# Properties

 Label 8280.2.a.bj.1.2 Level $8280$ Weight $2$ Character 8280.1 Self dual yes Analytic conductor $66.116$ Analytic rank $0$ 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: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.2597.1 Defining polynomial: $$x^{3} - x^{2} - 9x + 8$$ x^3 - x^2 - 9*x + 8 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 920) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.2 Root $$0.878468$$ of defining polynomial Character $$\chi$$ $$=$$ 8280.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{5} +0.121532 q^{7} +O(q^{10})$$ $$q-1.00000 q^{5} +0.121532 q^{7} -2.87847 q^{11} +5.22829 q^{13} +2.22829 q^{17} +1.22829 q^{19} -1.00000 q^{23} +1.00000 q^{25} -9.34983 q^{29} -2.12153 q^{31} -0.121532 q^{35} +5.59289 q^{37} -8.22829 q^{41} +8.00000 q^{43} +10.4566 q^{47} -6.98523 q^{49} +3.59289 q^{53} +2.87847 q^{55} +0.650174 q^{59} -7.33506 q^{61} -5.22829 q^{65} +5.59289 q^{67} +13.9852 q^{71} +12.9427 q^{73} -0.349826 q^{77} -3.51387 q^{79} +11.1068 q^{83} -2.22829 q^{85} +0.486128 q^{89} +0.635404 q^{91} -1.22829 q^{95} +0.635404 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q - 3 q^{5} + 2 q^{7}+O(q^{10})$$ 3 * q - 3 * q^5 + 2 * q^7 $$3 q - 3 q^{5} + 2 q^{7} - 7 q^{11} - q^{13} - 10 q^{17} - 13 q^{19} - 3 q^{23} + 3 q^{25} - 13 q^{29} - 8 q^{31} - 2 q^{35} + 5 q^{37} - 8 q^{41} + 24 q^{43} - 2 q^{47} - q^{49} - q^{53} + 7 q^{55} + 17 q^{59} + 13 q^{61} + q^{65} + 5 q^{67} + 22 q^{71} + 12 q^{73} + 14 q^{77} - 4 q^{79} + 15 q^{83} + 10 q^{85} + 8 q^{89} - 3 q^{91} + 13 q^{95} - 3 q^{97}+O(q^{100})$$ 3 * q - 3 * q^5 + 2 * q^7 - 7 * q^11 - q^13 - 10 * q^17 - 13 * q^19 - 3 * q^23 + 3 * q^25 - 13 * q^29 - 8 * q^31 - 2 * q^35 + 5 * q^37 - 8 * q^41 + 24 * q^43 - 2 * q^47 - q^49 - q^53 + 7 * q^55 + 17 * q^59 + 13 * q^61 + q^65 + 5 * q^67 + 22 * q^71 + 12 * q^73 + 14 * q^77 - 4 * q^79 + 15 * q^83 + 10 * q^85 + 8 * q^89 - 3 * q^91 + 13 * q^95 - 3 * 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
$$7$$ 0.121532 0.0459347 0.0229674 0.999736i $$-0.492689\pi$$
0.0229674 + 0.999736i $$0.492689\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −2.87847 −0.867891 −0.433945 0.900939i $$-0.642879\pi$$
−0.433945 + 0.900939i $$0.642879\pi$$
$$12$$ 0 0
$$13$$ 5.22829 1.45007 0.725034 0.688713i $$-0.241824\pi$$
0.725034 + 0.688713i $$0.241824\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.22829 0.540441 0.270220 0.962799i $$-0.412903\pi$$
0.270220 + 0.962799i $$0.412903\pi$$
$$18$$ 0 0
$$19$$ 1.22829 0.281790 0.140895 0.990025i $$-0.455002\pi$$
0.140895 + 0.990025i $$0.455002\pi$$
$$20$$ 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
$$29$$ −9.34983 −1.73622 −0.868110 0.496373i $$-0.834665\pi$$
−0.868110 + 0.496373i $$0.834665\pi$$
$$30$$ 0 0
$$31$$ −2.12153 −0.381038 −0.190519 0.981683i $$-0.561017\pi$$
−0.190519 + 0.981683i $$0.561017\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −0.121532 −0.0205426
$$36$$ 0 0
$$37$$ 5.59289 0.919465 0.459733 0.888057i $$-0.347945\pi$$
0.459733 + 0.888057i $$0.347945\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −8.22829 −1.28504 −0.642522 0.766267i $$-0.722112\pi$$
−0.642522 + 0.766267i $$0.722112\pi$$
$$42$$ 0 0
$$43$$ 8.00000 1.21999 0.609994 0.792406i $$-0.291172\pi$$
0.609994 + 0.792406i $$0.291172\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 10.4566 1.52525 0.762625 0.646841i $$-0.223910\pi$$
0.762625 + 0.646841i $$0.223910\pi$$
$$48$$ 0 0
$$49$$ −6.98523 −0.997890
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 3.59289 0.493521 0.246761 0.969076i $$-0.420634\pi$$
0.246761 + 0.969076i $$0.420634\pi$$
$$54$$ 0 0
$$55$$ 2.87847 0.388133
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0.650174 0.0846455 0.0423227 0.999104i $$-0.486524\pi$$
0.0423227 + 0.999104i $$0.486524\pi$$
$$60$$ 0 0
$$61$$ −7.33506 −0.939158 −0.469579 0.882891i $$-0.655594\pi$$
−0.469579 + 0.882891i $$0.655594\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −5.22829 −0.648490
$$66$$ 0 0
$$67$$ 5.59289 0.683280 0.341640 0.939831i $$-0.389018\pi$$
0.341640 + 0.939831i $$0.389018\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 13.9852 1.65974 0.829871 0.557956i $$-0.188414\pi$$
0.829871 + 0.557956i $$0.188414\pi$$
$$72$$ 0 0
$$73$$ 12.9427 1.51483 0.757415 0.652934i $$-0.226462\pi$$
0.757415 + 0.652934i $$0.226462\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −0.349826 −0.0398663
$$78$$ 0 0
$$79$$ −3.51387 −0.395342 −0.197671 0.980268i $$-0.563338\pi$$
−0.197671 + 0.980268i $$0.563338\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 11.1068 1.21913 0.609563 0.792738i $$-0.291345\pi$$
0.609563 + 0.792738i $$0.291345\pi$$
$$84$$ 0 0
$$85$$ −2.22829 −0.241692
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0.486128 0.0515294 0.0257647 0.999668i $$-0.491798\pi$$
0.0257647 + 0.999668i $$0.491798\pi$$
$$90$$ 0 0
$$91$$ 0.635404 0.0666085
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −1.22829 −0.126020
$$96$$ 0 0
$$97$$ 0.635404 0.0645155 0.0322578 0.999480i $$-0.489730\pi$$
0.0322578 + 0.999480i $$0.489730\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −13.3498 −1.32836 −0.664179 0.747574i $$-0.731219\pi$$
−0.664179 + 0.747574i $$0.731219\pi$$
$$102$$ 0 0
$$103$$ −7.33506 −0.722745 −0.361372 0.932422i $$-0.617692\pi$$
−0.361372 + 0.932422i $$0.617692\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −16.0495 −1.55156 −0.775781 0.631003i $$-0.782644\pi$$
−0.775781 + 0.631003i $$0.782644\pi$$
$$108$$ 0 0
$$109$$ 1.01477 0.0971973 0.0485987 0.998818i $$-0.484524\pi$$
0.0485987 + 0.998818i $$0.484524\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −17.3203 −1.62936 −0.814678 0.579914i $$-0.803086\pi$$
−0.814678 + 0.579914i $$0.803086\pi$$
$$114$$ 0 0
$$115$$ 1.00000 0.0932505
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0.270809 0.0248250
$$120$$ 0 0
$$121$$ −2.71442 −0.246766
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 1.75694 0.155903 0.0779514 0.996957i $$-0.475162\pi$$
0.0779514 + 0.996957i $$0.475162\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 20.2135 1.76606 0.883032 0.469313i $$-0.155498\pi$$
0.883032 + 0.469313i $$0.155498\pi$$
$$132$$ 0 0
$$133$$ 0.149277 0.0129439
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 17.9279 1.53169 0.765844 0.643027i $$-0.222322\pi$$
0.765844 + 0.643027i $$0.222322\pi$$
$$138$$ 0 0
$$139$$ −10.8637 −0.921447 −0.460723 0.887544i $$-0.652410\pi$$
−0.460723 + 0.887544i $$0.652410\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −15.0495 −1.25850
$$144$$ 0 0
$$145$$ 9.34983 0.776461
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 15.7144 1.28738 0.643688 0.765288i $$-0.277404\pi$$
0.643688 + 0.765288i $$0.277404\pi$$
$$150$$ 0 0
$$151$$ −8.39234 −0.682959 −0.341479 0.939889i $$-0.610928\pi$$
−0.341479 + 0.939889i $$0.610928\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 2.12153 0.170406
$$156$$ 0 0
$$157$$ −19.5633 −1.56133 −0.780663 0.624953i $$-0.785118\pi$$
−0.780663 + 0.624953i $$0.785118\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −0.121532 −0.00957805
$$162$$ 0 0
$$163$$ 1.01477 0.0794829 0.0397415 0.999210i $$-0.487347\pi$$
0.0397415 + 0.999210i $$0.487347\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 8.00000 0.619059 0.309529 0.950890i $$-0.399829\pi$$
0.309529 + 0.950890i $$0.399829\pi$$
$$168$$ 0 0
$$169$$ 14.3351 1.10270
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 2.63540 0.200366 0.100183 0.994969i $$-0.468057\pi$$
0.100183 + 0.994969i $$0.468057\pi$$
$$174$$ 0 0
$$175$$ 0.121532 0.00918695
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 14.4566 1.08054 0.540268 0.841493i $$-0.318323\pi$$
0.540268 + 0.841493i $$0.318323\pi$$
$$180$$ 0 0
$$181$$ 10.7422 0.798459 0.399229 0.916851i $$-0.369278\pi$$
0.399229 + 0.916851i $$0.369278\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −5.59289 −0.411197
$$186$$ 0 0
$$187$$ −6.41407 −0.469043
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 22.6701 1.64035 0.820176 0.572112i $$-0.193876\pi$$
0.820176 + 0.572112i $$0.193876\pi$$
$$192$$ 0 0
$$193$$ 2.24306 0.161459 0.0807296 0.996736i $$-0.474275\pi$$
0.0807296 + 0.996736i $$0.474275\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 7.57812 0.539919 0.269959 0.962872i $$-0.412990\pi$$
0.269959 + 0.962872i $$0.412990\pi$$
$$198$$ 0 0
$$199$$ −14.0000 −0.992434 −0.496217 0.868199i $$-0.665278\pi$$
−0.496217 + 0.868199i $$0.665278\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −1.13630 −0.0797528
$$204$$ 0 0
$$205$$ 8.22829 0.574689
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −3.53560 −0.244563
$$210$$ 0 0
$$211$$ −3.10676 −0.213878 −0.106939 0.994266i $$-0.534105\pi$$
−0.106939 + 0.994266i $$0.534105\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −8.00000 −0.545595
$$216$$ 0 0
$$217$$ −0.257834 −0.0175029
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 11.6502 0.783676
$$222$$ 0 0
$$223$$ 18.2135 1.21967 0.609834 0.792529i $$-0.291236\pi$$
0.609834 + 0.792529i $$0.291236\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −13.9705 −0.927252 −0.463626 0.886031i $$-0.653452\pi$$
−0.463626 + 0.886031i $$0.653452\pi$$
$$228$$ 0 0
$$229$$ 12.2135 0.807092 0.403546 0.914959i $$-0.367777\pi$$
0.403546 + 0.914959i $$0.367777\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −9.75694 −0.639198 −0.319599 0.947553i $$-0.603548\pi$$
−0.319599 + 0.947553i $$0.603548\pi$$
$$234$$ 0 0
$$235$$ −10.4566 −0.682113
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −8.62063 −0.557622 −0.278811 0.960346i $$-0.589940\pi$$
−0.278811 + 0.960346i $$0.589940\pi$$
$$240$$ 0 0
$$241$$ 3.18578 0.205214 0.102607 0.994722i $$-0.467282\pi$$
0.102607 + 0.994722i $$0.467282\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 6.98523 0.446270
$$246$$ 0 0
$$247$$ 6.42188 0.408614
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 25.2283 1.59240 0.796198 0.605036i $$-0.206841\pi$$
0.796198 + 0.605036i $$0.206841\pi$$
$$252$$ 0 0
$$253$$ 2.87847 0.180968
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 10.6701 0.665583 0.332792 0.943000i $$-0.392009\pi$$
0.332792 + 0.943000i $$0.392009\pi$$
$$258$$ 0 0
$$259$$ 0.679714 0.0422354
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 18.6849 1.15216 0.576080 0.817394i $$-0.304582\pi$$
0.576080 + 0.817394i $$0.304582\pi$$
$$264$$ 0 0
$$265$$ −3.59289 −0.220709
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 24.8637 1.51597 0.757983 0.652274i $$-0.226185\pi$$
0.757983 + 0.652274i $$0.226185\pi$$
$$270$$ 0 0
$$271$$ 0.578119 0.0351183 0.0175591 0.999846i $$-0.494410\pi$$
0.0175591 + 0.999846i $$0.494410\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −2.87847 −0.173578
$$276$$ 0 0
$$277$$ −9.51387 −0.571633 −0.285817 0.958284i $$-0.592265\pi$$
−0.285817 + 0.958284i $$0.592265\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 13.1562 0.784835 0.392418 0.919787i $$-0.371639\pi$$
0.392418 + 0.919787i $$0.371639\pi$$
$$282$$ 0 0
$$283$$ 24.5061 1.45673 0.728367 0.685187i $$-0.240280\pi$$
0.728367 + 0.685187i $$0.240280\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −1.00000 −0.0590281
$$288$$ 0 0
$$289$$ −12.0347 −0.707924
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 6.29254 0.367614 0.183807 0.982962i $$-0.441158\pi$$
0.183807 + 0.982962i $$0.441158\pi$$
$$294$$ 0 0
$$295$$ −0.650174 −0.0378546
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −5.22829 −0.302360
$$300$$ 0 0
$$301$$ 0.972255 0.0560398
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 7.33506 0.420004
$$306$$ 0 0
$$307$$ 13.3351 0.761072 0.380536 0.924766i $$-0.375740\pi$$
0.380536 + 0.924766i $$0.375740\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 24.4270 1.38513 0.692565 0.721355i $$-0.256480\pi$$
0.692565 + 0.721355i $$0.256480\pi$$
$$312$$ 0 0
$$313$$ 26.5486 1.50061 0.750307 0.661089i $$-0.229906\pi$$
0.750307 + 0.661089i $$0.229906\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 16.9852 0.953986 0.476993 0.878907i $$-0.341727\pi$$
0.476993 + 0.878907i $$0.341727\pi$$
$$318$$ 0 0
$$319$$ 26.9132 1.50685
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2.73700 0.152291
$$324$$ 0 0
$$325$$ 5.22829 0.290014
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 1.27081 0.0700620
$$330$$ 0 0
$$331$$ 17.8914 0.983403 0.491701 0.870764i $$-0.336375\pi$$
0.491701 + 0.870764i $$0.336375\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −5.59289 −0.305572
$$336$$ 0 0
$$337$$ −4.52864 −0.246691 −0.123345 0.992364i $$-0.539362\pi$$
−0.123345 + 0.992364i $$0.539362\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 6.10676 0.330700
$$342$$ 0 0
$$343$$ −1.69965 −0.0917725
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.0937869 0.00503475 0.00251737 0.999997i $$-0.499199\pi$$
0.00251737 + 0.999997i $$0.499199\pi$$
$$348$$ 0 0
$$349$$ 8.07902 0.432460 0.216230 0.976342i $$-0.430624\pi$$
0.216230 + 0.976342i $$0.430624\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 8.00000 0.425797 0.212899 0.977074i $$-0.431710\pi$$
0.212899 + 0.977074i $$0.431710\pi$$
$$354$$ 0 0
$$355$$ −13.9852 −0.742259
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −8.69965 −0.459150 −0.229575 0.973291i $$-0.573734\pi$$
−0.229575 + 0.973291i $$0.573734\pi$$
$$360$$ 0 0
$$361$$ −17.4913 −0.920594
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −12.9427 −0.677453
$$366$$ 0 0
$$367$$ 31.8064 1.66028 0.830141 0.557554i $$-0.188260\pi$$
0.830141 + 0.557554i $$0.188260\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0.436651 0.0226698
$$372$$ 0 0
$$373$$ −13.4288 −0.695319 −0.347660 0.937621i $$-0.613023\pi$$
−0.347660 + 0.937621i $$0.613023\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −48.8836 −2.51764
$$378$$ 0 0
$$379$$ 31.8212 1.63454 0.817272 0.576252i $$-0.195485\pi$$
0.817272 + 0.576252i $$0.195485\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −34.3480 −1.75510 −0.877551 0.479483i $$-0.840824\pi$$
−0.877551 + 0.479483i $$0.840824\pi$$
$$384$$ 0 0
$$385$$ 0.349826 0.0178288
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −8.14928 −0.413185 −0.206592 0.978427i $$-0.566237\pi$$
−0.206592 + 0.978427i $$0.566237\pi$$
$$390$$ 0 0
$$391$$ −2.22829 −0.112690
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 3.51387 0.176802
$$396$$ 0 0
$$397$$ 19.0625 0.956717 0.478359 0.878165i $$-0.341232\pi$$
0.478359 + 0.878165i $$0.341232\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −19.9705 −0.997277 −0.498639 0.866810i $$-0.666167\pi$$
−0.498639 + 0.866810i $$0.666167\pi$$
$$402$$ 0 0
$$403$$ −11.0920 −0.552531
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −16.0990 −0.797996
$$408$$ 0 0
$$409$$ −10.3351 −0.511036 −0.255518 0.966804i $$-0.582246\pi$$
−0.255518 + 0.966804i $$0.582246\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0.0790169 0.00388817
$$414$$ 0 0
$$415$$ −11.1068 −0.545209
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −5.72740 −0.279802 −0.139901 0.990166i $$-0.544678\pi$$
−0.139901 + 0.990166i $$0.544678\pi$$
$$420$$ 0 0
$$421$$ −8.44361 −0.411516 −0.205758 0.978603i $$-0.565966\pi$$
−0.205758 + 0.978603i $$0.565966\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2.22829 0.108088
$$426$$ 0 0
$$427$$ −0.891443 −0.0431400
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −35.3698 −1.70370 −0.851851 0.523785i $$-0.824520\pi$$
−0.851851 + 0.523785i $$0.824520\pi$$
$$432$$ 0 0
$$433$$ 13.3923 0.643595 0.321797 0.946809i $$-0.395713\pi$$
0.321797 + 0.946809i $$0.395713\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −1.22829 −0.0587573
$$438$$ 0 0
$$439$$ −21.1137 −1.00770 −0.503852 0.863790i $$-0.668084\pi$$
−0.503852 + 0.863790i $$0.668084\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 31.1692 1.48089 0.740447 0.672115i $$-0.234614\pi$$
0.740447 + 0.672115i $$0.234614\pi$$
$$444$$ 0 0
$$445$$ −0.486128 −0.0230447
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 6.09199 0.287499 0.143749 0.989614i $$-0.454084\pi$$
0.143749 + 0.989614i $$0.454084\pi$$
$$450$$ 0 0
$$451$$ 23.6849 1.11528
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −0.635404 −0.0297882
$$456$$ 0 0
$$457$$ 22.1345 1.03541 0.517704 0.855560i $$-0.326787\pi$$
0.517704 + 0.855560i $$0.326787\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 11.5434 0.537630 0.268815 0.963192i $$-0.413368\pi$$
0.268815 + 0.963192i $$0.413368\pi$$
$$462$$ 0 0
$$463$$ 30.4270 1.41406 0.707032 0.707181i $$-0.250033\pi$$
0.707032 + 0.707181i $$0.250033\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −10.3776 −0.480217 −0.240108 0.970746i $$-0.577183\pi$$
−0.240108 + 0.970746i $$0.577183\pi$$
$$468$$ 0 0
$$469$$ 0.679714 0.0313863
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −23.0277 −1.05882
$$474$$ 0 0
$$475$$ 1.22829 0.0563580
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 29.6128 1.35304 0.676522 0.736422i $$-0.263486\pi$$
0.676522 + 0.736422i $$0.263486\pi$$
$$480$$ 0 0
$$481$$ 29.2413 1.33329
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −0.635404 −0.0288522
$$486$$ 0 0
$$487$$ 11.1562 0.505537 0.252769 0.967527i $$-0.418659\pi$$
0.252769 + 0.967527i $$0.418659\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −38.2630 −1.72679 −0.863393 0.504533i $$-0.831665\pi$$
−0.863393 + 0.504533i $$0.831665\pi$$
$$492$$ 0 0
$$493$$ −20.8342 −0.938323
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 1.69965 0.0762398
$$498$$ 0 0
$$499$$ 6.40711 0.286822 0.143411 0.989663i $$-0.454193\pi$$
0.143411 + 0.989663i $$0.454193\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 18.0920 0.806682 0.403341 0.915050i $$-0.367849\pi$$
0.403341 + 0.915050i $$0.367849\pi$$
$$504$$ 0 0
$$505$$ 13.3498 0.594059
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 34.1285 1.51272 0.756359 0.654156i $$-0.226976\pi$$
0.756359 + 0.654156i $$0.226976\pi$$
$$510$$ 0 0
$$511$$ 1.57295 0.0695833
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 7.33506 0.323221
$$516$$ 0 0
$$517$$ −30.0990 −1.32375
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −35.8854 −1.57217 −0.786085 0.618119i $$-0.787895\pi$$
−0.786085 + 0.618119i $$0.787895\pi$$
$$522$$ 0 0
$$523$$ 11.7865 0.515387 0.257693 0.966227i $$-0.417038\pi$$
0.257693 + 0.966227i $$0.417038\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −4.72740 −0.205929
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −43.0199 −1.86340
$$534$$ 0 0
$$535$$ 16.0495 0.693879
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 20.1068 0.866060
$$540$$ 0 0
$$541$$ −17.2413 −0.741260 −0.370630 0.928781i $$-0.620858\pi$$
−0.370630 + 0.928781i $$0.620858\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −1.01477 −0.0434680
$$546$$ 0 0
$$547$$ 14.6571 0.626694 0.313347 0.949639i $$-0.398550\pi$$
0.313347 + 0.949639i $$0.398550\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −11.4843 −0.489249
$$552$$ 0 0
$$553$$ −0.427048 −0.0181599
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −2.07902 −0.0880908 −0.0440454 0.999030i $$-0.514025\pi$$
−0.0440454 + 0.999030i $$0.514025\pi$$
$$558$$ 0 0
$$559$$ 41.8264 1.76907
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 5.10676 0.215224 0.107612 0.994193i $$-0.465680\pi$$
0.107612 + 0.994193i $$0.465680\pi$$
$$564$$ 0 0
$$565$$ 17.3203 0.728670
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −6.00000 −0.251533 −0.125767 0.992060i $$-0.540139\pi$$
−0.125767 + 0.992060i $$0.540139\pi$$
$$570$$ 0 0
$$571$$ 10.0642 0.421176 0.210588 0.977575i $$-0.432462\pi$$
0.210588 + 0.977575i $$0.432462\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ −15.7274 −0.654740 −0.327370 0.944896i $$-0.606162\pi$$
−0.327370 + 0.944896i $$0.606162\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 1.34983 0.0560002
$$582$$ 0 0
$$583$$ −10.3420 −0.428323
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 18.7344 0.773250 0.386625 0.922237i $$-0.373641\pi$$
0.386625 + 0.922237i $$0.373641\pi$$
$$588$$ 0 0
$$589$$ −2.60586 −0.107373
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 3.21532 0.132037 0.0660187 0.997818i $$-0.478970\pi$$
0.0660187 + 0.997818i $$0.478970\pi$$
$$594$$ 0 0
$$595$$ −0.270809 −0.0111021
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −22.7639 −0.930108 −0.465054 0.885282i $$-0.653965\pi$$
−0.465054 + 0.885282i $$0.653965\pi$$
$$600$$ 0 0
$$601$$ 4.30552 0.175626 0.0878128 0.996137i $$-0.472012\pi$$
0.0878128 + 0.996137i $$0.472012\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2.71442 0.110357
$$606$$ 0 0
$$607$$ 11.0868 0.450000 0.225000 0.974359i $$-0.427762\pi$$
0.225000 + 0.974359i $$0.427762\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 54.6701 2.21172
$$612$$ 0 0
$$613$$ 29.9409 1.20930 0.604651 0.796490i $$-0.293313\pi$$
0.604651 + 0.796490i $$0.293313\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −35.0130 −1.40957 −0.704785 0.709421i $$-0.748956\pi$$
−0.704785 + 0.709421i $$0.748956\pi$$
$$618$$ 0 0
$$619$$ 4.98523 0.200373 0.100187 0.994969i $$-0.468056\pi$$
0.100187 + 0.994969i $$0.468056\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0.0590800 0.00236699
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 12.4626 0.496916
$$630$$ 0 0
$$631$$ −3.64237 −0.145000 −0.0725002 0.997368i $$-0.523098\pi$$
−0.0725002 + 0.997368i $$0.523098\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −1.75694 −0.0697219
$$636$$ 0 0
$$637$$ −36.5208 −1.44701
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −38.6997 −1.52854 −0.764272 0.644894i $$-0.776902\pi$$
−0.764272 + 0.644894i $$0.776902\pi$$
$$642$$ 0 0
$$643$$ −28.8637 −1.13827 −0.569137 0.822243i $$-0.692722\pi$$
−0.569137 + 0.822243i $$0.692722\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 19.8854 0.781777 0.390888 0.920438i $$-0.372168\pi$$
0.390888 + 0.920438i $$0.372168\pi$$
$$648$$ 0 0
$$649$$ −1.87151 −0.0734630
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 27.1988 1.06437 0.532185 0.846628i $$-0.321371\pi$$
0.532185 + 0.846628i $$0.321371\pi$$
$$654$$ 0 0
$$655$$ −20.2135 −0.789808
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 17.7274 0.690561 0.345281 0.938499i $$-0.387784\pi$$
0.345281 + 0.938499i $$0.387784\pi$$
$$660$$ 0 0
$$661$$ 40.7048 1.58323 0.791617 0.611018i $$-0.209240\pi$$
0.791617 + 0.611018i $$0.209240\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −0.149277 −0.00578871
$$666$$ 0 0
$$667$$ 9.34983 0.362027
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 21.1137 0.815086
$$672$$ 0 0
$$673$$ 12.2135 0.470797 0.235398 0.971899i $$-0.424361\pi$$
0.235398 + 0.971899i $$0.424361\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −16.5061 −0.634380 −0.317190 0.948362i $$-0.602739\pi$$
−0.317190 + 0.948362i $$0.602739\pi$$
$$678$$ 0 0
$$679$$ 0.0772219 0.00296350
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 29.1988 1.11726 0.558630 0.829417i $$-0.311327\pi$$
0.558630 + 0.829417i $$0.311327\pi$$
$$684$$ 0 0
$$685$$ −17.9279 −0.684992
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 18.7847 0.715639
$$690$$ 0 0
$$691$$ −15.9150 −0.605434 −0.302717 0.953080i $$-0.597894\pi$$
−0.302717 + 0.953080i $$0.597894\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 10.8637 0.412084
$$696$$ 0 0
$$697$$ −18.3351 −0.694490
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −34.5981 −1.30675 −0.653375 0.757034i $$-0.726648\pi$$
−0.653375 + 0.757034i $$0.726648\pi$$
$$702$$ 0 0
$$703$$ 6.86971 0.259096
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1.62243 −0.0610177
$$708$$ 0 0
$$709$$ 35.8212 1.34529 0.672646 0.739964i $$-0.265158\pi$$
0.672646 + 0.739964i $$0.265158\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 2.12153 0.0794520
$$714$$ 0 0
$$715$$ 15.0495 0.562819
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 32.5781 1.21496 0.607479 0.794335i $$-0.292181\pi$$
0.607479 + 0.794335i $$0.292181\pi$$
$$720$$ 0 0
$$721$$ −0.891443 −0.0331991
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −9.34983 −0.347244
$$726$$ 0 0
$$727$$ −31.9557 −1.18517 −0.592585 0.805508i $$-0.701893\pi$$
−0.592585 + 0.805508i $$0.701893\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 17.8264 0.659331
$$732$$ 0 0
$$733$$ −2.19359 −0.0810220 −0.0405110 0.999179i $$-0.512899\pi$$
−0.0405110 + 0.999179i $$0.512899\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −16.0990 −0.593013
$$738$$ 0 0
$$739$$ −51.7473 −1.90356 −0.951778 0.306787i $$-0.900746\pi$$
−0.951778 + 0.306787i $$0.900746\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 14.4436 0.529885 0.264942 0.964264i $$-0.414647\pi$$
0.264942 + 0.964264i $$0.414647\pi$$
$$744$$ 0 0
$$745$$ −15.7144 −0.575732
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −1.95052 −0.0712706
$$750$$ 0 0
$$751$$ 17.4288 0.635987 0.317994 0.948093i $$-0.396991\pi$$
0.317994 + 0.948093i $$0.396991\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 8.39234 0.305429
$$756$$ 0 0
$$757$$ −34.9331 −1.26967 −0.634833 0.772650i $$-0.718931\pi$$
−0.634833 + 0.772650i $$0.718931\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 23.2482 0.842748 0.421374 0.906887i $$-0.361548\pi$$
0.421374 + 0.906887i $$0.361548\pi$$
$$762$$ 0 0
$$763$$ 0.123327 0.00446473
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 3.39930 0.122742
$$768$$ 0 0
$$769$$ −48.6997 −1.75615 −0.878077 0.478519i $$-0.841174\pi$$
−0.878077 + 0.478519i $$0.841174\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 15.6128 0.561554 0.280777 0.959773i $$-0.409408\pi$$
0.280777 + 0.959773i $$0.409408\pi$$
$$774$$ 0 0
$$775$$ −2.12153 −0.0762077
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −10.1068 −0.362112
$$780$$ 0 0
$$781$$ −40.2560 −1.44047
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 19.5633 0.698246
$$786$$ 0 0
$$787$$ 24.2630 0.864883 0.432441 0.901662i $$-0.357652\pi$$
0.432441 + 0.901662i $$0.357652\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −2.10497 −0.0748440
$$792$$ 0 0
$$793$$ −38.3498 −1.36184
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −44.5911 −1.57950 −0.789749 0.613430i $$-0.789789\pi$$
−0.789749 + 0.613430i $$0.789789\pi$$
$$798$$ 0 0
$$799$$ 23.3003 0.824307
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −37.2552 −1.31471
$$804$$ 0 0
$$805$$ 0.121532 0.00428344
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 44.7144 1.57208 0.786038 0.618179i $$-0.212129\pi$$
0.786038 + 0.618179i $$0.212129\pi$$
$$810$$ 0 0
$$811$$ 1.19179 0.0418495 0.0209247 0.999781i $$-0.493339\pi$$
0.0209247 + 0.999781i $$0.493339\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −1.01477 −0.0355458
$$816$$ 0 0
$$817$$ 9.82635 0.343780
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −10.0000 −0.349002 −0.174501 0.984657i $$-0.555831\pi$$
−0.174501 + 0.984657i $$0.555831\pi$$
$$822$$ 0 0
$$823$$ 26.7551 0.932626 0.466313 0.884620i $$-0.345582\pi$$
0.466313 + 0.884620i $$0.345582\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 27.2907 0.948992 0.474496 0.880258i $$-0.342630\pi$$
0.474496 + 0.880258i $$0.342630\pi$$
$$828$$ 0 0
$$829$$ 34.2925 1.19103 0.595515 0.803344i $$-0.296948\pi$$
0.595515 + 0.803344i $$0.296948\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −15.5651 −0.539300
$$834$$ 0 0
$$835$$ −8.00000 −0.276851
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 40.6701 1.40409 0.702044 0.712133i $$-0.252271\pi$$
0.702044 + 0.712133i $$0.252271\pi$$
$$840$$ 0 0
$$841$$ 58.4192 2.01446
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −14.3351 −0.493141
$$846$$ 0 0
$$847$$ −0.329889 −0.0113351
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −5.59289 −0.191722
$$852$$ 0 0
$$853$$ −34.6276 −1.18563 −0.592813 0.805340i $$-0.701983\pi$$
−0.592813 + 0.805340i $$0.701983\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −26.4861 −0.904749 −0.452374 0.891828i $$-0.649423\pi$$
−0.452374 + 0.891828i $$0.649423\pi$$
$$858$$ 0 0
$$859$$ 40.9627 1.39763 0.698814 0.715304i $$-0.253712\pi$$
0.698814 + 0.715304i $$0.253712\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 18.5712 0.632170 0.316085 0.948731i $$-0.397632\pi$$
0.316085 + 0.948731i $$0.397632\pi$$
$$864$$ 0 0
$$865$$ −2.63540 −0.0896064
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 10.1146 0.343113
$$870$$ 0 0
$$871$$ 29.2413 0.990803
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ −0.121532 −0.00410853
$$876$$ 0 0
$$877$$ −28.4913 −0.962083 −0.481041 0.876698i $$-0.659741\pi$$
−0.481041 + 0.876698i $$0.659741\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 4.91318 0.165529 0.0827645 0.996569i $$-0.473625\pi$$
0.0827645 + 0.996569i $$0.473625\pi$$
$$882$$ 0 0
$$883$$ 30.1710 1.01534 0.507668 0.861553i $$-0.330508\pi$$
0.507668 + 0.861553i $$0.330508\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −25.7865 −0.865825 −0.432913 0.901436i $$-0.642514\pi$$
−0.432913 + 0.901436i $$0.642514\pi$$
$$888$$ 0 0
$$889$$ 0.213524 0.00716136
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 12.8438 0.429800
$$894$$ 0 0
$$895$$ −14.4566 −0.483230
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 19.8360 0.661566
$$900$$ 0 0
$$901$$ 8.00601 0.266719
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −10.7422 −0.357082
$$906$$ 0 0
$$907$$ −44.3776 −1.47353 −0.736767 0.676147i $$-0.763648\pi$$
−0.736767 + 0.676147i $$0.763648\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −47.7968 −1.58358 −0.791789 0.610794i $$-0.790850\pi$$
−0.791789 + 0.610794i $$0.790850\pi$$
$$912$$ 0 0
$$913$$ −31.9705 −1.05807
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 2.45659 0.0811237
$$918$$ 0 0
$$919$$ 8.00000 0.263896 0.131948 0.991257i $$-0.457877\pi$$
0.131948 + 0.991257i $$0.457877\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 73.1189 2.40674
$$924$$ 0 0
$$925$$ 5.59289 0.183893
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −24.0199 −0.788069 −0.394034 0.919096i $$-0.628921\pi$$
−0.394034 + 0.919096i $$0.628921\pi$$
$$930$$ 0 0
$$931$$ −8.57991 −0.281195
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 6.41407 0.209763
$$936$$ 0 0
$$937$$ 0.384533 0.0125621 0.00628107 0.999980i $$-0.498001\pi$$
0.00628107 + 0.999980i $$0.498001\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −25.0920 −0.817976 −0.408988 0.912540i $$-0.634118\pi$$
−0.408988 + 0.912540i $$0.634118\pi$$
$$942$$ 0 0
$$943$$ 8.22829 0.267950
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −44.7126 −1.45297 −0.726483 0.687185i $$-0.758846\pi$$
−0.726483 + 0.687185i $$0.758846\pi$$
$$948$$ 0 0
$$949$$ 67.6683 2.19661
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 21.2500 0.688356 0.344178 0.938904i $$-0.388158\pi$$
0.344178 + 0.938904i $$0.388158\pi$$
$$954$$ 0 0
$$955$$ −22.6701 −0.733588
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 2.17882 0.0703577
$$960$$ 0 0
$$961$$ −26.4991 −0.854810
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −2.24306 −0.0722068
$$966$$ 0 0
$$967$$ −41.0417 −1.31981 −0.659906 0.751349i $$-0.729404\pi$$
−0.659906 + 0.751349i $$0.729404\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −35.2760 −1.13206 −0.566030 0.824385i $$-0.691521\pi$$
−0.566030 + 0.824385i $$0.691521\pi$$
$$972$$ 0 0
$$973$$ −1.32029 −0.0423264
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 6.79164 0.217284 0.108642 0.994081i $$-0.465350\pi$$
0.108642 + 0.994081i $$0.465350\pi$$
$$978$$ 0 0
$$979$$ −1.39930 −0.0447219
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −19.5981 −0.625081 −0.312540 0.949904i $$-0.601180\pi$$
−0.312540 + 0.949904i $$0.601180\pi$$
$$984$$ 0 0
$$985$$ −7.57812 −0.241459
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −8.00000 −0.254385
$$990$$ 0 0
$$991$$ −37.2995 −1.18486 −0.592429 0.805623i $$-0.701831\pi$$
−0.592429 + 0.805623i $$0.701831\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 14.0000 0.443830
$$996$$ 0 0
$$997$$ −19.7274 −0.624773 −0.312386 0.949955i $$-0.601128\pi$$
−0.312386 + 0.949955i $$0.601128\pi$$
$$998$$ 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.bj.1.2 3
3.2 odd 2 920.2.a.h.1.2 3
12.11 even 2 1840.2.a.s.1.2 3
15.2 even 4 4600.2.e.p.4049.3 6
15.8 even 4 4600.2.e.p.4049.4 6
15.14 odd 2 4600.2.a.x.1.2 3
24.5 odd 2 7360.2.a.by.1.2 3
24.11 even 2 7360.2.a.cc.1.2 3
60.59 even 2 9200.2.a.ce.1.2 3

By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.h.1.2 3 3.2 odd 2
1840.2.a.s.1.2 3 12.11 even 2
4600.2.a.x.1.2 3 15.14 odd 2
4600.2.e.p.4049.3 6 15.2 even 4
4600.2.e.p.4049.4 6 15.8 even 4
7360.2.a.by.1.2 3 24.5 odd 2
7360.2.a.cc.1.2 3 24.11 even 2
8280.2.a.bj.1.2 3 1.1 even 1 trivial
9200.2.a.ce.1.2 3 60.59 even 2