# Properties

 Label 640.2.f.f.449.1 Level $640$ Weight $2$ Character 640.449 Analytic conductor $5.110$ Analytic rank $0$ Dimension $4$ CM discriminant -20 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$640 = 2^{7} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 640.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.11042572936$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-5})$$ Defining polynomial: $$x^{4} - 4 x^{2} + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 449.1 Root $$1.58114 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 640.449 Dual form 640.2.f.f.449.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.16228 q^{3} -2.23607i q^{5} -4.24264i q^{7} +7.00000 q^{9} +O(q^{10})$$ $$q-3.16228 q^{3} -2.23607i q^{5} -4.24264i q^{7} +7.00000 q^{9} +7.07107i q^{15} +13.4164i q^{21} -1.41421i q^{23} -5.00000 q^{25} -12.6491 q^{27} -8.94427i q^{29} -9.48683 q^{35} -12.0000 q^{41} -3.16228 q^{43} -15.6525i q^{45} +9.89949i q^{47} -11.0000 q^{49} +13.4164i q^{61} -29.6985i q^{63} +15.8114 q^{67} +4.47214i q^{69} +15.8114 q^{75} +19.0000 q^{81} -9.48683 q^{83} +28.2843i q^{87} -6.00000 q^{89} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 28 q^{9} + O(q^{10})$$ $$4 q + 28 q^{9} - 20 q^{25} - 48 q^{41} - 44 q^{49} + 76 q^{81} - 24 q^{89} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$261$$ $$511$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$3$$ −3.16228 −1.82574 −0.912871 0.408248i $$-0.866140\pi$$
−0.912871 + 0.408248i $$0.866140\pi$$
$$4$$ 0 0
$$5$$ − 2.23607i − 1.00000i
$$6$$ 0 0
$$7$$ − 4.24264i − 1.60357i −0.597614 0.801784i $$-0.703885\pi$$
0.597614 0.801784i $$-0.296115\pi$$
$$8$$ 0 0
$$9$$ 7.00000 2.33333
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 7.07107i 1.82574i
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 13.4164i 2.92770i
$$22$$ 0 0
$$23$$ − 1.41421i − 0.294884i −0.989071 0.147442i $$-0.952896\pi$$
0.989071 0.147442i $$-0.0471040\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 0 0
$$27$$ −12.6491 −2.43432
$$28$$ 0 0
$$29$$ − 8.94427i − 1.66091i −0.557086 0.830455i $$-0.688081\pi$$
0.557086 0.830455i $$-0.311919\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −9.48683 −1.60357
$$36$$ 0 0
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −12.0000 −1.87409 −0.937043 0.349215i $$-0.886448\pi$$
−0.937043 + 0.349215i $$0.886448\pi$$
$$42$$ 0 0
$$43$$ −3.16228 −0.482243 −0.241121 0.970495i $$-0.577515\pi$$
−0.241121 + 0.970495i $$0.577515\pi$$
$$44$$ 0 0
$$45$$ − 15.6525i − 2.33333i
$$46$$ 0 0
$$47$$ 9.89949i 1.44399i 0.691898 + 0.721995i $$0.256775\pi$$
−0.691898 + 0.721995i $$0.743225\pi$$
$$48$$ 0 0
$$49$$ −11.0000 −1.57143
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 13.4164i 1.71780i 0.512148 + 0.858898i $$0.328850\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 0 0
$$63$$ − 29.6985i − 3.74166i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 15.8114 1.93167 0.965834 0.259161i $$-0.0834459\pi$$
0.965834 + 0.259161i $$0.0834459\pi$$
$$68$$ 0 0
$$69$$ 4.47214i 0.538382i
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 15.8114 1.82574
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 19.0000 2.11111
$$82$$ 0 0
$$83$$ −9.48683 −1.04132 −0.520658 0.853766i $$-0.674313\pi$$
−0.520658 + 0.853766i $$0.674313\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 28.2843i 3.03239i
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 8.94427i 0.889988i 0.895533 + 0.444994i $$0.146794\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 0 0
$$103$$ − 12.7279i − 1.25412i −0.778971 0.627060i $$-0.784258\pi$$
0.778971 0.627060i $$-0.215742\pi$$
$$104$$ 0 0
$$105$$ 30.0000 2.92770
$$106$$ 0 0
$$107$$ −9.48683 −0.917127 −0.458563 0.888662i $$-0.651636\pi$$
−0.458563 + 0.888662i $$0.651636\pi$$
$$108$$ 0 0
$$109$$ − 13.4164i − 1.28506i −0.766261 0.642529i $$-0.777885\pi$$
0.766261 0.642529i $$-0.222115\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ −3.16228 −0.294884
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 0 0
$$123$$ 37.9473 3.42160
$$124$$ 0 0
$$125$$ 11.1803i 1.00000i
$$126$$ 0 0
$$127$$ − 4.24264i − 0.376473i −0.982124 0.188237i $$-0.939723\pi$$
0.982124 0.188237i $$-0.0602772\pi$$
$$128$$ 0 0
$$129$$ 10.0000 0.880451
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 28.2843i 2.43432i
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ − 31.3050i − 2.63635i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −20.0000 −1.66091
$$146$$ 0 0
$$147$$ 34.7851 2.86902
$$148$$ 0 0
$$149$$ 4.47214i 0.366372i 0.983078 + 0.183186i $$0.0586410\pi$$
−0.983078 + 0.183186i $$0.941359\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −6.00000 −0.472866
$$162$$ 0 0
$$163$$ 22.1359 1.73382 0.866910 0.498464i $$-0.166102\pi$$
0.866910 + 0.498464i $$0.166102\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ − 24.0416i − 1.86040i −0.367057 0.930199i $$-0.619634\pi$$
0.367057 0.930199i $$-0.380366\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 21.2132i 1.60357i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ − 26.8328i − 1.99447i −0.0743294 0.997234i $$-0.523682\pi$$
0.0743294 0.997234i $$-0.476318\pi$$
$$182$$ 0 0
$$183$$ − 42.4264i − 3.13625i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 53.6656i 3.90360i
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −50.0000 −3.52673
$$202$$ 0 0
$$203$$ −37.9473 −2.66338
$$204$$ 0 0
$$205$$ 26.8328i 1.87409i
$$206$$ 0 0
$$207$$ − 9.89949i − 0.688062i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 7.07107i 0.482243i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 29.6985i 1.98876i 0.105881 + 0.994379i $$0.466234\pi$$
−0.105881 + 0.994379i $$0.533766\pi$$
$$224$$ 0 0
$$225$$ −35.0000 −2.33333
$$226$$ 0 0
$$227$$ −28.4605 −1.88899 −0.944495 0.328526i $$-0.893448\pi$$
−0.944495 + 0.328526i $$0.893448\pi$$
$$228$$ 0 0
$$229$$ − 26.8328i − 1.77316i −0.462573 0.886581i $$-0.653074\pi$$
0.462573 0.886581i $$-0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 22.1359 1.44399
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 28.0000 1.80364 0.901819 0.432113i $$-0.142232\pi$$
0.901819 + 0.432113i $$0.142232\pi$$
$$242$$ 0 0
$$243$$ −22.1359 −1.42002
$$244$$ 0 0
$$245$$ 24.5967i 1.57143i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 30.0000 1.90117
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ − 62.6099i − 3.87546i
$$262$$ 0 0
$$263$$ − 15.5563i − 0.959246i −0.877475 0.479623i $$-0.840774\pi$$
0.877475 0.479623i $$-0.159226\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 18.9737 1.16117
$$268$$ 0 0
$$269$$ − 22.3607i − 1.36335i −0.731653 0.681677i $$-0.761251\pi$$
0.731653 0.681677i $$-0.238749\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 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
$$283$$ 15.8114 0.939889 0.469945 0.882696i $$-0.344274\pi$$
0.469945 + 0.882696i $$0.344274\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 50.9117i 3.00522i
$$288$$ 0 0
$$289$$ 17.0000 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 13.4164i 0.773309i
$$302$$ 0 0
$$303$$ − 28.2843i − 1.62489i
$$304$$ 0 0
$$305$$ 30.0000 1.71780
$$306$$ 0 0
$$307$$ −34.7851 −1.98529 −0.992644 0.121070i $$-0.961367\pi$$
−0.992644 + 0.121070i $$0.961367\pi$$
$$308$$ 0 0
$$309$$ 40.2492i 2.28970i
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ −66.4078 −3.74166
$$316$$ 0 0
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 30.0000 1.67444
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 42.4264i 2.34619i
$$328$$ 0 0
$$329$$ 42.0000 2.31553
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ − 35.3553i − 1.93167i
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 16.9706i 0.916324i
$$344$$ 0 0
$$345$$ 10.0000 0.538382
$$346$$ 0 0
$$347$$ −28.4605 −1.52784 −0.763920 0.645311i $$-0.776728\pi$$
−0.763920 + 0.645311i $$0.776728\pi$$
$$348$$ 0 0
$$349$$ 26.8328i 1.43633i 0.695874 + 0.718164i $$0.255017\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ 19.0000 1.00000
$$362$$ 0 0
$$363$$ −34.7851 −1.82574
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ − 38.1838i − 1.99318i −0.0825348 0.996588i $$-0.526302\pi$$
0.0825348 0.996588i $$-0.473698\pi$$
$$368$$ 0 0
$$369$$ −84.0000 −4.37287
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$374$$ 0 0
$$375$$ − 35.3553i − 1.82574i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 13.4164i 0.687343i
$$382$$ 0 0
$$383$$ − 26.8701i − 1.37300i −0.727132 0.686498i $$-0.759147\pi$$
0.727132 0.686498i $$-0.240853\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −22.1359 −1.12523
$$388$$ 0 0
$$389$$ − 31.3050i − 1.58722i −0.608424 0.793612i $$-0.708198\pi$$
0.608424 0.793612i $$-0.291802\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ − 42.4853i − 2.11111i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 4.00000 0.197787 0.0988936 0.995098i $$-0.468470\pi$$
0.0988936 + 0.995098i $$0.468470\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 21.2132i 1.04132i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 40.2492i 1.96163i 0.194948 + 0.980814i $$0.437546\pi$$
−0.194948 + 0.980814i $$0.562454\pi$$
$$422$$ 0 0
$$423$$ 69.2965i 3.36931i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 56.9210 2.75460
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 63.2456 3.03239
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ −77.0000 −3.66667
$$442$$ 0 0
$$443$$ −9.48683 −0.450733 −0.225367 0.974274i $$-0.572358\pi$$
−0.225367 + 0.974274i $$0.572358\pi$$
$$444$$ 0 0
$$445$$ 13.4164i 0.635999i
$$446$$ 0 0
$$447$$ − 14.1421i − 0.668900i
$$448$$ 0 0
$$449$$ −36.0000 −1.69895 −0.849473 0.527633i $$-0.823080\pi$$
−0.849473 + 0.527633i $$0.823080\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ − 8.94427i − 0.416576i −0.978068 0.208288i $$-0.933211\pi$$
0.978068 0.208288i $$-0.0667892\pi$$
$$462$$ 0 0
$$463$$ − 12.7279i − 0.591517i −0.955263 0.295758i $$-0.904428\pi$$
0.955263 0.295758i $$-0.0955723\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −28.4605 −1.31699 −0.658497 0.752583i $$-0.728808\pi$$
−0.658497 + 0.752583i $$0.728808\pi$$
$$468$$ 0 0
$$469$$ − 67.0820i − 3.09756i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 18.9737 0.863332
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ − 38.1838i − 1.73027i −0.501538 0.865136i $$-0.667232\pi$$
0.501538 0.865136i $$-0.332768\pi$$
$$488$$ 0 0
$$489$$ −70.0000 −3.16551
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 76.0263i 3.39661i
$$502$$ 0 0
$$503$$ 43.8406i 1.95476i 0.211498 + 0.977378i $$0.432166\pi$$
−0.211498 + 0.977378i $$0.567834\pi$$
$$504$$ 0 0
$$505$$ 20.0000 0.889988
$$506$$ 0 0
$$507$$ 41.1096 1.82574
$$508$$ 0 0
$$509$$ − 44.7214i − 1.98224i −0.132973 0.991120i $$-0.542452\pi$$
0.132973 0.991120i $$-0.457548\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −28.4605 −1.25412
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 42.0000 1.84005 0.920027 0.391856i $$-0.128167\pi$$
0.920027 + 0.391856i $$0.128167\pi$$
$$522$$ 0 0
$$523$$ −34.7851 −1.52104 −0.760522 0.649312i $$-0.775057\pi$$
−0.760522 + 0.649312i $$0.775057\pi$$
$$524$$ 0 0
$$525$$ − 67.0820i − 2.92770i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 21.0000 0.913043
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 21.2132i 0.917127i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 26.8328i 1.15363i 0.816874 + 0.576816i $$0.195705\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 0 0
$$543$$ 84.8528i 3.64138i
$$544$$ 0 0
$$545$$ −30.0000 −1.28506
$$546$$ 0 0
$$547$$ −3.16228 −0.135209 −0.0676046 0.997712i $$-0.521536\pi$$
−0.0676046 + 0.997712i $$0.521536\pi$$
$$548$$ 0 0
$$549$$ 93.9149i 4.00819i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 47.4342 1.99911 0.999556 0.0298010i $$-0.00948736\pi$$
0.999556 + 0.0298010i $$0.00948736\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ − 80.6102i − 3.38531i
$$568$$ 0 0
$$569$$ 36.0000 1.50920 0.754599 0.656186i $$-0.227831\pi$$
0.754599 + 0.656186i $$0.227831\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 7.07107i 0.294884i
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 40.2492i 1.66982i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 47.4342 1.95782 0.978909 0.204298i $$-0.0654911\pi$$
0.978909 + 0.204298i $$0.0654911\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −28.0000 −1.14214 −0.571072 0.820900i $$-0.693472\pi$$
−0.571072 + 0.820900i $$0.693472\pi$$
$$602$$ 0 0
$$603$$ 110.680 4.50723
$$604$$ 0 0
$$605$$ − 24.5967i − 1.00000i
$$606$$ 0 0
$$607$$ − 46.6690i − 1.89424i −0.320882 0.947119i $$-0.603979\pi$$
0.320882 0.947119i $$-0.396021\pi$$
$$608$$ 0 0
$$609$$ 120.000 4.86265
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ − 84.8528i − 3.42160i
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 17.8885i 0.717843i
$$622$$ 0 0
$$623$$ 25.4558i 1.01987i
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −9.48683 −0.376473
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 12.0000 0.473972 0.236986 0.971513i $$-0.423841\pi$$
0.236986 + 0.971513i $$0.423841\pi$$
$$642$$ 0 0
$$643$$ 41.1096 1.62120 0.810602 0.585597i $$-0.199140\pi$$
0.810602 + 0.585597i $$0.199140\pi$$
$$644$$ 0 0
$$645$$ − 22.3607i − 0.880451i
$$646$$ 0 0
$$647$$ 18.3848i 0.722780i 0.932415 + 0.361390i $$0.117698\pi$$
−0.932415 + 0.361390i $$0.882302\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ − 40.2492i − 1.56551i −0.622328 0.782757i $$-0.713813\pi$$
0.622328 0.782757i $$-0.286187\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −12.6491 −0.489776
$$668$$ 0 0
$$669$$ − 93.9149i − 3.63096i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 63.2456 2.43432
$$676$$ 0 0
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 90.0000 3.44881
$$682$$ 0 0
$$683$$ −28.4605 −1.08901 −0.544505 0.838757i $$-0.683283\pi$$
−0.544505 + 0.838757i $$0.683283\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 84.8528i 3.23734i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 22.3607i 0.844551i 0.906467 + 0.422276i $$0.138769\pi$$
−0.906467 + 0.422276i $$0.861231\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ −70.0000 −2.63635
$$706$$ 0 0
$$707$$ 37.9473 1.42716
$$708$$ 0 0
$$709$$ − 26.8328i − 1.00773i −0.863783 0.503864i $$-0.831911\pi$$
0.863783 0.503864i $$-0.168089\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ −54.0000 −2.01107
$$722$$ 0 0
$$723$$ −88.5438 −3.29298
$$724$$ 0 0
$$725$$ 44.7214i 1.66091i
$$726$$ 0 0
$$727$$ − 4.24264i − 0.157351i −0.996900 0.0786754i $$-0.974931\pi$$
0.996900 0.0786754i $$-0.0250691\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ − 77.7817i − 2.86902i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ − 26.8701i − 0.985767i −0.870095 0.492883i $$-0.835943\pi$$
0.870095 0.492883i $$-0.164057\pi$$
$$744$$ 0 0
$$745$$ 10.0000 0.366372
$$746$$ 0 0
$$747$$ −66.4078 −2.42974
$$748$$ 0 0
$$749$$ 40.2492i 1.47067i
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −42.0000 −1.52250 −0.761249 0.648459i $$-0.775414\pi$$
−0.761249 + 0.648459i $$0.775414\pi$$
$$762$$ 0 0
$$763$$ −56.9210 −2.06068
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 113.137i 4.04319i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 41.1096 1.46540 0.732700 0.680552i $$-0.238260\pi$$
0.732700 + 0.680552i $$0.238260\pi$$
$$788$$ 0 0
$$789$$ 49.1935i 1.75133i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −42.0000 −1.48400
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 13.4164i 0.472866i
$$806$$ 0 0
$$807$$ 70.7107i 2.48913i
$$808$$ 0 0
$$809$$ −54.0000 −1.89854 −0.949269 0.314464i $$-0.898175\pi$$
−0.949269 + 0.314464i $$0.898175\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ − 49.4975i − 1.73382i
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 31.3050i 1.09255i 0.837606 + 0.546275i $$0.183955\pi$$
−0.837606 + 0.546275i $$0.816045\pi$$
$$822$$ 0 0
$$823$$ 55.1543i 1.92256i 0.275575 + 0.961280i $$0.411132\pi$$
−0.275575 + 0.961280i $$0.588868\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 47.4342 1.64945 0.824724 0.565536i $$-0.191331\pi$$
0.824724 + 0.565536i $$0.191331\pi$$
$$828$$ 0 0
$$829$$ 13.4164i 0.465971i 0.972480 + 0.232986i $$0.0748495\pi$$
−0.972480 + 0.232986i $$0.925151\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −53.7587 −1.86040
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ −51.0000 −1.75862
$$842$$ 0 0
$$843$$ 37.9473 1.30698
$$844$$ 0 0
$$845$$ 29.0689i 1.00000i
$$846$$ 0 0
$$847$$ − 46.6690i − 1.60357i
$$848$$ 0 0
$$849$$ −50.0000 −1.71600
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ − 160.997i − 5.48676i
$$862$$ 0 0
$$863$$ − 57.9828i − 1.97376i −0.161468 0.986878i $$-0.551623\pi$$
0.161468 0.986878i $$-0.448377\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −53.7587 −1.82574
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 47.4342 1.60357
$$876$$ 0 0
$$877$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 12.0000 0.404290 0.202145 0.979356i $$-0.435209\pi$$
0.202145 + 0.979356i $$0.435209\pi$$
$$882$$ 0 0
$$883$$ 22.1359 0.744934 0.372467 0.928045i $$-0.378512\pi$$
0.372467 + 0.928045i $$0.378512\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 52.3259i 1.75693i 0.477805 + 0.878466i $$0.341433\pi$$
−0.477805 + 0.878466i $$0.658567\pi$$
$$888$$ 0 0
$$889$$ −18.0000 −0.603701
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ − 42.4264i − 1.41186i
$$904$$ 0 0
$$905$$ −60.0000 −1.99447
$$906$$ 0 0
$$907$$ −60.0833 −1.99503 −0.997516 0.0704373i $$-0.977561\pi$$
−0.997516 + 0.0704373i $$0.977561\pi$$
$$908$$ 0 0
$$909$$ 62.6099i 2.07664i
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ −94.8683 −3.13625
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ 110.000 3.62462
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ − 89.0955i − 2.92628i
$$928$$ 0 0
$$929$$ −36.0000 −1.18112 −0.590561 0.806993i $$-0.701093\pi$$
−0.590561 + 0.806993i $$0.701093\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ − 44.7214i − 1.45787i −0.684580 0.728937i $$-0.740015\pi$$
0.684580 0.728937i $$-0.259985\pi$$
$$942$$ 0 0
$$943$$ 16.9706i 0.552638i
$$944$$ 0 0
$$945$$ 120.000 3.90360
$$946$$ 0 0
$$947$$ −9.48683 −0.308281 −0.154140 0.988049i $$-0.549261\pi$$
−0.154140 + 0.988049i $$0.549261\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ −66.4078 −2.13996
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ − 46.6690i − 1.50078i −0.660998 0.750388i $$-0.729867\pi$$
0.660998 0.750388i $$-0.270133\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ − 93.9149i − 2.99847i
$$982$$ 0 0
$$983$$ 41.0122i 1.30809i 0.756457 + 0.654043i $$0.226928\pi$$
−0.756457 + 0.654043i $$0.773072\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −132.816 −4.22757
$$988$$ 0 0
$$989$$ 4.47214i 0.142206i
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 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 640.2.f.f.449.1 4
4.3 odd 2 inner 640.2.f.f.449.3 yes 4
5.2 odd 4 3200.2.d.i.1601.4 4
5.3 odd 4 3200.2.d.i.1601.1 4
5.4 even 2 inner 640.2.f.f.449.3 yes 4
8.3 odd 2 inner 640.2.f.f.449.2 yes 4
8.5 even 2 inner 640.2.f.f.449.4 yes 4
16.3 odd 4 1280.2.c.f.769.3 4
16.5 even 4 1280.2.c.f.769.4 4
16.11 odd 4 1280.2.c.f.769.2 4
16.13 even 4 1280.2.c.f.769.1 4
20.3 even 4 3200.2.d.i.1601.4 4
20.7 even 4 3200.2.d.i.1601.1 4
20.19 odd 2 CM 640.2.f.f.449.1 4
40.3 even 4 3200.2.d.i.1601.2 4
40.13 odd 4 3200.2.d.i.1601.3 4
40.19 odd 2 inner 640.2.f.f.449.4 yes 4
40.27 even 4 3200.2.d.i.1601.3 4
40.29 even 2 inner 640.2.f.f.449.2 yes 4
40.37 odd 4 3200.2.d.i.1601.2 4
80.3 even 4 6400.2.a.cv.1.1 4
80.13 odd 4 6400.2.a.cv.1.4 4
80.19 odd 4 1280.2.c.f.769.1 4
80.27 even 4 6400.2.a.cv.1.2 4
80.29 even 4 1280.2.c.f.769.3 4
80.37 odd 4 6400.2.a.cv.1.3 4
80.43 even 4 6400.2.a.cv.1.3 4
80.53 odd 4 6400.2.a.cv.1.2 4
80.59 odd 4 1280.2.c.f.769.4 4
80.67 even 4 6400.2.a.cv.1.4 4
80.69 even 4 1280.2.c.f.769.2 4
80.77 odd 4 6400.2.a.cv.1.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.f.f.449.1 4 1.1 even 1 trivial
640.2.f.f.449.1 4 20.19 odd 2 CM
640.2.f.f.449.2 yes 4 8.3 odd 2 inner
640.2.f.f.449.2 yes 4 40.29 even 2 inner
640.2.f.f.449.3 yes 4 4.3 odd 2 inner
640.2.f.f.449.3 yes 4 5.4 even 2 inner
640.2.f.f.449.4 yes 4 8.5 even 2 inner
640.2.f.f.449.4 yes 4 40.19 odd 2 inner
1280.2.c.f.769.1 4 16.13 even 4
1280.2.c.f.769.1 4 80.19 odd 4
1280.2.c.f.769.2 4 16.11 odd 4
1280.2.c.f.769.2 4 80.69 even 4
1280.2.c.f.769.3 4 16.3 odd 4
1280.2.c.f.769.3 4 80.29 even 4
1280.2.c.f.769.4 4 16.5 even 4
1280.2.c.f.769.4 4 80.59 odd 4
3200.2.d.i.1601.1 4 5.3 odd 4
3200.2.d.i.1601.1 4 20.7 even 4
3200.2.d.i.1601.2 4 40.3 even 4
3200.2.d.i.1601.2 4 40.37 odd 4
3200.2.d.i.1601.3 4 40.13 odd 4
3200.2.d.i.1601.3 4 40.27 even 4
3200.2.d.i.1601.4 4 5.2 odd 4
3200.2.d.i.1601.4 4 20.3 even 4
6400.2.a.cv.1.1 4 80.3 even 4
6400.2.a.cv.1.1 4 80.77 odd 4
6400.2.a.cv.1.2 4 80.27 even 4
6400.2.a.cv.1.2 4 80.53 odd 4
6400.2.a.cv.1.3 4 80.37 odd 4
6400.2.a.cv.1.3 4 80.43 even 4
6400.2.a.cv.1.4 4 80.13 odd 4
6400.2.a.cv.1.4 4 80.67 even 4