Properties

 Label 8550.2.a.z.1.1 Level $8550$ Weight $2$ Character 8550.1 Self dual yes Analytic conductor $68.272$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 8550.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$68.2720937282$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 2850) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 8550.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} -1.00000 q^{11} +4.00000 q^{13} +1.00000 q^{16} -4.00000 q^{17} -1.00000 q^{19} -1.00000 q^{22} -5.00000 q^{23} +4.00000 q^{26} -3.00000 q^{29} -5.00000 q^{31} +1.00000 q^{32} -4.00000 q^{34} -6.00000 q^{37} -1.00000 q^{38} +2.00000 q^{41} +4.00000 q^{43} -1.00000 q^{44} -5.00000 q^{46} -7.00000 q^{49} +4.00000 q^{52} -9.00000 q^{53} -3.00000 q^{58} -11.0000 q^{61} -5.00000 q^{62} +1.00000 q^{64} -1.00000 q^{67} -4.00000 q^{68} -2.00000 q^{71} -3.00000 q^{73} -6.00000 q^{74} -1.00000 q^{76} +17.0000 q^{79} +2.00000 q^{82} -3.00000 q^{83} +4.00000 q^{86} -1.00000 q^{88} -7.00000 q^{89} -5.00000 q^{92} +10.0000 q^{97} -7.00000 q^{98} +O(q^{100})$$

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
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.00000 −0.301511 −0.150756 0.988571i $$-0.548171\pi$$
−0.150756 + 0.988571i $$0.548171\pi$$
$$12$$ 0 0
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −4.00000 −0.970143 −0.485071 0.874475i $$-0.661206\pi$$
−0.485071 + 0.874475i $$0.661206\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −0.229416
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −1.00000 −0.213201
$$23$$ −5.00000 −1.04257 −0.521286 0.853382i $$-0.674548\pi$$
−0.521286 + 0.853382i $$0.674548\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 4.00000 0.784465
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −3.00000 −0.557086 −0.278543 0.960424i $$-0.589851\pi$$
−0.278543 + 0.960424i $$0.589851\pi$$
$$30$$ 0 0
$$31$$ −5.00000 −0.898027 −0.449013 0.893525i $$-0.648224\pi$$
−0.449013 + 0.893525i $$0.648224\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −4.00000 −0.685994
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −6.00000 −0.986394 −0.493197 0.869918i $$-0.664172\pi$$
−0.493197 + 0.869918i $$0.664172\pi$$
$$38$$ −1.00000 −0.162221
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ −1.00000 −0.150756
$$45$$ 0 0
$$46$$ −5.00000 −0.737210
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 4.00000 0.554700
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −3.00000 −0.393919
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −11.0000 −1.40841 −0.704203 0.709999i $$-0.748695\pi$$
−0.704203 + 0.709999i $$0.748695\pi$$
$$62$$ −5.00000 −0.635001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.00000 −0.122169 −0.0610847 0.998133i $$-0.519456\pi$$
−0.0610847 + 0.998133i $$0.519456\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ 0 0
$$73$$ −3.00000 −0.351123 −0.175562 0.984468i $$-0.556174\pi$$
−0.175562 + 0.984468i $$0.556174\pi$$
$$74$$ −6.00000 −0.697486
$$75$$ 0 0
$$76$$ −1.00000 −0.114708
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 17.0000 1.91265 0.956325 0.292306i $$-0.0944227\pi$$
0.956325 + 0.292306i $$0.0944227\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 2.00000 0.220863
$$83$$ −3.00000 −0.329293 −0.164646 0.986353i $$-0.552648\pi$$
−0.164646 + 0.986353i $$0.552648\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 4.00000 0.431331
$$87$$ 0 0
$$88$$ −1.00000 −0.106600
$$89$$ −7.00000 −0.741999 −0.370999 0.928633i $$-0.620985\pi$$
−0.370999 + 0.928633i $$0.620985\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −5.00000 −0.521286
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ −7.00000 −0.707107
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 8.00000 0.796030 0.398015 0.917379i $$-0.369699\pi$$
0.398015 + 0.917379i $$0.369699\pi$$
$$102$$ 0 0
$$103$$ 13.0000 1.28093 0.640464 0.767988i $$-0.278742\pi$$
0.640464 + 0.767988i $$0.278742\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 0 0
$$106$$ −9.00000 −0.874157
$$107$$ −10.0000 −0.966736 −0.483368 0.875417i $$-0.660587\pi$$
−0.483368 + 0.875417i $$0.660587\pi$$
$$108$$ 0 0
$$109$$ 6.00000 0.574696 0.287348 0.957826i $$-0.407226\pi$$
0.287348 + 0.957826i $$0.407226\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −5.00000 −0.470360 −0.235180 0.971952i $$-0.575568\pi$$
−0.235180 + 0.971952i $$0.575568\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −3.00000 −0.278543
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ −11.0000 −0.995893
$$123$$ 0 0
$$124$$ −5.00000 −0.449013
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −5.00000 −0.443678 −0.221839 0.975083i $$-0.571206\pi$$
−0.221839 + 0.975083i $$0.571206\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −15.0000 −1.31056 −0.655278 0.755388i $$-0.727449\pi$$
−0.655278 + 0.755388i $$0.727449\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −1.00000 −0.0863868
$$135$$ 0 0
$$136$$ −4.00000 −0.342997
$$137$$ 4.00000 0.341743 0.170872 0.985293i $$-0.445342\pi$$
0.170872 + 0.985293i $$0.445342\pi$$
$$138$$ 0 0
$$139$$ −2.00000 −0.169638 −0.0848189 0.996396i $$-0.527031\pi$$
−0.0848189 + 0.996396i $$0.527031\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −2.00000 −0.167836
$$143$$ −4.00000 −0.334497
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −3.00000 −0.248282
$$147$$ 0 0
$$148$$ −6.00000 −0.493197
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ −24.0000 −1.95309 −0.976546 0.215308i $$-0.930924\pi$$
−0.976546 + 0.215308i $$0.930924\pi$$
$$152$$ −1.00000 −0.0811107
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 14.0000 1.11732 0.558661 0.829396i $$-0.311315\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ 17.0000 1.35245
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 10.0000 0.783260 0.391630 0.920123i $$-0.371911\pi$$
0.391630 + 0.920123i $$0.371911\pi$$
$$164$$ 2.00000 0.156174
$$165$$ 0 0
$$166$$ −3.00000 −0.232845
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 4.00000 0.304997
$$173$$ −7.00000 −0.532200 −0.266100 0.963945i $$-0.585735\pi$$
−0.266100 + 0.963945i $$0.585735\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1.00000 −0.0753778
$$177$$ 0 0
$$178$$ −7.00000 −0.524672
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −5.00000 −0.368605
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 4.00000 0.292509
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −11.0000 −0.795932 −0.397966 0.917400i $$-0.630284\pi$$
−0.397966 + 0.917400i $$0.630284\pi$$
$$192$$ 0 0
$$193$$ 10.0000 0.719816 0.359908 0.932988i $$-0.382808\pi$$
0.359908 + 0.932988i $$0.382808\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ −7.00000 −0.500000
$$197$$ 20.0000 1.42494 0.712470 0.701702i $$-0.247576\pi$$
0.712470 + 0.701702i $$0.247576\pi$$
$$198$$ 0 0
$$199$$ 6.00000 0.425329 0.212664 0.977125i $$-0.431786\pi$$
0.212664 + 0.977125i $$0.431786\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 8.00000 0.562878
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 13.0000 0.905753
$$207$$ 0 0
$$208$$ 4.00000 0.277350
$$209$$ 1.00000 0.0691714
$$210$$ 0 0
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ −9.00000 −0.618123
$$213$$ 0 0
$$214$$ −10.0000 −0.683586
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 6.00000 0.406371
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −16.0000 −1.07628
$$222$$ 0 0
$$223$$ −15.0000 −1.00447 −0.502237 0.864730i $$-0.667490\pi$$
−0.502237 + 0.864730i $$0.667490\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −5.00000 −0.332595
$$227$$ −2.00000 −0.132745 −0.0663723 0.997795i $$-0.521143\pi$$
−0.0663723 + 0.997795i $$0.521143\pi$$
$$228$$ 0 0
$$229$$ 5.00000 0.330409 0.165205 0.986259i $$-0.447172\pi$$
0.165205 + 0.986259i $$0.447172\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −3.00000 −0.196960
$$233$$ 24.0000 1.57229 0.786146 0.618041i $$-0.212073\pi$$
0.786146 + 0.618041i $$0.212073\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −4.00000 −0.257663 −0.128831 0.991667i $$-0.541123\pi$$
−0.128831 + 0.991667i $$0.541123\pi$$
$$242$$ −10.0000 −0.642824
$$243$$ 0 0
$$244$$ −11.0000 −0.704203
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −4.00000 −0.254514
$$248$$ −5.00000 −0.317500
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −16.0000 −1.00991 −0.504956 0.863145i $$-0.668491\pi$$
−0.504956 + 0.863145i $$0.668491\pi$$
$$252$$ 0 0
$$253$$ 5.00000 0.314347
$$254$$ −5.00000 −0.313728
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −7.00000 −0.436648 −0.218324 0.975876i $$-0.570059\pi$$
−0.218324 + 0.975876i $$0.570059\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −15.0000 −0.926703
$$263$$ 11.0000 0.678289 0.339145 0.940734i $$-0.389862\pi$$
0.339145 + 0.940734i $$0.389862\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −1.00000 −0.0610847
$$269$$ 2.00000 0.121942 0.0609711 0.998140i $$-0.480580\pi$$
0.0609711 + 0.998140i $$0.480580\pi$$
$$270$$ 0 0
$$271$$ 2.00000 0.121491 0.0607457 0.998153i $$-0.480652\pi$$
0.0607457 + 0.998153i $$0.480652\pi$$
$$272$$ −4.00000 −0.242536
$$273$$ 0 0
$$274$$ 4.00000 0.241649
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −1.00000 −0.0600842 −0.0300421 0.999549i $$-0.509564\pi$$
−0.0300421 + 0.999549i $$0.509564\pi$$
$$278$$ −2.00000 −0.119952
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 3.00000 0.178965 0.0894825 0.995988i $$-0.471479\pi$$
0.0894825 + 0.995988i $$0.471479\pi$$
$$282$$ 0 0
$$283$$ −8.00000 −0.475551 −0.237775 0.971320i $$-0.576418\pi$$
−0.237775 + 0.971320i $$0.576418\pi$$
$$284$$ −2.00000 −0.118678
$$285$$ 0 0
$$286$$ −4.00000 −0.236525
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −3.00000 −0.175562
$$293$$ −11.0000 −0.642627 −0.321313 0.946973i $$-0.604124\pi$$
−0.321313 + 0.946973i $$0.604124\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −6.00000 −0.348743
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −20.0000 −1.15663
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −24.0000 −1.38104
$$303$$ 0 0
$$304$$ −1.00000 −0.0573539
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −25.0000 −1.42683 −0.713413 0.700744i $$-0.752851\pi$$
−0.713413 + 0.700744i $$0.752851\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −32.0000 −1.81455 −0.907277 0.420534i $$-0.861843\pi$$
−0.907277 + 0.420534i $$0.861843\pi$$
$$312$$ 0 0
$$313$$ 21.0000 1.18699 0.593495 0.804838i $$-0.297748\pi$$
0.593495 + 0.804838i $$0.297748\pi$$
$$314$$ 14.0000 0.790066
$$315$$ 0 0
$$316$$ 17.0000 0.956325
$$317$$ 13.0000 0.730153 0.365076 0.930978i $$-0.381043\pi$$
0.365076 + 0.930978i $$0.381043\pi$$
$$318$$ 0 0
$$319$$ 3.00000 0.167968
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 4.00000 0.222566
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 10.0000 0.553849
$$327$$ 0 0
$$328$$ 2.00000 0.110432
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 13.0000 0.714545 0.357272 0.934000i $$-0.383707\pi$$
0.357272 + 0.934000i $$0.383707\pi$$
$$332$$ −3.00000 −0.164646
$$333$$ 0 0
$$334$$ −18.0000 −0.984916
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −8.00000 −0.435788 −0.217894 0.975972i $$-0.569919\pi$$
−0.217894 + 0.975972i $$0.569919\pi$$
$$338$$ 3.00000 0.163178
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 5.00000 0.270765
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ −7.00000 −0.376322
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ 0 0
$$349$$ −1.00000 −0.0535288 −0.0267644 0.999642i $$-0.508520\pi$$
−0.0267644 + 0.999642i $$0.508520\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −1.00000 −0.0533002
$$353$$ −28.0000 −1.49029 −0.745145 0.666903i $$-0.767620\pi$$
−0.745145 + 0.666903i $$0.767620\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −7.00000 −0.370999
$$357$$ 0 0
$$358$$ 4.00000 0.211407
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −18.0000 −0.939592 −0.469796 0.882775i $$-0.655673\pi$$
−0.469796 + 0.882775i $$0.655673\pi$$
$$368$$ −5.00000 −0.260643
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 28.0000 1.44979 0.724893 0.688862i $$-0.241889\pi$$
0.724893 + 0.688862i $$0.241889\pi$$
$$374$$ 4.00000 0.206835
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −11.0000 −0.562809
$$383$$ 6.00000 0.306586 0.153293 0.988181i $$-0.451012\pi$$
0.153293 + 0.988181i $$0.451012\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 10.0000 0.508987
$$387$$ 0 0
$$388$$ 10.0000 0.507673
$$389$$ −26.0000 −1.31825 −0.659126 0.752032i $$-0.729074\pi$$
−0.659126 + 0.752032i $$0.729074\pi$$
$$390$$ 0 0
$$391$$ 20.0000 1.01144
$$392$$ −7.00000 −0.353553
$$393$$ 0 0
$$394$$ 20.0000 1.00759
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −3.00000 −0.150566 −0.0752828 0.997162i $$-0.523986\pi$$
−0.0752828 + 0.997162i $$0.523986\pi$$
$$398$$ 6.00000 0.300753
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 17.0000 0.848939 0.424470 0.905442i $$-0.360461\pi$$
0.424470 + 0.905442i $$0.360461\pi$$
$$402$$ 0 0
$$403$$ −20.0000 −0.996271
$$404$$ 8.00000 0.398015
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 6.00000 0.297409
$$408$$ 0 0
$$409$$ 6.00000 0.296681 0.148340 0.988936i $$-0.452607\pi$$
0.148340 + 0.988936i $$0.452607\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 13.0000 0.640464
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 4.00000 0.196116
$$417$$ 0 0
$$418$$ 1.00000 0.0489116
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −34.0000 −1.65706 −0.828529 0.559946i $$-0.810822\pi$$
−0.828529 + 0.559946i $$0.810822\pi$$
$$422$$ −13.0000 −0.632830
$$423$$ 0 0
$$424$$ −9.00000 −0.437079
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −10.0000 −0.483368
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −38.0000 −1.83040 −0.915198 0.403005i $$-0.867966\pi$$
−0.915198 + 0.403005i $$0.867966\pi$$
$$432$$ 0 0
$$433$$ −22.0000 −1.05725 −0.528626 0.848855i $$-0.677293\pi$$
−0.528626 + 0.848855i $$0.677293\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 6.00000 0.287348
$$437$$ 5.00000 0.239182
$$438$$ 0 0
$$439$$ 21.0000 1.00228 0.501138 0.865368i $$-0.332915\pi$$
0.501138 + 0.865368i $$0.332915\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −16.0000 −0.761042
$$443$$ 13.0000 0.617649 0.308824 0.951119i $$-0.400064\pi$$
0.308824 + 0.951119i $$0.400064\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −15.0000 −0.710271
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 27.0000 1.27421 0.637104 0.770778i $$-0.280132\pi$$
0.637104 + 0.770778i $$0.280132\pi$$
$$450$$ 0 0
$$451$$ −2.00000 −0.0941763
$$452$$ −5.00000 −0.235180
$$453$$ 0 0
$$454$$ −2.00000 −0.0938647
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −18.0000 −0.842004 −0.421002 0.907060i $$-0.638322\pi$$
−0.421002 + 0.907060i $$0.638322\pi$$
$$458$$ 5.00000 0.233635
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −4.00000 −0.186299 −0.0931493 0.995652i $$-0.529693\pi$$
−0.0931493 + 0.995652i $$0.529693\pi$$
$$462$$ 0 0
$$463$$ 4.00000 0.185896 0.0929479 0.995671i $$-0.470371\pi$$
0.0929479 + 0.995671i $$0.470371\pi$$
$$464$$ −3.00000 −0.139272
$$465$$ 0 0
$$466$$ 24.0000 1.11178
$$467$$ 11.0000 0.509019 0.254510 0.967070i $$-0.418086\pi$$
0.254510 + 0.967070i $$0.418086\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −4.00000 −0.183920
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 37.0000 1.69057 0.845287 0.534313i $$-0.179430\pi$$
0.845287 + 0.534313i $$0.179430\pi$$
$$480$$ 0 0
$$481$$ −24.0000 −1.09431
$$482$$ −4.00000 −0.182195
$$483$$ 0 0
$$484$$ −10.0000 −0.454545
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 8.00000 0.362515 0.181257 0.983436i $$-0.441983\pi$$
0.181257 + 0.983436i $$0.441983\pi$$
$$488$$ −11.0000 −0.497947
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −36.0000 −1.62466 −0.812329 0.583200i $$-0.801800\pi$$
−0.812329 + 0.583200i $$0.801800\pi$$
$$492$$ 0 0
$$493$$ 12.0000 0.540453
$$494$$ −4.00000 −0.179969
$$495$$ 0 0
$$496$$ −5.00000 −0.224507
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −24.0000 −1.07439 −0.537194 0.843459i $$-0.680516\pi$$
−0.537194 + 0.843459i $$0.680516\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −16.0000 −0.714115
$$503$$ 36.0000 1.60516 0.802580 0.596544i $$-0.203460\pi$$
0.802580 + 0.596544i $$0.203460\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 5.00000 0.222277
$$507$$ 0 0
$$508$$ −5.00000 −0.221839
$$509$$ 27.0000 1.19675 0.598377 0.801215i $$-0.295813\pi$$
0.598377 + 0.801215i $$0.295813\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −7.00000 −0.308757
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −3.00000 −0.131432 −0.0657162 0.997838i $$-0.520933\pi$$
−0.0657162 + 0.997838i $$0.520933\pi$$
$$522$$ 0 0
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ −15.0000 −0.655278
$$525$$ 0 0
$$526$$ 11.0000 0.479623
$$527$$ 20.0000 0.871214
$$528$$ 0 0
$$529$$ 2.00000 0.0869565
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 8.00000 0.346518
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −1.00000 −0.0431934
$$537$$ 0 0
$$538$$ 2.00000 0.0862261
$$539$$ 7.00000 0.301511
$$540$$ 0 0
$$541$$ −13.0000 −0.558914 −0.279457 0.960158i $$-0.590154\pi$$
−0.279457 + 0.960158i $$0.590154\pi$$
$$542$$ 2.00000 0.0859074
$$543$$ 0 0
$$544$$ −4.00000 −0.171499
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1.00000 0.0427569 0.0213785 0.999771i $$-0.493195\pi$$
0.0213785 + 0.999771i $$0.493195\pi$$
$$548$$ 4.00000 0.170872
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 3.00000 0.127804
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −1.00000 −0.0424859
$$555$$ 0 0
$$556$$ −2.00000 −0.0848189
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 16.0000 0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 3.00000 0.126547
$$563$$ −26.0000 −1.09577 −0.547885 0.836554i $$-0.684567\pi$$
−0.547885 + 0.836554i $$0.684567\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −8.00000 −0.336265
$$567$$ 0 0
$$568$$ −2.00000 −0.0839181
$$569$$ −22.0000 −0.922288 −0.461144 0.887325i $$-0.652561\pi$$
−0.461144 + 0.887325i $$0.652561\pi$$
$$570$$ 0 0
$$571$$ −26.0000 −1.08807 −0.544033 0.839064i $$-0.683103\pi$$
−0.544033 + 0.839064i $$0.683103\pi$$
$$572$$ −4.00000 −0.167248
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −27.0000 −1.12402 −0.562012 0.827129i $$-0.689973\pi$$
−0.562012 + 0.827129i $$0.689973\pi$$
$$578$$ −1.00000 −0.0415945
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 9.00000 0.372742
$$584$$ −3.00000 −0.124141
$$585$$ 0 0
$$586$$ −11.0000 −0.454406
$$587$$ 17.0000 0.701665 0.350833 0.936438i $$-0.385899\pi$$
0.350833 + 0.936438i $$0.385899\pi$$
$$588$$ 0 0
$$589$$ 5.00000 0.206021
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −6.00000 −0.246598
$$593$$ 28.0000 1.14982 0.574911 0.818216i $$-0.305037\pi$$
0.574911 + 0.818216i $$0.305037\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ −20.0000 −0.817861
$$599$$ −28.0000 −1.14405 −0.572024 0.820237i $$-0.693842\pi$$
−0.572024 + 0.820237i $$0.693842\pi$$
$$600$$ 0 0
$$601$$ −2.00000 −0.0815817 −0.0407909 0.999168i $$-0.512988\pi$$
−0.0407909 + 0.999168i $$0.512988\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −24.0000 −0.976546
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −25.0000 −1.01472 −0.507359 0.861735i $$-0.669378\pi$$
−0.507359 + 0.861735i $$0.669378\pi$$
$$608$$ −1.00000 −0.0405554
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 26.0000 1.05013 0.525065 0.851062i $$-0.324041\pi$$
0.525065 + 0.851062i $$0.324041\pi$$
$$614$$ −25.0000 −1.00892
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 46.0000 1.85189 0.925945 0.377658i $$-0.123271\pi$$
0.925945 + 0.377658i $$0.123271\pi$$
$$618$$ 0 0
$$619$$ −8.00000 −0.321547 −0.160774 0.986991i $$-0.551399\pi$$
−0.160774 + 0.986991i $$0.551399\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −32.0000 −1.28308
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 21.0000 0.839329
$$627$$ 0 0
$$628$$ 14.0000 0.558661
$$629$$ 24.0000 0.956943
$$630$$ 0 0
$$631$$ 28.0000 1.11466 0.557331 0.830290i $$-0.311825\pi$$
0.557331 + 0.830290i $$0.311825\pi$$
$$632$$ 17.0000 0.676224
$$633$$ 0 0
$$634$$ 13.0000 0.516296
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −28.0000 −1.10940
$$638$$ 3.00000 0.118771
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −6.00000 −0.236986 −0.118493 0.992955i $$-0.537806\pi$$
−0.118493 + 0.992955i $$0.537806\pi$$
$$642$$ 0 0
$$643$$ −14.0000 −0.552106 −0.276053 0.961142i $$-0.589027\pi$$
−0.276053 + 0.961142i $$0.589027\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 4.00000 0.157378
$$647$$ 21.0000 0.825595 0.412798 0.910823i $$-0.364552\pi$$
0.412798 + 0.910823i $$0.364552\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 10.0000 0.391630
$$653$$ 48.0000 1.87839 0.939193 0.343391i $$-0.111576\pi$$
0.939193 + 0.343391i $$0.111576\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 2.00000 0.0780869
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ 0 0
$$661$$ −32.0000 −1.24466 −0.622328 0.782757i $$-0.713813\pi$$
−0.622328 + 0.782757i $$0.713813\pi$$
$$662$$ 13.0000 0.505259
$$663$$ 0 0
$$664$$ −3.00000 −0.116423
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 15.0000 0.580802
$$668$$ −18.0000 −0.696441
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 11.0000 0.424650
$$672$$ 0 0
$$673$$ 44.0000 1.69608 0.848038 0.529936i $$-0.177784\pi$$
0.848038 + 0.529936i $$0.177784\pi$$
$$674$$ −8.00000 −0.308148
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ 15.0000 0.576497 0.288248 0.957556i $$-0.406927\pi$$
0.288248 + 0.957556i $$0.406927\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 5.00000 0.191460
$$683$$ 18.0000 0.688751 0.344375 0.938832i $$-0.388091\pi$$
0.344375 + 0.938832i $$0.388091\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 4.00000 0.152499
$$689$$ −36.0000 −1.37149
$$690$$ 0 0
$$691$$ 26.0000 0.989087 0.494543 0.869153i $$-0.335335\pi$$
0.494543 + 0.869153i $$0.335335\pi$$
$$692$$ −7.00000 −0.266100
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −8.00000 −0.303022
$$698$$ −1.00000 −0.0378506
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 6.00000 0.226294
$$704$$ −1.00000 −0.0376889
$$705$$ 0 0
$$706$$ −28.0000 −1.05379
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −43.0000 −1.61490 −0.807449 0.589937i $$-0.799153\pi$$
−0.807449 + 0.589937i $$0.799153\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −7.00000 −0.262336
$$713$$ 25.0000 0.936257
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 4.00000 0.149487
$$717$$ 0 0
$$718$$ −24.0000 −0.895672
$$719$$ 29.0000 1.08152 0.540759 0.841178i $$-0.318137\pi$$
0.540759 + 0.841178i $$0.318137\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1.00000 0.0372161
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −10.0000 −0.370879 −0.185440 0.982656i $$-0.559371\pi$$
−0.185440 + 0.982656i $$0.559371\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −16.0000 −0.591781
$$732$$ 0 0
$$733$$ 41.0000 1.51437 0.757185 0.653201i $$-0.226574\pi$$
0.757185 + 0.653201i $$0.226574\pi$$
$$734$$ −18.0000 −0.664392
$$735$$ 0 0
$$736$$ −5.00000 −0.184302
$$737$$ 1.00000 0.0368355
$$738$$ 0 0
$$739$$ −20.0000 −0.735712 −0.367856 0.929883i $$-0.619908\pi$$
−0.367856 + 0.929883i $$0.619908\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 16.0000 0.586983 0.293492 0.955962i $$-0.405183\pi$$
0.293492 + 0.955962i $$0.405183\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 28.0000 1.02515
$$747$$ 0 0
$$748$$ 4.00000 0.146254
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −12.0000 −0.437014
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −23.0000 −0.835949 −0.417975 0.908459i $$-0.637260\pi$$
−0.417975 + 0.908459i $$0.637260\pi$$
$$758$$ −8.00000 −0.290573
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 30.0000 1.08750 0.543750 0.839248i $$-0.317004\pi$$
0.543750 + 0.839248i $$0.317004\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −11.0000 −0.397966
$$765$$ 0 0
$$766$$ 6.00000 0.216789
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 35.0000 1.26213 0.631066 0.775729i $$-0.282618\pi$$
0.631066 + 0.775729i $$0.282618\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 10.0000 0.359908
$$773$$ −18.0000 −0.647415 −0.323708 0.946157i $$-0.604929\pi$$
−0.323708 + 0.946157i $$0.604929\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 10.0000 0.358979
$$777$$ 0 0
$$778$$ −26.0000 −0.932145
$$779$$ −2.00000 −0.0716574
$$780$$ 0 0
$$781$$ 2.00000 0.0715656
$$782$$ 20.0000 0.715199
$$783$$ 0 0
$$784$$ −7.00000 −0.250000
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 37.0000 1.31891 0.659454 0.751745i $$-0.270788\pi$$
0.659454 + 0.751745i $$0.270788\pi$$
$$788$$ 20.0000 0.712470
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −44.0000 −1.56249
$$794$$ −3.00000 −0.106466
$$795$$ 0 0
$$796$$ 6.00000 0.212664
$$797$$ 18.0000 0.637593 0.318796 0.947823i $$-0.396721\pi$$
0.318796 + 0.947823i $$0.396721\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 17.0000 0.600291
$$803$$ 3.00000 0.105868
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −20.0000 −0.704470
$$807$$ 0 0
$$808$$ 8.00000 0.281439
$$809$$ 44.0000 1.54696 0.773479 0.633822i $$-0.218515\pi$$
0.773479 + 0.633822i $$0.218515\pi$$
$$810$$ 0 0
$$811$$ −35.0000 −1.22902 −0.614508 0.788911i $$-0.710645\pi$$
−0.614508 + 0.788911i $$0.710645\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 6.00000 0.210300
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −4.00000 −0.139942
$$818$$ 6.00000 0.209785
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −26.0000 −0.907406 −0.453703 0.891153i $$-0.649897\pi$$
−0.453703 + 0.891153i $$0.649897\pi$$
$$822$$ 0 0
$$823$$ −26.0000 −0.906303 −0.453152 0.891434i $$-0.649700\pi$$
−0.453152 + 0.891434i $$0.649700\pi$$
$$824$$ 13.0000 0.452876
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −48.0000 −1.66912 −0.834562 0.550914i $$-0.814279\pi$$
−0.834562 + 0.550914i $$0.814279\pi$$
$$828$$ 0 0
$$829$$ −50.0000 −1.73657 −0.868286 0.496064i $$-0.834778\pi$$
−0.868286 + 0.496064i $$0.834778\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 4.00000 0.138675
$$833$$ 28.0000 0.970143
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 1.00000 0.0345857
$$837$$ 0 0
$$838$$ 12.0000 0.414533
$$839$$ 12.0000 0.414286 0.207143 0.978311i $$-0.433583\pi$$
0.207143 + 0.978311i $$0.433583\pi$$
$$840$$ 0 0
$$841$$ −20.0000 −0.689655
$$842$$ −34.0000 −1.17172
$$843$$ 0 0
$$844$$ −13.0000 −0.447478
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −9.00000 −0.309061
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 30.0000 1.02839
$$852$$ 0 0
$$853$$ 10.0000 0.342393 0.171197 0.985237i $$-0.445237\pi$$
0.171197 + 0.985237i $$0.445237\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −10.0000 −0.341793
$$857$$ 38.0000 1.29806 0.649028 0.760765i $$-0.275176\pi$$
0.649028 + 0.760765i $$0.275176\pi$$
$$858$$ 0 0
$$859$$ −18.0000 −0.614152 −0.307076 0.951685i $$-0.599351\pi$$
−0.307076 + 0.951685i $$0.599351\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −38.0000 −1.29429
$$863$$ −4.00000 −0.136162 −0.0680808 0.997680i $$-0.521688\pi$$
−0.0680808 + 0.997680i $$0.521688\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ −22.0000 −0.747590
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −17.0000 −0.576686
$$870$$ 0 0
$$871$$ −4.00000 −0.135535
$$872$$ 6.00000 0.203186
$$873$$ 0 0
$$874$$ 5.00000 0.169128
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −2.00000 −0.0675352 −0.0337676 0.999430i $$-0.510751\pi$$
−0.0337676 + 0.999430i $$0.510751\pi$$
$$878$$ 21.0000 0.708716
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 48.0000 1.61716 0.808581 0.588386i $$-0.200236\pi$$
0.808581 + 0.588386i $$0.200236\pi$$
$$882$$ 0 0
$$883$$ −38.0000 −1.27880 −0.639401 0.768874i $$-0.720818\pi$$
−0.639401 + 0.768874i $$0.720818\pi$$
$$884$$ −16.0000 −0.538138
$$885$$ 0 0
$$886$$ 13.0000 0.436744
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −15.0000 −0.502237
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 27.0000 0.901002
$$899$$ 15.0000 0.500278
$$900$$ 0 0
$$901$$ 36.0000 1.19933
$$902$$ −2.00000 −0.0665927
$$903$$ 0 0
$$904$$ −5.00000 −0.166298
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 8.00000 0.265636 0.132818 0.991140i $$-0.457597\pi$$
0.132818 + 0.991140i $$0.457597\pi$$
$$908$$ −2.00000 −0.0663723
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 18.0000 0.596367 0.298183 0.954509i $$-0.403619\pi$$
0.298183 + 0.954509i $$0.403619\pi$$
$$912$$ 0 0
$$913$$ 3.00000 0.0992855
$$914$$ −18.0000 −0.595387
$$915$$ 0 0
$$916$$ 5.00000 0.165205
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 14.0000 0.461817 0.230909 0.972975i $$-0.425830\pi$$
0.230909 + 0.972975i $$0.425830\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −4.00000 −0.131733
$$923$$ −8.00000 −0.263323
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 4.00000 0.131448
$$927$$ 0 0
$$928$$ −3.00000 −0.0984798
$$929$$ 12.0000 0.393707 0.196854 0.980433i $$-0.436928\pi$$
0.196854 + 0.980433i $$0.436928\pi$$
$$930$$ 0 0
$$931$$ 7.00000 0.229416
$$932$$ 24.0000 0.786146
$$933$$ 0 0
$$934$$ 11.0000 0.359931
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −10.0000 −0.326686 −0.163343 0.986569i $$-0.552228\pi$$
−0.163343 + 0.986569i $$0.552228\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −33.0000 −1.07577 −0.537885 0.843018i $$-0.680776\pi$$
−0.537885 + 0.843018i $$0.680776\pi$$
$$942$$ 0 0
$$943$$ −10.0000 −0.325645
$$944$$ 0 0
$$945$$ 0 0
$$946$$ −4.00000 −0.130051
$$947$$ −20.0000 −0.649913 −0.324956 0.945729i $$-0.605350\pi$$
−0.324956 + 0.945729i $$0.605350\pi$$
$$948$$ 0 0
$$949$$ −12.0000 −0.389536
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −3.00000 −0.0971795 −0.0485898 0.998819i $$-0.515473\pi$$
−0.0485898 + 0.998819i $$0.515473\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 37.0000 1.19542
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ −24.0000 −0.773791
$$963$$ 0 0
$$964$$ −4.00000 −0.128831
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 14.0000 0.450210 0.225105 0.974335i $$-0.427728\pi$$
0.225105 + 0.974335i $$0.427728\pi$$
$$968$$ −10.0000 −0.321412
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 12.0000 0.385098 0.192549 0.981287i $$-0.438325\pi$$
0.192549 + 0.981287i $$0.438325\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 8.00000 0.256337
$$975$$ 0 0
$$976$$ −11.0000 −0.352101
$$977$$ −46.0000 −1.47167 −0.735835 0.677161i $$-0.763210\pi$$
−0.735835 + 0.677161i $$0.763210\pi$$
$$978$$ 0 0
$$979$$ 7.00000 0.223721
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −36.0000 −1.14881
$$983$$ −34.0000 −1.08443 −0.542216 0.840239i $$-0.682414\pi$$
−0.542216 + 0.840239i $$0.682414\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 12.0000 0.382158
$$987$$ 0 0
$$988$$ −4.00000 −0.127257
$$989$$ −20.0000 −0.635963
$$990$$ 0 0
$$991$$ 13.0000 0.412959 0.206479 0.978451i $$-0.433799\pi$$
0.206479 + 0.978451i $$0.433799\pi$$
$$992$$ −5.00000 −0.158750
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 37.0000 1.17180 0.585901 0.810383i $$-0.300741\pi$$
0.585901 + 0.810383i $$0.300741\pi$$
$$998$$ −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 8550.2.a.z.1.1 1
3.2 odd 2 2850.2.a.l.1.1 1
5.4 even 2 8550.2.a.h.1.1 1
15.2 even 4 2850.2.d.g.799.1 2
15.8 even 4 2850.2.d.g.799.2 2
15.14 odd 2 2850.2.a.u.1.1 yes 1

By twisted newform
Twist Min Dim Char Parity Ord Type
2850.2.a.l.1.1 1 3.2 odd 2
2850.2.a.u.1.1 yes 1 15.14 odd 2
2850.2.d.g.799.1 2 15.2 even 4
2850.2.d.g.799.2 2 15.8 even 4
8550.2.a.h.1.1 1 5.4 even 2
8550.2.a.z.1.1 1 1.1 even 1 trivial