Properties

 Label 644.2.a.a.1.1 Level $644$ Weight $2$ Character 644.1 Self dual yes Analytic conductor $5.142$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$644 = 2^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 644.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$5.14236589017$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 644.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} +1.00000 q^{7} -2.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} +1.00000 q^{7} -2.00000 q^{9} -2.00000 q^{11} -3.00000 q^{13} -1.00000 q^{21} -1.00000 q^{23} -5.00000 q^{25} +5.00000 q^{27} +1.00000 q^{29} -5.00000 q^{31} +2.00000 q^{33} -8.00000 q^{37} +3.00000 q^{39} -7.00000 q^{41} -4.00000 q^{43} +3.00000 q^{47} +1.00000 q^{49} -12.0000 q^{53} +4.00000 q^{59} -6.00000 q^{61} -2.00000 q^{63} -12.0000 q^{67} +1.00000 q^{69} +13.0000 q^{71} +3.00000 q^{73} +5.00000 q^{75} -2.00000 q^{77} +4.00000 q^{79} +1.00000 q^{81} +16.0000 q^{83} -1.00000 q^{87} +4.00000 q^{89} -3.00000 q^{91} +5.00000 q^{93} +10.0000 q^{97} +4.00000 q^{99} +O(q^{100})$$

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 −0.288675 0.957427i $$-0.593215\pi$$
−0.288675 + 0.957427i $$0.593215\pi$$
$$4$$ 0 0
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 0 0
$$9$$ −2.00000 −0.666667
$$10$$ 0 0
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ −3.00000 −0.832050 −0.416025 0.909353i $$-0.636577\pi$$
−0.416025 + 0.909353i $$0.636577\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 0 0
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ 1.00000 0.185695 0.0928477 0.995680i $$-0.470403\pi$$
0.0928477 + 0.995680i $$0.470403\pi$$
$$30$$ 0 0
$$31$$ −5.00000 −0.898027 −0.449013 0.893525i $$-0.648224\pi$$
−0.449013 + 0.893525i $$0.648224\pi$$
$$32$$ 0 0
$$33$$ 2.00000 0.348155
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −8.00000 −1.31519 −0.657596 0.753371i $$-0.728427\pi$$
−0.657596 + 0.753371i $$0.728427\pi$$
$$38$$ 0 0
$$39$$ 3.00000 0.480384
$$40$$ 0 0
$$41$$ −7.00000 −1.09322 −0.546608 0.837389i $$-0.684081\pi$$
−0.546608 + 0.837389i $$0.684081\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 0.437595 0.218797 0.975770i $$-0.429787\pi$$
0.218797 + 0.975770i $$0.429787\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −12.0000 −1.64833 −0.824163 0.566352i $$-0.808354\pi$$
−0.824163 + 0.566352i $$0.808354\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 0 0
$$63$$ −2.00000 −0.251976
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ 0 0
$$69$$ 1.00000 0.120386
$$70$$ 0 0
$$71$$ 13.0000 1.54282 0.771408 0.636341i $$-0.219553\pi$$
0.771408 + 0.636341i $$0.219553\pi$$
$$72$$ 0 0
$$73$$ 3.00000 0.351123 0.175562 0.984468i $$-0.443826\pi$$
0.175562 + 0.984468i $$0.443826\pi$$
$$74$$ 0 0
$$75$$ 5.00000 0.577350
$$76$$ 0 0
$$77$$ −2.00000 −0.227921
$$78$$ 0 0
$$79$$ 4.00000 0.450035 0.225018 0.974355i $$-0.427756\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 16.0000 1.75623 0.878114 0.478451i $$-0.158802\pi$$
0.878114 + 0.478451i $$0.158802\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −1.00000 −0.107211
$$88$$ 0 0
$$89$$ 4.00000 0.423999 0.212000 0.977270i $$-0.432002\pi$$
0.212000 + 0.977270i $$0.432002\pi$$
$$90$$ 0 0
$$91$$ −3.00000 −0.314485
$$92$$ 0 0
$$93$$ 5.00000 0.518476
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 0 0
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ −10.0000 −0.995037 −0.497519 0.867453i $$-0.665755\pi$$
−0.497519 + 0.867453i $$0.665755\pi$$
$$102$$ 0 0
$$103$$ 14.0000 1.37946 0.689730 0.724066i $$-0.257729\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −8.00000 −0.773389 −0.386695 0.922208i $$-0.626383\pi$$
−0.386695 + 0.922208i $$0.626383\pi$$
$$108$$ 0 0
$$109$$ −4.00000 −0.383131 −0.191565 0.981480i $$-0.561356\pi$$
−0.191565 + 0.981480i $$0.561356\pi$$
$$110$$ 0 0
$$111$$ 8.00000 0.759326
$$112$$ 0 0
$$113$$ 4.00000 0.376288 0.188144 0.982141i $$-0.439753\pi$$
0.188144 + 0.982141i $$0.439753\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 6.00000 0.554700
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ 7.00000 0.631169
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 7.00000 0.621150 0.310575 0.950549i $$-0.399478\pi$$
0.310575 + 0.950549i $$0.399478\pi$$
$$128$$ 0 0
$$129$$ 4.00000 0.352180
$$130$$ 0 0
$$131$$ 3.00000 0.262111 0.131056 0.991375i $$-0.458163\pi$$
0.131056 + 0.991375i $$0.458163\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 10.0000 0.854358 0.427179 0.904167i $$-0.359507\pi$$
0.427179 + 0.904167i $$0.359507\pi$$
$$138$$ 0 0
$$139$$ 1.00000 0.0848189 0.0424094 0.999100i $$-0.486497\pi$$
0.0424094 + 0.999100i $$0.486497\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ 0 0
$$143$$ 6.00000 0.501745
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −1.00000 −0.0824786
$$148$$ 0 0
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ −11.0000 −0.895167 −0.447584 0.894242i $$-0.647715\pi$$
−0.447584 + 0.894242i $$0.647715\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 12.0000 0.957704 0.478852 0.877896i $$-0.341053\pi$$
0.478852 + 0.877896i $$0.341053\pi$$
$$158$$ 0 0
$$159$$ 12.0000 0.951662
$$160$$ 0 0
$$161$$ −1.00000 −0.0788110
$$162$$ 0 0
$$163$$ −9.00000 −0.704934 −0.352467 0.935824i $$-0.614657\pi$$
−0.352467 + 0.935824i $$0.614657\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 26.0000 1.97674 0.988372 0.152057i $$-0.0485898\pi$$
0.988372 + 0.152057i $$0.0485898\pi$$
$$174$$ 0 0
$$175$$ −5.00000 −0.377964
$$176$$ 0 0
$$177$$ −4.00000 −0.300658
$$178$$ 0 0
$$179$$ 3.00000 0.224231 0.112115 0.993695i $$-0.464237\pi$$
0.112115 + 0.993695i $$0.464237\pi$$
$$180$$ 0 0
$$181$$ −18.0000 −1.33793 −0.668965 0.743294i $$-0.733262\pi$$
−0.668965 + 0.743294i $$0.733262\pi$$
$$182$$ 0 0
$$183$$ 6.00000 0.443533
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 5.00000 0.363696
$$190$$ 0 0
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ 0 0
$$193$$ −19.0000 −1.36765 −0.683825 0.729646i $$-0.739685\pi$$
−0.683825 + 0.729646i $$0.739685\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 9.00000 0.641223 0.320612 0.947211i $$-0.396112\pi$$
0.320612 + 0.947211i $$0.396112\pi$$
$$198$$ 0 0
$$199$$ −2.00000 −0.141776 −0.0708881 0.997484i $$-0.522583\pi$$
−0.0708881 + 0.997484i $$0.522583\pi$$
$$200$$ 0 0
$$201$$ 12.0000 0.846415
$$202$$ 0 0
$$203$$ 1.00000 0.0701862
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 2.00000 0.139010
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 0 0
$$213$$ −13.0000 −0.890745
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −5.00000 −0.339422
$$218$$ 0 0
$$219$$ −3.00000 −0.202721
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 20.0000 1.33930 0.669650 0.742677i $$-0.266444\pi$$
0.669650 + 0.742677i $$0.266444\pi$$
$$224$$ 0 0
$$225$$ 10.0000 0.666667
$$226$$ 0 0
$$227$$ −20.0000 −1.32745 −0.663723 0.747978i $$-0.731025\pi$$
−0.663723 + 0.747978i $$0.731025\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 0 0
$$231$$ 2.00000 0.131590
$$232$$ 0 0
$$233$$ −1.00000 −0.0655122 −0.0327561 0.999463i $$-0.510428\pi$$
−0.0327561 + 0.999463i $$0.510428\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −4.00000 −0.259828
$$238$$ 0 0
$$239$$ −15.0000 −0.970269 −0.485135 0.874439i $$-0.661229\pi$$
−0.485135 + 0.874439i $$0.661229\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ −16.0000 −1.02640
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −16.0000 −1.01396
$$250$$ 0 0
$$251$$ −2.00000 −0.126239 −0.0631194 0.998006i $$-0.520105\pi$$
−0.0631194 + 0.998006i $$0.520105\pi$$
$$252$$ 0 0
$$253$$ 2.00000 0.125739
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 5.00000 0.311891 0.155946 0.987766i $$-0.450158\pi$$
0.155946 + 0.987766i $$0.450158\pi$$
$$258$$ 0 0
$$259$$ −8.00000 −0.497096
$$260$$ 0 0
$$261$$ −2.00000 −0.123797
$$262$$ 0 0
$$263$$ 18.0000 1.10993 0.554964 0.831875i $$-0.312732\pi$$
0.554964 + 0.831875i $$0.312732\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −4.00000 −0.244796
$$268$$ 0 0
$$269$$ −5.00000 −0.304855 −0.152428 0.988315i $$-0.548709\pi$$
−0.152428 + 0.988315i $$0.548709\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 3.00000 0.181568
$$274$$ 0 0
$$275$$ 10.0000 0.603023
$$276$$ 0 0
$$277$$ −3.00000 −0.180253 −0.0901263 0.995930i $$-0.528727\pi$$
−0.0901263 + 0.995930i $$0.528727\pi$$
$$278$$ 0 0
$$279$$ 10.0000 0.598684
$$280$$ 0 0
$$281$$ 22.0000 1.31241 0.656205 0.754583i $$-0.272161\pi$$
0.656205 + 0.754583i $$0.272161\pi$$
$$282$$ 0 0
$$283$$ −10.0000 −0.594438 −0.297219 0.954809i $$-0.596059\pi$$
−0.297219 + 0.954809i $$0.596059\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −7.00000 −0.413197
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ −10.0000 −0.586210
$$292$$ 0 0
$$293$$ −22.0000 −1.28525 −0.642627 0.766179i $$-0.722155\pi$$
−0.642627 + 0.766179i $$0.722155\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −10.0000 −0.580259
$$298$$ 0 0
$$299$$ 3.00000 0.173494
$$300$$ 0 0
$$301$$ −4.00000 −0.230556
$$302$$ 0 0
$$303$$ 10.0000 0.574485
$$304$$ 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
$$309$$ −14.0000 −0.796432
$$310$$ 0 0
$$311$$ −13.0000 −0.737162 −0.368581 0.929596i $$-0.620156\pi$$
−0.368581 + 0.929596i $$0.620156\pi$$
$$312$$ 0 0
$$313$$ 14.0000 0.791327 0.395663 0.918396i $$-0.370515\pi$$
0.395663 + 0.918396i $$0.370515\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 6.00000 0.336994 0.168497 0.985702i $$-0.446109\pi$$
0.168497 + 0.985702i $$0.446109\pi$$
$$318$$ 0 0
$$319$$ −2.00000 −0.111979
$$320$$ 0 0
$$321$$ 8.00000 0.446516
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 15.0000 0.832050
$$326$$ 0 0
$$327$$ 4.00000 0.221201
$$328$$ 0 0
$$329$$ 3.00000 0.165395
$$330$$ 0 0
$$331$$ −29.0000 −1.59398 −0.796992 0.603990i $$-0.793577\pi$$
−0.796992 + 0.603990i $$0.793577\pi$$
$$332$$ 0 0
$$333$$ 16.0000 0.876795
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ 0 0
$$339$$ −4.00000 −0.217250
$$340$$ 0 0
$$341$$ 10.0000 0.541530
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −12.0000 −0.644194 −0.322097 0.946707i $$-0.604388\pi$$
−0.322097 + 0.946707i $$0.604388\pi$$
$$348$$ 0 0
$$349$$ −25.0000 −1.33822 −0.669110 0.743164i $$-0.733324\pi$$
−0.669110 + 0.743164i $$0.733324\pi$$
$$350$$ 0 0
$$351$$ −15.0000 −0.800641
$$352$$ 0 0
$$353$$ 7.00000 0.372572 0.186286 0.982496i $$-0.440355\pi$$
0.186286 + 0.982496i $$0.440355\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 0 0
$$363$$ 7.00000 0.367405
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 24.0000 1.25279 0.626395 0.779506i $$-0.284530\pi$$
0.626395 + 0.779506i $$0.284530\pi$$
$$368$$ 0 0
$$369$$ 14.0000 0.728811
$$370$$ 0 0
$$371$$ −12.0000 −0.623009
$$372$$ 0 0
$$373$$ 10.0000 0.517780 0.258890 0.965907i $$-0.416643\pi$$
0.258890 + 0.965907i $$0.416643\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −3.00000 −0.154508
$$378$$ 0 0
$$379$$ −14.0000 −0.719132 −0.359566 0.933120i $$-0.617075\pi$$
−0.359566 + 0.933120i $$0.617075\pi$$
$$380$$ 0 0
$$381$$ −7.00000 −0.358621
$$382$$ 0 0
$$383$$ 14.0000 0.715367 0.357683 0.933843i $$-0.383567\pi$$
0.357683 + 0.933843i $$0.383567\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 8.00000 0.406663
$$388$$ 0 0
$$389$$ 4.00000 0.202808 0.101404 0.994845i $$-0.467667\pi$$
0.101404 + 0.994845i $$0.467667\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −3.00000 −0.151330
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −27.0000 −1.35509 −0.677546 0.735481i $$-0.736956\pi$$
−0.677546 + 0.735481i $$0.736956\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −18.0000 −0.898877 −0.449439 0.893311i $$-0.648376\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ 0 0
$$403$$ 15.0000 0.747203
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 16.0000 0.793091
$$408$$ 0 0
$$409$$ −21.0000 −1.03838 −0.519192 0.854658i $$-0.673767\pi$$
−0.519192 + 0.854658i $$0.673767\pi$$
$$410$$ 0 0
$$411$$ −10.0000 −0.493264
$$412$$ 0 0
$$413$$ 4.00000 0.196827
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −1.00000 −0.0489702
$$418$$ 0 0
$$419$$ 4.00000 0.195413 0.0977064 0.995215i $$-0.468849\pi$$
0.0977064 + 0.995215i $$0.468849\pi$$
$$420$$ 0 0
$$421$$ −28.0000 −1.36464 −0.682318 0.731055i $$-0.739028\pi$$
−0.682318 + 0.731055i $$0.739028\pi$$
$$422$$ 0 0
$$423$$ −6.00000 −0.291730
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −6.00000 −0.290360
$$428$$ 0 0
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ −30.0000 −1.44505 −0.722525 0.691345i $$-0.757018\pi$$
−0.722525 + 0.691345i $$0.757018\pi$$
$$432$$ 0 0
$$433$$ 6.00000 0.288342 0.144171 0.989553i $$-0.453949\pi$$
0.144171 + 0.989553i $$0.453949\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −7.00000 −0.334092 −0.167046 0.985949i $$-0.553423\pi$$
−0.167046 + 0.985949i $$0.553423\pi$$
$$440$$ 0 0
$$441$$ −2.00000 −0.0952381
$$442$$ 0 0
$$443$$ −23.0000 −1.09276 −0.546381 0.837536i $$-0.683995\pi$$
−0.546381 + 0.837536i $$0.683995\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 14.0000 0.659234
$$452$$ 0 0
$$453$$ 11.0000 0.516825
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 8.00000 0.374224 0.187112 0.982339i $$-0.440087\pi$$
0.187112 + 0.982339i $$0.440087\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 15.0000 0.698620 0.349310 0.937007i $$-0.386416\pi$$
0.349310 + 0.937007i $$0.386416\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −42.0000 −1.94353 −0.971764 0.235954i $$-0.924178\pi$$
−0.971764 + 0.235954i $$0.924178\pi$$
$$468$$ 0 0
$$469$$ −12.0000 −0.554109
$$470$$ 0 0
$$471$$ −12.0000 −0.552931
$$472$$ 0 0
$$473$$ 8.00000 0.367840
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 24.0000 1.09888
$$478$$ 0 0
$$479$$ 18.0000 0.822441 0.411220 0.911536i $$-0.365103\pi$$
0.411220 + 0.911536i $$0.365103\pi$$
$$480$$ 0 0
$$481$$ 24.0000 1.09431
$$482$$ 0 0
$$483$$ 1.00000 0.0455016
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 31.0000 1.40474 0.702372 0.711810i $$-0.252124\pi$$
0.702372 + 0.711810i $$0.252124\pi$$
$$488$$ 0 0
$$489$$ 9.00000 0.406994
$$490$$ 0 0
$$491$$ −17.0000 −0.767199 −0.383600 0.923499i $$-0.625316\pi$$
−0.383600 + 0.923499i $$0.625316\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 13.0000 0.583130
$$498$$ 0 0
$$499$$ −19.0000 −0.850557 −0.425278 0.905063i $$-0.639824\pi$$
−0.425278 + 0.905063i $$0.639824\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 16.0000 0.713405 0.356702 0.934218i $$-0.383901\pi$$
0.356702 + 0.934218i $$0.383901\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 4.00000 0.177646
$$508$$ 0 0
$$509$$ 15.0000 0.664863 0.332432 0.943127i $$-0.392131\pi$$
0.332432 + 0.943127i $$0.392131\pi$$
$$510$$ 0 0
$$511$$ 3.00000 0.132712
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −6.00000 −0.263880
$$518$$ 0 0
$$519$$ −26.0000 −1.14127
$$520$$ 0 0
$$521$$ −32.0000 −1.40195 −0.700973 0.713188i $$-0.747251\pi$$
−0.700973 + 0.713188i $$0.747251\pi$$
$$522$$ 0 0
$$523$$ −10.0000 −0.437269 −0.218635 0.975807i $$-0.570160\pi$$
−0.218635 + 0.975807i $$0.570160\pi$$
$$524$$ 0 0
$$525$$ 5.00000 0.218218
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ −8.00000 −0.347170
$$532$$ 0 0
$$533$$ 21.0000 0.909611
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −3.00000 −0.129460
$$538$$ 0 0
$$539$$ −2.00000 −0.0861461
$$540$$ 0 0
$$541$$ 45.0000 1.93470 0.967351 0.253442i $$-0.0815627\pi$$
0.967351 + 0.253442i $$0.0815627\pi$$
$$542$$ 0 0
$$543$$ 18.0000 0.772454
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −17.0000 −0.726868 −0.363434 0.931620i $$-0.618396\pi$$
−0.363434 + 0.931620i $$0.618396\pi$$
$$548$$ 0 0
$$549$$ 12.0000 0.512148
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 4.00000 0.170097
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 30.0000 1.27114 0.635570 0.772043i $$-0.280765\pi$$
0.635570 + 0.772043i $$0.280765\pi$$
$$558$$ 0 0
$$559$$ 12.0000 0.507546
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 30.0000 1.26435 0.632175 0.774826i $$-0.282163\pi$$
0.632175 + 0.774826i $$0.282163\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1.00000 0.0419961
$$568$$ 0 0
$$569$$ −4.00000 −0.167689 −0.0838444 0.996479i $$-0.526720\pi$$
−0.0838444 + 0.996479i $$0.526720\pi$$
$$570$$ 0 0
$$571$$ 10.0000 0.418487 0.209243 0.977864i $$-0.432900\pi$$
0.209243 + 0.977864i $$0.432900\pi$$
$$572$$ 0 0
$$573$$ 8.00000 0.334205
$$574$$ 0 0
$$575$$ 5.00000 0.208514
$$576$$ 0 0
$$577$$ 19.0000 0.790980 0.395490 0.918470i $$-0.370575\pi$$
0.395490 + 0.918470i $$0.370575\pi$$
$$578$$ 0 0
$$579$$ 19.0000 0.789613
$$580$$ 0 0
$$581$$ 16.0000 0.663792
$$582$$ 0 0
$$583$$ 24.0000 0.993978
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 7.00000 0.288921 0.144460 0.989511i $$-0.453855\pi$$
0.144460 + 0.989511i $$0.453855\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −9.00000 −0.370211
$$592$$ 0 0
$$593$$ −6.00000 −0.246390 −0.123195 0.992382i $$-0.539314\pi$$
−0.123195 + 0.992382i $$0.539314\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 2.00000 0.0818546
$$598$$ 0 0
$$599$$ −12.0000 −0.490307 −0.245153 0.969484i $$-0.578838\pi$$
−0.245153 + 0.969484i $$0.578838\pi$$
$$600$$ 0 0
$$601$$ −45.0000 −1.83559 −0.917794 0.397057i $$-0.870032\pi$$
−0.917794 + 0.397057i $$0.870032\pi$$
$$602$$ 0 0
$$603$$ 24.0000 0.977356
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −8.00000 −0.324710 −0.162355 0.986732i $$-0.551909\pi$$
−0.162355 + 0.986732i $$0.551909\pi$$
$$608$$ 0 0
$$609$$ −1.00000 −0.0405220
$$610$$ 0 0
$$611$$ −9.00000 −0.364101
$$612$$ 0 0
$$613$$ 6.00000 0.242338 0.121169 0.992632i $$-0.461336\pi$$
0.121169 + 0.992632i $$0.461336\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 12.0000 0.483102 0.241551 0.970388i $$-0.422344\pi$$
0.241551 + 0.970388i $$0.422344\pi$$
$$618$$ 0 0
$$619$$ 10.0000 0.401934 0.200967 0.979598i $$-0.435592\pi$$
0.200967 + 0.979598i $$0.435592\pi$$
$$620$$ 0 0
$$621$$ −5.00000 −0.200643
$$622$$ 0 0
$$623$$ 4.00000 0.160257
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 16.0000 0.636950 0.318475 0.947931i $$-0.396829\pi$$
0.318475 + 0.947931i $$0.396829\pi$$
$$632$$ 0 0
$$633$$ −12.0000 −0.476957
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −3.00000 −0.118864
$$638$$ 0 0
$$639$$ −26.0000 −1.02854
$$640$$ 0 0
$$641$$ 4.00000 0.157991 0.0789953 0.996875i $$-0.474829\pi$$
0.0789953 + 0.996875i $$0.474829\pi$$
$$642$$ 0 0
$$643$$ 28.0000 1.10421 0.552106 0.833774i $$-0.313824\pi$$
0.552106 + 0.833774i $$0.313824\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −21.0000 −0.825595 −0.412798 0.910823i $$-0.635448\pi$$
−0.412798 + 0.910823i $$0.635448\pi$$
$$648$$ 0 0
$$649$$ −8.00000 −0.314027
$$650$$ 0 0
$$651$$ 5.00000 0.195965
$$652$$ 0 0
$$653$$ −5.00000 −0.195665 −0.0978326 0.995203i $$-0.531191\pi$$
−0.0978326 + 0.995203i $$0.531191\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −6.00000 −0.234082
$$658$$ 0 0
$$659$$ −14.0000 −0.545363 −0.272681 0.962104i $$-0.587910\pi$$
−0.272681 + 0.962104i $$0.587910\pi$$
$$660$$ 0 0
$$661$$ 40.0000 1.55582 0.777910 0.628376i $$-0.216280\pi$$
0.777910 + 0.628376i $$0.216280\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −1.00000 −0.0387202
$$668$$ 0 0
$$669$$ −20.0000 −0.773245
$$670$$ 0 0
$$671$$ 12.0000 0.463255
$$672$$ 0 0
$$673$$ 43.0000 1.65753 0.828764 0.559598i $$-0.189045\pi$$
0.828764 + 0.559598i $$0.189045\pi$$
$$674$$ 0 0
$$675$$ −25.0000 −0.962250
$$676$$ 0 0
$$677$$ −12.0000 −0.461197 −0.230599 0.973049i $$-0.574068\pi$$
−0.230599 + 0.973049i $$0.574068\pi$$
$$678$$ 0 0
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ 20.0000 0.766402
$$682$$ 0 0
$$683$$ 23.0000 0.880071 0.440035 0.897980i $$-0.354966\pi$$
0.440035 + 0.897980i $$0.354966\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −10.0000 −0.381524
$$688$$ 0 0
$$689$$ 36.0000 1.37149
$$690$$ 0 0
$$691$$ 12.0000 0.456502 0.228251 0.973602i $$-0.426699\pi$$
0.228251 + 0.973602i $$0.426699\pi$$
$$692$$ 0 0
$$693$$ 4.00000 0.151947
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 1.00000 0.0378235
$$700$$ 0 0
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −10.0000 −0.376089
$$708$$ 0 0
$$709$$ 16.0000 0.600893 0.300446 0.953799i $$-0.402864\pi$$
0.300446 + 0.953799i $$0.402864\pi$$
$$710$$ 0 0
$$711$$ −8.00000 −0.300023
$$712$$ 0 0
$$713$$ 5.00000 0.187251
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 15.0000 0.560185
$$718$$ 0 0
$$719$$ −40.0000 −1.49175 −0.745874 0.666087i $$-0.767968\pi$$
−0.745874 + 0.666087i $$0.767968\pi$$
$$720$$ 0 0
$$721$$ 14.0000 0.521387
$$722$$ 0 0
$$723$$ 18.0000 0.669427
$$724$$ 0 0
$$725$$ −5.00000 −0.185695
$$726$$ 0 0
$$727$$ 20.0000 0.741759 0.370879 0.928681i $$-0.379056\pi$$
0.370879 + 0.928681i $$0.379056\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −24.0000 −0.886460 −0.443230 0.896408i $$-0.646168\pi$$
−0.443230 + 0.896408i $$0.646168\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 24.0000 0.884051
$$738$$ 0 0
$$739$$ −9.00000 −0.331070 −0.165535 0.986204i $$-0.552935\pi$$
−0.165535 + 0.986204i $$0.552935\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −16.0000 −0.586983 −0.293492 0.955962i $$-0.594817\pi$$
−0.293492 + 0.955962i $$0.594817\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −32.0000 −1.17082
$$748$$ 0 0
$$749$$ −8.00000 −0.292314
$$750$$ 0 0
$$751$$ 12.0000 0.437886 0.218943 0.975738i $$-0.429739\pi$$
0.218943 + 0.975738i $$0.429739\pi$$
$$752$$ 0 0
$$753$$ 2.00000 0.0728841
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −46.0000 −1.67190 −0.835949 0.548807i $$-0.815082\pi$$
−0.835949 + 0.548807i $$0.815082\pi$$
$$758$$ 0 0
$$759$$ −2.00000 −0.0725954
$$760$$ 0 0
$$761$$ −37.0000 −1.34125 −0.670624 0.741797i $$-0.733974\pi$$
−0.670624 + 0.741797i $$0.733974\pi$$
$$762$$ 0 0
$$763$$ −4.00000 −0.144810
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −12.0000 −0.433295
$$768$$ 0 0
$$769$$ −40.0000 −1.44244 −0.721218 0.692708i $$-0.756418\pi$$
−0.721218 + 0.692708i $$0.756418\pi$$
$$770$$ 0 0
$$771$$ −5.00000 −0.180071
$$772$$ 0 0
$$773$$ 26.0000 0.935155 0.467578 0.883952i $$-0.345127\pi$$
0.467578 + 0.883952i $$0.345127\pi$$
$$774$$ 0 0
$$775$$ 25.0000 0.898027
$$776$$ 0 0
$$777$$ 8.00000 0.286998
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −26.0000 −0.930353
$$782$$ 0 0
$$783$$ 5.00000 0.178685
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 8.00000 0.285169 0.142585 0.989783i $$-0.454459\pi$$
0.142585 + 0.989783i $$0.454459\pi$$
$$788$$ 0 0
$$789$$ −18.0000 −0.640817
$$790$$ 0 0
$$791$$ 4.00000 0.142224
$$792$$ 0 0
$$793$$ 18.0000 0.639199
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 32.0000 1.13350 0.566749 0.823890i $$-0.308201\pi$$
0.566749 + 0.823890i $$0.308201\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −8.00000 −0.282666
$$802$$ 0 0
$$803$$ −6.00000 −0.211735
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 5.00000 0.176008
$$808$$ 0 0
$$809$$ 42.0000 1.47664 0.738321 0.674450i $$-0.235619\pi$$
0.738321 + 0.674450i $$0.235619\pi$$
$$810$$ 0 0
$$811$$ −37.0000 −1.29925 −0.649623 0.760257i $$-0.725073\pi$$
−0.649623 + 0.760257i $$0.725073\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 6.00000 0.209657
$$820$$ 0 0
$$821$$ 6.00000 0.209401 0.104701 0.994504i $$-0.466612\pi$$
0.104701 + 0.994504i $$0.466612\pi$$
$$822$$ 0 0
$$823$$ −11.0000 −0.383436 −0.191718 0.981450i $$-0.561406\pi$$
−0.191718 + 0.981450i $$0.561406\pi$$
$$824$$ 0 0
$$825$$ −10.0000 −0.348155
$$826$$ 0 0
$$827$$ −12.0000 −0.417281 −0.208640 0.977992i $$-0.566904\pi$$
−0.208640 + 0.977992i $$0.566904\pi$$
$$828$$ 0 0
$$829$$ 34.0000 1.18087 0.590434 0.807086i $$-0.298956\pi$$
0.590434 + 0.807086i $$0.298956\pi$$
$$830$$ 0 0
$$831$$ 3.00000 0.104069
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −25.0000 −0.864126
$$838$$ 0 0
$$839$$ 30.0000 1.03572 0.517858 0.855467i $$-0.326730\pi$$
0.517858 + 0.855467i $$0.326730\pi$$
$$840$$ 0 0
$$841$$ −28.0000 −0.965517
$$842$$ 0 0
$$843$$ −22.0000 −0.757720
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ −7.00000 −0.240523
$$848$$ 0 0
$$849$$ 10.0000 0.343199
$$850$$ 0 0
$$851$$ 8.00000 0.274236
$$852$$ 0 0
$$853$$ −34.0000 −1.16414 −0.582069 0.813139i $$-0.697757\pi$$
−0.582069 + 0.813139i $$0.697757\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −51.0000 −1.74213 −0.871063 0.491171i $$-0.836569\pi$$
−0.871063 + 0.491171i $$0.836569\pi$$
$$858$$ 0 0
$$859$$ −29.0000 −0.989467 −0.494734 0.869045i $$-0.664734\pi$$
−0.494734 + 0.869045i $$0.664734\pi$$
$$860$$ 0 0
$$861$$ 7.00000 0.238559
$$862$$ 0 0
$$863$$ −57.0000 −1.94030 −0.970151 0.242500i $$-0.922032\pi$$
−0.970151 + 0.242500i $$0.922032\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 17.0000 0.577350
$$868$$ 0 0
$$869$$ −8.00000 −0.271381
$$870$$ 0 0
$$871$$ 36.0000 1.21981
$$872$$ 0 0
$$873$$ −20.0000 −0.676897
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 22.0000 0.742887 0.371444 0.928456i $$-0.378863\pi$$
0.371444 + 0.928456i $$0.378863\pi$$
$$878$$ 0 0
$$879$$ 22.0000 0.742042
$$880$$ 0 0
$$881$$ −58.0000 −1.95407 −0.977035 0.213080i $$-0.931651\pi$$
−0.977035 + 0.213080i $$0.931651\pi$$
$$882$$ 0 0
$$883$$ 12.0000 0.403832 0.201916 0.979403i $$-0.435283\pi$$
0.201916 + 0.979403i $$0.435283\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −25.0000 −0.839418 −0.419709 0.907659i $$-0.637868\pi$$
−0.419709 + 0.907659i $$0.637868\pi$$
$$888$$ 0 0
$$889$$ 7.00000 0.234772
$$890$$ 0 0
$$891$$ −2.00000 −0.0670025
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −3.00000 −0.100167
$$898$$ 0 0
$$899$$ −5.00000 −0.166759
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 4.00000 0.133112
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −28.0000 −0.929725 −0.464862 0.885383i $$-0.653896\pi$$
−0.464862 + 0.885383i $$0.653896\pi$$
$$908$$ 0 0
$$909$$ 20.0000 0.663358
$$910$$ 0 0
$$911$$ −10.0000 −0.331315 −0.165657 0.986183i $$-0.552975\pi$$
−0.165657 + 0.986183i $$0.552975\pi$$
$$912$$ 0 0
$$913$$ −32.0000 −1.05905
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 3.00000 0.0990687
$$918$$ 0 0
$$919$$ 18.0000 0.593765 0.296883 0.954914i $$-0.404053\pi$$
0.296883 + 0.954914i $$0.404053\pi$$
$$920$$ 0 0
$$921$$ 20.0000 0.659022
$$922$$ 0 0
$$923$$ −39.0000 −1.28370
$$924$$ 0 0
$$925$$ 40.0000 1.31519
$$926$$ 0 0
$$927$$ −28.0000 −0.919641
$$928$$ 0 0
$$929$$ −15.0000 −0.492134 −0.246067 0.969253i $$-0.579138\pi$$
−0.246067 + 0.969253i $$0.579138\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 13.0000 0.425601
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 4.00000 0.130674 0.0653372 0.997863i $$-0.479188\pi$$
0.0653372 + 0.997863i $$0.479188\pi$$
$$938$$ 0 0
$$939$$ −14.0000 −0.456873
$$940$$ 0 0
$$941$$ −18.0000 −0.586783 −0.293392 0.955992i $$-0.594784\pi$$
−0.293392 + 0.955992i $$0.594784\pi$$
$$942$$ 0 0
$$943$$ 7.00000 0.227951
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −27.0000 −0.877382 −0.438691 0.898638i $$-0.644558\pi$$
−0.438691 + 0.898638i $$0.644558\pi$$
$$948$$ 0 0
$$949$$ −9.00000 −0.292152
$$950$$ 0 0
$$951$$ −6.00000 −0.194563
$$952$$ 0 0
$$953$$ −10.0000 −0.323932 −0.161966 0.986796i $$-0.551783\pi$$
−0.161966 + 0.986796i $$0.551783\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 2.00000 0.0646508
$$958$$ 0 0
$$959$$ 10.0000 0.322917
$$960$$ 0 0
$$961$$ −6.00000 −0.193548
$$962$$ 0 0
$$963$$ 16.0000 0.515593
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −41.0000 −1.31847 −0.659236 0.751936i $$-0.729120\pi$$
−0.659236 + 0.751936i $$0.729120\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −52.0000 −1.66876 −0.834380 0.551190i $$-0.814174\pi$$
−0.834380 + 0.551190i $$0.814174\pi$$
$$972$$ 0 0
$$973$$ 1.00000 0.0320585
$$974$$ 0 0
$$975$$ −15.0000 −0.480384
$$976$$ 0 0
$$977$$ −16.0000 −0.511885 −0.255943 0.966692i $$-0.582386\pi$$
−0.255943 + 0.966692i $$0.582386\pi$$
$$978$$ 0 0
$$979$$ −8.00000 −0.255681
$$980$$ 0 0
$$981$$ 8.00000 0.255420
$$982$$ 0 0
$$983$$ 56.0000 1.78612 0.893061 0.449935i $$-0.148553\pi$$
0.893061 + 0.449935i $$0.148553\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −3.00000 −0.0954911
$$988$$ 0 0
$$989$$ 4.00000 0.127193
$$990$$ 0 0
$$991$$ 8.00000 0.254128 0.127064 0.991894i $$-0.459445\pi$$
0.127064 + 0.991894i $$0.459445\pi$$
$$992$$ 0 0
$$993$$ 29.0000 0.920287
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 34.0000 1.07679 0.538395 0.842692i $$-0.319031\pi$$
0.538395 + 0.842692i $$0.319031\pi$$
$$998$$ 0 0
$$999$$ −40.0000 −1.26554
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 644.2.a.a.1.1 1
3.2 odd 2 5796.2.a.e.1.1 1
4.3 odd 2 2576.2.a.l.1.1 1
7.6 odd 2 4508.2.a.c.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
644.2.a.a.1.1 1 1.1 even 1 trivial
2576.2.a.l.1.1 1 4.3 odd 2
4508.2.a.c.1.1 1 7.6 odd 2
5796.2.a.e.1.1 1 3.2 odd 2