# Properties

 Label 2800.2.a.u.1.1 Level $2800$ Weight $2$ Character 2800.1 Self dual yes Analytic conductor $22.358$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2800 = 2^{4} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2800.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$22.3581125660$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2800.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +1.00000 q^{11} +1.00000 q^{13} +3.00000 q^{17} +4.00000 q^{19} -1.00000 q^{21} +2.00000 q^{23} -5.00000 q^{27} -1.00000 q^{29} +6.00000 q^{31} +1.00000 q^{33} -2.00000 q^{37} +1.00000 q^{39} -10.0000 q^{41} +9.00000 q^{47} +1.00000 q^{49} +3.00000 q^{51} +14.0000 q^{53} +4.00000 q^{57} -6.00000 q^{59} -4.00000 q^{61} +2.00000 q^{63} +10.0000 q^{67} +2.00000 q^{69} +16.0000 q^{71} -10.0000 q^{73} -1.00000 q^{77} +11.0000 q^{79} +1.00000 q^{81} +4.00000 q^{83} -1.00000 q^{87} +12.0000 q^{89} -1.00000 q^{91} +6.00000 q^{93} +19.0000 q^{97} -2.00000 q^{99} +O(q^{100})$$

## 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
$$3$$ 1.00000 0.577350 0.288675 0.957427i $$-0.406785\pi$$
0.288675 + 0.957427i $$0.406785\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −1.00000 −0.377964
$$8$$ 0 0
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ 1.00000 0.301511 0.150756 0.988571i $$-0.451829\pi$$
0.150756 + 0.988571i $$0.451829\pi$$
$$12$$ 0 0
$$13$$ 1.00000 0.277350 0.138675 0.990338i $$-0.455716\pi$$
0.138675 + 0.990338i $$0.455716\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ 2.00000 0.417029 0.208514 0.978019i $$-0.433137\pi$$
0.208514 + 0.978019i $$0.433137\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ −1.00000 −0.185695 −0.0928477 0.995680i $$-0.529597\pi$$
−0.0928477 + 0.995680i $$0.529597\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ 0 0
$$33$$ 1.00000 0.174078
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0 0
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 9.00000 1.31278 0.656392 0.754420i $$-0.272082\pi$$
0.656392 + 0.754420i $$0.272082\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 3.00000 0.420084
$$52$$ 0 0
$$53$$ 14.0000 1.92305 0.961524 0.274721i $$-0.0885855\pi$$
0.961524 + 0.274721i $$0.0885855\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 4.00000 0.529813
$$58$$ 0 0
$$59$$ −6.00000 −0.781133 −0.390567 0.920575i $$-0.627721\pi$$
−0.390567 + 0.920575i $$0.627721\pi$$
$$60$$ 0 0
$$61$$ −4.00000 −0.512148 −0.256074 0.966657i $$-0.582429\pi$$
−0.256074 + 0.966657i $$0.582429\pi$$
$$62$$ 0 0
$$63$$ 2.00000 0.251976
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 10.0000 1.22169 0.610847 0.791748i $$-0.290829\pi$$
0.610847 + 0.791748i $$0.290829\pi$$
$$68$$ 0 0
$$69$$ 2.00000 0.240772
$$70$$ 0 0
$$71$$ 16.0000 1.89885 0.949425 0.313993i $$-0.101667\pi$$
0.949425 + 0.313993i $$0.101667\pi$$
$$72$$ 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
$$76$$ 0 0
$$77$$ −1.00000 −0.113961
$$78$$ 0 0
$$79$$ 11.0000 1.23760 0.618798 0.785550i $$-0.287620\pi$$
0.618798 + 0.785550i $$0.287620\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −1.00000 −0.107211
$$88$$ 0 0
$$89$$ 12.0000 1.27200 0.635999 0.771690i $$-0.280588\pi$$
0.635999 + 0.771690i $$0.280588\pi$$
$$90$$ 0 0
$$91$$ −1.00000 −0.104828
$$92$$ 0 0
$$93$$ 6.00000 0.622171
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 19.0000 1.92916 0.964579 0.263795i $$-0.0849741\pi$$
0.964579 + 0.263795i $$0.0849741\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 1.00000 0.0985329 0.0492665 0.998786i $$-0.484312\pi$$
0.0492665 + 0.998786i $$0.484312\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 16.0000 1.54678 0.773389 0.633932i $$-0.218560\pi$$
0.773389 + 0.633932i $$0.218560\pi$$
$$108$$ 0 0
$$109$$ −15.0000 −1.43674 −0.718370 0.695662i $$-0.755111\pi$$
−0.718370 + 0.695662i $$0.755111\pi$$
$$110$$ 0 0
$$111$$ −2.00000 −0.189832
$$112$$ 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
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ −3.00000 −0.275010
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ 0 0
$$123$$ −10.0000 −0.901670
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 18.0000 1.59724 0.798621 0.601834i $$-0.205563\pi$$
0.798621 + 0.601834i $$0.205563\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −6.00000 −0.524222 −0.262111 0.965038i $$-0.584419\pi$$
−0.262111 + 0.965038i $$0.584419\pi$$
$$132$$ 0 0
$$133$$ −4.00000 −0.346844
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 8.00000 0.683486 0.341743 0.939793i $$-0.388983\pi$$
0.341743 + 0.939793i $$0.388983\pi$$
$$138$$ 0 0
$$139$$ 14.0000 1.18746 0.593732 0.804663i $$-0.297654\pi$$
0.593732 + 0.804663i $$0.297654\pi$$
$$140$$ 0 0
$$141$$ 9.00000 0.757937
$$142$$ 0 0
$$143$$ 1.00000 0.0836242
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 1.00000 0.0824786
$$148$$ 0 0
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ −13.0000 −1.05792 −0.528962 0.848645i $$-0.677419\pi$$
−0.528962 + 0.848645i $$0.677419\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 14.0000 1.11732 0.558661 0.829396i $$-0.311315\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ 0 0
$$159$$ 14.0000 1.11027
$$160$$ 0 0
$$161$$ −2.00000 −0.157622
$$162$$ 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
$$167$$ −15.0000 −1.16073 −0.580367 0.814355i $$-0.697091\pi$$
−0.580367 + 0.814355i $$0.697091\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ −8.00000 −0.611775
$$172$$ 0 0
$$173$$ 15.0000 1.14043 0.570214 0.821496i $$-0.306860\pi$$
0.570214 + 0.821496i $$0.306860\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −6.00000 −0.450988
$$178$$ 0 0
$$179$$ −20.0000 −1.49487 −0.747435 0.664335i $$-0.768715\pi$$
−0.747435 + 0.664335i $$0.768715\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ −4.00000 −0.295689
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 3.00000 0.219382
$$188$$ 0 0
$$189$$ 5.00000 0.363696
$$190$$ 0 0
$$191$$ −3.00000 −0.217072 −0.108536 0.994092i $$-0.534616\pi$$
−0.108536 + 0.994092i $$0.534616\pi$$
$$192$$ 0 0
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ −10.0000 −0.708881 −0.354441 0.935079i $$-0.615329\pi$$
−0.354441 + 0.935079i $$0.615329\pi$$
$$200$$ 0 0
$$201$$ 10.0000 0.705346
$$202$$ 0 0
$$203$$ 1.00000 0.0701862
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −4.00000 −0.278019
$$208$$ 0 0
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ −1.00000 −0.0688428 −0.0344214 0.999407i $$-0.510959\pi$$
−0.0344214 + 0.999407i $$0.510959\pi$$
$$212$$ 0 0
$$213$$ 16.0000 1.09630
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −6.00000 −0.407307
$$218$$ 0 0
$$219$$ −10.0000 −0.675737
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 0 0
$$223$$ −15.0000 −1.00447 −0.502237 0.864730i $$-0.667490\pi$$
−0.502237 + 0.864730i $$0.667490\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −7.00000 −0.464606 −0.232303 0.972643i $$-0.574626\pi$$
−0.232303 + 0.972643i $$0.574626\pi$$
$$228$$ 0 0
$$229$$ 18.0000 1.18947 0.594737 0.803921i $$-0.297256\pi$$
0.594737 + 0.803921i $$0.297256\pi$$
$$230$$ 0 0
$$231$$ −1.00000 −0.0657952
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 11.0000 0.714527
$$238$$ 0 0
$$239$$ −17.0000 −1.09964 −0.549819 0.835284i $$-0.685303\pi$$
−0.549819 + 0.835284i $$0.685303\pi$$
$$240$$ 0 0
$$241$$ 2.00000 0.128831 0.0644157 0.997923i $$-0.479482\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$242$$ 0 0
$$243$$ 16.0000 1.02640
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 4.00000 0.254514
$$248$$ 0 0
$$249$$ 4.00000 0.253490
$$250$$ 0 0
$$251$$ −10.0000 −0.631194 −0.315597 0.948893i $$-0.602205\pi$$
−0.315597 + 0.948893i $$0.602205\pi$$
$$252$$ 0 0
$$253$$ 2.00000 0.125739
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ 2.00000 0.124274
$$260$$ 0 0
$$261$$ 2.00000 0.123797
$$262$$ 0 0
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ 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 $$-0.461232\pi$$
0.121491 + 0.992592i $$0.461232\pi$$
$$272$$ 0 0
$$273$$ −1.00000 −0.0605228
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 18.0000 1.08152 0.540758 0.841178i $$-0.318138\pi$$
0.540758 + 0.841178i $$0.318138\pi$$
$$278$$ 0 0
$$279$$ −12.0000 −0.718421
$$280$$ 0 0
$$281$$ 15.0000 0.894825 0.447412 0.894328i $$-0.352346\pi$$
0.447412 + 0.894328i $$0.352346\pi$$
$$282$$ 0 0
$$283$$ −21.0000 −1.24832 −0.624160 0.781296i $$-0.714559\pi$$
−0.624160 + 0.781296i $$0.714559\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 10.0000 0.590281
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 19.0000 1.11380
$$292$$ 0 0
$$293$$ 31.0000 1.81104 0.905520 0.424304i $$-0.139481\pi$$
0.905520 + 0.424304i $$0.139481\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −5.00000 −0.290129
$$298$$ 0 0
$$299$$ 2.00000 0.115663
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −25.0000 −1.42683 −0.713413 0.700744i $$-0.752851\pi$$
−0.713413 + 0.700744i $$0.752851\pi$$
$$308$$ 0 0
$$309$$ 1.00000 0.0568880
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ −7.00000 −0.395663 −0.197832 0.980236i $$-0.563390\pi$$
−0.197832 + 0.980236i $$0.563390\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −12.0000 −0.673987 −0.336994 0.941507i $$-0.609410\pi$$
−0.336994 + 0.941507i $$0.609410\pi$$
$$318$$ 0 0
$$319$$ −1.00000 −0.0559893
$$320$$ 0 0
$$321$$ 16.0000 0.893033
$$322$$ 0 0
$$323$$ 12.0000 0.667698
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −15.0000 −0.829502
$$328$$ 0 0
$$329$$ −9.00000 −0.496186
$$330$$ 0 0
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ 0 0
$$333$$ 4.00000 0.219199
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −34.0000 −1.85210 −0.926049 0.377403i $$-0.876817\pi$$
−0.926049 + 0.377403i $$0.876817\pi$$
$$338$$ 0 0
$$339$$ −14.0000 −0.760376
$$340$$ 0 0
$$341$$ 6.00000 0.324918
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −22.0000 −1.18102 −0.590511 0.807030i $$-0.701074\pi$$
−0.590511 + 0.807030i $$0.701074\pi$$
$$348$$ 0 0
$$349$$ 8.00000 0.428230 0.214115 0.976808i $$-0.431313\pi$$
0.214115 + 0.976808i $$0.431313\pi$$
$$350$$ 0 0
$$351$$ −5.00000 −0.266880
$$352$$ 0 0
$$353$$ −9.00000 −0.479022 −0.239511 0.970894i $$-0.576987\pi$$
−0.239511 + 0.970894i $$0.576987\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −3.00000 −0.158777
$$358$$ 0 0
$$359$$ −4.00000 −0.211112 −0.105556 0.994413i $$-0.533662\pi$$
−0.105556 + 0.994413i $$0.533662\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ −10.0000 −0.524864
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 17.0000 0.887393 0.443696 0.896177i $$-0.353667\pi$$
0.443696 + 0.896177i $$0.353667\pi$$
$$368$$ 0 0
$$369$$ 20.0000 1.04116
$$370$$ 0 0
$$371$$ −14.0000 −0.726844
$$372$$ 0 0
$$373$$ −20.0000 −1.03556 −0.517780 0.855514i $$-0.673242\pi$$
−0.517780 + 0.855514i $$0.673242\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −1.00000 −0.0515026
$$378$$ 0 0
$$379$$ 28.0000 1.43826 0.719132 0.694874i $$-0.244540\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$380$$ 0 0
$$381$$ 18.0000 0.922168
$$382$$ 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
$$389$$ 9.00000 0.456318 0.228159 0.973624i $$-0.426729\pi$$
0.228159 + 0.973624i $$0.426729\pi$$
$$390$$ 0 0
$$391$$ 6.00000 0.303433
$$392$$ 0 0
$$393$$ −6.00000 −0.302660
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 15.0000 0.752828 0.376414 0.926451i $$-0.377157\pi$$
0.376414 + 0.926451i $$0.377157\pi$$
$$398$$ 0 0
$$399$$ −4.00000 −0.200250
$$400$$ 0 0
$$401$$ 13.0000 0.649189 0.324595 0.945853i $$-0.394772\pi$$
0.324595 + 0.945853i $$0.394772\pi$$
$$402$$ 0 0
$$403$$ 6.00000 0.298881
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −2.00000 −0.0991363
$$408$$ 0 0
$$409$$ −28.0000 −1.38451 −0.692255 0.721653i $$-0.743383\pi$$
−0.692255 + 0.721653i $$0.743383\pi$$
$$410$$ 0 0
$$411$$ 8.00000 0.394611
$$412$$ 0 0
$$413$$ 6.00000 0.295241
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 14.0000 0.685583
$$418$$ 0 0
$$419$$ 30.0000 1.46560 0.732798 0.680446i $$-0.238214\pi$$
0.732798 + 0.680446i $$0.238214\pi$$
$$420$$ 0 0
$$421$$ 1.00000 0.0487370 0.0243685 0.999703i $$-0.492242\pi$$
0.0243685 + 0.999703i $$0.492242\pi$$
$$422$$ 0 0
$$423$$ −18.0000 −0.875190
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 4.00000 0.193574
$$428$$ 0 0
$$429$$ 1.00000 0.0482805
$$430$$ 0 0
$$431$$ −31.0000 −1.49322 −0.746609 0.665263i $$-0.768319\pi$$
−0.746609 + 0.665263i $$0.768319\pi$$
$$432$$ 0 0
$$433$$ −6.00000 −0.288342 −0.144171 0.989553i $$-0.546051\pi$$
−0.144171 + 0.989553i $$0.546051\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 8.00000 0.382692
$$438$$ 0 0
$$439$$ 30.0000 1.43182 0.715911 0.698192i $$-0.246012\pi$$
0.715911 + 0.698192i $$0.246012\pi$$
$$440$$ 0 0
$$441$$ −2.00000 −0.0952381
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −6.00000 −0.283790
$$448$$ 0 0
$$449$$ 27.0000 1.27421 0.637104 0.770778i $$-0.280132\pi$$
0.637104 + 0.770778i $$0.280132\pi$$
$$450$$ 0 0
$$451$$ −10.0000 −0.470882
$$452$$ 0 0
$$453$$ −13.0000 −0.610793
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −18.0000 −0.842004 −0.421002 0.907060i $$-0.638322\pi$$
−0.421002 + 0.907060i $$0.638322\pi$$
$$458$$ 0 0
$$459$$ −15.0000 −0.700140
$$460$$ 0 0
$$461$$ 12.0000 0.558896 0.279448 0.960161i $$-0.409849\pi$$
0.279448 + 0.960161i $$0.409849\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 27.0000 1.24941 0.624705 0.780860i $$-0.285219\pi$$
0.624705 + 0.780860i $$0.285219\pi$$
$$468$$ 0 0
$$469$$ −10.0000 −0.461757
$$470$$ 0 0
$$471$$ 14.0000 0.645086
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −28.0000 −1.28203
$$478$$ 0 0
$$479$$ −2.00000 −0.0913823 −0.0456912 0.998956i $$-0.514549\pi$$
−0.0456912 + 0.998956i $$0.514549\pi$$
$$480$$ 0 0
$$481$$ −2.00000 −0.0911922
$$482$$ 0 0
$$483$$ −2.00000 −0.0910032
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −38.0000 −1.72194 −0.860972 0.508652i $$-0.830144\pi$$
−0.860972 + 0.508652i $$0.830144\pi$$
$$488$$ 0 0
$$489$$ 10.0000 0.452216
$$490$$ 0 0
$$491$$ −5.00000 −0.225647 −0.112823 0.993615i $$-0.535989\pi$$
−0.112823 + 0.993615i $$0.535989\pi$$
$$492$$ 0 0
$$493$$ −3.00000 −0.135113
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −16.0000 −0.717698
$$498$$ 0 0
$$499$$ −23.0000 −1.02962 −0.514811 0.857304i $$-0.672138\pi$$
−0.514811 + 0.857304i $$0.672138\pi$$
$$500$$ 0 0
$$501$$ −15.0000 −0.670151
$$502$$ 0 0
$$503$$ −29.0000 −1.29305 −0.646523 0.762894i $$-0.723778\pi$$
−0.646523 + 0.762894i $$0.723778\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −12.0000 −0.532939
$$508$$ 0 0
$$509$$ 10.0000 0.443242 0.221621 0.975133i $$-0.428865\pi$$
0.221621 + 0.975133i $$0.428865\pi$$
$$510$$ 0 0
$$511$$ 10.0000 0.442374
$$512$$ 0 0
$$513$$ −20.0000 −0.883022
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 9.00000 0.395820
$$518$$ 0 0
$$519$$ 15.0000 0.658427
$$520$$ 0 0
$$521$$ −8.00000 −0.350486 −0.175243 0.984525i $$-0.556071\pi$$
−0.175243 + 0.984525i $$0.556071\pi$$
$$522$$ 0 0
$$523$$ −28.0000 −1.22435 −0.612177 0.790721i $$-0.709706\pi$$
−0.612177 + 0.790721i $$0.709706\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 18.0000 0.784092
$$528$$ 0 0
$$529$$ −19.0000 −0.826087
$$530$$ 0 0
$$531$$ 12.0000 0.520756
$$532$$ 0 0
$$533$$ −10.0000 −0.433148
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −20.0000 −0.863064
$$538$$ 0 0
$$539$$ 1.00000 0.0430730
$$540$$ 0 0
$$541$$ −41.0000 −1.76273 −0.881364 0.472438i $$-0.843374\pi$$
−0.881364 + 0.472438i $$0.843374\pi$$
$$542$$ 0 0
$$543$$ −2.00000 −0.0858282
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 4.00000 0.171028 0.0855138 0.996337i $$-0.472747\pi$$
0.0855138 + 0.996337i $$0.472747\pi$$
$$548$$ 0 0
$$549$$ 8.00000 0.341432
$$550$$ 0 0
$$551$$ −4.00000 −0.170406
$$552$$ 0 0
$$553$$ −11.0000 −0.467768
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 36.0000 1.52537 0.762684 0.646771i $$-0.223881\pi$$
0.762684 + 0.646771i $$0.223881\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 3.00000 0.126660
$$562$$ 0 0
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −1.00000 −0.0419961
$$568$$ 0 0
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ 44.0000 1.84134 0.920671 0.390339i $$-0.127642\pi$$
0.920671 + 0.390339i $$0.127642\pi$$
$$572$$ 0 0
$$573$$ −3.00000 −0.125327
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −31.0000 −1.29055 −0.645273 0.763952i $$-0.723257\pi$$
−0.645273 + 0.763952i $$0.723257\pi$$
$$578$$ 0 0
$$579$$ −4.00000 −0.166234
$$580$$ 0 0
$$581$$ −4.00000 −0.165948
$$582$$ 0 0
$$583$$ 14.0000 0.579821
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −20.0000 −0.825488 −0.412744 0.910847i $$-0.635430\pi$$
−0.412744 + 0.910847i $$0.635430\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ 0 0
$$591$$ 6.00000 0.246807
$$592$$ 0 0
$$593$$ −19.0000 −0.780236 −0.390118 0.920765i $$-0.627566\pi$$
−0.390118 + 0.920765i $$0.627566\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −10.0000 −0.409273
$$598$$ 0 0
$$599$$ −7.00000 −0.286012 −0.143006 0.989722i $$-0.545677\pi$$
−0.143006 + 0.989722i $$0.545677\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 0 0
$$603$$ −20.0000 −0.814463
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −1.00000 −0.0405887 −0.0202944 0.999794i $$-0.506460\pi$$
−0.0202944 + 0.999794i $$0.506460\pi$$
$$608$$ 0 0
$$609$$ 1.00000 0.0405220
$$610$$ 0 0
$$611$$ 9.00000 0.364101
$$612$$ 0 0
$$613$$ 4.00000 0.161558 0.0807792 0.996732i $$-0.474259\pi$$
0.0807792 + 0.996732i $$0.474259\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −2.00000 −0.0805170 −0.0402585 0.999189i $$-0.512818\pi$$
−0.0402585 + 0.999189i $$0.512818\pi$$
$$618$$ 0 0
$$619$$ 38.0000 1.52735 0.763674 0.645601i $$-0.223393\pi$$
0.763674 + 0.645601i $$0.223393\pi$$
$$620$$ 0 0
$$621$$ −10.0000 −0.401286
$$622$$ 0 0
$$623$$ −12.0000 −0.480770
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 4.00000 0.159745
$$628$$ 0 0
$$629$$ −6.00000 −0.239236
$$630$$ 0 0
$$631$$ 13.0000 0.517522 0.258761 0.965941i $$-0.416686\pi$$
0.258761 + 0.965941i $$0.416686\pi$$
$$632$$ 0 0
$$633$$ −1.00000 −0.0397464
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.00000 0.0396214
$$638$$ 0 0
$$639$$ −32.0000 −1.26590
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 0 0
$$643$$ −15.0000 −0.591542 −0.295771 0.955259i $$-0.595577\pi$$
−0.295771 + 0.955259i $$0.595577\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −32.0000 −1.25805 −0.629025 0.777385i $$-0.716546\pi$$
−0.629025 + 0.777385i $$0.716546\pi$$
$$648$$ 0 0
$$649$$ −6.00000 −0.235521
$$650$$ 0 0
$$651$$ −6.00000 −0.235159
$$652$$ 0 0
$$653$$ 24.0000 0.939193 0.469596 0.882881i $$-0.344399\pi$$
0.469596 + 0.882881i $$0.344399\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 20.0000 0.780274
$$658$$ 0 0
$$659$$ 21.0000 0.818044 0.409022 0.912525i $$-0.365870\pi$$
0.409022 + 0.912525i $$0.365870\pi$$
$$660$$ 0 0
$$661$$ −28.0000 −1.08907 −0.544537 0.838737i $$-0.683295\pi$$
−0.544537 + 0.838737i $$0.683295\pi$$
$$662$$ 0 0
$$663$$ 3.00000 0.116510
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −2.00000 −0.0774403
$$668$$ 0 0
$$669$$ −15.0000 −0.579934
$$670$$ 0 0
$$671$$ −4.00000 −0.154418
$$672$$ 0 0
$$673$$ 20.0000 0.770943 0.385472 0.922720i $$-0.374039\pi$$
0.385472 + 0.922720i $$0.374039\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −3.00000 −0.115299 −0.0576497 0.998337i $$-0.518361\pi$$
−0.0576497 + 0.998337i $$0.518361\pi$$
$$678$$ 0 0
$$679$$ −19.0000 −0.729153
$$680$$ 0 0
$$681$$ −7.00000 −0.268241
$$682$$ 0 0
$$683$$ −4.00000 −0.153056 −0.0765279 0.997067i $$-0.524383\pi$$
−0.0765279 + 0.997067i $$0.524383\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 18.0000 0.686743
$$688$$ 0 0
$$689$$ 14.0000 0.533358
$$690$$ 0 0
$$691$$ 48.0000 1.82601 0.913003 0.407953i $$-0.133757\pi$$
0.913003 + 0.407953i $$0.133757\pi$$
$$692$$ 0 0
$$693$$ 2.00000 0.0759737
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −30.0000 −1.13633
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −41.0000 −1.54855 −0.774274 0.632850i $$-0.781885\pi$$
−0.774274 + 0.632850i $$0.781885\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −17.0000 −0.638448 −0.319224 0.947679i $$-0.603422\pi$$
−0.319224 + 0.947679i $$0.603422\pi$$
$$710$$ 0 0
$$711$$ −22.0000 −0.825064
$$712$$ 0 0
$$713$$ 12.0000 0.449404
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −17.0000 −0.634877
$$718$$ 0 0
$$719$$ 50.0000 1.86469 0.932343 0.361576i $$-0.117761\pi$$
0.932343 + 0.361576i $$0.117761\pi$$
$$720$$ 0 0
$$721$$ −1.00000 −0.0372419
$$722$$ 0 0
$$723$$ 2.00000 0.0743808
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −36.0000 −1.33517 −0.667583 0.744535i $$-0.732671\pi$$
−0.667583 + 0.744535i $$0.732671\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 9.00000 0.332423 0.166211 0.986090i $$-0.446847\pi$$
0.166211 + 0.986090i $$0.446847\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 10.0000 0.368355
$$738$$ 0 0
$$739$$ −15.0000 −0.551784 −0.275892 0.961189i $$-0.588973\pi$$
−0.275892 + 0.961189i $$0.588973\pi$$
$$740$$ 0 0
$$741$$ 4.00000 0.146944
$$742$$ 0 0
$$743$$ 42.0000 1.54083 0.770415 0.637542i $$-0.220049\pi$$
0.770415 + 0.637542i $$0.220049\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −8.00000 −0.292705
$$748$$ 0 0
$$749$$ −16.0000 −0.584627
$$750$$ 0 0
$$751$$ −17.0000 −0.620339 −0.310169 0.950681i $$-0.600386\pi$$
−0.310169 + 0.950681i $$0.600386\pi$$
$$752$$ 0 0
$$753$$ −10.0000 −0.364420
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −8.00000 −0.290765 −0.145382 0.989376i $$-0.546441\pi$$
−0.145382 + 0.989376i $$0.546441\pi$$
$$758$$ 0 0
$$759$$ 2.00000 0.0725954
$$760$$ 0 0
$$761$$ 22.0000 0.797499 0.398750 0.917060i $$-0.369444\pi$$
0.398750 + 0.917060i $$0.369444\pi$$
$$762$$ 0 0
$$763$$ 15.0000 0.543036
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −6.00000 −0.216647
$$768$$ 0 0
$$769$$ −8.00000 −0.288487 −0.144244 0.989542i $$-0.546075\pi$$
−0.144244 + 0.989542i $$0.546075\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 0 0
$$773$$ 13.0000 0.467578 0.233789 0.972287i $$-0.424888\pi$$
0.233789 + 0.972287i $$0.424888\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 2.00000 0.0717496
$$778$$ 0 0
$$779$$ −40.0000 −1.43315
$$780$$ 0 0
$$781$$ 16.0000 0.572525
$$782$$ 0 0
$$783$$ 5.00000 0.178685
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −31.0000 −1.10503 −0.552515 0.833503i $$-0.686332\pi$$
−0.552515 + 0.833503i $$0.686332\pi$$
$$788$$ 0 0
$$789$$ 24.0000 0.854423
$$790$$ 0 0
$$791$$ 14.0000 0.497783
$$792$$ 0 0
$$793$$ −4.00000 −0.142044
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 27.0000 0.956389 0.478195 0.878254i $$-0.341291\pi$$
0.478195 + 0.878254i $$0.341291\pi$$
$$798$$ 0 0
$$799$$ 27.0000 0.955191
$$800$$ 0 0
$$801$$ −24.0000 −0.847998
$$802$$ 0 0
$$803$$ −10.0000 −0.352892
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −6.00000 −0.211210
$$808$$ 0 0
$$809$$ −51.0000 −1.79306 −0.896532 0.442978i $$-0.853922\pi$$
−0.896532 + 0.442978i $$0.853922\pi$$
$$810$$ 0 0
$$811$$ 42.0000 1.47482 0.737410 0.675446i $$-0.236049\pi$$
0.737410 + 0.675446i $$0.236049\pi$$
$$812$$ 0 0
$$813$$ 4.00000 0.140286
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 2.00000 0.0698857
$$820$$ 0 0
$$821$$ 45.0000 1.57051 0.785255 0.619172i $$-0.212532\pi$$
0.785255 + 0.619172i $$0.212532\pi$$
$$822$$ 0 0
$$823$$ −10.0000 −0.348578 −0.174289 0.984695i $$-0.555763\pi$$
−0.174289 + 0.984695i $$0.555763\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −42.0000 −1.46048 −0.730242 0.683189i $$-0.760592\pi$$
−0.730242 + 0.683189i $$0.760592\pi$$
$$828$$ 0 0
$$829$$ −50.0000 −1.73657 −0.868286 0.496064i $$-0.834778\pi$$
−0.868286 + 0.496064i $$0.834778\pi$$
$$830$$ 0 0
$$831$$ 18.0000 0.624413
$$832$$ 0 0
$$833$$ 3.00000 0.103944
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −30.0000 −1.03695
$$838$$ 0 0
$$839$$ −54.0000 −1.86429 −0.932144 0.362089i $$-0.882064\pi$$
−0.932144 + 0.362089i $$0.882064\pi$$
$$840$$ 0 0
$$841$$ −28.0000 −0.965517
$$842$$ 0 0
$$843$$ 15.0000 0.516627
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 10.0000 0.343604
$$848$$ 0 0
$$849$$ −21.0000 −0.720718
$$850$$ 0 0
$$851$$ −4.00000 −0.137118
$$852$$ 0 0
$$853$$ −14.0000 −0.479351 −0.239675 0.970853i $$-0.577041\pi$$
−0.239675 + 0.970853i $$0.577041\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 10.0000 0.341593 0.170797 0.985306i $$-0.445366\pi$$
0.170797 + 0.985306i $$0.445366\pi$$
$$858$$ 0 0
$$859$$ 8.00000 0.272956 0.136478 0.990643i $$-0.456422\pi$$
0.136478 + 0.990643i $$0.456422\pi$$
$$860$$ 0 0
$$861$$ 10.0000 0.340799
$$862$$ 0 0
$$863$$ 6.00000 0.204242 0.102121 0.994772i $$-0.467437\pi$$
0.102121 + 0.994772i $$0.467437\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −8.00000 −0.271694
$$868$$ 0 0
$$869$$ 11.0000 0.373149
$$870$$ 0 0
$$871$$ 10.0000 0.338837
$$872$$ 0 0
$$873$$ −38.0000 −1.28611
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −52.0000 −1.75592 −0.877958 0.478738i $$-0.841094\pi$$
−0.877958 + 0.478738i $$0.841094\pi$$
$$878$$ 0 0
$$879$$ 31.0000 1.04560
$$880$$ 0 0
$$881$$ 16.0000 0.539054 0.269527 0.962993i $$-0.413133\pi$$
0.269527 + 0.962993i $$0.413133\pi$$
$$882$$ 0 0
$$883$$ 16.0000 0.538443 0.269221 0.963078i $$-0.413234\pi$$
0.269221 + 0.963078i $$0.413234\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 12.0000 0.402921 0.201460 0.979497i $$-0.435431\pi$$
0.201460 + 0.979497i $$0.435431\pi$$
$$888$$ 0 0
$$889$$ −18.0000 −0.603701
$$890$$ 0 0
$$891$$ 1.00000 0.0335013
$$892$$ 0 0
$$893$$ 36.0000 1.20469
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 2.00000 0.0667781
$$898$$ 0 0
$$899$$ −6.00000 −0.200111
$$900$$ 0 0
$$901$$ 42.0000 1.39922
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 14.0000 0.464862 0.232431 0.972613i $$-0.425332\pi$$
0.232431 + 0.972613i $$0.425332\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ 4.00000 0.132381
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 6.00000 0.198137
$$918$$ 0 0
$$919$$ 27.0000 0.890648 0.445324 0.895370i $$-0.353089\pi$$
0.445324 + 0.895370i $$0.353089\pi$$
$$920$$ 0 0
$$921$$ −25.0000 −0.823778
$$922$$ 0 0
$$923$$ 16.0000 0.526646
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −2.00000 −0.0656886
$$928$$ 0 0
$$929$$ 14.0000 0.459325 0.229663 0.973270i $$-0.426238\pi$$
0.229663 + 0.973270i $$0.426238\pi$$
$$930$$ 0 0
$$931$$ 4.00000 0.131095
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −1.00000 −0.0326686 −0.0163343 0.999867i $$-0.505200\pi$$
−0.0163343 + 0.999867i $$0.505200\pi$$
$$938$$ 0 0
$$939$$ −7.00000 −0.228436
$$940$$ 0 0
$$941$$ −28.0000 −0.912774 −0.456387 0.889781i $$-0.650857\pi$$
−0.456387 + 0.889781i $$0.650857\pi$$
$$942$$ 0 0
$$943$$ −20.0000 −0.651290
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 30.0000 0.974869 0.487435 0.873160i $$-0.337933\pi$$
0.487435 + 0.873160i $$0.337933\pi$$
$$948$$ 0 0
$$949$$ −10.0000 −0.324614
$$950$$ 0 0
$$951$$ −12.0000 −0.389127
$$952$$ 0 0
$$953$$ −30.0000 −0.971795 −0.485898 0.874016i $$-0.661507\pi$$
−0.485898 + 0.874016i $$0.661507\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −1.00000 −0.0323254
$$958$$ 0 0
$$959$$ −8.00000 −0.258333
$$960$$ 0 0
$$961$$ 5.00000 0.161290
$$962$$ 0 0
$$963$$ −32.0000 −1.03119
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −32.0000 −1.02905 −0.514525 0.857475i $$-0.672032\pi$$
−0.514525 + 0.857475i $$0.672032\pi$$
$$968$$ 0 0
$$969$$ 12.0000 0.385496
$$970$$ 0 0
$$971$$ 18.0000 0.577647 0.288824 0.957382i $$-0.406736\pi$$
0.288824 + 0.957382i $$0.406736\pi$$
$$972$$ 0 0
$$973$$ −14.0000 −0.448819
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −40.0000 −1.27971 −0.639857 0.768494i $$-0.721006\pi$$
−0.639857 + 0.768494i $$0.721006\pi$$
$$978$$ 0 0
$$979$$ 12.0000 0.383522
$$980$$ 0 0
$$981$$ 30.0000 0.957826
$$982$$ 0 0
$$983$$ −1.00000 −0.0318950 −0.0159475 0.999873i $$-0.505076\pi$$
−0.0159475 + 0.999873i $$0.505076\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −9.00000 −0.286473
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −40.0000 −1.27064 −0.635321 0.772248i $$-0.719132\pi$$
−0.635321 + 0.772248i $$0.719132\pi$$
$$992$$ 0 0
$$993$$ −28.0000 −0.888553
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 27.0000 0.855099 0.427549 0.903992i $$-0.359377\pi$$
0.427549 + 0.903992i $$0.359377\pi$$
$$998$$ 0 0
$$999$$ 10.0000 0.316386
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 2800.2.a.u.1.1 1
4.3 odd 2 1400.2.a.d.1.1 1
5.2 odd 4 560.2.g.d.449.1 2
5.3 odd 4 560.2.g.d.449.2 2
5.4 even 2 2800.2.a.k.1.1 1
15.2 even 4 5040.2.t.a.1009.2 2
15.8 even 4 5040.2.t.a.1009.1 2
20.3 even 4 280.2.g.a.169.1 2
20.7 even 4 280.2.g.a.169.2 yes 2
20.19 odd 2 1400.2.a.j.1.1 1
28.27 even 2 9800.2.a.bb.1.1 1
40.3 even 4 2240.2.g.b.449.2 2
40.13 odd 4 2240.2.g.a.449.1 2
40.27 even 4 2240.2.g.b.449.1 2
40.37 odd 4 2240.2.g.a.449.2 2
60.23 odd 4 2520.2.t.a.1009.1 2
60.47 odd 4 2520.2.t.a.1009.2 2
140.27 odd 4 1960.2.g.a.1569.1 2
140.83 odd 4 1960.2.g.a.1569.2 2
140.139 even 2 9800.2.a.p.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.g.a.169.1 2 20.3 even 4
280.2.g.a.169.2 yes 2 20.7 even 4
560.2.g.d.449.1 2 5.2 odd 4
560.2.g.d.449.2 2 5.3 odd 4
1400.2.a.d.1.1 1 4.3 odd 2
1400.2.a.j.1.1 1 20.19 odd 2
1960.2.g.a.1569.1 2 140.27 odd 4
1960.2.g.a.1569.2 2 140.83 odd 4
2240.2.g.a.449.1 2 40.13 odd 4
2240.2.g.a.449.2 2 40.37 odd 4
2240.2.g.b.449.1 2 40.27 even 4
2240.2.g.b.449.2 2 40.3 even 4
2520.2.t.a.1009.1 2 60.23 odd 4
2520.2.t.a.1009.2 2 60.47 odd 4
2800.2.a.k.1.1 1 5.4 even 2
2800.2.a.u.1.1 1 1.1 even 1 trivial
5040.2.t.a.1009.1 2 15.8 even 4
5040.2.t.a.1009.2 2 15.2 even 4
9800.2.a.p.1.1 1 140.139 even 2
9800.2.a.bb.1.1 1 28.27 even 2