# Properties

 Label 8280.2.a.bi.1.3 Level $8280$ Weight $2$ Character 8280.1 Self dual yes Analytic conductor $66.116$ Analytic rank $1$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 8280.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$66.1161328736$$ Analytic rank: $$1$$ Dimension: $$3$$ Coefficient field: 3.3.568.1 Defining polynomial: $$x^{3} - x^{2} - 6x - 2$$ x^3 - x^2 - 6*x - 2 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 2760) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$-0.363328$$ of defining polynomial Character $$\chi$$ $$=$$ 8280.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{5} +4.86799 q^{7} +O(q^{10})$$ $$q-1.00000 q^{5} +4.86799 q^{7} -4.77801 q^{11} +2.77801 q^{13} +0.636672 q^{17} -3.50466 q^{19} +1.00000 q^{23} +1.00000 q^{25} -7.36333 q^{29} -5.15066 q^{31} -4.86799 q^{35} +2.86799 q^{37} +6.19269 q^{41} -8.28267 q^{43} -7.50466 q^{47} +16.6974 q^{49} +4.91934 q^{53} +4.77801 q^{55} +8.65533 q^{59} -15.0607 q^{61} -2.77801 q^{65} -13.4333 q^{67} +11.0993 q^{71} -15.2406 q^{73} -23.2593 q^{77} -1.45331 q^{79} -6.63667 q^{83} -0.636672 q^{85} -9.29200 q^{89} +13.5233 q^{91} +3.50466 q^{95} -14.7453 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q - 3 q^{5} + 2 q^{7}+O(q^{10})$$ 3 * q - 3 * q^5 + 2 * q^7 $$3 q - 3 q^{5} + 2 q^{7} - 8 q^{11} + 2 q^{13} + 4 q^{17} + 3 q^{23} + 3 q^{25} - 20 q^{29} + 14 q^{31} - 2 q^{35} - 4 q^{37} + 8 q^{41} - 8 q^{43} - 12 q^{47} + 29 q^{49} + 8 q^{55} - 14 q^{59} - 22 q^{61} - 2 q^{65} + 6 q^{67} + 6 q^{71} - 10 q^{73} + 8 q^{77} + 4 q^{79} - 22 q^{83} - 4 q^{85} + 10 q^{89} - 12 q^{91} + 2 q^{97}+O(q^{100})$$ 3 * q - 3 * q^5 + 2 * q^7 - 8 * q^11 + 2 * q^13 + 4 * q^17 + 3 * q^23 + 3 * q^25 - 20 * q^29 + 14 * q^31 - 2 * q^35 - 4 * q^37 + 8 * q^41 - 8 * q^43 - 12 * q^47 + 29 * q^49 + 8 * q^55 - 14 * q^59 - 22 * q^61 - 2 * q^65 + 6 * q^67 + 6 * q^71 - 10 * q^73 + 8 * q^77 + 4 * q^79 - 22 * q^83 - 4 * q^85 + 10 * q^89 - 12 * q^91 + 2 * q^97

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ 4.86799 1.83993 0.919964 0.392003i $$-0.128218\pi$$
0.919964 + 0.392003i $$0.128218\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −4.77801 −1.44062 −0.720312 0.693650i $$-0.756001\pi$$
−0.720312 + 0.693650i $$0.756001\pi$$
$$12$$ 0 0
$$13$$ 2.77801 0.770481 0.385240 0.922816i $$-0.374119\pi$$
0.385240 + 0.922816i $$0.374119\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0.636672 0.154416 0.0772078 0.997015i $$-0.475400\pi$$
0.0772078 + 0.997015i $$0.475400\pi$$
$$18$$ 0 0
$$19$$ −3.50466 −0.804025 −0.402013 0.915634i $$-0.631689\pi$$
−0.402013 + 0.915634i $$0.631689\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.00000 0.208514
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −7.36333 −1.36734 −0.683668 0.729793i $$-0.739616\pi$$
−0.683668 + 0.729793i $$0.739616\pi$$
$$30$$ 0 0
$$31$$ −5.15066 −0.925087 −0.462543 0.886597i $$-0.653063\pi$$
−0.462543 + 0.886597i $$0.653063\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −4.86799 −0.822841
$$36$$ 0 0
$$37$$ 2.86799 0.471495 0.235748 0.971814i $$-0.424246\pi$$
0.235748 + 0.971814i $$0.424246\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.19269 0.967135 0.483568 0.875307i $$-0.339341\pi$$
0.483568 + 0.875307i $$0.339341\pi$$
$$42$$ 0 0
$$43$$ −8.28267 −1.26310 −0.631548 0.775337i $$-0.717580\pi$$
−0.631548 + 0.775337i $$0.717580\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −7.50466 −1.09467 −0.547334 0.836914i $$-0.684357\pi$$
−0.547334 + 0.836914i $$0.684357\pi$$
$$48$$ 0 0
$$49$$ 16.6974 2.38534
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 4.91934 0.675724 0.337862 0.941196i $$-0.390296\pi$$
0.337862 + 0.941196i $$0.390296\pi$$
$$54$$ 0 0
$$55$$ 4.77801 0.644266
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 8.65533 1.12683 0.563414 0.826175i $$-0.309488\pi$$
0.563414 + 0.826175i $$0.309488\pi$$
$$60$$ 0 0
$$61$$ −15.0607 −1.92832 −0.964161 0.265317i $$-0.914523\pi$$
−0.964161 + 0.265317i $$0.914523\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −2.77801 −0.344569
$$66$$ 0 0
$$67$$ −13.4333 −1.64114 −0.820572 0.571544i $$-0.806345\pi$$
−0.820572 + 0.571544i $$0.806345\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 11.0993 1.31725 0.658623 0.752473i $$-0.271139\pi$$
0.658623 + 0.752473i $$0.271139\pi$$
$$72$$ 0 0
$$73$$ −15.2406 −1.78378 −0.891892 0.452249i $$-0.850622\pi$$
−0.891892 + 0.452249i $$0.850622\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −23.2593 −2.65064
$$78$$ 0 0
$$79$$ −1.45331 −0.163510 −0.0817552 0.996652i $$-0.526053\pi$$
−0.0817552 + 0.996652i $$0.526053\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −6.63667 −0.728469 −0.364235 0.931307i $$-0.618669\pi$$
−0.364235 + 0.931307i $$0.618669\pi$$
$$84$$ 0 0
$$85$$ −0.636672 −0.0690567
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −9.29200 −0.984950 −0.492475 0.870327i $$-0.663908\pi$$
−0.492475 + 0.870327i $$0.663908\pi$$
$$90$$ 0 0
$$91$$ 13.5233 1.41763
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 3.50466 0.359571
$$96$$ 0 0
$$97$$ −14.7453 −1.49716 −0.748580 0.663045i $$-0.769264\pi$$
−0.748580 + 0.663045i $$0.769264\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 17.3820 1.72957 0.864786 0.502140i $$-0.167454\pi$$
0.864786 + 0.502140i $$0.167454\pi$$
$$102$$ 0 0
$$103$$ 15.2920 1.50677 0.753383 0.657582i $$-0.228421\pi$$
0.753383 + 0.657582i $$0.228421\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −15.3820 −1.48703 −0.743516 0.668718i $$-0.766843\pi$$
−0.743516 + 0.668718i $$0.766843\pi$$
$$108$$ 0 0
$$109$$ −15.2406 −1.45979 −0.729895 0.683560i $$-0.760431\pi$$
−0.729895 + 0.683560i $$0.760431\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −6.19269 −0.582559 −0.291280 0.956638i $$-0.594081\pi$$
−0.291280 + 0.956638i $$0.594081\pi$$
$$114$$ 0 0
$$115$$ −1.00000 −0.0932505
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 3.09931 0.284114
$$120$$ 0 0
$$121$$ 11.8294 1.07540
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −4.77801 −0.423980 −0.211990 0.977272i $$-0.567994\pi$$
−0.211990 + 0.977272i $$0.567994\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −6.54669 −0.571987 −0.285993 0.958232i $$-0.592324\pi$$
−0.285993 + 0.958232i $$0.592324\pi$$
$$132$$ 0 0
$$133$$ −17.0607 −1.47935
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 10.7453 0.918034 0.459017 0.888427i $$-0.348202\pi$$
0.459017 + 0.888427i $$0.348202\pi$$
$$138$$ 0 0
$$139$$ 14.4240 1.22343 0.611714 0.791079i $$-0.290480\pi$$
0.611714 + 0.791079i $$0.290480\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −13.2733 −1.10997
$$144$$ 0 0
$$145$$ 7.36333 0.611491
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −6.67531 −0.546862 −0.273431 0.961892i $$-0.588159\pi$$
−0.273431 + 0.961892i $$0.588159\pi$$
$$150$$ 0 0
$$151$$ 18.3013 1.48934 0.744671 0.667432i $$-0.232607\pi$$
0.744671 + 0.667432i $$0.232607\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 5.15066 0.413711
$$156$$ 0 0
$$157$$ 18.4427 1.47188 0.735942 0.677044i $$-0.236739\pi$$
0.735942 + 0.677044i $$0.236739\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.86799 0.383652
$$162$$ 0 0
$$163$$ −0.282672 −0.0221406 −0.0110703 0.999939i $$-0.503524\pi$$
−0.0110703 + 0.999939i $$0.503524\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −6.51399 −0.504068 −0.252034 0.967718i $$-0.581099\pi$$
−0.252034 + 0.967718i $$0.581099\pi$$
$$168$$ 0 0
$$169$$ −5.28267 −0.406359
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −8.30133 −0.631138 −0.315569 0.948903i $$-0.602195\pi$$
−0.315569 + 0.948903i $$0.602195\pi$$
$$174$$ 0 0
$$175$$ 4.86799 0.367986
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −5.17064 −0.386472 −0.193236 0.981152i $$-0.561898\pi$$
−0.193236 + 0.981152i $$0.561898\pi$$
$$180$$ 0 0
$$181$$ 21.8573 1.62464 0.812322 0.583209i $$-0.198203\pi$$
0.812322 + 0.583209i $$0.198203\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −2.86799 −0.210859
$$186$$ 0 0
$$187$$ −3.04202 −0.222455
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 8.49534 0.614701 0.307350 0.951596i $$-0.400558\pi$$
0.307350 + 0.951596i $$0.400558\pi$$
$$192$$ 0 0
$$193$$ 7.83869 0.564241 0.282121 0.959379i $$-0.408962\pi$$
0.282121 + 0.959379i $$0.408962\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 17.5747 1.25214 0.626072 0.779765i $$-0.284662\pi$$
0.626072 + 0.779765i $$0.284662\pi$$
$$198$$ 0 0
$$199$$ 4.17997 0.296310 0.148155 0.988964i $$-0.452667\pi$$
0.148155 + 0.988964i $$0.452667\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −35.8446 −2.51580
$$204$$ 0 0
$$205$$ −6.19269 −0.432516
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 16.7453 1.15830
$$210$$ 0 0
$$211$$ −22.4240 −1.54373 −0.771866 0.635785i $$-0.780676\pi$$
−0.771866 + 0.635785i $$0.780676\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 8.28267 0.564874
$$216$$ 0 0
$$217$$ −25.0734 −1.70209
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1.76868 0.118974
$$222$$ 0 0
$$223$$ −12.2827 −0.822509 −0.411254 0.911521i $$-0.634909\pi$$
−0.411254 + 0.911521i $$0.634909\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −24.5653 −1.63046 −0.815230 0.579138i $$-0.803389\pi$$
−0.815230 + 0.579138i $$0.803389\pi$$
$$228$$ 0 0
$$229$$ −5.82003 −0.384598 −0.192299 0.981336i $$-0.561594\pi$$
−0.192299 + 0.981336i $$0.561594\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 2.28267 0.149543 0.0747714 0.997201i $$-0.476177\pi$$
0.0747714 + 0.997201i $$0.476177\pi$$
$$234$$ 0 0
$$235$$ 7.50466 0.489550
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −2.53397 −0.163909 −0.0819544 0.996636i $$-0.526116\pi$$
−0.0819544 + 0.996636i $$0.526116\pi$$
$$240$$ 0 0
$$241$$ 2.67531 0.172332 0.0861658 0.996281i $$-0.472539\pi$$
0.0861658 + 0.996281i $$0.472539\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −16.6974 −1.06675
$$246$$ 0 0
$$247$$ −9.73599 −0.619486
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −12.2827 −0.775275 −0.387638 0.921812i $$-0.626709\pi$$
−0.387638 + 0.921812i $$0.626709\pi$$
$$252$$ 0 0
$$253$$ −4.77801 −0.300391
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −9.89004 −0.616924 −0.308462 0.951237i $$-0.599814\pi$$
−0.308462 + 0.951237i $$0.599814\pi$$
$$258$$ 0 0
$$259$$ 13.9614 0.867517
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 4.26995 0.263297 0.131648 0.991296i $$-0.457973\pi$$
0.131648 + 0.991296i $$0.457973\pi$$
$$264$$ 0 0
$$265$$ −4.91934 −0.302193
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −30.5526 −1.86283 −0.931413 0.363963i $$-0.881423\pi$$
−0.931413 + 0.363963i $$0.881423\pi$$
$$270$$ 0 0
$$271$$ −23.6974 −1.43951 −0.719756 0.694227i $$-0.755746\pi$$
−0.719756 + 0.694227i $$0.755746\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −4.77801 −0.288125
$$276$$ 0 0
$$277$$ 20.5840 1.23677 0.618386 0.785874i $$-0.287787\pi$$
0.618386 + 0.785874i $$0.287787\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −8.61670 −0.514029 −0.257014 0.966408i $$-0.582739\pi$$
−0.257014 + 0.966408i $$0.582739\pi$$
$$282$$ 0 0
$$283$$ 7.02930 0.417849 0.208924 0.977932i $$-0.433004\pi$$
0.208924 + 0.977932i $$0.433004\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 30.1460 1.77946
$$288$$ 0 0
$$289$$ −16.5946 −0.976156
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 21.2793 1.24315 0.621574 0.783355i $$-0.286493\pi$$
0.621574 + 0.783355i $$0.286493\pi$$
$$294$$ 0 0
$$295$$ −8.65533 −0.503933
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 2.77801 0.160656
$$300$$ 0 0
$$301$$ −40.3200 −2.32401
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 15.0607 0.862372
$$306$$ 0 0
$$307$$ 13.0607 0.745412 0.372706 0.927949i $$-0.378430\pi$$
0.372706 + 0.927949i $$0.378430\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −5.45331 −0.309229 −0.154615 0.987975i $$-0.549414\pi$$
−0.154615 + 0.987975i $$0.549414\pi$$
$$312$$ 0 0
$$313$$ 4.60398 0.260232 0.130116 0.991499i $$-0.458465\pi$$
0.130116 + 0.991499i $$0.458465\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 30.3527 1.70478 0.852388 0.522910i $$-0.175153\pi$$
0.852388 + 0.522910i $$0.175153\pi$$
$$318$$ 0 0
$$319$$ 35.1820 1.96982
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −2.23132 −0.124154
$$324$$ 0 0
$$325$$ 2.77801 0.154096
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −36.5327 −2.01411
$$330$$ 0 0
$$331$$ 6.42401 0.353095 0.176548 0.984292i $$-0.443507\pi$$
0.176548 + 0.984292i $$0.443507\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 13.4333 0.733942
$$336$$ 0 0
$$337$$ −25.1120 −1.36794 −0.683970 0.729510i $$-0.739748\pi$$
−0.683970 + 0.729510i $$0.739748\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 24.6099 1.33270
$$342$$ 0 0
$$343$$ 47.2066 2.54892
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −8.46264 −0.454298 −0.227149 0.973860i $$-0.572941\pi$$
−0.227149 + 0.973860i $$0.572941\pi$$
$$348$$ 0 0
$$349$$ −6.40535 −0.342871 −0.171435 0.985195i $$-0.554840\pi$$
−0.171435 + 0.985195i $$0.554840\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 25.7873 1.37252 0.686261 0.727356i $$-0.259251\pi$$
0.686261 + 0.727356i $$0.259251\pi$$
$$354$$ 0 0
$$355$$ −11.0993 −0.589090
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −5.94865 −0.313958 −0.156979 0.987602i $$-0.550175\pi$$
−0.156979 + 0.987602i $$0.550175\pi$$
$$360$$ 0 0
$$361$$ −6.71733 −0.353544
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 15.2406 0.797732
$$366$$ 0 0
$$367$$ −10.5013 −0.548162 −0.274081 0.961707i $$-0.588374\pi$$
−0.274081 + 0.961707i $$0.588374\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 23.9473 1.24328
$$372$$ 0 0
$$373$$ −7.17064 −0.371282 −0.185641 0.982618i $$-0.559436\pi$$
−0.185641 + 0.982618i $$0.559436\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −20.4554 −1.05351
$$378$$ 0 0
$$379$$ −7.11203 −0.365321 −0.182660 0.983176i $$-0.558471\pi$$
−0.182660 + 0.983176i $$0.558471\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −7.80731 −0.398935 −0.199468 0.979904i $$-0.563921\pi$$
−0.199468 + 0.979904i $$0.563921\pi$$
$$384$$ 0 0
$$385$$ 23.2593 1.18540
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −27.5933 −1.39904 −0.699519 0.714614i $$-0.746602\pi$$
−0.699519 + 0.714614i $$0.746602\pi$$
$$390$$ 0 0
$$391$$ 0.636672 0.0321979
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 1.45331 0.0731241
$$396$$ 0 0
$$397$$ −14.6426 −0.734892 −0.367446 0.930045i $$-0.619768\pi$$
−0.367446 + 0.930045i $$0.619768\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 3.55602 0.177579 0.0887895 0.996050i $$-0.471700\pi$$
0.0887895 + 0.996050i $$0.471700\pi$$
$$402$$ 0 0
$$403$$ −14.3086 −0.712762
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −13.7033 −0.679247
$$408$$ 0 0
$$409$$ 28.9894 1.43343 0.716716 0.697366i $$-0.245645\pi$$
0.716716 + 0.697366i $$0.245645\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 42.1341 2.07328
$$414$$ 0 0
$$415$$ 6.63667 0.325781
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −28.3527 −1.38512 −0.692560 0.721361i $$-0.743517\pi$$
−0.692560 + 0.721361i $$0.743517\pi$$
$$420$$ 0 0
$$421$$ 9.32469 0.454458 0.227229 0.973841i $$-0.427033\pi$$
0.227229 + 0.973841i $$0.427033\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0.636672 0.0308831
$$426$$ 0 0
$$427$$ −73.3153 −3.54798
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 3.89730 0.187726 0.0938631 0.995585i $$-0.470078\pi$$
0.0938631 + 0.995585i $$0.470078\pi$$
$$432$$ 0 0
$$433$$ −28.4613 −1.36776 −0.683882 0.729593i $$-0.739710\pi$$
−0.683882 + 0.729593i $$0.739710\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3.50466 −0.167651
$$438$$ 0 0
$$439$$ 19.0866 0.910953 0.455477 0.890248i $$-0.349469\pi$$
0.455477 + 0.890248i $$0.349469\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.47668 −0.307716 −0.153858 0.988093i $$-0.549170\pi$$
−0.153858 + 0.988093i $$0.549170\pi$$
$$444$$ 0 0
$$445$$ 9.29200 0.440483
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −16.8166 −0.793626 −0.396813 0.917899i $$-0.629884\pi$$
−0.396813 + 0.917899i $$0.629884\pi$$
$$450$$ 0 0
$$451$$ −29.5887 −1.39328
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −13.5233 −0.633983
$$456$$ 0 0
$$457$$ −4.52671 −0.211751 −0.105875 0.994379i $$-0.533764\pi$$
−0.105875 + 0.994379i $$0.533764\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 8.44398 0.393276 0.196638 0.980476i $$-0.436998\pi$$
0.196638 + 0.980476i $$0.436998\pi$$
$$462$$ 0 0
$$463$$ −30.5140 −1.41811 −0.709053 0.705155i $$-0.750877\pi$$
−0.709053 + 0.705155i $$0.750877\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −12.2700 −0.567786 −0.283893 0.958856i $$-0.591626\pi$$
−0.283893 + 0.958856i $$0.591626\pi$$
$$468$$ 0 0
$$469$$ −65.3934 −3.01959
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 39.5747 1.81965
$$474$$ 0 0
$$475$$ −3.50466 −0.160805
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 1.06068 0.0484637 0.0242319 0.999706i $$-0.492286\pi$$
0.0242319 + 0.999706i $$0.492286\pi$$
$$480$$ 0 0
$$481$$ 7.96731 0.363278
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 14.7453 0.669550
$$486$$ 0 0
$$487$$ −5.13795 −0.232823 −0.116411 0.993201i $$-0.537139\pi$$
−0.116411 + 0.993201i $$0.537139\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −2.81664 −0.127113 −0.0635566 0.997978i $$-0.520244\pi$$
−0.0635566 + 0.997978i $$0.520244\pi$$
$$492$$ 0 0
$$493$$ −4.68802 −0.211138
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 54.0314 2.42364
$$498$$ 0 0
$$499$$ 13.2534 0.593302 0.296651 0.954986i $$-0.404130\pi$$
0.296651 + 0.954986i $$0.404130\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 28.2300 1.25871 0.629357 0.777116i $$-0.283318\pi$$
0.629357 + 0.777116i $$0.283318\pi$$
$$504$$ 0 0
$$505$$ −17.3820 −0.773488
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −2.70800 −0.120030 −0.0600150 0.998197i $$-0.519115\pi$$
−0.0600150 + 0.998197i $$0.519115\pi$$
$$510$$ 0 0
$$511$$ −74.1914 −3.28203
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −15.2920 −0.673846
$$516$$ 0 0
$$517$$ 35.8573 1.57700
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −23.4206 −1.02608 −0.513038 0.858366i $$-0.671480\pi$$
−0.513038 + 0.858366i $$0.671480\pi$$
$$522$$ 0 0
$$523$$ 2.01866 0.0882697 0.0441349 0.999026i $$-0.485947\pi$$
0.0441349 + 0.999026i $$0.485947\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −3.27928 −0.142848
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 17.2033 0.745159
$$534$$ 0 0
$$535$$ 15.3820 0.665021
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −79.7801 −3.43637
$$540$$ 0 0
$$541$$ 11.8387 0.508985 0.254492 0.967075i $$-0.418092\pi$$
0.254492 + 0.967075i $$0.418092\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 15.2406 0.652838
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 25.8060 1.09937
$$552$$ 0 0
$$553$$ −7.07472 −0.300848
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 36.9193 1.56432 0.782161 0.623076i $$-0.214117\pi$$
0.782161 + 0.623076i $$0.214117\pi$$
$$558$$ 0 0
$$559$$ −23.0093 −0.973191
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −37.7860 −1.59249 −0.796245 0.604974i $$-0.793184\pi$$
−0.796245 + 0.604974i $$0.793184\pi$$
$$564$$ 0 0
$$565$$ 6.19269 0.260528
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 25.9346 1.08724 0.543618 0.839333i $$-0.317054\pi$$
0.543618 + 0.839333i $$0.317054\pi$$
$$570$$ 0 0
$$571$$ 2.69396 0.112739 0.0563694 0.998410i $$-0.482048\pi$$
0.0563694 + 0.998410i $$0.482048\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.00000 0.0417029
$$576$$ 0 0
$$577$$ 17.3947 0.724151 0.362075 0.932149i $$-0.382068\pi$$
0.362075 + 0.932149i $$0.382068\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −32.3073 −1.34033
$$582$$ 0 0
$$583$$ −23.5047 −0.973464
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −25.2080 −1.04044 −0.520222 0.854031i $$-0.674151\pi$$
−0.520222 + 0.854031i $$0.674151\pi$$
$$588$$ 0 0
$$589$$ 18.0514 0.743793
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −44.7313 −1.83689 −0.918447 0.395545i $$-0.870556\pi$$
−0.918447 + 0.395545i $$0.870556\pi$$
$$594$$ 0 0
$$595$$ −3.09931 −0.127059
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −23.0093 −0.940136 −0.470068 0.882630i $$-0.655771\pi$$
−0.470068 + 0.882630i $$0.655771\pi$$
$$600$$ 0 0
$$601$$ 40.8867 1.66780 0.833901 0.551915i $$-0.186103\pi$$
0.833901 + 0.551915i $$0.186103\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −11.8294 −0.480932
$$606$$ 0 0
$$607$$ −2.65665 −0.107830 −0.0539150 0.998546i $$-0.517170\pi$$
−0.0539150 + 0.998546i $$0.517170\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −20.8480 −0.843420
$$612$$ 0 0
$$613$$ −38.0000 −1.53481 −0.767403 0.641165i $$-0.778451\pi$$
−0.767403 + 0.641165i $$0.778451\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 40.0314 1.61160 0.805801 0.592186i $$-0.201735\pi$$
0.805801 + 0.592186i $$0.201735\pi$$
$$618$$ 0 0
$$619$$ 22.9066 0.920695 0.460348 0.887739i $$-0.347725\pi$$
0.460348 + 0.887739i $$0.347725\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −45.2334 −1.81224
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1.82597 0.0728062
$$630$$ 0 0
$$631$$ −31.1566 −1.24032 −0.620162 0.784473i $$-0.712933\pi$$
−0.620162 + 0.784473i $$0.712933\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 4.77801 0.189609
$$636$$ 0 0
$$637$$ 46.3854 1.83786
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 37.7474 1.49093 0.745466 0.666544i $$-0.232227\pi$$
0.745466 + 0.666544i $$0.232227\pi$$
$$642$$ 0 0
$$643$$ 21.8187 0.860446 0.430223 0.902723i $$-0.358435\pi$$
0.430223 + 0.902723i $$0.358435\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −32.4554 −1.27595 −0.637976 0.770056i $$-0.720228\pi$$
−0.637976 + 0.770056i $$0.720228\pi$$
$$648$$ 0 0
$$649$$ −41.3552 −1.62333
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −15.0607 −0.589370 −0.294685 0.955594i $$-0.595215\pi$$
−0.294685 + 0.955594i $$0.595215\pi$$
$$654$$ 0 0
$$655$$ 6.54669 0.255800
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −32.2500 −1.25628 −0.628140 0.778100i $$-0.716184\pi$$
−0.628140 + 0.778100i $$0.716184\pi$$
$$660$$ 0 0
$$661$$ −37.0093 −1.43950 −0.719748 0.694235i $$-0.755743\pi$$
−0.719748 + 0.694235i $$0.755743\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 17.0607 0.661585
$$666$$ 0 0
$$667$$ −7.36333 −0.285109
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 71.9600 2.77799
$$672$$ 0 0
$$673$$ −0.411290 −0.0158541 −0.00792704 0.999969i $$-0.502523\pi$$
−0.00792704 + 0.999969i $$0.502523\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 1.98728 0.0763774 0.0381887 0.999271i $$-0.487841\pi$$
0.0381887 + 0.999271i $$0.487841\pi$$
$$678$$ 0 0
$$679$$ −71.7801 −2.75467
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −17.3179 −0.662652 −0.331326 0.943516i $$-0.607496\pi$$
−0.331326 + 0.943516i $$0.607496\pi$$
$$684$$ 0 0
$$685$$ −10.7453 −0.410557
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 13.6660 0.520632
$$690$$ 0 0
$$691$$ −5.94139 −0.226021 −0.113011 0.993594i $$-0.536049\pi$$
−0.113011 + 0.993594i $$0.536049\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −14.4240 −0.547134
$$696$$ 0 0
$$697$$ 3.94271 0.149341
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −34.2127 −1.29219 −0.646097 0.763255i $$-0.723600\pi$$
−0.646097 + 0.763255i $$0.723600\pi$$
$$702$$ 0 0
$$703$$ −10.0514 −0.379094
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 84.6154 3.18229
$$708$$ 0 0
$$709$$ 18.6354 0.699865 0.349933 0.936775i $$-0.386204\pi$$
0.349933 + 0.936775i $$0.386204\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −5.15066 −0.192894
$$714$$ 0 0
$$715$$ 13.2733 0.496395
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −10.5594 −0.393799 −0.196900 0.980424i $$-0.563087\pi$$
−0.196900 + 0.980424i $$0.563087\pi$$
$$720$$ 0 0
$$721$$ 74.4413 2.77234
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −7.36333 −0.273467
$$726$$ 0 0
$$727$$ −47.3493 −1.75609 −0.878044 0.478580i $$-0.841152\pi$$
−0.878044 + 0.478580i $$0.841152\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −5.27334 −0.195042
$$732$$ 0 0
$$733$$ −42.1600 −1.55721 −0.778607 0.627511i $$-0.784074\pi$$
−0.778607 + 0.627511i $$0.784074\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 64.1846 2.36427
$$738$$ 0 0
$$739$$ 13.2933 0.489003 0.244501 0.969649i $$-0.421376\pi$$
0.244501 + 0.969649i $$0.421376\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −3.47197 −0.127374 −0.0636871 0.997970i $$-0.520286\pi$$
−0.0636871 + 0.997970i $$0.520286\pi$$
$$744$$ 0 0
$$745$$ 6.67531 0.244564
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −74.8794 −2.73603
$$750$$ 0 0
$$751$$ 22.5513 0.822909 0.411454 0.911430i $$-0.365021\pi$$
0.411454 + 0.911430i $$0.365021\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −18.3013 −0.666054
$$756$$ 0 0
$$757$$ −13.9028 −0.505304 −0.252652 0.967557i $$-0.581303\pi$$
−0.252652 + 0.967557i $$0.581303\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −29.8701 −1.08279 −0.541394 0.840769i $$-0.682103\pi$$
−0.541394 + 0.840769i $$0.682103\pi$$
$$762$$ 0 0
$$763$$ −74.1914 −2.68591
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 24.0446 0.868199
$$768$$ 0 0
$$769$$ 10.4299 0.376114 0.188057 0.982158i $$-0.439781\pi$$
0.188057 + 0.982158i $$0.439781\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 50.5000 1.81636 0.908179 0.418583i $$-0.137473\pi$$
0.908179 + 0.418583i $$0.137473\pi$$
$$774$$ 0 0
$$775$$ −5.15066 −0.185017
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −21.7033 −0.777601
$$780$$ 0 0
$$781$$ −53.0326 −1.89766
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −18.4427 −0.658247
$$786$$ 0 0
$$787$$ 41.2907 1.47185 0.735927 0.677061i $$-0.236747\pi$$
0.735927 + 0.677061i $$0.236747\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −30.1460 −1.07187
$$792$$ 0 0
$$793$$ −41.8387 −1.48574
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −25.4847 −0.902714 −0.451357 0.892343i $$-0.649060\pi$$
−0.451357 + 0.892343i $$0.649060\pi$$
$$798$$ 0 0
$$799$$ −4.77801 −0.169034
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 72.8199 2.56976
$$804$$ 0 0
$$805$$ −4.86799 −0.171574
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 30.9380 1.08772 0.543861 0.839175i $$-0.316962\pi$$
0.543861 + 0.839175i $$0.316962\pi$$
$$810$$ 0 0
$$811$$ 31.5946 1.10944 0.554719 0.832038i $$-0.312826\pi$$
0.554719 + 0.832038i $$0.312826\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0.282672 0.00990158
$$816$$ 0 0
$$817$$ 29.0280 1.01556
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 56.7640 1.98108 0.990538 0.137238i $$-0.0438225\pi$$
0.990538 + 0.137238i $$0.0438225\pi$$
$$822$$ 0 0
$$823$$ −10.9066 −0.380181 −0.190091 0.981767i $$-0.560878\pi$$
−0.190091 + 0.981767i $$0.560878\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −8.75803 −0.304547 −0.152273 0.988338i $$-0.548659\pi$$
−0.152273 + 0.988338i $$0.548659\pi$$
$$828$$ 0 0
$$829$$ 21.2720 0.738808 0.369404 0.929269i $$-0.379562\pi$$
0.369404 + 0.929269i $$0.379562\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 10.6307 0.368333
$$834$$ 0 0
$$835$$ 6.51399 0.225426
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 14.6240 0.504875 0.252437 0.967613i $$-0.418768\pi$$
0.252437 + 0.967613i $$0.418768\pi$$
$$840$$ 0 0
$$841$$ 25.2186 0.869607
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 5.28267 0.181729
$$846$$ 0 0
$$847$$ 57.5852 1.97865
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 2.86799 0.0983135
$$852$$ 0 0
$$853$$ −52.6867 −1.80396 −0.901979 0.431779i $$-0.857886\pi$$
−0.901979 + 0.431779i $$0.857886\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 6.77075 0.231284 0.115642 0.993291i $$-0.463107\pi$$
0.115642 + 0.993291i $$0.463107\pi$$
$$858$$ 0 0
$$859$$ −47.9146 −1.63483 −0.817413 0.576052i $$-0.804593\pi$$
−0.817413 + 0.576052i $$0.804593\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 27.8573 0.948275 0.474138 0.880451i $$-0.342760\pi$$
0.474138 + 0.880451i $$0.342760\pi$$
$$864$$ 0 0
$$865$$ 8.30133 0.282254
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 6.94394 0.235557
$$870$$ 0 0
$$871$$ −37.3179 −1.26447
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −4.86799 −0.164568
$$876$$ 0 0
$$877$$ 12.4440 0.420203 0.210102 0.977680i $$-0.432620\pi$$
0.210102 + 0.977680i $$0.432620\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 7.70329 0.259530 0.129765 0.991545i $$-0.458578\pi$$
0.129765 + 0.991545i $$0.458578\pi$$
$$882$$ 0 0
$$883$$ −47.9274 −1.61288 −0.806442 0.591313i $$-0.798610\pi$$
−0.806442 + 0.591313i $$0.798610\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 7.61462 0.255674 0.127837 0.991795i $$-0.459197\pi$$
0.127837 + 0.991795i $$0.459197\pi$$
$$888$$ 0 0
$$889$$ −23.2593 −0.780092
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 26.3013 0.880140
$$894$$ 0 0
$$895$$ 5.17064 0.172835
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 37.9260 1.26490
$$900$$ 0 0
$$901$$ 3.13201 0.104342
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −21.8573 −0.726563
$$906$$ 0 0
$$907$$ 50.0759 1.66274 0.831372 0.555716i $$-0.187556\pi$$
0.831372 + 0.555716i $$0.187556\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −14.5840 −0.483190 −0.241595 0.970377i $$-0.577670\pi$$
−0.241595 + 0.970377i $$0.577670\pi$$
$$912$$ 0 0
$$913$$ 31.7101 1.04945
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −31.8692 −1.05241
$$918$$ 0 0
$$919$$ 8.03731 0.265127 0.132563 0.991175i $$-0.457679\pi$$
0.132563 + 0.991175i $$0.457679\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 30.8340 1.01491
$$924$$ 0 0
$$925$$ 2.86799 0.0942990
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −14.3353 −0.470327 −0.235164 0.971956i $$-0.575563\pi$$
−0.235164 + 0.971956i $$0.575563\pi$$
$$930$$ 0 0
$$931$$ −58.5186 −1.91787
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 3.04202 0.0994848
$$936$$ 0 0
$$937$$ 14.7080 0.480489 0.240245 0.970712i $$-0.422772\pi$$
0.240245 + 0.970712i $$0.422772\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −2.77801 −0.0905605 −0.0452802 0.998974i $$-0.514418\pi$$
−0.0452802 + 0.998974i $$0.514418\pi$$
$$942$$ 0 0
$$943$$ 6.19269 0.201662
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 32.6680 1.06157 0.530784 0.847507i $$-0.321897\pi$$
0.530784 + 0.847507i $$0.321897\pi$$
$$948$$ 0 0
$$949$$ −42.3386 −1.37437
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 25.4347 0.823909 0.411955 0.911204i $$-0.364846\pi$$
0.411955 + 0.911204i $$0.364846\pi$$
$$954$$ 0 0
$$955$$ −8.49534 −0.274903
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 52.3081 1.68912
$$960$$ 0 0
$$961$$ −4.47065 −0.144215
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −7.83869 −0.252336
$$966$$ 0 0
$$967$$ −46.4740 −1.49450 −0.747252 0.664541i $$-0.768627\pi$$
−0.747252 + 0.664541i $$0.768627\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −59.6120 −1.91304 −0.956520 0.291667i $$-0.905790\pi$$
−0.956520 + 0.291667i $$0.905790\pi$$
$$972$$ 0 0
$$973$$ 70.2160 2.25102
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −11.2207 −0.358981 −0.179491 0.983760i $$-0.557445\pi$$
−0.179491 + 0.983760i $$0.557445\pi$$
$$978$$ 0 0
$$979$$ 44.3973 1.41894
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −4.29539 −0.137002 −0.0685008 0.997651i $$-0.521822\pi$$
−0.0685008 + 0.997651i $$0.521822\pi$$
$$984$$ 0 0
$$985$$ −17.5747 −0.559976
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −8.28267 −0.263374
$$990$$ 0 0
$$991$$ 26.3841 0.838117 0.419059 0.907959i $$-0.362360\pi$$
0.419059 + 0.907959i $$0.362360\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −4.17997 −0.132514
$$996$$ 0 0
$$997$$ 13.2547 0.419780 0.209890 0.977725i $$-0.432689\pi$$
0.209890 + 0.977725i $$0.432689\pi$$
$$998$$ 0 0
$$999$$ 0 0
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 8280.2.a.bi.1.3 3
3.2 odd 2 2760.2.a.u.1.3 3
12.11 even 2 5520.2.a.bz.1.1 3

By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.u.1.3 3 3.2 odd 2
5520.2.a.bz.1.1 3 12.11 even 2
8280.2.a.bi.1.3 3 1.1 even 1 trivial