# Properties

 Label 320.2.c.d.129.2 Level $320$ Weight $2$ Character 320.129 Analytic conductor $2.555$ Analytic rank $0$ Dimension $4$ CM discriminant -20 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 320.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.55521286468$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 160) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 129.2 Root $$-0.618034i$$ of defining polynomial Character $$\chi$$ $$=$$ 320.129 Dual form 320.2.c.d.129.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.23607i q^{3} +2.23607 q^{5} +5.23607i q^{7} +1.47214 q^{9} +O(q^{10})$$ $$q-1.23607i q^{3} +2.23607 q^{5} +5.23607i q^{7} +1.47214 q^{9} -2.76393i q^{15} +6.47214 q^{21} -7.70820i q^{23} +5.00000 q^{25} -5.52786i q^{27} -6.00000 q^{29} +11.7082i q^{35} +4.47214 q^{41} +6.76393i q^{43} +3.29180 q^{45} +0.291796i q^{47} -20.4164 q^{49} -13.4164 q^{61} +7.70820i q^{63} -14.1803i q^{67} -9.52786 q^{69} -6.18034i q^{75} -2.41641 q^{81} -4.29180i q^{83} +7.41641i q^{87} -6.00000 q^{89} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 12 q^{9} + O(q^{10})$$ $$4 q - 12 q^{9} + 8 q^{21} + 20 q^{25} - 24 q^{29} + 40 q^{45} - 28 q^{49} - 56 q^{69} + 44 q^{81} - 24 q^{89} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$257$$ $$261$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ − 1.23607i − 0.713644i −0.934172 0.356822i $$-0.883860\pi$$
0.934172 0.356822i $$-0.116140\pi$$
$$4$$ 0 0
$$5$$ 2.23607 1.00000
$$6$$ 0 0
$$7$$ 5.23607i 1.97905i 0.144370 + 0.989524i $$0.453885\pi$$
−0.144370 + 0.989524i $$0.546115\pi$$
$$8$$ 0 0
$$9$$ 1.47214 0.490712
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ − 2.76393i − 0.713644i
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 6.47214 1.41234
$$22$$ 0 0
$$23$$ − 7.70820i − 1.60727i −0.595121 0.803636i $$-0.702896\pi$$
0.595121 0.803636i $$-0.297104\pi$$
$$24$$ 0 0
$$25$$ 5.00000 1.00000
$$26$$ 0 0
$$27$$ − 5.52786i − 1.06384i
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 11.7082i 1.97905i
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 4.47214 0.698430 0.349215 0.937043i $$-0.386448\pi$$
0.349215 + 0.937043i $$0.386448\pi$$
$$42$$ 0 0
$$43$$ 6.76393i 1.03149i 0.856742 + 0.515745i $$0.172485\pi$$
−0.856742 + 0.515745i $$0.827515\pi$$
$$44$$ 0 0
$$45$$ 3.29180 0.490712
$$46$$ 0 0
$$47$$ 0.291796i 0.0425628i 0.999774 + 0.0212814i $$0.00677460\pi$$
−0.999774 + 0.0212814i $$0.993225\pi$$
$$48$$ 0 0
$$49$$ −20.4164 −2.91663
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −13.4164 −1.71780 −0.858898 0.512148i $$-0.828850\pi$$
−0.858898 + 0.512148i $$0.828850\pi$$
$$62$$ 0 0
$$63$$ 7.70820i 0.971142i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ − 14.1803i − 1.73240i −0.499694 0.866202i $$-0.666554\pi$$
0.499694 0.866202i $$-0.333446\pi$$
$$68$$ 0 0
$$69$$ −9.52786 −1.14702
$$70$$ 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
$$75$$ − 6.18034i − 0.713644i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ −2.41641 −0.268490
$$82$$ 0 0
$$83$$ − 4.29180i − 0.471086i −0.971864 0.235543i $$-0.924313\pi$$
0.971864 0.235543i $$-0.0756868\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 7.41641i 0.795122i
$$88$$ 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
$$101$$ 18.0000 1.79107 0.895533 0.444994i $$-0.146794\pi$$
0.895533 + 0.444994i $$0.146794\pi$$
$$102$$ 0 0
$$103$$ 2.18034i 0.214835i 0.994214 + 0.107418i $$0.0342582\pi$$
−0.994214 + 0.107418i $$0.965742\pi$$
$$104$$ 0 0
$$105$$ 14.4721 1.41234
$$106$$ 0 0
$$107$$ 19.7082i 1.90526i 0.304125 + 0.952632i $$0.401636\pi$$
−0.304125 + 0.952632i $$0.598364\pi$$
$$108$$ 0 0
$$109$$ −13.4164 −1.28506 −0.642529 0.766261i $$-0.722115\pi$$
−0.642529 + 0.766261i $$0.722115\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ − 17.2361i − 1.60727i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ − 5.52786i − 0.498431i
$$124$$ 0 0
$$125$$ 11.1803 1.00000
$$126$$ 0 0
$$127$$ − 12.6525i − 1.12273i −0.827570 0.561363i $$-0.810277\pi$$
0.827570 0.561363i $$-0.189723\pi$$
$$128$$ 0 0
$$129$$ 8.36068 0.736117
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ − 12.3607i − 1.06384i
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0.360680 0.0303747
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −13.4164 −1.11417
$$146$$ 0 0
$$147$$ 25.2361i 2.08144i
$$148$$ 0 0
$$149$$ 4.47214 0.366372 0.183186 0.983078i $$-0.441359\pi$$
0.183186 + 0.983078i $$0.441359\pi$$
$$150$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 40.3607 3.18087
$$162$$ 0 0
$$163$$ 24.6525i 1.93093i 0.260531 + 0.965465i $$0.416102\pi$$
−0.260531 + 0.965465i $$0.583898\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ − 23.7082i − 1.83460i −0.398202 0.917298i $$-0.630366\pi$$
0.398202 0.917298i $$-0.369634\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 26.1803i 1.97905i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 16.5836i 1.22589i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 28.9443 2.10539
$$190$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −17.5279 −1.23632
$$202$$ 0 0
$$203$$ − 31.4164i − 2.20500i
$$204$$ 0 0
$$205$$ 10.0000 0.698430
$$206$$ 0 0
$$207$$ − 11.3475i − 0.788707i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 15.1246i 1.03149i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ − 18.7639i − 1.25653i −0.778001 0.628263i $$-0.783766\pi$$
0.778001 0.628263i $$-0.216234\pi$$
$$224$$ 0 0
$$225$$ 7.36068 0.490712
$$226$$ 0 0
$$227$$ − 27.1246i − 1.80032i −0.435556 0.900162i $$-0.643448\pi$$
0.435556 0.900162i $$-0.356552\pi$$
$$228$$ 0 0
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 0.652476i 0.0425628i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −13.4164 −0.864227 −0.432113 0.901819i $$-0.642232\pi$$
−0.432113 + 0.901819i $$0.642232\pi$$
$$242$$ 0 0
$$243$$ − 13.5967i − 0.872232i
$$244$$ 0 0
$$245$$ −45.6525 −2.91663
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −5.30495 −0.336188
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −8.83282 −0.546738
$$262$$ 0 0
$$263$$ 31.1246i 1.91923i 0.281324 + 0.959613i $$0.409226\pi$$
−0.281324 + 0.959613i $$0.590774\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 7.41641i 0.453877i
$$268$$ 0 0
$$269$$ 22.3607 1.36335 0.681677 0.731653i $$-0.261251\pi$$
0.681677 + 0.731653i $$0.261251\pi$$
$$270$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −31.3050 −1.86750 −0.933748 0.357930i $$-0.883483\pi$$
−0.933748 + 0.357930i $$0.883483\pi$$
$$282$$ 0 0
$$283$$ 9.81966i 0.583718i 0.956461 + 0.291859i $$0.0942738\pi$$
−0.956461 + 0.291859i $$0.905726\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 23.4164i 1.38223i
$$288$$ 0 0
$$289$$ 17.0000 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −35.4164 −2.04137
$$302$$ 0 0
$$303$$ − 22.2492i − 1.27818i
$$304$$ 0 0
$$305$$ −30.0000 −1.71780
$$306$$ 0 0
$$307$$ 21.5967i 1.23259i 0.787515 + 0.616296i $$0.211367\pi$$
−0.787515 + 0.616296i $$0.788633\pi$$
$$308$$ 0 0
$$309$$ 2.69505 0.153316
$$310$$ 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
$$315$$ 17.2361i 0.971142i
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 24.3607 1.35968
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 16.5836i 0.917075i
$$328$$ 0 0
$$329$$ −1.52786 −0.0842339
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ − 31.7082i − 1.73240i
$$336$$ 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
$$343$$ − 70.2492i − 3.79310i
$$344$$ 0 0
$$345$$ −21.3050 −1.14702
$$346$$ 0 0
$$347$$ − 3.12461i − 0.167738i −0.996477 0.0838690i $$-0.973272\pi$$
0.996477 0.0838690i $$-0.0267277\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 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
$$363$$ 13.5967i 0.713644i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 29.2361i 1.52611i 0.646333 + 0.763055i $$0.276302\pi$$
−0.646333 + 0.763055i $$0.723698\pi$$
$$368$$ 0 0
$$369$$ 6.58359 0.342728
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ − 13.8197i − 0.713644i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ −15.6393 −0.801227
$$382$$ 0 0
$$383$$ 39.1246i 1.99917i 0.0287325 + 0.999587i $$0.490853\pi$$
−0.0287325 + 0.999587i $$0.509147\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 9.95743i 0.506164i
$$388$$ 0 0
$$389$$ −31.3050 −1.58722 −0.793612 0.608424i $$-0.791802\pi$$
−0.793612 + 0.608424i $$0.791802\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 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
$$405$$ −5.40325 −0.268490
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 40.2492 1.99020 0.995098 0.0988936i $$-0.0315304\pi$$
0.995098 + 0.0988936i $$0.0315304\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ − 9.59675i − 0.471086i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 40.2492 1.96163 0.980814 0.194948i $$-0.0624538\pi$$
0.980814 + 0.194948i $$0.0624538\pi$$
$$422$$ 0 0
$$423$$ 0.429563i 0.0208861i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ − 70.2492i − 3.39960i
$$428$$ 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
$$435$$ 16.5836i 0.795122i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ −30.0557 −1.43123
$$442$$ 0 0
$$443$$ 35.7082i 1.69655i 0.529558 + 0.848274i $$0.322358\pi$$
−0.529558 + 0.848274i $$0.677642\pi$$
$$444$$ 0 0
$$445$$ −13.4164 −0.635999
$$446$$ 0 0
$$447$$ − 5.52786i − 0.261459i
$$448$$ 0 0
$$449$$ 22.3607 1.05527 0.527633 0.849473i $$-0.323080\pi$$
0.527633 + 0.849473i $$0.323080\pi$$
$$450$$ 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
$$461$$ 42.0000 1.95614 0.978068 0.208288i $$-0.0667892\pi$$
0.978068 + 0.208288i $$0.0667892\pi$$
$$462$$ 0 0
$$463$$ 20.0689i 0.932680i 0.884606 + 0.466340i $$0.154428\pi$$
−0.884606 + 0.466340i $$0.845572\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ − 43.1246i − 1.99557i −0.0665285 0.997785i $$-0.521192\pi$$
0.0665285 0.997785i $$-0.478808\pi$$
$$468$$ 0 0
$$469$$ 74.2492 3.42851
$$470$$ 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
$$483$$ − 49.8885i − 2.27001i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 11.3475i 0.514205i 0.966384 + 0.257103i $$0.0827679\pi$$
−0.966384 + 0.257103i $$0.917232\pi$$
$$488$$ 0 0
$$489$$ 30.4721 1.37800
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 0 0
$$501$$ −29.3050 −1.30925
$$502$$ 0 0
$$503$$ 24.2918i 1.08312i 0.840663 + 0.541559i $$0.182166\pi$$
−0.840663 + 0.541559i $$0.817834\pi$$
$$504$$ 0 0
$$505$$ 40.2492 1.79107
$$506$$ 0 0
$$507$$ − 16.0689i − 0.713644i
$$508$$ 0 0
$$509$$ −6.00000 −0.265945 −0.132973 0.991120i $$-0.542452\pi$$
−0.132973 + 0.991120i $$0.542452\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 4.87539i 0.214835i
$$516$$ 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
$$523$$ 45.5967i 1.99381i 0.0786374 + 0.996903i $$0.474943\pi$$
−0.0786374 + 0.996903i $$0.525057\pi$$
$$524$$ 0 0
$$525$$ 32.3607 1.41234
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −36.4164 −1.58332
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 44.0689i 1.90526i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −38.0000 −1.63375 −0.816874 0.576816i $$-0.804295\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 0 0
$$543$$ − 2.47214i − 0.106090i
$$544$$ 0 0
$$545$$ −30.0000 −1.28506
$$546$$ 0 0
$$547$$ 30.7639i 1.31537i 0.753293 + 0.657685i $$0.228464\pi$$
−0.753293 + 0.657685i $$0.771536\pi$$
$$548$$ 0 0
$$549$$ −19.7508 −0.842943
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 34.5410i 1.45573i 0.685720 + 0.727865i $$0.259487\pi$$
−0.685720 + 0.727865i $$0.740513\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ − 12.6525i − 0.531354i
$$568$$ 0 0
$$569$$ −31.3050 −1.31237 −0.656186 0.754599i $$-0.727831\pi$$
−0.656186 + 0.754599i $$0.727831\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ − 38.5410i − 1.60727i
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 22.4721 0.932301
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 26.5410i 1.09547i 0.836653 + 0.547733i $$0.184509\pi$$
−0.836653 + 0.547733i $$0.815491\pi$$
$$588$$ 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
$$601$$ 40.2492 1.64180 0.820900 0.571072i $$-0.193472\pi$$
0.820900 + 0.571072i $$0.193472\pi$$
$$602$$ 0 0
$$603$$ − 20.8754i − 0.850112i
$$604$$ 0 0
$$605$$ −24.5967 −1.00000
$$606$$ 0 0
$$607$$ − 21.8197i − 0.885633i −0.896612 0.442816i $$-0.853979\pi$$
0.896612 0.442816i $$-0.146021\pi$$
$$608$$ 0 0
$$609$$ −38.8328 −1.57359
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ − 12.3607i − 0.498431i
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ −42.6099 −1.70988
$$622$$ 0 0
$$623$$ − 31.4164i − 1.25867i
$$624$$ 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
$$635$$ − 28.2918i − 1.12273i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −49.1935 −1.94303 −0.971513 0.236986i $$-0.923841\pi$$
−0.971513 + 0.236986i $$0.923841\pi$$
$$642$$ 0 0
$$643$$ − 8.06888i − 0.318206i −0.987262 0.159103i $$-0.949140\pi$$
0.987262 0.159103i $$-0.0508601\pi$$
$$644$$ 0 0
$$645$$ 18.6950 0.736117
$$646$$ 0 0
$$647$$ − 46.5410i − 1.82972i −0.403775 0.914858i $$-0.632302\pi$$
0.403775 0.914858i $$-0.367698\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 40.2492 1.56551 0.782757 0.622328i $$-0.213813\pi$$
0.782757 + 0.622328i $$0.213813\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 46.2492i 1.79078i
$$668$$ 0 0
$$669$$ −23.1935 −0.896712
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ − 27.6393i − 1.06384i
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −33.5279 −1.28479
$$682$$ 0 0
$$683$$ − 51.1246i − 1.95623i −0.208068 0.978114i $$-0.566717\pi$$
0.208068 0.978114i $$-0.433283\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 17.3050i 0.660225i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 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
$$701$$ 22.3607 0.844551 0.422276 0.906467i $$-0.361231\pi$$
0.422276 + 0.906467i $$0.361231\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0.806504 0.0303747
$$706$$ 0 0
$$707$$ 94.2492i 3.54461i
$$708$$ 0 0
$$709$$ −46.0000 −1.72757 −0.863783 0.503864i $$-0.831911\pi$$
−0.863783 + 0.503864i $$0.831911\pi$$
$$710$$ 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
$$721$$ −11.4164 −0.425169
$$722$$ 0 0
$$723$$ 16.5836i 0.616750i
$$724$$ 0 0
$$725$$ −30.0000 −1.11417
$$726$$ 0 0
$$727$$ 41.0132i 1.52109i 0.649283 + 0.760547i $$0.275069\pi$$
−0.649283 + 0.760547i $$0.724931\pi$$
$$728$$ 0 0
$$729$$ −24.0557 −0.890953
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 56.4296i 2.08144i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ − 14.5410i − 0.533458i −0.963772 0.266729i $$-0.914057\pi$$
0.963772 0.266729i $$-0.0859429\pi$$
$$744$$ 0 0
$$745$$ 10.0000 0.366372
$$746$$ 0 0
$$747$$ − 6.31811i − 0.231167i
$$748$$ 0 0
$$749$$ −103.193 −3.77061
$$750$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 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
$$763$$ − 70.2492i − 2.54319i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 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
$$783$$ 33.1672i 1.18530i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ − 56.0689i − 1.99864i −0.0368739 0.999320i $$-0.511740\pi$$
0.0368739 0.999320i $$-0.488260\pi$$
$$788$$ 0 0
$$789$$ 38.4721 1.36964
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −8.83282 −0.312092
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 90.2492 3.18087
$$806$$ 0 0
$$807$$ − 27.6393i − 0.972950i
$$808$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 55.1246i 1.93093i
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −31.3050 −1.09255 −0.546275 0.837606i $$-0.683955\pi$$
−0.546275 + 0.837606i $$0.683955\pi$$
$$822$$ 0 0
$$823$$ 50.1803i 1.74918i 0.484866 + 0.874588i $$0.338868\pi$$
−0.484866 + 0.874588i $$0.661132\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 10.5410i 0.366547i 0.983062 + 0.183274i $$0.0586694\pi$$
−0.983062 + 0.183274i $$0.941331\pi$$
$$828$$ 0 0
$$829$$ −13.4164 −0.465971 −0.232986 0.972480i $$-0.574849\pi$$
−0.232986 + 0.972480i $$0.574849\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ − 53.0132i − 1.83460i
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ 38.6950i 1.33273i
$$844$$ 0 0
$$845$$ 29.0689 1.00000
$$846$$ 0 0
$$847$$ − 57.5967i − 1.97905i
$$848$$ 0 0
$$849$$ 12.1378 0.416567
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 28.9443 0.986418
$$862$$ 0 0
$$863$$ − 47.7082i − 1.62401i −0.583653 0.812003i $$-0.698377\pi$$
0.583653 0.812003i $$-0.301623\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ − 21.0132i − 0.713644i
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 58.5410i 1.97905i
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 58.1378 1.95871 0.979356 0.202145i $$-0.0647913\pi$$
0.979356 + 0.202145i $$0.0647913\pi$$
$$882$$ 0 0
$$883$$ − 23.3475i − 0.785707i −0.919601 0.392853i $$-0.871488\pi$$
0.919601 0.392853i $$-0.128512\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ − 16.8754i − 0.566620i −0.959028 0.283310i $$-0.908567\pi$$
0.959028 0.283310i $$-0.0914325\pi$$
$$888$$ 0 0
$$889$$ 66.2492 2.22193
$$890$$ 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
$$903$$ 43.7771i 1.45681i
$$904$$ 0 0
$$905$$ 4.47214 0.148659
$$906$$ 0 0
$$907$$ 39.4853i 1.31109i 0.755157 + 0.655544i $$0.227561\pi$$
−0.755157 + 0.655544i $$0.772439\pi$$
$$908$$ 0 0
$$909$$ 26.4984 0.878898
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 37.0820i 1.22589i
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ 26.6950 0.879632
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 3.20976i 0.105422i
$$928$$ 0 0
$$929$$ −49.1935 −1.61399 −0.806993 0.590561i $$-0.798907\pi$$
−0.806993 + 0.590561i $$0.798907\pi$$
$$930$$ 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
$$941$$ 42.0000 1.36916 0.684580 0.728937i $$-0.259985\pi$$
0.684580 + 0.728937i $$0.259985\pi$$
$$942$$ 0 0
$$943$$ − 34.4721i − 1.12257i
$$944$$ 0 0
$$945$$ 64.7214 2.10539
$$946$$ 0 0
$$947$$ − 36.2918i − 1.17932i −0.807650 0.589662i $$-0.799261\pi$$
0.807650 0.589662i $$-0.200739\pi$$
$$948$$ 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
$$963$$ 29.0132i 0.934936i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ − 3.93112i − 0.126416i −0.998000 0.0632081i $$-0.979867\pi$$
0.998000 0.0632081i $$-0.0201332\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 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
$$981$$ −19.7508 −0.630594
$$982$$ 0 0
$$983$$ − 62.5410i − 1.99475i −0.0724180 0.997374i $$-0.523072\pi$$
0.0724180 0.997374i $$-0.476928\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 1.88854i 0.0601130i
$$988$$ 0 0
$$989$$ 52.1378 1.65788
$$990$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 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 320.2.c.d.129.2 4
3.2 odd 2 2880.2.f.w.1729.2 4
4.3 odd 2 inner 320.2.c.d.129.3 4
5.2 odd 4 1600.2.a.bd.1.1 2
5.3 odd 4 1600.2.a.z.1.2 2
5.4 even 2 inner 320.2.c.d.129.3 4
8.3 odd 2 160.2.c.b.129.2 4
8.5 even 2 160.2.c.b.129.3 yes 4
12.11 even 2 2880.2.f.w.1729.1 4
15.14 odd 2 2880.2.f.w.1729.1 4
16.3 odd 4 1280.2.f.h.129.1 4
16.5 even 4 1280.2.f.h.129.2 4
16.11 odd 4 1280.2.f.g.129.4 4
16.13 even 4 1280.2.f.g.129.3 4
20.3 even 4 1600.2.a.bd.1.1 2
20.7 even 4 1600.2.a.z.1.2 2
20.19 odd 2 CM 320.2.c.d.129.2 4
24.5 odd 2 1440.2.f.i.289.4 4
24.11 even 2 1440.2.f.i.289.3 4
40.3 even 4 800.2.a.j.1.2 2
40.13 odd 4 800.2.a.n.1.1 2
40.19 odd 2 160.2.c.b.129.3 yes 4
40.27 even 4 800.2.a.n.1.1 2
40.29 even 2 160.2.c.b.129.2 4
40.37 odd 4 800.2.a.j.1.2 2
60.59 even 2 2880.2.f.w.1729.2 4
80.19 odd 4 1280.2.f.g.129.3 4
80.29 even 4 1280.2.f.h.129.1 4
80.59 odd 4 1280.2.f.h.129.2 4
80.69 even 4 1280.2.f.g.129.4 4
120.29 odd 2 1440.2.f.i.289.3 4
120.53 even 4 7200.2.a.cr.1.2 2
120.59 even 2 1440.2.f.i.289.4 4
120.77 even 4 7200.2.a.cb.1.1 2
120.83 odd 4 7200.2.a.cb.1.1 2
120.107 odd 4 7200.2.a.cr.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.2 4 8.3 odd 2
160.2.c.b.129.2 4 40.29 even 2
160.2.c.b.129.3 yes 4 8.5 even 2
160.2.c.b.129.3 yes 4 40.19 odd 2
320.2.c.d.129.2 4 1.1 even 1 trivial
320.2.c.d.129.2 4 20.19 odd 2 CM
320.2.c.d.129.3 4 4.3 odd 2 inner
320.2.c.d.129.3 4 5.4 even 2 inner
800.2.a.j.1.2 2 40.3 even 4
800.2.a.j.1.2 2 40.37 odd 4
800.2.a.n.1.1 2 40.13 odd 4
800.2.a.n.1.1 2 40.27 even 4
1280.2.f.g.129.3 4 16.13 even 4
1280.2.f.g.129.3 4 80.19 odd 4
1280.2.f.g.129.4 4 16.11 odd 4
1280.2.f.g.129.4 4 80.69 even 4
1280.2.f.h.129.1 4 16.3 odd 4
1280.2.f.h.129.1 4 80.29 even 4
1280.2.f.h.129.2 4 16.5 even 4
1280.2.f.h.129.2 4 80.59 odd 4
1440.2.f.i.289.3 4 24.11 even 2
1440.2.f.i.289.3 4 120.29 odd 2
1440.2.f.i.289.4 4 24.5 odd 2
1440.2.f.i.289.4 4 120.59 even 2
1600.2.a.z.1.2 2 5.3 odd 4
1600.2.a.z.1.2 2 20.7 even 4
1600.2.a.bd.1.1 2 5.2 odd 4
1600.2.a.bd.1.1 2 20.3 even 4
2880.2.f.w.1729.1 4 12.11 even 2
2880.2.f.w.1729.1 4 15.14 odd 2
2880.2.f.w.1729.2 4 3.2 odd 2
2880.2.f.w.1729.2 4 60.59 even 2
7200.2.a.cb.1.1 2 120.77 even 4
7200.2.a.cb.1.1 2 120.83 odd 4
7200.2.a.cr.1.2 2 120.53 even 4
7200.2.a.cr.1.2 2 120.107 odd 4