# Properties

 Label 6762.2.a.m.1.1 Level $6762$ Weight $2$ Character 6762.1 Self dual yes Analytic conductor $53.995$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6762.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$53.9948418468$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 966) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 6762.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} -4.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} -2.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} -2.00000 q^{20} +4.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} -6.00000 q^{29} +2.00000 q^{30} -6.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -4.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} -2.00000 q^{38} +4.00000 q^{39} +2.00000 q^{40} +10.0000 q^{41} +8.00000 q^{43} -4.00000 q^{44} -2.00000 q^{45} -1.00000 q^{46} -10.0000 q^{47} +1.00000 q^{48} +1.00000 q^{50} +4.00000 q^{51} +4.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} +8.00000 q^{55} +2.00000 q^{57} +6.00000 q^{58} +12.0000 q^{59} -2.00000 q^{60} +10.0000 q^{61} +6.00000 q^{62} +1.00000 q^{64} -8.00000 q^{65} +4.00000 q^{66} +8.00000 q^{67} +4.00000 q^{68} +1.00000 q^{69} -4.00000 q^{71} -1.00000 q^{72} +2.00000 q^{73} +2.00000 q^{74} -1.00000 q^{75} +2.00000 q^{76} -4.00000 q^{78} -8.00000 q^{79} -2.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +6.00000 q^{83} -8.00000 q^{85} -8.00000 q^{86} -6.00000 q^{87} +4.00000 q^{88} +2.00000 q^{90} +1.00000 q^{92} -6.00000 q^{93} +10.0000 q^{94} -4.00000 q^{95} -1.00000 q^{96} +8.00000 q^{97} -4.00000 q^{99} +O(q^{100})$$

## 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
$$3$$ 1.00000 0.577350
$$4$$ 1.00000 0.500000
$$5$$ −2.00000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ −1.00000 −0.408248
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 2.00000 0.632456
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ −2.00000 −0.516398
$$16$$ 1.00000 0.250000
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ −2.00000 −0.447214
$$21$$ 0 0
$$22$$ 4.00000 0.852803
$$23$$ 1.00000 0.208514
$$24$$ −1.00000 −0.204124
$$25$$ −1.00000 −0.200000
$$26$$ −4.00000 −0.784465
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 2.00000 0.365148
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ −4.00000 −0.696311
$$34$$ −4.00000 −0.685994
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ −2.00000 −0.324443
$$39$$ 4.00000 0.640513
$$40$$ 2.00000 0.316228
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ −2.00000 −0.298142
$$46$$ −1.00000 −0.147442
$$47$$ −10.0000 −1.45865 −0.729325 0.684167i $$-0.760166\pi$$
−0.729325 + 0.684167i $$0.760166\pi$$
$$48$$ 1.00000 0.144338
$$49$$ 0 0
$$50$$ 1.00000 0.141421
$$51$$ 4.00000 0.560112
$$52$$ 4.00000 0.554700
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 8.00000 1.07872
$$56$$ 0 0
$$57$$ 2.00000 0.264906
$$58$$ 6.00000 0.787839
$$59$$ 12.0000 1.56227 0.781133 0.624364i $$-0.214642\pi$$
0.781133 + 0.624364i $$0.214642\pi$$
$$60$$ −2.00000 −0.258199
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ 6.00000 0.762001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −8.00000 −0.992278
$$66$$ 4.00000 0.492366
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 4.00000 0.485071
$$69$$ 1.00000 0.120386
$$70$$ 0 0
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ 2.00000 0.232495
$$75$$ −1.00000 −0.115470
$$76$$ 2.00000 0.229416
$$77$$ 0 0
$$78$$ −4.00000 −0.452911
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ −2.00000 −0.223607
$$81$$ 1.00000 0.111111
$$82$$ −10.0000 −1.10432
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ −8.00000 −0.867722
$$86$$ −8.00000 −0.862662
$$87$$ −6.00000 −0.643268
$$88$$ 4.00000 0.426401
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 2.00000 0.210819
$$91$$ 0 0
$$92$$ 1.00000 0.104257
$$93$$ −6.00000 −0.622171
$$94$$ 10.0000 1.03142
$$95$$ −4.00000 −0.410391
$$96$$ −1.00000 −0.102062
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ 0 0
$$99$$ −4.00000 −0.402015
$$100$$ −1.00000 −0.100000
$$101$$ −16.0000 −1.59206 −0.796030 0.605257i $$-0.793070\pi$$
−0.796030 + 0.605257i $$0.793070\pi$$
$$102$$ −4.00000 −0.396059
$$103$$ −12.0000 −1.18240 −0.591198 0.806527i $$-0.701345\pi$$
−0.591198 + 0.806527i $$0.701345\pi$$
$$104$$ −4.00000 −0.392232
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −20.0000 −1.93347 −0.966736 0.255774i $$-0.917670\pi$$
−0.966736 + 0.255774i $$0.917670\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ −8.00000 −0.762770
$$111$$ −2.00000 −0.189832
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ −2.00000 −0.187317
$$115$$ −2.00000 −0.186501
$$116$$ −6.00000 −0.557086
$$117$$ 4.00000 0.369800
$$118$$ −12.0000 −1.10469
$$119$$ 0 0
$$120$$ 2.00000 0.182574
$$121$$ 5.00000 0.454545
$$122$$ −10.0000 −0.905357
$$123$$ 10.0000 0.901670
$$124$$ −6.00000 −0.538816
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 20.0000 1.77471 0.887357 0.461084i $$-0.152539\pi$$
0.887357 + 0.461084i $$0.152539\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 8.00000 0.704361
$$130$$ 8.00000 0.701646
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ −4.00000 −0.348155
$$133$$ 0 0
$$134$$ −8.00000 −0.691095
$$135$$ −2.00000 −0.172133
$$136$$ −4.00000 −0.342997
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ −1.00000 −0.0851257
$$139$$ 16.0000 1.35710 0.678551 0.734553i $$-0.262608\pi$$
0.678551 + 0.734553i $$0.262608\pi$$
$$140$$ 0 0
$$141$$ −10.0000 −0.842152
$$142$$ 4.00000 0.335673
$$143$$ −16.0000 −1.33799
$$144$$ 1.00000 0.0833333
$$145$$ 12.0000 0.996546
$$146$$ −2.00000 −0.165521
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 1.00000 0.0816497
$$151$$ 4.00000 0.325515 0.162758 0.986666i $$-0.447961\pi$$
0.162758 + 0.986666i $$0.447961\pi$$
$$152$$ −2.00000 −0.162221
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 12.0000 0.963863
$$156$$ 4.00000 0.320256
$$157$$ −10.0000 −0.798087 −0.399043 0.916932i $$-0.630658\pi$$
−0.399043 + 0.916932i $$0.630658\pi$$
$$158$$ 8.00000 0.636446
$$159$$ −6.00000 −0.475831
$$160$$ 2.00000 0.158114
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 12.0000 0.939913 0.469956 0.882690i $$-0.344270\pi$$
0.469956 + 0.882690i $$0.344270\pi$$
$$164$$ 10.0000 0.780869
$$165$$ 8.00000 0.622799
$$166$$ −6.00000 −0.465690
$$167$$ 18.0000 1.39288 0.696441 0.717614i $$-0.254766\pi$$
0.696441 + 0.717614i $$0.254766\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 8.00000 0.613572
$$171$$ 2.00000 0.152944
$$172$$ 8.00000 0.609994
$$173$$ −16.0000 −1.21646 −0.608229 0.793762i $$-0.708120\pi$$
−0.608229 + 0.793762i $$0.708120\pi$$
$$174$$ 6.00000 0.454859
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ 12.0000 0.901975
$$178$$ 0 0
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ −2.00000 −0.149071
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 10.0000 0.739221
$$184$$ −1.00000 −0.0737210
$$185$$ 4.00000 0.294086
$$186$$ 6.00000 0.439941
$$187$$ −16.0000 −1.17004
$$188$$ −10.0000 −0.729325
$$189$$ 0 0
$$190$$ 4.00000 0.290191
$$191$$ 16.0000 1.15772 0.578860 0.815427i $$-0.303498\pi$$
0.578860 + 0.815427i $$0.303498\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 6.00000 0.431889 0.215945 0.976406i $$-0.430717\pi$$
0.215945 + 0.976406i $$0.430717\pi$$
$$194$$ −8.00000 −0.574367
$$195$$ −8.00000 −0.572892
$$196$$ 0 0
$$197$$ −26.0000 −1.85242 −0.926212 0.377004i $$-0.876954\pi$$
−0.926212 + 0.377004i $$0.876954\pi$$
$$198$$ 4.00000 0.284268
$$199$$ 12.0000 0.850657 0.425329 0.905039i $$-0.360158\pi$$
0.425329 + 0.905039i $$0.360158\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 8.00000 0.564276
$$202$$ 16.0000 1.12576
$$203$$ 0 0
$$204$$ 4.00000 0.280056
$$205$$ −20.0000 −1.39686
$$206$$ 12.0000 0.836080
$$207$$ 1.00000 0.0695048
$$208$$ 4.00000 0.277350
$$209$$ −8.00000 −0.553372
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ −4.00000 −0.274075
$$214$$ 20.0000 1.36717
$$215$$ −16.0000 −1.09119
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ 2.00000 0.135147
$$220$$ 8.00000 0.539360
$$221$$ 16.0000 1.07628
$$222$$ 2.00000 0.134231
$$223$$ 14.0000 0.937509 0.468755 0.883328i $$-0.344703\pi$$
0.468755 + 0.883328i $$0.344703\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 6.00000 0.399114
$$227$$ 10.0000 0.663723 0.331862 0.943328i $$-0.392323\pi$$
0.331862 + 0.943328i $$0.392323\pi$$
$$228$$ 2.00000 0.132453
$$229$$ −6.00000 −0.396491 −0.198246 0.980152i $$-0.563524\pi$$
−0.198246 + 0.980152i $$0.563524\pi$$
$$230$$ 2.00000 0.131876
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ −4.00000 −0.261488
$$235$$ 20.0000 1.30466
$$236$$ 12.0000 0.781133
$$237$$ −8.00000 −0.519656
$$238$$ 0 0
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ −2.00000 −0.129099
$$241$$ −12.0000 −0.772988 −0.386494 0.922292i $$-0.626314\pi$$
−0.386494 + 0.922292i $$0.626314\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 1.00000 0.0641500
$$244$$ 10.0000 0.640184
$$245$$ 0 0
$$246$$ −10.0000 −0.637577
$$247$$ 8.00000 0.509028
$$248$$ 6.00000 0.381000
$$249$$ 6.00000 0.380235
$$250$$ −12.0000 −0.758947
$$251$$ −26.0000 −1.64111 −0.820553 0.571571i $$-0.806334\pi$$
−0.820553 + 0.571571i $$0.806334\pi$$
$$252$$ 0 0
$$253$$ −4.00000 −0.251478
$$254$$ −20.0000 −1.25491
$$255$$ −8.00000 −0.500979
$$256$$ 1.00000 0.0625000
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ −8.00000 −0.498058
$$259$$ 0 0
$$260$$ −8.00000 −0.496139
$$261$$ −6.00000 −0.371391
$$262$$ −12.0000 −0.741362
$$263$$ 16.0000 0.986602 0.493301 0.869859i $$-0.335790\pi$$
0.493301 + 0.869859i $$0.335790\pi$$
$$264$$ 4.00000 0.246183
$$265$$ 12.0000 0.737154
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 8.00000 0.488678
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 2.00000 0.121716
$$271$$ 26.0000 1.57939 0.789694 0.613501i $$-0.210239\pi$$
0.789694 + 0.613501i $$0.210239\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ 4.00000 0.241209
$$276$$ 1.00000 0.0601929
$$277$$ 14.0000 0.841178 0.420589 0.907251i $$-0.361823\pi$$
0.420589 + 0.907251i $$0.361823\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ −6.00000 −0.359211
$$280$$ 0 0
$$281$$ 14.0000 0.835170 0.417585 0.908638i $$-0.362877\pi$$
0.417585 + 0.908638i $$0.362877\pi$$
$$282$$ 10.0000 0.595491
$$283$$ 18.0000 1.06999 0.534994 0.844856i $$-0.320314\pi$$
0.534994 + 0.844856i $$0.320314\pi$$
$$284$$ −4.00000 −0.237356
$$285$$ −4.00000 −0.236940
$$286$$ 16.0000 0.946100
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −1.00000 −0.0588235
$$290$$ −12.0000 −0.704664
$$291$$ 8.00000 0.468968
$$292$$ 2.00000 0.117041
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 0 0
$$295$$ −24.0000 −1.39733
$$296$$ 2.00000 0.116248
$$297$$ −4.00000 −0.232104
$$298$$ −6.00000 −0.347571
$$299$$ 4.00000 0.231326
$$300$$ −1.00000 −0.0577350
$$301$$ 0 0
$$302$$ −4.00000 −0.230174
$$303$$ −16.0000 −0.919176
$$304$$ 2.00000 0.114708
$$305$$ −20.0000 −1.14520
$$306$$ −4.00000 −0.228665
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ −12.0000 −0.682656
$$310$$ −12.0000 −0.681554
$$311$$ 30.0000 1.70114 0.850572 0.525859i $$-0.176256\pi$$
0.850572 + 0.525859i $$0.176256\pi$$
$$312$$ −4.00000 −0.226455
$$313$$ 20.0000 1.13047 0.565233 0.824931i $$-0.308786\pi$$
0.565233 + 0.824931i $$0.308786\pi$$
$$314$$ 10.0000 0.564333
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ 30.0000 1.68497 0.842484 0.538721i $$-0.181092\pi$$
0.842484 + 0.538721i $$0.181092\pi$$
$$318$$ 6.00000 0.336463
$$319$$ 24.0000 1.34374
$$320$$ −2.00000 −0.111803
$$321$$ −20.0000 −1.11629
$$322$$ 0 0
$$323$$ 8.00000 0.445132
$$324$$ 1.00000 0.0555556
$$325$$ −4.00000 −0.221880
$$326$$ −12.0000 −0.664619
$$327$$ 2.00000 0.110600
$$328$$ −10.0000 −0.552158
$$329$$ 0 0
$$330$$ −8.00000 −0.440386
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ 6.00000 0.329293
$$333$$ −2.00000 −0.109599
$$334$$ −18.0000 −0.984916
$$335$$ −16.0000 −0.874173
$$336$$ 0 0
$$337$$ −10.0000 −0.544735 −0.272367 0.962193i $$-0.587807\pi$$
−0.272367 + 0.962193i $$0.587807\pi$$
$$338$$ −3.00000 −0.163178
$$339$$ −6.00000 −0.325875
$$340$$ −8.00000 −0.433861
$$341$$ 24.0000 1.29967
$$342$$ −2.00000 −0.108148
$$343$$ 0 0
$$344$$ −8.00000 −0.431331
$$345$$ −2.00000 −0.107676
$$346$$ 16.0000 0.860165
$$347$$ 28.0000 1.50312 0.751559 0.659665i $$-0.229302\pi$$
0.751559 + 0.659665i $$0.229302\pi$$
$$348$$ −6.00000 −0.321634
$$349$$ 16.0000 0.856460 0.428230 0.903670i $$-0.359137\pi$$
0.428230 + 0.903670i $$0.359137\pi$$
$$350$$ 0 0
$$351$$ 4.00000 0.213504
$$352$$ 4.00000 0.213201
$$353$$ 2.00000 0.106449 0.0532246 0.998583i $$-0.483050\pi$$
0.0532246 + 0.998583i $$0.483050\pi$$
$$354$$ −12.0000 −0.637793
$$355$$ 8.00000 0.424596
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −4.00000 −0.211407
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 2.00000 0.105409
$$361$$ −15.0000 −0.789474
$$362$$ −2.00000 −0.105118
$$363$$ 5.00000 0.262432
$$364$$ 0 0
$$365$$ −4.00000 −0.209370
$$366$$ −10.0000 −0.522708
$$367$$ −28.0000 −1.46159 −0.730794 0.682598i $$-0.760850\pi$$
−0.730794 + 0.682598i $$0.760850\pi$$
$$368$$ 1.00000 0.0521286
$$369$$ 10.0000 0.520579
$$370$$ −4.00000 −0.207950
$$371$$ 0 0
$$372$$ −6.00000 −0.311086
$$373$$ 6.00000 0.310668 0.155334 0.987862i $$-0.450355\pi$$
0.155334 + 0.987862i $$0.450355\pi$$
$$374$$ 16.0000 0.827340
$$375$$ 12.0000 0.619677
$$376$$ 10.0000 0.515711
$$377$$ −24.0000 −1.23606
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ −4.00000 −0.205196
$$381$$ 20.0000 1.02463
$$382$$ −16.0000 −0.818631
$$383$$ −32.0000 −1.63512 −0.817562 0.575841i $$-0.804675\pi$$
−0.817562 + 0.575841i $$0.804675\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −6.00000 −0.305392
$$387$$ 8.00000 0.406663
$$388$$ 8.00000 0.406138
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 8.00000 0.405096
$$391$$ 4.00000 0.202289
$$392$$ 0 0
$$393$$ 12.0000 0.605320
$$394$$ 26.0000 1.30986
$$395$$ 16.0000 0.805047
$$396$$ −4.00000 −0.201008
$$397$$ −28.0000 −1.40528 −0.702640 0.711546i $$-0.747995\pi$$
−0.702640 + 0.711546i $$0.747995\pi$$
$$398$$ −12.0000 −0.601506
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ −2.00000 −0.0998752 −0.0499376 0.998752i $$-0.515902\pi$$
−0.0499376 + 0.998752i $$0.515902\pi$$
$$402$$ −8.00000 −0.399004
$$403$$ −24.0000 −1.19553
$$404$$ −16.0000 −0.796030
$$405$$ −2.00000 −0.0993808
$$406$$ 0 0
$$407$$ 8.00000 0.396545
$$408$$ −4.00000 −0.198030
$$409$$ 30.0000 1.48340 0.741702 0.670729i $$-0.234019\pi$$
0.741702 + 0.670729i $$0.234019\pi$$
$$410$$ 20.0000 0.987730
$$411$$ 6.00000 0.295958
$$412$$ −12.0000 −0.591198
$$413$$ 0 0
$$414$$ −1.00000 −0.0491473
$$415$$ −12.0000 −0.589057
$$416$$ −4.00000 −0.196116
$$417$$ 16.0000 0.783523
$$418$$ 8.00000 0.391293
$$419$$ 22.0000 1.07477 0.537385 0.843337i $$-0.319412\pi$$
0.537385 + 0.843337i $$0.319412\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ −4.00000 −0.194717
$$423$$ −10.0000 −0.486217
$$424$$ 6.00000 0.291386
$$425$$ −4.00000 −0.194029
$$426$$ 4.00000 0.193801
$$427$$ 0 0
$$428$$ −20.0000 −0.966736
$$429$$ −16.0000 −0.772487
$$430$$ 16.0000 0.771589
$$431$$ 32.0000 1.54139 0.770693 0.637207i $$-0.219910\pi$$
0.770693 + 0.637207i $$0.219910\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ 16.0000 0.768911 0.384455 0.923144i $$-0.374389\pi$$
0.384455 + 0.923144i $$0.374389\pi$$
$$434$$ 0 0
$$435$$ 12.0000 0.575356
$$436$$ 2.00000 0.0957826
$$437$$ 2.00000 0.0956730
$$438$$ −2.00000 −0.0955637
$$439$$ 14.0000 0.668184 0.334092 0.942541i $$-0.391570\pi$$
0.334092 + 0.942541i $$0.391570\pi$$
$$440$$ −8.00000 −0.381385
$$441$$ 0 0
$$442$$ −16.0000 −0.761042
$$443$$ −4.00000 −0.190046 −0.0950229 0.995475i $$-0.530292\pi$$
−0.0950229 + 0.995475i $$0.530292\pi$$
$$444$$ −2.00000 −0.0949158
$$445$$ 0 0
$$446$$ −14.0000 −0.662919
$$447$$ 6.00000 0.283790
$$448$$ 0 0
$$449$$ 14.0000 0.660701 0.330350 0.943858i $$-0.392833\pi$$
0.330350 + 0.943858i $$0.392833\pi$$
$$450$$ 1.00000 0.0471405
$$451$$ −40.0000 −1.88353
$$452$$ −6.00000 −0.282216
$$453$$ 4.00000 0.187936
$$454$$ −10.0000 −0.469323
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ 18.0000 0.842004 0.421002 0.907060i $$-0.361678\pi$$
0.421002 + 0.907060i $$0.361678\pi$$
$$458$$ 6.00000 0.280362
$$459$$ 4.00000 0.186704
$$460$$ −2.00000 −0.0932505
$$461$$ 24.0000 1.11779 0.558896 0.829238i $$-0.311225\pi$$
0.558896 + 0.829238i $$0.311225\pi$$
$$462$$ 0 0
$$463$$ −32.0000 −1.48717 −0.743583 0.668644i $$-0.766875\pi$$
−0.743583 + 0.668644i $$0.766875\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 12.0000 0.556487
$$466$$ −6.00000 −0.277945
$$467$$ −22.0000 −1.01804 −0.509019 0.860755i $$-0.669992\pi$$
−0.509019 + 0.860755i $$0.669992\pi$$
$$468$$ 4.00000 0.184900
$$469$$ 0 0
$$470$$ −20.0000 −0.922531
$$471$$ −10.0000 −0.460776
$$472$$ −12.0000 −0.552345
$$473$$ −32.0000 −1.47136
$$474$$ 8.00000 0.367452
$$475$$ −2.00000 −0.0917663
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ −20.0000 −0.914779
$$479$$ −4.00000 −0.182765 −0.0913823 0.995816i $$-0.529129\pi$$
−0.0913823 + 0.995816i $$0.529129\pi$$
$$480$$ 2.00000 0.0912871
$$481$$ −8.00000 −0.364769
$$482$$ 12.0000 0.546585
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ −16.0000 −0.726523
$$486$$ −1.00000 −0.0453609
$$487$$ 16.0000 0.725029 0.362515 0.931978i $$-0.381918\pi$$
0.362515 + 0.931978i $$0.381918\pi$$
$$488$$ −10.0000 −0.452679
$$489$$ 12.0000 0.542659
$$490$$ 0 0
$$491$$ −28.0000 −1.26362 −0.631811 0.775122i $$-0.717688\pi$$
−0.631811 + 0.775122i $$0.717688\pi$$
$$492$$ 10.0000 0.450835
$$493$$ −24.0000 −1.08091
$$494$$ −8.00000 −0.359937
$$495$$ 8.00000 0.359573
$$496$$ −6.00000 −0.269408
$$497$$ 0 0
$$498$$ −6.00000 −0.268866
$$499$$ 28.0000 1.25345 0.626726 0.779240i $$-0.284395\pi$$
0.626726 + 0.779240i $$0.284395\pi$$
$$500$$ 12.0000 0.536656
$$501$$ 18.0000 0.804181
$$502$$ 26.0000 1.16044
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ 32.0000 1.42398
$$506$$ 4.00000 0.177822
$$507$$ 3.00000 0.133235
$$508$$ 20.0000 0.887357
$$509$$ 24.0000 1.06378 0.531891 0.846813i $$-0.321482\pi$$
0.531891 + 0.846813i $$0.321482\pi$$
$$510$$ 8.00000 0.354246
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 2.00000 0.0883022
$$514$$ 2.00000 0.0882162
$$515$$ 24.0000 1.05757
$$516$$ 8.00000 0.352180
$$517$$ 40.0000 1.75920
$$518$$ 0 0
$$519$$ −16.0000 −0.702322
$$520$$ 8.00000 0.350823
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 6.00000 0.262613
$$523$$ 34.0000 1.48672 0.743358 0.668894i $$-0.233232\pi$$
0.743358 + 0.668894i $$0.233232\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ −16.0000 −0.697633
$$527$$ −24.0000 −1.04546
$$528$$ −4.00000 −0.174078
$$529$$ 1.00000 0.0434783
$$530$$ −12.0000 −0.521247
$$531$$ 12.0000 0.520756
$$532$$ 0 0
$$533$$ 40.0000 1.73259
$$534$$ 0 0
$$535$$ 40.0000 1.72935
$$536$$ −8.00000 −0.345547
$$537$$ 4.00000 0.172613
$$538$$ 0 0
$$539$$ 0 0
$$540$$ −2.00000 −0.0860663
$$541$$ 30.0000 1.28980 0.644900 0.764267i $$-0.276899\pi$$
0.644900 + 0.764267i $$0.276899\pi$$
$$542$$ −26.0000 −1.11680
$$543$$ 2.00000 0.0858282
$$544$$ −4.00000 −0.171499
$$545$$ −4.00000 −0.171341
$$546$$ 0 0
$$547$$ 44.0000 1.88130 0.940652 0.339372i $$-0.110215\pi$$
0.940652 + 0.339372i $$0.110215\pi$$
$$548$$ 6.00000 0.256307
$$549$$ 10.0000 0.426790
$$550$$ −4.00000 −0.170561
$$551$$ −12.0000 −0.511217
$$552$$ −1.00000 −0.0425628
$$553$$ 0 0
$$554$$ −14.0000 −0.594803
$$555$$ 4.00000 0.169791
$$556$$ 16.0000 0.678551
$$557$$ 14.0000 0.593199 0.296600 0.955002i $$-0.404147\pi$$
0.296600 + 0.955002i $$0.404147\pi$$
$$558$$ 6.00000 0.254000
$$559$$ 32.0000 1.35346
$$560$$ 0 0
$$561$$ −16.0000 −0.675521
$$562$$ −14.0000 −0.590554
$$563$$ 22.0000 0.927189 0.463595 0.886047i $$-0.346559\pi$$
0.463595 + 0.886047i $$0.346559\pi$$
$$564$$ −10.0000 −0.421076
$$565$$ 12.0000 0.504844
$$566$$ −18.0000 −0.756596
$$567$$ 0 0
$$568$$ 4.00000 0.167836
$$569$$ −10.0000 −0.419222 −0.209611 0.977785i $$-0.567220\pi$$
−0.209611 + 0.977785i $$0.567220\pi$$
$$570$$ 4.00000 0.167542
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ −16.0000 −0.668994
$$573$$ 16.0000 0.668410
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 1.00000 0.0416667
$$577$$ −38.0000 −1.58196 −0.790980 0.611842i $$-0.790429\pi$$
−0.790980 + 0.611842i $$0.790429\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ 6.00000 0.249351
$$580$$ 12.0000 0.498273
$$581$$ 0 0
$$582$$ −8.00000 −0.331611
$$583$$ 24.0000 0.993978
$$584$$ −2.00000 −0.0827606
$$585$$ −8.00000 −0.330759
$$586$$ −6.00000 −0.247858
$$587$$ −16.0000 −0.660391 −0.330195 0.943913i $$-0.607115\pi$$
−0.330195 + 0.943913i $$0.607115\pi$$
$$588$$ 0 0
$$589$$ −12.0000 −0.494451
$$590$$ 24.0000 0.988064
$$591$$ −26.0000 −1.06950
$$592$$ −2.00000 −0.0821995
$$593$$ 30.0000 1.23195 0.615976 0.787765i $$-0.288762\pi$$
0.615976 + 0.787765i $$0.288762\pi$$
$$594$$ 4.00000 0.164122
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ 12.0000 0.491127
$$598$$ −4.00000 −0.163572
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 1.00000 0.0408248
$$601$$ −22.0000 −0.897399 −0.448699 0.893683i $$-0.648113\pi$$
−0.448699 + 0.893683i $$0.648113\pi$$
$$602$$ 0 0
$$603$$ 8.00000 0.325785
$$604$$ 4.00000 0.162758
$$605$$ −10.0000 −0.406558
$$606$$ 16.0000 0.649956
$$607$$ 2.00000 0.0811775 0.0405887 0.999176i $$-0.487077\pi$$
0.0405887 + 0.999176i $$0.487077\pi$$
$$608$$ −2.00000 −0.0811107
$$609$$ 0 0
$$610$$ 20.0000 0.809776
$$611$$ −40.0000 −1.61823
$$612$$ 4.00000 0.161690
$$613$$ −38.0000 −1.53481 −0.767403 0.641165i $$-0.778451\pi$$
−0.767403 + 0.641165i $$0.778451\pi$$
$$614$$ 0 0
$$615$$ −20.0000 −0.806478
$$616$$ 0 0
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ 12.0000 0.482711
$$619$$ 14.0000 0.562708 0.281354 0.959604i $$-0.409217\pi$$
0.281354 + 0.959604i $$0.409217\pi$$
$$620$$ 12.0000 0.481932
$$621$$ 1.00000 0.0401286
$$622$$ −30.0000 −1.20289
$$623$$ 0 0
$$624$$ 4.00000 0.160128
$$625$$ −19.0000 −0.760000
$$626$$ −20.0000 −0.799361
$$627$$ −8.00000 −0.319489
$$628$$ −10.0000 −0.399043
$$629$$ −8.00000 −0.318981
$$630$$ 0 0
$$631$$ −32.0000 −1.27390 −0.636950 0.770905i $$-0.719804\pi$$
−0.636950 + 0.770905i $$0.719804\pi$$
$$632$$ 8.00000 0.318223
$$633$$ 4.00000 0.158986
$$634$$ −30.0000 −1.19145
$$635$$ −40.0000 −1.58735
$$636$$ −6.00000 −0.237915
$$637$$ 0 0
$$638$$ −24.0000 −0.950169
$$639$$ −4.00000 −0.158238
$$640$$ 2.00000 0.0790569
$$641$$ −42.0000 −1.65890 −0.829450 0.558581i $$-0.811346\pi$$
−0.829450 + 0.558581i $$0.811346\pi$$
$$642$$ 20.0000 0.789337
$$643$$ −10.0000 −0.394362 −0.197181 0.980367i $$-0.563179\pi$$
−0.197181 + 0.980367i $$0.563179\pi$$
$$644$$ 0 0
$$645$$ −16.0000 −0.629999
$$646$$ −8.00000 −0.314756
$$647$$ −14.0000 −0.550397 −0.275198 0.961387i $$-0.588744\pi$$
−0.275198 + 0.961387i $$0.588744\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ −48.0000 −1.88416
$$650$$ 4.00000 0.156893
$$651$$ 0 0
$$652$$ 12.0000 0.469956
$$653$$ −22.0000 −0.860927 −0.430463 0.902608i $$-0.641650\pi$$
−0.430463 + 0.902608i $$0.641650\pi$$
$$654$$ −2.00000 −0.0782062
$$655$$ −24.0000 −0.937758
$$656$$ 10.0000 0.390434
$$657$$ 2.00000 0.0780274
$$658$$ 0 0
$$659$$ 40.0000 1.55818 0.779089 0.626913i $$-0.215682\pi$$
0.779089 + 0.626913i $$0.215682\pi$$
$$660$$ 8.00000 0.311400
$$661$$ 50.0000 1.94477 0.972387 0.233373i $$-0.0749763\pi$$
0.972387 + 0.233373i $$0.0749763\pi$$
$$662$$ 4.00000 0.155464
$$663$$ 16.0000 0.621389
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 2.00000 0.0774984
$$667$$ −6.00000 −0.232321
$$668$$ 18.0000 0.696441
$$669$$ 14.0000 0.541271
$$670$$ 16.0000 0.618134
$$671$$ −40.0000 −1.54418
$$672$$ 0 0
$$673$$ 30.0000 1.15642 0.578208 0.815890i $$-0.303752\pi$$
0.578208 + 0.815890i $$0.303752\pi$$
$$674$$ 10.0000 0.385186
$$675$$ −1.00000 −0.0384900
$$676$$ 3.00000 0.115385
$$677$$ 6.00000 0.230599 0.115299 0.993331i $$-0.463217\pi$$
0.115299 + 0.993331i $$0.463217\pi$$
$$678$$ 6.00000 0.230429
$$679$$ 0 0
$$680$$ 8.00000 0.306786
$$681$$ 10.0000 0.383201
$$682$$ −24.0000 −0.919007
$$683$$ −44.0000 −1.68361 −0.841807 0.539779i $$-0.818508\pi$$
−0.841807 + 0.539779i $$0.818508\pi$$
$$684$$ 2.00000 0.0764719
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ −6.00000 −0.228914
$$688$$ 8.00000 0.304997
$$689$$ −24.0000 −0.914327
$$690$$ 2.00000 0.0761387
$$691$$ −8.00000 −0.304334 −0.152167 0.988355i $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ −16.0000 −0.608229
$$693$$ 0 0
$$694$$ −28.0000 −1.06287
$$695$$ −32.0000 −1.21383
$$696$$ 6.00000 0.227429
$$697$$ 40.0000 1.51511
$$698$$ −16.0000 −0.605609
$$699$$ 6.00000 0.226941
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ −4.00000 −0.150970
$$703$$ −4.00000 −0.150863
$$704$$ −4.00000 −0.150756
$$705$$ 20.0000 0.753244
$$706$$ −2.00000 −0.0752710
$$707$$ 0 0
$$708$$ 12.0000 0.450988
$$709$$ −18.0000 −0.676004 −0.338002 0.941145i $$-0.609751\pi$$
−0.338002 + 0.941145i $$0.609751\pi$$
$$710$$ −8.00000 −0.300235
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ −6.00000 −0.224702
$$714$$ 0 0
$$715$$ 32.0000 1.19673
$$716$$ 4.00000 0.149487
$$717$$ 20.0000 0.746914
$$718$$ −16.0000 −0.597115
$$719$$ −6.00000 −0.223762 −0.111881 0.993722i $$-0.535688\pi$$
−0.111881 + 0.993722i $$0.535688\pi$$
$$720$$ −2.00000 −0.0745356
$$721$$ 0 0
$$722$$ 15.0000 0.558242
$$723$$ −12.0000 −0.446285
$$724$$ 2.00000 0.0743294
$$725$$ 6.00000 0.222834
$$726$$ −5.00000 −0.185567
$$727$$ −20.0000 −0.741759 −0.370879 0.928681i $$-0.620944\pi$$
−0.370879 + 0.928681i $$0.620944\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 4.00000 0.148047
$$731$$ 32.0000 1.18356
$$732$$ 10.0000 0.369611
$$733$$ −34.0000 −1.25582 −0.627909 0.778287i $$-0.716089\pi$$
−0.627909 + 0.778287i $$0.716089\pi$$
$$734$$ 28.0000 1.03350
$$735$$ 0 0
$$736$$ −1.00000 −0.0368605
$$737$$ −32.0000 −1.17874
$$738$$ −10.0000 −0.368105
$$739$$ 52.0000 1.91285 0.956425 0.291977i $$-0.0943129\pi$$
0.956425 + 0.291977i $$0.0943129\pi$$
$$740$$ 4.00000 0.147043
$$741$$ 8.00000 0.293887
$$742$$ 0 0
$$743$$ 16.0000 0.586983 0.293492 0.955962i $$-0.405183\pi$$
0.293492 + 0.955962i $$0.405183\pi$$
$$744$$ 6.00000 0.219971
$$745$$ −12.0000 −0.439646
$$746$$ −6.00000 −0.219676
$$747$$ 6.00000 0.219529
$$748$$ −16.0000 −0.585018
$$749$$ 0 0
$$750$$ −12.0000 −0.438178
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ −10.0000 −0.364662
$$753$$ −26.0000 −0.947493
$$754$$ 24.0000 0.874028
$$755$$ −8.00000 −0.291150
$$756$$ 0 0
$$757$$ −6.00000 −0.218074 −0.109037 0.994038i $$-0.534777\pi$$
−0.109037 + 0.994038i $$0.534777\pi$$
$$758$$ 28.0000 1.01701
$$759$$ −4.00000 −0.145191
$$760$$ 4.00000 0.145095
$$761$$ −26.0000 −0.942499 −0.471250 0.882000i $$-0.656197\pi$$
−0.471250 + 0.882000i $$0.656197\pi$$
$$762$$ −20.0000 −0.724524
$$763$$ 0 0
$$764$$ 16.0000 0.578860
$$765$$ −8.00000 −0.289241
$$766$$ 32.0000 1.15621
$$767$$ 48.0000 1.73318
$$768$$ 1.00000 0.0360844
$$769$$ 28.0000 1.00971 0.504853 0.863205i $$-0.331547\pi$$
0.504853 + 0.863205i $$0.331547\pi$$
$$770$$ 0 0
$$771$$ −2.00000 −0.0720282
$$772$$ 6.00000 0.215945
$$773$$ 18.0000 0.647415 0.323708 0.946157i $$-0.395071\pi$$
0.323708 + 0.946157i $$0.395071\pi$$
$$774$$ −8.00000 −0.287554
$$775$$ 6.00000 0.215526
$$776$$ −8.00000 −0.287183
$$777$$ 0 0
$$778$$ 6.00000 0.215110
$$779$$ 20.0000 0.716574
$$780$$ −8.00000 −0.286446
$$781$$ 16.0000 0.572525
$$782$$ −4.00000 −0.143040
$$783$$ −6.00000 −0.214423
$$784$$ 0 0
$$785$$ 20.0000 0.713831
$$786$$ −12.0000 −0.428026
$$787$$ 6.00000 0.213877 0.106938 0.994266i $$-0.465895\pi$$
0.106938 + 0.994266i $$0.465895\pi$$
$$788$$ −26.0000 −0.926212
$$789$$ 16.0000 0.569615
$$790$$ −16.0000 −0.569254
$$791$$ 0 0
$$792$$ 4.00000 0.142134
$$793$$ 40.0000 1.42044
$$794$$ 28.0000 0.993683
$$795$$ 12.0000 0.425596
$$796$$ 12.0000 0.425329
$$797$$ 18.0000 0.637593 0.318796 0.947823i $$-0.396721\pi$$
0.318796 + 0.947823i $$0.396721\pi$$
$$798$$ 0 0
$$799$$ −40.0000 −1.41510
$$800$$ 1.00000 0.0353553
$$801$$ 0 0
$$802$$ 2.00000 0.0706225
$$803$$ −8.00000 −0.282314
$$804$$ 8.00000 0.282138
$$805$$ 0 0
$$806$$ 24.0000 0.845364
$$807$$ 0 0
$$808$$ 16.0000 0.562878
$$809$$ 30.0000 1.05474 0.527372 0.849635i $$-0.323177\pi$$
0.527372 + 0.849635i $$0.323177\pi$$
$$810$$ 2.00000 0.0702728
$$811$$ 20.0000 0.702295 0.351147 0.936320i $$-0.385792\pi$$
0.351147 + 0.936320i $$0.385792\pi$$
$$812$$ 0 0
$$813$$ 26.0000 0.911860
$$814$$ −8.00000 −0.280400
$$815$$ −24.0000 −0.840683
$$816$$ 4.00000 0.140028
$$817$$ 16.0000 0.559769
$$818$$ −30.0000 −1.04893
$$819$$ 0 0
$$820$$ −20.0000 −0.698430
$$821$$ −2.00000 −0.0698005 −0.0349002 0.999391i $$-0.511111\pi$$
−0.0349002 + 0.999391i $$0.511111\pi$$
$$822$$ −6.00000 −0.209274
$$823$$ −20.0000 −0.697156 −0.348578 0.937280i $$-0.613335\pi$$
−0.348578 + 0.937280i $$0.613335\pi$$
$$824$$ 12.0000 0.418040
$$825$$ 4.00000 0.139262
$$826$$ 0 0
$$827$$ 36.0000 1.25184 0.625921 0.779886i $$-0.284723\pi$$
0.625921 + 0.779886i $$0.284723\pi$$
$$828$$ 1.00000 0.0347524
$$829$$ −20.0000 −0.694629 −0.347314 0.937749i $$-0.612906\pi$$
−0.347314 + 0.937749i $$0.612906\pi$$
$$830$$ 12.0000 0.416526
$$831$$ 14.0000 0.485655
$$832$$ 4.00000 0.138675
$$833$$ 0 0
$$834$$ −16.0000 −0.554035
$$835$$ −36.0000 −1.24583
$$836$$ −8.00000 −0.276686
$$837$$ −6.00000 −0.207390
$$838$$ −22.0000 −0.759977
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ −10.0000 −0.344623
$$843$$ 14.0000 0.482186
$$844$$ 4.00000 0.137686
$$845$$ −6.00000 −0.206406
$$846$$ 10.0000 0.343807
$$847$$ 0 0
$$848$$ −6.00000 −0.206041
$$849$$ 18.0000 0.617758
$$850$$ 4.00000 0.137199
$$851$$ −2.00000 −0.0685591
$$852$$ −4.00000 −0.137038
$$853$$ −12.0000 −0.410872 −0.205436 0.978671i $$-0.565861\pi$$
−0.205436 + 0.978671i $$0.565861\pi$$
$$854$$ 0 0
$$855$$ −4.00000 −0.136797
$$856$$ 20.0000 0.683586
$$857$$ 10.0000 0.341593 0.170797 0.985306i $$-0.445366\pi$$
0.170797 + 0.985306i $$0.445366\pi$$
$$858$$ 16.0000 0.546231
$$859$$ −8.00000 −0.272956 −0.136478 0.990643i $$-0.543578\pi$$
−0.136478 + 0.990643i $$0.543578\pi$$
$$860$$ −16.0000 −0.545595
$$861$$ 0 0
$$862$$ −32.0000 −1.08992
$$863$$ −4.00000 −0.136162 −0.0680808 0.997680i $$-0.521688\pi$$
−0.0680808 + 0.997680i $$0.521688\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 32.0000 1.08803
$$866$$ −16.0000 −0.543702
$$867$$ −1.00000 −0.0339618
$$868$$ 0 0
$$869$$ 32.0000 1.08553
$$870$$ −12.0000 −0.406838
$$871$$ 32.0000 1.08428
$$872$$ −2.00000 −0.0677285
$$873$$ 8.00000 0.270759
$$874$$ −2.00000 −0.0676510
$$875$$ 0 0
$$876$$ 2.00000 0.0675737
$$877$$ −14.0000 −0.472746 −0.236373 0.971662i $$-0.575959\pi$$
−0.236373 + 0.971662i $$0.575959\pi$$
$$878$$ −14.0000 −0.472477
$$879$$ 6.00000 0.202375
$$880$$ 8.00000 0.269680
$$881$$ −20.0000 −0.673817 −0.336909 0.941537i $$-0.609381\pi$$
−0.336909 + 0.941537i $$0.609381\pi$$
$$882$$ 0 0
$$883$$ 20.0000 0.673054 0.336527 0.941674i $$-0.390748\pi$$
0.336527 + 0.941674i $$0.390748\pi$$
$$884$$ 16.0000 0.538138
$$885$$ −24.0000 −0.806751
$$886$$ 4.00000 0.134383
$$887$$ −6.00000 −0.201460 −0.100730 0.994914i $$-0.532118\pi$$
−0.100730 + 0.994914i $$0.532118\pi$$
$$888$$ 2.00000 0.0671156
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −4.00000 −0.134005
$$892$$ 14.0000 0.468755
$$893$$ −20.0000 −0.669274
$$894$$ −6.00000 −0.200670
$$895$$ −8.00000 −0.267411
$$896$$ 0 0
$$897$$ 4.00000 0.133556
$$898$$ −14.0000 −0.467186
$$899$$ 36.0000 1.20067
$$900$$ −1.00000 −0.0333333
$$901$$ −24.0000 −0.799556
$$902$$ 40.0000 1.33185
$$903$$ 0 0
$$904$$ 6.00000 0.199557
$$905$$ −4.00000 −0.132964
$$906$$ −4.00000 −0.132891
$$907$$ −28.0000 −0.929725 −0.464862 0.885383i $$-0.653896\pi$$
−0.464862 + 0.885383i $$0.653896\pi$$
$$908$$ 10.0000 0.331862
$$909$$ −16.0000 −0.530687
$$910$$ 0 0
$$911$$ −24.0000 −0.795155 −0.397578 0.917568i $$-0.630149\pi$$
−0.397578 + 0.917568i $$0.630149\pi$$
$$912$$ 2.00000 0.0662266
$$913$$ −24.0000 −0.794284
$$914$$ −18.0000 −0.595387
$$915$$ −20.0000 −0.661180
$$916$$ −6.00000 −0.198246
$$917$$ 0 0
$$918$$ −4.00000 −0.132020
$$919$$ 48.0000 1.58337 0.791687 0.610927i $$-0.209203\pi$$
0.791687 + 0.610927i $$0.209203\pi$$
$$920$$ 2.00000 0.0659380
$$921$$ 0 0
$$922$$ −24.0000 −0.790398
$$923$$ −16.0000 −0.526646
$$924$$ 0 0
$$925$$ 2.00000 0.0657596
$$926$$ 32.0000 1.05159
$$927$$ −12.0000 −0.394132
$$928$$ 6.00000 0.196960
$$929$$ 10.0000 0.328089 0.164045 0.986453i $$-0.447546\pi$$
0.164045 + 0.986453i $$0.447546\pi$$
$$930$$ −12.0000 −0.393496
$$931$$ 0 0
$$932$$ 6.00000 0.196537
$$933$$ 30.0000 0.982156
$$934$$ 22.0000 0.719862
$$935$$ 32.0000 1.04651
$$936$$ −4.00000 −0.130744
$$937$$ −4.00000 −0.130674 −0.0653372 0.997863i $$-0.520812\pi$$
−0.0653372 + 0.997863i $$0.520812\pi$$
$$938$$ 0 0
$$939$$ 20.0000 0.652675
$$940$$ 20.0000 0.652328
$$941$$ −10.0000 −0.325991 −0.162995 0.986627i $$-0.552116\pi$$
−0.162995 + 0.986627i $$0.552116\pi$$
$$942$$ 10.0000 0.325818
$$943$$ 10.0000 0.325645
$$944$$ 12.0000 0.390567
$$945$$ 0 0
$$946$$ 32.0000 1.04041
$$947$$ 28.0000 0.909878 0.454939 0.890523i $$-0.349661\pi$$
0.454939 + 0.890523i $$0.349661\pi$$
$$948$$ −8.00000 −0.259828
$$949$$ 8.00000 0.259691
$$950$$ 2.00000 0.0648886
$$951$$ 30.0000 0.972817
$$952$$ 0 0
$$953$$ −30.0000 −0.971795 −0.485898 0.874016i $$-0.661507\pi$$
−0.485898 + 0.874016i $$0.661507\pi$$
$$954$$ 6.00000 0.194257
$$955$$ −32.0000 −1.03550
$$956$$ 20.0000 0.646846
$$957$$ 24.0000 0.775810
$$958$$ 4.00000 0.129234
$$959$$ 0 0
$$960$$ −2.00000 −0.0645497
$$961$$ 5.00000 0.161290
$$962$$ 8.00000 0.257930
$$963$$ −20.0000 −0.644491
$$964$$ −12.0000 −0.386494
$$965$$ −12.0000 −0.386294
$$966$$ 0 0
$$967$$ 24.0000 0.771788 0.385894 0.922543i $$-0.373893\pi$$
0.385894 + 0.922543i $$0.373893\pi$$
$$968$$ −5.00000 −0.160706
$$969$$ 8.00000 0.256997
$$970$$ 16.0000 0.513729
$$971$$ −42.0000 −1.34784 −0.673922 0.738802i $$-0.735392\pi$$
−0.673922 + 0.738802i $$0.735392\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 0 0
$$974$$ −16.0000 −0.512673
$$975$$ −4.00000 −0.128103
$$976$$ 10.0000 0.320092
$$977$$ −10.0000 −0.319928 −0.159964 0.987123i $$-0.551138\pi$$
−0.159964 + 0.987123i $$0.551138\pi$$
$$978$$ −12.0000 −0.383718
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 2.00000 0.0638551
$$982$$ 28.0000 0.893516
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ −10.0000 −0.318788
$$985$$ 52.0000 1.65686
$$986$$ 24.0000 0.764316
$$987$$ 0 0
$$988$$ 8.00000 0.254514
$$989$$ 8.00000 0.254385
$$990$$ −8.00000 −0.254257
$$991$$ −20.0000 −0.635321 −0.317660 0.948205i $$-0.602897\pi$$
−0.317660 + 0.948205i $$0.602897\pi$$
$$992$$ 6.00000 0.190500
$$993$$ −4.00000 −0.126936
$$994$$ 0 0
$$995$$ −24.0000 −0.760851
$$996$$ 6.00000 0.190117
$$997$$ 52.0000 1.64686 0.823428 0.567420i $$-0.192059\pi$$
0.823428 + 0.567420i $$0.192059\pi$$
$$998$$ −28.0000 −0.886325
$$999$$ −2.00000 −0.0632772
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 6762.2.a.m.1.1 1
7.6 odd 2 966.2.a.c.1.1 1
21.20 even 2 2898.2.a.l.1.1 1
28.27 even 2 7728.2.a.t.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.a.c.1.1 1 7.6 odd 2
2898.2.a.l.1.1 1 21.20 even 2
6762.2.a.m.1.1 1 1.1 even 1 trivial
7728.2.a.t.1.1 1 28.27 even 2