Properties

 Label 7056.2.a.bv.1.1 Level $7056$ Weight $2$ Character 7056.1 Self dual yes Analytic conductor $56.342$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$7056 = 2^{4} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7056.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$56.3424436662$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 504) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 7056.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{5} +O(q^{10})$$ $$q+2.00000 q^{5} +6.00000 q^{11} +6.00000 q^{13} -2.00000 q^{17} +4.00000 q^{19} +2.00000 q^{23} -1.00000 q^{25} -8.00000 q^{29} +4.00000 q^{31} -6.00000 q^{37} +10.0000 q^{41} +4.00000 q^{43} +4.00000 q^{47} +4.00000 q^{53} +12.0000 q^{55} +12.0000 q^{59} +2.00000 q^{61} +12.0000 q^{65} -12.0000 q^{67} +6.00000 q^{71} +2.00000 q^{73} +8.00000 q^{79} -4.00000 q^{85} -14.0000 q^{89} +8.00000 q^{95} +2.00000 q^{97} +O(q^{100})$$

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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 2.00000 0.894427 0.447214 0.894427i $$-0.352416\pi$$
0.447214 + 0.894427i $$0.352416\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 0 0
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.00000 0.417029 0.208514 0.978019i $$-0.433137\pi$$
0.208514 + 0.978019i $$0.433137\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −8.00000 −1.48556 −0.742781 0.669534i $$-0.766494\pi$$
−0.742781 + 0.669534i $$0.766494\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −6.00000 −0.986394 −0.493197 0.869918i $$-0.664172\pi$$
−0.493197 + 0.869918i $$0.664172\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 4.00000 0.583460 0.291730 0.956501i $$-0.405769\pi$$
0.291730 + 0.956501i $$0.405769\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 4.00000 0.549442 0.274721 0.961524i $$-0.411414\pi$$
0.274721 + 0.961524i $$0.411414\pi$$
$$54$$ 0 0
$$55$$ 12.0000 1.61808
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 12.0000 1.56227 0.781133 0.624364i $$-0.214642\pi$$
0.781133 + 0.624364i $$0.214642\pi$$
$$60$$ 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
$$64$$ 0 0
$$65$$ 12.0000 1.48842
$$66$$ 0 0
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −14.0000 −1.48400 −0.741999 0.670402i $$-0.766122\pi$$
−0.741999 + 0.670402i $$0.766122\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 8.00000 0.820783
$$96$$ 0 0
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −18.0000 −1.79107 −0.895533 0.444994i $$-0.853206\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 0 0
$$103$$ −12.0000 −1.18240 −0.591198 0.806527i $$-0.701345\pi$$
−0.591198 + 0.806527i $$0.701345\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −18.0000 −1.74013 −0.870063 0.492941i $$-0.835922\pi$$
−0.870063 + 0.492941i $$0.835922\pi$$
$$108$$ 0 0
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 4.00000 0.373002
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 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 $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −20.0000 −1.70872 −0.854358 0.519685i $$-0.826049\pi$$
−0.854358 + 0.519685i $$0.826049\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 36.0000 3.01047
$$144$$ 0 0
$$145$$ −16.0000 −1.32873
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −4.00000 −0.327693 −0.163846 0.986486i $$-0.552390\pi$$
−0.163846 + 0.986486i $$0.552390\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 8.00000 0.642575
$$156$$ 0 0
$$157$$ 18.0000 1.43656 0.718278 0.695756i $$-0.244931\pi$$
0.718278 + 0.695756i $$0.244931\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −4.00000 −0.313304 −0.156652 0.987654i $$-0.550070\pi$$
−0.156652 + 0.987654i $$0.550070\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −10.0000 −0.760286 −0.380143 0.924928i $$-0.624125\pi$$
−0.380143 + 0.924928i $$0.624125\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 2.00000 0.149487 0.0747435 0.997203i $$-0.476186\pi$$
0.0747435 + 0.997203i $$0.476186\pi$$
$$180$$ 0 0
$$181$$ 22.0000 1.63525 0.817624 0.575753i $$-0.195291\pi$$
0.817624 + 0.575753i $$0.195291\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −12.0000 −0.882258
$$186$$ 0 0
$$187$$ −12.0000 −0.877527
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −2.00000 −0.144715 −0.0723575 0.997379i $$-0.523052\pi$$
−0.0723575 + 0.997379i $$0.523052\pi$$
$$192$$ 0 0
$$193$$ 6.00000 0.431889 0.215945 0.976406i $$-0.430717\pi$$
0.215945 + 0.976406i $$0.430717\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 20.0000 1.39686
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 24.0000 1.66011
$$210$$ 0 0
$$211$$ 28.0000 1.92760 0.963800 0.266627i $$-0.0859092\pi$$
0.963800 + 0.266627i $$0.0859092\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 8.00000 0.545595
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −12.0000 −0.807207
$$222$$ 0 0
$$223$$ 24.0000 1.60716 0.803579 0.595198i $$-0.202926\pi$$
0.803579 + 0.595198i $$0.202926\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −20.0000 −1.32745 −0.663723 0.747978i $$-0.731025\pi$$
−0.663723 + 0.747978i $$0.731025\pi$$
$$228$$ 0 0
$$229$$ −2.00000 −0.132164 −0.0660819 0.997814i $$-0.521050\pi$$
−0.0660819 + 0.997814i $$0.521050\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 4.00000 0.262049 0.131024 0.991379i $$-0.458173\pi$$
0.131024 + 0.991379i $$0.458173\pi$$
$$234$$ 0 0
$$235$$ 8.00000 0.521862
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 26.0000 1.68180 0.840900 0.541190i $$-0.182026\pi$$
0.840900 + 0.541190i $$0.182026\pi$$
$$240$$ 0 0
$$241$$ −22.0000 −1.41714 −0.708572 0.705638i $$-0.750660\pi$$
−0.708572 + 0.705638i $$0.750660\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 24.0000 1.52708
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −4.00000 −0.252478 −0.126239 0.992000i $$-0.540291\pi$$
−0.126239 + 0.992000i $$0.540291\pi$$
$$252$$ 0 0
$$253$$ 12.0000 0.754434
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −6.00000 −0.369976 −0.184988 0.982741i $$-0.559225\pi$$
−0.184988 + 0.982741i $$0.559225\pi$$
$$264$$ 0 0
$$265$$ 8.00000 0.491436
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −6.00000 −0.365826 −0.182913 0.983129i $$-0.558553\pi$$
−0.182913 + 0.983129i $$0.558553\pi$$
$$270$$ 0 0
$$271$$ −4.00000 −0.242983 −0.121491 0.992592i $$-0.538768\pi$$
−0.121491 + 0.992592i $$0.538768\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −6.00000 −0.361814
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ 20.0000 1.18888 0.594438 0.804141i $$-0.297374\pi$$
0.594438 + 0.804141i $$0.297374\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 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
$$295$$ 24.0000 1.39733
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 12.0000 0.693978
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 4.00000 0.229039
$$306$$ 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
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ −2.00000 −0.113047 −0.0565233 0.998401i $$-0.518002\pi$$
−0.0565233 + 0.998401i $$0.518002\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 12.0000 0.673987 0.336994 0.941507i $$-0.390590\pi$$
0.336994 + 0.941507i $$0.390590\pi$$
$$318$$ 0 0
$$319$$ −48.0000 −2.68748
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −8.00000 −0.445132
$$324$$ 0 0
$$325$$ −6.00000 −0.332820
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 28.0000 1.53902 0.769510 0.638635i $$-0.220501\pi$$
0.769510 + 0.638635i $$0.220501\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −24.0000 −1.31126
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 24.0000 1.29967
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 18.0000 0.966291 0.483145 0.875540i $$-0.339494\pi$$
0.483145 + 0.875540i $$0.339494\pi$$
$$348$$ 0 0
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ 0 0
$$355$$ 12.0000 0.636894
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 30.0000 1.58334 0.791670 0.610949i $$-0.209212\pi$$
0.791670 + 0.610949i $$0.209212\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 4.00000 0.209370
$$366$$ 0 0
$$367$$ −16.0000 −0.835193 −0.417597 0.908633i $$-0.637127\pi$$
−0.417597 + 0.908633i $$0.637127\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −10.0000 −0.517780 −0.258890 0.965907i $$-0.583357\pi$$
−0.258890 + 0.965907i $$0.583357\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −48.0000 −2.47213
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −16.0000 −0.811232 −0.405616 0.914044i $$-0.632943\pi$$
−0.405616 + 0.914044i $$0.632943\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 16.0000 0.805047
$$396$$ 0 0
$$397$$ 2.00000 0.100377 0.0501886 0.998740i $$-0.484018\pi$$
0.0501886 + 0.998740i $$0.484018\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −12.0000 −0.599251 −0.299626 0.954057i $$-0.596862\pi$$
−0.299626 + 0.954057i $$0.596862\pi$$
$$402$$ 0 0
$$403$$ 24.0000 1.19553
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −36.0000 −1.78445
$$408$$ 0 0
$$409$$ 18.0000 0.890043 0.445021 0.895520i $$-0.353196\pi$$
0.445021 + 0.895520i $$0.353196\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 28.0000 1.36789 0.683945 0.729534i $$-0.260263\pi$$
0.683945 + 0.729534i $$0.260263\pi$$
$$420$$ 0 0
$$421$$ −2.00000 −0.0974740 −0.0487370 0.998812i $$-0.515520\pi$$
−0.0487370 + 0.998812i $$0.515520\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2.00000 0.0970143
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −18.0000 −0.867029 −0.433515 0.901146i $$-0.642727\pi$$
−0.433515 + 0.901146i $$0.642727\pi$$
$$432$$ 0 0
$$433$$ 38.0000 1.82616 0.913082 0.407777i $$-0.133696\pi$$
0.913082 + 0.407777i $$0.133696\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 8.00000 0.382692
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −22.0000 −1.04525 −0.522626 0.852562i $$-0.675047\pi$$
−0.522626 + 0.852562i $$0.675047\pi$$
$$444$$ 0 0
$$445$$ −28.0000 −1.32733
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 8.00000 0.377543 0.188772 0.982021i $$-0.439549\pi$$
0.188772 + 0.982021i $$0.439549\pi$$
$$450$$ 0 0
$$451$$ 60.0000 2.82529
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 30.0000 1.39724 0.698620 0.715493i $$-0.253798\pi$$
0.698620 + 0.715493i $$0.253798\pi$$
$$462$$ 0 0
$$463$$ −32.0000 −1.48717 −0.743583 0.668644i $$-0.766875\pi$$
−0.743583 + 0.668644i $$0.766875\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 24.0000 1.10352
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −4.00000 −0.182765 −0.0913823 0.995816i $$-0.529129\pi$$
−0.0913823 + 0.995816i $$0.529129\pi$$
$$480$$ 0 0
$$481$$ −36.0000 −1.64146
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 4.00000 0.181631
$$486$$ 0 0
$$487$$ −40.0000 −1.81257 −0.906287 0.422664i $$-0.861095\pi$$
−0.906287 + 0.422664i $$0.861095\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 18.0000 0.812329 0.406164 0.913800i $$-0.366866\pi$$
0.406164 + 0.913800i $$0.366866\pi$$
$$492$$ 0 0
$$493$$ 16.0000 0.720604
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −28.0000 −1.25345 −0.626726 0.779240i $$-0.715605\pi$$
−0.626726 + 0.779240i $$0.715605\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 32.0000 1.42681 0.713405 0.700752i $$-0.247152\pi$$
0.713405 + 0.700752i $$0.247152\pi$$
$$504$$ 0 0
$$505$$ −36.0000 −1.60198
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −30.0000 −1.32973 −0.664863 0.746965i $$-0.731510\pi$$
−0.664863 + 0.746965i $$0.731510\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −24.0000 −1.05757
$$516$$ 0 0
$$517$$ 24.0000 1.05552
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 30.0000 1.31432 0.657162 0.753749i $$-0.271757\pi$$
0.657162 + 0.753749i $$0.271757\pi$$
$$522$$ 0 0
$$523$$ −16.0000 −0.699631 −0.349816 0.936819i $$-0.613756\pi$$
−0.349816 + 0.936819i $$0.613756\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −8.00000 −0.348485
$$528$$ 0 0
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 60.0000 2.59889
$$534$$ 0 0
$$535$$ −36.0000 −1.55642
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 22.0000 0.945854 0.472927 0.881102i $$-0.343197\pi$$
0.472927 + 0.881102i $$0.343197\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −28.0000 −1.19939
$$546$$ 0 0
$$547$$ −28.0000 −1.19719 −0.598597 0.801050i $$-0.704275\pi$$
−0.598597 + 0.801050i $$0.704275\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −32.0000 −1.36325
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 20.0000 0.847427 0.423714 0.905796i $$-0.360726\pi$$
0.423714 + 0.905796i $$0.360726\pi$$
$$558$$ 0 0
$$559$$ 24.0000 1.01509
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −28.0000 −1.18006 −0.590030 0.807382i $$-0.700884\pi$$
−0.590030 + 0.807382i $$0.700884\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −12.0000 −0.503066 −0.251533 0.967849i $$-0.580935\pi$$
−0.251533 + 0.967849i $$0.580935\pi$$
$$570$$ 0 0
$$571$$ 28.0000 1.17176 0.585882 0.810397i $$-0.300748\pi$$
0.585882 + 0.810397i $$0.300748\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −2.00000 −0.0834058
$$576$$ 0 0
$$577$$ 30.0000 1.24892 0.624458 0.781058i $$-0.285320\pi$$
0.624458 + 0.781058i $$0.285320\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 24.0000 0.993978
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −28.0000 −1.15568 −0.577842 0.816149i $$-0.696105\pi$$
−0.577842 + 0.816149i $$0.696105\pi$$
$$588$$ 0 0
$$589$$ 16.0000 0.659269
$$590$$ 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
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −26.0000 −1.06233 −0.531166 0.847268i $$-0.678246\pi$$
−0.531166 + 0.847268i $$0.678246\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 50.0000 2.03279
$$606$$ 0 0
$$607$$ −8.00000 −0.324710 −0.162355 0.986732i $$-0.551909\pi$$
−0.162355 + 0.986732i $$0.551909\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 24.0000 0.970936
$$612$$ 0 0
$$613$$ 22.0000 0.888572 0.444286 0.895885i $$-0.353457\pi$$
0.444286 + 0.895885i $$0.353457\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −12.0000 −0.483102 −0.241551 0.970388i $$-0.577656\pi$$
−0.241551 + 0.970388i $$0.577656\pi$$
$$618$$ 0 0
$$619$$ 24.0000 0.964641 0.482321 0.875995i $$-0.339794\pi$$
0.482321 + 0.875995i $$0.339794\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 12.0000 0.478471
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −16.0000 −0.634941
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 20.0000 0.789953 0.394976 0.918691i $$-0.370753\pi$$
0.394976 + 0.918691i $$0.370753\pi$$
$$642$$ 0 0
$$643$$ 28.0000 1.10421 0.552106 0.833774i $$-0.313824\pi$$
0.552106 + 0.833774i $$0.313824\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −36.0000 −1.41531 −0.707653 0.706560i $$-0.750246\pi$$
−0.707653 + 0.706560i $$0.750246\pi$$
$$648$$ 0 0
$$649$$ 72.0000 2.82625
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −8.00000 −0.313064 −0.156532 0.987673i $$-0.550031\pi$$
−0.156532 + 0.987673i $$0.550031\pi$$
$$654$$ 0 0
$$655$$ −16.0000 −0.625172
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −34.0000 −1.32445 −0.662226 0.749304i $$-0.730388\pi$$
−0.662226 + 0.749304i $$0.730388\pi$$
$$660$$ 0 0
$$661$$ −14.0000 −0.544537 −0.272268 0.962221i $$-0.587774\pi$$
−0.272268 + 0.962221i $$0.587774\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −16.0000 −0.619522
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 12.0000 0.463255
$$672$$ 0 0
$$673$$ −2.00000 −0.0770943 −0.0385472 0.999257i $$-0.512273\pi$$
−0.0385472 + 0.999257i $$0.512273\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −18.0000 −0.691796 −0.345898 0.938272i $$-0.612426\pi$$
−0.345898 + 0.938272i $$0.612426\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −6.00000 −0.229584 −0.114792 0.993390i $$-0.536620\pi$$
−0.114792 + 0.993390i $$0.536620\pi$$
$$684$$ 0 0
$$685$$ −40.0000 −1.52832
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −20.0000 −0.757554
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −40.0000 −1.51078 −0.755390 0.655276i $$-0.772552\pi$$
−0.755390 + 0.655276i $$0.772552\pi$$
$$702$$ 0 0
$$703$$ −24.0000 −0.905177
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 10.0000 0.375558 0.187779 0.982211i $$-0.439871\pi$$
0.187779 + 0.982211i $$0.439871\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 8.00000 0.299602
$$714$$ 0 0
$$715$$ 72.0000 2.69265
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −48.0000 −1.79010 −0.895049 0.445968i $$-0.852860\pi$$
−0.895049 + 0.445968i $$0.852860\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 8.00000 0.297113
$$726$$ 0 0
$$727$$ 20.0000 0.741759 0.370879 0.928681i $$-0.379056\pi$$
0.370879 + 0.928681i $$0.379056\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −8.00000 −0.295891
$$732$$ 0 0
$$733$$ −34.0000 −1.25582 −0.627909 0.778287i $$-0.716089\pi$$
−0.627909 + 0.778287i $$0.716089\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −72.0000 −2.65215
$$738$$ 0 0
$$739$$ −4.00000 −0.147142 −0.0735712 0.997290i $$-0.523440\pi$$
−0.0735712 + 0.997290i $$0.523440\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −10.0000 −0.366864 −0.183432 0.983032i $$-0.558721\pi$$
−0.183432 + 0.983032i $$0.558721\pi$$
$$744$$ 0 0
$$745$$ −8.00000 −0.293097
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −8.00000 −0.291924 −0.145962 0.989290i $$-0.546628\pi$$
−0.145962 + 0.989290i $$0.546628\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 16.0000 0.582300
$$756$$ 0 0
$$757$$ 10.0000 0.363456 0.181728 0.983349i $$-0.441831\pi$$
0.181728 + 0.983349i $$0.441831\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 42.0000 1.52250 0.761249 0.648459i $$-0.224586\pi$$
0.761249 + 0.648459i $$0.224586\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 72.0000 2.59977
$$768$$ 0 0
$$769$$ −10.0000 −0.360609 −0.180305 0.983611i $$-0.557708\pi$$
−0.180305 + 0.983611i $$0.557708\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 22.0000 0.791285 0.395643 0.918405i $$-0.370522\pi$$
0.395643 + 0.918405i $$0.370522\pi$$
$$774$$ 0 0
$$775$$ −4.00000 −0.143684
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 40.0000 1.43315
$$780$$ 0 0
$$781$$ 36.0000 1.28818
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 36.0000 1.28490
$$786$$ 0 0
$$787$$ 16.0000 0.570338 0.285169 0.958477i $$-0.407950\pi$$
0.285169 + 0.958477i $$0.407950\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 12.0000 0.426132
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −18.0000 −0.637593 −0.318796 0.947823i $$-0.603279\pi$$
−0.318796 + 0.947823i $$0.603279\pi$$
$$798$$ 0 0
$$799$$ −8.00000 −0.283020
$$800$$ 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
$$809$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$810$$ 0 0
$$811$$ −48.0000 −1.68551 −0.842754 0.538299i $$-0.819067\pi$$
−0.842754 + 0.538299i $$0.819067\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −8.00000 −0.280228
$$816$$ 0 0
$$817$$ 16.0000 0.559769
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 12.0000 0.418803 0.209401 0.977830i $$-0.432848\pi$$
0.209401 + 0.977830i $$0.432848\pi$$
$$822$$ 0 0
$$823$$ 16.0000 0.557725 0.278862 0.960331i $$-0.410043\pi$$
0.278862 + 0.960331i $$0.410043\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −18.0000 −0.625921 −0.312961 0.949766i $$-0.601321\pi$$
−0.312961 + 0.949766i $$0.601321\pi$$
$$828$$ 0 0
$$829$$ −26.0000 −0.903017 −0.451509 0.892267i $$-0.649114\pi$$
−0.451509 + 0.892267i $$0.649114\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −24.0000 −0.830554
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 12.0000 0.414286 0.207143 0.978311i $$-0.433583\pi$$
0.207143 + 0.978311i $$0.433583\pi$$
$$840$$ 0 0
$$841$$ 35.0000 1.20690
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 46.0000 1.58245
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −12.0000 −0.411355
$$852$$ 0 0
$$853$$ 2.00000 0.0684787 0.0342393 0.999414i $$-0.489099\pi$$
0.0342393 + 0.999414i $$0.489099\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ 4.00000 0.136478 0.0682391 0.997669i $$-0.478262\pi$$
0.0682391 + 0.997669i $$0.478262\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 26.0000 0.885050 0.442525 0.896756i $$-0.354083\pi$$
0.442525 + 0.896756i $$0.354083\pi$$
$$864$$ 0 0
$$865$$ −20.0000 −0.680020
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 48.0000 1.62829
$$870$$ 0 0
$$871$$ −72.0000 −2.43963
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −34.0000 −1.14810 −0.574049 0.818821i $$-0.694628\pi$$
−0.574049 + 0.818821i $$0.694628\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −2.00000 −0.0673817 −0.0336909 0.999432i $$-0.510726\pi$$
−0.0336909 + 0.999432i $$0.510726\pi$$
$$882$$ 0 0
$$883$$ 20.0000 0.673054 0.336527 0.941674i $$-0.390748\pi$$
0.336527 + 0.941674i $$0.390748\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 36.0000 1.20876 0.604381 0.796696i $$-0.293421\pi$$
0.604381 + 0.796696i $$0.293421\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 16.0000 0.535420
$$894$$ 0 0
$$895$$ 4.00000 0.133705
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −32.0000 −1.06726
$$900$$ 0 0
$$901$$ −8.00000 −0.266519
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 44.0000 1.46261
$$906$$ 0 0
$$907$$ 28.0000 0.929725 0.464862 0.885383i $$-0.346104\pi$$
0.464862 + 0.885383i $$0.346104\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −2.00000 −0.0662630 −0.0331315 0.999451i $$-0.510548\pi$$
−0.0331315 + 0.999451i $$0.510548\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 32.0000 1.05558 0.527791 0.849374i $$-0.323020\pi$$
0.527791 + 0.849374i $$0.323020\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 36.0000 1.18495
$$924$$ 0 0
$$925$$ 6.00000 0.197279
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 10.0000 0.328089 0.164045 0.986453i $$-0.447546\pi$$
0.164045 + 0.986453i $$0.447546\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −24.0000 −0.784884
$$936$$ 0 0
$$937$$ 30.0000 0.980057 0.490029 0.871706i $$-0.336986\pi$$
0.490029 + 0.871706i $$0.336986\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −6.00000 −0.195594 −0.0977972 0.995206i $$-0.531180\pi$$
−0.0977972 + 0.995206i $$0.531180\pi$$
$$942$$ 0 0
$$943$$ 20.0000 0.651290
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 22.0000 0.714904 0.357452 0.933932i $$-0.383646\pi$$
0.357452 + 0.933932i $$0.383646\pi$$
$$948$$ 0 0
$$949$$ 12.0000 0.389536
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −40.0000 −1.29573 −0.647864 0.761756i $$-0.724337\pi$$
−0.647864 + 0.761756i $$0.724337\pi$$
$$954$$ 0 0
$$955$$ −4.00000 −0.129437
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 12.0000 0.386294
$$966$$ 0 0
$$967$$ −48.0000 −1.54358 −0.771788 0.635880i $$-0.780637\pi$$
−0.771788 + 0.635880i $$0.780637\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −16.0000 −0.513464 −0.256732 0.966483i $$-0.582646\pi$$
−0.256732 + 0.966483i $$0.582646\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 36.0000 1.15174 0.575871 0.817541i $$-0.304663\pi$$
0.575871 + 0.817541i $$0.304663\pi$$
$$978$$ 0 0
$$979$$ −84.0000 −2.68465
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −24.0000 −0.765481 −0.382741 0.923856i $$-0.625020\pi$$
−0.382741 + 0.923856i $$0.625020\pi$$
$$984$$ 0 0
$$985$$ −24.0000 −0.764704
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 8.00000 0.254385
$$990$$ 0 0
$$991$$ 24.0000 0.762385 0.381193 0.924496i $$-0.375513\pi$$
0.381193 + 0.924496i $$0.375513\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −32.0000 −1.01447
$$996$$ 0 0
$$997$$ −46.0000 −1.45683 −0.728417 0.685134i $$-0.759744\pi$$
−0.728417 + 0.685134i $$0.759744\pi$$
$$998$$ 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 7056.2.a.bv.1.1 1
3.2 odd 2 7056.2.a.j.1.1 1
4.3 odd 2 3528.2.a.t.1.1 1
7.6 odd 2 1008.2.a.c.1.1 1
12.11 even 2 3528.2.a.g.1.1 1
21.20 even 2 1008.2.a.i.1.1 1
28.3 even 6 3528.2.s.z.3313.1 2
28.11 odd 6 3528.2.s.k.3313.1 2
28.19 even 6 3528.2.s.z.361.1 2
28.23 odd 6 3528.2.s.k.361.1 2
28.27 even 2 504.2.a.d.1.1 1
56.13 odd 2 4032.2.a.ba.1.1 1
56.27 even 2 4032.2.a.bl.1.1 1
84.11 even 6 3528.2.s.s.3313.1 2
84.23 even 6 3528.2.s.s.361.1 2
84.47 odd 6 3528.2.s.c.361.1 2
84.59 odd 6 3528.2.s.c.3313.1 2
84.83 odd 2 504.2.a.g.1.1 yes 1
168.83 odd 2 4032.2.a.j.1.1 1
168.125 even 2 4032.2.a.i.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.a.d.1.1 1 28.27 even 2
504.2.a.g.1.1 yes 1 84.83 odd 2
1008.2.a.c.1.1 1 7.6 odd 2
1008.2.a.i.1.1 1 21.20 even 2
3528.2.a.g.1.1 1 12.11 even 2
3528.2.a.t.1.1 1 4.3 odd 2
3528.2.s.c.361.1 2 84.47 odd 6
3528.2.s.c.3313.1 2 84.59 odd 6
3528.2.s.k.361.1 2 28.23 odd 6
3528.2.s.k.3313.1 2 28.11 odd 6
3528.2.s.s.361.1 2 84.23 even 6
3528.2.s.s.3313.1 2 84.11 even 6
3528.2.s.z.361.1 2 28.19 even 6
3528.2.s.z.3313.1 2 28.3 even 6
4032.2.a.i.1.1 1 168.125 even 2
4032.2.a.j.1.1 1 168.83 odd 2
4032.2.a.ba.1.1 1 56.13 odd 2
4032.2.a.bl.1.1 1 56.27 even 2
7056.2.a.j.1.1 1 3.2 odd 2
7056.2.a.bv.1.1 1 1.1 even 1 trivial