# Properties

 Label 4851.2.a.j.1.1 Level $4851$ Weight $2$ Character 4851.1 Self dual yes Analytic conductor $38.735$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4851 = 3^{2} \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4851.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$38.7354300205$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 77) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 4851.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{4} -1.00000 q^{5} +O(q^{10})$$ $$q-2.00000 q^{4} -1.00000 q^{5} +1.00000 q^{11} +4.00000 q^{13} +4.00000 q^{16} +2.00000 q^{17} +6.00000 q^{19} +2.00000 q^{20} +5.00000 q^{23} -4.00000 q^{25} -10.0000 q^{29} -1.00000 q^{31} -5.00000 q^{37} -2.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} +8.00000 q^{47} -8.00000 q^{52} +6.00000 q^{53} -1.00000 q^{55} +3.00000 q^{59} +2.00000 q^{61} -8.00000 q^{64} -4.00000 q^{65} -3.00000 q^{67} -4.00000 q^{68} -1.00000 q^{71} -10.0000 q^{73} -12.0000 q^{76} +6.00000 q^{79} -4.00000 q^{80} +12.0000 q^{83} -2.00000 q^{85} -15.0000 q^{89} -10.0000 q^{92} -6.00000 q^{95} +5.00000 q^{97} +O(q^{100})$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$3$$ 0 0
$$4$$ −2.00000 −1.00000
$$5$$ −1.00000 −0.447214 −0.223607 0.974679i $$-0.571783\pi$$
−0.223607 + 0.974679i $$0.571783\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.00000 0.301511
$$12$$ 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
$$16$$ 4.00000 1.00000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ 6.00000 1.37649 0.688247 0.725476i $$-0.258380\pi$$
0.688247 + 0.725476i $$0.258380\pi$$
$$20$$ 2.00000 0.447214
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 5.00000 1.04257 0.521286 0.853382i $$-0.325452\pi$$
0.521286 + 0.853382i $$0.325452\pi$$
$$24$$ 0 0
$$25$$ −4.00000 −0.800000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −10.0000 −1.85695 −0.928477 0.371391i $$-0.878881\pi$$
−0.928477 + 0.371391i $$0.878881\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −0.179605 −0.0898027 0.995960i $$-0.528624\pi$$
−0.0898027 + 0.995960i $$0.528624\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ 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 $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ −2.00000 −0.301511
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 8.00000 1.16692 0.583460 0.812142i $$-0.301699\pi$$
0.583460 + 0.812142i $$0.301699\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −8.00000 −1.10940
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ −1.00000 −0.134840
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 3.00000 0.390567 0.195283 0.980747i $$-0.437437\pi$$
0.195283 + 0.980747i $$0.437437\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ −4.00000 −0.496139
$$66$$ 0 0
$$67$$ −3.00000 −0.366508 −0.183254 0.983066i $$-0.558663\pi$$
−0.183254 + 0.983066i $$0.558663\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −1.00000 −0.118678 −0.0593391 0.998238i $$-0.518899\pi$$
−0.0593391 + 0.998238i $$0.518899\pi$$
$$72$$ 0 0
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −12.0000 −1.37649
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 6.00000 0.675053 0.337526 0.941316i $$-0.390410\pi$$
0.337526 + 0.941316i $$0.390410\pi$$
$$80$$ −4.00000 −0.447214
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −15.0000 −1.59000 −0.794998 0.606612i $$-0.792528\pi$$
−0.794998 + 0.606612i $$0.792528\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −10.0000 −1.04257
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −6.00000 −0.615587
$$96$$ 0 0
$$97$$ 5.00000 0.507673 0.253837 0.967247i $$-0.418307\pi$$
0.253837 + 0.967247i $$0.418307\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 8.00000 0.800000
$$101$$ −12.0000 −1.19404 −0.597022 0.802225i $$-0.703650\pi$$
−0.597022 + 0.802225i $$0.703650\pi$$
$$102$$ 0 0
$$103$$ 12.0000 1.18240 0.591198 0.806527i $$-0.298655\pi$$
0.591198 + 0.806527i $$0.298655\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 10.0000 0.966736 0.483368 0.875417i $$-0.339413\pi$$
0.483368 + 0.875417i $$0.339413\pi$$
$$108$$ 0 0
$$109$$ 4.00000 0.383131 0.191565 0.981480i $$-0.438644\pi$$
0.191565 + 0.981480i $$0.438644\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 19.0000 1.78737 0.893685 0.448695i $$-0.148111\pi$$
0.893685 + 0.448695i $$0.148111\pi$$
$$114$$ 0 0
$$115$$ −5.00000 −0.466252
$$116$$ 20.0000 1.85695
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 0.0909091
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 2.00000 0.179605
$$125$$ 9.00000 0.804984
$$126$$ 0 0
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 18.0000 1.57267 0.786334 0.617802i $$-0.211977\pi$$
0.786334 + 0.617802i $$0.211977\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 3.00000 0.256307 0.128154 0.991754i $$-0.459095\pi$$
0.128154 + 0.991754i $$0.459095\pi$$
$$138$$ 0 0
$$139$$ 10.0000 0.848189 0.424094 0.905618i $$-0.360592\pi$$
0.424094 + 0.905618i $$0.360592\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 4.00000 0.334497
$$144$$ 0 0
$$145$$ 10.0000 0.830455
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 10.0000 0.821995
$$149$$ 22.0000 1.80231 0.901155 0.433497i $$-0.142720\pi$$
0.901155 + 0.433497i $$0.142720\pi$$
$$150$$ 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
$$155$$ 1.00000 0.0803219
$$156$$ 0 0
$$157$$ −7.00000 −0.558661 −0.279330 0.960195i $$-0.590112\pi$$
−0.279330 + 0.960195i $$0.590112\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ 4.00000 0.312348
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.00000 −0.154765 −0.0773823 0.997001i $$-0.524656\pi$$
−0.0773823 + 0.997001i $$0.524656\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 16.0000 1.21999
$$173$$ 16.0000 1.21646 0.608229 0.793762i $$-0.291880\pi$$
0.608229 + 0.793762i $$0.291880\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 4.00000 0.301511
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1.00000 −0.0747435 −0.0373718 0.999301i $$-0.511899\pi$$
−0.0373718 + 0.999301i $$0.511899\pi$$
$$180$$ 0 0
$$181$$ −5.00000 −0.371647 −0.185824 0.982583i $$-0.559495\pi$$
−0.185824 + 0.982583i $$0.559495\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 5.00000 0.367607
$$186$$ 0 0
$$187$$ 2.00000 0.146254
$$188$$ −16.0000 −1.16692
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −5.00000 −0.361787 −0.180894 0.983503i $$-0.557899\pi$$
−0.180894 + 0.983503i $$0.557899\pi$$
$$192$$ 0 0
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 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
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 2.00000 0.139686
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 16.0000 1.10940
$$209$$ 6.00000 0.415029
$$210$$ 0 0
$$211$$ −2.00000 −0.137686 −0.0688428 0.997628i $$-0.521931\pi$$
−0.0688428 + 0.997628i $$0.521931\pi$$
$$212$$ −12.0000 −0.824163
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 8.00000 0.545595
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 2.00000 0.134840
$$221$$ 8.00000 0.538138
$$222$$ 0 0
$$223$$ −1.00000 −0.0669650 −0.0334825 0.999439i $$-0.510660\pi$$
−0.0334825 + 0.999439i $$0.510660\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 4.00000 0.265489 0.132745 0.991150i $$-0.457621\pi$$
0.132745 + 0.991150i $$0.457621\pi$$
$$228$$ 0 0
$$229$$ 7.00000 0.462573 0.231287 0.972886i $$-0.425707\pi$$
0.231287 + 0.972886i $$0.425707\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ −8.00000 −0.521862
$$236$$ −6.00000 −0.390567
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −4.00000 −0.258738 −0.129369 0.991596i $$-0.541295\pi$$
−0.129369 + 0.991596i $$0.541295\pi$$
$$240$$ 0 0
$$241$$ 12.0000 0.772988 0.386494 0.922292i $$-0.373686\pi$$
0.386494 + 0.922292i $$0.373686\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ −4.00000 −0.256074
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 24.0000 1.52708
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −21.0000 −1.32551 −0.662754 0.748837i $$-0.730613\pi$$
−0.662754 + 0.748837i $$0.730613\pi$$
$$252$$ 0 0
$$253$$ 5.00000 0.314347
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 8.00000 0.496139
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −18.0000 −1.10993 −0.554964 0.831875i $$-0.687268\pi$$
−0.554964 + 0.831875i $$0.687268\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 6.00000 0.366508
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ −16.0000 −0.971931 −0.485965 0.873978i $$-0.661532\pi$$
−0.485965 + 0.873978i $$0.661532\pi$$
$$272$$ 8.00000 0.485071
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −4.00000 −0.241209
$$276$$ 0 0
$$277$$ 24.0000 1.44202 0.721010 0.692925i $$-0.243678\pi$$
0.721010 + 0.692925i $$0.243678\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 4.00000 0.238620 0.119310 0.992857i $$-0.461932\pi$$
0.119310 + 0.992857i $$0.461932\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 2.00000 0.118678
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 20.0000 1.17041
$$293$$ −6.00000 −0.350524 −0.175262 0.984522i $$-0.556077\pi$$
−0.175262 + 0.984522i $$0.556077\pi$$
$$294$$ 0 0
$$295$$ −3.00000 −0.174667
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 20.0000 1.15663
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 24.0000 1.37649
$$305$$ −2.00000 −0.114520
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 8.00000 0.453638 0.226819 0.973937i $$-0.427167\pi$$
0.226819 + 0.973937i $$0.427167\pi$$
$$312$$ 0 0
$$313$$ 23.0000 1.30004 0.650018 0.759918i $$-0.274761\pi$$
0.650018 + 0.759918i $$0.274761\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −12.0000 −0.675053
$$317$$ −9.00000 −0.505490 −0.252745 0.967533i $$-0.581333\pi$$
−0.252745 + 0.967533i $$0.581333\pi$$
$$318$$ 0 0
$$319$$ −10.0000 −0.559893
$$320$$ 8.00000 0.447214
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 12.0000 0.667698
$$324$$ 0 0
$$325$$ −16.0000 −0.887520
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −17.0000 −0.934405 −0.467202 0.884150i $$-0.654738\pi$$
−0.467202 + 0.884150i $$0.654738\pi$$
$$332$$ −24.0000 −1.31717
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 3.00000 0.163908
$$336$$ 0 0
$$337$$ −18.0000 −0.980522 −0.490261 0.871576i $$-0.663099\pi$$
−0.490261 + 0.871576i $$0.663099\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 4.00000 0.216930
$$341$$ −1.00000 −0.0541530
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −14.0000 −0.751559 −0.375780 0.926709i $$-0.622625\pi$$
−0.375780 + 0.926709i $$0.622625\pi$$
$$348$$ 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
$$353$$ 9.00000 0.479022 0.239511 0.970894i $$-0.423013\pi$$
0.239511 + 0.970894i $$0.423013\pi$$
$$354$$ 0 0
$$355$$ 1.00000 0.0530745
$$356$$ 30.0000 1.59000
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −8.00000 −0.422224 −0.211112 0.977462i $$-0.567708\pi$$
−0.211112 + 0.977462i $$0.567708\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 10.0000 0.523424
$$366$$ 0 0
$$367$$ 11.0000 0.574195 0.287098 0.957901i $$-0.407310\pi$$
0.287098 + 0.957901i $$0.407310\pi$$
$$368$$ 20.0000 1.04257
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −4.00000 −0.207112 −0.103556 0.994624i $$-0.533022\pi$$
−0.103556 + 0.994624i $$0.533022\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −40.0000 −2.06010
$$378$$ 0 0
$$379$$ −29.0000 −1.48963 −0.744815 0.667271i $$-0.767462\pi$$
−0.744815 + 0.667271i $$0.767462\pi$$
$$380$$ 12.0000 0.615587
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 17.0000 0.868659 0.434330 0.900754i $$-0.356985\pi$$
0.434330 + 0.900754i $$0.356985\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ −10.0000 −0.507673
$$389$$ −9.00000 −0.456318 −0.228159 0.973624i $$-0.573271\pi$$
−0.228159 + 0.973624i $$0.573271\pi$$
$$390$$ 0 0
$$391$$ 10.0000 0.505722
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −6.00000 −0.301893
$$396$$ 0 0
$$397$$ −18.0000 −0.903394 −0.451697 0.892171i $$-0.649181\pi$$
−0.451697 + 0.892171i $$0.649181\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −16.0000 −0.800000
$$401$$ 6.00000 0.299626 0.149813 0.988714i $$-0.452133\pi$$
0.149813 + 0.988714i $$0.452133\pi$$
$$402$$ 0 0
$$403$$ −4.00000 −0.199254
$$404$$ 24.0000 1.19404
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −5.00000 −0.247841
$$408$$ 0 0
$$409$$ 26.0000 1.28562 0.642809 0.766027i $$-0.277769\pi$$
0.642809 + 0.766027i $$0.277769\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −24.0000 −1.18240
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −12.0000 −0.589057
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 16.0000 0.781651 0.390826 0.920465i $$-0.372190\pi$$
0.390826 + 0.920465i $$0.372190\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −8.00000 −0.388057
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −20.0000 −0.966736
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 20.0000 0.963366 0.481683 0.876346i $$-0.340026\pi$$
0.481683 + 0.876346i $$0.340026\pi$$
$$432$$ 0 0
$$433$$ 25.0000 1.20142 0.600712 0.799466i $$-0.294884\pi$$
0.600712 + 0.799466i $$0.294884\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −8.00000 −0.383131
$$437$$ 30.0000 1.43509
$$438$$ 0 0
$$439$$ 14.0000 0.668184 0.334092 0.942541i $$-0.391570\pi$$
0.334092 + 0.942541i $$0.391570\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 39.0000 1.85295 0.926473 0.376361i $$-0.122825\pi$$
0.926473 + 0.376361i $$0.122825\pi$$
$$444$$ 0 0
$$445$$ 15.0000 0.711068
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −15.0000 −0.707894 −0.353947 0.935266i $$-0.615161\pi$$
−0.353947 + 0.935266i $$0.615161\pi$$
$$450$$ 0 0
$$451$$ −2.00000 −0.0941763
$$452$$ −38.0000 −1.78737
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 8.00000 0.374224 0.187112 0.982339i $$-0.440087\pi$$
0.187112 + 0.982339i $$0.440087\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 10.0000 0.466252
$$461$$ 18.0000 0.838344 0.419172 0.907907i $$-0.362320\pi$$
0.419172 + 0.907907i $$0.362320\pi$$
$$462$$ 0 0
$$463$$ 13.0000 0.604161 0.302081 0.953282i $$-0.402319\pi$$
0.302081 + 0.953282i $$0.402319\pi$$
$$464$$ −40.0000 −1.85695
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 3.00000 0.138823 0.0694117 0.997588i $$-0.477888\pi$$
0.0694117 + 0.997588i $$0.477888\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −8.00000 −0.367840
$$474$$ 0 0
$$475$$ −24.0000 −1.10120
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −28.0000 −1.27935 −0.639676 0.768644i $$-0.720932\pi$$
−0.639676 + 0.768644i $$0.720932\pi$$
$$480$$ 0 0
$$481$$ −20.0000 −0.911922
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −2.00000 −0.0909091
$$485$$ −5.00000 −0.227038
$$486$$ 0 0
$$487$$ −13.0000 −0.589086 −0.294543 0.955638i $$-0.595167\pi$$
−0.294543 + 0.955638i $$0.595167\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 30.0000 1.35388 0.676941 0.736038i $$-0.263305\pi$$
0.676941 + 0.736038i $$0.263305\pi$$
$$492$$ 0 0
$$493$$ −20.0000 −0.900755
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 44.0000 1.96971 0.984855 0.173379i $$-0.0554684\pi$$
0.984855 + 0.173379i $$0.0554684\pi$$
$$500$$ −18.0000 −0.804984
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 12.0000 0.533993
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −4.00000 −0.177471
$$509$$ −31.0000 −1.37405 −0.687025 0.726633i $$-0.741084\pi$$
−0.687025 + 0.726633i $$0.741084\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −12.0000 −0.528783
$$516$$ 0 0
$$517$$ 8.00000 0.351840
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 7.00000 0.306676 0.153338 0.988174i $$-0.450998\pi$$
0.153338 + 0.988174i $$0.450998\pi$$
$$522$$ 0 0
$$523$$ −32.0000 −1.39926 −0.699631 0.714504i $$-0.746652\pi$$
−0.699631 + 0.714504i $$0.746652\pi$$
$$524$$ −36.0000 −1.57267
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.00000 −0.0871214
$$528$$ 0 0
$$529$$ 2.00000 0.0869565
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −8.00000 −0.346518
$$534$$ 0 0
$$535$$ −10.0000 −0.432338
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 32.0000 1.37579 0.687894 0.725811i $$-0.258536\pi$$
0.687894 + 0.725811i $$0.258536\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −4.00000 −0.171341
$$546$$ 0 0
$$547$$ −24.0000 −1.02617 −0.513083 0.858339i $$-0.671497\pi$$
−0.513083 + 0.858339i $$0.671497\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −60.0000 −2.55609
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −20.0000 −0.848189
$$557$$ −14.0000 −0.593199 −0.296600 0.955002i $$-0.595853\pi$$
−0.296600 + 0.955002i $$0.595853\pi$$
$$558$$ 0 0
$$559$$ −32.0000 −1.35346
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 20.0000 0.842900 0.421450 0.906852i $$-0.361521\pi$$
0.421450 + 0.906852i $$0.361521\pi$$
$$564$$ 0 0
$$565$$ −19.0000 −0.799336
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 0 0
$$571$$ −20.0000 −0.836974 −0.418487 0.908223i $$-0.637439\pi$$
−0.418487 + 0.908223i $$0.637439\pi$$
$$572$$ −8.00000 −0.334497
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −20.0000 −0.834058
$$576$$ 0 0
$$577$$ 25.0000 1.04076 0.520382 0.853934i $$-0.325790\pi$$
0.520382 + 0.853934i $$0.325790\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ −20.0000 −0.830455
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 6.00000 0.248495
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 36.0000 1.48588 0.742940 0.669359i $$-0.233431\pi$$
0.742940 + 0.669359i $$0.233431\pi$$
$$588$$ 0 0
$$589$$ −6.00000 −0.247226
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −20.0000 −0.821995
$$593$$ 30.0000 1.23195 0.615976 0.787765i $$-0.288762\pi$$
0.615976 + 0.787765i $$0.288762\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −44.0000 −1.80231
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 48.0000 1.96123 0.980613 0.195952i $$-0.0627798\pi$$
0.980613 + 0.195952i $$0.0627798\pi$$
$$600$$ 0 0
$$601$$ −8.00000 −0.326327 −0.163163 0.986599i $$-0.552170\pi$$
−0.163163 + 0.986599i $$0.552170\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −12.0000 −0.488273
$$605$$ −1.00000 −0.0406558
$$606$$ 0 0
$$607$$ 10.0000 0.405887 0.202944 0.979190i $$-0.434949\pi$$
0.202944 + 0.979190i $$0.434949\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 32.0000 1.29458
$$612$$ 0 0
$$613$$ 16.0000 0.646234 0.323117 0.946359i $$-0.395269\pi$$
0.323117 + 0.946359i $$0.395269\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 30.0000 1.20775 0.603877 0.797077i $$-0.293622\pi$$
0.603877 + 0.797077i $$0.293622\pi$$
$$618$$ 0 0
$$619$$ −17.0000 −0.683288 −0.341644 0.939829i $$-0.610984\pi$$
−0.341644 + 0.939829i $$0.610984\pi$$
$$620$$ −2.00000 −0.0803219
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 14.0000 0.558661
$$629$$ −10.0000 −0.398726
$$630$$ 0 0
$$631$$ 27.0000 1.07485 0.537427 0.843311i $$-0.319397\pi$$
0.537427 + 0.843311i $$0.319397\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −2.00000 −0.0793676
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −15.0000 −0.592464 −0.296232 0.955116i $$-0.595730\pi$$
−0.296232 + 0.955116i $$0.595730\pi$$
$$642$$ 0 0
$$643$$ 29.0000 1.14365 0.571824 0.820376i $$-0.306236\pi$$
0.571824 + 0.820376i $$0.306236\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −21.0000 −0.825595 −0.412798 0.910823i $$-0.635448\pi$$
−0.412798 + 0.910823i $$0.635448\pi$$
$$648$$ 0 0
$$649$$ 3.00000 0.117760
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −8.00000 −0.313304
$$653$$ 17.0000 0.665261 0.332631 0.943057i $$-0.392064\pi$$
0.332631 + 0.943057i $$0.392064\pi$$
$$654$$ 0 0
$$655$$ −18.0000 −0.703318
$$656$$ −8.00000 −0.312348
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 2.00000 0.0779089 0.0389545 0.999241i $$-0.487597\pi$$
0.0389545 + 0.999241i $$0.487597\pi$$
$$660$$ 0 0
$$661$$ −35.0000 −1.36134 −0.680671 0.732589i $$-0.738312\pi$$
−0.680671 + 0.732589i $$0.738312\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −50.0000 −1.93601
$$668$$ 4.00000 0.154765
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 2.00000 0.0772091
$$672$$ 0 0
$$673$$ 4.00000 0.154189 0.0770943 0.997024i $$-0.475436\pi$$
0.0770943 + 0.997024i $$0.475436\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −6.00000 −0.230769
$$677$$ 38.0000 1.46046 0.730229 0.683202i $$-0.239413\pi$$
0.730229 + 0.683202i $$0.239413\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ −3.00000 −0.114624
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −32.0000 −1.21999
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ −15.0000 −0.570627 −0.285313 0.958434i $$-0.592098\pi$$
−0.285313 + 0.958434i $$0.592098\pi$$
$$692$$ −32.0000 −1.21646
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −10.0000 −0.379322
$$696$$ 0 0
$$697$$ −4.00000 −0.151511
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ −30.0000 −1.13147
$$704$$ −8.00000 −0.301511
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 39.0000 1.46468 0.732338 0.680941i $$-0.238429\pi$$
0.732338 + 0.680941i $$0.238429\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −5.00000 −0.187251
$$714$$ 0 0
$$715$$ −4.00000 −0.149592
$$716$$ 2.00000 0.0747435
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −11.0000 −0.410231 −0.205115 0.978738i $$-0.565757\pi$$
−0.205115 + 0.978738i $$0.565757\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 10.0000 0.371647
$$725$$ 40.0000 1.48556
$$726$$ 0 0
$$727$$ 19.0000 0.704671 0.352335 0.935874i $$-0.385388\pi$$
0.352335 + 0.935874i $$0.385388\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −16.0000 −0.591781
$$732$$ 0 0
$$733$$ 4.00000 0.147743 0.0738717 0.997268i $$-0.476464\pi$$
0.0738717 + 0.997268i $$0.476464\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −3.00000 −0.110506
$$738$$ 0 0
$$739$$ −18.0000 −0.662141 −0.331070 0.943606i $$-0.607410\pi$$
−0.331070 + 0.943606i $$0.607410\pi$$
$$740$$ −10.0000 −0.367607
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.0000 0.880475 0.440237 0.897881i $$-0.354894\pi$$
0.440237 + 0.897881i $$0.354894\pi$$
$$744$$ 0 0
$$745$$ −22.0000 −0.806018
$$746$$ 0 0
$$747$$ 0 0
$$748$$ −4.00000 −0.146254
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −23.0000 −0.839282 −0.419641 0.907690i $$-0.637844\pi$$
−0.419641 + 0.907690i $$0.637844\pi$$
$$752$$ 32.0000 1.16692
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −6.00000 −0.218362
$$756$$ 0 0
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −48.0000 −1.74000 −0.869999 0.493053i $$-0.835881\pi$$
−0.869999 + 0.493053i $$0.835881\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 10.0000 0.361787
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 12.0000 0.433295
$$768$$ 0 0
$$769$$ −40.0000 −1.44244 −0.721218 0.692708i $$-0.756418\pi$$
−0.721218 + 0.692708i $$0.756418\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −28.0000 −1.00774
$$773$$ −6.00000 −0.215805 −0.107903 0.994161i $$-0.534413\pi$$
−0.107903 + 0.994161i $$0.534413\pi$$
$$774$$ 0 0
$$775$$ 4.00000 0.143684
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −12.0000 −0.429945
$$780$$ 0 0
$$781$$ −1.00000 −0.0357828
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 7.00000 0.249841
$$786$$ 0 0
$$787$$ 22.0000 0.784215 0.392108 0.919919i $$-0.371746\pi$$
0.392108 + 0.919919i $$0.371746\pi$$
$$788$$ 36.0000 1.28245
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 8.00000 0.284088
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −16.0000 −0.567105
$$797$$ 23.0000 0.814702 0.407351 0.913272i $$-0.366453\pi$$
0.407351 + 0.913272i $$0.366453\pi$$
$$798$$ 0 0
$$799$$ 16.0000 0.566039
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −10.0000 −0.352892
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −30.0000 −1.05474 −0.527372 0.849635i $$-0.676823\pi$$
−0.527372 + 0.849635i $$0.676823\pi$$
$$810$$ 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
$$815$$ −4.00000 −0.140114
$$816$$ 0 0
$$817$$ −48.0000 −1.67931
$$818$$ 0 0
$$819$$ 0 0
$$820$$ −4.00000 −0.139686
$$821$$ −18.0000 −0.628204 −0.314102 0.949389i $$-0.601703\pi$$
−0.314102 + 0.949389i $$0.601703\pi$$
$$822$$ 0 0
$$823$$ −25.0000 −0.871445 −0.435723 0.900081i $$-0.643507\pi$$
−0.435723 + 0.900081i $$0.643507\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −20.0000 −0.695468 −0.347734 0.937593i $$-0.613049\pi$$
−0.347734 + 0.937593i $$0.613049\pi$$
$$828$$ 0 0
$$829$$ 29.0000 1.00721 0.503606 0.863934i $$-0.332006\pi$$
0.503606 + 0.863934i $$0.332006\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −32.0000 −1.10940
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 2.00000 0.0692129
$$836$$ −12.0000 −0.415029
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 45.0000 1.55357 0.776786 0.629764i $$-0.216849\pi$$
0.776786 + 0.629764i $$0.216849\pi$$
$$840$$ 0 0
$$841$$ 71.0000 2.44828
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 4.00000 0.137686
$$845$$ −3.00000 −0.103203
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 24.0000 0.824163
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −25.0000 −0.856989
$$852$$ 0 0
$$853$$ 34.0000 1.16414 0.582069 0.813139i $$-0.302243\pi$$
0.582069 + 0.813139i $$0.302243\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −28.0000 −0.956462 −0.478231 0.878234i $$-0.658722\pi$$
−0.478231 + 0.878234i $$0.658722\pi$$
$$858$$ 0 0
$$859$$ −55.0000 −1.87658 −0.938288 0.345855i $$-0.887589\pi$$
−0.938288 + 0.345855i $$0.887589\pi$$
$$860$$ −16.0000 −0.545595
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −52.0000 −1.77010 −0.885050 0.465495i $$-0.845876\pi$$
−0.885050 + 0.465495i $$0.845876\pi$$
$$864$$ 0 0
$$865$$ −16.0000 −0.544016
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 6.00000 0.203536
$$870$$ 0 0
$$871$$ −12.0000 −0.406604
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −38.0000 −1.28317 −0.641584 0.767052i $$-0.721723\pi$$
−0.641584 + 0.767052i $$0.721723\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ −4.00000 −0.134840
$$881$$ 27.0000 0.909653 0.454827 0.890580i $$-0.349701\pi$$
0.454827 + 0.890580i $$0.349701\pi$$
$$882$$ 0 0
$$883$$ −44.0000 −1.48072 −0.740359 0.672212i $$-0.765344\pi$$
−0.740359 + 0.672212i $$0.765344\pi$$
$$884$$ −16.0000 −0.538138
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −2.00000 −0.0671534 −0.0335767 0.999436i $$-0.510690\pi$$
−0.0335767 + 0.999436i $$0.510690\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 2.00000 0.0669650
$$893$$ 48.0000 1.60626
$$894$$ 0 0
$$895$$ 1.00000 0.0334263
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 10.0000 0.333519
$$900$$ 0 0
$$901$$ 12.0000 0.399778
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 5.00000 0.166206
$$906$$ 0 0
$$907$$ −40.0000 −1.32818 −0.664089 0.747653i $$-0.731180\pi$$
−0.664089 + 0.747653i $$0.731180\pi$$
$$908$$ −8.00000 −0.265489
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 12.0000 0.397142
$$914$$ 0 0
$$915$$ 0 0
$$916$$ −14.0000 −0.462573
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 48.0000 1.58337 0.791687 0.610927i $$-0.209203\pi$$
0.791687 + 0.610927i $$0.209203\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −4.00000 −0.131662
$$924$$ 0 0
$$925$$ 20.0000 0.657596
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −30.0000 −0.984268 −0.492134 0.870519i $$-0.663783\pi$$
−0.492134 + 0.870519i $$0.663783\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 12.0000 0.393073
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −2.00000 −0.0654070
$$936$$ 0 0
$$937$$ −36.0000 −1.17607 −0.588034 0.808836i $$-0.700098\pi$$
−0.588034 + 0.808836i $$0.700098\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 16.0000 0.521862
$$941$$ 58.0000 1.89075 0.945373 0.325991i $$-0.105698\pi$$
0.945373 + 0.325991i $$0.105698\pi$$
$$942$$ 0 0
$$943$$ −10.0000 −0.325645
$$944$$ 12.0000 0.390567
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −5.00000 −0.162478 −0.0812391 0.996695i $$-0.525888\pi$$
−0.0812391 + 0.996695i $$0.525888\pi$$
$$948$$ 0 0
$$949$$ −40.0000 −1.29845
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −44.0000 −1.42530 −0.712650 0.701520i $$-0.752505\pi$$
−0.712650 + 0.701520i $$0.752505\pi$$
$$954$$ 0 0
$$955$$ 5.00000 0.161796
$$956$$ 8.00000 0.258738
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −30.0000 −0.967742
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −24.0000 −0.772988
$$965$$ −14.0000 −0.450676
$$966$$ 0 0
$$967$$ −34.0000 −1.09337 −0.546683 0.837340i $$-0.684110\pi$$
−0.546683 + 0.837340i $$0.684110\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 29.0000 0.930654 0.465327 0.885139i $$-0.345937\pi$$
0.465327 + 0.885139i $$0.345937\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 8.00000 0.256074
$$977$$ 31.0000 0.991778 0.495889 0.868386i $$-0.334842\pi$$
0.495889 + 0.868386i $$0.334842\pi$$
$$978$$ 0 0
$$979$$ −15.0000 −0.479402
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −27.0000 −0.861166 −0.430583 0.902551i $$-0.641692\pi$$
−0.430583 + 0.902551i $$0.641692\pi$$
$$984$$ 0 0
$$985$$ 18.0000 0.573528
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −48.0000 −1.52708
$$989$$ −40.0000 −1.27193
$$990$$ 0 0
$$991$$ −32.0000 −1.01651 −0.508257 0.861206i $$-0.669710\pi$$
−0.508257 + 0.861206i $$0.669710\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −8.00000 −0.253617
$$996$$ 0 0
$$997$$ 12.0000 0.380044 0.190022 0.981780i $$-0.439144\pi$$
0.190022 + 0.981780i $$0.439144\pi$$
$$998$$ 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 4851.2.a.j.1.1 1
3.2 odd 2 539.2.a.c.1.1 1
7.6 odd 2 693.2.a.c.1.1 1
12.11 even 2 8624.2.a.a.1.1 1
21.2 odd 6 539.2.e.c.67.1 2
21.5 even 6 539.2.e.f.67.1 2
21.11 odd 6 539.2.e.c.177.1 2
21.17 even 6 539.2.e.f.177.1 2
21.20 even 2 77.2.a.a.1.1 1
33.32 even 2 5929.2.a.f.1.1 1
77.76 even 2 7623.2.a.j.1.1 1
84.83 odd 2 1232.2.a.l.1.1 1
105.62 odd 4 1925.2.b.e.1849.2 2
105.83 odd 4 1925.2.b.e.1849.1 2
105.104 even 2 1925.2.a.h.1.1 1
168.83 odd 2 4928.2.a.a.1.1 1
168.125 even 2 4928.2.a.bj.1.1 1
231.20 even 10 847.2.f.i.323.1 4
231.41 odd 10 847.2.f.h.372.1 4
231.62 odd 10 847.2.f.h.148.1 4
231.83 odd 10 847.2.f.h.729.1 4
231.104 even 10 847.2.f.i.729.1 4
231.125 even 10 847.2.f.i.148.1 4
231.146 even 10 847.2.f.i.372.1 4
231.167 odd 10 847.2.f.h.323.1 4
231.230 odd 2 847.2.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.a.a.1.1 1 21.20 even 2
539.2.a.c.1.1 1 3.2 odd 2
539.2.e.c.67.1 2 21.2 odd 6
539.2.e.c.177.1 2 21.11 odd 6
539.2.e.f.67.1 2 21.5 even 6
539.2.e.f.177.1 2 21.17 even 6
693.2.a.c.1.1 1 7.6 odd 2
847.2.a.b.1.1 1 231.230 odd 2
847.2.f.h.148.1 4 231.62 odd 10
847.2.f.h.323.1 4 231.167 odd 10
847.2.f.h.372.1 4 231.41 odd 10
847.2.f.h.729.1 4 231.83 odd 10
847.2.f.i.148.1 4 231.125 even 10
847.2.f.i.323.1 4 231.20 even 10
847.2.f.i.372.1 4 231.146 even 10
847.2.f.i.729.1 4 231.104 even 10
1232.2.a.l.1.1 1 84.83 odd 2
1925.2.a.h.1.1 1 105.104 even 2
1925.2.b.e.1849.1 2 105.83 odd 4
1925.2.b.e.1849.2 2 105.62 odd 4
4851.2.a.j.1.1 1 1.1 even 1 trivial
4928.2.a.a.1.1 1 168.83 odd 2
4928.2.a.bj.1.1 1 168.125 even 2
5929.2.a.f.1.1 1 33.32 even 2
7623.2.a.j.1.1 1 77.76 even 2
8624.2.a.a.1.1 1 12.11 even 2