# Properties

 Label 5390.2.a.q.1.1 Level $5390$ Weight $2$ Character 5390.1 Self dual yes Analytic conductor $43.039$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5390.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$43.0393666895$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 770) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 5390.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.00000 q^{12} -2.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -1.00000 q^{20} -1.00000 q^{22} -4.00000 q^{23} -2.00000 q^{24} +1.00000 q^{25} -4.00000 q^{27} +2.00000 q^{29} +2.00000 q^{30} +2.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} +1.00000 q^{36} -6.00000 q^{37} +1.00000 q^{40} -8.00000 q^{41} -12.0000 q^{43} +1.00000 q^{44} -1.00000 q^{45} +4.00000 q^{46} +6.00000 q^{47} +2.00000 q^{48} -1.00000 q^{50} -6.00000 q^{53} +4.00000 q^{54} -1.00000 q^{55} -2.00000 q^{58} +10.0000 q^{59} -2.00000 q^{60} +4.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -2.00000 q^{66} -8.00000 q^{67} -8.00000 q^{69} -4.00000 q^{71} -1.00000 q^{72} +4.00000 q^{73} +6.00000 q^{74} +2.00000 q^{75} -16.0000 q^{79} -1.00000 q^{80} -11.0000 q^{81} +8.00000 q^{82} +12.0000 q^{86} +4.00000 q^{87} -1.00000 q^{88} +6.00000 q^{89} +1.00000 q^{90} -4.00000 q^{92} +4.00000 q^{93} -6.00000 q^{94} -2.00000 q^{96} -14.0000 q^{97} +1.00000 q^{99} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 2.00000 1.15470 0.577350 0.816497i $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ 1.00000 0.500000
$$5$$ −1.00000 −0.447214
$$6$$ −2.00000 −0.816497
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 1.00000 0.316228
$$11$$ 1.00000 0.301511
$$12$$ 2.00000 0.577350
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ −2.00000 −0.516398
$$16$$ 1.00000 0.250000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ −1.00000 −0.213201
$$23$$ −4.00000 −0.834058 −0.417029 0.908893i $$-0.636929\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ −2.00000 −0.408248
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 2.00000 0.365148
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 2.00000 0.348155
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −6.00000 −0.986394 −0.493197 0.869918i $$-0.664172\pi$$
−0.493197 + 0.869918i $$0.664172\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ −8.00000 −1.24939 −0.624695 0.780869i $$-0.714777\pi$$
−0.624695 + 0.780869i $$0.714777\pi$$
$$42$$ 0 0
$$43$$ −12.0000 −1.82998 −0.914991 0.403473i $$-0.867803\pi$$
−0.914991 + 0.403473i $$0.867803\pi$$
$$44$$ 1.00000 0.150756
$$45$$ −1.00000 −0.149071
$$46$$ 4.00000 0.589768
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ 2.00000 0.288675
$$49$$ 0 0
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 4.00000 0.544331
$$55$$ −1.00000 −0.134840
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −2.00000 −0.262613
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ −2.00000 −0.258199
$$61$$ 4.00000 0.512148 0.256074 0.966657i $$-0.417571\pi$$
0.256074 + 0.966657i $$0.417571\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −2.00000 −0.246183
$$67$$ −8.00000 −0.977356 −0.488678 0.872464i $$-0.662521\pi$$
−0.488678 + 0.872464i $$0.662521\pi$$
$$68$$ 0 0
$$69$$ −8.00000 −0.963087
$$70$$ 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
$$73$$ 4.00000 0.468165 0.234082 0.972217i $$-0.424791\pi$$
0.234082 + 0.972217i $$0.424791\pi$$
$$74$$ 6.00000 0.697486
$$75$$ 2.00000 0.230940
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ −11.0000 −1.22222
$$82$$ 8.00000 0.883452
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 12.0000 1.29399
$$87$$ 4.00000 0.428845
$$88$$ −1.00000 −0.106600
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 1.00000 0.105409
$$91$$ 0 0
$$92$$ −4.00000 −0.417029
$$93$$ 4.00000 0.414781
$$94$$ −6.00000 −0.618853
$$95$$ 0 0
$$96$$ −2.00000 −0.204124
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ 1.00000 0.100504
$$100$$ 1.00000 0.100000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 14.0000 1.37946 0.689730 0.724066i $$-0.257729\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ −4.00000 −0.384900
$$109$$ −6.00000 −0.574696 −0.287348 0.957826i $$-0.592774\pi$$
−0.287348 + 0.957826i $$0.592774\pi$$
$$110$$ 1.00000 0.0953463
$$111$$ −12.0000 −1.13899
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ 4.00000 0.373002
$$116$$ 2.00000 0.185695
$$117$$ 0 0
$$118$$ −10.0000 −0.920575
$$119$$ 0 0
$$120$$ 2.00000 0.182574
$$121$$ 1.00000 0.0909091
$$122$$ −4.00000 −0.362143
$$123$$ −16.0000 −1.44267
$$124$$ 2.00000 0.179605
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −24.0000 −2.11308
$$130$$ 0 0
$$131$$ −4.00000 −0.349482 −0.174741 0.984614i $$-0.555909\pi$$
−0.174741 + 0.984614i $$0.555909\pi$$
$$132$$ 2.00000 0.174078
$$133$$ 0 0
$$134$$ 8.00000 0.691095
$$135$$ 4.00000 0.344265
$$136$$ 0 0
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 8.00000 0.681005
$$139$$ −8.00000 −0.678551 −0.339276 0.940687i $$-0.610182\pi$$
−0.339276 + 0.940687i $$0.610182\pi$$
$$140$$ 0 0
$$141$$ 12.0000 1.01058
$$142$$ 4.00000 0.335673
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ −2.00000 −0.166091
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ −6.00000 −0.493197
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ −2.00000 −0.163299
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −2.00000 −0.160644
$$156$$ 0 0
$$157$$ −6.00000 −0.478852 −0.239426 0.970915i $$-0.576959\pi$$
−0.239426 + 0.970915i $$0.576959\pi$$
$$158$$ 16.0000 1.27289
$$159$$ −12.0000 −0.951662
$$160$$ 1.00000 0.0790569
$$161$$ 0 0
$$162$$ 11.0000 0.864242
$$163$$ −8.00000 −0.626608 −0.313304 0.949653i $$-0.601436\pi$$
−0.313304 + 0.949653i $$0.601436\pi$$
$$164$$ −8.00000 −0.624695
$$165$$ −2.00000 −0.155700
$$166$$ 0 0
$$167$$ −16.0000 −1.23812 −0.619059 0.785345i $$-0.712486\pi$$
−0.619059 + 0.785345i $$0.712486\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −12.0000 −0.914991
$$173$$ −24.0000 −1.82469 −0.912343 0.409426i $$-0.865729\pi$$
−0.912343 + 0.409426i $$0.865729\pi$$
$$174$$ −4.00000 −0.303239
$$175$$ 0 0
$$176$$ 1.00000 0.0753778
$$177$$ 20.0000 1.50329
$$178$$ −6.00000 −0.449719
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ −1.00000 −0.0745356
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ 0 0
$$183$$ 8.00000 0.591377
$$184$$ 4.00000 0.294884
$$185$$ 6.00000 0.441129
$$186$$ −4.00000 −0.293294
$$187$$ 0 0
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ 2.00000 0.144338
$$193$$ −22.0000 −1.58359 −0.791797 0.610784i $$-0.790854\pi$$
−0.791797 + 0.610784i $$0.790854\pi$$
$$194$$ 14.0000 1.00514
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 14.0000 0.997459 0.498729 0.866758i $$-0.333800\pi$$
0.498729 + 0.866758i $$0.333800\pi$$
$$198$$ −1.00000 −0.0710669
$$199$$ 6.00000 0.425329 0.212664 0.977125i $$-0.431786\pi$$
0.212664 + 0.977125i $$0.431786\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ −16.0000 −1.12855
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 8.00000 0.558744
$$206$$ −14.0000 −0.975426
$$207$$ −4.00000 −0.278019
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ −8.00000 −0.548151
$$214$$ −12.0000 −0.820303
$$215$$ 12.0000 0.818393
$$216$$ 4.00000 0.272166
$$217$$ 0 0
$$218$$ 6.00000 0.406371
$$219$$ 8.00000 0.540590
$$220$$ −1.00000 −0.0674200
$$221$$ 0 0
$$222$$ 12.0000 0.805387
$$223$$ 6.00000 0.401790 0.200895 0.979613i $$-0.435615\pi$$
0.200895 + 0.979613i $$0.435615\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ −2.00000 −0.133038
$$227$$ −4.00000 −0.265489 −0.132745 0.991150i $$-0.542379\pi$$
−0.132745 + 0.991150i $$0.542379\pi$$
$$228$$ 0 0
$$229$$ −2.00000 −0.132164 −0.0660819 0.997814i $$-0.521050\pi$$
−0.0660819 + 0.997814i $$0.521050\pi$$
$$230$$ −4.00000 −0.263752
$$231$$ 0 0
$$232$$ −2.00000 −0.131306
$$233$$ −18.0000 −1.17922 −0.589610 0.807688i $$-0.700718\pi$$
−0.589610 + 0.807688i $$0.700718\pi$$
$$234$$ 0 0
$$235$$ −6.00000 −0.391397
$$236$$ 10.0000 0.650945
$$237$$ −32.0000 −2.07862
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ −2.00000 −0.129099
$$241$$ 16.0000 1.03065 0.515325 0.856995i $$-0.327671\pi$$
0.515325 + 0.856995i $$0.327671\pi$$
$$242$$ −1.00000 −0.0642824
$$243$$ −10.0000 −0.641500
$$244$$ 4.00000 0.256074
$$245$$ 0 0
$$246$$ 16.0000 1.02012
$$247$$ 0 0
$$248$$ −2.00000 −0.127000
$$249$$ 0 0
$$250$$ 1.00000 0.0632456
$$251$$ −10.0000 −0.631194 −0.315597 0.948893i $$-0.602205\pi$$
−0.315597 + 0.948893i $$0.602205\pi$$
$$252$$ 0 0
$$253$$ −4.00000 −0.251478
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 14.0000 0.873296 0.436648 0.899632i $$-0.356166\pi$$
0.436648 + 0.899632i $$0.356166\pi$$
$$258$$ 24.0000 1.49417
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 2.00000 0.123797
$$262$$ 4.00000 0.247121
$$263$$ −24.0000 −1.47990 −0.739952 0.672660i $$-0.765152\pi$$
−0.739952 + 0.672660i $$0.765152\pi$$
$$264$$ −2.00000 −0.123091
$$265$$ 6.00000 0.368577
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ −8.00000 −0.488678
$$269$$ −10.0000 −0.609711 −0.304855 0.952399i $$-0.598608\pi$$
−0.304855 + 0.952399i $$0.598608\pi$$
$$270$$ −4.00000 −0.243432
$$271$$ −20.0000 −1.21491 −0.607457 0.794353i $$-0.707810\pi$$
−0.607457 + 0.794353i $$0.707810\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ 1.00000 0.0603023
$$276$$ −8.00000 −0.481543
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 8.00000 0.479808
$$279$$ 2.00000 0.119737
$$280$$ 0 0
$$281$$ −2.00000 −0.119310 −0.0596550 0.998219i $$-0.519000\pi$$
−0.0596550 + 0.998219i $$0.519000\pi$$
$$282$$ −12.0000 −0.714590
$$283$$ −28.0000 −1.66443 −0.832214 0.554455i $$-0.812927\pi$$
−0.832214 + 0.554455i $$0.812927\pi$$
$$284$$ −4.00000 −0.237356
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −17.0000 −1.00000
$$290$$ 2.00000 0.117444
$$291$$ −28.0000 −1.64139
$$292$$ 4.00000 0.234082
$$293$$ 4.00000 0.233682 0.116841 0.993151i $$-0.462723\pi$$
0.116841 + 0.993151i $$0.462723\pi$$
$$294$$ 0 0
$$295$$ −10.0000 −0.582223
$$296$$ 6.00000 0.348743
$$297$$ −4.00000 −0.232104
$$298$$ −6.00000 −0.347571
$$299$$ 0 0
$$300$$ 2.00000 0.115470
$$301$$ 0 0
$$302$$ 8.00000 0.460348
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −4.00000 −0.229039
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ 28.0000 1.59286
$$310$$ 2.00000 0.113592
$$311$$ 6.00000 0.340229 0.170114 0.985424i $$-0.445586\pi$$
0.170114 + 0.985424i $$0.445586\pi$$
$$312$$ 0 0
$$313$$ −2.00000 −0.113047 −0.0565233 0.998401i $$-0.518002\pi$$
−0.0565233 + 0.998401i $$0.518002\pi$$
$$314$$ 6.00000 0.338600
$$315$$ 0 0
$$316$$ −16.0000 −0.900070
$$317$$ −2.00000 −0.112331 −0.0561656 0.998421i $$-0.517887\pi$$
−0.0561656 + 0.998421i $$0.517887\pi$$
$$318$$ 12.0000 0.672927
$$319$$ 2.00000 0.111979
$$320$$ −1.00000 −0.0559017
$$321$$ 24.0000 1.33955
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −11.0000 −0.611111
$$325$$ 0 0
$$326$$ 8.00000 0.443079
$$327$$ −12.0000 −0.663602
$$328$$ 8.00000 0.441726
$$329$$ 0 0
$$330$$ 2.00000 0.110096
$$331$$ 28.0000 1.53902 0.769510 0.638635i $$-0.220501\pi$$
0.769510 + 0.638635i $$0.220501\pi$$
$$332$$ 0 0
$$333$$ −6.00000 −0.328798
$$334$$ 16.0000 0.875481
$$335$$ 8.00000 0.437087
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 13.0000 0.707107
$$339$$ 4.00000 0.217250
$$340$$ 0 0
$$341$$ 2.00000 0.108306
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 12.0000 0.646997
$$345$$ 8.00000 0.430706
$$346$$ 24.0000 1.29025
$$347$$ 28.0000 1.50312 0.751559 0.659665i $$-0.229302\pi$$
0.751559 + 0.659665i $$0.229302\pi$$
$$348$$ 4.00000 0.214423
$$349$$ 20.0000 1.07058 0.535288 0.844670i $$-0.320203\pi$$
0.535288 + 0.844670i $$0.320203\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −1.00000 −0.0533002
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ −20.0000 −1.06299
$$355$$ 4.00000 0.212298
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ −8.00000 −0.422224 −0.211112 0.977462i $$-0.567708\pi$$
−0.211112 + 0.977462i $$0.567708\pi$$
$$360$$ 1.00000 0.0527046
$$361$$ −19.0000 −1.00000
$$362$$ −6.00000 −0.315353
$$363$$ 2.00000 0.104973
$$364$$ 0 0
$$365$$ −4.00000 −0.209370
$$366$$ −8.00000 −0.418167
$$367$$ 22.0000 1.14839 0.574195 0.818718i $$-0.305315\pi$$
0.574195 + 0.818718i $$0.305315\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ −8.00000 −0.416463
$$370$$ −6.00000 −0.311925
$$371$$ 0 0
$$372$$ 4.00000 0.207390
$$373$$ 14.0000 0.724893 0.362446 0.932005i $$-0.381942\pi$$
0.362446 + 0.932005i $$0.381942\pi$$
$$374$$ 0 0
$$375$$ −2.00000 −0.103280
$$376$$ −6.00000 −0.309426
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −16.0000 −0.821865 −0.410932 0.911666i $$-0.634797\pi$$
−0.410932 + 0.911666i $$0.634797\pi$$
$$380$$ 0 0
$$381$$ 16.0000 0.819705
$$382$$ 8.00000 0.409316
$$383$$ 2.00000 0.102195 0.0510976 0.998694i $$-0.483728\pi$$
0.0510976 + 0.998694i $$0.483728\pi$$
$$384$$ −2.00000 −0.102062
$$385$$ 0 0
$$386$$ 22.0000 1.11977
$$387$$ −12.0000 −0.609994
$$388$$ −14.0000 −0.710742
$$389$$ 22.0000 1.11544 0.557722 0.830028i $$-0.311675\pi$$
0.557722 + 0.830028i $$0.311675\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −8.00000 −0.403547
$$394$$ −14.0000 −0.705310
$$395$$ 16.0000 0.805047
$$396$$ 1.00000 0.0502519
$$397$$ 34.0000 1.70641 0.853206 0.521575i $$-0.174655\pi$$
0.853206 + 0.521575i $$0.174655\pi$$
$$398$$ −6.00000 −0.300753
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 16.0000 0.798007
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 11.0000 0.546594
$$406$$ 0 0
$$407$$ −6.00000 −0.297409
$$408$$ 0 0
$$409$$ −4.00000 −0.197787 −0.0988936 0.995098i $$-0.531530\pi$$
−0.0988936 + 0.995098i $$0.531530\pi$$
$$410$$ −8.00000 −0.395092
$$411$$ 12.0000 0.591916
$$412$$ 14.0000 0.689730
$$413$$ 0 0
$$414$$ 4.00000 0.196589
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −16.0000 −0.783523
$$418$$ 0 0
$$419$$ 26.0000 1.27018 0.635092 0.772437i $$-0.280962\pi$$
0.635092 + 0.772437i $$0.280962\pi$$
$$420$$ 0 0
$$421$$ 18.0000 0.877266 0.438633 0.898666i $$-0.355463\pi$$
0.438633 + 0.898666i $$0.355463\pi$$
$$422$$ 12.0000 0.584151
$$423$$ 6.00000 0.291730
$$424$$ 6.00000 0.291386
$$425$$ 0 0
$$426$$ 8.00000 0.387601
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ −12.0000 −0.578691
$$431$$ 8.00000 0.385346 0.192673 0.981263i $$-0.438284\pi$$
0.192673 + 0.981263i $$0.438284\pi$$
$$432$$ −4.00000 −0.192450
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ 0 0
$$435$$ −4.00000 −0.191785
$$436$$ −6.00000 −0.287348
$$437$$ 0 0
$$438$$ −8.00000 −0.382255
$$439$$ −4.00000 −0.190910 −0.0954548 0.995434i $$-0.530431\pi$$
−0.0954548 + 0.995434i $$0.530431\pi$$
$$440$$ 1.00000 0.0476731
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −20.0000 −0.950229 −0.475114 0.879924i $$-0.657593\pi$$
−0.475114 + 0.879924i $$0.657593\pi$$
$$444$$ −12.0000 −0.569495
$$445$$ −6.00000 −0.284427
$$446$$ −6.00000 −0.284108
$$447$$ 12.0000 0.567581
$$448$$ 0 0
$$449$$ −10.0000 −0.471929 −0.235965 0.971762i $$-0.575825\pi$$
−0.235965 + 0.971762i $$0.575825\pi$$
$$450$$ −1.00000 −0.0471405
$$451$$ −8.00000 −0.376705
$$452$$ 2.00000 0.0940721
$$453$$ −16.0000 −0.751746
$$454$$ 4.00000 0.187729
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 26.0000 1.21623 0.608114 0.793849i $$-0.291926\pi$$
0.608114 + 0.793849i $$0.291926\pi$$
$$458$$ 2.00000 0.0934539
$$459$$ 0 0
$$460$$ 4.00000 0.186501
$$461$$ 20.0000 0.931493 0.465746 0.884918i $$-0.345786\pi$$
0.465746 + 0.884918i $$0.345786\pi$$
$$462$$ 0 0
$$463$$ 4.00000 0.185896 0.0929479 0.995671i $$-0.470371\pi$$
0.0929479 + 0.995671i $$0.470371\pi$$
$$464$$ 2.00000 0.0928477
$$465$$ −4.00000 −0.185496
$$466$$ 18.0000 0.833834
$$467$$ 30.0000 1.38823 0.694117 0.719862i $$-0.255795\pi$$
0.694117 + 0.719862i $$0.255795\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 6.00000 0.276759
$$471$$ −12.0000 −0.552931
$$472$$ −10.0000 −0.460287
$$473$$ −12.0000 −0.551761
$$474$$ 32.0000 1.46981
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ 0 0
$$479$$ −20.0000 −0.913823 −0.456912 0.889512i $$-0.651044\pi$$
−0.456912 + 0.889512i $$0.651044\pi$$
$$480$$ 2.00000 0.0912871
$$481$$ 0 0
$$482$$ −16.0000 −0.728780
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 14.0000 0.635707
$$486$$ 10.0000 0.453609
$$487$$ 20.0000 0.906287 0.453143 0.891438i $$-0.350303\pi$$
0.453143 + 0.891438i $$0.350303\pi$$
$$488$$ −4.00000 −0.181071
$$489$$ −16.0000 −0.723545
$$490$$ 0 0
$$491$$ 36.0000 1.62466 0.812329 0.583200i $$-0.198200\pi$$
0.812329 + 0.583200i $$0.198200\pi$$
$$492$$ −16.0000 −0.721336
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −1.00000 −0.0449467
$$496$$ 2.00000 0.0898027
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −40.0000 −1.79065 −0.895323 0.445418i $$-0.853055\pi$$
−0.895323 + 0.445418i $$0.853055\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ −32.0000 −1.42965
$$502$$ 10.0000 0.446322
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 4.00000 0.177822
$$507$$ −26.0000 −1.15470
$$508$$ 8.00000 0.354943
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −14.0000 −0.617514
$$515$$ −14.0000 −0.616914
$$516$$ −24.0000 −1.05654
$$517$$ 6.00000 0.263880
$$518$$ 0 0
$$519$$ −48.0000 −2.10697
$$520$$ 0 0
$$521$$ 34.0000 1.48957 0.744784 0.667306i $$-0.232553\pi$$
0.744784 + 0.667306i $$0.232553\pi$$
$$522$$ −2.00000 −0.0875376
$$523$$ −28.0000 −1.22435 −0.612177 0.790721i $$-0.709706\pi$$
−0.612177 + 0.790721i $$0.709706\pi$$
$$524$$ −4.00000 −0.174741
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ 0 0
$$528$$ 2.00000 0.0870388
$$529$$ −7.00000 −0.304348
$$530$$ −6.00000 −0.260623
$$531$$ 10.0000 0.433963
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −12.0000 −0.519291
$$535$$ −12.0000 −0.518805
$$536$$ 8.00000 0.345547
$$537$$ 24.0000 1.03568
$$538$$ 10.0000 0.431131
$$539$$ 0 0
$$540$$ 4.00000 0.172133
$$541$$ −10.0000 −0.429934 −0.214967 0.976621i $$-0.568964\pi$$
−0.214967 + 0.976621i $$0.568964\pi$$
$$542$$ 20.0000 0.859074
$$543$$ 12.0000 0.514969
$$544$$ 0 0
$$545$$ 6.00000 0.257012
$$546$$ 0 0
$$547$$ −44.0000 −1.88130 −0.940652 0.339372i $$-0.889785\pi$$
−0.940652 + 0.339372i $$0.889785\pi$$
$$548$$ 6.00000 0.256307
$$549$$ 4.00000 0.170716
$$550$$ −1.00000 −0.0426401
$$551$$ 0 0
$$552$$ 8.00000 0.340503
$$553$$ 0 0
$$554$$ 2.00000 0.0849719
$$555$$ 12.0000 0.509372
$$556$$ −8.00000 −0.339276
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ −2.00000 −0.0846668
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 2.00000 0.0843649
$$563$$ −32.0000 −1.34864 −0.674320 0.738440i $$-0.735563\pi$$
−0.674320 + 0.738440i $$0.735563\pi$$
$$564$$ 12.0000 0.505291
$$565$$ −2.00000 −0.0841406
$$566$$ 28.0000 1.17693
$$567$$ 0 0
$$568$$ 4.00000 0.167836
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 0 0
$$573$$ −16.0000 −0.668410
$$574$$ 0 0
$$575$$ −4.00000 −0.166812
$$576$$ 1.00000 0.0416667
$$577$$ 26.0000 1.08239 0.541197 0.840896i $$-0.317971\pi$$
0.541197 + 0.840896i $$0.317971\pi$$
$$578$$ 17.0000 0.707107
$$579$$ −44.0000 −1.82858
$$580$$ −2.00000 −0.0830455
$$581$$ 0 0
$$582$$ 28.0000 1.16064
$$583$$ −6.00000 −0.248495
$$584$$ −4.00000 −0.165521
$$585$$ 0 0
$$586$$ −4.00000 −0.165238
$$587$$ −2.00000 −0.0825488 −0.0412744 0.999148i $$-0.513142\pi$$
−0.0412744 + 0.999148i $$0.513142\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 10.0000 0.411693
$$591$$ 28.0000 1.15177
$$592$$ −6.00000 −0.246598
$$593$$ 12.0000 0.492781 0.246390 0.969171i $$-0.420755\pi$$
0.246390 + 0.969171i $$0.420755\pi$$
$$594$$ 4.00000 0.164122
$$595$$ 0 0
$$596$$ 6.00000 0.245770
$$597$$ 12.0000 0.491127
$$598$$ 0 0
$$599$$ 20.0000 0.817178 0.408589 0.912719i $$-0.366021\pi$$
0.408589 + 0.912719i $$0.366021\pi$$
$$600$$ −2.00000 −0.0816497
$$601$$ 8.00000 0.326327 0.163163 0.986599i $$-0.447830\pi$$
0.163163 + 0.986599i $$0.447830\pi$$
$$602$$ 0 0
$$603$$ −8.00000 −0.325785
$$604$$ −8.00000 −0.325515
$$605$$ −1.00000 −0.0406558
$$606$$ 0 0
$$607$$ −24.0000 −0.974130 −0.487065 0.873366i $$-0.661933\pi$$
−0.487065 + 0.873366i $$0.661933\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 4.00000 0.161955
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 16.0000 0.645182
$$616$$ 0 0
$$617$$ −42.0000 −1.69086 −0.845428 0.534089i $$-0.820655\pi$$
−0.845428 + 0.534089i $$0.820655\pi$$
$$618$$ −28.0000 −1.12633
$$619$$ 22.0000 0.884255 0.442127 0.896952i $$-0.354224\pi$$
0.442127 + 0.896952i $$0.354224\pi$$
$$620$$ −2.00000 −0.0803219
$$621$$ 16.0000 0.642058
$$622$$ −6.00000 −0.240578
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 2.00000 0.0799361
$$627$$ 0 0
$$628$$ −6.00000 −0.239426
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 16.0000 0.636446
$$633$$ −24.0000 −0.953914
$$634$$ 2.00000 0.0794301
$$635$$ −8.00000 −0.317470
$$636$$ −12.0000 −0.475831
$$637$$ 0 0
$$638$$ −2.00000 −0.0791808
$$639$$ −4.00000 −0.158238
$$640$$ 1.00000 0.0395285
$$641$$ 46.0000 1.81689 0.908445 0.418004i $$-0.137270\pi$$
0.908445 + 0.418004i $$0.137270\pi$$
$$642$$ −24.0000 −0.947204
$$643$$ −34.0000 −1.34083 −0.670415 0.741987i $$-0.733884\pi$$
−0.670415 + 0.741987i $$0.733884\pi$$
$$644$$ 0 0
$$645$$ 24.0000 0.944999
$$646$$ 0 0
$$647$$ 42.0000 1.65119 0.825595 0.564263i $$-0.190840\pi$$
0.825595 + 0.564263i $$0.190840\pi$$
$$648$$ 11.0000 0.432121
$$649$$ 10.0000 0.392534
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −8.00000 −0.313304
$$653$$ 22.0000 0.860927 0.430463 0.902608i $$-0.358350\pi$$
0.430463 + 0.902608i $$0.358350\pi$$
$$654$$ 12.0000 0.469237
$$655$$ 4.00000 0.156293
$$656$$ −8.00000 −0.312348
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ −20.0000 −0.779089 −0.389545 0.921008i $$-0.627368\pi$$
−0.389545 + 0.921008i $$0.627368\pi$$
$$660$$ −2.00000 −0.0778499
$$661$$ −46.0000 −1.78919 −0.894596 0.446875i $$-0.852537\pi$$
−0.894596 + 0.446875i $$0.852537\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ −8.00000 −0.309761
$$668$$ −16.0000 −0.619059
$$669$$ 12.0000 0.463947
$$670$$ −8.00000 −0.309067
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ 14.0000 0.539660 0.269830 0.962908i $$-0.413032\pi$$
0.269830 + 0.962908i $$0.413032\pi$$
$$674$$ −14.0000 −0.539260
$$675$$ −4.00000 −0.153960
$$676$$ −13.0000 −0.500000
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ −4.00000 −0.153619
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −8.00000 −0.306561
$$682$$ −2.00000 −0.0765840
$$683$$ 20.0000 0.765279 0.382639 0.923898i $$-0.375015\pi$$
0.382639 + 0.923898i $$0.375015\pi$$
$$684$$ 0 0
$$685$$ −6.00000 −0.229248
$$686$$ 0 0
$$687$$ −4.00000 −0.152610
$$688$$ −12.0000 −0.457496
$$689$$ 0 0
$$690$$ −8.00000 −0.304555
$$691$$ −6.00000 −0.228251 −0.114125 0.993466i $$-0.536407\pi$$
−0.114125 + 0.993466i $$0.536407\pi$$
$$692$$ −24.0000 −0.912343
$$693$$ 0 0
$$694$$ −28.0000 −1.06287
$$695$$ 8.00000 0.303457
$$696$$ −4.00000 −0.151620
$$697$$ 0 0
$$698$$ −20.0000 −0.757011
$$699$$ −36.0000 −1.36165
$$700$$ 0 0
$$701$$ −14.0000 −0.528773 −0.264386 0.964417i $$-0.585169\pi$$
−0.264386 + 0.964417i $$0.585169\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 1.00000 0.0376889
$$705$$ −12.0000 −0.451946
$$706$$ 18.0000 0.677439
$$707$$ 0 0
$$708$$ 20.0000 0.751646
$$709$$ 30.0000 1.12667 0.563337 0.826227i $$-0.309517\pi$$
0.563337 + 0.826227i $$0.309517\pi$$
$$710$$ −4.00000 −0.150117
$$711$$ −16.0000 −0.600047
$$712$$ −6.00000 −0.224860
$$713$$ −8.00000 −0.299602
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 0 0
$$718$$ 8.00000 0.298557
$$719$$ 34.0000 1.26799 0.633993 0.773339i $$-0.281415\pi$$
0.633993 + 0.773339i $$0.281415\pi$$
$$720$$ −1.00000 −0.0372678
$$721$$ 0 0
$$722$$ 19.0000 0.707107
$$723$$ 32.0000 1.19009
$$724$$ 6.00000 0.222988
$$725$$ 2.00000 0.0742781
$$726$$ −2.00000 −0.0742270
$$727$$ −14.0000 −0.519231 −0.259616 0.965712i $$-0.583596\pi$$
−0.259616 + 0.965712i $$0.583596\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 4.00000 0.148047
$$731$$ 0 0
$$732$$ 8.00000 0.295689
$$733$$ −4.00000 −0.147743 −0.0738717 0.997268i $$-0.523536\pi$$
−0.0738717 + 0.997268i $$0.523536\pi$$
$$734$$ −22.0000 −0.812035
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ −8.00000 −0.294684
$$738$$ 8.00000 0.294484
$$739$$ 12.0000 0.441427 0.220714 0.975339i $$-0.429161\pi$$
0.220714 + 0.975339i $$0.429161\pi$$
$$740$$ 6.00000 0.220564
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −8.00000 −0.293492 −0.146746 0.989174i $$-0.546880\pi$$
−0.146746 + 0.989174i $$0.546880\pi$$
$$744$$ −4.00000 −0.146647
$$745$$ −6.00000 −0.219823
$$746$$ −14.0000 −0.512576
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 2.00000 0.0730297
$$751$$ 52.0000 1.89751 0.948753 0.316017i $$-0.102346\pi$$
0.948753 + 0.316017i $$0.102346\pi$$
$$752$$ 6.00000 0.218797
$$753$$ −20.0000 −0.728841
$$754$$ 0 0
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ −26.0000 −0.944986 −0.472493 0.881334i $$-0.656646\pi$$
−0.472493 + 0.881334i $$0.656646\pi$$
$$758$$ 16.0000 0.581146
$$759$$ −8.00000 −0.290382
$$760$$ 0 0
$$761$$ −12.0000 −0.435000 −0.217500 0.976060i $$-0.569790\pi$$
−0.217500 + 0.976060i $$0.569790\pi$$
$$762$$ −16.0000 −0.579619
$$763$$ 0 0
$$764$$ −8.00000 −0.289430
$$765$$ 0 0
$$766$$ −2.00000 −0.0722629
$$767$$ 0 0
$$768$$ 2.00000 0.0721688
$$769$$ −12.0000 −0.432731 −0.216366 0.976312i $$-0.569420\pi$$
−0.216366 + 0.976312i $$0.569420\pi$$
$$770$$ 0 0
$$771$$ 28.0000 1.00840
$$772$$ −22.0000 −0.791797
$$773$$ −18.0000 −0.647415 −0.323708 0.946157i $$-0.604929\pi$$
−0.323708 + 0.946157i $$0.604929\pi$$
$$774$$ 12.0000 0.431331
$$775$$ 2.00000 0.0718421
$$776$$ 14.0000 0.502571
$$777$$ 0 0
$$778$$ −22.0000 −0.788738
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −4.00000 −0.143131
$$782$$ 0 0
$$783$$ −8.00000 −0.285897
$$784$$ 0 0
$$785$$ 6.00000 0.214149
$$786$$ 8.00000 0.285351
$$787$$ −48.0000 −1.71102 −0.855508 0.517790i $$-0.826755\pi$$
−0.855508 + 0.517790i $$0.826755\pi$$
$$788$$ 14.0000 0.498729
$$789$$ −48.0000 −1.70885
$$790$$ −16.0000 −0.569254
$$791$$ 0 0
$$792$$ −1.00000 −0.0355335
$$793$$ 0 0
$$794$$ −34.0000 −1.20661
$$795$$ 12.0000 0.425596
$$796$$ 6.00000 0.212664
$$797$$ −6.00000 −0.212531 −0.106265 0.994338i $$-0.533889\pi$$
−0.106265 + 0.994338i $$0.533889\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −1.00000 −0.0353553
$$801$$ 6.00000 0.212000
$$802$$ 6.00000 0.211867
$$803$$ 4.00000 0.141157
$$804$$ −16.0000 −0.564276
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −20.0000 −0.704033
$$808$$ 0 0
$$809$$ 18.0000 0.632846 0.316423 0.948618i $$-0.397518\pi$$
0.316423 + 0.948618i $$0.397518\pi$$
$$810$$ −11.0000 −0.386501
$$811$$ 44.0000 1.54505 0.772524 0.634985i $$-0.218994\pi$$
0.772524 + 0.634985i $$0.218994\pi$$
$$812$$ 0 0
$$813$$ −40.0000 −1.40286
$$814$$ 6.00000 0.210300
$$815$$ 8.00000 0.280228
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 4.00000 0.139857
$$819$$ 0 0
$$820$$ 8.00000 0.279372
$$821$$ −34.0000 −1.18661 −0.593304 0.804978i $$-0.702177\pi$$
−0.593304 + 0.804978i $$0.702177\pi$$
$$822$$ −12.0000 −0.418548
$$823$$ 32.0000 1.11545 0.557725 0.830026i $$-0.311674\pi$$
0.557725 + 0.830026i $$0.311674\pi$$
$$824$$ −14.0000 −0.487713
$$825$$ 2.00000 0.0696311
$$826$$ 0 0
$$827$$ −36.0000 −1.25184 −0.625921 0.779886i $$-0.715277\pi$$
−0.625921 + 0.779886i $$0.715277\pi$$
$$828$$ −4.00000 −0.139010
$$829$$ 10.0000 0.347314 0.173657 0.984806i $$-0.444442\pi$$
0.173657 + 0.984806i $$0.444442\pi$$
$$830$$ 0 0
$$831$$ −4.00000 −0.138758
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 16.0000 0.554035
$$835$$ 16.0000 0.553703
$$836$$ 0 0
$$837$$ −8.00000 −0.276520
$$838$$ −26.0000 −0.898155
$$839$$ 10.0000 0.345238 0.172619 0.984989i $$-0.444777\pi$$
0.172619 + 0.984989i $$0.444777\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ −18.0000 −0.620321
$$843$$ −4.00000 −0.137767
$$844$$ −12.0000 −0.413057
$$845$$ 13.0000 0.447214
$$846$$ −6.00000 −0.206284
$$847$$ 0 0
$$848$$ −6.00000 −0.206041
$$849$$ −56.0000 −1.92192
$$850$$ 0 0
$$851$$ 24.0000 0.822709
$$852$$ −8.00000 −0.274075
$$853$$ 8.00000 0.273915 0.136957 0.990577i $$-0.456268\pi$$
0.136957 + 0.990577i $$0.456268\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ −12.0000 −0.409912 −0.204956 0.978771i $$-0.565705\pi$$
−0.204956 + 0.978771i $$0.565705\pi$$
$$858$$ 0 0
$$859$$ −2.00000 −0.0682391 −0.0341196 0.999418i $$-0.510863\pi$$
−0.0341196 + 0.999418i $$0.510863\pi$$
$$860$$ 12.0000 0.409197
$$861$$ 0 0
$$862$$ −8.00000 −0.272481
$$863$$ −32.0000 −1.08929 −0.544646 0.838666i $$-0.683336\pi$$
−0.544646 + 0.838666i $$0.683336\pi$$
$$864$$ 4.00000 0.136083
$$865$$ 24.0000 0.816024
$$866$$ 14.0000 0.475739
$$867$$ −34.0000 −1.15470
$$868$$ 0 0
$$869$$ −16.0000 −0.542763
$$870$$ 4.00000 0.135613
$$871$$ 0 0
$$872$$ 6.00000 0.203186
$$873$$ −14.0000 −0.473828
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 8.00000 0.270295
$$877$$ 10.0000 0.337676 0.168838 0.985644i $$-0.445999\pi$$
0.168838 + 0.985644i $$0.445999\pi$$
$$878$$ 4.00000 0.134993
$$879$$ 8.00000 0.269833
$$880$$ −1.00000 −0.0337100
$$881$$ 26.0000 0.875962 0.437981 0.898984i $$-0.355694\pi$$
0.437981 + 0.898984i $$0.355694\pi$$
$$882$$ 0 0
$$883$$ −44.0000 −1.48072 −0.740359 0.672212i $$-0.765344\pi$$
−0.740359 + 0.672212i $$0.765344\pi$$
$$884$$ 0 0
$$885$$ −20.0000 −0.672293
$$886$$ 20.0000 0.671913
$$887$$ 52.0000 1.74599 0.872995 0.487730i $$-0.162175\pi$$
0.872995 + 0.487730i $$0.162175\pi$$
$$888$$ 12.0000 0.402694
$$889$$ 0 0
$$890$$ 6.00000 0.201120
$$891$$ −11.0000 −0.368514
$$892$$ 6.00000 0.200895
$$893$$ 0 0
$$894$$ −12.0000 −0.401340
$$895$$ −12.0000 −0.401116
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 10.0000 0.333704
$$899$$ 4.00000 0.133407
$$900$$ 1.00000 0.0333333
$$901$$ 0 0
$$902$$ 8.00000 0.266371
$$903$$ 0 0
$$904$$ −2.00000 −0.0665190
$$905$$ −6.00000 −0.199447
$$906$$ 16.0000 0.531564
$$907$$ 48.0000 1.59381 0.796907 0.604102i $$-0.206468\pi$$
0.796907 + 0.604102i $$0.206468\pi$$
$$908$$ −4.00000 −0.132745
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 28.0000 0.927681 0.463841 0.885919i $$-0.346471\pi$$
0.463841 + 0.885919i $$0.346471\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ −26.0000 −0.860004
$$915$$ −8.00000 −0.264472
$$916$$ −2.00000 −0.0660819
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −8.00000 −0.263896 −0.131948 0.991257i $$-0.542123\pi$$
−0.131948 + 0.991257i $$0.542123\pi$$
$$920$$ −4.00000 −0.131876
$$921$$ −56.0000 −1.84526
$$922$$ −20.0000 −0.658665
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −6.00000 −0.197279
$$926$$ −4.00000 −0.131448
$$927$$ 14.0000 0.459820
$$928$$ −2.00000 −0.0656532
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 4.00000 0.131165
$$931$$ 0 0
$$932$$ −18.0000 −0.589610
$$933$$ 12.0000 0.392862
$$934$$ −30.0000 −0.981630
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −36.0000 −1.17607 −0.588034 0.808836i $$-0.700098\pi$$
−0.588034 + 0.808836i $$0.700098\pi$$
$$938$$ 0 0
$$939$$ −4.00000 −0.130535
$$940$$ −6.00000 −0.195698
$$941$$ 60.0000 1.95594 0.977972 0.208736i $$-0.0669349\pi$$
0.977972 + 0.208736i $$0.0669349\pi$$
$$942$$ 12.0000 0.390981
$$943$$ 32.0000 1.04206
$$944$$ 10.0000 0.325472
$$945$$ 0 0
$$946$$ 12.0000 0.390154
$$947$$ −12.0000 −0.389948 −0.194974 0.980808i $$-0.562462\pi$$
−0.194974 + 0.980808i $$0.562462\pi$$
$$948$$ −32.0000 −1.03931
$$949$$ 0 0
$$950$$ 0 0
$$951$$ −4.00000 −0.129709
$$952$$ 0 0
$$953$$ −6.00000 −0.194359 −0.0971795 0.995267i $$-0.530982\pi$$
−0.0971795 + 0.995267i $$0.530982\pi$$
$$954$$ 6.00000 0.194257
$$955$$ 8.00000 0.258874
$$956$$ 0 0
$$957$$ 4.00000 0.129302
$$958$$ 20.0000 0.646171
$$959$$ 0 0
$$960$$ −2.00000 −0.0645497
$$961$$ −27.0000 −0.870968
$$962$$ 0 0
$$963$$ 12.0000 0.386695
$$964$$ 16.0000 0.515325
$$965$$ 22.0000 0.708205
$$966$$ 0 0
$$967$$ −48.0000 −1.54358 −0.771788 0.635880i $$-0.780637\pi$$
−0.771788 + 0.635880i $$0.780637\pi$$
$$968$$ −1.00000 −0.0321412
$$969$$ 0 0
$$970$$ −14.0000 −0.449513
$$971$$ −26.0000 −0.834380 −0.417190 0.908819i $$-0.636985\pi$$
−0.417190 + 0.908819i $$0.636985\pi$$
$$972$$ −10.0000 −0.320750
$$973$$ 0 0
$$974$$ −20.0000 −0.640841
$$975$$ 0 0
$$976$$ 4.00000 0.128037
$$977$$ 42.0000 1.34370 0.671850 0.740688i $$-0.265500\pi$$
0.671850 + 0.740688i $$0.265500\pi$$
$$978$$ 16.0000 0.511624
$$979$$ 6.00000 0.191761
$$980$$ 0 0
$$981$$ −6.00000 −0.191565
$$982$$ −36.0000 −1.14881
$$983$$ 22.0000 0.701691 0.350846 0.936433i $$-0.385894\pi$$
0.350846 + 0.936433i $$0.385894\pi$$
$$984$$ 16.0000 0.510061
$$985$$ −14.0000 −0.446077
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 48.0000 1.52631
$$990$$ 1.00000 0.0317821
$$991$$ −4.00000 −0.127064 −0.0635321 0.997980i $$-0.520237\pi$$
−0.0635321 + 0.997980i $$0.520237\pi$$
$$992$$ −2.00000 −0.0635001
$$993$$ 56.0000 1.77711
$$994$$ 0 0
$$995$$ −6.00000 −0.190213
$$996$$ 0 0
$$997$$ 48.0000 1.52018 0.760088 0.649821i $$-0.225156\pi$$
0.760088 + 0.649821i $$0.225156\pi$$
$$998$$ 40.0000 1.26618
$$999$$ 24.0000 0.759326
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 5390.2.a.q.1.1 1
7.6 odd 2 770.2.a.b.1.1 1
21.20 even 2 6930.2.a.s.1.1 1
28.27 even 2 6160.2.a.p.1.1 1
35.13 even 4 3850.2.c.p.1849.2 2
35.27 even 4 3850.2.c.p.1849.1 2
35.34 odd 2 3850.2.a.bb.1.1 1
77.76 even 2 8470.2.a.v.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.a.b.1.1 1 7.6 odd 2
3850.2.a.bb.1.1 1 35.34 odd 2
3850.2.c.p.1849.1 2 35.27 even 4
3850.2.c.p.1849.2 2 35.13 even 4
5390.2.a.q.1.1 1 1.1 even 1 trivial
6160.2.a.p.1.1 1 28.27 even 2
6930.2.a.s.1.1 1 21.20 even 2
8470.2.a.v.1.1 1 77.76 even 2