# Properties

 Label 5520.2.a.ba.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 1380) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

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

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{3} -1.00000 q^{5} +5.00000 q^{7} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{3} -1.00000 q^{5} +5.00000 q^{7} +1.00000 q^{9} +4.00000 q^{13} -1.00000 q^{15} -3.00000 q^{17} +4.00000 q^{19} +5.00000 q^{21} +1.00000 q^{23} +1.00000 q^{25} +1.00000 q^{27} +1.00000 q^{29} -1.00000 q^{31} -5.00000 q^{35} -1.00000 q^{37} +4.00000 q^{39} +11.0000 q^{41} -4.00000 q^{43} -1.00000 q^{45} -6.00000 q^{47} +18.0000 q^{49} -3.00000 q^{51} +1.00000 q^{53} +4.00000 q^{57} +1.00000 q^{59} +6.00000 q^{61} +5.00000 q^{63} -4.00000 q^{65} +9.00000 q^{67} +1.00000 q^{69} -13.0000 q^{71} +1.00000 q^{75} -16.0000 q^{79} +1.00000 q^{81} -9.00000 q^{83} +3.00000 q^{85} +1.00000 q^{87} +8.00000 q^{89} +20.0000 q^{91} -1.00000 q^{93} -4.00000 q^{95} +2.00000 q^{97} +O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.00000 0.577350
$$4$$ 0 0
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 5.00000 1.88982 0.944911 0.327327i $$-0.106148\pi$$
0.944911 + 0.327327i $$0.106148\pi$$
$$8$$ 0 0
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 4.00000 1.10940 0.554700 0.832050i $$-0.312833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −0.258199
$$16$$ 0 0
$$17$$ −3.00000 −0.727607 −0.363803 0.931476i $$-0.618522\pi$$
−0.363803 + 0.931476i $$0.618522\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 5.00000 1.09109
$$22$$ 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
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −5.00000 −0.845154
$$36$$ 0 0
$$37$$ −1.00000 −0.164399 −0.0821995 0.996616i $$-0.526194\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ 0 0
$$39$$ 4.00000 0.640513
$$40$$ 0 0
$$41$$ 11.0000 1.71791 0.858956 0.512050i $$-0.171114\pi$$
0.858956 + 0.512050i $$0.171114\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ −1.00000 −0.149071
$$46$$ 0 0
$$47$$ −6.00000 −0.875190 −0.437595 0.899172i $$-0.644170\pi$$
−0.437595 + 0.899172i $$0.644170\pi$$
$$48$$ 0 0
$$49$$ 18.0000 2.57143
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 0 0
$$53$$ 1.00000 0.137361 0.0686803 0.997639i $$-0.478121\pi$$
0.0686803 + 0.997639i $$0.478121\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 4.00000 0.529813
$$58$$ 0 0
$$59$$ 1.00000 0.130189 0.0650945 0.997879i $$-0.479265\pi$$
0.0650945 + 0.997879i $$0.479265\pi$$
$$60$$ 0 0
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 0 0
$$63$$ 5.00000 0.629941
$$64$$ 0 0
$$65$$ −4.00000 −0.496139
$$66$$ 0 0
$$67$$ 9.00000 1.09952 0.549762 0.835321i $$-0.314718\pi$$
0.549762 + 0.835321i $$0.314718\pi$$
$$68$$ 0 0
$$69$$ 1.00000 0.120386
$$70$$ 0 0
$$71$$ −13.0000 −1.54282 −0.771408 0.636341i $$-0.780447\pi$$
−0.771408 + 0.636341i $$0.780447\pi$$
$$72$$ 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
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ −9.00000 −0.987878 −0.493939 0.869496i $$-0.664443\pi$$
−0.493939 + 0.869496i $$0.664443\pi$$
$$84$$ 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 $$-0.360626\pi$$
0.423999 + 0.905663i $$0.360626\pi$$
$$90$$ 0 0
$$91$$ 20.0000 2.09657
$$92$$ 0 0
$$93$$ −1.00000 −0.103695
$$94$$ 0 0
$$95$$ −4.00000 −0.410391
$$96$$ 0 0
$$97$$ 2.00000 0.203069 0.101535 0.994832i $$-0.467625\pi$$
0.101535 + 0.994832i $$0.467625\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −7.00000 −0.696526 −0.348263 0.937397i $$-0.613228\pi$$
−0.348263 + 0.937397i $$0.613228\pi$$
$$102$$ 0 0
$$103$$ 16.0000 1.57653 0.788263 0.615338i $$-0.210980\pi$$
0.788263 + 0.615338i $$0.210980\pi$$
$$104$$ 0 0
$$105$$ −5.00000 −0.487950
$$106$$ 0 0
$$107$$ 3.00000 0.290021 0.145010 0.989430i $$-0.453678\pi$$
0.145010 + 0.989430i $$0.453678\pi$$
$$108$$ 0 0
$$109$$ −12.0000 −1.14939 −0.574696 0.818367i $$-0.694880\pi$$
−0.574696 + 0.818367i $$0.694880\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 0 0
$$113$$ 1.00000 0.0940721 0.0470360 0.998893i $$-0.485022\pi$$
0.0470360 + 0.998893i $$0.485022\pi$$
$$114$$ 0 0
$$115$$ −1.00000 −0.0932505
$$116$$ 0 0
$$117$$ 4.00000 0.369800
$$118$$ 0 0
$$119$$ −15.0000 −1.37505
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ 11.0000 0.991837
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 18.0000 1.59724 0.798621 0.601834i $$-0.205563\pi$$
0.798621 + 0.601834i $$0.205563\pi$$
$$128$$ 0 0
$$129$$ −4.00000 −0.352180
$$130$$ 0 0
$$131$$ −20.0000 −1.74741 −0.873704 0.486458i $$-0.838289\pi$$
−0.873704 + 0.486458i $$0.838289\pi$$
$$132$$ 0 0
$$133$$ 20.0000 1.73422
$$134$$ 0 0
$$135$$ −1.00000 −0.0860663
$$136$$ 0 0
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 0 0
$$139$$ −11.0000 −0.933008 −0.466504 0.884519i $$-0.654487\pi$$
−0.466504 + 0.884519i $$0.654487\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −1.00000 −0.0830455
$$146$$ 0 0
$$147$$ 18.0000 1.48461
$$148$$ 0 0
$$149$$ 22.0000 1.80231 0.901155 0.433497i $$-0.142720\pi$$
0.901155 + 0.433497i $$0.142720\pi$$
$$150$$ 0 0
$$151$$ 16.0000 1.30206 0.651031 0.759051i $$-0.274337\pi$$
0.651031 + 0.759051i $$0.274337\pi$$
$$152$$ 0 0
$$153$$ −3.00000 −0.242536
$$154$$ 0 0
$$155$$ 1.00000 0.0803219
$$156$$ 0 0
$$157$$ 5.00000 0.399043 0.199522 0.979893i $$-0.436061\pi$$
0.199522 + 0.979893i $$0.436061\pi$$
$$158$$ 0 0
$$159$$ 1.00000 0.0793052
$$160$$ 0 0
$$161$$ 5.00000 0.394055
$$162$$ 0 0
$$163$$ −18.0000 −1.40987 −0.704934 0.709273i $$-0.749024\pi$$
−0.704934 + 0.709273i $$0.749024\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 6.00000 0.464294 0.232147 0.972681i $$-0.425425\pi$$
0.232147 + 0.972681i $$0.425425\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ 4.00000 0.305888
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 5.00000 0.377964
$$176$$ 0 0
$$177$$ 1.00000 0.0751646
$$178$$ 0 0
$$179$$ −24.0000 −1.79384 −0.896922 0.442189i $$-0.854202\pi$$
−0.896922 + 0.442189i $$0.854202\pi$$
$$180$$ 0 0
$$181$$ −8.00000 −0.594635 −0.297318 0.954779i $$-0.596092\pi$$
−0.297318 + 0.954779i $$0.596092\pi$$
$$182$$ 0 0
$$183$$ 6.00000 0.443533
$$184$$ 0 0
$$185$$ 1.00000 0.0735215
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 5.00000 0.363696
$$190$$ 0 0
$$191$$ 10.0000 0.723575 0.361787 0.932261i $$-0.382167\pi$$
0.361787 + 0.932261i $$0.382167\pi$$
$$192$$ 0 0
$$193$$ 12.0000 0.863779 0.431889 0.901927i $$-0.357847\pi$$
0.431889 + 0.901927i $$0.357847\pi$$
$$194$$ 0 0
$$195$$ −4.00000 −0.286446
$$196$$ 0 0
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ 0 0
$$199$$ −2.00000 −0.141776 −0.0708881 0.997484i $$-0.522583\pi$$
−0.0708881 + 0.997484i $$0.522583\pi$$
$$200$$ 0 0
$$201$$ 9.00000 0.634811
$$202$$ 0 0
$$203$$ 5.00000 0.350931
$$204$$ 0 0
$$205$$ −11.0000 −0.768273
$$206$$ 0 0
$$207$$ 1.00000 0.0695048
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 23.0000 1.58339 0.791693 0.610920i $$-0.209200\pi$$
0.791693 + 0.610920i $$0.209200\pi$$
$$212$$ 0 0
$$213$$ −13.0000 −0.890745
$$214$$ 0 0
$$215$$ 4.00000 0.272798
$$216$$ 0 0
$$217$$ −5.00000 −0.339422
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −12.0000 −0.807207
$$222$$ 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
$$227$$ −28.0000 −1.85843 −0.929213 0.369546i $$-0.879513\pi$$
−0.929213 + 0.369546i $$0.879513\pi$$
$$228$$ 0 0
$$229$$ −20.0000 −1.32164 −0.660819 0.750546i $$-0.729791\pi$$
−0.660819 + 0.750546i $$0.729791\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 8.00000 0.524097 0.262049 0.965055i $$-0.415602\pi$$
0.262049 + 0.965055i $$0.415602\pi$$
$$234$$ 0 0
$$235$$ 6.00000 0.391397
$$236$$ 0 0
$$237$$ −16.0000 −1.03931
$$238$$ 0 0
$$239$$ 21.0000 1.35838 0.679189 0.733964i $$-0.262332\pi$$
0.679189 + 0.733964i $$0.262332\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 0 0
$$243$$ 1.00000 0.0641500
$$244$$ 0 0
$$245$$ −18.0000 −1.14998
$$246$$ 0 0
$$247$$ 16.0000 1.01806
$$248$$ 0 0
$$249$$ −9.00000 −0.570352
$$250$$ 0 0
$$251$$ −6.00000 −0.378717 −0.189358 0.981908i $$-0.560641\pi$$
−0.189358 + 0.981908i $$0.560641\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 3.00000 0.187867
$$256$$ 0 0
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ −5.00000 −0.310685
$$260$$ 0 0
$$261$$ 1.00000 0.0618984
$$262$$ 0 0
$$263$$ 29.0000 1.78822 0.894108 0.447851i $$-0.147810\pi$$
0.894108 + 0.447851i $$0.147810\pi$$
$$264$$ 0 0
$$265$$ −1.00000 −0.0614295
$$266$$ 0 0
$$267$$ 8.00000 0.489592
$$268$$ 0 0
$$269$$ 15.0000 0.914566 0.457283 0.889321i $$-0.348823\pi$$
0.457283 + 0.889321i $$0.348823\pi$$
$$270$$ 0 0
$$271$$ 13.0000 0.789694 0.394847 0.918747i $$-0.370798\pi$$
0.394847 + 0.918747i $$0.370798\pi$$
$$272$$ 0 0
$$273$$ 20.0000 1.21046
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 10.0000 0.600842 0.300421 0.953807i $$-0.402873\pi$$
0.300421 + 0.953807i $$0.402873\pi$$
$$278$$ 0 0
$$279$$ −1.00000 −0.0598684
$$280$$ 0 0
$$281$$ 20.0000 1.19310 0.596550 0.802576i $$-0.296538\pi$$
0.596550 + 0.802576i $$0.296538\pi$$
$$282$$ 0 0
$$283$$ −1.00000 −0.0594438 −0.0297219 0.999558i $$-0.509462\pi$$
−0.0297219 + 0.999558i $$0.509462\pi$$
$$284$$ 0 0
$$285$$ −4.00000 −0.236940
$$286$$ 0 0
$$287$$ 55.0000 3.24655
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 2.00000 0.117242
$$292$$ 0 0
$$293$$ 7.00000 0.408944 0.204472 0.978872i $$-0.434452\pi$$
0.204472 + 0.978872i $$0.434452\pi$$
$$294$$ 0 0
$$295$$ −1.00000 −0.0582223
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 4.00000 0.231326
$$300$$ 0 0
$$301$$ −20.0000 −1.15278
$$302$$ 0 0
$$303$$ −7.00000 −0.402139
$$304$$ 0 0
$$305$$ −6.00000 −0.343559
$$306$$ 0 0
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ 16.0000 0.910208
$$310$$ 0 0
$$311$$ 32.0000 1.81455 0.907277 0.420534i $$-0.138157\pi$$
0.907277 + 0.420534i $$0.138157\pi$$
$$312$$ 0 0
$$313$$ 21.0000 1.18699 0.593495 0.804838i $$-0.297748\pi$$
0.593495 + 0.804838i $$0.297748\pi$$
$$314$$ 0 0
$$315$$ −5.00000 −0.281718
$$316$$ 0 0
$$317$$ −6.00000 −0.336994 −0.168497 0.985702i $$-0.553891\pi$$
−0.168497 + 0.985702i $$0.553891\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 3.00000 0.167444
$$322$$ 0 0
$$323$$ −12.0000 −0.667698
$$324$$ 0 0
$$325$$ 4.00000 0.221880
$$326$$ 0 0
$$327$$ −12.0000 −0.663602
$$328$$ 0 0
$$329$$ −30.0000 −1.65395
$$330$$ 0 0
$$331$$ −25.0000 −1.37412 −0.687062 0.726599i $$-0.741100\pi$$
−0.687062 + 0.726599i $$0.741100\pi$$
$$332$$ 0 0
$$333$$ −1.00000 −0.0547997
$$334$$ 0 0
$$335$$ −9.00000 −0.491723
$$336$$ 0 0
$$337$$ 10.0000 0.544735 0.272367 0.962193i $$-0.412193\pi$$
0.272367 + 0.962193i $$0.412193\pi$$
$$338$$ 0 0
$$339$$ 1.00000 0.0543125
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 55.0000 2.96972
$$344$$ 0 0
$$345$$ −1.00000 −0.0538382
$$346$$ 0 0
$$347$$ 8.00000 0.429463 0.214731 0.976673i $$-0.431112\pi$$
0.214731 + 0.976673i $$0.431112\pi$$
$$348$$ 0 0
$$349$$ 19.0000 1.01705 0.508523 0.861048i $$-0.330192\pi$$
0.508523 + 0.861048i $$0.330192\pi$$
$$350$$ 0 0
$$351$$ 4.00000 0.213504
$$352$$ 0 0
$$353$$ −18.0000 −0.958043 −0.479022 0.877803i $$-0.659008\pi$$
−0.479022 + 0.877803i $$0.659008\pi$$
$$354$$ 0 0
$$355$$ 13.0000 0.689968
$$356$$ 0 0
$$357$$ −15.0000 −0.793884
$$358$$ 0 0
$$359$$ 10.0000 0.527780 0.263890 0.964553i $$-0.414994\pi$$
0.263890 + 0.964553i $$0.414994\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ −11.0000 −0.577350
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 7.00000 0.365397 0.182699 0.983169i $$-0.441517\pi$$
0.182699 + 0.983169i $$0.441517\pi$$
$$368$$ 0 0
$$369$$ 11.0000 0.572637
$$370$$ 0 0
$$371$$ 5.00000 0.259587
$$372$$ 0 0
$$373$$ −22.0000 −1.13912 −0.569558 0.821951i $$-0.692886\pi$$
−0.569558 + 0.821951i $$0.692886\pi$$
$$374$$ 0 0
$$375$$ −1.00000 −0.0516398
$$376$$ 0 0
$$377$$ 4.00000 0.206010
$$378$$ 0 0
$$379$$ 24.0000 1.23280 0.616399 0.787434i $$-0.288591\pi$$
0.616399 + 0.787434i $$0.288591\pi$$
$$380$$ 0 0
$$381$$ 18.0000 0.922168
$$382$$ 0 0
$$383$$ −27.0000 −1.37964 −0.689818 0.723983i $$-0.742309\pi$$
−0.689818 + 0.723983i $$0.742309\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −4.00000 −0.203331
$$388$$ 0 0
$$389$$ 10.0000 0.507020 0.253510 0.967333i $$-0.418415\pi$$
0.253510 + 0.967333i $$0.418415\pi$$
$$390$$ 0 0
$$391$$ −3.00000 −0.151717
$$392$$ 0 0
$$393$$ −20.0000 −1.00887
$$394$$ 0 0
$$395$$ 16.0000 0.805047
$$396$$ 0 0
$$397$$ 32.0000 1.60603 0.803017 0.595956i $$-0.203227\pi$$
0.803017 + 0.595956i $$0.203227\pi$$
$$398$$ 0 0
$$399$$ 20.0000 1.00125
$$400$$ 0 0
$$401$$ 38.0000 1.89763 0.948815 0.315833i $$-0.102284\pi$$
0.948815 + 0.315833i $$0.102284\pi$$
$$402$$ 0 0
$$403$$ −4.00000 −0.199254
$$404$$ 0 0
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −7.00000 −0.346128 −0.173064 0.984911i $$-0.555367\pi$$
−0.173064 + 0.984911i $$0.555367\pi$$
$$410$$ 0 0
$$411$$ 2.00000 0.0986527
$$412$$ 0 0
$$413$$ 5.00000 0.246034
$$414$$ 0 0
$$415$$ 9.00000 0.441793
$$416$$ 0 0
$$417$$ −11.0000 −0.538672
$$418$$ 0 0
$$419$$ −20.0000 −0.977064 −0.488532 0.872546i $$-0.662467\pi$$
−0.488532 + 0.872546i $$0.662467\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ 0 0
$$423$$ −6.00000 −0.291730
$$424$$ 0 0
$$425$$ −3.00000 −0.145521
$$426$$ 0 0
$$427$$ 30.0000 1.45180
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ −17.0000 −0.816968 −0.408484 0.912766i $$-0.633942\pi$$
−0.408484 + 0.912766i $$0.633942\pi$$
$$434$$ 0 0
$$435$$ −1.00000 −0.0479463
$$436$$ 0 0
$$437$$ 4.00000 0.191346
$$438$$ 0 0
$$439$$ −24.0000 −1.14546 −0.572729 0.819745i $$-0.694115\pi$$
−0.572729 + 0.819745i $$0.694115\pi$$
$$440$$ 0 0
$$441$$ 18.0000 0.857143
$$442$$ 0 0
$$443$$ 2.00000 0.0950229 0.0475114 0.998871i $$-0.484871\pi$$
0.0475114 + 0.998871i $$0.484871\pi$$
$$444$$ 0 0
$$445$$ −8.00000 −0.379236
$$446$$ 0 0
$$447$$ 22.0000 1.04056
$$448$$ 0 0
$$449$$ 1.00000 0.0471929 0.0235965 0.999722i $$-0.492488\pi$$
0.0235965 + 0.999722i $$0.492488\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 16.0000 0.751746
$$454$$ 0 0
$$455$$ −20.0000 −0.937614
$$456$$ 0 0
$$457$$ 9.00000 0.421002 0.210501 0.977594i $$-0.432490\pi$$
0.210501 + 0.977594i $$0.432490\pi$$
$$458$$ 0 0
$$459$$ −3.00000 −0.140028
$$460$$ 0 0
$$461$$ 34.0000 1.58354 0.791769 0.610821i $$-0.209160\pi$$
0.791769 + 0.610821i $$0.209160\pi$$
$$462$$ 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
$$467$$ 3.00000 0.138823 0.0694117 0.997588i $$-0.477888\pi$$
0.0694117 + 0.997588i $$0.477888\pi$$
$$468$$ 0 0
$$469$$ 45.0000 2.07791
$$470$$ 0 0
$$471$$ 5.00000 0.230388
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 4.00000 0.183533
$$476$$ 0 0
$$477$$ 1.00000 0.0457869
$$478$$ 0 0
$$479$$ −38.0000 −1.73626 −0.868132 0.496333i $$-0.834679\pi$$
−0.868132 + 0.496333i $$0.834679\pi$$
$$480$$ 0 0
$$481$$ −4.00000 −0.182384
$$482$$ 0 0
$$483$$ 5.00000 0.227508
$$484$$ 0 0
$$485$$ −2.00000 −0.0908153
$$486$$ 0 0
$$487$$ 14.0000 0.634401 0.317200 0.948359i $$-0.397257\pi$$
0.317200 + 0.948359i $$0.397257\pi$$
$$488$$ 0 0
$$489$$ −18.0000 −0.813988
$$490$$ 0 0
$$491$$ −1.00000 −0.0451294 −0.0225647 0.999745i $$-0.507183\pi$$
−0.0225647 + 0.999745i $$0.507183\pi$$
$$492$$ 0 0
$$493$$ −3.00000 −0.135113
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −65.0000 −2.91565
$$498$$ 0 0
$$499$$ −3.00000 −0.134298 −0.0671492 0.997743i $$-0.521390\pi$$
−0.0671492 + 0.997743i $$0.521390\pi$$
$$500$$ 0 0
$$501$$ 6.00000 0.268060
$$502$$ 0 0
$$503$$ −31.0000 −1.38222 −0.691111 0.722749i $$-0.742878\pi$$
−0.691111 + 0.722749i $$0.742878\pi$$
$$504$$ 0 0
$$505$$ 7.00000 0.311496
$$506$$ 0 0
$$507$$ 3.00000 0.133235
$$508$$ 0 0
$$509$$ −18.0000 −0.797836 −0.398918 0.916987i $$-0.630614\pi$$
−0.398918 + 0.916987i $$0.630614\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 4.00000 0.176604
$$514$$ 0 0
$$515$$ −16.0000 −0.705044
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 32.0000 1.40195 0.700973 0.713188i $$-0.252749\pi$$
0.700973 + 0.713188i $$0.252749\pi$$
$$522$$ 0 0
$$523$$ −28.0000 −1.22435 −0.612177 0.790721i $$-0.709706\pi$$
−0.612177 + 0.790721i $$0.709706\pi$$
$$524$$ 0 0
$$525$$ 5.00000 0.218218
$$526$$ 0 0
$$527$$ 3.00000 0.130682
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 1.00000 0.0433963
$$532$$ 0 0
$$533$$ 44.0000 1.90585
$$534$$ 0 0
$$535$$ −3.00000 −0.129701
$$536$$ 0 0
$$537$$ −24.0000 −1.03568
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 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
$$545$$ 12.0000 0.514024
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ 0 0
$$549$$ 6.00000 0.256074
$$550$$ 0 0
$$551$$ 4.00000 0.170406
$$552$$ 0 0
$$553$$ −80.0000 −3.40195
$$554$$ 0 0
$$555$$ 1.00000 0.0424476
$$556$$ 0 0
$$557$$ −23.0000 −0.974541 −0.487271 0.873251i $$-0.662007\pi$$
−0.487271 + 0.873251i $$0.662007\pi$$
$$558$$ 0 0
$$559$$ −16.0000 −0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −27.0000 −1.13791 −0.568957 0.822367i $$-0.692653\pi$$
−0.568957 + 0.822367i $$0.692653\pi$$
$$564$$ 0 0
$$565$$ −1.00000 −0.0420703
$$566$$ 0 0
$$567$$ 5.00000 0.209980
$$568$$ 0 0
$$569$$ −30.0000 −1.25767 −0.628833 0.777541i $$-0.716467\pi$$
−0.628833 + 0.777541i $$0.716467\pi$$
$$570$$ 0 0
$$571$$ −10.0000 −0.418487 −0.209243 0.977864i $$-0.567100\pi$$
−0.209243 + 0.977864i $$0.567100\pi$$
$$572$$ 0 0
$$573$$ 10.0000 0.417756
$$574$$ 0 0
$$575$$ 1.00000 0.0417029
$$576$$ 0 0
$$577$$ 4.00000 0.166522 0.0832611 0.996528i $$-0.473466\pi$$
0.0832611 + 0.996528i $$0.473466\pi$$
$$578$$ 0 0
$$579$$ 12.0000 0.498703
$$580$$ 0 0
$$581$$ −45.0000 −1.86691
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ −4.00000 −0.165380
$$586$$ 0 0
$$587$$ 6.00000 0.247647 0.123823 0.992304i $$-0.460484\pi$$
0.123823 + 0.992304i $$0.460484\pi$$
$$588$$ 0 0
$$589$$ −4.00000 −0.164817
$$590$$ 0 0
$$591$$ 2.00000 0.0822690
$$592$$ 0 0
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ 15.0000 0.614940
$$596$$ 0 0
$$597$$ −2.00000 −0.0818546
$$598$$ 0 0
$$599$$ 44.0000 1.79779 0.898896 0.438163i $$-0.144371\pi$$
0.898896 + 0.438163i $$0.144371\pi$$
$$600$$ 0 0
$$601$$ 7.00000 0.285536 0.142768 0.989756i $$-0.454400\pi$$
0.142768 + 0.989756i $$0.454400\pi$$
$$602$$ 0 0
$$603$$ 9.00000 0.366508
$$604$$ 0 0
$$605$$ 11.0000 0.447214
$$606$$ 0 0
$$607$$ −22.0000 −0.892952 −0.446476 0.894795i $$-0.647321\pi$$
−0.446476 + 0.894795i $$0.647321\pi$$
$$608$$ 0 0
$$609$$ 5.00000 0.202610
$$610$$ 0 0
$$611$$ −24.0000 −0.970936
$$612$$ 0 0
$$613$$ 14.0000 0.565455 0.282727 0.959200i $$-0.408761\pi$$
0.282727 + 0.959200i $$0.408761\pi$$
$$614$$ 0 0
$$615$$ −11.0000 −0.443563
$$616$$ 0 0
$$617$$ −1.00000 −0.0402585 −0.0201292 0.999797i $$-0.506408\pi$$
−0.0201292 + 0.999797i $$0.506408\pi$$
$$618$$ 0 0
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ 0 0
$$621$$ 1.00000 0.0401286
$$622$$ 0 0
$$623$$ 40.0000 1.60257
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ −38.0000 −1.51276 −0.756378 0.654135i $$-0.773033\pi$$
−0.756378 + 0.654135i $$0.773033\pi$$
$$632$$ 0 0
$$633$$ 23.0000 0.914168
$$634$$ 0 0
$$635$$ −18.0000 −0.714308
$$636$$ 0 0
$$637$$ 72.0000 2.85274
$$638$$ 0 0
$$639$$ −13.0000 −0.514272
$$640$$ 0 0
$$641$$ 24.0000 0.947943 0.473972 0.880540i $$-0.342820\pi$$
0.473972 + 0.880540i $$0.342820\pi$$
$$642$$ 0 0
$$643$$ 1.00000 0.0394362 0.0197181 0.999806i $$-0.493723\pi$$
0.0197181 + 0.999806i $$0.493723\pi$$
$$644$$ 0 0
$$645$$ 4.00000 0.157500
$$646$$ 0 0
$$647$$ 48.0000 1.88707 0.943537 0.331266i $$-0.107476\pi$$
0.943537 + 0.331266i $$0.107476\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −5.00000 −0.195965
$$652$$ 0 0
$$653$$ −44.0000 −1.72185 −0.860927 0.508729i $$-0.830115\pi$$
−0.860927 + 0.508729i $$0.830115\pi$$
$$654$$ 0 0
$$655$$ 20.0000 0.781465
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −24.0000 −0.934907 −0.467454 0.884018i $$-0.654829\pi$$
−0.467454 + 0.884018i $$0.654829\pi$$
$$660$$ 0 0
$$661$$ −14.0000 −0.544537 −0.272268 0.962221i $$-0.587774\pi$$
−0.272268 + 0.962221i $$0.587774\pi$$
$$662$$ 0 0
$$663$$ −12.0000 −0.466041
$$664$$ 0 0
$$665$$ −20.0000 −0.775567
$$666$$ 0 0
$$667$$ 1.00000 0.0387202
$$668$$ 0 0
$$669$$ −14.0000 −0.541271
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −6.00000 −0.231283 −0.115642 0.993291i $$-0.536892\pi$$
−0.115642 + 0.993291i $$0.536892\pi$$
$$674$$ 0 0
$$675$$ 1.00000 0.0384900
$$676$$ 0 0
$$677$$ 39.0000 1.49889 0.749446 0.662066i $$-0.230320\pi$$
0.749446 + 0.662066i $$0.230320\pi$$
$$678$$ 0 0
$$679$$ 10.0000 0.383765
$$680$$ 0 0
$$681$$ −28.0000 −1.07296
$$682$$ 0 0
$$683$$ −34.0000 −1.30097 −0.650487 0.759517i $$-0.725435\pi$$
−0.650487 + 0.759517i $$0.725435\pi$$
$$684$$ 0 0
$$685$$ −2.00000 −0.0764161
$$686$$ 0 0
$$687$$ −20.0000 −0.763048
$$688$$ 0 0
$$689$$ 4.00000 0.152388
$$690$$ 0 0
$$691$$ −8.00000 −0.304334 −0.152167 0.988355i $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 11.0000 0.417254
$$696$$ 0 0
$$697$$ −33.0000 −1.24996
$$698$$ 0 0
$$699$$ 8.00000 0.302588
$$700$$ 0 0
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ 0 0
$$703$$ −4.00000 −0.150863
$$704$$ 0 0
$$705$$ 6.00000 0.225973
$$706$$ 0 0
$$707$$ −35.0000 −1.31631
$$708$$ 0 0
$$709$$ 18.0000 0.676004 0.338002 0.941145i $$-0.390249\pi$$
0.338002 + 0.941145i $$0.390249\pi$$
$$710$$ 0 0
$$711$$ −16.0000 −0.600047
$$712$$ 0 0
$$713$$ −1.00000 −0.0374503
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 21.0000 0.784259
$$718$$ 0 0
$$719$$ 25.0000 0.932343 0.466171 0.884694i $$-0.345633\pi$$
0.466171 + 0.884694i $$0.345633\pi$$
$$720$$ 0 0
$$721$$ 80.0000 2.97936
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 1.00000 0.0371391
$$726$$ 0 0
$$727$$ −13.0000 −0.482143 −0.241072 0.970507i $$-0.577499\pi$$
−0.241072 + 0.970507i $$0.577499\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 12.0000 0.443836
$$732$$ 0 0
$$733$$ −21.0000 −0.775653 −0.387826 0.921732i $$-0.626774\pi$$
−0.387826 + 0.921732i $$0.626774\pi$$
$$734$$ 0 0
$$735$$ −18.0000 −0.663940
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −45.0000 −1.65535 −0.827676 0.561206i $$-0.810337\pi$$
−0.827676 + 0.561206i $$0.810337\pi$$
$$740$$ 0 0
$$741$$ 16.0000 0.587775
$$742$$ 0 0
$$743$$ −16.0000 −0.586983 −0.293492 0.955962i $$-0.594817\pi$$
−0.293492 + 0.955962i $$0.594817\pi$$
$$744$$ 0 0
$$745$$ −22.0000 −0.806018
$$746$$ 0 0
$$747$$ −9.00000 −0.329293
$$748$$ 0 0
$$749$$ 15.0000 0.548088
$$750$$ 0 0
$$751$$ −20.0000 −0.729810 −0.364905 0.931045i $$-0.618899\pi$$
−0.364905 + 0.931045i $$0.618899\pi$$
$$752$$ 0 0
$$753$$ −6.00000 −0.218652
$$754$$ 0 0
$$755$$ −16.0000 −0.582300
$$756$$ 0 0
$$757$$ 29.0000 1.05402 0.527011 0.849858i $$-0.323312\pi$$
0.527011 + 0.849858i $$0.323312\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −45.0000 −1.63125 −0.815624 0.578582i $$-0.803606\pi$$
−0.815624 + 0.578582i $$0.803606\pi$$
$$762$$ 0 0
$$763$$ −60.0000 −2.17215
$$764$$ 0 0
$$765$$ 3.00000 0.108465
$$766$$ 0 0
$$767$$ 4.00000 0.144432
$$768$$ 0 0
$$769$$ 10.0000 0.360609 0.180305 0.983611i $$-0.442292\pi$$
0.180305 + 0.983611i $$0.442292\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 0 0
$$773$$ −6.00000 −0.215805 −0.107903 0.994161i $$-0.534413\pi$$
−0.107903 + 0.994161i $$0.534413\pi$$
$$774$$ 0 0
$$775$$ −1.00000 −0.0359211
$$776$$ 0 0
$$777$$ −5.00000 −0.179374
$$778$$ 0 0
$$779$$ 44.0000 1.57646
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 1.00000 0.0357371
$$784$$ 0 0
$$785$$ −5.00000 −0.178458
$$786$$ 0 0
$$787$$ −23.0000 −0.819861 −0.409931 0.912117i $$-0.634447\pi$$
−0.409931 + 0.912117i $$0.634447\pi$$
$$788$$ 0 0
$$789$$ 29.0000 1.03243
$$790$$ 0 0
$$791$$ 5.00000 0.177780
$$792$$ 0 0
$$793$$ 24.0000 0.852265
$$794$$ 0 0
$$795$$ −1.00000 −0.0354663
$$796$$ 0 0
$$797$$ 15.0000 0.531327 0.265664 0.964066i $$-0.414409\pi$$
0.265664 + 0.964066i $$0.414409\pi$$
$$798$$ 0 0
$$799$$ 18.0000 0.636794
$$800$$ 0 0
$$801$$ 8.00000 0.282666
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ −5.00000 −0.176227
$$806$$ 0 0
$$807$$ 15.0000 0.528025
$$808$$ 0 0
$$809$$ 13.0000 0.457056 0.228528 0.973537i $$-0.426609\pi$$
0.228528 + 0.973537i $$0.426609\pi$$
$$810$$ 0 0
$$811$$ 39.0000 1.36948 0.684738 0.728790i $$-0.259917\pi$$
0.684738 + 0.728790i $$0.259917\pi$$
$$812$$ 0 0
$$813$$ 13.0000 0.455930
$$814$$ 0 0
$$815$$ 18.0000 0.630512
$$816$$ 0 0
$$817$$ −16.0000 −0.559769
$$818$$ 0 0
$$819$$ 20.0000 0.698857
$$820$$ 0 0
$$821$$ −42.0000 −1.46581 −0.732905 0.680331i $$-0.761836\pi$$
−0.732905 + 0.680331i $$0.761836\pi$$
$$822$$ 0 0
$$823$$ −40.0000 −1.39431 −0.697156 0.716919i $$-0.745552\pi$$
−0.697156 + 0.716919i $$0.745552\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −27.0000 −0.938882 −0.469441 0.882964i $$-0.655545\pi$$
−0.469441 + 0.882964i $$0.655545\pi$$
$$828$$ 0 0
$$829$$ 17.0000 0.590434 0.295217 0.955430i $$-0.404608\pi$$
0.295217 + 0.955430i $$0.404608\pi$$
$$830$$ 0 0
$$831$$ 10.0000 0.346896
$$832$$ 0 0
$$833$$ −54.0000 −1.87099
$$834$$ 0 0
$$835$$ −6.00000 −0.207639
$$836$$ 0 0
$$837$$ −1.00000 −0.0345651
$$838$$ 0 0
$$839$$ 26.0000 0.897620 0.448810 0.893627i $$-0.351848\pi$$
0.448810 + 0.893627i $$0.351848\pi$$
$$840$$ 0 0
$$841$$ −28.0000 −0.965517
$$842$$ 0 0
$$843$$ 20.0000 0.688837
$$844$$ 0 0
$$845$$ −3.00000 −0.103203
$$846$$ 0 0
$$847$$ −55.0000 −1.88982
$$848$$ 0 0
$$849$$ −1.00000 −0.0343199
$$850$$ 0 0
$$851$$ −1.00000 −0.0342796
$$852$$ 0 0
$$853$$ −54.0000 −1.84892 −0.924462 0.381273i $$-0.875486\pi$$
−0.924462 + 0.381273i $$0.875486\pi$$
$$854$$ 0 0
$$855$$ −4.00000 −0.136797
$$856$$ 0 0
$$857$$ −2.00000 −0.0683187 −0.0341593 0.999416i $$-0.510875\pi$$
−0.0341593 + 0.999416i $$0.510875\pi$$
$$858$$ 0 0
$$859$$ 27.0000 0.921228 0.460614 0.887601i $$-0.347629\pi$$
0.460614 + 0.887601i $$0.347629\pi$$
$$860$$ 0 0
$$861$$ 55.0000 1.87439
$$862$$ 0 0
$$863$$ −42.0000 −1.42970 −0.714848 0.699280i $$-0.753504\pi$$
−0.714848 + 0.699280i $$0.753504\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −8.00000 −0.271694
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 36.0000 1.21981
$$872$$ 0 0
$$873$$ 2.00000 0.0676897
$$874$$ 0 0
$$875$$ −5.00000 −0.169031
$$876$$ 0 0
$$877$$ 42.0000 1.41824 0.709120 0.705088i $$-0.249093\pi$$
0.709120 + 0.705088i $$0.249093\pi$$
$$878$$ 0 0
$$879$$ 7.00000 0.236104
$$880$$ 0 0
$$881$$ −6.00000 −0.202145 −0.101073 0.994879i $$-0.532227\pi$$
−0.101073 + 0.994879i $$0.532227\pi$$
$$882$$ 0 0
$$883$$ −46.0000 −1.54802 −0.774012 0.633171i $$-0.781753\pi$$
−0.774012 + 0.633171i $$0.781753\pi$$
$$884$$ 0 0
$$885$$ −1.00000 −0.0336146
$$886$$ 0 0
$$887$$ −38.0000 −1.27592 −0.637958 0.770072i $$-0.720220\pi$$
−0.637958 + 0.770072i $$0.720220\pi$$
$$888$$ 0 0
$$889$$ 90.0000 3.01850
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −24.0000 −0.803129
$$894$$ 0 0
$$895$$ 24.0000 0.802232
$$896$$ 0 0
$$897$$ 4.00000 0.133556
$$898$$ 0 0
$$899$$ −1.00000 −0.0333519
$$900$$ 0 0
$$901$$ −3.00000 −0.0999445
$$902$$ 0 0
$$903$$ −20.0000 −0.665558
$$904$$ 0 0
$$905$$ 8.00000 0.265929
$$906$$ 0 0
$$907$$ 17.0000 0.564476 0.282238 0.959344i $$-0.408923\pi$$
0.282238 + 0.959344i $$0.408923\pi$$
$$908$$ 0 0
$$909$$ −7.00000 −0.232175
$$910$$ 0 0
$$911$$ 24.0000 0.795155 0.397578 0.917568i $$-0.369851\pi$$
0.397578 + 0.917568i $$0.369851\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ −6.00000 −0.198354
$$916$$ 0 0
$$917$$ −100.000 −3.30229
$$918$$ 0 0
$$919$$ −48.0000 −1.58337 −0.791687 0.610927i $$-0.790797\pi$$
−0.791687 + 0.610927i $$0.790797\pi$$
$$920$$ 0 0
$$921$$ −12.0000 −0.395413
$$922$$ 0 0
$$923$$ −52.0000 −1.71160
$$924$$ 0 0
$$925$$ −1.00000 −0.0328798
$$926$$ 0 0
$$927$$ 16.0000 0.525509
$$928$$ 0 0
$$929$$ 5.00000 0.164045 0.0820223 0.996630i $$-0.473862\pi$$
0.0820223 + 0.996630i $$0.473862\pi$$
$$930$$ 0 0
$$931$$ 72.0000 2.35970
$$932$$ 0 0
$$933$$ 32.0000 1.04763
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 2.00000 0.0653372 0.0326686 0.999466i $$-0.489599\pi$$
0.0326686 + 0.999466i $$0.489599\pi$$
$$938$$ 0 0
$$939$$ 21.0000 0.685309
$$940$$ 0 0
$$941$$ 6.00000 0.195594 0.0977972 0.995206i $$-0.468820\pi$$
0.0977972 + 0.995206i $$0.468820\pi$$
$$942$$ 0 0
$$943$$ 11.0000 0.358209
$$944$$ 0 0
$$945$$ −5.00000 −0.162650
$$946$$ 0 0
$$947$$ 8.00000 0.259965 0.129983 0.991516i $$-0.458508\pi$$
0.129983 + 0.991516i $$0.458508\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ −6.00000 −0.194563
$$952$$ 0 0
$$953$$ −6.00000 −0.194359 −0.0971795 0.995267i $$-0.530982\pi$$
−0.0971795 + 0.995267i $$0.530982\pi$$
$$954$$ 0 0
$$955$$ −10.0000 −0.323592
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 10.0000 0.322917
$$960$$ 0 0
$$961$$ −30.0000 −0.967742
$$962$$ 0 0
$$963$$ 3.00000 0.0966736
$$964$$ 0 0
$$965$$ −12.0000 −0.386294
$$966$$ 0 0
$$967$$ −2.00000 −0.0643157 −0.0321578 0.999483i $$-0.510238\pi$$
−0.0321578 + 0.999483i $$0.510238\pi$$
$$968$$ 0 0
$$969$$ −12.0000 −0.385496
$$970$$ 0 0
$$971$$ −20.0000 −0.641831 −0.320915 0.947108i $$-0.603990\pi$$
−0.320915 + 0.947108i $$0.603990\pi$$
$$972$$ 0 0
$$973$$ −55.0000 −1.76322
$$974$$ 0 0
$$975$$ 4.00000 0.128103
$$976$$ 0 0
$$977$$ 31.0000 0.991778 0.495889 0.868386i $$-0.334842\pi$$
0.495889 + 0.868386i $$0.334842\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −12.0000 −0.383131
$$982$$ 0 0
$$983$$ 11.0000 0.350846 0.175423 0.984493i $$-0.443871\pi$$
0.175423 + 0.984493i $$0.443871\pi$$
$$984$$ 0 0
$$985$$ −2.00000 −0.0637253
$$986$$ 0 0
$$987$$ −30.0000 −0.954911
$$988$$ 0 0
$$989$$ −4.00000 −0.127193
$$990$$ 0 0
$$991$$ 35.0000 1.11181 0.555906 0.831245i $$-0.312372\pi$$
0.555906 + 0.831245i $$0.312372\pi$$
$$992$$ 0 0
$$993$$ −25.0000 −0.793351
$$994$$ 0 0
$$995$$ 2.00000 0.0634043
$$996$$ 0 0
$$997$$ 40.0000 1.26681 0.633406 0.773819i $$-0.281656\pi$$
0.633406 + 0.773819i $$0.281656\pi$$
$$998$$ 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.ba.1.1 1
4.3 odd 2 1380.2.a.a.1.1 1
12.11 even 2 4140.2.a.e.1.1 1
20.3 even 4 6900.2.f.f.6349.1 2
20.7 even 4 6900.2.f.f.6349.2 2
20.19 odd 2 6900.2.a.i.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1380.2.a.a.1.1 1 4.3 odd 2
4140.2.a.e.1.1 1 12.11 even 2
5520.2.a.ba.1.1 1 1.1 even 1 trivial
6900.2.a.i.1.1 1 20.19 odd 2
6900.2.f.f.6349.1 2 20.3 even 4
6900.2.f.f.6349.2 2 20.7 even 4