# Properties

 Label 9016.2.a.w.1.1 Level $9016$ Weight $2$ Character 9016.1 Self dual yes Analytic conductor $71.993$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$9016 = 2^{3} \cdot 7^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 9016.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$71.9931224624$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{17})$$ Defining polynomial: $$x^{2} - x - 4$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 184) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-1.56155$$ of defining polynomial Character $$\chi$$ $$=$$ 9016.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.56155 q^{3} -2.00000 q^{5} -0.561553 q^{9} +O(q^{10})$$ $$q-1.56155 q^{3} -2.00000 q^{5} -0.561553 q^{9} -3.12311 q^{11} -0.438447 q^{13} +3.12311 q^{15} -5.12311 q^{17} +3.12311 q^{19} -1.00000 q^{23} -1.00000 q^{25} +5.56155 q^{27} +3.56155 q^{29} +2.43845 q^{31} +4.87689 q^{33} +8.24621 q^{37} +0.684658 q^{39} +9.80776 q^{41} -8.00000 q^{43} +1.12311 q^{45} +0.684658 q^{47} +8.00000 q^{51} +2.00000 q^{53} +6.24621 q^{55} -4.87689 q^{57} -10.2462 q^{59} +4.24621 q^{61} +0.876894 q^{65} +3.12311 q^{67} +1.56155 q^{69} +13.5616 q^{71} +14.6847 q^{73} +1.56155 q^{75} +3.12311 q^{79} -7.00000 q^{81} -14.2462 q^{83} +10.2462 q^{85} -5.56155 q^{87} -11.3693 q^{89} -3.80776 q^{93} -6.24621 q^{95} -11.3693 q^{97} +1.75379 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{3} - 4 q^{5} + 3 q^{9} + O(q^{10})$$ $$2 q + q^{3} - 4 q^{5} + 3 q^{9} + 2 q^{11} - 5 q^{13} - 2 q^{15} - 2 q^{17} - 2 q^{19} - 2 q^{23} - 2 q^{25} + 7 q^{27} + 3 q^{29} + 9 q^{31} + 18 q^{33} - 11 q^{39} - q^{41} - 16 q^{43} - 6 q^{45} - 11 q^{47} + 16 q^{51} + 4 q^{53} - 4 q^{55} - 18 q^{57} - 4 q^{59} - 8 q^{61} + 10 q^{65} - 2 q^{67} - q^{69} + 23 q^{71} + 17 q^{73} - q^{75} - 2 q^{79} - 14 q^{81} - 12 q^{83} + 4 q^{85} - 7 q^{87} + 2 q^{89} + 13 q^{93} + 4 q^{95} + 2 q^{97} + 20 q^{99} + O(q^{100})$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.56155 −0.901563 −0.450781 0.892634i $$-0.648855\pi$$
−0.450781 + 0.892634i $$0.648855\pi$$
$$4$$ 0 0
$$5$$ −2.00000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −0.561553 −0.187184
$$10$$ 0 0
$$11$$ −3.12311 −0.941652 −0.470826 0.882226i $$-0.656044\pi$$
−0.470826 + 0.882226i $$0.656044\pi$$
$$12$$ 0 0
$$13$$ −0.438447 −0.121603 −0.0608017 0.998150i $$-0.519366\pi$$
−0.0608017 + 0.998150i $$0.519366\pi$$
$$14$$ 0 0
$$15$$ 3.12311 0.806382
$$16$$ 0 0
$$17$$ −5.12311 −1.24254 −0.621268 0.783598i $$-0.713382\pi$$
−0.621268 + 0.783598i $$0.713382\pi$$
$$18$$ 0 0
$$19$$ 3.12311 0.716490 0.358245 0.933628i $$-0.383375\pi$$
0.358245 + 0.933628i $$0.383375\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1.00000 −0.208514
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 5.56155 1.07032
$$28$$ 0 0
$$29$$ 3.56155 0.661364 0.330682 0.943742i $$-0.392721\pi$$
0.330682 + 0.943742i $$0.392721\pi$$
$$30$$ 0 0
$$31$$ 2.43845 0.437958 0.218979 0.975730i $$-0.429727\pi$$
0.218979 + 0.975730i $$0.429727\pi$$
$$32$$ 0 0
$$33$$ 4.87689 0.848958
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 8.24621 1.35567 0.677834 0.735215i $$-0.262919\pi$$
0.677834 + 0.735215i $$0.262919\pi$$
$$38$$ 0 0
$$39$$ 0.684658 0.109633
$$40$$ 0 0
$$41$$ 9.80776 1.53172 0.765858 0.643010i $$-0.222315\pi$$
0.765858 + 0.643010i $$0.222315\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ 1.12311 0.167423
$$46$$ 0 0
$$47$$ 0.684658 0.0998677 0.0499338 0.998753i $$-0.484099\pi$$
0.0499338 + 0.998753i $$0.484099\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 8.00000 1.12022
$$52$$ 0 0
$$53$$ 2.00000 0.274721 0.137361 0.990521i $$-0.456138\pi$$
0.137361 + 0.990521i $$0.456138\pi$$
$$54$$ 0 0
$$55$$ 6.24621 0.842239
$$56$$ 0 0
$$57$$ −4.87689 −0.645960
$$58$$ 0 0
$$59$$ −10.2462 −1.33394 −0.666972 0.745083i $$-0.732410\pi$$
−0.666972 + 0.745083i $$0.732410\pi$$
$$60$$ 0 0
$$61$$ 4.24621 0.543672 0.271836 0.962344i $$-0.412369\pi$$
0.271836 + 0.962344i $$0.412369\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0.876894 0.108765
$$66$$ 0 0
$$67$$ 3.12311 0.381548 0.190774 0.981634i $$-0.438900\pi$$
0.190774 + 0.981634i $$0.438900\pi$$
$$68$$ 0 0
$$69$$ 1.56155 0.187989
$$70$$ 0 0
$$71$$ 13.5616 1.60946 0.804730 0.593641i $$-0.202310\pi$$
0.804730 + 0.593641i $$0.202310\pi$$
$$72$$ 0 0
$$73$$ 14.6847 1.71871 0.859355 0.511380i $$-0.170866\pi$$
0.859355 + 0.511380i $$0.170866\pi$$
$$74$$ 0 0
$$75$$ 1.56155 0.180313
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 3.12311 0.351377 0.175688 0.984446i $$-0.443785\pi$$
0.175688 + 0.984446i $$0.443785\pi$$
$$80$$ 0 0
$$81$$ −7.00000 −0.777778
$$82$$ 0 0
$$83$$ −14.2462 −1.56372 −0.781862 0.623451i $$-0.785730\pi$$
−0.781862 + 0.623451i $$0.785730\pi$$
$$84$$ 0 0
$$85$$ 10.2462 1.11136
$$86$$ 0 0
$$87$$ −5.56155 −0.596261
$$88$$ 0 0
$$89$$ −11.3693 −1.20515 −0.602573 0.798064i $$-0.705858\pi$$
−0.602573 + 0.798064i $$0.705858\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −3.80776 −0.394847
$$94$$ 0 0
$$95$$ −6.24621 −0.640848
$$96$$ 0 0
$$97$$ −11.3693 −1.15438 −0.577190 0.816610i $$-0.695851\pi$$
−0.577190 + 0.816610i $$0.695851\pi$$
$$98$$ 0 0
$$99$$ 1.75379 0.176262
$$100$$ 0 0
$$101$$ −12.2462 −1.21854 −0.609272 0.792961i $$-0.708538\pi$$
−0.609272 + 0.792961i $$0.708538\pi$$
$$102$$ 0 0
$$103$$ 14.2462 1.40372 0.701860 0.712314i $$-0.252353\pi$$
0.701860 + 0.712314i $$0.252353\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 11.1231 1.07531 0.537656 0.843165i $$-0.319310\pi$$
0.537656 + 0.843165i $$0.319310\pi$$
$$108$$ 0 0
$$109$$ 13.1231 1.25697 0.628483 0.777824i $$-0.283676\pi$$
0.628483 + 0.777824i $$0.283676\pi$$
$$110$$ 0 0
$$111$$ −12.8769 −1.22222
$$112$$ 0 0
$$113$$ −2.87689 −0.270635 −0.135318 0.990802i $$-0.543206\pi$$
−0.135318 + 0.990802i $$0.543206\pi$$
$$114$$ 0 0
$$115$$ 2.00000 0.186501
$$116$$ 0 0
$$117$$ 0.246211 0.0227622
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1.24621 −0.113292
$$122$$ 0 0
$$123$$ −15.3153 −1.38094
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 0.684658 0.0607536 0.0303768 0.999539i $$-0.490329\pi$$
0.0303768 + 0.999539i $$0.490329\pi$$
$$128$$ 0 0
$$129$$ 12.4924 1.09990
$$130$$ 0 0
$$131$$ −3.31534 −0.289663 −0.144831 0.989456i $$-0.546264\pi$$
−0.144831 + 0.989456i $$0.546264\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −11.1231 −0.957325
$$136$$ 0 0
$$137$$ 6.87689 0.587533 0.293766 0.955877i $$-0.405091\pi$$
0.293766 + 0.955877i $$0.405091\pi$$
$$138$$ 0 0
$$139$$ 3.31534 0.281204 0.140602 0.990066i $$-0.455096\pi$$
0.140602 + 0.990066i $$0.455096\pi$$
$$140$$ 0 0
$$141$$ −1.06913 −0.0900370
$$142$$ 0 0
$$143$$ 1.36932 0.114508
$$144$$ 0 0
$$145$$ −7.12311 −0.591542
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −20.2462 −1.65863 −0.829317 0.558778i $$-0.811270\pi$$
−0.829317 + 0.558778i $$0.811270\pi$$
$$150$$ 0 0
$$151$$ −10.4384 −0.849469 −0.424734 0.905318i $$-0.639633\pi$$
−0.424734 + 0.905318i $$0.639633\pi$$
$$152$$ 0 0
$$153$$ 2.87689 0.232583
$$154$$ 0 0
$$155$$ −4.87689 −0.391722
$$156$$ 0 0
$$157$$ −21.1231 −1.68581 −0.842904 0.538064i $$-0.819156\pi$$
−0.842904 + 0.538064i $$0.819156\pi$$
$$158$$ 0 0
$$159$$ −3.12311 −0.247678
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 18.9309 1.48278 0.741390 0.671074i $$-0.234167\pi$$
0.741390 + 0.671074i $$0.234167\pi$$
$$164$$ 0 0
$$165$$ −9.75379 −0.759331
$$166$$ 0 0
$$167$$ 16.0000 1.23812 0.619059 0.785345i $$-0.287514\pi$$
0.619059 + 0.785345i $$0.287514\pi$$
$$168$$ 0 0
$$169$$ −12.8078 −0.985213
$$170$$ 0 0
$$171$$ −1.75379 −0.134116
$$172$$ 0 0
$$173$$ 10.0000 0.760286 0.380143 0.924928i $$-0.375875\pi$$
0.380143 + 0.924928i $$0.375875\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 16.0000 1.20263
$$178$$ 0 0
$$179$$ −3.31534 −0.247800 −0.123900 0.992295i $$-0.539540\pi$$
−0.123900 + 0.992295i $$0.539540\pi$$
$$180$$ 0 0
$$181$$ −3.75379 −0.279017 −0.139508 0.990221i $$-0.544552\pi$$
−0.139508 + 0.990221i $$0.544552\pi$$
$$182$$ 0 0
$$183$$ −6.63068 −0.490154
$$184$$ 0 0
$$185$$ −16.4924 −1.21255
$$186$$ 0 0
$$187$$ 16.0000 1.17004
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 25.3693 1.83566 0.917830 0.396974i $$-0.129940\pi$$
0.917830 + 0.396974i $$0.129940\pi$$
$$192$$ 0 0
$$193$$ −0.438447 −0.0315601 −0.0157801 0.999875i $$-0.505023\pi$$
−0.0157801 + 0.999875i $$0.505023\pi$$
$$194$$ 0 0
$$195$$ −1.36932 −0.0980588
$$196$$ 0 0
$$197$$ −16.9309 −1.20627 −0.603137 0.797637i $$-0.706083\pi$$
−0.603137 + 0.797637i $$0.706083\pi$$
$$198$$ 0 0
$$199$$ −11.1231 −0.788496 −0.394248 0.919004i $$-0.628995\pi$$
−0.394248 + 0.919004i $$0.628995\pi$$
$$200$$ 0 0
$$201$$ −4.87689 −0.343990
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −19.6155 −1.37001
$$206$$ 0 0
$$207$$ 0.561553 0.0390306
$$208$$ 0 0
$$209$$ −9.75379 −0.674684
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ −21.1771 −1.45103
$$214$$ 0 0
$$215$$ 16.0000 1.09119
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −22.9309 −1.54952
$$220$$ 0 0
$$221$$ 2.24621 0.151097
$$222$$ 0 0
$$223$$ 28.4924 1.90799 0.953997 0.299817i $$-0.0969255\pi$$
0.953997 + 0.299817i $$0.0969255\pi$$
$$224$$ 0 0
$$225$$ 0.561553 0.0374369
$$226$$ 0 0
$$227$$ 6.24621 0.414576 0.207288 0.978280i $$-0.433536\pi$$
0.207288 + 0.978280i $$0.433536\pi$$
$$228$$ 0 0
$$229$$ −14.8769 −0.983093 −0.491546 0.870851i $$-0.663568\pi$$
−0.491546 + 0.870851i $$0.663568\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −16.0540 −1.05173 −0.525865 0.850568i $$-0.676258\pi$$
−0.525865 + 0.850568i $$0.676258\pi$$
$$234$$ 0 0
$$235$$ −1.36932 −0.0893244
$$236$$ 0 0
$$237$$ −4.87689 −0.316788
$$238$$ 0 0
$$239$$ 26.0540 1.68529 0.842646 0.538468i $$-0.180997\pi$$
0.842646 + 0.538468i $$0.180997\pi$$
$$240$$ 0 0
$$241$$ −6.49242 −0.418214 −0.209107 0.977893i $$-0.567056\pi$$
−0.209107 + 0.977893i $$0.567056\pi$$
$$242$$ 0 0
$$243$$ −5.75379 −0.369106
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1.36932 −0.0871275
$$248$$ 0 0
$$249$$ 22.2462 1.40980
$$250$$ 0 0
$$251$$ 6.24621 0.394257 0.197129 0.980378i $$-0.436838\pi$$
0.197129 + 0.980378i $$0.436838\pi$$
$$252$$ 0 0
$$253$$ 3.12311 0.196348
$$254$$ 0 0
$$255$$ −16.0000 −1.00196
$$256$$ 0 0
$$257$$ 5.31534 0.331562 0.165781 0.986163i $$-0.446986\pi$$
0.165781 + 0.986163i $$0.446986\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −2.00000 −0.123797
$$262$$ 0 0
$$263$$ −19.1231 −1.17918 −0.589591 0.807702i $$-0.700711\pi$$
−0.589591 + 0.807702i $$0.700711\pi$$
$$264$$ 0 0
$$265$$ −4.00000 −0.245718
$$266$$ 0 0
$$267$$ 17.7538 1.08651
$$268$$ 0 0
$$269$$ −13.3153 −0.811851 −0.405925 0.913906i $$-0.633051\pi$$
−0.405925 + 0.913906i $$0.633051\pi$$
$$270$$ 0 0
$$271$$ −24.0000 −1.45790 −0.728948 0.684569i $$-0.759990\pi$$
−0.728948 + 0.684569i $$0.759990\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 3.12311 0.188330
$$276$$ 0 0
$$277$$ 17.8078 1.06996 0.534982 0.844863i $$-0.320318\pi$$
0.534982 + 0.844863i $$0.320318\pi$$
$$278$$ 0 0
$$279$$ −1.36932 −0.0819789
$$280$$ 0 0
$$281$$ 5.12311 0.305619 0.152809 0.988256i $$-0.451168\pi$$
0.152809 + 0.988256i $$0.451168\pi$$
$$282$$ 0 0
$$283$$ −3.12311 −0.185649 −0.0928247 0.995682i $$-0.529590\pi$$
−0.0928247 + 0.995682i $$0.529590\pi$$
$$284$$ 0 0
$$285$$ 9.75379 0.577765
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 9.24621 0.543895
$$290$$ 0 0
$$291$$ 17.7538 1.04075
$$292$$ 0 0
$$293$$ 15.3693 0.897885 0.448943 0.893561i $$-0.351801\pi$$
0.448943 + 0.893561i $$0.351801\pi$$
$$294$$ 0 0
$$295$$ 20.4924 1.19311
$$296$$ 0 0
$$297$$ −17.3693 −1.00787
$$298$$ 0 0
$$299$$ 0.438447 0.0253561
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 19.1231 1.09859
$$304$$ 0 0
$$305$$ −8.49242 −0.486275
$$306$$ 0 0
$$307$$ 18.2462 1.04137 0.520683 0.853750i $$-0.325677\pi$$
0.520683 + 0.853750i $$0.325677\pi$$
$$308$$ 0 0
$$309$$ −22.2462 −1.26554
$$310$$ 0 0
$$311$$ −5.56155 −0.315367 −0.157683 0.987490i $$-0.550403\pi$$
−0.157683 + 0.987490i $$0.550403\pi$$
$$312$$ 0 0
$$313$$ 15.3693 0.868725 0.434363 0.900738i $$-0.356974\pi$$
0.434363 + 0.900738i $$0.356974\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −3.75379 −0.210834 −0.105417 0.994428i $$-0.533618\pi$$
−0.105417 + 0.994428i $$0.533618\pi$$
$$318$$ 0 0
$$319$$ −11.1231 −0.622774
$$320$$ 0 0
$$321$$ −17.3693 −0.969461
$$322$$ 0 0
$$323$$ −16.0000 −0.890264
$$324$$ 0 0
$$325$$ 0.438447 0.0243207
$$326$$ 0 0
$$327$$ −20.4924 −1.13323
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 31.4233 1.72718 0.863590 0.504194i $$-0.168211\pi$$
0.863590 + 0.504194i $$0.168211\pi$$
$$332$$ 0 0
$$333$$ −4.63068 −0.253760
$$334$$ 0 0
$$335$$ −6.24621 −0.341267
$$336$$ 0 0
$$337$$ −21.6155 −1.17747 −0.588736 0.808325i $$-0.700374\pi$$
−0.588736 + 0.808325i $$0.700374\pi$$
$$338$$ 0 0
$$339$$ 4.49242 0.243995
$$340$$ 0 0
$$341$$ −7.61553 −0.412404
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −3.12311 −0.168142
$$346$$ 0 0
$$347$$ −16.4924 −0.885360 −0.442680 0.896680i $$-0.645972\pi$$
−0.442680 + 0.896680i $$0.645972\pi$$
$$348$$ 0 0
$$349$$ 34.6847 1.85663 0.928314 0.371798i $$-0.121259\pi$$
0.928314 + 0.371798i $$0.121259\pi$$
$$350$$ 0 0
$$351$$ −2.43845 −0.130155
$$352$$ 0 0
$$353$$ −15.5616 −0.828258 −0.414129 0.910218i $$-0.635914\pi$$
−0.414129 + 0.910218i $$0.635914\pi$$
$$354$$ 0 0
$$355$$ −27.1231 −1.43954
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −23.6155 −1.24638 −0.623190 0.782071i $$-0.714164\pi$$
−0.623190 + 0.782071i $$0.714164\pi$$
$$360$$ 0 0
$$361$$ −9.24621 −0.486643
$$362$$ 0 0
$$363$$ 1.94602 0.102140
$$364$$ 0 0
$$365$$ −29.3693 −1.53726
$$366$$ 0 0
$$367$$ 14.2462 0.743646 0.371823 0.928304i $$-0.378733\pi$$
0.371823 + 0.928304i $$0.378733\pi$$
$$368$$ 0 0
$$369$$ −5.50758 −0.286713
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −10.4924 −0.543277 −0.271639 0.962399i $$-0.587566\pi$$
−0.271639 + 0.962399i $$0.587566\pi$$
$$374$$ 0 0
$$375$$ −18.7386 −0.967659
$$376$$ 0 0
$$377$$ −1.56155 −0.0804241
$$378$$ 0 0
$$379$$ −12.4924 −0.641693 −0.320846 0.947131i $$-0.603967\pi$$
−0.320846 + 0.947131i $$0.603967\pi$$
$$380$$ 0 0
$$381$$ −1.06913 −0.0547732
$$382$$ 0 0
$$383$$ −9.75379 −0.498395 −0.249198 0.968453i $$-0.580167\pi$$
−0.249198 + 0.968453i $$0.580167\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 4.49242 0.228363
$$388$$ 0 0
$$389$$ −23.3693 −1.18487 −0.592436 0.805618i $$-0.701834\pi$$
−0.592436 + 0.805618i $$0.701834\pi$$
$$390$$ 0 0
$$391$$ 5.12311 0.259087
$$392$$ 0 0
$$393$$ 5.17708 0.261149
$$394$$ 0 0
$$395$$ −6.24621 −0.314281
$$396$$ 0 0
$$397$$ −16.4384 −0.825022 −0.412511 0.910953i $$-0.635348\pi$$
−0.412511 + 0.910953i $$0.635348\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −28.2462 −1.41055 −0.705274 0.708935i $$-0.749176\pi$$
−0.705274 + 0.708935i $$0.749176\pi$$
$$402$$ 0 0
$$403$$ −1.06913 −0.0532572
$$404$$ 0 0
$$405$$ 14.0000 0.695666
$$406$$ 0 0
$$407$$ −25.7538 −1.27657
$$408$$ 0 0
$$409$$ −26.3002 −1.30046 −0.650230 0.759737i $$-0.725328\pi$$
−0.650230 + 0.759737i $$0.725328\pi$$
$$410$$ 0 0
$$411$$ −10.7386 −0.529698
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 28.4924 1.39864
$$416$$ 0 0
$$417$$ −5.17708 −0.253523
$$418$$ 0 0
$$419$$ −20.4924 −1.00112 −0.500560 0.865702i $$-0.666873\pi$$
−0.500560 + 0.865702i $$0.666873\pi$$
$$420$$ 0 0
$$421$$ −18.8769 −0.920004 −0.460002 0.887918i $$-0.652151\pi$$
−0.460002 + 0.887918i $$0.652151\pi$$
$$422$$ 0 0
$$423$$ −0.384472 −0.0186937
$$424$$ 0 0
$$425$$ 5.12311 0.248507
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −2.13826 −0.103236
$$430$$ 0 0
$$431$$ 4.49242 0.216392 0.108196 0.994130i $$-0.465493\pi$$
0.108196 + 0.994130i $$0.465493\pi$$
$$432$$ 0 0
$$433$$ 24.7386 1.18886 0.594431 0.804146i $$-0.297377\pi$$
0.594431 + 0.804146i $$0.297377\pi$$
$$434$$ 0 0
$$435$$ 11.1231 0.533312
$$436$$ 0 0
$$437$$ −3.12311 −0.149398
$$438$$ 0 0
$$439$$ 26.0540 1.24349 0.621744 0.783220i $$-0.286424\pi$$
0.621744 + 0.783220i $$0.286424\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −34.9309 −1.65962 −0.829808 0.558049i $$-0.811550\pi$$
−0.829808 + 0.558049i $$0.811550\pi$$
$$444$$ 0 0
$$445$$ 22.7386 1.07791
$$446$$ 0 0
$$447$$ 31.6155 1.49536
$$448$$ 0 0
$$449$$ 8.24621 0.389163 0.194581 0.980886i $$-0.437665\pi$$
0.194581 + 0.980886i $$0.437665\pi$$
$$450$$ 0 0
$$451$$ −30.6307 −1.44234
$$452$$ 0 0
$$453$$ 16.3002 0.765850
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 19.3693 0.906058 0.453029 0.891496i $$-0.350343\pi$$
0.453029 + 0.891496i $$0.350343\pi$$
$$458$$ 0 0
$$459$$ −28.4924 −1.32991
$$460$$ 0 0
$$461$$ −9.80776 −0.456793 −0.228397 0.973568i $$-0.573348\pi$$
−0.228397 + 0.973568i $$0.573348\pi$$
$$462$$ 0 0
$$463$$ −20.4924 −0.952364 −0.476182 0.879347i $$-0.657980\pi$$
−0.476182 + 0.879347i $$0.657980\pi$$
$$464$$ 0 0
$$465$$ 7.61553 0.353162
$$466$$ 0 0
$$467$$ −9.36932 −0.433560 −0.216780 0.976220i $$-0.569555\pi$$
−0.216780 + 0.976220i $$0.569555\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 32.9848 1.51986
$$472$$ 0 0
$$473$$ 24.9848 1.14880
$$474$$ 0 0
$$475$$ −3.12311 −0.143298
$$476$$ 0 0
$$477$$ −1.12311 −0.0514235
$$478$$ 0 0
$$479$$ 6.24621 0.285397 0.142698 0.989766i $$-0.454422\pi$$
0.142698 + 0.989766i $$0.454422\pi$$
$$480$$ 0 0
$$481$$ −3.61553 −0.164854
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 22.7386 1.03251
$$486$$ 0 0
$$487$$ 24.6847 1.11857 0.559284 0.828976i $$-0.311076\pi$$
0.559284 + 0.828976i $$0.311076\pi$$
$$488$$ 0 0
$$489$$ −29.5616 −1.33682
$$490$$ 0 0
$$491$$ −7.80776 −0.352359 −0.176180 0.984358i $$-0.556374\pi$$
−0.176180 + 0.984358i $$0.556374\pi$$
$$492$$ 0 0
$$493$$ −18.2462 −0.821768
$$494$$ 0 0
$$495$$ −3.50758 −0.157654
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 14.0540 0.629142 0.314571 0.949234i $$-0.398139\pi$$
0.314571 + 0.949234i $$0.398139\pi$$
$$500$$ 0 0
$$501$$ −24.9848 −1.11624
$$502$$ 0 0
$$503$$ 17.3693 0.774460 0.387230 0.921983i $$-0.373432\pi$$
0.387230 + 0.921983i $$0.373432\pi$$
$$504$$ 0 0
$$505$$ 24.4924 1.08990
$$506$$ 0 0
$$507$$ 20.0000 0.888231
$$508$$ 0 0
$$509$$ −38.3002 −1.69763 −0.848813 0.528693i $$-0.822682\pi$$
−0.848813 + 0.528693i $$0.822682\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 17.3693 0.766874
$$514$$ 0 0
$$515$$ −28.4924 −1.25553
$$516$$ 0 0
$$517$$ −2.13826 −0.0940406
$$518$$ 0 0
$$519$$ −15.6155 −0.685446
$$520$$ 0 0
$$521$$ 21.6155 0.946993 0.473497 0.880796i $$-0.342992\pi$$
0.473497 + 0.880796i $$0.342992\pi$$
$$522$$ 0 0
$$523$$ −22.2462 −0.972759 −0.486379 0.873748i $$-0.661683\pi$$
−0.486379 + 0.873748i $$0.661683\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −12.4924 −0.544178
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 5.75379 0.249693
$$532$$ 0 0
$$533$$ −4.30019 −0.186262
$$534$$ 0 0
$$535$$ −22.2462 −0.961788
$$536$$ 0 0
$$537$$ 5.17708 0.223408
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 7.06913 0.303926 0.151963 0.988386i $$-0.451441\pi$$
0.151963 + 0.988386i $$0.451441\pi$$
$$542$$ 0 0
$$543$$ 5.86174 0.251551
$$544$$ 0 0
$$545$$ −26.2462 −1.12426
$$546$$ 0 0
$$547$$ −26.5464 −1.13504 −0.567521 0.823359i $$-0.692097\pi$$
−0.567521 + 0.823359i $$0.692097\pi$$
$$548$$ 0 0
$$549$$ −2.38447 −0.101767
$$550$$ 0 0
$$551$$ 11.1231 0.473860
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 25.7538 1.09319
$$556$$ 0 0
$$557$$ −9.12311 −0.386558 −0.193279 0.981144i $$-0.561912\pi$$
−0.193279 + 0.981144i $$0.561912\pi$$
$$558$$ 0 0
$$559$$ 3.50758 0.148355
$$560$$ 0 0
$$561$$ −24.9848 −1.05486
$$562$$ 0 0
$$563$$ −22.2462 −0.937566 −0.468783 0.883313i $$-0.655307\pi$$
−0.468783 + 0.883313i $$0.655307\pi$$
$$564$$ 0 0
$$565$$ 5.75379 0.242064
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 8.24621 0.345699 0.172850 0.984948i $$-0.444703\pi$$
0.172850 + 0.984948i $$0.444703\pi$$
$$570$$ 0 0
$$571$$ −44.4924 −1.86195 −0.930975 0.365083i $$-0.881041\pi$$
−0.930975 + 0.365083i $$0.881041\pi$$
$$572$$ 0 0
$$573$$ −39.6155 −1.65496
$$574$$ 0 0
$$575$$ 1.00000 0.0417029
$$576$$ 0 0
$$577$$ 12.9309 0.538319 0.269160 0.963096i $$-0.413254\pi$$
0.269160 + 0.963096i $$0.413254\pi$$
$$578$$ 0 0
$$579$$ 0.684658 0.0284534
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −6.24621 −0.258692
$$584$$ 0 0
$$585$$ −0.492423 −0.0203592
$$586$$ 0 0
$$587$$ −14.0540 −0.580070 −0.290035 0.957016i $$-0.593667\pi$$
−0.290035 + 0.957016i $$0.593667\pi$$
$$588$$ 0 0
$$589$$ 7.61553 0.313792
$$590$$ 0 0
$$591$$ 26.4384 1.08753
$$592$$ 0 0
$$593$$ −4.73863 −0.194592 −0.0972962 0.995255i $$-0.531019\pi$$
−0.0972962 + 0.995255i $$0.531019\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 17.3693 0.710879
$$598$$ 0 0
$$599$$ 8.00000 0.326871 0.163436 0.986554i $$-0.447742\pi$$
0.163436 + 0.986554i $$0.447742\pi$$
$$600$$ 0 0
$$601$$ 18.1922 0.742077 0.371038 0.928618i $$-0.379002\pi$$
0.371038 + 0.928618i $$0.379002\pi$$
$$602$$ 0 0
$$603$$ −1.75379 −0.0714198
$$604$$ 0 0
$$605$$ 2.49242 0.101331
$$606$$ 0 0
$$607$$ −34.7386 −1.41000 −0.704999 0.709208i $$-0.749052\pi$$
−0.704999 + 0.709208i $$0.749052\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −0.300187 −0.0121442
$$612$$ 0 0
$$613$$ 46.1080 1.86228 0.931141 0.364659i $$-0.118814\pi$$
0.931141 + 0.364659i $$0.118814\pi$$
$$614$$ 0 0
$$615$$ 30.6307 1.23515
$$616$$ 0 0
$$617$$ −30.9848 −1.24740 −0.623701 0.781663i $$-0.714372\pi$$
−0.623701 + 0.781663i $$0.714372\pi$$
$$618$$ 0 0
$$619$$ 4.49242 0.180566 0.0902829 0.995916i $$-0.471223\pi$$
0.0902829 + 0.995916i $$0.471223\pi$$
$$620$$ 0 0
$$621$$ −5.56155 −0.223177
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ 15.2311 0.608270
$$628$$ 0 0
$$629$$ −42.2462 −1.68447
$$630$$ 0 0
$$631$$ 42.7386 1.70140 0.850699 0.525653i $$-0.176179\pi$$
0.850699 + 0.525653i $$0.176179\pi$$
$$632$$ 0 0
$$633$$ 6.24621 0.248265
$$634$$ 0 0
$$635$$ −1.36932 −0.0543397
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −7.61553 −0.301266
$$640$$ 0 0
$$641$$ 11.3693 0.449061 0.224531 0.974467i $$-0.427915\pi$$
0.224531 + 0.974467i $$0.427915\pi$$
$$642$$ 0 0
$$643$$ −1.36932 −0.0540006 −0.0270003 0.999635i $$-0.508596\pi$$
−0.0270003 + 0.999635i $$0.508596\pi$$
$$644$$ 0 0
$$645$$ −24.9848 −0.983777
$$646$$ 0 0
$$647$$ −24.3002 −0.955339 −0.477669 0.878540i $$-0.658518\pi$$
−0.477669 + 0.878540i $$0.658518\pi$$
$$648$$ 0 0
$$649$$ 32.0000 1.25611
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −12.0540 −0.471709 −0.235854 0.971788i $$-0.575789\pi$$
−0.235854 + 0.971788i $$0.575789\pi$$
$$654$$ 0 0
$$655$$ 6.63068 0.259082
$$656$$ 0 0
$$657$$ −8.24621 −0.321715
$$658$$ 0 0
$$659$$ −14.2462 −0.554954 −0.277477 0.960732i $$-0.589498\pi$$
−0.277477 + 0.960732i $$0.589498\pi$$
$$660$$ 0 0
$$661$$ −16.2462 −0.631904 −0.315952 0.948775i $$-0.602324\pi$$
−0.315952 + 0.948775i $$0.602324\pi$$
$$662$$ 0 0
$$663$$ −3.50758 −0.136223
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −3.56155 −0.137904
$$668$$ 0 0
$$669$$ −44.4924 −1.72018
$$670$$ 0 0
$$671$$ −13.2614 −0.511949
$$672$$ 0 0
$$673$$ −40.0540 −1.54397 −0.771984 0.635642i $$-0.780735\pi$$
−0.771984 + 0.635642i $$0.780735\pi$$
$$674$$ 0 0
$$675$$ −5.56155 −0.214064
$$676$$ 0 0
$$677$$ −26.9848 −1.03711 −0.518556 0.855044i $$-0.673530\pi$$
−0.518556 + 0.855044i $$0.673530\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −9.75379 −0.373766
$$682$$ 0 0
$$683$$ 28.6847 1.09759 0.548794 0.835958i $$-0.315087\pi$$
0.548794 + 0.835958i $$0.315087\pi$$
$$684$$ 0 0
$$685$$ −13.7538 −0.525505
$$686$$ 0 0
$$687$$ 23.2311 0.886320
$$688$$ 0 0
$$689$$ −0.876894 −0.0334070
$$690$$ 0 0
$$691$$ 44.9848 1.71130 0.855652 0.517551i $$-0.173156\pi$$
0.855652 + 0.517551i $$0.173156\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −6.63068 −0.251516
$$696$$ 0 0
$$697$$ −50.2462 −1.90321
$$698$$ 0 0
$$699$$ 25.0691 0.948202
$$700$$ 0 0
$$701$$ −27.8617 −1.05232 −0.526162 0.850385i $$-0.676369\pi$$
−0.526162 + 0.850385i $$0.676369\pi$$
$$702$$ 0 0
$$703$$ 25.7538 0.971323
$$704$$ 0 0
$$705$$ 2.13826 0.0805316
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −12.6307 −0.474355 −0.237178 0.971466i $$-0.576222\pi$$
−0.237178 + 0.971466i $$0.576222\pi$$
$$710$$ 0 0
$$711$$ −1.75379 −0.0657722
$$712$$ 0 0
$$713$$ −2.43845 −0.0913206
$$714$$ 0 0
$$715$$ −2.73863 −0.102419
$$716$$ 0 0
$$717$$ −40.6847 −1.51940
$$718$$ 0 0
$$719$$ 28.4924 1.06259 0.531294 0.847187i $$-0.321706\pi$$
0.531294 + 0.847187i $$0.321706\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 10.1383 0.377046
$$724$$ 0 0
$$725$$ −3.56155 −0.132273
$$726$$ 0 0
$$727$$ 14.6307 0.542622 0.271311 0.962492i $$-0.412543\pi$$
0.271311 + 0.962492i $$0.412543\pi$$
$$728$$ 0 0
$$729$$ 29.9848 1.11055
$$730$$ 0 0
$$731$$ 40.9848 1.51588
$$732$$ 0 0
$$733$$ −24.6307 −0.909755 −0.454878 0.890554i $$-0.650317\pi$$
−0.454878 + 0.890554i $$0.650317\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −9.75379 −0.359285
$$738$$ 0 0
$$739$$ 12.6847 0.466613 0.233306 0.972403i $$-0.425046\pi$$
0.233306 + 0.972403i $$0.425046\pi$$
$$740$$ 0 0
$$741$$ 2.13826 0.0785510
$$742$$ 0 0
$$743$$ 17.7538 0.651323 0.325662 0.945486i $$-0.394413\pi$$
0.325662 + 0.945486i $$0.394413\pi$$
$$744$$ 0 0
$$745$$ 40.4924 1.48353
$$746$$ 0 0
$$747$$ 8.00000 0.292705
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −24.9848 −0.911710 −0.455855 0.890054i $$-0.650666\pi$$
−0.455855 + 0.890054i $$0.650666\pi$$
$$752$$ 0 0
$$753$$ −9.75379 −0.355448
$$754$$ 0 0
$$755$$ 20.8769 0.759788
$$756$$ 0 0
$$757$$ −34.4924 −1.25365 −0.626824 0.779161i $$-0.715646\pi$$
−0.626824 + 0.779161i $$0.715646\pi$$
$$758$$ 0 0
$$759$$ −4.87689 −0.177020
$$760$$ 0 0
$$761$$ 30.6847 1.11232 0.556159 0.831076i $$-0.312275\pi$$
0.556159 + 0.831076i $$0.312275\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −5.75379 −0.208029
$$766$$ 0 0
$$767$$ 4.49242 0.162212
$$768$$ 0 0
$$769$$ 6.00000 0.216366 0.108183 0.994131i $$-0.465497\pi$$
0.108183 + 0.994131i $$0.465497\pi$$
$$770$$ 0 0
$$771$$ −8.30019 −0.298924
$$772$$ 0 0
$$773$$ −27.3693 −0.984406 −0.492203 0.870480i $$-0.663808\pi$$
−0.492203 + 0.870480i $$0.663808\pi$$
$$774$$ 0 0
$$775$$ −2.43845 −0.0875916
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 30.6307 1.09746
$$780$$ 0 0
$$781$$ −42.3542 −1.51555
$$782$$ 0 0
$$783$$ 19.8078 0.707872
$$784$$ 0 0
$$785$$ 42.2462 1.50783
$$786$$ 0 0
$$787$$ 9.75379 0.347685 0.173843 0.984773i $$-0.444382\pi$$
0.173843 + 0.984773i $$0.444382\pi$$
$$788$$ 0 0
$$789$$ 29.8617 1.06311
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −1.86174 −0.0661123
$$794$$ 0 0
$$795$$ 6.24621 0.221530
$$796$$ 0 0
$$797$$ 4.24621 0.150409 0.0752043 0.997168i $$-0.476039\pi$$
0.0752043 + 0.997168i $$0.476039\pi$$
$$798$$ 0 0
$$799$$ −3.50758 −0.124089
$$800$$ 0 0
$$801$$ 6.38447 0.225584
$$802$$ 0 0
$$803$$ −45.8617 −1.61843
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 20.7926 0.731935
$$808$$ 0 0
$$809$$ 26.0000 0.914111 0.457056 0.889438i $$-0.348904\pi$$
0.457056 + 0.889438i $$0.348904\pi$$
$$810$$ 0 0
$$811$$ −5.06913 −0.178001 −0.0890006 0.996032i $$-0.528367\pi$$
−0.0890006 + 0.996032i $$0.528367\pi$$
$$812$$ 0 0
$$813$$ 37.4773 1.31439
$$814$$ 0 0
$$815$$ −37.8617 −1.32624
$$816$$ 0 0
$$817$$ −24.9848 −0.874109
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 24.7386 0.863384 0.431692 0.902021i $$-0.357917\pi$$
0.431692 + 0.902021i $$0.357917\pi$$
$$822$$ 0 0
$$823$$ 53.5616 1.86704 0.933519 0.358527i $$-0.116721\pi$$
0.933519 + 0.358527i $$0.116721\pi$$
$$824$$ 0 0
$$825$$ −4.87689 −0.169792
$$826$$ 0 0
$$827$$ −28.4924 −0.990779 −0.495389 0.868671i $$-0.664975\pi$$
−0.495389 + 0.868671i $$0.664975\pi$$
$$828$$ 0 0
$$829$$ 3.75379 0.130374 0.0651872 0.997873i $$-0.479236\pi$$
0.0651872 + 0.997873i $$0.479236\pi$$
$$830$$ 0 0
$$831$$ −27.8078 −0.964641
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −32.0000 −1.10741
$$836$$ 0 0
$$837$$ 13.5616 0.468756
$$838$$ 0 0
$$839$$ −33.7538 −1.16531 −0.582655 0.812720i $$-0.697986\pi$$
−0.582655 + 0.812720i $$0.697986\pi$$
$$840$$ 0 0
$$841$$ −16.3153 −0.562598
$$842$$ 0 0
$$843$$ −8.00000 −0.275535
$$844$$ 0 0
$$845$$ 25.6155 0.881201
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 4.87689 0.167375
$$850$$ 0 0
$$851$$ −8.24621 −0.282676
$$852$$ 0 0
$$853$$ −30.9848 −1.06090 −0.530450 0.847716i $$-0.677977\pi$$
−0.530450 + 0.847716i $$0.677977\pi$$
$$854$$ 0 0
$$855$$ 3.50758 0.119957
$$856$$ 0 0
$$857$$ −12.4384 −0.424889 −0.212445 0.977173i $$-0.568143\pi$$
−0.212445 + 0.977173i $$0.568143\pi$$
$$858$$ 0 0
$$859$$ −54.0540 −1.84430 −0.922149 0.386835i $$-0.873568\pi$$
−0.922149 + 0.386835i $$0.873568\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 37.1771 1.26552 0.632761 0.774347i $$-0.281921\pi$$
0.632761 + 0.774347i $$0.281921\pi$$
$$864$$ 0 0
$$865$$ −20.0000 −0.680020
$$866$$ 0 0
$$867$$ −14.4384 −0.490355
$$868$$ 0 0
$$869$$ −9.75379 −0.330875
$$870$$ 0 0
$$871$$ −1.36932 −0.0463975
$$872$$ 0 0
$$873$$ 6.38447 0.216082
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −34.9848 −1.18135 −0.590677 0.806908i $$-0.701139\pi$$
−0.590677 + 0.806908i $$0.701139\pi$$
$$878$$ 0 0
$$879$$ −24.0000 −0.809500
$$880$$ 0 0
$$881$$ −13.1231 −0.442129 −0.221064 0.975259i $$-0.570953\pi$$
−0.221064 + 0.975259i $$0.570953\pi$$
$$882$$ 0 0
$$883$$ −28.9848 −0.975418 −0.487709 0.873006i $$-0.662167\pi$$
−0.487709 + 0.873006i $$0.662167\pi$$
$$884$$ 0 0
$$885$$ −32.0000 −1.07567
$$886$$ 0 0
$$887$$ −7.31534 −0.245625 −0.122813 0.992430i $$-0.539191\pi$$
−0.122813 + 0.992430i $$0.539191\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 21.8617 0.732396
$$892$$ 0 0
$$893$$ 2.13826 0.0715542
$$894$$ 0 0
$$895$$ 6.63068 0.221639
$$896$$ 0 0
$$897$$ −0.684658 −0.0228601
$$898$$ 0 0
$$899$$ 8.68466 0.289650
$$900$$ 0 0
$$901$$ −10.2462 −0.341351
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 7.50758 0.249560
$$906$$ 0 0
$$907$$ 51.1231 1.69751 0.848757 0.528782i $$-0.177351\pi$$
0.848757 + 0.528782i $$0.177351\pi$$
$$908$$ 0 0
$$909$$ 6.87689 0.228092
$$910$$ 0 0
$$911$$ −28.8769 −0.956734 −0.478367 0.878160i $$-0.658771\pi$$
−0.478367 + 0.878160i $$0.658771\pi$$
$$912$$ 0 0
$$913$$ 44.4924 1.47248
$$914$$ 0 0
$$915$$ 13.2614 0.438407
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 54.2462 1.78942 0.894709 0.446650i $$-0.147383\pi$$
0.894709 + 0.446650i $$0.147383\pi$$
$$920$$ 0 0
$$921$$ −28.4924 −0.938857
$$922$$ 0 0
$$923$$ −5.94602 −0.195716
$$924$$ 0 0
$$925$$ −8.24621 −0.271134
$$926$$ 0 0
$$927$$ −8.00000 −0.262754
$$928$$ 0 0
$$929$$ −14.1922 −0.465632 −0.232816 0.972521i $$-0.574794\pi$$
−0.232816 + 0.972521i $$0.574794\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 8.68466 0.284323
$$934$$ 0 0
$$935$$ −32.0000 −1.04651
$$936$$ 0 0
$$937$$ −32.2462 −1.05344 −0.526719 0.850040i $$-0.676578\pi$$
−0.526719 + 0.850040i $$0.676578\pi$$
$$938$$ 0 0
$$939$$ −24.0000 −0.783210
$$940$$ 0 0
$$941$$ −30.8769 −1.00656 −0.503279 0.864124i $$-0.667873\pi$$
−0.503279 + 0.864124i $$0.667873\pi$$
$$942$$ 0 0
$$943$$ −9.80776 −0.319385
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 1.56155 0.0507436 0.0253718 0.999678i $$-0.491923\pi$$
0.0253718 + 0.999678i $$0.491923\pi$$
$$948$$ 0 0
$$949$$ −6.43845 −0.209001
$$950$$ 0 0
$$951$$ 5.86174 0.190080
$$952$$ 0 0
$$953$$ 27.7538 0.899033 0.449517 0.893272i $$-0.351596\pi$$
0.449517 + 0.893272i $$0.351596\pi$$
$$954$$ 0 0
$$955$$ −50.7386 −1.64186
$$956$$ 0 0
$$957$$ 17.3693 0.561470
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −25.0540 −0.808193
$$962$$ 0 0
$$963$$ −6.24621 −0.201281
$$964$$ 0 0
$$965$$ 0.876894 0.0282282
$$966$$ 0 0
$$967$$ −2.05398 −0.0660514 −0.0330257 0.999455i $$-0.510514\pi$$
−0.0330257 + 0.999455i $$0.510514\pi$$
$$968$$ 0 0
$$969$$ 24.9848 0.802629
$$970$$ 0 0
$$971$$ −6.63068 −0.212789 −0.106394 0.994324i $$-0.533931\pi$$
−0.106394 + 0.994324i $$0.533931\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ −0.684658 −0.0219266
$$976$$ 0 0
$$977$$ 25.2311 0.807213 0.403607 0.914933i $$-0.367756\pi$$
0.403607 + 0.914933i $$0.367756\pi$$
$$978$$ 0 0
$$979$$ 35.5076 1.13483
$$980$$ 0 0
$$981$$ −7.36932 −0.235284
$$982$$ 0 0
$$983$$ 52.1080 1.66199 0.830993 0.556283i $$-0.187773\pi$$
0.830993 + 0.556283i $$0.187773\pi$$
$$984$$ 0 0
$$985$$ 33.8617 1.07892
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 8.00000 0.254385
$$990$$ 0 0
$$991$$ −56.9848 −1.81018 −0.905092 0.425217i $$-0.860198\pi$$
−0.905092 + 0.425217i $$0.860198\pi$$
$$992$$ 0 0
$$993$$ −49.0691 −1.55716
$$994$$ 0 0
$$995$$ 22.2462 0.705252
$$996$$ 0 0
$$997$$ −14.0000 −0.443384 −0.221692 0.975117i $$-0.571158\pi$$
−0.221692 + 0.975117i $$0.571158\pi$$
$$998$$ 0 0
$$999$$ 45.8617 1.45100
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 9016.2.a.w.1.1 2
7.6 odd 2 184.2.a.e.1.2 2
21.20 even 2 1656.2.a.j.1.2 2
28.27 even 2 368.2.a.i.1.1 2
35.13 even 4 4600.2.e.o.4049.3 4
35.27 even 4 4600.2.e.o.4049.2 4
35.34 odd 2 4600.2.a.s.1.1 2
56.13 odd 2 1472.2.a.u.1.1 2
56.27 even 2 1472.2.a.p.1.2 2
84.83 odd 2 3312.2.a.t.1.1 2
140.139 even 2 9200.2.a.br.1.2 2
161.160 even 2 4232.2.a.o.1.2 2
644.643 odd 2 8464.2.a.bd.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
184.2.a.e.1.2 2 7.6 odd 2
368.2.a.i.1.1 2 28.27 even 2
1472.2.a.p.1.2 2 56.27 even 2
1472.2.a.u.1.1 2 56.13 odd 2
1656.2.a.j.1.2 2 21.20 even 2
3312.2.a.t.1.1 2 84.83 odd 2
4232.2.a.o.1.2 2 161.160 even 2
4600.2.a.s.1.1 2 35.34 odd 2
4600.2.e.o.4049.2 4 35.27 even 4
4600.2.e.o.4049.3 4 35.13 even 4
8464.2.a.bd.1.1 2 644.643 odd 2
9016.2.a.w.1.1 2 1.1 even 1 trivial
9200.2.a.br.1.2 2 140.139 even 2