# Properties

 Label 3744.2.a.a.1.1 Level $3744$ Weight $2$ Character 3744.1 Self dual yes Analytic conductor $29.896$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3744 = 2^{5} \cdot 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3744.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$29.8959905168$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1248) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 3744.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{5} -2.00000 q^{7} +O(q^{10})$$ $$q-2.00000 q^{5} -2.00000 q^{7} -2.00000 q^{11} -1.00000 q^{13} -6.00000 q^{17} -2.00000 q^{19} -1.00000 q^{25} -2.00000 q^{29} +2.00000 q^{31} +4.00000 q^{35} +10.0000 q^{37} -2.00000 q^{41} +8.00000 q^{43} +2.00000 q^{47} -3.00000 q^{49} +2.00000 q^{53} +4.00000 q^{55} -10.0000 q^{59} +6.00000 q^{61} +2.00000 q^{65} +14.0000 q^{67} +14.0000 q^{71} -6.00000 q^{73} +4.00000 q^{77} -4.00000 q^{79} -6.00000 q^{83} +12.0000 q^{85} -10.0000 q^{89} +2.00000 q^{91} +4.00000 q^{95} +10.0000 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −2.00000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0 0
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 4.00000 0.676123
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.00000 0.291730 0.145865 0.989305i $$-0.453403\pi$$
0.145865 + 0.989305i $$0.453403\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 2.00000 0.274721 0.137361 0.990521i $$-0.456138\pi$$
0.137361 + 0.990521i $$0.456138\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −10.0000 −1.30189 −0.650945 0.759125i $$-0.725627\pi$$
−0.650945 + 0.759125i $$0.725627\pi$$
$$60$$ 0 0
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 2.00000 0.248069
$$66$$ 0 0
$$67$$ 14.0000 1.71037 0.855186 0.518321i $$-0.173443\pi$$
0.855186 + 0.518321i $$0.173443\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 14.0000 1.66149 0.830747 0.556650i $$-0.187914\pi$$
0.830747 + 0.556650i $$0.187914\pi$$
$$72$$ 0 0
$$73$$ −6.00000 −0.702247 −0.351123 0.936329i $$-0.614200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.00000 0.455842
$$78$$ 0 0
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 4.00000 0.410391
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −4.00000 −0.386695 −0.193347 0.981130i $$-0.561934\pi$$
−0.193347 + 0.981130i $$0.561934\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 12.0000 1.10004
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 4.00000 0.349482 0.174741 0.984614i $$-0.444091\pi$$
0.174741 + 0.984614i $$0.444091\pi$$
$$132$$ 0 0
$$133$$ 4.00000 0.346844
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 0.512615 0.256307 0.966595i $$-0.417494\pi$$
0.256307 + 0.966595i $$0.417494\pi$$
$$138$$ 0 0
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.00000 0.167248
$$144$$ 0 0
$$145$$ 4.00000 0.332182
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 6.00000 0.488273 0.244137 0.969741i $$-0.421495\pi$$
0.244137 + 0.969741i $$0.421495\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −4.00000 −0.321288
$$156$$ 0 0
$$157$$ 2.00000 0.159617 0.0798087 0.996810i $$-0.474569\pi$$
0.0798087 + 0.996810i $$0.474569\pi$$
$$158$$ 0 0
$$159$$ 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 $$0.371911\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.00000 0.154765 0.0773823 0.997001i $$-0.475344\pi$$
0.0773823 + 0.997001i $$0.475344\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ 0 0
$$175$$ 2.00000 0.151186
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 24.0000 1.79384 0.896922 0.442189i $$-0.145798\pi$$
0.896922 + 0.442189i $$0.145798\pi$$
$$180$$ 0 0
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −20.0000 −1.47043
$$186$$ 0 0
$$187$$ 12.0000 0.877527
$$188$$ 0 0
$$189$$ 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
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 4.00000 0.280745
$$204$$ 0 0
$$205$$ 4.00000 0.279372
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −16.0000 −1.09119
$$216$$ 0 0
$$217$$ −4.00000 −0.271538
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 6.00000 0.403604
$$222$$ 0 0
$$223$$ −14.0000 −0.937509 −0.468755 0.883328i $$-0.655297\pi$$
−0.468755 + 0.883328i $$0.655297\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 18.0000 1.19470 0.597351 0.801980i $$-0.296220\pi$$
0.597351 + 0.801980i $$0.296220\pi$$
$$228$$ 0 0
$$229$$ −22.0000 −1.45380 −0.726900 0.686743i $$-0.759040\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ −4.00000 −0.260931
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 30.0000 1.94054 0.970269 0.242028i $$-0.0778125\pi$$
0.970269 + 0.242028i $$0.0778125\pi$$
$$240$$ 0 0
$$241$$ −14.0000 −0.901819 −0.450910 0.892570i $$-0.648900\pi$$
−0.450910 + 0.892570i $$0.648900\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 6.00000 0.383326
$$246$$ 0 0
$$247$$ 2.00000 0.127257
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −2.00000 −0.124757 −0.0623783 0.998053i $$-0.519869\pi$$
−0.0623783 + 0.998053i $$0.519869\pi$$
$$258$$ 0 0
$$259$$ −20.0000 −1.24274
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −12.0000 −0.739952 −0.369976 0.929041i $$-0.620634\pi$$
−0.369976 + 0.929041i $$0.620634\pi$$
$$264$$ 0 0
$$265$$ −4.00000 −0.245718
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 30.0000 1.82913 0.914566 0.404436i $$-0.132532\pi$$
0.914566 + 0.404436i $$0.132532\pi$$
$$270$$ 0 0
$$271$$ 6.00000 0.364474 0.182237 0.983255i $$-0.441666\pi$$
0.182237 + 0.983255i $$0.441666\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 2.00000 0.120605
$$276$$ 0 0
$$277$$ −26.0000 −1.56219 −0.781094 0.624413i $$-0.785338\pi$$
−0.781094 + 0.624413i $$0.785338\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 30.0000 1.78965 0.894825 0.446417i $$-0.147300\pi$$
0.894825 + 0.446417i $$0.147300\pi$$
$$282$$ 0 0
$$283$$ 8.00000 0.475551 0.237775 0.971320i $$-0.423582\pi$$
0.237775 + 0.971320i $$0.423582\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 4.00000 0.236113
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 0 0
$$295$$ 20.0000 1.16445
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −16.0000 −0.922225
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −12.0000 −0.687118
$$306$$ 0 0
$$307$$ 18.0000 1.02731 0.513657 0.857996i $$-0.328290\pi$$
0.513657 + 0.857996i $$0.328290\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 0 0
$$313$$ −26.0000 −1.46961 −0.734803 0.678280i $$-0.762726\pi$$
−0.734803 + 0.678280i $$0.762726\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ 4.00000 0.223957
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 12.0000 0.667698
$$324$$ 0 0
$$325$$ 1.00000 0.0554700
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −4.00000 −0.220527
$$330$$ 0 0
$$331$$ −10.0000 −0.549650 −0.274825 0.961494i $$-0.588620\pi$$
−0.274825 + 0.961494i $$0.588620\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −28.0000 −1.52980
$$336$$ 0 0
$$337$$ −10.0000 −0.544735 −0.272367 0.962193i $$-0.587807\pi$$
−0.272367 + 0.962193i $$0.587807\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −4.00000 −0.216612
$$342$$ 0 0
$$343$$ 20.0000 1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −28.0000 −1.50312 −0.751559 0.659665i $$-0.770698\pi$$
−0.751559 + 0.659665i $$0.770698\pi$$
$$348$$ 0 0
$$349$$ 34.0000 1.81998 0.909989 0.414632i $$-0.136090\pi$$
0.909989 + 0.414632i $$0.136090\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −10.0000 −0.532246 −0.266123 0.963939i $$-0.585743\pi$$
−0.266123 + 0.963939i $$0.585743\pi$$
$$354$$ 0 0
$$355$$ −28.0000 −1.48609
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 10.0000 0.527780 0.263890 0.964553i $$-0.414994\pi$$
0.263890 + 0.964553i $$0.414994\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 12.0000 0.628109
$$366$$ 0 0
$$367$$ −36.0000 −1.87918 −0.939592 0.342296i $$-0.888796\pi$$
−0.939592 + 0.342296i $$0.888796\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −4.00000 −0.207670
$$372$$ 0 0
$$373$$ 26.0000 1.34623 0.673114 0.739538i $$-0.264956\pi$$
0.673114 + 0.739538i $$0.264956\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 2.00000 0.103005
$$378$$ 0 0
$$379$$ 22.0000 1.13006 0.565032 0.825069i $$-0.308864\pi$$
0.565032 + 0.825069i $$0.308864\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −34.0000 −1.73732 −0.868659 0.495410i $$-0.835018\pi$$
−0.868659 + 0.495410i $$0.835018\pi$$
$$384$$ 0 0
$$385$$ −8.00000 −0.407718
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 8.00000 0.402524
$$396$$ 0 0
$$397$$ 10.0000 0.501886 0.250943 0.968002i $$-0.419259\pi$$
0.250943 + 0.968002i $$0.419259\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −10.0000 −0.499376 −0.249688 0.968326i $$-0.580328\pi$$
−0.249688 + 0.968326i $$0.580328\pi$$
$$402$$ 0 0
$$403$$ −2.00000 −0.0996271
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −20.0000 −0.991363
$$408$$ 0 0
$$409$$ 34.0000 1.68119 0.840596 0.541663i $$-0.182205\pi$$
0.840596 + 0.541663i $$0.182205\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 20.0000 0.984136
$$414$$ 0 0
$$415$$ 12.0000 0.589057
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −20.0000 −0.977064 −0.488532 0.872546i $$-0.662467\pi$$
−0.488532 + 0.872546i $$0.662467\pi$$
$$420$$ 0 0
$$421$$ 2.00000 0.0974740 0.0487370 0.998812i $$-0.484480\pi$$
0.0487370 + 0.998812i $$0.484480\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 6.00000 0.291043
$$426$$ 0 0
$$427$$ −12.0000 −0.580721
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 30.0000 1.44505 0.722525 0.691345i $$-0.242982\pi$$
0.722525 + 0.691345i $$0.242982\pi$$
$$432$$ 0 0
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −8.00000 −0.381819 −0.190910 0.981608i $$-0.561144\pi$$
−0.190910 + 0.981608i $$0.561144\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −12.0000 −0.570137 −0.285069 0.958507i $$-0.592016\pi$$
−0.285069 + 0.958507i $$0.592016\pi$$
$$444$$ 0 0
$$445$$ 20.0000 0.948091
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −10.0000 −0.471929 −0.235965 0.971762i $$-0.575825\pi$$
−0.235965 + 0.971762i $$0.575825\pi$$
$$450$$ 0 0
$$451$$ 4.00000 0.188353
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −4.00000 −0.187523
$$456$$ 0 0
$$457$$ 2.00000 0.0935561 0.0467780 0.998905i $$-0.485105\pi$$
0.0467780 + 0.998905i $$0.485105\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ −34.0000 −1.58011 −0.790057 0.613033i $$-0.789949\pi$$
−0.790057 + 0.613033i $$0.789949\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 16.0000 0.740392 0.370196 0.928954i $$-0.379291\pi$$
0.370196 + 0.928954i $$0.379291\pi$$
$$468$$ 0 0
$$469$$ −28.0000 −1.29292
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −16.0000 −0.735681
$$474$$ 0 0
$$475$$ 2.00000 0.0917663
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 18.0000 0.822441 0.411220 0.911536i $$-0.365103\pi$$
0.411220 + 0.911536i $$0.365103\pi$$
$$480$$ 0 0
$$481$$ −10.0000 −0.455961
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −20.0000 −0.908153
$$486$$ 0 0
$$487$$ 34.0000 1.54069 0.770344 0.637629i $$-0.220085\pi$$
0.770344 + 0.637629i $$0.220085\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 16.0000 0.722070 0.361035 0.932552i $$-0.382424\pi$$
0.361035 + 0.932552i $$0.382424\pi$$
$$492$$ 0 0
$$493$$ 12.0000 0.540453
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −28.0000 −1.25597
$$498$$ 0 0
$$499$$ 6.00000 0.268597 0.134298 0.990941i $$-0.457122\pi$$
0.134298 + 0.990941i $$0.457122\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 12.0000 0.535054 0.267527 0.963550i $$-0.413794\pi$$
0.267527 + 0.963550i $$0.413794\pi$$
$$504$$ 0 0
$$505$$ 12.0000 0.533993
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 30.0000 1.32973 0.664863 0.746965i $$-0.268490\pi$$
0.664863 + 0.746965i $$0.268490\pi$$
$$510$$ 0 0
$$511$$ 12.0000 0.530849
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −4.00000 −0.175920
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 42.0000 1.84005 0.920027 0.391856i $$-0.128167\pi$$
0.920027 + 0.391856i $$0.128167\pi$$
$$522$$ 0 0
$$523$$ −36.0000 −1.57417 −0.787085 0.616844i $$-0.788411\pi$$
−0.787085 + 0.616844i $$0.788411\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −12.0000 −0.522728
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 2.00000 0.0866296
$$534$$ 0 0
$$535$$ 8.00000 0.345870
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 6.00000 0.258438
$$540$$ 0 0
$$541$$ 10.0000 0.429934 0.214967 0.976621i $$-0.431036\pi$$
0.214967 + 0.976621i $$0.431036\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −4.00000 −0.171341
$$546$$ 0 0
$$547$$ −36.0000 −1.53925 −0.769624 0.638497i $$-0.779557\pi$$
−0.769624 + 0.638497i $$0.779557\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 4.00000 0.170406
$$552$$ 0 0
$$553$$ 8.00000 0.340195
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −2.00000 −0.0847427 −0.0423714 0.999102i $$-0.513491\pi$$
−0.0423714 + 0.999102i $$0.513491\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −24.0000 −1.01148 −0.505740 0.862686i $$-0.668780\pi$$
−0.505740 + 0.862686i $$0.668780\pi$$
$$564$$ 0 0
$$565$$ 28.0000 1.17797
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −26.0000 −1.08998 −0.544988 0.838444i $$-0.683466\pi$$
−0.544988 + 0.838444i $$0.683466\pi$$
$$570$$ 0 0
$$571$$ −8.00000 −0.334790 −0.167395 0.985890i $$-0.553535\pi$$
−0.167395 + 0.985890i $$0.553535\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 42.0000 1.74848 0.874241 0.485491i $$-0.161359\pi$$
0.874241 + 0.485491i $$0.161359\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 12.0000 0.497844
$$582$$ 0 0
$$583$$ −4.00000 −0.165663
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 18.0000 0.742940 0.371470 0.928445i $$-0.378854\pi$$
0.371470 + 0.928445i $$0.378854\pi$$
$$588$$ 0 0
$$589$$ −4.00000 −0.164817
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −18.0000 −0.739171 −0.369586 0.929197i $$-0.620500\pi$$
−0.369586 + 0.929197i $$0.620500\pi$$
$$594$$ 0 0
$$595$$ −24.0000 −0.983904
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −28.0000 −1.14405 −0.572024 0.820237i $$-0.693842\pi$$
−0.572024 + 0.820237i $$0.693842\pi$$
$$600$$ 0 0
$$601$$ 22.0000 0.897399 0.448699 0.893683i $$-0.351887\pi$$
0.448699 + 0.893683i $$0.351887\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 14.0000 0.569181
$$606$$ 0 0
$$607$$ 20.0000 0.811775 0.405887 0.913923i $$-0.366962\pi$$
0.405887 + 0.913923i $$0.366962\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −2.00000 −0.0809113
$$612$$ 0 0
$$613$$ −6.00000 −0.242338 −0.121169 0.992632i $$-0.538664\pi$$
−0.121169 + 0.992632i $$0.538664\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ 0 0
$$619$$ −6.00000 −0.241160 −0.120580 0.992704i $$-0.538475\pi$$
−0.120580 + 0.992704i $$0.538475\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 20.0000 0.801283
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −60.0000 −2.39236
$$630$$ 0 0
$$631$$ −10.0000 −0.398094 −0.199047 0.979990i $$-0.563785\pi$$
−0.199047 + 0.979990i $$0.563785\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −16.0000 −0.634941
$$636$$ 0 0
$$637$$ 3.00000 0.118864
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 26.0000 1.02694 0.513469 0.858108i $$-0.328360\pi$$
0.513469 + 0.858108i $$0.328360\pi$$
$$642$$ 0 0
$$643$$ −42.0000 −1.65632 −0.828159 0.560493i $$-0.810612\pi$$
−0.828159 + 0.560493i $$0.810612\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 0 0
$$649$$ 20.0000 0.785069
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −34.0000 −1.33052 −0.665261 0.746611i $$-0.731680\pi$$
−0.665261 + 0.746611i $$0.731680\pi$$
$$654$$ 0 0
$$655$$ −8.00000 −0.312586
$$656$$ 0 0
$$657$$ 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
$$661$$ −22.0000 −0.855701 −0.427850 0.903850i $$-0.640729\pi$$
−0.427850 + 0.903850i $$0.640729\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −8.00000 −0.310227
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 2.00000 0.0768662 0.0384331 0.999261i $$-0.487763\pi$$
0.0384331 + 0.999261i $$0.487763\pi$$
$$678$$ 0 0
$$679$$ −20.0000 −0.767530
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 30.0000 1.14792 0.573959 0.818884i $$-0.305407\pi$$
0.573959 + 0.818884i $$0.305407\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −2.00000 −0.0761939
$$690$$ 0 0
$$691$$ 22.0000 0.836919 0.418460 0.908235i $$-0.362570\pi$$
0.418460 + 0.908235i $$0.362570\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −40.0000 −1.51729
$$696$$ 0 0
$$697$$ 12.0000 0.454532
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ −20.0000 −0.754314
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 12.0000 0.451306
$$708$$ 0 0
$$709$$ 34.0000 1.27690 0.638448 0.769665i $$-0.279577\pi$$
0.638448 + 0.769665i $$0.279577\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −4.00000 −0.149592
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.00000 0.0742781
$$726$$ 0 0
$$727$$ 24.0000 0.890111 0.445055 0.895503i $$-0.353184\pi$$
0.445055 + 0.895503i $$0.353184\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −48.0000 −1.77534
$$732$$ 0 0
$$733$$ 50.0000 1.84679 0.923396 0.383849i $$-0.125402\pi$$
0.923396 + 0.383849i $$0.125402\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −28.0000 −1.03139
$$738$$ 0 0
$$739$$ −38.0000 −1.39785 −0.698926 0.715194i $$-0.746338\pi$$
−0.698926 + 0.715194i $$0.746338\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 6.00000 0.220119 0.110059 0.993925i $$-0.464896\pi$$
0.110059 + 0.993925i $$0.464896\pi$$
$$744$$ 0 0
$$745$$ −12.0000 −0.439646
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 8.00000 0.292314
$$750$$ 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
$$754$$ 0 0
$$755$$ −12.0000 −0.436725
$$756$$ 0 0
$$757$$ 30.0000 1.09037 0.545184 0.838316i $$-0.316460\pi$$
0.545184 + 0.838316i $$0.316460\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −42.0000 −1.52250 −0.761249 0.648459i $$-0.775414\pi$$
−0.761249 + 0.648459i $$0.775414\pi$$
$$762$$ 0 0
$$763$$ −4.00000 −0.144810
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 10.0000 0.361079
$$768$$ 0 0
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −18.0000 −0.647415 −0.323708 0.946157i $$-0.604929\pi$$
−0.323708 + 0.946157i $$0.604929\pi$$
$$774$$ 0 0
$$775$$ −2.00000 −0.0718421
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 4.00000 0.143315
$$780$$ 0 0
$$781$$ −28.0000 −1.00192
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −4.00000 −0.142766
$$786$$ 0 0
$$787$$ −6.00000 −0.213877 −0.106938 0.994266i $$-0.534105\pi$$
−0.106938 + 0.994266i $$0.534105\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 28.0000 0.995565
$$792$$ 0 0
$$793$$ −6.00000 −0.213066
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 30.0000 1.06265 0.531327 0.847167i $$-0.321693\pi$$
0.531327 + 0.847167i $$0.321693\pi$$
$$798$$ 0 0
$$799$$ −12.0000 −0.424529
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 12.0000 0.423471
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −22.0000 −0.773479 −0.386739 0.922189i $$-0.626399\pi$$
−0.386739 + 0.922189i $$0.626399\pi$$
$$810$$ 0 0
$$811$$ 22.0000 0.772524 0.386262 0.922389i $$-0.373766\pi$$
0.386262 + 0.922389i $$0.373766\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −20.0000 −0.700569
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −2.00000 −0.0698005 −0.0349002 0.999391i $$-0.511111\pi$$
−0.0349002 + 0.999391i $$0.511111\pi$$
$$822$$ 0 0
$$823$$ −32.0000 −1.11545 −0.557725 0.830026i $$-0.688326\pi$$
−0.557725 + 0.830026i $$0.688326\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 22.0000 0.765015 0.382507 0.923952i $$-0.375061\pi$$
0.382507 + 0.923952i $$0.375061\pi$$
$$828$$ 0 0
$$829$$ 14.0000 0.486240 0.243120 0.969996i $$-0.421829\pi$$
0.243120 + 0.969996i $$0.421829\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 18.0000 0.623663
$$834$$ 0 0
$$835$$ −4.00000 −0.138426
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 2.00000 0.0690477 0.0345238 0.999404i $$-0.489009\pi$$
0.0345238 + 0.999404i $$0.489009\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −2.00000 −0.0688021
$$846$$ 0 0
$$847$$ 14.0000 0.481046
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −30.0000 −1.02718 −0.513590 0.858036i $$-0.671685\pi$$
−0.513590 + 0.858036i $$0.671685\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −10.0000 −0.341593 −0.170797 0.985306i $$-0.554634\pi$$
−0.170797 + 0.985306i $$0.554634\pi$$
$$858$$ 0 0
$$859$$ 44.0000 1.50126 0.750630 0.660722i $$-0.229750\pi$$
0.750630 + 0.660722i $$0.229750\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 14.0000 0.476566 0.238283 0.971196i $$-0.423415\pi$$
0.238283 + 0.971196i $$0.423415\pi$$
$$864$$ 0 0
$$865$$ −36.0000 −1.22404
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 8.00000 0.271381
$$870$$ 0 0
$$871$$ −14.0000 −0.474372
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −24.0000 −0.811348
$$876$$ 0 0
$$877$$ 10.0000 0.337676 0.168838 0.985644i $$-0.445999\pi$$
0.168838 + 0.985644i $$0.445999\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 30.0000 1.01073 0.505363 0.862907i $$-0.331359\pi$$
0.505363 + 0.862907i $$0.331359\pi$$
$$882$$ 0 0
$$883$$ −40.0000 −1.34611 −0.673054 0.739594i $$-0.735018\pi$$
−0.673054 + 0.739594i $$0.735018\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −12.0000 −0.402921 −0.201460 0.979497i $$-0.564569\pi$$
−0.201460 + 0.979497i $$0.564569\pi$$
$$888$$ 0 0
$$889$$ −16.0000 −0.536623
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −4.00000 −0.133855
$$894$$ 0 0
$$895$$ −48.0000 −1.60446
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −4.00000 −0.133407
$$900$$ 0 0
$$901$$ −12.0000 −0.399778
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 44.0000 1.46261
$$906$$ 0 0
$$907$$ −56.0000 −1.85945 −0.929725 0.368255i $$-0.879955\pi$$
−0.929725 + 0.368255i $$0.879955\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −12.0000 −0.397578 −0.198789 0.980042i $$-0.563701\pi$$
−0.198789 + 0.980042i $$0.563701\pi$$
$$912$$ 0 0
$$913$$ 12.0000 0.397142
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −8.00000 −0.264183
$$918$$ 0 0
$$919$$ 12.0000 0.395843 0.197922 0.980218i $$-0.436581\pi$$
0.197922 + 0.980218i $$0.436581\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −14.0000 −0.460816
$$924$$ 0 0
$$925$$ −10.0000 −0.328798
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −42.0000 −1.37798 −0.688988 0.724773i $$-0.741945\pi$$
−0.688988 + 0.724773i $$0.741945\pi$$
$$930$$ 0 0
$$931$$ 6.00000 0.196642
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −24.0000 −0.784884
$$936$$ 0 0
$$937$$ 26.0000 0.849383 0.424691 0.905338i $$-0.360383\pi$$
0.424691 + 0.905338i $$0.360383\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −10.0000 −0.325991 −0.162995 0.986627i $$-0.552116\pi$$
−0.162995 + 0.986627i $$0.552116\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −18.0000 −0.584921 −0.292461 0.956278i $$-0.594474\pi$$
−0.292461 + 0.956278i $$0.594474\pi$$
$$948$$ 0 0
$$949$$ 6.00000 0.194768
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 54.0000 1.74923 0.874616 0.484817i $$-0.161114\pi$$
0.874616 + 0.484817i $$0.161114\pi$$
$$954$$ 0 0
$$955$$ −24.0000 −0.776622
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −12.0000 −0.387500
$$960$$ 0 0
$$961$$ −27.0000 −0.870968
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 12.0000 0.386294
$$966$$ 0 0
$$967$$ 18.0000 0.578841 0.289420 0.957202i $$-0.406537\pi$$
0.289420 + 0.957202i $$0.406537\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 28.0000 0.898563 0.449281 0.893390i $$-0.351680\pi$$
0.449281 + 0.893390i $$0.351680\pi$$
$$972$$ 0 0
$$973$$ −40.0000 −1.28234
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −2.00000 −0.0639857 −0.0319928 0.999488i $$-0.510185\pi$$
−0.0319928 + 0.999488i $$0.510185\pi$$
$$978$$ 0 0
$$979$$ 20.0000 0.639203
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −6.00000 −0.191370 −0.0956851 0.995412i $$-0.530504\pi$$
−0.0956851 + 0.995412i $$0.530504\pi$$
$$984$$ 0 0
$$985$$ 4.00000 0.127451
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −52.0000 −1.65183 −0.825917 0.563791i $$-0.809342\pi$$
−0.825917 + 0.563791i $$0.809342\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −16.0000 −0.507234
$$996$$ 0 0
$$997$$ 30.0000 0.950110 0.475055 0.879956i $$-0.342428\pi$$
0.475055 + 0.879956i $$0.342428\pi$$
$$998$$ 0 0
$$999$$ 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 3744.2.a.a.1.1 1
3.2 odd 2 1248.2.a.e.1.1 1
4.3 odd 2 3744.2.a.d.1.1 1
8.3 odd 2 7488.2.a.bv.1.1 1
8.5 even 2 7488.2.a.bo.1.1 1
12.11 even 2 1248.2.a.j.1.1 yes 1
24.5 odd 2 2496.2.a.r.1.1 1
24.11 even 2 2496.2.a.d.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1248.2.a.e.1.1 1 3.2 odd 2
1248.2.a.j.1.1 yes 1 12.11 even 2
2496.2.a.d.1.1 1 24.11 even 2
2496.2.a.r.1.1 1 24.5 odd 2
3744.2.a.a.1.1 1 1.1 even 1 trivial
3744.2.a.d.1.1 1 4.3 odd 2
7488.2.a.bo.1.1 1 8.5 even 2
7488.2.a.bv.1.1 1 8.3 odd 2