# Properties

 Label 5520.2.a.n.1.1 Level $5520$ Weight $2$ Character 5520.1 Self dual yes Analytic conductor $44.077$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5520.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$44.0774219157$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 2760) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 5520.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{3} +1.00000 q^{5} +3.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{3} +1.00000 q^{5} +3.00000 q^{7} +1.00000 q^{9} +4.00000 q^{11} -1.00000 q^{15} +3.00000 q^{17} +4.00000 q^{19} -3.00000 q^{21} -1.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} +1.00000 q^{29} -1.00000 q^{31} -4.00000 q^{33} +3.00000 q^{35} +1.00000 q^{37} +3.00000 q^{41} +12.0000 q^{43} +1.00000 q^{45} +10.0000 q^{47} +2.00000 q^{49} -3.00000 q^{51} -9.00000 q^{53} +4.00000 q^{55} -4.00000 q^{57} +9.00000 q^{59} -10.0000 q^{61} +3.00000 q^{63} -1.00000 q^{67} +1.00000 q^{69} -5.00000 q^{71} -1.00000 q^{75} +12.0000 q^{77} -4.00000 q^{79} +1.00000 q^{81} +9.00000 q^{83} +3.00000 q^{85} -1.00000 q^{87} -8.00000 q^{89} +1.00000 q^{93} +4.00000 q^{95} -10.0000 q^{97} +4.00000 q^{99} +O(q^{100})$$

## 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
$$4$$ 0 0
$$5$$ 1.00000 0.447214
$$6$$ 0 0
$$7$$ 3.00000 1.13389 0.566947 0.823754i $$-0.308125\pi$$
0.566947 + 0.823754i $$0.308125\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −0.258199
$$16$$ 0 0
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ −3.00000 −0.654654
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 1.00000 0.185695 0.0928477 0.995680i $$-0.470403\pi$$
0.0928477 + 0.995680i $$0.470403\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −0.179605 −0.0898027 0.995960i $$-0.528624\pi$$
−0.0898027 + 0.995960i $$0.528624\pi$$
$$32$$ 0 0
$$33$$ −4.00000 −0.696311
$$34$$ 0 0
$$35$$ 3.00000 0.507093
$$36$$ 0 0
$$37$$ 1.00000 0.164399 0.0821995 0.996616i $$-0.473806\pi$$
0.0821995 + 0.996616i $$0.473806\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.00000 0.468521 0.234261 0.972174i $$-0.424733\pi$$
0.234261 + 0.972174i $$0.424733\pi$$
$$42$$ 0 0
$$43$$ 12.0000 1.82998 0.914991 0.403473i $$-0.132197\pi$$
0.914991 + 0.403473i $$0.132197\pi$$
$$44$$ 0 0
$$45$$ 1.00000 0.149071
$$46$$ 0 0
$$47$$ 10.0000 1.45865 0.729325 0.684167i $$-0.239834\pi$$
0.729325 + 0.684167i $$0.239834\pi$$
$$48$$ 0 0
$$49$$ 2.00000 0.285714
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 0 0
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ −4.00000 −0.529813
$$58$$ 0 0
$$59$$ 9.00000 1.17170 0.585850 0.810419i $$-0.300761\pi$$
0.585850 + 0.810419i $$0.300761\pi$$
$$60$$ 0 0
$$61$$ −10.0000 −1.28037 −0.640184 0.768221i $$-0.721142\pi$$
−0.640184 + 0.768221i $$0.721142\pi$$
$$62$$ 0 0
$$63$$ 3.00000 0.377964
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.00000 −0.122169 −0.0610847 0.998133i $$-0.519456\pi$$
−0.0610847 + 0.998133i $$0.519456\pi$$
$$68$$ 0 0
$$69$$ 1.00000 0.120386
$$70$$ 0 0
$$71$$ −5.00000 −0.593391 −0.296695 0.954972i $$-0.595885\pi$$
−0.296695 + 0.954972i $$0.595885\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 0 0
$$75$$ −1.00000 −0.115470
$$76$$ 0 0
$$77$$ 12.0000 1.36753
$$78$$ 0 0
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 9.00000 0.987878 0.493939 0.869496i $$-0.335557\pi$$
0.493939 + 0.869496i $$0.335557\pi$$
$$84$$ 0 0
$$85$$ 3.00000 0.325396
$$86$$ 0 0
$$87$$ −1.00000 −0.107211
$$88$$ 0 0
$$89$$ −8.00000 −0.847998 −0.423999 0.905663i $$-0.639374\pi$$
−0.423999 + 0.905663i $$0.639374\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 1.00000 0.103695
$$94$$ 0 0
$$95$$ 4.00000 0.410391
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ −15.0000 −1.49256 −0.746278 0.665635i $$-0.768161\pi$$
−0.746278 + 0.665635i $$0.768161\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ −3.00000 −0.292770
$$106$$ 0 0
$$107$$ −11.0000 −1.06341 −0.531705 0.846930i $$-0.678449\pi$$
−0.531705 + 0.846930i $$0.678449\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 0 0
$$113$$ −9.00000 −0.846649 −0.423324 0.905978i $$-0.639137\pi$$
−0.423324 + 0.905978i $$0.639137\pi$$
$$114$$ 0 0
$$115$$ −1.00000 −0.0932505
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 9.00000 0.825029
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 0 0
$$123$$ −3.00000 −0.270501
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 0 0
$$129$$ −12.0000 −1.05654
$$130$$ 0 0
$$131$$ −4.00000 −0.349482 −0.174741 0.984614i $$-0.555909\pi$$
−0.174741 + 0.984614i $$0.555909\pi$$
$$132$$ 0 0
$$133$$ 12.0000 1.04053
$$134$$ 0 0
$$135$$ −1.00000 −0.0860663
$$136$$ 0 0
$$137$$ 14.0000 1.19610 0.598050 0.801459i $$-0.295942\pi$$
0.598050 + 0.801459i $$0.295942\pi$$
$$138$$ 0 0
$$139$$ 5.00000 0.424094 0.212047 0.977259i $$-0.431987\pi$$
0.212047 + 0.977259i $$0.431987\pi$$
$$140$$ 0 0
$$141$$ −10.0000 −0.842152
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 1.00000 0.0830455
$$146$$ 0 0
$$147$$ −2.00000 −0.164957
$$148$$ 0 0
$$149$$ 2.00000 0.163846 0.0819232 0.996639i $$-0.473894\pi$$
0.0819232 + 0.996639i $$0.473894\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 3.00000 0.242536
$$154$$ 0 0
$$155$$ −1.00000 −0.0803219
$$156$$ 0 0
$$157$$ 3.00000 0.239426 0.119713 0.992809i $$-0.461803\pi$$
0.119713 + 0.992809i $$0.461803\pi$$
$$158$$ 0 0
$$159$$ 9.00000 0.713746
$$160$$ 0 0
$$161$$ −3.00000 −0.236433
$$162$$ 0 0
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ 0 0
$$165$$ −4.00000 −0.311400
$$166$$ 0 0
$$167$$ −22.0000 −1.70241 −0.851206 0.524832i $$-0.824128\pi$$
−0.851206 + 0.524832i $$0.824128\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ 0 0
$$173$$ 8.00000 0.608229 0.304114 0.952636i $$-0.401639\pi$$
0.304114 + 0.952636i $$0.401639\pi$$
$$174$$ 0 0
$$175$$ 3.00000 0.226779
$$176$$ 0 0
$$177$$ −9.00000 −0.676481
$$178$$ 0 0
$$179$$ 24.0000 1.79384 0.896922 0.442189i $$-0.145798\pi$$
0.896922 + 0.442189i $$0.145798\pi$$
$$180$$ 0 0
$$181$$ 8.00000 0.594635 0.297318 0.954779i $$-0.403908\pi$$
0.297318 + 0.954779i $$0.403908\pi$$
$$182$$ 0 0
$$183$$ 10.0000 0.739221
$$184$$ 0 0
$$185$$ 1.00000 0.0735215
$$186$$ 0 0
$$187$$ 12.0000 0.877527
$$188$$ 0 0
$$189$$ −3.00000 −0.218218
$$190$$ 0 0
$$191$$ 18.0000 1.30243 0.651217 0.758891i $$-0.274259\pi$$
0.651217 + 0.758891i $$0.274259\pi$$
$$192$$ 0 0
$$193$$ 16.0000 1.15171 0.575853 0.817554i $$-0.304670\pi$$
0.575853 + 0.817554i $$0.304670\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 26.0000 1.85242 0.926212 0.377004i $$-0.123046\pi$$
0.926212 + 0.377004i $$0.123046\pi$$
$$198$$ 0 0
$$199$$ −6.00000 −0.425329 −0.212664 0.977125i $$-0.568214\pi$$
−0.212664 + 0.977125i $$0.568214\pi$$
$$200$$ 0 0
$$201$$ 1.00000 0.0705346
$$202$$ 0 0
$$203$$ 3.00000 0.210559
$$204$$ 0 0
$$205$$ 3.00000 0.209529
$$206$$ 0 0
$$207$$ −1.00000 −0.0695048
$$208$$ 0 0
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ −9.00000 −0.619586 −0.309793 0.950804i $$-0.600260\pi$$
−0.309793 + 0.950804i $$0.600260\pi$$
$$212$$ 0 0
$$213$$ 5.00000 0.342594
$$214$$ 0 0
$$215$$ 12.0000 0.818393
$$216$$ 0 0
$$217$$ −3.00000 −0.203653
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −14.0000 −0.937509 −0.468755 0.883328i $$-0.655297\pi$$
−0.468755 + 0.883328i $$0.655297\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ 4.00000 0.265489 0.132745 0.991150i $$-0.457621\pi$$
0.132745 + 0.991150i $$0.457621\pi$$
$$228$$ 0 0
$$229$$ 8.00000 0.528655 0.264327 0.964433i $$-0.414850\pi$$
0.264327 + 0.964433i $$0.414850\pi$$
$$230$$ 0 0
$$231$$ −12.0000 −0.789542
$$232$$ 0 0
$$233$$ −4.00000 −0.262049 −0.131024 0.991379i $$-0.541827\pi$$
−0.131024 + 0.991379i $$0.541827\pi$$
$$234$$ 0 0
$$235$$ 10.0000 0.652328
$$236$$ 0 0
$$237$$ 4.00000 0.259828
$$238$$ 0 0
$$239$$ 21.0000 1.35838 0.679189 0.733964i $$-0.262332\pi$$
0.679189 + 0.733964i $$0.262332\pi$$
$$240$$ 0 0
$$241$$ 4.00000 0.257663 0.128831 0.991667i $$-0.458877\pi$$
0.128831 + 0.991667i $$0.458877\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 0 0
$$245$$ 2.00000 0.127775
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −9.00000 −0.570352
$$250$$ 0 0
$$251$$ −10.0000 −0.631194 −0.315597 0.948893i $$-0.602205\pi$$
−0.315597 + 0.948893i $$0.602205\pi$$
$$252$$ 0 0
$$253$$ −4.00000 −0.251478
$$254$$ 0 0
$$255$$ −3.00000 −0.187867
$$256$$ 0 0
$$257$$ −26.0000 −1.62184 −0.810918 0.585160i $$-0.801032\pi$$
−0.810918 + 0.585160i $$0.801032\pi$$
$$258$$ 0 0
$$259$$ 3.00000 0.186411
$$260$$ 0 0
$$261$$ 1.00000 0.0618984
$$262$$ 0 0
$$263$$ 3.00000 0.184988 0.0924940 0.995713i $$-0.470516\pi$$
0.0924940 + 0.995713i $$0.470516\pi$$
$$264$$ 0 0
$$265$$ −9.00000 −0.552866
$$266$$ 0 0
$$267$$ 8.00000 0.489592
$$268$$ 0 0
$$269$$ −9.00000 −0.548740 −0.274370 0.961624i $$-0.588469\pi$$
−0.274370 + 0.961624i $$0.588469\pi$$
$$270$$ 0 0
$$271$$ −27.0000 −1.64013 −0.820067 0.572268i $$-0.806064\pi$$
−0.820067 + 0.572268i $$0.806064\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 4.00000 0.241209
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 0 0
$$279$$ −1.00000 −0.0598684
$$280$$ 0 0
$$281$$ −16.0000 −0.954480 −0.477240 0.878773i $$-0.658363\pi$$
−0.477240 + 0.878773i $$0.658363\pi$$
$$282$$ 0 0
$$283$$ 1.00000 0.0594438 0.0297219 0.999558i $$-0.490538\pi$$
0.0297219 + 0.999558i $$0.490538\pi$$
$$284$$ 0 0
$$285$$ −4.00000 −0.236940
$$286$$ 0 0
$$287$$ 9.00000 0.531253
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 10.0000 0.586210
$$292$$ 0 0
$$293$$ 25.0000 1.46052 0.730258 0.683172i $$-0.239400\pi$$
0.730258 + 0.683172i $$0.239400\pi$$
$$294$$ 0 0
$$295$$ 9.00000 0.524000
$$296$$ 0 0
$$297$$ −4.00000 −0.232104
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 36.0000 2.07501
$$302$$ 0 0
$$303$$ 15.0000 0.861727
$$304$$ 0 0
$$305$$ −10.0000 −0.572598
$$306$$ 0 0
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 16.0000 0.907277 0.453638 0.891186i $$-0.350126\pi$$
0.453638 + 0.891186i $$0.350126\pi$$
$$312$$ 0 0
$$313$$ −5.00000 −0.282617 −0.141308 0.989966i $$-0.545131\pi$$
−0.141308 + 0.989966i $$0.545131\pi$$
$$314$$ 0 0
$$315$$ 3.00000 0.169031
$$316$$ 0 0
$$317$$ 2.00000 0.112331 0.0561656 0.998421i $$-0.482113\pi$$
0.0561656 + 0.998421i $$0.482113\pi$$
$$318$$ 0 0
$$319$$ 4.00000 0.223957
$$320$$ 0 0
$$321$$ 11.0000 0.613960
$$322$$ 0 0
$$323$$ 12.0000 0.667698
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 30.0000 1.65395
$$330$$ 0 0
$$331$$ −17.0000 −0.934405 −0.467202 0.884150i $$-0.654738\pi$$
−0.467202 + 0.884150i $$0.654738\pi$$
$$332$$ 0 0
$$333$$ 1.00000 0.0547997
$$334$$ 0 0
$$335$$ −1.00000 −0.0546358
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 0 0
$$339$$ 9.00000 0.488813
$$340$$ 0 0
$$341$$ −4.00000 −0.216612
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ 0 0
$$345$$ 1.00000 0.0538382
$$346$$ 0 0
$$347$$ 12.0000 0.644194 0.322097 0.946707i $$-0.395612\pi$$
0.322097 + 0.946707i $$0.395612\pi$$
$$348$$ 0 0
$$349$$ 11.0000 0.588817 0.294408 0.955680i $$-0.404877\pi$$
0.294408 + 0.955680i $$0.404877\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2.00000 0.106449 0.0532246 0.998583i $$-0.483050\pi$$
0.0532246 + 0.998583i $$0.483050\pi$$
$$354$$ 0 0
$$355$$ −5.00000 −0.265372
$$356$$ 0 0
$$357$$ −9.00000 −0.476331
$$358$$ 0 0
$$359$$ 18.0000 0.950004 0.475002 0.879985i $$-0.342447\pi$$
0.475002 + 0.879985i $$0.342447\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ −5.00000 −0.262432
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 17.0000 0.887393 0.443696 0.896177i $$-0.353667\pi$$
0.443696 + 0.896177i $$0.353667\pi$$
$$368$$ 0 0
$$369$$ 3.00000 0.156174
$$370$$ 0 0
$$371$$ −27.0000 −1.40177
$$372$$ 0 0
$$373$$ 22.0000 1.13912 0.569558 0.821951i $$-0.307114\pi$$
0.569558 + 0.821951i $$0.307114\pi$$
$$374$$ 0 0
$$375$$ −1.00000 −0.0516398
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 8.00000 0.410932 0.205466 0.978664i $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ 0 0
$$381$$ −2.00000 −0.102463
$$382$$ 0 0
$$383$$ 27.0000 1.37964 0.689818 0.723983i $$-0.257691\pi$$
0.689818 + 0.723983i $$0.257691\pi$$
$$384$$ 0 0
$$385$$ 12.0000 0.611577
$$386$$ 0 0
$$387$$ 12.0000 0.609994
$$388$$ 0 0
$$389$$ −30.0000 −1.52106 −0.760530 0.649303i $$-0.775061\pi$$
−0.760530 + 0.649303i $$0.775061\pi$$
$$390$$ 0 0
$$391$$ −3.00000 −0.151717
$$392$$ 0 0
$$393$$ 4.00000 0.201773
$$394$$ 0 0
$$395$$ −4.00000 −0.201262
$$396$$ 0 0
$$397$$ 20.0000 1.00377 0.501886 0.864934i $$-0.332640\pi$$
0.501886 + 0.864934i $$0.332640\pi$$
$$398$$ 0 0
$$399$$ −12.0000 −0.600751
$$400$$ 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
$$405$$ 1.00000 0.0496904
$$406$$ 0 0
$$407$$ 4.00000 0.198273
$$408$$ 0 0
$$409$$ 17.0000 0.840596 0.420298 0.907386i $$-0.361926\pi$$
0.420298 + 0.907386i $$0.361926\pi$$
$$410$$ 0 0
$$411$$ −14.0000 −0.690569
$$412$$ 0 0
$$413$$ 27.0000 1.32858
$$414$$ 0 0
$$415$$ 9.00000 0.441793
$$416$$ 0 0
$$417$$ −5.00000 −0.244851
$$418$$ 0 0
$$419$$ 36.0000 1.75872 0.879358 0.476162i $$-0.157972\pi$$
0.879358 + 0.476162i $$0.157972\pi$$
$$420$$ 0 0
$$421$$ 8.00000 0.389896 0.194948 0.980814i $$-0.437546\pi$$
0.194948 + 0.980814i $$0.437546\pi$$
$$422$$ 0 0
$$423$$ 10.0000 0.486217
$$424$$ 0 0
$$425$$ 3.00000 0.145521
$$426$$ 0 0
$$427$$ −30.0000 −1.45180
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 0 0
$$433$$ 9.00000 0.432512 0.216256 0.976337i $$-0.430615\pi$$
0.216256 + 0.976337i $$0.430615\pi$$
$$434$$ 0 0
$$435$$ −1.00000 −0.0479463
$$436$$ 0 0
$$437$$ −4.00000 −0.191346
$$438$$ 0 0
$$439$$ −40.0000 −1.90910 −0.954548 0.298057i $$-0.903661\pi$$
−0.954548 + 0.298057i $$0.903661\pi$$
$$440$$ 0 0
$$441$$ 2.00000 0.0952381
$$442$$ 0 0
$$443$$ 10.0000 0.475114 0.237557 0.971374i $$-0.423653\pi$$
0.237557 + 0.971374i $$0.423653\pi$$
$$444$$ 0 0
$$445$$ −8.00000 −0.379236
$$446$$ 0 0
$$447$$ −2.00000 −0.0945968
$$448$$ 0 0
$$449$$ −15.0000 −0.707894 −0.353947 0.935266i $$-0.615161\pi$$
−0.353947 + 0.935266i $$0.615161\pi$$
$$450$$ 0 0
$$451$$ 12.0000 0.565058
$$452$$ 0 0
$$453$$ 16.0000 0.751746
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −25.0000 −1.16945 −0.584725 0.811231i $$-0.698798\pi$$
−0.584725 + 0.811231i $$0.698798\pi$$
$$458$$ 0 0
$$459$$ −3.00000 −0.140028
$$460$$ 0 0
$$461$$ −22.0000 −1.02464 −0.512321 0.858794i $$-0.671214\pi$$
−0.512321 + 0.858794i $$0.671214\pi$$
$$462$$ 0 0
$$463$$ −32.0000 −1.48717 −0.743583 0.668644i $$-0.766875\pi$$
−0.743583 + 0.668644i $$0.766875\pi$$
$$464$$ 0 0
$$465$$ 1.00000 0.0463739
$$466$$ 0 0
$$467$$ 13.0000 0.601568 0.300784 0.953692i $$-0.402752\pi$$
0.300784 + 0.953692i $$0.402752\pi$$
$$468$$ 0 0
$$469$$ −3.00000 −0.138527
$$470$$ 0 0
$$471$$ −3.00000 −0.138233
$$472$$ 0 0
$$473$$ 48.0000 2.20704
$$474$$ 0 0
$$475$$ 4.00000 0.183533
$$476$$ 0 0
$$477$$ −9.00000 −0.412082
$$478$$ 0 0
$$479$$ 2.00000 0.0913823 0.0456912 0.998956i $$-0.485451\pi$$
0.0456912 + 0.998956i $$0.485451\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 3.00000 0.136505
$$484$$ 0 0
$$485$$ −10.0000 −0.454077
$$486$$ 0 0
$$487$$ −34.0000 −1.54069 −0.770344 0.637629i $$-0.779915\pi$$
−0.770344 + 0.637629i $$0.779915\pi$$
$$488$$ 0 0
$$489$$ 10.0000 0.452216
$$490$$ 0 0
$$491$$ −9.00000 −0.406164 −0.203082 0.979162i $$-0.565096\pi$$
−0.203082 + 0.979162i $$0.565096\pi$$
$$492$$ 0 0
$$493$$ 3.00000 0.135113
$$494$$ 0 0
$$495$$ 4.00000 0.179787
$$496$$ 0 0
$$497$$ −15.0000 −0.672842
$$498$$ 0 0
$$499$$ 29.0000 1.29822 0.649109 0.760695i $$-0.275142\pi$$
0.649109 + 0.760695i $$0.275142\pi$$
$$500$$ 0 0
$$501$$ 22.0000 0.982888
$$502$$ 0 0
$$503$$ 7.00000 0.312115 0.156057 0.987748i $$-0.450122\pi$$
0.156057 + 0.987748i $$0.450122\pi$$
$$504$$ 0 0
$$505$$ −15.0000 −0.667491
$$506$$ 0 0
$$507$$ 13.0000 0.577350
$$508$$ 0 0
$$509$$ −2.00000 −0.0886484 −0.0443242 0.999017i $$-0.514113\pi$$
−0.0443242 + 0.999017i $$0.514113\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −4.00000 −0.176604
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 40.0000 1.75920
$$518$$ 0 0
$$519$$ −8.00000 −0.351161
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 4.00000 0.174908 0.0874539 0.996169i $$-0.472127\pi$$
0.0874539 + 0.996169i $$0.472127\pi$$
$$524$$ 0 0
$$525$$ −3.00000 −0.130931
$$526$$ 0 0
$$527$$ −3.00000 −0.130682
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 9.00000 0.390567
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −11.0000 −0.475571
$$536$$ 0 0
$$537$$ −24.0000 −1.03568
$$538$$ 0 0
$$539$$ 8.00000 0.344584
$$540$$ 0 0
$$541$$ −18.0000 −0.773880 −0.386940 0.922105i $$-0.626468\pi$$
−0.386940 + 0.922105i $$0.626468\pi$$
$$542$$ 0 0
$$543$$ −8.00000 −0.343313
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 36.0000 1.53925 0.769624 0.638497i $$-0.220443\pi$$
0.769624 + 0.638497i $$0.220443\pi$$
$$548$$ 0 0
$$549$$ −10.0000 −0.426790
$$550$$ 0 0
$$551$$ 4.00000 0.170406
$$552$$ 0 0
$$553$$ −12.0000 −0.510292
$$554$$ 0 0
$$555$$ −1.00000 −0.0424476
$$556$$ 0 0
$$557$$ 15.0000 0.635570 0.317785 0.948163i $$-0.397061\pi$$
0.317785 + 0.948163i $$0.397061\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −12.0000 −0.506640
$$562$$ 0 0
$$563$$ −37.0000 −1.55936 −0.779682 0.626176i $$-0.784619\pi$$
−0.779682 + 0.626176i $$0.784619\pi$$
$$564$$ 0 0
$$565$$ −9.00000 −0.378633
$$566$$ 0 0
$$567$$ 3.00000 0.125988
$$568$$ 0 0
$$569$$ 6.00000 0.251533 0.125767 0.992060i $$-0.459861\pi$$
0.125767 + 0.992060i $$0.459861\pi$$
$$570$$ 0 0
$$571$$ 6.00000 0.251092 0.125546 0.992088i $$-0.459932\pi$$
0.125546 + 0.992088i $$0.459932\pi$$
$$572$$ 0 0
$$573$$ −18.0000 −0.751961
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ −4.00000 −0.166522 −0.0832611 0.996528i $$-0.526534\pi$$
−0.0832611 + 0.996528i $$0.526534\pi$$
$$578$$ 0 0
$$579$$ −16.0000 −0.664937
$$580$$ 0 0
$$581$$ 27.0000 1.12015
$$582$$ 0 0
$$583$$ −36.0000 −1.49097
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −2.00000 −0.0825488 −0.0412744 0.999148i $$-0.513142\pi$$
−0.0412744 + 0.999148i $$0.513142\pi$$
$$588$$ 0 0
$$589$$ −4.00000 −0.164817
$$590$$ 0 0
$$591$$ −26.0000 −1.06950
$$592$$ 0 0
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 0 0
$$595$$ 9.00000 0.368964
$$596$$ 0 0
$$597$$ 6.00000 0.245564
$$598$$ 0 0
$$599$$ −20.0000 −0.817178 −0.408589 0.912719i $$-0.633979\pi$$
−0.408589 + 0.912719i $$0.633979\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −0.0407909 −0.0203954 0.999792i $$-0.506493\pi$$
−0.0203954 + 0.999792i $$0.506493\pi$$
$$602$$ 0 0
$$603$$ −1.00000 −0.0407231
$$604$$ 0 0
$$605$$ 5.00000 0.203279
$$606$$ 0 0
$$607$$ 38.0000 1.54237 0.771186 0.636610i $$-0.219664\pi$$
0.771186 + 0.636610i $$0.219664\pi$$
$$608$$ 0 0
$$609$$ −3.00000 −0.121566
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 34.0000 1.37325 0.686624 0.727013i $$-0.259092\pi$$
0.686624 + 0.727013i $$0.259092\pi$$
$$614$$ 0 0
$$615$$ −3.00000 −0.120972
$$616$$ 0 0
$$617$$ 41.0000 1.65060 0.825299 0.564696i $$-0.191007\pi$$
0.825299 + 0.564696i $$0.191007\pi$$
$$618$$ 0 0
$$619$$ 4.00000 0.160774 0.0803868 0.996764i $$-0.474384\pi$$
0.0803868 + 0.996764i $$0.474384\pi$$
$$620$$ 0 0
$$621$$ 1.00000 0.0401286
$$622$$ 0 0
$$623$$ −24.0000 −0.961540
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ −16.0000 −0.638978
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ −26.0000 −1.03504 −0.517522 0.855670i $$-0.673145\pi$$
−0.517522 + 0.855670i $$0.673145\pi$$
$$632$$ 0 0
$$633$$ 9.00000 0.357718
$$634$$ 0 0
$$635$$ 2.00000 0.0793676
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −5.00000 −0.197797
$$640$$ 0 0
$$641$$ 12.0000 0.473972 0.236986 0.971513i $$-0.423841\pi$$
0.236986 + 0.971513i $$0.423841\pi$$
$$642$$ 0 0
$$643$$ 23.0000 0.907031 0.453516 0.891248i $$-0.350170\pi$$
0.453516 + 0.891248i $$0.350170\pi$$
$$644$$ 0 0
$$645$$ −12.0000 −0.472500
$$646$$ 0 0
$$647$$ −36.0000 −1.41531 −0.707653 0.706560i $$-0.750246\pi$$
−0.707653 + 0.706560i $$0.750246\pi$$
$$648$$ 0 0
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ 3.00000 0.117579
$$652$$ 0 0
$$653$$ −4.00000 −0.156532 −0.0782660 0.996933i $$-0.524938\pi$$
−0.0782660 + 0.996933i $$0.524938\pi$$
$$654$$ 0 0
$$655$$ −4.00000 −0.156293
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −4.00000 −0.155818 −0.0779089 0.996960i $$-0.524824\pi$$
−0.0779089 + 0.996960i $$0.524824\pi$$
$$660$$ 0 0
$$661$$ −18.0000 −0.700119 −0.350059 0.936727i $$-0.613839\pi$$
−0.350059 + 0.936727i $$0.613839\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 12.0000 0.465340
$$666$$ 0 0
$$667$$ −1.00000 −0.0387202
$$668$$ 0 0
$$669$$ 14.0000 0.541271
$$670$$ 0 0
$$671$$ −40.0000 −1.54418
$$672$$ 0 0
$$673$$ −2.00000 −0.0770943 −0.0385472 0.999257i $$-0.512273\pi$$
−0.0385472 + 0.999257i $$0.512273\pi$$
$$674$$ 0 0
$$675$$ −1.00000 −0.0384900
$$676$$ 0 0
$$677$$ 41.0000 1.57576 0.787879 0.615830i $$-0.211179\pi$$
0.787879 + 0.615830i $$0.211179\pi$$
$$678$$ 0 0
$$679$$ −30.0000 −1.15129
$$680$$ 0 0
$$681$$ −4.00000 −0.153280
$$682$$ 0 0
$$683$$ 26.0000 0.994862 0.497431 0.867503i $$-0.334277\pi$$
0.497431 + 0.867503i $$0.334277\pi$$
$$684$$ 0 0
$$685$$ 14.0000 0.534913
$$686$$ 0 0
$$687$$ −8.00000 −0.305219
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 8.00000 0.304334 0.152167 0.988355i $$-0.451375\pi$$
0.152167 + 0.988355i $$0.451375\pi$$
$$692$$ 0 0
$$693$$ 12.0000 0.455842
$$694$$ 0 0
$$695$$ 5.00000 0.189661
$$696$$ 0 0
$$697$$ 9.00000 0.340899
$$698$$ 0 0
$$699$$ 4.00000 0.151294
$$700$$ 0 0
$$701$$ −42.0000 −1.58632 −0.793159 0.609015i $$-0.791565\pi$$
−0.793159 + 0.609015i $$0.791565\pi$$
$$702$$ 0 0
$$703$$ 4.00000 0.150863
$$704$$ 0 0
$$705$$ −10.0000 −0.376622
$$706$$ 0 0
$$707$$ −45.0000 −1.69240
$$708$$ 0 0
$$709$$ −34.0000 −1.27690 −0.638448 0.769665i $$-0.720423\pi$$
−0.638448 + 0.769665i $$0.720423\pi$$
$$710$$ 0 0
$$711$$ −4.00000 −0.150012
$$712$$ 0 0
$$713$$ 1.00000 0.0374503
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −21.0000 −0.784259
$$718$$ 0 0
$$719$$ 9.00000 0.335643 0.167822 0.985817i $$-0.446327\pi$$
0.167822 + 0.985817i $$0.446327\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −4.00000 −0.148762
$$724$$ 0 0
$$725$$ 1.00000 0.0371391
$$726$$ 0 0
$$727$$ 5.00000 0.185440 0.0927199 0.995692i $$-0.470444\pi$$
0.0927199 + 0.995692i $$0.470444\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 36.0000 1.33151
$$732$$ 0 0
$$733$$ −11.0000 −0.406294 −0.203147 0.979148i $$-0.565117\pi$$
−0.203147 + 0.979148i $$0.565117\pi$$
$$734$$ 0 0
$$735$$ −2.00000 −0.0737711
$$736$$ 0 0
$$737$$ −4.00000 −0.147342
$$738$$ 0 0
$$739$$ −53.0000 −1.94964 −0.974818 0.223001i $$-0.928415\pi$$
−0.974818 + 0.223001i $$0.928415\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −32.0000 −1.17397 −0.586983 0.809599i $$-0.699684\pi$$
−0.586983 + 0.809599i $$0.699684\pi$$
$$744$$ 0 0
$$745$$ 2.00000 0.0732743
$$746$$ 0 0
$$747$$ 9.00000 0.329293
$$748$$ 0 0
$$749$$ −33.0000 −1.20579
$$750$$ 0 0
$$751$$ −32.0000 −1.16770 −0.583848 0.811863i $$-0.698454\pi$$
−0.583848 + 0.811863i $$0.698454\pi$$
$$752$$ 0 0
$$753$$ 10.0000 0.364420
$$754$$ 0 0
$$755$$ −16.0000 −0.582300
$$756$$ 0 0
$$757$$ 19.0000 0.690567 0.345283 0.938498i $$-0.387783\pi$$
0.345283 + 0.938498i $$0.387783\pi$$
$$758$$ 0 0
$$759$$ 4.00000 0.145191
$$760$$ 0 0
$$761$$ 35.0000 1.26875 0.634375 0.773026i $$-0.281258\pi$$
0.634375 + 0.773026i $$0.281258\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 3.00000 0.108465
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −42.0000 −1.51456 −0.757279 0.653091i $$-0.773472\pi$$
−0.757279 + 0.653091i $$0.773472\pi$$
$$770$$ 0 0
$$771$$ 26.0000 0.936367
$$772$$ 0 0
$$773$$ −18.0000 −0.647415 −0.323708 0.946157i $$-0.604929\pi$$
−0.323708 + 0.946157i $$0.604929\pi$$
$$774$$ 0 0
$$775$$ −1.00000 −0.0359211
$$776$$ 0 0
$$777$$ −3.00000 −0.107624
$$778$$ 0 0
$$779$$ 12.0000 0.429945
$$780$$ 0 0
$$781$$ −20.0000 −0.715656
$$782$$ 0 0
$$783$$ −1.00000 −0.0357371
$$784$$ 0 0
$$785$$ 3.00000 0.107075
$$786$$ 0 0
$$787$$ −25.0000 −0.891154 −0.445577 0.895244i $$-0.647001\pi$$
−0.445577 + 0.895244i $$0.647001\pi$$
$$788$$ 0 0
$$789$$ −3.00000 −0.106803
$$790$$ 0 0
$$791$$ −27.0000 −0.960009
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 9.00000 0.319197
$$796$$ 0 0
$$797$$ −23.0000 −0.814702 −0.407351 0.913272i $$-0.633547\pi$$
−0.407351 + 0.913272i $$0.633547\pi$$
$$798$$ 0 0
$$799$$ 30.0000 1.06132
$$800$$ 0 0
$$801$$ −8.00000 −0.282666
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ −3.00000 −0.105736
$$806$$ 0 0
$$807$$ 9.00000 0.316815
$$808$$ 0 0
$$809$$ −27.0000 −0.949269 −0.474635 0.880183i $$-0.657420\pi$$
−0.474635 + 0.880183i $$0.657420\pi$$
$$810$$ 0 0
$$811$$ −17.0000 −0.596951 −0.298475 0.954417i $$-0.596478\pi$$
−0.298475 + 0.954417i $$0.596478\pi$$
$$812$$ 0 0
$$813$$ 27.0000 0.946931
$$814$$ 0 0
$$815$$ −10.0000 −0.350285
$$816$$ 0 0
$$817$$ 48.0000 1.67931
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −10.0000 −0.349002 −0.174501 0.984657i $$-0.555831\pi$$
−0.174501 + 0.984657i $$0.555831\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ −4.00000 −0.139262
$$826$$ 0 0
$$827$$ 3.00000 0.104320 0.0521601 0.998639i $$-0.483389\pi$$
0.0521601 + 0.998639i $$0.483389\pi$$
$$828$$ 0 0
$$829$$ −47.0000 −1.63238 −0.816189 0.577785i $$-0.803917\pi$$
−0.816189 + 0.577785i $$0.803917\pi$$
$$830$$ 0 0
$$831$$ 2.00000 0.0693792
$$832$$ 0 0
$$833$$ 6.00000 0.207888
$$834$$ 0 0
$$835$$ −22.0000 −0.761341
$$836$$ 0 0
$$837$$ 1.00000 0.0345651
$$838$$ 0 0
$$839$$ −34.0000 −1.17381 −0.586905 0.809656i $$-0.699654\pi$$
−0.586905 + 0.809656i $$0.699654\pi$$
$$840$$ 0 0
$$841$$ −28.0000 −0.965517
$$842$$ 0 0
$$843$$ 16.0000 0.551069
$$844$$ 0 0
$$845$$ −13.0000 −0.447214
$$846$$ 0 0
$$847$$ 15.0000 0.515406
$$848$$ 0 0
$$849$$ −1.00000 −0.0343199
$$850$$ 0 0
$$851$$ −1.00000 −0.0342796
$$852$$ 0 0
$$853$$ 14.0000 0.479351 0.239675 0.970853i $$-0.422959\pi$$
0.239675 + 0.970853i $$0.422959\pi$$
$$854$$ 0 0
$$855$$ 4.00000 0.136797
$$856$$ 0 0
$$857$$ 14.0000 0.478231 0.239115 0.970991i $$-0.423143\pi$$
0.239115 + 0.970991i $$0.423143\pi$$
$$858$$ 0 0
$$859$$ 35.0000 1.19418 0.597092 0.802173i $$-0.296323\pi$$
0.597092 + 0.802173i $$0.296323\pi$$
$$860$$ 0 0
$$861$$ −9.00000 −0.306719
$$862$$ 0 0
$$863$$ 34.0000 1.15737 0.578687 0.815550i $$-0.303565\pi$$
0.578687 + 0.815550i $$0.303565\pi$$
$$864$$ 0 0
$$865$$ 8.00000 0.272008
$$866$$ 0 0
$$867$$ 8.00000 0.271694
$$868$$ 0 0
$$869$$ −16.0000 −0.542763
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ −10.0000 −0.338449
$$874$$ 0 0
$$875$$ 3.00000 0.101419
$$876$$ 0 0
$$877$$ −14.0000 −0.472746 −0.236373 0.971662i $$-0.575959\pi$$
−0.236373 + 0.971662i $$0.575959\pi$$
$$878$$ 0 0
$$879$$ −25.0000 −0.843229
$$880$$ 0 0
$$881$$ 26.0000 0.875962 0.437981 0.898984i $$-0.355694\pi$$
0.437981 + 0.898984i $$0.355694\pi$$
$$882$$ 0 0
$$883$$ −22.0000 −0.740359 −0.370179 0.928960i $$-0.620704\pi$$
−0.370179 + 0.928960i $$0.620704\pi$$
$$884$$ 0 0
$$885$$ −9.00000 −0.302532
$$886$$ 0 0
$$887$$ −30.0000 −1.00730 −0.503651 0.863907i $$-0.668010\pi$$
−0.503651 + 0.863907i $$0.668010\pi$$
$$888$$ 0 0
$$889$$ 6.00000 0.201234
$$890$$ 0 0
$$891$$ 4.00000 0.134005
$$892$$ 0 0
$$893$$ 40.0000 1.33855
$$894$$ 0 0
$$895$$ 24.0000 0.802232
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −1.00000 −0.0333519
$$900$$ 0 0
$$901$$ −27.0000 −0.899500
$$902$$ 0 0
$$903$$ −36.0000 −1.19800
$$904$$ 0 0
$$905$$ 8.00000 0.265929
$$906$$ 0 0
$$907$$ −49.0000 −1.62702 −0.813509 0.581552i $$-0.802446\pi$$
−0.813509 + 0.581552i $$0.802446\pi$$
$$908$$ 0 0
$$909$$ −15.0000 −0.497519
$$910$$ 0 0
$$911$$ 12.0000 0.397578 0.198789 0.980042i $$-0.436299\pi$$
0.198789 + 0.980042i $$0.436299\pi$$
$$912$$ 0 0
$$913$$ 36.0000 1.19143
$$914$$ 0 0
$$915$$ 10.0000 0.330590
$$916$$ 0 0
$$917$$ −12.0000 −0.396275
$$918$$ 0 0
$$919$$ 52.0000 1.71532 0.857661 0.514216i $$-0.171917\pi$$
0.857661 + 0.514216i $$0.171917\pi$$
$$920$$ 0 0
$$921$$ −4.00000 −0.131804
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 1.00000 0.0328798
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 21.0000 0.688988 0.344494 0.938789i $$-0.388051\pi$$
0.344494 + 0.938789i $$0.388051\pi$$
$$930$$ 0 0
$$931$$ 8.00000 0.262189
$$932$$ 0 0
$$933$$ −16.0000 −0.523816
$$934$$ 0 0
$$935$$ 12.0000 0.392442
$$936$$ 0 0
$$937$$ −42.0000 −1.37208 −0.686040 0.727564i $$-0.740653\pi$$
−0.686040 + 0.727564i $$0.740653\pi$$
$$938$$ 0 0
$$939$$ 5.00000 0.163169
$$940$$ 0 0
$$941$$ −26.0000 −0.847576 −0.423788 0.905761i $$-0.639300\pi$$
−0.423788 + 0.905761i $$0.639300\pi$$
$$942$$ 0 0
$$943$$ −3.00000 −0.0976934
$$944$$ 0 0
$$945$$ −3.00000 −0.0975900
$$946$$ 0 0
$$947$$ 36.0000 1.16984 0.584921 0.811090i $$-0.301125\pi$$
0.584921 + 0.811090i $$0.301125\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ −2.00000 −0.0648544
$$952$$ 0 0
$$953$$ −26.0000 −0.842223 −0.421111 0.907009i $$-0.638360\pi$$
−0.421111 + 0.907009i $$0.638360\pi$$
$$954$$ 0 0
$$955$$ 18.0000 0.582466
$$956$$ 0 0
$$957$$ −4.00000 −0.129302
$$958$$ 0 0
$$959$$ 42.0000 1.35625
$$960$$ 0 0
$$961$$ −30.0000 −0.967742
$$962$$ 0 0
$$963$$ −11.0000 −0.354470
$$964$$ 0 0
$$965$$ 16.0000 0.515058
$$966$$ 0 0
$$967$$ −42.0000 −1.35063 −0.675314 0.737530i $$-0.735992\pi$$
−0.675314 + 0.737530i $$0.735992\pi$$
$$968$$ 0 0
$$969$$ −12.0000 −0.385496
$$970$$ 0 0
$$971$$ 48.0000 1.54039 0.770197 0.637806i $$-0.220158\pi$$
0.770197 + 0.637806i $$0.220158\pi$$
$$972$$ 0 0
$$973$$ 15.0000 0.480878
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 1.00000 0.0319928 0.0159964 0.999872i $$-0.494908\pi$$
0.0159964 + 0.999872i $$0.494908\pi$$
$$978$$ 0 0
$$979$$ −32.0000 −1.02272
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 37.0000 1.18012 0.590058 0.807361i $$-0.299105\pi$$
0.590058 + 0.807361i $$0.299105\pi$$
$$984$$ 0 0
$$985$$ 26.0000 0.828429
$$986$$ 0 0
$$987$$ −30.0000 −0.954911
$$988$$ 0 0
$$989$$ −12.0000 −0.381578
$$990$$ 0 0
$$991$$ −13.0000 −0.412959 −0.206479 0.978451i $$-0.566201\pi$$
−0.206479 + 0.978451i $$0.566201\pi$$
$$992$$ 0 0
$$993$$ 17.0000 0.539479
$$994$$ 0 0
$$995$$ −6.00000 −0.190213
$$996$$ 0 0
$$997$$ −48.0000 −1.52018 −0.760088 0.649821i $$-0.774844\pi$$
−0.760088 + 0.649821i $$0.774844\pi$$
$$998$$ 0 0
$$999$$ −1.00000 −0.0316386
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 5520.2.a.n.1.1 1
4.3 odd 2 2760.2.a.j.1.1 1
12.11 even 2 8280.2.a.a.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.j.1.1 1 4.3 odd 2
5520.2.a.n.1.1 1 1.1 even 1 trivial
8280.2.a.a.1.1 1 12.11 even 2