# Properties

 Label 1900.2.a.k.1.2 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: $$x^{6} - 9x^{4} + 14x^{2} - 4$$ 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 1.2 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 $$6 q + 10 q^{9} + 18 q^{11} + 6 q^{19} + 4 q^{21} - 4 q^{29} + 8 q^{31} - 4 q^{39} + 4 q^{41} + 12 q^{49} + 36 q^{51} + 28 q^{59} + 30 q^{61} - 32 q^{69} + 44 q^{71} + 24 q^{79} + 50 q^{81} + 8 q^{89} + 24 q^{91} + 90 q^{99}+O(q^{100})$$ 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

## 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 $$-0.655146\pi$$
−0.468336 + 0.883551i $$0.655146\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −4.74397 −1.79305 −0.896525 0.442993i $$-0.853917\pi$$
−0.896525 + 0.442993i $$0.853917\pi$$
$$8$$ 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 $$-0.537305\pi$$
−0.116928 + 0.993140i $$0.537305\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −5.52315 −1.33956 −0.669781 0.742559i $$-0.733612\pi$$
−0.669781 + 0.742559i $$0.733612\pi$$
$$18$$ 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 $$-0.474113\pi$$
0.0812358 + 0.996695i $$0.474113\pi$$
$$24$$ 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 $$-0.542576\pi$$
−0.133357 + 0.991068i $$0.542576\pi$$
$$38$$ 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 $$-0.235905\pi$$
0.737715 + 0.675112i $$0.235905\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −3.18559 −0.464666 −0.232333 0.972636i $$-0.574636\pi$$
−0.232333 + 0.972636i $$0.574636\pi$$
$$48$$ 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 $$-0.360488\pi$$
0.424390 + 0.905479i $$0.360488\pi$$
$$54$$ 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 $$-0.136521\pi$$
0.909427 + 0.415864i $$0.136521\pi$$
$$68$$ 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 $$-0.700828\pi$$
−0.589888 + 0.807485i $$0.700828\pi$$
$$74$$ 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 $$-0.513616\pi$$
−0.0427634 + 0.999085i $$0.513616\pi$$
$$84$$ 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 $$-0.398431\pi$$
0.313702 + 0.949521i $$0.398431\pi$$
$$98$$ 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 $$-0.558568\pi$$
−0.182960 + 0.983120i $$0.558568\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 10.2031 0.986374 0.493187 0.869923i $$-0.335832\pi$$
0.493187 + 0.869923i $$0.335832\pi$$
$$108$$ 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 $$-0.608167\pi$$
−0.333315 + 0.942815i $$0.608167\pi$$
$$114$$ 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 $$-0.356846\pi$$
0.434723 + 0.900564i $$0.356846\pi$$
$$128$$ 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 $$-0.375920\pi$$
0.380012 + 0.924981i $$0.375920\pi$$
$$138$$ 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 $$-0.229035\pi$$
0.752112 + 0.659035i $$0.229035\pi$$
$$158$$ 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 $$-0.469217\pi$$
0.0965580 + 0.995327i $$0.469217\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −7.49134 −0.579697 −0.289849 0.957072i $$-0.593605\pi$$
−0.289849 + 0.957072i $$0.593605\pi$$
$$168$$ 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 $$-0.776160\pi$$
−0.762768 + 0.646673i $$0.776160\pi$$
$$174$$ 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 $$-0.257823\pi$$
0.689516 + 0.724271i $$0.257823\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 3.37271 0.240295 0.120148 0.992756i $$-0.461663\pi$$
0.120148 + 0.992756i $$0.461663\pi$$
$$198$$ 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 $$-0.283493\pi$$
0.628931 + 0.777461i $$0.283493\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −0.843176 −0.0559636 −0.0279818 0.999608i $$-0.508908\pi$$
−0.0279818 + 0.999608i $$0.508908\pi$$
$$228$$ 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 $$-0.551341\pi$$
−0.160593 + 0.987021i $$0.551341\pi$$
$$234$$ 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 $$-0.596292\pi$$
−0.297916 + 0.954592i $$0.596292\pi$$
$$258$$ 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 $$-0.595103\pi$$
−0.294349 + 0.955698i $$0.595103\pi$$
$$264$$ 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 $$-0.465598\pi$$
0.107868 + 0.994165i $$0.465598\pi$$
$$278$$ 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 $$-0.708252\pi$$
−0.608559 + 0.793508i $$0.708252\pi$$
$$284$$ 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 $$-0.310949\pi$$
0.559615 + 0.828753i $$0.310949\pi$$
$$294$$ 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 $$-0.867479\pi$$
−0.914580 + 0.404404i $$0.867479\pi$$
$$308$$ 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 $$-0.362703\pi$$
0.418082 + 0.908409i $$0.362703\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 16.9485 0.951925 0.475962 0.879466i $$-0.342100\pi$$
0.475962 + 0.879466i $$0.342100\pi$$
$$318$$ 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 $$-0.776022\pi$$
−0.762488 + 0.647002i $$0.776022\pi$$
$$338$$ 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 $$-0.348189\pi$$
0.459052 + 0.888409i $$0.348189\pi$$
$$348$$ 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 $$-0.563334\pi$$
−0.197659 + 0.980271i $$0.563334\pi$$
$$354$$ 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 $$-0.261269\pi$$
0.681636 + 0.731692i $$0.261269\pi$$
$$368$$ 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 $$-0.496389\pi$$
0.0113450 + 0.999936i $$0.496389\pi$$
$$374$$ 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 $$-0.306893\pi$$
0.570130 + 0.821555i $$0.306893\pi$$
$$384$$ 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 $$-0.364540\pi$$
0.412831 + 0.910808i $$0.364540\pi$$
$$398$$ 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 $$-0.690422\pi$$
−0.563179 + 0.826335i $$0.690422\pi$$
$$434$$ 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 $$-0.344265\pi$$
0.469970 + 0.882682i $$0.344265\pi$$
$$444$$ 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 $$-0.446068\pi$$
0.168623 + 0.985681i $$0.446068\pi$$
$$458$$ 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 $$-0.565077\pi$$
−0.203025 + 0.979174i $$0.565077\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 17.3584 0.803249 0.401624 0.915804i $$-0.368446\pi$$
0.401624 + 0.915804i $$0.368446\pi$$
$$468$$ 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 $$-0.515550\pi$$
−0.0488330 + 0.998807i $$0.515550\pi$$
$$488$$ 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 $$-0.435095\pi$$
0.202495 + 0.979283i $$0.435095\pi$$
$$504$$ 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 $$-0.714292\pi$$
−0.623504 + 0.781820i $$0.714292\pi$$
$$524$$ 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 $$-0.574543\pi$$
−0.232049 + 0.972704i $$0.574543\pi$$
$$548$$ 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 $$-0.369042\pi$$
0.399907 + 0.916556i $$0.369042\pi$$
$$558$$ 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 $$-0.655599\pi$$
−0.469591 + 0.882884i $$0.655599\pi$$
$$564$$ 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 $$-0.830820\pi$$
−0.862050 + 0.506823i $$0.830820\pi$$
$$578$$ 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 $$-0.500388\pi$$
−0.00122035 + 0.999999i $$0.500388\pi$$
$$588$$ 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 $$-0.157212\pi$$
0.880493 + 0.474059i $$0.157212\pi$$
$$594$$ 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 $$-0.482824\pi$$
0.0539325 + 0.998545i $$0.482824\pi$$
$$608$$ 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 $$-0.258161\pi$$
0.688748 + 0.725001i $$0.258161\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 29.9226 1.20464 0.602319 0.798255i $$-0.294244\pi$$
0.602319 + 0.798255i $$0.294244\pi$$
$$618$$ 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 $$-0.251389\pi$$
0.704015 + 0.710185i $$0.251389\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 15.2881 0.601036 0.300518 0.953776i $$-0.402840\pi$$
0.300518 + 0.953776i $$0.402840\pi$$
$$648$$ 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 $$-0.395681\pi$$
0.321892 + 0.946776i $$0.395681\pi$$
$$654$$ 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 $$-0.456389\pi$$
0.136580 + 0.990629i $$0.456389\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −17.6095 −0.676786 −0.338393 0.941005i $$-0.609883\pi$$
−0.338393 + 0.941005i $$0.609883\pi$$
$$678$$ 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 $$-0.669849\pi$$
−0.508632 + 0.860984i $$0.669849\pi$$
$$684$$ 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 $$-0.331641\pi$$
0.504596 + 0.863355i $$0.331641\pi$$
$$728$$ 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 $$-0.764591\pi$$
−0.738765 + 0.673963i $$0.764591\pi$$
$$734$$ 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 $$-0.655912\pi$$
−0.470459 + 0.882422i $$0.655912\pi$$
$$744$$ 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 $$-0.516035\pi$$
−0.0503554 + 0.998731i $$0.516035\pi$$
$$758$$ 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 $$-0.398446\pi$$
0.313655 + 0.949537i $$0.398446\pi$$
$$774$$ 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 $$-0.685208\pi$$
−0.549568 + 0.835449i $$0.685208\pi$$
$$788$$ 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 $$-0.263976\pi$$
0.675387 + 0.737463i $$0.263976\pi$$
$$798$$ 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 $$-0.241580\pi$$
0.725562 + 0.688157i $$0.241580\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −7.54814 −0.262475 −0.131237 0.991351i $$-0.541895\pi$$
−0.131237 + 0.991351i $$0.541895\pi$$
$$828$$ 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 $$-0.558485\pi$$
−0.182702 + 0.983168i $$0.558485\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −29.7119 −1.01494 −0.507470 0.861669i $$-0.669419\pi$$
−0.507470 + 0.861669i $$0.669419\pi$$
$$858$$ 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 $$-0.735235\pi$$
−0.673559 + 0.739134i $$0.735235\pi$$
$$864$$ 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 $$-0.199793\pi$$
0.809398 + 0.587260i $$0.199793\pi$$
$$878$$ 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 $$-0.303564\pi$$
0.578690 + 0.815548i $$0.303564\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −44.1002 −1.48074 −0.740370 0.672200i $$-0.765350\pi$$
−0.740370 + 0.672200i $$0.765350\pi$$
$$888$$ 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 $$-0.361606\pi$$
0.421208 + 0.906964i $$0.361606\pi$$
$$908$$ 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 $$-0.495591\pi$$
0.0138520 + 0.999904i $$0.495591\pi$$
$$938$$ 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 $$-0.638762\pi$$
−0.422257 + 0.906476i $$0.638762\pi$$
$$948$$ 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 $$-0.264428\pi$$
0.674340 + 0.738421i $$0.264428\pi$$
$$954$$ 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 $$-0.431580\pi$$
0.213296 + 0.976988i $$0.431580\pi$$
$$968$$ 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 $$-0.801691\pi$$
−0.812128 + 0.583479i $$0.801691\pi$$
$$978$$ 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 $$-0.242203\pi$$
0.724214 + 0.689575i $$0.242203\pi$$
$$984$$ 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 $$-0.107695\pi$$
0.943309 + 0.331917i $$0.107695\pi$$
$$998$$ 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.1.2 6
4.3 odd 2 7600.2.a.cj.1.5 6
5.2 odd 4 380.2.c.b.229.5 yes 6
5.3 odd 4 380.2.c.b.229.2 6
5.4 even 2 inner 1900.2.a.k.1.5 6
15.2 even 4 3420.2.f.c.1369.6 6
15.8 even 4 3420.2.f.c.1369.5 6
20.3 even 4 1520.2.d.i.609.5 6
20.7 even 4 1520.2.d.i.609.2 6
20.19 odd 2 7600.2.a.cj.1.2 6

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