# Properties

 Label 5054.2.a.a.1.1 Level $5054$ Weight $2$ Character 5054.1 Self dual yes Analytic conductor $40.356$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5054 = 2 \cdot 7 \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5054.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$40.3563931816$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 266) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 5054.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{10} -2.00000 q^{11} +5.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{18} +1.00000 q^{20} +2.00000 q^{22} +1.00000 q^{23} -4.00000 q^{25} -5.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} +1.00000 q^{35} -3.00000 q^{36} +4.00000 q^{37} -1.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} -3.00000 q^{45} -1.00000 q^{46} +1.00000 q^{49} +4.00000 q^{50} +5.00000 q^{52} +2.00000 q^{53} -2.00000 q^{55} -1.00000 q^{56} +6.00000 q^{58} +7.00000 q^{59} -7.00000 q^{61} +4.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +5.00000 q^{65} -12.0000 q^{67} -1.00000 q^{70} +15.0000 q^{71} +3.00000 q^{72} -14.0000 q^{73} -4.00000 q^{74} -2.00000 q^{77} +4.00000 q^{79} +1.00000 q^{80} +9.00000 q^{81} -2.00000 q^{82} -7.00000 q^{83} +8.00000 q^{86} +2.00000 q^{88} +3.00000 q^{90} +5.00000 q^{91} +1.00000 q^{92} -12.0000 q^{97} -1.00000 q^{98} +6.00000 q^{99} +O(q^{100})$$

## 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
$$3$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 1.00000 0.447214 0.223607 0.974679i $$-0.428217\pi$$
0.223607 + 0.974679i $$0.428217\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ −1.00000 −0.353553
$$9$$ −3.00000 −1.00000
$$10$$ −1.00000 −0.316228
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 5.00000 1.38675 0.693375 0.720577i $$-0.256123\pi$$
0.693375 + 0.720577i $$0.256123\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 3.00000 0.707107
$$19$$ 0 0
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ 2.00000 0.426401
$$23$$ 1.00000 0.208514 0.104257 0.994550i $$-0.466753\pi$$
0.104257 + 0.994550i $$0.466753\pi$$
$$24$$ 0 0
$$25$$ −4.00000 −0.800000
$$26$$ −5.00000 −0.980581
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 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
$$34$$ 0 0
$$35$$ 1.00000 0.169031
$$36$$ −3.00000 −0.500000
$$37$$ 4.00000 0.657596 0.328798 0.944400i $$-0.393356\pi$$
0.328798 + 0.944400i $$0.393356\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −1.00000 −0.158114
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ −2.00000 −0.301511
$$45$$ −3.00000 −0.447214
$$46$$ −1.00000 −0.147442
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 4.00000 0.565685
$$51$$ 0 0
$$52$$ 5.00000 0.693375
$$53$$ 2.00000 0.274721 0.137361 0.990521i $$-0.456138\pi$$
0.137361 + 0.990521i $$0.456138\pi$$
$$54$$ 0 0
$$55$$ −2.00000 −0.269680
$$56$$ −1.00000 −0.133631
$$57$$ 0 0
$$58$$ 6.00000 0.787839
$$59$$ 7.00000 0.911322 0.455661 0.890153i $$-0.349403\pi$$
0.455661 + 0.890153i $$0.349403\pi$$
$$60$$ 0 0
$$61$$ −7.00000 −0.896258 −0.448129 0.893969i $$-0.647910\pi$$
−0.448129 + 0.893969i $$0.647910\pi$$
$$62$$ 4.00000 0.508001
$$63$$ −3.00000 −0.377964
$$64$$ 1.00000 0.125000
$$65$$ 5.00000 0.620174
$$66$$ 0 0
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −1.00000 −0.119523
$$71$$ 15.0000 1.78017 0.890086 0.455792i $$-0.150644\pi$$
0.890086 + 0.455792i $$0.150644\pi$$
$$72$$ 3.00000 0.353553
$$73$$ −14.0000 −1.63858 −0.819288 0.573382i $$-0.805631\pi$$
−0.819288 + 0.573382i $$0.805631\pi$$
$$74$$ −4.00000 −0.464991
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −2.00000 −0.227921
$$78$$ 0 0
$$79$$ 4.00000 0.450035 0.225018 0.974355i $$-0.427756\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 1.00000 0.111803
$$81$$ 9.00000 1.00000
$$82$$ −2.00000 −0.220863
$$83$$ −7.00000 −0.768350 −0.384175 0.923260i $$-0.625514\pi$$
−0.384175 + 0.923260i $$0.625514\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 8.00000 0.862662
$$87$$ 0 0
$$88$$ 2.00000 0.213201
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 3.00000 0.316228
$$91$$ 5.00000 0.524142
$$92$$ 1.00000 0.104257
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −12.0000 −1.21842 −0.609208 0.793011i $$-0.708512\pi$$
−0.609208 + 0.793011i $$0.708512\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 6.00000 0.603023
$$100$$ −4.00000 −0.400000
$$101$$ −18.0000 −1.79107 −0.895533 0.444994i $$-0.853206\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 0 0
$$103$$ −6.00000 −0.591198 −0.295599 0.955312i $$-0.595519\pi$$
−0.295599 + 0.955312i $$0.595519\pi$$
$$104$$ −5.00000 −0.490290
$$105$$ 0 0
$$106$$ −2.00000 −0.194257
$$107$$ 18.0000 1.74013 0.870063 0.492941i $$-0.164078\pi$$
0.870063 + 0.492941i $$0.164078\pi$$
$$108$$ 0 0
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ 2.00000 0.190693
$$111$$ 0 0
$$112$$ 1.00000 0.0944911
$$113$$ 5.00000 0.470360 0.235180 0.971952i $$-0.424432\pi$$
0.235180 + 0.971952i $$0.424432\pi$$
$$114$$ 0 0
$$115$$ 1.00000 0.0932505
$$116$$ −6.00000 −0.557086
$$117$$ −15.0000 −1.38675
$$118$$ −7.00000 −0.644402
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 7.00000 0.633750
$$123$$ 0 0
$$124$$ −4.00000 −0.359211
$$125$$ −9.00000 −0.804984
$$126$$ 3.00000 0.267261
$$127$$ −13.0000 −1.15356 −0.576782 0.816898i $$-0.695692\pi$$
−0.576782 + 0.816898i $$0.695692\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ −5.00000 −0.438529
$$131$$ 15.0000 1.31056 0.655278 0.755388i $$-0.272551\pi$$
0.655278 + 0.755388i $$0.272551\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −9.00000 −0.768922 −0.384461 0.923141i $$-0.625613\pi$$
−0.384461 + 0.923141i $$0.625613\pi$$
$$138$$ 0 0
$$139$$ −12.0000 −1.01783 −0.508913 0.860818i $$-0.669953\pi$$
−0.508913 + 0.860818i $$0.669953\pi$$
$$140$$ 1.00000 0.0845154
$$141$$ 0 0
$$142$$ −15.0000 −1.25877
$$143$$ −10.0000 −0.836242
$$144$$ −3.00000 −0.250000
$$145$$ −6.00000 −0.498273
$$146$$ 14.0000 1.15865
$$147$$ 0 0
$$148$$ 4.00000 0.328798
$$149$$ −4.00000 −0.327693 −0.163846 0.986486i $$-0.552390\pi$$
−0.163846 + 0.986486i $$0.552390\pi$$
$$150$$ 0 0
$$151$$ −19.0000 −1.54620 −0.773099 0.634285i $$-0.781294\pi$$
−0.773099 + 0.634285i $$0.781294\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 2.00000 0.161165
$$155$$ −4.00000 −0.321288
$$156$$ 0 0
$$157$$ 7.00000 0.558661 0.279330 0.960195i $$-0.409888\pi$$
0.279330 + 0.960195i $$0.409888\pi$$
$$158$$ −4.00000 −0.318223
$$159$$ 0 0
$$160$$ −1.00000 −0.0790569
$$161$$ 1.00000 0.0788110
$$162$$ −9.00000 −0.707107
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 2.00000 0.156174
$$165$$ 0 0
$$166$$ 7.00000 0.543305
$$167$$ −2.00000 −0.154765 −0.0773823 0.997001i $$-0.524656\pi$$
−0.0773823 + 0.997001i $$0.524656\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −8.00000 −0.609994
$$173$$ 13.0000 0.988372 0.494186 0.869356i $$-0.335466\pi$$
0.494186 + 0.869356i $$0.335466\pi$$
$$174$$ 0 0
$$175$$ −4.00000 −0.302372
$$176$$ −2.00000 −0.150756
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ −3.00000 −0.223607
$$181$$ −23.0000 −1.70958 −0.854788 0.518977i $$-0.826313\pi$$
−0.854788 + 0.518977i $$0.826313\pi$$
$$182$$ −5.00000 −0.370625
$$183$$ 0 0
$$184$$ −1.00000 −0.0737210
$$185$$ 4.00000 0.294086
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 17.0000 1.23008 0.615038 0.788497i $$-0.289140\pi$$
0.615038 + 0.788497i $$0.289140\pi$$
$$192$$ 0 0
$$193$$ 3.00000 0.215945 0.107972 0.994154i $$-0.465564\pi$$
0.107972 + 0.994154i $$0.465564\pi$$
$$194$$ 12.0000 0.861550
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ −6.00000 −0.426401
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 4.00000 0.282843
$$201$$ 0 0
$$202$$ 18.0000 1.26648
$$203$$ −6.00000 −0.421117
$$204$$ 0 0
$$205$$ 2.00000 0.139686
$$206$$ 6.00000 0.418040
$$207$$ −3.00000 −0.208514
$$208$$ 5.00000 0.346688
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ 2.00000 0.137361
$$213$$ 0 0
$$214$$ −18.0000 −1.23045
$$215$$ −8.00000 −0.545595
$$216$$ 0 0
$$217$$ −4.00000 −0.271538
$$218$$ −10.0000 −0.677285
$$219$$ 0 0
$$220$$ −2.00000 −0.134840
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 2.00000 0.133930 0.0669650 0.997755i $$-0.478668\pi$$
0.0669650 + 0.997755i $$0.478668\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 12.0000 0.800000
$$226$$ −5.00000 −0.332595
$$227$$ 3.00000 0.199117 0.0995585 0.995032i $$-0.468257\pi$$
0.0995585 + 0.995032i $$0.468257\pi$$
$$228$$ 0 0
$$229$$ 27.0000 1.78421 0.892105 0.451828i $$-0.149228\pi$$
0.892105 + 0.451828i $$0.149228\pi$$
$$230$$ −1.00000 −0.0659380
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ −11.0000 −0.720634 −0.360317 0.932830i $$-0.617331\pi$$
−0.360317 + 0.932830i $$0.617331\pi$$
$$234$$ 15.0000 0.980581
$$235$$ 0 0
$$236$$ 7.00000 0.455661
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −5.00000 −0.323423 −0.161712 0.986838i $$-0.551701\pi$$
−0.161712 + 0.986838i $$0.551701\pi$$
$$240$$ 0 0
$$241$$ 4.00000 0.257663 0.128831 0.991667i $$-0.458877\pi$$
0.128831 + 0.991667i $$0.458877\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 0 0
$$244$$ −7.00000 −0.448129
$$245$$ 1.00000 0.0638877
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 4.00000 0.254000
$$249$$ 0 0
$$250$$ 9.00000 0.569210
$$251$$ 9.00000 0.568075 0.284037 0.958813i $$-0.408326\pi$$
0.284037 + 0.958813i $$0.408326\pi$$
$$252$$ −3.00000 −0.188982
$$253$$ −2.00000 −0.125739
$$254$$ 13.0000 0.815693
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −14.0000 −0.873296 −0.436648 0.899632i $$-0.643834\pi$$
−0.436648 + 0.899632i $$0.643834\pi$$
$$258$$ 0 0
$$259$$ 4.00000 0.248548
$$260$$ 5.00000 0.310087
$$261$$ 18.0000 1.11417
$$262$$ −15.0000 −0.926703
$$263$$ −3.00000 −0.184988 −0.0924940 0.995713i $$-0.529484\pi$$
−0.0924940 + 0.995713i $$0.529484\pi$$
$$264$$ 0 0
$$265$$ 2.00000 0.122859
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −12.0000 −0.733017
$$269$$ −14.0000 −0.853595 −0.426798 0.904347i $$-0.640358\pi$$
−0.426798 + 0.904347i $$0.640358\pi$$
$$270$$ 0 0
$$271$$ −20.0000 −1.21491 −0.607457 0.794353i $$-0.707810\pi$$
−0.607457 + 0.794353i $$0.707810\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 9.00000 0.543710
$$275$$ 8.00000 0.482418
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 12.0000 0.719712
$$279$$ 12.0000 0.718421
$$280$$ −1.00000 −0.0597614
$$281$$ 22.0000 1.31241 0.656205 0.754583i $$-0.272161\pi$$
0.656205 + 0.754583i $$0.272161\pi$$
$$282$$ 0 0
$$283$$ −7.00000 −0.416107 −0.208053 0.978117i $$-0.566713\pi$$
−0.208053 + 0.978117i $$0.566713\pi$$
$$284$$ 15.0000 0.890086
$$285$$ 0 0
$$286$$ 10.0000 0.591312
$$287$$ 2.00000 0.118056
$$288$$ 3.00000 0.176777
$$289$$ −17.0000 −1.00000
$$290$$ 6.00000 0.352332
$$291$$ 0 0
$$292$$ −14.0000 −0.819288
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 0 0
$$295$$ 7.00000 0.407556
$$296$$ −4.00000 −0.232495
$$297$$ 0 0
$$298$$ 4.00000 0.231714
$$299$$ 5.00000 0.289157
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 19.0000 1.09333
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −7.00000 −0.400819
$$306$$ 0 0
$$307$$ −19.0000 −1.08439 −0.542194 0.840254i $$-0.682406\pi$$
−0.542194 + 0.840254i $$0.682406\pi$$
$$308$$ −2.00000 −0.113961
$$309$$ 0 0
$$310$$ 4.00000 0.227185
$$311$$ 18.0000 1.02069 0.510343 0.859971i $$-0.329518\pi$$
0.510343 + 0.859971i $$0.329518\pi$$
$$312$$ 0 0
$$313$$ 28.0000 1.58265 0.791327 0.611393i $$-0.209391\pi$$
0.791327 + 0.611393i $$0.209391\pi$$
$$314$$ −7.00000 −0.395033
$$315$$ −3.00000 −0.169031
$$316$$ 4.00000 0.225018
$$317$$ −22.0000 −1.23564 −0.617822 0.786318i $$-0.711985\pi$$
−0.617822 + 0.786318i $$0.711985\pi$$
$$318$$ 0 0
$$319$$ 12.0000 0.671871
$$320$$ 1.00000 0.0559017
$$321$$ 0 0
$$322$$ −1.00000 −0.0557278
$$323$$ 0 0
$$324$$ 9.00000 0.500000
$$325$$ −20.0000 −1.10940
$$326$$ 4.00000 0.221540
$$327$$ 0 0
$$328$$ −2.00000 −0.110432
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 18.0000 0.989369 0.494685 0.869072i $$-0.335284\pi$$
0.494685 + 0.869072i $$0.335284\pi$$
$$332$$ −7.00000 −0.384175
$$333$$ −12.0000 −0.657596
$$334$$ 2.00000 0.109435
$$335$$ −12.0000 −0.655630
$$336$$ 0 0
$$337$$ −13.0000 −0.708155 −0.354078 0.935216i $$-0.615205\pi$$
−0.354078 + 0.935216i $$0.615205\pi$$
$$338$$ −12.0000 −0.652714
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8.00000 0.433224
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 8.00000 0.431331
$$345$$ 0 0
$$346$$ −13.0000 −0.698884
$$347$$ 18.0000 0.966291 0.483145 0.875540i $$-0.339494\pi$$
0.483145 + 0.875540i $$0.339494\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ 2.00000 0.106600
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 0 0
$$355$$ 15.0000 0.796117
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ −4.00000 −0.211112 −0.105556 0.994413i $$-0.533662\pi$$
−0.105556 + 0.994413i $$0.533662\pi$$
$$360$$ 3.00000 0.158114
$$361$$ 0 0
$$362$$ 23.0000 1.20885
$$363$$ 0 0
$$364$$ 5.00000 0.262071
$$365$$ −14.0000 −0.732793
$$366$$ 0 0
$$367$$ −18.0000 −0.939592 −0.469796 0.882775i $$-0.655673\pi$$
−0.469796 + 0.882775i $$0.655673\pi$$
$$368$$ 1.00000 0.0521286
$$369$$ −6.00000 −0.312348
$$370$$ −4.00000 −0.207950
$$371$$ 2.00000 0.103835
$$372$$ 0 0
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −30.0000 −1.54508
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −17.0000 −0.869796
$$383$$ −36.0000 −1.83951 −0.919757 0.392488i $$-0.871614\pi$$
−0.919757 + 0.392488i $$0.871614\pi$$
$$384$$ 0 0
$$385$$ −2.00000 −0.101929
$$386$$ −3.00000 −0.152696
$$387$$ 24.0000 1.21999
$$388$$ −12.0000 −0.609208
$$389$$ −30.0000 −1.52106 −0.760530 0.649303i $$-0.775061\pi$$
−0.760530 + 0.649303i $$0.775061\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −1.00000 −0.0505076
$$393$$ 0 0
$$394$$ −2.00000 −0.100759
$$395$$ 4.00000 0.201262
$$396$$ 6.00000 0.301511
$$397$$ −6.00000 −0.301131 −0.150566 0.988600i $$-0.548110\pi$$
−0.150566 + 0.988600i $$0.548110\pi$$
$$398$$ 4.00000 0.200502
$$399$$ 0 0
$$400$$ −4.00000 −0.200000
$$401$$ 25.0000 1.24844 0.624220 0.781248i $$-0.285417\pi$$
0.624220 + 0.781248i $$0.285417\pi$$
$$402$$ 0 0
$$403$$ −20.0000 −0.996271
$$404$$ −18.0000 −0.895533
$$405$$ 9.00000 0.447214
$$406$$ 6.00000 0.297775
$$407$$ −8.00000 −0.396545
$$408$$ 0 0
$$409$$ 4.00000 0.197787 0.0988936 0.995098i $$-0.468470\pi$$
0.0988936 + 0.995098i $$0.468470\pi$$
$$410$$ −2.00000 −0.0987730
$$411$$ 0 0
$$412$$ −6.00000 −0.295599
$$413$$ 7.00000 0.344447
$$414$$ 3.00000 0.147442
$$415$$ −7.00000 −0.343616
$$416$$ −5.00000 −0.245145
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ 0 0
$$421$$ −34.0000 −1.65706 −0.828529 0.559946i $$-0.810822\pi$$
−0.828529 + 0.559946i $$0.810822\pi$$
$$422$$ −8.00000 −0.389434
$$423$$ 0 0
$$424$$ −2.00000 −0.0971286
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −7.00000 −0.338754
$$428$$ 18.0000 0.870063
$$429$$ 0 0
$$430$$ 8.00000 0.385794
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ −2.00000 −0.0961139 −0.0480569 0.998845i $$-0.515303\pi$$
−0.0480569 + 0.998845i $$0.515303\pi$$
$$434$$ 4.00000 0.192006
$$435$$ 0 0
$$436$$ 10.0000 0.478913
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 20.0000 0.954548 0.477274 0.878755i $$-0.341625\pi$$
0.477274 + 0.878755i $$0.341625\pi$$
$$440$$ 2.00000 0.0953463
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ −34.0000 −1.61539 −0.807694 0.589601i $$-0.799285\pi$$
−0.807694 + 0.589601i $$0.799285\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −2.00000 −0.0947027
$$447$$ 0 0
$$448$$ 1.00000 0.0472456
$$449$$ −37.0000 −1.74614 −0.873069 0.487597i $$-0.837874\pi$$
−0.873069 + 0.487597i $$0.837874\pi$$
$$450$$ −12.0000 −0.565685
$$451$$ −4.00000 −0.188353
$$452$$ 5.00000 0.235180
$$453$$ 0 0
$$454$$ −3.00000 −0.140797
$$455$$ 5.00000 0.234404
$$456$$ 0 0
$$457$$ −39.0000 −1.82434 −0.912172 0.409809i $$-0.865595\pi$$
−0.912172 + 0.409809i $$0.865595\pi$$
$$458$$ −27.0000 −1.26163
$$459$$ 0 0
$$460$$ 1.00000 0.0466252
$$461$$ −37.0000 −1.72326 −0.861631 0.507535i $$-0.830557\pi$$
−0.861631 + 0.507535i $$0.830557\pi$$
$$462$$ 0 0
$$463$$ −5.00000 −0.232370 −0.116185 0.993228i $$-0.537067\pi$$
−0.116185 + 0.993228i $$0.537067\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 0 0
$$466$$ 11.0000 0.509565
$$467$$ −36.0000 −1.66588 −0.832941 0.553362i $$-0.813345\pi$$
−0.832941 + 0.553362i $$0.813345\pi$$
$$468$$ −15.0000 −0.693375
$$469$$ −12.0000 −0.554109
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −7.00000 −0.322201
$$473$$ 16.0000 0.735681
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ 5.00000 0.228695
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 20.0000 0.911922
$$482$$ −4.00000 −0.182195
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ −12.0000 −0.544892
$$486$$ 0 0
$$487$$ 16.0000 0.725029 0.362515 0.931978i $$-0.381918\pi$$
0.362515 + 0.931978i $$0.381918\pi$$
$$488$$ 7.00000 0.316875
$$489$$ 0 0
$$490$$ −1.00000 −0.0451754
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 6.00000 0.269680
$$496$$ −4.00000 −0.179605
$$497$$ 15.0000 0.672842
$$498$$ 0 0
$$499$$ 24.0000 1.07439 0.537194 0.843459i $$-0.319484\pi$$
0.537194 + 0.843459i $$0.319484\pi$$
$$500$$ −9.00000 −0.402492
$$501$$ 0 0
$$502$$ −9.00000 −0.401690
$$503$$ 16.0000 0.713405 0.356702 0.934218i $$-0.383901\pi$$
0.356702 + 0.934218i $$0.383901\pi$$
$$504$$ 3.00000 0.133631
$$505$$ −18.0000 −0.800989
$$506$$ 2.00000 0.0889108
$$507$$ 0 0
$$508$$ −13.0000 −0.576782
$$509$$ −35.0000 −1.55135 −0.775674 0.631134i $$-0.782590\pi$$
−0.775674 + 0.631134i $$0.782590\pi$$
$$510$$ 0 0
$$511$$ −14.0000 −0.619324
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 14.0000 0.617514
$$515$$ −6.00000 −0.264392
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −4.00000 −0.175750
$$519$$ 0 0
$$520$$ −5.00000 −0.219265
$$521$$ 38.0000 1.66481 0.832405 0.554168i $$-0.186963\pi$$
0.832405 + 0.554168i $$0.186963\pi$$
$$522$$ −18.0000 −0.787839
$$523$$ 28.0000 1.22435 0.612177 0.790721i $$-0.290294\pi$$
0.612177 + 0.790721i $$0.290294\pi$$
$$524$$ 15.0000 0.655278
$$525$$ 0 0
$$526$$ 3.00000 0.130806
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −22.0000 −0.956522
$$530$$ −2.00000 −0.0868744
$$531$$ −21.0000 −0.911322
$$532$$ 0 0
$$533$$ 10.0000 0.433148
$$534$$ 0 0
$$535$$ 18.0000 0.778208
$$536$$ 12.0000 0.518321
$$537$$ 0 0
$$538$$ 14.0000 0.603583
$$539$$ −2.00000 −0.0861461
$$540$$ 0 0
$$541$$ 36.0000 1.54776 0.773880 0.633332i $$-0.218313\pi$$
0.773880 + 0.633332i $$0.218313\pi$$
$$542$$ 20.0000 0.859074
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 10.0000 0.428353
$$546$$ 0 0
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ −9.00000 −0.384461
$$549$$ 21.0000 0.896258
$$550$$ −8.00000 −0.341121
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 4.00000 0.170097
$$554$$ 2.00000 0.0849719
$$555$$ 0 0
$$556$$ −12.0000 −0.508913
$$557$$ −2.00000 −0.0847427 −0.0423714 0.999102i $$-0.513491\pi$$
−0.0423714 + 0.999102i $$0.513491\pi$$
$$558$$ −12.0000 −0.508001
$$559$$ −40.0000 −1.69182
$$560$$ 1.00000 0.0422577
$$561$$ 0 0
$$562$$ −22.0000 −0.928014
$$563$$ 3.00000 0.126435 0.0632175 0.998000i $$-0.479864\pi$$
0.0632175 + 0.998000i $$0.479864\pi$$
$$564$$ 0 0
$$565$$ 5.00000 0.210352
$$566$$ 7.00000 0.294232
$$567$$ 9.00000 0.377964
$$568$$ −15.0000 −0.629386
$$569$$ −31.0000 −1.29959 −0.649794 0.760111i $$-0.725145\pi$$
−0.649794 + 0.760111i $$0.725145\pi$$
$$570$$ 0 0
$$571$$ −30.0000 −1.25546 −0.627730 0.778431i $$-0.716016\pi$$
−0.627730 + 0.778431i $$0.716016\pi$$
$$572$$ −10.0000 −0.418121
$$573$$ 0 0
$$574$$ −2.00000 −0.0834784
$$575$$ −4.00000 −0.166812
$$576$$ −3.00000 −0.125000
$$577$$ 32.0000 1.33218 0.666089 0.745873i $$-0.267967\pi$$
0.666089 + 0.745873i $$0.267967\pi$$
$$578$$ 17.0000 0.707107
$$579$$ 0 0
$$580$$ −6.00000 −0.249136
$$581$$ −7.00000 −0.290409
$$582$$ 0 0
$$583$$ −4.00000 −0.165663
$$584$$ 14.0000 0.579324
$$585$$ −15.0000 −0.620174
$$586$$ 21.0000 0.867502
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −7.00000 −0.288185
$$591$$ 0 0
$$592$$ 4.00000 0.164399
$$593$$ 42.0000 1.72473 0.862367 0.506284i $$-0.168981\pi$$
0.862367 + 0.506284i $$0.168981\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −4.00000 −0.163846
$$597$$ 0 0
$$598$$ −5.00000 −0.204465
$$599$$ −5.00000 −0.204294 −0.102147 0.994769i $$-0.532571\pi$$
−0.102147 + 0.994769i $$0.532571\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 8.00000 0.326056
$$603$$ 36.0000 1.46603
$$604$$ −19.0000 −0.773099
$$605$$ −7.00000 −0.284590
$$606$$ 0 0
$$607$$ 8.00000 0.324710 0.162355 0.986732i $$-0.448091\pi$$
0.162355 + 0.986732i $$0.448091\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 7.00000 0.283422
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −24.0000 −0.969351 −0.484675 0.874694i $$-0.661062\pi$$
−0.484675 + 0.874694i $$0.661062\pi$$
$$614$$ 19.0000 0.766778
$$615$$ 0 0
$$616$$ 2.00000 0.0805823
$$617$$ 13.0000 0.523360 0.261680 0.965155i $$-0.415723\pi$$
0.261680 + 0.965155i $$0.415723\pi$$
$$618$$ 0 0
$$619$$ −17.0000 −0.683288 −0.341644 0.939829i $$-0.610984\pi$$
−0.341644 + 0.939829i $$0.610984\pi$$
$$620$$ −4.00000 −0.160644
$$621$$ 0 0
$$622$$ −18.0000 −0.721734
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ −28.0000 −1.11911
$$627$$ 0 0
$$628$$ 7.00000 0.279330
$$629$$ 0 0
$$630$$ 3.00000 0.119523
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ −4.00000 −0.159111
$$633$$ 0 0
$$634$$ 22.0000 0.873732
$$635$$ −13.0000 −0.515889
$$636$$ 0 0
$$637$$ 5.00000 0.198107
$$638$$ −12.0000 −0.475085
$$639$$ −45.0000 −1.78017
$$640$$ −1.00000 −0.0395285
$$641$$ −39.0000 −1.54041 −0.770204 0.637798i $$-0.779845\pi$$
−0.770204 + 0.637798i $$0.779845\pi$$
$$642$$ 0 0
$$643$$ −9.00000 −0.354925 −0.177463 0.984128i $$-0.556789\pi$$
−0.177463 + 0.984128i $$0.556789\pi$$
$$644$$ 1.00000 0.0394055
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ −9.00000 −0.353553
$$649$$ −14.0000 −0.549548
$$650$$ 20.0000 0.784465
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ 24.0000 0.939193 0.469596 0.882881i $$-0.344399\pi$$
0.469596 + 0.882881i $$0.344399\pi$$
$$654$$ 0 0
$$655$$ 15.0000 0.586098
$$656$$ 2.00000 0.0780869
$$657$$ 42.0000 1.63858
$$658$$ 0 0
$$659$$ 22.0000 0.856998 0.428499 0.903542i $$-0.359042\pi$$
0.428499 + 0.903542i $$0.359042\pi$$
$$660$$ 0 0
$$661$$ −17.0000 −0.661223 −0.330612 0.943767i $$-0.607255\pi$$
−0.330612 + 0.943767i $$0.607255\pi$$
$$662$$ −18.0000 −0.699590
$$663$$ 0 0
$$664$$ 7.00000 0.271653
$$665$$ 0 0
$$666$$ 12.0000 0.464991
$$667$$ −6.00000 −0.232321
$$668$$ −2.00000 −0.0773823
$$669$$ 0 0
$$670$$ 12.0000 0.463600
$$671$$ 14.0000 0.540464
$$672$$ 0 0
$$673$$ −23.0000 −0.886585 −0.443292 0.896377i $$-0.646190\pi$$
−0.443292 + 0.896377i $$0.646190\pi$$
$$674$$ 13.0000 0.500741
$$675$$ 0 0
$$676$$ 12.0000 0.461538
$$677$$ −34.0000 −1.30673 −0.653363 0.757045i $$-0.726642\pi$$
−0.653363 + 0.757045i $$0.726642\pi$$
$$678$$ 0 0
$$679$$ −12.0000 −0.460518
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −8.00000 −0.306336
$$683$$ 30.0000 1.14792 0.573959 0.818884i $$-0.305407\pi$$
0.573959 + 0.818884i $$0.305407\pi$$
$$684$$ 0 0
$$685$$ −9.00000 −0.343872
$$686$$ −1.00000 −0.0381802
$$687$$ 0 0
$$688$$ −8.00000 −0.304997
$$689$$ 10.0000 0.380970
$$690$$ 0 0
$$691$$ −29.0000 −1.10321 −0.551606 0.834105i $$-0.685985\pi$$
−0.551606 + 0.834105i $$0.685985\pi$$
$$692$$ 13.0000 0.494186
$$693$$ 6.00000 0.227921
$$694$$ −18.0000 −0.683271
$$695$$ −12.0000 −0.455186
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 14.0000 0.529908
$$699$$ 0 0
$$700$$ −4.00000 −0.151186
$$701$$ 6.00000 0.226617 0.113308 0.993560i $$-0.463855\pi$$
0.113308 + 0.993560i $$0.463855\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −2.00000 −0.0753778
$$705$$ 0 0
$$706$$ −18.0000 −0.677439
$$707$$ −18.0000 −0.676960
$$708$$ 0 0
$$709$$ −34.0000 −1.27690 −0.638448 0.769665i $$-0.720423\pi$$
−0.638448 + 0.769665i $$0.720423\pi$$
$$710$$ −15.0000 −0.562940
$$711$$ −12.0000 −0.450035
$$712$$ 0 0
$$713$$ −4.00000 −0.149801
$$714$$ 0 0
$$715$$ −10.0000 −0.373979
$$716$$ −12.0000 −0.448461
$$717$$ 0 0
$$718$$ 4.00000 0.149279
$$719$$ 50.0000 1.86469 0.932343 0.361576i $$-0.117761\pi$$
0.932343 + 0.361576i $$0.117761\pi$$
$$720$$ −3.00000 −0.111803
$$721$$ −6.00000 −0.223452
$$722$$ 0 0
$$723$$ 0 0
$$724$$ −23.0000 −0.854788
$$725$$ 24.0000 0.891338
$$726$$ 0 0
$$727$$ 40.0000 1.48352 0.741759 0.670667i $$-0.233992\pi$$
0.741759 + 0.670667i $$0.233992\pi$$
$$728$$ −5.00000 −0.185312
$$729$$ −27.0000 −1.00000
$$730$$ 14.0000 0.518163
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 13.0000 0.480166 0.240083 0.970752i $$-0.422825\pi$$
0.240083 + 0.970752i $$0.422825\pi$$
$$734$$ 18.0000 0.664392
$$735$$ 0 0
$$736$$ −1.00000 −0.0368605
$$737$$ 24.0000 0.884051
$$738$$ 6.00000 0.220863
$$739$$ −38.0000 −1.39785 −0.698926 0.715194i $$-0.746338\pi$$
−0.698926 + 0.715194i $$0.746338\pi$$
$$740$$ 4.00000 0.147043
$$741$$ 0 0
$$742$$ −2.00000 −0.0734223
$$743$$ 43.0000 1.57752 0.788759 0.614703i $$-0.210724\pi$$
0.788759 + 0.614703i $$0.210724\pi$$
$$744$$ 0 0
$$745$$ −4.00000 −0.146549
$$746$$ −4.00000 −0.146450
$$747$$ 21.0000 0.768350
$$748$$ 0 0
$$749$$ 18.0000 0.657706
$$750$$ 0 0
$$751$$ 48.0000 1.75154 0.875772 0.482724i $$-0.160353\pi$$
0.875772 + 0.482724i $$0.160353\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 30.0000 1.09254
$$755$$ −19.0000 −0.691481
$$756$$ 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
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 0 0
$$763$$ 10.0000 0.362024
$$764$$ 17.0000 0.615038
$$765$$ 0 0
$$766$$ 36.0000 1.30073
$$767$$ 35.0000 1.26378
$$768$$ 0 0
$$769$$ −12.0000 −0.432731 −0.216366 0.976312i $$-0.569420\pi$$
−0.216366 + 0.976312i $$0.569420\pi$$
$$770$$ 2.00000 0.0720750
$$771$$ 0 0
$$772$$ 3.00000 0.107972
$$773$$ −17.0000 −0.611448 −0.305724 0.952120i $$-0.598898\pi$$
−0.305724 + 0.952120i $$0.598898\pi$$
$$774$$ −24.0000 −0.862662
$$775$$ 16.0000 0.574737
$$776$$ 12.0000 0.430775
$$777$$ 0 0
$$778$$ 30.0000 1.07555
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −30.0000 −1.07348
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 7.00000 0.249841
$$786$$ 0 0
$$787$$ −25.0000 −0.891154 −0.445577 0.895244i $$-0.647001\pi$$
−0.445577 + 0.895244i $$0.647001\pi$$
$$788$$ 2.00000 0.0712470
$$789$$ 0 0
$$790$$ −4.00000 −0.142314
$$791$$ 5.00000 0.177780
$$792$$ −6.00000 −0.213201
$$793$$ −35.0000 −1.24289
$$794$$ 6.00000 0.212932
$$795$$ 0 0
$$796$$ −4.00000 −0.141776
$$797$$ −7.00000 −0.247953 −0.123976 0.992285i $$-0.539565\pi$$
−0.123976 + 0.992285i $$0.539565\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 4.00000 0.141421
$$801$$ 0 0
$$802$$ −25.0000 −0.882781
$$803$$ 28.0000 0.988099
$$804$$ 0 0
$$805$$ 1.00000 0.0352454
$$806$$ 20.0000 0.704470
$$807$$ 0 0
$$808$$ 18.0000 0.633238
$$809$$ 33.0000 1.16022 0.580109 0.814539i $$-0.303010\pi$$
0.580109 + 0.814539i $$0.303010\pi$$
$$810$$ −9.00000 −0.316228
$$811$$ 12.0000 0.421377 0.210688 0.977553i $$-0.432429\pi$$
0.210688 + 0.977553i $$0.432429\pi$$
$$812$$ −6.00000 −0.210559
$$813$$ 0 0
$$814$$ 8.00000 0.280400
$$815$$ −4.00000 −0.140114
$$816$$ 0 0
$$817$$ 0 0
$$818$$ −4.00000 −0.139857
$$819$$ −15.0000 −0.524142
$$820$$ 2.00000 0.0698430
$$821$$ −48.0000 −1.67521 −0.837606 0.546275i $$-0.816045\pi$$
−0.837606 + 0.546275i $$0.816045\pi$$
$$822$$ 0 0
$$823$$ 5.00000 0.174289 0.0871445 0.996196i $$-0.472226\pi$$
0.0871445 + 0.996196i $$0.472226\pi$$
$$824$$ 6.00000 0.209020
$$825$$ 0 0
$$826$$ −7.00000 −0.243561
$$827$$ −6.00000 −0.208640 −0.104320 0.994544i $$-0.533267\pi$$
−0.104320 + 0.994544i $$0.533267\pi$$
$$828$$ −3.00000 −0.104257
$$829$$ 31.0000 1.07667 0.538337 0.842729i $$-0.319053\pi$$
0.538337 + 0.842729i $$0.319053\pi$$
$$830$$ 7.00000 0.242974
$$831$$ 0 0
$$832$$ 5.00000 0.173344
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −2.00000 −0.0692129
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 28.0000 0.967244
$$839$$ −54.0000 −1.86429 −0.932144 0.362089i $$-0.882064\pi$$
−0.932144 + 0.362089i $$0.882064\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 34.0000 1.17172
$$843$$ 0 0
$$844$$ 8.00000 0.275371
$$845$$ 12.0000 0.412813
$$846$$ 0 0
$$847$$ −7.00000 −0.240523
$$848$$ 2.00000 0.0686803
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 4.00000 0.137118
$$852$$ 0 0
$$853$$ 26.0000 0.890223 0.445112 0.895475i $$-0.353164\pi$$
0.445112 + 0.895475i $$0.353164\pi$$
$$854$$ 7.00000 0.239535
$$855$$ 0 0
$$856$$ −18.0000 −0.615227
$$857$$ −14.0000 −0.478231 −0.239115 0.970991i $$-0.576857\pi$$
−0.239115 + 0.970991i $$0.576857\pi$$
$$858$$ 0 0
$$859$$ 28.0000 0.955348 0.477674 0.878537i $$-0.341480\pi$$
0.477674 + 0.878537i $$0.341480\pi$$
$$860$$ −8.00000 −0.272798
$$861$$ 0 0
$$862$$ 12.0000 0.408722
$$863$$ 32.0000 1.08929 0.544646 0.838666i $$-0.316664\pi$$
0.544646 + 0.838666i $$0.316664\pi$$
$$864$$ 0 0
$$865$$ 13.0000 0.442013
$$866$$ 2.00000 0.0679628
$$867$$ 0 0
$$868$$ −4.00000 −0.135769
$$869$$ −8.00000 −0.271381
$$870$$ 0 0
$$871$$ −60.0000 −2.03302
$$872$$ −10.0000 −0.338643
$$873$$ 36.0000 1.21842
$$874$$ 0 0
$$875$$ −9.00000 −0.304256
$$876$$ 0 0
$$877$$ 46.0000 1.55331 0.776655 0.629926i $$-0.216915\pi$$
0.776655 + 0.629926i $$0.216915\pi$$
$$878$$ −20.0000 −0.674967
$$879$$ 0 0
$$880$$ −2.00000 −0.0674200
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 3.00000 0.101015
$$883$$ 34.0000 1.14419 0.572096 0.820187i $$-0.306131\pi$$
0.572096 + 0.820187i $$0.306131\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 34.0000 1.14225
$$887$$ 42.0000 1.41022 0.705111 0.709097i $$-0.250897\pi$$
0.705111 + 0.709097i $$0.250897\pi$$
$$888$$ 0 0
$$889$$ −13.0000 −0.436006
$$890$$ 0 0
$$891$$ −18.0000 −0.603023
$$892$$ 2.00000 0.0669650
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −12.0000 −0.401116
$$896$$ −1.00000 −0.0334077
$$897$$ 0 0
$$898$$ 37.0000 1.23471
$$899$$ 24.0000 0.800445
$$900$$ 12.0000 0.400000
$$901$$ 0 0
$$902$$ 4.00000 0.133185
$$903$$ 0 0
$$904$$ −5.00000 −0.166298
$$905$$ −23.0000 −0.764546
$$906$$ 0 0
$$907$$ 10.0000 0.332045 0.166022 0.986122i $$-0.446908\pi$$
0.166022 + 0.986122i $$0.446908\pi$$
$$908$$ 3.00000 0.0995585
$$909$$ 54.0000 1.79107
$$910$$ −5.00000 −0.165748
$$911$$ −9.00000 −0.298183 −0.149092 0.988823i $$-0.547635\pi$$
−0.149092 + 0.988823i $$0.547635\pi$$
$$912$$ 0 0
$$913$$ 14.0000 0.463332
$$914$$ 39.0000 1.29001
$$915$$ 0 0
$$916$$ 27.0000 0.892105
$$917$$ 15.0000 0.495344
$$918$$ 0 0
$$919$$ 3.00000 0.0989609 0.0494804 0.998775i $$-0.484243\pi$$
0.0494804 + 0.998775i $$0.484243\pi$$
$$920$$ −1.00000 −0.0329690
$$921$$ 0 0
$$922$$ 37.0000 1.21853
$$923$$ 75.0000 2.46866
$$924$$ 0 0
$$925$$ −16.0000 −0.526077
$$926$$ 5.00000 0.164310
$$927$$ 18.0000 0.591198
$$928$$ 6.00000 0.196960
$$929$$ 36.0000 1.18112 0.590561 0.806993i $$-0.298907\pi$$
0.590561 + 0.806993i $$0.298907\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −11.0000 −0.360317
$$933$$ 0 0
$$934$$ 36.0000 1.17796
$$935$$ 0 0
$$936$$ 15.0000 0.490290
$$937$$ 58.0000 1.89478 0.947389 0.320085i $$-0.103712\pi$$
0.947389 + 0.320085i $$0.103712\pi$$
$$938$$ 12.0000 0.391814
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −17.0000 −0.554184 −0.277092 0.960843i $$-0.589371\pi$$
−0.277092 + 0.960843i $$0.589371\pi$$
$$942$$ 0 0
$$943$$ 2.00000 0.0651290
$$944$$ 7.00000 0.227831
$$945$$ 0 0
$$946$$ −16.0000 −0.520205
$$947$$ −18.0000 −0.584921 −0.292461 0.956278i $$-0.594474\pi$$
−0.292461 + 0.956278i $$0.594474\pi$$
$$948$$ 0 0
$$949$$ −70.0000 −2.27230
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 22.0000 0.712650 0.356325 0.934362i $$-0.384030\pi$$
0.356325 + 0.934362i $$0.384030\pi$$
$$954$$ 6.00000 0.194257
$$955$$ 17.0000 0.550107
$$956$$ −5.00000 −0.161712
$$957$$ 0 0
$$958$$ −24.0000 −0.775405
$$959$$ −9.00000 −0.290625
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ −20.0000 −0.644826
$$963$$ −54.0000 −1.74013
$$964$$ 4.00000 0.128831
$$965$$ 3.00000 0.0965734
$$966$$ 0 0
$$967$$ −57.0000 −1.83300 −0.916498 0.400039i $$-0.868997\pi$$
−0.916498 + 0.400039i $$0.868997\pi$$
$$968$$ 7.00000 0.224989
$$969$$ 0 0
$$970$$ 12.0000 0.385297
$$971$$ 41.0000 1.31575 0.657876 0.753126i $$-0.271455\pi$$
0.657876 + 0.753126i $$0.271455\pi$$
$$972$$ 0 0
$$973$$ −12.0000 −0.384702
$$974$$ −16.0000 −0.512673
$$975$$ 0 0
$$976$$ −7.00000 −0.224065
$$977$$ 37.0000 1.18373 0.591867 0.806035i $$-0.298391\pi$$
0.591867 + 0.806035i $$0.298391\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 1.00000 0.0319438
$$981$$ −30.0000 −0.957826
$$982$$ −20.0000 −0.638226
$$983$$ −42.0000 −1.33959 −0.669796 0.742545i $$-0.733618\pi$$
−0.669796 + 0.742545i $$0.733618\pi$$
$$984$$ 0 0
$$985$$ 2.00000 0.0637253
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −8.00000 −0.254385
$$990$$ −6.00000 −0.190693
$$991$$ 31.0000 0.984747 0.492374 0.870384i $$-0.336129\pi$$
0.492374 + 0.870384i $$0.336129\pi$$
$$992$$ 4.00000 0.127000
$$993$$ 0 0
$$994$$ −15.0000 −0.475771
$$995$$ −4.00000 −0.126809
$$996$$ 0 0
$$997$$ 17.0000 0.538395 0.269198 0.963085i $$-0.413241\pi$$
0.269198 + 0.963085i $$0.413241\pi$$
$$998$$ −24.0000 −0.759707
$$999$$ 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 5054.2.a.a.1.1 1
19.8 odd 6 266.2.f.a.197.1 2
19.12 odd 6 266.2.f.a.239.1 yes 2
19.18 odd 2 5054.2.a.b.1.1 1
57.8 even 6 2394.2.o.i.1261.1 2
57.50 even 6 2394.2.o.i.505.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
266.2.f.a.197.1 2 19.8 odd 6
266.2.f.a.239.1 yes 2 19.12 odd 6
2394.2.o.i.505.1 2 57.50 even 6
2394.2.o.i.1261.1 2 57.8 even 6
5054.2.a.a.1.1 1 1.1 even 1 trivial
5054.2.a.b.1.1 1 19.18 odd 2