# Properties

 Label 2925.2.a.bh.1.3 Level $2925$ Weight $2$ Character 2925.1 Self dual yes Analytic conductor $23.356$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2925 = 3^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2925.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$23.3562425912$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.316.1 Defining polynomial: $$x^{3} - x^{2} - 4x + 2$$ x^3 - x^2 - 4*x + 2 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 195) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$0.470683$$ of defining polynomial Character $$\chi$$ $$=$$ 2925.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.77846 q^{2} +5.71982 q^{4} +2.71982 q^{7} +10.3354 q^{8} +O(q^{10})$$ $$q+2.77846 q^{2} +5.71982 q^{4} +2.71982 q^{7} +10.3354 q^{8} +2.71982 q^{11} -1.00000 q^{13} +7.55691 q^{14} +17.2767 q^{16} -2.83709 q^{17} -3.55691 q^{19} +7.55691 q^{22} -4.83709 q^{23} -2.77846 q^{26} +15.5569 q^{28} -6.00000 q^{29} +7.55691 q^{31} +27.3319 q^{32} -7.88273 q^{34} +4.27674 q^{37} -9.88273 q^{38} -2.83709 q^{41} -11.1138 q^{43} +15.5569 q^{44} -13.4396 q^{46} -11.5569 q^{47} +0.397442 q^{49} -5.71982 q^{52} +1.16291 q^{53} +28.1104 q^{56} -16.6707 q^{58} +2.11727 q^{59} +6.60256 q^{61} +20.9966 q^{62} +41.3871 q^{64} -1.88273 q^{67} -16.2277 q^{68} +6.71982 q^{71} -9.11383 q^{73} +11.8827 q^{74} -20.3449 q^{76} +7.39744 q^{77} +10.2767 q^{79} -7.88273 q^{82} +2.11727 q^{83} -30.8793 q^{86} +28.1104 q^{88} -1.16291 q^{89} -2.71982 q^{91} -27.6673 q^{92} -32.1104 q^{94} +10.8371 q^{97} +1.10428 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 8 q^{4} - q^{7} + 6 q^{8}+O(q^{10})$$ 3 * q + 8 * q^4 - q^7 + 6 * q^8 $$3 q + 8 q^{4} - q^{7} + 6 q^{8} - q^{11} - 3 q^{13} + 6 q^{14} + 26 q^{16} - q^{17} + 6 q^{19} + 6 q^{22} - 7 q^{23} + 30 q^{28} - 18 q^{29} + 6 q^{31} + 22 q^{32} - 22 q^{34} - 13 q^{37} - 28 q^{38} - q^{41} + 30 q^{44} - 22 q^{46} - 18 q^{47} + 12 q^{49} - 8 q^{52} + 11 q^{53} + 16 q^{56} + 8 q^{59} + 9 q^{61} + 28 q^{62} + 30 q^{64} - 4 q^{67} + 18 q^{68} + 11 q^{71} + 6 q^{73} + 34 q^{74} + 4 q^{76} + 33 q^{77} + 5 q^{79} - 22 q^{82} + 8 q^{83} - 56 q^{86} + 16 q^{88} - 11 q^{89} + q^{91} + 2 q^{92} - 28 q^{94} + 25 q^{97} + 10 q^{98}+O(q^{100})$$ 3 * q + 8 * q^4 - q^7 + 6 * q^8 - q^11 - 3 * q^13 + 6 * q^14 + 26 * q^16 - q^17 + 6 * q^19 + 6 * q^22 - 7 * q^23 + 30 * q^28 - 18 * q^29 + 6 * q^31 + 22 * q^32 - 22 * q^34 - 13 * q^37 - 28 * q^38 - q^41 + 30 * q^44 - 22 * q^46 - 18 * q^47 + 12 * q^49 - 8 * q^52 + 11 * q^53 + 16 * q^56 + 8 * q^59 + 9 * q^61 + 28 * q^62 + 30 * q^64 - 4 * q^67 + 18 * q^68 + 11 * q^71 + 6 * q^73 + 34 * q^74 + 4 * q^76 + 33 * q^77 + 5 * q^79 - 22 * q^82 + 8 * q^83 - 56 * q^86 + 16 * q^88 - 11 * q^89 + q^91 + 2 * q^92 - 28 * q^94 + 25 * q^97 + 10 * q^98

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.77846 1.96467 0.982333 0.187142i $$-0.0599223\pi$$
0.982333 + 0.187142i $$0.0599223\pi$$
$$3$$ 0 0
$$4$$ 5.71982 2.85991
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.71982 1.02800 0.513998 0.857791i $$-0.328164\pi$$
0.513998 + 0.857791i $$0.328164\pi$$
$$8$$ 10.3354 3.65411
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.71982 0.820058 0.410029 0.912073i $$-0.365519\pi$$
0.410029 + 0.912073i $$0.365519\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 7.55691 2.01967
$$15$$ 0 0
$$16$$ 17.2767 4.31918
$$17$$ −2.83709 −0.688095 −0.344048 0.938952i $$-0.611798\pi$$
−0.344048 + 0.938952i $$0.611798\pi$$
$$18$$ 0 0
$$19$$ −3.55691 −0.816012 −0.408006 0.912979i $$-0.633776\pi$$
−0.408006 + 0.912979i $$0.633776\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 7.55691 1.61114
$$23$$ −4.83709 −1.00860 −0.504302 0.863528i $$-0.668250\pi$$
−0.504302 + 0.863528i $$0.668250\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −2.77846 −0.544900
$$27$$ 0 0
$$28$$ 15.5569 2.93998
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 7.55691 1.35726 0.678631 0.734479i $$-0.262574\pi$$
0.678631 + 0.734479i $$0.262574\pi$$
$$32$$ 27.3319 4.83165
$$33$$ 0 0
$$34$$ −7.88273 −1.35188
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 4.27674 0.703091 0.351546 0.936171i $$-0.385656\pi$$
0.351546 + 0.936171i $$0.385656\pi$$
$$38$$ −9.88273 −1.60319
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2.83709 −0.443079 −0.221540 0.975151i $$-0.571108\pi$$
−0.221540 + 0.975151i $$0.571108\pi$$
$$42$$ 0 0
$$43$$ −11.1138 −1.69484 −0.847421 0.530921i $$-0.821846\pi$$
−0.847421 + 0.530921i $$0.821846\pi$$
$$44$$ 15.5569 2.34529
$$45$$ 0 0
$$46$$ −13.4396 −1.98157
$$47$$ −11.5569 −1.68575 −0.842875 0.538110i $$-0.819138\pi$$
−0.842875 + 0.538110i $$0.819138\pi$$
$$48$$ 0 0
$$49$$ 0.397442 0.0567775
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −5.71982 −0.793197
$$53$$ 1.16291 0.159738 0.0798690 0.996805i $$-0.474550\pi$$
0.0798690 + 0.996805i $$0.474550\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 28.1104 3.75641
$$57$$ 0 0
$$58$$ −16.6707 −2.18898
$$59$$ 2.11727 0.275645 0.137822 0.990457i $$-0.455990\pi$$
0.137822 + 0.990457i $$0.455990\pi$$
$$60$$ 0 0
$$61$$ 6.60256 0.845371 0.422685 0.906276i $$-0.361088\pi$$
0.422685 + 0.906276i $$0.361088\pi$$
$$62$$ 20.9966 2.66657
$$63$$ 0 0
$$64$$ 41.3871 5.17339
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.88273 −0.230013 −0.115006 0.993365i $$-0.536689\pi$$
−0.115006 + 0.993365i $$0.536689\pi$$
$$68$$ −16.2277 −1.96789
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 6.71982 0.797496 0.398748 0.917060i $$-0.369445\pi$$
0.398748 + 0.917060i $$0.369445\pi$$
$$72$$ 0 0
$$73$$ −9.11383 −1.06669 −0.533346 0.845897i $$-0.679066\pi$$
−0.533346 + 0.845897i $$0.679066\pi$$
$$74$$ 11.8827 1.38134
$$75$$ 0 0
$$76$$ −20.3449 −2.33372
$$77$$ 7.39744 0.843017
$$78$$ 0 0
$$79$$ 10.2767 1.15622 0.578112 0.815958i $$-0.303790\pi$$
0.578112 + 0.815958i $$0.303790\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −7.88273 −0.870502
$$83$$ 2.11727 0.232400 0.116200 0.993226i $$-0.462929\pi$$
0.116200 + 0.993226i $$0.462929\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −30.8793 −3.32980
$$87$$ 0 0
$$88$$ 28.1104 2.99658
$$89$$ −1.16291 −0.123268 −0.0616341 0.998099i $$-0.519631\pi$$
−0.0616341 + 0.998099i $$0.519631\pi$$
$$90$$ 0 0
$$91$$ −2.71982 −0.285115
$$92$$ −27.6673 −2.88452
$$93$$ 0 0
$$94$$ −32.1104 −3.31193
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.8371 1.10034 0.550170 0.835053i $$-0.314563\pi$$
0.550170 + 0.835053i $$0.314563\pi$$
$$98$$ 1.10428 0.111549
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −7.67418 −0.763610 −0.381805 0.924243i $$-0.624697\pi$$
−0.381805 + 0.924243i $$0.624697\pi$$
$$102$$ 0 0
$$103$$ −3.76547 −0.371023 −0.185511 0.982642i $$-0.559394\pi$$
−0.185511 + 0.982642i $$0.559394\pi$$
$$104$$ −10.3354 −1.01347
$$105$$ 0 0
$$106$$ 3.23109 0.313832
$$107$$ −12.6026 −1.21834 −0.609168 0.793041i $$-0.708496\pi$$
−0.609168 + 0.793041i $$0.708496\pi$$
$$108$$ 0 0
$$109$$ 11.4396 1.09572 0.547860 0.836570i $$-0.315443\pi$$
0.547860 + 0.836570i $$0.315443\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 46.9897 4.44011
$$113$$ −13.1138 −1.23365 −0.616823 0.787102i $$-0.711580\pi$$
−0.616823 + 0.787102i $$0.711580\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −34.3189 −3.18643
$$117$$ 0 0
$$118$$ 5.88273 0.541550
$$119$$ −7.71639 −0.707360
$$120$$ 0 0
$$121$$ −3.60256 −0.327505
$$122$$ 18.3449 1.66087
$$123$$ 0 0
$$124$$ 43.2242 3.88165
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 13.4396 1.19258 0.596288 0.802771i $$-0.296642\pi$$
0.596288 + 0.802771i $$0.296642\pi$$
$$128$$ 60.3285 5.33234
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 9.43965 0.824746 0.412373 0.911015i $$-0.364700\pi$$
0.412373 + 0.911015i $$0.364700\pi$$
$$132$$ 0 0
$$133$$ −9.67418 −0.838858
$$134$$ −5.23109 −0.451898
$$135$$ 0 0
$$136$$ −29.3224 −2.51437
$$137$$ 1.76547 0.150834 0.0754170 0.997152i $$-0.475971\pi$$
0.0754170 + 0.997152i $$0.475971\pi$$
$$138$$ 0 0
$$139$$ −6.27674 −0.532386 −0.266193 0.963920i $$-0.585766\pi$$
−0.266193 + 0.963920i $$0.585766\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 18.6707 1.56681
$$143$$ −2.71982 −0.227443
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −25.3224 −2.09570
$$147$$ 0 0
$$148$$ 24.4622 2.01078
$$149$$ 20.8302 1.70648 0.853239 0.521520i $$-0.174635\pi$$
0.853239 + 0.521520i $$0.174635\pi$$
$$150$$ 0 0
$$151$$ 4.99656 0.406614 0.203307 0.979115i $$-0.434831\pi$$
0.203307 + 0.979115i $$0.434831\pi$$
$$152$$ −36.7620 −2.98179
$$153$$ 0 0
$$154$$ 20.5535 1.65625
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −8.87930 −0.708645 −0.354322 0.935123i $$-0.615288\pi$$
−0.354322 + 0.935123i $$0.615288\pi$$
$$158$$ 28.5535 2.27159
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −13.1560 −1.03684
$$162$$ 0 0
$$163$$ 13.8337 1.08354 0.541768 0.840528i $$-0.317755\pi$$
0.541768 + 0.840528i $$0.317755\pi$$
$$164$$ −16.2277 −1.26717
$$165$$ 0 0
$$166$$ 5.88273 0.456589
$$167$$ −9.88273 −0.764749 −0.382374 0.924007i $$-0.624894\pi$$
−0.382374 + 0.924007i $$0.624894\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −63.5691 −4.84710
$$173$$ 13.1138 0.997026 0.498513 0.866882i $$-0.333880\pi$$
0.498513 + 0.866882i $$0.333880\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 46.9897 3.54198
$$177$$ 0 0
$$178$$ −3.23109 −0.242181
$$179$$ −8.55348 −0.639317 −0.319658 0.947533i $$-0.603568\pi$$
−0.319658 + 0.947533i $$0.603568\pi$$
$$180$$ 0 0
$$181$$ 3.72326 0.276748 0.138374 0.990380i $$-0.455812\pi$$
0.138374 + 0.990380i $$0.455812\pi$$
$$182$$ −7.55691 −0.560156
$$183$$ 0 0
$$184$$ −49.9931 −3.68554
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −7.71639 −0.564278
$$188$$ −66.1035 −4.82109
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 4.23453 0.306400 0.153200 0.988195i $$-0.451042\pi$$
0.153200 + 0.988195i $$0.451042\pi$$
$$192$$ 0 0
$$193$$ 23.3906 1.68369 0.841845 0.539719i $$-0.181470\pi$$
0.841845 + 0.539719i $$0.181470\pi$$
$$194$$ 30.1104 2.16180
$$195$$ 0 0
$$196$$ 2.27330 0.162379
$$197$$ 14.5535 1.03689 0.518446 0.855110i $$-0.326511\pi$$
0.518446 + 0.855110i $$0.326511\pi$$
$$198$$ 0 0
$$199$$ −15.1138 −1.07139 −0.535695 0.844411i $$-0.679950\pi$$
−0.535695 + 0.844411i $$0.679950\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −21.3224 −1.50024
$$203$$ −16.3189 −1.14537
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −10.4622 −0.728935
$$207$$ 0 0
$$208$$ −17.2767 −1.19793
$$209$$ −9.67418 −0.669177
$$210$$ 0 0
$$211$$ −18.2277 −1.25484 −0.627422 0.778680i $$-0.715890\pi$$
−0.627422 + 0.778680i $$0.715890\pi$$
$$212$$ 6.65164 0.456836
$$213$$ 0 0
$$214$$ −35.0157 −2.39362
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 20.5535 1.39526
$$218$$ 31.7846 2.15272
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 2.83709 0.190843
$$222$$ 0 0
$$223$$ −10.1173 −0.677502 −0.338751 0.940876i $$-0.610004\pi$$
−0.338751 + 0.940876i $$0.610004\pi$$
$$224$$ 74.3380 4.96692
$$225$$ 0 0
$$226$$ −36.4362 −2.42370
$$227$$ 11.3224 0.751493 0.375746 0.926723i $$-0.377386\pi$$
0.375746 + 0.926723i $$0.377386\pi$$
$$228$$ 0 0
$$229$$ −6.23453 −0.411990 −0.205995 0.978553i $$-0.566043\pi$$
−0.205995 + 0.978553i $$0.566043\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −62.0122 −4.07130
$$233$$ 6.83709 0.447913 0.223956 0.974599i $$-0.428103\pi$$
0.223956 + 0.974599i $$0.428103\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 12.1104 0.788319
$$237$$ 0 0
$$238$$ −21.4396 −1.38973
$$239$$ −1.28018 −0.0828077 −0.0414039 0.999142i $$-0.513183\pi$$
−0.0414039 + 0.999142i $$0.513183\pi$$
$$240$$ 0 0
$$241$$ −6.00000 −0.386494 −0.193247 0.981150i $$-0.561902\pi$$
−0.193247 + 0.981150i $$0.561902\pi$$
$$242$$ −10.0096 −0.643438
$$243$$ 0 0
$$244$$ 37.7655 2.41769
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3.55691 0.226321
$$248$$ 78.1035 4.95958
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −18.2277 −1.15052 −0.575260 0.817971i $$-0.695099\pi$$
−0.575260 + 0.817971i $$0.695099\pi$$
$$252$$ 0 0
$$253$$ −13.1560 −0.827113
$$254$$ 37.3415 2.34301
$$255$$ 0 0
$$256$$ 84.8459 5.30287
$$257$$ 1.11383 0.0694787 0.0347394 0.999396i $$-0.488940\pi$$
0.0347394 + 0.999396i $$0.488940\pi$$
$$258$$ 0 0
$$259$$ 11.6320 0.722776
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 26.2277 1.62035
$$263$$ 8.00000 0.493301 0.246651 0.969104i $$-0.420670\pi$$
0.246651 + 0.969104i $$0.420670\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −26.8793 −1.64808
$$267$$ 0 0
$$268$$ −10.7689 −0.657816
$$269$$ −15.6742 −0.955672 −0.477836 0.878449i $$-0.658579\pi$$
−0.477836 + 0.878449i $$0.658579\pi$$
$$270$$ 0 0
$$271$$ 0.443086 0.0269155 0.0134578 0.999909i $$-0.495716\pi$$
0.0134578 + 0.999909i $$0.495716\pi$$
$$272$$ −49.0157 −2.97201
$$273$$ 0 0
$$274$$ 4.90528 0.296339
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 4.87930 0.293168 0.146584 0.989198i $$-0.453172\pi$$
0.146584 + 0.989198i $$0.453172\pi$$
$$278$$ −17.4396 −1.04596
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 9.11383 0.543685 0.271843 0.962342i $$-0.412367\pi$$
0.271843 + 0.962342i $$0.412367\pi$$
$$282$$ 0 0
$$283$$ −33.3415 −1.98195 −0.990973 0.134063i $$-0.957198\pi$$
−0.990973 + 0.134063i $$0.957198\pi$$
$$284$$ 38.4362 2.28077
$$285$$ 0 0
$$286$$ −7.55691 −0.446850
$$287$$ −7.71639 −0.455484
$$288$$ 0 0
$$289$$ −8.95092 −0.526525
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −52.1295 −3.05065
$$293$$ −29.4328 −1.71948 −0.859740 0.510731i $$-0.829375\pi$$
−0.859740 + 0.510731i $$0.829375\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 44.2017 2.56917
$$297$$ 0 0
$$298$$ 57.8759 3.35266
$$299$$ 4.83709 0.279736
$$300$$ 0 0
$$301$$ −30.2277 −1.74229
$$302$$ 13.8827 0.798862
$$303$$ 0 0
$$304$$ −61.4519 −3.52451
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 21.8337 1.24611 0.623056 0.782177i $$-0.285891\pi$$
0.623056 + 0.782177i $$0.285891\pi$$
$$308$$ 42.3121 2.41095
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −25.1070 −1.42368 −0.711842 0.702339i $$-0.752139\pi$$
−0.711842 + 0.702339i $$0.752139\pi$$
$$312$$ 0 0
$$313$$ −8.22766 −0.465055 −0.232527 0.972590i $$-0.574700\pi$$
−0.232527 + 0.972590i $$0.574700\pi$$
$$314$$ −24.6707 −1.39225
$$315$$ 0 0
$$316$$ 58.7811 3.30670
$$317$$ 27.6742 1.55434 0.777168 0.629293i $$-0.216655\pi$$
0.777168 + 0.629293i $$0.216655\pi$$
$$318$$ 0 0
$$319$$ −16.3189 −0.913685
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −36.5535 −2.03705
$$323$$ 10.0913 0.561494
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 38.4362 2.12878
$$327$$ 0 0
$$328$$ −29.3224 −1.61906
$$329$$ −31.4328 −1.73294
$$330$$ 0 0
$$331$$ −13.2311 −0.727247 −0.363623 0.931546i $$-0.618460\pi$$
−0.363623 + 0.931546i $$0.618460\pi$$
$$332$$ 12.1104 0.664644
$$333$$ 0 0
$$334$$ −27.4588 −1.50248
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 4.32582 0.235642 0.117821 0.993035i $$-0.462409\pi$$
0.117821 + 0.993035i $$0.462409\pi$$
$$338$$ 2.77846 0.151128
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 20.5535 1.11303
$$342$$ 0 0
$$343$$ −17.9578 −0.969630
$$344$$ −114.866 −6.19314
$$345$$ 0 0
$$346$$ 36.4362 1.95882
$$347$$ 6.27674 0.336953 0.168476 0.985706i $$-0.446115\pi$$
0.168476 + 0.985706i $$0.446115\pi$$
$$348$$ 0 0
$$349$$ 17.6673 0.945709 0.472855 0.881140i $$-0.343224\pi$$
0.472855 + 0.881140i $$0.343224\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 74.3380 3.96223
$$353$$ −13.7655 −0.732662 −0.366331 0.930485i $$-0.619386\pi$$
−0.366331 + 0.930485i $$0.619386\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −6.65164 −0.352536
$$357$$ 0 0
$$358$$ −23.7655 −1.25604
$$359$$ −0.996562 −0.0525965 −0.0262983 0.999654i $$-0.508372\pi$$
−0.0262983 + 0.999654i $$0.508372\pi$$
$$360$$ 0 0
$$361$$ −6.34836 −0.334124
$$362$$ 10.3449 0.543717
$$363$$ 0 0
$$364$$ −15.5569 −0.815404
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −14.2277 −0.742678 −0.371339 0.928497i $$-0.621101\pi$$
−0.371339 + 0.928497i $$0.621101\pi$$
$$368$$ −83.5691 −4.35634
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 3.16291 0.164210
$$372$$ 0 0
$$373$$ −15.6742 −0.811578 −0.405789 0.913967i $$-0.633003\pi$$
−0.405789 + 0.913967i $$0.633003\pi$$
$$374$$ −21.4396 −1.10862
$$375$$ 0 0
$$376$$ −119.445 −6.15991
$$377$$ 6.00000 0.309016
$$378$$ 0 0
$$379$$ 26.2017 1.34589 0.672945 0.739693i $$-0.265029\pi$$
0.672945 + 0.739693i $$0.265029\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 11.7655 0.601974
$$383$$ 22.4362 1.14644 0.573218 0.819403i $$-0.305695\pi$$
0.573218 + 0.819403i $$0.305695\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 64.9897 3.30789
$$387$$ 0 0
$$388$$ 61.9862 3.14687
$$389$$ −31.6742 −1.60594 −0.802972 0.596016i $$-0.796749\pi$$
−0.802972 + 0.596016i $$0.796749\pi$$
$$390$$ 0 0
$$391$$ 13.7233 0.694015
$$392$$ 4.10771 0.207471
$$393$$ 0 0
$$394$$ 40.4362 2.03715
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −17.9509 −0.900931 −0.450465 0.892794i $$-0.648742\pi$$
−0.450465 + 0.892794i $$0.648742\pi$$
$$398$$ −41.9931 −2.10493
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −13.5829 −0.678297 −0.339149 0.940733i $$-0.610139\pi$$
−0.339149 + 0.940733i $$0.610139\pi$$
$$402$$ 0 0
$$403$$ −7.55691 −0.376437
$$404$$ −43.8950 −2.18386
$$405$$ 0 0
$$406$$ −45.3415 −2.25026
$$407$$ 11.6320 0.576576
$$408$$ 0 0
$$409$$ −14.0000 −0.692255 −0.346128 0.938187i $$-0.612504\pi$$
−0.346128 + 0.938187i $$0.612504\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −21.5378 −1.06109
$$413$$ 5.75859 0.283362
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −27.3319 −1.34006
$$417$$ 0 0
$$418$$ −26.8793 −1.31471
$$419$$ −12.3189 −0.601820 −0.300910 0.953653i $$-0.597290\pi$$
−0.300910 + 0.953653i $$0.597290\pi$$
$$420$$ 0 0
$$421$$ 22.7880 1.11062 0.555310 0.831644i $$-0.312600\pi$$
0.555310 + 0.831644i $$0.312600\pi$$
$$422$$ −50.6448 −2.46535
$$423$$ 0 0
$$424$$ 12.0191 0.583699
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 17.9578 0.869039
$$428$$ −72.0844 −3.48433
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 8.99656 0.433349 0.216675 0.976244i $$-0.430479\pi$$
0.216675 + 0.976244i $$0.430479\pi$$
$$432$$ 0 0
$$433$$ 20.3258 0.976797 0.488398 0.872621i $$-0.337581\pi$$
0.488398 + 0.872621i $$0.337581\pi$$
$$434$$ 57.1070 2.74122
$$435$$ 0 0
$$436$$ 65.4328 3.13366
$$437$$ 17.2051 0.823032
$$438$$ 0 0
$$439$$ −25.3906 −1.21183 −0.605913 0.795531i $$-0.707192\pi$$
−0.605913 + 0.795531i $$0.707192\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 7.88273 0.374943
$$443$$ 10.9284 0.519223 0.259611 0.965713i $$-0.416406\pi$$
0.259611 + 0.965713i $$0.416406\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −28.1104 −1.33107
$$447$$ 0 0
$$448$$ 112.566 5.31823
$$449$$ −2.83709 −0.133891 −0.0669453 0.997757i $$-0.521325\pi$$
−0.0669453 + 0.997757i $$0.521325\pi$$
$$450$$ 0 0
$$451$$ −7.71639 −0.363350
$$452$$ −75.0088 −3.52812
$$453$$ 0 0
$$454$$ 31.4588 1.47643
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 13.7164 0.641625 0.320813 0.947143i $$-0.396044\pi$$
0.320813 + 0.947143i $$0.396044\pi$$
$$458$$ −17.3224 −0.809422
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 19.6251 0.914032 0.457016 0.889458i $$-0.348918\pi$$
0.457016 + 0.889458i $$0.348918\pi$$
$$462$$ 0 0
$$463$$ −27.0388 −1.25660 −0.628299 0.777972i $$-0.716249\pi$$
−0.628299 + 0.777972i $$0.716249\pi$$
$$464$$ −103.660 −4.81231
$$465$$ 0 0
$$466$$ 18.9966 0.879999
$$467$$ 28.9215 1.33833 0.669164 0.743115i $$-0.266652\pi$$
0.669164 + 0.743115i $$0.266652\pi$$
$$468$$ 0 0
$$469$$ −5.12070 −0.236452
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 21.8827 1.00723
$$473$$ −30.2277 −1.38987
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −44.1364 −2.02299
$$477$$ 0 0
$$478$$ −3.55691 −0.162689
$$479$$ 12.1595 0.555580 0.277790 0.960642i $$-0.410398\pi$$
0.277790 + 0.960642i $$0.410398\pi$$
$$480$$ 0 0
$$481$$ −4.27674 −0.195002
$$482$$ −16.6707 −0.759332
$$483$$ 0 0
$$484$$ −20.6060 −0.936636
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0.159472 0.00722636 0.00361318 0.999993i $$-0.498850\pi$$
0.00361318 + 0.999993i $$0.498850\pi$$
$$488$$ 68.2399 3.08907
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 42.2277 1.90571 0.952854 0.303430i $$-0.0981318\pi$$
0.952854 + 0.303430i $$0.0981318\pi$$
$$492$$ 0 0
$$493$$ 17.0225 0.766657
$$494$$ 9.88273 0.444645
$$495$$ 0 0
$$496$$ 130.559 5.86226
$$497$$ 18.2767 0.819824
$$498$$ 0 0
$$499$$ 7.79145 0.348793 0.174397 0.984676i $$-0.444203\pi$$
0.174397 + 0.984676i $$0.444203\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −50.6448 −2.26039
$$503$$ 27.3484 1.21940 0.609702 0.792631i $$-0.291289\pi$$
0.609702 + 0.792631i $$0.291289\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −36.5535 −1.62500
$$507$$ 0 0
$$508$$ 76.8724 3.41066
$$509$$ 33.4819 1.48406 0.742029 0.670368i $$-0.233864\pi$$
0.742029 + 0.670368i $$0.233864\pi$$
$$510$$ 0 0
$$511$$ −24.7880 −1.09656
$$512$$ 115.084 5.08603
$$513$$ 0 0
$$514$$ 3.09472 0.136502
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −31.4328 −1.38241
$$518$$ 32.3189 1.42001
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 17.3484 0.760045 0.380023 0.924977i $$-0.375916\pi$$
0.380023 + 0.924977i $$0.375916\pi$$
$$522$$ 0 0
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ 53.9931 2.35870
$$525$$ 0 0
$$526$$ 22.2277 0.969172
$$527$$ −21.4396 −0.933926
$$528$$ 0 0
$$529$$ 0.397442 0.0172801
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −55.3346 −2.39906
$$533$$ 2.83709 0.122888
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −19.4588 −0.840490
$$537$$ 0 0
$$538$$ −43.5500 −1.87758
$$539$$ 1.08097 0.0465608
$$540$$ 0 0
$$541$$ −32.6448 −1.40351 −0.701754 0.712419i $$-0.747599\pi$$
−0.701754 + 0.712419i $$0.747599\pi$$
$$542$$ 1.23109 0.0528800
$$543$$ 0 0
$$544$$ −77.5432 −3.32464
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −34.2277 −1.46347 −0.731734 0.681590i $$-0.761289\pi$$
−0.731734 + 0.681590i $$0.761289\pi$$
$$548$$ 10.0982 0.431372
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 21.3415 0.909178
$$552$$ 0 0
$$553$$ 27.9509 1.18859
$$554$$ 13.5569 0.575978
$$555$$ 0 0
$$556$$ −35.9018 −1.52258
$$557$$ 6.65164 0.281839 0.140919 0.990021i $$-0.454994\pi$$
0.140919 + 0.990021i $$0.454994\pi$$
$$558$$ 0 0
$$559$$ 11.1138 0.470065
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 25.3224 1.06816
$$563$$ 40.2699 1.69717 0.848586 0.529057i $$-0.177454\pi$$
0.848586 + 0.529057i $$0.177454\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −92.6379 −3.89386
$$567$$ 0 0
$$568$$ 69.4519 2.91414
$$569$$ 13.4328 0.563131 0.281566 0.959542i $$-0.409146\pi$$
0.281566 + 0.959542i $$0.409146\pi$$
$$570$$ 0 0
$$571$$ −35.7164 −1.49468 −0.747342 0.664439i $$-0.768670\pi$$
−0.747342 + 0.664439i $$0.768670\pi$$
$$572$$ −15.5569 −0.650467
$$573$$ 0 0
$$574$$ −21.4396 −0.894874
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 13.7164 0.571021 0.285510 0.958376i $$-0.407837\pi$$
0.285510 + 0.958376i $$0.407837\pi$$
$$578$$ −24.8697 −1.03444
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 5.75859 0.238907
$$582$$ 0 0
$$583$$ 3.16291 0.130994
$$584$$ −94.1948 −3.89781
$$585$$ 0 0
$$586$$ −81.7777 −3.37821
$$587$$ 30.6707 1.26592 0.632959 0.774186i $$-0.281840\pi$$
0.632959 + 0.774186i $$0.281840\pi$$
$$588$$ 0 0
$$589$$ −26.8793 −1.10754
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 73.8881 3.03678
$$593$$ −45.6673 −1.87533 −0.937666 0.347538i $$-0.887018\pi$$
−0.937666 + 0.347538i $$0.887018\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 119.145 4.88038
$$597$$ 0 0
$$598$$ 13.4396 0.549588
$$599$$ 40.2208 1.64338 0.821688 0.569937i $$-0.193032\pi$$
0.821688 + 0.569937i $$0.193032\pi$$
$$600$$ 0 0
$$601$$ 17.3974 0.709656 0.354828 0.934932i $$-0.384539\pi$$
0.354828 + 0.934932i $$0.384539\pi$$
$$602$$ −83.9862 −3.42302
$$603$$ 0 0
$$604$$ 28.5795 1.16288
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 14.2277 0.577483 0.288741 0.957407i $$-0.406763\pi$$
0.288741 + 0.957407i $$0.406763\pi$$
$$608$$ −97.2173 −3.94268
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 11.5569 0.467543
$$612$$ 0 0
$$613$$ 40.8302 1.64912 0.824558 0.565777i $$-0.191424\pi$$
0.824558 + 0.565777i $$0.191424\pi$$
$$614$$ 60.6639 2.44819
$$615$$ 0 0
$$616$$ 76.4553 3.08047
$$617$$ 5.11383 0.205875 0.102937 0.994688i $$-0.467176\pi$$
0.102937 + 0.994688i $$0.467176\pi$$
$$618$$ 0 0
$$619$$ 11.5569 0.464512 0.232256 0.972655i $$-0.425389\pi$$
0.232256 + 0.972655i $$0.425389\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −69.7586 −2.79706
$$623$$ −3.16291 −0.126719
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −22.8602 −0.913677
$$627$$ 0 0
$$628$$ −50.7880 −2.02666
$$629$$ −12.1335 −0.483794
$$630$$ 0 0
$$631$$ 35.2242 1.40225 0.701127 0.713036i $$-0.252681\pi$$
0.701127 + 0.713036i $$0.252681\pi$$
$$632$$ 106.214 4.22496
$$633$$ 0 0
$$634$$ 76.8915 3.05375
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −0.397442 −0.0157472
$$638$$ −45.3415 −1.79509
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 21.9018 0.865071 0.432535 0.901617i $$-0.357619\pi$$
0.432535 + 0.901617i $$0.357619\pi$$
$$642$$ 0 0
$$643$$ −7.50783 −0.296080 −0.148040 0.988981i $$-0.547296\pi$$
−0.148040 + 0.988981i $$0.547296\pi$$
$$644$$ −75.2502 −2.96527
$$645$$ 0 0
$$646$$ 28.0382 1.10315
$$647$$ −14.0422 −0.552056 −0.276028 0.961150i $$-0.589018\pi$$
−0.276028 + 0.961150i $$0.589018\pi$$
$$648$$ 0 0
$$649$$ 5.75859 0.226044
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 79.1261 3.09882
$$653$$ 7.99312 0.312795 0.156398 0.987694i $$-0.450012\pi$$
0.156398 + 0.987694i $$0.450012\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −49.0157 −1.91374
$$657$$ 0 0
$$658$$ −87.3346 −3.40466
$$659$$ 25.3415 0.987164 0.493582 0.869699i $$-0.335687\pi$$
0.493582 + 0.869699i $$0.335687\pi$$
$$660$$ 0 0
$$661$$ 27.4396 1.06728 0.533639 0.845712i $$-0.320824\pi$$
0.533639 + 0.845712i $$0.320824\pi$$
$$662$$ −36.7620 −1.42880
$$663$$ 0 0
$$664$$ 21.8827 0.849215
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 29.0225 1.12376
$$668$$ −56.5275 −2.18711
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 17.9578 0.693253
$$672$$ 0 0
$$673$$ −27.1070 −1.04490 −0.522448 0.852671i $$-0.674981\pi$$
−0.522448 + 0.852671i $$0.674981\pi$$
$$674$$ 12.0191 0.462959
$$675$$ 0 0
$$676$$ 5.71982 0.219993
$$677$$ −36.5957 −1.40649 −0.703243 0.710949i $$-0.748265\pi$$
−0.703243 + 0.710949i $$0.748265\pi$$
$$678$$ 0 0
$$679$$ 29.4750 1.13115
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 57.1070 2.18674
$$683$$ −13.4656 −0.515248 −0.257624 0.966245i $$-0.582940\pi$$
−0.257624 + 0.966245i $$0.582940\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −49.8950 −1.90500
$$687$$ 0 0
$$688$$ −192.011 −7.32034
$$689$$ −1.16291 −0.0443033
$$690$$ 0 0
$$691$$ 29.5500 1.12414 0.562068 0.827091i $$-0.310006\pi$$
0.562068 + 0.827091i $$0.310006\pi$$
$$692$$ 75.0088 2.85141
$$693$$ 0 0
$$694$$ 17.4396 0.662000
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 8.04908 0.304881
$$698$$ 49.0878 1.85800
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −43.6604 −1.64903 −0.824516 0.565839i $$-0.808552\pi$$
−0.824516 + 0.565839i $$0.808552\pi$$
$$702$$ 0 0
$$703$$ −15.2120 −0.573731
$$704$$ 112.566 4.24248
$$705$$ 0 0
$$706$$ −38.2468 −1.43944
$$707$$ −20.8724 −0.784988
$$708$$ 0 0
$$709$$ −26.7880 −1.00604 −0.503022 0.864273i $$-0.667779\pi$$
−0.503022 + 0.864273i $$0.667779\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −12.0191 −0.450435
$$713$$ −36.5535 −1.36894
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −48.9244 −1.82839
$$717$$ 0 0
$$718$$ −2.76891 −0.103335
$$719$$ 34.8793 1.30078 0.650389 0.759601i $$-0.274606\pi$$
0.650389 + 0.759601i $$0.274606\pi$$
$$720$$ 0 0
$$721$$ −10.2414 −0.381410
$$722$$ −17.6386 −0.656443
$$723$$ 0 0
$$724$$ 21.2964 0.791475
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −37.4396 −1.38856 −0.694280 0.719705i $$-0.744277\pi$$
−0.694280 + 0.719705i $$0.744277\pi$$
$$728$$ −28.1104 −1.04184
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 31.5309 1.16621
$$732$$ 0 0
$$733$$ 47.1560 1.74175 0.870874 0.491506i $$-0.163554\pi$$
0.870874 + 0.491506i $$0.163554\pi$$
$$734$$ −39.5309 −1.45911
$$735$$ 0 0
$$736$$ −132.207 −4.87322
$$737$$ −5.12070 −0.188624
$$738$$ 0 0
$$739$$ −31.7914 −1.16947 −0.584734 0.811225i $$-0.698801\pi$$
−0.584734 + 0.811225i $$0.698801\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 8.78801 0.322618
$$743$$ 16.6776 0.611842 0.305921 0.952057i $$-0.401036\pi$$
0.305921 + 0.952057i $$0.401036\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −43.5500 −1.59448
$$747$$ 0 0
$$748$$ −44.1364 −1.61379
$$749$$ −34.2767 −1.25244
$$750$$ 0 0
$$751$$ 16.1855 0.590616 0.295308 0.955402i $$-0.404578\pi$$
0.295308 + 0.955402i $$0.404578\pi$$
$$752$$ −199.666 −7.28106
$$753$$ 0 0
$$754$$ 16.6707 0.607113
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −12.3258 −0.447990 −0.223995 0.974590i $$-0.571910\pi$$
−0.223995 + 0.974590i $$0.571910\pi$$
$$758$$ 72.8002 2.64422
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0.00687569 0.000249244 0 0.000124622 1.00000i $$-0.499960\pi$$
0.000124622 1.00000i $$0.499960\pi$$
$$762$$ 0 0
$$763$$ 31.1138 1.12640
$$764$$ 24.2208 0.876277
$$765$$ 0 0
$$766$$ 62.3380 2.25237
$$767$$ −2.11727 −0.0764501
$$768$$ 0 0
$$769$$ −20.3258 −0.732968 −0.366484 0.930424i $$-0.619439\pi$$
−0.366484 + 0.930424i $$0.619439\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 133.790 4.81520
$$773$$ 9.90184 0.356144 0.178072 0.984017i $$-0.443014\pi$$
0.178072 + 0.984017i $$0.443014\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 112.005 4.02076
$$777$$ 0 0
$$778$$ −88.0054 −3.15514
$$779$$ 10.0913 0.361558
$$780$$ 0 0
$$781$$ 18.2767 0.653993
$$782$$ 38.1295 1.36351
$$783$$ 0 0
$$784$$ 6.86651 0.245232
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −36.3449 −1.29556 −0.647778 0.761829i $$-0.724302\pi$$
−0.647778 + 0.761829i $$0.724302\pi$$
$$788$$ 83.2433 2.96542
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −35.6673 −1.26818
$$792$$ 0 0
$$793$$ −6.60256 −0.234464
$$794$$ −49.8759 −1.77003
$$795$$ 0 0
$$796$$ −86.4484 −3.06408
$$797$$ 18.8371 0.667244 0.333622 0.942707i $$-0.391729\pi$$
0.333622 + 0.942707i $$0.391729\pi$$
$$798$$ 0 0
$$799$$ 32.7880 1.15996
$$800$$ 0 0
$$801$$ 0 0
$$802$$ −37.7395 −1.33263
$$803$$ −24.7880 −0.874750
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −20.9966 −0.739572
$$807$$ 0 0
$$808$$ −79.3155 −2.79031
$$809$$ −32.2277 −1.13306 −0.566532 0.824040i $$-0.691715\pi$$
−0.566532 + 0.824040i $$0.691715\pi$$
$$810$$ 0 0
$$811$$ −23.0034 −0.807760 −0.403880 0.914812i $$-0.632339\pi$$
−0.403880 + 0.914812i $$0.632339\pi$$
$$812$$ −93.3415 −3.27564
$$813$$ 0 0
$$814$$ 32.3189 1.13278
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 39.5309 1.38301
$$818$$ −38.8984 −1.36005
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −49.9372 −1.74282 −0.871410 0.490556i $$-0.836794\pi$$
−0.871410 + 0.490556i $$0.836794\pi$$
$$822$$ 0 0
$$823$$ −28.2345 −0.984194 −0.492097 0.870540i $$-0.663769\pi$$
−0.492097 + 0.870540i $$0.663769\pi$$
$$824$$ −38.9175 −1.35576
$$825$$ 0 0
$$826$$ 16.0000 0.556711
$$827$$ −9.55004 −0.332087 −0.166044 0.986118i $$-0.553099\pi$$
−0.166044 + 0.986118i $$0.553099\pi$$
$$828$$ 0 0
$$829$$ −37.9862 −1.31932 −0.659658 0.751565i $$-0.729299\pi$$
−0.659658 + 0.751565i $$0.729299\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −41.3871 −1.43484
$$833$$ −1.12758 −0.0390683
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −55.3346 −1.91379
$$837$$ 0 0
$$838$$ −34.2277 −1.18237
$$839$$ 4.72670 0.163184 0.0815919 0.996666i $$-0.474000\pi$$
0.0815919 + 0.996666i $$0.474000\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 63.3155 2.18200
$$843$$ 0 0
$$844$$ −104.259 −3.58874
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −9.79832 −0.336674
$$848$$ 20.0913 0.689938
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −20.6870 −0.709140
$$852$$ 0 0
$$853$$ 48.3611 1.65585 0.827927 0.560836i $$-0.189520\pi$$
0.827927 + 0.560836i $$0.189520\pi$$
$$854$$ 49.8950 1.70737
$$855$$ 0 0
$$856$$ −130.252 −4.45193
$$857$$ 6.83709 0.233551 0.116775 0.993158i $$-0.462744\pi$$
0.116775 + 0.993158i $$0.462744\pi$$
$$858$$ 0 0
$$859$$ 12.6026 0.429994 0.214997 0.976615i $$-0.431026\pi$$
0.214997 + 0.976615i $$0.431026\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 24.9966 0.851386
$$863$$ 8.20855 0.279422 0.139711 0.990192i $$-0.455383\pi$$
0.139711 + 0.990192i $$0.455383\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 56.4744 1.91908
$$867$$ 0 0
$$868$$ 117.562 3.99032
$$869$$ 27.9509 0.948170
$$870$$ 0 0
$$871$$ 1.88273 0.0637940
$$872$$ 118.233 4.00387
$$873$$ 0 0
$$874$$ 47.8037 1.61698
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −13.5309 −0.456907 −0.228454 0.973555i $$-0.573367\pi$$
−0.228454 + 0.973555i $$0.573367\pi$$
$$878$$ −70.5466 −2.38083
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 9.34836 0.314954 0.157477 0.987523i $$-0.449664\pi$$
0.157477 + 0.987523i $$0.449664\pi$$
$$882$$ 0 0
$$883$$ 55.1001 1.85427 0.927133 0.374733i $$-0.122266\pi$$
0.927133 + 0.374733i $$0.122266\pi$$
$$884$$ 16.2277 0.545795
$$885$$ 0 0
$$886$$ 30.3640 1.02010
$$887$$ 0.133492 0.00448223 0.00224112 0.999997i $$-0.499287\pi$$
0.00224112 + 0.999997i $$0.499287\pi$$
$$888$$ 0 0
$$889$$ 36.5535 1.22596
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −57.8690 −1.93760
$$893$$ 41.1070 1.37559
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 164.083 5.48162
$$897$$ 0 0
$$898$$ −7.88273 −0.263050
$$899$$ −45.3415 −1.51222
$$900$$ 0 0
$$901$$ −3.29928 −0.109915
$$902$$ −21.4396 −0.713862
$$903$$ 0 0
$$904$$ −135.536 −4.50787
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 58.5466 1.94401 0.972004 0.234964i $$-0.0754973\pi$$
0.972004 + 0.234964i $$0.0754973\pi$$
$$908$$ 64.7620 2.14920
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −50.4622 −1.67189 −0.835943 0.548816i $$-0.815079\pi$$
−0.835943 + 0.548816i $$0.815079\pi$$
$$912$$ 0 0
$$913$$ 5.75859 0.190582
$$914$$ 38.1104 1.26058
$$915$$ 0 0
$$916$$ −35.6604 −1.17825
$$917$$ 25.6742 0.847836
$$918$$ 0 0
$$919$$ 56.9735 1.87938 0.939691 0.342026i $$-0.111113\pi$$
0.939691 + 0.342026i $$0.111113\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 54.5275 1.79577
$$923$$ −6.71982 −0.221186
$$924$$ 0 0
$$925$$ 0 0
$$926$$ −75.1261 −2.46880
$$927$$ 0 0
$$928$$ −163.992 −5.38329
$$929$$ 36.5957 1.20067 0.600333 0.799750i $$-0.295035\pi$$
0.600333 + 0.799750i $$0.295035\pi$$
$$930$$ 0 0
$$931$$ −1.41367 −0.0463311
$$932$$ 39.1070 1.28099
$$933$$ 0 0
$$934$$ 80.3572 2.62937
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 47.1070 1.53892 0.769459 0.638697i $$-0.220526\pi$$
0.769459 + 0.638697i $$0.220526\pi$$
$$938$$ −14.2277 −0.464549
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 36.3611 1.18534 0.592670 0.805446i $$-0.298074\pi$$
0.592670 + 0.805446i $$0.298074\pi$$
$$942$$ 0 0
$$943$$ 13.7233 0.446891
$$944$$ 36.5795 1.19056
$$945$$ 0 0
$$946$$ −83.9862 −2.73063
$$947$$ 44.5795 1.44864 0.724319 0.689465i $$-0.242154\pi$$
0.724319 + 0.689465i $$0.242154\pi$$
$$948$$ 0 0
$$949$$ 9.11383 0.295847
$$950$$ 0 0
$$951$$ 0 0
$$952$$ −79.7517 −2.58477
$$953$$ 19.8596 0.643317 0.321658 0.946856i $$-0.395760\pi$$
0.321658 + 0.946856i $$0.395760\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ −7.32238 −0.236823
$$957$$ 0 0
$$958$$ 33.7846 1.09153
$$959$$ 4.80176 0.155057
$$960$$ 0 0
$$961$$ 26.1070 0.842160
$$962$$ −11.8827 −0.383115
$$963$$ 0 0
$$964$$ −34.3189 −1.10534
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −47.4068 −1.52450 −0.762250 0.647283i $$-0.775905\pi$$
−0.762250 + 0.647283i $$0.775905\pi$$
$$968$$ −37.2338 −1.19674
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 10.6448 0.341607 0.170803 0.985305i $$-0.445364\pi$$
0.170803 + 0.985305i $$0.445364\pi$$
$$972$$ 0 0
$$973$$ −17.0716 −0.547291
$$974$$ 0.443086 0.0141974
$$975$$ 0 0
$$976$$ 114.071 3.65131
$$977$$ −1.21199 −0.0387750 −0.0193875 0.999812i $$-0.506172\pi$$
−0.0193875 + 0.999812i $$0.506172\pi$$
$$978$$ 0 0
$$979$$ −3.16291 −0.101087
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 117.328 3.74408
$$983$$ 51.8759 1.65458 0.827291 0.561773i $$-0.189881\pi$$
0.827291 + 0.561773i $$0.189881\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 47.2964 1.50622
$$987$$ 0 0
$$988$$ 20.3449 0.647258
$$989$$ 53.7586 1.70942
$$990$$ 0 0
$$991$$ −21.6251 −0.686944 −0.343472 0.939163i $$-0.611603\pi$$
−0.343472 + 0.939163i $$0.611603\pi$$
$$992$$ 206.545 6.55781
$$993$$ 0 0
$$994$$ 50.7811 1.61068
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −23.2051 −0.734913 −0.367457 0.930041i $$-0.619771\pi$$
−0.367457 + 0.930041i $$0.619771\pi$$
$$998$$ 21.6482 0.685262
$$999$$ 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 2925.2.a.bh.1.3 3
3.2 odd 2 975.2.a.o.1.1 3
5.2 odd 4 2925.2.c.w.2224.6 6
5.3 odd 4 2925.2.c.w.2224.1 6
5.4 even 2 585.2.a.n.1.1 3
15.2 even 4 975.2.c.i.274.1 6
15.8 even 4 975.2.c.i.274.6 6
15.14 odd 2 195.2.a.e.1.3 3
20.19 odd 2 9360.2.a.dd.1.3 3
60.59 even 2 3120.2.a.bj.1.3 3
65.64 even 2 7605.2.a.bx.1.3 3
105.104 even 2 9555.2.a.bq.1.3 3
195.194 odd 2 2535.2.a.bc.1.1 3

By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.e.1.3 3 15.14 odd 2
585.2.a.n.1.1 3 5.4 even 2
975.2.a.o.1.1 3 3.2 odd 2
975.2.c.i.274.1 6 15.2 even 4
975.2.c.i.274.6 6 15.8 even 4
2535.2.a.bc.1.1 3 195.194 odd 2
2925.2.a.bh.1.3 3 1.1 even 1 trivial
2925.2.c.w.2224.1 6 5.3 odd 4
2925.2.c.w.2224.6 6 5.2 odd 4
3120.2.a.bj.1.3 3 60.59 even 2
7605.2.a.bx.1.3 3 65.64 even 2
9360.2.a.dd.1.3 3 20.19 odd 2
9555.2.a.bq.1.3 3 105.104 even 2