# Properties

 Label 1900.2.a.k.1.5 Level $1900$ Weight $2$ Character 1900.1 Self dual yes Analytic conductor $15.172$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1900.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$15.1715763840$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.6.56310016.1 Defining polynomial: $$x^{6} - 9 x^{4} + 14 x^{2} - 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 380) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.5 Root $$1.23277$$ of defining polynomial Character $$\chi$$ $$=$$ 1900.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.62236 q^{3} +4.74397 q^{7} -0.367938 q^{9} +O(q^{10})$$ $$q+1.62236 q^{3} +4.74397 q^{7} -0.367938 q^{9} +4.48028 q^{11} +0.843176 q^{13} +5.52315 q^{17} +1.00000 q^{19} +7.69643 q^{21} -0.779187 q^{23} -5.46402 q^{27} -10.6570 q^{29} -8.65699 q^{31} +7.26864 q^{33} +1.62236 q^{37} +1.36794 q^{39} +4.73588 q^{41} -9.67504 q^{43} +3.18559 q^{47} +15.5052 q^{49} +8.96056 q^{51} -6.17922 q^{53} +1.62236 q^{57} +11.6964 q^{59} +6.48028 q^{61} -1.74549 q^{63} -14.8880 q^{67} -1.26412 q^{69} +0.303566 q^{71} +10.0800 q^{73} +21.2543 q^{77} +4.00000 q^{79} -7.76081 q^{81} +0.779187 q^{83} -17.2895 q^{87} -5.69643 q^{89} +4.00000 q^{91} -14.0448 q^{93} -6.17922 q^{97} -1.64847 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 10 q^{9} + O(q^{10})$$ $$6 q + 10 q^{9} + 18 q^{11} + 6 q^{19} + 4 q^{21} - 4 q^{29} + 8 q^{31} - 4 q^{39} + 4 q^{41} + 12 q^{49} + 36 q^{51} + 28 q^{59} + 30 q^{61} - 32 q^{69} + 44 q^{71} + 24 q^{79} + 50 q^{81} + 8 q^{89} + 24 q^{91} + 90 q^{99} + O(q^{100})$$

## 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
$$3$$ 1.62236 0.936672 0.468336 0.883551i $$-0.344854\pi$$
0.468336 + 0.883551i $$0.344854\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 4.74397 1.79305 0.896525 0.442993i $$-0.146083\pi$$
0.896525 + 0.442993i $$0.146083\pi$$
$$8$$ 0 0
$$9$$ −0.367938 −0.122646
$$10$$ 0 0
$$11$$ 4.48028 1.35085 0.675427 0.737426i $$-0.263959\pi$$
0.675427 + 0.737426i $$0.263959\pi$$
$$12$$ 0 0
$$13$$ 0.843176 0.233855 0.116928 0.993140i $$-0.462695\pi$$
0.116928 + 0.993140i $$0.462695\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 5.52315 1.33956 0.669781 0.742559i $$-0.266388\pi$$
0.669781 + 0.742559i $$0.266388\pi$$
$$18$$ 0 0
$$19$$ 1.00000 0.229416
$$20$$ 0 0
$$21$$ 7.69643 1.67950
$$22$$ 0 0
$$23$$ −0.779187 −0.162472 −0.0812358 0.996695i $$-0.525887\pi$$
−0.0812358 + 0.996695i $$0.525887\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −5.46402 −1.05155
$$28$$ 0 0
$$29$$ −10.6570 −1.97895 −0.989477 0.144691i $$-0.953781\pi$$
−0.989477 + 0.144691i $$0.953781\pi$$
$$30$$ 0 0
$$31$$ −8.65699 −1.55484 −0.777421 0.628981i $$-0.783472\pi$$
−0.777421 + 0.628981i $$0.783472\pi$$
$$32$$ 0 0
$$33$$ 7.26864 1.26531
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 1.62236 0.266715 0.133357 0.991068i $$-0.457424\pi$$
0.133357 + 0.991068i $$0.457424\pi$$
$$38$$ 0 0
$$39$$ 1.36794 0.219045
$$40$$ 0 0
$$41$$ 4.73588 0.739620 0.369810 0.929107i $$-0.379423\pi$$
0.369810 + 0.929107i $$0.379423\pi$$
$$42$$ 0 0
$$43$$ −9.67504 −1.47543 −0.737715 0.675112i $$-0.764095\pi$$
−0.737715 + 0.675112i $$0.764095\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.18559 0.464666 0.232333 0.972636i $$-0.425364\pi$$
0.232333 + 0.972636i $$0.425364\pi$$
$$48$$ 0 0
$$49$$ 15.5052 2.21503
$$50$$ 0 0
$$51$$ 8.96056 1.25473
$$52$$ 0 0
$$53$$ −6.17922 −0.848780 −0.424390 0.905479i $$-0.639512\pi$$
−0.424390 + 0.905479i $$0.639512\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.62236 0.214887
$$58$$ 0 0
$$59$$ 11.6964 1.52275 0.761373 0.648314i $$-0.224526\pi$$
0.761373 + 0.648314i $$0.224526\pi$$
$$60$$ 0 0
$$61$$ 6.48028 0.829715 0.414857 0.909886i $$-0.363831\pi$$
0.414857 + 0.909886i $$0.363831\pi$$
$$62$$ 0 0
$$63$$ −1.74549 −0.219911
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −14.8880 −1.81885 −0.909427 0.415864i $$-0.863479\pi$$
−0.909427 + 0.415864i $$0.863479\pi$$
$$68$$ 0 0
$$69$$ −1.26412 −0.152183
$$70$$ 0 0
$$71$$ 0.303566 0.0360266 0.0180133 0.999838i $$-0.494266\pi$$
0.0180133 + 0.999838i $$0.494266\pi$$
$$72$$ 0 0
$$73$$ 10.0800 1.17978 0.589888 0.807485i $$-0.299172\pi$$
0.589888 + 0.807485i $$0.299172\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 21.2543 2.42215
$$78$$ 0 0
$$79$$ 4.00000 0.450035 0.225018 0.974355i $$-0.427756\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 0 0
$$81$$ −7.76081 −0.862312
$$82$$ 0 0
$$83$$ 0.779187 0.0855268 0.0427634 0.999085i $$-0.486384\pi$$
0.0427634 + 0.999085i $$0.486384\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −17.2895 −1.85363
$$88$$ 0 0
$$89$$ −5.69643 −0.603821 −0.301910 0.953336i $$-0.597624\pi$$
−0.301910 + 0.953336i $$0.597624\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ 0 0
$$93$$ −14.0448 −1.45638
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −6.17922 −0.627404 −0.313702 0.949521i $$-0.601569\pi$$
−0.313702 + 0.949521i $$0.601569\pi$$
$$98$$ 0 0
$$99$$ −1.64847 −0.165677
$$100$$ 0 0
$$101$$ 3.36794 0.335122 0.167561 0.985862i $$-0.446411\pi$$
0.167561 + 0.985862i $$0.446411\pi$$
$$102$$ 0 0
$$103$$ 3.71368 0.365919 0.182960 0.983120i $$-0.441432\pi$$
0.182960 + 0.983120i $$0.441432\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −10.2031 −0.986374 −0.493187 0.869923i $$-0.664168\pi$$
−0.493187 + 0.869923i $$0.664168\pi$$
$$108$$ 0 0
$$109$$ 2.96056 0.283570 0.141785 0.989897i $$-0.454716\pi$$
0.141785 + 0.989897i $$0.454716\pi$$
$$110$$ 0 0
$$111$$ 2.63206 0.249824
$$112$$ 0 0
$$113$$ 7.08638 0.666631 0.333315 0.942815i $$-0.391833\pi$$
0.333315 + 0.942815i $$0.391833\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −0.310237 −0.0286814
$$118$$ 0 0
$$119$$ 26.2016 2.40190
$$120$$ 0 0
$$121$$ 9.07290 0.824809
$$122$$ 0 0
$$123$$ 7.68331 0.692781
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −9.79817 −0.869447 −0.434723 0.900564i $$-0.643154\pi$$
−0.434723 + 0.900564i $$0.643154\pi$$
$$128$$ 0 0
$$129$$ −15.6964 −1.38199
$$130$$ 0 0
$$131$$ 12.5841 1.09948 0.549739 0.835337i $$-0.314727\pi$$
0.549739 + 0.835337i $$0.314727\pi$$
$$132$$ 0 0
$$133$$ 4.74397 0.411354
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −8.89586 −0.760024 −0.380012 0.924981i $$-0.624080\pi$$
−0.380012 + 0.924981i $$0.624080\pi$$
$$138$$ 0 0
$$139$$ 6.25560 0.530593 0.265296 0.964167i $$-0.414530\pi$$
0.265296 + 0.964167i $$0.414530\pi$$
$$140$$ 0 0
$$141$$ 5.16819 0.435240
$$142$$ 0 0
$$143$$ 3.77767 0.315904
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 25.1551 2.07476
$$148$$ 0 0
$$149$$ 2.48028 0.203192 0.101596 0.994826i $$-0.467605\pi$$
0.101596 + 0.994826i $$0.467605\pi$$
$$150$$ 0 0
$$151$$ 3.69643 0.300812 0.150406 0.988624i $$-0.451942\pi$$
0.150406 + 0.988624i $$0.451942\pi$$
$$152$$ 0 0
$$153$$ −2.03218 −0.164292
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −18.8479 −1.50422 −0.752112 0.659035i $$-0.770965\pi$$
−0.752112 + 0.659035i $$0.770965\pi$$
$$158$$ 0 0
$$159$$ −10.0249 −0.795029
$$160$$ 0 0
$$161$$ −3.69643 −0.291320
$$162$$ 0 0
$$163$$ −2.46554 −0.193116 −0.0965580 0.995327i $$-0.530783\pi$$
−0.0965580 + 0.995327i $$0.530783\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 7.49134 0.579697 0.289849 0.957072i $$-0.406395\pi$$
0.289849 + 0.957072i $$0.406395\pi$$
$$168$$ 0 0
$$169$$ −12.2891 −0.945312
$$170$$ 0 0
$$171$$ −0.367938 −0.0281369
$$172$$ 0 0
$$173$$ 20.0653 1.52554 0.762768 0.646673i $$-0.223840\pi$$
0.762768 + 0.646673i $$0.223840\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 18.9759 1.42631
$$178$$ 0 0
$$179$$ −3.69643 −0.276284 −0.138142 0.990412i $$-0.544113\pi$$
−0.138142 + 0.990412i $$0.544113\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 10.5134 0.777170
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 24.7453 1.80955
$$188$$ 0 0
$$189$$ −25.9211 −1.88548
$$190$$ 0 0
$$191$$ 0.887659 0.0642288 0.0321144 0.999484i $$-0.489776\pi$$
0.0321144 + 0.999484i $$0.489776\pi$$
$$192$$ 0 0
$$193$$ −19.1581 −1.37903 −0.689516 0.724271i $$-0.742177\pi$$
−0.689516 + 0.724271i $$0.742177\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −3.37271 −0.240295 −0.120148 0.992756i $$-0.538337\pi$$
−0.120148 + 0.992756i $$0.538337\pi$$
$$198$$ 0 0
$$199$$ 4.58409 0.324958 0.162479 0.986712i $$-0.448051\pi$$
0.162479 + 0.986712i $$0.448051\pi$$
$$200$$ 0 0
$$201$$ −24.1537 −1.70367
$$202$$ 0 0
$$203$$ −50.5564 −3.54836
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0.286693 0.0199265
$$208$$ 0 0
$$209$$ 4.48028 0.309907
$$210$$ 0 0
$$211$$ −14.8817 −1.02450 −0.512248 0.858837i $$-0.671187\pi$$
−0.512248 + 0.858837i $$0.671187\pi$$
$$212$$ 0 0
$$213$$ 0.492494 0.0337451
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −41.0685 −2.78791
$$218$$ 0 0
$$219$$ 16.3534 1.10506
$$220$$ 0 0
$$221$$ 4.65699 0.313263
$$222$$ 0 0
$$223$$ −18.7839 −1.25786 −0.628931 0.777461i $$-0.716507\pi$$
−0.628931 + 0.777461i $$0.716507\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0.843176 0.0559636 0.0279818 0.999608i $$-0.491092\pi$$
0.0279818 + 0.999608i $$0.491092\pi$$
$$228$$ 0 0
$$229$$ −4.86273 −0.321338 −0.160669 0.987008i $$-0.551365\pi$$
−0.160669 + 0.987008i $$0.551365\pi$$
$$230$$ 0 0
$$231$$ 34.4822 2.26876
$$232$$ 0 0
$$233$$ 4.90268 0.321185 0.160593 0.987021i $$-0.448659\pi$$
0.160593 + 0.987021i $$0.448659\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 6.48945 0.421535
$$238$$ 0 0
$$239$$ −6.20164 −0.401151 −0.200575 0.979678i $$-0.564281\pi$$
−0.200575 + 0.979678i $$0.564281\pi$$
$$240$$ 0 0
$$241$$ −3.26412 −0.210261 −0.105130 0.994458i $$-0.533526\pi$$
−0.105130 + 0.994458i $$0.533526\pi$$
$$242$$ 0 0
$$243$$ 3.80121 0.243848
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0.843176 0.0536500
$$248$$ 0 0
$$249$$ 1.26412 0.0801106
$$250$$ 0 0
$$251$$ 28.4263 1.79425 0.897127 0.441773i $$-0.145650\pi$$
0.897127 + 0.441773i $$0.145650\pi$$
$$252$$ 0 0
$$253$$ −3.49097 −0.219476
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 9.55192 0.595832 0.297916 0.954592i $$-0.403708\pi$$
0.297916 + 0.954592i $$0.403708\pi$$
$$258$$ 0 0
$$259$$ 7.69643 0.478233
$$260$$ 0 0
$$261$$ 3.92112 0.242711
$$262$$ 0 0
$$263$$ 9.54706 0.588697 0.294349 0.955698i $$-0.404897\pi$$
0.294349 + 0.955698i $$0.404897\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −9.24168 −0.565582
$$268$$ 0 0
$$269$$ −14.3534 −0.875144 −0.437572 0.899183i $$-0.644161\pi$$
−0.437572 + 0.899183i $$0.644161\pi$$
$$270$$ 0 0
$$271$$ −12.1038 −0.735254 −0.367627 0.929973i $$-0.619830\pi$$
−0.367627 + 0.929973i $$0.619830\pi$$
$$272$$ 0 0
$$273$$ 6.48945 0.392760
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −3.59055 −0.215735 −0.107868 0.994165i $$-0.534402\pi$$
−0.107868 + 0.994165i $$0.534402\pi$$
$$278$$ 0 0
$$279$$ 3.18524 0.190695
$$280$$ 0 0
$$281$$ 26.7069 1.59320 0.796599 0.604509i $$-0.206631\pi$$
0.796599 + 0.604509i $$0.206631\pi$$
$$282$$ 0 0
$$283$$ 20.4751 1.21712 0.608559 0.793508i $$-0.291748\pi$$
0.608559 + 0.793508i $$0.291748\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 22.4668 1.32618
$$288$$ 0 0
$$289$$ 13.5052 0.794424
$$290$$ 0 0
$$291$$ −10.0249 −0.587672
$$292$$ 0 0
$$293$$ −19.1581 −1.11923 −0.559615 0.828753i $$-0.689051\pi$$
−0.559615 + 0.828753i $$0.689051\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −24.4803 −1.42049
$$298$$ 0 0
$$299$$ −0.656992 −0.0379948
$$300$$ 0 0
$$301$$ −45.8981 −2.64552
$$302$$ 0 0
$$303$$ 5.46402 0.313900
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 32.0495 1.82916 0.914580 0.404404i $$-0.132521\pi$$
0.914580 + 0.404404i $$0.132521\pi$$
$$308$$ 0 0
$$309$$ 6.02493 0.342746
$$310$$ 0 0
$$311$$ −20.5301 −1.16416 −0.582079 0.813132i $$-0.697760\pi$$
−0.582079 + 0.813132i $$0.697760\pi$$
$$312$$ 0 0
$$313$$ −14.7932 −0.836163 −0.418082 0.908409i $$-0.637297\pi$$
−0.418082 + 0.908409i $$0.637297\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −16.9485 −0.951925 −0.475962 0.879466i $$-0.657900\pi$$
−0.475962 + 0.879466i $$0.657900\pi$$
$$318$$ 0 0
$$319$$ −47.7463 −2.67328
$$320$$ 0 0
$$321$$ −16.5532 −0.923908
$$322$$ 0 0
$$323$$ 5.52315 0.307316
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 4.80310 0.265612
$$328$$ 0 0
$$329$$ 15.1123 0.833170
$$330$$ 0 0
$$331$$ −22.1287 −1.21631 −0.608153 0.793820i $$-0.708089\pi$$
−0.608153 + 0.793820i $$0.708089\pi$$
$$332$$ 0 0
$$333$$ −0.596929 −0.0327115
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 27.9948 1.52498 0.762488 0.647002i $$-0.223978\pi$$
0.762488 + 0.647002i $$0.223978\pi$$
$$338$$ 0 0
$$339$$ 11.4967 0.624414
$$340$$ 0 0
$$341$$ −38.7857 −2.10037
$$342$$ 0 0
$$343$$ 40.3484 2.17861
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −17.1024 −0.918105 −0.459052 0.888409i $$-0.651811\pi$$
−0.459052 + 0.888409i $$0.651811\pi$$
$$348$$ 0 0
$$349$$ −19.2411 −1.02995 −0.514976 0.857205i $$-0.672199\pi$$
−0.514976 + 0.857205i $$0.672199\pi$$
$$350$$ 0 0
$$351$$ −4.60713 −0.245910
$$352$$ 0 0
$$353$$ 7.42735 0.395318 0.197659 0.980271i $$-0.436666\pi$$
0.197659 + 0.980271i $$0.436666\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 42.5086 2.24979
$$358$$ 0 0
$$359$$ 28.1767 1.48711 0.743555 0.668675i $$-0.233138\pi$$
0.743555 + 0.668675i $$0.233138\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 0 0
$$363$$ 14.7195 0.772575
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −26.1165 −1.36327 −0.681636 0.731692i $$-0.738731\pi$$
−0.681636 + 0.731692i $$0.738731\pi$$
$$368$$ 0 0
$$369$$ −1.74251 −0.0907115
$$370$$ 0 0
$$371$$ −29.3140 −1.52191
$$372$$ 0 0
$$373$$ −0.438217 −0.0226900 −0.0113450 0.999936i $$-0.503611\pi$$
−0.0113450 + 0.999936i $$0.503611\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −8.98572 −0.462788
$$378$$ 0 0
$$379$$ −13.7753 −0.707591 −0.353795 0.935323i $$-0.615109\pi$$
−0.353795 + 0.935323i $$0.615109\pi$$
$$380$$ 0 0
$$381$$ −15.8962 −0.814386
$$382$$ 0 0
$$383$$ −22.3153 −1.14026 −0.570130 0.821555i $$-0.693107\pi$$
−0.570130 + 0.821555i $$0.693107\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 3.55982 0.180956
$$388$$ 0 0
$$389$$ 14.4263 0.731444 0.365722 0.930724i $$-0.380822\pi$$
0.365722 + 0.930724i $$0.380822\pi$$
$$390$$ 0 0
$$391$$ −4.30357 −0.217641
$$392$$ 0 0
$$393$$ 20.4160 1.02985
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −16.4512 −0.825662 −0.412831 0.910808i $$-0.635460\pi$$
−0.412831 + 0.910808i $$0.635460\pi$$
$$398$$ 0 0
$$399$$ 7.69643 0.385304
$$400$$ 0 0
$$401$$ 2.96056 0.147843 0.0739216 0.997264i $$-0.476449\pi$$
0.0739216 + 0.997264i $$0.476449\pi$$
$$402$$ 0 0
$$403$$ −7.29937 −0.363608
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 7.26864 0.360293
$$408$$ 0 0
$$409$$ 17.0893 0.845012 0.422506 0.906360i $$-0.361151\pi$$
0.422506 + 0.906360i $$0.361151\pi$$
$$410$$ 0 0
$$411$$ −14.4323 −0.711893
$$412$$ 0 0
$$413$$ 55.4875 2.73036
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 10.1489 0.496991
$$418$$ 0 0
$$419$$ −15.3929 −0.751991 −0.375995 0.926622i $$-0.622699\pi$$
−0.375995 + 0.926622i $$0.622699\pi$$
$$420$$ 0 0
$$421$$ −16.4323 −0.800862 −0.400431 0.916327i $$-0.631140\pi$$
−0.400431 + 0.916327i $$0.631140\pi$$
$$422$$ 0 0
$$423$$ −1.17210 −0.0569895
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 30.7422 1.48772
$$428$$ 0 0
$$429$$ 6.12874 0.295899
$$430$$ 0 0
$$431$$ 15.1852 0.731447 0.365724 0.930724i $$-0.380822\pi$$
0.365724 + 0.930724i $$0.380822\pi$$
$$432$$ 0 0
$$433$$ 23.4380 1.12636 0.563179 0.826335i $$-0.309578\pi$$
0.563179 + 0.826335i $$0.309578\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −0.779187 −0.0372735
$$438$$ 0 0
$$439$$ 0.511196 0.0243980 0.0121990 0.999926i $$-0.496117\pi$$
0.0121990 + 0.999926i $$0.496117\pi$$
$$440$$ 0 0
$$441$$ −5.70496 −0.271665
$$442$$ 0 0
$$443$$ −19.7834 −0.939940 −0.469970 0.882682i $$-0.655735\pi$$
−0.469970 + 0.882682i $$0.655735\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 4.02391 0.190325
$$448$$ 0 0
$$449$$ 31.1682 1.47092 0.735459 0.677569i $$-0.236967\pi$$
0.735459 + 0.677569i $$0.236967\pi$$
$$450$$ 0 0
$$451$$ 21.2180 0.999119
$$452$$ 0 0
$$453$$ 5.99696 0.281762
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −7.20950 −0.337246 −0.168623 0.985681i $$-0.553932\pi$$
−0.168623 + 0.985681i $$0.553932\pi$$
$$458$$ 0 0
$$459$$ −30.1786 −1.40862
$$460$$ 0 0
$$461$$ −5.41591 −0.252244 −0.126122 0.992015i $$-0.540253\pi$$
−0.126122 + 0.992015i $$0.540253\pi$$
$$462$$ 0 0
$$463$$ 8.73715 0.406050 0.203025 0.979174i $$-0.434923\pi$$
0.203025 + 0.979174i $$0.434923\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −17.3584 −0.803249 −0.401624 0.915804i $$-0.631554\pi$$
−0.401624 + 0.915804i $$0.631554\pi$$
$$468$$ 0 0
$$469$$ −70.6280 −3.26130
$$470$$ 0 0
$$471$$ −30.5781 −1.40896
$$472$$ 0 0
$$473$$ −43.3469 −1.99309
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 2.27357 0.104100
$$478$$ 0 0
$$479$$ 7.44682 0.340254 0.170127 0.985422i $$-0.445582\pi$$
0.170127 + 0.985422i $$0.445582\pi$$
$$480$$ 0 0
$$481$$ 1.36794 0.0623726
$$482$$ 0 0
$$483$$ −5.99696 −0.272871
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 2.15530 0.0976661 0.0488330 0.998807i $$-0.484450\pi$$
0.0488330 + 0.998807i $$0.484450\pi$$
$$488$$ 0 0
$$489$$ −4.00000 −0.180886
$$490$$ 0 0
$$491$$ 29.3140 1.32292 0.661461 0.749980i $$-0.269937\pi$$
0.661461 + 0.749980i $$0.269937\pi$$
$$492$$ 0 0
$$493$$ −58.8602 −2.65093
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 1.44011 0.0645976
$$498$$ 0 0
$$499$$ −23.5696 −1.05512 −0.527560 0.849518i $$-0.676893\pi$$
−0.527560 + 0.849518i $$0.676893\pi$$
$$500$$ 0 0
$$501$$ 12.1537 0.542986
$$502$$ 0 0
$$503$$ −9.08297 −0.404990 −0.202495 0.979283i $$-0.564905\pi$$
−0.202495 + 0.979283i $$0.564905\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −19.9373 −0.885447
$$508$$ 0 0
$$509$$ −18.5112 −0.820494 −0.410247 0.911974i $$-0.634558\pi$$
−0.410247 + 0.911974i $$0.634558\pi$$
$$510$$ 0 0
$$511$$ 47.8192 2.11540
$$512$$ 0 0
$$513$$ −5.46402 −0.241242
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 14.2723 0.627697
$$518$$ 0 0
$$519$$ 32.5532 1.42893
$$520$$ 0 0
$$521$$ −25.0893 −1.09918 −0.549591 0.835434i $$-0.685216\pi$$
−0.549591 + 0.835434i $$0.685216\pi$$
$$522$$ 0 0
$$523$$ 28.5181 1.24701 0.623504 0.781820i $$-0.285708\pi$$
0.623504 + 0.781820i $$0.285708\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −47.8139 −2.08281
$$528$$ 0 0
$$529$$ −22.3929 −0.973603
$$530$$ 0 0
$$531$$ −4.30357 −0.186759
$$532$$ 0 0
$$533$$ 3.99318 0.172964
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −5.99696 −0.258788
$$538$$ 0 0
$$539$$ 69.4677 2.99218
$$540$$ 0 0
$$541$$ −15.6485 −0.672780 −0.336390 0.941723i $$-0.609206\pi$$
−0.336390 + 0.941723i $$0.609206\pi$$
$$542$$ 0 0
$$543$$ −3.24473 −0.139245
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 10.8543 0.464098 0.232049 0.972704i $$-0.425457\pi$$
0.232049 + 0.972704i $$0.425457\pi$$
$$548$$ 0 0
$$549$$ −2.38434 −0.101761
$$550$$ 0 0
$$551$$ −10.6570 −0.454003
$$552$$ 0 0
$$553$$ 18.9759 0.806936
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −18.8763 −0.799814 −0.399907 0.916556i $$-0.630958\pi$$
−0.399907 + 0.916556i $$0.630958\pi$$
$$558$$ 0 0
$$559$$ −8.15777 −0.345037
$$560$$ 0 0
$$561$$ 40.1458 1.69496
$$562$$ 0 0
$$563$$ 22.2846 0.939183 0.469591 0.882884i $$-0.344401\pi$$
0.469591 + 0.882884i $$0.344401\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −36.8170 −1.54617
$$568$$ 0 0
$$569$$ −7.11833 −0.298416 −0.149208 0.988806i $$-0.547672\pi$$
−0.149208 + 0.988806i $$0.547672\pi$$
$$570$$ 0 0
$$571$$ 1.21017 0.0506440 0.0253220 0.999679i $$-0.491939\pi$$
0.0253220 + 0.999679i $$0.491939\pi$$
$$572$$ 0 0
$$573$$ 1.44011 0.0601613
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 41.4143 1.72410 0.862050 0.506823i $$-0.169180\pi$$
0.862050 + 0.506823i $$0.169180\pi$$
$$578$$ 0 0
$$579$$ −31.0814 −1.29170
$$580$$ 0 0
$$581$$ 3.69643 0.153354
$$582$$ 0 0
$$583$$ −27.6846 −1.14658
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0.0591336 0.00244071 0.00122035 0.999999i $$-0.499612\pi$$
0.00122035 + 0.999999i $$0.499612\pi$$
$$588$$ 0 0
$$589$$ −8.65699 −0.356705
$$590$$ 0 0
$$591$$ −5.47175 −0.225078
$$592$$ 0 0
$$593$$ −42.8828 −1.76099 −0.880493 0.474059i $$-0.842788\pi$$
−0.880493 + 0.474059i $$0.842788\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 7.43706 0.304379
$$598$$ 0 0
$$599$$ 15.3430 0.626898 0.313449 0.949605i $$-0.398515\pi$$
0.313449 + 0.949605i $$0.398515\pi$$
$$600$$ 0 0
$$601$$ −12.5781 −0.513072 −0.256536 0.966535i $$-0.582581\pi$$
−0.256536 + 0.966535i $$0.582581\pi$$
$$602$$ 0 0
$$603$$ 5.47785 0.223075
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −2.65751 −0.107865 −0.0539325 0.998545i $$-0.517176\pi$$
−0.0539325 + 0.998545i $$0.517176\pi$$
$$608$$ 0 0
$$609$$ −82.0208 −3.32365
$$610$$ 0 0
$$611$$ 2.68602 0.108665
$$612$$ 0 0
$$613$$ −34.1052 −1.37750 −0.688748 0.725001i $$-0.741839\pi$$
−0.688748 + 0.725001i $$0.741839\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −29.9226 −1.20464 −0.602319 0.798255i $$-0.705756\pi$$
−0.602319 + 0.798255i $$0.705756\pi$$
$$618$$ 0 0
$$619$$ 17.2102 0.691735 0.345868 0.938283i $$-0.387585\pi$$
0.345868 + 0.938283i $$0.387585\pi$$
$$620$$ 0 0
$$621$$ 4.25749 0.170847
$$622$$ 0 0
$$623$$ −27.0237 −1.08268
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 7.26864 0.290281
$$628$$ 0 0
$$629$$ 8.96056 0.357281
$$630$$ 0 0
$$631$$ −3.36195 −0.133837 −0.0669186 0.997758i $$-0.521317\pi$$
−0.0669186 + 0.997758i $$0.521317\pi$$
$$632$$ 0 0
$$633$$ −24.1435 −0.959617
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 13.0736 0.517996
$$638$$ 0 0
$$639$$ −0.111693 −0.00441853
$$640$$ 0 0
$$641$$ −16.2745 −0.642806 −0.321403 0.946943i $$-0.604154\pi$$
−0.321403 + 0.946943i $$0.604154\pi$$
$$642$$ 0 0
$$643$$ −35.7040 −1.40803 −0.704015 0.710185i $$-0.748611\pi$$
−0.704015 + 0.710185i $$0.748611\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −15.2881 −0.601036 −0.300518 0.953776i $$-0.597160\pi$$
−0.300518 + 0.953776i $$0.597160\pi$$
$$648$$ 0 0
$$649$$ 52.4033 2.05701
$$650$$ 0 0
$$651$$ −66.6280 −2.61136
$$652$$ 0 0
$$653$$ −16.4512 −0.643785 −0.321892 0.946776i $$-0.604319\pi$$
−0.321892 + 0.946776i $$0.604319\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −3.70882 −0.144695
$$658$$ 0 0
$$659$$ 7.03944 0.274218 0.137109 0.990556i $$-0.456219\pi$$
0.137109 + 0.990556i $$0.456219\pi$$
$$660$$ 0 0
$$661$$ 6.35343 0.247120 0.123560 0.992337i $$-0.460569\pi$$
0.123560 + 0.992337i $$0.460569\pi$$
$$662$$ 0 0
$$663$$ 7.55533 0.293425
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 8.30378 0.321524
$$668$$ 0 0
$$669$$ −30.4743 −1.17820
$$670$$ 0 0
$$671$$ 29.0335 1.12082
$$672$$ 0 0
$$673$$ −7.08638 −0.273160 −0.136580 0.990629i $$-0.543611\pi$$
−0.136580 + 0.990629i $$0.543611\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 17.6095 0.676786 0.338393 0.941005i $$-0.390117\pi$$
0.338393 + 0.941005i $$0.390117\pi$$
$$678$$ 0 0
$$679$$ −29.3140 −1.12497
$$680$$ 0 0
$$681$$ 1.36794 0.0524195
$$682$$ 0 0
$$683$$ 26.5855 1.01726 0.508632 0.860984i $$-0.330151\pi$$
0.508632 + 0.860984i $$0.330151\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −7.88911 −0.300988
$$688$$ 0 0
$$689$$ −5.21017 −0.198492
$$690$$ 0 0
$$691$$ 49.4907 1.88271 0.941357 0.337411i $$-0.109551\pi$$
0.941357 + 0.337411i $$0.109551\pi$$
$$692$$ 0 0
$$693$$ −7.82027 −0.297067
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 26.1570 0.990766
$$698$$ 0 0
$$699$$ 7.95392 0.300845
$$700$$ 0 0
$$701$$ 29.3389 1.10812 0.554058 0.832478i $$-0.313079\pi$$
0.554058 + 0.832478i $$0.313079\pi$$
$$702$$ 0 0
$$703$$ 1.62236 0.0611886
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 15.9774 0.600891
$$708$$ 0 0
$$709$$ 24.7359 0.928975 0.464488 0.885580i $$-0.346238\pi$$
0.464488 + 0.885580i $$0.346238\pi$$
$$710$$ 0 0
$$711$$ −1.47175 −0.0551951
$$712$$ 0 0
$$713$$ 6.74541 0.252618
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −10.0613 −0.375747
$$718$$ 0 0
$$719$$ 26.7548 0.997786 0.498893 0.866663i $$-0.333740\pi$$
0.498893 + 0.866663i $$0.333740\pi$$
$$720$$ 0 0
$$721$$ 17.6175 0.656112
$$722$$ 0 0
$$723$$ −5.29559 −0.196945
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −27.2108 −1.00919 −0.504596 0.863355i $$-0.668359\pi$$
−0.504596 + 0.863355i $$0.668359\pi$$
$$728$$ 0 0
$$729$$ 29.4494 1.09072
$$730$$ 0 0
$$731$$ −53.4367 −1.97643
$$732$$ 0 0
$$733$$ 40.0026 1.47753 0.738765 0.673963i $$-0.235409\pi$$
0.738765 + 0.673963i $$0.235409\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −66.7022 −2.45701
$$738$$ 0 0
$$739$$ 35.1123 1.29163 0.645814 0.763495i $$-0.276518\pi$$
0.645814 + 0.763495i $$0.276518\pi$$
$$740$$ 0 0
$$741$$ 1.36794 0.0502525
$$742$$ 0 0
$$743$$ 25.6476 0.940918 0.470459 0.882422i $$-0.344088\pi$$
0.470459 + 0.882422i $$0.344088\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −0.286693 −0.0104895
$$748$$ 0 0
$$749$$ −48.4033 −1.76862
$$750$$ 0 0
$$751$$ −13.2641 −0.484015 −0.242007 0.970274i $$-0.577806\pi$$
−0.242007 + 0.970274i $$0.577806\pi$$
$$752$$ 0 0
$$753$$ 46.1178 1.68063
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 2.77092 0.100711 0.0503554 0.998731i $$-0.483965\pi$$
0.0503554 + 0.998731i $$0.483965\pi$$
$$758$$ 0 0
$$759$$ −5.66363 −0.205577
$$760$$ 0 0
$$761$$ 10.7838 0.390914 0.195457 0.980712i $$-0.437381\pi$$
0.195457 + 0.980712i $$0.437381\pi$$
$$762$$ 0 0
$$763$$ 14.0448 0.508455
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 9.86216 0.356102
$$768$$ 0 0
$$769$$ −40.6090 −1.46440 −0.732199 0.681090i $$-0.761506\pi$$
−0.732199 + 0.681090i $$0.761506\pi$$
$$770$$ 0 0
$$771$$ 15.4967 0.558099
$$772$$ 0 0
$$773$$ −17.4410 −0.627310 −0.313655 0.949537i $$-0.601554\pi$$
−0.313655 + 0.949537i $$0.601554\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 12.4864 0.447947
$$778$$ 0 0
$$779$$ 4.73588 0.169680
$$780$$ 0 0
$$781$$ 1.36006 0.0486668
$$782$$ 0 0
$$783$$ 58.2300 2.08097
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 30.8346 1.09914 0.549568 0.835449i $$-0.314792\pi$$
0.549568 + 0.835449i $$0.314792\pi$$
$$788$$ 0 0
$$789$$ 15.4888 0.551416
$$790$$ 0 0
$$791$$ 33.6175 1.19530
$$792$$ 0 0
$$793$$ 5.46402 0.194033
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −38.1340 −1.35077 −0.675387 0.737463i $$-0.736024\pi$$
−0.675387 + 0.737463i $$0.736024\pi$$
$$798$$ 0 0
$$799$$ 17.5945 0.622449
$$800$$ 0 0
$$801$$ 2.09594 0.0740563
$$802$$ 0 0
$$803$$ 45.1612 1.59371
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −23.2865 −0.819722
$$808$$ 0 0
$$809$$ 30.7917 1.08258 0.541290 0.840836i $$-0.317936\pi$$
0.541290 + 0.840836i $$0.317936\pi$$
$$810$$ 0 0
$$811$$ −19.0275 −0.668145 −0.334072 0.942547i $$-0.608423\pi$$
−0.334072 + 0.942547i $$0.608423\pi$$
$$812$$ 0 0
$$813$$ −19.6368 −0.688692
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −9.67504 −0.338487
$$818$$ 0 0
$$819$$ −1.47175 −0.0514272
$$820$$ 0 0
$$821$$ −42.1228 −1.47009 −0.735047 0.678016i $$-0.762840\pi$$
−0.735047 + 0.678016i $$0.762840\pi$$
$$822$$ 0 0
$$823$$ −41.6298 −1.45112 −0.725562 0.688157i $$-0.758420\pi$$
−0.725562 + 0.688157i $$0.758420\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 7.54814 0.262475 0.131237 0.991351i $$-0.458105\pi$$
0.131237 + 0.991351i $$0.458105\pi$$
$$828$$ 0 0
$$829$$ 51.6674 1.79448 0.897242 0.441540i $$-0.145568\pi$$
0.897242 + 0.441540i $$0.145568\pi$$
$$830$$ 0 0
$$831$$ −5.82518 −0.202073
$$832$$ 0 0
$$833$$ 85.6376 2.96717
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 47.3020 1.63500
$$838$$ 0 0
$$839$$ 45.1682 1.55938 0.779689 0.626166i $$-0.215377\pi$$
0.779689 + 0.626166i $$0.215377\pi$$
$$840$$ 0 0
$$841$$ 84.5715 2.91626
$$842$$ 0 0
$$843$$ 43.3282 1.49230
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 43.0415 1.47892
$$848$$ 0 0
$$849$$ 33.2180 1.14004
$$850$$ 0 0
$$851$$ −1.26412 −0.0433336
$$852$$ 0 0
$$853$$ 10.6721 0.365405 0.182702 0.983168i $$-0.441515\pi$$
0.182702 + 0.983168i $$0.441515\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 29.7119 1.01494 0.507470 0.861669i $$-0.330581\pi$$
0.507470 + 0.861669i $$0.330581\pi$$
$$858$$ 0 0
$$859$$ −15.6734 −0.534769 −0.267385 0.963590i $$-0.586159\pi$$
−0.267385 + 0.963590i $$0.586159\pi$$
$$860$$ 0 0
$$861$$ 36.4494 1.24219
$$862$$ 0 0
$$863$$ 39.5741 1.34712 0.673559 0.739134i $$-0.264765\pi$$
0.673559 + 0.739134i $$0.264765\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 21.9104 0.744115
$$868$$ 0 0
$$869$$ 17.9211 0.607932
$$870$$ 0 0
$$871$$ −12.5532 −0.425348
$$872$$ 0 0
$$873$$ 2.27357 0.0769487
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −47.9393 −1.61880 −0.809398 0.587260i $$-0.800207\pi$$
−0.809398 + 0.587260i $$0.800207\pi$$
$$878$$ 0 0
$$879$$ −31.0814 −1.04835
$$880$$ 0 0
$$881$$ −2.32251 −0.0782473 −0.0391237 0.999234i $$-0.512457\pi$$
−0.0391237 + 0.999234i $$0.512457\pi$$
$$882$$ 0 0
$$883$$ −34.3919 −1.15738 −0.578690 0.815548i $$-0.696436\pi$$
−0.578690 + 0.815548i $$0.696436\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 44.1002 1.48074 0.740370 0.672200i $$-0.234650\pi$$
0.740370 + 0.672200i $$0.234650\pi$$
$$888$$ 0 0
$$889$$ −46.4822 −1.55896
$$890$$ 0 0
$$891$$ −34.7706 −1.16486
$$892$$ 0 0
$$893$$ 3.18559 0.106602
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ −1.06588 −0.0355887
$$898$$ 0 0
$$899$$ 92.2575 3.07696
$$900$$ 0 0
$$901$$ −34.1287 −1.13699
$$902$$ 0 0
$$903$$ −74.4633 −2.47798
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −25.3706 −0.842417 −0.421208 0.906964i $$-0.638394\pi$$
−0.421208 + 0.906964i $$0.638394\pi$$
$$908$$ 0 0
$$909$$ −1.23919 −0.0411015
$$910$$ 0 0
$$911$$ 29.8252 0.988152 0.494076 0.869419i $$-0.335506\pi$$
0.494076 + 0.869419i $$0.335506\pi$$
$$912$$ 0 0
$$913$$ 3.49097 0.115534
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 59.6985 1.97142
$$918$$ 0 0
$$919$$ −15.8422 −0.522587 −0.261293 0.965259i $$-0.584149\pi$$
−0.261293 + 0.965259i $$0.584149\pi$$
$$920$$ 0 0
$$921$$ 51.9959 1.71332
$$922$$ 0 0
$$923$$ 0.255960 0.00842501
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −1.36640 −0.0448786
$$928$$ 0 0
$$929$$ −7.97098 −0.261519 −0.130760 0.991414i $$-0.541742\pi$$
−0.130760 + 0.991414i $$0.541742\pi$$
$$930$$ 0 0
$$931$$ 15.5052 0.508163
$$932$$ 0 0
$$933$$ −33.3073 −1.09043
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −0.848033 −0.0277040 −0.0138520 0.999904i $$-0.504409\pi$$
−0.0138520 + 0.999904i $$0.504409\pi$$
$$938$$ 0 0
$$939$$ −24.0000 −0.783210
$$940$$ 0 0
$$941$$ 31.3140 1.02081 0.510403 0.859935i $$-0.329496\pi$$
0.510403 + 0.859935i $$0.329496\pi$$
$$942$$ 0 0
$$943$$ −3.69013 −0.120167
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 25.9885 0.844514 0.422257 0.906476i $$-0.361238\pi$$
0.422257 + 0.906476i $$0.361238\pi$$
$$948$$ 0 0
$$949$$ 8.49922 0.275896
$$950$$ 0 0
$$951$$ −27.4967 −0.891641
$$952$$ 0 0
$$953$$ −41.6347 −1.34868 −0.674340 0.738421i $$-0.735572\pi$$
−0.674340 + 0.738421i $$0.735572\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ −77.4618 −2.50399
$$958$$ 0 0
$$959$$ −42.2016 −1.36276
$$960$$ 0 0
$$961$$ 43.9435 1.41753
$$962$$ 0 0
$$963$$ 3.75412 0.120975
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −13.2656 −0.426593 −0.213296 0.976988i $$-0.568420\pi$$
−0.213296 + 0.976988i $$0.568420\pi$$
$$968$$ 0 0
$$969$$ 8.96056 0.287855
$$970$$ 0 0
$$971$$ 25.3140 0.812364 0.406182 0.913792i $$-0.366860\pi$$
0.406182 + 0.913792i $$0.366860\pi$$
$$972$$ 0 0
$$973$$ 29.6763 0.951380
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 50.7694 1.62426 0.812128 0.583479i $$-0.198309\pi$$
0.812128 + 0.583479i $$0.198309\pi$$
$$978$$ 0 0
$$979$$ −25.5216 −0.815674
$$980$$ 0 0
$$981$$ −1.08930 −0.0347788
$$982$$ 0 0
$$983$$ −45.4123 −1.44843 −0.724214 0.689575i $$-0.757797\pi$$
−0.724214 + 0.689575i $$0.757797\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 24.5177 0.780407
$$988$$ 0 0
$$989$$ 7.53866 0.239716
$$990$$ 0 0
$$991$$ 45.6175 1.44909 0.724545 0.689228i $$-0.242050\pi$$
0.724545 + 0.689228i $$0.242050\pi$$
$$992$$ 0 0
$$993$$ −35.9009 −1.13928
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −59.5705 −1.88662 −0.943309 0.331917i $$-0.892305\pi$$
−0.943309 + 0.331917i $$0.892305\pi$$
$$998$$ 0 0
$$999$$ −8.86462 −0.280464
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 1900.2.a.k.1.5 6
4.3 odd 2 7600.2.a.cj.1.2 6
5.2 odd 4 380.2.c.b.229.2 6
5.3 odd 4 380.2.c.b.229.5 yes 6
5.4 even 2 inner 1900.2.a.k.1.2 6
15.2 even 4 3420.2.f.c.1369.5 6
15.8 even 4 3420.2.f.c.1369.6 6
20.3 even 4 1520.2.d.i.609.2 6
20.7 even 4 1520.2.d.i.609.5 6
20.19 odd 2 7600.2.a.cj.1.5 6

By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.c.b.229.2 6 5.2 odd 4
380.2.c.b.229.5 yes 6 5.3 odd 4
1520.2.d.i.609.2 6 20.3 even 4
1520.2.d.i.609.5 6 20.7 even 4
1900.2.a.k.1.2 6 5.4 even 2 inner
1900.2.a.k.1.5 6 1.1 even 1 trivial
3420.2.f.c.1369.5 6 15.2 even 4
3420.2.f.c.1369.6 6 15.8 even 4
7600.2.a.cj.1.2 6 4.3 odd 2
7600.2.a.cj.1.5 6 20.19 odd 2