# Properties

 Label 1656.2.a.j.1.1 Level $1656$ Weight $2$ Character 1656.1 Self dual yes Analytic conductor $13.223$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1656 = 2^{3} \cdot 3^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1656.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$13.2232265747$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{17})$$ Defining polynomial: $$x^{2} - x - 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ 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 $$\chi$$ $$=$$ 1656.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{5} +O(q^{10})$$ $$q-2.00000 q^{5} -5.12311 q^{11} +4.56155 q^{13} +3.12311 q^{17} +5.12311 q^{19} +1.00000 q^{23} -1.00000 q^{25} +0.561553 q^{29} -6.56155 q^{31} -8.24621 q^{37} -10.8078 q^{41} -8.00000 q^{43} -11.6847 q^{47} -7.00000 q^{49} -2.00000 q^{53} +10.2462 q^{55} +6.24621 q^{59} +12.2462 q^{61} -9.12311 q^{65} -5.12311 q^{67} -9.43845 q^{71} -2.31534 q^{73} -5.12311 q^{79} +2.24621 q^{83} -6.24621 q^{85} +13.3693 q^{89} -10.2462 q^{95} -13.3693 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 4 q^{5} + O(q^{10})$$ $$2 q - 4 q^{5} - 2 q^{11} + 5 q^{13} - 2 q^{17} + 2 q^{19} + 2 q^{23} - 2 q^{25} - 3 q^{29} - 9 q^{31} - q^{41} - 16 q^{43} - 11 q^{47} - 14 q^{49} - 4 q^{53} + 4 q^{55} - 4 q^{59} + 8 q^{61} - 10 q^{65} - 2 q^{67} - 23 q^{71} - 17 q^{73} - 2 q^{79} - 12 q^{83} + 4 q^{85} + 2 q^{89} - 4 q^{95} - 2 q^{97} + O(q^{100})$$

## 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
$$3$$ 0 0
$$4$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −5.12311 −1.54467 −0.772337 0.635213i $$-0.780912\pi$$
−0.772337 + 0.635213i $$0.780912\pi$$
$$12$$ 0 0
$$13$$ 4.56155 1.26515 0.632574 0.774500i $$-0.281999\pi$$
0.632574 + 0.774500i $$0.281999\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 3.12311 0.757464 0.378732 0.925506i $$-0.376360\pi$$
0.378732 + 0.925506i $$0.376360\pi$$
$$18$$ 0 0
$$19$$ 5.12311 1.17532 0.587661 0.809108i $$-0.300049\pi$$
0.587661 + 0.809108i $$0.300049\pi$$
$$20$$ 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
$$29$$ 0.561553 0.104278 0.0521389 0.998640i $$-0.483396\pi$$
0.0521389 + 0.998640i $$0.483396\pi$$
$$30$$ 0 0
$$31$$ −6.56155 −1.17849 −0.589245 0.807955i $$-0.700575\pi$$
−0.589245 + 0.807955i $$0.700575\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −8.24621 −1.35567 −0.677834 0.735215i $$-0.737081\pi$$
−0.677834 + 0.735215i $$0.737081\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −10.8078 −1.68789 −0.843945 0.536430i $$-0.819772\pi$$
−0.843945 + 0.536430i $$0.819772\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −11.6847 −1.70438 −0.852191 0.523230i $$-0.824727\pi$$
−0.852191 + 0.523230i $$0.824727\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ 0 0
$$55$$ 10.2462 1.38160
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 6.24621 0.813187 0.406594 0.913609i $$-0.366716\pi$$
0.406594 + 0.913609i $$0.366716\pi$$
$$60$$ 0 0
$$61$$ 12.2462 1.56797 0.783983 0.620782i $$-0.213185\pi$$
0.783983 + 0.620782i $$0.213185\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −9.12311 −1.13158
$$66$$ 0 0
$$67$$ −5.12311 −0.625887 −0.312943 0.949772i $$-0.601315\pi$$
−0.312943 + 0.949772i $$0.601315\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −9.43845 −1.12014 −0.560069 0.828446i $$-0.689225\pi$$
−0.560069 + 0.828446i $$0.689225\pi$$
$$72$$ 0 0
$$73$$ −2.31534 −0.270990 −0.135495 0.990778i $$-0.543263\pi$$
−0.135495 + 0.990778i $$0.543263\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −5.12311 −0.576394 −0.288197 0.957571i $$-0.593056\pi$$
−0.288197 + 0.957571i $$0.593056\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 2.24621 0.246554 0.123277 0.992372i $$-0.460660\pi$$
0.123277 + 0.992372i $$0.460660\pi$$
$$84$$ 0 0
$$85$$ −6.24621 −0.677497
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 13.3693 1.41714 0.708572 0.705638i $$-0.249340\pi$$
0.708572 + 0.705638i $$0.249340\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −10.2462 −1.05124
$$96$$ 0 0
$$97$$ −13.3693 −1.35745 −0.678724 0.734393i $$-0.737467\pi$$
−0.678724 + 0.734393i $$0.737467\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 4.24621 0.422514 0.211257 0.977431i $$-0.432244\pi$$
0.211257 + 0.977431i $$0.432244\pi$$
$$102$$ 0 0
$$103$$ 2.24621 0.221326 0.110663 0.993858i $$-0.464703\pi$$
0.110663 + 0.993858i $$0.464703\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −2.87689 −0.278120 −0.139060 0.990284i $$-0.544408\pi$$
−0.139060 + 0.990284i $$0.544408\pi$$
$$108$$ 0 0
$$109$$ 4.87689 0.467122 0.233561 0.972342i $$-0.424962\pi$$
0.233561 + 0.972342i $$0.424962\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 11.1231 1.04637 0.523187 0.852218i $$-0.324743\pi$$
0.523187 + 0.852218i $$0.324743\pi$$
$$114$$ 0 0
$$115$$ −2.00000 −0.186501
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 15.2462 1.38602
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ −11.6847 −1.03685 −0.518423 0.855124i $$-0.673481\pi$$
−0.518423 + 0.855124i $$0.673481\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −15.6847 −1.37037 −0.685187 0.728367i $$-0.740280\pi$$
−0.685187 + 0.728367i $$0.740280\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −15.1231 −1.29205 −0.646027 0.763315i $$-0.723571\pi$$
−0.646027 + 0.763315i $$0.723571\pi$$
$$138$$ 0 0
$$139$$ −15.6847 −1.33036 −0.665178 0.746685i $$-0.731644\pi$$
−0.665178 + 0.746685i $$0.731644\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −23.3693 −1.95424
$$144$$ 0 0
$$145$$ −1.12311 −0.0932688
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 3.75379 0.307522 0.153761 0.988108i $$-0.450861\pi$$
0.153761 + 0.988108i $$0.450861\pi$$
$$150$$ 0 0
$$151$$ −14.5616 −1.18500 −0.592501 0.805570i $$-0.701859\pi$$
−0.592501 + 0.805570i $$0.701859\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 13.1231 1.05407
$$156$$ 0 0
$$157$$ 12.8769 1.02769 0.513844 0.857884i $$-0.328221\pi$$
0.513844 + 0.857884i $$0.328221\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −9.93087 −0.777846 −0.388923 0.921270i $$-0.627153\pi$$
−0.388923 + 0.921270i $$0.627153\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 16.0000 1.23812 0.619059 0.785345i $$-0.287514\pi$$
0.619059 + 0.785345i $$0.287514\pi$$
$$168$$ 0 0
$$169$$ 7.80776 0.600597
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 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
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 15.6847 1.17233 0.586163 0.810193i $$-0.300638\pi$$
0.586163 + 0.810193i $$0.300638\pi$$
$$180$$ 0 0
$$181$$ 20.2462 1.50489 0.752445 0.658656i $$-0.228875\pi$$
0.752445 + 0.658656i $$0.228875\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 16.4924 1.21255
$$186$$ 0 0
$$187$$ −16.0000 −1.17004
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −0.630683 −0.0456346 −0.0228173 0.999740i $$-0.507264\pi$$
−0.0228173 + 0.999740i $$0.507264\pi$$
$$192$$ 0 0
$$193$$ −4.56155 −0.328348 −0.164174 0.986431i $$-0.552496\pi$$
−0.164174 + 0.986431i $$0.552496\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −11.9309 −0.850039 −0.425020 0.905184i $$-0.639733\pi$$
−0.425020 + 0.905184i $$0.639733\pi$$
$$198$$ 0 0
$$199$$ 2.87689 0.203938 0.101969 0.994788i $$-0.467486\pi$$
0.101969 + 0.994788i $$0.467486\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 21.6155 1.50969
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −26.2462 −1.81549
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 16.0000 1.09119
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 14.2462 0.958304
$$222$$ 0 0
$$223$$ 4.49242 0.300835 0.150417 0.988623i $$-0.451938\pi$$
0.150417 + 0.988623i $$0.451938\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −10.2462 −0.680065 −0.340032 0.940414i $$-0.610438\pi$$
−0.340032 + 0.940414i $$0.610438\pi$$
$$228$$ 0 0
$$229$$ 23.1231 1.52802 0.764009 0.645206i $$-0.223228\pi$$
0.764009 + 0.645206i $$0.223228\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −21.0540 −1.37929 −0.689646 0.724147i $$-0.742234\pi$$
−0.689646 + 0.724147i $$0.742234\pi$$
$$234$$ 0 0
$$235$$ 23.3693 1.52445
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 11.0540 0.715022 0.357511 0.933909i $$-0.383625\pi$$
0.357511 + 0.933909i $$0.383625\pi$$
$$240$$ 0 0
$$241$$ −26.4924 −1.70653 −0.853263 0.521480i $$-0.825380\pi$$
−0.853263 + 0.521480i $$0.825380\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 14.0000 0.894427
$$246$$ 0 0
$$247$$ 23.3693 1.48695
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −10.2462 −0.646735 −0.323368 0.946273i $$-0.604815\pi$$
−0.323368 + 0.946273i $$0.604815\pi$$
$$252$$ 0 0
$$253$$ −5.12311 −0.322087
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 17.6847 1.10314 0.551569 0.834129i $$-0.314029\pi$$
0.551569 + 0.834129i $$0.314029\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 10.8769 0.670698 0.335349 0.942094i $$-0.391146\pi$$
0.335349 + 0.942094i $$0.391146\pi$$
$$264$$ 0 0
$$265$$ 4.00000 0.245718
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −25.6847 −1.56602 −0.783011 0.622008i $$-0.786317\pi$$
−0.783011 + 0.622008i $$0.786317\pi$$
$$270$$ 0 0
$$271$$ 24.0000 1.45790 0.728948 0.684569i $$-0.240010\pi$$
0.728948 + 0.684569i $$0.240010\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 5.12311 0.308935
$$276$$ 0 0
$$277$$ −2.80776 −0.168702 −0.0843511 0.996436i $$-0.526882\pi$$
−0.0843511 + 0.996436i $$0.526882\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 3.12311 0.186309 0.0931544 0.995652i $$-0.470305\pi$$
0.0931544 + 0.995652i $$0.470305\pi$$
$$282$$ 0 0
$$283$$ −5.12311 −0.304537 −0.152269 0.988339i $$-0.548658\pi$$
−0.152269 + 0.988339i $$0.548658\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −7.24621 −0.426248
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −9.36932 −0.547361 −0.273681 0.961821i $$-0.588241\pi$$
−0.273681 + 0.961821i $$0.588241\pi$$
$$294$$ 0 0
$$295$$ −12.4924 −0.727337
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 4.56155 0.263801
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −24.4924 −1.40243
$$306$$ 0 0
$$307$$ −1.75379 −0.100094 −0.0500470 0.998747i $$-0.515937\pi$$
−0.0500470 + 0.998747i $$0.515937\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.43845 −0.0815669 −0.0407834 0.999168i $$-0.512985\pi$$
−0.0407834 + 0.999168i $$0.512985\pi$$
$$312$$ 0 0
$$313$$ 9.36932 0.529585 0.264793 0.964305i $$-0.414697\pi$$
0.264793 + 0.964305i $$0.414697\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 20.2462 1.13714 0.568570 0.822635i $$-0.307497\pi$$
0.568570 + 0.822635i $$0.307497\pi$$
$$318$$ 0 0
$$319$$ −2.87689 −0.161075
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 16.0000 0.890264
$$324$$ 0 0
$$325$$ −4.56155 −0.253029
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −30.4233 −1.67222 −0.836108 0.548565i $$-0.815174\pi$$
−0.836108 + 0.548565i $$0.815174\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 10.2462 0.559810
$$336$$ 0 0
$$337$$ 19.6155 1.06853 0.534263 0.845318i $$-0.320589\pi$$
0.534263 + 0.845318i $$0.320589\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 33.6155 1.82038
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −16.4924 −0.885360 −0.442680 0.896680i $$-0.645972\pi$$
−0.442680 + 0.896680i $$0.645972\pi$$
$$348$$ 0 0
$$349$$ −22.3153 −1.19451 −0.597256 0.802050i $$-0.703743\pi$$
−0.597256 + 0.802050i $$0.703743\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −11.4384 −0.608807 −0.304404 0.952543i $$-0.598457\pi$$
−0.304404 + 0.952543i $$0.598457\pi$$
$$354$$ 0 0
$$355$$ 18.8769 1.00188
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −17.6155 −0.929712 −0.464856 0.885386i $$-0.653894\pi$$
−0.464856 + 0.885386i $$0.653894\pi$$
$$360$$ 0 0
$$361$$ 7.24621 0.381380
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 4.63068 0.242381
$$366$$ 0 0
$$367$$ 2.24621 0.117251 0.0586256 0.998280i $$-0.481328\pi$$
0.0586256 + 0.998280i $$0.481328\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 22.4924 1.16461 0.582307 0.812969i $$-0.302150\pi$$
0.582307 + 0.812969i $$0.302150\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 2.56155 0.131927
$$378$$ 0 0
$$379$$ 20.4924 1.05263 0.526313 0.850291i $$-0.323574\pi$$
0.526313 + 0.850291i $$0.323574\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −26.2462 −1.34112 −0.670559 0.741856i $$-0.733946\pi$$
−0.670559 + 0.741856i $$0.733946\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1.36932 −0.0694271 −0.0347136 0.999397i $$-0.511052\pi$$
−0.0347136 + 0.999397i $$0.511052\pi$$
$$390$$ 0 0
$$391$$ 3.12311 0.157942
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 10.2462 0.515543
$$396$$ 0 0
$$397$$ 20.5616 1.03195 0.515977 0.856602i $$-0.327429\pi$$
0.515977 + 0.856602i $$0.327429\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 11.7538 0.586956 0.293478 0.955966i $$-0.405187\pi$$
0.293478 + 0.955966i $$0.405187\pi$$
$$402$$ 0 0
$$403$$ −29.9309 −1.49096
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 42.2462 2.09407
$$408$$ 0 0
$$409$$ −27.3002 −1.34991 −0.674954 0.737860i $$-0.735836\pi$$
−0.674954 + 0.737860i $$0.735836\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −4.49242 −0.220524
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 12.4924 0.610295 0.305147 0.952305i $$-0.401294\pi$$
0.305147 + 0.952305i $$0.401294\pi$$
$$420$$ 0 0
$$421$$ −27.1231 −1.32190 −0.660950 0.750430i $$-0.729846\pi$$
−0.660950 + 0.750430i $$0.729846\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −3.12311 −0.151493
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 28.4924 1.37243 0.686216 0.727398i $$-0.259271\pi$$
0.686216 + 0.727398i $$0.259271\pi$$
$$432$$ 0 0
$$433$$ 24.7386 1.18886 0.594431 0.804146i $$-0.297377\pi$$
0.594431 + 0.804146i $$0.297377\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 5.12311 0.245071
$$438$$ 0 0
$$439$$ 11.0540 0.527577 0.263789 0.964580i $$-0.415028\pi$$
0.263789 + 0.964580i $$0.415028\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 6.06913 0.288353 0.144177 0.989552i $$-0.453947\pi$$
0.144177 + 0.989552i $$0.453947\pi$$
$$444$$ 0 0
$$445$$ −26.7386 −1.26753
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 8.24621 0.389163 0.194581 0.980886i $$-0.437665\pi$$
0.194581 + 0.980886i $$0.437665\pi$$
$$450$$ 0 0
$$451$$ 55.3693 2.60724
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.36932 −0.251166 −0.125583 0.992083i $$-0.540080\pi$$
−0.125583 + 0.992083i $$0.540080\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 10.8078 0.503368 0.251684 0.967809i $$-0.419016\pi$$
0.251684 + 0.967809i $$0.419016\pi$$
$$462$$ 0 0
$$463$$ 12.4924 0.580572 0.290286 0.956940i $$-0.406250\pi$$
0.290286 + 0.956940i $$0.406250\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 15.3693 0.711207 0.355604 0.934637i $$-0.384275\pi$$
0.355604 + 0.934637i $$0.384275\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 40.9848 1.88449
$$474$$ 0 0
$$475$$ −5.12311 −0.235064
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −10.2462 −0.468161 −0.234081 0.972217i $$-0.575208\pi$$
−0.234081 + 0.972217i $$0.575208\pi$$
$$480$$ 0 0
$$481$$ −37.6155 −1.71512
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 26.7386 1.21414
$$486$$ 0 0
$$487$$ 12.3153 0.558061 0.279031 0.960282i $$-0.409987\pi$$
0.279031 + 0.960282i $$0.409987\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −12.8078 −0.578006 −0.289003 0.957328i $$-0.593324\pi$$
−0.289003 + 0.957328i $$0.593324\pi$$
$$492$$ 0 0
$$493$$ 1.75379 0.0789867
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −23.0540 −1.03204 −0.516019 0.856577i $$-0.672587\pi$$
−0.516019 + 0.856577i $$0.672587\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −7.36932 −0.328582 −0.164291 0.986412i $$-0.552534\pi$$
−0.164291 + 0.986412i $$0.552534\pi$$
$$504$$ 0 0
$$505$$ −8.49242 −0.377908
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 15.3002 0.678169 0.339084 0.940756i $$-0.389883\pi$$
0.339084 + 0.940756i $$0.389883\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −4.49242 −0.197960
$$516$$ 0 0
$$517$$ 59.8617 2.63272
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −19.6155 −0.859372 −0.429686 0.902978i $$-0.641376\pi$$
−0.429686 + 0.902978i $$0.641376\pi$$
$$522$$ 0 0
$$523$$ 5.75379 0.251596 0.125798 0.992056i $$-0.459851\pi$$
0.125798 + 0.992056i $$0.459851\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −20.4924 −0.892664
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −49.3002 −2.13543
$$534$$ 0 0
$$535$$ 5.75379 0.248758
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 35.8617 1.54467
$$540$$ 0 0
$$541$$ 35.9309 1.54479 0.772394 0.635143i $$-0.219059\pi$$
0.772394 + 0.635143i $$0.219059\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −9.75379 −0.417806
$$546$$ 0 0
$$547$$ 43.5464 1.86191 0.930955 0.365135i $$-0.118977\pi$$
0.930955 + 0.365135i $$0.118977\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 2.87689 0.122560
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0.876894 0.0371552 0.0185776 0.999827i $$-0.494086\pi$$
0.0185776 + 0.999827i $$0.494086\pi$$
$$558$$ 0 0
$$559$$ −36.4924 −1.54347
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −5.75379 −0.242493 −0.121247 0.992622i $$-0.538689\pi$$
−0.121247 + 0.992622i $$0.538689\pi$$
$$564$$ 0 0
$$565$$ −22.2462 −0.935905
$$566$$ 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
$$571$$ −11.5076 −0.481577 −0.240789 0.970578i $$-0.577406\pi$$
−0.240789 + 0.970578i $$0.577406\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ 15.9309 0.663211 0.331605 0.943418i $$-0.392410\pi$$
0.331605 + 0.943418i $$0.392410\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 10.2462 0.424355
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 23.0540 0.951539 0.475770 0.879570i $$-0.342170\pi$$
0.475770 + 0.879570i $$0.342170\pi$$
$$588$$ 0 0
$$589$$ −33.6155 −1.38510
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 44.7386 1.83720 0.918598 0.395194i $$-0.129323\pi$$
0.918598 + 0.395194i $$0.129323\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −8.00000 −0.326871 −0.163436 0.986554i $$-0.552258\pi$$
−0.163436 + 0.986554i $$0.552258\pi$$
$$600$$ 0 0
$$601$$ −38.8078 −1.58300 −0.791501 0.611168i $$-0.790700\pi$$
−0.791501 + 0.611168i $$0.790700\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −30.4924 −1.23969
$$606$$ 0 0
$$607$$ −14.7386 −0.598223 −0.299111 0.954218i $$-0.596690\pi$$
−0.299111 + 0.954218i $$0.596690\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −53.3002 −2.15629
$$612$$ 0 0
$$613$$ −28.1080 −1.13527 −0.567635 0.823281i $$-0.692141\pi$$
−0.567635 + 0.823281i $$0.692141\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −34.9848 −1.40844 −0.704218 0.709983i $$-0.748702\pi$$
−0.704218 + 0.709983i $$0.748702\pi$$
$$618$$ 0 0
$$619$$ 28.4924 1.14521 0.572604 0.819832i $$-0.305933\pi$$
0.572604 + 0.819832i $$0.305933\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −25.7538 −1.02687
$$630$$ 0 0
$$631$$ −6.73863 −0.268261 −0.134130 0.990964i $$-0.542824\pi$$
−0.134130 + 0.990964i $$0.542824\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 23.3693 0.927383
$$636$$ 0 0
$$637$$ −31.9309 −1.26515
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 13.3693 0.528056 0.264028 0.964515i $$-0.414949\pi$$
0.264028 + 0.964515i $$0.414949\pi$$
$$642$$ 0 0
$$643$$ −23.3693 −0.921596 −0.460798 0.887505i $$-0.652437\pi$$
−0.460798 + 0.887505i $$0.652437\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 29.3002 1.15191 0.575955 0.817482i $$-0.304630\pi$$
0.575955 + 0.817482i $$0.304630\pi$$
$$648$$ 0 0
$$649$$ −32.0000 −1.25611
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −25.0540 −0.980438 −0.490219 0.871599i $$-0.663083\pi$$
−0.490219 + 0.871599i $$0.663083\pi$$
$$654$$ 0 0
$$655$$ 31.3693 1.22570
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −2.24621 −0.0875000 −0.0437500 0.999043i $$-0.513930\pi$$
−0.0437500 + 0.999043i $$0.513930\pi$$
$$660$$ 0 0
$$661$$ −0.246211 −0.00957651 −0.00478825 0.999989i $$-0.501524\pi$$
−0.00478825 + 0.999989i $$0.501524\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0.561553 0.0217434
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −62.7386 −2.42200
$$672$$ 0 0
$$673$$ −2.94602 −0.113561 −0.0567805 0.998387i $$-0.518084\pi$$
−0.0567805 + 0.998387i $$0.518084\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 38.9848 1.49831 0.749155 0.662395i $$-0.230460\pi$$
0.749155 + 0.662395i $$0.230460\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −16.3153 −0.624289 −0.312145 0.950035i $$-0.601047\pi$$
−0.312145 + 0.950035i $$0.601047\pi$$
$$684$$ 0 0
$$685$$ 30.2462 1.15565
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −9.12311 −0.347563
$$690$$ 0 0
$$691$$ 20.9848 0.798301 0.399151 0.916885i $$-0.369305\pi$$
0.399151 + 0.916885i $$0.369305\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 31.3693 1.18991
$$696$$ 0 0
$$697$$ −33.7538 −1.27852
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −29.8617 −1.12786 −0.563931 0.825822i $$-0.690712\pi$$
−0.563931 + 0.825822i $$0.690712\pi$$
$$702$$ 0 0
$$703$$ −42.2462 −1.59335
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −37.3693 −1.40343 −0.701717 0.712456i $$-0.747583\pi$$
−0.701717 + 0.712456i $$0.747583\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −6.56155 −0.245732
$$714$$ 0 0
$$715$$ 46.7386 1.74793
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −4.49242 −0.167539 −0.0837695 0.996485i $$-0.526696\pi$$
−0.0837695 + 0.996485i $$0.526696\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −0.561553 −0.0208555
$$726$$ 0 0
$$727$$ −39.3693 −1.46013 −0.730064 0.683379i $$-0.760510\pi$$
−0.730064 + 0.683379i $$0.760510\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −24.9848 −0.924098
$$732$$ 0 0
$$733$$ 49.3693 1.82350 0.911749 0.410749i $$-0.134733\pi$$
0.911749 + 0.410749i $$0.134733\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 26.2462 0.966792
$$738$$ 0 0
$$739$$ 0.315342 0.0116000 0.00580001 0.999983i $$-0.498154\pi$$
0.00580001 + 0.999983i $$0.498154\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −34.2462 −1.25637 −0.628186 0.778063i $$-0.716202\pi$$
−0.628186 + 0.778063i $$0.716202\pi$$
$$744$$ 0 0
$$745$$ −7.50758 −0.275056
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 40.9848 1.49556 0.747779 0.663948i $$-0.231120\pi$$
0.747779 + 0.663948i $$0.231120\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 29.1231 1.05990
$$756$$ 0 0
$$757$$ −1.50758 −0.0547938 −0.0273969 0.999625i $$-0.508722\pi$$
−0.0273969 + 0.999625i $$0.508722\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 18.3153 0.663931 0.331965 0.943292i $$-0.392288\pi$$
0.331965 + 0.943292i $$0.392288\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 28.4924 1.02880
$$768$$ 0 0
$$769$$ −6.00000 −0.216366 −0.108183 0.994131i $$-0.534503\pi$$
−0.108183 + 0.994131i $$0.534503\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.63068 −0.0946191 −0.0473095 0.998880i $$-0.515065\pi$$
−0.0473095 + 0.998880i $$0.515065\pi$$
$$774$$ 0 0
$$775$$ 6.56155 0.235698
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −55.3693 −1.98381
$$780$$ 0 0
$$781$$ 48.3542 1.73025
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −25.7538 −0.919192
$$786$$ 0 0
$$787$$ −26.2462 −0.935576 −0.467788 0.883841i $$-0.654949\pi$$
−0.467788 + 0.883841i $$0.654949\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 55.8617 1.98371
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −12.2462 −0.433783 −0.216892 0.976196i $$-0.569592\pi$$
−0.216892 + 0.976196i $$0.569592\pi$$
$$798$$ 0 0
$$799$$ −36.4924 −1.29101
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 11.8617 0.418592
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −26.0000 −0.914111 −0.457056 0.889438i $$-0.651096\pi$$
−0.457056 + 0.889438i $$0.651096\pi$$
$$810$$ 0 0
$$811$$ 33.9309 1.19147 0.595737 0.803180i $$-0.296860\pi$$
0.595737 + 0.803180i $$0.296860\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 19.8617 0.695726
$$816$$ 0 0
$$817$$ −40.9848 −1.43388
$$818$$ 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
$$823$$ 49.4384 1.72332 0.861658 0.507489i $$-0.169426\pi$$
0.861658 + 0.507489i $$0.169426\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −4.49242 −0.156217 −0.0781084 0.996945i $$-0.524888\pi$$
−0.0781084 + 0.996945i $$0.524888\pi$$
$$828$$ 0 0
$$829$$ −20.2462 −0.703180 −0.351590 0.936154i $$-0.614359\pi$$
−0.351590 + 0.936154i $$0.614359\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −21.8617 −0.757464
$$834$$ 0 0
$$835$$ −32.0000 −1.10741
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ −50.2462 −1.73469 −0.867346 0.497706i $$-0.834176\pi$$
−0.867346 + 0.497706i $$0.834176\pi$$
$$840$$ 0 0
$$841$$ −28.6847 −0.989126
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −15.6155 −0.537190
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ −8.24621 −0.282676
$$852$$ 0 0
$$853$$ −34.9848 −1.19786 −0.598929 0.800802i $$-0.704407\pi$$
−0.598929 + 0.800802i $$0.704407\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −16.5616 −0.565732 −0.282866 0.959159i $$-0.591285\pi$$
−0.282866 + 0.959159i $$0.591285\pi$$
$$858$$ 0 0
$$859$$ 16.9460 0.578191 0.289095 0.957300i $$-0.406646\pi$$
0.289095 + 0.957300i $$0.406646\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 8.17708 0.278351 0.139176 0.990268i $$-0.455555\pi$$
0.139176 + 0.990268i $$0.455555\pi$$
$$864$$ 0 0
$$865$$ −20.0000 −0.680020
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 26.2462 0.890342
$$870$$ 0 0
$$871$$ −23.3693 −0.791839
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 30.9848 1.04628 0.523142 0.852246i $$-0.324760\pi$$
0.523142 + 0.852246i $$0.324760\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −4.87689 −0.164307 −0.0821534 0.996620i $$-0.526180\pi$$
−0.0821534 + 0.996620i $$0.526180\pi$$
$$882$$ 0 0
$$883$$ 36.9848 1.24464 0.622320 0.782763i $$-0.286190\pi$$
0.622320 + 0.782763i $$0.286190\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −19.6847 −0.660946 −0.330473 0.943815i $$-0.607208\pi$$
−0.330473 + 0.943815i $$0.607208\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −59.8617 −2.00320
$$894$$ 0 0
$$895$$ −31.3693 −1.04856
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −3.68466 −0.122890
$$900$$ 0 0
$$901$$ −6.24621 −0.208091
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −40.4924 −1.34601
$$906$$ 0 0
$$907$$ 42.8769 1.42370 0.711852 0.702330i $$-0.247857\pi$$
0.711852 + 0.702330i $$0.247857\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 37.1231 1.22994 0.614972 0.788549i $$-0.289167\pi$$
0.614972 + 0.788549i $$0.289167\pi$$
$$912$$ 0 0
$$913$$ −11.5076 −0.380845
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 37.7538 1.24538 0.622691 0.782468i $$-0.286039\pi$$
0.622691 + 0.782468i $$0.286039\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −43.0540 −1.41714
$$924$$ 0 0
$$925$$ 8.24621 0.271134
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −34.8078 −1.14201 −0.571003 0.820948i $$-0.693445\pi$$
−0.571003 + 0.820948i $$0.693445\pi$$
$$930$$ 0 0
$$931$$ −35.8617 −1.17532
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 32.0000 1.04651
$$936$$ 0 0
$$937$$ 15.7538 0.514654 0.257327 0.966324i $$-0.417158\pi$$
0.257327 + 0.966324i $$0.417158\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −39.1231 −1.27538 −0.637688 0.770294i $$-0.720109\pi$$
−0.637688 + 0.770294i $$0.720109\pi$$
$$942$$ 0 0
$$943$$ −10.8078 −0.351949
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 2.56155 0.0832393 0.0416196 0.999134i $$-0.486748\pi$$
0.0416196 + 0.999134i $$0.486748\pi$$
$$948$$ 0 0
$$949$$ −10.5616 −0.342843
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −44.2462 −1.43328 −0.716638 0.697446i $$-0.754320\pi$$
−0.716638 + 0.697446i $$0.754320\pi$$
$$954$$ 0 0
$$955$$ 1.26137 0.0408169
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 12.0540 0.388838
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 9.12311 0.293683
$$966$$ 0 0
$$967$$ 35.0540 1.12726 0.563630 0.826027i $$-0.309404\pi$$
0.563630 + 0.826027i $$0.309404\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −31.3693 −1.00669 −0.503345 0.864086i $$-0.667897\pi$$
−0.503345 + 0.864086i $$0.667897\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 57.2311 1.83098 0.915492 0.402337i $$-0.131802\pi$$
0.915492 + 0.402337i $$0.131802\pi$$
$$978$$ 0 0
$$979$$ −68.4924 −2.18903
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −22.1080 −0.705134 −0.352567 0.935787i $$-0.614691\pi$$
−0.352567 + 0.935787i $$0.614691\pi$$
$$984$$ 0 0
$$985$$ 23.8617 0.760298
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −8.00000 −0.254385
$$990$$ 0 0
$$991$$ 8.98485 0.285413 0.142707 0.989765i $$-0.454419\pi$$
0.142707 + 0.989765i $$0.454419\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ −5.75379 −0.182407
$$996$$ 0 0
$$997$$ 14.0000 0.443384 0.221692 0.975117i $$-0.428842\pi$$
0.221692 + 0.975117i $$0.428842\pi$$
$$998$$ 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 1656.2.a.j.1.1 2
3.2 odd 2 184.2.a.e.1.1 2
4.3 odd 2 3312.2.a.t.1.2 2
12.11 even 2 368.2.a.i.1.2 2
15.2 even 4 4600.2.e.o.4049.4 4
15.8 even 4 4600.2.e.o.4049.1 4
15.14 odd 2 4600.2.a.s.1.2 2
21.20 even 2 9016.2.a.w.1.2 2
24.5 odd 2 1472.2.a.u.1.2 2
24.11 even 2 1472.2.a.p.1.1 2
60.59 even 2 9200.2.a.br.1.1 2
69.68 even 2 4232.2.a.o.1.1 2
276.275 odd 2 8464.2.a.bd.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
184.2.a.e.1.1 2 3.2 odd 2
368.2.a.i.1.2 2 12.11 even 2
1472.2.a.p.1.1 2 24.11 even 2
1472.2.a.u.1.2 2 24.5 odd 2
1656.2.a.j.1.1 2 1.1 even 1 trivial
3312.2.a.t.1.2 2 4.3 odd 2
4232.2.a.o.1.1 2 69.68 even 2
4600.2.a.s.1.2 2 15.14 odd 2
4600.2.e.o.4049.1 4 15.8 even 4
4600.2.e.o.4049.4 4 15.2 even 4
8464.2.a.bd.1.2 2 276.275 odd 2
9016.2.a.w.1.2 2 21.20 even 2
9200.2.a.br.1.1 2 60.59 even 2