# Properties

 Label 2898.2.a.a.1.1 Level $2898$ Weight $2$ Character 2898.1 Self dual yes Analytic conductor $23.141$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2898.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$23.1406465058$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 966) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2898.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} +3.00000 q^{10} -4.00000 q^{11} -3.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} -3.00000 q^{20} +4.00000 q^{22} -1.00000 q^{23} +4.00000 q^{25} +3.00000 q^{26} -1.00000 q^{28} -3.00000 q^{29} -6.00000 q^{31} -1.00000 q^{32} -4.00000 q^{34} +3.00000 q^{35} -9.00000 q^{37} +3.00000 q^{40} -9.00000 q^{41} -3.00000 q^{43} -4.00000 q^{44} +1.00000 q^{46} +7.00000 q^{47} +1.00000 q^{49} -4.00000 q^{50} -3.00000 q^{52} +4.00000 q^{53} +12.0000 q^{55} +1.00000 q^{56} +3.00000 q^{58} -6.00000 q^{59} +10.0000 q^{61} +6.00000 q^{62} +1.00000 q^{64} +9.00000 q^{65} +4.00000 q^{67} +4.00000 q^{68} -3.00000 q^{70} +6.00000 q^{71} -8.00000 q^{73} +9.00000 q^{74} +4.00000 q^{77} +8.00000 q^{79} -3.00000 q^{80} +9.00000 q^{82} -4.00000 q^{83} -12.0000 q^{85} +3.00000 q^{86} +4.00000 q^{88} +14.0000 q^{89} +3.00000 q^{91} -1.00000 q^{92} -7.00000 q^{94} -7.00000 q^{97} -1.00000 q^{98} +O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −3.00000 −1.34164 −0.670820 0.741620i $$-0.734058\pi$$
−0.670820 + 0.741620i $$0.734058\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 3.00000 0.948683
$$11$$ −4.00000 −1.20605 −0.603023 0.797724i $$-0.706037\pi$$
−0.603023 + 0.797724i $$0.706037\pi$$
$$12$$ 0 0
$$13$$ −3.00000 −0.832050 −0.416025 0.909353i $$-0.636577\pi$$
−0.416025 + 0.909353i $$0.636577\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ −3.00000 −0.670820
$$21$$ 0 0
$$22$$ 4.00000 0.852803
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 4.00000 0.800000
$$26$$ 3.00000 0.588348
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ −3.00000 −0.557086 −0.278543 0.960424i $$-0.589851\pi$$
−0.278543 + 0.960424i $$0.589851\pi$$
$$30$$ 0 0
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ −4.00000 −0.685994
$$35$$ 3.00000 0.507093
$$36$$ 0 0
$$37$$ −9.00000 −1.47959 −0.739795 0.672832i $$-0.765078\pi$$
−0.739795 + 0.672832i $$0.765078\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 3.00000 0.474342
$$41$$ −9.00000 −1.40556 −0.702782 0.711405i $$-0.748059\pi$$
−0.702782 + 0.711405i $$0.748059\pi$$
$$42$$ 0 0
$$43$$ −3.00000 −0.457496 −0.228748 0.973486i $$-0.573463\pi$$
−0.228748 + 0.973486i $$0.573463\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 0 0
$$46$$ 1.00000 0.147442
$$47$$ 7.00000 1.02105 0.510527 0.859861i $$-0.329450\pi$$
0.510527 + 0.859861i $$0.329450\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ −4.00000 −0.565685
$$51$$ 0 0
$$52$$ −3.00000 −0.416025
$$53$$ 4.00000 0.549442 0.274721 0.961524i $$-0.411414\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 0 0
$$55$$ 12.0000 1.61808
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ 3.00000 0.393919
$$59$$ −6.00000 −0.781133 −0.390567 0.920575i $$-0.627721\pi$$
−0.390567 + 0.920575i $$0.627721\pi$$
$$60$$ 0 0
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ 6.00000 0.762001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 9.00000 1.11631
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ 4.00000 0.485071
$$69$$ 0 0
$$70$$ −3.00000 −0.358569
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ −8.00000 −0.936329 −0.468165 0.883641i $$-0.655085\pi$$
−0.468165 + 0.883641i $$0.655085\pi$$
$$74$$ 9.00000 1.04623
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.00000 0.455842
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ −3.00000 −0.335410
$$81$$ 0 0
$$82$$ 9.00000 0.993884
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ −12.0000 −1.30158
$$86$$ 3.00000 0.323498
$$87$$ 0 0
$$88$$ 4.00000 0.426401
$$89$$ 14.0000 1.48400 0.741999 0.670402i $$-0.233878\pi$$
0.741999 + 0.670402i $$0.233878\pi$$
$$90$$ 0 0
$$91$$ 3.00000 0.314485
$$92$$ −1.00000 −0.104257
$$93$$ 0 0
$$94$$ −7.00000 −0.721995
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −7.00000 −0.710742 −0.355371 0.934725i $$-0.615646\pi$$
−0.355371 + 0.934725i $$0.615646\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0 0
$$100$$ 4.00000 0.400000
$$101$$ 14.0000 1.39305 0.696526 0.717532i $$-0.254728\pi$$
0.696526 + 0.717532i $$0.254728\pi$$
$$102$$ 0 0
$$103$$ 5.00000 0.492665 0.246332 0.969185i $$-0.420775\pi$$
0.246332 + 0.969185i $$0.420775\pi$$
$$104$$ 3.00000 0.294174
$$105$$ 0 0
$$106$$ −4.00000 −0.388514
$$107$$ −8.00000 −0.773389 −0.386695 0.922208i $$-0.626383\pi$$
−0.386695 + 0.922208i $$0.626383\pi$$
$$108$$ 0 0
$$109$$ 3.00000 0.287348 0.143674 0.989625i $$-0.454108\pi$$
0.143674 + 0.989625i $$0.454108\pi$$
$$110$$ −12.0000 −1.14416
$$111$$ 0 0
$$112$$ −1.00000 −0.0944911
$$113$$ −9.00000 −0.846649 −0.423324 0.905978i $$-0.639137\pi$$
−0.423324 + 0.905978i $$0.639137\pi$$
$$114$$ 0 0
$$115$$ 3.00000 0.279751
$$116$$ −3.00000 −0.278543
$$117$$ 0 0
$$118$$ 6.00000 0.552345
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ −10.0000 −0.905357
$$123$$ 0 0
$$124$$ −6.00000 −0.538816
$$125$$ 3.00000 0.268328
$$126$$ 0 0
$$127$$ 7.00000 0.621150 0.310575 0.950549i $$-0.399478\pi$$
0.310575 + 0.950549i $$0.399478\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ −9.00000 −0.789352
$$131$$ 6.00000 0.524222 0.262111 0.965038i $$-0.415581\pi$$
0.262111 + 0.965038i $$0.415581\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ −4.00000 −0.342997
$$137$$ 15.0000 1.28154 0.640768 0.767734i $$-0.278616\pi$$
0.640768 + 0.767734i $$0.278616\pi$$
$$138$$ 0 0
$$139$$ 9.00000 0.763370 0.381685 0.924292i $$-0.375344\pi$$
0.381685 + 0.924292i $$0.375344\pi$$
$$140$$ 3.00000 0.253546
$$141$$ 0 0
$$142$$ −6.00000 −0.503509
$$143$$ 12.0000 1.00349
$$144$$ 0 0
$$145$$ 9.00000 0.747409
$$146$$ 8.00000 0.662085
$$147$$ 0 0
$$148$$ −9.00000 −0.739795
$$149$$ −16.0000 −1.31077 −0.655386 0.755295i $$-0.727494\pi$$
−0.655386 + 0.755295i $$0.727494\pi$$
$$150$$ 0 0
$$151$$ 15.0000 1.22068 0.610341 0.792139i $$-0.291032\pi$$
0.610341 + 0.792139i $$0.291032\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ −4.00000 −0.322329
$$155$$ 18.0000 1.44579
$$156$$ 0 0
$$157$$ −8.00000 −0.638470 −0.319235 0.947676i $$-0.603426\pi$$
−0.319235 + 0.947676i $$0.603426\pi$$
$$158$$ −8.00000 −0.636446
$$159$$ 0 0
$$160$$ 3.00000 0.237171
$$161$$ 1.00000 0.0788110
$$162$$ 0 0
$$163$$ 16.0000 1.25322 0.626608 0.779334i $$-0.284443\pi$$
0.626608 + 0.779334i $$0.284443\pi$$
$$164$$ −9.00000 −0.702782
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ 20.0000 1.54765 0.773823 0.633402i $$-0.218342\pi$$
0.773823 + 0.633402i $$0.218342\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 12.0000 0.920358
$$171$$ 0 0
$$172$$ −3.00000 −0.228748
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ −4.00000 −0.302372
$$176$$ −4.00000 −0.301511
$$177$$ 0 0
$$178$$ −14.0000 −1.04934
$$179$$ −19.0000 −1.42013 −0.710063 0.704138i $$-0.751334\pi$$
−0.710063 + 0.704138i $$0.751334\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ −3.00000 −0.222375
$$183$$ 0 0
$$184$$ 1.00000 0.0737210
$$185$$ 27.0000 1.98508
$$186$$ 0 0
$$187$$ −16.0000 −1.17004
$$188$$ 7.00000 0.510527
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ −17.0000 −1.22369 −0.611843 0.790979i $$-0.709572\pi$$
−0.611843 + 0.790979i $$0.709572\pi$$
$$194$$ 7.00000 0.502571
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ 23.0000 1.63868 0.819341 0.573306i $$-0.194340\pi$$
0.819341 + 0.573306i $$0.194340\pi$$
$$198$$ 0 0
$$199$$ −5.00000 −0.354441 −0.177220 0.984171i $$-0.556711\pi$$
−0.177220 + 0.984171i $$0.556711\pi$$
$$200$$ −4.00000 −0.282843
$$201$$ 0 0
$$202$$ −14.0000 −0.985037
$$203$$ 3.00000 0.210559
$$204$$ 0 0
$$205$$ 27.0000 1.88576
$$206$$ −5.00000 −0.348367
$$207$$ 0 0
$$208$$ −3.00000 −0.208013
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 4.00000 0.274721
$$213$$ 0 0
$$214$$ 8.00000 0.546869
$$215$$ 9.00000 0.613795
$$216$$ 0 0
$$217$$ 6.00000 0.407307
$$218$$ −3.00000 −0.203186
$$219$$ 0 0
$$220$$ 12.0000 0.809040
$$221$$ −12.0000 −0.807207
$$222$$ 0 0
$$223$$ −14.0000 −0.937509 −0.468755 0.883328i $$-0.655297\pi$$
−0.468755 + 0.883328i $$0.655297\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ 9.00000 0.598671
$$227$$ −11.0000 −0.730096 −0.365048 0.930989i $$-0.618947\pi$$
−0.365048 + 0.930989i $$0.618947\pi$$
$$228$$ 0 0
$$229$$ 12.0000 0.792982 0.396491 0.918039i $$-0.370228\pi$$
0.396491 + 0.918039i $$0.370228\pi$$
$$230$$ −3.00000 −0.197814
$$231$$ 0 0
$$232$$ 3.00000 0.196960
$$233$$ 10.0000 0.655122 0.327561 0.944830i $$-0.393773\pi$$
0.327561 + 0.944830i $$0.393773\pi$$
$$234$$ 0 0
$$235$$ −21.0000 −1.36989
$$236$$ −6.00000 −0.390567
$$237$$ 0 0
$$238$$ 4.00000 0.259281
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −5.00000 −0.322078 −0.161039 0.986948i $$-0.551485\pi$$
−0.161039 + 0.986948i $$0.551485\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 0 0
$$244$$ 10.0000 0.640184
$$245$$ −3.00000 −0.191663
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 6.00000 0.381000
$$249$$ 0 0
$$250$$ −3.00000 −0.189737
$$251$$ −19.0000 −1.19927 −0.599635 0.800274i $$-0.704687\pi$$
−0.599635 + 0.800274i $$0.704687\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ −7.00000 −0.439219
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 26.0000 1.62184 0.810918 0.585160i $$-0.198968\pi$$
0.810918 + 0.585160i $$0.198968\pi$$
$$258$$ 0 0
$$259$$ 9.00000 0.559233
$$260$$ 9.00000 0.558156
$$261$$ 0 0
$$262$$ −6.00000 −0.370681
$$263$$ −21.0000 −1.29492 −0.647458 0.762101i $$-0.724168\pi$$
−0.647458 + 0.762101i $$0.724168\pi$$
$$264$$ 0 0
$$265$$ −12.0000 −0.737154
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 4.00000 0.244339
$$269$$ 6.00000 0.365826 0.182913 0.983129i $$-0.441447\pi$$
0.182913 + 0.983129i $$0.441447\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ −15.0000 −0.906183
$$275$$ −16.0000 −0.964836
$$276$$ 0 0
$$277$$ 20.0000 1.20168 0.600842 0.799368i $$-0.294832\pi$$
0.600842 + 0.799368i $$0.294832\pi$$
$$278$$ −9.00000 −0.539784
$$279$$ 0 0
$$280$$ −3.00000 −0.179284
$$281$$ −23.0000 −1.37206 −0.686032 0.727571i $$-0.740649\pi$$
−0.686032 + 0.727571i $$0.740649\pi$$
$$282$$ 0 0
$$283$$ −6.00000 −0.356663 −0.178331 0.983970i $$-0.557070\pi$$
−0.178331 + 0.983970i $$0.557070\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 0 0
$$286$$ −12.0000 −0.709575
$$287$$ 9.00000 0.531253
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ −9.00000 −0.528498
$$291$$ 0 0
$$292$$ −8.00000 −0.468165
$$293$$ −6.00000 −0.350524 −0.175262 0.984522i $$-0.556077\pi$$
−0.175262 + 0.984522i $$0.556077\pi$$
$$294$$ 0 0
$$295$$ 18.0000 1.04800
$$296$$ 9.00000 0.523114
$$297$$ 0 0
$$298$$ 16.0000 0.926855
$$299$$ 3.00000 0.173494
$$300$$ 0 0
$$301$$ 3.00000 0.172917
$$302$$ −15.0000 −0.863153
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −30.0000 −1.71780
$$306$$ 0 0
$$307$$ 15.0000 0.856095 0.428048 0.903756i $$-0.359202\pi$$
0.428048 + 0.903756i $$0.359202\pi$$
$$308$$ 4.00000 0.227921
$$309$$ 0 0
$$310$$ −18.0000 −1.02233
$$311$$ 28.0000 1.58773 0.793867 0.608091i $$-0.208065\pi$$
0.793867 + 0.608091i $$0.208065\pi$$
$$312$$ 0 0
$$313$$ 34.0000 1.92179 0.960897 0.276907i $$-0.0893093\pi$$
0.960897 + 0.276907i $$0.0893093\pi$$
$$314$$ 8.00000 0.451466
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ −5.00000 −0.280828 −0.140414 0.990093i $$-0.544843\pi$$
−0.140414 + 0.990093i $$0.544843\pi$$
$$318$$ 0 0
$$319$$ 12.0000 0.671871
$$320$$ −3.00000 −0.167705
$$321$$ 0 0
$$322$$ −1.00000 −0.0557278
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −12.0000 −0.665640
$$326$$ −16.0000 −0.886158
$$327$$ 0 0
$$328$$ 9.00000 0.496942
$$329$$ −7.00000 −0.385922
$$330$$ 0 0
$$331$$ 8.00000 0.439720 0.219860 0.975531i $$-0.429440\pi$$
0.219860 + 0.975531i $$0.429440\pi$$
$$332$$ −4.00000 −0.219529
$$333$$ 0 0
$$334$$ −20.0000 −1.09435
$$335$$ −12.0000 −0.655630
$$336$$ 0 0
$$337$$ −12.0000 −0.653682 −0.326841 0.945079i $$-0.605984\pi$$
−0.326841 + 0.945079i $$0.605984\pi$$
$$338$$ 4.00000 0.217571
$$339$$ 0 0
$$340$$ −12.0000 −0.650791
$$341$$ 24.0000 1.29967
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 3.00000 0.161749
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ −23.0000 −1.23470 −0.617352 0.786687i $$-0.711795\pi$$
−0.617352 + 0.786687i $$0.711795\pi$$
$$348$$ 0 0
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ 4.00000 0.213201
$$353$$ 29.0000 1.54351 0.771757 0.635917i $$-0.219378\pi$$
0.771757 + 0.635917i $$0.219378\pi$$
$$354$$ 0 0
$$355$$ −18.0000 −0.955341
$$356$$ 14.0000 0.741999
$$357$$ 0 0
$$358$$ 19.0000 1.00418
$$359$$ 1.00000 0.0527780 0.0263890 0.999652i $$-0.491599\pi$$
0.0263890 + 0.999652i $$0.491599\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 2.00000 0.105118
$$363$$ 0 0
$$364$$ 3.00000 0.157243
$$365$$ 24.0000 1.25622
$$366$$ 0 0
$$367$$ 31.0000 1.61819 0.809093 0.587680i $$-0.199959\pi$$
0.809093 + 0.587680i $$0.199959\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ 0 0
$$370$$ −27.0000 −1.40366
$$371$$ −4.00000 −0.207670
$$372$$ 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
$$376$$ −7.00000 −0.360997
$$377$$ 9.00000 0.463524
$$378$$ 0 0
$$379$$ −25.0000 −1.28416 −0.642082 0.766636i $$-0.721929\pi$$
−0.642082 + 0.766636i $$0.721929\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −12.0000 −0.613973
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ −12.0000 −0.611577
$$386$$ 17.0000 0.865277
$$387$$ 0 0
$$388$$ −7.00000 −0.355371
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ −1.00000 −0.0505076
$$393$$ 0 0
$$394$$ −23.0000 −1.15872
$$395$$ −24.0000 −1.20757
$$396$$ 0 0
$$397$$ 34.0000 1.70641 0.853206 0.521575i $$-0.174655\pi$$
0.853206 + 0.521575i $$0.174655\pi$$
$$398$$ 5.00000 0.250627
$$399$$ 0 0
$$400$$ 4.00000 0.200000
$$401$$ −38.0000 −1.89763 −0.948815 0.315833i $$-0.897716\pi$$
−0.948815 + 0.315833i $$0.897716\pi$$
$$402$$ 0 0
$$403$$ 18.0000 0.896644
$$404$$ 14.0000 0.696526
$$405$$ 0 0
$$406$$ −3.00000 −0.148888
$$407$$ 36.0000 1.78445
$$408$$ 0 0
$$409$$ 16.0000 0.791149 0.395575 0.918434i $$-0.370545\pi$$
0.395575 + 0.918434i $$0.370545\pi$$
$$410$$ −27.0000 −1.33343
$$411$$ 0 0
$$412$$ 5.00000 0.246332
$$413$$ 6.00000 0.295241
$$414$$ 0 0
$$415$$ 12.0000 0.589057
$$416$$ 3.00000 0.147087
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 4.00000 0.195413 0.0977064 0.995215i $$-0.468849\pi$$
0.0977064 + 0.995215i $$0.468849\pi$$
$$420$$ 0 0
$$421$$ −21.0000 −1.02348 −0.511739 0.859141i $$-0.670998\pi$$
−0.511739 + 0.859141i $$0.670998\pi$$
$$422$$ 12.0000 0.584151
$$423$$ 0 0
$$424$$ −4.00000 −0.194257
$$425$$ 16.0000 0.776114
$$426$$ 0 0
$$427$$ −10.0000 −0.483934
$$428$$ −8.00000 −0.386695
$$429$$ 0 0
$$430$$ −9.00000 −0.434019
$$431$$ −21.0000 −1.01153 −0.505767 0.862670i $$-0.668791\pi$$
−0.505767 + 0.862670i $$0.668791\pi$$
$$432$$ 0 0
$$433$$ 23.0000 1.10531 0.552655 0.833410i $$-0.313615\pi$$
0.552655 + 0.833410i $$0.313615\pi$$
$$434$$ −6.00000 −0.288009
$$435$$ 0 0
$$436$$ 3.00000 0.143674
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −10.0000 −0.477274 −0.238637 0.971109i $$-0.576701\pi$$
−0.238637 + 0.971109i $$0.576701\pi$$
$$440$$ −12.0000 −0.572078
$$441$$ 0 0
$$442$$ 12.0000 0.570782
$$443$$ −25.0000 −1.18779 −0.593893 0.804544i $$-0.702410\pi$$
−0.593893 + 0.804544i $$0.702410\pi$$
$$444$$ 0 0
$$445$$ −42.0000 −1.99099
$$446$$ 14.0000 0.662919
$$447$$ 0 0
$$448$$ −1.00000 −0.0472456
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 36.0000 1.69517
$$452$$ −9.00000 −0.423324
$$453$$ 0 0
$$454$$ 11.0000 0.516256
$$455$$ −9.00000 −0.421927
$$456$$ 0 0
$$457$$ 24.0000 1.12267 0.561336 0.827588i $$-0.310287\pi$$
0.561336 + 0.827588i $$0.310287\pi$$
$$458$$ −12.0000 −0.560723
$$459$$ 0 0
$$460$$ 3.00000 0.139876
$$461$$ 22.0000 1.02464 0.512321 0.858794i $$-0.328786\pi$$
0.512321 + 0.858794i $$0.328786\pi$$
$$462$$ 0 0
$$463$$ 13.0000 0.604161 0.302081 0.953282i $$-0.402319\pi$$
0.302081 + 0.953282i $$0.402319\pi$$
$$464$$ −3.00000 −0.139272
$$465$$ 0 0
$$466$$ −10.0000 −0.463241
$$467$$ −13.0000 −0.601568 −0.300784 0.953692i $$-0.597248\pi$$
−0.300784 + 0.953692i $$0.597248\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ 21.0000 0.968658
$$471$$ 0 0
$$472$$ 6.00000 0.276172
$$473$$ 12.0000 0.551761
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −4.00000 −0.183340
$$477$$ 0 0
$$478$$ −12.0000 −0.548867
$$479$$ −30.0000 −1.37073 −0.685367 0.728197i $$-0.740358\pi$$
−0.685367 + 0.728197i $$0.740358\pi$$
$$480$$ 0 0
$$481$$ 27.0000 1.23109
$$482$$ 5.00000 0.227744
$$483$$ 0 0
$$484$$ 5.00000 0.227273
$$485$$ 21.0000 0.953561
$$486$$ 0 0
$$487$$ 13.0000 0.589086 0.294543 0.955638i $$-0.404833\pi$$
0.294543 + 0.955638i $$0.404833\pi$$
$$488$$ −10.0000 −0.452679
$$489$$ 0 0
$$490$$ 3.00000 0.135526
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ 0 0
$$493$$ −12.0000 −0.540453
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −6.00000 −0.269408
$$497$$ −6.00000 −0.269137
$$498$$ 0 0
$$499$$ 34.0000 1.52205 0.761025 0.648723i $$-0.224697\pi$$
0.761025 + 0.648723i $$0.224697\pi$$
$$500$$ 3.00000 0.134164
$$501$$ 0 0
$$502$$ 19.0000 0.848012
$$503$$ 30.0000 1.33763 0.668817 0.743427i $$-0.266801\pi$$
0.668817 + 0.743427i $$0.266801\pi$$
$$504$$ 0 0
$$505$$ −42.0000 −1.86898
$$506$$ −4.00000 −0.177822
$$507$$ 0 0
$$508$$ 7.00000 0.310575
$$509$$ −44.0000 −1.95027 −0.975133 0.221621i $$-0.928865\pi$$
−0.975133 + 0.221621i $$0.928865\pi$$
$$510$$ 0 0
$$511$$ 8.00000 0.353899
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −26.0000 −1.14681
$$515$$ −15.0000 −0.660979
$$516$$ 0 0
$$517$$ −28.0000 −1.23144
$$518$$ −9.00000 −0.395437
$$519$$ 0 0
$$520$$ −9.00000 −0.394676
$$521$$ 6.00000 0.262865 0.131432 0.991325i $$-0.458042\pi$$
0.131432 + 0.991325i $$0.458042\pi$$
$$522$$ 0 0
$$523$$ 42.0000 1.83653 0.918266 0.395964i $$-0.129590\pi$$
0.918266 + 0.395964i $$0.129590\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ 21.0000 0.915644
$$527$$ −24.0000 −1.04546
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 12.0000 0.521247
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 27.0000 1.16950
$$534$$ 0 0
$$535$$ 24.0000 1.03761
$$536$$ −4.00000 −0.172774
$$537$$ 0 0
$$538$$ −6.00000 −0.258678
$$539$$ −4.00000 −0.172292
$$540$$ 0 0
$$541$$ −28.0000 −1.20381 −0.601907 0.798566i $$-0.705592\pi$$
−0.601907 + 0.798566i $$0.705592\pi$$
$$542$$ −20.0000 −0.859074
$$543$$ 0 0
$$544$$ −4.00000 −0.171499
$$545$$ −9.00000 −0.385518
$$546$$ 0 0
$$547$$ 22.0000 0.940652 0.470326 0.882493i $$-0.344136\pi$$
0.470326 + 0.882493i $$0.344136\pi$$
$$548$$ 15.0000 0.640768
$$549$$ 0 0
$$550$$ 16.0000 0.682242
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −8.00000 −0.340195
$$554$$ −20.0000 −0.849719
$$555$$ 0 0
$$556$$ 9.00000 0.381685
$$557$$ −24.0000 −1.01691 −0.508456 0.861088i $$-0.669784\pi$$
−0.508456 + 0.861088i $$0.669784\pi$$
$$558$$ 0 0
$$559$$ 9.00000 0.380659
$$560$$ 3.00000 0.126773
$$561$$ 0 0
$$562$$ 23.0000 0.970196
$$563$$ −15.0000 −0.632175 −0.316087 0.948730i $$-0.602369\pi$$
−0.316087 + 0.948730i $$0.602369\pi$$
$$564$$ 0 0
$$565$$ 27.0000 1.13590
$$566$$ 6.00000 0.252199
$$567$$ 0 0
$$568$$ −6.00000 −0.251754
$$569$$ 13.0000 0.544988 0.272494 0.962157i $$-0.412151\pi$$
0.272494 + 0.962157i $$0.412151\pi$$
$$570$$ 0 0
$$571$$ −20.0000 −0.836974 −0.418487 0.908223i $$-0.637439\pi$$
−0.418487 + 0.908223i $$0.637439\pi$$
$$572$$ 12.0000 0.501745
$$573$$ 0 0
$$574$$ −9.00000 −0.375653
$$575$$ −4.00000 −0.166812
$$576$$ 0 0
$$577$$ −30.0000 −1.24892 −0.624458 0.781058i $$-0.714680\pi$$
−0.624458 + 0.781058i $$0.714680\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ 0 0
$$580$$ 9.00000 0.373705
$$581$$ 4.00000 0.165948
$$582$$ 0 0
$$583$$ −16.0000 −0.662652
$$584$$ 8.00000 0.331042
$$585$$ 0 0
$$586$$ 6.00000 0.247858
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −18.0000 −0.741048
$$591$$ 0 0
$$592$$ −9.00000 −0.369898
$$593$$ −29.0000 −1.19089 −0.595444 0.803397i $$-0.703024\pi$$
−0.595444 + 0.803397i $$0.703024\pi$$
$$594$$ 0 0
$$595$$ 12.0000 0.491952
$$596$$ −16.0000 −0.655386
$$597$$ 0 0
$$598$$ −3.00000 −0.122679
$$599$$ 40.0000 1.63436 0.817178 0.576386i $$-0.195537\pi$$
0.817178 + 0.576386i $$0.195537\pi$$
$$600$$ 0 0
$$601$$ −28.0000 −1.14214 −0.571072 0.820900i $$-0.693472\pi$$
−0.571072 + 0.820900i $$0.693472\pi$$
$$602$$ −3.00000 −0.122271
$$603$$ 0 0
$$604$$ 15.0000 0.610341
$$605$$ −15.0000 −0.609837
$$606$$ 0 0
$$607$$ 30.0000 1.21766 0.608831 0.793300i $$-0.291639\pi$$
0.608831 + 0.793300i $$0.291639\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 30.0000 1.21466
$$611$$ −21.0000 −0.849569
$$612$$ 0 0
$$613$$ 25.0000 1.00974 0.504870 0.863195i $$-0.331540\pi$$
0.504870 + 0.863195i $$0.331540\pi$$
$$614$$ −15.0000 −0.605351
$$615$$ 0 0
$$616$$ −4.00000 −0.161165
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ 0 0
$$619$$ 2.00000 0.0803868 0.0401934 0.999192i $$-0.487203\pi$$
0.0401934 + 0.999192i $$0.487203\pi$$
$$620$$ 18.0000 0.722897
$$621$$ 0 0
$$622$$ −28.0000 −1.12270
$$623$$ −14.0000 −0.560898
$$624$$ 0 0
$$625$$ −29.0000 −1.16000
$$626$$ −34.0000 −1.35891
$$627$$ 0 0
$$628$$ −8.00000 −0.319235
$$629$$ −36.0000 −1.43541
$$630$$ 0 0
$$631$$ 16.0000 0.636950 0.318475 0.947931i $$-0.396829\pi$$
0.318475 + 0.947931i $$0.396829\pi$$
$$632$$ −8.00000 −0.318223
$$633$$ 0 0
$$634$$ 5.00000 0.198575
$$635$$ −21.0000 −0.833360
$$636$$ 0 0
$$637$$ −3.00000 −0.118864
$$638$$ −12.0000 −0.475085
$$639$$ 0 0
$$640$$ 3.00000 0.118585
$$641$$ −15.0000 −0.592464 −0.296232 0.955116i $$-0.595730\pi$$
−0.296232 + 0.955116i $$0.595730\pi$$
$$642$$ 0 0
$$643$$ −26.0000 −1.02534 −0.512670 0.858586i $$-0.671344\pi$$
−0.512670 + 0.858586i $$0.671344\pi$$
$$644$$ 1.00000 0.0394055
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 24.0000 0.943537 0.471769 0.881722i $$-0.343616\pi$$
0.471769 + 0.881722i $$0.343616\pi$$
$$648$$ 0 0
$$649$$ 24.0000 0.942082
$$650$$ 12.0000 0.470679
$$651$$ 0 0
$$652$$ 16.0000 0.626608
$$653$$ −31.0000 −1.21312 −0.606562 0.795036i $$-0.707452\pi$$
−0.606562 + 0.795036i $$0.707452\pi$$
$$654$$ 0 0
$$655$$ −18.0000 −0.703318
$$656$$ −9.00000 −0.351391
$$657$$ 0 0
$$658$$ 7.00000 0.272888
$$659$$ 12.0000 0.467454 0.233727 0.972302i $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ 0 0
$$661$$ −38.0000 −1.47803 −0.739014 0.673690i $$-0.764708\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ −8.00000 −0.310929
$$663$$ 0 0
$$664$$ 4.00000 0.155230
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 3.00000 0.116160
$$668$$ 20.0000 0.773823
$$669$$ 0 0
$$670$$ 12.0000 0.463600
$$671$$ −40.0000 −1.54418
$$672$$ 0 0
$$673$$ 19.0000 0.732396 0.366198 0.930537i $$-0.380659\pi$$
0.366198 + 0.930537i $$0.380659\pi$$
$$674$$ 12.0000 0.462223
$$675$$ 0 0
$$676$$ −4.00000 −0.153846
$$677$$ −46.0000 −1.76792 −0.883962 0.467559i $$-0.845134\pi$$
−0.883962 + 0.467559i $$0.845134\pi$$
$$678$$ 0 0
$$679$$ 7.00000 0.268635
$$680$$ 12.0000 0.460179
$$681$$ 0 0
$$682$$ −24.0000 −0.919007
$$683$$ 4.00000 0.153056 0.0765279 0.997067i $$-0.475617\pi$$
0.0765279 + 0.997067i $$0.475617\pi$$
$$684$$ 0 0
$$685$$ −45.0000 −1.71936
$$686$$ 1.00000 0.0381802
$$687$$ 0 0
$$688$$ −3.00000 −0.114374
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ −5.00000 −0.190209 −0.0951045 0.995467i $$-0.530319\pi$$
−0.0951045 + 0.995467i $$0.530319\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ 23.0000 0.873068
$$695$$ −27.0000 −1.02417
$$696$$ 0 0
$$697$$ −36.0000 −1.36360
$$698$$ 26.0000 0.984115
$$699$$ 0 0
$$700$$ −4.00000 −0.151186
$$701$$ −36.0000 −1.35970 −0.679851 0.733351i $$-0.737955\pi$$
−0.679851 + 0.733351i $$0.737955\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −4.00000 −0.150756
$$705$$ 0 0
$$706$$ −29.0000 −1.09143
$$707$$ −14.0000 −0.526524
$$708$$ 0 0
$$709$$ −34.0000 −1.27690 −0.638448 0.769665i $$-0.720423\pi$$
−0.638448 + 0.769665i $$0.720423\pi$$
$$710$$ 18.0000 0.675528
$$711$$ 0 0
$$712$$ −14.0000 −0.524672
$$713$$ 6.00000 0.224702
$$714$$ 0 0
$$715$$ −36.0000 −1.34632
$$716$$ −19.0000 −0.710063
$$717$$ 0 0
$$718$$ −1.00000 −0.0373197
$$719$$ 7.00000 0.261056 0.130528 0.991445i $$-0.458333\pi$$
0.130528 + 0.991445i $$0.458333\pi$$
$$720$$ 0 0
$$721$$ −5.00000 −0.186210
$$722$$ 19.0000 0.707107
$$723$$ 0 0
$$724$$ −2.00000 −0.0743294
$$725$$ −12.0000 −0.445669
$$726$$ 0 0
$$727$$ −44.0000 −1.63187 −0.815935 0.578144i $$-0.803777\pi$$
−0.815935 + 0.578144i $$0.803777\pi$$
$$728$$ −3.00000 −0.111187
$$729$$ 0 0
$$730$$ −24.0000 −0.888280
$$731$$ −12.0000 −0.443836
$$732$$ 0 0
$$733$$ −16.0000 −0.590973 −0.295487 0.955347i $$-0.595482\pi$$
−0.295487 + 0.955347i $$0.595482\pi$$
$$734$$ −31.0000 −1.14423
$$735$$ 0 0
$$736$$ 1.00000 0.0368605
$$737$$ −16.0000 −0.589368
$$738$$ 0 0
$$739$$ 26.0000 0.956425 0.478213 0.878244i $$-0.341285\pi$$
0.478213 + 0.878244i $$0.341285\pi$$
$$740$$ 27.0000 0.992540
$$741$$ 0 0
$$742$$ 4.00000 0.146845
$$743$$ −40.0000 −1.46746 −0.733729 0.679442i $$-0.762222\pi$$
−0.733729 + 0.679442i $$0.762222\pi$$
$$744$$ 0 0
$$745$$ 48.0000 1.75858
$$746$$ −22.0000 −0.805477
$$747$$ 0 0
$$748$$ −16.0000 −0.585018
$$749$$ 8.00000 0.292314
$$750$$ 0 0
$$751$$ −40.0000 −1.45962 −0.729810 0.683650i $$-0.760392\pi$$
−0.729810 + 0.683650i $$0.760392\pi$$
$$752$$ 7.00000 0.255264
$$753$$ 0 0
$$754$$ −9.00000 −0.327761
$$755$$ −45.0000 −1.63772
$$756$$ 0 0
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ 25.0000 0.908041
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 42.0000 1.52250 0.761249 0.648459i $$-0.224586\pi$$
0.761249 + 0.648459i $$0.224586\pi$$
$$762$$ 0 0
$$763$$ −3.00000 −0.108607
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 18.0000 0.649942
$$768$$ 0 0
$$769$$ 5.00000 0.180305 0.0901523 0.995928i $$-0.471265\pi$$
0.0901523 + 0.995928i $$0.471265\pi$$
$$770$$ 12.0000 0.432450
$$771$$ 0 0
$$772$$ −17.0000 −0.611843
$$773$$ −19.0000 −0.683383 −0.341691 0.939812i $$-0.611000\pi$$
−0.341691 + 0.939812i $$0.611000\pi$$
$$774$$ 0 0
$$775$$ −24.0000 −0.862105
$$776$$ 7.00000 0.251285
$$777$$ 0 0
$$778$$ 18.0000 0.645331
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −24.0000 −0.858788
$$782$$ 4.00000 0.143040
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 24.0000 0.856597
$$786$$ 0 0
$$787$$ −40.0000 −1.42585 −0.712923 0.701242i $$-0.752629\pi$$
−0.712923 + 0.701242i $$0.752629\pi$$
$$788$$ 23.0000 0.819341
$$789$$ 0 0
$$790$$ 24.0000 0.853882
$$791$$ 9.00000 0.320003
$$792$$ 0 0
$$793$$ −30.0000 −1.06533
$$794$$ −34.0000 −1.20661
$$795$$ 0 0
$$796$$ −5.00000 −0.177220
$$797$$ 49.0000 1.73567 0.867835 0.496853i $$-0.165511\pi$$
0.867835 + 0.496853i $$0.165511\pi$$
$$798$$ 0 0
$$799$$ 28.0000 0.990569
$$800$$ −4.00000 −0.141421
$$801$$ 0 0
$$802$$ 38.0000 1.34183
$$803$$ 32.0000 1.12926
$$804$$ 0 0
$$805$$ −3.00000 −0.105736
$$806$$ −18.0000 −0.634023
$$807$$ 0 0
$$808$$ −14.0000 −0.492518
$$809$$ 16.0000 0.562530 0.281265 0.959630i $$-0.409246\pi$$
0.281265 + 0.959630i $$0.409246\pi$$
$$810$$ 0 0
$$811$$ 33.0000 1.15879 0.579393 0.815048i $$-0.303290\pi$$
0.579393 + 0.815048i $$0.303290\pi$$
$$812$$ 3.00000 0.105279
$$813$$ 0 0
$$814$$ −36.0000 −1.26180
$$815$$ −48.0000 −1.68137
$$816$$ 0 0
$$817$$ 0 0
$$818$$ −16.0000 −0.559427
$$819$$ 0 0
$$820$$ 27.0000 0.942881
$$821$$ 30.0000 1.04701 0.523504 0.852023i $$-0.324625\pi$$
0.523504 + 0.852023i $$0.324625\pi$$
$$822$$ 0 0
$$823$$ 7.00000 0.244005 0.122002 0.992530i $$-0.461068\pi$$
0.122002 + 0.992530i $$0.461068\pi$$
$$824$$ −5.00000 −0.174183
$$825$$ 0 0
$$826$$ −6.00000 −0.208767
$$827$$ 30.0000 1.04320 0.521601 0.853189i $$-0.325335\pi$$
0.521601 + 0.853189i $$0.325335\pi$$
$$828$$ 0 0
$$829$$ 38.0000 1.31979 0.659897 0.751356i $$-0.270600\pi$$
0.659897 + 0.751356i $$0.270600\pi$$
$$830$$ −12.0000 −0.416526
$$831$$ 0 0
$$832$$ −3.00000 −0.104006
$$833$$ 4.00000 0.138592
$$834$$ 0 0
$$835$$ −60.0000 −2.07639
$$836$$ 0 0
$$837$$ 0 0
$$838$$ −4.00000 −0.138178
$$839$$ −6.00000 −0.207143 −0.103572 0.994622i $$-0.533027\pi$$
−0.103572 + 0.994622i $$0.533027\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ 21.0000 0.723708
$$843$$ 0 0
$$844$$ −12.0000 −0.413057
$$845$$ 12.0000 0.412813
$$846$$ 0 0
$$847$$ −5.00000 −0.171802
$$848$$ 4.00000 0.137361
$$849$$ 0 0
$$850$$ −16.0000 −0.548795
$$851$$ 9.00000 0.308516
$$852$$ 0 0
$$853$$ 7.00000 0.239675 0.119838 0.992793i $$-0.461763\pi$$
0.119838 + 0.992793i $$0.461763\pi$$
$$854$$ 10.0000 0.342193
$$855$$ 0 0
$$856$$ 8.00000 0.273434
$$857$$ −33.0000 −1.12726 −0.563629 0.826028i $$-0.690595\pi$$
−0.563629 + 0.826028i $$0.690595\pi$$
$$858$$ 0 0
$$859$$ 13.0000 0.443554 0.221777 0.975097i $$-0.428814\pi$$
0.221777 + 0.975097i $$0.428814\pi$$
$$860$$ 9.00000 0.306897
$$861$$ 0 0
$$862$$ 21.0000 0.715263
$$863$$ 8.00000 0.272323 0.136162 0.990687i $$-0.456523\pi$$
0.136162 + 0.990687i $$0.456523\pi$$
$$864$$ 0 0
$$865$$ −18.0000 −0.612018
$$866$$ −23.0000 −0.781572
$$867$$ 0 0
$$868$$ 6.00000 0.203653
$$869$$ −32.0000 −1.08553
$$870$$ 0 0
$$871$$ −12.0000 −0.406604
$$872$$ −3.00000 −0.101593
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −3.00000 −0.101419
$$876$$ 0 0
$$877$$ −36.0000 −1.21563 −0.607817 0.794077i $$-0.707955\pi$$
−0.607817 + 0.794077i $$0.707955\pi$$
$$878$$ 10.0000 0.337484
$$879$$ 0 0
$$880$$ 12.0000 0.404520
$$881$$ −6.00000 −0.202145 −0.101073 0.994879i $$-0.532227\pi$$
−0.101073 + 0.994879i $$0.532227\pi$$
$$882$$ 0 0
$$883$$ 54.0000 1.81724 0.908622 0.417619i $$-0.137135\pi$$
0.908622 + 0.417619i $$0.137135\pi$$
$$884$$ −12.0000 −0.403604
$$885$$ 0 0
$$886$$ 25.0000 0.839891
$$887$$ 24.0000 0.805841 0.402921 0.915235i $$-0.367995\pi$$
0.402921 + 0.915235i $$0.367995\pi$$
$$888$$ 0 0
$$889$$ −7.00000 −0.234772
$$890$$ 42.0000 1.40784
$$891$$ 0 0
$$892$$ −14.0000 −0.468755
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 57.0000 1.90530
$$896$$ 1.00000 0.0334077
$$897$$ 0 0
$$898$$ 30.0000 1.00111
$$899$$ 18.0000 0.600334
$$900$$ 0 0
$$901$$ 16.0000 0.533037
$$902$$ −36.0000 −1.19867
$$903$$ 0 0
$$904$$ 9.00000 0.299336
$$905$$ 6.00000 0.199447
$$906$$ 0 0
$$907$$ −53.0000 −1.75984 −0.879918 0.475125i $$-0.842403\pi$$
−0.879918 + 0.475125i $$0.842403\pi$$
$$908$$ −11.0000 −0.365048
$$909$$ 0 0
$$910$$ 9.00000 0.298347
$$911$$ 49.0000 1.62344 0.811721 0.584045i $$-0.198531\pi$$
0.811721 + 0.584045i $$0.198531\pi$$
$$912$$ 0 0
$$913$$ 16.0000 0.529523
$$914$$ −24.0000 −0.793849
$$915$$ 0 0
$$916$$ 12.0000 0.396491
$$917$$ −6.00000 −0.198137
$$918$$ 0 0
$$919$$ 24.0000 0.791687 0.395843 0.918318i $$-0.370452\pi$$
0.395843 + 0.918318i $$0.370452\pi$$
$$920$$ −3.00000 −0.0989071
$$921$$ 0 0
$$922$$ −22.0000 −0.724531
$$923$$ −18.0000 −0.592477
$$924$$ 0 0
$$925$$ −36.0000 −1.18367
$$926$$ −13.0000 −0.427207
$$927$$ 0 0
$$928$$ 3.00000 0.0984798
$$929$$ −9.00000 −0.295280 −0.147640 0.989041i $$-0.547168\pi$$
−0.147640 + 0.989041i $$0.547168\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 10.0000 0.327561
$$933$$ 0 0
$$934$$ 13.0000 0.425373
$$935$$ 48.0000 1.56977
$$936$$ 0 0
$$937$$ 25.0000 0.816714 0.408357 0.912822i $$-0.366102\pi$$
0.408357 + 0.912822i $$0.366102\pi$$
$$938$$ 4.00000 0.130605
$$939$$ 0 0
$$940$$ −21.0000 −0.684944
$$941$$ −3.00000 −0.0977972 −0.0488986 0.998804i $$-0.515571\pi$$
−0.0488986 + 0.998804i $$0.515571\pi$$
$$942$$ 0 0
$$943$$ 9.00000 0.293080
$$944$$ −6.00000 −0.195283
$$945$$ 0 0
$$946$$ −12.0000 −0.390154
$$947$$ 31.0000 1.00736 0.503682 0.863889i $$-0.331978\pi$$
0.503682 + 0.863889i $$0.331978\pi$$
$$948$$ 0 0
$$949$$ 24.0000 0.779073
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 4.00000 0.129641
$$953$$ −34.0000 −1.10137 −0.550684 0.834714i $$-0.685633\pi$$
−0.550684 + 0.834714i $$0.685633\pi$$
$$954$$ 0 0
$$955$$ −36.0000 −1.16493
$$956$$ 12.0000 0.388108
$$957$$ 0 0
$$958$$ 30.0000 0.969256
$$959$$ −15.0000 −0.484375
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ −27.0000 −0.870515
$$963$$ 0 0
$$964$$ −5.00000 −0.161039
$$965$$ 51.0000 1.64175
$$966$$ 0 0
$$967$$ 4.00000 0.128631 0.0643157 0.997930i $$-0.479514\pi$$
0.0643157 + 0.997930i $$0.479514\pi$$
$$968$$ −5.00000 −0.160706
$$969$$ 0 0
$$970$$ −21.0000 −0.674269
$$971$$ 24.0000 0.770197 0.385098 0.922876i $$-0.374168\pi$$
0.385098 + 0.922876i $$0.374168\pi$$
$$972$$ 0 0
$$973$$ −9.00000 −0.288527
$$974$$ −13.0000 −0.416547
$$975$$ 0 0
$$976$$ 10.0000 0.320092
$$977$$ −13.0000 −0.415907 −0.207953 0.978139i $$-0.566680\pi$$
−0.207953 + 0.978139i $$0.566680\pi$$
$$978$$ 0 0
$$979$$ −56.0000 −1.78977
$$980$$ −3.00000 −0.0958315
$$981$$ 0 0
$$982$$ −12.0000 −0.382935
$$983$$ 54.0000 1.72233 0.861166 0.508323i $$-0.169735\pi$$
0.861166 + 0.508323i $$0.169735\pi$$
$$984$$ 0 0
$$985$$ −69.0000 −2.19852
$$986$$ 12.0000 0.382158
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 3.00000 0.0953945
$$990$$ 0 0
$$991$$ −36.0000 −1.14358 −0.571789 0.820401i $$-0.693750\pi$$
−0.571789 + 0.820401i $$0.693750\pi$$
$$992$$ 6.00000 0.190500
$$993$$ 0 0
$$994$$ 6.00000 0.190308
$$995$$ 15.0000 0.475532
$$996$$ 0 0
$$997$$ −46.0000 −1.45683 −0.728417 0.685134i $$-0.759744\pi$$
−0.728417 + 0.685134i $$0.759744\pi$$
$$998$$ −34.0000 −1.07625
$$999$$ 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 2898.2.a.a.1.1 1
3.2 odd 2 966.2.a.k.1.1 1
12.11 even 2 7728.2.a.j.1.1 1
21.20 even 2 6762.2.a.y.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.a.k.1.1 1 3.2 odd 2
2898.2.a.a.1.1 1 1.1 even 1 trivial
6762.2.a.y.1.1 1 21.20 even 2
7728.2.a.j.1.1 1 12.11 even 2