# Properties

 Label 7605.2.a.q.1.1 Level $7605$ Weight $2$ Character 7605.1 Self dual yes Analytic conductor $60.726$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$7605 = 3^{2} \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7605.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$60.7262307372$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 585) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7605.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{7} -3.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{7} -3.00000 q^{8} +1.00000 q^{10} +4.00000 q^{11} -2.00000 q^{14} -1.00000 q^{16} -4.00000 q^{17} -6.00000 q^{19} -1.00000 q^{20} +4.00000 q^{22} +1.00000 q^{25} +2.00000 q^{28} -4.00000 q^{29} +10.0000 q^{31} +5.00000 q^{32} -4.00000 q^{34} -2.00000 q^{35} +2.00000 q^{37} -6.00000 q^{38} -3.00000 q^{40} +6.00000 q^{41} -8.00000 q^{43} -4.00000 q^{44} +8.00000 q^{47} -3.00000 q^{49} +1.00000 q^{50} -4.00000 q^{53} +4.00000 q^{55} +6.00000 q^{56} -4.00000 q^{58} -12.0000 q^{59} +2.00000 q^{61} +10.0000 q^{62} +7.00000 q^{64} +10.0000 q^{67} +4.00000 q^{68} -2.00000 q^{70} +6.00000 q^{73} +2.00000 q^{74} +6.00000 q^{76} -8.00000 q^{77} +12.0000 q^{79} -1.00000 q^{80} +6.00000 q^{82} +4.00000 q^{83} -4.00000 q^{85} -8.00000 q^{86} -12.0000 q^{88} -14.0000 q^{89} +8.00000 q^{94} -6.00000 q^{95} +14.0000 q^{97} -3.00000 q^{98} +O(q^{100})$$

## 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 0.353553 0.935414i $$-0.384973\pi$$
0.353553 + 0.935414i $$0.384973\pi$$
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ −3.00000 −1.06066
$$9$$ 0 0
$$10$$ 1.00000 0.316228
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 0 0
$$13$$ 0 0
$$14$$ −2.00000 −0.534522
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ −4.00000 −0.970143 −0.485071 0.874475i $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ 0 0
$$19$$ −6.00000 −1.37649 −0.688247 0.725476i $$-0.741620\pi$$
−0.688247 + 0.725476i $$0.741620\pi$$
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ 4.00000 0.852803
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 2.00000 0.377964
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ 10.0000 1.79605 0.898027 0.439941i $$-0.145001\pi$$
0.898027 + 0.439941i $$0.145001\pi$$
$$32$$ 5.00000 0.883883
$$33$$ 0 0
$$34$$ −4.00000 −0.685994
$$35$$ −2.00000 −0.338062
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ −6.00000 −0.973329
$$39$$ 0 0
$$40$$ −3.00000 −0.474342
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 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
$$46$$ 0 0
$$47$$ 8.00000 1.16692 0.583460 0.812142i $$-0.301699\pi$$
0.583460 + 0.812142i $$0.301699\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −4.00000 −0.549442 −0.274721 0.961524i $$-0.588586\pi$$
−0.274721 + 0.961524i $$0.588586\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 6.00000 0.801784
$$57$$ 0 0
$$58$$ −4.00000 −0.525226
$$59$$ −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 $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 10.0000 1.27000
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 10.0000 1.22169 0.610847 0.791748i $$-0.290829\pi$$
0.610847 + 0.791748i $$0.290829\pi$$
$$68$$ 4.00000 0.485071
$$69$$ 0 0
$$70$$ −2.00000 −0.239046
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 2.00000 0.232495
$$75$$ 0 0
$$76$$ 6.00000 0.688247
$$77$$ −8.00000 −0.911685
$$78$$ 0 0
$$79$$ 12.0000 1.35011 0.675053 0.737769i $$-0.264121\pi$$
0.675053 + 0.737769i $$0.264121\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ −8.00000 −0.862662
$$87$$ 0 0
$$88$$ −12.0000 −1.27920
$$89$$ −14.0000 −1.48400 −0.741999 0.670402i $$-0.766122\pi$$
−0.741999 + 0.670402i $$0.766122\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 8.00000 0.825137
$$95$$ −6.00000 −0.615587
$$96$$ 0 0
$$97$$ 14.0000 1.42148 0.710742 0.703452i $$-0.248359\pi$$
0.710742 + 0.703452i $$0.248359\pi$$
$$98$$ −3.00000 −0.303046
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ 12.0000 1.19404 0.597022 0.802225i $$-0.296350\pi$$
0.597022 + 0.802225i $$0.296350\pi$$
$$102$$ 0 0
$$103$$ −4.00000 −0.394132 −0.197066 0.980390i $$-0.563141\pi$$
−0.197066 + 0.980390i $$0.563141\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −4.00000 −0.388514
$$107$$ 4.00000 0.386695 0.193347 0.981130i $$-0.438066\pi$$
0.193347 + 0.981130i $$0.438066\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 4.00000 0.381385
$$111$$ 0 0
$$112$$ 2.00000 0.188982
$$113$$ 16.0000 1.50515 0.752577 0.658505i $$-0.228811\pi$$
0.752577 + 0.658505i $$0.228811\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 4.00000 0.371391
$$117$$ 0 0
$$118$$ −12.0000 −1.10469
$$119$$ 8.00000 0.733359
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 2.00000 0.181071
$$123$$ 0 0
$$124$$ −10.0000 −0.898027
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ −3.00000 −0.265165
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −16.0000 −1.39793 −0.698963 0.715158i $$-0.746355\pi$$
−0.698963 + 0.715158i $$0.746355\pi$$
$$132$$ 0 0
$$133$$ 12.0000 1.04053
$$134$$ 10.0000 0.863868
$$135$$ 0 0
$$136$$ 12.0000 1.02899
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 0 0
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 2.00000 0.169031
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −4.00000 −0.332182
$$146$$ 6.00000 0.496564
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ 18.0000 1.47462 0.737309 0.675556i $$-0.236096\pi$$
0.737309 + 0.675556i $$0.236096\pi$$
$$150$$ 0 0
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ 18.0000 1.45999
$$153$$ 0 0
$$154$$ −8.00000 −0.644658
$$155$$ 10.0000 0.803219
$$156$$ 0 0
$$157$$ 18.0000 1.43656 0.718278 0.695756i $$-0.244931\pi$$
0.718278 + 0.695756i $$0.244931\pi$$
$$158$$ 12.0000 0.954669
$$159$$ 0 0
$$160$$ 5.00000 0.395285
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −6.00000 −0.469956 −0.234978 0.972001i $$-0.575502\pi$$
−0.234978 + 0.972001i $$0.575502\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ 24.0000 1.85718 0.928588 0.371113i $$-0.121024\pi$$
0.928588 + 0.371113i $$0.121024\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ −4.00000 −0.306786
$$171$$ 0 0
$$172$$ 8.00000 0.609994
$$173$$ 24.0000 1.82469 0.912343 0.409426i $$-0.134271\pi$$
0.912343 + 0.409426i $$0.134271\pi$$
$$174$$ 0 0
$$175$$ −2.00000 −0.151186
$$176$$ −4.00000 −0.301511
$$177$$ 0 0
$$178$$ −14.0000 −1.04934
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 2.00000 0.147043
$$186$$ 0 0
$$187$$ −16.0000 −1.17004
$$188$$ −8.00000 −0.583460
$$189$$ 0 0
$$190$$ −6.00000 −0.435286
$$191$$ −12.0000 −0.868290 −0.434145 0.900843i $$-0.642949\pi$$
−0.434145 + 0.900843i $$0.642949\pi$$
$$192$$ 0 0
$$193$$ 26.0000 1.87152 0.935760 0.352636i $$-0.114715\pi$$
0.935760 + 0.352636i $$0.114715\pi$$
$$194$$ 14.0000 1.00514
$$195$$ 0 0
$$196$$ 3.00000 0.214286
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ −3.00000 −0.212132
$$201$$ 0 0
$$202$$ 12.0000 0.844317
$$203$$ 8.00000 0.561490
$$204$$ 0 0
$$205$$ 6.00000 0.419058
$$206$$ −4.00000 −0.278693
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −24.0000 −1.66011
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 4.00000 0.274721
$$213$$ 0 0
$$214$$ 4.00000 0.273434
$$215$$ −8.00000 −0.545595
$$216$$ 0 0
$$217$$ −20.0000 −1.35769
$$218$$ 2.00000 0.135457
$$219$$ 0 0
$$220$$ −4.00000 −0.269680
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 14.0000 0.937509 0.468755 0.883328i $$-0.344703\pi$$
0.468755 + 0.883328i $$0.344703\pi$$
$$224$$ −10.0000 −0.668153
$$225$$ 0 0
$$226$$ 16.0000 1.06430
$$227$$ 20.0000 1.32745 0.663723 0.747978i $$-0.268975\pi$$
0.663723 + 0.747978i $$0.268975\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 12.0000 0.787839
$$233$$ −8.00000 −0.524097 −0.262049 0.965055i $$-0.584398\pi$$
−0.262049 + 0.965055i $$0.584398\pi$$
$$234$$ 0 0
$$235$$ 8.00000 0.521862
$$236$$ 12.0000 0.781133
$$237$$ 0 0
$$238$$ 8.00000 0.518563
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −22.0000 −1.41714 −0.708572 0.705638i $$-0.750660\pi$$
−0.708572 + 0.705638i $$0.750660\pi$$
$$242$$ 5.00000 0.321412
$$243$$ 0 0
$$244$$ −2.00000 −0.128037
$$245$$ −3.00000 −0.191663
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −30.0000 −1.90500
$$249$$ 0 0
$$250$$ 1.00000 0.0632456
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ 8.00000 0.499026 0.249513 0.968371i $$-0.419729\pi$$
0.249513 + 0.968371i $$0.419729\pi$$
$$258$$ 0 0
$$259$$ −4.00000 −0.248548
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −16.0000 −0.988483
$$263$$ −4.00000 −0.246651 −0.123325 0.992366i $$-0.539356\pi$$
−0.123325 + 0.992366i $$0.539356\pi$$
$$264$$ 0 0
$$265$$ −4.00000 −0.245718
$$266$$ 12.0000 0.735767
$$267$$ 0 0
$$268$$ −10.0000 −0.610847
$$269$$ 12.0000 0.731653 0.365826 0.930683i $$-0.380786\pi$$
0.365826 + 0.930683i $$0.380786\pi$$
$$270$$ 0 0
$$271$$ −14.0000 −0.850439 −0.425220 0.905090i $$-0.639803\pi$$
−0.425220 + 0.905090i $$0.639803\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ −10.0000 −0.604122
$$275$$ 4.00000 0.241209
$$276$$ 0 0
$$277$$ 10.0000 0.600842 0.300421 0.953807i $$-0.402873\pi$$
0.300421 + 0.953807i $$0.402873\pi$$
$$278$$ 12.0000 0.719712
$$279$$ 0 0
$$280$$ 6.00000 0.358569
$$281$$ 30.0000 1.78965 0.894825 0.446417i $$-0.147300\pi$$
0.894825 + 0.446417i $$0.147300\pi$$
$$282$$ 0 0
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −12.0000 −0.708338
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ −4.00000 −0.234888
$$291$$ 0 0
$$292$$ −6.00000 −0.351123
$$293$$ 2.00000 0.116841 0.0584206 0.998292i $$-0.481394\pi$$
0.0584206 + 0.998292i $$0.481394\pi$$
$$294$$ 0 0
$$295$$ −12.0000 −0.698667
$$296$$ −6.00000 −0.348743
$$297$$ 0 0
$$298$$ 18.0000 1.04271
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 16.0000 0.922225
$$302$$ −10.0000 −0.575435
$$303$$ 0 0
$$304$$ 6.00000 0.344124
$$305$$ 2.00000 0.114520
$$306$$ 0 0
$$307$$ 22.0000 1.25561 0.627803 0.778372i $$-0.283954\pi$$
0.627803 + 0.778372i $$0.283954\pi$$
$$308$$ 8.00000 0.455842
$$309$$ 0 0
$$310$$ 10.0000 0.567962
$$311$$ −4.00000 −0.226819 −0.113410 0.993548i $$-0.536177\pi$$
−0.113410 + 0.993548i $$0.536177\pi$$
$$312$$ 0 0
$$313$$ 2.00000 0.113047 0.0565233 0.998401i $$-0.481998\pi$$
0.0565233 + 0.998401i $$0.481998\pi$$
$$314$$ 18.0000 1.01580
$$315$$ 0 0
$$316$$ −12.0000 −0.675053
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ −16.0000 −0.895828
$$320$$ 7.00000 0.391312
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 24.0000 1.33540
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −6.00000 −0.332309
$$327$$ 0 0
$$328$$ −18.0000 −0.993884
$$329$$ −16.0000 −0.882109
$$330$$ 0 0
$$331$$ −18.0000 −0.989369 −0.494685 0.869072i $$-0.664716\pi$$
−0.494685 + 0.869072i $$0.664716\pi$$
$$332$$ −4.00000 −0.219529
$$333$$ 0 0
$$334$$ 24.0000 1.31322
$$335$$ 10.0000 0.546358
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 4.00000 0.216930
$$341$$ 40.0000 2.16612
$$342$$ 0 0
$$343$$ 20.0000 1.07990
$$344$$ 24.0000 1.29399
$$345$$ 0 0
$$346$$ 24.0000 1.29025
$$347$$ 32.0000 1.71785 0.858925 0.512101i $$-0.171133\pi$$
0.858925 + 0.512101i $$0.171133\pi$$
$$348$$ 0 0
$$349$$ 6.00000 0.321173 0.160586 0.987022i $$-0.448662\pi$$
0.160586 + 0.987022i $$0.448662\pi$$
$$350$$ −2.00000 −0.106904
$$351$$ 0 0
$$352$$ 20.0000 1.06600
$$353$$ 6.00000 0.319348 0.159674 0.987170i $$-0.448956\pi$$
0.159674 + 0.987170i $$0.448956\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 14.0000 0.741999
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ −10.0000 −0.525588
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 6.00000 0.314054
$$366$$ 0 0
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 2.00000 0.103975
$$371$$ 8.00000 0.415339
$$372$$ 0 0
$$373$$ 22.0000 1.13912 0.569558 0.821951i $$-0.307114\pi$$
0.569558 + 0.821951i $$0.307114\pi$$
$$374$$ −16.0000 −0.827340
$$375$$ 0 0
$$376$$ −24.0000 −1.23771
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 2.00000 0.102733 0.0513665 0.998680i $$-0.483642\pi$$
0.0513665 + 0.998680i $$0.483642\pi$$
$$380$$ 6.00000 0.307794
$$381$$ 0 0
$$382$$ −12.0000 −0.613973
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ −8.00000 −0.407718
$$386$$ 26.0000 1.32337
$$387$$ 0 0
$$388$$ −14.0000 −0.710742
$$389$$ 8.00000 0.405616 0.202808 0.979219i $$-0.434993\pi$$
0.202808 + 0.979219i $$0.434993\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 9.00000 0.454569
$$393$$ 0 0
$$394$$ −18.0000 −0.906827
$$395$$ 12.0000 0.603786
$$396$$ 0 0
$$397$$ 18.0000 0.903394 0.451697 0.892171i $$-0.350819\pi$$
0.451697 + 0.892171i $$0.350819\pi$$
$$398$$ 8.00000 0.401004
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ −22.0000 −1.09863 −0.549314 0.835616i $$-0.685111\pi$$
−0.549314 + 0.835616i $$0.685111\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −12.0000 −0.597022
$$405$$ 0 0
$$406$$ 8.00000 0.397033
$$407$$ 8.00000 0.396545
$$408$$ 0 0
$$409$$ −30.0000 −1.48340 −0.741702 0.670729i $$-0.765981\pi$$
−0.741702 + 0.670729i $$0.765981\pi$$
$$410$$ 6.00000 0.296319
$$411$$ 0 0
$$412$$ 4.00000 0.197066
$$413$$ 24.0000 1.18096
$$414$$ 0 0
$$415$$ 4.00000 0.196352
$$416$$ 0 0
$$417$$ 0 0
$$418$$ −24.0000 −1.17388
$$419$$ −16.0000 −0.781651 −0.390826 0.920465i $$-0.627810\pi$$
−0.390826 + 0.920465i $$0.627810\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 12.0000 0.582772
$$425$$ −4.00000 −0.194029
$$426$$ 0 0
$$427$$ −4.00000 −0.193574
$$428$$ −4.00000 −0.193347
$$429$$ 0 0
$$430$$ −8.00000 −0.385794
$$431$$ 40.0000 1.92673 0.963366 0.268190i $$-0.0864254\pi$$
0.963366 + 0.268190i $$0.0864254\pi$$
$$432$$ 0 0
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ −20.0000 −0.960031
$$435$$ 0 0
$$436$$ −2.00000 −0.0957826
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −36.0000 −1.71819 −0.859093 0.511819i $$-0.828972\pi$$
−0.859093 + 0.511819i $$0.828972\pi$$
$$440$$ −12.0000 −0.572078
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 20.0000 0.950229 0.475114 0.879924i $$-0.342407\pi$$
0.475114 + 0.879924i $$0.342407\pi$$
$$444$$ 0 0
$$445$$ −14.0000 −0.663664
$$446$$ 14.0000 0.662919
$$447$$ 0 0
$$448$$ −14.0000 −0.661438
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 24.0000 1.13012
$$452$$ −16.0000 −0.752577
$$453$$ 0 0
$$454$$ 20.0000 0.938647
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 10.0000 0.467269
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 14.0000 0.652045 0.326023 0.945362i $$-0.394291\pi$$
0.326023 + 0.945362i $$0.394291\pi$$
$$462$$ 0 0
$$463$$ −18.0000 −0.836531 −0.418265 0.908325i $$-0.637362\pi$$
−0.418265 + 0.908325i $$0.637362\pi$$
$$464$$ 4.00000 0.185695
$$465$$ 0 0
$$466$$ −8.00000 −0.370593
$$467$$ 8.00000 0.370196 0.185098 0.982720i $$-0.440740\pi$$
0.185098 + 0.982720i $$0.440740\pi$$
$$468$$ 0 0
$$469$$ −20.0000 −0.923514
$$470$$ 8.00000 0.369012
$$471$$ 0 0
$$472$$ 36.0000 1.65703
$$473$$ −32.0000 −1.47136
$$474$$ 0 0
$$475$$ −6.00000 −0.275299
$$476$$ −8.00000 −0.366679
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −22.0000 −1.00207
$$483$$ 0 0
$$484$$ −5.00000 −0.227273
$$485$$ 14.0000 0.635707
$$486$$ 0 0
$$487$$ 22.0000 0.996915 0.498458 0.866914i $$-0.333900\pi$$
0.498458 + 0.866914i $$0.333900\pi$$
$$488$$ −6.00000 −0.271607
$$489$$ 0 0
$$490$$ −3.00000 −0.135526
$$491$$ 36.0000 1.62466 0.812329 0.583200i $$-0.198200\pi$$
0.812329 + 0.583200i $$0.198200\pi$$
$$492$$ 0 0
$$493$$ 16.0000 0.720604
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −10.0000 −0.449013
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 38.0000 1.70111 0.850557 0.525883i $$-0.176265\pi$$
0.850557 + 0.525883i $$0.176265\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 0 0
$$502$$ 12.0000 0.535586
$$503$$ 12.0000 0.535054 0.267527 0.963550i $$-0.413794\pi$$
0.267527 + 0.963550i $$0.413794\pi$$
$$504$$ 0 0
$$505$$ 12.0000 0.533993
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 8.00000 0.354943
$$509$$ −42.0000 −1.86162 −0.930809 0.365507i $$-0.880896\pi$$
−0.930809 + 0.365507i $$0.880896\pi$$
$$510$$ 0 0
$$511$$ −12.0000 −0.530849
$$512$$ −11.0000 −0.486136
$$513$$ 0 0
$$514$$ 8.00000 0.352865
$$515$$ −4.00000 −0.176261
$$516$$ 0 0
$$517$$ 32.0000 1.40736
$$518$$ −4.00000 −0.175750
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 12.0000 0.525730 0.262865 0.964833i $$-0.415333\pi$$
0.262865 + 0.964833i $$0.415333\pi$$
$$522$$ 0 0
$$523$$ −12.0000 −0.524723 −0.262362 0.964970i $$-0.584501\pi$$
−0.262362 + 0.964970i $$0.584501\pi$$
$$524$$ 16.0000 0.698963
$$525$$ 0 0
$$526$$ −4.00000 −0.174408
$$527$$ −40.0000 −1.74243
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ −4.00000 −0.173749
$$531$$ 0 0
$$532$$ −12.0000 −0.520266
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 4.00000 0.172935
$$536$$ −30.0000 −1.29580
$$537$$ 0 0
$$538$$ 12.0000 0.517357
$$539$$ −12.0000 −0.516877
$$540$$ 0 0
$$541$$ −14.0000 −0.601907 −0.300954 0.953639i $$-0.597305\pi$$
−0.300954 + 0.953639i $$0.597305\pi$$
$$542$$ −14.0000 −0.601351
$$543$$ 0 0
$$544$$ −20.0000 −0.857493
$$545$$ 2.00000 0.0856706
$$546$$ 0 0
$$547$$ −36.0000 −1.53925 −0.769624 0.638497i $$-0.779557\pi$$
−0.769624 + 0.638497i $$0.779557\pi$$
$$548$$ 10.0000 0.427179
$$549$$ 0 0
$$550$$ 4.00000 0.170561
$$551$$ 24.0000 1.02243
$$552$$ 0 0
$$553$$ −24.0000 −1.02058
$$554$$ 10.0000 0.424859
$$555$$ 0 0
$$556$$ −12.0000 −0.508913
$$557$$ 26.0000 1.10166 0.550828 0.834619i $$-0.314312\pi$$
0.550828 + 0.834619i $$0.314312\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 2.00000 0.0845154
$$561$$ 0 0
$$562$$ 30.0000 1.26547
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 0 0
$$565$$ 16.0000 0.673125
$$566$$ −4.00000 −0.168133
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 28.0000 1.17382 0.586911 0.809652i $$-0.300344\pi$$
0.586911 + 0.809652i $$0.300344\pi$$
$$570$$ 0 0
$$571$$ −12.0000 −0.502184 −0.251092 0.967963i $$-0.580790\pi$$
−0.251092 + 0.967963i $$0.580790\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −12.0000 −0.500870
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −38.0000 −1.58196 −0.790980 0.611842i $$-0.790429\pi$$
−0.790980 + 0.611842i $$0.790429\pi$$
$$578$$ −1.00000 −0.0415945
$$579$$ 0 0
$$580$$ 4.00000 0.166091
$$581$$ −8.00000 −0.331896
$$582$$ 0 0
$$583$$ −16.0000 −0.662652
$$584$$ −18.0000 −0.744845
$$585$$ 0 0
$$586$$ 2.00000 0.0826192
$$587$$ 20.0000 0.825488 0.412744 0.910847i $$-0.364570\pi$$
0.412744 + 0.910847i $$0.364570\pi$$
$$588$$ 0 0
$$589$$ −60.0000 −2.47226
$$590$$ −12.0000 −0.494032
$$591$$ 0 0
$$592$$ −2.00000 −0.0821995
$$593$$ −14.0000 −0.574911 −0.287456 0.957794i $$-0.592809\pi$$
−0.287456 + 0.957794i $$0.592809\pi$$
$$594$$ 0 0
$$595$$ 8.00000 0.327968
$$596$$ −18.0000 −0.737309
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 8.00000 0.326871 0.163436 0.986554i $$-0.447742\pi$$
0.163436 + 0.986554i $$0.447742\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 16.0000 0.652111
$$603$$ 0 0
$$604$$ 10.0000 0.406894
$$605$$ 5.00000 0.203279
$$606$$ 0 0
$$607$$ −8.00000 −0.324710 −0.162355 0.986732i $$-0.551909\pi$$
−0.162355 + 0.986732i $$0.551909\pi$$
$$608$$ −30.0000 −1.21666
$$609$$ 0 0
$$610$$ 2.00000 0.0809776
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ 22.0000 0.887848
$$615$$ 0 0
$$616$$ 24.0000 0.966988
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ 0 0
$$619$$ −22.0000 −0.884255 −0.442127 0.896952i $$-0.645776\pi$$
−0.442127 + 0.896952i $$0.645776\pi$$
$$620$$ −10.0000 −0.401610
$$621$$ 0 0
$$622$$ −4.00000 −0.160385
$$623$$ 28.0000 1.12180
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 2.00000 0.0799361
$$627$$ 0 0
$$628$$ −18.0000 −0.718278
$$629$$ −8.00000 −0.318981
$$630$$ 0 0
$$631$$ 14.0000 0.557331 0.278666 0.960388i $$-0.410108\pi$$
0.278666 + 0.960388i $$0.410108\pi$$
$$632$$ −36.0000 −1.43200
$$633$$ 0 0
$$634$$ −18.0000 −0.714871
$$635$$ −8.00000 −0.317470
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −16.0000 −0.633446
$$639$$ 0 0
$$640$$ −3.00000 −0.118585
$$641$$ −40.0000 −1.57991 −0.789953 0.613168i $$-0.789895\pi$$
−0.789953 + 0.613168i $$0.789895\pi$$
$$642$$ 0 0
$$643$$ −14.0000 −0.552106 −0.276053 0.961142i $$-0.589027\pi$$
−0.276053 + 0.961142i $$0.589027\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 24.0000 0.944267
$$647$$ −28.0000 −1.10079 −0.550397 0.834903i $$-0.685524\pi$$
−0.550397 + 0.834903i $$0.685524\pi$$
$$648$$ 0 0
$$649$$ −48.0000 −1.88416
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 6.00000 0.234978
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ −16.0000 −0.625172
$$656$$ −6.00000 −0.234261
$$657$$ 0 0
$$658$$ −16.0000 −0.623745
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ 0 0
$$661$$ −26.0000 −1.01128 −0.505641 0.862744i $$-0.668744\pi$$
−0.505641 + 0.862744i $$0.668744\pi$$
$$662$$ −18.0000 −0.699590
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ 12.0000 0.465340
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −24.0000 −0.928588
$$669$$ 0 0
$$670$$ 10.0000 0.386334
$$671$$ 8.00000 0.308837
$$672$$ 0 0
$$673$$ −18.0000 −0.693849 −0.346925 0.937893i $$-0.612774\pi$$
−0.346925 + 0.937893i $$0.612774\pi$$
$$674$$ 14.0000 0.539260
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −36.0000 −1.38359 −0.691796 0.722093i $$-0.743180\pi$$
−0.691796 + 0.722093i $$0.743180\pi$$
$$678$$ 0 0
$$679$$ −28.0000 −1.07454
$$680$$ 12.0000 0.460179
$$681$$ 0 0
$$682$$ 40.0000 1.53168
$$683$$ −4.00000 −0.153056 −0.0765279 0.997067i $$-0.524383\pi$$
−0.0765279 + 0.997067i $$0.524383\pi$$
$$684$$ 0 0
$$685$$ −10.0000 −0.382080
$$686$$ 20.0000 0.763604
$$687$$ 0 0
$$688$$ 8.00000 0.304997
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −34.0000 −1.29342 −0.646710 0.762736i $$-0.723856\pi$$
−0.646710 + 0.762736i $$0.723856\pi$$
$$692$$ −24.0000 −0.912343
$$693$$ 0 0
$$694$$ 32.0000 1.21470
$$695$$ 12.0000 0.455186
$$696$$ 0 0
$$697$$ −24.0000 −0.909065
$$698$$ 6.00000 0.227103
$$699$$ 0 0
$$700$$ 2.00000 0.0755929
$$701$$ 40.0000 1.51078 0.755390 0.655276i $$-0.227448\pi$$
0.755390 + 0.655276i $$0.227448\pi$$
$$702$$ 0 0
$$703$$ −12.0000 −0.452589
$$704$$ 28.0000 1.05529
$$705$$ 0 0
$$706$$ 6.00000 0.225813
$$707$$ −24.0000 −0.902613
$$708$$ 0 0
$$709$$ 50.0000 1.87779 0.938895 0.344204i $$-0.111851\pi$$
0.938895 + 0.344204i $$0.111851\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 42.0000 1.57402
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 16.0000 0.597115
$$719$$ −20.0000 −0.745874 −0.372937 0.927857i $$-0.621649\pi$$
−0.372937 + 0.927857i $$0.621649\pi$$
$$720$$ 0 0
$$721$$ 8.00000 0.297936
$$722$$ 17.0000 0.632674
$$723$$ 0 0
$$724$$ 10.0000 0.371647
$$725$$ −4.00000 −0.148556
$$726$$ 0 0
$$727$$ −24.0000 −0.890111 −0.445055 0.895503i $$-0.646816\pi$$
−0.445055 + 0.895503i $$0.646816\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 6.00000 0.222070
$$731$$ 32.0000 1.18356
$$732$$ 0 0
$$733$$ −34.0000 −1.25582 −0.627909 0.778287i $$-0.716089\pi$$
−0.627909 + 0.778287i $$0.716089\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 40.0000 1.47342
$$738$$ 0 0
$$739$$ −30.0000 −1.10357 −0.551784 0.833987i $$-0.686053\pi$$
−0.551784 + 0.833987i $$0.686053\pi$$
$$740$$ −2.00000 −0.0735215
$$741$$ 0 0
$$742$$ 8.00000 0.293689
$$743$$ −24.0000 −0.880475 −0.440237 0.897881i $$-0.645106\pi$$
−0.440237 + 0.897881i $$0.645106\pi$$
$$744$$ 0 0
$$745$$ 18.0000 0.659469
$$746$$ 22.0000 0.805477
$$747$$ 0 0
$$748$$ 16.0000 0.585018
$$749$$ −8.00000 −0.292314
$$750$$ 0 0
$$751$$ 20.0000 0.729810 0.364905 0.931045i $$-0.381101\pi$$
0.364905 + 0.931045i $$0.381101\pi$$
$$752$$ −8.00000 −0.291730
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −10.0000 −0.363937
$$756$$ 0 0
$$757$$ −34.0000 −1.23575 −0.617876 0.786276i $$-0.712006\pi$$
−0.617876 + 0.786276i $$0.712006\pi$$
$$758$$ 2.00000 0.0726433
$$759$$ 0 0
$$760$$ 18.0000 0.652929
$$761$$ −18.0000 −0.652499 −0.326250 0.945284i $$-0.605785\pi$$
−0.326250 + 0.945284i $$0.605785\pi$$
$$762$$ 0 0
$$763$$ −4.00000 −0.144810
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ 24.0000 0.867155
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −2.00000 −0.0721218 −0.0360609 0.999350i $$-0.511481\pi$$
−0.0360609 + 0.999350i $$0.511481\pi$$
$$770$$ −8.00000 −0.288300
$$771$$ 0 0
$$772$$ −26.0000 −0.935760
$$773$$ 50.0000 1.79838 0.899188 0.437564i $$-0.144158\pi$$
0.899188 + 0.437564i $$0.144158\pi$$
$$774$$ 0 0
$$775$$ 10.0000 0.359211
$$776$$ −42.0000 −1.50771
$$777$$ 0 0
$$778$$ 8.00000 0.286814
$$779$$ −36.0000 −1.28983
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 3.00000 0.107143
$$785$$ 18.0000 0.642448
$$786$$ 0 0
$$787$$ 22.0000 0.784215 0.392108 0.919919i $$-0.371746\pi$$
0.392108 + 0.919919i $$0.371746\pi$$
$$788$$ 18.0000 0.641223
$$789$$ 0 0
$$790$$ 12.0000 0.426941
$$791$$ −32.0000 −1.13779
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 18.0000 0.638796
$$795$$ 0 0
$$796$$ −8.00000 −0.283552
$$797$$ −12.0000 −0.425062 −0.212531 0.977154i $$-0.568171\pi$$
−0.212531 + 0.977154i $$0.568171\pi$$
$$798$$ 0 0
$$799$$ −32.0000 −1.13208
$$800$$ 5.00000 0.176777
$$801$$ 0 0
$$802$$ −22.0000 −0.776847
$$803$$ 24.0000 0.846942
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −36.0000 −1.26648
$$809$$ 28.0000 0.984428 0.492214 0.870474i $$-0.336188\pi$$
0.492214 + 0.870474i $$0.336188\pi$$
$$810$$ 0 0
$$811$$ −30.0000 −1.05344 −0.526721 0.850038i $$-0.676579\pi$$
−0.526721 + 0.850038i $$0.676579\pi$$
$$812$$ −8.00000 −0.280745
$$813$$ 0 0
$$814$$ 8.00000 0.280400
$$815$$ −6.00000 −0.210171
$$816$$ 0 0
$$817$$ 48.0000 1.67931
$$818$$ −30.0000 −1.04893
$$819$$ 0 0
$$820$$ −6.00000 −0.209529
$$821$$ 10.0000 0.349002 0.174501 0.984657i $$-0.444169\pi$$
0.174501 + 0.984657i $$0.444169\pi$$
$$822$$ 0 0
$$823$$ −4.00000 −0.139431 −0.0697156 0.997567i $$-0.522209\pi$$
−0.0697156 + 0.997567i $$0.522209\pi$$
$$824$$ 12.0000 0.418040
$$825$$ 0 0
$$826$$ 24.0000 0.835067
$$827$$ 20.0000 0.695468 0.347734 0.937593i $$-0.386951\pi$$
0.347734 + 0.937593i $$0.386951\pi$$
$$828$$ 0 0
$$829$$ −2.00000 −0.0694629 −0.0347314 0.999397i $$-0.511058\pi$$
−0.0347314 + 0.999397i $$0.511058\pi$$
$$830$$ 4.00000 0.138842
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 12.0000 0.415775
$$834$$ 0 0
$$835$$ 24.0000 0.830554
$$836$$ 24.0000 0.830057
$$837$$ 0 0
$$838$$ −16.0000 −0.552711
$$839$$ 40.0000 1.38095 0.690477 0.723355i $$-0.257401\pi$$
0.690477 + 0.723355i $$0.257401\pi$$
$$840$$ 0 0
$$841$$ −13.0000 −0.448276
$$842$$ −22.0000 −0.758170
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −10.0000 −0.343604
$$848$$ 4.00000 0.137361
$$849$$ 0 0
$$850$$ −4.00000 −0.137199
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −30.0000 −1.02718 −0.513590 0.858036i $$-0.671685\pi$$
−0.513590 + 0.858036i $$0.671685\pi$$
$$854$$ −4.00000 −0.136877
$$855$$ 0 0
$$856$$ −12.0000 −0.410152
$$857$$ −48.0000 −1.63965 −0.819824 0.572615i $$-0.805929\pi$$
−0.819824 + 0.572615i $$0.805929\pi$$
$$858$$ 0 0
$$859$$ 16.0000 0.545913 0.272956 0.962026i $$-0.411998\pi$$
0.272956 + 0.962026i $$0.411998\pi$$
$$860$$ 8.00000 0.272798
$$861$$ 0 0
$$862$$ 40.0000 1.36241
$$863$$ 48.0000 1.63394 0.816970 0.576681i $$-0.195652\pi$$
0.816970 + 0.576681i $$0.195652\pi$$
$$864$$ 0 0
$$865$$ 24.0000 0.816024
$$866$$ −2.00000 −0.0679628
$$867$$ 0 0
$$868$$ 20.0000 0.678844
$$869$$ 48.0000 1.62829
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −6.00000 −0.203186
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −2.00000 −0.0676123
$$876$$ 0 0
$$877$$ 42.0000 1.41824 0.709120 0.705088i $$-0.249093\pi$$
0.709120 + 0.705088i $$0.249093\pi$$
$$878$$ −36.0000 −1.21494
$$879$$ 0 0
$$880$$ −4.00000 −0.134840
$$881$$ −28.0000 −0.943344 −0.471672 0.881774i $$-0.656349\pi$$
−0.471672 + 0.881774i $$0.656349\pi$$
$$882$$ 0 0
$$883$$ −4.00000 −0.134611 −0.0673054 0.997732i $$-0.521440\pi$$
−0.0673054 + 0.997732i $$0.521440\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 20.0000 0.671913
$$887$$ −56.0000 −1.88030 −0.940148 0.340766i $$-0.889313\pi$$
−0.940148 + 0.340766i $$0.889313\pi$$
$$888$$ 0 0
$$889$$ 16.0000 0.536623
$$890$$ −14.0000 −0.469281
$$891$$ 0 0
$$892$$ −14.0000 −0.468755
$$893$$ −48.0000 −1.60626
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 6.00000 0.200446
$$897$$ 0 0
$$898$$ −30.0000 −1.00111
$$899$$ −40.0000 −1.33407
$$900$$ 0 0
$$901$$ 16.0000 0.533037
$$902$$ 24.0000 0.799113
$$903$$ 0 0
$$904$$ −48.0000 −1.59646
$$905$$ −10.0000 −0.332411
$$906$$ 0 0
$$907$$ 44.0000 1.46100 0.730498 0.682915i $$-0.239288\pi$$
0.730498 + 0.682915i $$0.239288\pi$$
$$908$$ −20.0000 −0.663723
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ 16.0000 0.529523
$$914$$ 22.0000 0.727695
$$915$$ 0 0
$$916$$ −10.0000 −0.330409
$$917$$ 32.0000 1.05673
$$918$$ 0 0
$$919$$ 44.0000 1.45143 0.725713 0.687998i $$-0.241510\pi$$
0.725713 + 0.687998i $$0.241510\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 14.0000 0.461065
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 2.00000 0.0657596
$$926$$ −18.0000 −0.591517
$$927$$ 0 0
$$928$$ −20.0000 −0.656532
$$929$$ −10.0000 −0.328089 −0.164045 0.986453i $$-0.552454\pi$$
−0.164045 + 0.986453i $$0.552454\pi$$
$$930$$ 0 0
$$931$$ 18.0000 0.589926
$$932$$ 8.00000 0.262049
$$933$$ 0 0
$$934$$ 8.00000 0.261768
$$935$$ −16.0000 −0.523256
$$936$$ 0 0
$$937$$ 54.0000 1.76410 0.882052 0.471153i $$-0.156162\pi$$
0.882052 + 0.471153i $$0.156162\pi$$
$$938$$ −20.0000 −0.653023
$$939$$ 0 0
$$940$$ −8.00000 −0.260931
$$941$$ −6.00000 −0.195594 −0.0977972 0.995206i $$-0.531180\pi$$
−0.0977972 + 0.995206i $$0.531180\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 12.0000 0.390567
$$945$$ 0 0
$$946$$ −32.0000 −1.04041
$$947$$ −12.0000 −0.389948 −0.194974 0.980808i $$-0.562462\pi$$
−0.194974 + 0.980808i $$0.562462\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ −6.00000 −0.194666
$$951$$ 0 0
$$952$$ −24.0000 −0.777844
$$953$$ −48.0000 −1.55487 −0.777436 0.628962i $$-0.783480\pi$$
−0.777436 + 0.628962i $$0.783480\pi$$
$$954$$ 0 0
$$955$$ −12.0000 −0.388311
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 24.0000 0.775405
$$959$$ 20.0000 0.645834
$$960$$ 0 0
$$961$$ 69.0000 2.22581
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 22.0000 0.708572
$$965$$ 26.0000 0.836970
$$966$$ 0 0
$$967$$ −58.0000 −1.86515 −0.932577 0.360971i $$-0.882445\pi$$
−0.932577 + 0.360971i $$0.882445\pi$$
$$968$$ −15.0000 −0.482118
$$969$$ 0 0
$$970$$ 14.0000 0.449513
$$971$$ −52.0000 −1.66876 −0.834380 0.551190i $$-0.814174\pi$$
−0.834380 + 0.551190i $$0.814174\pi$$
$$972$$ 0 0
$$973$$ −24.0000 −0.769405
$$974$$ 22.0000 0.704925
$$975$$ 0 0
$$976$$ −2.00000 −0.0640184
$$977$$ −54.0000 −1.72761 −0.863807 0.503824i $$-0.831926\pi$$
−0.863807 + 0.503824i $$0.831926\pi$$
$$978$$ 0 0
$$979$$ −56.0000 −1.78977
$$980$$ 3.00000 0.0958315
$$981$$ 0 0
$$982$$ 36.0000 1.14881
$$983$$ 16.0000 0.510321 0.255160 0.966899i $$-0.417872\pi$$
0.255160 + 0.966899i $$0.417872\pi$$
$$984$$ 0 0
$$985$$ −18.0000 −0.573528
$$986$$ 16.0000 0.509544
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −48.0000 −1.52477 −0.762385 0.647124i $$-0.775972\pi$$
−0.762385 + 0.647124i $$0.775972\pi$$
$$992$$ 50.0000 1.58750
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 8.00000 0.253617
$$996$$ 0 0
$$997$$ −58.0000 −1.83688 −0.918439 0.395562i $$-0.870550\pi$$
−0.918439 + 0.395562i $$0.870550\pi$$
$$998$$ 38.0000 1.20287
$$999$$ 0 0
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 7605.2.a.q.1.1 1
3.2 odd 2 7605.2.a.c.1.1 1
13.12 even 2 585.2.a.d.1.1 1
39.38 odd 2 585.2.a.i.1.1 yes 1
52.51 odd 2 9360.2.a.i.1.1 1
65.12 odd 4 2925.2.c.g.2224.1 2
65.38 odd 4 2925.2.c.g.2224.2 2
65.64 even 2 2925.2.a.m.1.1 1
156.155 even 2 9360.2.a.be.1.1 1
195.38 even 4 2925.2.c.k.2224.1 2
195.77 even 4 2925.2.c.k.2224.2 2
195.194 odd 2 2925.2.a.c.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.a.d.1.1 1 13.12 even 2
585.2.a.i.1.1 yes 1 39.38 odd 2
2925.2.a.c.1.1 1 195.194 odd 2
2925.2.a.m.1.1 1 65.64 even 2
2925.2.c.g.2224.1 2 65.12 odd 4
2925.2.c.g.2224.2 2 65.38 odd 4
2925.2.c.k.2224.1 2 195.38 even 4
2925.2.c.k.2224.2 2 195.77 even 4
7605.2.a.c.1.1 1 3.2 odd 2
7605.2.a.q.1.1 1 1.1 even 1 trivial
9360.2.a.i.1.1 1 52.51 odd 2
9360.2.a.be.1.1 1 156.155 even 2