# Properties

 Label 1950.2.a.k.1.1 Level $1950$ Weight $2$ Character 1950.1 Self dual yes Analytic conductor $15.571$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$15.5708283941$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1950.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +4.00000 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} -4.00000 q^{22} -8.00000 q^{23} -1.00000 q^{24} +1.00000 q^{26} +1.00000 q^{27} +6.00000 q^{29} -8.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} -6.00000 q^{34} +1.00000 q^{36} +10.0000 q^{37} -4.00000 q^{38} -1.00000 q^{39} -6.00000 q^{41} -4.00000 q^{43} +4.00000 q^{44} +8.00000 q^{46} +1.00000 q^{48} -7.00000 q^{49} +6.00000 q^{51} -1.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} +4.00000 q^{57} -6.00000 q^{58} +4.00000 q^{59} -2.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} -4.00000 q^{66} +12.0000 q^{67} +6.00000 q^{68} -8.00000 q^{69} +16.0000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -10.0000 q^{74} +4.00000 q^{76} +1.00000 q^{78} -16.0000 q^{79} +1.00000 q^{81} +6.00000 q^{82} +12.0000 q^{83} +4.00000 q^{86} +6.00000 q^{87} -4.00000 q^{88} +10.0000 q^{89} -8.00000 q^{92} -8.00000 q^{93} -1.00000 q^{96} +6.00000 q^{97} +7.00000 q^{98} +4.00000 q^{99} +O(q^{100})$$

## 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
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −1.00000 −0.277350
$$14$$ 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
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −4.00000 −0.852803
$$23$$ −8.00000 −1.66812 −0.834058 0.551677i $$-0.813988\pi$$
−0.834058 + 0.551677i $$0.813988\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 0 0
$$26$$ 1.00000 0.196116
$$27$$ 1.00000 0.192450
$$28$$ 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 $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 4.00000 0.696311
$$34$$ −6.00000 −1.02899
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ −4.00000 −0.648886
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ 6.00000 0.840168
$$52$$ −1.00000 −0.138675
$$53$$ 10.0000 1.37361 0.686803 0.726844i $$-0.259014\pi$$
0.686803 + 0.726844i $$0.259014\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 4.00000 0.529813
$$58$$ −6.00000 −0.787839
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 8.00000 1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −4.00000 −0.492366
$$67$$ 12.0000 1.46603 0.733017 0.680211i $$-0.238112\pi$$
0.733017 + 0.680211i $$0.238112\pi$$
$$68$$ 6.00000 0.727607
$$69$$ −8.00000 −0.963087
$$70$$ 0 0
$$71$$ 16.0000 1.89885 0.949425 0.313993i $$-0.101667\pi$$
0.949425 + 0.313993i $$0.101667\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ −10.0000 −1.16248
$$75$$ 0 0
$$76$$ 4.00000 0.458831
$$77$$ 0 0
$$78$$ 1.00000 0.113228
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 6.00000 0.662589
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ 6.00000 0.643268
$$88$$ −4.00000 −0.426401
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −8.00000 −0.834058
$$93$$ −8.00000 −0.829561
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 6.00000 0.609208 0.304604 0.952479i $$-0.401476\pi$$
0.304604 + 0.952479i $$0.401476\pi$$
$$98$$ 7.00000 0.707107
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ −2.00000 −0.199007 −0.0995037 0.995037i $$-0.531726\pi$$
−0.0995037 + 0.995037i $$0.531726\pi$$
$$102$$ −6.00000 −0.594089
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ 0 0
$$106$$ −10.0000 −0.971286
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 0 0
$$111$$ 10.0000 0.949158
$$112$$ 0 0
$$113$$ −10.0000 −0.940721 −0.470360 0.882474i $$-0.655876\pi$$
−0.470360 + 0.882474i $$0.655876\pi$$
$$114$$ −4.00000 −0.374634
$$115$$ 0 0
$$116$$ 6.00000 0.557086
$$117$$ −1.00000 −0.0924500
$$118$$ −4.00000 −0.368230
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 2.00000 0.181071
$$123$$ −6.00000 −0.541002
$$124$$ −8.00000 −0.718421
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ 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
$$134$$ −12.0000 −1.03664
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 8.00000 0.681005
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −16.0000 −1.34269
$$143$$ −4.00000 −0.334497
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 2.00000 0.165521
$$147$$ −7.00000 −0.577350
$$148$$ 10.0000 0.821995
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ −4.00000 −0.324443
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −1.00000 −0.0800641
$$157$$ 2.00000 0.159617 0.0798087 0.996810i $$-0.474569\pi$$
0.0798087 + 0.996810i $$0.474569\pi$$
$$158$$ 16.0000 1.27289
$$159$$ 10.0000 0.793052
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ −12.0000 −0.931381
$$167$$ −8.00000 −0.619059 −0.309529 0.950890i $$-0.600171\pi$$
−0.309529 + 0.950890i $$0.600171\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ −4.00000 −0.304997
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ −6.00000 −0.454859
$$175$$ 0 0
$$176$$ 4.00000 0.301511
$$177$$ 4.00000 0.300658
$$178$$ −10.0000 −0.749532
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ 0 0
$$183$$ −2.00000 −0.147844
$$184$$ 8.00000 0.589768
$$185$$ 0 0
$$186$$ 8.00000 0.586588
$$187$$ 24.0000 1.75505
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ −10.0000 −0.719816 −0.359908 0.932988i $$-0.617192\pi$$
−0.359908 + 0.932988i $$0.617192\pi$$
$$194$$ −6.00000 −0.430775
$$195$$ 0 0
$$196$$ −7.00000 −0.500000
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ −4.00000 −0.284268
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ 12.0000 0.846415
$$202$$ 2.00000 0.140720
$$203$$ 0 0
$$204$$ 6.00000 0.420084
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −8.00000 −0.556038
$$208$$ −1.00000 −0.0693375
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 10.0000 0.686803
$$213$$ 16.0000 1.09630
$$214$$ −12.0000 −0.820303
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 10.0000 0.677285
$$219$$ −2.00000 −0.135147
$$220$$ 0 0
$$221$$ −6.00000 −0.403604
$$222$$ −10.0000 −0.671156
$$223$$ −8.00000 −0.535720 −0.267860 0.963458i $$-0.586316\pi$$
−0.267860 + 0.963458i $$0.586316\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 10.0000 0.665190
$$227$$ −4.00000 −0.265489 −0.132745 0.991150i $$-0.542379\pi$$
−0.132745 + 0.991150i $$0.542379\pi$$
$$228$$ 4.00000 0.264906
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ 14.0000 0.917170 0.458585 0.888650i $$-0.348356\pi$$
0.458585 + 0.888650i $$0.348356\pi$$
$$234$$ 1.00000 0.0653720
$$235$$ 0 0
$$236$$ 4.00000 0.260378
$$237$$ −16.0000 −1.03931
$$238$$ 0 0
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ 0 0
$$241$$ 18.0000 1.15948 0.579741 0.814801i $$-0.303154\pi$$
0.579741 + 0.814801i $$0.303154\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 1.00000 0.0641500
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ 6.00000 0.382546
$$247$$ −4.00000 −0.254514
$$248$$ 8.00000 0.508001
$$249$$ 12.0000 0.760469
$$250$$ 0 0
$$251$$ −28.0000 −1.76734 −0.883672 0.468106i $$-0.844936\pi$$
−0.883672 + 0.468106i $$0.844936\pi$$
$$252$$ 0 0
$$253$$ −32.0000 −2.01182
$$254$$ 8.00000 0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 4.00000 0.249029
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 6.00000 0.371391
$$262$$ −12.0000 −0.741362
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ −4.00000 −0.246183
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 10.0000 0.611990
$$268$$ 12.0000 0.733017
$$269$$ −26.0000 −1.58525 −0.792624 0.609711i $$-0.791286\pi$$
−0.792624 + 0.609711i $$0.791286\pi$$
$$270$$ 0 0
$$271$$ 24.0000 1.45790 0.728948 0.684569i $$-0.240010\pi$$
0.728948 + 0.684569i $$0.240010\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ 10.0000 0.604122
$$275$$ 0 0
$$276$$ −8.00000 −0.481543
$$277$$ 10.0000 0.600842 0.300421 0.953807i $$-0.402873\pi$$
0.300421 + 0.953807i $$0.402873\pi$$
$$278$$ −12.0000 −0.719712
$$279$$ −8.00000 −0.478947
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 0 0
$$283$$ −20.0000 −1.18888 −0.594438 0.804141i $$-0.702626\pi$$
−0.594438 + 0.804141i $$0.702626\pi$$
$$284$$ 16.0000 0.949425
$$285$$ 0 0
$$286$$ 4.00000 0.236525
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 6.00000 0.351726
$$292$$ −2.00000 −0.117041
$$293$$ 26.0000 1.51894 0.759468 0.650545i $$-0.225459\pi$$
0.759468 + 0.650545i $$0.225459\pi$$
$$294$$ 7.00000 0.408248
$$295$$ 0 0
$$296$$ −10.0000 −0.581238
$$297$$ 4.00000 0.232104
$$298$$ −6.00000 −0.347571
$$299$$ 8.00000 0.462652
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −2.00000 −0.114897
$$304$$ 4.00000 0.229416
$$305$$ 0 0
$$306$$ −6.00000 −0.342997
$$307$$ 12.0000 0.684876 0.342438 0.939540i $$-0.388747\pi$$
0.342438 + 0.939540i $$0.388747\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 1.00000 0.0566139
$$313$$ 22.0000 1.24351 0.621757 0.783210i $$-0.286419\pi$$
0.621757 + 0.783210i $$0.286419\pi$$
$$314$$ −2.00000 −0.112867
$$315$$ 0 0
$$316$$ −16.0000 −0.900070
$$317$$ 2.00000 0.112331 0.0561656 0.998421i $$-0.482113\pi$$
0.0561656 + 0.998421i $$0.482113\pi$$
$$318$$ −10.0000 −0.560772
$$319$$ 24.0000 1.34374
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 24.0000 1.33540
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 4.00000 0.221540
$$327$$ −10.0000 −0.553001
$$328$$ 6.00000 0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ 12.0000 0.658586
$$333$$ 10.0000 0.547997
$$334$$ 8.00000 0.437741
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ −1.00000 −0.0543928
$$339$$ −10.0000 −0.543125
$$340$$ 0 0
$$341$$ −32.0000 −1.73290
$$342$$ −4.00000 −0.216295
$$343$$ 0 0
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ −18.0000 −0.967686
$$347$$ −20.0000 −1.07366 −0.536828 0.843692i $$-0.680378\pi$$
−0.536828 + 0.843692i $$0.680378\pi$$
$$348$$ 6.00000 0.321634
$$349$$ 6.00000 0.321173 0.160586 0.987022i $$-0.448662\pi$$
0.160586 + 0.987022i $$0.448662\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −0.0533761
$$352$$ −4.00000 −0.213201
$$353$$ 30.0000 1.59674 0.798369 0.602168i $$-0.205696\pi$$
0.798369 + 0.602168i $$0.205696\pi$$
$$354$$ −4.00000 −0.212598
$$355$$ 0 0
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −6.00000 −0.315353
$$363$$ 5.00000 0.262432
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 2.00000 0.104542
$$367$$ 24.0000 1.25279 0.626395 0.779506i $$-0.284530\pi$$
0.626395 + 0.779506i $$0.284530\pi$$
$$368$$ −8.00000 −0.417029
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −8.00000 −0.414781
$$373$$ −22.0000 −1.13912 −0.569558 0.821951i $$-0.692886\pi$$
−0.569558 + 0.821951i $$0.692886\pi$$
$$374$$ −24.0000 −1.24101
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −6.00000 −0.309016
$$378$$ 0 0
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ 0 0
$$381$$ −8.00000 −0.409852
$$382$$ 0 0
$$383$$ −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
$$386$$ 10.0000 0.508987
$$387$$ −4.00000 −0.203331
$$388$$ 6.00000 0.304604
$$389$$ −34.0000 −1.72387 −0.861934 0.507020i $$-0.830747\pi$$
−0.861934 + 0.507020i $$0.830747\pi$$
$$390$$ 0 0
$$391$$ −48.0000 −2.42746
$$392$$ 7.00000 0.353553
$$393$$ 12.0000 0.605320
$$394$$ 6.00000 0.302276
$$395$$ 0 0
$$396$$ 4.00000 0.201008
$$397$$ −30.0000 −1.50566 −0.752828 0.658217i $$-0.771311\pi$$
−0.752828 + 0.658217i $$0.771311\pi$$
$$398$$ 8.00000 0.401004
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 34.0000 1.69788 0.848939 0.528490i $$-0.177242\pi$$
0.848939 + 0.528490i $$0.177242\pi$$
$$402$$ −12.0000 −0.598506
$$403$$ 8.00000 0.398508
$$404$$ −2.00000 −0.0995037
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 40.0000 1.98273
$$408$$ −6.00000 −0.297044
$$409$$ −22.0000 −1.08783 −0.543915 0.839140i $$-0.683059\pi$$
−0.543915 + 0.839140i $$0.683059\pi$$
$$410$$ 0 0
$$411$$ −10.0000 −0.493264
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 8.00000 0.393179
$$415$$ 0 0
$$416$$ 1.00000 0.0490290
$$417$$ 12.0000 0.587643
$$418$$ −16.0000 −0.782586
$$419$$ −4.00000 −0.195413 −0.0977064 0.995215i $$-0.531151\pi$$
−0.0977064 + 0.995215i $$0.531151\pi$$
$$420$$ 0 0
$$421$$ −34.0000 −1.65706 −0.828529 0.559946i $$-0.810822\pi$$
−0.828529 + 0.559946i $$0.810822\pi$$
$$422$$ 12.0000 0.584151
$$423$$ 0 0
$$424$$ −10.0000 −0.485643
$$425$$ 0 0
$$426$$ −16.0000 −0.775203
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ −4.00000 −0.193122
$$430$$ 0 0
$$431$$ −24.0000 −1.15604 −0.578020 0.816023i $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 1.00000 0.0481125
$$433$$ −34.0000 −1.63394 −0.816968 0.576683i $$-0.804347\pi$$
−0.816968 + 0.576683i $$0.804347\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −10.0000 −0.478913
$$437$$ −32.0000 −1.53077
$$438$$ 2.00000 0.0955637
$$439$$ −40.0000 −1.90910 −0.954548 0.298057i $$-0.903661\pi$$
−0.954548 + 0.298057i $$0.903661\pi$$
$$440$$ 0 0
$$441$$ −7.00000 −0.333333
$$442$$ 6.00000 0.285391
$$443$$ −36.0000 −1.71041 −0.855206 0.518289i $$-0.826569\pi$$
−0.855206 + 0.518289i $$0.826569\pi$$
$$444$$ 10.0000 0.474579
$$445$$ 0 0
$$446$$ 8.00000 0.378811
$$447$$ 6.00000 0.283790
$$448$$ 0 0
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ −24.0000 −1.13012
$$452$$ −10.0000 −0.470360
$$453$$ 0 0
$$454$$ 4.00000 0.187729
$$455$$ 0 0
$$456$$ −4.00000 −0.187317
$$457$$ −34.0000 −1.59045 −0.795226 0.606313i $$-0.792648\pi$$
−0.795226 + 0.606313i $$0.792648\pi$$
$$458$$ −14.0000 −0.654177
$$459$$ 6.00000 0.280056
$$460$$ 0 0
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ 6.00000 0.278543
$$465$$ 0 0
$$466$$ −14.0000 −0.648537
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ −1.00000 −0.0462250
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 2.00000 0.0921551
$$472$$ −4.00000 −0.184115
$$473$$ −16.0000 −0.735681
$$474$$ 16.0000 0.734904
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 10.0000 0.457869
$$478$$ 8.00000 0.365911
$$479$$ −8.00000 −0.365529 −0.182765 0.983157i $$-0.558505\pi$$
−0.182765 + 0.983157i $$0.558505\pi$$
$$480$$ 0 0
$$481$$ −10.0000 −0.455961
$$482$$ −18.0000 −0.819878
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 16.0000 0.725029 0.362515 0.931978i $$-0.381918\pi$$
0.362515 + 0.931978i $$0.381918\pi$$
$$488$$ 2.00000 0.0905357
$$489$$ −4.00000 −0.180886
$$490$$ 0 0
$$491$$ 4.00000 0.180517 0.0902587 0.995918i $$-0.471231\pi$$
0.0902587 + 0.995918i $$0.471231\pi$$
$$492$$ −6.00000 −0.270501
$$493$$ 36.0000 1.62136
$$494$$ 4.00000 0.179969
$$495$$ 0 0
$$496$$ −8.00000 −0.359211
$$497$$ 0 0
$$498$$ −12.0000 −0.537733
$$499$$ 20.0000 0.895323 0.447661 0.894203i $$-0.352257\pi$$
0.447661 + 0.894203i $$0.352257\pi$$
$$500$$ 0 0
$$501$$ −8.00000 −0.357414
$$502$$ 28.0000 1.24970
$$503$$ −8.00000 −0.356702 −0.178351 0.983967i $$-0.557076\pi$$
−0.178351 + 0.983967i $$0.557076\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 32.0000 1.42257
$$507$$ 1.00000 0.0444116
$$508$$ −8.00000 −0.354943
$$509$$ 30.0000 1.32973 0.664863 0.746965i $$-0.268490\pi$$
0.664863 + 0.746965i $$0.268490\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 4.00000 0.176604
$$514$$ −6.00000 −0.264649
$$515$$ 0 0
$$516$$ −4.00000 −0.176090
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 18.0000 0.790112
$$520$$ 0 0
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ −6.00000 −0.262613
$$523$$ −36.0000 −1.57417 −0.787085 0.616844i $$-0.788411\pi$$
−0.787085 + 0.616844i $$0.788411\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ −48.0000 −2.09091
$$528$$ 4.00000 0.174078
$$529$$ 41.0000 1.78261
$$530$$ 0 0
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ 6.00000 0.259889
$$534$$ −10.0000 −0.432742
$$535$$ 0 0
$$536$$ −12.0000 −0.518321
$$537$$ 12.0000 0.517838
$$538$$ 26.0000 1.12094
$$539$$ −28.0000 −1.20605
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ −24.0000 −1.03089
$$543$$ 6.00000 0.257485
$$544$$ −6.00000 −0.257248
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ −10.0000 −0.427179
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ 24.0000 1.02243
$$552$$ 8.00000 0.340503
$$553$$ 0 0
$$554$$ −10.0000 −0.424859
$$555$$ 0 0
$$556$$ 12.0000 0.508913
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ 8.00000 0.338667
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ 24.0000 1.01328
$$562$$ −10.0000 −0.421825
$$563$$ −12.0000 −0.505740 −0.252870 0.967500i $$-0.581374\pi$$
−0.252870 + 0.967500i $$0.581374\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 20.0000 0.840663
$$567$$ 0 0
$$568$$ −16.0000 −0.671345
$$569$$ 10.0000 0.419222 0.209611 0.977785i $$-0.432780\pi$$
0.209611 + 0.977785i $$0.432780\pi$$
$$570$$ 0 0
$$571$$ 28.0000 1.17176 0.585882 0.810397i $$-0.300748\pi$$
0.585882 + 0.810397i $$0.300748\pi$$
$$572$$ −4.00000 −0.167248
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −42.0000 −1.74848 −0.874241 0.485491i $$-0.838641\pi$$
−0.874241 + 0.485491i $$0.838641\pi$$
$$578$$ −19.0000 −0.790296
$$579$$ −10.0000 −0.415586
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −6.00000 −0.248708
$$583$$ 40.0000 1.65663
$$584$$ 2.00000 0.0827606
$$585$$ 0 0
$$586$$ −26.0000 −1.07405
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ −7.00000 −0.288675
$$589$$ −32.0000 −1.31854
$$590$$ 0 0
$$591$$ −6.00000 −0.246807
$$592$$ 10.0000 0.410997
$$593$$ −34.0000 −1.39621 −0.698106 0.715994i $$-0.745974\pi$$
−0.698106 + 0.715994i $$0.745974\pi$$
$$594$$ −4.00000 −0.164122
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ −8.00000 −0.327418
$$598$$ −8.00000 −0.327144
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ −6.00000 −0.244745 −0.122373 0.992484i $$-0.539050\pi$$
−0.122373 + 0.992484i $$0.539050\pi$$
$$602$$ 0 0
$$603$$ 12.0000 0.488678
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 2.00000 0.0812444
$$607$$ 8.00000 0.324710 0.162355 0.986732i $$-0.448091\pi$$
0.162355 + 0.986732i $$0.448091\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 6.00000 0.242536
$$613$$ 10.0000 0.403896 0.201948 0.979396i $$-0.435273\pi$$
0.201948 + 0.979396i $$0.435273\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ −8.00000 −0.321029
$$622$$ 24.0000 0.962312
$$623$$ 0 0
$$624$$ −1.00000 −0.0400320
$$625$$ 0 0
$$626$$ −22.0000 −0.879297
$$627$$ 16.0000 0.638978
$$628$$ 2.00000 0.0798087
$$629$$ 60.0000 2.39236
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 16.0000 0.636446
$$633$$ −12.0000 −0.476957
$$634$$ −2.00000 −0.0794301
$$635$$ 0 0
$$636$$ 10.0000 0.396526
$$637$$ 7.00000 0.277350
$$638$$ −24.0000 −0.950169
$$639$$ 16.0000 0.632950
$$640$$ 0 0
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ −12.0000 −0.473602
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −24.0000 −0.944267
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 16.0000 0.628055
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ 34.0000 1.33052 0.665261 0.746611i $$-0.268320\pi$$
0.665261 + 0.746611i $$0.268320\pi$$
$$654$$ 10.0000 0.391031
$$655$$ 0 0
$$656$$ −6.00000 −0.234261
$$657$$ −2.00000 −0.0780274
$$658$$ 0 0
$$659$$ −20.0000 −0.779089 −0.389545 0.921008i $$-0.627368\pi$$
−0.389545 + 0.921008i $$0.627368\pi$$
$$660$$ 0 0
$$661$$ 14.0000 0.544537 0.272268 0.962221i $$-0.412226\pi$$
0.272268 + 0.962221i $$0.412226\pi$$
$$662$$ 20.0000 0.777322
$$663$$ −6.00000 −0.233021
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ −10.0000 −0.387492
$$667$$ −48.0000 −1.85857
$$668$$ −8.00000 −0.309529
$$669$$ −8.00000 −0.309298
$$670$$ 0 0
$$671$$ −8.00000 −0.308837
$$672$$ 0 0
$$673$$ −34.0000 −1.31060 −0.655302 0.755367i $$-0.727459\pi$$
−0.655302 + 0.755367i $$0.727459\pi$$
$$674$$ 2.00000 0.0770371
$$675$$ 0 0
$$676$$ 1.00000 0.0384615
$$677$$ −22.0000 −0.845529 −0.422764 0.906240i $$-0.638940\pi$$
−0.422764 + 0.906240i $$0.638940\pi$$
$$678$$ 10.0000 0.384048
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −4.00000 −0.153280
$$682$$ 32.0000 1.22534
$$683$$ −28.0000 −1.07139 −0.535695 0.844411i $$-0.679950\pi$$
−0.535695 + 0.844411i $$0.679950\pi$$
$$684$$ 4.00000 0.152944
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 14.0000 0.534133
$$688$$ −4.00000 −0.152499
$$689$$ −10.0000 −0.380970
$$690$$ 0 0
$$691$$ −12.0000 −0.456502 −0.228251 0.973602i $$-0.573301\pi$$
−0.228251 + 0.973602i $$0.573301\pi$$
$$692$$ 18.0000 0.684257
$$693$$ 0 0
$$694$$ 20.0000 0.759190
$$695$$ 0 0
$$696$$ −6.00000 −0.227429
$$697$$ −36.0000 −1.36360
$$698$$ −6.00000 −0.227103
$$699$$ 14.0000 0.529529
$$700$$ 0 0
$$701$$ 22.0000 0.830929 0.415464 0.909610i $$-0.363619\pi$$
0.415464 + 0.909610i $$0.363619\pi$$
$$702$$ 1.00000 0.0377426
$$703$$ 40.0000 1.50863
$$704$$ 4.00000 0.150756
$$705$$ 0 0
$$706$$ −30.0000 −1.12906
$$707$$ 0 0
$$708$$ 4.00000 0.150329
$$709$$ −50.0000 −1.87779 −0.938895 0.344204i $$-0.888149\pi$$
−0.938895 + 0.344204i $$0.888149\pi$$
$$710$$ 0 0
$$711$$ −16.0000 −0.600047
$$712$$ −10.0000 −0.374766
$$713$$ 64.0000 2.39682
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ −8.00000 −0.298765
$$718$$ −16.0000 −0.597115
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 3.00000 0.111648
$$723$$ 18.0000 0.669427
$$724$$ 6.00000 0.222988
$$725$$ 0 0
$$726$$ −5.00000 −0.185567
$$727$$ 16.0000 0.593407 0.296704 0.954970i $$-0.404113\pi$$
0.296704 + 0.954970i $$0.404113\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −24.0000 −0.887672
$$732$$ −2.00000 −0.0739221
$$733$$ 50.0000 1.84679 0.923396 0.383849i $$-0.125402\pi$$
0.923396 + 0.383849i $$0.125402\pi$$
$$734$$ −24.0000 −0.885856
$$735$$ 0 0
$$736$$ 8.00000 0.294884
$$737$$ 48.0000 1.76810
$$738$$ 6.00000 0.220863
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 0 0
$$741$$ −4.00000 −0.146944
$$742$$ 0 0
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 8.00000 0.293294
$$745$$ 0 0
$$746$$ 22.0000 0.805477
$$747$$ 12.0000 0.439057
$$748$$ 24.0000 0.877527
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 0 0
$$753$$ −28.0000 −1.02038
$$754$$ 6.00000 0.218507
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 42.0000 1.52652 0.763258 0.646094i $$-0.223599\pi$$
0.763258 + 0.646094i $$0.223599\pi$$
$$758$$ 4.00000 0.145287
$$759$$ −32.0000 −1.16153
$$760$$ 0 0
$$761$$ 42.0000 1.52250 0.761249 0.648459i $$-0.224586\pi$$
0.761249 + 0.648459i $$0.224586\pi$$
$$762$$ 8.00000 0.289809
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 32.0000 1.15621
$$767$$ −4.00000 −0.144432
$$768$$ 1.00000 0.0360844
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ 6.00000 0.216085
$$772$$ −10.0000 −0.359908
$$773$$ −38.0000 −1.36677 −0.683383 0.730061i $$-0.739492\pi$$
−0.683383 + 0.730061i $$0.739492\pi$$
$$774$$ 4.00000 0.143777
$$775$$ 0 0
$$776$$ −6.00000 −0.215387
$$777$$ 0 0
$$778$$ 34.0000 1.21896
$$779$$ −24.0000 −0.859889
$$780$$ 0 0
$$781$$ 64.0000 2.29010
$$782$$ 48.0000 1.71648
$$783$$ 6.00000 0.214423
$$784$$ −7.00000 −0.250000
$$785$$ 0 0
$$786$$ −12.0000 −0.428026
$$787$$ −4.00000 −0.142585 −0.0712923 0.997455i $$-0.522712\pi$$
−0.0712923 + 0.997455i $$0.522712\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −4.00000 −0.142134
$$793$$ 2.00000 0.0710221
$$794$$ 30.0000 1.06466
$$795$$ 0 0
$$796$$ −8.00000 −0.283552
$$797$$ 2.00000 0.0708436 0.0354218 0.999372i $$-0.488723\pi$$
0.0354218 + 0.999372i $$0.488723\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 10.0000 0.353333
$$802$$ −34.0000 −1.20058
$$803$$ −8.00000 −0.282314
$$804$$ 12.0000 0.423207
$$805$$ 0 0
$$806$$ −8.00000 −0.281788
$$807$$ −26.0000 −0.915243
$$808$$ 2.00000 0.0703598
$$809$$ 42.0000 1.47664 0.738321 0.674450i $$-0.235619\pi$$
0.738321 + 0.674450i $$0.235619\pi$$
$$810$$ 0 0
$$811$$ 12.0000 0.421377 0.210688 0.977553i $$-0.432429\pi$$
0.210688 + 0.977553i $$0.432429\pi$$
$$812$$ 0 0
$$813$$ 24.0000 0.841717
$$814$$ −40.0000 −1.40200
$$815$$ 0 0
$$816$$ 6.00000 0.210042
$$817$$ −16.0000 −0.559769
$$818$$ 22.0000 0.769212
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 6.00000 0.209401 0.104701 0.994504i $$-0.466612\pi$$
0.104701 + 0.994504i $$0.466612\pi$$
$$822$$ 10.0000 0.348790
$$823$$ −16.0000 −0.557725 −0.278862 0.960331i $$-0.589957\pi$$
−0.278862 + 0.960331i $$0.589957\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 36.0000 1.25184 0.625921 0.779886i $$-0.284723\pi$$
0.625921 + 0.779886i $$0.284723\pi$$
$$828$$ −8.00000 −0.278019
$$829$$ −2.00000 −0.0694629 −0.0347314 0.999397i $$-0.511058\pi$$
−0.0347314 + 0.999397i $$0.511058\pi$$
$$830$$ 0 0
$$831$$ 10.0000 0.346896
$$832$$ −1.00000 −0.0346688
$$833$$ −42.0000 −1.45521
$$834$$ −12.0000 −0.415526
$$835$$ 0 0
$$836$$ 16.0000 0.553372
$$837$$ −8.00000 −0.276520
$$838$$ 4.00000 0.138178
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 34.0000 1.17172
$$843$$ 10.0000 0.344418
$$844$$ −12.0000 −0.413057
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 10.0000 0.343401
$$849$$ −20.0000 −0.686398
$$850$$ 0 0
$$851$$ −80.0000 −2.74236
$$852$$ 16.0000 0.548151
$$853$$ 26.0000 0.890223 0.445112 0.895475i $$-0.353164\pi$$
0.445112 + 0.895475i $$0.353164\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ −18.0000 −0.614868 −0.307434 0.951569i $$-0.599470\pi$$
−0.307434 + 0.951569i $$0.599470\pi$$
$$858$$ 4.00000 0.136558
$$859$$ −20.0000 −0.682391 −0.341196 0.939992i $$-0.610832\pi$$
−0.341196 + 0.939992i $$0.610832\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 24.0000 0.817443
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 0 0
$$866$$ 34.0000 1.15537
$$867$$ 19.0000 0.645274
$$868$$ 0 0
$$869$$ −64.0000 −2.17105
$$870$$ 0 0
$$871$$ −12.0000 −0.406604
$$872$$ 10.0000 0.338643
$$873$$ 6.00000 0.203069
$$874$$ 32.0000 1.08242
$$875$$ 0 0
$$876$$ −2.00000 −0.0675737
$$877$$ −14.0000 −0.472746 −0.236373 0.971662i $$-0.575959\pi$$
−0.236373 + 0.971662i $$0.575959\pi$$
$$878$$ 40.0000 1.34993
$$879$$ 26.0000 0.876958
$$880$$ 0 0
$$881$$ 2.00000 0.0673817 0.0336909 0.999432i $$-0.489274\pi$$
0.0336909 + 0.999432i $$0.489274\pi$$
$$882$$ 7.00000 0.235702
$$883$$ 36.0000 1.21150 0.605748 0.795656i $$-0.292874\pi$$
0.605748 + 0.795656i $$0.292874\pi$$
$$884$$ −6.00000 −0.201802
$$885$$ 0 0
$$886$$ 36.0000 1.20944
$$887$$ −8.00000 −0.268614 −0.134307 0.990940i $$-0.542881\pi$$
−0.134307 + 0.990940i $$0.542881\pi$$
$$888$$ −10.0000 −0.335578
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 4.00000 0.134005
$$892$$ −8.00000 −0.267860
$$893$$ 0 0
$$894$$ −6.00000 −0.200670
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 8.00000 0.267112
$$898$$ −18.0000 −0.600668
$$899$$ −48.0000 −1.60089
$$900$$ 0 0
$$901$$ 60.0000 1.99889
$$902$$ 24.0000 0.799113
$$903$$ 0 0
$$904$$ 10.0000 0.332595
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 12.0000 0.398453 0.199227 0.979953i $$-0.436157\pi$$
0.199227 + 0.979953i $$0.436157\pi$$
$$908$$ −4.00000 −0.132745
$$909$$ −2.00000 −0.0663358
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 4.00000 0.132453
$$913$$ 48.0000 1.58857
$$914$$ 34.0000 1.12462
$$915$$ 0 0
$$916$$ 14.0000 0.462573
$$917$$ 0 0
$$918$$ −6.00000 −0.198030
$$919$$ −56.0000 −1.84727 −0.923635 0.383274i $$-0.874797\pi$$
−0.923635 + 0.383274i $$0.874797\pi$$
$$920$$ 0 0
$$921$$ 12.0000 0.395413
$$922$$ 18.0000 0.592798
$$923$$ −16.0000 −0.526646
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 8.00000 0.262896
$$927$$ 0 0
$$928$$ −6.00000 −0.196960
$$929$$ −14.0000 −0.459325 −0.229663 0.973270i $$-0.573762\pi$$
−0.229663 + 0.973270i $$0.573762\pi$$
$$930$$ 0 0
$$931$$ −28.0000 −0.917663
$$932$$ 14.0000 0.458585
$$933$$ −24.0000 −0.785725
$$934$$ 12.0000 0.392652
$$935$$ 0 0
$$936$$ 1.00000 0.0326860
$$937$$ 22.0000 0.718709 0.359354 0.933201i $$-0.382997\pi$$
0.359354 + 0.933201i $$0.382997\pi$$
$$938$$ 0 0
$$939$$ 22.0000 0.717943
$$940$$ 0 0
$$941$$ 30.0000 0.977972 0.488986 0.872292i $$-0.337367\pi$$
0.488986 + 0.872292i $$0.337367\pi$$
$$942$$ −2.00000 −0.0651635
$$943$$ 48.0000 1.56310
$$944$$ 4.00000 0.130189
$$945$$ 0 0
$$946$$ 16.0000 0.520205
$$947$$ −52.0000 −1.68977 −0.844886 0.534946i $$-0.820332\pi$$
−0.844886 + 0.534946i $$0.820332\pi$$
$$948$$ −16.0000 −0.519656
$$949$$ 2.00000 0.0649227
$$950$$ 0 0
$$951$$ 2.00000 0.0648544
$$952$$ 0 0
$$953$$ −34.0000 −1.10137 −0.550684 0.834714i $$-0.685633\pi$$
−0.550684 + 0.834714i $$0.685633\pi$$
$$954$$ −10.0000 −0.323762
$$955$$ 0 0
$$956$$ −8.00000 −0.258738
$$957$$ 24.0000 0.775810
$$958$$ 8.00000 0.258468
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 33.0000 1.06452
$$962$$ 10.0000 0.322413
$$963$$ 12.0000 0.386695
$$964$$ 18.0000 0.579741
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −16.0000 −0.514525 −0.257263 0.966342i $$-0.582821\pi$$
−0.257263 + 0.966342i $$0.582821\pi$$
$$968$$ −5.00000 −0.160706
$$969$$ 24.0000 0.770991
$$970$$ 0 0
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ 1.00000 0.0320750
$$973$$ 0 0
$$974$$ −16.0000 −0.512673
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ 30.0000 0.959785 0.479893 0.877327i $$-0.340676\pi$$
0.479893 + 0.877327i $$0.340676\pi$$
$$978$$ 4.00000 0.127906
$$979$$ 40.0000 1.27841
$$980$$ 0 0
$$981$$ −10.0000 −0.319275
$$982$$ −4.00000 −0.127645
$$983$$ −8.00000 −0.255160 −0.127580 0.991828i $$-0.540721\pi$$
−0.127580 + 0.991828i $$0.540721\pi$$
$$984$$ 6.00000 0.191273
$$985$$ 0 0
$$986$$ −36.0000 −1.14647
$$987$$ 0 0
$$988$$ −4.00000 −0.127257
$$989$$ 32.0000 1.01754
$$990$$ 0 0
$$991$$ −16.0000 −0.508257 −0.254128 0.967170i $$-0.581789\pi$$
−0.254128 + 0.967170i $$0.581789\pi$$
$$992$$ 8.00000 0.254000
$$993$$ −20.0000 −0.634681
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 12.0000 0.380235
$$997$$ 58.0000 1.83688 0.918439 0.395562i $$-0.129450\pi$$
0.918439 + 0.395562i $$0.129450\pi$$
$$998$$ −20.0000 −0.633089
$$999$$ 10.0000 0.316386
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 1950.2.a.k.1.1 1
3.2 odd 2 5850.2.a.bo.1.1 1
5.2 odd 4 1950.2.e.g.1249.1 2
5.3 odd 4 1950.2.e.g.1249.2 2
5.4 even 2 390.2.a.f.1.1 1
15.2 even 4 5850.2.e.e.5149.2 2
15.8 even 4 5850.2.e.e.5149.1 2
15.14 odd 2 1170.2.a.a.1.1 1
20.19 odd 2 3120.2.a.w.1.1 1
60.59 even 2 9360.2.a.p.1.1 1
65.34 odd 4 5070.2.b.d.1351.2 2
65.44 odd 4 5070.2.b.d.1351.1 2
65.64 even 2 5070.2.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.a.f.1.1 1 5.4 even 2
1170.2.a.a.1.1 1 15.14 odd 2
1950.2.a.k.1.1 1 1.1 even 1 trivial
1950.2.e.g.1249.1 2 5.2 odd 4
1950.2.e.g.1249.2 2 5.3 odd 4
3120.2.a.w.1.1 1 20.19 odd 2
5070.2.a.a.1.1 1 65.64 even 2
5070.2.b.d.1351.1 2 65.44 odd 4
5070.2.b.d.1351.2 2 65.34 odd 4
5850.2.a.bo.1.1 1 3.2 odd 2
5850.2.e.e.5149.1 2 15.8 even 4
5850.2.e.e.5149.2 2 15.2 even 4
9360.2.a.p.1.1 1 60.59 even 2