Properties

 Label 570.2.a.k.1.1 Level $570$ Weight $2$ Character 570.1 Self dual yes Analytic conductor $4.551$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 570.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +6.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} +2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -6.00000 q^{17} +1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{21} +6.00000 q^{22} +1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} -1.00000 q^{30} +8.00000 q^{31} +1.00000 q^{32} +6.00000 q^{33} -6.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} +8.00000 q^{37} +1.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} -12.0000 q^{41} +2.00000 q^{42} +2.00000 q^{43} +6.00000 q^{44} -1.00000 q^{45} +1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} -6.00000 q^{51} -4.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} -6.00000 q^{55} +2.00000 q^{56} +1.00000 q^{57} -12.0000 q^{59} -1.00000 q^{60} +2.00000 q^{61} +8.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +6.00000 q^{66} -16.0000 q^{67} -6.00000 q^{68} -2.00000 q^{70} +1.00000 q^{72} -10.0000 q^{73} +8.00000 q^{74} +1.00000 q^{75} +1.00000 q^{76} +12.0000 q^{77} -4.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} +2.00000 q^{84} +6.00000 q^{85} +2.00000 q^{86} +6.00000 q^{88} -12.0000 q^{89} -1.00000 q^{90} -8.00000 q^{91} +8.00000 q^{93} -1.00000 q^{95} +1.00000 q^{96} +8.00000 q^{97} -3.00000 q^{98} +6.00000 q^{99} +O(q^{100})$$

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
$$5$$ −1.00000 −0.447214
$$6$$ 1.00000 0.408248
$$7$$ 2.00000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ −1.00000 −0.316228
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 2.00000 0.534522
$$15$$ −1.00000 −0.258199
$$16$$ 1.00000 0.250000
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 1.00000 0.229416
$$20$$ −1.00000 −0.223607
$$21$$ 2.00000 0.436436
$$22$$ 6.00000 1.27920
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 1.00000 0.200000
$$26$$ −4.00000 −0.784465
$$27$$ 1.00000 0.192450
$$28$$ 2.00000 0.377964
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ −1.00000 −0.182574
$$31$$ 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
$$35$$ −2.00000 −0.338062
$$36$$ 1.00000 0.166667
$$37$$ 8.00000 1.31519 0.657596 0.753371i $$-0.271573\pi$$
0.657596 + 0.753371i $$0.271573\pi$$
$$38$$ 1.00000 0.162221
$$39$$ −4.00000 −0.640513
$$40$$ −1.00000 −0.158114
$$41$$ −12.0000 −1.87409 −0.937043 0.349215i $$-0.886448\pi$$
−0.937043 + 0.349215i $$0.886448\pi$$
$$42$$ 2.00000 0.308607
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 6.00000 0.904534
$$45$$ −1.00000 −0.149071
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −3.00000 −0.428571
$$50$$ 1.00000 0.141421
$$51$$ −6.00000 −0.840168
$$52$$ −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
$$55$$ −6.00000 −0.809040
$$56$$ 2.00000 0.267261
$$57$$ 1.00000 0.132453
$$58$$ 0 0
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ −1.00000 −0.129099
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 8.00000 1.01600
$$63$$ 2.00000 0.251976
$$64$$ 1.00000 0.125000
$$65$$ 4.00000 0.496139
$$66$$ 6.00000 0.738549
$$67$$ −16.0000 −1.95471 −0.977356 0.211604i $$-0.932131\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ −6.00000 −0.727607
$$69$$ 0 0
$$70$$ −2.00000 −0.239046
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 8.00000 0.929981
$$75$$ 1.00000 0.115470
$$76$$ 1.00000 0.114708
$$77$$ 12.0000 1.36753
$$78$$ −4.00000 −0.452911
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 1.00000 0.111111
$$82$$ −12.0000 −1.32518
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 2.00000 0.218218
$$85$$ 6.00000 0.650791
$$86$$ 2.00000 0.215666
$$87$$ 0 0
$$88$$ 6.00000 0.639602
$$89$$ −12.0000 −1.27200 −0.635999 0.771690i $$-0.719412\pi$$
−0.635999 + 0.771690i $$0.719412\pi$$
$$90$$ −1.00000 −0.105409
$$91$$ −8.00000 −0.838628
$$92$$ 0 0
$$93$$ 8.00000 0.829561
$$94$$ 0 0
$$95$$ −1.00000 −0.102598
$$96$$ 1.00000 0.102062
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ −3.00000 −0.303046
$$99$$ 6.00000 0.603023
$$100$$ 1.00000 0.100000
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ −6.00000 −0.594089
$$103$$ −16.0000 −1.57653 −0.788263 0.615338i $$-0.789020\pi$$
−0.788263 + 0.615338i $$0.789020\pi$$
$$104$$ −4.00000 −0.392232
$$105$$ −2.00000 −0.195180
$$106$$ −6.00000 −0.582772
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ −6.00000 −0.572078
$$111$$ 8.00000 0.759326
$$112$$ 2.00000 0.188982
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 1.00000 0.0936586
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −4.00000 −0.369800
$$118$$ −12.0000 −1.10469
$$119$$ −12.0000 −1.10004
$$120$$ −1.00000 −0.0912871
$$121$$ 25.0000 2.27273
$$122$$ 2.00000 0.181071
$$123$$ −12.0000 −1.08200
$$124$$ 8.00000 0.718421
$$125$$ −1.00000 −0.0894427
$$126$$ 2.00000 0.178174
$$127$$ 20.0000 1.77471 0.887357 0.461084i $$-0.152539\pi$$
0.887357 + 0.461084i $$0.152539\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 2.00000 0.176090
$$130$$ 4.00000 0.350823
$$131$$ 18.0000 1.57267 0.786334 0.617802i $$-0.211977\pi$$
0.786334 + 0.617802i $$0.211977\pi$$
$$132$$ 6.00000 0.522233
$$133$$ 2.00000 0.173422
$$134$$ −16.0000 −1.38219
$$135$$ −1.00000 −0.0860663
$$136$$ −6.00000 −0.514496
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 0 0
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ −2.00000 −0.169031
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −24.0000 −2.00698
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −10.0000 −0.827606
$$147$$ −3.00000 −0.247436
$$148$$ 8.00000 0.657596
$$149$$ −18.0000 −1.47462 −0.737309 0.675556i $$-0.763904\pi$$
−0.737309 + 0.675556i $$0.763904\pi$$
$$150$$ 1.00000 0.0816497
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 1.00000 0.0811107
$$153$$ −6.00000 −0.485071
$$154$$ 12.0000 0.966988
$$155$$ −8.00000 −0.642575
$$156$$ −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
$$160$$ −1.00000 −0.0790569
$$161$$ 0 0
$$162$$ 1.00000 0.0785674
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ −12.0000 −0.937043
$$165$$ −6.00000 −0.467099
$$166$$ 0 0
$$167$$ 24.0000 1.85718 0.928588 0.371113i $$-0.121024\pi$$
0.928588 + 0.371113i $$0.121024\pi$$
$$168$$ 2.00000 0.154303
$$169$$ 3.00000 0.230769
$$170$$ 6.00000 0.460179
$$171$$ 1.00000 0.0764719
$$172$$ 2.00000 0.152499
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 2.00000 0.151186
$$176$$ 6.00000 0.452267
$$177$$ −12.0000 −0.901975
$$178$$ −12.0000 −0.899438
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ −1.00000 −0.0745356
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ −8.00000 −0.592999
$$183$$ 2.00000 0.147844
$$184$$ 0 0
$$185$$ −8.00000 −0.588172
$$186$$ 8.00000 0.586588
$$187$$ −36.0000 −2.63258
$$188$$ 0 0
$$189$$ 2.00000 0.145479
$$190$$ −1.00000 −0.0725476
$$191$$ 6.00000 0.434145 0.217072 0.976156i $$-0.430349\pi$$
0.217072 + 0.976156i $$0.430349\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 20.0000 1.43963 0.719816 0.694165i $$-0.244226\pi$$
0.719816 + 0.694165i $$0.244226\pi$$
$$194$$ 8.00000 0.574367
$$195$$ 4.00000 0.286446
$$196$$ −3.00000 −0.214286
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 6.00000 0.426401
$$199$$ 20.0000 1.41776 0.708881 0.705328i $$-0.249200\pi$$
0.708881 + 0.705328i $$0.249200\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ −16.0000 −1.12855
$$202$$ 6.00000 0.422159
$$203$$ 0 0
$$204$$ −6.00000 −0.420084
$$205$$ 12.0000 0.838116
$$206$$ −16.0000 −1.11477
$$207$$ 0 0
$$208$$ −4.00000 −0.277350
$$209$$ 6.00000 0.415029
$$210$$ −2.00000 −0.138013
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 0 0
$$214$$ −12.0000 −0.820303
$$215$$ −2.00000 −0.136399
$$216$$ 1.00000 0.0680414
$$217$$ 16.0000 1.08615
$$218$$ 2.00000 0.135457
$$219$$ −10.0000 −0.675737
$$220$$ −6.00000 −0.404520
$$221$$ 24.0000 1.61441
$$222$$ 8.00000 0.536925
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ 2.00000 0.133631
$$225$$ 1.00000 0.0666667
$$226$$ −6.00000 −0.399114
$$227$$ 12.0000 0.796468 0.398234 0.917284i $$-0.369623\pi$$
0.398234 + 0.917284i $$0.369623\pi$$
$$228$$ 1.00000 0.0662266
$$229$$ 2.00000 0.132164 0.0660819 0.997814i $$-0.478950\pi$$
0.0660819 + 0.997814i $$0.478950\pi$$
$$230$$ 0 0
$$231$$ 12.0000 0.789542
$$232$$ 0 0
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ −4.00000 −0.261488
$$235$$ 0 0
$$236$$ −12.0000 −0.781133
$$237$$ 8.00000 0.519656
$$238$$ −12.0000 −0.777844
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ −1.00000 −0.0645497
$$241$$ 2.00000 0.128831 0.0644157 0.997923i $$-0.479482\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$242$$ 25.0000 1.60706
$$243$$ 1.00000 0.0641500
$$244$$ 2.00000 0.128037
$$245$$ 3.00000 0.191663
$$246$$ −12.0000 −0.765092
$$247$$ −4.00000 −0.254514
$$248$$ 8.00000 0.508001
$$249$$ 0 0
$$250$$ −1.00000 −0.0632456
$$251$$ 6.00000 0.378717 0.189358 0.981908i $$-0.439359\pi$$
0.189358 + 0.981908i $$0.439359\pi$$
$$252$$ 2.00000 0.125988
$$253$$ 0 0
$$254$$ 20.0000 1.25491
$$255$$ 6.00000 0.375735
$$256$$ 1.00000 0.0625000
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 2.00000 0.124515
$$259$$ 16.0000 0.994192
$$260$$ 4.00000 0.248069
$$261$$ 0 0
$$262$$ 18.0000 1.11204
$$263$$ −12.0000 −0.739952 −0.369976 0.929041i $$-0.620634\pi$$
−0.369976 + 0.929041i $$0.620634\pi$$
$$264$$ 6.00000 0.369274
$$265$$ 6.00000 0.368577
$$266$$ 2.00000 0.122628
$$267$$ −12.0000 −0.734388
$$268$$ −16.0000 −0.977356
$$269$$ 24.0000 1.46331 0.731653 0.681677i $$-0.238749\pi$$
0.731653 + 0.681677i $$0.238749\pi$$
$$270$$ −1.00000 −0.0608581
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ −6.00000 −0.363803
$$273$$ −8.00000 −0.484182
$$274$$ 6.00000 0.362473
$$275$$ 6.00000 0.361814
$$276$$ 0 0
$$277$$ −10.0000 −0.600842 −0.300421 0.953807i $$-0.597127\pi$$
−0.300421 + 0.953807i $$0.597127\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 8.00000 0.478947
$$280$$ −2.00000 −0.119523
$$281$$ 24.0000 1.43172 0.715860 0.698244i $$-0.246035\pi$$
0.715860 + 0.698244i $$0.246035\pi$$
$$282$$ 0 0
$$283$$ 14.0000 0.832214 0.416107 0.909316i $$-0.363394\pi$$
0.416107 + 0.909316i $$0.363394\pi$$
$$284$$ 0 0
$$285$$ −1.00000 −0.0592349
$$286$$ −24.0000 −1.41915
$$287$$ −24.0000 −1.41668
$$288$$ 1.00000 0.0589256
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ −10.0000 −0.585206
$$293$$ −18.0000 −1.05157 −0.525786 0.850617i $$-0.676229\pi$$
−0.525786 + 0.850617i $$0.676229\pi$$
$$294$$ −3.00000 −0.174964
$$295$$ 12.0000 0.698667
$$296$$ 8.00000 0.464991
$$297$$ 6.00000 0.348155
$$298$$ −18.0000 −1.04271
$$299$$ 0 0
$$300$$ 1.00000 0.0577350
$$301$$ 4.00000 0.230556
$$302$$ 8.00000 0.460348
$$303$$ 6.00000 0.344691
$$304$$ 1.00000 0.0573539
$$305$$ −2.00000 −0.114520
$$306$$ −6.00000 −0.342997
$$307$$ −16.0000 −0.913168 −0.456584 0.889680i $$-0.650927\pi$$
−0.456584 + 0.889680i $$0.650927\pi$$
$$308$$ 12.0000 0.683763
$$309$$ −16.0000 −0.910208
$$310$$ −8.00000 −0.454369
$$311$$ −18.0000 −1.02069 −0.510343 0.859971i $$-0.670482\pi$$
−0.510343 + 0.859971i $$0.670482\pi$$
$$312$$ −4.00000 −0.226455
$$313$$ 26.0000 1.46961 0.734803 0.678280i $$-0.237274\pi$$
0.734803 + 0.678280i $$0.237274\pi$$
$$314$$ −10.0000 −0.564333
$$315$$ −2.00000 −0.112687
$$316$$ 8.00000 0.450035
$$317$$ −30.0000 −1.68497 −0.842484 0.538721i $$-0.818908\pi$$
−0.842484 + 0.538721i $$0.818908\pi$$
$$318$$ −6.00000 −0.336463
$$319$$ 0 0
$$320$$ −1.00000 −0.0559017
$$321$$ −12.0000 −0.669775
$$322$$ 0 0
$$323$$ −6.00000 −0.333849
$$324$$ 1.00000 0.0555556
$$325$$ −4.00000 −0.221880
$$326$$ −10.0000 −0.553849
$$327$$ 2.00000 0.110600
$$328$$ −12.0000 −0.662589
$$329$$ 0 0
$$330$$ −6.00000 −0.330289
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ 0 0
$$333$$ 8.00000 0.438397
$$334$$ 24.0000 1.31322
$$335$$ 16.0000 0.874173
$$336$$ 2.00000 0.109109
$$337$$ 8.00000 0.435788 0.217894 0.975972i $$-0.430081\pi$$
0.217894 + 0.975972i $$0.430081\pi$$
$$338$$ 3.00000 0.163178
$$339$$ −6.00000 −0.325875
$$340$$ 6.00000 0.325396
$$341$$ 48.0000 2.59935
$$342$$ 1.00000 0.0540738
$$343$$ −20.0000 −1.07990
$$344$$ 2.00000 0.107833
$$345$$ 0 0
$$346$$ 6.00000 0.322562
$$347$$ 24.0000 1.28839 0.644194 0.764862i $$-0.277193\pi$$
0.644194 + 0.764862i $$0.277193\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 2.00000 0.106904
$$351$$ −4.00000 −0.213504
$$352$$ 6.00000 0.319801
$$353$$ 30.0000 1.59674 0.798369 0.602168i $$-0.205696\pi$$
0.798369 + 0.602168i $$0.205696\pi$$
$$354$$ −12.0000 −0.637793
$$355$$ 0 0
$$356$$ −12.0000 −0.635999
$$357$$ −12.0000 −0.635107
$$358$$ −12.0000 −0.634220
$$359$$ 6.00000 0.316668 0.158334 0.987386i $$-0.449388\pi$$
0.158334 + 0.987386i $$0.449388\pi$$
$$360$$ −1.00000 −0.0527046
$$361$$ 1.00000 0.0526316
$$362$$ 2.00000 0.105118
$$363$$ 25.0000 1.31216
$$364$$ −8.00000 −0.419314
$$365$$ 10.0000 0.523424
$$366$$ 2.00000 0.104542
$$367$$ −34.0000 −1.77479 −0.887393 0.461014i $$-0.847486\pi$$
−0.887393 + 0.461014i $$0.847486\pi$$
$$368$$ 0 0
$$369$$ −12.0000 −0.624695
$$370$$ −8.00000 −0.415900
$$371$$ −12.0000 −0.623009
$$372$$ 8.00000 0.414781
$$373$$ −4.00000 −0.207112 −0.103556 0.994624i $$-0.533022\pi$$
−0.103556 + 0.994624i $$0.533022\pi$$
$$374$$ −36.0000 −1.86152
$$375$$ −1.00000 −0.0516398
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 2.00000 0.102869
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ −1.00000 −0.0512989
$$381$$ 20.0000 1.02463
$$382$$ 6.00000 0.306987
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ −12.0000 −0.611577
$$386$$ 20.0000 1.01797
$$387$$ 2.00000 0.101666
$$388$$ 8.00000 0.406138
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 4.00000 0.202548
$$391$$ 0 0
$$392$$ −3.00000 −0.151523
$$393$$ 18.0000 0.907980
$$394$$ 6.00000 0.302276
$$395$$ −8.00000 −0.402524
$$396$$ 6.00000 0.301511
$$397$$ 14.0000 0.702640 0.351320 0.936255i $$-0.385733\pi$$
0.351320 + 0.936255i $$0.385733\pi$$
$$398$$ 20.0000 1.00251
$$399$$ 2.00000 0.100125
$$400$$ 1.00000 0.0500000
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ −16.0000 −0.798007
$$403$$ −32.0000 −1.59403
$$404$$ 6.00000 0.298511
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ 48.0000 2.37927
$$408$$ −6.00000 −0.297044
$$409$$ 14.0000 0.692255 0.346128 0.938187i $$-0.387496\pi$$
0.346128 + 0.938187i $$0.387496\pi$$
$$410$$ 12.0000 0.592638
$$411$$ 6.00000 0.295958
$$412$$ −16.0000 −0.788263
$$413$$ −24.0000 −1.18096
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −4.00000 −0.196116
$$417$$ 8.00000 0.391762
$$418$$ 6.00000 0.293470
$$419$$ 30.0000 1.46560 0.732798 0.680446i $$-0.238214\pi$$
0.732798 + 0.680446i $$0.238214\pi$$
$$420$$ −2.00000 −0.0975900
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ −4.00000 −0.194717
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ −6.00000 −0.291043
$$426$$ 0 0
$$427$$ 4.00000 0.193574
$$428$$ −12.0000 −0.580042
$$429$$ −24.0000 −1.15873
$$430$$ −2.00000 −0.0964486
$$431$$ 12.0000 0.578020 0.289010 0.957326i $$-0.406674\pi$$
0.289010 + 0.957326i $$0.406674\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −4.00000 −0.192228 −0.0961139 0.995370i $$-0.530641\pi$$
−0.0961139 + 0.995370i $$0.530641\pi$$
$$434$$ 16.0000 0.768025
$$435$$ 0 0
$$436$$ 2.00000 0.0957826
$$437$$ 0 0
$$438$$ −10.0000 −0.477818
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ −6.00000 −0.286039
$$441$$ −3.00000 −0.142857
$$442$$ 24.0000 1.14156
$$443$$ −36.0000 −1.71041 −0.855206 0.518289i $$-0.826569\pi$$
−0.855206 + 0.518289i $$0.826569\pi$$
$$444$$ 8.00000 0.379663
$$445$$ 12.0000 0.568855
$$446$$ −16.0000 −0.757622
$$447$$ −18.0000 −0.851371
$$448$$ 2.00000 0.0944911
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ 1.00000 0.0471405
$$451$$ −72.0000 −3.39035
$$452$$ −6.00000 −0.282216
$$453$$ 8.00000 0.375873
$$454$$ 12.0000 0.563188
$$455$$ 8.00000 0.375046
$$456$$ 1.00000 0.0468293
$$457$$ −22.0000 −1.02912 −0.514558 0.857455i $$-0.672044\pi$$
−0.514558 + 0.857455i $$0.672044\pi$$
$$458$$ 2.00000 0.0934539
$$459$$ −6.00000 −0.280056
$$460$$ 0 0
$$461$$ −42.0000 −1.95614 −0.978068 0.208288i $$-0.933211\pi$$
−0.978068 + 0.208288i $$0.933211\pi$$
$$462$$ 12.0000 0.558291
$$463$$ 14.0000 0.650635 0.325318 0.945605i $$-0.394529\pi$$
0.325318 + 0.945605i $$0.394529\pi$$
$$464$$ 0 0
$$465$$ −8.00000 −0.370991
$$466$$ 6.00000 0.277945
$$467$$ 36.0000 1.66588 0.832941 0.553362i $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ −4.00000 −0.184900
$$469$$ −32.0000 −1.47762
$$470$$ 0 0
$$471$$ −10.0000 −0.460776
$$472$$ −12.0000 −0.552345
$$473$$ 12.0000 0.551761
$$474$$ 8.00000 0.367452
$$475$$ 1.00000 0.0458831
$$476$$ −12.0000 −0.550019
$$477$$ −6.00000 −0.274721
$$478$$ −6.00000 −0.274434
$$479$$ 30.0000 1.37073 0.685367 0.728197i $$-0.259642\pi$$
0.685367 + 0.728197i $$0.259642\pi$$
$$480$$ −1.00000 −0.0456435
$$481$$ −32.0000 −1.45907
$$482$$ 2.00000 0.0910975
$$483$$ 0 0
$$484$$ 25.0000 1.13636
$$485$$ −8.00000 −0.363261
$$486$$ 1.00000 0.0453609
$$487$$ −16.0000 −0.725029 −0.362515 0.931978i $$-0.618082\pi$$
−0.362515 + 0.931978i $$0.618082\pi$$
$$488$$ 2.00000 0.0905357
$$489$$ −10.0000 −0.452216
$$490$$ 3.00000 0.135526
$$491$$ −6.00000 −0.270776 −0.135388 0.990793i $$-0.543228\pi$$
−0.135388 + 0.990793i $$0.543228\pi$$
$$492$$ −12.0000 −0.541002
$$493$$ 0 0
$$494$$ −4.00000 −0.179969
$$495$$ −6.00000 −0.269680
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 32.0000 1.43252 0.716258 0.697835i $$-0.245853\pi$$
0.716258 + 0.697835i $$0.245853\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 24.0000 1.07224
$$502$$ 6.00000 0.267793
$$503$$ 12.0000 0.535054 0.267527 0.963550i $$-0.413794\pi$$
0.267527 + 0.963550i $$0.413794\pi$$
$$504$$ 2.00000 0.0890871
$$505$$ −6.00000 −0.266996
$$506$$ 0 0
$$507$$ 3.00000 0.133235
$$508$$ 20.0000 0.887357
$$509$$ −36.0000 −1.59567 −0.797836 0.602875i $$-0.794022\pi$$
−0.797836 + 0.602875i $$0.794022\pi$$
$$510$$ 6.00000 0.265684
$$511$$ −20.0000 −0.884748
$$512$$ 1.00000 0.0441942
$$513$$ 1.00000 0.0441511
$$514$$ −6.00000 −0.264649
$$515$$ 16.0000 0.705044
$$516$$ 2.00000 0.0880451
$$517$$ 0 0
$$518$$ 16.0000 0.703000
$$519$$ 6.00000 0.263371
$$520$$ 4.00000 0.175412
$$521$$ −24.0000 −1.05146 −0.525730 0.850652i $$-0.676208\pi$$
−0.525730 + 0.850652i $$0.676208\pi$$
$$522$$ 0 0
$$523$$ −4.00000 −0.174908 −0.0874539 0.996169i $$-0.527873\pi$$
−0.0874539 + 0.996169i $$0.527873\pi$$
$$524$$ 18.0000 0.786334
$$525$$ 2.00000 0.0872872
$$526$$ −12.0000 −0.523225
$$527$$ −48.0000 −2.09091
$$528$$ 6.00000 0.261116
$$529$$ −23.0000 −1.00000
$$530$$ 6.00000 0.260623
$$531$$ −12.0000 −0.520756
$$532$$ 2.00000 0.0867110
$$533$$ 48.0000 2.07911
$$534$$ −12.0000 −0.519291
$$535$$ 12.0000 0.518805
$$536$$ −16.0000 −0.691095
$$537$$ −12.0000 −0.517838
$$538$$ 24.0000 1.03471
$$539$$ −18.0000 −0.775315
$$540$$ −1.00000 −0.0430331
$$541$$ −10.0000 −0.429934 −0.214967 0.976621i $$-0.568964\pi$$
−0.214967 + 0.976621i $$0.568964\pi$$
$$542$$ 20.0000 0.859074
$$543$$ 2.00000 0.0858282
$$544$$ −6.00000 −0.257248
$$545$$ −2.00000 −0.0856706
$$546$$ −8.00000 −0.342368
$$547$$ −16.0000 −0.684111 −0.342055 0.939680i $$-0.611123\pi$$
−0.342055 + 0.939680i $$0.611123\pi$$
$$548$$ 6.00000 0.256307
$$549$$ 2.00000 0.0853579
$$550$$ 6.00000 0.255841
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ −10.0000 −0.424859
$$555$$ −8.00000 −0.339581
$$556$$ 8.00000 0.339276
$$557$$ −30.0000 −1.27114 −0.635570 0.772043i $$-0.719235\pi$$
−0.635570 + 0.772043i $$0.719235\pi$$
$$558$$ 8.00000 0.338667
$$559$$ −8.00000 −0.338364
$$560$$ −2.00000 −0.0845154
$$561$$ −36.0000 −1.51992
$$562$$ 24.0000 1.01238
$$563$$ 12.0000 0.505740 0.252870 0.967500i $$-0.418626\pi$$
0.252870 + 0.967500i $$0.418626\pi$$
$$564$$ 0 0
$$565$$ 6.00000 0.252422
$$566$$ 14.0000 0.588464
$$567$$ 2.00000 0.0839921
$$568$$ 0 0
$$569$$ −36.0000 −1.50920 −0.754599 0.656186i $$-0.772169\pi$$
−0.754599 + 0.656186i $$0.772169\pi$$
$$570$$ −1.00000 −0.0418854
$$571$$ −16.0000 −0.669579 −0.334790 0.942293i $$-0.608665\pi$$
−0.334790 + 0.942293i $$0.608665\pi$$
$$572$$ −24.0000 −1.00349
$$573$$ 6.00000 0.250654
$$574$$ −24.0000 −1.00174
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ 19.0000 0.790296
$$579$$ 20.0000 0.831172
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 8.00000 0.331611
$$583$$ −36.0000 −1.49097
$$584$$ −10.0000 −0.413803
$$585$$ 4.00000 0.165380
$$586$$ −18.0000 −0.743573
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ −3.00000 −0.123718
$$589$$ 8.00000 0.329634
$$590$$ 12.0000 0.494032
$$591$$ 6.00000 0.246807
$$592$$ 8.00000 0.328798
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 6.00000 0.246183
$$595$$ 12.0000 0.491952
$$596$$ −18.0000 −0.737309
$$597$$ 20.0000 0.818546
$$598$$ 0 0
$$599$$ −12.0000 −0.490307 −0.245153 0.969484i $$-0.578838\pi$$
−0.245153 + 0.969484i $$0.578838\pi$$
$$600$$ 1.00000 0.0408248
$$601$$ −34.0000 −1.38689 −0.693444 0.720510i $$-0.743908\pi$$
−0.693444 + 0.720510i $$0.743908\pi$$
$$602$$ 4.00000 0.163028
$$603$$ −16.0000 −0.651570
$$604$$ 8.00000 0.325515
$$605$$ −25.0000 −1.01639
$$606$$ 6.00000 0.243733
$$607$$ 8.00000 0.324710 0.162355 0.986732i $$-0.448091\pi$$
0.162355 + 0.986732i $$0.448091\pi$$
$$608$$ 1.00000 0.0405554
$$609$$ 0 0
$$610$$ −2.00000 −0.0809776
$$611$$ 0 0
$$612$$ −6.00000 −0.242536
$$613$$ 38.0000 1.53481 0.767403 0.641165i $$-0.221549\pi$$
0.767403 + 0.641165i $$0.221549\pi$$
$$614$$ −16.0000 −0.645707
$$615$$ 12.0000 0.483887
$$616$$ 12.0000 0.483494
$$617$$ −30.0000 −1.20775 −0.603877 0.797077i $$-0.706378\pi$$
−0.603877 + 0.797077i $$0.706378\pi$$
$$618$$ −16.0000 −0.643614
$$619$$ −16.0000 −0.643094 −0.321547 0.946894i $$-0.604203\pi$$
−0.321547 + 0.946894i $$0.604203\pi$$
$$620$$ −8.00000 −0.321288
$$621$$ 0 0
$$622$$ −18.0000 −0.721734
$$623$$ −24.0000 −0.961540
$$624$$ −4.00000 −0.160128
$$625$$ 1.00000 0.0400000
$$626$$ 26.0000 1.03917
$$627$$ 6.00000 0.239617
$$628$$ −10.0000 −0.399043
$$629$$ −48.0000 −1.91389
$$630$$ −2.00000 −0.0796819
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 8.00000 0.318223
$$633$$ −4.00000 −0.158986
$$634$$ −30.0000 −1.19145
$$635$$ −20.0000 −0.793676
$$636$$ −6.00000 −0.237915
$$637$$ 12.0000 0.475457
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.00000 −0.0395285
$$641$$ 12.0000 0.473972 0.236986 0.971513i $$-0.423841\pi$$
0.236986 + 0.971513i $$0.423841\pi$$
$$642$$ −12.0000 −0.473602
$$643$$ 14.0000 0.552106 0.276053 0.961142i $$-0.410973\pi$$
0.276053 + 0.961142i $$0.410973\pi$$
$$644$$ 0 0
$$645$$ −2.00000 −0.0787499
$$646$$ −6.00000 −0.236067
$$647$$ −12.0000 −0.471769 −0.235884 0.971781i $$-0.575799\pi$$
−0.235884 + 0.971781i $$0.575799\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ −72.0000 −2.82625
$$650$$ −4.00000 −0.156893
$$651$$ 16.0000 0.627089
$$652$$ −10.0000 −0.391630
$$653$$ 30.0000 1.17399 0.586995 0.809590i $$-0.300311\pi$$
0.586995 + 0.809590i $$0.300311\pi$$
$$654$$ 2.00000 0.0782062
$$655$$ −18.0000 −0.703318
$$656$$ −12.0000 −0.468521
$$657$$ −10.0000 −0.390137
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ −6.00000 −0.233550
$$661$$ 50.0000 1.94477 0.972387 0.233373i $$-0.0749763\pi$$
0.972387 + 0.233373i $$0.0749763\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 24.0000 0.932083
$$664$$ 0 0
$$665$$ −2.00000 −0.0775567
$$666$$ 8.00000 0.309994
$$667$$ 0 0
$$668$$ 24.0000 0.928588
$$669$$ −16.0000 −0.618596
$$670$$ 16.0000 0.618134
$$671$$ 12.0000 0.463255
$$672$$ 2.00000 0.0771517
$$673$$ 8.00000 0.308377 0.154189 0.988041i $$-0.450724\pi$$
0.154189 + 0.988041i $$0.450724\pi$$
$$674$$ 8.00000 0.308148
$$675$$ 1.00000 0.0384900
$$676$$ 3.00000 0.115385
$$677$$ 42.0000 1.61419 0.807096 0.590421i $$-0.201038\pi$$
0.807096 + 0.590421i $$0.201038\pi$$
$$678$$ −6.00000 −0.230429
$$679$$ 16.0000 0.614024
$$680$$ 6.00000 0.230089
$$681$$ 12.0000 0.459841
$$682$$ 48.0000 1.83801
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 1.00000 0.0382360
$$685$$ −6.00000 −0.229248
$$686$$ −20.0000 −0.763604
$$687$$ 2.00000 0.0763048
$$688$$ 2.00000 0.0762493
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 12.0000 0.455842
$$694$$ 24.0000 0.911028
$$695$$ −8.00000 −0.303457
$$696$$ 0 0
$$697$$ 72.0000 2.72719
$$698$$ 14.0000 0.529908
$$699$$ 6.00000 0.226941
$$700$$ 2.00000 0.0755929
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ −4.00000 −0.150970
$$703$$ 8.00000 0.301726
$$704$$ 6.00000 0.226134
$$705$$ 0 0
$$706$$ 30.0000 1.12906
$$707$$ 12.0000 0.451306
$$708$$ −12.0000 −0.450988
$$709$$ −46.0000 −1.72757 −0.863783 0.503864i $$-0.831911\pi$$
−0.863783 + 0.503864i $$0.831911\pi$$
$$710$$ 0 0
$$711$$ 8.00000 0.300023
$$712$$ −12.0000 −0.449719
$$713$$ 0 0
$$714$$ −12.0000 −0.449089
$$715$$ 24.0000 0.897549
$$716$$ −12.0000 −0.448461
$$717$$ −6.00000 −0.224074
$$718$$ 6.00000 0.223918
$$719$$ 18.0000 0.671287 0.335643 0.941989i $$-0.391046\pi$$
0.335643 + 0.941989i $$0.391046\pi$$
$$720$$ −1.00000 −0.0372678
$$721$$ −32.0000 −1.19174
$$722$$ 1.00000 0.0372161
$$723$$ 2.00000 0.0743808
$$724$$ 2.00000 0.0743294
$$725$$ 0 0
$$726$$ 25.0000 0.927837
$$727$$ −10.0000 −0.370879 −0.185440 0.982656i $$-0.559371\pi$$
−0.185440 + 0.982656i $$0.559371\pi$$
$$728$$ −8.00000 −0.296500
$$729$$ 1.00000 0.0370370
$$730$$ 10.0000 0.370117
$$731$$ −12.0000 −0.443836
$$732$$ 2.00000 0.0739221
$$733$$ −22.0000 −0.812589 −0.406294 0.913742i $$-0.633179\pi$$
−0.406294 + 0.913742i $$0.633179\pi$$
$$734$$ −34.0000 −1.25496
$$735$$ 3.00000 0.110657
$$736$$ 0 0
$$737$$ −96.0000 −3.53621
$$738$$ −12.0000 −0.441726
$$739$$ 44.0000 1.61857 0.809283 0.587419i $$-0.199856\pi$$
0.809283 + 0.587419i $$0.199856\pi$$
$$740$$ −8.00000 −0.294086
$$741$$ −4.00000 −0.146944
$$742$$ −12.0000 −0.440534
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 8.00000 0.293294
$$745$$ 18.0000 0.659469
$$746$$ −4.00000 −0.146450
$$747$$ 0 0
$$748$$ −36.0000 −1.31629
$$749$$ −24.0000 −0.876941
$$750$$ −1.00000 −0.0365148
$$751$$ −16.0000 −0.583848 −0.291924 0.956441i $$-0.594295\pi$$
−0.291924 + 0.956441i $$0.594295\pi$$
$$752$$ 0 0
$$753$$ 6.00000 0.218652
$$754$$ 0 0
$$755$$ −8.00000 −0.291150
$$756$$ 2.00000 0.0727393
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ −4.00000 −0.145287
$$759$$ 0 0
$$760$$ −1.00000 −0.0362738
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 20.0000 0.724524
$$763$$ 4.00000 0.144810
$$764$$ 6.00000 0.217072
$$765$$ 6.00000 0.216930
$$766$$ 24.0000 0.867155
$$767$$ 48.0000 1.73318
$$768$$ 1.00000 0.0360844
$$769$$ 50.0000 1.80305 0.901523 0.432731i $$-0.142450\pi$$
0.901523 + 0.432731i $$0.142450\pi$$
$$770$$ −12.0000 −0.432450
$$771$$ −6.00000 −0.216085
$$772$$ 20.0000 0.719816
$$773$$ −30.0000 −1.07903 −0.539513 0.841978i $$-0.681391\pi$$
−0.539513 + 0.841978i $$0.681391\pi$$
$$774$$ 2.00000 0.0718885
$$775$$ 8.00000 0.287368
$$776$$ 8.00000 0.287183
$$777$$ 16.0000 0.573997
$$778$$ 18.0000 0.645331
$$779$$ −12.0000 −0.429945
$$780$$ 4.00000 0.143223
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −3.00000 −0.107143
$$785$$ 10.0000 0.356915
$$786$$ 18.0000 0.642039
$$787$$ −28.0000 −0.998092 −0.499046 0.866575i $$-0.666316\pi$$
−0.499046 + 0.866575i $$0.666316\pi$$
$$788$$ 6.00000 0.213741
$$789$$ −12.0000 −0.427211
$$790$$ −8.00000 −0.284627
$$791$$ −12.0000 −0.426671
$$792$$ 6.00000 0.213201
$$793$$ −8.00000 −0.284088
$$794$$ 14.0000 0.496841
$$795$$ 6.00000 0.212798
$$796$$ 20.0000 0.708881
$$797$$ −42.0000 −1.48772 −0.743858 0.668338i $$-0.767006\pi$$
−0.743858 + 0.668338i $$0.767006\pi$$
$$798$$ 2.00000 0.0707992
$$799$$ 0 0
$$800$$ 1.00000 0.0353553
$$801$$ −12.0000 −0.423999
$$802$$ 0 0
$$803$$ −60.0000 −2.11735
$$804$$ −16.0000 −0.564276
$$805$$ 0 0
$$806$$ −32.0000 −1.12715
$$807$$ 24.0000 0.844840
$$808$$ 6.00000 0.211079
$$809$$ −30.0000 −1.05474 −0.527372 0.849635i $$-0.676823\pi$$
−0.527372 + 0.849635i $$0.676823\pi$$
$$810$$ −1.00000 −0.0351364
$$811$$ 20.0000 0.702295 0.351147 0.936320i $$-0.385792\pi$$
0.351147 + 0.936320i $$0.385792\pi$$
$$812$$ 0 0
$$813$$ 20.0000 0.701431
$$814$$ 48.0000 1.68240
$$815$$ 10.0000 0.350285
$$816$$ −6.00000 −0.210042
$$817$$ 2.00000 0.0699711
$$818$$ 14.0000 0.489499
$$819$$ −8.00000 −0.279543
$$820$$ 12.0000 0.419058
$$821$$ 30.0000 1.04701 0.523504 0.852023i $$-0.324625\pi$$
0.523504 + 0.852023i $$0.324625\pi$$
$$822$$ 6.00000 0.209274
$$823$$ 14.0000 0.488009 0.244005 0.969774i $$-0.421539\pi$$
0.244005 + 0.969774i $$0.421539\pi$$
$$824$$ −16.0000 −0.557386
$$825$$ 6.00000 0.208893
$$826$$ −24.0000 −0.835067
$$827$$ 12.0000 0.417281 0.208640 0.977992i $$-0.433096\pi$$
0.208640 + 0.977992i $$0.433096\pi$$
$$828$$ 0 0
$$829$$ 2.00000 0.0694629 0.0347314 0.999397i $$-0.488942\pi$$
0.0347314 + 0.999397i $$0.488942\pi$$
$$830$$ 0 0
$$831$$ −10.0000 −0.346896
$$832$$ −4.00000 −0.138675
$$833$$ 18.0000 0.623663
$$834$$ 8.00000 0.277017
$$835$$ −24.0000 −0.830554
$$836$$ 6.00000 0.207514
$$837$$ 8.00000 0.276520
$$838$$ 30.0000 1.03633
$$839$$ 24.0000 0.828572 0.414286 0.910147i $$-0.364031\pi$$
0.414286 + 0.910147i $$0.364031\pi$$
$$840$$ −2.00000 −0.0690066
$$841$$ −29.0000 −1.00000
$$842$$ −10.0000 −0.344623
$$843$$ 24.0000 0.826604
$$844$$ −4.00000 −0.137686
$$845$$ −3.00000 −0.103203
$$846$$ 0 0
$$847$$ 50.0000 1.71802
$$848$$ −6.00000 −0.206041
$$849$$ 14.0000 0.480479
$$850$$ −6.00000 −0.205798
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −22.0000 −0.753266 −0.376633 0.926363i $$-0.622918\pi$$
−0.376633 + 0.926363i $$0.622918\pi$$
$$854$$ 4.00000 0.136877
$$855$$ −1.00000 −0.0341993
$$856$$ −12.0000 −0.410152
$$857$$ 6.00000 0.204956 0.102478 0.994735i $$-0.467323\pi$$
0.102478 + 0.994735i $$0.467323\pi$$
$$858$$ −24.0000 −0.819346
$$859$$ −52.0000 −1.77422 −0.887109 0.461561i $$-0.847290\pi$$
−0.887109 + 0.461561i $$0.847290\pi$$
$$860$$ −2.00000 −0.0681994
$$861$$ −24.0000 −0.817918
$$862$$ 12.0000 0.408722
$$863$$ 24.0000 0.816970 0.408485 0.912765i $$-0.366057\pi$$
0.408485 + 0.912765i $$0.366057\pi$$
$$864$$ 1.00000 0.0340207
$$865$$ −6.00000 −0.204006
$$866$$ −4.00000 −0.135926
$$867$$ 19.0000 0.645274
$$868$$ 16.0000 0.543075
$$869$$ 48.0000 1.62829
$$870$$ 0 0
$$871$$ 64.0000 2.16856
$$872$$ 2.00000 0.0677285
$$873$$ 8.00000 0.270759
$$874$$ 0 0
$$875$$ −2.00000 −0.0676123
$$876$$ −10.0000 −0.337869
$$877$$ 20.0000 0.675352 0.337676 0.941262i $$-0.390359\pi$$
0.337676 + 0.941262i $$0.390359\pi$$
$$878$$ 8.00000 0.269987
$$879$$ −18.0000 −0.607125
$$880$$ −6.00000 −0.202260
$$881$$ 30.0000 1.01073 0.505363 0.862907i $$-0.331359\pi$$
0.505363 + 0.862907i $$0.331359\pi$$
$$882$$ −3.00000 −0.101015
$$883$$ −34.0000 −1.14419 −0.572096 0.820187i $$-0.693869\pi$$
−0.572096 + 0.820187i $$0.693869\pi$$
$$884$$ 24.0000 0.807207
$$885$$ 12.0000 0.403376
$$886$$ −36.0000 −1.20944
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 8.00000 0.268462
$$889$$ 40.0000 1.34156
$$890$$ 12.0000 0.402241
$$891$$ 6.00000 0.201008
$$892$$ −16.0000 −0.535720
$$893$$ 0 0
$$894$$ −18.0000 −0.602010
$$895$$ 12.0000 0.401116
$$896$$ 2.00000 0.0668153
$$897$$ 0 0
$$898$$ 12.0000 0.400445
$$899$$ 0 0
$$900$$ 1.00000 0.0333333
$$901$$ 36.0000 1.19933
$$902$$ −72.0000 −2.39734
$$903$$ 4.00000 0.133112
$$904$$ −6.00000 −0.199557
$$905$$ −2.00000 −0.0664822
$$906$$ 8.00000 0.265782
$$907$$ 44.0000 1.46100 0.730498 0.682915i $$-0.239288\pi$$
0.730498 + 0.682915i $$0.239288\pi$$
$$908$$ 12.0000 0.398234
$$909$$ 6.00000 0.199007
$$910$$ 8.00000 0.265197
$$911$$ 48.0000 1.59031 0.795155 0.606406i $$-0.207389\pi$$
0.795155 + 0.606406i $$0.207389\pi$$
$$912$$ 1.00000 0.0331133
$$913$$ 0 0
$$914$$ −22.0000 −0.727695
$$915$$ −2.00000 −0.0661180
$$916$$ 2.00000 0.0660819
$$917$$ 36.0000 1.18882
$$918$$ −6.00000 −0.198030
$$919$$ 56.0000 1.84727 0.923635 0.383274i $$-0.125203\pi$$
0.923635 + 0.383274i $$0.125203\pi$$
$$920$$ 0 0
$$921$$ −16.0000 −0.527218
$$922$$ −42.0000 −1.38320
$$923$$ 0 0
$$924$$ 12.0000 0.394771
$$925$$ 8.00000 0.263038
$$926$$ 14.0000 0.460069
$$927$$ −16.0000 −0.525509
$$928$$ 0 0
$$929$$ 18.0000 0.590561 0.295280 0.955411i $$-0.404587\pi$$
0.295280 + 0.955411i $$0.404587\pi$$
$$930$$ −8.00000 −0.262330
$$931$$ −3.00000 −0.0983210
$$932$$ 6.00000 0.196537
$$933$$ −18.0000 −0.589294
$$934$$ 36.0000 1.17796
$$935$$ 36.0000 1.17733
$$936$$ −4.00000 −0.130744
$$937$$ −10.0000 −0.326686 −0.163343 0.986569i $$-0.552228\pi$$
−0.163343 + 0.986569i $$0.552228\pi$$
$$938$$ −32.0000 −1.04484
$$939$$ 26.0000 0.848478
$$940$$ 0 0
$$941$$ −24.0000 −0.782378 −0.391189 0.920310i $$-0.627936\pi$$
−0.391189 + 0.920310i $$0.627936\pi$$
$$942$$ −10.0000 −0.325818
$$943$$ 0 0
$$944$$ −12.0000 −0.390567
$$945$$ −2.00000 −0.0650600
$$946$$ 12.0000 0.390154
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 8.00000 0.259828
$$949$$ 40.0000 1.29845
$$950$$ 1.00000 0.0324443
$$951$$ −30.0000 −0.972817
$$952$$ −12.0000 −0.388922
$$953$$ 18.0000 0.583077 0.291539 0.956559i $$-0.405833\pi$$
0.291539 + 0.956559i $$0.405833\pi$$
$$954$$ −6.00000 −0.194257
$$955$$ −6.00000 −0.194155
$$956$$ −6.00000 −0.194054
$$957$$ 0 0
$$958$$ 30.0000 0.969256
$$959$$ 12.0000 0.387500
$$960$$ −1.00000 −0.0322749
$$961$$ 33.0000 1.06452
$$962$$ −32.0000 −1.03172
$$963$$ −12.0000 −0.386695
$$964$$ 2.00000 0.0644157
$$965$$ −20.0000 −0.643823
$$966$$ 0 0
$$967$$ −34.0000 −1.09337 −0.546683 0.837340i $$-0.684110\pi$$
−0.546683 + 0.837340i $$0.684110\pi$$
$$968$$ 25.0000 0.803530
$$969$$ −6.00000 −0.192748
$$970$$ −8.00000 −0.256865
$$971$$ −24.0000 −0.770197 −0.385098 0.922876i $$-0.625832\pi$$
−0.385098 + 0.922876i $$0.625832\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 16.0000 0.512936
$$974$$ −16.0000 −0.512673
$$975$$ −4.00000 −0.128103
$$976$$ 2.00000 0.0640184
$$977$$ 30.0000 0.959785 0.479893 0.877327i $$-0.340676\pi$$
0.479893 + 0.877327i $$0.340676\pi$$
$$978$$ −10.0000 −0.319765
$$979$$ −72.0000 −2.30113
$$980$$ 3.00000 0.0958315
$$981$$ 2.00000 0.0638551
$$982$$ −6.00000 −0.191468
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ −12.0000 −0.382546
$$985$$ −6.00000 −0.191176
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −4.00000 −0.127257
$$989$$ 0 0
$$990$$ −6.00000 −0.190693
$$991$$ 32.0000 1.01651 0.508257 0.861206i $$-0.330290\pi$$
0.508257 + 0.861206i $$0.330290\pi$$
$$992$$ 8.00000 0.254000
$$993$$ −28.0000 −0.888553
$$994$$ 0 0
$$995$$ −20.0000 −0.634043
$$996$$ 0 0
$$997$$ −10.0000 −0.316703 −0.158352 0.987383i $$-0.550618\pi$$
−0.158352 + 0.987383i $$0.550618\pi$$
$$998$$ 32.0000 1.01294
$$999$$ 8.00000 0.253109
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 570.2.a.k.1.1 1
3.2 odd 2 1710.2.a.j.1.1 1
4.3 odd 2 4560.2.a.b.1.1 1
5.2 odd 4 2850.2.d.t.799.2 2
5.3 odd 4 2850.2.d.t.799.1 2
5.4 even 2 2850.2.a.c.1.1 1
15.14 odd 2 8550.2.a.v.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.k.1.1 1 1.1 even 1 trivial
1710.2.a.j.1.1 1 3.2 odd 2
2850.2.a.c.1.1 1 5.4 even 2
2850.2.d.t.799.1 2 5.3 odd 4
2850.2.d.t.799.2 2 5.2 odd 4
4560.2.a.b.1.1 1 4.3 odd 2
8550.2.a.v.1.1 1 15.14 odd 2