# Properties

 Label 1764.4.a.b.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 12) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-18.0000 q^{5} +O(q^{10})$$ $$q-18.0000 q^{5} -36.0000 q^{11} +10.0000 q^{13} +18.0000 q^{17} +100.000 q^{19} -72.0000 q^{23} +199.000 q^{25} +234.000 q^{29} +16.0000 q^{31} -226.000 q^{37} +90.0000 q^{41} +452.000 q^{43} +432.000 q^{47} -414.000 q^{53} +648.000 q^{55} -684.000 q^{59} -422.000 q^{61} -180.000 q^{65} +332.000 q^{67} +360.000 q^{71} -26.0000 q^{73} +512.000 q^{79} -1188.00 q^{83} -324.000 q^{85} -630.000 q^{89} -1800.00 q^{95} +1054.00 q^{97} +O(q^{100})$$

## 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
$$5$$ −18.0000 −1.60997 −0.804984 0.593296i $$-0.797826\pi$$
−0.804984 + 0.593296i $$0.797826\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −36.0000 −0.986764 −0.493382 0.869813i $$-0.664240\pi$$
−0.493382 + 0.869813i $$0.664240\pi$$
$$12$$ 0 0
$$13$$ 10.0000 0.213346 0.106673 0.994294i $$-0.465980\pi$$
0.106673 + 0.994294i $$0.465980\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 18.0000 0.256802 0.128401 0.991722i $$-0.459015\pi$$
0.128401 + 0.991722i $$0.459015\pi$$
$$18$$ 0 0
$$19$$ 100.000 1.20745 0.603726 0.797192i $$-0.293682\pi$$
0.603726 + 0.797192i $$0.293682\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −72.0000 −0.652741 −0.326370 0.945242i $$-0.605826\pi$$
−0.326370 + 0.945242i $$0.605826\pi$$
$$24$$ 0 0
$$25$$ 199.000 1.59200
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 234.000 1.49837 0.749185 0.662361i $$-0.230446\pi$$
0.749185 + 0.662361i $$0.230446\pi$$
$$30$$ 0 0
$$31$$ 16.0000 0.0926995 0.0463498 0.998925i $$-0.485241\pi$$
0.0463498 + 0.998925i $$0.485241\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −226.000 −1.00417 −0.502083 0.864819i $$-0.667433\pi$$
−0.502083 + 0.864819i $$0.667433\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 90.0000 0.342820 0.171410 0.985200i $$-0.445168\pi$$
0.171410 + 0.985200i $$0.445168\pi$$
$$42$$ 0 0
$$43$$ 452.000 1.60301 0.801504 0.597989i $$-0.204033\pi$$
0.801504 + 0.597989i $$0.204033\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 432.000 1.34072 0.670358 0.742038i $$-0.266140\pi$$
0.670358 + 0.742038i $$0.266140\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −414.000 −1.07297 −0.536484 0.843911i $$-0.680248\pi$$
−0.536484 + 0.843911i $$0.680248\pi$$
$$54$$ 0 0
$$55$$ 648.000 1.58866
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −684.000 −1.50931 −0.754654 0.656123i $$-0.772195\pi$$
−0.754654 + 0.656123i $$0.772195\pi$$
$$60$$ 0 0
$$61$$ −422.000 −0.885763 −0.442882 0.896580i $$-0.646044\pi$$
−0.442882 + 0.896580i $$0.646044\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −180.000 −0.343481
$$66$$ 0 0
$$67$$ 332.000 0.605377 0.302688 0.953090i $$-0.402116\pi$$
0.302688 + 0.953090i $$0.402116\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 360.000 0.601748 0.300874 0.953664i $$-0.402722\pi$$
0.300874 + 0.953664i $$0.402722\pi$$
$$72$$ 0 0
$$73$$ −26.0000 −0.0416859 −0.0208429 0.999783i $$-0.506635\pi$$
−0.0208429 + 0.999783i $$0.506635\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 512.000 0.729171 0.364585 0.931170i $$-0.381211\pi$$
0.364585 + 0.931170i $$0.381211\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1188.00 −1.57108 −0.785542 0.618809i $$-0.787616\pi$$
−0.785542 + 0.618809i $$0.787616\pi$$
$$84$$ 0 0
$$85$$ −324.000 −0.413444
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −630.000 −0.750336 −0.375168 0.926957i $$-0.622415\pi$$
−0.375168 + 0.926957i $$0.622415\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −1800.00 −1.94396
$$96$$ 0 0
$$97$$ 1054.00 1.10327 0.551637 0.834085i $$-0.314004\pi$$
0.551637 + 0.834085i $$0.314004\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 558.000 0.549733 0.274867 0.961482i $$-0.411366\pi$$
0.274867 + 0.961482i $$0.411366\pi$$
$$102$$ 0 0
$$103$$ −8.00000 −0.00765304 −0.00382652 0.999993i $$-0.501218\pi$$
−0.00382652 + 0.999993i $$0.501218\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1764.00 −1.59376 −0.796880 0.604138i $$-0.793518\pi$$
−0.796880 + 0.604138i $$0.793518\pi$$
$$108$$ 0 0
$$109$$ 1622.00 1.42532 0.712658 0.701512i $$-0.247491\pi$$
0.712658 + 0.701512i $$0.247491\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1134.00 0.944051 0.472025 0.881585i $$-0.343523\pi$$
0.472025 + 0.881585i $$0.343523\pi$$
$$114$$ 0 0
$$115$$ 1296.00 1.05089
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −35.0000 −0.0262960
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1332.00 −0.953102
$$126$$ 0 0
$$127$$ −592.000 −0.413634 −0.206817 0.978380i $$-0.566310\pi$$
−0.206817 + 0.978380i $$0.566310\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1908.00 −1.27254 −0.636270 0.771466i $$-0.719524\pi$$
−0.636270 + 0.771466i $$0.719524\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −954.000 −0.594932 −0.297466 0.954732i $$-0.596142\pi$$
−0.297466 + 0.954732i $$0.596142\pi$$
$$138$$ 0 0
$$139$$ −2564.00 −1.56457 −0.782286 0.622919i $$-0.785947\pi$$
−0.782286 + 0.622919i $$0.785947\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −360.000 −0.210522
$$144$$ 0 0
$$145$$ −4212.00 −2.41233
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 738.000 0.405767 0.202884 0.979203i $$-0.434969\pi$$
0.202884 + 0.979203i $$0.434969\pi$$
$$150$$ 0 0
$$151$$ −2440.00 −1.31500 −0.657498 0.753456i $$-0.728385\pi$$
−0.657498 + 0.753456i $$0.728385\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −288.000 −0.149243
$$156$$ 0 0
$$157$$ 2554.00 1.29829 0.649145 0.760665i $$-0.275127\pi$$
0.649145 + 0.760665i $$0.275127\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −820.000 −0.394033 −0.197016 0.980400i $$-0.563125\pi$$
−0.197016 + 0.980400i $$0.563125\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1944.00 0.900786 0.450393 0.892830i $$-0.351284\pi$$
0.450393 + 0.892830i $$0.351284\pi$$
$$168$$ 0 0
$$169$$ −2097.00 −0.954483
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1242.00 −0.545824 −0.272912 0.962039i $$-0.587987\pi$$
−0.272912 + 0.962039i $$0.587987\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1116.00 −0.465999 −0.232999 0.972477i $$-0.574854\pi$$
−0.232999 + 0.972477i $$0.574854\pi$$
$$180$$ 0 0
$$181$$ −1070.00 −0.439406 −0.219703 0.975567i $$-0.570509\pi$$
−0.219703 + 0.975567i $$0.570509\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 4068.00 1.61668
$$186$$ 0 0
$$187$$ −648.000 −0.253403
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 576.000 0.218209 0.109104 0.994030i $$-0.465202\pi$$
0.109104 + 0.994030i $$0.465202\pi$$
$$192$$ 0 0
$$193$$ −1342.00 −0.500514 −0.250257 0.968179i $$-0.580515\pi$$
−0.250257 + 0.968179i $$0.580515\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1422.00 −0.514281 −0.257140 0.966374i $$-0.582780\pi$$
−0.257140 + 0.966374i $$0.582780\pi$$
$$198$$ 0 0
$$199$$ −872.000 −0.310625 −0.155313 0.987865i $$-0.549639\pi$$
−0.155313 + 0.987865i $$0.549639\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −1620.00 −0.551930
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −3600.00 −1.19147
$$210$$ 0 0
$$211$$ 1340.00 0.437201 0.218600 0.975814i $$-0.429851\pi$$
0.218600 + 0.975814i $$0.429851\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −8136.00 −2.58079
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 180.000 0.0547878
$$222$$ 0 0
$$223$$ −4880.00 −1.46542 −0.732711 0.680540i $$-0.761745\pi$$
−0.732711 + 0.680540i $$0.761745\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 2700.00 0.789451 0.394725 0.918799i $$-0.370840\pi$$
0.394725 + 0.918799i $$0.370840\pi$$
$$228$$ 0 0
$$229$$ −254.000 −0.0732960 −0.0366480 0.999328i $$-0.511668\pi$$
−0.0366480 + 0.999328i $$0.511668\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −4410.00 −1.23995 −0.619976 0.784621i $$-0.712858\pi$$
−0.619976 + 0.784621i $$0.712858\pi$$
$$234$$ 0 0
$$235$$ −7776.00 −2.15851
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3888.00 1.05228 0.526138 0.850399i $$-0.323640\pi$$
0.526138 + 0.850399i $$0.323640\pi$$
$$240$$ 0 0
$$241$$ −5138.00 −1.37331 −0.686655 0.726984i $$-0.740922\pi$$
−0.686655 + 0.726984i $$0.740922\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1000.00 0.257605
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 4788.00 1.20405 0.602024 0.798478i $$-0.294361\pi$$
0.602024 + 0.798478i $$0.294361\pi$$
$$252$$ 0 0
$$253$$ 2592.00 0.644101
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −5886.00 −1.42863 −0.714316 0.699823i $$-0.753262\pi$$
−0.714316 + 0.699823i $$0.753262\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −2232.00 −0.523312 −0.261656 0.965161i $$-0.584269\pi$$
−0.261656 + 0.965161i $$0.584269\pi$$
$$264$$ 0 0
$$265$$ 7452.00 1.72744
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −666.000 −0.150954 −0.0754772 0.997148i $$-0.524048\pi$$
−0.0754772 + 0.997148i $$0.524048\pi$$
$$270$$ 0 0
$$271$$ 5536.00 1.24092 0.620458 0.784240i $$-0.286947\pi$$
0.620458 + 0.784240i $$0.286947\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −7164.00 −1.57093
$$276$$ 0 0
$$277$$ 2126.00 0.461151 0.230576 0.973054i $$-0.425939\pi$$
0.230576 + 0.973054i $$0.425939\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 2934.00 0.622875 0.311437 0.950267i $$-0.399190\pi$$
0.311437 + 0.950267i $$0.399190\pi$$
$$282$$ 0 0
$$283$$ −2036.00 −0.427659 −0.213830 0.976871i $$-0.568594\pi$$
−0.213830 + 0.976871i $$0.568594\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4589.00 −0.934053
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 2286.00 0.455800 0.227900 0.973684i $$-0.426814\pi$$
0.227900 + 0.973684i $$0.426814\pi$$
$$294$$ 0 0
$$295$$ 12312.0 2.42994
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −720.000 −0.139260
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 7596.00 1.42605
$$306$$ 0 0
$$307$$ −1244.00 −0.231267 −0.115633 0.993292i $$-0.536890\pi$$
−0.115633 + 0.993292i $$0.536890\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 1224.00 0.223173 0.111586 0.993755i $$-0.464407\pi$$
0.111586 + 0.993755i $$0.464407\pi$$
$$312$$ 0 0
$$313$$ −1898.00 −0.342752 −0.171376 0.985206i $$-0.554821\pi$$
−0.171376 + 0.985206i $$0.554821\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 9162.00 1.62331 0.811655 0.584137i $$-0.198567\pi$$
0.811655 + 0.584137i $$0.198567\pi$$
$$318$$ 0 0
$$319$$ −8424.00 −1.47854
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 1800.00 0.310076
$$324$$ 0 0
$$325$$ 1990.00 0.339647
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −4348.00 −0.722017 −0.361009 0.932562i $$-0.617568\pi$$
−0.361009 + 0.932562i $$0.617568\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −5976.00 −0.974638
$$336$$ 0 0
$$337$$ 7154.00 1.15639 0.578195 0.815899i $$-0.303757\pi$$
0.578195 + 0.815899i $$0.303757\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −576.000 −0.0914726
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1836.00 0.284039 0.142020 0.989864i $$-0.454640\pi$$
0.142020 + 0.989864i $$0.454640\pi$$
$$348$$ 0 0
$$349$$ −5894.00 −0.904007 −0.452004 0.892016i $$-0.649291\pi$$
−0.452004 + 0.892016i $$0.649291\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 11106.0 1.67454 0.837270 0.546789i $$-0.184150\pi$$
0.837270 + 0.546789i $$0.184150\pi$$
$$354$$ 0 0
$$355$$ −6480.00 −0.968796
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −13176.0 −1.93705 −0.968527 0.248907i $$-0.919929\pi$$
−0.968527 + 0.248907i $$0.919929\pi$$
$$360$$ 0 0
$$361$$ 3141.00 0.457938
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 468.000 0.0671130
$$366$$ 0 0
$$367$$ 6112.00 0.869329 0.434665 0.900592i $$-0.356867\pi$$
0.434665 + 0.900592i $$0.356867\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −13618.0 −1.89038 −0.945192 0.326515i $$-0.894126\pi$$
−0.945192 + 0.326515i $$0.894126\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 2340.00 0.319671
$$378$$ 0 0
$$379$$ 692.000 0.0937880 0.0468940 0.998900i $$-0.485068\pi$$
0.0468940 + 0.998900i $$0.485068\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −8064.00 −1.07585 −0.537926 0.842992i $$-0.680792\pi$$
−0.537926 + 0.842992i $$0.680792\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −12654.0 −1.64931 −0.824657 0.565633i $$-0.808632\pi$$
−0.824657 + 0.565633i $$0.808632\pi$$
$$390$$ 0 0
$$391$$ −1296.00 −0.167625
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −9216.00 −1.17394
$$396$$ 0 0
$$397$$ 106.000 0.0134005 0.00670024 0.999978i $$-0.497867\pi$$
0.00670024 + 0.999978i $$0.497867\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 4014.00 0.499874 0.249937 0.968262i $$-0.419590\pi$$
0.249937 + 0.968262i $$0.419590\pi$$
$$402$$ 0 0
$$403$$ 160.000 0.0197771
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 8136.00 0.990876
$$408$$ 0 0
$$409$$ −3914.00 −0.473190 −0.236595 0.971608i $$-0.576032\pi$$
−0.236595 + 0.971608i $$0.576032\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 21384.0 2.52940
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 4428.00 0.516282 0.258141 0.966107i $$-0.416890\pi$$
0.258141 + 0.966107i $$0.416890\pi$$
$$420$$ 0 0
$$421$$ −15490.0 −1.79320 −0.896599 0.442843i $$-0.853970\pi$$
−0.896599 + 0.442843i $$0.853970\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 3582.00 0.408829
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −6768.00 −0.756388 −0.378194 0.925726i $$-0.623455\pi$$
−0.378194 + 0.925726i $$0.623455\pi$$
$$432$$ 0 0
$$433$$ −1298.00 −0.144060 −0.0720299 0.997402i $$-0.522948\pi$$
−0.0720299 + 0.997402i $$0.522948\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −7200.00 −0.788153
$$438$$ 0 0
$$439$$ 2248.00 0.244399 0.122200 0.992506i $$-0.461005\pi$$
0.122200 + 0.992506i $$0.461005\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 9612.00 1.03088 0.515440 0.856926i $$-0.327628\pi$$
0.515440 + 0.856926i $$0.327628\pi$$
$$444$$ 0 0
$$445$$ 11340.0 1.20802
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −162.000 −0.0170273 −0.00851364 0.999964i $$-0.502710\pi$$
−0.00851364 + 0.999964i $$0.502710\pi$$
$$450$$ 0 0
$$451$$ −3240.00 −0.338283
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 1370.00 0.140232 0.0701159 0.997539i $$-0.477663\pi$$
0.0701159 + 0.997539i $$0.477663\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −15354.0 −1.55121 −0.775604 0.631220i $$-0.782555\pi$$
−0.775604 + 0.631220i $$0.782555\pi$$
$$462$$ 0 0
$$463$$ −13024.0 −1.30729 −0.653646 0.756800i $$-0.726762\pi$$
−0.653646 + 0.756800i $$0.726762\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −14436.0 −1.43045 −0.715223 0.698896i $$-0.753675\pi$$
−0.715223 + 0.698896i $$0.753675\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −16272.0 −1.58179
$$474$$ 0 0
$$475$$ 19900.0 1.92226
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 12096.0 1.15382 0.576911 0.816807i $$-0.304258\pi$$
0.576911 + 0.816807i $$0.304258\pi$$
$$480$$ 0 0
$$481$$ −2260.00 −0.214235
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −18972.0 −1.77624
$$486$$ 0 0
$$487$$ 6056.00 0.563498 0.281749 0.959488i $$-0.409085\pi$$
0.281749 + 0.959488i $$0.409085\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −7524.00 −0.691555 −0.345777 0.938317i $$-0.612385\pi$$
−0.345777 + 0.938317i $$0.612385\pi$$
$$492$$ 0 0
$$493$$ 4212.00 0.384785
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 5276.00 0.473319 0.236660 0.971593i $$-0.423947\pi$$
0.236660 + 0.971593i $$0.423947\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4968.00 0.440382 0.220191 0.975457i $$-0.429332\pi$$
0.220191 + 0.975457i $$0.429332\pi$$
$$504$$ 0 0
$$505$$ −10044.0 −0.885054
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 10998.0 0.957717 0.478858 0.877892i $$-0.341051\pi$$
0.478858 + 0.877892i $$0.341051\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 144.000 0.0123212
$$516$$ 0 0
$$517$$ −15552.0 −1.32297
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −8838.00 −0.743186 −0.371593 0.928396i $$-0.621188\pi$$
−0.371593 + 0.928396i $$0.621188\pi$$
$$522$$ 0 0
$$523$$ −22436.0 −1.87583 −0.937914 0.346869i $$-0.887245\pi$$
−0.937914 + 0.346869i $$0.887245\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 288.000 0.0238055
$$528$$ 0 0
$$529$$ −6983.00 −0.573929
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 900.000 0.0731395
$$534$$ 0 0
$$535$$ 31752.0 2.56590
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −4762.00 −0.378437 −0.189218 0.981935i $$-0.560595\pi$$
−0.189218 + 0.981935i $$0.560595\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −29196.0 −2.29471
$$546$$ 0 0
$$547$$ −6004.00 −0.469310 −0.234655 0.972079i $$-0.575396\pi$$
−0.234655 + 0.972079i $$0.575396\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 23400.0 1.80921
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 5274.00 0.401197 0.200598 0.979674i $$-0.435711\pi$$
0.200598 + 0.979674i $$0.435711\pi$$
$$558$$ 0 0
$$559$$ 4520.00 0.341996
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −12420.0 −0.929735 −0.464867 0.885380i $$-0.653898\pi$$
−0.464867 + 0.885380i $$0.653898\pi$$
$$564$$ 0 0
$$565$$ −20412.0 −1.51989
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 21366.0 1.57418 0.787091 0.616837i $$-0.211586\pi$$
0.787091 + 0.616837i $$0.211586\pi$$
$$570$$ 0 0
$$571$$ 21140.0 1.54935 0.774677 0.632357i $$-0.217912\pi$$
0.774677 + 0.632357i $$0.217912\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −14328.0 −1.03916
$$576$$ 0 0
$$577$$ −3266.00 −0.235642 −0.117821 0.993035i $$-0.537591\pi$$
−0.117821 + 0.993035i $$0.537591\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 14904.0 1.05877
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 17028.0 1.19731 0.598655 0.801007i $$-0.295702\pi$$
0.598655 + 0.801007i $$0.295702\pi$$
$$588$$ 0 0
$$589$$ 1600.00 0.111930
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 9522.00 0.659396 0.329698 0.944086i $$-0.393053\pi$$
0.329698 + 0.944086i $$0.393053\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 10296.0 0.702309 0.351155 0.936318i $$-0.385789\pi$$
0.351155 + 0.936318i $$0.385789\pi$$
$$600$$ 0 0
$$601$$ 3382.00 0.229542 0.114771 0.993392i $$-0.463387\pi$$
0.114771 + 0.993392i $$0.463387\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 630.000 0.0423358
$$606$$ 0 0
$$607$$ 20656.0 1.38122 0.690611 0.723227i $$-0.257342\pi$$
0.690611 + 0.723227i $$0.257342\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 4320.00 0.286037
$$612$$ 0 0
$$613$$ −22114.0 −1.45706 −0.728529 0.685015i $$-0.759795\pi$$
−0.728529 + 0.685015i $$0.759795\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −19962.0 −1.30250 −0.651248 0.758865i $$-0.725754\pi$$
−0.651248 + 0.758865i $$0.725754\pi$$
$$618$$ 0 0
$$619$$ 604.000 0.0392194 0.0196097 0.999808i $$-0.493758\pi$$
0.0196097 + 0.999808i $$0.493758\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −899.000 −0.0575360
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −4068.00 −0.257872
$$630$$ 0 0
$$631$$ 152.000 0.00958958 0.00479479 0.999989i $$-0.498474\pi$$
0.00479479 + 0.999989i $$0.498474\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 10656.0 0.665938
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −4194.00 −0.258429 −0.129215 0.991617i $$-0.541246\pi$$
−0.129215 + 0.991617i $$0.541246\pi$$
$$642$$ 0 0
$$643$$ 7252.00 0.444776 0.222388 0.974958i $$-0.428615\pi$$
0.222388 + 0.974958i $$0.428615\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −6696.00 −0.406873 −0.203437 0.979088i $$-0.565211\pi$$
−0.203437 + 0.979088i $$0.565211\pi$$
$$648$$ 0 0
$$649$$ 24624.0 1.48933
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −28422.0 −1.70328 −0.851638 0.524131i $$-0.824390\pi$$
−0.851638 + 0.524131i $$0.824390\pi$$
$$654$$ 0 0
$$655$$ 34344.0 2.04875
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 19908.0 1.17679 0.588396 0.808573i $$-0.299760\pi$$
0.588396 + 0.808573i $$0.299760\pi$$
$$660$$ 0 0
$$661$$ −14318.0 −0.842520 −0.421260 0.906940i $$-0.638412\pi$$
−0.421260 + 0.906940i $$0.638412\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −16848.0 −0.978047
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 15192.0 0.874040
$$672$$ 0 0
$$673$$ 30050.0 1.72116 0.860581 0.509313i $$-0.170101\pi$$
0.860581 + 0.509313i $$0.170101\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 22158.0 1.25790 0.628952 0.777444i $$-0.283484\pi$$
0.628952 + 0.777444i $$0.283484\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 3132.00 0.175465 0.0877325 0.996144i $$-0.472038\pi$$
0.0877325 + 0.996144i $$0.472038\pi$$
$$684$$ 0 0
$$685$$ 17172.0 0.957822
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −4140.00 −0.228914
$$690$$ 0 0
$$691$$ 20932.0 1.15237 0.576187 0.817318i $$-0.304540\pi$$
0.576187 + 0.817318i $$0.304540\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 46152.0 2.51891
$$696$$ 0 0
$$697$$ 1620.00 0.0880371
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 21834.0 1.17640 0.588202 0.808714i $$-0.299836\pi$$
0.588202 + 0.808714i $$0.299836\pi$$
$$702$$ 0 0
$$703$$ −22600.0 −1.21248
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 12446.0 0.659266 0.329633 0.944109i $$-0.393075\pi$$
0.329633 + 0.944109i $$0.393075\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −1152.00 −0.0605088
$$714$$ 0 0
$$715$$ 6480.00 0.338935
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −12528.0 −0.649813 −0.324907 0.945746i $$-0.605333\pi$$
−0.324907 + 0.945746i $$0.605333\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 46566.0 2.38540
$$726$$ 0 0
$$727$$ −11576.0 −0.590550 −0.295275 0.955412i $$-0.595411\pi$$
−0.295275 + 0.955412i $$0.595411\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 8136.00 0.411656
$$732$$ 0 0
$$733$$ 29338.0 1.47834 0.739170 0.673519i $$-0.235218\pi$$
0.739170 + 0.673519i $$0.235218\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −11952.0 −0.597364
$$738$$ 0 0
$$739$$ 2540.00 0.126435 0.0632175 0.998000i $$-0.479864\pi$$
0.0632175 + 0.998000i $$0.479864\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 18792.0 0.927876 0.463938 0.885868i $$-0.346436\pi$$
0.463938 + 0.885868i $$0.346436\pi$$
$$744$$ 0 0
$$745$$ −13284.0 −0.653273
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 4832.00 0.234783 0.117392 0.993086i $$-0.462547\pi$$
0.117392 + 0.993086i $$0.462547\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 43920.0 2.11710
$$756$$ 0 0
$$757$$ −20818.0 −0.999529 −0.499764 0.866161i $$-0.666580\pi$$
−0.499764 + 0.866161i $$0.666580\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 12042.0 0.573617 0.286808 0.957988i $$-0.407406\pi$$
0.286808 + 0.957988i $$0.407406\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −6840.00 −0.322005
$$768$$ 0 0
$$769$$ −13058.0 −0.612332 −0.306166 0.951978i $$-0.599046\pi$$
−0.306166 + 0.951978i $$0.599046\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −11826.0 −0.550261 −0.275130 0.961407i $$-0.588721\pi$$
−0.275130 + 0.961407i $$0.588721\pi$$
$$774$$ 0 0
$$775$$ 3184.00 0.147578
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 9000.00 0.413939
$$780$$ 0 0
$$781$$ −12960.0 −0.593784
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −45972.0 −2.09021
$$786$$ 0 0
$$787$$ −11996.0 −0.543343 −0.271672 0.962390i $$-0.587576\pi$$
−0.271672 + 0.962390i $$0.587576\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −4220.00 −0.188974
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 6966.00 0.309596 0.154798 0.987946i $$-0.450527\pi$$
0.154798 + 0.987946i $$0.450527\pi$$
$$798$$ 0 0
$$799$$ 7776.00 0.344299
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 936.000 0.0411342
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 40806.0 1.77338 0.886689 0.462367i $$-0.153000\pi$$
0.886689 + 0.462367i $$0.153000\pi$$
$$810$$ 0 0
$$811$$ 17980.0 0.778500 0.389250 0.921132i $$-0.372734\pi$$
0.389250 + 0.921132i $$0.372734\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 14760.0 0.634381
$$816$$ 0 0
$$817$$ 45200.0 1.93555
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 12834.0 0.545566 0.272783 0.962076i $$-0.412056\pi$$
0.272783 + 0.962076i $$0.412056\pi$$
$$822$$ 0 0
$$823$$ −37864.0 −1.60371 −0.801857 0.597516i $$-0.796154\pi$$
−0.801857 + 0.597516i $$0.796154\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −42516.0 −1.78770 −0.893849 0.448368i $$-0.852005\pi$$
−0.893849 + 0.448368i $$0.852005\pi$$
$$828$$ 0 0
$$829$$ −45638.0 −1.91203 −0.956015 0.293317i $$-0.905241\pi$$
−0.956015 + 0.293317i $$0.905241\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −34992.0 −1.45024
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 17496.0 0.719939 0.359970 0.932964i $$-0.382787\pi$$
0.359970 + 0.932964i $$0.382787\pi$$
$$840$$ 0 0
$$841$$ 30367.0 1.24511
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 37746.0 1.53669
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 16272.0 0.655461
$$852$$ 0 0
$$853$$ −32174.0 −1.29146 −0.645731 0.763565i $$-0.723447\pi$$
−0.645731 + 0.763565i $$0.723447\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −38934.0 −1.55188 −0.775939 0.630807i $$-0.782724\pi$$
−0.775939 + 0.630807i $$0.782724\pi$$
$$858$$ 0 0
$$859$$ −29780.0 −1.18286 −0.591432 0.806355i $$-0.701437\pi$$
−0.591432 + 0.806355i $$0.701437\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 48096.0 1.89711 0.948556 0.316611i $$-0.102545\pi$$
0.948556 + 0.316611i $$0.102545\pi$$
$$864$$ 0 0
$$865$$ 22356.0 0.878759
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −18432.0 −0.719520
$$870$$ 0 0
$$871$$ 3320.00 0.129155
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 21302.0 0.820202 0.410101 0.912040i $$-0.365493\pi$$
0.410101 + 0.912040i $$0.365493\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −7470.00 −0.285665 −0.142832 0.989747i $$-0.545621\pi$$
−0.142832 + 0.989747i $$0.545621\pi$$
$$882$$ 0 0
$$883$$ 764.000 0.0291174 0.0145587 0.999894i $$-0.495366\pi$$
0.0145587 + 0.999894i $$0.495366\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 32328.0 1.22375 0.611876 0.790954i $$-0.290415\pi$$
0.611876 + 0.790954i $$0.290415\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 43200.0 1.61885
$$894$$ 0 0
$$895$$ 20088.0 0.750243
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 3744.00 0.138898
$$900$$ 0 0
$$901$$ −7452.00 −0.275541
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 19260.0 0.707430
$$906$$ 0 0
$$907$$ −36316.0 −1.32950 −0.664748 0.747068i $$-0.731461\pi$$
−0.664748 + 0.747068i $$0.731461\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 13392.0 0.487044 0.243522 0.969895i $$-0.421697\pi$$
0.243522 + 0.969895i $$0.421697\pi$$
$$912$$ 0 0
$$913$$ 42768.0 1.55029
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 38072.0 1.36657 0.683286 0.730151i $$-0.260550\pi$$
0.683286 + 0.730151i $$0.260550\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 3600.00 0.128381
$$924$$ 0 0
$$925$$ −44974.0 −1.59863
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −12798.0 −0.451979 −0.225990 0.974130i $$-0.572562\pi$$
−0.225990 + 0.974130i $$0.572562\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 11664.0 0.407972
$$936$$ 0 0
$$937$$ −34874.0 −1.21588 −0.607942 0.793981i $$-0.708005\pi$$
−0.607942 + 0.793981i $$0.708005\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 17190.0 0.595513 0.297757 0.954642i $$-0.403762\pi$$
0.297757 + 0.954642i $$0.403762\pi$$
$$942$$ 0 0
$$943$$ −6480.00 −0.223773
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −40284.0 −1.38232 −0.691158 0.722703i $$-0.742899\pi$$
−0.691158 + 0.722703i $$0.742899\pi$$
$$948$$ 0 0
$$949$$ −260.000 −0.00889353
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −15498.0 −0.526789 −0.263394 0.964688i $$-0.584842\pi$$
−0.263394 + 0.964688i $$0.584842\pi$$
$$954$$ 0 0
$$955$$ −10368.0 −0.351310
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −29535.0 −0.991407
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 24156.0 0.805813
$$966$$ 0 0
$$967$$ 37160.0 1.23577 0.617883 0.786270i $$-0.287991\pi$$
0.617883 + 0.786270i $$0.287991\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 18468.0 0.610367 0.305183 0.952294i $$-0.401282\pi$$
0.305183 + 0.952294i $$0.401282\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −10386.0 −0.340100 −0.170050 0.985435i $$-0.554393\pi$$
−0.170050 + 0.985435i $$0.554393\pi$$
$$978$$ 0 0
$$979$$ 22680.0 0.740404
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 44136.0 1.43206 0.716032 0.698067i $$-0.245956\pi$$
0.716032 + 0.698067i $$0.245956\pi$$
$$984$$ 0 0
$$985$$ 25596.0 0.827976
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −32544.0 −1.04635
$$990$$ 0 0
$$991$$ −28432.0 −0.911375 −0.455687 0.890140i $$-0.650606\pi$$
−0.455687 + 0.890140i $$0.650606\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 15696.0 0.500097
$$996$$ 0 0
$$997$$ 39778.0 1.26357 0.631786 0.775143i $$-0.282322\pi$$
0.631786 + 0.775143i $$0.282322\pi$$
$$998$$ 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.b.1.1 1
3.2 odd 2 588.4.a.c.1.1 1
7.2 even 3 1764.4.k.o.361.1 2
7.3 odd 6 1764.4.k.b.1549.1 2
7.4 even 3 1764.4.k.o.1549.1 2
7.5 odd 6 1764.4.k.b.361.1 2
7.6 odd 2 36.4.a.a.1.1 1
12.11 even 2 2352.4.a.bk.1.1 1
21.2 odd 6 588.4.i.e.361.1 2
21.5 even 6 588.4.i.d.361.1 2
21.11 odd 6 588.4.i.e.373.1 2
21.17 even 6 588.4.i.d.373.1 2
21.20 even 2 12.4.a.a.1.1 1
28.27 even 2 144.4.a.g.1.1 1
35.13 even 4 900.4.d.c.649.1 2
35.27 even 4 900.4.d.c.649.2 2
35.34 odd 2 900.4.a.g.1.1 1
56.13 odd 2 576.4.a.b.1.1 1
56.27 even 2 576.4.a.a.1.1 1
63.13 odd 6 324.4.e.a.217.1 2
63.20 even 6 324.4.e.h.109.1 2
63.34 odd 6 324.4.e.a.109.1 2
63.41 even 6 324.4.e.h.217.1 2
84.83 odd 2 48.4.a.a.1.1 1
105.62 odd 4 300.4.d.e.49.1 2
105.83 odd 4 300.4.d.e.49.2 2
105.104 even 2 300.4.a.b.1.1 1
168.83 odd 2 192.4.a.l.1.1 1
168.125 even 2 192.4.a.f.1.1 1
231.230 odd 2 1452.4.a.d.1.1 1
273.83 odd 4 2028.4.b.c.337.2 2
273.125 odd 4 2028.4.b.c.337.1 2
273.272 even 2 2028.4.a.c.1.1 1
336.83 odd 4 768.4.d.j.385.1 2
336.125 even 4 768.4.d.g.385.2 2
336.251 odd 4 768.4.d.j.385.2 2
336.293 even 4 768.4.d.g.385.1 2
420.83 even 4 1200.4.f.d.49.1 2
420.167 even 4 1200.4.f.d.49.2 2
420.419 odd 2 1200.4.a.be.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
12.4.a.a.1.1 1 21.20 even 2
36.4.a.a.1.1 1 7.6 odd 2
48.4.a.a.1.1 1 84.83 odd 2
144.4.a.g.1.1 1 28.27 even 2
192.4.a.f.1.1 1 168.125 even 2
192.4.a.l.1.1 1 168.83 odd 2
300.4.a.b.1.1 1 105.104 even 2
300.4.d.e.49.1 2 105.62 odd 4
300.4.d.e.49.2 2 105.83 odd 4
324.4.e.a.109.1 2 63.34 odd 6
324.4.e.a.217.1 2 63.13 odd 6
324.4.e.h.109.1 2 63.20 even 6
324.4.e.h.217.1 2 63.41 even 6
576.4.a.a.1.1 1 56.27 even 2
576.4.a.b.1.1 1 56.13 odd 2
588.4.a.c.1.1 1 3.2 odd 2
588.4.i.d.361.1 2 21.5 even 6
588.4.i.d.373.1 2 21.17 even 6
588.4.i.e.361.1 2 21.2 odd 6
588.4.i.e.373.1 2 21.11 odd 6
768.4.d.g.385.1 2 336.293 even 4
768.4.d.g.385.2 2 336.125 even 4
768.4.d.j.385.1 2 336.83 odd 4
768.4.d.j.385.2 2 336.251 odd 4
900.4.a.g.1.1 1 35.34 odd 2
900.4.d.c.649.1 2 35.13 even 4
900.4.d.c.649.2 2 35.27 even 4
1200.4.a.be.1.1 1 420.419 odd 2
1200.4.f.d.49.1 2 420.83 even 4
1200.4.f.d.49.2 2 420.167 even 4
1452.4.a.d.1.1 1 231.230 odd 2
1764.4.a.b.1.1 1 1.1 even 1 trivial
1764.4.k.b.361.1 2 7.5 odd 6
1764.4.k.b.1549.1 2 7.3 odd 6
1764.4.k.o.361.1 2 7.2 even 3
1764.4.k.o.1549.1 2 7.4 even 3
2028.4.a.c.1.1 1 273.272 even 2
2028.4.b.c.337.1 2 273.125 odd 4
2028.4.b.c.337.2 2 273.83 odd 4
2352.4.a.bk.1.1 1 12.11 even 2