# Properties

 Label 1960.2.a.m.1.1 Level $1960$ Weight $2$ Character 1960.1 Self dual yes Analytic conductor $15.651$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1960 = 2^{3} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1960.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$15.6506787962$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1960.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000 q^{3} +1.00000 q^{5} +1.00000 q^{9} +O(q^{10})$$ $$q+2.00000 q^{3} +1.00000 q^{5} +1.00000 q^{9} -1.00000 q^{11} +3.00000 q^{13} +2.00000 q^{15} +2.00000 q^{17} +5.00000 q^{19} +7.00000 q^{23} +1.00000 q^{25} -4.00000 q^{27} -6.00000 q^{29} -4.00000 q^{31} -2.00000 q^{33} -5.00000 q^{37} +6.00000 q^{39} +5.00000 q^{41} +6.00000 q^{43} +1.00000 q^{45} +9.00000 q^{47} +4.00000 q^{51} +11.0000 q^{53} -1.00000 q^{55} +10.0000 q^{57} -8.00000 q^{59} +12.0000 q^{61} +3.00000 q^{65} -4.00000 q^{67} +14.0000 q^{69} -4.00000 q^{71} -12.0000 q^{73} +2.00000 q^{75} +14.0000 q^{79} -11.0000 q^{81} +4.00000 q^{83} +2.00000 q^{85} -12.0000 q^{87} -6.00000 q^{89} -8.00000 q^{93} +5.00000 q^{95} -6.00000 q^{97} -1.00000 q^{99} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 2.00000 1.15470 0.577350 0.816497i $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ 0 0
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ −1.00000 −0.301511 −0.150756 0.988571i $$-0.548171\pi$$
−0.150756 + 0.988571i $$0.548171\pi$$
$$12$$ 0 0
$$13$$ 3.00000 0.832050 0.416025 0.909353i $$-0.363423\pi$$
0.416025 + 0.909353i $$0.363423\pi$$
$$14$$ 0 0
$$15$$ 2.00000 0.516398
$$16$$ 0 0
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ 5.00000 1.14708 0.573539 0.819178i $$-0.305570\pi$$
0.573539 + 0.819178i $$0.305570\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 7.00000 1.45960 0.729800 0.683660i $$-0.239613\pi$$
0.729800 + 0.683660i $$0.239613\pi$$
$$24$$ 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 $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ −2.00000 −0.348155
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ 0 0
$$39$$ 6.00000 0.960769
$$40$$ 0 0
$$41$$ 5.00000 0.780869 0.390434 0.920631i $$-0.372325\pi$$
0.390434 + 0.920631i $$0.372325\pi$$
$$42$$ 0 0
$$43$$ 6.00000 0.914991 0.457496 0.889212i $$-0.348747\pi$$
0.457496 + 0.889212i $$0.348747\pi$$
$$44$$ 0 0
$$45$$ 1.00000 0.149071
$$46$$ 0 0
$$47$$ 9.00000 1.31278 0.656392 0.754420i $$-0.272082\pi$$
0.656392 + 0.754420i $$0.272082\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ 0 0
$$53$$ 11.0000 1.51097 0.755483 0.655168i $$-0.227402\pi$$
0.755483 + 0.655168i $$0.227402\pi$$
$$54$$ 0 0
$$55$$ −1.00000 −0.134840
$$56$$ 0 0
$$57$$ 10.0000 1.32453
$$58$$ 0 0
$$59$$ −8.00000 −1.04151 −0.520756 0.853706i $$-0.674350\pi$$
−0.520756 + 0.853706i $$0.674350\pi$$
$$60$$ 0 0
$$61$$ 12.0000 1.53644 0.768221 0.640184i $$-0.221142\pi$$
0.768221 + 0.640184i $$0.221142\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 3.00000 0.372104
$$66$$ 0 0
$$67$$ −4.00000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ 0 0
$$69$$ 14.0000 1.68540
$$70$$ 0 0
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ 0 0
$$73$$ −12.0000 −1.40449 −0.702247 0.711934i $$-0.747820\pi$$
−0.702247 + 0.711934i $$0.747820\pi$$
$$74$$ 0 0
$$75$$ 2.00000 0.230940
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 14.0000 1.57512 0.787562 0.616236i $$-0.211343\pi$$
0.787562 + 0.616236i $$0.211343\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ 0 0
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ 0 0
$$85$$ 2.00000 0.216930
$$86$$ 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
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −8.00000 −0.829561
$$94$$ 0 0
$$95$$ 5.00000 0.512989
$$96$$ 0 0
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 0 0
$$99$$ −1.00000 −0.100504
$$100$$ 0 0
$$101$$ −12.0000 −1.19404 −0.597022 0.802225i $$-0.703650\pi$$
−0.597022 + 0.802225i $$0.703650\pi$$
$$102$$ 0 0
$$103$$ −20.0000 −1.97066 −0.985329 0.170664i $$-0.945409\pi$$
−0.985329 + 0.170664i $$0.945409\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −4.00000 −0.383131 −0.191565 0.981480i $$-0.561356\pi$$
−0.191565 + 0.981480i $$0.561356\pi$$
$$110$$ 0 0
$$111$$ −10.0000 −0.949158
$$112$$ 0 0
$$113$$ 20.0000 1.88144 0.940721 0.339182i $$-0.110150\pi$$
0.940721 + 0.339182i $$0.110150\pi$$
$$114$$ 0 0
$$115$$ 7.00000 0.652753
$$116$$ 0 0
$$117$$ 3.00000 0.277350
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ 0 0
$$123$$ 10.0000 0.901670
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 17.0000 1.50851 0.754253 0.656584i $$-0.227999\pi$$
0.754253 + 0.656584i $$0.227999\pi$$
$$128$$ 0 0
$$129$$ 12.0000 1.05654
$$130$$ 0 0
$$131$$ −7.00000 −0.611593 −0.305796 0.952097i $$-0.598923\pi$$
−0.305796 + 0.952097i $$0.598923\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −4.00000 −0.344265
$$136$$ 0 0
$$137$$ −12.0000 −1.02523 −0.512615 0.858619i $$-0.671323\pi$$
−0.512615 + 0.858619i $$0.671323\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ 18.0000 1.51587
$$142$$ 0 0
$$143$$ −3.00000 −0.250873
$$144$$ 0 0
$$145$$ −6.00000 −0.498273
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 10.0000 0.819232 0.409616 0.912258i $$-0.365663\pi$$
0.409616 + 0.912258i $$0.365663\pi$$
$$150$$ 0 0
$$151$$ −10.0000 −0.813788 −0.406894 0.913475i $$-0.633388\pi$$
−0.406894 + 0.913475i $$0.633388\pi$$
$$152$$ 0 0
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ −4.00000 −0.321288
$$156$$ 0 0
$$157$$ −5.00000 −0.399043 −0.199522 0.979893i $$-0.563939\pi$$
−0.199522 + 0.979893i $$0.563939\pi$$
$$158$$ 0 0
$$159$$ 22.0000 1.74471
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ 0 0
$$165$$ −2.00000 −0.155700
$$166$$ 0 0
$$167$$ −5.00000 −0.386912 −0.193456 0.981109i $$-0.561970\pi$$
−0.193456 + 0.981109i $$0.561970\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ 5.00000 0.382360
$$172$$ 0 0
$$173$$ −19.0000 −1.44454 −0.722272 0.691609i $$-0.756902\pi$$
−0.722272 + 0.691609i $$0.756902\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −16.0000 −1.20263
$$178$$ 0 0
$$179$$ 9.00000 0.672692 0.336346 0.941739i $$-0.390809\pi$$
0.336346 + 0.941739i $$0.390809\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 24.0000 1.77413
$$184$$ 0 0
$$185$$ −5.00000 −0.367607
$$186$$ 0 0
$$187$$ −2.00000 −0.146254
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ −20.0000 −1.43963 −0.719816 0.694165i $$-0.755774\pi$$
−0.719816 + 0.694165i $$0.755774\pi$$
$$194$$ 0 0
$$195$$ 6.00000 0.429669
$$196$$ 0 0
$$197$$ −27.0000 −1.92367 −0.961835 0.273629i $$-0.911776\pi$$
−0.961835 + 0.273629i $$0.911776\pi$$
$$198$$ 0 0
$$199$$ 4.00000 0.283552 0.141776 0.989899i $$-0.454719\pi$$
0.141776 + 0.989899i $$0.454719\pi$$
$$200$$ 0 0
$$201$$ −8.00000 −0.564276
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 5.00000 0.349215
$$206$$ 0 0
$$207$$ 7.00000 0.486534
$$208$$ 0 0
$$209$$ −5.00000 −0.345857
$$210$$ 0 0
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 0 0
$$213$$ −8.00000 −0.548151
$$214$$ 0 0
$$215$$ 6.00000 0.409197
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −24.0000 −1.62177
$$220$$ 0 0
$$221$$ 6.00000 0.403604
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ 8.00000 0.530979 0.265489 0.964114i $$-0.414466\pi$$
0.265489 + 0.964114i $$0.414466\pi$$
$$228$$ 0 0
$$229$$ 28.0000 1.85029 0.925146 0.379611i $$-0.123942\pi$$
0.925146 + 0.379611i $$0.123942\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 2.00000 0.131024 0.0655122 0.997852i $$-0.479132\pi$$
0.0655122 + 0.997852i $$0.479132\pi$$
$$234$$ 0 0
$$235$$ 9.00000 0.587095
$$236$$ 0 0
$$237$$ 28.0000 1.81880
$$238$$ 0 0
$$239$$ 6.00000 0.388108 0.194054 0.980991i $$-0.437836\pi$$
0.194054 + 0.980991i $$0.437836\pi$$
$$240$$ 0 0
$$241$$ −23.0000 −1.48156 −0.740780 0.671748i $$-0.765544\pi$$
−0.740780 + 0.671748i $$0.765544\pi$$
$$242$$ 0 0
$$243$$ −10.0000 −0.641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 15.0000 0.954427
$$248$$ 0 0
$$249$$ 8.00000 0.506979
$$250$$ 0 0
$$251$$ −29.0000 −1.83046 −0.915232 0.402928i $$-0.867993\pi$$
−0.915232 + 0.402928i $$0.867993\pi$$
$$252$$ 0 0
$$253$$ −7.00000 −0.440086
$$254$$ 0 0
$$255$$ 4.00000 0.250490
$$256$$ 0 0
$$257$$ −12.0000 −0.748539 −0.374270 0.927320i $$-0.622107\pi$$
−0.374270 + 0.927320i $$0.622107\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ 8.00000 0.493301 0.246651 0.969104i $$-0.420670\pi$$
0.246651 + 0.969104i $$0.420670\pi$$
$$264$$ 0 0
$$265$$ 11.0000 0.675725
$$266$$ 0 0
$$267$$ −12.0000 −0.734388
$$268$$ 0 0
$$269$$ 12.0000 0.731653 0.365826 0.930683i $$-0.380786\pi$$
0.365826 + 0.930683i $$0.380786\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.00000 −0.0603023
$$276$$ 0 0
$$277$$ 2.00000 0.120168 0.0600842 0.998193i $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ 0 0
$$279$$ −4.00000 −0.239474
$$280$$ 0 0
$$281$$ −3.00000 −0.178965 −0.0894825 0.995988i $$-0.528521\pi$$
−0.0894825 + 0.995988i $$0.528521\pi$$
$$282$$ 0 0
$$283$$ 22.0000 1.30776 0.653882 0.756596i $$-0.273139\pi$$
0.653882 + 0.756596i $$0.273139\pi$$
$$284$$ 0 0
$$285$$ 10.0000 0.592349
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ −12.0000 −0.703452
$$292$$ 0 0
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 0 0
$$295$$ −8.00000 −0.465778
$$296$$ 0 0
$$297$$ 4.00000 0.232104
$$298$$ 0 0
$$299$$ 21.0000 1.21446
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −24.0000 −1.37876
$$304$$ 0 0
$$305$$ 12.0000 0.687118
$$306$$ 0 0
$$307$$ 6.00000 0.342438 0.171219 0.985233i $$-0.445229\pi$$
0.171219 + 0.985233i $$0.445229\pi$$
$$308$$ 0 0
$$309$$ −40.0000 −2.27552
$$310$$ 0 0
$$311$$ 4.00000 0.226819 0.113410 0.993548i $$-0.463823\pi$$
0.113410 + 0.993548i $$0.463823\pi$$
$$312$$ 0 0
$$313$$ −16.0000 −0.904373 −0.452187 0.891923i $$-0.649356\pi$$
−0.452187 + 0.891923i $$0.649356\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2.00000 0.112331 0.0561656 0.998421i $$-0.482113\pi$$
0.0561656 + 0.998421i $$0.482113\pi$$
$$318$$ 0 0
$$319$$ 6.00000 0.335936
$$320$$ 0 0
$$321$$ 24.0000 1.33955
$$322$$ 0 0
$$323$$ 10.0000 0.556415
$$324$$ 0 0
$$325$$ 3.00000 0.166410
$$326$$ 0 0
$$327$$ −8.00000 −0.442401
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −27.0000 −1.48405 −0.742027 0.670370i $$-0.766135\pi$$
−0.742027 + 0.670370i $$0.766135\pi$$
$$332$$ 0 0
$$333$$ −5.00000 −0.273998
$$334$$ 0 0
$$335$$ −4.00000 −0.218543
$$336$$ 0 0
$$337$$ −26.0000 −1.41631 −0.708155 0.706057i $$-0.750472\pi$$
−0.708155 + 0.706057i $$0.750472\pi$$
$$338$$ 0 0
$$339$$ 40.0000 2.17250
$$340$$ 0 0
$$341$$ 4.00000 0.216612
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 14.0000 0.753735
$$346$$ 0 0
$$347$$ 8.00000 0.429463 0.214731 0.976673i $$-0.431112\pi$$
0.214731 + 0.976673i $$0.431112\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ −12.0000 −0.640513
$$352$$ 0 0
$$353$$ −20.0000 −1.06449 −0.532246 0.846590i $$-0.678652\pi$$
−0.532246 + 0.846590i $$0.678652\pi$$
$$354$$ 0 0
$$355$$ −4.00000 −0.212298
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 30.0000 1.58334 0.791670 0.610949i $$-0.209212\pi$$
0.791670 + 0.610949i $$0.209212\pi$$
$$360$$ 0 0
$$361$$ 6.00000 0.315789
$$362$$ 0 0
$$363$$ −20.0000 −1.04973
$$364$$ 0 0
$$365$$ −12.0000 −0.628109
$$366$$ 0 0
$$367$$ −19.0000 −0.991792 −0.495896 0.868382i $$-0.665160\pi$$
−0.495896 + 0.868382i $$0.665160\pi$$
$$368$$ 0 0
$$369$$ 5.00000 0.260290
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 14.0000 0.724893 0.362446 0.932005i $$-0.381942\pi$$
0.362446 + 0.932005i $$0.381942\pi$$
$$374$$ 0 0
$$375$$ 2.00000 0.103280
$$376$$ 0 0
$$377$$ −18.0000 −0.927047
$$378$$ 0 0
$$379$$ −21.0000 −1.07870 −0.539349 0.842082i $$-0.681330\pi$$
−0.539349 + 0.842082i $$0.681330\pi$$
$$380$$ 0 0
$$381$$ 34.0000 1.74187
$$382$$ 0 0
$$383$$ 21.0000 1.07305 0.536525 0.843884i $$-0.319737\pi$$
0.536525 + 0.843884i $$0.319737\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 6.00000 0.304997
$$388$$ 0 0
$$389$$ −16.0000 −0.811232 −0.405616 0.914044i $$-0.632943\pi$$
−0.405616 + 0.914044i $$0.632943\pi$$
$$390$$ 0 0
$$391$$ 14.0000 0.708010
$$392$$ 0 0
$$393$$ −14.0000 −0.706207
$$394$$ 0 0
$$395$$ 14.0000 0.704416
$$396$$ 0 0
$$397$$ −18.0000 −0.903394 −0.451697 0.892171i $$-0.649181\pi$$
−0.451697 + 0.892171i $$0.649181\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 13.0000 0.649189 0.324595 0.945853i $$-0.394772\pi$$
0.324595 + 0.945853i $$0.394772\pi$$
$$402$$ 0 0
$$403$$ −12.0000 −0.597763
$$404$$ 0 0
$$405$$ −11.0000 −0.546594
$$406$$ 0 0
$$407$$ 5.00000 0.247841
$$408$$ 0 0
$$409$$ 6.00000 0.296681 0.148340 0.988936i $$-0.452607\pi$$
0.148340 + 0.988936i $$0.452607\pi$$
$$410$$ 0 0
$$411$$ −24.0000 −1.18383
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 4.00000 0.196352
$$416$$ 0 0
$$417$$ −8.00000 −0.391762
$$418$$ 0 0
$$419$$ 5.00000 0.244266 0.122133 0.992514i $$-0.461027\pi$$
0.122133 + 0.992514i $$0.461027\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 0 0
$$423$$ 9.00000 0.437595
$$424$$ 0 0
$$425$$ 2.00000 0.0970143
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ −16.0000 −0.770693 −0.385346 0.922772i $$-0.625918\pi$$
−0.385346 + 0.922772i $$0.625918\pi$$
$$432$$ 0 0
$$433$$ −24.0000 −1.15337 −0.576683 0.816968i $$-0.695653\pi$$
−0.576683 + 0.816968i $$0.695653\pi$$
$$434$$ 0 0
$$435$$ −12.0000 −0.575356
$$436$$ 0 0
$$437$$ 35.0000 1.67428
$$438$$ 0 0
$$439$$ 10.0000 0.477274 0.238637 0.971109i $$-0.423299\pi$$
0.238637 + 0.971109i $$0.423299\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −32.0000 −1.52037 −0.760183 0.649709i $$-0.774891\pi$$
−0.760183 + 0.649709i $$0.774891\pi$$
$$444$$ 0 0
$$445$$ −6.00000 −0.284427
$$446$$ 0 0
$$447$$ 20.0000 0.945968
$$448$$ 0 0
$$449$$ 13.0000 0.613508 0.306754 0.951789i $$-0.400757\pi$$
0.306754 + 0.951789i $$0.400757\pi$$
$$450$$ 0 0
$$451$$ −5.00000 −0.235441
$$452$$ 0 0
$$453$$ −20.0000 −0.939682
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −22.0000 −1.02912 −0.514558 0.857455i $$-0.672044\pi$$
−0.514558 + 0.857455i $$0.672044\pi$$
$$458$$ 0 0
$$459$$ −8.00000 −0.373408
$$460$$ 0 0
$$461$$ −14.0000 −0.652045 −0.326023 0.945362i $$-0.605709\pi$$
−0.326023 + 0.945362i $$0.605709\pi$$
$$462$$ 0 0
$$463$$ 9.00000 0.418265 0.209133 0.977887i $$-0.432936\pi$$
0.209133 + 0.977887i $$0.432936\pi$$
$$464$$ 0 0
$$465$$ −8.00000 −0.370991
$$466$$ 0 0
$$467$$ 10.0000 0.462745 0.231372 0.972865i $$-0.425678\pi$$
0.231372 + 0.972865i $$0.425678\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −10.0000 −0.460776
$$472$$ 0 0
$$473$$ −6.00000 −0.275880
$$474$$ 0 0
$$475$$ 5.00000 0.229416
$$476$$ 0 0
$$477$$ 11.0000 0.503655
$$478$$ 0 0
$$479$$ 16.0000 0.731059 0.365529 0.930800i $$-0.380888\pi$$
0.365529 + 0.930800i $$0.380888\pi$$
$$480$$ 0 0
$$481$$ −15.0000 −0.683941
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −6.00000 −0.272446
$$486$$ 0 0
$$487$$ −8.00000 −0.362515 −0.181257 0.983436i $$-0.558017\pi$$
−0.181257 + 0.983436i $$0.558017\pi$$
$$488$$ 0 0
$$489$$ 8.00000 0.361773
$$490$$ 0 0
$$491$$ −20.0000 −0.902587 −0.451294 0.892375i $$-0.649037\pi$$
−0.451294 + 0.892375i $$0.649037\pi$$
$$492$$ 0 0
$$493$$ −12.0000 −0.540453
$$494$$ 0 0
$$495$$ −1.00000 −0.0449467
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 28.0000 1.25345 0.626726 0.779240i $$-0.284395\pi$$
0.626726 + 0.779240i $$0.284395\pi$$
$$500$$ 0 0
$$501$$ −10.0000 −0.446767
$$502$$ 0 0
$$503$$ −16.0000 −0.713405 −0.356702 0.934218i $$-0.616099\pi$$
−0.356702 + 0.934218i $$0.616099\pi$$
$$504$$ 0 0
$$505$$ −12.0000 −0.533993
$$506$$ 0 0
$$507$$ −8.00000 −0.355292
$$508$$ 0 0
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −20.0000 −0.883022
$$514$$ 0 0
$$515$$ −20.0000 −0.881305
$$516$$ 0 0
$$517$$ −9.00000 −0.395820
$$518$$ 0 0
$$519$$ −38.0000 −1.66801
$$520$$ 0 0
$$521$$ 15.0000 0.657162 0.328581 0.944476i $$-0.393430\pi$$
0.328581 + 0.944476i $$0.393430\pi$$
$$522$$ 0 0
$$523$$ −28.0000 −1.22435 −0.612177 0.790721i $$-0.709706\pi$$
−0.612177 + 0.790721i $$0.709706\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −8.00000 −0.348485
$$528$$ 0 0
$$529$$ 26.0000 1.13043
$$530$$ 0 0
$$531$$ −8.00000 −0.347170
$$532$$ 0 0
$$533$$ 15.0000 0.649722
$$534$$ 0 0
$$535$$ 12.0000 0.518805
$$536$$ 0 0
$$537$$ 18.0000 0.776757
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −40.0000 −1.71973 −0.859867 0.510518i $$-0.829454\pi$$
−0.859867 + 0.510518i $$0.829454\pi$$
$$542$$ 0 0
$$543$$ −4.00000 −0.171656
$$544$$ 0 0
$$545$$ −4.00000 −0.171341
$$546$$ 0 0
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ 0 0
$$549$$ 12.0000 0.512148
$$550$$ 0 0
$$551$$ −30.0000 −1.27804
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −10.0000 −0.424476
$$556$$ 0 0
$$557$$ 21.0000 0.889799 0.444899 0.895581i $$-0.353239\pi$$
0.444899 + 0.895581i $$0.353239\pi$$
$$558$$ 0 0
$$559$$ 18.0000 0.761319
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ 0 0
$$563$$ −6.00000 −0.252870 −0.126435 0.991975i $$-0.540353\pi$$
−0.126435 + 0.991975i $$0.540353\pi$$
$$564$$ 0 0
$$565$$ 20.0000 0.841406
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −11.0000 −0.461144 −0.230572 0.973055i $$-0.574060\pi$$
−0.230572 + 0.973055i $$0.574060\pi$$
$$570$$ 0 0
$$571$$ 28.0000 1.17176 0.585882 0.810397i $$-0.300748\pi$$
0.585882 + 0.810397i $$0.300748\pi$$
$$572$$ 0 0
$$573$$ 24.0000 1.00261
$$574$$ 0 0
$$575$$ 7.00000 0.291920
$$576$$ 0 0
$$577$$ 4.00000 0.166522 0.0832611 0.996528i $$-0.473466\pi$$
0.0832611 + 0.996528i $$0.473466\pi$$
$$578$$ 0 0
$$579$$ −40.0000 −1.66234
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −11.0000 −0.455573
$$584$$ 0 0
$$585$$ 3.00000 0.124035
$$586$$ 0 0
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ −20.0000 −0.824086
$$590$$ 0 0
$$591$$ −54.0000 −2.22126
$$592$$ 0 0
$$593$$ 12.0000 0.492781 0.246390 0.969171i $$-0.420755\pi$$
0.246390 + 0.969171i $$0.420755\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 8.00000 0.327418
$$598$$ 0 0
$$599$$ 34.0000 1.38920 0.694601 0.719395i $$-0.255581\pi$$
0.694601 + 0.719395i $$0.255581\pi$$
$$600$$ 0 0
$$601$$ 14.0000 0.571072 0.285536 0.958368i $$-0.407828\pi$$
0.285536 + 0.958368i $$0.407828\pi$$
$$602$$ 0 0
$$603$$ −4.00000 −0.162893
$$604$$ 0 0
$$605$$ −10.0000 −0.406558
$$606$$ 0 0
$$607$$ −33.0000 −1.33943 −0.669714 0.742619i $$-0.733583\pi$$
−0.669714 + 0.742619i $$0.733583\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 27.0000 1.09230
$$612$$ 0 0
$$613$$ −41.0000 −1.65597 −0.827987 0.560747i $$-0.810514\pi$$
−0.827987 + 0.560747i $$0.810514\pi$$
$$614$$ 0 0
$$615$$ 10.0000 0.403239
$$616$$ 0 0
$$617$$ 42.0000 1.69086 0.845428 0.534089i $$-0.179345\pi$$
0.845428 + 0.534089i $$0.179345\pi$$
$$618$$ 0 0
$$619$$ −35.0000 −1.40677 −0.703384 0.710810i $$-0.748329\pi$$
−0.703384 + 0.710810i $$0.748329\pi$$
$$620$$ 0 0
$$621$$ −28.0000 −1.12360
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ −10.0000 −0.399362
$$628$$ 0 0
$$629$$ −10.0000 −0.398726
$$630$$ 0 0
$$631$$ 40.0000 1.59237 0.796187 0.605050i $$-0.206847\pi$$
0.796187 + 0.605050i $$0.206847\pi$$
$$632$$ 0 0
$$633$$ −26.0000 −1.03341
$$634$$ 0 0
$$635$$ 17.0000 0.674624
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −4.00000 −0.158238
$$640$$ 0 0
$$641$$ 35.0000 1.38242 0.691208 0.722655i $$-0.257079\pi$$
0.691208 + 0.722655i $$0.257079\pi$$
$$642$$ 0 0
$$643$$ 34.0000 1.34083 0.670415 0.741987i $$-0.266116\pi$$
0.670415 + 0.741987i $$0.266116\pi$$
$$644$$ 0 0
$$645$$ 12.0000 0.472500
$$646$$ 0 0
$$647$$ −23.0000 −0.904223 −0.452112 0.891961i $$-0.649329\pi$$
−0.452112 + 0.891961i $$0.649329\pi$$
$$648$$ 0 0
$$649$$ 8.00000 0.314027
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 45.0000 1.76099 0.880493 0.474059i $$-0.157212\pi$$
0.880493 + 0.474059i $$0.157212\pi$$
$$654$$ 0 0
$$655$$ −7.00000 −0.273513
$$656$$ 0 0
$$657$$ −12.0000 −0.468165
$$658$$ 0 0
$$659$$ −16.0000 −0.623272 −0.311636 0.950202i $$-0.600877\pi$$
−0.311636 + 0.950202i $$0.600877\pi$$
$$660$$ 0 0
$$661$$ 36.0000 1.40024 0.700119 0.714026i $$-0.253130\pi$$
0.700119 + 0.714026i $$0.253130\pi$$
$$662$$ 0 0
$$663$$ 12.0000 0.466041
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −42.0000 −1.62625
$$668$$ 0 0
$$669$$ 32.0000 1.23719
$$670$$ 0 0
$$671$$ −12.0000 −0.463255
$$672$$ 0 0
$$673$$ −42.0000 −1.61898 −0.809491 0.587133i $$-0.800257\pi$$
−0.809491 + 0.587133i $$0.800257\pi$$
$$674$$ 0 0
$$675$$ −4.00000 −0.153960
$$676$$ 0 0
$$677$$ −21.0000 −0.807096 −0.403548 0.914959i $$-0.632223\pi$$
−0.403548 + 0.914959i $$0.632223\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 16.0000 0.613121
$$682$$ 0 0
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ 56.0000 2.13653
$$688$$ 0 0
$$689$$ 33.0000 1.25720
$$690$$ 0 0
$$691$$ −8.00000 −0.304334 −0.152167 0.988355i $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −4.00000 −0.151729
$$696$$ 0 0
$$697$$ 10.0000 0.378777
$$698$$ 0 0
$$699$$ 4.00000 0.151294
$$700$$ 0 0
$$701$$ 42.0000 1.58632 0.793159 0.609015i $$-0.208435\pi$$
0.793159 + 0.609015i $$0.208435\pi$$
$$702$$ 0 0
$$703$$ −25.0000 −0.942893
$$704$$ 0 0
$$705$$ 18.0000 0.677919
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −18.0000 −0.676004 −0.338002 0.941145i $$-0.609751\pi$$
−0.338002 + 0.941145i $$0.609751\pi$$
$$710$$ 0 0
$$711$$ 14.0000 0.525041
$$712$$ 0 0
$$713$$ −28.0000 −1.04861
$$714$$ 0 0
$$715$$ −3.00000 −0.112194
$$716$$ 0 0
$$717$$ 12.0000 0.448148
$$718$$ 0 0
$$719$$ 36.0000 1.34257 0.671287 0.741198i $$-0.265742\pi$$
0.671287 + 0.741198i $$0.265742\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −46.0000 −1.71076
$$724$$ 0 0
$$725$$ −6.00000 −0.222834
$$726$$ 0 0
$$727$$ −41.0000 −1.52061 −0.760303 0.649569i $$-0.774949\pi$$
−0.760303 + 0.649569i $$0.774949\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 12.0000 0.443836
$$732$$ 0 0
$$733$$ −31.0000 −1.14501 −0.572506 0.819901i $$-0.694029\pi$$
−0.572506 + 0.819901i $$0.694029\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 4.00000 0.147342
$$738$$ 0 0
$$739$$ −41.0000 −1.50821 −0.754105 0.656754i $$-0.771929\pi$$
−0.754105 + 0.656754i $$0.771929\pi$$
$$740$$ 0 0
$$741$$ 30.0000 1.10208
$$742$$ 0 0
$$743$$ −3.00000 −0.110059 −0.0550297 0.998485i $$-0.517525\pi$$
−0.0550297 + 0.998485i $$0.517525\pi$$
$$744$$ 0 0
$$745$$ 10.0000 0.366372
$$746$$ 0 0
$$747$$ 4.00000 0.146352
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 18.0000 0.656829 0.328415 0.944534i $$-0.393486\pi$$
0.328415 + 0.944534i $$0.393486\pi$$
$$752$$ 0 0
$$753$$ −58.0000 −2.11364
$$754$$ 0 0
$$755$$ −10.0000 −0.363937
$$756$$ 0 0
$$757$$ −6.00000 −0.218074 −0.109037 0.994038i $$-0.534777\pi$$
−0.109037 + 0.994038i $$0.534777\pi$$
$$758$$ 0 0
$$759$$ −14.0000 −0.508168
$$760$$ 0 0
$$761$$ 3.00000 0.108750 0.0543750 0.998521i $$-0.482683\pi$$
0.0543750 + 0.998521i $$0.482683\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 2.00000 0.0723102
$$766$$ 0 0
$$767$$ −24.0000 −0.866590
$$768$$ 0 0
$$769$$ 41.0000 1.47850 0.739249 0.673432i $$-0.235181\pi$$
0.739249 + 0.673432i $$0.235181\pi$$
$$770$$ 0 0
$$771$$ −24.0000 −0.864339
$$772$$ 0 0
$$773$$ −15.0000 −0.539513 −0.269756 0.962929i $$-0.586943\pi$$
−0.269756 + 0.962929i $$0.586943\pi$$
$$774$$ 0 0
$$775$$ −4.00000 −0.143684
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 25.0000 0.895718
$$780$$ 0 0
$$781$$ 4.00000 0.143131
$$782$$ 0 0
$$783$$ 24.0000 0.857690
$$784$$ 0 0
$$785$$ −5.00000 −0.178458
$$786$$ 0 0
$$787$$ 18.0000 0.641631 0.320815 0.947142i $$-0.396043\pi$$
0.320815 + 0.947142i $$0.396043\pi$$
$$788$$ 0 0
$$789$$ 16.0000 0.569615
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 36.0000 1.27840
$$794$$ 0 0
$$795$$ 22.0000 0.780260
$$796$$ 0 0
$$797$$ −2.00000 −0.0708436 −0.0354218 0.999372i $$-0.511277\pi$$
−0.0354218 + 0.999372i $$0.511277\pi$$
$$798$$ 0 0
$$799$$ 18.0000 0.636794
$$800$$ 0 0
$$801$$ −6.00000 −0.212000
$$802$$ 0 0
$$803$$ 12.0000 0.423471
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 24.0000 0.844840
$$808$$ 0 0
$$809$$ 55.0000 1.93370 0.966849 0.255351i $$-0.0821909\pi$$
0.966849 + 0.255351i $$0.0821909\pi$$
$$810$$ 0 0
$$811$$ 5.00000 0.175574 0.0877869 0.996139i $$-0.472021\pi$$
0.0877869 + 0.996139i $$0.472021\pi$$
$$812$$ 0 0
$$813$$ 16.0000 0.561144
$$814$$ 0 0
$$815$$ 4.00000 0.140114
$$816$$ 0 0
$$817$$ 30.0000 1.04957
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 30.0000 1.04701 0.523504 0.852023i $$-0.324625\pi$$
0.523504 + 0.852023i $$0.324625\pi$$
$$822$$ 0 0
$$823$$ 4.00000 0.139431 0.0697156 0.997567i $$-0.477791\pi$$
0.0697156 + 0.997567i $$0.477791\pi$$
$$824$$ 0 0
$$825$$ −2.00000 −0.0696311
$$826$$ 0 0
$$827$$ −14.0000 −0.486828 −0.243414 0.969923i $$-0.578267\pi$$
−0.243414 + 0.969923i $$0.578267\pi$$
$$828$$ 0 0
$$829$$ −38.0000 −1.31979 −0.659897 0.751356i $$-0.729400\pi$$
−0.659897 + 0.751356i $$0.729400\pi$$
$$830$$ 0 0
$$831$$ 4.00000 0.138758
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −5.00000 −0.173032
$$836$$ 0 0
$$837$$ 16.0000 0.553041
$$838$$ 0 0
$$839$$ 14.0000 0.483334 0.241667 0.970359i $$-0.422306\pi$$
0.241667 + 0.970359i $$0.422306\pi$$
$$840$$ 0 0
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ −6.00000 −0.206651
$$844$$ 0 0
$$845$$ −4.00000 −0.137604
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 44.0000 1.51008
$$850$$ 0 0
$$851$$ −35.0000 −1.19978
$$852$$ 0 0
$$853$$ −23.0000 −0.787505 −0.393753 0.919216i $$-0.628823\pi$$
−0.393753 + 0.919216i $$0.628823\pi$$
$$854$$ 0 0
$$855$$ 5.00000 0.170996
$$856$$ 0 0
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ −40.0000 −1.36478 −0.682391 0.730987i $$-0.739060\pi$$
−0.682391 + 0.730987i $$0.739060\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −13.0000 −0.442525 −0.221263 0.975214i $$-0.571018\pi$$
−0.221263 + 0.975214i $$0.571018\pi$$
$$864$$ 0 0
$$865$$ −19.0000 −0.646019
$$866$$ 0 0
$$867$$ −26.0000 −0.883006
$$868$$ 0 0
$$869$$ −14.0000 −0.474917
$$870$$ 0 0
$$871$$ −12.0000 −0.406604
$$872$$ 0 0
$$873$$ −6.00000 −0.203069
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 9.00000 0.303908 0.151954 0.988388i $$-0.451443\pi$$
0.151954 + 0.988388i $$0.451443\pi$$
$$878$$ 0 0
$$879$$ −42.0000 −1.41662
$$880$$ 0 0
$$881$$ 7.00000 0.235836 0.117918 0.993023i $$-0.462378\pi$$
0.117918 + 0.993023i $$0.462378\pi$$
$$882$$ 0 0
$$883$$ 8.00000 0.269221 0.134611 0.990899i $$-0.457022\pi$$
0.134611 + 0.990899i $$0.457022\pi$$
$$884$$ 0 0
$$885$$ −16.0000 −0.537834
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 11.0000 0.368514
$$892$$ 0 0
$$893$$ 45.0000 1.50587
$$894$$ 0 0
$$895$$ 9.00000 0.300837
$$896$$ 0 0
$$897$$ 42.0000 1.40234
$$898$$ 0 0
$$899$$ 24.0000 0.800445
$$900$$ 0 0
$$901$$ 22.0000 0.732926
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −2.00000 −0.0664822
$$906$$ 0 0
$$907$$ 22.0000 0.730498 0.365249 0.930910i $$-0.380984\pi$$
0.365249 + 0.930910i $$0.380984\pi$$
$$908$$ 0 0
$$909$$ −12.0000 −0.398015
$$910$$ 0 0
$$911$$ 42.0000 1.39152 0.695761 0.718273i $$-0.255067\pi$$
0.695761 + 0.718273i $$0.255067\pi$$
$$912$$ 0 0
$$913$$ −4.00000 −0.132381
$$914$$ 0 0
$$915$$ 24.0000 0.793416
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −18.0000 −0.593765 −0.296883 0.954914i $$-0.595947\pi$$
−0.296883 + 0.954914i $$0.595947\pi$$
$$920$$ 0 0
$$921$$ 12.0000 0.395413
$$922$$ 0 0
$$923$$ −12.0000 −0.394985
$$924$$ 0 0
$$925$$ −5.00000 −0.164399
$$926$$ 0 0
$$927$$ −20.0000 −0.656886
$$928$$ 0 0
$$929$$ 31.0000 1.01708 0.508539 0.861039i $$-0.330186\pi$$
0.508539 + 0.861039i $$0.330186\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 8.00000 0.261908
$$934$$ 0 0
$$935$$ −2.00000 −0.0654070
$$936$$ 0 0
$$937$$ 38.0000 1.24141 0.620703 0.784046i $$-0.286847\pi$$
0.620703 + 0.784046i $$0.286847\pi$$
$$938$$ 0 0
$$939$$ −32.0000 −1.04428
$$940$$ 0 0
$$941$$ −24.0000 −0.782378 −0.391189 0.920310i $$-0.627936\pi$$
−0.391189 + 0.920310i $$0.627936\pi$$
$$942$$ 0 0
$$943$$ 35.0000 1.13976
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 14.0000 0.454939 0.227469 0.973785i $$-0.426955\pi$$
0.227469 + 0.973785i $$0.426955\pi$$
$$948$$ 0 0
$$949$$ −36.0000 −1.16861
$$950$$ 0 0
$$951$$ 4.00000 0.129709
$$952$$ 0 0
$$953$$ −20.0000 −0.647864 −0.323932 0.946080i $$-0.605005\pi$$
−0.323932 + 0.946080i $$0.605005\pi$$
$$954$$ 0 0
$$955$$ 12.0000 0.388311
$$956$$ 0 0
$$957$$ 12.0000 0.387905
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −15.0000 −0.483871
$$962$$ 0 0
$$963$$ 12.0000 0.386695
$$964$$ 0 0
$$965$$ −20.0000 −0.643823
$$966$$ 0 0
$$967$$ −8.00000 −0.257263 −0.128631 0.991692i $$-0.541058\pi$$
−0.128631 + 0.991692i $$0.541058\pi$$
$$968$$ 0 0
$$969$$ 20.0000 0.642493
$$970$$ 0 0
$$971$$ −7.00000 −0.224641 −0.112320 0.993672i $$-0.535828\pi$$
−0.112320 + 0.993672i $$0.535828\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 6.00000 0.192154
$$976$$ 0 0
$$977$$ 18.0000 0.575871 0.287936 0.957650i $$-0.407031\pi$$
0.287936 + 0.957650i $$0.407031\pi$$
$$978$$ 0 0
$$979$$ 6.00000 0.191761
$$980$$ 0 0
$$981$$ −4.00000 −0.127710
$$982$$ 0 0
$$983$$ 3.00000 0.0956851 0.0478426 0.998855i $$-0.484765\pi$$
0.0478426 + 0.998855i $$0.484765\pi$$
$$984$$ 0 0
$$985$$ −27.0000 −0.860292
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 42.0000 1.33552
$$990$$ 0 0
$$991$$ 44.0000 1.39771 0.698853 0.715265i $$-0.253694\pi$$
0.698853 + 0.715265i $$0.253694\pi$$
$$992$$ 0 0
$$993$$ −54.0000 −1.71364
$$994$$ 0 0
$$995$$ 4.00000 0.126809
$$996$$ 0 0
$$997$$ −46.0000 −1.45683 −0.728417 0.685134i $$-0.759744\pi$$
−0.728417 + 0.685134i $$0.759744\pi$$
$$998$$ 0 0
$$999$$ 20.0000 0.632772
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 1960.2.a.m.1.1 1
4.3 odd 2 3920.2.a.i.1.1 1
5.4 even 2 9800.2.a.g.1.1 1
7.2 even 3 1960.2.q.c.361.1 2
7.3 odd 6 280.2.q.c.121.1 yes 2
7.4 even 3 1960.2.q.c.961.1 2
7.5 odd 6 280.2.q.c.81.1 2
7.6 odd 2 1960.2.a.a.1.1 1
21.5 even 6 2520.2.bi.e.361.1 2
21.17 even 6 2520.2.bi.e.1801.1 2
28.3 even 6 560.2.q.c.401.1 2
28.19 even 6 560.2.q.c.81.1 2
28.27 even 2 3920.2.a.bf.1.1 1
35.3 even 12 1400.2.bh.e.849.1 4
35.12 even 12 1400.2.bh.e.249.1 4
35.17 even 12 1400.2.bh.e.849.2 4
35.19 odd 6 1400.2.q.a.1201.1 2
35.24 odd 6 1400.2.q.a.401.1 2
35.33 even 12 1400.2.bh.e.249.2 4
35.34 odd 2 9800.2.a.bi.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.q.c.81.1 2 7.5 odd 6
280.2.q.c.121.1 yes 2 7.3 odd 6
560.2.q.c.81.1 2 28.19 even 6
560.2.q.c.401.1 2 28.3 even 6
1400.2.q.a.401.1 2 35.24 odd 6
1400.2.q.a.1201.1 2 35.19 odd 6
1400.2.bh.e.249.1 4 35.12 even 12
1400.2.bh.e.249.2 4 35.33 even 12
1400.2.bh.e.849.1 4 35.3 even 12
1400.2.bh.e.849.2 4 35.17 even 12
1960.2.a.a.1.1 1 7.6 odd 2
1960.2.a.m.1.1 1 1.1 even 1 trivial
1960.2.q.c.361.1 2 7.2 even 3
1960.2.q.c.961.1 2 7.4 even 3
2520.2.bi.e.361.1 2 21.5 even 6
2520.2.bi.e.1801.1 2 21.17 even 6
3920.2.a.i.1.1 1 4.3 odd 2
3920.2.a.bf.1.1 1 28.27 even 2
9800.2.a.g.1.1 1 5.4 even 2
9800.2.a.bi.1.1 1 35.34 odd 2