# Properties

 Label 8464.2.a.bd.1.2 Level $8464$ Weight $2$ Character 8464.1 Self dual yes Analytic conductor $67.585$ Analytic rank $0$ Dimension $2$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$8464 = 2^{4} \cdot 23^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 8464.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$67.5853802708$$ Analytic rank: $$0$$ 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 1.2 Root $$2.56155$$ of defining polynomial Character $$\chi$$ $$=$$ 8464.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.56155 q^{3} -2.00000 q^{5} +3.56155 q^{9} +O(q^{10})$$ $$q+2.56155 q^{3} -2.00000 q^{5} +3.56155 q^{9} +5.12311 q^{11} +4.56155 q^{13} -5.12311 q^{15} +3.12311 q^{17} +5.12311 q^{19} -1.00000 q^{25} +1.43845 q^{27} -0.561553 q^{29} +6.56155 q^{31} +13.1231 q^{33} +8.24621 q^{37} +11.6847 q^{39} +10.8078 q^{41} -8.00000 q^{43} -7.12311 q^{45} -11.6847 q^{47} -7.00000 q^{49} +8.00000 q^{51} -2.00000 q^{53} -10.2462 q^{55} +13.1231 q^{57} +6.24621 q^{59} -12.2462 q^{61} -9.12311 q^{65} -5.12311 q^{67} -9.43845 q^{71} -2.31534 q^{73} -2.56155 q^{75} -5.12311 q^{79} -7.00000 q^{81} -2.24621 q^{83} -6.24621 q^{85} -1.43845 q^{87} +13.3693 q^{89} +16.8078 q^{93} -10.2462 q^{95} +13.3693 q^{97} +18.2462 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{3} - 4 q^{5} + 3 q^{9} + O(q^{10})$$ $$2 q + q^{3} - 4 q^{5} + 3 q^{9} + 2 q^{11} + 5 q^{13} - 2 q^{15} - 2 q^{17} + 2 q^{19} - 2 q^{25} + 7 q^{27} + 3 q^{29} + 9 q^{31} + 18 q^{33} + 11 q^{39} + q^{41} - 16 q^{43} - 6 q^{45} - 11 q^{47} - 14 q^{49} + 16 q^{51} - 4 q^{53} - 4 q^{55} + 18 q^{57} - 4 q^{59} - 8 q^{61} - 10 q^{65} - 2 q^{67} - 23 q^{71} - 17 q^{73} - q^{75} - 2 q^{79} - 14 q^{81} + 12 q^{83} + 4 q^{85} - 7 q^{87} + 2 q^{89} + 13 q^{93} - 4 q^{95} + 2 q^{97} + 20 q^{99} + O(q^{100})$$

## 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
$$3$$ 2.56155 1.47891 0.739457 0.673204i $$-0.235083\pi$$
0.739457 + 0.673204i $$0.235083\pi$$
$$4$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ 3.56155 1.18718
$$10$$ 0 0
$$11$$ 5.12311 1.54467 0.772337 0.635213i $$-0.219088\pi$$
0.772337 + 0.635213i $$0.219088\pi$$
$$12$$ 0 0
$$13$$ 4.56155 1.26515 0.632574 0.774500i $$-0.281999\pi$$
0.632574 + 0.774500i $$0.281999\pi$$
$$14$$ 0 0
$$15$$ −5.12311 −1.32278
$$16$$ 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
$$23$$ 0 0
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 1.43845 0.276829
$$28$$ 0 0
$$29$$ −0.561553 −0.104278 −0.0521389 0.998640i $$-0.516604\pi$$
−0.0521389 + 0.998640i $$0.516604\pi$$
$$30$$ 0 0
$$31$$ 6.56155 1.17849 0.589245 0.807955i $$-0.299425\pi$$
0.589245 + 0.807955i $$0.299425\pi$$
$$32$$ 0 0
$$33$$ 13.1231 2.28444
$$34$$ 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
$$39$$ 11.6847 1.87104
$$40$$ 0 0
$$41$$ 10.8078 1.68789 0.843945 0.536430i $$-0.180228\pi$$
0.843945 + 0.536430i $$0.180228\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ −7.12311 −1.06185
$$46$$ 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
$$51$$ 8.00000 1.12022
$$52$$ 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
$$57$$ 13.1231 1.73820
$$58$$ 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 $$-0.786815\pi$$
−0.783983 + 0.620782i $$0.786815\pi$$
$$62$$ 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
$$75$$ −2.56155 −0.295783
$$76$$ 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
$$81$$ −7.00000 −0.777778
$$82$$ 0 0
$$83$$ −2.24621 −0.246554 −0.123277 0.992372i $$-0.539340\pi$$
−0.123277 + 0.992372i $$0.539340\pi$$
$$84$$ 0 0
$$85$$ −6.24621 −0.677497
$$86$$ 0 0
$$87$$ −1.43845 −0.154218
$$88$$ 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
$$93$$ 16.8078 1.74288
$$94$$ 0 0
$$95$$ −10.2462 −1.05124
$$96$$ 0 0
$$97$$ 13.3693 1.35745 0.678724 0.734393i $$-0.262533\pi$$
0.678724 + 0.734393i $$0.262533\pi$$
$$98$$ 0 0
$$99$$ 18.2462 1.83381
$$100$$ 0 0
$$101$$ −4.24621 −0.422514 −0.211257 0.977431i $$-0.567756\pi$$
−0.211257 + 0.977431i $$0.567756\pi$$
$$102$$ 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 $$-0.455592\pi$$
0.139060 + 0.990284i $$0.455592\pi$$
$$108$$ 0 0
$$109$$ −4.87689 −0.467122 −0.233561 0.972342i $$-0.575038\pi$$
−0.233561 + 0.972342i $$0.575038\pi$$
$$110$$ 0 0
$$111$$ 21.1231 2.00492
$$112$$ 0 0
$$113$$ 11.1231 1.04637 0.523187 0.852218i $$-0.324743\pi$$
0.523187 + 0.852218i $$0.324743\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 16.2462 1.50196
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 15.2462 1.38602
$$122$$ 0 0
$$123$$ 27.6847 2.49624
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 11.6847 1.03685 0.518423 0.855124i $$-0.326519\pi$$
0.518423 + 0.855124i $$0.326519\pi$$
$$128$$ 0 0
$$129$$ −20.4924 −1.80426
$$130$$ 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
$$135$$ −2.87689 −0.247604
$$136$$ 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 $$-0.268356\pi$$
0.665178 + 0.746685i $$0.268356\pi$$
$$140$$ 0 0
$$141$$ −29.9309 −2.52063
$$142$$ 0 0
$$143$$ 23.3693 1.95424
$$144$$ 0 0
$$145$$ 1.12311 0.0932688
$$146$$ 0 0
$$147$$ −17.9309 −1.47891
$$148$$ 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 $$-0.298141\pi$$
0.592501 + 0.805570i $$0.298141\pi$$
$$152$$ 0 0
$$153$$ 11.1231 0.899250
$$154$$ 0 0
$$155$$ −13.1231 −1.05407
$$156$$ 0 0
$$157$$ −12.8769 −1.02769 −0.513844 0.857884i $$-0.671779\pi$$
−0.513844 + 0.857884i $$0.671779\pi$$
$$158$$ 0 0
$$159$$ −5.12311 −0.406289
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 9.93087 0.777846 0.388923 0.921270i $$-0.372847\pi$$
0.388923 + 0.921270i $$0.372847\pi$$
$$164$$ 0 0
$$165$$ −26.2462 −2.04326
$$166$$ 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
$$171$$ 18.2462 1.39532
$$172$$ 0 0
$$173$$ −10.0000 −0.760286 −0.380143 0.924928i $$-0.624125\pi$$
−0.380143 + 0.924928i $$0.624125\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 16.0000 1.20263
$$178$$ 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 $$-0.771125\pi$$
−0.752445 + 0.658656i $$0.771125\pi$$
$$182$$ 0 0
$$183$$ −31.3693 −2.31889
$$184$$ 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 $$-0.492736\pi$$
0.0228173 + 0.999740i $$0.492736\pi$$
$$192$$ 0 0
$$193$$ −4.56155 −0.328348 −0.164174 0.986431i $$-0.552496\pi$$
−0.164174 + 0.986431i $$0.552496\pi$$
$$194$$ 0 0
$$195$$ −23.3693 −1.67351
$$196$$ 0 0
$$197$$ 11.9309 0.850039 0.425020 0.905184i $$-0.360267\pi$$
0.425020 + 0.905184i $$0.360267\pi$$
$$198$$ 0 0
$$199$$ 2.87689 0.203938 0.101969 0.994788i $$-0.467486\pi$$
0.101969 + 0.994788i $$0.467486\pi$$
$$200$$ 0 0
$$201$$ −13.1231 −0.925633
$$202$$ 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 $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 0 0
$$213$$ −24.1771 −1.65659
$$214$$ 0 0
$$215$$ 16.0000 1.09119
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −5.93087 −0.400771
$$220$$ 0 0
$$221$$ 14.2462 0.958304
$$222$$ 0 0
$$223$$ −4.49242 −0.300835 −0.150417 0.988623i $$-0.548062\pi$$
−0.150417 + 0.988623i $$0.548062\pi$$
$$224$$ 0 0
$$225$$ −3.56155 −0.237437
$$226$$ 0 0
$$227$$ 10.2462 0.680065 0.340032 0.940414i $$-0.389562\pi$$
0.340032 + 0.940414i $$0.389562\pi$$
$$228$$ 0 0
$$229$$ −23.1231 −1.52802 −0.764009 0.645206i $$-0.776772\pi$$
−0.764009 + 0.645206i $$0.776772\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 21.0540 1.37929 0.689646 0.724147i $$-0.257766\pi$$
0.689646 + 0.724147i $$0.257766\pi$$
$$234$$ 0 0
$$235$$ 23.3693 1.52445
$$236$$ 0 0
$$237$$ −13.1231 −0.852437
$$238$$ 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 $$-0.174620\pi$$
0.853263 + 0.521480i $$0.174620\pi$$
$$242$$ 0 0
$$243$$ −22.2462 −1.42710
$$244$$ 0 0
$$245$$ 14.0000 0.894427
$$246$$ 0 0
$$247$$ 23.3693 1.48695
$$248$$ 0 0
$$249$$ −5.75379 −0.364632
$$250$$ 0 0
$$251$$ 10.2462 0.646735 0.323368 0.946273i $$-0.395185\pi$$
0.323368 + 0.946273i $$0.395185\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ −16.0000 −1.00196
$$256$$ 0 0
$$257$$ −17.6847 −1.10314 −0.551569 0.834129i $$-0.685971\pi$$
−0.551569 + 0.834129i $$0.685971\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −2.00000 −0.123797
$$262$$ 0 0
$$263$$ −10.8769 −0.670698 −0.335349 0.942094i $$-0.608854\pi$$
−0.335349 + 0.942094i $$0.608854\pi$$
$$264$$ 0 0
$$265$$ 4.00000 0.245718
$$266$$ 0 0
$$267$$ 34.2462 2.09583
$$268$$ 0 0
$$269$$ 25.6847 1.56602 0.783011 0.622008i $$-0.213683\pi$$
0.783011 + 0.622008i $$0.213683\pi$$
$$270$$ 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
$$275$$ −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
$$279$$ 23.3693 1.39908
$$280$$ 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
$$285$$ −26.2462 −1.55469
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −7.24621 −0.426248
$$290$$ 0 0
$$291$$ 34.2462 2.00755
$$292$$ 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
$$297$$ 7.36932 0.427611
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −10.8769 −0.624861
$$304$$ 0 0
$$305$$ 24.4924 1.40243
$$306$$ 0 0
$$307$$ 1.75379 0.100094 0.0500470 0.998747i $$-0.484063\pi$$
0.0500470 + 0.998747i $$0.484063\pi$$
$$308$$ 0 0
$$309$$ 5.75379 0.327322
$$310$$ 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 $$-0.585303\pi$$
−0.264793 + 0.964305i $$0.585303\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −20.2462 −1.13714 −0.568570 0.822635i $$-0.692503\pi$$
−0.568570 + 0.822635i $$0.692503\pi$$
$$318$$ 0 0
$$319$$ −2.87689 −0.161075
$$320$$ 0 0
$$321$$ 7.36932 0.411315
$$322$$ 0 0
$$323$$ 16.0000 0.890264
$$324$$ 0 0
$$325$$ −4.56155 −0.253029
$$326$$ 0 0
$$327$$ −12.4924 −0.690833
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 30.4233 1.67222 0.836108 0.548565i $$-0.184826\pi$$
0.836108 + 0.548565i $$0.184826\pi$$
$$332$$ 0 0
$$333$$ 29.3693 1.60943
$$334$$ 0 0
$$335$$ 10.2462 0.559810
$$336$$ 0 0
$$337$$ −19.6155 −1.06853 −0.534263 0.845318i $$-0.679411\pi$$
−0.534263 + 0.845318i $$0.679411\pi$$
$$338$$ 0 0
$$339$$ 28.4924 1.54750
$$340$$ 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
$$351$$ 6.56155 0.350230
$$352$$ 0 0
$$353$$ 11.4384 0.608807 0.304404 0.952543i $$-0.401543\pi$$
0.304404 + 0.952543i $$0.401543\pi$$
$$354$$ 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 $$-0.346106\pi$$
0.464856 + 0.885386i $$0.346106\pi$$
$$360$$ 0 0
$$361$$ 7.24621 0.381380
$$362$$ 0 0
$$363$$ 39.0540 2.04980
$$364$$ 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
$$369$$ 38.4924 2.00384
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −22.4924 −1.16461 −0.582307 0.812969i $$-0.697850\pi$$
−0.582307 + 0.812969i $$0.697850\pi$$
$$374$$ 0 0
$$375$$ 30.7386 1.58734
$$376$$ 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
$$381$$ 29.9309 1.53340
$$382$$ 0 0
$$383$$ 26.2462 1.34112 0.670559 0.741856i $$-0.266054\pi$$
0.670559 + 0.741856i $$0.266054\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −28.4924 −1.44835
$$388$$ 0 0
$$389$$ −1.36932 −0.0694271 −0.0347136 0.999397i $$-0.511052\pi$$
−0.0347136 + 0.999397i $$0.511052\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −40.1771 −2.02667
$$394$$ 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
$$405$$ 14.0000 0.695666
$$406$$ 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
$$411$$ −38.7386 −1.91084
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 4.49242 0.220524
$$416$$ 0 0
$$417$$ 40.1771 1.96748
$$418$$ 0 0
$$419$$ −12.4924 −0.610295 −0.305147 0.952305i $$-0.598706\pi$$
−0.305147 + 0.952305i $$0.598706\pi$$
$$420$$ 0 0
$$421$$ 27.1231 1.32190 0.660950 0.750430i $$-0.270154\pi$$
0.660950 + 0.750430i $$0.270154\pi$$
$$422$$ 0 0
$$423$$ −41.6155 −2.02342
$$424$$ 0 0
$$425$$ −3.12311 −0.151493
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 59.8617 2.89015
$$430$$ 0 0
$$431$$ −28.4924 −1.37243 −0.686216 0.727398i $$-0.740729\pi$$
−0.686216 + 0.727398i $$0.740729\pi$$
$$432$$ 0 0
$$433$$ −24.7386 −1.18886 −0.594431 0.804146i $$-0.702623\pi$$
−0.594431 + 0.804146i $$0.702623\pi$$
$$434$$ 0 0
$$435$$ 2.87689 0.137937
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −11.0540 −0.527577 −0.263789 0.964580i $$-0.584972\pi$$
−0.263789 + 0.964580i $$0.584972\pi$$
$$440$$ 0 0
$$441$$ −24.9309 −1.18718
$$442$$ 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
$$447$$ 9.61553 0.454799
$$448$$ 0 0
$$449$$ −8.24621 −0.389163 −0.194581 0.980886i $$-0.562335\pi$$
−0.194581 + 0.980886i $$0.562335\pi$$
$$450$$ 0 0
$$451$$ 55.3693 2.60724
$$452$$ 0 0
$$453$$ 37.3002 1.75252
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5.36932 0.251166 0.125583 0.992083i $$-0.459920\pi$$
0.125583 + 0.992083i $$0.459920\pi$$
$$458$$ 0 0
$$459$$ 4.49242 0.209688
$$460$$ 0 0
$$461$$ −10.8078 −0.503368 −0.251684 0.967809i $$-0.580984\pi$$
−0.251684 + 0.967809i $$0.580984\pi$$
$$462$$ 0 0
$$463$$ −12.4924 −0.580572 −0.290286 0.956940i $$-0.593750\pi$$
−0.290286 + 0.956940i $$0.593750\pi$$
$$464$$ 0 0
$$465$$ −33.6155 −1.55888
$$466$$ 0 0
$$467$$ −15.3693 −0.711207 −0.355604 0.934637i $$-0.615725\pi$$
−0.355604 + 0.934637i $$0.615725\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −32.9848 −1.51986
$$472$$ 0 0
$$473$$ −40.9848 −1.88449
$$474$$ 0 0
$$475$$ −5.12311 −0.235064
$$476$$ 0 0
$$477$$ −7.12311 −0.326145
$$478$$ 0 0
$$479$$ 10.2462 0.468161 0.234081 0.972217i $$-0.424792\pi$$
0.234081 + 0.972217i $$0.424792\pi$$
$$480$$ 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 $$-0.590013\pi$$
−0.279031 + 0.960282i $$0.590013\pi$$
$$488$$ 0 0
$$489$$ 25.4384 1.15037
$$490$$ 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
$$495$$ −36.4924 −1.64021
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 23.0540 1.03204 0.516019 0.856577i $$-0.327413\pi$$
0.516019 + 0.856577i $$0.327413\pi$$
$$500$$ 0 0
$$501$$ 40.9848 1.83107
$$502$$ 0 0
$$503$$ 7.36932 0.328582 0.164291 0.986412i $$-0.447466\pi$$
0.164291 + 0.986412i $$0.447466\pi$$
$$504$$ 0 0
$$505$$ 8.49242 0.377908
$$506$$ 0 0
$$507$$ 20.0000 0.888231
$$508$$ 0 0
$$509$$ −15.3002 −0.678169 −0.339084 0.940756i $$-0.610117\pi$$
−0.339084 + 0.940756i $$0.610117\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 7.36932 0.325363
$$514$$ 0 0
$$515$$ −4.49242 −0.197960
$$516$$ 0 0
$$517$$ −59.8617 −2.63272
$$518$$ 0 0
$$519$$ −25.6155 −1.12440
$$520$$ 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
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 22.2462 0.965403
$$532$$ 0 0
$$533$$ 49.3002 2.13543
$$534$$ 0 0
$$535$$ −5.75379 −0.248758
$$536$$ 0 0
$$537$$ 40.1771 1.73377
$$538$$ 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
$$543$$ −51.8617 −2.22560
$$544$$ 0 0
$$545$$ 9.75379 0.417806
$$546$$ 0 0
$$547$$ −43.5464 −1.86191 −0.930955 0.365135i $$-0.881023\pi$$
−0.930955 + 0.365135i $$0.881023\pi$$
$$548$$ 0 0
$$549$$ −43.6155 −1.86147
$$550$$ 0 0
$$551$$ −2.87689 −0.122560
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −42.2462 −1.79325
$$556$$ 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
$$561$$ 40.9848 1.73038
$$562$$ 0 0
$$563$$ 5.75379 0.242493 0.121247 0.992622i $$-0.461311\pi$$
0.121247 + 0.992622i $$0.461311\pi$$
$$564$$ 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
$$573$$ 1.61553 0.0674897
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 15.9309 0.663211 0.331605 0.943418i $$-0.392410\pi$$
0.331605 + 0.943418i $$0.392410\pi$$
$$578$$ 0 0
$$579$$ −11.6847 −0.485598
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −10.2462 −0.424355
$$584$$ 0 0
$$585$$ −32.4924 −1.34340
$$586$$ 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
$$591$$ 30.5616 1.25713
$$592$$ 0 0
$$593$$ −44.7386 −1.83720 −0.918598 0.395194i $$-0.870677\pi$$
−0.918598 + 0.395194i $$0.870677\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 7.36932 0.301606
$$598$$ 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
$$603$$ −18.2462 −0.743043
$$604$$ 0 0
$$605$$ −30.4924 −1.23969
$$606$$ 0 0
$$607$$ 14.7386 0.598223 0.299111 0.954218i $$-0.403310\pi$$
0.299111 + 0.954218i $$0.403310\pi$$
$$608$$ 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 $$-0.307859\pi$$
0.567635 + 0.823281i $$0.307859\pi$$
$$614$$ 0 0
$$615$$ −55.3693 −2.23271
$$616$$ 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
$$627$$ 67.2311 2.68495
$$628$$ 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
$$633$$ 10.2462 0.407250
$$634$$ 0 0
$$635$$ −23.3693 −0.927383
$$636$$ 0 0
$$637$$ −31.9309 −1.26515
$$638$$ 0 0
$$639$$ −33.6155 −1.32981
$$640$$ 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
$$645$$ 40.9848 1.61378
$$646$$ 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 $$-0.336917\pi$$
0.490219 + 0.871599i $$0.336917\pi$$
$$654$$ 0 0
$$655$$ 31.3693 1.22570
$$656$$ 0 0
$$657$$ −8.24621 −0.321715
$$658$$ 0 0
$$659$$ 2.24621 0.0875000 0.0437500 0.999043i $$-0.486070\pi$$
0.0437500 + 0.999043i $$0.486070\pi$$
$$660$$ 0 0
$$661$$ 0.246211 0.00957651 0.00478825 0.999989i $$-0.498476\pi$$
0.00478825 + 0.999989i $$0.498476\pi$$
$$662$$ 0 0
$$663$$ 36.4924 1.41725
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −11.5076 −0.444909
$$670$$ 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
$$675$$ −1.43845 −0.0553659
$$676$$ 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
$$681$$ 26.2462 1.00576
$$682$$ 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
$$687$$ −59.2311 −2.25981
$$688$$ 0 0
$$689$$ −9.12311 −0.347563
$$690$$ 0 0
$$691$$ −20.9848 −0.798301 −0.399151 0.916885i $$-0.630695\pi$$
−0.399151 + 0.916885i $$0.630695\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −31.3693 −1.18991
$$696$$ 0 0
$$697$$ 33.7538 1.27852
$$698$$ 0 0
$$699$$ 53.9309 2.03985
$$700$$ 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
$$705$$ 59.8617 2.25452
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 37.3693 1.40343 0.701717 0.712456i $$-0.252417\pi$$
0.701717 + 0.712456i $$0.252417\pi$$
$$710$$ 0 0
$$711$$ −18.2462 −0.684286
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −46.7386 −1.74793
$$716$$ 0 0
$$717$$ 28.3153 1.05746
$$718$$ 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
$$723$$ 67.8617 2.52381
$$724$$ 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
$$729$$ −35.9848 −1.33277
$$730$$ 0 0
$$731$$ −24.9848 −0.924098
$$732$$ 0 0
$$733$$ −49.3693 −1.82350 −0.911749 0.410749i $$-0.865267\pi$$
−0.911749 + 0.410749i $$0.865267\pi$$
$$734$$ 0 0
$$735$$ 35.8617 1.32278
$$736$$ 0 0
$$737$$ −26.2462 −0.966792
$$738$$ 0 0
$$739$$ −0.315342 −0.0116000 −0.00580001 0.999983i $$-0.501846\pi$$
−0.00580001 + 0.999983i $$0.501846\pi$$
$$740$$ 0 0
$$741$$ 59.8617 2.19908
$$742$$ 0 0
$$743$$ 34.2462 1.25637 0.628186 0.778063i $$-0.283798\pi$$
0.628186 + 0.778063i $$0.283798\pi$$
$$744$$ 0 0
$$745$$ −7.50758 −0.275056
$$746$$ 0 0
$$747$$ −8.00000 −0.292705
$$748$$ 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
$$753$$ 26.2462 0.956465
$$754$$ 0 0
$$755$$ −29.1231 −1.05990
$$756$$ 0 0
$$757$$ 1.50758 0.0547938 0.0273969 0.999625i $$-0.491278\pi$$
0.0273969 + 0.999625i $$0.491278\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −18.3153 −0.663931 −0.331965 0.943292i $$-0.607712\pi$$
−0.331965 + 0.943292i $$0.607712\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −22.2462 −0.804313
$$766$$ 0 0
$$767$$ 28.4924 1.02880
$$768$$ 0 0
$$769$$ 6.00000 0.216366 0.108183 0.994131i $$-0.465497\pi$$
0.108183 + 0.994131i $$0.465497\pi$$
$$770$$ 0 0
$$771$$ −45.3002 −1.63145
$$772$$ 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
$$783$$ −0.807764 −0.0288671
$$784$$ 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
$$789$$ −27.8617 −0.991904
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −55.8617 −1.98371
$$794$$ 0 0
$$795$$ 10.2462 0.363396
$$796$$ 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
$$801$$ 47.6155 1.68241
$$802$$ 0 0
$$803$$ −11.8617 −0.418592
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 65.7926 2.31601
$$808$$ 0 0
$$809$$ 26.0000 0.914111 0.457056 0.889438i $$-0.348904\pi$$
0.457056 + 0.889438i $$0.348904\pi$$
$$810$$ 0 0
$$811$$ −33.9309 −1.19147 −0.595737 0.803180i $$-0.703140\pi$$
−0.595737 + 0.803180i $$0.703140\pi$$
$$812$$ 0 0
$$813$$ −61.4773 −2.15610
$$814$$ 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 $$-0.642083\pi$$
−0.431692 + 0.902021i $$0.642083\pi$$
$$822$$ 0 0
$$823$$ −49.4384 −1.72332 −0.861658 0.507489i $$-0.830574\pi$$
−0.861658 + 0.507489i $$0.830574\pi$$
$$824$$ 0 0
$$825$$ −13.1231 −0.456888
$$826$$ 0 0
$$827$$ 4.49242 0.156217 0.0781084 0.996945i $$-0.475112\pi$$
0.0781084 + 0.996945i $$0.475112\pi$$
$$828$$ 0 0
$$829$$ −20.2462 −0.703180 −0.351590 0.936154i $$-0.614359\pi$$
−0.351590 + 0.936154i $$0.614359\pi$$
$$830$$ 0 0
$$831$$ −7.19224 −0.249496
$$832$$ 0 0
$$833$$ −21.8617 −0.757464
$$834$$ 0 0
$$835$$ −32.0000 −1.10741
$$836$$ 0 0
$$837$$ 9.43845 0.326240
$$838$$ 0 0
$$839$$ 50.2462 1.73469 0.867346 0.497706i $$-0.165824\pi$$
0.867346 + 0.497706i $$0.165824\pi$$
$$840$$ 0 0
$$841$$ −28.6847 −0.989126
$$842$$ 0 0
$$843$$ 8.00000 0.275535
$$844$$ 0 0
$$845$$ −15.6155 −0.537190
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ −13.1231 −0.450384
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −34.9848 −1.19786 −0.598929 0.800802i $$-0.704407\pi$$
−0.598929 + 0.800802i $$0.704407\pi$$
$$854$$ 0 0
$$855$$ −36.4924 −1.24801
$$856$$ 0 0
$$857$$ 16.5616 0.565732 0.282866 0.959159i $$-0.408715\pi$$
0.282866 + 0.959159i $$0.408715\pi$$
$$858$$ 0 0
$$859$$ −16.9460 −0.578191 −0.289095 0.957300i $$-0.593354\pi$$
−0.289095 + 0.957300i $$0.593354\pi$$
$$860$$ 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
$$867$$ −18.5616 −0.630383
$$868$$ 0 0
$$869$$ −26.2462 −0.890342
$$870$$ 0 0
$$871$$ −23.3693 −0.791839
$$872$$ 0 0
$$873$$ 47.6155 1.61154
$$874$$ 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
$$879$$ −24.0000 −0.809500
$$880$$ 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 $$-0.713810\pi$$
−0.622320 + 0.782763i $$0.713810\pi$$
$$884$$ 0 0
$$885$$ −32.0000 −1.07567
$$886$$ 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
$$891$$ −35.8617 −1.20141
$$892$$ 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
$$909$$ −15.1231 −0.501602
$$910$$ 0 0
$$911$$ −37.1231 −1.22994 −0.614972 0.788549i $$-0.710833\pi$$
−0.614972 + 0.788549i $$0.710833\pi$$
$$912$$ 0 0
$$913$$ −11.5076 −0.380845
$$914$$ 0 0
$$915$$ 62.7386 2.07408
$$916$$ 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
$$921$$ 4.49242 0.148030
$$922$$ 0 0
$$923$$ −43.0540 −1.41714
$$924$$ 0 0
$$925$$ −8.24621 −0.271134
$$926$$ 0 0
$$927$$ 8.00000 0.262754
$$928$$ 0 0
$$929$$ 34.8078 1.14201 0.571003 0.820948i $$-0.306555\pi$$
0.571003 + 0.820948i $$0.306555\pi$$
$$930$$ 0 0
$$931$$ −35.8617 −1.17532
$$932$$ 0 0
$$933$$ −3.68466 −0.120630
$$934$$ 0 0
$$935$$ −32.0000 −1.04651
$$936$$ 0 0
$$937$$ −15.7538 −0.514654 −0.257327 0.966324i $$-0.582842\pi$$
−0.257327 + 0.966324i $$0.582842\pi$$
$$938$$ 0 0
$$939$$ −24.0000 −0.783210
$$940$$ 0 0
$$941$$ −39.1231 −1.27538 −0.637688 0.770294i $$-0.720109\pi$$
−0.637688 + 0.770294i $$0.720109\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 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
$$951$$ −51.8617 −1.68173
$$952$$ 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
$$957$$ −7.36932 −0.238216
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 12.0540 0.388838
$$962$$ 0 0
$$963$$ 10.2462 0.330180
$$964$$ 0 0
$$965$$ 9.12311 0.293683
$$966$$ 0 0
$$967$$ −35.0540 −1.12726 −0.563630 0.826027i $$-0.690596\pi$$
−0.563630 + 0.826027i $$0.690596\pi$$
$$968$$ 0 0
$$969$$ 40.9848 1.31662
$$970$$ 0 0
$$971$$ 31.3693 1.00669 0.503345 0.864086i $$-0.332103\pi$$
0.503345 + 0.864086i $$0.332103\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ −11.6847 −0.374209
$$976$$ 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
$$981$$ −17.3693 −0.554560
$$982$$ 0 0
$$983$$ 22.1080 0.705134 0.352567 0.935787i $$-0.385309\pi$$
0.352567 + 0.935787i $$0.385309\pi$$
$$984$$ 0 0
$$985$$ −23.8617 −0.760298
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −8.98485 −0.285413 −0.142707 0.989765i $$-0.545581\pi$$
−0.142707 + 0.989765i $$0.545581\pi$$
$$992$$ 0 0
$$993$$ 77.9309 2.47306
$$994$$ 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
$$999$$ 11.8617 0.375289
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 8464.2.a.bd.1.2 2
4.3 odd 2 4232.2.a.o.1.1 2
23.22 odd 2 368.2.a.i.1.2 2
69.68 even 2 3312.2.a.t.1.2 2
92.91 even 2 184.2.a.e.1.1 2
115.114 odd 2 9200.2.a.br.1.1 2
184.45 odd 2 1472.2.a.p.1.1 2
184.91 even 2 1472.2.a.u.1.2 2
276.275 odd 2 1656.2.a.j.1.1 2
460.183 odd 4 4600.2.e.o.4049.1 4
460.367 odd 4 4600.2.e.o.4049.4 4
460.459 even 2 4600.2.a.s.1.2 2
644.643 odd 2 9016.2.a.w.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
184.2.a.e.1.1 2 92.91 even 2
368.2.a.i.1.2 2 23.22 odd 2
1472.2.a.p.1.1 2 184.45 odd 2
1472.2.a.u.1.2 2 184.91 even 2
1656.2.a.j.1.1 2 276.275 odd 2
3312.2.a.t.1.2 2 69.68 even 2
4232.2.a.o.1.1 2 4.3 odd 2
4600.2.a.s.1.2 2 460.459 even 2
4600.2.e.o.4049.1 4 460.183 odd 4
4600.2.e.o.4049.4 4 460.367 odd 4
8464.2.a.bd.1.2 2 1.1 even 1 trivial
9016.2.a.w.1.2 2 644.643 odd 2
9200.2.a.br.1.1 2 115.114 odd 2