# Properties

 Label 720.4.a.c.1.1 Level $720$ Weight $4$ Character 720.1 Self dual yes Analytic conductor $42.481$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 720.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$42.4813752041$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 60) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 720.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-5.00000 q^{5} -32.0000 q^{7} +O(q^{10})$$ $$q-5.00000 q^{5} -32.0000 q^{7} +36.0000 q^{11} -10.0000 q^{13} +78.0000 q^{17} -140.000 q^{19} -192.000 q^{23} +25.0000 q^{25} -6.00000 q^{29} +16.0000 q^{31} +160.000 q^{35} -34.0000 q^{37} +390.000 q^{41} +52.0000 q^{43} +408.000 q^{47} +681.000 q^{49} +114.000 q^{53} -180.000 q^{55} +516.000 q^{59} -58.0000 q^{61} +50.0000 q^{65} +892.000 q^{67} -120.000 q^{71} -646.000 q^{73} -1152.00 q^{77} +1168.00 q^{79} -732.000 q^{83} -390.000 q^{85} +1590.00 q^{89} +320.000 q^{91} +700.000 q^{95} +194.000 q^{97} +O(q^{100})$$

## 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
$$5$$ −5.00000 −0.447214
$$6$$ 0 0
$$7$$ −32.0000 −1.72784 −0.863919 0.503631i $$-0.831997\pi$$
−0.863919 + 0.503631i $$0.831997\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 36.0000 0.986764 0.493382 0.869813i $$-0.335760\pi$$
0.493382 + 0.869813i $$0.335760\pi$$
$$12$$ 0 0
$$13$$ −10.0000 −0.213346 −0.106673 0.994294i $$-0.534020\pi$$
−0.106673 + 0.994294i $$0.534020\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 78.0000 1.11281 0.556405 0.830911i $$-0.312180\pi$$
0.556405 + 0.830911i $$0.312180\pi$$
$$18$$ 0 0
$$19$$ −140.000 −1.69043 −0.845216 0.534425i $$-0.820528\pi$$
−0.845216 + 0.534425i $$0.820528\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −192.000 −1.74064 −0.870321 0.492485i $$-0.836089\pi$$
−0.870321 + 0.492485i $$0.836089\pi$$
$$24$$ 0 0
$$25$$ 25.0000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −6.00000 −0.0384197 −0.0192099 0.999815i $$-0.506115\pi$$
−0.0192099 + 0.999815i $$0.506115\pi$$
$$30$$ 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
$$35$$ 160.000 0.772712
$$36$$ 0 0
$$37$$ −34.0000 −0.151069 −0.0755347 0.997143i $$-0.524066\pi$$
−0.0755347 + 0.997143i $$0.524066\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 390.000 1.48556 0.742778 0.669538i $$-0.233508\pi$$
0.742778 + 0.669538i $$0.233508\pi$$
$$42$$ 0 0
$$43$$ 52.0000 0.184417 0.0922084 0.995740i $$-0.470607\pi$$
0.0922084 + 0.995740i $$0.470607\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 408.000 1.26623 0.633116 0.774057i $$-0.281776\pi$$
0.633116 + 0.774057i $$0.281776\pi$$
$$48$$ 0 0
$$49$$ 681.000 1.98542
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 114.000 0.295455 0.147727 0.989028i $$-0.452804\pi$$
0.147727 + 0.989028i $$0.452804\pi$$
$$54$$ 0 0
$$55$$ −180.000 −0.441294
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 516.000 1.13860 0.569301 0.822129i $$-0.307214\pi$$
0.569301 + 0.822129i $$0.307214\pi$$
$$60$$ 0 0
$$61$$ −58.0000 −0.121740 −0.0608700 0.998146i $$-0.519388\pi$$
−0.0608700 + 0.998146i $$0.519388\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 50.0000 0.0954113
$$66$$ 0 0
$$67$$ 892.000 1.62649 0.813247 0.581918i $$-0.197698\pi$$
0.813247 + 0.581918i $$0.197698\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −120.000 −0.200583 −0.100291 0.994958i $$-0.531978\pi$$
−0.100291 + 0.994958i $$0.531978\pi$$
$$72$$ 0 0
$$73$$ −646.000 −1.03573 −0.517867 0.855461i $$-0.673274\pi$$
−0.517867 + 0.855461i $$0.673274\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −1152.00 −1.70497
$$78$$ 0 0
$$79$$ 1168.00 1.66342 0.831711 0.555209i $$-0.187362\pi$$
0.831711 + 0.555209i $$0.187362\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −732.000 −0.968041 −0.484021 0.875057i $$-0.660824\pi$$
−0.484021 + 0.875057i $$0.660824\pi$$
$$84$$ 0 0
$$85$$ −390.000 −0.497664
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1590.00 1.89370 0.946852 0.321669i $$-0.104244\pi$$
0.946852 + 0.321669i $$0.104244\pi$$
$$90$$ 0 0
$$91$$ 320.000 0.368628
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 700.000 0.755984
$$96$$ 0 0
$$97$$ 194.000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −798.000 −0.786178 −0.393089 0.919500i $$-0.628594\pi$$
−0.393089 + 0.919500i $$0.628594\pi$$
$$102$$ 0 0
$$103$$ −272.000 −0.260203 −0.130102 0.991501i $$-0.541530\pi$$
−0.130102 + 0.991501i $$0.541530\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 156.000 0.140945 0.0704724 0.997514i $$-0.477549\pi$$
0.0704724 + 0.997514i $$0.477549\pi$$
$$108$$ 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
$$113$$ −1074.00 −0.894101 −0.447051 0.894509i $$-0.647526\pi$$
−0.447051 + 0.894509i $$0.647526\pi$$
$$114$$ 0 0
$$115$$ 960.000 0.778439
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −2496.00 −1.92276
$$120$$ 0 0
$$121$$ −35.0000 −0.0262960
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −125.000 −0.0894427
$$126$$ 0 0
$$127$$ 1528.00 1.06762 0.533811 0.845604i $$-0.320759\pi$$
0.533811 + 0.845604i $$0.320759\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2412.00 1.60868 0.804341 0.594168i $$-0.202518\pi$$
0.804341 + 0.594168i $$0.202518\pi$$
$$132$$ 0 0
$$133$$ 4480.00 2.92079
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2106.00 −1.31334 −0.656671 0.754178i $$-0.728036\pi$$
−0.656671 + 0.754178i $$0.728036\pi$$
$$138$$ 0 0
$$139$$ 556.000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −360.000 −0.210522
$$144$$ 0 0
$$145$$ 30.0000 0.0171818
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 2418.00 1.32946 0.664732 0.747081i $$-0.268546\pi$$
0.664732 + 0.747081i $$0.268546\pi$$
$$150$$ 0 0
$$151$$ −2840.00 −1.53057 −0.765285 0.643692i $$-0.777402\pi$$
−0.765285 + 0.643692i $$0.777402\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −80.0000 −0.0414565
$$156$$ 0 0
$$157$$ 2054.00 1.04412 0.522061 0.852908i $$-0.325163\pi$$
0.522061 + 0.852908i $$0.325163\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 6144.00 3.00755
$$162$$ 0 0
$$163$$ 460.000 0.221043 0.110521 0.993874i $$-0.464748\pi$$
0.110521 + 0.993874i $$0.464748\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2016.00 0.934148 0.467074 0.884218i $$-0.345308\pi$$
0.467074 + 0.884218i $$0.345308\pi$$
$$168$$ 0 0
$$169$$ −2097.00 −0.954483
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 618.000 0.271593 0.135797 0.990737i $$-0.456641\pi$$
0.135797 + 0.990737i $$0.456641\pi$$
$$174$$ 0 0
$$175$$ −800.000 −0.345568
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −2964.00 −1.23765 −0.618826 0.785528i $$-0.712391\pi$$
−0.618826 + 0.785528i $$0.712391\pi$$
$$180$$ 0 0
$$181$$ −370.000 −0.151944 −0.0759721 0.997110i $$-0.524206\pi$$
−0.0759721 + 0.997110i $$0.524206\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 170.000 0.0675603
$$186$$ 0 0
$$187$$ 2808.00 1.09808
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1104.00 0.418234 0.209117 0.977891i $$-0.432941\pi$$
0.209117 + 0.977891i $$0.432941\pi$$
$$192$$ 0 0
$$193$$ −2398.00 −0.894362 −0.447181 0.894444i $$-0.647572\pi$$
−0.447181 + 0.894444i $$0.647572\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1278.00 −0.462202 −0.231101 0.972930i $$-0.574233\pi$$
−0.231101 + 0.972930i $$0.574233\pi$$
$$198$$ 0 0
$$199$$ −4472.00 −1.59302 −0.796512 0.604623i $$-0.793324\pi$$
−0.796512 + 0.604623i $$0.793324\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 192.000 0.0663830
$$204$$ 0 0
$$205$$ −1950.00 −0.664361
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −5040.00 −1.66806
$$210$$ 0 0
$$211$$ −1340.00 −0.437201 −0.218600 0.975814i $$-0.570149\pi$$
−0.218600 + 0.975814i $$0.570149\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −260.000 −0.0824737
$$216$$ 0 0
$$217$$ −512.000 −0.160170
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −780.000 −0.237414
$$222$$ 0 0
$$223$$ −2360.00 −0.708687 −0.354344 0.935115i $$-0.615296\pi$$
−0.354344 + 0.935115i $$0.615296\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 1380.00 0.403497 0.201748 0.979437i $$-0.435338\pi$$
0.201748 + 0.979437i $$0.435338\pi$$
$$228$$ 0 0
$$229$$ 1694.00 0.488833 0.244416 0.969670i $$-0.421404\pi$$
0.244416 + 0.969670i $$0.421404\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5190.00 1.45926 0.729631 0.683841i $$-0.239692\pi$$
0.729631 + 0.683841i $$0.239692\pi$$
$$234$$ 0 0
$$235$$ −2040.00 −0.566276
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 2352.00 0.636562 0.318281 0.947996i $$-0.396895\pi$$
0.318281 + 0.947996i $$0.396895\pi$$
$$240$$ 0 0
$$241$$ −3502.00 −0.936032 −0.468016 0.883720i $$-0.655031\pi$$
−0.468016 + 0.883720i $$0.655031\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −3405.00 −0.887908
$$246$$ 0 0
$$247$$ 1400.00 0.360647
$$248$$ 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
$$253$$ −6912.00 −1.71760
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1506.00 −0.365532 −0.182766 0.983156i $$-0.558505\pi$$
−0.182766 + 0.983156i $$0.558505\pi$$
$$258$$ 0 0
$$259$$ 1088.00 0.261023
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −432.000 −0.101286 −0.0506431 0.998717i $$-0.516127\pi$$
−0.0506431 + 0.998717i $$0.516127\pi$$
$$264$$ 0 0
$$265$$ −570.000 −0.132131
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −54.0000 −0.0122395 −0.00611977 0.999981i $$-0.501948\pi$$
−0.00611977 + 0.999981i $$0.501948\pi$$
$$270$$ 0 0
$$271$$ 6496.00 1.45610 0.728051 0.685522i $$-0.240426\pi$$
0.728051 + 0.685522i $$0.240426\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 900.000 0.197353
$$276$$ 0 0
$$277$$ −466.000 −0.101080 −0.0505401 0.998722i $$-0.516094\pi$$
−0.0505401 + 0.998722i $$0.516094\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 4854.00 1.03048 0.515241 0.857045i $$-0.327702\pi$$
0.515241 + 0.857045i $$0.327702\pi$$
$$282$$ 0 0
$$283$$ 4516.00 0.948581 0.474290 0.880368i $$-0.342705\pi$$
0.474290 + 0.880368i $$0.342705\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −12480.0 −2.56680
$$288$$ 0 0
$$289$$ 1171.00 0.238347
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −8574.00 −1.70955 −0.854775 0.518998i $$-0.826305\pi$$
−0.854775 + 0.518998i $$0.826305\pi$$
$$294$$ 0 0
$$295$$ −2580.00 −0.509198
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1920.00 0.371359
$$300$$ 0 0
$$301$$ −1664.00 −0.318642
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 290.000 0.0544438
$$306$$ 0 0
$$307$$ −3476.00 −0.646208 −0.323104 0.946363i $$-0.604726\pi$$
−0.323104 + 0.946363i $$0.604726\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 2424.00 0.441969 0.220985 0.975277i $$-0.429073\pi$$
0.220985 + 0.975277i $$0.429073\pi$$
$$312$$ 0 0
$$313$$ −1558.00 −0.281353 −0.140676 0.990056i $$-0.544928\pi$$
−0.140676 + 0.990056i $$0.544928\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 8538.00 1.51275 0.756375 0.654138i $$-0.226968\pi$$
0.756375 + 0.654138i $$0.226968\pi$$
$$318$$ 0 0
$$319$$ −216.000 −0.0379112
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −10920.0 −1.88113
$$324$$ 0 0
$$325$$ −250.000 −0.0426692
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −13056.0 −2.18784
$$330$$ 0 0
$$331$$ 988.000 0.164065 0.0820323 0.996630i $$-0.473859\pi$$
0.0820323 + 0.996630i $$0.473859\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −4460.00 −0.727391
$$336$$ 0 0
$$337$$ 2546.00 0.411541 0.205771 0.978600i $$-0.434030\pi$$
0.205771 + 0.978600i $$0.434030\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 576.000 0.0914726
$$342$$ 0 0
$$343$$ −10816.0 −1.70265
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 8556.00 1.32366 0.661830 0.749654i $$-0.269780\pi$$
0.661830 + 0.749654i $$0.269780\pi$$
$$348$$ 0 0
$$349$$ −3706.00 −0.568417 −0.284209 0.958762i $$-0.591731\pi$$
−0.284209 + 0.958762i $$0.591731\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −11394.0 −1.71796 −0.858982 0.512005i $$-0.828903\pi$$
−0.858982 + 0.512005i $$0.828903\pi$$
$$354$$ 0 0
$$355$$ 600.000 0.0897034
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −264.000 −0.0388117 −0.0194058 0.999812i $$-0.506177\pi$$
−0.0194058 + 0.999812i $$0.506177\pi$$
$$360$$ 0 0
$$361$$ 12741.0 1.85756
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3230.00 0.463194
$$366$$ 0 0
$$367$$ −10232.0 −1.45533 −0.727665 0.685933i $$-0.759394\pi$$
−0.727665 + 0.685933i $$0.759394\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −3648.00 −0.510498
$$372$$ 0 0
$$373$$ −562.000 −0.0780141 −0.0390070 0.999239i $$-0.512419\pi$$
−0.0390070 + 0.999239i $$0.512419\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 60.0000 0.00819670
$$378$$ 0 0
$$379$$ 7228.00 0.979624 0.489812 0.871828i $$-0.337065\pi$$
0.489812 + 0.871828i $$0.337065\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −5736.00 −0.765263 −0.382632 0.923901i $$-0.624982\pi$$
−0.382632 + 0.923901i $$0.624982\pi$$
$$384$$ 0 0
$$385$$ 5760.00 0.762485
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 9186.00 1.19730 0.598649 0.801012i $$-0.295705\pi$$
0.598649 + 0.801012i $$0.295705\pi$$
$$390$$ 0 0
$$391$$ −14976.0 −1.93700
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −5840.00 −0.743905
$$396$$ 0 0
$$397$$ −394.000 −0.0498093 −0.0249047 0.999690i $$-0.507928\pi$$
−0.0249047 + 0.999690i $$0.507928\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 1614.00 0.200996 0.100498 0.994937i $$-0.467956\pi$$
0.100498 + 0.994937i $$0.467956\pi$$
$$402$$ 0 0
$$403$$ −160.000 −0.0197771
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −1224.00 −0.149070
$$408$$ 0 0
$$409$$ 1034.00 0.125007 0.0625037 0.998045i $$-0.480091\pi$$
0.0625037 + 0.998045i $$0.480091\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −16512.0 −1.96732
$$414$$ 0 0
$$415$$ 3660.00 0.432921
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 3708.00 0.432333 0.216167 0.976356i $$-0.430645\pi$$
0.216167 + 0.976356i $$0.430645\pi$$
$$420$$ 0 0
$$421$$ −4930.00 −0.570721 −0.285360 0.958420i $$-0.592113\pi$$
−0.285360 + 0.958420i $$0.592113\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1950.00 0.222562
$$426$$ 0 0
$$427$$ 1856.00 0.210347
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −2592.00 −0.289680 −0.144840 0.989455i $$-0.546267\pi$$
−0.144840 + 0.989455i $$0.546267\pi$$
$$432$$ 0 0
$$433$$ 2162.00 0.239952 0.119976 0.992777i $$-0.461718\pi$$
0.119976 + 0.992777i $$0.461718\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 26880.0 2.94244
$$438$$ 0 0
$$439$$ −1352.00 −0.146987 −0.0734937 0.997296i $$-0.523415\pi$$
−0.0734937 + 0.997296i $$0.523415\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 5532.00 0.593303 0.296652 0.954986i $$-0.404130\pi$$
0.296652 + 0.954986i $$0.404130\pi$$
$$444$$ 0 0
$$445$$ −7950.00 −0.846890
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 3198.00 0.336131 0.168066 0.985776i $$-0.446248\pi$$
0.168066 + 0.985776i $$0.446248\pi$$
$$450$$ 0 0
$$451$$ 14040.0 1.46589
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −1600.00 −0.164855
$$456$$ 0 0
$$457$$ −1510.00 −0.154562 −0.0772810 0.997009i $$-0.524624\pi$$
−0.0772810 + 0.997009i $$0.524624\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −16086.0 −1.62516 −0.812581 0.582848i $$-0.801938\pi$$
−0.812581 + 0.582848i $$0.801938\pi$$
$$462$$ 0 0
$$463$$ −5384.00 −0.540423 −0.270211 0.962801i $$-0.587094\pi$$
−0.270211 + 0.962801i $$0.587094\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −2604.00 −0.258027 −0.129014 0.991643i $$-0.541181\pi$$
−0.129014 + 0.991643i $$0.541181\pi$$
$$468$$ 0 0
$$469$$ −28544.0 −2.81032
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 1872.00 0.181976
$$474$$ 0 0
$$475$$ −3500.00 −0.338086
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 11136.0 1.06225 0.531124 0.847294i $$-0.321770\pi$$
0.531124 + 0.847294i $$0.321770\pi$$
$$480$$ 0 0
$$481$$ 340.000 0.0322301
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −970.000 −0.0908153
$$486$$ 0 0
$$487$$ −14624.0 −1.36073 −0.680366 0.732872i $$-0.738179\pi$$
−0.680366 + 0.732872i $$0.738179\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 11844.0 1.08862 0.544310 0.838884i $$-0.316792\pi$$
0.544310 + 0.838884i $$0.316792\pi$$
$$492$$ 0 0
$$493$$ −468.000 −0.0427539
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 3840.00 0.346575
$$498$$ 0 0
$$499$$ 11284.0 1.01231 0.506154 0.862443i $$-0.331067\pi$$
0.506154 + 0.862443i $$0.331067\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4032.00 0.357412 0.178706 0.983903i $$-0.442809\pi$$
0.178706 + 0.983903i $$0.442809\pi$$
$$504$$ 0 0
$$505$$ 3990.00 0.351589
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 17562.0 1.52932 0.764658 0.644436i $$-0.222908\pi$$
0.764658 + 0.644436i $$0.222908\pi$$
$$510$$ 0 0
$$511$$ 20672.0 1.78958
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 1360.00 0.116367
$$516$$ 0 0
$$517$$ 14688.0 1.24947
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −3162.00 −0.265892 −0.132946 0.991123i $$-0.542444\pi$$
−0.132946 + 0.991123i $$0.542444\pi$$
$$522$$ 0 0
$$523$$ −6764.00 −0.565524 −0.282762 0.959190i $$-0.591251\pi$$
−0.282762 + 0.959190i $$0.591251\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 1248.00 0.103157
$$528$$ 0 0
$$529$$ 24697.0 2.02983
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3900.00 −0.316938
$$534$$ 0 0
$$535$$ −780.000 −0.0630324
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 24516.0 1.95914
$$540$$ 0 0
$$541$$ 17798.0 1.41441 0.707205 0.707009i $$-0.249956\pi$$
0.707205 + 0.707009i $$0.249956\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −8110.00 −0.637421
$$546$$ 0 0
$$547$$ 19996.0 1.56301 0.781506 0.623898i $$-0.214452\pi$$
0.781506 + 0.623898i $$0.214452\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 840.000 0.0649459
$$552$$ 0 0
$$553$$ −37376.0 −2.87412
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −11094.0 −0.843928 −0.421964 0.906613i $$-0.638659\pi$$
−0.421964 + 0.906613i $$0.638659\pi$$
$$558$$ 0 0
$$559$$ −520.000 −0.0393446
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 900.000 0.0673721 0.0336860 0.999432i $$-0.489275\pi$$
0.0336860 + 0.999432i $$0.489275\pi$$
$$564$$ 0 0
$$565$$ 5370.00 0.399854
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −7914.00 −0.583079 −0.291540 0.956559i $$-0.594168\pi$$
−0.291540 + 0.956559i $$0.594168\pi$$
$$570$$ 0 0
$$571$$ 2380.00 0.174431 0.0872153 0.996189i $$-0.472203\pi$$
0.0872153 + 0.996189i $$0.472203\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −4800.00 −0.348128
$$576$$ 0 0
$$577$$ −25726.0 −1.85613 −0.928065 0.372417i $$-0.878529\pi$$
−0.928065 + 0.372417i $$0.878529\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 23424.0 1.67262
$$582$$ 0 0
$$583$$ 4104.00 0.291544
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 3612.00 0.253975 0.126987 0.991904i $$-0.459469\pi$$
0.126987 + 0.991904i $$0.459469\pi$$
$$588$$ 0 0
$$589$$ −2240.00 −0.156702
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −2898.00 −0.200686 −0.100343 0.994953i $$-0.531994\pi$$
−0.100343 + 0.994953i $$0.531994\pi$$
$$594$$ 0 0
$$595$$ 12480.0 0.859883
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 2664.00 0.181716 0.0908582 0.995864i $$-0.471039\pi$$
0.0908582 + 0.995864i $$0.471039\pi$$
$$600$$ 0 0
$$601$$ −502.000 −0.0340716 −0.0170358 0.999855i $$-0.505423\pi$$
−0.0170358 + 0.999855i $$0.505423\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 175.000 0.0117599
$$606$$ 0 0
$$607$$ −7976.00 −0.533337 −0.266669 0.963788i $$-0.585923\pi$$
−0.266669 + 0.963788i $$0.585923\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −4080.00 −0.270146
$$612$$ 0 0
$$613$$ 20414.0 1.34505 0.672523 0.740076i $$-0.265210\pi$$
0.672523 + 0.740076i $$0.265210\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 6342.00 0.413808 0.206904 0.978361i $$-0.433661\pi$$
0.206904 + 0.978361i $$0.433661\pi$$
$$618$$ 0 0
$$619$$ −22676.0 −1.47242 −0.736208 0.676755i $$-0.763385\pi$$
−0.736208 + 0.676755i $$0.763385\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −50880.0 −3.27201
$$624$$ 0 0
$$625$$ 625.000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −2652.00 −0.168112
$$630$$ 0 0
$$631$$ 7048.00 0.444654 0.222327 0.974972i $$-0.428635\pi$$
0.222327 + 0.974972i $$0.428635\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −7640.00 −0.477455
$$636$$ 0 0
$$637$$ −6810.00 −0.423582
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 20286.0 1.25000 0.624999 0.780625i $$-0.285099\pi$$
0.624999 + 0.780625i $$0.285099\pi$$
$$642$$ 0 0
$$643$$ 16108.0 0.987928 0.493964 0.869482i $$-0.335548\pi$$
0.493964 + 0.869482i $$0.335548\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 27456.0 1.66833 0.834163 0.551518i $$-0.185951\pi$$
0.834163 + 0.551518i $$0.185951\pi$$
$$648$$ 0 0
$$649$$ 18576.0 1.12353
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 12522.0 0.750419 0.375210 0.926940i $$-0.377571\pi$$
0.375210 + 0.926940i $$0.377571\pi$$
$$654$$ 0 0
$$655$$ −12060.0 −0.719425
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −16308.0 −0.963990 −0.481995 0.876174i $$-0.660088\pi$$
−0.481995 + 0.876174i $$0.660088\pi$$
$$660$$ 0 0
$$661$$ 32078.0 1.88758 0.943789 0.330547i $$-0.107233\pi$$
0.943789 + 0.330547i $$0.107233\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −22400.0 −1.30622
$$666$$ 0 0
$$667$$ 1152.00 0.0668750
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −2088.00 −0.120129
$$672$$ 0 0
$$673$$ 4610.00 0.264045 0.132023 0.991247i $$-0.457853\pi$$
0.132023 + 0.991247i $$0.457853\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −10782.0 −0.612091 −0.306046 0.952017i $$-0.599006\pi$$
−0.306046 + 0.952017i $$0.599006\pi$$
$$678$$ 0 0
$$679$$ −6208.00 −0.350871
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 2892.00 0.162019 0.0810097 0.996713i $$-0.474186\pi$$
0.0810097 + 0.996713i $$0.474186\pi$$
$$684$$ 0 0
$$685$$ 10530.0 0.587344
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −1140.00 −0.0630342
$$690$$ 0 0
$$691$$ 29572.0 1.62803 0.814017 0.580841i $$-0.197276\pi$$
0.814017 + 0.580841i $$0.197276\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −2780.00 −0.151729
$$696$$ 0 0
$$697$$ 30420.0 1.65314
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −5766.00 −0.310669 −0.155334 0.987862i $$-0.549646\pi$$
−0.155334 + 0.987862i $$0.549646\pi$$
$$702$$ 0 0
$$703$$ 4760.00 0.255372
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 25536.0 1.35839
$$708$$ 0 0
$$709$$ 3326.00 0.176178 0.0880892 0.996113i $$-0.471924\pi$$
0.0880892 + 0.996113i $$0.471924\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −3072.00 −0.161357
$$714$$ 0 0
$$715$$ 1800.00 0.0941485
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −7728.00 −0.400843 −0.200421 0.979710i $$-0.564231\pi$$
−0.200421 + 0.979710i $$0.564231\pi$$
$$720$$ 0 0
$$721$$ 8704.00 0.449589
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −150.000 −0.00768395
$$726$$ 0 0
$$727$$ 21616.0 1.10274 0.551371 0.834260i $$-0.314105\pi$$
0.551371 + 0.834260i $$0.314105\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 4056.00 0.205221
$$732$$ 0 0
$$733$$ 10118.0 0.509846 0.254923 0.966961i $$-0.417950\pi$$
0.254923 + 0.966961i $$0.417950\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 32112.0 1.60497
$$738$$ 0 0
$$739$$ −10460.0 −0.520673 −0.260336 0.965518i $$-0.583833\pi$$
−0.260336 + 0.965518i $$0.583833\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 17232.0 0.850849 0.425424 0.904994i $$-0.360125\pi$$
0.425424 + 0.904994i $$0.360125\pi$$
$$744$$ 0 0
$$745$$ −12090.0 −0.594555
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −4992.00 −0.243530
$$750$$ 0 0
$$751$$ −26912.0 −1.30763 −0.653817 0.756653i $$-0.726833\pi$$
−0.653817 + 0.756653i $$0.726833\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 14200.0 0.684491
$$756$$ 0 0
$$757$$ 13838.0 0.664400 0.332200 0.943209i $$-0.392209\pi$$
0.332200 + 0.943209i $$0.392209\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 17238.0 0.821126 0.410563 0.911832i $$-0.365332\pi$$
0.410563 + 0.911832i $$0.365332\pi$$
$$762$$ 0 0
$$763$$ −51904.0 −2.46271
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −5160.00 −0.242916
$$768$$ 0 0
$$769$$ 21698.0 1.01749 0.508745 0.860917i $$-0.330110\pi$$
0.508745 + 0.860917i $$0.330110\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −18366.0 −0.854565 −0.427283 0.904118i $$-0.640529\pi$$
−0.427283 + 0.904118i $$0.640529\pi$$
$$774$$ 0 0
$$775$$ 400.000 0.0185399
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −54600.0 −2.51123
$$780$$ 0 0
$$781$$ −4320.00 −0.197928
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −10270.0 −0.466945
$$786$$ 0 0
$$787$$ 30316.0 1.37312 0.686562 0.727071i $$-0.259119\pi$$
0.686562 + 0.727071i $$0.259119\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 34368.0 1.54486
$$792$$ 0 0
$$793$$ 580.000 0.0259728
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −7494.00 −0.333063 −0.166531 0.986036i $$-0.553257\pi$$
−0.166531 + 0.986036i $$0.553257\pi$$
$$798$$ 0 0
$$799$$ 31824.0 1.40908
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −23256.0 −1.02203
$$804$$ 0 0
$$805$$ −30720.0 −1.34502
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 11526.0 0.500906 0.250453 0.968129i $$-0.419421\pi$$
0.250453 + 0.968129i $$0.419421\pi$$
$$810$$ 0 0
$$811$$ 33820.0 1.46434 0.732171 0.681121i $$-0.238507\pi$$
0.732171 + 0.681121i $$0.238507\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −2300.00 −0.0988534
$$816$$ 0 0
$$817$$ −7280.00 −0.311744
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −19566.0 −0.831739 −0.415870 0.909424i $$-0.636523\pi$$
−0.415870 + 0.909424i $$0.636523\pi$$
$$822$$ 0 0
$$823$$ 40096.0 1.69825 0.849124 0.528193i $$-0.177130\pi$$
0.849124 + 0.528193i $$0.177130\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 31884.0 1.34065 0.670324 0.742069i $$-0.266155\pi$$
0.670324 + 0.742069i $$0.266155\pi$$
$$828$$ 0 0
$$829$$ −24442.0 −1.02401 −0.512006 0.858982i $$-0.671097\pi$$
−0.512006 + 0.858982i $$0.671097\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 53118.0 2.20940
$$834$$ 0 0
$$835$$ −10080.0 −0.417764
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −31944.0 −1.31446 −0.657228 0.753691i $$-0.728271\pi$$
−0.657228 + 0.753691i $$0.728271\pi$$
$$840$$ 0 0
$$841$$ −24353.0 −0.998524
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 10485.0 0.426858
$$846$$ 0 0
$$847$$ 1120.00 0.0454352
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 6528.00 0.262958
$$852$$ 0 0
$$853$$ 17486.0 0.701887 0.350943 0.936397i $$-0.385861\pi$$
0.350943 + 0.936397i $$0.385861\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −43434.0 −1.73125 −0.865623 0.500697i $$-0.833077\pi$$
−0.865623 + 0.500697i $$0.833077\pi$$
$$858$$ 0 0
$$859$$ −10820.0 −0.429771 −0.214886 0.976639i $$-0.568938\pi$$
−0.214886 + 0.976639i $$0.568938\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 29976.0 1.18238 0.591191 0.806532i $$-0.298658\pi$$
0.591191 + 0.806532i $$0.298658\pi$$
$$864$$ 0 0
$$865$$ −3090.00 −0.121460
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 42048.0 1.64140
$$870$$ 0 0
$$871$$ −8920.00 −0.347007
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 4000.00 0.154542
$$876$$ 0 0
$$877$$ −40522.0 −1.56024 −0.780120 0.625630i $$-0.784842\pi$$
−0.780120 + 0.625630i $$0.784842\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −15570.0 −0.595422 −0.297711 0.954656i $$-0.596223\pi$$
−0.297711 + 0.954656i $$0.596223\pi$$
$$882$$ 0 0
$$883$$ 1084.00 0.0413131 0.0206566 0.999787i $$-0.493424\pi$$
0.0206566 + 0.999787i $$0.493424\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −8208.00 −0.310708 −0.155354 0.987859i $$-0.549652\pi$$
−0.155354 + 0.987859i $$0.549652\pi$$
$$888$$ 0 0
$$889$$ −48896.0 −1.84468
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −57120.0 −2.14048
$$894$$ 0 0
$$895$$ 14820.0 0.553495
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −96.0000 −0.00356149
$$900$$ 0 0
$$901$$ 8892.00 0.328785
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 1850.00 0.0679515
$$906$$ 0 0
$$907$$ −34076.0 −1.24749 −0.623746 0.781627i $$-0.714390\pi$$
−0.623746 + 0.781627i $$0.714390\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −15072.0 −0.548142 −0.274071 0.961709i $$-0.588370\pi$$
−0.274071 + 0.961709i $$0.588370\pi$$
$$912$$ 0 0
$$913$$ −26352.0 −0.955229
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −77184.0 −2.77954
$$918$$ 0 0
$$919$$ −24392.0 −0.875536 −0.437768 0.899088i $$-0.644231\pi$$
−0.437768 + 0.899088i $$0.644231\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 1200.00 0.0427936
$$924$$ 0 0
$$925$$ −850.000 −0.0302139
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −13602.0 −0.480374 −0.240187 0.970727i $$-0.577209\pi$$
−0.240187 + 0.970727i $$0.577209\pi$$
$$930$$ 0 0
$$931$$ −95340.0 −3.35622
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −14040.0 −0.491077
$$936$$ 0 0
$$937$$ −47974.0 −1.67262 −0.836309 0.548259i $$-0.815291\pi$$
−0.836309 + 0.548259i $$0.815291\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 48330.0 1.67430 0.837148 0.546976i $$-0.184221\pi$$
0.837148 + 0.546976i $$0.184221\pi$$
$$942$$ 0 0
$$943$$ −74880.0 −2.58582
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −9324.00 −0.319946 −0.159973 0.987121i $$-0.551141\pi$$
−0.159973 + 0.987121i $$0.551141\pi$$
$$948$$ 0 0
$$949$$ 6460.00 0.220970
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 14838.0 0.504355 0.252177 0.967681i $$-0.418853\pi$$
0.252177 + 0.967681i $$0.418853\pi$$
$$954$$ 0 0
$$955$$ −5520.00 −0.187040
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 67392.0 2.26924
$$960$$ 0 0
$$961$$ −29535.0 −0.991407
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 11990.0 0.399971
$$966$$ 0 0
$$967$$ −11360.0 −0.377780 −0.188890 0.981998i $$-0.560489\pi$$
−0.188890 + 0.981998i $$0.560489\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −6972.00 −0.230424 −0.115212 0.993341i $$-0.536755\pi$$
−0.115212 + 0.993341i $$0.536755\pi$$
$$972$$ 0 0
$$973$$ −17792.0 −0.586213
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 41166.0 1.34802 0.674011 0.738722i $$-0.264570\pi$$
0.674011 + 0.738722i $$0.264570\pi$$
$$978$$ 0 0
$$979$$ 57240.0 1.86864
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 22464.0 0.728881 0.364441 0.931227i $$-0.381260\pi$$
0.364441 + 0.931227i $$0.381260\pi$$
$$984$$ 0 0
$$985$$ 6390.00 0.206703
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −9984.00 −0.321004
$$990$$ 0 0
$$991$$ 10192.0 0.326700 0.163350 0.986568i $$-0.447770\pi$$
0.163350 + 0.986568i $$0.447770\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 22360.0 0.712422
$$996$$ 0 0
$$997$$ −322.000 −0.0102285 −0.00511426 0.999987i $$-0.501628\pi$$
−0.00511426 + 0.999987i $$0.501628\pi$$
$$998$$ 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 720.4.a.c.1.1 1
3.2 odd 2 240.4.a.j.1.1 1
4.3 odd 2 180.4.a.c.1.1 1
12.11 even 2 60.4.a.b.1.1 1
15.2 even 4 1200.4.f.e.49.1 2
15.8 even 4 1200.4.f.e.49.2 2
15.14 odd 2 1200.4.a.s.1.1 1
20.3 even 4 900.4.d.b.649.1 2
20.7 even 4 900.4.d.b.649.2 2
20.19 odd 2 900.4.a.b.1.1 1
24.5 odd 2 960.4.a.a.1.1 1
24.11 even 2 960.4.a.bb.1.1 1
36.7 odd 6 1620.4.i.g.1081.1 2
36.11 even 6 1620.4.i.a.1081.1 2
36.23 even 6 1620.4.i.a.541.1 2
36.31 odd 6 1620.4.i.g.541.1 2
60.23 odd 4 300.4.d.d.49.1 2
60.47 odd 4 300.4.d.d.49.2 2
60.59 even 2 300.4.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
60.4.a.b.1.1 1 12.11 even 2
180.4.a.c.1.1 1 4.3 odd 2
240.4.a.j.1.1 1 3.2 odd 2
300.4.a.e.1.1 1 60.59 even 2
300.4.d.d.49.1 2 60.23 odd 4
300.4.d.d.49.2 2 60.47 odd 4
720.4.a.c.1.1 1 1.1 even 1 trivial
900.4.a.b.1.1 1 20.19 odd 2
900.4.d.b.649.1 2 20.3 even 4
900.4.d.b.649.2 2 20.7 even 4
960.4.a.a.1.1 1 24.5 odd 2
960.4.a.bb.1.1 1 24.11 even 2
1200.4.a.s.1.1 1 15.14 odd 2
1200.4.f.e.49.1 2 15.2 even 4
1200.4.f.e.49.2 2 15.8 even 4
1620.4.i.a.541.1 2 36.23 even 6
1620.4.i.a.1081.1 2 36.11 even 6
1620.4.i.g.541.1 2 36.31 odd 6
1620.4.i.g.1081.1 2 36.7 odd 6