# Properties

 Label 600.2.a.d.1.1 Level $600$ Weight $2$ Character 600.1 Self dual yes Analytic conductor $4.791$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$600 = 2^{3} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 600.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$4.79102412128$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 120) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 600.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} +2.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} +2.00000 q^{7} +1.00000 q^{9} +2.00000 q^{11} -2.00000 q^{13} -6.00000 q^{17} +8.00000 q^{19} -2.00000 q^{21} +4.00000 q^{23} -1.00000 q^{27} +8.00000 q^{29} -2.00000 q^{33} +10.0000 q^{37} +2.00000 q^{39} +2.00000 q^{41} +12.0000 q^{43} -3.00000 q^{49} +6.00000 q^{51} -10.0000 q^{53} -8.00000 q^{57} -6.00000 q^{59} +2.00000 q^{61} +2.00000 q^{63} +8.00000 q^{67} -4.00000 q^{69} -4.00000 q^{71} -4.00000 q^{73} +4.00000 q^{77} -8.00000 q^{79} +1.00000 q^{81} -4.00000 q^{83} -8.00000 q^{87} +6.00000 q^{89} -4.00000 q^{91} -8.00000 q^{97} +2.00000 q^{99} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.00000 −0.577350
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.00000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ 8.00000 1.83533 0.917663 0.397360i $$-0.130073\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ −2.00000 −0.436436
$$22$$ 0 0
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 8.00000 1.48556 0.742781 0.669534i $$-0.233506\pi$$
0.742781 + 0.669534i $$0.233506\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ −2.00000 −0.348155
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 10.0000 1.64399 0.821995 0.569495i $$-0.192861\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 0 0
$$39$$ 2.00000 0.320256
$$40$$ 0 0
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 12.0000 1.82998 0.914991 0.403473i $$-0.132197\pi$$
0.914991 + 0.403473i $$0.132197\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 0 0
$$51$$ 6.00000 0.840168
$$52$$ 0 0
$$53$$ −10.0000 −1.37361 −0.686803 0.726844i $$-0.740986\pi$$
−0.686803 + 0.726844i $$0.740986\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −8.00000 −1.05963
$$58$$ 0 0
$$59$$ −6.00000 −0.781133 −0.390567 0.920575i $$-0.627721\pi$$
−0.390567 + 0.920575i $$0.627721\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 0 0
$$63$$ 2.00000 0.251976
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 0 0
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ 0 0
$$73$$ −4.00000 −0.468165 −0.234082 0.972217i $$-0.575209\pi$$
−0.234082 + 0.972217i $$0.575209\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.00000 0.455842
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −8.00000 −0.857690
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ −4.00000 −0.419314
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −8.00000 −0.812277 −0.406138 0.913812i $$-0.633125\pi$$
−0.406138 + 0.913812i $$0.633125\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 2.00000 0.197066 0.0985329 0.995134i $$-0.468585\pi$$
0.0985329 + 0.995134i $$0.468585\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −4.00000 −0.386695 −0.193347 0.981130i $$-0.561934\pi$$
−0.193347 + 0.981130i $$0.561934\pi$$
$$108$$ 0 0
$$109$$ −6.00000 −0.574696 −0.287348 0.957826i $$-0.592774\pi$$
−0.287348 + 0.957826i $$0.592774\pi$$
$$110$$ 0 0
$$111$$ −10.0000 −0.949158
$$112$$ 0 0
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −2.00000 −0.184900
$$118$$ 0 0
$$119$$ −12.0000 −1.10004
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ −2.00000 −0.180334
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 18.0000 1.59724 0.798621 0.601834i $$-0.205563\pi$$
0.798621 + 0.601834i $$0.205563\pi$$
$$128$$ 0 0
$$129$$ −12.0000 −1.05654
$$130$$ 0 0
$$131$$ −18.0000 −1.57267 −0.786334 0.617802i $$-0.788023\pi$$
−0.786334 + 0.617802i $$0.788023\pi$$
$$132$$ 0 0
$$133$$ 16.0000 1.38738
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −10.0000 −0.854358 −0.427179 0.904167i $$-0.640493\pi$$
−0.427179 + 0.904167i $$0.640493\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −4.00000 −0.334497
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 3.00000 0.247436
$$148$$ 0 0
$$149$$ −12.0000 −0.983078 −0.491539 0.870855i $$-0.663566\pi$$
−0.491539 + 0.870855i $$0.663566\pi$$
$$150$$ 0 0
$$151$$ 16.0000 1.30206 0.651031 0.759051i $$-0.274337\pi$$
0.651031 + 0.759051i $$0.274337\pi$$
$$152$$ 0 0
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 14.0000 1.11732 0.558661 0.829396i $$-0.311315\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ 0 0
$$159$$ 10.0000 0.793052
$$160$$ 0 0
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ −16.0000 −1.25322 −0.626608 0.779334i $$-0.715557\pi$$
−0.626608 + 0.779334i $$0.715557\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 8.00000 0.611775
$$172$$ 0 0
$$173$$ 18.0000 1.36851 0.684257 0.729241i $$-0.260127\pi$$
0.684257 + 0.729241i $$0.260127\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 6.00000 0.450988
$$178$$ 0 0
$$179$$ −22.0000 −1.64436 −0.822179 0.569230i $$-0.807242\pi$$
−0.822179 + 0.569230i $$0.807242\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ −2.00000 −0.147844
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −12.0000 −0.877527
$$188$$ 0 0
$$189$$ −2.00000 −0.145479
$$190$$ 0 0
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ 0 0
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ −8.00000 −0.564276
$$202$$ 0 0
$$203$$ 16.0000 1.12298
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 4.00000 0.278019
$$208$$ 0 0
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 0 0
$$213$$ 4.00000 0.274075
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 4.00000 0.270295
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ −6.00000 −0.401790 −0.200895 0.979613i $$-0.564385\pi$$
−0.200895 + 0.979613i $$0.564385\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 4.00000 0.265489 0.132745 0.991150i $$-0.457621\pi$$
0.132745 + 0.991150i $$0.457621\pi$$
$$228$$ 0 0
$$229$$ 6.00000 0.396491 0.198246 0.980152i $$-0.436476\pi$$
0.198246 + 0.980152i $$0.436476\pi$$
$$230$$ 0 0
$$231$$ −4.00000 −0.263181
$$232$$ 0 0
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 8.00000 0.519656
$$238$$ 0 0
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ −10.0000 −0.644157 −0.322078 0.946713i $$-0.604381\pi$$
−0.322078 + 0.946713i $$0.604381\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −16.0000 −1.01806
$$248$$ 0 0
$$249$$ 4.00000 0.253490
$$250$$ 0 0
$$251$$ −2.00000 −0.126239 −0.0631194 0.998006i $$-0.520105\pi$$
−0.0631194 + 0.998006i $$0.520105\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 0 0
$$259$$ 20.0000 1.24274
$$260$$ 0 0
$$261$$ 8.00000 0.495188
$$262$$ 0 0
$$263$$ −12.0000 −0.739952 −0.369976 0.929041i $$-0.620634\pi$$
−0.369976 + 0.929041i $$0.620634\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ 0 0
$$269$$ 24.0000 1.46331 0.731653 0.681677i $$-0.238749\pi$$
0.731653 + 0.681677i $$0.238749\pi$$
$$270$$ 0 0
$$271$$ −16.0000 −0.971931 −0.485965 0.873978i $$-0.661532\pi$$
−0.485965 + 0.873978i $$0.661532\pi$$
$$272$$ 0 0
$$273$$ 4.00000 0.242091
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −6.00000 −0.360505 −0.180253 0.983620i $$-0.557691\pi$$
−0.180253 + 0.983620i $$0.557691\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 4.00000 0.236113
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ 8.00000 0.468968
$$292$$ 0 0
$$293$$ 22.0000 1.28525 0.642627 0.766179i $$-0.277845\pi$$
0.642627 + 0.766179i $$0.277845\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −2.00000 −0.116052
$$298$$ 0 0
$$299$$ −8.00000 −0.462652
$$300$$ 0 0
$$301$$ 24.0000 1.38334
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ −2.00000 −0.113776
$$310$$ 0 0
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 0 0
$$313$$ −4.00000 −0.226093 −0.113047 0.993590i $$-0.536061\pi$$
−0.113047 + 0.993590i $$0.536061\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ 16.0000 0.895828
$$320$$ 0 0
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ −48.0000 −2.67079
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 6.00000 0.331801
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 16.0000 0.879440 0.439720 0.898135i $$-0.355078\pi$$
0.439720 + 0.898135i $$0.355078\pi$$
$$332$$ 0 0
$$333$$ 10.0000 0.547997
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −28.0000 −1.52526 −0.762629 0.646837i $$-0.776092\pi$$
−0.762629 + 0.646837i $$0.776092\pi$$
$$338$$ 0 0
$$339$$ 2.00000 0.108625
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 28.0000 1.50312 0.751559 0.659665i $$-0.229302\pi$$
0.751559 + 0.659665i $$0.229302\pi$$
$$348$$ 0 0
$$349$$ −22.0000 −1.17763 −0.588817 0.808267i $$-0.700406\pi$$
−0.588817 + 0.808267i $$0.700406\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ 0 0
$$353$$ −6.00000 −0.319348 −0.159674 0.987170i $$-0.551044\pi$$
−0.159674 + 0.987170i $$0.551044\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 12.0000 0.635107
$$358$$ 0 0
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −14.0000 −0.730794 −0.365397 0.930852i $$-0.619067\pi$$
−0.365397 + 0.930852i $$0.619067\pi$$
$$368$$ 0 0
$$369$$ 2.00000 0.104116
$$370$$ 0 0
$$371$$ −20.0000 −1.03835
$$372$$ 0 0
$$373$$ −2.00000 −0.103556 −0.0517780 0.998659i $$-0.516489\pi$$
−0.0517780 + 0.998659i $$0.516489\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −16.0000 −0.824042
$$378$$ 0 0
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ 0 0
$$381$$ −18.0000 −0.922168
$$382$$ 0 0
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 12.0000 0.609994
$$388$$ 0 0
$$389$$ 12.0000 0.608424 0.304212 0.952604i $$-0.401607\pi$$
0.304212 + 0.952604i $$0.401607\pi$$
$$390$$ 0 0
$$391$$ −24.0000 −1.21373
$$392$$ 0 0
$$393$$ 18.0000 0.907980
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −6.00000 −0.301131 −0.150566 0.988600i $$-0.548110\pi$$
−0.150566 + 0.988600i $$0.548110\pi$$
$$398$$ 0 0
$$399$$ −16.0000 −0.801002
$$400$$ 0 0
$$401$$ 22.0000 1.09863 0.549314 0.835616i $$-0.314889\pi$$
0.549314 + 0.835616i $$0.314889\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 20.0000 0.991363
$$408$$ 0 0
$$409$$ −10.0000 −0.494468 −0.247234 0.968956i $$-0.579522\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 0 0
$$411$$ 10.0000 0.493264
$$412$$ 0 0
$$413$$ −12.0000 −0.590481
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −4.00000 −0.195881
$$418$$ 0 0
$$419$$ 6.00000 0.293119 0.146560 0.989202i $$-0.453180\pi$$
0.146560 + 0.989202i $$0.453180\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 4.00000 0.193574
$$428$$ 0 0
$$429$$ 4.00000 0.193122
$$430$$ 0 0
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 0 0
$$433$$ 12.0000 0.576683 0.288342 0.957528i $$-0.406896\pi$$
0.288342 + 0.957528i $$0.406896\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 32.0000 1.53077
$$438$$ 0 0
$$439$$ 24.0000 1.14546 0.572729 0.819745i $$-0.305885\pi$$
0.572729 + 0.819745i $$0.305885\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 0 0
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 12.0000 0.567581
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ 4.00000 0.188353
$$452$$ 0 0
$$453$$ −16.0000 −0.751746
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 0 0
$$459$$ 6.00000 0.280056
$$460$$ 0 0
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ 22.0000 1.02243 0.511213 0.859454i $$-0.329196\pi$$
0.511213 + 0.859454i $$0.329196\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −36.0000 −1.66588 −0.832941 0.553362i $$-0.813345\pi$$
−0.832941 + 0.553362i $$0.813345\pi$$
$$468$$ 0 0
$$469$$ 16.0000 0.738811
$$470$$ 0 0
$$471$$ −14.0000 −0.645086
$$472$$ 0 0
$$473$$ 24.0000 1.10352
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −10.0000 −0.457869
$$478$$ 0 0
$$479$$ −28.0000 −1.27935 −0.639676 0.768644i $$-0.720932\pi$$
−0.639676 + 0.768644i $$0.720932\pi$$
$$480$$ 0 0
$$481$$ −20.0000 −0.911922
$$482$$ 0 0
$$483$$ −8.00000 −0.364013
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −34.0000 −1.54069 −0.770344 0.637629i $$-0.779915\pi$$
−0.770344 + 0.637629i $$0.779915\pi$$
$$488$$ 0 0
$$489$$ 16.0000 0.723545
$$490$$ 0 0
$$491$$ −34.0000 −1.53440 −0.767199 0.641409i $$-0.778350\pi$$
−0.767199 + 0.641409i $$0.778350\pi$$
$$492$$ 0 0
$$493$$ −48.0000 −2.16181
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −8.00000 −0.358849
$$498$$ 0 0
$$499$$ −40.0000 −1.79065 −0.895323 0.445418i $$-0.853055\pi$$
−0.895323 + 0.445418i $$0.853055\pi$$
$$500$$ 0 0
$$501$$ 12.0000 0.536120
$$502$$ 0 0
$$503$$ −16.0000 −0.713405 −0.356702 0.934218i $$-0.616099\pi$$
−0.356702 + 0.934218i $$0.616099\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 9.00000 0.399704
$$508$$ 0 0
$$509$$ −8.00000 −0.354594 −0.177297 0.984157i $$-0.556735\pi$$
−0.177297 + 0.984157i $$0.556735\pi$$
$$510$$ 0 0
$$511$$ −8.00000 −0.353899
$$512$$ 0 0
$$513$$ −8.00000 −0.353209
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −18.0000 −0.790112
$$520$$ 0 0
$$521$$ −26.0000 −1.13908 −0.569540 0.821963i $$-0.692879\pi$$
−0.569540 + 0.821963i $$0.692879\pi$$
$$522$$ 0 0
$$523$$ 16.0000 0.699631 0.349816 0.936819i $$-0.386244\pi$$
0.349816 + 0.936819i $$0.386244\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 0 0
$$531$$ −6.00000 −0.260378
$$532$$ 0 0
$$533$$ −4.00000 −0.173259
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 22.0000 0.949370
$$538$$ 0 0
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 10.0000 0.429934 0.214967 0.976621i $$-0.431036\pi$$
0.214967 + 0.976621i $$0.431036\pi$$
$$542$$ 0 0
$$543$$ 14.0000 0.600798
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 20.0000 0.855138 0.427569 0.903983i $$-0.359370\pi$$
0.427569 + 0.903983i $$0.359370\pi$$
$$548$$ 0 0
$$549$$ 2.00000 0.0853579
$$550$$ 0 0
$$551$$ 64.0000 2.72649
$$552$$ 0 0
$$553$$ −16.0000 −0.680389
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −18.0000 −0.762684 −0.381342 0.924434i $$-0.624538\pi$$
−0.381342 + 0.924434i $$0.624538\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ 0 0
$$563$$ 36.0000 1.51722 0.758610 0.651546i $$-0.225879\pi$$
0.758610 + 0.651546i $$0.225879\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 2.00000 0.0839921
$$568$$ 0 0
$$569$$ −42.0000 −1.76073 −0.880366 0.474295i $$-0.842703\pi$$
−0.880366 + 0.474295i $$0.842703\pi$$
$$570$$ 0 0
$$571$$ 16.0000 0.669579 0.334790 0.942293i $$-0.391335\pi$$
0.334790 + 0.942293i $$0.391335\pi$$
$$572$$ 0 0
$$573$$ −12.0000 −0.501307
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −16.0000 −0.666089 −0.333044 0.942911i $$-0.608076\pi$$
−0.333044 + 0.942911i $$0.608076\pi$$
$$578$$ 0 0
$$579$$ 4.00000 0.166234
$$580$$ 0 0
$$581$$ −8.00000 −0.331896
$$582$$ 0 0
$$583$$ −20.0000 −0.828315
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −4.00000 −0.165098 −0.0825488 0.996587i $$-0.526306\pi$$
−0.0825488 + 0.996587i $$0.526306\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −6.00000 −0.246807
$$592$$ 0 0
$$593$$ −34.0000 −1.39621 −0.698106 0.715994i $$-0.745974\pi$$
−0.698106 + 0.715994i $$0.745974\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 8.00000 0.327418
$$598$$ 0 0
$$599$$ 16.0000 0.653742 0.326871 0.945069i $$-0.394006\pi$$
0.326871 + 0.945069i $$0.394006\pi$$
$$600$$ 0 0
$$601$$ −30.0000 −1.22373 −0.611863 0.790964i $$-0.709580\pi$$
−0.611863 + 0.790964i $$0.709580\pi$$
$$602$$ 0 0
$$603$$ 8.00000 0.325785
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 22.0000 0.892952 0.446476 0.894795i $$-0.352679\pi$$
0.446476 + 0.894795i $$0.352679\pi$$
$$608$$ 0 0
$$609$$ −16.0000 −0.648353
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −14.0000 −0.565455 −0.282727 0.959200i $$-0.591239\pi$$
−0.282727 + 0.959200i $$0.591239\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 10.0000 0.402585 0.201292 0.979531i $$-0.435486\pi$$
0.201292 + 0.979531i $$0.435486\pi$$
$$618$$ 0 0
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 0 0
$$621$$ −4.00000 −0.160514
$$622$$ 0 0
$$623$$ 12.0000 0.480770
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −16.0000 −0.638978
$$628$$ 0 0
$$629$$ −60.0000 −2.39236
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ 0 0
$$633$$ −4.00000 −0.158986
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.00000 0.237729
$$638$$ 0 0
$$639$$ −4.00000 −0.158238
$$640$$ 0 0
$$641$$ 18.0000 0.710957 0.355479 0.934684i $$-0.384318\pi$$
0.355479 + 0.934684i $$0.384318\pi$$
$$642$$ 0 0
$$643$$ −24.0000 −0.946468 −0.473234 0.880937i $$-0.656913\pi$$
−0.473234 + 0.880937i $$0.656913\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 8.00000 0.314512 0.157256 0.987558i $$-0.449735\pi$$
0.157256 + 0.987558i $$0.449735\pi$$
$$648$$ 0 0
$$649$$ −12.0000 −0.471041
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −6.00000 −0.234798 −0.117399 0.993085i $$-0.537456\pi$$
−0.117399 + 0.993085i $$0.537456\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −4.00000 −0.156055
$$658$$ 0 0
$$659$$ 30.0000 1.16863 0.584317 0.811525i $$-0.301362\pi$$
0.584317 + 0.811525i $$0.301362\pi$$
$$660$$ 0 0
$$661$$ 2.00000 0.0777910 0.0388955 0.999243i $$-0.487616\pi$$
0.0388955 + 0.999243i $$0.487616\pi$$
$$662$$ 0 0
$$663$$ −12.0000 −0.466041
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 32.0000 1.23904
$$668$$ 0 0
$$669$$ 6.00000 0.231973
$$670$$ 0 0
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ 20.0000 0.770943 0.385472 0.922720i $$-0.374039\pi$$
0.385472 + 0.922720i $$0.374039\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −30.0000 −1.15299 −0.576497 0.817099i $$-0.695581\pi$$
−0.576497 + 0.817099i $$0.695581\pi$$
$$678$$ 0 0
$$679$$ −16.0000 −0.614024
$$680$$ 0 0
$$681$$ −4.00000 −0.153280
$$682$$ 0 0
$$683$$ −20.0000 −0.765279 −0.382639 0.923898i $$-0.624985\pi$$
−0.382639 + 0.923898i $$0.624985\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −6.00000 −0.228914
$$688$$ 0 0
$$689$$ 20.0000 0.761939
$$690$$ 0 0
$$691$$ 48.0000 1.82601 0.913003 0.407953i $$-0.133757\pi$$
0.913003 + 0.407953i $$0.133757\pi$$
$$692$$ 0 0
$$693$$ 4.00000 0.151947
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −12.0000 −0.454532
$$698$$ 0 0
$$699$$ 6.00000 0.226941
$$700$$ 0 0
$$701$$ −8.00000 −0.302156 −0.151078 0.988522i $$-0.548274\pi$$
−0.151078 + 0.988522i $$0.548274\pi$$
$$702$$ 0 0
$$703$$ 80.0000 3.01726
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 46.0000 1.72757 0.863783 0.503864i $$-0.168089\pi$$
0.863783 + 0.503864i $$0.168089\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −20.0000 −0.746914
$$718$$ 0 0
$$719$$ 40.0000 1.49175 0.745874 0.666087i $$-0.232032\pi$$
0.745874 + 0.666087i $$0.232032\pi$$
$$720$$ 0 0
$$721$$ 4.00000 0.148968
$$722$$ 0 0
$$723$$ 10.0000 0.371904
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 30.0000 1.11264 0.556319 0.830969i $$-0.312213\pi$$
0.556319 + 0.830969i $$0.312213\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −72.0000 −2.66302
$$732$$ 0 0
$$733$$ 42.0000 1.55131 0.775653 0.631160i $$-0.217421\pi$$
0.775653 + 0.631160i $$0.217421\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 16.0000 0.589368
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 16.0000 0.587775
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −4.00000 −0.146352
$$748$$ 0 0
$$749$$ −8.00000 −0.292314
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ 0 0
$$753$$ 2.00000 0.0728841
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −38.0000 −1.38113 −0.690567 0.723269i $$-0.742639\pi$$
−0.690567 + 0.723269i $$0.742639\pi$$
$$758$$ 0 0
$$759$$ −8.00000 −0.290382
$$760$$ 0 0
$$761$$ −2.00000 −0.0724999 −0.0362500 0.999343i $$-0.511541\pi$$
−0.0362500 + 0.999343i $$0.511541\pi$$
$$762$$ 0 0
$$763$$ −12.0000 −0.434429
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 12.0000 0.433295
$$768$$ 0 0
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ −6.00000 −0.216085
$$772$$ 0 0
$$773$$ −38.0000 −1.36677 −0.683383 0.730061i $$-0.739492\pi$$
−0.683383 + 0.730061i $$0.739492\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −20.0000 −0.717496
$$778$$ 0 0
$$779$$ 16.0000 0.573259
$$780$$ 0 0
$$781$$ −8.00000 −0.286263
$$782$$ 0 0
$$783$$ −8.00000 −0.285897
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −32.0000 −1.14068 −0.570338 0.821410i $$-0.693188\pi$$
−0.570338 + 0.821410i $$0.693188\pi$$
$$788$$ 0 0
$$789$$ 12.0000 0.427211
$$790$$ 0 0
$$791$$ −4.00000 −0.142224
$$792$$ 0 0
$$793$$ −4.00000 −0.142044
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −30.0000 −1.06265 −0.531327 0.847167i $$-0.678307\pi$$
−0.531327 + 0.847167i $$0.678307\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 6.00000 0.212000
$$802$$ 0 0
$$803$$ −8.00000 −0.282314
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −24.0000 −0.844840
$$808$$ 0 0
$$809$$ 18.0000 0.632846 0.316423 0.948618i $$-0.397518\pi$$
0.316423 + 0.948618i $$0.397518\pi$$
$$810$$ 0 0
$$811$$ 12.0000 0.421377 0.210688 0.977553i $$-0.432429\pi$$
0.210688 + 0.977553i $$0.432429\pi$$
$$812$$ 0 0
$$813$$ 16.0000 0.561144
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 96.0000 3.35861
$$818$$ 0 0
$$819$$ −4.00000 −0.139771
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ −26.0000 −0.906303 −0.453152 0.891434i $$-0.649700\pi$$
−0.453152 + 0.891434i $$0.649700\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 36.0000 1.25184 0.625921 0.779886i $$-0.284723\pi$$
0.625921 + 0.779886i $$0.284723\pi$$
$$828$$ 0 0
$$829$$ −14.0000 −0.486240 −0.243120 0.969996i $$-0.578171\pi$$
−0.243120 + 0.969996i $$0.578171\pi$$
$$830$$ 0 0
$$831$$ 6.00000 0.208138
$$832$$ 0 0
$$833$$ 18.0000 0.623663
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 24.0000 0.828572 0.414286 0.910147i $$-0.364031\pi$$
0.414286 + 0.910147i $$0.364031\pi$$
$$840$$ 0 0
$$841$$ 35.0000 1.20690
$$842$$ 0 0
$$843$$ 18.0000 0.619953
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −14.0000 −0.481046
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 40.0000 1.37118
$$852$$ 0 0
$$853$$ 10.0000 0.342393 0.171197 0.985237i $$-0.445237\pi$$
0.171197 + 0.985237i $$0.445237\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 34.0000 1.16142 0.580709 0.814111i $$-0.302775\pi$$
0.580709 + 0.814111i $$0.302775\pi$$
$$858$$ 0 0
$$859$$ 28.0000 0.955348 0.477674 0.878537i $$-0.341480\pi$$
0.477674 + 0.878537i $$0.341480\pi$$
$$860$$ 0 0
$$861$$ −4.00000 −0.136320
$$862$$ 0 0
$$863$$ 12.0000 0.408485 0.204242 0.978920i $$-0.434527\pi$$
0.204242 + 0.978920i $$0.434527\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −19.0000 −0.645274
$$868$$ 0 0
$$869$$ −16.0000 −0.542763
$$870$$ 0 0
$$871$$ −16.0000 −0.542139
$$872$$ 0 0
$$873$$ −8.00000 −0.270759
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 14.0000 0.472746 0.236373 0.971662i $$-0.424041\pi$$
0.236373 + 0.971662i $$0.424041\pi$$
$$878$$ 0 0
$$879$$ −22.0000 −0.742042
$$880$$ 0 0
$$881$$ −2.00000 −0.0673817 −0.0336909 0.999432i $$-0.510726\pi$$
−0.0336909 + 0.999432i $$0.510726\pi$$
$$882$$ 0 0
$$883$$ 8.00000 0.269221 0.134611 0.990899i $$-0.457022\pi$$
0.134611 + 0.990899i $$0.457022\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −12.0000 −0.402921 −0.201460 0.979497i $$-0.564569\pi$$
−0.201460 + 0.979497i $$0.564569\pi$$
$$888$$ 0 0
$$889$$ 36.0000 1.20740
$$890$$ 0 0
$$891$$ 2.00000 0.0670025
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 8.00000 0.267112
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 60.0000 1.99889
$$902$$ 0 0
$$903$$ −24.0000 −0.798670
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 28.0000 0.929725 0.464862 0.885383i $$-0.346104\pi$$
0.464862 + 0.885383i $$0.346104\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 48.0000 1.59031 0.795155 0.606406i $$-0.207389\pi$$
0.795155 + 0.606406i $$0.207389\pi$$
$$912$$ 0 0
$$913$$ −8.00000 −0.264761
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −36.0000 −1.18882
$$918$$ 0 0
$$919$$ −24.0000 −0.791687 −0.395843 0.918318i $$-0.629548\pi$$
−0.395843 + 0.918318i $$0.629548\pi$$
$$920$$ 0 0
$$921$$ 20.0000 0.659022
$$922$$ 0 0
$$923$$ 8.00000 0.263323
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 2.00000 0.0656886
$$928$$ 0 0
$$929$$ 14.0000 0.459325 0.229663 0.973270i $$-0.426238\pi$$
0.229663 + 0.973270i $$0.426238\pi$$
$$930$$ 0 0
$$931$$ −24.0000 −0.786568
$$932$$ 0 0
$$933$$ −12.0000 −0.392862
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 56.0000 1.82944 0.914720 0.404088i $$-0.132411\pi$$
0.914720 + 0.404088i $$0.132411\pi$$
$$938$$ 0 0
$$939$$ 4.00000 0.130535
$$940$$ 0 0
$$941$$ −4.00000 −0.130396 −0.0651981 0.997872i $$-0.520768\pi$$
−0.0651981 + 0.997872i $$0.520768\pi$$
$$942$$ 0 0
$$943$$ 8.00000 0.260516
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −36.0000 −1.16984 −0.584921 0.811090i $$-0.698875\pi$$
−0.584921 + 0.811090i $$0.698875\pi$$
$$948$$ 0 0
$$949$$ 8.00000 0.259691
$$950$$ 0 0
$$951$$ −18.0000 −0.583690
$$952$$ 0 0
$$953$$ −42.0000 −1.36051 −0.680257 0.732974i $$-0.738132\pi$$
−0.680257 + 0.732974i $$0.738132\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −16.0000 −0.517207
$$958$$ 0 0
$$959$$ −20.0000 −0.645834
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ −4.00000 −0.128898
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 26.0000 0.836104 0.418052 0.908423i $$-0.362713\pi$$
0.418052 + 0.908423i $$0.362713\pi$$
$$968$$ 0 0
$$969$$ 48.0000 1.54198
$$970$$ 0 0
$$971$$ 30.0000 0.962746 0.481373 0.876516i $$-0.340138\pi$$
0.481373 + 0.876516i $$0.340138\pi$$
$$972$$ 0 0
$$973$$ 8.00000 0.256468
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 2.00000 0.0639857 0.0319928 0.999488i $$-0.489815\pi$$
0.0319928 + 0.999488i $$0.489815\pi$$
$$978$$ 0 0
$$979$$ 12.0000 0.383522
$$980$$ 0 0
$$981$$ −6.00000 −0.191565
$$982$$ 0 0
$$983$$ −56.0000 −1.78612 −0.893061 0.449935i $$-0.851447\pi$$
−0.893061 + 0.449935i $$0.851447\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 48.0000 1.52631
$$990$$ 0 0
$$991$$ −32.0000 −1.01651 −0.508257 0.861206i $$-0.669710\pi$$
−0.508257 + 0.861206i $$0.669710\pi$$
$$992$$ 0 0
$$993$$ −16.0000 −0.507745
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −42.0000 −1.33015 −0.665077 0.746775i $$-0.731601\pi$$
−0.665077 + 0.746775i $$0.731601\pi$$
$$998$$ 0 0
$$999$$ −10.0000 −0.316386
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 600.2.a.d.1.1 1
3.2 odd 2 1800.2.a.q.1.1 1
4.3 odd 2 1200.2.a.l.1.1 1
5.2 odd 4 120.2.f.a.49.2 yes 2
5.3 odd 4 120.2.f.a.49.1 2
5.4 even 2 600.2.a.g.1.1 1
8.3 odd 2 4800.2.a.n.1.1 1
8.5 even 2 4800.2.a.ch.1.1 1
12.11 even 2 3600.2.a.n.1.1 1
15.2 even 4 360.2.f.a.289.2 2
15.8 even 4 360.2.f.a.289.1 2
15.14 odd 2 1800.2.a.g.1.1 1
20.3 even 4 240.2.f.c.49.2 2
20.7 even 4 240.2.f.c.49.1 2
20.19 odd 2 1200.2.a.h.1.1 1
40.3 even 4 960.2.f.b.769.1 2
40.13 odd 4 960.2.f.a.769.2 2
40.19 odd 2 4800.2.a.ci.1.1 1
40.27 even 4 960.2.f.b.769.2 2
40.29 even 2 4800.2.a.k.1.1 1
40.37 odd 4 960.2.f.a.769.1 2
60.23 odd 4 720.2.f.b.289.1 2
60.47 odd 4 720.2.f.b.289.2 2
60.59 even 2 3600.2.a.bi.1.1 1
80.3 even 4 3840.2.d.m.2689.1 2
80.13 odd 4 3840.2.d.ba.2689.1 2
80.27 even 4 3840.2.d.m.2689.2 2
80.37 odd 4 3840.2.d.ba.2689.2 2
80.43 even 4 3840.2.d.v.2689.2 2
80.53 odd 4 3840.2.d.d.2689.2 2
80.67 even 4 3840.2.d.v.2689.1 2
80.77 odd 4 3840.2.d.d.2689.1 2
120.53 even 4 2880.2.f.t.1729.2 2
120.77 even 4 2880.2.f.t.1729.1 2
120.83 odd 4 2880.2.f.r.1729.2 2
120.107 odd 4 2880.2.f.r.1729.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
120.2.f.a.49.1 2 5.3 odd 4
120.2.f.a.49.2 yes 2 5.2 odd 4
240.2.f.c.49.1 2 20.7 even 4
240.2.f.c.49.2 2 20.3 even 4
360.2.f.a.289.1 2 15.8 even 4
360.2.f.a.289.2 2 15.2 even 4
600.2.a.d.1.1 1 1.1 even 1 trivial
600.2.a.g.1.1 1 5.4 even 2
720.2.f.b.289.1 2 60.23 odd 4
720.2.f.b.289.2 2 60.47 odd 4
960.2.f.a.769.1 2 40.37 odd 4
960.2.f.a.769.2 2 40.13 odd 4
960.2.f.b.769.1 2 40.3 even 4
960.2.f.b.769.2 2 40.27 even 4
1200.2.a.h.1.1 1 20.19 odd 2
1200.2.a.l.1.1 1 4.3 odd 2
1800.2.a.g.1.1 1 15.14 odd 2
1800.2.a.q.1.1 1 3.2 odd 2
2880.2.f.r.1729.1 2 120.107 odd 4
2880.2.f.r.1729.2 2 120.83 odd 4
2880.2.f.t.1729.1 2 120.77 even 4
2880.2.f.t.1729.2 2 120.53 even 4
3600.2.a.n.1.1 1 12.11 even 2
3600.2.a.bi.1.1 1 60.59 even 2
3840.2.d.d.2689.1 2 80.77 odd 4
3840.2.d.d.2689.2 2 80.53 odd 4
3840.2.d.m.2689.1 2 80.3 even 4
3840.2.d.m.2689.2 2 80.27 even 4
3840.2.d.v.2689.1 2 80.67 even 4
3840.2.d.v.2689.2 2 80.43 even 4
3840.2.d.ba.2689.1 2 80.13 odd 4
3840.2.d.ba.2689.2 2 80.37 odd 4
4800.2.a.k.1.1 1 40.29 even 2
4800.2.a.n.1.1 1 8.3 odd 2
4800.2.a.ch.1.1 1 8.5 even 2
4800.2.a.ci.1.1 1 40.19 odd 2