# Properties

 Label 320.2.a.a.1.1 Level $320$ Weight $2$ Character 320.1 Self dual yes Analytic conductor $2.555$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 320.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$2.55521286468$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 20) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 320.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{3} +1.00000 q^{5} -2.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-2.00000 q^{3} +1.00000 q^{5} -2.00000 q^{7} +1.00000 q^{9} -2.00000 q^{13} -2.00000 q^{15} -6.00000 q^{17} -4.00000 q^{19} +4.00000 q^{21} -6.00000 q^{23} +1.00000 q^{25} +4.00000 q^{27} -6.00000 q^{29} +4.00000 q^{31} -2.00000 q^{35} -2.00000 q^{37} +4.00000 q^{39} +6.00000 q^{41} -10.0000 q^{43} +1.00000 q^{45} +6.00000 q^{47} -3.00000 q^{49} +12.0000 q^{51} +6.00000 q^{53} +8.00000 q^{57} +12.0000 q^{59} -2.00000 q^{61} -2.00000 q^{63} -2.00000 q^{65} +2.00000 q^{67} +12.0000 q^{69} +12.0000 q^{71} +2.00000 q^{73} -2.00000 q^{75} -8.00000 q^{79} -11.0000 q^{81} +6.00000 q^{83} -6.00000 q^{85} +12.0000 q^{87} -6.00000 q^{89} +4.00000 q^{91} -8.00000 q^{93} -4.00000 q^{95} +2.00000 q^{97} +O(q^{100})$$

## 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
$$3$$ −2.00000 −1.15470 −0.577350 0.816497i $$-0.695913\pi$$
−0.577350 + 0.816497i $$0.695913\pi$$
$$4$$ 0 0
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ −2.00000 −0.516398
$$16$$ 0 0
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ 0 0
$$21$$ 4.00000 0.872872
$$22$$ 0 0
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 4.00000 0.769800
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 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
$$35$$ −2.00000 −0.338062
$$36$$ 0 0
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0 0
$$39$$ 4.00000 0.640513
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ −10.0000 −1.52499 −0.762493 0.646997i $$-0.776025\pi$$
−0.762493 + 0.646997i $$0.776025\pi$$
$$44$$ 0 0
$$45$$ 1.00000 0.149071
$$46$$ 0 0
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 12.0000 1.68034
$$52$$ 0 0
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 8.00000 1.05963
$$58$$ 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 $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 0 0
$$63$$ −2.00000 −0.251976
$$64$$ 0 0
$$65$$ −2.00000 −0.248069
$$66$$ 0 0
$$67$$ 2.00000 0.244339 0.122169 0.992509i $$-0.461015\pi$$
0.122169 + 0.992509i $$0.461015\pi$$
$$68$$ 0 0
$$69$$ 12.0000 1.44463
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ 2.00000 0.234082 0.117041 0.993127i $$-0.462659\pi$$
0.117041 + 0.993127i $$0.462659\pi$$
$$74$$ 0 0
$$75$$ −2.00000 −0.230940
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 0 0
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ −6.00000 −0.650791
$$86$$ 0 0
$$87$$ 12.0000 1.28654
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ 0 0
$$93$$ −8.00000 −0.829561
$$94$$ 0 0
$$95$$ −4.00000 −0.410391
$$96$$ 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
$$101$$ −6.00000 −0.597022 −0.298511 0.954406i $$-0.596490\pi$$
−0.298511 + 0.954406i $$0.596490\pi$$
$$102$$ 0 0
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ 0 0
$$105$$ 4.00000 0.390360
$$106$$ 0 0
$$107$$ −6.00000 −0.580042 −0.290021 0.957020i $$-0.593662\pi$$
−0.290021 + 0.957020i $$0.593662\pi$$
$$108$$ 0 0
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ 4.00000 0.379663
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ −6.00000 −0.559503
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ 12.0000 1.10004
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ −12.0000 −1.08200
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ 0 0
$$129$$ 20.0000 1.76090
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 8.00000 0.693688
$$134$$ 0 0
$$135$$ 4.00000 0.344265
$$136$$ 0 0
$$137$$ 18.0000 1.53784 0.768922 0.639343i $$-0.220793\pi$$
0.768922 + 0.639343i $$0.220793\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ −12.0000 −1.01058
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −6.00000 −0.498273
$$146$$ 0 0
$$147$$ 6.00000 0.494872
$$148$$ 0 0
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ −20.0000 −1.62758 −0.813788 0.581161i $$-0.802599\pi$$
−0.813788 + 0.581161i $$0.802599\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 4.00000 0.321288
$$156$$ 0 0
$$157$$ 22.0000 1.75579 0.877896 0.478852i $$-0.158947\pi$$
0.877896 + 0.478852i $$0.158947\pi$$
$$158$$ 0 0
$$159$$ −12.0000 −0.951662
$$160$$ 0 0
$$161$$ 12.0000 0.945732
$$162$$ 0 0
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −18.0000 −1.39288 −0.696441 0.717614i $$-0.745234\pi$$
−0.696441 + 0.717614i $$0.745234\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −4.00000 −0.305888
$$172$$ 0 0
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ −2.00000 −0.151186
$$176$$ 0 0
$$177$$ −24.0000 −1.80395
$$178$$ 0 0
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 4.00000 0.295689
$$184$$ 0 0
$$185$$ −2.00000 −0.147043
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −8.00000 −0.581914
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ 26.0000 1.87152 0.935760 0.352636i $$-0.114715\pi$$
0.935760 + 0.352636i $$0.114715\pi$$
$$194$$ 0 0
$$195$$ 4.00000 0.286446
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ 0 0
$$203$$ 12.0000 0.842235
$$204$$ 0 0
$$205$$ 6.00000 0.419058
$$206$$ 0 0
$$207$$ −6.00000 −0.417029
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −16.0000 −1.10149 −0.550743 0.834675i $$-0.685655\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ 0 0
$$213$$ −24.0000 −1.64445
$$214$$ 0 0
$$215$$ −10.0000 −0.681994
$$216$$ 0 0
$$217$$ −8.00000 −0.543075
$$218$$ 0 0
$$219$$ −4.00000 −0.270295
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ 10.0000 0.669650 0.334825 0.942280i $$-0.391323\pi$$
0.334825 + 0.942280i $$0.391323\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ −6.00000 −0.398234 −0.199117 0.979976i $$-0.563807\pi$$
−0.199117 + 0.979976i $$0.563807\pi$$
$$228$$ 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
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 6.00000 0.391397
$$236$$ 0 0
$$237$$ 16.0000 1.03931
$$238$$ 0 0
$$239$$ 24.0000 1.55243 0.776215 0.630468i $$-0.217137\pi$$
0.776215 + 0.630468i $$0.217137\pi$$
$$240$$ 0 0
$$241$$ 14.0000 0.901819 0.450910 0.892570i $$-0.351100\pi$$
0.450910 + 0.892570i $$0.351100\pi$$
$$242$$ 0 0
$$243$$ 10.0000 0.641500
$$244$$ 0 0
$$245$$ −3.00000 −0.191663
$$246$$ 0 0
$$247$$ 8.00000 0.509028
$$248$$ 0 0
$$249$$ −12.0000 −0.760469
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 12.0000 0.751469
$$256$$ 0 0
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 0 0
$$259$$ 4.00000 0.248548
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ 18.0000 1.10993 0.554964 0.831875i $$-0.312732\pi$$
0.554964 + 0.831875i $$0.312732\pi$$
$$264$$ 0 0
$$265$$ 6.00000 0.368577
$$266$$ 0 0
$$267$$ 12.0000 0.734388
$$268$$ 0 0
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ −20.0000 −1.21491 −0.607457 0.794353i $$-0.707810\pi$$
−0.607457 + 0.794353i $$0.707810\pi$$
$$272$$ 0 0
$$273$$ −8.00000 −0.484182
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −26.0000 −1.56219 −0.781094 0.624413i $$-0.785338\pi$$
−0.781094 + 0.624413i $$0.785338\pi$$
$$278$$ 0 0
$$279$$ 4.00000 0.239474
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 14.0000 0.832214 0.416107 0.909316i $$-0.363394\pi$$
0.416107 + 0.909316i $$0.363394\pi$$
$$284$$ 0 0
$$285$$ 8.00000 0.473879
$$286$$ 0 0
$$287$$ −12.0000 −0.708338
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ −4.00000 −0.234484
$$292$$ 0 0
$$293$$ 30.0000 1.75262 0.876309 0.481749i $$-0.159998\pi$$
0.876309 + 0.481749i $$0.159998\pi$$
$$294$$ 0 0
$$295$$ 12.0000 0.698667
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 12.0000 0.693978
$$300$$ 0 0
$$301$$ 20.0000 1.15278
$$302$$ 0 0
$$303$$ 12.0000 0.689382
$$304$$ 0 0
$$305$$ −2.00000 −0.114520
$$306$$ 0 0
$$307$$ 2.00000 0.114146 0.0570730 0.998370i $$-0.481823\pi$$
0.0570730 + 0.998370i $$0.481823\pi$$
$$308$$ 0 0
$$309$$ 28.0000 1.59286
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ −22.0000 −1.24351 −0.621757 0.783210i $$-0.713581\pi$$
−0.621757 + 0.783210i $$0.713581\pi$$
$$314$$ 0 0
$$315$$ −2.00000 −0.112687
$$316$$ 0 0
$$317$$ 6.00000 0.336994 0.168497 0.985702i $$-0.446109\pi$$
0.168497 + 0.985702i $$0.446109\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 24.0000 1.33540
$$324$$ 0 0
$$325$$ −2.00000 −0.110940
$$326$$ 0 0
$$327$$ 4.00000 0.221201
$$328$$ 0 0
$$329$$ −12.0000 −0.661581
$$330$$ 0 0
$$331$$ 8.00000 0.439720 0.219860 0.975531i $$-0.429440\pi$$
0.219860 + 0.975531i $$0.429440\pi$$
$$332$$ 0 0
$$333$$ −2.00000 −0.109599
$$334$$ 0 0
$$335$$ 2.00000 0.109272
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 0 0
$$339$$ 12.0000 0.651751
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 20.0000 1.07990
$$344$$ 0 0
$$345$$ 12.0000 0.646058
$$346$$ 0 0
$$347$$ −30.0000 −1.61048 −0.805242 0.592946i $$-0.797965\pi$$
−0.805242 + 0.592946i $$0.797965\pi$$
$$348$$ 0 0
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ −8.00000 −0.427008
$$352$$ 0 0
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 0 0
$$355$$ 12.0000 0.636894
$$356$$ 0 0
$$357$$ −24.0000 −1.27021
$$358$$ 0 0
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ 22.0000 1.15470
$$364$$ 0 0
$$365$$ 2.00000 0.104685
$$366$$ 0 0
$$367$$ 22.0000 1.14839 0.574195 0.818718i $$-0.305315\pi$$
0.574195 + 0.818718i $$0.305315\pi$$
$$368$$ 0 0
$$369$$ 6.00000 0.312348
$$370$$ 0 0
$$371$$ −12.0000 −0.623009
$$372$$ 0 0
$$373$$ −26.0000 −1.34623 −0.673114 0.739538i $$-0.735044\pi$$
−0.673114 + 0.739538i $$0.735044\pi$$
$$374$$ 0 0
$$375$$ −2.00000 −0.103280
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ 0 0
$$381$$ 4.00000 0.204926
$$382$$ 0 0
$$383$$ −6.00000 −0.306586 −0.153293 0.988181i $$-0.548988\pi$$
−0.153293 + 0.988181i $$0.548988\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −10.0000 −0.508329
$$388$$ 0 0
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 36.0000 1.82060
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −8.00000 −0.402524
$$396$$ 0 0
$$397$$ −2.00000 −0.100377 −0.0501886 0.998740i $$-0.515982\pi$$
−0.0501886 + 0.998740i $$0.515982\pi$$
$$398$$ 0 0
$$399$$ −16.0000 −0.801002
$$400$$ 0 0
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 0 0
$$403$$ −8.00000 −0.398508
$$404$$ 0 0
$$405$$ −11.0000 −0.546594
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −34.0000 −1.68119 −0.840596 0.541663i $$-0.817795\pi$$
−0.840596 + 0.541663i $$0.817795\pi$$
$$410$$ 0 0
$$411$$ −36.0000 −1.77575
$$412$$ 0 0
$$413$$ −24.0000 −1.18096
$$414$$ 0 0
$$415$$ 6.00000 0.294528
$$416$$ 0 0
$$417$$ 8.00000 0.391762
$$418$$ 0 0
$$419$$ 36.0000 1.75872 0.879358 0.476162i $$-0.157972\pi$$
0.879358 + 0.476162i $$0.157972\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 0 0
$$423$$ 6.00000 0.291730
$$424$$ 0 0
$$425$$ −6.00000 −0.291043
$$426$$ 0 0
$$427$$ 4.00000 0.193574
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −36.0000 −1.73406 −0.867029 0.498257i $$-0.833974\pi$$
−0.867029 + 0.498257i $$0.833974\pi$$
$$432$$ 0 0
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 12.0000 0.575356
$$436$$ 0 0
$$437$$ 24.0000 1.14808
$$438$$ 0 0
$$439$$ −8.00000 −0.381819 −0.190910 0.981608i $$-0.561144\pi$$
−0.190910 + 0.981608i $$0.561144\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ 6.00000 0.285069 0.142534 0.989790i $$-0.454475\pi$$
0.142534 + 0.989790i $$0.454475\pi$$
$$444$$ 0 0
$$445$$ −6.00000 −0.284427
$$446$$ 0 0
$$447$$ −12.0000 −0.567581
$$448$$ 0 0
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 40.0000 1.87936
$$454$$ 0 0
$$455$$ 4.00000 0.187523
$$456$$ 0 0
$$457$$ 26.0000 1.21623 0.608114 0.793849i $$-0.291926\pi$$
0.608114 + 0.793849i $$0.291926\pi$$
$$458$$ 0 0
$$459$$ −24.0000 −1.12022
$$460$$ 0 0
$$461$$ −30.0000 −1.39724 −0.698620 0.715493i $$-0.746202\pi$$
−0.698620 + 0.715493i $$0.746202\pi$$
$$462$$ 0 0
$$463$$ −14.0000 −0.650635 −0.325318 0.945605i $$-0.605471\pi$$
−0.325318 + 0.945605i $$0.605471\pi$$
$$464$$ 0 0
$$465$$ −8.00000 −0.370991
$$466$$ 0 0
$$467$$ −30.0000 −1.38823 −0.694117 0.719862i $$-0.744205\pi$$
−0.694117 + 0.719862i $$0.744205\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ 0 0
$$471$$ −44.0000 −2.02741
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 0 0
$$479$$ 24.0000 1.09659 0.548294 0.836286i $$-0.315277\pi$$
0.548294 + 0.836286i $$0.315277\pi$$
$$480$$ 0 0
$$481$$ 4.00000 0.182384
$$482$$ 0 0
$$483$$ −24.0000 −1.09204
$$484$$ 0 0
$$485$$ 2.00000 0.0908153
$$486$$ 0 0
$$487$$ −26.0000 −1.17817 −0.589086 0.808070i $$-0.700512\pi$$
−0.589086 + 0.808070i $$0.700512\pi$$
$$488$$ 0 0
$$489$$ 20.0000 0.904431
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 36.0000 1.62136
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −24.0000 −1.07655
$$498$$ 0 0
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ 0 0
$$501$$ 36.0000 1.60836
$$502$$ 0 0
$$503$$ 18.0000 0.802580 0.401290 0.915951i $$-0.368562\pi$$
0.401290 + 0.915951i $$0.368562\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 0 0
$$507$$ 18.0000 0.799408
$$508$$ 0 0
$$509$$ −6.00000 −0.265945 −0.132973 0.991120i $$-0.542452\pi$$
−0.132973 + 0.991120i $$0.542452\pi$$
$$510$$ 0 0
$$511$$ −4.00000 −0.176950
$$512$$ 0 0
$$513$$ −16.0000 −0.706417
$$514$$ 0 0
$$515$$ −14.0000 −0.616914
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −12.0000 −0.526742
$$520$$ 0 0
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ 0 0
$$523$$ 14.0000 0.612177 0.306089 0.952003i $$-0.400980\pi$$
0.306089 + 0.952003i $$0.400980\pi$$
$$524$$ 0 0
$$525$$ 4.00000 0.174574
$$526$$ 0 0
$$527$$ −24.0000 −1.04546
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 12.0000 0.520756
$$532$$ 0 0
$$533$$ −12.0000 −0.519778
$$534$$ 0 0
$$535$$ −6.00000 −0.259403
$$536$$ 0 0
$$537$$ 24.0000 1.03568
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −14.0000 −0.601907 −0.300954 0.953639i $$-0.597305\pi$$
−0.300954 + 0.953639i $$0.597305\pi$$
$$542$$ 0 0
$$543$$ −20.0000 −0.858282
$$544$$ 0 0
$$545$$ −2.00000 −0.0856706
$$546$$ 0 0
$$547$$ 26.0000 1.11168 0.555840 0.831289i $$-0.312397\pi$$
0.555840 + 0.831289i $$0.312397\pi$$
$$548$$ 0 0
$$549$$ −2.00000 −0.0853579
$$550$$ 0 0
$$551$$ 24.0000 1.02243
$$552$$ 0 0
$$553$$ 16.0000 0.680389
$$554$$ 0 0
$$555$$ 4.00000 0.169791
$$556$$ 0 0
$$557$$ 30.0000 1.27114 0.635570 0.772043i $$-0.280765\pi$$
0.635570 + 0.772043i $$0.280765\pi$$
$$558$$ 0 0
$$559$$ 20.0000 0.845910
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −18.0000 −0.758610 −0.379305 0.925272i $$-0.623837\pi$$
−0.379305 + 0.925272i $$0.623837\pi$$
$$564$$ 0 0
$$565$$ −6.00000 −0.252422
$$566$$ 0 0
$$567$$ 22.0000 0.923913
$$568$$ 0 0
$$569$$ 30.0000 1.25767 0.628833 0.777541i $$-0.283533\pi$$
0.628833 + 0.777541i $$0.283533\pi$$
$$570$$ 0 0
$$571$$ 8.00000 0.334790 0.167395 0.985890i $$-0.446465\pi$$
0.167395 + 0.985890i $$0.446465\pi$$
$$572$$ 0 0
$$573$$ −24.0000 −1.00261
$$574$$ 0 0
$$575$$ −6.00000 −0.250217
$$576$$ 0 0
$$577$$ −22.0000 −0.915872 −0.457936 0.888985i $$-0.651411\pi$$
−0.457936 + 0.888985i $$0.651411\pi$$
$$578$$ 0 0
$$579$$ −52.0000 −2.16105
$$580$$ 0 0
$$581$$ −12.0000 −0.497844
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ −2.00000 −0.0826898
$$586$$ 0 0
$$587$$ −6.00000 −0.247647 −0.123823 0.992304i $$-0.539516\pi$$
−0.123823 + 0.992304i $$0.539516\pi$$
$$588$$ 0 0
$$589$$ −16.0000 −0.659269
$$590$$ 0 0
$$591$$ 36.0000 1.48084
$$592$$ 0 0
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 0 0
$$595$$ 12.0000 0.491952
$$596$$ 0 0
$$597$$ 16.0000 0.654836
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −10.0000 −0.407909 −0.203954 0.978980i $$-0.565379\pi$$
−0.203954 + 0.978980i $$0.565379\pi$$
$$602$$ 0 0
$$603$$ 2.00000 0.0814463
$$604$$ 0 0
$$605$$ −11.0000 −0.447214
$$606$$ 0 0
$$607$$ 22.0000 0.892952 0.446476 0.894795i $$-0.352679\pi$$
0.446476 + 0.894795i $$0.352679\pi$$
$$608$$ 0 0
$$609$$ −24.0000 −0.972529
$$610$$ 0 0
$$611$$ −12.0000 −0.485468
$$612$$ 0 0
$$613$$ −2.00000 −0.0807792 −0.0403896 0.999184i $$-0.512860\pi$$
−0.0403896 + 0.999184i $$0.512860\pi$$
$$614$$ 0 0
$$615$$ −12.0000 −0.483887
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 0 0
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ 0 0
$$621$$ −24.0000 −0.963087
$$622$$ 0 0
$$623$$ 12.0000 0.480770
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 12.0000 0.478471
$$630$$ 0 0
$$631$$ 28.0000 1.11466 0.557331 0.830290i $$-0.311825\pi$$
0.557331 + 0.830290i $$0.311825\pi$$
$$632$$ 0 0
$$633$$ 32.0000 1.27189
$$634$$ 0 0
$$635$$ −2.00000 −0.0793676
$$636$$ 0 0
$$637$$ 6.00000 0.237729
$$638$$ 0 0
$$639$$ 12.0000 0.474713
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 0 0
$$643$$ 14.0000 0.552106 0.276053 0.961142i $$-0.410973\pi$$
0.276053 + 0.961142i $$0.410973\pi$$
$$644$$ 0 0
$$645$$ 20.0000 0.787499
$$646$$ 0 0
$$647$$ −42.0000 −1.65119 −0.825595 0.564263i $$-0.809160\pi$$
−0.825595 + 0.564263i $$0.809160\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 16.0000 0.627089
$$652$$ 0 0
$$653$$ −42.0000 −1.64359 −0.821794 0.569785i $$-0.807026\pi$$
−0.821794 + 0.569785i $$0.807026\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 2.00000 0.0780274
$$658$$ 0 0
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ 0 0
$$661$$ 22.0000 0.855701 0.427850 0.903850i $$-0.359271\pi$$
0.427850 + 0.903850i $$0.359271\pi$$
$$662$$ 0 0
$$663$$ −24.0000 −0.932083
$$664$$ 0 0
$$665$$ 8.00000 0.310227
$$666$$ 0 0
$$667$$ 36.0000 1.39393
$$668$$ 0 0
$$669$$ −20.0000 −0.773245
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −46.0000 −1.77317 −0.886585 0.462566i $$-0.846929\pi$$
−0.886585 + 0.462566i $$0.846929\pi$$
$$674$$ 0 0
$$675$$ 4.00000 0.153960
$$676$$ 0 0
$$677$$ −18.0000 −0.691796 −0.345898 0.938272i $$-0.612426\pi$$
−0.345898 + 0.938272i $$0.612426\pi$$
$$678$$ 0 0
$$679$$ −4.00000 −0.153506
$$680$$ 0 0
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ −42.0000 −1.60709 −0.803543 0.595247i $$-0.797054\pi$$
−0.803543 + 0.595247i $$0.797054\pi$$
$$684$$ 0 0
$$685$$ 18.0000 0.687745
$$686$$ 0 0
$$687$$ 28.0000 1.06827
$$688$$ 0 0
$$689$$ −12.0000 −0.457164
$$690$$ 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
$$695$$ −4.00000 −0.151729
$$696$$ 0 0
$$697$$ −36.0000 −1.36360
$$698$$ 0 0
$$699$$ 12.0000 0.453882
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ 8.00000 0.301726
$$704$$ 0 0
$$705$$ −12.0000 −0.451946
$$706$$ 0 0
$$707$$ 12.0000 0.451306
$$708$$ 0 0
$$709$$ 34.0000 1.27690 0.638448 0.769665i $$-0.279577\pi$$
0.638448 + 0.769665i $$0.279577\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ −24.0000 −0.898807
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −48.0000 −1.79259
$$718$$ 0 0
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ 28.0000 1.04277
$$722$$ 0 0
$$723$$ −28.0000 −1.04133
$$724$$ 0 0
$$725$$ −6.00000 −0.222834
$$726$$ 0 0
$$727$$ 46.0000 1.70605 0.853023 0.521874i $$-0.174767\pi$$
0.853023 + 0.521874i $$0.174767\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 60.0000 2.21918
$$732$$ 0 0
$$733$$ 22.0000 0.812589 0.406294 0.913742i $$-0.366821\pi$$
0.406294 + 0.913742i $$0.366821\pi$$
$$734$$ 0 0
$$735$$ 6.00000 0.221313
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 0 0
$$741$$ −16.0000 −0.587775
$$742$$ 0 0
$$743$$ −6.00000 −0.220119 −0.110059 0.993925i $$-0.535104\pi$$
−0.110059 + 0.993925i $$0.535104\pi$$
$$744$$ 0 0
$$745$$ 6.00000 0.219823
$$746$$ 0 0
$$747$$ 6.00000 0.219529
$$748$$ 0 0
$$749$$ 12.0000 0.438470
$$750$$ 0 0
$$751$$ 4.00000 0.145962 0.0729810 0.997333i $$-0.476749\pi$$
0.0729810 + 0.997333i $$0.476749\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −20.0000 −0.727875
$$756$$ 0 0
$$757$$ 22.0000 0.799604 0.399802 0.916602i $$-0.369079\pi$$
0.399802 + 0.916602i $$0.369079\pi$$
$$758$$ 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
$$763$$ 4.00000 0.144810
$$764$$ 0 0
$$765$$ −6.00000 −0.216930
$$766$$ 0 0
$$767$$ −24.0000 −0.866590
$$768$$ 0 0
$$769$$ 2.00000 0.0721218 0.0360609 0.999350i $$-0.488519\pi$$
0.0360609 + 0.999350i $$0.488519\pi$$
$$770$$ 0 0
$$771$$ 12.0000 0.432169
$$772$$ 0 0
$$773$$ 30.0000 1.07903 0.539513 0.841978i $$-0.318609\pi$$
0.539513 + 0.841978i $$0.318609\pi$$
$$774$$ 0 0
$$775$$ 4.00000 0.143684
$$776$$ 0 0
$$777$$ −8.00000 −0.286998
$$778$$ 0 0
$$779$$ −24.0000 −0.859889
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −24.0000 −0.857690
$$784$$ 0 0
$$785$$ 22.0000 0.785214
$$786$$ 0 0
$$787$$ 26.0000 0.926800 0.463400 0.886149i $$-0.346629\pi$$
0.463400 + 0.886149i $$0.346629\pi$$
$$788$$ 0 0
$$789$$ −36.0000 −1.28163
$$790$$ 0 0
$$791$$ 12.0000 0.426671
$$792$$ 0 0
$$793$$ 4.00000 0.142044
$$794$$ 0 0
$$795$$ −12.0000 −0.425596
$$796$$ 0 0
$$797$$ −42.0000 −1.48772 −0.743858 0.668338i $$-0.767006\pi$$
−0.743858 + 0.668338i $$0.767006\pi$$
$$798$$ 0 0
$$799$$ −36.0000 −1.27359
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 12.0000 0.422944
$$806$$ 0 0
$$807$$ 36.0000 1.26726
$$808$$ 0 0
$$809$$ −6.00000 −0.210949 −0.105474 0.994422i $$-0.533636\pi$$
−0.105474 + 0.994422i $$0.533636\pi$$
$$810$$ 0 0
$$811$$ −16.0000 −0.561836 −0.280918 0.959732i $$-0.590639\pi$$
−0.280918 + 0.959732i $$0.590639\pi$$
$$812$$ 0 0
$$813$$ 40.0000 1.40286
$$814$$ 0 0
$$815$$ −10.0000 −0.350285
$$816$$ 0 0
$$817$$ 40.0000 1.39942
$$818$$ 0 0
$$819$$ 4.00000 0.139771
$$820$$ 0 0
$$821$$ 54.0000 1.88461 0.942306 0.334751i $$-0.108652\pi$$
0.942306 + 0.334751i $$0.108652\pi$$
$$822$$ 0 0
$$823$$ −38.0000 −1.32460 −0.662298 0.749240i $$-0.730419\pi$$
−0.662298 + 0.749240i $$0.730419\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −30.0000 −1.04320 −0.521601 0.853189i $$-0.674665\pi$$
−0.521601 + 0.853189i $$0.674665\pi$$
$$828$$ 0 0
$$829$$ −2.00000 −0.0694629 −0.0347314 0.999397i $$-0.511058\pi$$
−0.0347314 + 0.999397i $$0.511058\pi$$
$$830$$ 0 0
$$831$$ 52.0000 1.80386
$$832$$ 0 0
$$833$$ 18.0000 0.623663
$$834$$ 0 0
$$835$$ −18.0000 −0.622916
$$836$$ 0 0
$$837$$ 16.0000 0.553041
$$838$$ 0 0
$$839$$ 48.0000 1.65714 0.828572 0.559883i $$-0.189154\pi$$
0.828572 + 0.559883i $$0.189154\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ −12.0000 −0.413302
$$844$$ 0 0
$$845$$ −9.00000 −0.309609
$$846$$ 0 0
$$847$$ 22.0000 0.755929
$$848$$ 0 0
$$849$$ −28.0000 −0.960958
$$850$$ 0 0
$$851$$ 12.0000 0.411355
$$852$$ 0 0
$$853$$ −50.0000 −1.71197 −0.855984 0.517003i $$-0.827048\pi$$
−0.855984 + 0.517003i $$0.827048\pi$$
$$854$$ 0 0
$$855$$ −4.00000 −0.136797
$$856$$ 0 0
$$857$$ 18.0000 0.614868 0.307434 0.951569i $$-0.400530\pi$$
0.307434 + 0.951569i $$0.400530\pi$$
$$858$$ 0 0
$$859$$ −4.00000 −0.136478 −0.0682391 0.997669i $$-0.521738\pi$$
−0.0682391 + 0.997669i $$0.521738\pi$$
$$860$$ 0 0
$$861$$ 24.0000 0.817918
$$862$$ 0 0
$$863$$ −6.00000 −0.204242 −0.102121 0.994772i $$-0.532563\pi$$
−0.102121 + 0.994772i $$0.532563\pi$$
$$864$$ 0 0
$$865$$ 6.00000 0.204006
$$866$$ 0 0
$$867$$ −38.0000 −1.29055
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −4.00000 −0.135535
$$872$$ 0 0
$$873$$ 2.00000 0.0676897
$$874$$ 0 0
$$875$$ −2.00000 −0.0676123
$$876$$ 0 0
$$877$$ −26.0000 −0.877958 −0.438979 0.898497i $$-0.644660\pi$$
−0.438979 + 0.898497i $$0.644660\pi$$
$$878$$ 0 0
$$879$$ −60.0000 −2.02375
$$880$$ 0 0
$$881$$ −18.0000 −0.606435 −0.303218 0.952921i $$-0.598061\pi$$
−0.303218 + 0.952921i $$0.598061\pi$$
$$882$$ 0 0
$$883$$ 14.0000 0.471138 0.235569 0.971858i $$-0.424305\pi$$
0.235569 + 0.971858i $$0.424305\pi$$
$$884$$ 0 0
$$885$$ −24.0000 −0.806751
$$886$$ 0 0
$$887$$ −18.0000 −0.604381 −0.302190 0.953248i $$-0.597718\pi$$
−0.302190 + 0.953248i $$0.597718\pi$$
$$888$$ 0 0
$$889$$ 4.00000 0.134156
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −24.0000 −0.803129
$$894$$ 0 0
$$895$$ −12.0000 −0.401116
$$896$$ 0 0
$$897$$ −24.0000 −0.801337
$$898$$ 0 0
$$899$$ −24.0000 −0.800445
$$900$$ 0 0
$$901$$ −36.0000 −1.19933
$$902$$ 0 0
$$903$$ −40.0000 −1.33112
$$904$$ 0 0
$$905$$ 10.0000 0.332411
$$906$$ 0 0
$$907$$ −46.0000 −1.52740 −0.763702 0.645568i $$-0.776621\pi$$
−0.763702 + 0.645568i $$0.776621\pi$$
$$908$$ 0 0
$$909$$ −6.00000 −0.199007
$$910$$ 0 0
$$911$$ −12.0000 −0.397578 −0.198789 0.980042i $$-0.563701\pi$$
−0.198789 + 0.980042i $$0.563701\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 4.00000 0.132236
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 16.0000 0.527791 0.263896 0.964551i $$-0.414993\pi$$
0.263896 + 0.964551i $$0.414993\pi$$
$$920$$ 0 0
$$921$$ −4.00000 −0.131804
$$922$$ 0 0
$$923$$ −24.0000 −0.789970
$$924$$ 0 0
$$925$$ −2.00000 −0.0657596
$$926$$ 0 0
$$927$$ −14.0000 −0.459820
$$928$$ 0 0
$$929$$ −42.0000 −1.37798 −0.688988 0.724773i $$-0.741945\pi$$
−0.688988 + 0.724773i $$0.741945\pi$$
$$930$$ 0 0
$$931$$ 12.0000 0.393284
$$932$$ 0 0
$$933$$ 24.0000 0.785725
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −22.0000 −0.718709 −0.359354 0.933201i $$-0.617003\pi$$
−0.359354 + 0.933201i $$0.617003\pi$$
$$938$$ 0 0
$$939$$ 44.0000 1.43589
$$940$$ 0 0
$$941$$ 18.0000 0.586783 0.293392 0.955992i $$-0.405216\pi$$
0.293392 + 0.955992i $$0.405216\pi$$
$$942$$ 0 0
$$943$$ −36.0000 −1.17232
$$944$$ 0 0
$$945$$ −8.00000 −0.260240
$$946$$ 0 0
$$947$$ 18.0000 0.584921 0.292461 0.956278i $$-0.405526\pi$$
0.292461 + 0.956278i $$0.405526\pi$$
$$948$$ 0 0
$$949$$ −4.00000 −0.129845
$$950$$ 0 0
$$951$$ −12.0000 −0.389127
$$952$$ 0 0
$$953$$ −6.00000 −0.194359 −0.0971795 0.995267i $$-0.530982\pi$$
−0.0971795 + 0.995267i $$0.530982\pi$$
$$954$$ 0 0
$$955$$ 12.0000 0.388311
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −36.0000 −1.16250
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 0 0
$$963$$ −6.00000 −0.193347
$$964$$ 0 0
$$965$$ 26.0000 0.836970
$$966$$ 0 0
$$967$$ 22.0000 0.707472 0.353736 0.935345i $$-0.384911\pi$$
0.353736 + 0.935345i $$0.384911\pi$$
$$968$$ 0 0
$$969$$ −48.0000 −1.54198
$$970$$ 0 0
$$971$$ −24.0000 −0.770197 −0.385098 0.922876i $$-0.625832\pi$$
−0.385098 + 0.922876i $$0.625832\pi$$
$$972$$ 0 0
$$973$$ 8.00000 0.256468
$$974$$ 0 0
$$975$$ 4.00000 0.128103
$$976$$ 0 0
$$977$$ 18.0000 0.575871 0.287936 0.957650i $$-0.407031\pi$$
0.287936 + 0.957650i $$0.407031\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −2.00000 −0.0638551
$$982$$ 0 0
$$983$$ 18.0000 0.574111 0.287055 0.957914i $$-0.407324\pi$$
0.287055 + 0.957914i $$0.407324\pi$$
$$984$$ 0 0
$$985$$ −18.0000 −0.573528
$$986$$ 0 0
$$987$$ 24.0000 0.763928
$$988$$ 0 0
$$989$$ 60.0000 1.90789
$$990$$ 0 0
$$991$$ 4.00000 0.127064 0.0635321 0.997980i $$-0.479763\pi$$
0.0635321 + 0.997980i $$0.479763\pi$$
$$992$$ 0 0
$$993$$ −16.0000 −0.507745
$$994$$ 0 0
$$995$$ −8.00000 −0.253617
$$996$$ 0 0
$$997$$ −26.0000 −0.823428 −0.411714 0.911313i $$-0.635070\pi$$
−0.411714 + 0.911313i $$0.635070\pi$$
$$998$$ 0 0
$$999$$ −8.00000 −0.253109
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.a.a.1.1 1
3.2 odd 2 2880.2.a.f.1.1 1
4.3 odd 2 320.2.a.f.1.1 1
5.2 odd 4 1600.2.c.e.449.2 2
5.3 odd 4 1600.2.c.e.449.1 2
5.4 even 2 1600.2.a.w.1.1 1
8.3 odd 2 20.2.a.a.1.1 1
8.5 even 2 80.2.a.b.1.1 1
12.11 even 2 2880.2.a.m.1.1 1
16.3 odd 4 1280.2.d.c.641.2 2
16.5 even 4 1280.2.d.g.641.2 2
16.11 odd 4 1280.2.d.c.641.1 2
16.13 even 4 1280.2.d.g.641.1 2
20.3 even 4 1600.2.c.d.449.2 2
20.7 even 4 1600.2.c.d.449.1 2
20.19 odd 2 1600.2.a.c.1.1 1
24.5 odd 2 720.2.a.h.1.1 1
24.11 even 2 180.2.a.a.1.1 1
40.3 even 4 100.2.c.a.49.1 2
40.13 odd 4 400.2.c.b.49.2 2
40.19 odd 2 100.2.a.a.1.1 1
40.27 even 4 100.2.c.a.49.2 2
40.29 even 2 400.2.a.c.1.1 1
40.37 odd 4 400.2.c.b.49.1 2
56.3 even 6 980.2.i.c.961.1 2
56.11 odd 6 980.2.i.i.961.1 2
56.13 odd 2 3920.2.a.h.1.1 1
56.19 even 6 980.2.i.c.361.1 2
56.27 even 2 980.2.a.h.1.1 1
56.51 odd 6 980.2.i.i.361.1 2
72.11 even 6 1620.2.i.b.1081.1 2
72.43 odd 6 1620.2.i.h.1081.1 2
72.59 even 6 1620.2.i.b.541.1 2
72.67 odd 6 1620.2.i.h.541.1 2
88.21 odd 2 9680.2.a.ba.1.1 1
88.43 even 2 2420.2.a.a.1.1 1
104.51 odd 2 3380.2.a.c.1.1 1
104.83 even 4 3380.2.f.b.3041.2 2
104.99 even 4 3380.2.f.b.3041.1 2
120.29 odd 2 3600.2.a.be.1.1 1
120.53 even 4 3600.2.f.j.2449.2 2
120.59 even 2 900.2.a.b.1.1 1
120.77 even 4 3600.2.f.j.2449.1 2
120.83 odd 4 900.2.d.c.649.1 2
120.107 odd 4 900.2.d.c.649.2 2
136.67 odd 2 5780.2.a.f.1.1 1
136.115 odd 4 5780.2.c.a.5201.1 2
136.123 odd 4 5780.2.c.a.5201.2 2
152.75 even 2 7220.2.a.f.1.1 1
168.83 odd 2 8820.2.a.g.1.1 1
280.27 odd 4 4900.2.e.f.2549.1 2
280.83 odd 4 4900.2.e.f.2549.2 2
280.139 even 2 4900.2.a.e.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
20.2.a.a.1.1 1 8.3 odd 2
80.2.a.b.1.1 1 8.5 even 2
100.2.a.a.1.1 1 40.19 odd 2
100.2.c.a.49.1 2 40.3 even 4
100.2.c.a.49.2 2 40.27 even 4
180.2.a.a.1.1 1 24.11 even 2
320.2.a.a.1.1 1 1.1 even 1 trivial
320.2.a.f.1.1 1 4.3 odd 2
400.2.a.c.1.1 1 40.29 even 2
400.2.c.b.49.1 2 40.37 odd 4
400.2.c.b.49.2 2 40.13 odd 4
720.2.a.h.1.1 1 24.5 odd 2
900.2.a.b.1.1 1 120.59 even 2
900.2.d.c.649.1 2 120.83 odd 4
900.2.d.c.649.2 2 120.107 odd 4
980.2.a.h.1.1 1 56.27 even 2
980.2.i.c.361.1 2 56.19 even 6
980.2.i.c.961.1 2 56.3 even 6
980.2.i.i.361.1 2 56.51 odd 6
980.2.i.i.961.1 2 56.11 odd 6
1280.2.d.c.641.1 2 16.11 odd 4
1280.2.d.c.641.2 2 16.3 odd 4
1280.2.d.g.641.1 2 16.13 even 4
1280.2.d.g.641.2 2 16.5 even 4
1600.2.a.c.1.1 1 20.19 odd 2
1600.2.a.w.1.1 1 5.4 even 2
1600.2.c.d.449.1 2 20.7 even 4
1600.2.c.d.449.2 2 20.3 even 4
1600.2.c.e.449.1 2 5.3 odd 4
1600.2.c.e.449.2 2 5.2 odd 4
1620.2.i.b.541.1 2 72.59 even 6
1620.2.i.b.1081.1 2 72.11 even 6
1620.2.i.h.541.1 2 72.67 odd 6
1620.2.i.h.1081.1 2 72.43 odd 6
2420.2.a.a.1.1 1 88.43 even 2
2880.2.a.f.1.1 1 3.2 odd 2
2880.2.a.m.1.1 1 12.11 even 2
3380.2.a.c.1.1 1 104.51 odd 2
3380.2.f.b.3041.1 2 104.99 even 4
3380.2.f.b.3041.2 2 104.83 even 4
3600.2.a.be.1.1 1 120.29 odd 2
3600.2.f.j.2449.1 2 120.77 even 4
3600.2.f.j.2449.2 2 120.53 even 4
3920.2.a.h.1.1 1 56.13 odd 2
4900.2.a.e.1.1 1 280.139 even 2
4900.2.e.f.2549.1 2 280.27 odd 4
4900.2.e.f.2549.2 2 280.83 odd 4
5780.2.a.f.1.1 1 136.67 odd 2
5780.2.c.a.5201.1 2 136.115 odd 4
5780.2.c.a.5201.2 2 136.123 odd 4
7220.2.a.f.1.1 1 152.75 even 2
8820.2.a.g.1.1 1 168.83 odd 2
9680.2.a.ba.1.1 1 88.21 odd 2