# Properties

 Label 7350.2.a.c.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 1050) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} +1.00000 q^{19} +4.00000 q^{22} +2.00000 q^{23} +1.00000 q^{24} +1.00000 q^{26} -1.00000 q^{27} +4.00000 q^{29} -1.00000 q^{32} +4.00000 q^{33} +2.00000 q^{34} +1.00000 q^{36} -3.00000 q^{37} -1.00000 q^{38} +1.00000 q^{39} +12.0000 q^{41} -8.00000 q^{43} -4.00000 q^{44} -2.00000 q^{46} +6.00000 q^{47} -1.00000 q^{48} +2.00000 q^{51} -1.00000 q^{52} -2.00000 q^{53} +1.00000 q^{54} -1.00000 q^{57} -4.00000 q^{58} +6.00000 q^{59} -13.0000 q^{61} +1.00000 q^{64} -4.00000 q^{66} -3.00000 q^{67} -2.00000 q^{68} -2.00000 q^{69} +16.0000 q^{71} -1.00000 q^{72} +11.0000 q^{73} +3.00000 q^{74} +1.00000 q^{76} -1.00000 q^{78} +13.0000 q^{79} +1.00000 q^{81} -12.0000 q^{82} +6.00000 q^{83} +8.00000 q^{86} -4.00000 q^{87} +4.00000 q^{88} -2.00000 q^{89} +2.00000 q^{92} -6.00000 q^{94} +1.00000 q^{96} -17.0000 q^{97} -4.00000 q^{99} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ −1.00000 −0.577350
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 1.00000 0.408248
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ −1.00000 −0.277350 −0.138675 0.990338i $$-0.544284\pi$$
−0.138675 + 0.990338i $$0.544284\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 1.00000 0.229416 0.114708 0.993399i $$-0.463407\pi$$
0.114708 + 0.993399i $$0.463407\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 4.00000 0.852803
$$23$$ 2.00000 0.417029 0.208514 0.978019i $$-0.433137\pi$$
0.208514 + 0.978019i $$0.433137\pi$$
$$24$$ 1.00000 0.204124
$$25$$ 0 0
$$26$$ 1.00000 0.196116
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 4.00000 0.696311
$$34$$ 2.00000 0.342997
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −3.00000 −0.493197 −0.246598 0.969118i $$-0.579313\pi$$
−0.246598 + 0.969118i $$0.579313\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ 12.0000 1.87409 0.937043 0.349215i $$-0.113552\pi$$
0.937043 + 0.349215i $$0.113552\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 0 0
$$46$$ −2.00000 −0.294884
$$47$$ 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
$$52$$ −1.00000 −0.138675
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ 1.00000 0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.00000 −0.132453
$$58$$ −4.00000 −0.525226
$$59$$ 6.00000 0.781133 0.390567 0.920575i $$-0.372279\pi$$
0.390567 + 0.920575i $$0.372279\pi$$
$$60$$ 0 0
$$61$$ −13.0000 −1.66448 −0.832240 0.554416i $$-0.812942\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −4.00000 −0.492366
$$67$$ −3.00000 −0.366508 −0.183254 0.983066i $$-0.558663\pi$$
−0.183254 + 0.983066i $$0.558663\pi$$
$$68$$ −2.00000 −0.242536
$$69$$ −2.00000 −0.240772
$$70$$ 0 0
$$71$$ 16.0000 1.89885 0.949425 0.313993i $$-0.101667\pi$$
0.949425 + 0.313993i $$0.101667\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ 11.0000 1.28745 0.643726 0.765256i $$-0.277388\pi$$
0.643726 + 0.765256i $$0.277388\pi$$
$$74$$ 3.00000 0.348743
$$75$$ 0 0
$$76$$ 1.00000 0.114708
$$77$$ 0 0
$$78$$ −1.00000 −0.113228
$$79$$ 13.0000 1.46261 0.731307 0.682048i $$-0.238911\pi$$
0.731307 + 0.682048i $$0.238911\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ −12.0000 −1.32518
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 8.00000 0.862662
$$87$$ −4.00000 −0.428845
$$88$$ 4.00000 0.426401
$$89$$ −2.00000 −0.212000 −0.106000 0.994366i $$-0.533804\pi$$
−0.106000 + 0.994366i $$0.533804\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 2.00000 0.208514
$$93$$ 0 0
$$94$$ −6.00000 −0.618853
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ −17.0000 −1.72609 −0.863044 0.505128i $$-0.831445\pi$$
−0.863044 + 0.505128i $$0.831445\pi$$
$$98$$ 0 0
$$99$$ −4.00000 −0.402015
$$100$$ 0 0
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ −2.00000 −0.198030
$$103$$ −7.00000 −0.689730 −0.344865 0.938652i $$-0.612075\pi$$
−0.344865 + 0.938652i $$0.612075\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ 0 0
$$106$$ 2.00000 0.194257
$$107$$ −6.00000 −0.580042 −0.290021 0.957020i $$-0.593662\pi$$
−0.290021 + 0.957020i $$0.593662\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ −19.0000 −1.81987 −0.909935 0.414751i $$-0.863869\pi$$
−0.909935 + 0.414751i $$0.863869\pi$$
$$110$$ 0 0
$$111$$ 3.00000 0.284747
$$112$$ 0 0
$$113$$ −18.0000 −1.69330 −0.846649 0.532152i $$-0.821383\pi$$
−0.846649 + 0.532152i $$0.821383\pi$$
$$114$$ 1.00000 0.0936586
$$115$$ 0 0
$$116$$ 4.00000 0.371391
$$117$$ −1.00000 −0.0924500
$$118$$ −6.00000 −0.552345
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 13.0000 1.17696
$$123$$ −12.0000 −1.08200
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1.00000 0.0887357 0.0443678 0.999015i $$-0.485873\pi$$
0.0443678 + 0.999015i $$0.485873\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 8.00000 0.704361
$$130$$ 0 0
$$131$$ 2.00000 0.174741 0.0873704 0.996176i $$-0.472154\pi$$
0.0873704 + 0.996176i $$0.472154\pi$$
$$132$$ 4.00000 0.348155
$$133$$ 0 0
$$134$$ 3.00000 0.259161
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 2.00000 0.170251
$$139$$ −13.0000 −1.10265 −0.551323 0.834292i $$-0.685877\pi$$
−0.551323 + 0.834292i $$0.685877\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ −16.0000 −1.34269
$$143$$ 4.00000 0.334497
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −11.0000 −0.910366
$$147$$ 0 0
$$148$$ −3.00000 −0.246598
$$149$$ −16.0000 −1.31077 −0.655386 0.755295i $$-0.727494\pi$$
−0.655386 + 0.755295i $$0.727494\pi$$
$$150$$ 0 0
$$151$$ 19.0000 1.54620 0.773099 0.634285i $$-0.218706\pi$$
0.773099 + 0.634285i $$0.218706\pi$$
$$152$$ −1.00000 −0.0811107
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 1.00000 0.0800641
$$157$$ 21.0000 1.67598 0.837991 0.545684i $$-0.183730\pi$$
0.837991 + 0.545684i $$0.183730\pi$$
$$158$$ −13.0000 −1.03422
$$159$$ 2.00000 0.158610
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ −23.0000 −1.80150 −0.900750 0.434339i $$-0.856982\pi$$
−0.900750 + 0.434339i $$0.856982\pi$$
$$164$$ 12.0000 0.937043
$$165$$ 0 0
$$166$$ −6.00000 −0.465690
$$167$$ −10.0000 −0.773823 −0.386912 0.922117i $$-0.626458\pi$$
−0.386912 + 0.922117i $$0.626458\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 1.00000 0.0764719
$$172$$ −8.00000 −0.609994
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 4.00000 0.303239
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ −6.00000 −0.450988
$$178$$ 2.00000 0.149906
$$179$$ −8.00000 −0.597948 −0.298974 0.954261i $$-0.596644\pi$$
−0.298974 + 0.954261i $$0.596644\pi$$
$$180$$ 0 0
$$181$$ −18.0000 −1.33793 −0.668965 0.743294i $$-0.733262\pi$$
−0.668965 + 0.743294i $$0.733262\pi$$
$$182$$ 0 0
$$183$$ 13.0000 0.960988
$$184$$ −2.00000 −0.147442
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 8.00000 0.585018
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 20.0000 1.44715 0.723575 0.690246i $$-0.242498\pi$$
0.723575 + 0.690246i $$0.242498\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 10.0000 0.719816 0.359908 0.932988i $$-0.382808\pi$$
0.359908 + 0.932988i $$0.382808\pi$$
$$194$$ 17.0000 1.22053
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 4.00000 0.284268
$$199$$ 15.0000 1.06332 0.531661 0.846957i $$-0.321568\pi$$
0.531661 + 0.846957i $$0.321568\pi$$
$$200$$ 0 0
$$201$$ 3.00000 0.211604
$$202$$ −12.0000 −0.844317
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ 0 0
$$206$$ 7.00000 0.487713
$$207$$ 2.00000 0.139010
$$208$$ −1.00000 −0.0693375
$$209$$ −4.00000 −0.276686
$$210$$ 0 0
$$211$$ 3.00000 0.206529 0.103264 0.994654i $$-0.467071\pi$$
0.103264 + 0.994654i $$0.467071\pi$$
$$212$$ −2.00000 −0.137361
$$213$$ −16.0000 −1.09630
$$214$$ 6.00000 0.410152
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ 19.0000 1.28684
$$219$$ −11.0000 −0.743311
$$220$$ 0 0
$$221$$ 2.00000 0.134535
$$222$$ −3.00000 −0.201347
$$223$$ 19.0000 1.27233 0.636167 0.771551i $$-0.280519\pi$$
0.636167 + 0.771551i $$0.280519\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 18.0000 1.19734
$$227$$ 8.00000 0.530979 0.265489 0.964114i $$-0.414466\pi$$
0.265489 + 0.964114i $$0.414466\pi$$
$$228$$ −1.00000 −0.0662266
$$229$$ −7.00000 −0.462573 −0.231287 0.972886i $$-0.574293\pi$$
−0.231287 + 0.972886i $$0.574293\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −4.00000 −0.262613
$$233$$ 4.00000 0.262049 0.131024 0.991379i $$-0.458173\pi$$
0.131024 + 0.991379i $$0.458173\pi$$
$$234$$ 1.00000 0.0653720
$$235$$ 0 0
$$236$$ 6.00000 0.390567
$$237$$ −13.0000 −0.844441
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ 13.0000 0.837404 0.418702 0.908124i $$-0.362485\pi$$
0.418702 + 0.908124i $$0.362485\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ −1.00000 −0.0641500
$$244$$ −13.0000 −0.832240
$$245$$ 0 0
$$246$$ 12.0000 0.765092
$$247$$ −1.00000 −0.0636285
$$248$$ 0 0
$$249$$ −6.00000 −0.380235
$$250$$ 0 0
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ −8.00000 −0.502956
$$254$$ −1.00000 −0.0627456
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 8.00000 0.499026 0.249513 0.968371i $$-0.419729\pi$$
0.249513 + 0.968371i $$0.419729\pi$$
$$258$$ −8.00000 −0.498058
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 4.00000 0.247594
$$262$$ −2.00000 −0.123560
$$263$$ −32.0000 −1.97320 −0.986602 0.163144i $$-0.947836\pi$$
−0.986602 + 0.163144i $$0.947836\pi$$
$$264$$ −4.00000 −0.246183
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 2.00000 0.122398
$$268$$ −3.00000 −0.183254
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ −20.0000 −1.21491 −0.607457 0.794353i $$-0.707810\pi$$
−0.607457 + 0.794353i $$0.707810\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ 10.0000 0.604122
$$275$$ 0 0
$$276$$ −2.00000 −0.120386
$$277$$ −1.00000 −0.0600842 −0.0300421 0.999549i $$-0.509564\pi$$
−0.0300421 + 0.999549i $$0.509564\pi$$
$$278$$ 13.0000 0.779688
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 6.00000 0.357295
$$283$$ −13.0000 −0.772770 −0.386385 0.922338i $$-0.626276\pi$$
−0.386385 + 0.922338i $$0.626276\pi$$
$$284$$ 16.0000 0.949425
$$285$$ 0 0
$$286$$ −4.00000 −0.236525
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 17.0000 0.996558
$$292$$ 11.0000 0.643726
$$293$$ −12.0000 −0.701047 −0.350524 0.936554i $$-0.613996\pi$$
−0.350524 + 0.936554i $$0.613996\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 3.00000 0.174371
$$297$$ 4.00000 0.232104
$$298$$ 16.0000 0.926855
$$299$$ −2.00000 −0.115663
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −19.0000 −1.09333
$$303$$ −12.0000 −0.689382
$$304$$ 1.00000 0.0573539
$$305$$ 0 0
$$306$$ 2.00000 0.114332
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ 7.00000 0.398216
$$310$$ 0 0
$$311$$ −14.0000 −0.793867 −0.396934 0.917847i $$-0.629926\pi$$
−0.396934 + 0.917847i $$0.629926\pi$$
$$312$$ −1.00000 −0.0566139
$$313$$ 18.0000 1.01742 0.508710 0.860938i $$-0.330123\pi$$
0.508710 + 0.860938i $$0.330123\pi$$
$$314$$ −21.0000 −1.18510
$$315$$ 0 0
$$316$$ 13.0000 0.731307
$$317$$ −22.0000 −1.23564 −0.617822 0.786318i $$-0.711985\pi$$
−0.617822 + 0.786318i $$0.711985\pi$$
$$318$$ −2.00000 −0.112154
$$319$$ −16.0000 −0.895828
$$320$$ 0 0
$$321$$ 6.00000 0.334887
$$322$$ 0 0
$$323$$ −2.00000 −0.111283
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 23.0000 1.27385
$$327$$ 19.0000 1.05070
$$328$$ −12.0000 −0.662589
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 21.0000 1.15426 0.577132 0.816651i $$-0.304172\pi$$
0.577132 + 0.816651i $$0.304172\pi$$
$$332$$ 6.00000 0.329293
$$333$$ −3.00000 −0.164399
$$334$$ 10.0000 0.547176
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 12.0000 0.652714
$$339$$ 18.0000 0.977626
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −1.00000 −0.0540738
$$343$$ 0 0
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ 22.0000 1.18102 0.590511 0.807030i $$-0.298926\pi$$
0.590511 + 0.807030i $$0.298926\pi$$
$$348$$ −4.00000 −0.214423
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ 4.00000 0.213201
$$353$$ 20.0000 1.06449 0.532246 0.846590i $$-0.321348\pi$$
0.532246 + 0.846590i $$0.321348\pi$$
$$354$$ 6.00000 0.318896
$$355$$ 0 0
$$356$$ −2.00000 −0.106000
$$357$$ 0 0
$$358$$ 8.00000 0.422813
$$359$$ −6.00000 −0.316668 −0.158334 0.987386i $$-0.550612\pi$$
−0.158334 + 0.987386i $$0.550612\pi$$
$$360$$ 0 0
$$361$$ −18.0000 −0.947368
$$362$$ 18.0000 0.946059
$$363$$ −5.00000 −0.262432
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −13.0000 −0.679521
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 2.00000 0.104257
$$369$$ 12.0000 0.624695
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −23.0000 −1.19089 −0.595447 0.803394i $$-0.703025\pi$$
−0.595447 + 0.803394i $$0.703025\pi$$
$$374$$ −8.00000 −0.413670
$$375$$ 0 0
$$376$$ −6.00000 −0.309426
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ −5.00000 −0.256833 −0.128416 0.991720i $$-0.540989\pi$$
−0.128416 + 0.991720i $$0.540989\pi$$
$$380$$ 0 0
$$381$$ −1.00000 −0.0512316
$$382$$ −20.0000 −1.02329
$$383$$ 14.0000 0.715367 0.357683 0.933843i $$-0.383567\pi$$
0.357683 + 0.933843i $$0.383567\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ −10.0000 −0.508987
$$387$$ −8.00000 −0.406663
$$388$$ −17.0000 −0.863044
$$389$$ −20.0000 −1.01404 −0.507020 0.861934i $$-0.669253\pi$$
−0.507020 + 0.861934i $$0.669253\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ 0 0
$$393$$ −2.00000 −0.100887
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −4.00000 −0.201008
$$397$$ 18.0000 0.903394 0.451697 0.892171i $$-0.350819\pi$$
0.451697 + 0.892171i $$0.350819\pi$$
$$398$$ −15.0000 −0.751882
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 4.00000 0.199750 0.0998752 0.995000i $$-0.468156\pi$$
0.0998752 + 0.995000i $$0.468156\pi$$
$$402$$ −3.00000 −0.149626
$$403$$ 0 0
$$404$$ 12.0000 0.597022
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 12.0000 0.594818
$$408$$ −2.00000 −0.0990148
$$409$$ −11.0000 −0.543915 −0.271957 0.962309i $$-0.587671\pi$$
−0.271957 + 0.962309i $$0.587671\pi$$
$$410$$ 0 0
$$411$$ 10.0000 0.493264
$$412$$ −7.00000 −0.344865
$$413$$ 0 0
$$414$$ −2.00000 −0.0982946
$$415$$ 0 0
$$416$$ 1.00000 0.0490290
$$417$$ 13.0000 0.636613
$$418$$ 4.00000 0.195646
$$419$$ −16.0000 −0.781651 −0.390826 0.920465i $$-0.627810\pi$$
−0.390826 + 0.920465i $$0.627810\pi$$
$$420$$ 0 0
$$421$$ 1.00000 0.0487370 0.0243685 0.999703i $$-0.492242\pi$$
0.0243685 + 0.999703i $$0.492242\pi$$
$$422$$ −3.00000 −0.146038
$$423$$ 6.00000 0.291730
$$424$$ 2.00000 0.0971286
$$425$$ 0 0
$$426$$ 16.0000 0.775203
$$427$$ 0 0
$$428$$ −6.00000 −0.290021
$$429$$ −4.00000 −0.193122
$$430$$ 0 0
$$431$$ 6.00000 0.289010 0.144505 0.989504i $$-0.453841\pi$$
0.144505 + 0.989504i $$0.453841\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −19.0000 −0.909935
$$437$$ 2.00000 0.0956730
$$438$$ 11.0000 0.525600
$$439$$ −23.0000 −1.09773 −0.548865 0.835911i $$-0.684940\pi$$
−0.548865 + 0.835911i $$0.684940\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −2.00000 −0.0951303
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ 3.00000 0.142374
$$445$$ 0 0
$$446$$ −19.0000 −0.899676
$$447$$ 16.0000 0.756774
$$448$$ 0 0
$$449$$ 2.00000 0.0943858 0.0471929 0.998886i $$-0.484972\pi$$
0.0471929 + 0.998886i $$0.484972\pi$$
$$450$$ 0 0
$$451$$ −48.0000 −2.26023
$$452$$ −18.0000 −0.846649
$$453$$ −19.0000 −0.892698
$$454$$ −8.00000 −0.375459
$$455$$ 0 0
$$456$$ 1.00000 0.0468293
$$457$$ −37.0000 −1.73079 −0.865393 0.501093i $$-0.832931\pi$$
−0.865393 + 0.501093i $$0.832931\pi$$
$$458$$ 7.00000 0.327089
$$459$$ 2.00000 0.0933520
$$460$$ 0 0
$$461$$ 26.0000 1.21094 0.605470 0.795868i $$-0.292985\pi$$
0.605470 + 0.795868i $$0.292985\pi$$
$$462$$ 0 0
$$463$$ 3.00000 0.139422 0.0697109 0.997567i $$-0.477792\pi$$
0.0697109 + 0.997567i $$0.477792\pi$$
$$464$$ 4.00000 0.185695
$$465$$ 0 0
$$466$$ −4.00000 −0.185296
$$467$$ −30.0000 −1.38823 −0.694117 0.719862i $$-0.744205\pi$$
−0.694117 + 0.719862i $$0.744205\pi$$
$$468$$ −1.00000 −0.0462250
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −21.0000 −0.967629
$$472$$ −6.00000 −0.276172
$$473$$ 32.0000 1.47136
$$474$$ 13.0000 0.597110
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −2.00000 −0.0915737
$$478$$ 12.0000 0.548867
$$479$$ −34.0000 −1.55350 −0.776750 0.629809i $$-0.783133\pi$$
−0.776750 + 0.629809i $$0.783133\pi$$
$$480$$ 0 0
$$481$$ 3.00000 0.136788
$$482$$ −13.0000 −0.592134
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ −40.0000 −1.81257 −0.906287 0.422664i $$-0.861095\pi$$
−0.906287 + 0.422664i $$0.861095\pi$$
$$488$$ 13.0000 0.588482
$$489$$ 23.0000 1.04010
$$490$$ 0 0
$$491$$ 18.0000 0.812329 0.406164 0.913800i $$-0.366866\pi$$
0.406164 + 0.913800i $$0.366866\pi$$
$$492$$ −12.0000 −0.541002
$$493$$ −8.00000 −0.360302
$$494$$ 1.00000 0.0449921
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 6.00000 0.268866
$$499$$ −27.0000 −1.20869 −0.604343 0.796724i $$-0.706564\pi$$
−0.604343 + 0.796724i $$0.706564\pi$$
$$500$$ 0 0
$$501$$ 10.0000 0.446767
$$502$$ −24.0000 −1.07117
$$503$$ −4.00000 −0.178351 −0.0891756 0.996016i $$-0.528423\pi$$
−0.0891756 + 0.996016i $$0.528423\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 8.00000 0.355643
$$507$$ 12.0000 0.532939
$$508$$ 1.00000 0.0443678
$$509$$ −36.0000 −1.59567 −0.797836 0.602875i $$-0.794022\pi$$
−0.797836 + 0.602875i $$0.794022\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ −1.00000 −0.0441511
$$514$$ −8.00000 −0.352865
$$515$$ 0 0
$$516$$ 8.00000 0.352180
$$517$$ −24.0000 −1.05552
$$518$$ 0 0
$$519$$ −6.00000 −0.263371
$$520$$ 0 0
$$521$$ 6.00000 0.262865 0.131432 0.991325i $$-0.458042\pi$$
0.131432 + 0.991325i $$0.458042\pi$$
$$522$$ −4.00000 −0.175075
$$523$$ −16.0000 −0.699631 −0.349816 0.936819i $$-0.613756\pi$$
−0.349816 + 0.936819i $$0.613756\pi$$
$$524$$ 2.00000 0.0873704
$$525$$ 0 0
$$526$$ 32.0000 1.39527
$$527$$ 0 0
$$528$$ 4.00000 0.174078
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 6.00000 0.260378
$$532$$ 0 0
$$533$$ −12.0000 −0.519778
$$534$$ −2.00000 −0.0865485
$$535$$ 0 0
$$536$$ 3.00000 0.129580
$$537$$ 8.00000 0.345225
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 17.0000 0.730887 0.365444 0.930834i $$-0.380917\pi$$
0.365444 + 0.930834i $$0.380917\pi$$
$$542$$ 20.0000 0.859074
$$543$$ 18.0000 0.772454
$$544$$ 2.00000 0.0857493
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ −10.0000 −0.427179
$$549$$ −13.0000 −0.554826
$$550$$ 0 0
$$551$$ 4.00000 0.170406
$$552$$ 2.00000 0.0851257
$$553$$ 0 0
$$554$$ 1.00000 0.0424859
$$555$$ 0 0
$$556$$ −13.0000 −0.551323
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ −8.00000 −0.337760
$$562$$ 18.0000 0.759284
$$563$$ 28.0000 1.18006 0.590030 0.807382i $$-0.299116\pi$$
0.590030 + 0.807382i $$0.299116\pi$$
$$564$$ −6.00000 −0.252646
$$565$$ 0 0
$$566$$ 13.0000 0.546431
$$567$$ 0 0
$$568$$ −16.0000 −0.671345
$$569$$ −40.0000 −1.67689 −0.838444 0.544988i $$-0.816534\pi$$
−0.838444 + 0.544988i $$0.816534\pi$$
$$570$$ 0 0
$$571$$ −35.0000 −1.46470 −0.732352 0.680926i $$-0.761578\pi$$
−0.732352 + 0.680926i $$0.761578\pi$$
$$572$$ 4.00000 0.167248
$$573$$ −20.0000 −0.835512
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 0.0416667
$$577$$ −22.0000 −0.915872 −0.457936 0.888985i $$-0.651411\pi$$
−0.457936 + 0.888985i $$0.651411\pi$$
$$578$$ 13.0000 0.540729
$$579$$ −10.0000 −0.415586
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −17.0000 −0.704673
$$583$$ 8.00000 0.331326
$$584$$ −11.0000 −0.455183
$$585$$ 0 0
$$586$$ 12.0000 0.495715
$$587$$ 42.0000 1.73353 0.866763 0.498721i $$-0.166197\pi$$
0.866763 + 0.498721i $$0.166197\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −3.00000 −0.123299
$$593$$ −42.0000 −1.72473 −0.862367 0.506284i $$-0.831019\pi$$
−0.862367 + 0.506284i $$0.831019\pi$$
$$594$$ −4.00000 −0.164122
$$595$$ 0 0
$$596$$ −16.0000 −0.655386
$$597$$ −15.0000 −0.613909
$$598$$ 2.00000 0.0817861
$$599$$ −6.00000 −0.245153 −0.122577 0.992459i $$-0.539116\pi$$
−0.122577 + 0.992459i $$0.539116\pi$$
$$600$$ 0 0
$$601$$ −29.0000 −1.18293 −0.591467 0.806329i $$-0.701451\pi$$
−0.591467 + 0.806329i $$0.701451\pi$$
$$602$$ 0 0
$$603$$ −3.00000 −0.122169
$$604$$ 19.0000 0.773099
$$605$$ 0 0
$$606$$ 12.0000 0.487467
$$607$$ −1.00000 −0.0405887 −0.0202944 0.999794i $$-0.506460\pi$$
−0.0202944 + 0.999794i $$0.506460\pi$$
$$608$$ −1.00000 −0.0405554
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −6.00000 −0.242734
$$612$$ −2.00000 −0.0808452
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ 20.0000 0.807134
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −44.0000 −1.77137 −0.885687 0.464283i $$-0.846312\pi$$
−0.885687 + 0.464283i $$0.846312\pi$$
$$618$$ −7.00000 −0.281581
$$619$$ 44.0000 1.76851 0.884255 0.467005i $$-0.154667\pi$$
0.884255 + 0.467005i $$0.154667\pi$$
$$620$$ 0 0
$$621$$ −2.00000 −0.0802572
$$622$$ 14.0000 0.561349
$$623$$ 0 0
$$624$$ 1.00000 0.0400320
$$625$$ 0 0
$$626$$ −18.0000 −0.719425
$$627$$ 4.00000 0.159745
$$628$$ 21.0000 0.837991
$$629$$ 6.00000 0.239236
$$630$$ 0 0
$$631$$ 17.0000 0.676759 0.338380 0.941010i $$-0.390121\pi$$
0.338380 + 0.941010i $$0.390121\pi$$
$$632$$ −13.0000 −0.517112
$$633$$ −3.00000 −0.119239
$$634$$ 22.0000 0.873732
$$635$$ 0 0
$$636$$ 2.00000 0.0793052
$$637$$ 0 0
$$638$$ 16.0000 0.633446
$$639$$ 16.0000 0.632950
$$640$$ 0 0
$$641$$ 16.0000 0.631962 0.315981 0.948766i $$-0.397666\pi$$
0.315981 + 0.948766i $$0.397666\pi$$
$$642$$ −6.00000 −0.236801
$$643$$ −11.0000 −0.433798 −0.216899 0.976194i $$-0.569594\pi$$
−0.216899 + 0.976194i $$0.569594\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 2.00000 0.0786889
$$647$$ −12.0000 −0.471769 −0.235884 0.971781i $$-0.575799\pi$$
−0.235884 + 0.971781i $$0.575799\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ −24.0000 −0.942082
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −23.0000 −0.900750
$$653$$ 16.0000 0.626128 0.313064 0.949732i $$-0.398644\pi$$
0.313064 + 0.949732i $$0.398644\pi$$
$$654$$ −19.0000 −0.742959
$$655$$ 0 0
$$656$$ 12.0000 0.468521
$$657$$ 11.0000 0.429151
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ −25.0000 −0.972387 −0.486194 0.873851i $$-0.661615\pi$$
−0.486194 + 0.873851i $$0.661615\pi$$
$$662$$ −21.0000 −0.816188
$$663$$ −2.00000 −0.0776736
$$664$$ −6.00000 −0.232845
$$665$$ 0 0
$$666$$ 3.00000 0.116248
$$667$$ 8.00000 0.309761
$$668$$ −10.0000 −0.386912
$$669$$ −19.0000 −0.734582
$$670$$ 0 0
$$671$$ 52.0000 2.00744
$$672$$ 0 0
$$673$$ 9.00000 0.346925 0.173462 0.984841i $$-0.444505\pi$$
0.173462 + 0.984841i $$0.444505\pi$$
$$674$$ −18.0000 −0.693334
$$675$$ 0 0
$$676$$ −12.0000 −0.461538
$$677$$ 2.00000 0.0768662 0.0384331 0.999261i $$-0.487763\pi$$
0.0384331 + 0.999261i $$0.487763\pi$$
$$678$$ −18.0000 −0.691286
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −8.00000 −0.306561
$$682$$ 0 0
$$683$$ −48.0000 −1.83667 −0.918334 0.395805i $$-0.870466\pi$$
−0.918334 + 0.395805i $$0.870466\pi$$
$$684$$ 1.00000 0.0382360
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 7.00000 0.267067
$$688$$ −8.00000 −0.304997
$$689$$ 2.00000 0.0761939
$$690$$ 0 0
$$691$$ −39.0000 −1.48363 −0.741815 0.670605i $$-0.766035\pi$$
−0.741815 + 0.670605i $$0.766035\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ −22.0000 −0.835109
$$695$$ 0 0
$$696$$ 4.00000 0.151620
$$697$$ −24.0000 −0.909065
$$698$$ −2.00000 −0.0757011
$$699$$ −4.00000 −0.151294
$$700$$ 0 0
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ −1.00000 −0.0377426
$$703$$ −3.00000 −0.113147
$$704$$ −4.00000 −0.150756
$$705$$ 0 0
$$706$$ −20.0000 −0.752710
$$707$$ 0 0
$$708$$ −6.00000 −0.225494
$$709$$ −11.0000 −0.413114 −0.206557 0.978435i $$-0.566226\pi$$
−0.206557 + 0.978435i $$0.566226\pi$$
$$710$$ 0 0
$$711$$ 13.0000 0.487538
$$712$$ 2.00000 0.0749532
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −8.00000 −0.298974
$$717$$ 12.0000 0.448148
$$718$$ 6.00000 0.223918
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 18.0000 0.669891
$$723$$ −13.0000 −0.483475
$$724$$ −18.0000 −0.668965
$$725$$ 0 0
$$726$$ 5.00000 0.185567
$$727$$ 1.00000 0.0370879 0.0185440 0.999828i $$-0.494097\pi$$
0.0185440 + 0.999828i $$0.494097\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 16.0000 0.591781
$$732$$ 13.0000 0.480494
$$733$$ 35.0000 1.29275 0.646377 0.763018i $$-0.276283\pi$$
0.646377 + 0.763018i $$0.276283\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ −2.00000 −0.0737210
$$737$$ 12.0000 0.442026
$$738$$ −12.0000 −0.441726
$$739$$ −1.00000 −0.0367856 −0.0183928 0.999831i $$-0.505855\pi$$
−0.0183928 + 0.999831i $$0.505855\pi$$
$$740$$ 0 0
$$741$$ 1.00000 0.0367359
$$742$$ 0 0
$$743$$ 6.00000 0.220119 0.110059 0.993925i $$-0.464896\pi$$
0.110059 + 0.993925i $$0.464896\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 23.0000 0.842090
$$747$$ 6.00000 0.219529
$$748$$ 8.00000 0.292509
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 19.0000 0.693320 0.346660 0.937991i $$-0.387316\pi$$
0.346660 + 0.937991i $$0.387316\pi$$
$$752$$ 6.00000 0.218797
$$753$$ −24.0000 −0.874609
$$754$$ 4.00000 0.145671
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −1.00000 −0.0363456 −0.0181728 0.999835i $$-0.505785\pi$$
−0.0181728 + 0.999835i $$0.505785\pi$$
$$758$$ 5.00000 0.181608
$$759$$ 8.00000 0.290382
$$760$$ 0 0
$$761$$ 34.0000 1.23250 0.616250 0.787551i $$-0.288651\pi$$
0.616250 + 0.787551i $$0.288651\pi$$
$$762$$ 1.00000 0.0362262
$$763$$ 0 0
$$764$$ 20.0000 0.723575
$$765$$ 0 0
$$766$$ −14.0000 −0.505841
$$767$$ −6.00000 −0.216647
$$768$$ −1.00000 −0.0360844
$$769$$ −50.0000 −1.80305 −0.901523 0.432731i $$-0.857550\pi$$
−0.901523 + 0.432731i $$0.857550\pi$$
$$770$$ 0 0
$$771$$ −8.00000 −0.288113
$$772$$ 10.0000 0.359908
$$773$$ 32.0000 1.15096 0.575480 0.817816i $$-0.304815\pi$$
0.575480 + 0.817816i $$0.304815\pi$$
$$774$$ 8.00000 0.287554
$$775$$ 0 0
$$776$$ 17.0000 0.610264
$$777$$ 0 0
$$778$$ 20.0000 0.717035
$$779$$ 12.0000 0.429945
$$780$$ 0 0
$$781$$ −64.0000 −2.29010
$$782$$ 4.00000 0.143040
$$783$$ −4.00000 −0.142948
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 2.00000 0.0713376
$$787$$ −23.0000 −0.819861 −0.409931 0.912117i $$-0.634447\pi$$
−0.409931 + 0.912117i $$0.634447\pi$$
$$788$$ 0 0
$$789$$ 32.0000 1.13923
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 4.00000 0.142134
$$793$$ 13.0000 0.461644
$$794$$ −18.0000 −0.638796
$$795$$ 0 0
$$796$$ 15.0000 0.531661
$$797$$ −42.0000 −1.48772 −0.743858 0.668338i $$-0.767006\pi$$
−0.743858 + 0.668338i $$0.767006\pi$$
$$798$$ 0 0
$$799$$ −12.0000 −0.424529
$$800$$ 0 0
$$801$$ −2.00000 −0.0706665
$$802$$ −4.00000 −0.141245
$$803$$ −44.0000 −1.55273
$$804$$ 3.00000 0.105802
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −12.0000 −0.422159
$$809$$ 14.0000 0.492214 0.246107 0.969243i $$-0.420849\pi$$
0.246107 + 0.969243i $$0.420849\pi$$
$$810$$ 0 0
$$811$$ −5.00000 −0.175574 −0.0877869 0.996139i $$-0.527979\pi$$
−0.0877869 + 0.996139i $$0.527979\pi$$
$$812$$ 0 0
$$813$$ 20.0000 0.701431
$$814$$ −12.0000 −0.420600
$$815$$ 0 0
$$816$$ 2.00000 0.0700140
$$817$$ −8.00000 −0.279885
$$818$$ 11.0000 0.384606
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −44.0000 −1.53561 −0.767805 0.640683i $$-0.778651\pi$$
−0.767805 + 0.640683i $$0.778651\pi$$
$$822$$ −10.0000 −0.348790
$$823$$ −9.00000 −0.313720 −0.156860 0.987621i $$-0.550137\pi$$
−0.156860 + 0.987621i $$0.550137\pi$$
$$824$$ 7.00000 0.243857
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −40.0000 −1.39094 −0.695468 0.718557i $$-0.744803\pi$$
−0.695468 + 0.718557i $$0.744803\pi$$
$$828$$ 2.00000 0.0695048
$$829$$ −3.00000 −0.104194 −0.0520972 0.998642i $$-0.516591\pi$$
−0.0520972 + 0.998642i $$0.516591\pi$$
$$830$$ 0 0
$$831$$ 1.00000 0.0346896
$$832$$ −1.00000 −0.0346688
$$833$$ 0 0
$$834$$ −13.0000 −0.450153
$$835$$ 0 0
$$836$$ −4.00000 −0.138343
$$837$$ 0 0
$$838$$ 16.0000 0.552711
$$839$$ 50.0000 1.72619 0.863096 0.505040i $$-0.168522\pi$$
0.863096 + 0.505040i $$0.168522\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ −1.00000 −0.0344623
$$843$$ 18.0000 0.619953
$$844$$ 3.00000 0.103264
$$845$$ 0 0
$$846$$ −6.00000 −0.206284
$$847$$ 0 0
$$848$$ −2.00000 −0.0686803
$$849$$ 13.0000 0.446159
$$850$$ 0 0
$$851$$ −6.00000 −0.205677
$$852$$ −16.0000 −0.548151
$$853$$ 38.0000 1.30110 0.650548 0.759465i $$-0.274539\pi$$
0.650548 + 0.759465i $$0.274539\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 6.00000 0.205076
$$857$$ −26.0000 −0.888143 −0.444072 0.895991i $$-0.646466\pi$$
−0.444072 + 0.895991i $$0.646466\pi$$
$$858$$ 4.00000 0.136558
$$859$$ 4.00000 0.136478 0.0682391 0.997669i $$-0.478262\pi$$
0.0682391 + 0.997669i $$0.478262\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −6.00000 −0.204361
$$863$$ 34.0000 1.15737 0.578687 0.815550i $$-0.303565\pi$$
0.578687 + 0.815550i $$0.303565\pi$$
$$864$$ 1.00000 0.0340207
$$865$$ 0 0
$$866$$ −2.00000 −0.0679628
$$867$$ 13.0000 0.441503
$$868$$ 0 0
$$869$$ −52.0000 −1.76398
$$870$$ 0 0
$$871$$ 3.00000 0.101651
$$872$$ 19.0000 0.643421
$$873$$ −17.0000 −0.575363
$$874$$ −2.00000 −0.0676510
$$875$$ 0 0
$$876$$ −11.0000 −0.371656
$$877$$ 13.0000 0.438979 0.219489 0.975615i $$-0.429561\pi$$
0.219489 + 0.975615i $$0.429561\pi$$
$$878$$ 23.0000 0.776212
$$879$$ 12.0000 0.404750
$$880$$ 0 0
$$881$$ −40.0000 −1.34763 −0.673817 0.738898i $$-0.735346\pi$$
−0.673817 + 0.738898i $$0.735346\pi$$
$$882$$ 0 0
$$883$$ 1.00000 0.0336527 0.0168263 0.999858i $$-0.494644\pi$$
0.0168263 + 0.999858i $$0.494644\pi$$
$$884$$ 2.00000 0.0672673
$$885$$ 0 0
$$886$$ 6.00000 0.201574
$$887$$ 46.0000 1.54453 0.772264 0.635301i $$-0.219124\pi$$
0.772264 + 0.635301i $$0.219124\pi$$
$$888$$ −3.00000 −0.100673
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −4.00000 −0.134005
$$892$$ 19.0000 0.636167
$$893$$ 6.00000 0.200782
$$894$$ −16.0000 −0.535120
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 2.00000 0.0667781
$$898$$ −2.00000 −0.0667409
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 4.00000 0.133259
$$902$$ 48.0000 1.59823
$$903$$ 0 0
$$904$$ 18.0000 0.598671
$$905$$ 0 0
$$906$$ 19.0000 0.631233
$$907$$ 47.0000 1.56061 0.780305 0.625400i $$-0.215064\pi$$
0.780305 + 0.625400i $$0.215064\pi$$
$$908$$ 8.00000 0.265489
$$909$$ 12.0000 0.398015
$$910$$ 0 0
$$911$$ −46.0000 −1.52405 −0.762024 0.647549i $$-0.775794\pi$$
−0.762024 + 0.647549i $$0.775794\pi$$
$$912$$ −1.00000 −0.0331133
$$913$$ −24.0000 −0.794284
$$914$$ 37.0000 1.22385
$$915$$ 0 0
$$916$$ −7.00000 −0.231287
$$917$$ 0 0
$$918$$ −2.00000 −0.0660098
$$919$$ 16.0000 0.527791 0.263896 0.964551i $$-0.414993\pi$$
0.263896 + 0.964551i $$0.414993\pi$$
$$920$$ 0 0
$$921$$ 20.0000 0.659022
$$922$$ −26.0000 −0.856264
$$923$$ −16.0000 −0.526646
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −3.00000 −0.0985861
$$927$$ −7.00000 −0.229910
$$928$$ −4.00000 −0.131306
$$929$$ −20.0000 −0.656179 −0.328089 0.944647i $$-0.606405\pi$$
−0.328089 + 0.944647i $$0.606405\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 4.00000 0.131024
$$933$$ 14.0000 0.458339
$$934$$ 30.0000 0.981630
$$935$$ 0 0
$$936$$ 1.00000 0.0326860
$$937$$ −46.0000 −1.50275 −0.751377 0.659873i $$-0.770610\pi$$
−0.751377 + 0.659873i $$0.770610\pi$$
$$938$$ 0 0
$$939$$ −18.0000 −0.587408
$$940$$ 0 0
$$941$$ 42.0000 1.36916 0.684580 0.728937i $$-0.259985\pi$$
0.684580 + 0.728937i $$0.259985\pi$$
$$942$$ 21.0000 0.684217
$$943$$ 24.0000 0.781548
$$944$$ 6.00000 0.195283
$$945$$ 0 0
$$946$$ −32.0000 −1.04041
$$947$$ 38.0000 1.23483 0.617417 0.786636i $$-0.288179\pi$$
0.617417 + 0.786636i $$0.288179\pi$$
$$948$$ −13.0000 −0.422220
$$949$$ −11.0000 −0.357075
$$950$$ 0 0
$$951$$ 22.0000 0.713399
$$952$$ 0 0
$$953$$ 4.00000 0.129573 0.0647864 0.997899i $$-0.479363\pi$$
0.0647864 + 0.997899i $$0.479363\pi$$
$$954$$ 2.00000 0.0647524
$$955$$ 0 0
$$956$$ −12.0000 −0.388108
$$957$$ 16.0000 0.517207
$$958$$ 34.0000 1.09849
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ −3.00000 −0.0967239
$$963$$ −6.00000 −0.193347
$$964$$ 13.0000 0.418702
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 11.0000 0.353736 0.176868 0.984235i $$-0.443403\pi$$
0.176868 + 0.984235i $$0.443403\pi$$
$$968$$ −5.00000 −0.160706
$$969$$ 2.00000 0.0642493
$$970$$ 0 0
$$971$$ 16.0000 0.513464 0.256732 0.966483i $$-0.417354\pi$$
0.256732 + 0.966483i $$0.417354\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ 40.0000 1.28168
$$975$$ 0 0
$$976$$ −13.0000 −0.416120
$$977$$ 48.0000 1.53566 0.767828 0.640656i $$-0.221338\pi$$
0.767828 + 0.640656i $$0.221338\pi$$
$$978$$ −23.0000 −0.735459
$$979$$ 8.00000 0.255681
$$980$$ 0 0
$$981$$ −19.0000 −0.606623
$$982$$ −18.0000 −0.574403
$$983$$ −42.0000 −1.33959 −0.669796 0.742545i $$-0.733618\pi$$
−0.669796 + 0.742545i $$0.733618\pi$$
$$984$$ 12.0000 0.382546
$$985$$ 0 0
$$986$$ 8.00000 0.254772
$$987$$ 0 0
$$988$$ −1.00000 −0.0318142
$$989$$ −16.0000 −0.508770
$$990$$ 0 0
$$991$$ −8.00000 −0.254128 −0.127064 0.991894i $$-0.540555\pi$$
−0.127064 + 0.991894i $$0.540555\pi$$
$$992$$ 0 0
$$993$$ −21.0000 −0.666415
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −6.00000 −0.190117
$$997$$ −31.0000 −0.981780 −0.490890 0.871222i $$-0.663328\pi$$
−0.490890 + 0.871222i $$0.663328\pi$$
$$998$$ 27.0000 0.854670
$$999$$ 3.00000 0.0949158
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.c.1.1 1
5.4 even 2 7350.2.a.cl.1.1 1
7.2 even 3 1050.2.i.t.151.1 yes 2
7.4 even 3 1050.2.i.t.751.1 yes 2
7.6 odd 2 7350.2.a.y.1.1 1
35.2 odd 12 1050.2.o.k.949.1 4
35.4 even 6 1050.2.i.a.751.1 yes 2
35.9 even 6 1050.2.i.a.151.1 2
35.18 odd 12 1050.2.o.k.499.1 4
35.23 odd 12 1050.2.o.k.949.2 4
35.32 odd 12 1050.2.o.k.499.2 4
35.34 odd 2 7350.2.a.bp.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.a.151.1 2 35.9 even 6
1050.2.i.a.751.1 yes 2 35.4 even 6
1050.2.i.t.151.1 yes 2 7.2 even 3
1050.2.i.t.751.1 yes 2 7.4 even 3
1050.2.o.k.499.1 4 35.18 odd 12
1050.2.o.k.499.2 4 35.32 odd 12
1050.2.o.k.949.1 4 35.2 odd 12
1050.2.o.k.949.2 4 35.23 odd 12
7350.2.a.c.1.1 1 1.1 even 1 trivial
7350.2.a.y.1.1 1 7.6 odd 2
7350.2.a.bp.1.1 1 35.34 odd 2
7350.2.a.cl.1.1 1 5.4 even 2