$
$$642$$ 0 0
$$643$$ 19056.5 1.16877 0.584383 0.811478i $$-0.301337\pi$$
0.584383 + 0.811478i $$0.301337\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 4.00000 0.000243619 0
$$647$$ −9342.29 −0.567672 −0.283836 0.958873i $$-0.591607\pi$$
−0.283836 + 0.958873i $$0.591607\pi$$
$$648$$ 0 0
$$649$$ −6078.29 −0.367633
$$650$$ 27186.8 1.64055
$$651$$ 0 0
$$652$$ 13144.0 0.789507
$$653$$ −3774.00 −0.226169 −0.113084 0.993585i $$-0.536073\pi$$
−0.113084 + 0.993585i $$0.536073\pi$$
$$654$$ 0 0
$$655$$ 34356.0 2.04947
$$656$$ 2013.84 0.119859
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 21150.0 1.25021 0.625104 0.780541i $$-0.285057\pi$$
0.625104 + 0.780541i $$0.285057\pi$$
$$660$$ 0 0
$$661$$ −10377.5 −0.610647 −0.305324 0.952249i $$-0.598765\pi$$
−0.305324 + 0.952249i $$0.598765\pi$$
$$662$$ −11476.0 −0.673757
$$663$$ 0 0
$$664$$ −3382.80 −0.197708
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −40040.0 −2.32437
$$668$$ 5962.32 0.345343
$$669$$ 0 0
$$670$$ 27085.0 1.56177
$$671$$ 197.990 0.0113909
$$672$$ 0 0
$$673$$ −1164.00 −0.0666700 −0.0333350 0.999444i $$-0.510613\pi$$
−0.0333350 + 0.999444i $$0.510613\pi$$
$$674$$ −4508.00 −0.257629
$$675$$ 0 0
$$676$$ 1580.00 0.0898953
$$677$$ −27152.9 −1.54146 −0.770732 0.637160i $$-0.780109\pi$$
−0.770732 + 0.637160i $$0.780109\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −224.000 −0.0126324
$$681$$ 0 0
$$682$$ −2613.47 −0.146737
$$683$$ 16596.0 0.929763 0.464882 0.885373i $$-0.346097\pi$$
0.464882 + 0.885373i $$0.346097\pi$$
$$684$$ 0 0
$$685$$ −16393.6 −0.914403
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −544.000 −0.0301451
$$689$$ 3767.46 0.208315
$$690$$ 0 0
$$691$$ 11298.2 0.622000 0.311000 0.950410i $$-0.399336\pi$$
0.311000 + 0.950410i $$0.399336\pi$$
$$692$$ 8281.63 0.454943
$$693$$ 0 0
$$694$$ 3972.00 0.217255
$$695$$ −8428.00 −0.459989
$$696$$ 0 0
$$697$$ −178.000 −0.00967321
$$698$$ 13542.5 0.734372
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 2754.00 0.148384 0.0741920 0.997244i $$-0.476362\pi$$
0.0741920 + 0.997244i $$0.476362\pi$$
$$702$$ 0 0
$$703$$ 53.7401 0.00288314
$$704$$ 896.000 0.0479677
$$705$$ 0 0
$$706$$ −13986.6 −0.745597
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 29434.0 1.55912 0.779561 0.626327i $$-0.215442\pi$$
0.779561 + 0.626327i $$0.215442\pi$$
$$710$$ −23283.6 −1.23073
$$711$$ 0 0
$$712$$ −4944.09 −0.260235
$$713$$ 13067.3 0.686361
$$714$$ 0 0
$$715$$ 14112.0 0.738124
$$716$$ −2160.00 −0.112742
$$717$$ 0 0
$$718$$ −11888.0 −0.617906
$$719$$ 17669.2 0.916480 0.458240 0.888828i $$-0.348480\pi$$
0.458240 + 0.888828i $$0.348480\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −13714.0 −0.706901
$$723$$ 0 0
$$724$$ 15137.7 0.777058
$$725$$ 76362.0 3.91174
$$726$$ 0 0
$$727$$ 28445.5 1.45115 0.725574 0.688144i $$-0.241574\pi$$
0.725574 + 0.688144i $$0.241574\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −10696.0 −0.542297
$$731$$ 48.0833 0.00243286
$$732$$ 0 0
$$733$$ 22341.7 1.12580 0.562900 0.826525i $$-0.309686\pi$$
0.562900 + 0.826525i $$0.309686\pi$$
$$734$$ −1685.74 −0.0847710
$$735$$ 0 0
$$736$$ −4480.00 −0.224368
$$737$$ 9576.00 0.478611
$$738$$ 0 0
$$739$$ 20670.0 1.02890 0.514451 0.857520i $$-0.327996\pi$$
0.514451 + 0.857520i $$0.327996\pi$$
$$740$$ −3009.45 −0.149499
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 25400.0 1.25415 0.627076 0.778958i $$-0.284251\pi$$
0.627076 + 0.778958i $$0.284251\pi$$
$$744$$ 0 0
$$745$$ −40587.9 −1.99601
$$746$$ −11452.0 −0.562048
$$747$$ 0 0
$$748$$ −79.1960 −0.00387124
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 29180.0 1.41783 0.708917 0.705292i $$-0.249184\pi$$
0.708917 + 0.705292i $$0.249184\pi$$
$$752$$ −8372.14 −0.405985
$$753$$ 0 0
$$754$$ 29121.5 1.40655
$$755$$ −9345.12 −0.450469
$$756$$ 0 0
$$757$$ −26206.0 −1.25822 −0.629110 0.777316i $$-0.716581\pi$$
−0.629110 + 0.777316i $$0.716581\pi$$
$$758$$ 20660.0 0.989980
$$759$$ 0 0
$$760$$ −224.000 −0.0106912
$$761$$ −6863.18 −0.326925 −0.163463 0.986550i $$-0.552266\pi$$
−0.163463 + 0.986550i $$0.552266\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −4112.00 −0.194721
$$765$$ 0 0
$$766$$ −2008.18 −0.0947240
$$767$$ −22104.0 −1.04059
$$768$$ 0 0
$$769$$ −9058.04 −0.424761 −0.212380 0.977187i $$-0.568122\pi$$
−0.212380 + 0.977187i $$0.568122\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 18368.0 0.856320
$$773$$ 132.936 0.00618548 0.00309274 0.999995i $$-0.499016\pi$$
0.00309274 + 0.999995i $$0.499016\pi$$
$$774$$ 0 0
$$775$$ −24921.3 −1.15509
$$776$$ 11868.1 0.549020
$$777$$ 0 0
$$778$$ −10420.0 −0.480174
$$779$$ −178.000 −0.00818679
$$780$$ 0 0
$$781$$ −8232.00 −0.377163
$$782$$ 395.980 0.0181077
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −43792.0 −1.99109
$$786$$ 0 0
$$787$$ −8729.94 −0.395411 −0.197706 0.980261i $$-0.563349\pi$$
−0.197706 + 0.980261i $$0.563349\pi$$
$$788$$ −3176.00 −0.143579
$$789$$ 0 0
$$790$$ 48309.5 2.17567
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 720.000 0.0322421
$$794$$ −147.078 −0.00657382
$$795$$ 0 0
$$796$$ 9944.75 0.442817
$$797$$ −7517.96 −0.334128 −0.167064 0.985946i $$-0.553429\pi$$
−0.167064 + 0.985946i $$0.553429\pi$$
$$798$$ 0 0
$$799$$ 740.000 0.0327651
$$800$$ 8544.00 0.377595
$$801$$ 0 0
$$802$$ 996.000 0.0438528
$$803$$ −3781.61 −0.166189
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −9504.00 −0.415340
$$807$$ 0 0
$$808$$ −9028.34 −0.393089
$$809$$ −3776.00 −0.164100 −0.0820501 0.996628i $$-0.526147\pi$$
−0.0820501 + 0.996628i $$0.526147\pi$$
$$810$$ 0 0
$$811$$ −36227.9 −1.56860 −0.784300 0.620382i $$-0.786977\pi$$
−0.784300 + 0.620382i $$0.786977\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ −1064.00 −0.0458147
$$815$$ 65059.5 2.79624
$$816$$ 0 0
$$817$$ 48.0833 0.00205902
$$818$$ 6711.86 0.286888
$$819$$ 0 0
$$820$$ 9968.00 0.424509
$$821$$ 16410.0 0.697580 0.348790 0.937201i $$-0.386593\pi$$
0.348790 + 0.937201i $$0.386593\pi$$
$$822$$ 0 0
$$823$$ 22072.0 0.934850 0.467425 0.884033i $$-0.345182\pi$$
0.467425 + 0.884033i $$0.345182\pi$$
$$824$$ −6946.62 −0.293686
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 11628.0 0.488930 0.244465 0.969658i $$-0.421388\pi$$
0.244465 + 0.969658i $$0.421388\pi$$
$$828$$ 0 0
$$829$$ −30906.2 −1.29483 −0.647417 0.762136i $$-0.724151\pi$$
−0.647417 + 0.762136i $$0.724151\pi$$
$$830$$ −16744.0 −0.700232
$$831$$ 0 0
$$832$$ 3258.35 0.135773
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 29512.0 1.22312
$$836$$ −79.1960 −0.00327638
$$837$$ 0 0
$$838$$ −29090.4 −1.19918
$$839$$ −17884.1 −0.735911 −0.367955 0.929843i $$-0.619942\pi$$
−0.367955 + 0.929843i $$0.619942\pi$$
$$840$$ 0 0
$$841$$ 57407.0 2.35381
$$842$$ 21708.0 0.888488
$$843$$ 0 0
$$844$$ −10992.0 −0.448294
$$845$$ 7820.60 0.318387
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 1184.00 0.0479466
$$849$$ 0 0
$$850$$ −755.190 −0.0304739
$$851$$ 5320.00 0.214298
$$852$$ 0 0
$$853$$ −20755.0 −0.833104 −0.416552 0.909112i $$-0.636762\pi$$
−0.416552 + 0.909112i $$0.636762\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 13472.0 0.537925
$$857$$ −44919.7 −1.79046 −0.895231 0.445602i $$-0.852990\pi$$
−0.895231 + 0.445602i $$0.852990\pi$$
$$858$$ 0 0
$$859$$ 69.2965 0.00275246 0.00137623 0.999999i $$-0.499562\pi$$
0.00137623 + 0.999999i $$0.499562\pi$$
$$860$$ −2692.66 −0.106766
$$861$$ 0 0
$$862$$ 10728.0 0.423895
$$863$$ 5452.00 0.215050 0.107525 0.994202i $$-0.465707\pi$$
0.107525 + 0.994202i $$0.465707\pi$$
$$864$$ 0 0
$$865$$ 40992.0 1.61129
$$866$$ −12974.0 −0.509093
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 17080.0 0.666743
$$870$$ 0 0
$$871$$ 34823.6 1.35471
$$872$$ −6544.00 −0.254137
$$873$$ 0 0
$$874$$ 395.980 0.0153252
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 31106.0 1.19769 0.598845 0.800865i $$-0.295626\pi$$
0.598845 + 0.800865i $$0.295626\pi$$
$$878$$ 27865.7 1.07109
$$879$$ 0 0
$$880$$ 4434.97 0.169890
$$881$$ −5943.94 −0.227306 −0.113653 0.993521i $$-0.536255\pi$$
−0.113653 + 0.993521i $$0.536255\pi$$
$$882$$ 0 0
$$883$$ 34796.0 1.32614 0.663068 0.748559i $$-0.269254\pi$$
0.663068 + 0.748559i $$0.269254\pi$$
$$884$$ −288.000 −0.0109576
$$885$$ 0 0
$$886$$ −11992.0 −0.454717
$$887$$ −9964.55 −0.377200 −0.188600 0.982054i $$-0.560395\pi$$
−0.188600 + 0.982054i $$0.560395\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ −24472.0 −0.921689
$$891$$ 0 0
$$892$$ −13712.2 −0.514707
$$893$$ 740.000 0.0277303
$$894$$ 0 0
$$895$$ −10691.5 −0.399303
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −5244.00 −0.194871
$$899$$ −26694.7 −0.990343
$$900$$ 0 0
$$901$$ −104.652 −0.00386954
$$902$$ 3524.22 0.130093
$$903$$ 0 0
$$904$$ 4320.00 0.158939
$$905$$ 74928.0 2.75214
$$906$$ 0 0
$$907$$ −29756.0 −1.08934 −0.544670 0.838650i $$-0.683345\pi$$
−0.544670 + 0.838650i $$0.683345\pi$$
$$908$$ −21162.3 −0.773453
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −21440.0 −0.779735 −0.389868 0.920871i $$-0.627479\pi$$
−0.389868 + 0.920871i $$0.627479\pi$$
$$912$$ 0 0
$$913$$ −5919.90 −0.214589
$$914$$ 22416.0 0.811220
$$915$$ 0 0
$$916$$ −10996.9 −0.396669
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −8288.00 −0.297493 −0.148746 0.988875i $$-0.547524\pi$$
−0.148746 + 0.988875i $$0.547524\pi$$
$$920$$ −22174.9 −0.794656
$$921$$ 0 0
$$922$$ −19572.7 −0.699125
$$923$$ −29936.1 −1.06756
$$924$$ 0 0
$$925$$ −10146.0 −0.360647
$$926$$ 7904.00 0.280498
$$927$$ 0 0
$$928$$ 9152.00 0.323738
$$929$$ 45581.5 1.60978 0.804888 0.593427i $$-0.202226\pi$$
0.804888 + 0.593427i $$0.202226\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −288.000 −0.0101221
$$933$$ 0 0
$$934$$ −35013.1 −1.22662
$$935$$ −392.000 −0.0137110
$$936$$ 0 0
$$937$$ 11665.8 0.406731 0.203365 0.979103i $$-0.434812\pi$$
0.203365 + 0.979103i $$0.434812\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ −41440.0 −1.43790
$$941$$ −14.1421 −0.000489926 0 −0.000244963 1.00000i $$-0.500078\pi$$
−0.000244963 1.00000i $$0.500078\pi$$
$$942$$ 0 0
$$943$$ −17621.1 −0.608507
$$944$$ −6946.62 −0.239505
$$945$$ 0 0
$$946$$ −952.000 −0.0327190
$$947$$ −14034.0 −0.481567 −0.240783 0.970579i $$-0.577404\pi$$
−0.240783 + 0.970579i $$0.577404\pi$$
$$948$$ 0 0
$$949$$ −13752.0 −0.470399
$$950$$ −755.190 −0.0257912
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 42698.0 1.45134 0.725668 0.688045i $$-0.241531\pi$$
0.725668 + 0.688045i $$0.241531\pi$$
$$954$$ 0 0
$$955$$ −20353.4 −0.689654
$$956$$ −17232.0 −0.582974
$$957$$ 0 0
$$958$$ −4576.40 −0.154339
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −21079.0 −0.707563
$$962$$ −3869.29 −0.129679
$$963$$ 0 0
$$964$$ −6160.31 −0.205820
$$965$$ 90917.0 3.03287
$$966$$ 0 0
$$967$$ −48492.0 −1.61261 −0.806307 0.591497i $$-0.798537\pi$$
−0.806307 + 0.591497i $$0.798537\pi$$
$$968$$ −9080.00 −0.301490
$$969$$ 0 0
$$970$$ 58744.0 1.94449
$$971$$ −52669.6 −1.74073 −0.870364 0.492409i $$-0.836116\pi$$
−0.870364 + 0.492409i $$0.836116\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 1944.00 0.0639525
$$975$$ 0 0
$$976$$ 226.274 0.00742096
$$977$$ 55380.0 1.81347 0.906737 0.421698i $$-0.138566\pi$$
0.906737 + 0.421698i $$0.138566\pi$$
$$978$$ 0 0
$$979$$ −8652.16 −0.282456
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 14808.0 0.481204
$$983$$ 50535.5 1.63971 0.819854 0.572573i $$-0.194055\pi$$
0.819854 + 0.572573i $$0.194055\pi$$
$$984$$ 0 0
$$985$$ −15720.4 −0.508521
$$986$$ −808.930 −0.0261274
$$987$$ 0 0
$$988$$ −288.000 −0.00927379
$$989$$ 4760.00 0.153043
$$990$$ 0 0
$$991$$ −39712.0 −1.27295 −0.636475 0.771297i $$-0.719608\pi$$
−0.636475 + 0.771297i $$0.719608\pi$$
$$992$$ −2986.82 −0.0955964
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 49224.0 1.56835
$$996$$ 0 0
$$997$$ 2186.37 0.0694515 0.0347258 0.999397i $$-0.488944\pi$$
0.0347258 + 0.999397i $$0.488944\pi$$
$$998$$ −24488.0 −0.776708
$$999$$ 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 882.4.a.bg.1.2 2
3.2 odd 2 98.4.a.g.1.1 2
7.2 even 3 882.4.g.ba.361.1 4
7.3 odd 6 882.4.g.ba.667.2 4
7.4 even 3 882.4.g.ba.667.1 4
7.5 odd 6 882.4.g.ba.361.2 4
7.6 odd 2 inner 882.4.a.bg.1.1 2
12.11 even 2 784.4.a.y.1.2 2
15.14 odd 2 2450.4.a.bx.1.2 2
21.2 odd 6 98.4.c.h.67.2 4
21.5 even 6 98.4.c.h.67.1 4
21.11 odd 6 98.4.c.h.79.2 4
21.17 even 6 98.4.c.h.79.1 4
21.20 even 2 98.4.a.g.1.2 yes 2
84.83 odd 2 784.4.a.y.1.1 2
105.104 even 2 2450.4.a.bx.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
98.4.a.g.1.1 2 3.2 odd 2
98.4.a.g.1.2 yes 2 21.20 even 2
98.4.c.h.67.1 4 21.5 even 6
98.4.c.h.67.2 4 21.2 odd 6
98.4.c.h.79.1 4 21.17 even 6
98.4.c.h.79.2 4 21.11 odd 6
784.4.a.y.1.1 2 84.83 odd 2
784.4.a.y.1.2 2 12.11 even 2
882.4.a.bg.1.1 2 7.6 odd 2 inner
882.4.a.bg.1.2 2 1.1 even 1 trivial
882.4.g.ba.361.1 4 7.2 even 3
882.4.g.ba.361.2 4 7.5 odd 6
882.4.g.ba.667.1 4 7.4 even 3
882.4.g.ba.667.2 4 7.3 odd 6
2450.4.a.bx.1.1 2 105.104 even 2
2450.4.a.bx.1.2 2 15.14 odd 2