# Properties

 Label 4018.2.a.s.1.1 Level $4018$ Weight $2$ Character 4018.1 Self dual yes Analytic conductor $32.084$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4018 = 2 \cdot 7^{2} \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4018.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$32.0838915322$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 574) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 4018.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{6} +1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{6} +1.00000 q^{8} +6.00000 q^{9} +1.00000 q^{10} -2.00000 q^{11} +3.00000 q^{12} +3.00000 q^{15} +1.00000 q^{16} +3.00000 q^{17} +6.00000 q^{18} +8.00000 q^{19} +1.00000 q^{20} -2.00000 q^{22} -4.00000 q^{23} +3.00000 q^{24} -4.00000 q^{25} +9.00000 q^{27} -5.00000 q^{29} +3.00000 q^{30} +3.00000 q^{31} +1.00000 q^{32} -6.00000 q^{33} +3.00000 q^{34} +6.00000 q^{36} +10.0000 q^{37} +8.00000 q^{38} +1.00000 q^{40} +1.00000 q^{41} -5.00000 q^{43} -2.00000 q^{44} +6.00000 q^{45} -4.00000 q^{46} -6.00000 q^{47} +3.00000 q^{48} -4.00000 q^{50} +9.00000 q^{51} -9.00000 q^{53} +9.00000 q^{54} -2.00000 q^{55} +24.0000 q^{57} -5.00000 q^{58} +10.0000 q^{59} +3.00000 q^{60} -13.0000 q^{61} +3.00000 q^{62} +1.00000 q^{64} -6.00000 q^{66} -2.00000 q^{67} +3.00000 q^{68} -12.0000 q^{69} +9.00000 q^{71} +6.00000 q^{72} -4.00000 q^{73} +10.0000 q^{74} -12.0000 q^{75} +8.00000 q^{76} -11.0000 q^{79} +1.00000 q^{80} +9.00000 q^{81} +1.00000 q^{82} +14.0000 q^{83} +3.00000 q^{85} -5.00000 q^{86} -15.0000 q^{87} -2.00000 q^{88} +1.00000 q^{89} +6.00000 q^{90} -4.00000 q^{92} +9.00000 q^{93} -6.00000 q^{94} +8.00000 q^{95} +3.00000 q^{96} -7.00000 q^{97} -12.0000 q^{99} +O(q^{100})$$

## 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
$$3$$ 3.00000 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 1.00000 0.447214 0.223607 0.974679i $$-0.428217\pi$$
0.223607 + 0.974679i $$0.428217\pi$$
$$6$$ 3.00000 1.22474
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ 6.00000 2.00000
$$10$$ 1.00000 0.316228
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 3.00000 0.866025
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 3.00000 0.774597
$$16$$ 1.00000 0.250000
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 6.00000 1.41421
$$19$$ 8.00000 1.83533 0.917663 0.397360i $$-0.130073\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ −4.00000 −0.834058 −0.417029 0.908893i $$-0.636929\pi$$
−0.417029 + 0.908893i $$0.636929\pi$$
$$24$$ 3.00000 0.612372
$$25$$ −4.00000 −0.800000
$$26$$ 0 0
$$27$$ 9.00000 1.73205
$$28$$ 0 0
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 3.00000 0.547723
$$31$$ 3.00000 0.538816 0.269408 0.963026i $$-0.413172\pi$$
0.269408 + 0.963026i $$0.413172\pi$$
$$32$$ 1.00000 0.176777
$$33$$ −6.00000 −1.04447
$$34$$ 3.00000 0.514496
$$35$$ 0 0
$$36$$ 6.00000 1.00000
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 8.00000 1.29777
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ 1.00000 0.156174
$$42$$ 0 0
$$43$$ −5.00000 −0.762493 −0.381246 0.924473i $$-0.624505\pi$$
−0.381246 + 0.924473i $$0.624505\pi$$
$$44$$ −2.00000 −0.301511
$$45$$ 6.00000 0.894427
$$46$$ −4.00000 −0.589768
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ 3.00000 0.433013
$$49$$ 0 0
$$50$$ −4.00000 −0.565685
$$51$$ 9.00000 1.26025
$$52$$ 0 0
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ 9.00000 1.22474
$$55$$ −2.00000 −0.269680
$$56$$ 0 0
$$57$$ 24.0000 3.17888
$$58$$ −5.00000 −0.656532
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 3.00000 0.387298
$$61$$ −13.0000 −1.66448 −0.832240 0.554416i $$-0.812942\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 3.00000 0.381000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −6.00000 −0.738549
$$67$$ −2.00000 −0.244339 −0.122169 0.992509i $$-0.538985\pi$$
−0.122169 + 0.992509i $$0.538985\pi$$
$$68$$ 3.00000 0.363803
$$69$$ −12.0000 −1.44463
$$70$$ 0 0
$$71$$ 9.00000 1.06810 0.534052 0.845452i $$-0.320669\pi$$
0.534052 + 0.845452i $$0.320669\pi$$
$$72$$ 6.00000 0.707107
$$73$$ −4.00000 −0.468165 −0.234082 0.972217i $$-0.575209\pi$$
−0.234082 + 0.972217i $$0.575209\pi$$
$$74$$ 10.0000 1.16248
$$75$$ −12.0000 −1.38564
$$76$$ 8.00000 0.917663
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −11.0000 −1.23760 −0.618798 0.785550i $$-0.712380\pi$$
−0.618798 + 0.785550i $$0.712380\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 9.00000 1.00000
$$82$$ 1.00000 0.110432
$$83$$ 14.0000 1.53670 0.768350 0.640030i $$-0.221078\pi$$
0.768350 + 0.640030i $$0.221078\pi$$
$$84$$ 0 0
$$85$$ 3.00000 0.325396
$$86$$ −5.00000 −0.539164
$$87$$ −15.0000 −1.60817
$$88$$ −2.00000 −0.213201
$$89$$ 1.00000 0.106000 0.0529999 0.998595i $$-0.483122\pi$$
0.0529999 + 0.998595i $$0.483122\pi$$
$$90$$ 6.00000 0.632456
$$91$$ 0 0
$$92$$ −4.00000 −0.417029
$$93$$ 9.00000 0.933257
$$94$$ −6.00000 −0.618853
$$95$$ 8.00000 0.820783
$$96$$ 3.00000 0.306186
$$97$$ −7.00000 −0.710742 −0.355371 0.934725i $$-0.615646\pi$$
−0.355371 + 0.934725i $$0.615646\pi$$
$$98$$ 0 0
$$99$$ −12.0000 −1.20605
$$100$$ −4.00000 −0.400000
$$101$$ 10.0000 0.995037 0.497519 0.867453i $$-0.334245\pi$$
0.497519 + 0.867453i $$0.334245\pi$$
$$102$$ 9.00000 0.891133
$$103$$ −13.0000 −1.28093 −0.640464 0.767988i $$-0.721258\pi$$
−0.640464 + 0.767988i $$0.721258\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −9.00000 −0.874157
$$107$$ 3.00000 0.290021 0.145010 0.989430i $$-0.453678\pi$$
0.145010 + 0.989430i $$0.453678\pi$$
$$108$$ 9.00000 0.866025
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ −2.00000 −0.190693
$$111$$ 30.0000 2.84747
$$112$$ 0 0
$$113$$ 9.00000 0.846649 0.423324 0.905978i $$-0.360863\pi$$
0.423324 + 0.905978i $$0.360863\pi$$
$$114$$ 24.0000 2.24781
$$115$$ −4.00000 −0.373002
$$116$$ −5.00000 −0.464238
$$117$$ 0 0
$$118$$ 10.0000 0.920575
$$119$$ 0 0
$$120$$ 3.00000 0.273861
$$121$$ −7.00000 −0.636364
$$122$$ −13.0000 −1.17696
$$123$$ 3.00000 0.270501
$$124$$ 3.00000 0.269408
$$125$$ −9.00000 −0.804984
$$126$$ 0 0
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −15.0000 −1.32068
$$130$$ 0 0
$$131$$ 8.00000 0.698963 0.349482 0.936943i $$-0.386358\pi$$
0.349482 + 0.936943i $$0.386358\pi$$
$$132$$ −6.00000 −0.522233
$$133$$ 0 0
$$134$$ −2.00000 −0.172774
$$135$$ 9.00000 0.774597
$$136$$ 3.00000 0.257248
$$137$$ 12.0000 1.02523 0.512615 0.858619i $$-0.328677\pi$$
0.512615 + 0.858619i $$0.328677\pi$$
$$138$$ −12.0000 −1.02151
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 0 0
$$141$$ −18.0000 −1.51587
$$142$$ 9.00000 0.755263
$$143$$ 0 0
$$144$$ 6.00000 0.500000
$$145$$ −5.00000 −0.415227
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ 10.0000 0.821995
$$149$$ 3.00000 0.245770 0.122885 0.992421i $$-0.460785\pi$$
0.122885 + 0.992421i $$0.460785\pi$$
$$150$$ −12.0000 −0.979796
$$151$$ 19.0000 1.54620 0.773099 0.634285i $$-0.218706\pi$$
0.773099 + 0.634285i $$0.218706\pi$$
$$152$$ 8.00000 0.648886
$$153$$ 18.0000 1.45521
$$154$$ 0 0
$$155$$ 3.00000 0.240966
$$156$$ 0 0
$$157$$ −4.00000 −0.319235 −0.159617 0.987179i $$-0.551026\pi$$
−0.159617 + 0.987179i $$0.551026\pi$$
$$158$$ −11.0000 −0.875113
$$159$$ −27.0000 −2.14124
$$160$$ 1.00000 0.0790569
$$161$$ 0 0
$$162$$ 9.00000 0.707107
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 1.00000 0.0780869
$$165$$ −6.00000 −0.467099
$$166$$ 14.0000 1.08661
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 3.00000 0.230089
$$171$$ 48.0000 3.67065
$$172$$ −5.00000 −0.381246
$$173$$ 1.00000 0.0760286 0.0380143 0.999277i $$-0.487897\pi$$
0.0380143 + 0.999277i $$0.487897\pi$$
$$174$$ −15.0000 −1.13715
$$175$$ 0 0
$$176$$ −2.00000 −0.150756
$$177$$ 30.0000 2.25494
$$178$$ 1.00000 0.0749532
$$179$$ −16.0000 −1.19590 −0.597948 0.801535i $$-0.704017\pi$$
−0.597948 + 0.801535i $$0.704017\pi$$
$$180$$ 6.00000 0.447214
$$181$$ 14.0000 1.04061 0.520306 0.853980i $$-0.325818\pi$$
0.520306 + 0.853980i $$0.325818\pi$$
$$182$$ 0 0
$$183$$ −39.0000 −2.88296
$$184$$ −4.00000 −0.294884
$$185$$ 10.0000 0.735215
$$186$$ 9.00000 0.659912
$$187$$ −6.00000 −0.438763
$$188$$ −6.00000 −0.437595
$$189$$ 0 0
$$190$$ 8.00000 0.580381
$$191$$ −11.0000 −0.795932 −0.397966 0.917400i $$-0.630284\pi$$
−0.397966 + 0.917400i $$0.630284\pi$$
$$192$$ 3.00000 0.216506
$$193$$ 12.0000 0.863779 0.431889 0.901927i $$-0.357847\pi$$
0.431889 + 0.901927i $$0.357847\pi$$
$$194$$ −7.00000 −0.502571
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ −12.0000 −0.852803
$$199$$ 24.0000 1.70131 0.850657 0.525720i $$-0.176204\pi$$
0.850657 + 0.525720i $$0.176204\pi$$
$$200$$ −4.00000 −0.282843
$$201$$ −6.00000 −0.423207
$$202$$ 10.0000 0.703598
$$203$$ 0 0
$$204$$ 9.00000 0.630126
$$205$$ 1.00000 0.0698430
$$206$$ −13.0000 −0.905753
$$207$$ −24.0000 −1.66812
$$208$$ 0 0
$$209$$ −16.0000 −1.10674
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ −9.00000 −0.618123
$$213$$ 27.0000 1.85001
$$214$$ 3.00000 0.205076
$$215$$ −5.00000 −0.340997
$$216$$ 9.00000 0.612372
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ −12.0000 −0.810885
$$220$$ −2.00000 −0.134840
$$221$$ 0 0
$$222$$ 30.0000 2.01347
$$223$$ −21.0000 −1.40626 −0.703132 0.711059i $$-0.748216\pi$$
−0.703132 + 0.711059i $$0.748216\pi$$
$$224$$ 0 0
$$225$$ −24.0000 −1.60000
$$226$$ 9.00000 0.598671
$$227$$ −25.0000 −1.65931 −0.829654 0.558278i $$-0.811462\pi$$
−0.829654 + 0.558278i $$0.811462\pi$$
$$228$$ 24.0000 1.58944
$$229$$ −20.0000 −1.32164 −0.660819 0.750546i $$-0.729791\pi$$
−0.660819 + 0.750546i $$0.729791\pi$$
$$230$$ −4.00000 −0.263752
$$231$$ 0 0
$$232$$ −5.00000 −0.328266
$$233$$ 10.0000 0.655122 0.327561 0.944830i $$-0.393773\pi$$
0.327561 + 0.944830i $$0.393773\pi$$
$$234$$ 0 0
$$235$$ −6.00000 −0.391397
$$236$$ 10.0000 0.650945
$$237$$ −33.0000 −2.14358
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 3.00000 0.193649
$$241$$ 10.0000 0.644157 0.322078 0.946713i $$-0.395619\pi$$
0.322078 + 0.946713i $$0.395619\pi$$
$$242$$ −7.00000 −0.449977
$$243$$ 0 0
$$244$$ −13.0000 −0.832240
$$245$$ 0 0
$$246$$ 3.00000 0.191273
$$247$$ 0 0
$$248$$ 3.00000 0.190500
$$249$$ 42.0000 2.66164
$$250$$ −9.00000 −0.569210
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ 2.00000 0.125491
$$255$$ 9.00000 0.563602
$$256$$ 1.00000 0.0625000
$$257$$ 15.0000 0.935674 0.467837 0.883815i $$-0.345033\pi$$
0.467837 + 0.883815i $$0.345033\pi$$
$$258$$ −15.0000 −0.933859
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −30.0000 −1.85695
$$262$$ 8.00000 0.494242
$$263$$ −16.0000 −0.986602 −0.493301 0.869859i $$-0.664210\pi$$
−0.493301 + 0.869859i $$0.664210\pi$$
$$264$$ −6.00000 −0.369274
$$265$$ −9.00000 −0.552866
$$266$$ 0 0
$$267$$ 3.00000 0.183597
$$268$$ −2.00000 −0.122169
$$269$$ 10.0000 0.609711 0.304855 0.952399i $$-0.401392\pi$$
0.304855 + 0.952399i $$0.401392\pi$$
$$270$$ 9.00000 0.547723
$$271$$ −20.0000 −1.21491 −0.607457 0.794353i $$-0.707810\pi$$
−0.607457 + 0.794353i $$0.707810\pi$$
$$272$$ 3.00000 0.181902
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ 8.00000 0.482418
$$276$$ −12.0000 −0.722315
$$277$$ 26.0000 1.56219 0.781094 0.624413i $$-0.214662\pi$$
0.781094 + 0.624413i $$0.214662\pi$$
$$278$$ −14.0000 −0.839664
$$279$$ 18.0000 1.07763
$$280$$ 0 0
$$281$$ 2.00000 0.119310 0.0596550 0.998219i $$-0.481000\pi$$
0.0596550 + 0.998219i $$0.481000\pi$$
$$282$$ −18.0000 −1.07188
$$283$$ −18.0000 −1.06999 −0.534994 0.844856i $$-0.679686\pi$$
−0.534994 + 0.844856i $$0.679686\pi$$
$$284$$ 9.00000 0.534052
$$285$$ 24.0000 1.42164
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 6.00000 0.353553
$$289$$ −8.00000 −0.470588
$$290$$ −5.00000 −0.293610
$$291$$ −21.0000 −1.23104
$$292$$ −4.00000 −0.234082
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ 0 0
$$295$$ 10.0000 0.582223
$$296$$ 10.0000 0.581238
$$297$$ −18.0000 −1.04447
$$298$$ 3.00000 0.173785
$$299$$ 0 0
$$300$$ −12.0000 −0.692820
$$301$$ 0 0
$$302$$ 19.0000 1.09333
$$303$$ 30.0000 1.72345
$$304$$ 8.00000 0.458831
$$305$$ −13.0000 −0.744378
$$306$$ 18.0000 1.02899
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ −39.0000 −2.21863
$$310$$ 3.00000 0.170389
$$311$$ −18.0000 −1.02069 −0.510343 0.859971i $$-0.670482\pi$$
−0.510343 + 0.859971i $$0.670482\pi$$
$$312$$ 0 0
$$313$$ 22.0000 1.24351 0.621757 0.783210i $$-0.286419\pi$$
0.621757 + 0.783210i $$0.286419\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ 0 0
$$316$$ −11.0000 −0.618798
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ −27.0000 −1.51408
$$319$$ 10.0000 0.559893
$$320$$ 1.00000 0.0559017
$$321$$ 9.00000 0.502331
$$322$$ 0 0
$$323$$ 24.0000 1.33540
$$324$$ 9.00000 0.500000
$$325$$ 0 0
$$326$$ −4.00000 −0.221540
$$327$$ −6.00000 −0.331801
$$328$$ 1.00000 0.0552158
$$329$$ 0 0
$$330$$ −6.00000 −0.330289
$$331$$ −32.0000 −1.75888 −0.879440 0.476011i $$-0.842082\pi$$
−0.879440 + 0.476011i $$0.842082\pi$$
$$332$$ 14.0000 0.768350
$$333$$ 60.0000 3.28798
$$334$$ 0 0
$$335$$ −2.00000 −0.109272
$$336$$ 0 0
$$337$$ −19.0000 −1.03500 −0.517498 0.855684i $$-0.673136\pi$$
−0.517498 + 0.855684i $$0.673136\pi$$
$$338$$ −13.0000 −0.707107
$$339$$ 27.0000 1.46644
$$340$$ 3.00000 0.162698
$$341$$ −6.00000 −0.324918
$$342$$ 48.0000 2.59554
$$343$$ 0 0
$$344$$ −5.00000 −0.269582
$$345$$ −12.0000 −0.646058
$$346$$ 1.00000 0.0537603
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ −15.0000 −0.804084
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −2.00000 −0.106600
$$353$$ 24.0000 1.27739 0.638696 0.769460i $$-0.279474\pi$$
0.638696 + 0.769460i $$0.279474\pi$$
$$354$$ 30.0000 1.59448
$$355$$ 9.00000 0.477670
$$356$$ 1.00000 0.0529999
$$357$$ 0 0
$$358$$ −16.0000 −0.845626
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 6.00000 0.316228
$$361$$ 45.0000 2.36842
$$362$$ 14.0000 0.735824
$$363$$ −21.0000 −1.10221
$$364$$ 0 0
$$365$$ −4.00000 −0.209370
$$366$$ −39.0000 −2.03856
$$367$$ 17.0000 0.887393 0.443696 0.896177i $$-0.353667\pi$$
0.443696 + 0.896177i $$0.353667\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 6.00000 0.312348
$$370$$ 10.0000 0.519875
$$371$$ 0 0
$$372$$ 9.00000 0.466628
$$373$$ −18.0000 −0.932005 −0.466002 0.884783i $$-0.654306\pi$$
−0.466002 + 0.884783i $$0.654306\pi$$
$$374$$ −6.00000 −0.310253
$$375$$ −27.0000 −1.39427
$$376$$ −6.00000 −0.309426
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 37.0000 1.90056 0.950281 0.311393i $$-0.100796\pi$$
0.950281 + 0.311393i $$0.100796\pi$$
$$380$$ 8.00000 0.410391
$$381$$ 6.00000 0.307389
$$382$$ −11.0000 −0.562809
$$383$$ 22.0000 1.12415 0.562074 0.827087i $$-0.310004\pi$$
0.562074 + 0.827087i $$0.310004\pi$$
$$384$$ 3.00000 0.153093
$$385$$ 0 0
$$386$$ 12.0000 0.610784
$$387$$ −30.0000 −1.52499
$$388$$ −7.00000 −0.355371
$$389$$ −2.00000 −0.101404 −0.0507020 0.998714i $$-0.516146\pi$$
−0.0507020 + 0.998714i $$0.516146\pi$$
$$390$$ 0 0
$$391$$ −12.0000 −0.606866
$$392$$ 0 0
$$393$$ 24.0000 1.21064
$$394$$ −12.0000 −0.604551
$$395$$ −11.0000 −0.553470
$$396$$ −12.0000 −0.603023
$$397$$ −20.0000 −1.00377 −0.501886 0.864934i $$-0.667360\pi$$
−0.501886 + 0.864934i $$0.667360\pi$$
$$398$$ 24.0000 1.20301
$$399$$ 0 0
$$400$$ −4.00000 −0.200000
$$401$$ −25.0000 −1.24844 −0.624220 0.781248i $$-0.714583\pi$$
−0.624220 + 0.781248i $$0.714583\pi$$
$$402$$ −6.00000 −0.299253
$$403$$ 0 0
$$404$$ 10.0000 0.497519
$$405$$ 9.00000 0.447214
$$406$$ 0 0
$$407$$ −20.0000 −0.991363
$$408$$ 9.00000 0.445566
$$409$$ 10.0000 0.494468 0.247234 0.968956i $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ 1.00000 0.0493865
$$411$$ 36.0000 1.77575
$$412$$ −13.0000 −0.640464
$$413$$ 0 0
$$414$$ −24.0000 −1.17954
$$415$$ 14.0000 0.687233
$$416$$ 0 0
$$417$$ −42.0000 −2.05675
$$418$$ −16.0000 −0.782586
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ 0 0
$$421$$ −19.0000 −0.926003 −0.463002 0.886357i $$-0.653228\pi$$
−0.463002 + 0.886357i $$0.653228\pi$$
$$422$$ −12.0000 −0.584151
$$423$$ −36.0000 −1.75038
$$424$$ −9.00000 −0.437079
$$425$$ −12.0000 −0.582086
$$426$$ 27.0000 1.30815
$$427$$ 0 0
$$428$$ 3.00000 0.145010
$$429$$ 0 0
$$430$$ −5.00000 −0.241121
$$431$$ −16.0000 −0.770693 −0.385346 0.922772i $$-0.625918\pi$$
−0.385346 + 0.922772i $$0.625918\pi$$
$$432$$ 9.00000 0.433013
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ −15.0000 −0.719195
$$436$$ −2.00000 −0.0957826
$$437$$ −32.0000 −1.53077
$$438$$ −12.0000 −0.573382
$$439$$ −34.0000 −1.62273 −0.811366 0.584539i $$-0.801275\pi$$
−0.811366 + 0.584539i $$0.801275\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −25.0000 −1.18779 −0.593893 0.804544i $$-0.702410\pi$$
−0.593893 + 0.804544i $$0.702410\pi$$
$$444$$ 30.0000 1.42374
$$445$$ 1.00000 0.0474045
$$446$$ −21.0000 −0.994379
$$447$$ 9.00000 0.425685
$$448$$ 0 0
$$449$$ −33.0000 −1.55737 −0.778683 0.627417i $$-0.784112\pi$$
−0.778683 + 0.627417i $$0.784112\pi$$
$$450$$ −24.0000 −1.13137
$$451$$ −2.00000 −0.0941763
$$452$$ 9.00000 0.423324
$$453$$ 57.0000 2.67809
$$454$$ −25.0000 −1.17331
$$455$$ 0 0
$$456$$ 24.0000 1.12390
$$457$$ −18.0000 −0.842004 −0.421002 0.907060i $$-0.638322\pi$$
−0.421002 + 0.907060i $$0.638322\pi$$
$$458$$ −20.0000 −0.934539
$$459$$ 27.0000 1.26025
$$460$$ −4.00000 −0.186501
$$461$$ 21.0000 0.978068 0.489034 0.872265i $$-0.337349\pi$$
0.489034 + 0.872265i $$0.337349\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −5.00000 −0.232119
$$465$$ 9.00000 0.417365
$$466$$ 10.0000 0.463241
$$467$$ −6.00000 −0.277647 −0.138823 0.990317i $$-0.544332\pi$$
−0.138823 + 0.990317i $$0.544332\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −6.00000 −0.276759
$$471$$ −12.0000 −0.552931
$$472$$ 10.0000 0.460287
$$473$$ 10.0000 0.459800
$$474$$ −33.0000 −1.51574
$$475$$ −32.0000 −1.46826
$$476$$ 0 0
$$477$$ −54.0000 −2.47249
$$478$$ −12.0000 −0.548867
$$479$$ 10.0000 0.456912 0.228456 0.973554i $$-0.426632\pi$$
0.228456 + 0.973554i $$0.426632\pi$$
$$480$$ 3.00000 0.136931
$$481$$ 0 0
$$482$$ 10.0000 0.455488
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ −7.00000 −0.317854
$$486$$ 0 0
$$487$$ 12.0000 0.543772 0.271886 0.962329i $$-0.412353\pi$$
0.271886 + 0.962329i $$0.412353\pi$$
$$488$$ −13.0000 −0.588482
$$489$$ −12.0000 −0.542659
$$490$$ 0 0
$$491$$ 37.0000 1.66979 0.834893 0.550412i $$-0.185529\pi$$
0.834893 + 0.550412i $$0.185529\pi$$
$$492$$ 3.00000 0.135250
$$493$$ −15.0000 −0.675566
$$494$$ 0 0
$$495$$ −12.0000 −0.539360
$$496$$ 3.00000 0.134704
$$497$$ 0 0
$$498$$ 42.0000 1.88207
$$499$$ 10.0000 0.447661 0.223831 0.974628i $$-0.428144\pi$$
0.223831 + 0.974628i $$0.428144\pi$$
$$500$$ −9.00000 −0.402492
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 10.0000 0.444994
$$506$$ 8.00000 0.355643
$$507$$ −39.0000 −1.73205
$$508$$ 2.00000 0.0887357
$$509$$ 36.0000 1.59567 0.797836 0.602875i $$-0.205978\pi$$
0.797836 + 0.602875i $$0.205978\pi$$
$$510$$ 9.00000 0.398527
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 72.0000 3.17888
$$514$$ 15.0000 0.661622
$$515$$ −13.0000 −0.572848
$$516$$ −15.0000 −0.660338
$$517$$ 12.0000 0.527759
$$518$$ 0 0
$$519$$ 3.00000 0.131685
$$520$$ 0 0
$$521$$ 38.0000 1.66481 0.832405 0.554168i $$-0.186963\pi$$
0.832405 + 0.554168i $$0.186963\pi$$
$$522$$ −30.0000 −1.31306
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ 8.00000 0.349482
$$525$$ 0 0
$$526$$ −16.0000 −0.697633
$$527$$ 9.00000 0.392046
$$528$$ −6.00000 −0.261116
$$529$$ −7.00000 −0.304348
$$530$$ −9.00000 −0.390935
$$531$$ 60.0000 2.60378
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 3.00000 0.129823
$$535$$ 3.00000 0.129701
$$536$$ −2.00000 −0.0863868
$$537$$ −48.0000 −2.07135
$$538$$ 10.0000 0.431131
$$539$$ 0 0
$$540$$ 9.00000 0.387298
$$541$$ 10.0000 0.429934 0.214967 0.976621i $$-0.431036\pi$$
0.214967 + 0.976621i $$0.431036\pi$$
$$542$$ −20.0000 −0.859074
$$543$$ 42.0000 1.80239
$$544$$ 3.00000 0.128624
$$545$$ −2.00000 −0.0856706
$$546$$ 0 0
$$547$$ 2.00000 0.0855138 0.0427569 0.999086i $$-0.486386\pi$$
0.0427569 + 0.999086i $$0.486386\pi$$
$$548$$ 12.0000 0.512615
$$549$$ −78.0000 −3.32896
$$550$$ 8.00000 0.341121
$$551$$ −40.0000 −1.70406
$$552$$ −12.0000 −0.510754
$$553$$ 0 0
$$554$$ 26.0000 1.10463
$$555$$ 30.0000 1.27343
$$556$$ −14.0000 −0.593732
$$557$$ 33.0000 1.39825 0.699127 0.714997i $$-0.253572\pi$$
0.699127 + 0.714997i $$0.253572\pi$$
$$558$$ 18.0000 0.762001
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −18.0000 −0.759961
$$562$$ 2.00000 0.0843649
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ −18.0000 −0.757937
$$565$$ 9.00000 0.378633
$$566$$ −18.0000 −0.756596
$$567$$ 0 0
$$568$$ 9.00000 0.377632
$$569$$ −25.0000 −1.04805 −0.524027 0.851701i $$-0.675571\pi$$
−0.524027 + 0.851701i $$0.675571\pi$$
$$570$$ 24.0000 1.00525
$$571$$ −44.0000 −1.84134 −0.920671 0.390339i $$-0.872358\pi$$
−0.920671 + 0.390339i $$0.872358\pi$$
$$572$$ 0 0
$$573$$ −33.0000 −1.37859
$$574$$ 0 0
$$575$$ 16.0000 0.667246
$$576$$ 6.00000 0.250000
$$577$$ −46.0000 −1.91501 −0.957503 0.288425i $$-0.906868\pi$$
−0.957503 + 0.288425i $$0.906868\pi$$
$$578$$ −8.00000 −0.332756
$$579$$ 36.0000 1.49611
$$580$$ −5.00000 −0.207614
$$581$$ 0 0
$$582$$ −21.0000 −0.870478
$$583$$ 18.0000 0.745484
$$584$$ −4.00000 −0.165521
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ 21.0000 0.866763 0.433381 0.901211i $$-0.357320\pi$$
0.433381 + 0.901211i $$0.357320\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ 10.0000 0.411693
$$591$$ −36.0000 −1.48084
$$592$$ 10.0000 0.410997
$$593$$ 43.0000 1.76580 0.882899 0.469563i $$-0.155588\pi$$
0.882899 + 0.469563i $$0.155588\pi$$
$$594$$ −18.0000 −0.738549
$$595$$ 0 0
$$596$$ 3.00000 0.122885
$$597$$ 72.0000 2.94676
$$598$$ 0 0
$$599$$ −44.0000 −1.79779 −0.898896 0.438163i $$-0.855629\pi$$
−0.898896 + 0.438163i $$0.855629\pi$$
$$600$$ −12.0000 −0.489898
$$601$$ −21.0000 −0.856608 −0.428304 0.903635i $$-0.640889\pi$$
−0.428304 + 0.903635i $$0.640889\pi$$
$$602$$ 0 0
$$603$$ −12.0000 −0.488678
$$604$$ 19.0000 0.773099
$$605$$ −7.00000 −0.284590
$$606$$ 30.0000 1.21867
$$607$$ 43.0000 1.74532 0.872658 0.488332i $$-0.162394\pi$$
0.872658 + 0.488332i $$0.162394\pi$$
$$608$$ 8.00000 0.324443
$$609$$ 0 0
$$610$$ −13.0000 −0.526355
$$611$$ 0 0
$$612$$ 18.0000 0.727607
$$613$$ −16.0000 −0.646234 −0.323117 0.946359i $$-0.604731\pi$$
−0.323117 + 0.946359i $$0.604731\pi$$
$$614$$ 28.0000 1.12999
$$615$$ 3.00000 0.120972
$$616$$ 0 0
$$617$$ 30.0000 1.20775 0.603877 0.797077i $$-0.293622\pi$$
0.603877 + 0.797077i $$0.293622\pi$$
$$618$$ −39.0000 −1.56881
$$619$$ 24.0000 0.964641 0.482321 0.875995i $$-0.339794\pi$$
0.482321 + 0.875995i $$0.339794\pi$$
$$620$$ 3.00000 0.120483
$$621$$ −36.0000 −1.44463
$$622$$ −18.0000 −0.721734
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ 22.0000 0.879297
$$627$$ −48.0000 −1.91694
$$628$$ −4.00000 −0.159617
$$629$$ 30.0000 1.19618
$$630$$ 0 0
$$631$$ 30.0000 1.19428 0.597141 0.802137i $$-0.296303\pi$$
0.597141 + 0.802137i $$0.296303\pi$$
$$632$$ −11.0000 −0.437557
$$633$$ −36.0000 −1.43087
$$634$$ −18.0000 −0.714871
$$635$$ 2.00000 0.0793676
$$636$$ −27.0000 −1.07062
$$637$$ 0 0
$$638$$ 10.0000 0.395904
$$639$$ 54.0000 2.13621
$$640$$ 1.00000 0.0395285
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ 9.00000 0.355202
$$643$$ 7.00000 0.276053 0.138027 0.990429i $$-0.455924\pi$$
0.138027 + 0.990429i $$0.455924\pi$$
$$644$$ 0 0
$$645$$ −15.0000 −0.590624
$$646$$ 24.0000 0.944267
$$647$$ 3.00000 0.117942 0.0589711 0.998260i $$-0.481218\pi$$
0.0589711 + 0.998260i $$0.481218\pi$$
$$648$$ 9.00000 0.353553
$$649$$ −20.0000 −0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ 3.00000 0.117399 0.0586995 0.998276i $$-0.481305\pi$$
0.0586995 + 0.998276i $$0.481305\pi$$
$$654$$ −6.00000 −0.234619
$$655$$ 8.00000 0.312586
$$656$$ 1.00000 0.0390434
$$657$$ −24.0000 −0.936329
$$658$$ 0 0
$$659$$ 44.0000 1.71400 0.856998 0.515319i $$-0.172327\pi$$
0.856998 + 0.515319i $$0.172327\pi$$
$$660$$ −6.00000 −0.233550
$$661$$ 38.0000 1.47803 0.739014 0.673690i $$-0.235292\pi$$
0.739014 + 0.673690i $$0.235292\pi$$
$$662$$ −32.0000 −1.24372
$$663$$ 0 0
$$664$$ 14.0000 0.543305
$$665$$ 0 0
$$666$$ 60.0000 2.32495
$$667$$ 20.0000 0.774403
$$668$$ 0 0
$$669$$ −63.0000 −2.43572
$$670$$ −2.00000 −0.0772667
$$671$$ 26.0000 1.00372
$$672$$ 0 0
$$673$$ 30.0000 1.15642 0.578208 0.815890i $$-0.303752\pi$$
0.578208 + 0.815890i $$0.303752\pi$$
$$674$$ −19.0000 −0.731853
$$675$$ −36.0000 −1.38564
$$676$$ −13.0000 −0.500000
$$677$$ −6.00000 −0.230599 −0.115299 0.993331i $$-0.536783\pi$$
−0.115299 + 0.993331i $$0.536783\pi$$
$$678$$ 27.0000 1.03693
$$679$$ 0 0
$$680$$ 3.00000 0.115045
$$681$$ −75.0000 −2.87401
$$682$$ −6.00000 −0.229752
$$683$$ 40.0000 1.53056 0.765279 0.643699i $$-0.222601\pi$$
0.765279 + 0.643699i $$0.222601\pi$$
$$684$$ 48.0000 1.83533
$$685$$ 12.0000 0.458496
$$686$$ 0 0
$$687$$ −60.0000 −2.28914
$$688$$ −5.00000 −0.190623
$$689$$ 0 0
$$690$$ −12.0000 −0.456832
$$691$$ −13.0000 −0.494543 −0.247272 0.968946i $$-0.579534\pi$$
−0.247272 + 0.968946i $$0.579534\pi$$
$$692$$ 1.00000 0.0380143
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ −14.0000 −0.531050
$$696$$ −15.0000 −0.568574
$$697$$ 3.00000 0.113633
$$698$$ −14.0000 −0.529908
$$699$$ 30.0000 1.13470
$$700$$ 0 0
$$701$$ 16.0000 0.604312 0.302156 0.953259i $$-0.402294\pi$$
0.302156 + 0.953259i $$0.402294\pi$$
$$702$$ 0 0
$$703$$ 80.0000 3.01726
$$704$$ −2.00000 −0.0753778
$$705$$ −18.0000 −0.677919
$$706$$ 24.0000 0.903252
$$707$$ 0 0
$$708$$ 30.0000 1.12747
$$709$$ 3.00000 0.112667 0.0563337 0.998412i $$-0.482059\pi$$
0.0563337 + 0.998412i $$0.482059\pi$$
$$710$$ 9.00000 0.337764
$$711$$ −66.0000 −2.47519
$$712$$ 1.00000 0.0374766
$$713$$ −12.0000 −0.449404
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −16.0000 −0.597948
$$717$$ −36.0000 −1.34444
$$718$$ 24.0000 0.895672
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 6.00000 0.223607
$$721$$ 0 0
$$722$$ 45.0000 1.67473
$$723$$ 30.0000 1.11571
$$724$$ 14.0000 0.520306
$$725$$ 20.0000 0.742781
$$726$$ −21.0000 −0.779383
$$727$$ 28.0000 1.03846 0.519231 0.854634i $$-0.326218\pi$$
0.519231 + 0.854634i $$0.326218\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ −4.00000 −0.148047
$$731$$ −15.0000 −0.554795
$$732$$ −39.0000 −1.44148
$$733$$ −13.0000 −0.480166 −0.240083 0.970752i $$-0.577175\pi$$
−0.240083 + 0.970752i $$0.577175\pi$$
$$734$$ 17.0000 0.627481
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ 4.00000 0.147342
$$738$$ 6.00000 0.220863
$$739$$ 19.0000 0.698926 0.349463 0.936950i $$-0.386364\pi$$
0.349463 + 0.936950i $$0.386364\pi$$
$$740$$ 10.0000 0.367607
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −12.0000 −0.440237 −0.220119 0.975473i $$-0.570644\pi$$
−0.220119 + 0.975473i $$0.570644\pi$$
$$744$$ 9.00000 0.329956
$$745$$ 3.00000 0.109911
$$746$$ −18.0000 −0.659027
$$747$$ 84.0000 3.07340
$$748$$ −6.00000 −0.219382
$$749$$ 0 0
$$750$$ −27.0000 −0.985901
$$751$$ 24.0000 0.875772 0.437886 0.899030i $$-0.355727\pi$$
0.437886 + 0.899030i $$0.355727\pi$$
$$752$$ −6.00000 −0.218797
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 19.0000 0.691481
$$756$$ 0 0
$$757$$ −5.00000 −0.181728 −0.0908640 0.995863i $$-0.528963\pi$$
−0.0908640 + 0.995863i $$0.528963\pi$$
$$758$$ 37.0000 1.34390
$$759$$ 24.0000 0.871145
$$760$$ 8.00000 0.290191
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ 6.00000 0.217357
$$763$$ 0 0
$$764$$ −11.0000 −0.397966
$$765$$ 18.0000 0.650791
$$766$$ 22.0000 0.794892
$$767$$ 0 0
$$768$$ 3.00000 0.108253
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 45.0000 1.62064
$$772$$ 12.0000 0.431889
$$773$$ 38.0000 1.36677 0.683383 0.730061i $$-0.260508\pi$$
0.683383 + 0.730061i $$0.260508\pi$$
$$774$$ −30.0000 −1.07833
$$775$$ −12.0000 −0.431053
$$776$$ −7.00000 −0.251285
$$777$$ 0 0
$$778$$ −2.00000 −0.0717035
$$779$$ 8.00000 0.286630
$$780$$ 0 0
$$781$$ −18.0000 −0.644091
$$782$$ −12.0000 −0.429119
$$783$$ −45.0000 −1.60817
$$784$$ 0 0
$$785$$ −4.00000 −0.142766
$$786$$ 24.0000 0.856052
$$787$$ 52.0000 1.85360 0.926800 0.375555i $$-0.122548\pi$$
0.926800 + 0.375555i $$0.122548\pi$$
$$788$$ −12.0000 −0.427482
$$789$$ −48.0000 −1.70885
$$790$$ −11.0000 −0.391362
$$791$$ 0 0
$$792$$ −12.0000 −0.426401
$$793$$ 0 0
$$794$$ −20.0000 −0.709773
$$795$$ −27.0000 −0.957591
$$796$$ 24.0000 0.850657
$$797$$ −21.0000 −0.743858 −0.371929 0.928261i $$-0.621304\pi$$
−0.371929 + 0.928261i $$0.621304\pi$$
$$798$$ 0 0
$$799$$ −18.0000 −0.636794
$$800$$ −4.00000 −0.141421
$$801$$ 6.00000 0.212000
$$802$$ −25.0000 −0.882781
$$803$$ 8.00000 0.282314
$$804$$ −6.00000 −0.211604
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 30.0000 1.05605
$$808$$ 10.0000 0.351799
$$809$$ 54.0000 1.89854 0.949269 0.314464i $$-0.101825\pi$$
0.949269 + 0.314464i $$0.101825\pi$$
$$810$$ 9.00000 0.316228
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ −60.0000 −2.10429
$$814$$ −20.0000 −0.701000
$$815$$ −4.00000 −0.140114
$$816$$ 9.00000 0.315063
$$817$$ −40.0000 −1.39942
$$818$$ 10.0000 0.349642
$$819$$ 0 0
$$820$$ 1.00000 0.0349215
$$821$$ −4.00000 −0.139601 −0.0698005 0.997561i $$-0.522236\pi$$
−0.0698005 + 0.997561i $$0.522236\pi$$
$$822$$ 36.0000 1.25564
$$823$$ −51.0000 −1.77775 −0.888874 0.458151i $$-0.848512\pi$$
−0.888874 + 0.458151i $$0.848512\pi$$
$$824$$ −13.0000 −0.452876
$$825$$ 24.0000 0.835573
$$826$$ 0 0
$$827$$ 30.0000 1.04320 0.521601 0.853189i $$-0.325335\pi$$
0.521601 + 0.853189i $$0.325335\pi$$
$$828$$ −24.0000 −0.834058
$$829$$ −11.0000 −0.382046 −0.191023 0.981586i $$-0.561180\pi$$
−0.191023 + 0.981586i $$0.561180\pi$$
$$830$$ 14.0000 0.485947
$$831$$ 78.0000 2.70579
$$832$$ 0 0
$$833$$ 0 0
$$834$$ −42.0000 −1.45434
$$835$$ 0 0
$$836$$ −16.0000 −0.553372
$$837$$ 27.0000 0.933257
$$838$$ −28.0000 −0.967244
$$839$$ −14.0000 −0.483334 −0.241667 0.970359i $$-0.577694\pi$$
−0.241667 + 0.970359i $$0.577694\pi$$
$$840$$ 0 0
$$841$$ −4.00000 −0.137931
$$842$$ −19.0000 −0.654783
$$843$$ 6.00000 0.206651
$$844$$ −12.0000 −0.413057
$$845$$ −13.0000 −0.447214
$$846$$ −36.0000 −1.23771
$$847$$ 0 0
$$848$$ −9.00000 −0.309061
$$849$$ −54.0000 −1.85328
$$850$$ −12.0000 −0.411597
$$851$$ −40.0000 −1.37118
$$852$$ 27.0000 0.925005
$$853$$ 21.0000 0.719026 0.359513 0.933140i $$-0.382943\pi$$
0.359513 + 0.933140i $$0.382943\pi$$
$$854$$ 0 0
$$855$$ 48.0000 1.64157
$$856$$ 3.00000 0.102538
$$857$$ 38.0000 1.29806 0.649028 0.760765i $$-0.275176\pi$$
0.649028 + 0.760765i $$0.275176\pi$$
$$858$$ 0 0
$$859$$ 8.00000 0.272956 0.136478 0.990643i $$-0.456422\pi$$
0.136478 + 0.990643i $$0.456422\pi$$
$$860$$ −5.00000 −0.170499
$$861$$ 0 0
$$862$$ −16.0000 −0.544962
$$863$$ −32.0000 −1.08929 −0.544646 0.838666i $$-0.683336\pi$$
−0.544646 + 0.838666i $$0.683336\pi$$
$$864$$ 9.00000 0.306186
$$865$$ 1.00000 0.0340010
$$866$$ 0 0
$$867$$ −24.0000 −0.815083
$$868$$ 0 0
$$869$$ 22.0000 0.746299
$$870$$ −15.0000 −0.508548
$$871$$ 0 0
$$872$$ −2.00000 −0.0677285
$$873$$ −42.0000 −1.42148
$$874$$ −32.0000 −1.08242
$$875$$ 0 0
$$876$$ −12.0000 −0.405442
$$877$$ −32.0000 −1.08056 −0.540282 0.841484i $$-0.681682\pi$$
−0.540282 + 0.841484i $$0.681682\pi$$
$$878$$ −34.0000 −1.14744
$$879$$ −42.0000 −1.41662
$$880$$ −2.00000 −0.0674200
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ −26.0000 −0.874970 −0.437485 0.899226i $$-0.644131\pi$$
−0.437485 + 0.899226i $$0.644131\pi$$
$$884$$ 0 0
$$885$$ 30.0000 1.00844
$$886$$ −25.0000 −0.839891
$$887$$ −20.0000 −0.671534 −0.335767 0.941945i $$-0.608996\pi$$
−0.335767 + 0.941945i $$0.608996\pi$$
$$888$$ 30.0000 1.00673
$$889$$ 0 0
$$890$$ 1.00000 0.0335201
$$891$$ −18.0000 −0.603023
$$892$$ −21.0000 −0.703132
$$893$$ −48.0000 −1.60626
$$894$$ 9.00000 0.301005
$$895$$ −16.0000 −0.534821
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −33.0000 −1.10122
$$899$$ −15.0000 −0.500278
$$900$$ −24.0000 −0.800000
$$901$$ −27.0000 −0.899500
$$902$$ −2.00000 −0.0665927
$$903$$ 0 0
$$904$$ 9.00000 0.299336
$$905$$ 14.0000 0.465376
$$906$$ 57.0000 1.89370
$$907$$ 19.0000 0.630885 0.315442 0.948945i $$-0.397847\pi$$
0.315442 + 0.948945i $$0.397847\pi$$
$$908$$ −25.0000 −0.829654
$$909$$ 60.0000 1.99007
$$910$$ 0 0
$$911$$ 2.00000 0.0662630 0.0331315 0.999451i $$-0.489452\pi$$
0.0331315 + 0.999451i $$0.489452\pi$$
$$912$$ 24.0000 0.794719
$$913$$ −28.0000 −0.926665
$$914$$ −18.0000 −0.595387
$$915$$ −39.0000 −1.28930
$$916$$ −20.0000 −0.660819
$$917$$ 0 0
$$918$$ 27.0000 0.891133
$$919$$ 3.00000 0.0989609 0.0494804 0.998775i $$-0.484243\pi$$
0.0494804 + 0.998775i $$0.484243\pi$$
$$920$$ −4.00000 −0.131876
$$921$$ 84.0000 2.76789
$$922$$ 21.0000 0.691598
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −40.0000 −1.31519
$$926$$ 16.0000 0.525793
$$927$$ −78.0000 −2.56186
$$928$$ −5.00000 −0.164133
$$929$$ 50.0000 1.64045 0.820223 0.572043i $$-0.193849\pi$$
0.820223 + 0.572043i $$0.193849\pi$$
$$930$$ 9.00000 0.295122
$$931$$ 0 0
$$932$$ 10.0000 0.327561
$$933$$ −54.0000 −1.76788
$$934$$ −6.00000 −0.196326
$$935$$ −6.00000 −0.196221
$$936$$ 0 0
$$937$$ −7.00000 −0.228680 −0.114340 0.993442i $$-0.536475\pi$$
−0.114340 + 0.993442i $$0.536475\pi$$
$$938$$ 0 0
$$939$$ 66.0000 2.15383
$$940$$ −6.00000 −0.195698
$$941$$ −18.0000 −0.586783 −0.293392 0.955992i $$-0.594784\pi$$
−0.293392 + 0.955992i $$0.594784\pi$$
$$942$$ −12.0000 −0.390981
$$943$$ −4.00000 −0.130258
$$944$$ 10.0000 0.325472
$$945$$ 0 0
$$946$$ 10.0000 0.325128
$$947$$ −4.00000 −0.129983 −0.0649913 0.997886i $$-0.520702\pi$$
−0.0649913 + 0.997886i $$0.520702\pi$$
$$948$$ −33.0000 −1.07179
$$949$$ 0 0
$$950$$ −32.0000 −1.03822
$$951$$ −54.0000 −1.75107
$$952$$ 0 0
$$953$$ 30.0000 0.971795 0.485898 0.874016i $$-0.338493\pi$$
0.485898 + 0.874016i $$0.338493\pi$$
$$954$$ −54.0000 −1.74831
$$955$$ −11.0000 −0.355952
$$956$$ −12.0000 −0.388108
$$957$$ 30.0000 0.969762
$$958$$ 10.0000 0.323085
$$959$$ 0 0
$$960$$ 3.00000 0.0968246
$$961$$ −22.0000 −0.709677
$$962$$ 0 0
$$963$$ 18.0000 0.580042
$$964$$ 10.0000 0.322078
$$965$$ 12.0000 0.386294
$$966$$ 0 0
$$967$$ −47.0000 −1.51142 −0.755709 0.654907i $$-0.772708\pi$$
−0.755709 + 0.654907i $$0.772708\pi$$
$$968$$ −7.00000 −0.224989
$$969$$ 72.0000 2.31297
$$970$$ −7.00000 −0.224756
$$971$$ −13.0000 −0.417190 −0.208595 0.978002i $$-0.566889\pi$$
−0.208595 + 0.978002i $$0.566889\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 12.0000 0.384505
$$975$$ 0 0
$$976$$ −13.0000 −0.416120
$$977$$ 54.0000 1.72761 0.863807 0.503824i $$-0.168074\pi$$
0.863807 + 0.503824i $$0.168074\pi$$
$$978$$ −12.0000 −0.383718
$$979$$ −2.00000 −0.0639203
$$980$$ 0 0
$$981$$ −12.0000 −0.383131
$$982$$ 37.0000 1.18072
$$983$$ 3.00000 0.0956851 0.0478426 0.998855i $$-0.484765\pi$$
0.0478426 + 0.998855i $$0.484765\pi$$
$$984$$ 3.00000 0.0956365
$$985$$ −12.0000 −0.382352
$$986$$ −15.0000 −0.477697
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 20.0000 0.635963
$$990$$ −12.0000 −0.381385
$$991$$ 40.0000 1.27064 0.635321 0.772248i $$-0.280868\pi$$
0.635321 + 0.772248i $$0.280868\pi$$
$$992$$ 3.00000 0.0952501
$$993$$ −96.0000 −3.04647
$$994$$ 0 0
$$995$$ 24.0000 0.760851
$$996$$ 42.0000 1.33082
$$997$$ −4.00000 −0.126681 −0.0633406 0.997992i $$-0.520175\pi$$
−0.0633406 + 0.997992i $$0.520175\pi$$
$$998$$ 10.0000 0.316544
$$999$$ 90.0000 2.84747
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 4018.2.a.s.1.1 1
7.6 odd 2 574.2.a.g.1.1 1
21.20 even 2 5166.2.a.o.1.1 1
28.27 even 2 4592.2.a.l.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.a.g.1.1 1 7.6 odd 2
4018.2.a.s.1.1 1 1.1 even 1 trivial
4592.2.a.l.1.1 1 28.27 even 2
5166.2.a.o.1.1 1 21.20 even 2