# Properties

 Label 2450.2.a.bf.1.1 Level $2450$ Weight $2$ Character 2450.1 Self dual yes Analytic conductor $19.563$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2450 = 2 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2450.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$19.5633484952$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 70) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2450.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{11} +2.00000 q^{12} +1.00000 q^{13} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} +3.00000 q^{22} -9.00000 q^{23} +2.00000 q^{24} +1.00000 q^{26} -4.00000 q^{27} +6.00000 q^{29} +8.00000 q^{31} +1.00000 q^{32} +6.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} +7.00000 q^{37} -1.00000 q^{38} +2.00000 q^{39} +3.00000 q^{41} -2.00000 q^{43} +3.00000 q^{44} -9.00000 q^{46} -9.00000 q^{47} +2.00000 q^{48} +12.0000 q^{51} +1.00000 q^{52} -9.00000 q^{53} -4.00000 q^{54} -2.00000 q^{57} +6.00000 q^{58} +8.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +6.00000 q^{66} -8.00000 q^{67} +6.00000 q^{68} -18.0000 q^{69} +1.00000 q^{72} +4.00000 q^{73} +7.00000 q^{74} -1.00000 q^{76} +2.00000 q^{78} -10.0000 q^{79} -11.0000 q^{81} +3.00000 q^{82} -2.00000 q^{86} +12.0000 q^{87} +3.00000 q^{88} +6.00000 q^{89} -9.00000 q^{92} +16.0000 q^{93} -9.00000 q^{94} +2.00000 q^{96} +10.0000 q^{97} +3.00000 q^{99} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 2.00000 1.15470 0.577350 0.816497i $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 2.00000 0.816497
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 2.00000 0.577350
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −1.00000 −0.229416 −0.114708 0.993399i $$-0.536593\pi$$
−0.114708 + 0.993399i $$0.536593\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 3.00000 0.639602
$$23$$ −9.00000 −1.87663 −0.938315 0.345782i $$-0.887614\pi$$
−0.938315 + 0.345782i $$0.887614\pi$$
$$24$$ 2.00000 0.408248
$$25$$ 0 0
$$26$$ 1.00000 0.196116
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 6.00000 1.04447
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 7.00000 1.15079 0.575396 0.817875i $$-0.304848\pi$$
0.575396 + 0.817875i $$0.304848\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ 2.00000 0.320256
$$40$$ 0 0
$$41$$ 3.00000 0.468521 0.234261 0.972174i $$-0.424733\pi$$
0.234261 + 0.972174i $$0.424733\pi$$
$$42$$ 0 0
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 0 0
$$46$$ −9.00000 −1.32698
$$47$$ −9.00000 −1.31278 −0.656392 0.754420i $$-0.727918\pi$$
−0.656392 + 0.754420i $$0.727918\pi$$
$$48$$ 2.00000 0.288675
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 12.0000 1.68034
$$52$$ 1.00000 0.138675
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ −4.00000 −0.544331
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −2.00000 −0.264906
$$58$$ 6.00000 0.787839
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 8.00000 1.02430 0.512148 0.858898i $$-0.328850\pi$$
0.512148 + 0.858898i $$0.328850\pi$$
$$62$$ 8.00000 1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 6.00000 0.738549
$$67$$ −8.00000 −0.977356 −0.488678 0.872464i $$-0.662521\pi$$
−0.488678 + 0.872464i $$0.662521\pi$$
$$68$$ 6.00000 0.727607
$$69$$ −18.0000 −2.16695
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 1.00000 0.117851
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 7.00000 0.813733
$$75$$ 0 0
$$76$$ −1.00000 −0.114708
$$77$$ 0 0
$$78$$ 2.00000 0.226455
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 3.00000 0.331295
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 −0.215666
$$87$$ 12.0000 1.28654
$$88$$ 3.00000 0.319801
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −9.00000 −0.938315
$$93$$ 16.0000 1.65912
$$94$$ −9.00000 −0.928279
$$95$$ 0 0
$$96$$ 2.00000 0.204124
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 0 0
$$99$$ 3.00000 0.301511
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 12.0000 1.18818
$$103$$ 4.00000 0.394132 0.197066 0.980390i $$-0.436859\pi$$
0.197066 + 0.980390i $$0.436859\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ 0 0
$$106$$ −9.00000 −0.874157
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ −4.00000 −0.384900
$$109$$ −16.0000 −1.53252 −0.766261 0.642529i $$-0.777885\pi$$
−0.766261 + 0.642529i $$0.777885\pi$$
$$110$$ 0 0
$$111$$ 14.0000 1.32882
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ −2.00000 −0.187317
$$115$$ 0 0
$$116$$ 6.00000 0.557086
$$117$$ 1.00000 0.0924500
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 8.00000 0.724286
$$123$$ 6.00000 0.541002
$$124$$ 8.00000 0.718421
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1.00000 0.0887357 0.0443678 0.999015i $$-0.485873\pi$$
0.0443678 + 0.999015i $$0.485873\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ 3.00000 0.262111 0.131056 0.991375i $$-0.458163\pi$$
0.131056 + 0.991375i $$0.458163\pi$$
$$132$$ 6.00000 0.522233
$$133$$ 0 0
$$134$$ −8.00000 −0.691095
$$135$$ 0 0
$$136$$ 6.00000 0.514496
$$137$$ −12.0000 −1.02523 −0.512615 0.858619i $$-0.671323\pi$$
−0.512615 + 0.858619i $$0.671323\pi$$
$$138$$ −18.0000 −1.53226
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ −18.0000 −1.51587
$$142$$ 0 0
$$143$$ 3.00000 0.250873
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 4.00000 0.331042
$$147$$ 0 0
$$148$$ 7.00000 0.575396
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ −1.00000 −0.0811107
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 2.00000 0.160128
$$157$$ −23.0000 −1.83560 −0.917800 0.397043i $$-0.870036\pi$$
−0.917800 + 0.397043i $$0.870036\pi$$
$$158$$ −10.0000 −0.795557
$$159$$ −18.0000 −1.42749
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −11.0000 −0.864242
$$163$$ −20.0000 −1.56652 −0.783260 0.621694i $$-0.786445\pi$$
−0.783260 + 0.621694i $$0.786445\pi$$
$$164$$ 3.00000 0.234261
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −3.00000 −0.232147 −0.116073 0.993241i $$-0.537031\pi$$
−0.116073 + 0.993241i $$0.537031\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −1.00000 −0.0764719
$$172$$ −2.00000 −0.152499
$$173$$ −9.00000 −0.684257 −0.342129 0.939653i $$-0.611148\pi$$
−0.342129 + 0.939653i $$0.611148\pi$$
$$174$$ 12.0000 0.909718
$$175$$ 0 0
$$176$$ 3.00000 0.226134
$$177$$ 0 0
$$178$$ 6.00000 0.449719
$$179$$ −3.00000 −0.224231 −0.112115 0.993695i $$-0.535763\pi$$
−0.112115 + 0.993695i $$0.535763\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 16.0000 1.18275
$$184$$ −9.00000 −0.663489
$$185$$ 0 0
$$186$$ 16.0000 1.17318
$$187$$ 18.0000 1.31629
$$188$$ −9.00000 −0.656392
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 2.00000 0.144338
$$193$$ 16.0000 1.15171 0.575853 0.817554i $$-0.304670\pi$$
0.575853 + 0.817554i $$0.304670\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −15.0000 −1.06871 −0.534353 0.845262i $$-0.679445\pi$$
−0.534353 + 0.845262i $$0.679445\pi$$
$$198$$ 3.00000 0.213201
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ −16.0000 −1.12855
$$202$$ 12.0000 0.844317
$$203$$ 0 0
$$204$$ 12.0000 0.840168
$$205$$ 0 0
$$206$$ 4.00000 0.278693
$$207$$ −9.00000 −0.625543
$$208$$ 1.00000 0.0693375
$$209$$ −3.00000 −0.207514
$$210$$ 0 0
$$211$$ 23.0000 1.58339 0.791693 0.610920i $$-0.209200\pi$$
0.791693 + 0.610920i $$0.209200\pi$$
$$212$$ −9.00000 −0.618123
$$213$$ 0 0
$$214$$ 12.0000 0.820303
$$215$$ 0 0
$$216$$ −4.00000 −0.272166
$$217$$ 0 0
$$218$$ −16.0000 −1.08366
$$219$$ 8.00000 0.540590
$$220$$ 0 0
$$221$$ 6.00000 0.403604
$$222$$ 14.0000 0.939618
$$223$$ −8.00000 −0.535720 −0.267860 0.963458i $$-0.586316\pi$$
−0.267860 + 0.963458i $$0.586316\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ −2.00000 −0.132453
$$229$$ −4.00000 −0.264327 −0.132164 0.991228i $$-0.542192\pi$$
−0.132164 + 0.991228i $$0.542192\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 1.00000 0.0653720
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −20.0000 −1.29914
$$238$$ 0 0
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ 0 0
$$241$$ −1.00000 −0.0644157 −0.0322078 0.999481i $$-0.510254\pi$$
−0.0322078 + 0.999481i $$0.510254\pi$$
$$242$$ −2.00000 −0.128565
$$243$$ −10.0000 −0.641500
$$244$$ 8.00000 0.512148
$$245$$ 0 0
$$246$$ 6.00000 0.382546
$$247$$ −1.00000 −0.0636285
$$248$$ 8.00000 0.508001
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −15.0000 −0.946792 −0.473396 0.880850i $$-0.656972\pi$$
−0.473396 + 0.880850i $$0.656972\pi$$
$$252$$ 0 0
$$253$$ −27.0000 −1.69748
$$254$$ 1.00000 0.0627456
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ 3.00000 0.185341
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 6.00000 0.369274
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ −8.00000 −0.488678
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ −16.0000 −0.971931 −0.485965 0.873978i $$-0.661532\pi$$
−0.485965 + 0.873978i $$0.661532\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ −12.0000 −0.724947
$$275$$ 0 0
$$276$$ −18.0000 −1.08347
$$277$$ 10.0000 0.600842 0.300421 0.953807i $$-0.402873\pi$$
0.300421 + 0.953807i $$0.402873\pi$$
$$278$$ −4.00000 −0.239904
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ −27.0000 −1.61068 −0.805342 0.592810i $$-0.798019\pi$$
−0.805342 + 0.592810i $$0.798019\pi$$
$$282$$ −18.0000 −1.07188
$$283$$ −14.0000 −0.832214 −0.416107 0.909316i $$-0.636606\pi$$
−0.416107 + 0.909316i $$0.636606\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 3.00000 0.177394
$$287$$ 0 0
$$288$$ 1.00000 0.0589256
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 20.0000 1.17242
$$292$$ 4.00000 0.234082
$$293$$ 9.00000 0.525786 0.262893 0.964825i $$-0.415323\pi$$
0.262893 + 0.964825i $$0.415323\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 7.00000 0.406867
$$297$$ −12.0000 −0.696311
$$298$$ −6.00000 −0.347571
$$299$$ −9.00000 −0.520483
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −10.0000 −0.575435
$$303$$ 24.0000 1.37876
$$304$$ −1.00000 −0.0573539
$$305$$ 0 0
$$306$$ 6.00000 0.342997
$$307$$ −14.0000 −0.799022 −0.399511 0.916728i $$-0.630820\pi$$
−0.399511 + 0.916728i $$0.630820\pi$$
$$308$$ 0 0
$$309$$ 8.00000 0.455104
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 2.00000 0.113228
$$313$$ 28.0000 1.58265 0.791327 0.611393i $$-0.209391\pi$$
0.791327 + 0.611393i $$0.209391\pi$$
$$314$$ −23.0000 −1.29797
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ −6.00000 −0.336994 −0.168497 0.985702i $$-0.553891\pi$$
−0.168497 + 0.985702i $$0.553891\pi$$
$$318$$ −18.0000 −1.00939
$$319$$ 18.0000 1.00781
$$320$$ 0 0
$$321$$ 24.0000 1.33955
$$322$$ 0 0
$$323$$ −6.00000 −0.333849
$$324$$ −11.0000 −0.611111
$$325$$ 0 0
$$326$$ −20.0000 −1.10770
$$327$$ −32.0000 −1.76960
$$328$$ 3.00000 0.165647
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −7.00000 −0.384755 −0.192377 0.981321i $$-0.561620\pi$$
−0.192377 + 0.981321i $$0.561620\pi$$
$$332$$ 0 0
$$333$$ 7.00000 0.383598
$$334$$ −3.00000 −0.164153
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 22.0000 1.19842 0.599208 0.800593i $$-0.295482\pi$$
0.599208 + 0.800593i $$0.295482\pi$$
$$338$$ −12.0000 −0.652714
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 24.0000 1.29967
$$342$$ −1.00000 −0.0540738
$$343$$ 0 0
$$344$$ −2.00000 −0.107833
$$345$$ 0 0
$$346$$ −9.00000 −0.483843
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 12.0000 0.643268
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ −4.00000 −0.213504
$$352$$ 3.00000 0.159901
$$353$$ −12.0000 −0.638696 −0.319348 0.947638i $$-0.603464\pi$$
−0.319348 + 0.947638i $$0.603464\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −3.00000 −0.158555
$$359$$ 18.0000 0.950004 0.475002 0.879985i $$-0.342447\pi$$
0.475002 + 0.879985i $$0.342447\pi$$
$$360$$ 0 0
$$361$$ −18.0000 −0.947368
$$362$$ 2.00000 0.105118
$$363$$ −4.00000 −0.209946
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 16.0000 0.836333
$$367$$ 19.0000 0.991792 0.495896 0.868382i $$-0.334840\pi$$
0.495896 + 0.868382i $$0.334840\pi$$
$$368$$ −9.00000 −0.469157
$$369$$ 3.00000 0.156174
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 16.0000 0.829561
$$373$$ −2.00000 −0.103556 −0.0517780 0.998659i $$-0.516489\pi$$
−0.0517780 + 0.998659i $$0.516489\pi$$
$$374$$ 18.0000 0.930758
$$375$$ 0 0
$$376$$ −9.00000 −0.464140
$$377$$ 6.00000 0.309016
$$378$$ 0 0
$$379$$ 23.0000 1.18143 0.590715 0.806880i $$-0.298846\pi$$
0.590715 + 0.806880i $$0.298846\pi$$
$$380$$ 0 0
$$381$$ 2.00000 0.102463
$$382$$ 12.0000 0.613973
$$383$$ −21.0000 −1.07305 −0.536525 0.843884i $$-0.680263\pi$$
−0.536525 + 0.843884i $$0.680263\pi$$
$$384$$ 2.00000 0.102062
$$385$$ 0 0
$$386$$ 16.0000 0.814379
$$387$$ −2.00000 −0.101666
$$388$$ 10.0000 0.507673
$$389$$ −12.0000 −0.608424 −0.304212 0.952604i $$-0.598393\pi$$
−0.304212 + 0.952604i $$0.598393\pi$$
$$390$$ 0 0
$$391$$ −54.0000 −2.73090
$$392$$ 0 0
$$393$$ 6.00000 0.302660
$$394$$ −15.0000 −0.755689
$$395$$ 0 0
$$396$$ 3.00000 0.150756
$$397$$ −14.0000 −0.702640 −0.351320 0.936255i $$-0.614267\pi$$
−0.351320 + 0.936255i $$0.614267\pi$$
$$398$$ −16.0000 −0.802008
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −27.0000 −1.34832 −0.674158 0.738587i $$-0.735493\pi$$
−0.674158 + 0.738587i $$0.735493\pi$$
$$402$$ −16.0000 −0.798007
$$403$$ 8.00000 0.398508
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 21.0000 1.04093
$$408$$ 12.0000 0.594089
$$409$$ 26.0000 1.28562 0.642809 0.766027i $$-0.277769\pi$$
0.642809 + 0.766027i $$0.277769\pi$$
$$410$$ 0 0
$$411$$ −24.0000 −1.18383
$$412$$ 4.00000 0.197066
$$413$$ 0 0
$$414$$ −9.00000 −0.442326
$$415$$ 0 0
$$416$$ 1.00000 0.0490290
$$417$$ −8.00000 −0.391762
$$418$$ −3.00000 −0.146735
$$419$$ −9.00000 −0.439679 −0.219839 0.975536i $$-0.570553\pi$$
−0.219839 + 0.975536i $$0.570553\pi$$
$$420$$ 0 0
$$421$$ 2.00000 0.0974740 0.0487370 0.998812i $$-0.484480\pi$$
0.0487370 + 0.998812i $$0.484480\pi$$
$$422$$ 23.0000 1.11962
$$423$$ −9.00000 −0.437595
$$424$$ −9.00000 −0.437079
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ 6.00000 0.289683
$$430$$ 0 0
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ −4.00000 −0.192450
$$433$$ 40.0000 1.92228 0.961139 0.276066i $$-0.0890309\pi$$
0.961139 + 0.276066i $$0.0890309\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −16.0000 −0.766261
$$437$$ 9.00000 0.430528
$$438$$ 8.00000 0.382255
$$439$$ 26.0000 1.24091 0.620456 0.784241i $$-0.286947\pi$$
0.620456 + 0.784241i $$0.286947\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 6.00000 0.285391
$$443$$ −12.0000 −0.570137 −0.285069 0.958507i $$-0.592016\pi$$
−0.285069 + 0.958507i $$0.592016\pi$$
$$444$$ 14.0000 0.664411
$$445$$ 0 0
$$446$$ −8.00000 −0.378811
$$447$$ −12.0000 −0.567581
$$448$$ 0 0
$$449$$ 21.0000 0.991051 0.495526 0.868593i $$-0.334975\pi$$
0.495526 + 0.868593i $$0.334975\pi$$
$$450$$ 0 0
$$451$$ 9.00000 0.423793
$$452$$ 0 0
$$453$$ −20.0000 −0.939682
$$454$$ 12.0000 0.563188
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ −14.0000 −0.654892 −0.327446 0.944870i $$-0.606188\pi$$
−0.327446 + 0.944870i $$0.606188\pi$$
$$458$$ −4.00000 −0.186908
$$459$$ −24.0000 −1.12022
$$460$$ 0 0
$$461$$ −30.0000 −1.39724 −0.698620 0.715493i $$-0.746202\pi$$
−0.698620 + 0.715493i $$0.746202\pi$$
$$462$$ 0 0
$$463$$ 1.00000 0.0464739 0.0232370 0.999730i $$-0.492603\pi$$
0.0232370 + 0.999730i $$0.492603\pi$$
$$464$$ 6.00000 0.278543
$$465$$ 0 0
$$466$$ 6.00000 0.277945
$$467$$ 6.00000 0.277647 0.138823 0.990317i $$-0.455668\pi$$
0.138823 + 0.990317i $$0.455668\pi$$
$$468$$ 1.00000 0.0462250
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −46.0000 −2.11957
$$472$$ 0 0
$$473$$ −6.00000 −0.275880
$$474$$ −20.0000 −0.918630
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −9.00000 −0.412082
$$478$$ −6.00000 −0.274434
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 7.00000 0.319173
$$482$$ −1.00000 −0.0455488
$$483$$ 0 0
$$484$$ −2.00000 −0.0909091
$$485$$ 0 0
$$486$$ −10.0000 −0.453609
$$487$$ 16.0000 0.725029 0.362515 0.931978i $$-0.381918\pi$$
0.362515 + 0.931978i $$0.381918\pi$$
$$488$$ 8.00000 0.362143
$$489$$ −40.0000 −1.80886
$$490$$ 0 0
$$491$$ 36.0000 1.62466 0.812329 0.583200i $$-0.198200\pi$$
0.812329 + 0.583200i $$0.198200\pi$$
$$492$$ 6.00000 0.270501
$$493$$ 36.0000 1.62136
$$494$$ −1.00000 −0.0449921
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ 0 0
$$501$$ −6.00000 −0.268060
$$502$$ −15.0000 −0.669483
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −27.0000 −1.20030
$$507$$ −24.0000 −1.06588
$$508$$ 1.00000 0.0443678
$$509$$ −42.0000 −1.86162 −0.930809 0.365507i $$-0.880896\pi$$
−0.930809 + 0.365507i $$0.880896\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 4.00000 0.176604
$$514$$ 0 0
$$515$$ 0 0
$$516$$ −4.00000 −0.176090
$$517$$ −27.0000 −1.18746
$$518$$ 0 0
$$519$$ −18.0000 −0.790112
$$520$$ 0 0
$$521$$ −15.0000 −0.657162 −0.328581 0.944476i $$-0.606570\pi$$
−0.328581 + 0.944476i $$0.606570\pi$$
$$522$$ 6.00000 0.262613
$$523$$ 28.0000 1.22435 0.612177 0.790721i $$-0.290294\pi$$
0.612177 + 0.790721i $$0.290294\pi$$
$$524$$ 3.00000 0.131056
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 48.0000 2.09091
$$528$$ 6.00000 0.261116
$$529$$ 58.0000 2.52174
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 3.00000 0.129944
$$534$$ 12.0000 0.519291
$$535$$ 0 0
$$536$$ −8.00000 −0.345547
$$537$$ −6.00000 −0.258919
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 8.00000 0.343947 0.171973 0.985102i $$-0.444986\pi$$
0.171973 + 0.985102i $$0.444986\pi$$
$$542$$ −16.0000 −0.687259
$$543$$ 4.00000 0.171656
$$544$$ 6.00000 0.257248
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ −12.0000 −0.512615
$$549$$ 8.00000 0.341432
$$550$$ 0 0
$$551$$ −6.00000 −0.255609
$$552$$ −18.0000 −0.766131
$$553$$ 0 0
$$554$$ 10.0000 0.424859
$$555$$ 0 0
$$556$$ −4.00000 −0.169638
$$557$$ 9.00000 0.381342 0.190671 0.981654i $$-0.438934\pi$$
0.190671 + 0.981654i $$0.438934\pi$$
$$558$$ 8.00000 0.338667
$$559$$ −2.00000 −0.0845910
$$560$$ 0 0
$$561$$ 36.0000 1.51992
$$562$$ −27.0000 −1.13893
$$563$$ −42.0000 −1.77009 −0.885044 0.465506i $$-0.845872\pi$$
−0.885044 + 0.465506i $$0.845872\pi$$
$$564$$ −18.0000 −0.757937
$$565$$ 0 0
$$566$$ −14.0000 −0.588464
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 21.0000 0.880366 0.440183 0.897908i $$-0.354914\pi$$
0.440183 + 0.897908i $$0.354914\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 3.00000 0.125436
$$573$$ 24.0000 1.00261
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −44.0000 −1.83174 −0.915872 0.401470i $$-0.868499\pi$$
−0.915872 + 0.401470i $$0.868499\pi$$
$$578$$ 19.0000 0.790296
$$579$$ 32.0000 1.32987
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 20.0000 0.829027
$$583$$ −27.0000 −1.11823
$$584$$ 4.00000 0.165521
$$585$$ 0 0
$$586$$ 9.00000 0.371787
$$587$$ 24.0000 0.990586 0.495293 0.868726i $$-0.335061\pi$$
0.495293 + 0.868726i $$0.335061\pi$$
$$588$$ 0 0
$$589$$ −8.00000 −0.329634
$$590$$ 0 0
$$591$$ −30.0000 −1.23404
$$592$$ 7.00000 0.287698
$$593$$ −24.0000 −0.985562 −0.492781 0.870153i $$-0.664020\pi$$
−0.492781 + 0.870153i $$0.664020\pi$$
$$594$$ −12.0000 −0.492366
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ −32.0000 −1.30967
$$598$$ −9.00000 −0.368037
$$599$$ −42.0000 −1.71607 −0.858037 0.513588i $$-0.828316\pi$$
−0.858037 + 0.513588i $$0.828316\pi$$
$$600$$ 0 0
$$601$$ 26.0000 1.06056 0.530281 0.847822i $$-0.322086\pi$$
0.530281 + 0.847822i $$0.322086\pi$$
$$602$$ 0 0
$$603$$ −8.00000 −0.325785
$$604$$ −10.0000 −0.406894
$$605$$ 0 0
$$606$$ 24.0000 0.974933
$$607$$ 1.00000 0.0405887 0.0202944 0.999794i $$-0.493540\pi$$
0.0202944 + 0.999794i $$0.493540\pi$$
$$608$$ −1.00000 −0.0405554
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −9.00000 −0.364101
$$612$$ 6.00000 0.242536
$$613$$ −29.0000 −1.17130 −0.585649 0.810564i $$-0.699160\pi$$
−0.585649 + 0.810564i $$0.699160\pi$$
$$614$$ −14.0000 −0.564994
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000 0.724653 0.362326 0.932051i $$-0.381983\pi$$
0.362326 + 0.932051i $$0.381983\pi$$
$$618$$ 8.00000 0.321807
$$619$$ 23.0000 0.924448 0.462224 0.886763i $$-0.347052\pi$$
0.462224 + 0.886763i $$0.347052\pi$$
$$620$$ 0 0
$$621$$ 36.0000 1.44463
$$622$$ −24.0000 −0.962312
$$623$$ 0 0
$$624$$ 2.00000 0.0800641
$$625$$ 0 0
$$626$$ 28.0000 1.11911
$$627$$ −6.00000 −0.239617
$$628$$ −23.0000 −0.917800
$$629$$ 42.0000 1.67465
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ −10.0000 −0.397779
$$633$$ 46.0000 1.82834
$$634$$ −6.00000 −0.238290
$$635$$ 0 0
$$636$$ −18.0000 −0.713746
$$637$$ 0 0
$$638$$ 18.0000 0.712627
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 27.0000 1.06644 0.533218 0.845978i $$-0.320983\pi$$
0.533218 + 0.845978i $$0.320983\pi$$
$$642$$ 24.0000 0.947204
$$643$$ −2.00000 −0.0788723 −0.0394362 0.999222i $$-0.512556\pi$$
−0.0394362 + 0.999222i $$0.512556\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −6.00000 −0.236067
$$647$$ −33.0000 −1.29736 −0.648682 0.761060i $$-0.724679\pi$$
−0.648682 + 0.761060i $$0.724679\pi$$
$$648$$ −11.0000 −0.432121
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −20.0000 −0.783260
$$653$$ 9.00000 0.352197 0.176099 0.984373i $$-0.443652\pi$$
0.176099 + 0.984373i $$0.443652\pi$$
$$654$$ −32.0000 −1.25130
$$655$$ 0 0
$$656$$ 3.00000 0.117130
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ −24.0000 −0.934907 −0.467454 0.884018i $$-0.654829\pi$$
−0.467454 + 0.884018i $$0.654829\pi$$
$$660$$ 0 0
$$661$$ −28.0000 −1.08907 −0.544537 0.838737i $$-0.683295\pi$$
−0.544537 + 0.838737i $$0.683295\pi$$
$$662$$ −7.00000 −0.272063
$$663$$ 12.0000 0.466041
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 7.00000 0.271244
$$667$$ −54.0000 −2.09089
$$668$$ −3.00000 −0.116073
$$669$$ −16.0000 −0.618596
$$670$$ 0 0
$$671$$ 24.0000 0.926510
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 22.0000 0.847408
$$675$$ 0 0
$$676$$ −12.0000 −0.461538
$$677$$ 9.00000 0.345898 0.172949 0.984931i $$-0.444670\pi$$
0.172949 + 0.984931i $$0.444670\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 24.0000 0.919682
$$682$$ 24.0000 0.919007
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ −1.00000 −0.0382360
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −8.00000 −0.305219
$$688$$ −2.00000 −0.0762493
$$689$$ −9.00000 −0.342873
$$690$$ 0 0
$$691$$ 32.0000 1.21734 0.608669 0.793424i $$-0.291704\pi$$
0.608669 + 0.793424i $$0.291704\pi$$
$$692$$ −9.00000 −0.342129
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 12.0000 0.454859
$$697$$ 18.0000 0.681799
$$698$$ 26.0000 0.984115
$$699$$ 12.0000 0.453882
$$700$$ 0 0
$$701$$ −30.0000 −1.13308 −0.566542 0.824033i $$-0.691719\pi$$
−0.566542 + 0.824033i $$0.691719\pi$$
$$702$$ −4.00000 −0.150970
$$703$$ −7.00000 −0.264010
$$704$$ 3.00000 0.113067
$$705$$ 0 0
$$706$$ −12.0000 −0.451626
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −46.0000 −1.72757 −0.863783 0.503864i $$-0.831911\pi$$
−0.863783 + 0.503864i $$0.831911\pi$$
$$710$$ 0 0
$$711$$ −10.0000 −0.375029
$$712$$ 6.00000 0.224860
$$713$$ −72.0000 −2.69642
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −3.00000 −0.112115
$$717$$ −12.0000 −0.448148
$$718$$ 18.0000 0.671754
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −18.0000 −0.669891
$$723$$ −2.00000 −0.0743808
$$724$$ 2.00000 0.0743294
$$725$$ 0 0
$$726$$ −4.00000 −0.148454
$$727$$ 1.00000 0.0370879 0.0185440 0.999828i $$-0.494097\pi$$
0.0185440 + 0.999828i $$0.494097\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ −12.0000 −0.443836
$$732$$ 16.0000 0.591377
$$733$$ 43.0000 1.58824 0.794121 0.607760i $$-0.207932\pi$$
0.794121 + 0.607760i $$0.207932\pi$$
$$734$$ 19.0000 0.701303
$$735$$ 0 0
$$736$$ −9.00000 −0.331744
$$737$$ −24.0000 −0.884051
$$738$$ 3.00000 0.110432
$$739$$ 35.0000 1.28750 0.643748 0.765238i $$-0.277379\pi$$
0.643748 + 0.765238i $$0.277379\pi$$
$$740$$ 0 0
$$741$$ −2.00000 −0.0734718
$$742$$ 0 0
$$743$$ 45.0000 1.65089 0.825445 0.564483i $$-0.190924\pi$$
0.825445 + 0.564483i $$0.190924\pi$$
$$744$$ 16.0000 0.586588
$$745$$ 0 0
$$746$$ −2.00000 −0.0732252
$$747$$ 0 0
$$748$$ 18.0000 0.658145
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −10.0000 −0.364905 −0.182453 0.983215i $$-0.558404\pi$$
−0.182453 + 0.983215i $$0.558404\pi$$
$$752$$ −9.00000 −0.328196
$$753$$ −30.0000 −1.09326
$$754$$ 6.00000 0.218507
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −38.0000 −1.38113 −0.690567 0.723269i $$-0.742639\pi$$
−0.690567 + 0.723269i $$0.742639\pi$$
$$758$$ 23.0000 0.835398
$$759$$ −54.0000 −1.96008
$$760$$ 0 0
$$761$$ −27.0000 −0.978749 −0.489375 0.872074i $$-0.662775\pi$$
−0.489375 + 0.872074i $$0.662775\pi$$
$$762$$ 2.00000 0.0724524
$$763$$ 0 0
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ −21.0000 −0.758761
$$767$$ 0 0
$$768$$ 2.00000 0.0721688
$$769$$ 23.0000 0.829401 0.414701 0.909958i $$-0.363886\pi$$
0.414701 + 0.909958i $$0.363886\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 16.0000 0.575853
$$773$$ 51.0000 1.83434 0.917171 0.398493i $$-0.130467\pi$$
0.917171 + 0.398493i $$0.130467\pi$$
$$774$$ −2.00000 −0.0718885
$$775$$ 0 0
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ −12.0000 −0.430221
$$779$$ −3.00000 −0.107486
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −54.0000 −1.93104
$$783$$ −24.0000 −0.857690
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 6.00000 0.214013
$$787$$ 22.0000 0.784215 0.392108 0.919919i $$-0.371746\pi$$
0.392108 + 0.919919i $$0.371746\pi$$
$$788$$ −15.0000 −0.534353
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 3.00000 0.106600
$$793$$ 8.00000 0.284088
$$794$$ −14.0000 −0.496841
$$795$$ 0 0
$$796$$ −16.0000 −0.567105
$$797$$ −6.00000 −0.212531 −0.106265 0.994338i $$-0.533889\pi$$
−0.106265 + 0.994338i $$0.533889\pi$$
$$798$$ 0 0
$$799$$ −54.0000 −1.91038
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ −27.0000 −0.953403
$$803$$ 12.0000 0.423471
$$804$$ −16.0000 −0.564276
$$805$$ 0 0
$$806$$ 8.00000 0.281788
$$807$$ 0 0
$$808$$ 12.0000 0.422159
$$809$$ −9.00000 −0.316423 −0.158212 0.987405i $$-0.550573\pi$$
−0.158212 + 0.987405i $$0.550573\pi$$
$$810$$ 0 0
$$811$$ −25.0000 −0.877869 −0.438934 0.898519i $$-0.644644\pi$$
−0.438934 + 0.898519i $$0.644644\pi$$
$$812$$ 0 0
$$813$$ −32.0000 −1.12229
$$814$$ 21.0000 0.736050
$$815$$ 0 0
$$816$$ 12.0000 0.420084
$$817$$ 2.00000 0.0699711
$$818$$ 26.0000 0.909069
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 30.0000 1.04701 0.523504 0.852023i $$-0.324625\pi$$
0.523504 + 0.852023i $$0.324625\pi$$
$$822$$ −24.0000 −0.837096
$$823$$ 4.00000 0.139431 0.0697156 0.997567i $$-0.477791\pi$$
0.0697156 + 0.997567i $$0.477791\pi$$
$$824$$ 4.00000 0.139347
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −6.00000 −0.208640 −0.104320 0.994544i $$-0.533267\pi$$
−0.104320 + 0.994544i $$0.533267\pi$$
$$828$$ −9.00000 −0.312772
$$829$$ 14.0000 0.486240 0.243120 0.969996i $$-0.421829\pi$$
0.243120 + 0.969996i $$0.421829\pi$$
$$830$$ 0 0
$$831$$ 20.0000 0.693792
$$832$$ 1.00000 0.0346688
$$833$$ 0 0
$$834$$ −8.00000 −0.277017
$$835$$ 0 0
$$836$$ −3.00000 −0.103757
$$837$$ −32.0000 −1.10608
$$838$$ −9.00000 −0.310900
$$839$$ −30.0000 −1.03572 −0.517858 0.855467i $$-0.673270\pi$$
−0.517858 + 0.855467i $$0.673270\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 2.00000 0.0689246
$$843$$ −54.0000 −1.85986
$$844$$ 23.0000 0.791693
$$845$$ 0 0
$$846$$ −9.00000 −0.309426
$$847$$ 0 0
$$848$$ −9.00000 −0.309061
$$849$$ −28.0000 −0.960958
$$850$$ 0 0
$$851$$ −63.0000 −2.15961
$$852$$ 0 0
$$853$$ 19.0000 0.650548 0.325274 0.945620i $$-0.394544\pi$$
0.325274 + 0.945620i $$0.394544\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 12.0000 0.410152
$$857$$ 18.0000 0.614868 0.307434 0.951569i $$-0.400530\pi$$
0.307434 + 0.951569i $$0.400530\pi$$
$$858$$ 6.00000 0.204837
$$859$$ 32.0000 1.09183 0.545913 0.837842i $$-0.316183\pi$$
0.545913 + 0.837842i $$0.316183\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 12.0000 0.408722
$$863$$ 3.00000 0.102121 0.0510606 0.998696i $$-0.483740\pi$$
0.0510606 + 0.998696i $$0.483740\pi$$
$$864$$ −4.00000 −0.136083
$$865$$ 0 0
$$866$$ 40.0000 1.35926
$$867$$ 38.0000 1.29055
$$868$$ 0 0
$$869$$ −30.0000 −1.01768
$$870$$ 0 0
$$871$$ −8.00000 −0.271070
$$872$$ −16.0000 −0.541828
$$873$$ 10.0000 0.338449
$$874$$ 9.00000 0.304430
$$875$$ 0 0
$$876$$ 8.00000 0.270295
$$877$$ 13.0000 0.438979 0.219489 0.975615i $$-0.429561\pi$$
0.219489 + 0.975615i $$0.429561\pi$$
$$878$$ 26.0000 0.877457
$$879$$ 18.0000 0.607125
$$880$$ 0 0
$$881$$ 33.0000 1.11180 0.555899 0.831250i $$-0.312374\pi$$
0.555899 + 0.831250i $$0.312374\pi$$
$$882$$ 0 0
$$883$$ −8.00000 −0.269221 −0.134611 0.990899i $$-0.542978\pi$$
−0.134611 + 0.990899i $$0.542978\pi$$
$$884$$ 6.00000 0.201802
$$885$$ 0 0
$$886$$ −12.0000 −0.403148
$$887$$ 48.0000 1.61168 0.805841 0.592132i $$-0.201714\pi$$
0.805841 + 0.592132i $$0.201714\pi$$
$$888$$ 14.0000 0.469809
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −33.0000 −1.10554
$$892$$ −8.00000 −0.267860
$$893$$ 9.00000 0.301174
$$894$$ −12.0000 −0.401340
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −18.0000 −0.601003
$$898$$ 21.0000 0.700779
$$899$$ 48.0000 1.60089
$$900$$ 0 0
$$901$$ −54.0000 −1.79900
$$902$$ 9.00000 0.299667
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ −20.0000 −0.664455
$$907$$ 10.0000 0.332045 0.166022 0.986122i $$-0.446908\pi$$
0.166022 + 0.986122i $$0.446908\pi$$
$$908$$ 12.0000 0.398234
$$909$$ 12.0000 0.398015
$$910$$ 0 0
$$911$$ −30.0000 −0.993944 −0.496972 0.867766i $$-0.665555\pi$$
−0.496972 + 0.867766i $$0.665555\pi$$
$$912$$ −2.00000 −0.0662266
$$913$$ 0 0
$$914$$ −14.0000 −0.463079
$$915$$ 0 0
$$916$$ −4.00000 −0.132164
$$917$$ 0 0
$$918$$ −24.0000 −0.792118
$$919$$ −22.0000 −0.725713 −0.362857 0.931845i $$-0.618198\pi$$
−0.362857 + 0.931845i $$0.618198\pi$$
$$920$$ 0 0
$$921$$ −28.0000 −0.922631
$$922$$ −30.0000 −0.987997
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 1.00000 0.0328620
$$927$$ 4.00000 0.131377
$$928$$ 6.00000 0.196960
$$929$$ 57.0000 1.87011 0.935055 0.354504i $$-0.115350\pi$$
0.935055 + 0.354504i $$0.115350\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 6.00000 0.196537
$$933$$ −48.0000 −1.57145
$$934$$ 6.00000 0.196326
$$935$$ 0 0
$$936$$ 1.00000 0.0326860
$$937$$ 10.0000 0.326686 0.163343 0.986569i $$-0.447772\pi$$
0.163343 + 0.986569i $$0.447772\pi$$
$$938$$ 0 0
$$939$$ 56.0000 1.82749
$$940$$ 0 0
$$941$$ 48.0000 1.56476 0.782378 0.622804i $$-0.214007\pi$$
0.782378 + 0.622804i $$0.214007\pi$$
$$942$$ −46.0000 −1.49876
$$943$$ −27.0000 −0.879241
$$944$$ 0 0
$$945$$ 0 0
$$946$$ −6.00000 −0.195077
$$947$$ −6.00000 −0.194974 −0.0974869 0.995237i $$-0.531080\pi$$
−0.0974869 + 0.995237i $$0.531080\pi$$
$$948$$ −20.0000 −0.649570
$$949$$ 4.00000 0.129845
$$950$$ 0 0
$$951$$ −12.0000 −0.389127
$$952$$ 0 0
$$953$$ −36.0000 −1.16615 −0.583077 0.812417i $$-0.698151\pi$$
−0.583077 + 0.812417i $$0.698151\pi$$
$$954$$ −9.00000 −0.291386
$$955$$ 0 0
$$956$$ −6.00000 −0.194054
$$957$$ 36.0000 1.16371
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 7.00000 0.225689
$$963$$ 12.0000 0.386695
$$964$$ −1.00000 −0.0322078
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −32.0000 −1.02905 −0.514525 0.857475i $$-0.672032\pi$$
−0.514525 + 0.857475i $$0.672032\pi$$
$$968$$ −2.00000 −0.0642824
$$969$$ −12.0000 −0.385496
$$970$$ 0 0
$$971$$ −45.0000 −1.44412 −0.722059 0.691831i $$-0.756804\pi$$
−0.722059 + 0.691831i $$0.756804\pi$$
$$972$$ −10.0000 −0.320750
$$973$$ 0 0
$$974$$ 16.0000 0.512673
$$975$$ 0 0
$$976$$ 8.00000 0.256074
$$977$$ 42.0000 1.34370 0.671850 0.740688i $$-0.265500\pi$$
0.671850 + 0.740688i $$0.265500\pi$$
$$978$$ −40.0000 −1.27906
$$979$$ 18.0000 0.575282
$$980$$ 0 0
$$981$$ −16.0000 −0.510841
$$982$$ 36.0000 1.14881
$$983$$ −3.00000 −0.0956851 −0.0478426 0.998855i $$-0.515235\pi$$
−0.0478426 + 0.998855i $$0.515235\pi$$
$$984$$ 6.00000 0.191273
$$985$$ 0 0
$$986$$ 36.0000 1.14647
$$987$$ 0 0
$$988$$ −1.00000 −0.0318142
$$989$$ 18.0000 0.572367
$$990$$ 0 0
$$991$$ 44.0000 1.39771 0.698853 0.715265i $$-0.253694\pi$$
0.698853 + 0.715265i $$0.253694\pi$$
$$992$$ 8.00000 0.254000
$$993$$ −14.0000 −0.444277
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 22.0000 0.696747 0.348373 0.937356i $$-0.386734\pi$$
0.348373 + 0.937356i $$0.386734\pi$$
$$998$$ −4.00000 −0.126618
$$999$$ −28.0000 −0.885881
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 2450.2.a.bf.1.1 1
5.2 odd 4 2450.2.c.q.99.2 2
5.3 odd 4 2450.2.c.q.99.1 2
5.4 even 2 490.2.a.a.1.1 1
7.2 even 3 350.2.e.b.151.1 2
7.4 even 3 350.2.e.b.51.1 2
7.6 odd 2 2450.2.a.v.1.1 1
15.14 odd 2 4410.2.a.x.1.1 1
20.19 odd 2 3920.2.a.bh.1.1 1
35.2 odd 12 350.2.j.d.249.2 4
35.4 even 6 70.2.e.d.51.1 yes 2
35.9 even 6 70.2.e.d.11.1 2
35.13 even 4 2450.2.c.e.99.1 2
35.18 odd 12 350.2.j.d.149.2 4
35.19 odd 6 490.2.e.g.361.1 2
35.23 odd 12 350.2.j.d.249.1 4
35.24 odd 6 490.2.e.g.471.1 2
35.27 even 4 2450.2.c.e.99.2 2
35.32 odd 12 350.2.j.d.149.1 4
35.34 odd 2 490.2.a.d.1.1 1
105.44 odd 6 630.2.k.d.361.1 2
105.74 odd 6 630.2.k.d.541.1 2
105.104 even 2 4410.2.a.bg.1.1 1
140.39 odd 6 560.2.q.b.401.1 2
140.79 odd 6 560.2.q.b.81.1 2
140.139 even 2 3920.2.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.e.d.11.1 2 35.9 even 6
70.2.e.d.51.1 yes 2 35.4 even 6
350.2.e.b.51.1 2 7.4 even 3
350.2.e.b.151.1 2 7.2 even 3
350.2.j.d.149.1 4 35.32 odd 12
350.2.j.d.149.2 4 35.18 odd 12
350.2.j.d.249.1 4 35.23 odd 12
350.2.j.d.249.2 4 35.2 odd 12
490.2.a.a.1.1 1 5.4 even 2
490.2.a.d.1.1 1 35.34 odd 2
490.2.e.g.361.1 2 35.19 odd 6
490.2.e.g.471.1 2 35.24 odd 6
560.2.q.b.81.1 2 140.79 odd 6
560.2.q.b.401.1 2 140.39 odd 6
630.2.k.d.361.1 2 105.44 odd 6
630.2.k.d.541.1 2 105.74 odd 6
2450.2.a.v.1.1 1 7.6 odd 2
2450.2.a.bf.1.1 1 1.1 even 1 trivial
2450.2.c.e.99.1 2 35.13 even 4
2450.2.c.e.99.2 2 35.27 even 4
2450.2.c.q.99.1 2 5.3 odd 4
2450.2.c.q.99.2 2 5.2 odd 4
3920.2.a.e.1.1 1 140.139 even 2
3920.2.a.bh.1.1 1 20.19 odd 2
4410.2.a.x.1.1 1 15.14 odd 2
4410.2.a.bg.1.1 1 105.104 even 2