# Properties

 Label 1764.4.a.c.1.1 Level $1764$ Weight $4$ Character 1764.1 Self dual yes Analytic conductor $104.079$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1764.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$104.079369250$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 28) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1764.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-8.00000 q^{5} +O(q^{10})$$ $$q-8.00000 q^{5} +40.0000 q^{11} +12.0000 q^{13} -58.0000 q^{17} -26.0000 q^{19} +64.0000 q^{23} -61.0000 q^{25} +62.0000 q^{29} -252.000 q^{31} +26.0000 q^{37} +6.00000 q^{41} +416.000 q^{43} -396.000 q^{47} +450.000 q^{53} -320.000 q^{55} +274.000 q^{59} +576.000 q^{61} -96.0000 q^{65} -476.000 q^{67} +448.000 q^{71} +158.000 q^{73} -936.000 q^{79} +530.000 q^{83} +464.000 q^{85} -390.000 q^{89} +208.000 q^{95} -214.000 q^{97} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −8.00000 −0.715542 −0.357771 0.933809i $$-0.616463\pi$$
−0.357771 + 0.933809i $$0.616463\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 40.0000 1.09640 0.548202 0.836346i $$-0.315312\pi$$
0.548202 + 0.836346i $$0.315312\pi$$
$$12$$ 0 0
$$13$$ 12.0000 0.256015 0.128008 0.991773i $$-0.459142\pi$$
0.128008 + 0.991773i $$0.459142\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −58.0000 −0.827474 −0.413737 0.910396i $$-0.635777\pi$$
−0.413737 + 0.910396i $$0.635777\pi$$
$$18$$ 0 0
$$19$$ −26.0000 −0.313937 −0.156969 0.987604i $$-0.550172\pi$$
−0.156969 + 0.987604i $$0.550172\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 64.0000 0.580214 0.290107 0.956994i $$-0.406309\pi$$
0.290107 + 0.956994i $$0.406309\pi$$
$$24$$ 0 0
$$25$$ −61.0000 −0.488000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 62.0000 0.397004 0.198502 0.980101i $$-0.436392\pi$$
0.198502 + 0.980101i $$0.436392\pi$$
$$30$$ 0 0
$$31$$ −252.000 −1.46002 −0.730009 0.683438i $$-0.760484\pi$$
−0.730009 + 0.683438i $$0.760484\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 26.0000 0.115524 0.0577618 0.998330i $$-0.481604\pi$$
0.0577618 + 0.998330i $$0.481604\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.00000 0.0228547 0.0114273 0.999935i $$-0.496362\pi$$
0.0114273 + 0.999935i $$0.496362\pi$$
$$42$$ 0 0
$$43$$ 416.000 1.47534 0.737668 0.675164i $$-0.235927\pi$$
0.737668 + 0.675164i $$0.235927\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −396.000 −1.22899 −0.614495 0.788921i $$-0.710640\pi$$
−0.614495 + 0.788921i $$0.710640\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 450.000 1.16627 0.583134 0.812376i $$-0.301826\pi$$
0.583134 + 0.812376i $$0.301826\pi$$
$$54$$ 0 0
$$55$$ −320.000 −0.784523
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 274.000 0.604606 0.302303 0.953212i $$-0.402245\pi$$
0.302303 + 0.953212i $$0.402245\pi$$
$$60$$ 0 0
$$61$$ 576.000 1.20900 0.604502 0.796604i $$-0.293372\pi$$
0.604502 + 0.796604i $$0.293372\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −96.0000 −0.183190
$$66$$ 0 0
$$67$$ −476.000 −0.867950 −0.433975 0.900925i $$-0.642889\pi$$
−0.433975 + 0.900925i $$0.642889\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 448.000 0.748843 0.374421 0.927259i $$-0.377841\pi$$
0.374421 + 0.927259i $$0.377841\pi$$
$$72$$ 0 0
$$73$$ 158.000 0.253322 0.126661 0.991946i $$-0.459574\pi$$
0.126661 + 0.991946i $$0.459574\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −936.000 −1.33302 −0.666508 0.745498i $$-0.732212\pi$$
−0.666508 + 0.745498i $$0.732212\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 530.000 0.700904 0.350452 0.936581i $$-0.386028\pi$$
0.350452 + 0.936581i $$0.386028\pi$$
$$84$$ 0 0
$$85$$ 464.000 0.592093
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −390.000 −0.464493 −0.232247 0.972657i $$-0.574608\pi$$
−0.232247 + 0.972657i $$0.574608\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 208.000 0.224635
$$96$$ 0 0
$$97$$ −214.000 −0.224004 −0.112002 0.993708i $$-0.535726\pi$$
−0.112002 + 0.993708i $$0.535726\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1432.00 1.41079 0.705393 0.708817i $$-0.250771\pi$$
0.705393 + 0.708817i $$0.250771\pi$$
$$102$$ 0 0
$$103$$ −764.000 −0.730866 −0.365433 0.930838i $$-0.619079\pi$$
−0.365433 + 0.930838i $$0.619079\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −324.000 −0.292731 −0.146366 0.989231i $$-0.546758\pi$$
−0.146366 + 0.989231i $$0.546758\pi$$
$$108$$ 0 0
$$109$$ −1334.00 −1.17224 −0.586119 0.810225i $$-0.699345\pi$$
−0.586119 + 0.810225i $$0.699345\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1798.00 −1.49683 −0.748414 0.663232i $$-0.769184\pi$$
−0.748414 + 0.663232i $$0.769184\pi$$
$$114$$ 0 0
$$115$$ −512.000 −0.415167
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 269.000 0.202104
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1488.00 1.06473
$$126$$ 0 0
$$127$$ −384.000 −0.268303 −0.134152 0.990961i $$-0.542831\pi$$
−0.134152 + 0.990961i $$0.542831\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1814.00 −1.20985 −0.604923 0.796284i $$-0.706796\pi$$
−0.604923 + 0.796284i $$0.706796\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1666.00 −1.03895 −0.519474 0.854486i $$-0.673872\pi$$
−0.519474 + 0.854486i $$0.673872\pi$$
$$138$$ 0 0
$$139$$ −1126.00 −0.687094 −0.343547 0.939135i $$-0.611628\pi$$
−0.343547 + 0.939135i $$0.611628\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 480.000 0.280697
$$144$$ 0 0
$$145$$ −496.000 −0.284073
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2694.00 −1.48122 −0.740608 0.671938i $$-0.765462\pi$$
−0.740608 + 0.671938i $$0.765462\pi$$
$$150$$ 0 0
$$151$$ −2648.00 −1.42709 −0.713547 0.700607i $$-0.752912\pi$$
−0.713547 + 0.700607i $$0.752912\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 2016.00 1.04470
$$156$$ 0 0
$$157$$ 556.000 0.282635 0.141317 0.989964i $$-0.454866\pi$$
0.141317 + 0.989964i $$0.454866\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −328.000 −0.157613 −0.0788066 0.996890i $$-0.525111\pi$$
−0.0788066 + 0.996890i $$0.525111\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −4268.00 −1.97765 −0.988826 0.149077i $$-0.952370\pi$$
−0.988826 + 0.149077i $$0.952370\pi$$
$$168$$ 0 0
$$169$$ −2053.00 −0.934456
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −3476.00 −1.52760 −0.763802 0.645451i $$-0.776669\pi$$
−0.763802 + 0.645451i $$0.776669\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −2268.00 −0.947029 −0.473515 0.880786i $$-0.657015\pi$$
−0.473515 + 0.880786i $$0.657015\pi$$
$$180$$ 0 0
$$181$$ 276.000 0.113342 0.0566710 0.998393i $$-0.481951\pi$$
0.0566710 + 0.998393i $$0.481951\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −208.000 −0.0826620
$$186$$ 0 0
$$187$$ −2320.00 −0.907247
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3000.00 1.13650 0.568252 0.822854i $$-0.307620\pi$$
0.568252 + 0.822854i $$0.307620\pi$$
$$192$$ 0 0
$$193$$ 3278.00 1.22257 0.611284 0.791411i $$-0.290653\pi$$
0.611284 + 0.791411i $$0.290653\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2362.00 0.854241 0.427121 0.904195i $$-0.359528\pi$$
0.427121 + 0.904195i $$0.359528\pi$$
$$198$$ 0 0
$$199$$ 1036.00 0.369046 0.184523 0.982828i $$-0.440926\pi$$
0.184523 + 0.982828i $$0.440926\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −48.0000 −0.0163535
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −1040.00 −0.344202
$$210$$ 0 0
$$211$$ 3524.00 1.14977 0.574887 0.818233i $$-0.305046\pi$$
0.574887 + 0.818233i $$0.305046\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −3328.00 −1.05566
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −696.000 −0.211846
$$222$$ 0 0
$$223$$ 1336.00 0.401189 0.200595 0.979674i $$-0.435713\pi$$
0.200595 + 0.979674i $$0.435713\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1290.00 0.377182 0.188591 0.982056i $$-0.439608\pi$$
0.188591 + 0.982056i $$0.439608\pi$$
$$228$$ 0 0
$$229$$ −5524.00 −1.59404 −0.797022 0.603950i $$-0.793593\pi$$
−0.797022 + 0.603950i $$0.793593\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6314.00 −1.77530 −0.887648 0.460523i $$-0.847662\pi$$
−0.887648 + 0.460523i $$0.847662\pi$$
$$234$$ 0 0
$$235$$ 3168.00 0.879394
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3960.00 1.07176 0.535881 0.844294i $$-0.319980\pi$$
0.535881 + 0.844294i $$0.319980\pi$$
$$240$$ 0 0
$$241$$ 7018.00 1.87581 0.937903 0.346898i $$-0.112765\pi$$
0.937903 + 0.346898i $$0.112765\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −312.000 −0.0803728
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −2394.00 −0.602024 −0.301012 0.953620i $$-0.597324\pi$$
−0.301012 + 0.953620i $$0.597324\pi$$
$$252$$ 0 0
$$253$$ 2560.00 0.636149
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −2766.00 −0.671355 −0.335678 0.941977i $$-0.608965\pi$$
−0.335678 + 0.941977i $$0.608965\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −7968.00 −1.86817 −0.934084 0.357055i $$-0.883781\pi$$
−0.934084 + 0.357055i $$0.883781\pi$$
$$264$$ 0 0
$$265$$ −3600.00 −0.834514
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −2900.00 −0.657309 −0.328654 0.944450i $$-0.606595\pi$$
−0.328654 + 0.944450i $$0.606595\pi$$
$$270$$ 0 0
$$271$$ −2640.00 −0.591766 −0.295883 0.955224i $$-0.595614\pi$$
−0.295883 + 0.955224i $$0.595614\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −2440.00 −0.535046
$$276$$ 0 0
$$277$$ −1522.00 −0.330138 −0.165069 0.986282i $$-0.552785\pi$$
−0.165069 + 0.986282i $$0.552785\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 4534.00 0.962547 0.481274 0.876570i $$-0.340174\pi$$
0.481274 + 0.876570i $$0.340174\pi$$
$$282$$ 0 0
$$283$$ −4834.00 −1.01538 −0.507688 0.861541i $$-0.669500\pi$$
−0.507688 + 0.861541i $$0.669500\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1549.00 −0.315286
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −4656.00 −0.928350 −0.464175 0.885744i $$-0.653649\pi$$
−0.464175 + 0.885744i $$0.653649\pi$$
$$294$$ 0 0
$$295$$ −2192.00 −0.432621
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 768.000 0.148544
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −4608.00 −0.865093
$$306$$ 0 0
$$307$$ 7238.00 1.34558 0.672792 0.739831i $$-0.265095\pi$$
0.672792 + 0.739831i $$0.265095\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1096.00 0.199834 0.0999171 0.994996i $$-0.468142\pi$$
0.0999171 + 0.994996i $$0.468142\pi$$
$$312$$ 0 0
$$313$$ 3818.00 0.689476 0.344738 0.938699i $$-0.387968\pi$$
0.344738 + 0.938699i $$0.387968\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1998.00 −0.354003 −0.177001 0.984211i $$-0.556640\pi$$
−0.177001 + 0.984211i $$0.556640\pi$$
$$318$$ 0 0
$$319$$ 2480.00 0.435277
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 1508.00 0.259775
$$324$$ 0 0
$$325$$ −732.000 −0.124936
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −7936.00 −1.31783 −0.658915 0.752217i $$-0.728984\pi$$
−0.658915 + 0.752217i $$0.728984\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 3808.00 0.621055
$$336$$ 0 0
$$337$$ 2766.00 0.447103 0.223551 0.974692i $$-0.428235\pi$$
0.223551 + 0.974692i $$0.428235\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −10080.0 −1.60077
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −8352.00 −1.29210 −0.646050 0.763295i $$-0.723580\pi$$
−0.646050 + 0.763295i $$0.723580\pi$$
$$348$$ 0 0
$$349$$ 5924.00 0.908609 0.454304 0.890847i $$-0.349888\pi$$
0.454304 + 0.890847i $$0.349888\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2226.00 0.335632 0.167816 0.985818i $$-0.446329\pi$$
0.167816 + 0.985818i $$0.446329\pi$$
$$354$$ 0 0
$$355$$ −3584.00 −0.535828
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −3880.00 −0.570414 −0.285207 0.958466i $$-0.592062\pi$$
−0.285207 + 0.958466i $$0.592062\pi$$
$$360$$ 0 0
$$361$$ −6183.00 −0.901443
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1264.00 −0.181262
$$366$$ 0 0
$$367$$ 2584.00 0.367531 0.183765 0.982970i $$-0.441171\pi$$
0.183765 + 0.982970i $$0.441171\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 10534.0 1.46228 0.731139 0.682228i $$-0.238989\pi$$
0.731139 + 0.682228i $$0.238989\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 744.000 0.101639
$$378$$ 0 0
$$379$$ −4472.00 −0.606098 −0.303049 0.952975i $$-0.598005\pi$$
−0.303049 + 0.952975i $$0.598005\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 2468.00 0.329266 0.164633 0.986355i $$-0.447356\pi$$
0.164633 + 0.986355i $$0.447356\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 1046.00 0.136335 0.0681675 0.997674i $$-0.478285\pi$$
0.0681675 + 0.997674i $$0.478285\pi$$
$$390$$ 0 0
$$391$$ −3712.00 −0.480112
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 7488.00 0.953828
$$396$$ 0 0
$$397$$ −2124.00 −0.268515 −0.134258 0.990946i $$-0.542865\pi$$
−0.134258 + 0.990946i $$0.542865\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −11598.0 −1.44433 −0.722165 0.691721i $$-0.756853\pi$$
−0.722165 + 0.691721i $$0.756853\pi$$
$$402$$ 0 0
$$403$$ −3024.00 −0.373787
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1040.00 0.126661
$$408$$ 0 0
$$409$$ 2770.00 0.334884 0.167442 0.985882i $$-0.446449\pi$$
0.167442 + 0.985882i $$0.446449\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −4240.00 −0.501526
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 9438.00 1.10042 0.550211 0.835026i $$-0.314547\pi$$
0.550211 + 0.835026i $$0.314547\pi$$
$$420$$ 0 0
$$421$$ 5550.00 0.642495 0.321248 0.946995i $$-0.395898\pi$$
0.321248 + 0.946995i $$0.395898\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 3538.00 0.403808
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 3000.00 0.335278 0.167639 0.985848i $$-0.446386\pi$$
0.167639 + 0.985848i $$0.446386\pi$$
$$432$$ 0 0
$$433$$ −12926.0 −1.43460 −0.717302 0.696762i $$-0.754623\pi$$
−0.717302 + 0.696762i $$0.754623\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −1664.00 −0.182151
$$438$$ 0 0
$$439$$ 408.000 0.0443571 0.0221786 0.999754i $$-0.492940\pi$$
0.0221786 + 0.999754i $$0.492940\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 14452.0 1.54997 0.774983 0.631982i $$-0.217758\pi$$
0.774983 + 0.631982i $$0.217758\pi$$
$$444$$ 0 0
$$445$$ 3120.00 0.332364
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −10258.0 −1.07818 −0.539092 0.842247i $$-0.681233\pi$$
−0.539092 + 0.842247i $$0.681233\pi$$
$$450$$ 0 0
$$451$$ 240.000 0.0250580
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5498.00 −0.562769 −0.281385 0.959595i $$-0.590794\pi$$
−0.281385 + 0.959595i $$0.590794\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −16316.0 −1.64840 −0.824199 0.566300i $$-0.808375\pi$$
−0.824199 + 0.566300i $$0.808375\pi$$
$$462$$ 0 0
$$463$$ 8944.00 0.897760 0.448880 0.893592i $$-0.351823\pi$$
0.448880 + 0.893592i $$0.351823\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −9422.00 −0.933615 −0.466807 0.884359i $$-0.654596\pi$$
−0.466807 + 0.884359i $$0.654596\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 16640.0 1.61756
$$474$$ 0 0
$$475$$ 1586.00 0.153201
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 13820.0 1.31827 0.659136 0.752024i $$-0.270922\pi$$
0.659136 + 0.752024i $$0.270922\pi$$
$$480$$ 0 0
$$481$$ 312.000 0.0295758
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 1712.00 0.160284
$$486$$ 0 0
$$487$$ −13264.0 −1.23419 −0.617094 0.786890i $$-0.711690\pi$$
−0.617094 + 0.786890i $$0.711690\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 5940.00 0.545964 0.272982 0.962019i $$-0.411990\pi$$
0.272982 + 0.962019i $$0.411990\pi$$
$$492$$ 0 0
$$493$$ −3596.00 −0.328511
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −8252.00 −0.740301 −0.370151 0.928972i $$-0.620694\pi$$
−0.370151 + 0.928972i $$0.620694\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4704.00 0.416980 0.208490 0.978024i $$-0.433145\pi$$
0.208490 + 0.978024i $$0.433145\pi$$
$$504$$ 0 0
$$505$$ −11456.0 −1.00948
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −10788.0 −0.939430 −0.469715 0.882818i $$-0.655643\pi$$
−0.469715 + 0.882818i $$0.655643\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 6112.00 0.522965
$$516$$ 0 0
$$517$$ −15840.0 −1.34747
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −14586.0 −1.22653 −0.613267 0.789876i $$-0.710145\pi$$
−0.613267 + 0.789876i $$0.710145\pi$$
$$522$$ 0 0
$$523$$ −26.0000 −0.00217381 −0.00108690 0.999999i $$-0.500346\pi$$
−0.00108690 + 0.999999i $$0.500346\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 14616.0 1.20813
$$528$$ 0 0
$$529$$ −8071.00 −0.663352
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 72.0000 0.00585116
$$534$$ 0 0
$$535$$ 2592.00 0.209462
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 11214.0 0.891178 0.445589 0.895238i $$-0.352994\pi$$
0.445589 + 0.895238i $$0.352994\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 10672.0 0.838786
$$546$$ 0 0
$$547$$ −5424.00 −0.423973 −0.211987 0.977273i $$-0.567993\pi$$
−0.211987 + 0.977273i $$0.567993\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1612.00 −0.124634
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 17618.0 1.34021 0.670106 0.742265i $$-0.266248\pi$$
0.670106 + 0.742265i $$0.266248\pi$$
$$558$$ 0 0
$$559$$ 4992.00 0.377709
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −3562.00 −0.266644 −0.133322 0.991073i $$-0.542564\pi$$
−0.133322 + 0.991073i $$0.542564\pi$$
$$564$$ 0 0
$$565$$ 14384.0 1.07104
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −2838.00 −0.209095 −0.104548 0.994520i $$-0.533339\pi$$
−0.104548 + 0.994520i $$0.533339\pi$$
$$570$$ 0 0
$$571$$ −360.000 −0.0263845 −0.0131922 0.999913i $$-0.504199\pi$$
−0.0131922 + 0.999913i $$0.504199\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −3904.00 −0.283144
$$576$$ 0 0
$$577$$ −22018.0 −1.58860 −0.794299 0.607527i $$-0.792162\pi$$
−0.794299 + 0.607527i $$0.792162\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 18000.0 1.27870
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 1454.00 0.102237 0.0511184 0.998693i $$-0.483721\pi$$
0.0511184 + 0.998693i $$0.483721\pi$$
$$588$$ 0 0
$$589$$ 6552.00 0.458354
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 13818.0 0.956892 0.478446 0.878117i $$-0.341200\pi$$
0.478446 + 0.878117i $$0.341200\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −6696.00 −0.456746 −0.228373 0.973574i $$-0.573341\pi$$
−0.228373 + 0.973574i $$0.573341\pi$$
$$600$$ 0 0
$$601$$ −10010.0 −0.679395 −0.339698 0.940535i $$-0.610325\pi$$
−0.339698 + 0.940535i $$0.610325\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −2152.00 −0.144614
$$606$$ 0 0
$$607$$ −2880.00 −0.192579 −0.0962896 0.995353i $$-0.530697\pi$$
−0.0962896 + 0.995353i $$0.530697\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −4752.00 −0.314640
$$612$$ 0 0
$$613$$ 6522.00 0.429724 0.214862 0.976644i $$-0.431070\pi$$
0.214862 + 0.976644i $$0.431070\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −6614.00 −0.431555 −0.215778 0.976443i $$-0.569229\pi$$
−0.215778 + 0.976443i $$0.569229\pi$$
$$618$$ 0 0
$$619$$ −5266.00 −0.341936 −0.170968 0.985277i $$-0.554689\pi$$
−0.170968 + 0.985277i $$0.554689\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −4279.00 −0.273856
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −1508.00 −0.0955928
$$630$$ 0 0
$$631$$ 3344.00 0.210971 0.105485 0.994421i $$-0.466360\pi$$
0.105485 + 0.994421i $$0.466360\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 3072.00 0.191982
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 4882.00 0.300823 0.150411 0.988623i $$-0.451940\pi$$
0.150411 + 0.988623i $$0.451940\pi$$
$$642$$ 0 0
$$643$$ 15898.0 0.975048 0.487524 0.873110i $$-0.337900\pi$$
0.487524 + 0.873110i $$0.337900\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 6132.00 0.372602 0.186301 0.982493i $$-0.440350\pi$$
0.186301 + 0.982493i $$0.440350\pi$$
$$648$$ 0 0
$$649$$ 10960.0 0.662893
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 24198.0 1.45014 0.725070 0.688676i $$-0.241808\pi$$
0.725070 + 0.688676i $$0.241808\pi$$
$$654$$ 0 0
$$655$$ 14512.0 0.865696
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −17456.0 −1.03185 −0.515925 0.856634i $$-0.672552\pi$$
−0.515925 + 0.856634i $$0.672552\pi$$
$$660$$ 0 0
$$661$$ 656.000 0.0386013 0.0193006 0.999814i $$-0.493856\pi$$
0.0193006 + 0.999814i $$0.493856\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 3968.00 0.230347
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 23040.0 1.32556
$$672$$ 0 0
$$673$$ −18214.0 −1.04324 −0.521618 0.853179i $$-0.674671\pi$$
−0.521618 + 0.853179i $$0.674671\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 30252.0 1.71740 0.858699 0.512480i $$-0.171273\pi$$
0.858699 + 0.512480i $$0.171273\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 10836.0 0.607069 0.303534 0.952820i $$-0.401833\pi$$
0.303534 + 0.952820i $$0.401833\pi$$
$$684$$ 0 0
$$685$$ 13328.0 0.743411
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 5400.00 0.298583
$$690$$ 0 0
$$691$$ −9578.00 −0.527300 −0.263650 0.964618i $$-0.584926\pi$$
−0.263650 + 0.964618i $$0.584926\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 9008.00 0.491644
$$696$$ 0 0
$$697$$ −348.000 −0.0189117
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −12442.0 −0.670368 −0.335184 0.942153i $$-0.608798\pi$$
−0.335184 + 0.942153i $$0.608798\pi$$
$$702$$ 0 0
$$703$$ −676.000 −0.0362672
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −25174.0 −1.33347 −0.666734 0.745295i $$-0.732308\pi$$
−0.666734 + 0.745295i $$0.732308\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −16128.0 −0.847123
$$714$$ 0 0
$$715$$ −3840.00 −0.200850
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 34188.0 1.77329 0.886646 0.462448i $$-0.153029\pi$$
0.886646 + 0.462448i $$0.153029\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −3782.00 −0.193738
$$726$$ 0 0
$$727$$ 5204.00 0.265482 0.132741 0.991151i $$-0.457622\pi$$
0.132741 + 0.991151i $$0.457622\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −24128.0 −1.22080
$$732$$ 0 0
$$733$$ 32880.0 1.65682 0.828411 0.560121i $$-0.189245\pi$$
0.828411 + 0.560121i $$0.189245\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −19040.0 −0.951625
$$738$$ 0 0
$$739$$ −3912.00 −0.194730 −0.0973648 0.995249i $$-0.531041\pi$$
−0.0973648 + 0.995249i $$0.531041\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 16008.0 0.790413 0.395206 0.918592i $$-0.370673\pi$$
0.395206 + 0.918592i $$0.370673\pi$$
$$744$$ 0 0
$$745$$ 21552.0 1.05987
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 9960.00 0.483949 0.241974 0.970283i $$-0.422205\pi$$
0.241974 + 0.970283i $$0.422205\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 21184.0 1.02115
$$756$$ 0 0
$$757$$ 12378.0 0.594301 0.297151 0.954831i $$-0.403964\pi$$
0.297151 + 0.954831i $$0.403964\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 34670.0 1.65149 0.825747 0.564041i $$-0.190754\pi$$
0.825747 + 0.564041i $$0.190754\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 3288.00 0.154789
$$768$$ 0 0
$$769$$ 10898.0 0.511043 0.255521 0.966803i $$-0.417753\pi$$
0.255521 + 0.966803i $$0.417753\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −25808.0 −1.20084 −0.600420 0.799685i $$-0.705000\pi$$
−0.600420 + 0.799685i $$0.705000\pi$$
$$774$$ 0 0
$$775$$ 15372.0 0.712488
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −156.000 −0.00717494
$$780$$ 0 0
$$781$$ 17920.0 0.821035
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −4448.00 −0.202237
$$786$$ 0 0
$$787$$ 21054.0 0.953614 0.476807 0.879008i $$-0.341794\pi$$
0.476807 + 0.879008i $$0.341794\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 6912.00 0.309524
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −24276.0 −1.07892 −0.539461 0.842011i $$-0.681372\pi$$
−0.539461 + 0.842011i $$0.681372\pi$$
$$798$$ 0 0
$$799$$ 22968.0 1.01696
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 6320.00 0.277743
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −21526.0 −0.935493 −0.467747 0.883863i $$-0.654934\pi$$
−0.467747 + 0.883863i $$0.654934\pi$$
$$810$$ 0 0
$$811$$ 12806.0 0.554475 0.277238 0.960801i $$-0.410581\pi$$
0.277238 + 0.960801i $$0.410581\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 2624.00 0.112779
$$816$$ 0 0
$$817$$ −10816.0 −0.463163
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −13214.0 −0.561720 −0.280860 0.959749i $$-0.590620\pi$$
−0.280860 + 0.959749i $$0.590620\pi$$
$$822$$ 0 0
$$823$$ 32248.0 1.36585 0.682925 0.730488i $$-0.260708\pi$$
0.682925 + 0.730488i $$0.260708\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 14316.0 0.601954 0.300977 0.953631i $$-0.402687\pi$$
0.300977 + 0.953631i $$0.402687\pi$$
$$828$$ 0 0
$$829$$ −25168.0 −1.05443 −0.527214 0.849733i $$-0.676763\pi$$
−0.527214 + 0.849733i $$0.676763\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 34144.0 1.41509
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 9356.00 0.384988 0.192494 0.981298i $$-0.438342\pi$$
0.192494 + 0.981298i $$0.438342\pi$$
$$840$$ 0 0
$$841$$ −20545.0 −0.842388
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 16424.0 0.668642
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 1664.00 0.0670284
$$852$$ 0 0
$$853$$ −2372.00 −0.0952119 −0.0476059 0.998866i $$-0.515159\pi$$
−0.0476059 + 0.998866i $$0.515159\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 11694.0 0.466114 0.233057 0.972463i $$-0.425127\pi$$
0.233057 + 0.972463i $$0.425127\pi$$
$$858$$ 0 0
$$859$$ 20506.0 0.814500 0.407250 0.913317i $$-0.366488\pi$$
0.407250 + 0.913317i $$0.366488\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 28136.0 1.10980 0.554902 0.831916i $$-0.312756\pi$$
0.554902 + 0.831916i $$0.312756\pi$$
$$864$$ 0 0
$$865$$ 27808.0 1.09306
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −37440.0 −1.46152
$$870$$ 0 0
$$871$$ −5712.00 −0.222209
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −37070.0 −1.42733 −0.713663 0.700489i $$-0.752965\pi$$
−0.713663 + 0.700489i $$0.752965\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −6198.00 −0.237021 −0.118511 0.992953i $$-0.537812\pi$$
−0.118511 + 0.992953i $$0.537812\pi$$
$$882$$ 0 0
$$883$$ −31876.0 −1.21485 −0.607425 0.794377i $$-0.707798\pi$$
−0.607425 + 0.794377i $$0.707798\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −132.000 −0.00499676 −0.00249838 0.999997i $$-0.500795\pi$$
−0.00249838 + 0.999997i $$0.500795\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 10296.0 0.385826
$$894$$ 0 0
$$895$$ 18144.0 0.677639
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −15624.0 −0.579632
$$900$$ 0 0
$$901$$ −26100.0 −0.965058
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −2208.00 −0.0811010
$$906$$ 0 0
$$907$$ 38244.0 1.40008 0.700039 0.714104i $$-0.253166\pi$$
0.700039 + 0.714104i $$0.253166\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 7008.00 0.254869 0.127434 0.991847i $$-0.459326\pi$$
0.127434 + 0.991847i $$0.459326\pi$$
$$912$$ 0 0
$$913$$ 21200.0 0.768475
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 36664.0 1.31603 0.658016 0.753004i $$-0.271396\pi$$
0.658016 + 0.753004i $$0.271396\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 5376.00 0.191715
$$924$$ 0 0
$$925$$ −1586.00 −0.0563755
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 45510.0 1.60725 0.803625 0.595136i $$-0.202902\pi$$
0.803625 + 0.595136i $$0.202902\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 18560.0 0.649173
$$936$$ 0 0
$$937$$ 3838.00 0.133812 0.0669061 0.997759i $$-0.478687\pi$$
0.0669061 + 0.997759i $$0.478687\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −16832.0 −0.583111 −0.291556 0.956554i $$-0.594173\pi$$
−0.291556 + 0.956554i $$0.594173\pi$$
$$942$$ 0 0
$$943$$ 384.000 0.0132606
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 40928.0 1.40442 0.702208 0.711972i $$-0.252198\pi$$
0.702208 + 0.711972i $$0.252198\pi$$
$$948$$ 0 0
$$949$$ 1896.00 0.0648543
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 24070.0 0.818157 0.409079 0.912499i $$-0.365850\pi$$
0.409079 + 0.912499i $$0.365850\pi$$
$$954$$ 0 0
$$955$$ −24000.0 −0.813217
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33713.0 1.13165
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −26224.0 −0.874798
$$966$$ 0 0
$$967$$ −17152.0 −0.570394 −0.285197 0.958469i $$-0.592059\pi$$
−0.285197 + 0.958469i $$0.592059\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −32910.0 −1.08767 −0.543837 0.839191i $$-0.683029\pi$$
−0.543837 + 0.839191i $$0.683029\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 6822.00 0.223393 0.111697 0.993742i $$-0.464372\pi$$
0.111697 + 0.993742i $$0.464372\pi$$
$$978$$ 0 0
$$979$$ −15600.0 −0.509273
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −48420.0 −1.57107 −0.785533 0.618820i $$-0.787611\pi$$
−0.785533 + 0.618820i $$0.787611\pi$$
$$984$$ 0 0
$$985$$ −18896.0 −0.611245
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 26624.0 0.856010
$$990$$ 0 0
$$991$$ −49216.0 −1.57760 −0.788798 0.614652i $$-0.789296\pi$$
−0.788798 + 0.614652i $$0.789296\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −8288.00 −0.264068
$$996$$ 0 0
$$997$$ −35264.0 −1.12018 −0.560091 0.828431i $$-0.689234\pi$$
−0.560091 + 0.828431i $$0.689234\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1764.4.a.c.1.1 1
3.2 odd 2 196.4.a.d.1.1 1
7.2 even 3 1764.4.k.m.361.1 2
7.3 odd 6 1764.4.k.d.1549.1 2
7.4 even 3 1764.4.k.m.1549.1 2
7.5 odd 6 1764.4.k.d.361.1 2
7.6 odd 2 252.4.a.d.1.1 1
12.11 even 2 784.4.a.a.1.1 1
21.2 odd 6 196.4.e.a.165.1 2
21.5 even 6 196.4.e.f.165.1 2
21.11 odd 6 196.4.e.a.177.1 2
21.17 even 6 196.4.e.f.177.1 2
21.20 even 2 28.4.a.a.1.1 1
28.27 even 2 1008.4.a.o.1.1 1
84.83 odd 2 112.4.a.g.1.1 1
105.62 odd 4 700.4.e.a.449.2 2
105.83 odd 4 700.4.e.a.449.1 2
105.104 even 2 700.4.a.n.1.1 1
168.83 odd 2 448.4.a.a.1.1 1
168.125 even 2 448.4.a.p.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.a.a.1.1 1 21.20 even 2
112.4.a.g.1.1 1 84.83 odd 2
196.4.a.d.1.1 1 3.2 odd 2
196.4.e.a.165.1 2 21.2 odd 6
196.4.e.a.177.1 2 21.11 odd 6
196.4.e.f.165.1 2 21.5 even 6
196.4.e.f.177.1 2 21.17 even 6
252.4.a.d.1.1 1 7.6 odd 2
448.4.a.a.1.1 1 168.83 odd 2
448.4.a.p.1.1 1 168.125 even 2
700.4.a.n.1.1 1 105.104 even 2
700.4.e.a.449.1 2 105.83 odd 4
700.4.e.a.449.2 2 105.62 odd 4
784.4.a.a.1.1 1 12.11 even 2
1008.4.a.o.1.1 1 28.27 even 2
1764.4.a.c.1.1 1 1.1 even 1 trivial
1764.4.k.d.361.1 2 7.5 odd 6
1764.4.k.d.1549.1 2 7.3 odd 6
1764.4.k.m.361.1 2 7.2 even 3
1764.4.k.m.1549.1 2 7.4 even 3