# Properties

 Label 7350.2.a.m.1.1 Level 7350 Weight 2 Character 7350.1 Self dual yes Analytic conductor 58.690 Analytic rank 1 Dimension 1 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7350.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$58.6900454856$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1470) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7350.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} +8.00000 q^{23} +1.00000 q^{24} -2.00000 q^{26} -1.00000 q^{27} -8.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} -2.00000 q^{34} +1.00000 q^{36} -6.00000 q^{37} +2.00000 q^{38} -2.00000 q^{39} -10.0000 q^{41} +2.00000 q^{43} -8.00000 q^{46} +6.00000 q^{47} -1.00000 q^{48} -2.00000 q^{51} +2.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} +2.00000 q^{57} +8.00000 q^{58} -12.0000 q^{59} -2.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -14.0000 q^{67} +2.00000 q^{68} -8.00000 q^{69} +6.00000 q^{71} -1.00000 q^{72} +10.0000 q^{73} +6.00000 q^{74} -2.00000 q^{76} +2.00000 q^{78} +4.00000 q^{79} +1.00000 q^{81} +10.0000 q^{82} -12.0000 q^{83} -2.00000 q^{86} +8.00000 q^{87} +14.0000 q^{89} +8.00000 q^{92} +4.00000 q^{93} -6.00000 q^{94} +1.00000 q^{96} -14.0000 q^{97} +O(q^{100})$$

## 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
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 8.00000 1.66812 0.834058 0.551677i $$-0.186012\pi$$
0.834058 + 0.551677i $$0.186012\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 0 0
$$26$$ −2.00000 −0.392232
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −8.00000 −1.48556 −0.742781 0.669534i $$-0.766494\pi$$
−0.742781 + 0.669534i $$0.766494\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −6.00000 −0.986394 −0.493197 0.869918i $$-0.664172\pi$$
−0.493197 + 0.869918i $$0.664172\pi$$
$$38$$ 2.00000 0.324443
$$39$$ −2.00000 −0.320256
$$40$$ 0 0
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −8.00000 −1.17954
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −2.00000 −0.280056
$$52$$ 2.00000 0.277350
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 2.00000 0.264906
$$58$$ 8.00000 1.05045
$$59$$ −12.0000 −1.56227 −0.781133 0.624364i $$-0.785358\pi$$
−0.781133 + 0.624364i $$0.785358\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 4.00000 0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −14.0000 −1.71037 −0.855186 0.518321i $$-0.826557\pi$$
−0.855186 + 0.518321i $$0.826557\pi$$
$$68$$ 2.00000 0.242536
$$69$$ −8.00000 −0.963087
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ 10.0000 1.17041 0.585206 0.810885i $$-0.301014\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ 6.00000 0.697486
$$75$$ 0 0
$$76$$ −2.00000 −0.229416
$$77$$ 0 0
$$78$$ 2.00000 0.226455
$$79$$ 4.00000 0.450035 0.225018 0.974355i $$-0.427756\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 10.0000 1.10432
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 −0.215666
$$87$$ 8.00000 0.857690
$$88$$ 0 0
$$89$$ 14.0000 1.48400 0.741999 0.670402i $$-0.233878\pi$$
0.741999 + 0.670402i $$0.233878\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 8.00000 0.834058
$$93$$ 4.00000 0.414781
$$94$$ −6.00000 −0.618853
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 2.00000 0.198030
$$103$$ 4.00000 0.394132 0.197066 0.980390i $$-0.436859\pi$$
0.197066 + 0.980390i $$0.436859\pi$$
$$104$$ −2.00000 −0.196116
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ 6.00000 0.569495
$$112$$ 0 0
$$113$$ 10.0000 0.940721 0.470360 0.882474i $$-0.344124\pi$$
0.470360 + 0.882474i $$0.344124\pi$$
$$114$$ −2.00000 −0.187317
$$115$$ 0 0
$$116$$ −8.00000 −0.742781
$$117$$ 2.00000 0.184900
$$118$$ 12.0000 1.10469
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 2.00000 0.181071
$$123$$ 10.0000 0.901670
$$124$$ −4.00000 −0.359211
$$125$$ 0 0
$$126$$ 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
$$129$$ −2.00000 −0.176090
$$130$$ 0 0
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 14.0000 1.20942
$$135$$ 0 0
$$136$$ −2.00000 −0.171499
$$137$$ −2.00000 −0.170872 −0.0854358 0.996344i $$-0.527228\pi$$
−0.0854358 + 0.996344i $$0.527228\pi$$
$$138$$ 8.00000 0.681005
$$139$$ −22.0000 −1.86602 −0.933008 0.359856i $$-0.882826\pi$$
−0.933008 + 0.359856i $$0.882826\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ −6.00000 −0.503509
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −10.0000 −0.827606
$$147$$ 0 0
$$148$$ −6.00000 −0.493197
$$149$$ 20.0000 1.63846 0.819232 0.573462i $$-0.194400\pi$$
0.819232 + 0.573462i $$0.194400\pi$$
$$150$$ 0 0
$$151$$ 20.0000 1.62758 0.813788 0.581161i $$-0.197401\pi$$
0.813788 + 0.581161i $$0.197401\pi$$
$$152$$ 2.00000 0.162221
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −2.00000 −0.160128
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ −4.00000 −0.318223
$$159$$ −6.00000 −0.475831
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 2.00000 0.156652 0.0783260 0.996928i $$-0.475042\pi$$
0.0783260 + 0.996928i $$0.475042\pi$$
$$164$$ −10.0000 −0.780869
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ 2.00000 0.154765 0.0773823 0.997001i $$-0.475344\pi$$
0.0773823 + 0.997001i $$0.475344\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −2.00000 −0.152944
$$172$$ 2.00000 0.152499
$$173$$ −12.0000 −0.912343 −0.456172 0.889892i $$-0.650780\pi$$
−0.456172 + 0.889892i $$0.650780\pi$$
$$174$$ −8.00000 −0.606478
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 12.0000 0.901975
$$178$$ −14.0000 −1.04934
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ −8.00000 −0.589768
$$185$$ 0 0
$$186$$ −4.00000 −0.293294
$$187$$ 0 0
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 22.0000 1.59186 0.795932 0.605386i $$-0.206981\pi$$
0.795932 + 0.605386i $$0.206981\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ −20.0000 −1.43963 −0.719816 0.694165i $$-0.755774\pi$$
−0.719816 + 0.694165i $$0.755774\pi$$
$$194$$ 14.0000 1.00514
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ 14.0000 0.987484
$$202$$ −6.00000 −0.422159
$$203$$ 0 0
$$204$$ −2.00000 −0.140028
$$205$$ 0 0
$$206$$ −4.00000 −0.278693
$$207$$ 8.00000 0.556038
$$208$$ 2.00000 0.138675
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 6.00000 0.412082
$$213$$ −6.00000 −0.411113
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ 2.00000 0.135457
$$219$$ −10.0000 −0.675737
$$220$$ 0 0
$$221$$ 4.00000 0.269069
$$222$$ −6.00000 −0.402694
$$223$$ −20.0000 −1.33930 −0.669650 0.742677i $$-0.733556\pi$$
−0.669650 + 0.742677i $$0.733556\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −10.0000 −0.665190
$$227$$ 16.0000 1.06196 0.530979 0.847385i $$-0.321824\pi$$
0.530979 + 0.847385i $$0.321824\pi$$
$$228$$ 2.00000 0.132453
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 8.00000 0.525226
$$233$$ −14.0000 −0.917170 −0.458585 0.888650i $$-0.651644\pi$$
−0.458585 + 0.888650i $$0.651644\pi$$
$$234$$ −2.00000 −0.130744
$$235$$ 0 0
$$236$$ −12.0000 −0.781133
$$237$$ −4.00000 −0.259828
$$238$$ 0 0
$$239$$ 18.0000 1.16432 0.582162 0.813073i $$-0.302207\pi$$
0.582162 + 0.813073i $$0.302207\pi$$
$$240$$ 0 0
$$241$$ −24.0000 −1.54598 −0.772988 0.634421i $$-0.781239\pi$$
−0.772988 + 0.634421i $$0.781239\pi$$
$$242$$ 11.0000 0.707107
$$243$$ −1.00000 −0.0641500
$$244$$ −2.00000 −0.128037
$$245$$ 0 0
$$246$$ −10.0000 −0.637577
$$247$$ −4.00000 −0.254514
$$248$$ 4.00000 0.254000
$$249$$ 12.0000 0.760469
$$250$$ 0 0
$$251$$ −24.0000 −1.51487 −0.757433 0.652913i $$-0.773547\pi$$
−0.757433 + 0.652913i $$0.773547\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 30.0000 1.87135 0.935674 0.352865i $$-0.114792\pi$$
0.935674 + 0.352865i $$0.114792\pi$$
$$258$$ 2.00000 0.124515
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −8.00000 −0.495188
$$262$$ 8.00000 0.494242
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −14.0000 −0.856786
$$268$$ −14.0000 −0.855186
$$269$$ −30.0000 −1.82913 −0.914566 0.404436i $$-0.867468\pi$$
−0.914566 + 0.404436i $$0.867468\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 2.00000 0.120824
$$275$$ 0 0
$$276$$ −8.00000 −0.481543
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 22.0000 1.31947
$$279$$ −4.00000 −0.239474
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 6.00000 0.357295
$$283$$ 20.0000 1.18888 0.594438 0.804141i $$-0.297374\pi$$
0.594438 + 0.804141i $$0.297374\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 14.0000 0.820695
$$292$$ 10.0000 0.585206
$$293$$ −24.0000 −1.40209 −0.701047 0.713115i $$-0.747284\pi$$
−0.701047 + 0.713115i $$0.747284\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 6.00000 0.348743
$$297$$ 0 0
$$298$$ −20.0000 −1.15857
$$299$$ 16.0000 0.925304
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −20.0000 −1.15087
$$303$$ −6.00000 −0.344691
$$304$$ −2.00000 −0.114708
$$305$$ 0 0
$$306$$ −2.00000 −0.114332
$$307$$ 12.0000 0.684876 0.342438 0.939540i $$-0.388747\pi$$
0.342438 + 0.939540i $$0.388747\pi$$
$$308$$ 0 0
$$309$$ −4.00000 −0.227552
$$310$$ 0 0
$$311$$ −8.00000 −0.453638 −0.226819 0.973937i $$-0.572833\pi$$
−0.226819 + 0.973937i $$0.572833\pi$$
$$312$$ 2.00000 0.113228
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 2.00000 0.112867
$$315$$ 0 0
$$316$$ 4.00000 0.225018
$$317$$ 34.0000 1.90963 0.954815 0.297200i $$-0.0960529\pi$$
0.954815 + 0.297200i $$0.0960529\pi$$
$$318$$ 6.00000 0.336463
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −4.00000 −0.222566
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −2.00000 −0.110770
$$327$$ 2.00000 0.110600
$$328$$ 10.0000 0.552158
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 28.0000 1.53902 0.769510 0.638635i $$-0.220501\pi$$
0.769510 + 0.638635i $$0.220501\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ −6.00000 −0.328798
$$334$$ −2.00000 −0.109435
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −12.0000 −0.653682 −0.326841 0.945079i $$-0.605984\pi$$
−0.326841 + 0.945079i $$0.605984\pi$$
$$338$$ 9.00000 0.489535
$$339$$ −10.0000 −0.543125
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 2.00000 0.108148
$$343$$ 0 0
$$344$$ −2.00000 −0.107833
$$345$$ 0 0
$$346$$ 12.0000 0.645124
$$347$$ 28.0000 1.50312 0.751559 0.659665i $$-0.229302\pi$$
0.751559 + 0.659665i $$0.229302\pi$$
$$348$$ 8.00000 0.428845
$$349$$ −30.0000 −1.60586 −0.802932 0.596071i $$-0.796728\pi$$
−0.802932 + 0.596071i $$0.796728\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −0.106752
$$352$$ 0 0
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ −12.0000 −0.637793
$$355$$ 0 0
$$356$$ 14.0000 0.741999
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ −14.0000 −0.738892 −0.369446 0.929252i $$-0.620452\pi$$
−0.369446 + 0.929252i $$0.620452\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 2.00000 0.105118
$$363$$ 11.0000 0.577350
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −2.00000 −0.104542
$$367$$ 16.0000 0.835193 0.417597 0.908633i $$-0.362873\pi$$
0.417597 + 0.908633i $$0.362873\pi$$
$$368$$ 8.00000 0.417029
$$369$$ −10.0000 −0.520579
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 4.00000 0.207390
$$373$$ −22.0000 −1.13912 −0.569558 0.821951i $$-0.692886\pi$$
−0.569558 + 0.821951i $$0.692886\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −6.00000 −0.309426
$$377$$ −16.0000 −0.824042
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 0 0
$$381$$ −8.00000 −0.409852
$$382$$ −22.0000 −1.12562
$$383$$ −26.0000 −1.32854 −0.664269 0.747494i $$-0.731257\pi$$
−0.664269 + 0.747494i $$0.731257\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ 20.0000 1.01797
$$387$$ 2.00000 0.101666
$$388$$ −14.0000 −0.710742
$$389$$ −4.00000 −0.202808 −0.101404 0.994845i $$-0.532333\pi$$
−0.101404 + 0.994845i $$0.532333\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ 0 0
$$393$$ 8.00000 0.403547
$$394$$ 6.00000 0.302276
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −38.0000 −1.90717 −0.953583 0.301131i $$-0.902636\pi$$
−0.953583 + 0.301131i $$0.902636\pi$$
$$398$$ 16.0000 0.802008
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 10.0000 0.499376 0.249688 0.968326i $$-0.419672\pi$$
0.249688 + 0.968326i $$0.419672\pi$$
$$402$$ −14.0000 −0.698257
$$403$$ −8.00000 −0.398508
$$404$$ 6.00000 0.298511
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 2.00000 0.0990148
$$409$$ −24.0000 −1.18672 −0.593362 0.804936i $$-0.702200\pi$$
−0.593362 + 0.804936i $$0.702200\pi$$
$$410$$ 0 0
$$411$$ 2.00000 0.0986527
$$412$$ 4.00000 0.197066
$$413$$ 0 0
$$414$$ −8.00000 −0.393179
$$415$$ 0 0
$$416$$ −2.00000 −0.0980581
$$417$$ 22.0000 1.07734
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ −18.0000 −0.877266 −0.438633 0.898666i $$-0.644537\pi$$
−0.438633 + 0.898666i $$0.644537\pi$$
$$422$$ 4.00000 0.194717
$$423$$ 6.00000 0.291730
$$424$$ −6.00000 −0.291386
$$425$$ 0 0
$$426$$ 6.00000 0.290701
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −10.0000 −0.481683 −0.240842 0.970564i $$-0.577423\pi$$
−0.240842 + 0.970564i $$0.577423\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −2.00000 −0.0957826
$$437$$ −16.0000 −0.765384
$$438$$ 10.0000 0.477818
$$439$$ 36.0000 1.71819 0.859093 0.511819i $$-0.171028\pi$$
0.859093 + 0.511819i $$0.171028\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −4.00000 −0.190261
$$443$$ −4.00000 −0.190046 −0.0950229 0.995475i $$-0.530292\pi$$
−0.0950229 + 0.995475i $$0.530292\pi$$
$$444$$ 6.00000 0.284747
$$445$$ 0 0
$$446$$ 20.0000 0.947027
$$447$$ −20.0000 −0.945968
$$448$$ 0 0
$$449$$ −26.0000 −1.22702 −0.613508 0.789689i $$-0.710242\pi$$
−0.613508 + 0.789689i $$0.710242\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 10.0000 0.470360
$$453$$ −20.0000 −0.939682
$$454$$ −16.0000 −0.750917
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ −32.0000 −1.49690 −0.748448 0.663193i $$-0.769201\pi$$
−0.748448 + 0.663193i $$0.769201\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ −2.00000 −0.0933520
$$460$$ 0 0
$$461$$ 14.0000 0.652045 0.326023 0.945362i $$-0.394291\pi$$
0.326023 + 0.945362i $$0.394291\pi$$
$$462$$ 0 0
$$463$$ −4.00000 −0.185896 −0.0929479 0.995671i $$-0.529629\pi$$
−0.0929479 + 0.995671i $$0.529629\pi$$
$$464$$ −8.00000 −0.371391
$$465$$ 0 0
$$466$$ 14.0000 0.648537
$$467$$ −36.0000 −1.66588 −0.832941 0.553362i $$-0.813345\pi$$
−0.832941 + 0.553362i $$0.813345\pi$$
$$468$$ 2.00000 0.0924500
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 2.00000 0.0921551
$$472$$ 12.0000 0.552345
$$473$$ 0 0
$$474$$ 4.00000 0.183726
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ −18.0000 −0.823301
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 0 0
$$481$$ −12.0000 −0.547153
$$482$$ 24.0000 1.09317
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ −32.0000 −1.45006 −0.725029 0.688718i $$-0.758174\pi$$
−0.725029 + 0.688718i $$0.758174\pi$$
$$488$$ 2.00000 0.0905357
$$489$$ −2.00000 −0.0904431
$$490$$ 0 0
$$491$$ −4.00000 −0.180517 −0.0902587 0.995918i $$-0.528769\pi$$
−0.0902587 + 0.995918i $$0.528769\pi$$
$$492$$ 10.0000 0.450835
$$493$$ −16.0000 −0.720604
$$494$$ 4.00000 0.179969
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ 0 0
$$498$$ −12.0000 −0.537733
$$499$$ −12.0000 −0.537194 −0.268597 0.963253i $$-0.586560\pi$$
−0.268597 + 0.963253i $$0.586560\pi$$
$$500$$ 0 0
$$501$$ −2.00000 −0.0893534
$$502$$ 24.0000 1.07117
$$503$$ 26.0000 1.15928 0.579641 0.814872i $$-0.303193\pi$$
0.579641 + 0.814872i $$0.303193\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 9.00000 0.399704
$$508$$ 8.00000 0.354943
$$509$$ −14.0000 −0.620539 −0.310270 0.950649i $$-0.600419\pi$$
−0.310270 + 0.950649i $$0.600419\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 2.00000 0.0883022
$$514$$ −30.0000 −1.32324
$$515$$ 0 0
$$516$$ −2.00000 −0.0880451
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 12.0000 0.526742
$$520$$ 0 0
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 8.00000 0.350150
$$523$$ −4.00000 −0.174908 −0.0874539 0.996169i $$-0.527873\pi$$
−0.0874539 + 0.996169i $$0.527873\pi$$
$$524$$ −8.00000 −0.349482
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −8.00000 −0.348485
$$528$$ 0 0
$$529$$ 41.0000 1.78261
$$530$$ 0 0
$$531$$ −12.0000 −0.520756
$$532$$ 0 0
$$533$$ −20.0000 −0.866296
$$534$$ 14.0000 0.605839
$$535$$ 0 0
$$536$$ 14.0000 0.604708
$$537$$ 12.0000 0.517838
$$538$$ 30.0000 1.29339
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −30.0000 −1.28980 −0.644900 0.764267i $$-0.723101\pi$$
−0.644900 + 0.764267i $$0.723101\pi$$
$$542$$ −20.0000 −0.859074
$$543$$ 2.00000 0.0858282
$$544$$ −2.00000 −0.0857493
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 26.0000 1.11168 0.555840 0.831289i $$-0.312397\pi$$
0.555840 + 0.831289i $$0.312397\pi$$
$$548$$ −2.00000 −0.0854358
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ 16.0000 0.681623
$$552$$ 8.00000 0.340503
$$553$$ 0 0
$$554$$ 2.00000 0.0849719
$$555$$ 0 0
$$556$$ −22.0000 −0.933008
$$557$$ 18.0000 0.762684 0.381342 0.924434i $$-0.375462\pi$$
0.381342 + 0.924434i $$0.375462\pi$$
$$558$$ 4.00000 0.169334
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −18.0000 −0.759284
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ −6.00000 −0.252646
$$565$$ 0 0
$$566$$ −20.0000 −0.840663
$$567$$ 0 0
$$568$$ −6.00000 −0.251754
$$569$$ 10.0000 0.419222 0.209611 0.977785i $$-0.432780\pi$$
0.209611 + 0.977785i $$0.432780\pi$$
$$570$$ 0 0
$$571$$ 4.00000 0.167395 0.0836974 0.996491i $$-0.473327\pi$$
0.0836974 + 0.996491i $$0.473327\pi$$
$$572$$ 0 0
$$573$$ −22.0000 −0.919063
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −26.0000 −1.08239 −0.541197 0.840896i $$-0.682029\pi$$
−0.541197 + 0.840896i $$0.682029\pi$$
$$578$$ 13.0000 0.540729
$$579$$ 20.0000 0.831172
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −14.0000 −0.580319
$$583$$ 0 0
$$584$$ −10.0000 −0.413803
$$585$$ 0 0
$$586$$ 24.0000 0.991431
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 8.00000 0.329634
$$590$$ 0 0
$$591$$ 6.00000 0.246807
$$592$$ −6.00000 −0.246598
$$593$$ −14.0000 −0.574911 −0.287456 0.957794i $$-0.592809\pi$$
−0.287456 + 0.957794i $$0.592809\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 20.0000 0.819232
$$597$$ 16.0000 0.654836
$$598$$ −16.0000 −0.654289
$$599$$ −34.0000 −1.38920 −0.694601 0.719395i $$-0.744419\pi$$
−0.694601 + 0.719395i $$0.744419\pi$$
$$600$$ 0 0
$$601$$ −8.00000 −0.326327 −0.163163 0.986599i $$-0.552170\pi$$
−0.163163 + 0.986599i $$0.552170\pi$$
$$602$$ 0 0
$$603$$ −14.0000 −0.570124
$$604$$ 20.0000 0.813788
$$605$$ 0 0
$$606$$ 6.00000 0.243733
$$607$$ −12.0000 −0.487065 −0.243532 0.969893i $$-0.578306\pi$$
−0.243532 + 0.969893i $$0.578306\pi$$
$$608$$ 2.00000 0.0811107
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 12.0000 0.485468
$$612$$ 2.00000 0.0808452
$$613$$ 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
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 4.00000 0.160904
$$619$$ 22.0000 0.884255 0.442127 0.896952i $$-0.354224\pi$$
0.442127 + 0.896952i $$0.354224\pi$$
$$620$$ 0 0
$$621$$ −8.00000 −0.321029
$$622$$ 8.00000 0.320771
$$623$$ 0 0
$$624$$ −2.00000 −0.0800641
$$625$$ 0 0
$$626$$ −6.00000 −0.239808
$$627$$ 0 0
$$628$$ −2.00000 −0.0798087
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −24.0000 −0.955425 −0.477712 0.878516i $$-0.658534\pi$$
−0.477712 + 0.878516i $$0.658534\pi$$
$$632$$ −4.00000 −0.159111
$$633$$ 4.00000 0.158986
$$634$$ −34.0000 −1.35031
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 6.00000 0.237356
$$640$$ 0 0
$$641$$ −42.0000 −1.65890 −0.829450 0.558581i $$-0.811346\pi$$
−0.829450 + 0.558581i $$0.811346\pi$$
$$642$$ 0 0
$$643$$ −36.0000 −1.41970 −0.709851 0.704352i $$-0.751238\pi$$
−0.709851 + 0.704352i $$0.751238\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 4.00000 0.157378
$$647$$ 14.0000 0.550397 0.275198 0.961387i $$-0.411256\pi$$
0.275198 + 0.961387i $$0.411256\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 2.00000 0.0783260
$$653$$ 14.0000 0.547862 0.273931 0.961749i $$-0.411676\pi$$
0.273931 + 0.961749i $$0.411676\pi$$
$$654$$ −2.00000 −0.0782062
$$655$$ 0 0
$$656$$ −10.0000 −0.390434
$$657$$ 10.0000 0.390137
$$658$$ 0 0
$$659$$ 16.0000 0.623272 0.311636 0.950202i $$-0.399123\pi$$
0.311636 + 0.950202i $$0.399123\pi$$
$$660$$ 0 0
$$661$$ 22.0000 0.855701 0.427850 0.903850i $$-0.359271\pi$$
0.427850 + 0.903850i $$0.359271\pi$$
$$662$$ −28.0000 −1.08825
$$663$$ −4.00000 −0.155347
$$664$$ 12.0000 0.465690
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ −64.0000 −2.47809
$$668$$ 2.00000 0.0773823
$$669$$ 20.0000 0.773245
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −20.0000 −0.770943 −0.385472 0.922720i $$-0.625961\pi$$
−0.385472 + 0.922720i $$0.625961\pi$$
$$674$$ 12.0000 0.462223
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −12.0000 −0.461197 −0.230599 0.973049i $$-0.574068\pi$$
−0.230599 + 0.973049i $$0.574068\pi$$
$$678$$ 10.0000 0.384048
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −16.0000 −0.613121
$$682$$ 0 0
$$683$$ 24.0000 0.918334 0.459167 0.888350i $$-0.348148\pi$$
0.459167 + 0.888350i $$0.348148\pi$$
$$684$$ −2.00000 −0.0764719
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −10.0000 −0.381524
$$688$$ 2.00000 0.0762493
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ −34.0000 −1.29342 −0.646710 0.762736i $$-0.723856\pi$$
−0.646710 + 0.762736i $$0.723856\pi$$
$$692$$ −12.0000 −0.456172
$$693$$ 0 0
$$694$$ −28.0000 −1.06287
$$695$$ 0 0
$$696$$ −8.00000 −0.303239
$$697$$ −20.0000 −0.757554
$$698$$ 30.0000 1.13552
$$699$$ 14.0000 0.529529
$$700$$ 0 0
$$701$$ −8.00000 −0.302156 −0.151078 0.988522i $$-0.548274\pi$$
−0.151078 + 0.988522i $$0.548274\pi$$
$$702$$ 2.00000 0.0754851
$$703$$ 12.0000 0.452589
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −6.00000 −0.225813
$$707$$ 0 0
$$708$$ 12.0000 0.450988
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 0 0
$$711$$ 4.00000 0.150012
$$712$$ −14.0000 −0.524672
$$713$$ −32.0000 −1.19841
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −12.0000 −0.448461
$$717$$ −18.0000 −0.672222
$$718$$ 14.0000 0.522475
$$719$$ −8.00000 −0.298350 −0.149175 0.988811i $$-0.547662\pi$$
−0.149175 + 0.988811i $$0.547662\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 15.0000 0.558242
$$723$$ 24.0000 0.892570
$$724$$ −2.00000 −0.0743294
$$725$$ 0 0
$$726$$ −11.0000 −0.408248
$$727$$ 36.0000 1.33517 0.667583 0.744535i $$-0.267329\pi$$
0.667583 + 0.744535i $$0.267329\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 4.00000 0.147945
$$732$$ 2.00000 0.0739221
$$733$$ 2.00000 0.0738717 0.0369358 0.999318i $$-0.488240\pi$$
0.0369358 + 0.999318i $$0.488240\pi$$
$$734$$ −16.0000 −0.590571
$$735$$ 0 0
$$736$$ −8.00000 −0.294884
$$737$$ 0 0
$$738$$ 10.0000 0.368105
$$739$$ −4.00000 −0.147142 −0.0735712 0.997290i $$-0.523440\pi$$
−0.0735712 + 0.997290i $$0.523440\pi$$
$$740$$ 0 0
$$741$$ 4.00000 0.146944
$$742$$ 0 0
$$743$$ −32.0000 −1.17397 −0.586983 0.809599i $$-0.699684\pi$$
−0.586983 + 0.809599i $$0.699684\pi$$
$$744$$ −4.00000 −0.146647
$$745$$ 0 0
$$746$$ 22.0000 0.805477
$$747$$ −12.0000 −0.439057
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −24.0000 −0.875772 −0.437886 0.899030i $$-0.644273\pi$$
−0.437886 + 0.899030i $$0.644273\pi$$
$$752$$ 6.00000 0.218797
$$753$$ 24.0000 0.874609
$$754$$ 16.0000 0.582686
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 34.0000 1.23575 0.617876 0.786276i $$-0.287994\pi$$
0.617876 + 0.786276i $$0.287994\pi$$
$$758$$ −12.0000 −0.435860
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 34.0000 1.23250 0.616250 0.787551i $$-0.288651\pi$$
0.616250 + 0.787551i $$0.288651\pi$$
$$762$$ 8.00000 0.289809
$$763$$ 0 0
$$764$$ 22.0000 0.795932
$$765$$ 0 0
$$766$$ 26.0000 0.939418
$$767$$ −24.0000 −0.866590
$$768$$ −1.00000 −0.0360844
$$769$$ 20.0000 0.721218 0.360609 0.932717i $$-0.382569\pi$$
0.360609 + 0.932717i $$0.382569\pi$$
$$770$$ 0 0
$$771$$ −30.0000 −1.08042
$$772$$ −20.0000 −0.719816
$$773$$ −24.0000 −0.863220 −0.431610 0.902060i $$-0.642054\pi$$
−0.431610 + 0.902060i $$0.642054\pi$$
$$774$$ −2.00000 −0.0718885
$$775$$ 0 0
$$776$$ 14.0000 0.502571
$$777$$ 0 0
$$778$$ 4.00000 0.143407
$$779$$ 20.0000 0.716574
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −16.0000 −0.572159
$$783$$ 8.00000 0.285897
$$784$$ 0 0
$$785$$ 0 0
$$786$$ −8.00000 −0.285351
$$787$$ −28.0000 −0.998092 −0.499046 0.866575i $$-0.666316\pi$$
−0.499046 + 0.866575i $$0.666316\pi$$
$$788$$ −6.00000 −0.213741
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −4.00000 −0.142044
$$794$$ 38.0000 1.34857
$$795$$ 0 0
$$796$$ −16.0000 −0.567105
$$797$$ −20.0000 −0.708436 −0.354218 0.935163i $$-0.615253\pi$$
−0.354218 + 0.935163i $$0.615253\pi$$
$$798$$ 0 0
$$799$$ 12.0000 0.424529
$$800$$ 0 0
$$801$$ 14.0000 0.494666
$$802$$ −10.0000 −0.353112
$$803$$ 0 0
$$804$$ 14.0000 0.493742
$$805$$ 0 0
$$806$$ 8.00000 0.281788
$$807$$ 30.0000 1.05605
$$808$$ −6.00000 −0.211079
$$809$$ 18.0000 0.632846 0.316423 0.948618i $$-0.397518\pi$$
0.316423 + 0.948618i $$0.397518\pi$$
$$810$$ 0 0
$$811$$ −22.0000 −0.772524 −0.386262 0.922389i $$-0.626234\pi$$
−0.386262 + 0.922389i $$0.626234\pi$$
$$812$$ 0 0
$$813$$ −20.0000 −0.701431
$$814$$ 0 0
$$815$$ 0 0
$$816$$ −2.00000 −0.0700140
$$817$$ −4.00000 −0.139942
$$818$$ 24.0000 0.839140
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ −2.00000 −0.0697580
$$823$$ −4.00000 −0.139431 −0.0697156 0.997567i $$-0.522209\pi$$
−0.0697156 + 0.997567i $$0.522209\pi$$
$$824$$ −4.00000 −0.139347
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −12.0000 −0.417281 −0.208640 0.977992i $$-0.566904\pi$$
−0.208640 + 0.977992i $$0.566904\pi$$
$$828$$ 8.00000 0.278019
$$829$$ −22.0000 −0.764092 −0.382046 0.924143i $$-0.624780\pi$$
−0.382046 + 0.924143i $$0.624780\pi$$
$$830$$ 0 0
$$831$$ 2.00000 0.0693792
$$832$$ 2.00000 0.0693375
$$833$$ 0 0
$$834$$ −22.0000 −0.761798
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 4.00000 0.138260
$$838$$ 12.0000 0.414533
$$839$$ −24.0000 −0.828572 −0.414286 0.910147i $$-0.635969\pi$$
−0.414286 + 0.910147i $$0.635969\pi$$
$$840$$ 0 0
$$841$$ 35.0000 1.20690
$$842$$ 18.0000 0.620321
$$843$$ −18.0000 −0.619953
$$844$$ −4.00000 −0.137686
$$845$$ 0 0
$$846$$ −6.00000 −0.206284
$$847$$ 0 0
$$848$$ 6.00000 0.206041
$$849$$ −20.0000 −0.686398
$$850$$ 0 0
$$851$$ −48.0000 −1.64542
$$852$$ −6.00000 −0.205557
$$853$$ 10.0000 0.342393 0.171197 0.985237i $$-0.445237\pi$$
0.171197 + 0.985237i $$0.445237\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −10.0000 −0.341593 −0.170797 0.985306i $$-0.554634\pi$$
−0.170797 + 0.985306i $$0.554634\pi$$
$$858$$ 0 0
$$859$$ −42.0000 −1.43302 −0.716511 0.697576i $$-0.754262\pi$$
−0.716511 + 0.697576i $$0.754262\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 10.0000 0.340601
$$863$$ 32.0000 1.08929 0.544646 0.838666i $$-0.316664\pi$$
0.544646 + 0.838666i $$0.316664\pi$$
$$864$$ 1.00000 0.0340207
$$865$$ 0 0
$$866$$ 14.0000 0.475739
$$867$$ 13.0000 0.441503
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −28.0000 −0.948744
$$872$$ 2.00000 0.0677285
$$873$$ −14.0000 −0.473828
$$874$$ 16.0000 0.541208
$$875$$ 0 0
$$876$$ −10.0000 −0.337869
$$877$$ −42.0000 −1.41824 −0.709120 0.705088i $$-0.750907\pi$$
−0.709120 + 0.705088i $$0.750907\pi$$
$$878$$ −36.0000 −1.21494
$$879$$ 24.0000 0.809500
$$880$$ 0 0
$$881$$ 18.0000 0.606435 0.303218 0.952921i $$-0.401939\pi$$
0.303218 + 0.952921i $$0.401939\pi$$
$$882$$ 0 0
$$883$$ 10.0000 0.336527 0.168263 0.985742i $$-0.446184\pi$$
0.168263 + 0.985742i $$0.446184\pi$$
$$884$$ 4.00000 0.134535
$$885$$ 0 0
$$886$$ 4.00000 0.134383
$$887$$ −30.0000 −1.00730 −0.503651 0.863907i $$-0.668010\pi$$
−0.503651 + 0.863907i $$0.668010\pi$$
$$888$$ −6.00000 −0.201347
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −20.0000 −0.669650
$$893$$ −12.0000 −0.401565
$$894$$ 20.0000 0.668900
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −16.0000 −0.534224
$$898$$ 26.0000 0.867631
$$899$$ 32.0000 1.06726
$$900$$ 0 0
$$901$$ 12.0000 0.399778
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −10.0000 −0.332595
$$905$$ 0 0
$$906$$ 20.0000 0.664455
$$907$$ −38.0000 −1.26177 −0.630885 0.775877i $$-0.717308\pi$$
−0.630885 + 0.775877i $$0.717308\pi$$
$$908$$ 16.0000 0.530979
$$909$$ 6.00000 0.199007
$$910$$ 0 0
$$911$$ 22.0000 0.728893 0.364446 0.931224i $$-0.381258\pi$$
0.364446 + 0.931224i $$0.381258\pi$$
$$912$$ 2.00000 0.0662266
$$913$$ 0 0
$$914$$ 32.0000 1.05847
$$915$$ 0 0
$$916$$ 10.0000 0.330409
$$917$$ 0 0
$$918$$ 2.00000 0.0660098
$$919$$ −16.0000 −0.527791 −0.263896 0.964551i $$-0.585007\pi$$
−0.263896 + 0.964551i $$0.585007\pi$$
$$920$$ 0 0
$$921$$ −12.0000 −0.395413
$$922$$ −14.0000 −0.461065
$$923$$ 12.0000 0.394985
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 4.00000 0.131448
$$927$$ 4.00000 0.131377
$$928$$ 8.00000 0.262613
$$929$$ −22.0000 −0.721797 −0.360898 0.932605i $$-0.617530\pi$$
−0.360898 + 0.932605i $$0.617530\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −14.0000 −0.458585
$$933$$ 8.00000 0.261908
$$934$$ 36.0000 1.17796
$$935$$ 0 0
$$936$$ −2.00000 −0.0653720
$$937$$ −42.0000 −1.37208 −0.686040 0.727564i $$-0.740653\pi$$
−0.686040 + 0.727564i $$0.740653\pi$$
$$938$$ 0 0
$$939$$ −6.00000 −0.195803
$$940$$ 0 0
$$941$$ −14.0000 −0.456387 −0.228193 0.973616i $$-0.573282\pi$$
−0.228193 + 0.973616i $$0.573282\pi$$
$$942$$ −2.00000 −0.0651635
$$943$$ −80.0000 −2.60516
$$944$$ −12.0000 −0.390567
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 24.0000 0.779895 0.389948 0.920837i $$-0.372493\pi$$
0.389948 + 0.920837i $$0.372493\pi$$
$$948$$ −4.00000 −0.129914
$$949$$ 20.0000 0.649227
$$950$$ 0 0
$$951$$ −34.0000 −1.10253
$$952$$ 0 0
$$953$$ 34.0000 1.10137 0.550684 0.834714i $$-0.314367\pi$$
0.550684 + 0.834714i $$0.314367\pi$$
$$954$$ −6.00000 −0.194257
$$955$$ 0 0
$$956$$ 18.0000 0.582162
$$957$$ 0 0
$$958$$ 24.0000 0.775405
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 12.0000 0.386896
$$963$$ 0 0
$$964$$ −24.0000 −0.772988
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 32.0000 1.02905 0.514525 0.857475i $$-0.327968\pi$$
0.514525 + 0.857475i $$0.327968\pi$$
$$968$$ 11.0000 0.353553
$$969$$ 4.00000 0.128499
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ 32.0000 1.02535
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ 34.0000 1.08776 0.543878 0.839164i $$-0.316955\pi$$
0.543878 + 0.839164i $$0.316955\pi$$
$$978$$ 2.00000 0.0639529
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −2.00000 −0.0638551
$$982$$ 4.00000 0.127645
$$983$$ −18.0000 −0.574111 −0.287055 0.957914i $$-0.592676\pi$$
−0.287055 + 0.957914i $$0.592676\pi$$
$$984$$ −10.0000 −0.318788
$$985$$ 0 0
$$986$$ 16.0000 0.509544
$$987$$ 0 0
$$988$$ −4.00000 −0.127257
$$989$$ 16.0000 0.508770
$$990$$ 0 0
$$991$$ 16.0000 0.508257 0.254128 0.967170i $$-0.418211\pi$$
0.254128 + 0.967170i $$0.418211\pi$$
$$992$$ 4.00000 0.127000
$$993$$ −28.0000 −0.888553
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 12.0000 0.380235
$$997$$ −6.00000 −0.190022 −0.0950110 0.995476i $$-0.530289\pi$$
−0.0950110 + 0.995476i $$0.530289\pi$$
$$998$$ 12.0000 0.379853
$$999$$ 6.00000 0.189832
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 7350.2.a.m.1.1 1
5.2 odd 4 1470.2.g.d.589.1 yes 2
5.3 odd 4 1470.2.g.d.589.2 yes 2
5.4 even 2 7350.2.a.cr.1.1 1
7.6 odd 2 7350.2.a.bc.1.1 1
35.2 odd 12 1470.2.n.d.949.1 4
35.3 even 12 1470.2.n.e.79.1 4
35.12 even 12 1470.2.n.e.949.1 4
35.13 even 4 1470.2.g.c.589.2 yes 2
35.17 even 12 1470.2.n.e.79.2 4
35.18 odd 12 1470.2.n.d.79.1 4
35.23 odd 12 1470.2.n.d.949.2 4
35.27 even 4 1470.2.g.c.589.1 2
35.32 odd 12 1470.2.n.d.79.2 4
35.33 even 12 1470.2.n.e.949.2 4
35.34 odd 2 7350.2.a.bx.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.g.c.589.1 2 35.27 even 4
1470.2.g.c.589.2 yes 2 35.13 even 4
1470.2.g.d.589.1 yes 2 5.2 odd 4
1470.2.g.d.589.2 yes 2 5.3 odd 4
1470.2.n.d.79.1 4 35.18 odd 12
1470.2.n.d.79.2 4 35.32 odd 12
1470.2.n.d.949.1 4 35.2 odd 12
1470.2.n.d.949.2 4 35.23 odd 12
1470.2.n.e.79.1 4 35.3 even 12
1470.2.n.e.79.2 4 35.17 even 12
1470.2.n.e.949.1 4 35.12 even 12
1470.2.n.e.949.2 4 35.33 even 12
7350.2.a.m.1.1 1 1.1 even 1 trivial
7350.2.a.bc.1.1 1 7.6 odd 2
7350.2.a.bx.1.1 1 35.34 odd 2
7350.2.a.cr.1.1 1 5.4 even 2