# Properties

 Label 2576.2.a.bb.1.1 Level $2576$ Weight $2$ Character 2576.1 Self dual yes Analytic conductor $20.569$ Analytic rank $0$ Dimension $5$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2576 = 2^{4} \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2576.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$20.5694635607$$ Analytic rank: $$0$$ Dimension: $$5$$ Coefficient field: 5.5.6963152.1 Defining polynomial: $$x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10$$ x^5 - 2*x^4 - 10*x^3 + 10*x^2 + 29*x + 10 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 644) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Root $$-2.25688$$ of defining polynomial Character $$\chi$$ $$=$$ 2576.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.25688 q^{3} -3.04771 q^{5} +1.00000 q^{7} +7.60729 q^{9} +O(q^{10})$$ $$q-3.25688 q^{3} -3.04771 q^{5} +1.00000 q^{7} +7.60729 q^{9} -5.22523 q^{11} +3.38206 q^{13} +9.92604 q^{15} -2.63895 q^{17} -3.39461 q^{19} -3.25688 q^{21} +1.00000 q^{23} +4.28854 q^{25} -15.0054 q^{27} -4.00190 q^{29} -6.97185 q^{31} +17.0180 q^{33} -3.04771 q^{35} -5.11916 q^{37} -11.0150 q^{39} -5.89583 q^{41} +7.90838 q^{43} -23.1848 q^{45} -9.54893 q^{47} +1.00000 q^{49} +8.59475 q^{51} -11.8200 q^{53} +15.9250 q^{55} +11.0558 q^{57} -1.51979 q^{59} +1.13934 q^{61} +7.60729 q^{63} -10.3076 q^{65} +8.80688 q^{67} -3.25688 q^{69} +14.5333 q^{71} -13.2271 q^{73} -13.9673 q^{75} -5.22523 q^{77} -14.4398 q^{79} +26.0490 q^{81} +0.693795 q^{83} +8.04275 q^{85} +13.0337 q^{87} +10.8511 q^{89} +3.38206 q^{91} +22.7065 q^{93} +10.3458 q^{95} -3.23476 q^{97} -39.7498 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$5 q - 3 q^{3} + 2 q^{5} + 5 q^{7} + 10 q^{9}+O(q^{10})$$ 5 * q - 3 * q^3 + 2 * q^5 + 5 * q^7 + 10 * q^9 $$5 q - 3 q^{3} + 2 q^{5} + 5 q^{7} + 10 q^{9} - 2 q^{11} + 13 q^{13} - 4 q^{15} + 4 q^{17} - 12 q^{19} - 3 q^{21} + 5 q^{23} + 19 q^{25} - 15 q^{27} + 13 q^{29} + 3 q^{31} + 24 q^{33} + 2 q^{35} - 4 q^{37} - 3 q^{39} + q^{41} + 8 q^{43} - 16 q^{45} - 5 q^{47} + 5 q^{49} + 16 q^{51} - 8 q^{53} + 2 q^{55} + 12 q^{57} - 12 q^{59} + 20 q^{61} + 10 q^{63} - 12 q^{65} + 12 q^{67} - 3 q^{69} - 9 q^{71} - 9 q^{73} - 35 q^{75} - 2 q^{77} + 8 q^{79} - 11 q^{81} + 28 q^{83} + 16 q^{85} + 15 q^{87} + 32 q^{89} + 13 q^{91} - 15 q^{93} + 36 q^{95} + 4 q^{97} - 28 q^{99}+O(q^{100})$$ 5 * q - 3 * q^3 + 2 * q^5 + 5 * q^7 + 10 * q^9 - 2 * q^11 + 13 * q^13 - 4 * q^15 + 4 * q^17 - 12 * q^19 - 3 * q^21 + 5 * q^23 + 19 * q^25 - 15 * q^27 + 13 * q^29 + 3 * q^31 + 24 * q^33 + 2 * q^35 - 4 * q^37 - 3 * q^39 + q^41 + 8 * q^43 - 16 * q^45 - 5 * q^47 + 5 * q^49 + 16 * q^51 - 8 * q^53 + 2 * q^55 + 12 * q^57 - 12 * q^59 + 20 * q^61 + 10 * q^63 - 12 * q^65 + 12 * q^67 - 3 * q^69 - 9 * q^71 - 9 * q^73 - 35 * q^75 - 2 * q^77 + 8 * q^79 - 11 * q^81 + 28 * q^83 + 16 * q^85 + 15 * q^87 + 32 * q^89 + 13 * q^91 - 15 * q^93 + 36 * q^95 + 4 * q^97 - 28 * q^99

## 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
$$3$$ −3.25688 −1.88036 −0.940181 0.340675i $$-0.889345\pi$$
−0.940181 + 0.340675i $$0.889345\pi$$
$$4$$ 0 0
$$5$$ −3.04771 −1.36298 −0.681489 0.731828i $$-0.738667\pi$$
−0.681489 + 0.731828i $$0.738667\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 0 0
$$9$$ 7.60729 2.53576
$$10$$ 0 0
$$11$$ −5.22523 −1.57546 −0.787732 0.616018i $$-0.788745\pi$$
−0.787732 + 0.616018i $$0.788745\pi$$
$$12$$ 0 0
$$13$$ 3.38206 0.938016 0.469008 0.883194i $$-0.344612\pi$$
0.469008 + 0.883194i $$0.344612\pi$$
$$14$$ 0 0
$$15$$ 9.92604 2.56289
$$16$$ 0 0
$$17$$ −2.63895 −0.640039 −0.320019 0.947411i $$-0.603689\pi$$
−0.320019 + 0.947411i $$0.603689\pi$$
$$18$$ 0 0
$$19$$ −3.39461 −0.778777 −0.389388 0.921074i $$-0.627314\pi$$
−0.389388 + 0.921074i $$0.627314\pi$$
$$20$$ 0 0
$$21$$ −3.25688 −0.710710
$$22$$ 0 0
$$23$$ 1.00000 0.208514
$$24$$ 0 0
$$25$$ 4.28854 0.857708
$$26$$ 0 0
$$27$$ −15.0054 −2.88779
$$28$$ 0 0
$$29$$ −4.00190 −0.743134 −0.371567 0.928406i $$-0.621179\pi$$
−0.371567 + 0.928406i $$0.621179\pi$$
$$30$$ 0 0
$$31$$ −6.97185 −1.25218 −0.626091 0.779750i $$-0.715346\pi$$
−0.626091 + 0.779750i $$0.715346\pi$$
$$32$$ 0 0
$$33$$ 17.0180 2.96245
$$34$$ 0 0
$$35$$ −3.04771 −0.515157
$$36$$ 0 0
$$37$$ −5.11916 −0.841585 −0.420792 0.907157i $$-0.638248\pi$$
−0.420792 + 0.907157i $$0.638248\pi$$
$$38$$ 0 0
$$39$$ −11.0150 −1.76381
$$40$$ 0 0
$$41$$ −5.89583 −0.920774 −0.460387 0.887718i $$-0.652289\pi$$
−0.460387 + 0.887718i $$0.652289\pi$$
$$42$$ 0 0
$$43$$ 7.90838 1.20602 0.603008 0.797735i $$-0.293969\pi$$
0.603008 + 0.797735i $$0.293969\pi$$
$$44$$ 0 0
$$45$$ −23.1848 −3.45619
$$46$$ 0 0
$$47$$ −9.54893 −1.39286 −0.696428 0.717627i $$-0.745228\pi$$
−0.696428 + 0.717627i $$0.745228\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ 0 0
$$51$$ 8.59475 1.20351
$$52$$ 0 0
$$53$$ −11.8200 −1.62360 −0.811799 0.583937i $$-0.801512\pi$$
−0.811799 + 0.583937i $$0.801512\pi$$
$$54$$ 0 0
$$55$$ 15.9250 2.14732
$$56$$ 0 0
$$57$$ 11.0558 1.46438
$$58$$ 0 0
$$59$$ −1.51979 −0.197860 −0.0989299 0.995094i $$-0.531542\pi$$
−0.0989299 + 0.995094i $$0.531542\pi$$
$$60$$ 0 0
$$61$$ 1.13934 0.145877 0.0729385 0.997336i $$-0.476762\pi$$
0.0729385 + 0.997336i $$0.476762\pi$$
$$62$$ 0 0
$$63$$ 7.60729 0.958428
$$64$$ 0 0
$$65$$ −10.3076 −1.27849
$$66$$ 0 0
$$67$$ 8.80688 1.07593 0.537966 0.842967i $$-0.319193\pi$$
0.537966 + 0.842967i $$0.319193\pi$$
$$68$$ 0 0
$$69$$ −3.25688 −0.392083
$$70$$ 0 0
$$71$$ 14.5333 1.72479 0.862394 0.506237i $$-0.168964\pi$$
0.862394 + 0.506237i $$0.168964\pi$$
$$72$$ 0 0
$$73$$ −13.2271 −1.54812 −0.774059 0.633114i $$-0.781777\pi$$
−0.774059 + 0.633114i $$0.781777\pi$$
$$74$$ 0 0
$$75$$ −13.9673 −1.61280
$$76$$ 0 0
$$77$$ −5.22523 −0.595470
$$78$$ 0 0
$$79$$ −14.4398 −1.62461 −0.812303 0.583236i $$-0.801786\pi$$
−0.812303 + 0.583236i $$0.801786\pi$$
$$80$$ 0 0
$$81$$ 26.0490 2.89433
$$82$$ 0 0
$$83$$ 0.693795 0.0761538 0.0380769 0.999275i $$-0.487877\pi$$
0.0380769 + 0.999275i $$0.487877\pi$$
$$84$$ 0 0
$$85$$ 8.04275 0.872359
$$86$$ 0 0
$$87$$ 13.0337 1.39736
$$88$$ 0 0
$$89$$ 10.8511 1.15021 0.575106 0.818079i $$-0.304961\pi$$
0.575106 + 0.818079i $$0.304961\pi$$
$$90$$ 0 0
$$91$$ 3.38206 0.354537
$$92$$ 0 0
$$93$$ 22.7065 2.35456
$$94$$ 0 0
$$95$$ 10.3458 1.06146
$$96$$ 0 0
$$97$$ −3.23476 −0.328440 −0.164220 0.986424i $$-0.552511\pi$$
−0.164220 + 0.986424i $$0.552511\pi$$
$$98$$ 0 0
$$99$$ −39.7498 −3.99501
$$100$$ 0 0
$$101$$ −8.32672 −0.828540 −0.414270 0.910154i $$-0.635963\pi$$
−0.414270 + 0.910154i $$0.635963\pi$$
$$102$$ 0 0
$$103$$ −0.418345 −0.0412208 −0.0206104 0.999788i $$-0.506561\pi$$
−0.0206104 + 0.999788i $$0.506561\pi$$
$$104$$ 0 0
$$105$$ 9.92604 0.968682
$$106$$ 0 0
$$107$$ 11.9084 1.15123 0.575613 0.817722i $$-0.304763\pi$$
0.575613 + 0.817722i $$0.304763\pi$$
$$108$$ 0 0
$$109$$ 17.9154 1.71598 0.857992 0.513663i $$-0.171712\pi$$
0.857992 + 0.513663i $$0.171712\pi$$
$$110$$ 0 0
$$111$$ 16.6725 1.58248
$$112$$ 0 0
$$113$$ −12.6375 −1.18884 −0.594418 0.804156i $$-0.702617\pi$$
−0.594418 + 0.804156i $$0.702617\pi$$
$$114$$ 0 0
$$115$$ −3.04771 −0.284201
$$116$$ 0 0
$$117$$ 25.7283 2.37859
$$118$$ 0 0
$$119$$ −2.63895 −0.241912
$$120$$ 0 0
$$121$$ 16.3030 1.48209
$$122$$ 0 0
$$123$$ 19.2020 1.73139
$$124$$ 0 0
$$125$$ 2.16832 0.193940
$$126$$ 0 0
$$127$$ 3.22333 0.286024 0.143012 0.989721i $$-0.454321\pi$$
0.143012 + 0.989721i $$0.454321\pi$$
$$128$$ 0 0
$$129$$ −25.7567 −2.26775
$$130$$ 0 0
$$131$$ 14.0910 1.23114 0.615569 0.788083i $$-0.288926\pi$$
0.615569 + 0.788083i $$0.288926\pi$$
$$132$$ 0 0
$$133$$ −3.39461 −0.294350
$$134$$ 0 0
$$135$$ 45.7321 3.93600
$$136$$ 0 0
$$137$$ 2.67250 0.228327 0.114164 0.993462i $$-0.463581\pi$$
0.114164 + 0.993462i $$0.463581\pi$$
$$138$$ 0 0
$$139$$ −6.23315 −0.528689 −0.264344 0.964428i $$-0.585156\pi$$
−0.264344 + 0.964428i $$0.585156\pi$$
$$140$$ 0 0
$$141$$ 31.0998 2.61907
$$142$$ 0 0
$$143$$ −17.6721 −1.47781
$$144$$ 0 0
$$145$$ 12.1966 1.01287
$$146$$ 0 0
$$147$$ −3.25688 −0.268623
$$148$$ 0 0
$$149$$ −5.58165 −0.457267 −0.228633 0.973513i $$-0.573426\pi$$
−0.228633 + 0.973513i $$0.573426\pi$$
$$150$$ 0 0
$$151$$ 11.8325 0.962916 0.481458 0.876469i $$-0.340107\pi$$
0.481458 + 0.876469i $$0.340107\pi$$
$$152$$ 0 0
$$153$$ −20.0752 −1.62299
$$154$$ 0 0
$$155$$ 21.2482 1.70670
$$156$$ 0 0
$$157$$ 17.3015 1.38081 0.690406 0.723422i $$-0.257432\pi$$
0.690406 + 0.723422i $$0.257432\pi$$
$$158$$ 0 0
$$159$$ 38.4963 3.05295
$$160$$ 0 0
$$161$$ 1.00000 0.0788110
$$162$$ 0 0
$$163$$ −14.3212 −1.12172 −0.560861 0.827910i $$-0.689530\pi$$
−0.560861 + 0.827910i $$0.689530\pi$$
$$164$$ 0 0
$$165$$ −51.8658 −4.03775
$$166$$ 0 0
$$167$$ −6.28358 −0.486238 −0.243119 0.969996i $$-0.578171\pi$$
−0.243119 + 0.969996i $$0.578171\pi$$
$$168$$ 0 0
$$169$$ −1.56164 −0.120126
$$170$$ 0 0
$$171$$ −25.8238 −1.97479
$$172$$ 0 0
$$173$$ −2.60539 −0.198084 −0.0990421 0.995083i $$-0.531578\pi$$
−0.0990421 + 0.995083i $$0.531578\pi$$
$$174$$ 0 0
$$175$$ 4.28854 0.324183
$$176$$ 0 0
$$177$$ 4.94978 0.372048
$$178$$ 0 0
$$179$$ −25.2341 −1.88609 −0.943044 0.332667i $$-0.892051\pi$$
−0.943044 + 0.332667i $$0.892051\pi$$
$$180$$ 0 0
$$181$$ −1.36485 −0.101448 −0.0507242 0.998713i $$-0.516153\pi$$
−0.0507242 + 0.998713i $$0.516153\pi$$
$$182$$ 0 0
$$183$$ −3.71068 −0.274302
$$184$$ 0 0
$$185$$ 15.6017 1.14706
$$186$$ 0 0
$$187$$ 13.7891 1.00836
$$188$$ 0 0
$$189$$ −15.0054 −1.09148
$$190$$ 0 0
$$191$$ 22.1467 1.60248 0.801239 0.598344i $$-0.204174\pi$$
0.801239 + 0.598344i $$0.204174\pi$$
$$192$$ 0 0
$$193$$ 18.3653 1.32197 0.660983 0.750401i $$-0.270139\pi$$
0.660983 + 0.750401i $$0.270139\pi$$
$$194$$ 0 0
$$195$$ 33.5705 2.40403
$$196$$ 0 0
$$197$$ −1.07831 −0.0768261 −0.0384131 0.999262i $$-0.512230\pi$$
−0.0384131 + 0.999262i $$0.512230\pi$$
$$198$$ 0 0
$$199$$ 5.55335 0.393666 0.196833 0.980437i $$-0.436934\pi$$
0.196833 + 0.980437i $$0.436934\pi$$
$$200$$ 0 0
$$201$$ −28.6830 −2.02314
$$202$$ 0 0
$$203$$ −4.00190 −0.280878
$$204$$ 0 0
$$205$$ 17.9688 1.25499
$$206$$ 0 0
$$207$$ 7.60729 0.528743
$$208$$ 0 0
$$209$$ 17.7376 1.22693
$$210$$ 0 0
$$211$$ 19.3543 1.33240 0.666201 0.745772i $$-0.267919\pi$$
0.666201 + 0.745772i $$0.267919\pi$$
$$212$$ 0 0
$$213$$ −47.3334 −3.24323
$$214$$ 0 0
$$215$$ −24.1024 −1.64377
$$216$$ 0 0
$$217$$ −6.97185 −0.473280
$$218$$ 0 0
$$219$$ 43.0792 2.91102
$$220$$ 0 0
$$221$$ −8.92509 −0.600367
$$222$$ 0 0
$$223$$ 2.69234 0.180293 0.0901464 0.995929i $$-0.471267\pi$$
0.0901464 + 0.995929i $$0.471267\pi$$
$$224$$ 0 0
$$225$$ 32.6242 2.17495
$$226$$ 0 0
$$227$$ 8.26663 0.548675 0.274338 0.961633i $$-0.411541\pi$$
0.274338 + 0.961633i $$0.411541\pi$$
$$228$$ 0 0
$$229$$ 26.2369 1.73378 0.866891 0.498499i $$-0.166115\pi$$
0.866891 + 0.498499i $$0.166115\pi$$
$$230$$ 0 0
$$231$$ 17.0180 1.11970
$$232$$ 0 0
$$233$$ 1.17735 0.0771310 0.0385655 0.999256i $$-0.487721\pi$$
0.0385655 + 0.999256i $$0.487721\pi$$
$$234$$ 0 0
$$235$$ 29.1024 1.89843
$$236$$ 0 0
$$237$$ 47.0288 3.05485
$$238$$ 0 0
$$239$$ −5.56911 −0.360236 −0.180118 0.983645i $$-0.557648\pi$$
−0.180118 + 0.983645i $$0.557648\pi$$
$$240$$ 0 0
$$241$$ 8.12518 0.523389 0.261694 0.965151i $$-0.415719\pi$$
0.261694 + 0.965151i $$0.415719\pi$$
$$242$$ 0 0
$$243$$ −39.8223 −2.55460
$$244$$ 0 0
$$245$$ −3.04771 −0.194711
$$246$$ 0 0
$$247$$ −11.4808 −0.730505
$$248$$ 0 0
$$249$$ −2.25961 −0.143197
$$250$$ 0 0
$$251$$ −2.78542 −0.175814 −0.0879071 0.996129i $$-0.528018\pi$$
−0.0879071 + 0.996129i $$0.528018\pi$$
$$252$$ 0 0
$$253$$ −5.22523 −0.328507
$$254$$ 0 0
$$255$$ −26.1943 −1.64035
$$256$$ 0 0
$$257$$ −24.1150 −1.50425 −0.752126 0.659020i $$-0.770971\pi$$
−0.752126 + 0.659020i $$0.770971\pi$$
$$258$$ 0 0
$$259$$ −5.11916 −0.318089
$$260$$ 0 0
$$261$$ −30.4436 −1.88441
$$262$$ 0 0
$$263$$ −3.40905 −0.210211 −0.105106 0.994461i $$-0.533518\pi$$
−0.105106 + 0.994461i $$0.533518\pi$$
$$264$$ 0 0
$$265$$ 36.0239 2.21293
$$266$$ 0 0
$$267$$ −35.3407 −2.16282
$$268$$ 0 0
$$269$$ 5.29044 0.322564 0.161282 0.986908i $$-0.448437\pi$$
0.161282 + 0.986908i $$0.448437\pi$$
$$270$$ 0 0
$$271$$ −16.2206 −0.985331 −0.492666 0.870219i $$-0.663977\pi$$
−0.492666 + 0.870219i $$0.663977\pi$$
$$272$$ 0 0
$$273$$ −11.0150 −0.666658
$$274$$ 0 0
$$275$$ −22.4086 −1.35129
$$276$$ 0 0
$$277$$ −22.2211 −1.33513 −0.667567 0.744550i $$-0.732664\pi$$
−0.667567 + 0.744550i $$0.732664\pi$$
$$278$$ 0 0
$$279$$ −53.0369 −3.17524
$$280$$ 0 0
$$281$$ −5.74964 −0.342995 −0.171497 0.985185i $$-0.554860\pi$$
−0.171497 + 0.985185i $$0.554860\pi$$
$$282$$ 0 0
$$283$$ 14.0108 0.832857 0.416428 0.909169i $$-0.363282\pi$$
0.416428 + 0.909169i $$0.363282\pi$$
$$284$$ 0 0
$$285$$ −33.6950 −1.99592
$$286$$ 0 0
$$287$$ −5.89583 −0.348020
$$288$$ 0 0
$$289$$ −10.0360 −0.590350
$$290$$ 0 0
$$291$$ 10.5352 0.617586
$$292$$ 0 0
$$293$$ 15.7616 0.920801 0.460400 0.887711i $$-0.347706\pi$$
0.460400 + 0.887711i $$0.347706\pi$$
$$294$$ 0 0
$$295$$ 4.63188 0.269678
$$296$$ 0 0
$$297$$ 78.4066 4.54961
$$298$$ 0 0
$$299$$ 3.38206 0.195590
$$300$$ 0 0
$$301$$ 7.90838 0.455831
$$302$$ 0 0
$$303$$ 27.1192 1.55795
$$304$$ 0 0
$$305$$ −3.47237 −0.198827
$$306$$ 0 0
$$307$$ −11.4944 −0.656018 −0.328009 0.944675i $$-0.606378\pi$$
−0.328009 + 0.944675i $$0.606378\pi$$
$$308$$ 0 0
$$309$$ 1.36250 0.0775100
$$310$$ 0 0
$$311$$ −4.41105 −0.250128 −0.125064 0.992149i $$-0.539914\pi$$
−0.125064 + 0.992149i $$0.539914\pi$$
$$312$$ 0 0
$$313$$ −6.20154 −0.350532 −0.175266 0.984521i $$-0.556079\pi$$
−0.175266 + 0.984521i $$0.556079\pi$$
$$314$$ 0 0
$$315$$ −23.1848 −1.30632
$$316$$ 0 0
$$317$$ −9.50769 −0.534005 −0.267003 0.963696i $$-0.586033\pi$$
−0.267003 + 0.963696i $$0.586033\pi$$
$$318$$ 0 0
$$319$$ 20.9108 1.17078
$$320$$ 0 0
$$321$$ −38.7842 −2.16472
$$322$$ 0 0
$$323$$ 8.95819 0.498447
$$324$$ 0 0
$$325$$ 14.5041 0.804544
$$326$$ 0 0
$$327$$ −58.3484 −3.22667
$$328$$ 0 0
$$329$$ −9.54893 −0.526450
$$330$$ 0 0
$$331$$ −10.0087 −0.550130 −0.275065 0.961426i $$-0.588699\pi$$
−0.275065 + 0.961426i $$0.588699\pi$$
$$332$$ 0 0
$$333$$ −38.9429 −2.13406
$$334$$ 0 0
$$335$$ −26.8408 −1.46647
$$336$$ 0 0
$$337$$ 16.5389 0.900929 0.450464 0.892794i $$-0.351258\pi$$
0.450464 + 0.892794i $$0.351258\pi$$
$$338$$ 0 0
$$339$$ 41.1589 2.23544
$$340$$ 0 0
$$341$$ 36.4295 1.97277
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 0 0
$$345$$ 9.92604 0.534400
$$346$$ 0 0
$$347$$ −34.8917 −1.87308 −0.936541 0.350558i $$-0.885992\pi$$
−0.936541 + 0.350558i $$0.885992\pi$$
$$348$$ 0 0
$$349$$ 6.92337 0.370599 0.185300 0.982682i $$-0.440674\pi$$
0.185300 + 0.982682i $$0.440674\pi$$
$$350$$ 0 0
$$351$$ −50.7493 −2.70880
$$352$$ 0 0
$$353$$ 21.6050 1.14992 0.574959 0.818182i $$-0.305018\pi$$
0.574959 + 0.818182i $$0.305018\pi$$
$$354$$ 0 0
$$355$$ −44.2934 −2.35085
$$356$$ 0 0
$$357$$ 8.59475 0.454882
$$358$$ 0 0
$$359$$ 26.2085 1.38323 0.691616 0.722265i $$-0.256899\pi$$
0.691616 + 0.722265i $$0.256899\pi$$
$$360$$ 0 0
$$361$$ −7.47664 −0.393507
$$362$$ 0 0
$$363$$ −53.0969 −2.78687
$$364$$ 0 0
$$365$$ 40.3124 2.11005
$$366$$ 0 0
$$367$$ −16.5650 −0.864688 −0.432344 0.901709i $$-0.642313\pi$$
−0.432344 + 0.901709i $$0.642313\pi$$
$$368$$ 0 0
$$369$$ −44.8513 −2.33487
$$370$$ 0 0
$$371$$ −11.8200 −0.613662
$$372$$ 0 0
$$373$$ 15.6116 0.808340 0.404170 0.914684i $$-0.367560\pi$$
0.404170 + 0.914684i $$0.367560\pi$$
$$374$$ 0 0
$$375$$ −7.06197 −0.364678
$$376$$ 0 0
$$377$$ −13.5347 −0.697071
$$378$$ 0 0
$$379$$ 9.80933 0.503871 0.251936 0.967744i $$-0.418933\pi$$
0.251936 + 0.967744i $$0.418933\pi$$
$$380$$ 0 0
$$381$$ −10.4980 −0.537829
$$382$$ 0 0
$$383$$ 18.4925 0.944921 0.472461 0.881352i $$-0.343366\pi$$
0.472461 + 0.881352i $$0.343366\pi$$
$$384$$ 0 0
$$385$$ 15.9250 0.811612
$$386$$ 0 0
$$387$$ 60.1613 3.05817
$$388$$ 0 0
$$389$$ 11.3030 0.573084 0.286542 0.958068i $$-0.407494\pi$$
0.286542 + 0.958068i $$0.407494\pi$$
$$390$$ 0 0
$$391$$ −2.63895 −0.133457
$$392$$ 0 0
$$393$$ −45.8928 −2.31498
$$394$$ 0 0
$$395$$ 44.0084 2.21430
$$396$$ 0 0
$$397$$ −1.20204 −0.0603285 −0.0301643 0.999545i $$-0.509603\pi$$
−0.0301643 + 0.999545i $$0.509603\pi$$
$$398$$ 0 0
$$399$$ 11.0558 0.553484
$$400$$ 0 0
$$401$$ −3.01127 −0.150376 −0.0751878 0.997169i $$-0.523956\pi$$
−0.0751878 + 0.997169i $$0.523956\pi$$
$$402$$ 0 0
$$403$$ −23.5793 −1.17457
$$404$$ 0 0
$$405$$ −79.3898 −3.94491
$$406$$ 0 0
$$407$$ 26.7488 1.32589
$$408$$ 0 0
$$409$$ −33.4725 −1.65511 −0.827553 0.561387i $$-0.810268\pi$$
−0.827553 + 0.561387i $$0.810268\pi$$
$$410$$ 0 0
$$411$$ −8.70404 −0.429338
$$412$$ 0 0
$$413$$ −1.51979 −0.0747839
$$414$$ 0 0
$$415$$ −2.11449 −0.103796
$$416$$ 0 0
$$417$$ 20.3006 0.994126
$$418$$ 0 0
$$419$$ 6.40028 0.312674 0.156337 0.987704i $$-0.450031\pi$$
0.156337 + 0.987704i $$0.450031\pi$$
$$420$$ 0 0
$$421$$ −8.01082 −0.390423 −0.195212 0.980761i $$-0.562539\pi$$
−0.195212 + 0.980761i $$0.562539\pi$$
$$422$$ 0 0
$$423$$ −72.6415 −3.53195
$$424$$ 0 0
$$425$$ −11.3172 −0.548967
$$426$$ 0 0
$$427$$ 1.13934 0.0551363
$$428$$ 0 0
$$429$$ 57.5558 2.77882
$$430$$ 0 0
$$431$$ 27.6084 1.32985 0.664925 0.746910i $$-0.268463\pi$$
0.664925 + 0.746910i $$0.268463\pi$$
$$432$$ 0 0
$$433$$ −14.8797 −0.715074 −0.357537 0.933899i $$-0.616383\pi$$
−0.357537 + 0.933899i $$0.616383\pi$$
$$434$$ 0 0
$$435$$ −39.7230 −1.90457
$$436$$ 0 0
$$437$$ −3.39461 −0.162386
$$438$$ 0 0
$$439$$ 36.1931 1.72740 0.863702 0.504004i $$-0.168140\pi$$
0.863702 + 0.504004i $$0.168140\pi$$
$$440$$ 0 0
$$441$$ 7.60729 0.362252
$$442$$ 0 0
$$443$$ 10.5546 0.501465 0.250733 0.968056i $$-0.419329\pi$$
0.250733 + 0.968056i $$0.419329\pi$$
$$444$$ 0 0
$$445$$ −33.0710 −1.56771
$$446$$ 0 0
$$447$$ 18.1788 0.859828
$$448$$ 0 0
$$449$$ 39.9560 1.88564 0.942821 0.333301i $$-0.108162\pi$$
0.942821 + 0.333301i $$0.108162\pi$$
$$450$$ 0 0
$$451$$ 30.8071 1.45065
$$452$$ 0 0
$$453$$ −38.5371 −1.81063
$$454$$ 0 0
$$455$$ −10.3076 −0.483226
$$456$$ 0 0
$$457$$ 10.1870 0.476530 0.238265 0.971200i $$-0.423421\pi$$
0.238265 + 0.971200i $$0.423421\pi$$
$$458$$ 0 0
$$459$$ 39.5985 1.84830
$$460$$ 0 0
$$461$$ −6.70956 −0.312495 −0.156248 0.987718i $$-0.549940\pi$$
−0.156248 + 0.987718i $$0.549940\pi$$
$$462$$ 0 0
$$463$$ −16.6512 −0.773848 −0.386924 0.922112i $$-0.626462\pi$$
−0.386924 + 0.922112i $$0.626462\pi$$
$$464$$ 0 0
$$465$$ −69.2029 −3.20921
$$466$$ 0 0
$$467$$ −39.1863 −1.81332 −0.906662 0.421857i $$-0.861378\pi$$
−0.906662 + 0.421857i $$0.861378\pi$$
$$468$$ 0 0
$$469$$ 8.80688 0.406664
$$470$$ 0 0
$$471$$ −56.3491 −2.59643
$$472$$ 0 0
$$473$$ −41.3230 −1.90004
$$474$$ 0 0
$$475$$ −14.5579 −0.667963
$$476$$ 0 0
$$477$$ −89.9180 −4.11706
$$478$$ 0 0
$$479$$ 36.2704 1.65724 0.828619 0.559813i $$-0.189127\pi$$
0.828619 + 0.559813i $$0.189127\pi$$
$$480$$ 0 0
$$481$$ −17.3133 −0.789420
$$482$$ 0 0
$$483$$ −3.25688 −0.148193
$$484$$ 0 0
$$485$$ 9.85861 0.447656
$$486$$ 0 0
$$487$$ −23.7517 −1.07629 −0.538146 0.842851i $$-0.680875\pi$$
−0.538146 + 0.842851i $$0.680875\pi$$
$$488$$ 0 0
$$489$$ 46.6425 2.10925
$$490$$ 0 0
$$491$$ 22.3752 1.00978 0.504889 0.863185i $$-0.331534\pi$$
0.504889 + 0.863185i $$0.331534\pi$$
$$492$$ 0 0
$$493$$ 10.5608 0.475635
$$494$$ 0 0
$$495$$ 121.146 5.44510
$$496$$ 0 0
$$497$$ 14.5333 0.651909
$$498$$ 0 0
$$499$$ −16.2296 −0.726535 −0.363268 0.931685i $$-0.618339\pi$$
−0.363268 + 0.931685i $$0.618339\pi$$
$$500$$ 0 0
$$501$$ 20.4649 0.914304
$$502$$ 0 0
$$503$$ 2.57708 0.114906 0.0574532 0.998348i $$-0.481702\pi$$
0.0574532 + 0.998348i $$0.481702\pi$$
$$504$$ 0 0
$$505$$ 25.3774 1.12928
$$506$$ 0 0
$$507$$ 5.08608 0.225881
$$508$$ 0 0
$$509$$ 33.4091 1.48083 0.740417 0.672148i $$-0.234628\pi$$
0.740417 + 0.672148i $$0.234628\pi$$
$$510$$ 0 0
$$511$$ −13.2271 −0.585134
$$512$$ 0 0
$$513$$ 50.9375 2.24894
$$514$$ 0 0
$$515$$ 1.27500 0.0561830
$$516$$ 0 0
$$517$$ 49.8953 2.19439
$$518$$ 0 0
$$519$$ 8.48546 0.372470
$$520$$ 0 0
$$521$$ 12.4303 0.544580 0.272290 0.962215i $$-0.412219\pi$$
0.272290 + 0.962215i $$0.412219\pi$$
$$522$$ 0 0
$$523$$ −1.05262 −0.0460279 −0.0230140 0.999735i $$-0.507326\pi$$
−0.0230140 + 0.999735i $$0.507326\pi$$
$$524$$ 0 0
$$525$$ −13.9673 −0.609582
$$526$$ 0 0
$$527$$ 18.3984 0.801445
$$528$$ 0 0
$$529$$ 1.00000 0.0434783
$$530$$ 0 0
$$531$$ −11.5615 −0.501725
$$532$$ 0 0
$$533$$ −19.9401 −0.863701
$$534$$ 0 0
$$535$$ −36.2933 −1.56910
$$536$$ 0 0
$$537$$ 82.1847 3.54653
$$538$$ 0 0
$$539$$ −5.22523 −0.225066
$$540$$ 0 0
$$541$$ 29.4265 1.26514 0.632572 0.774502i $$-0.281999\pi$$
0.632572 + 0.774502i $$0.281999\pi$$
$$542$$ 0 0
$$543$$ 4.44515 0.190760
$$544$$ 0 0
$$545$$ −54.6009 −2.33885
$$546$$ 0 0
$$547$$ 36.3851 1.55571 0.777857 0.628441i $$-0.216307\pi$$
0.777857 + 0.628441i $$0.216307\pi$$
$$548$$ 0 0
$$549$$ 8.66726 0.369910
$$550$$ 0 0
$$551$$ 13.5849 0.578735
$$552$$ 0 0
$$553$$ −14.4398 −0.614043
$$554$$ 0 0
$$555$$ −50.8130 −2.15689
$$556$$ 0 0
$$557$$ −22.2666 −0.943467 −0.471734 0.881741i $$-0.656372\pi$$
−0.471734 + 0.881741i $$0.656372\pi$$
$$558$$ 0 0
$$559$$ 26.7466 1.13126
$$560$$ 0 0
$$561$$ −44.9095 −1.89608
$$562$$ 0 0
$$563$$ −22.0300 −0.928453 −0.464227 0.885717i $$-0.653668\pi$$
−0.464227 + 0.885717i $$0.653668\pi$$
$$564$$ 0 0
$$565$$ 38.5154 1.62036
$$566$$ 0 0
$$567$$ 26.0490 1.09395
$$568$$ 0 0
$$569$$ 27.9918 1.17348 0.586738 0.809777i $$-0.300412\pi$$
0.586738 + 0.809777i $$0.300412\pi$$
$$570$$ 0 0
$$571$$ −19.7000 −0.824421 −0.412210 0.911089i $$-0.635243\pi$$
−0.412210 + 0.911089i $$0.635243\pi$$
$$572$$ 0 0
$$573$$ −72.1292 −3.01324
$$574$$ 0 0
$$575$$ 4.28854 0.178845
$$576$$ 0 0
$$577$$ 11.9624 0.498000 0.249000 0.968503i $$-0.419898\pi$$
0.249000 + 0.968503i $$0.419898\pi$$
$$578$$ 0 0
$$579$$ −59.8138 −2.48578
$$580$$ 0 0
$$581$$ 0.693795 0.0287834
$$582$$ 0 0
$$583$$ 61.7620 2.55792
$$584$$ 0 0
$$585$$ −78.4126 −3.24196
$$586$$ 0 0
$$587$$ 19.3278 0.797743 0.398872 0.917007i $$-0.369402\pi$$
0.398872 + 0.917007i $$0.369402\pi$$
$$588$$ 0 0
$$589$$ 23.6667 0.975170
$$590$$ 0 0
$$591$$ 3.51192 0.144461
$$592$$ 0 0
$$593$$ 8.45045 0.347018 0.173509 0.984832i $$-0.444489\pi$$
0.173509 + 0.984832i $$0.444489\pi$$
$$594$$ 0 0
$$595$$ 8.04275 0.329721
$$596$$ 0 0
$$597$$ −18.0866 −0.740235
$$598$$ 0 0
$$599$$ −5.56581 −0.227413 −0.113706 0.993514i $$-0.536272\pi$$
−0.113706 + 0.993514i $$0.536272\pi$$
$$600$$ 0 0
$$601$$ −18.2258 −0.743445 −0.371722 0.928344i $$-0.621233\pi$$
−0.371722 + 0.928344i $$0.621233\pi$$
$$602$$ 0 0
$$603$$ 66.9965 2.72831
$$604$$ 0 0
$$605$$ −49.6868 −2.02005
$$606$$ 0 0
$$607$$ −28.3740 −1.15166 −0.575832 0.817568i $$-0.695322\pi$$
−0.575832 + 0.817568i $$0.695322\pi$$
$$608$$ 0 0
$$609$$ 13.0337 0.528153
$$610$$ 0 0
$$611$$ −32.2951 −1.30652
$$612$$ 0 0
$$613$$ 15.8620 0.640660 0.320330 0.947306i $$-0.396206\pi$$
0.320330 + 0.947306i $$0.396206\pi$$
$$614$$ 0 0
$$615$$ −58.5223 −2.35985
$$616$$ 0 0
$$617$$ −14.9140 −0.600417 −0.300208 0.953874i $$-0.597056\pi$$
−0.300208 + 0.953874i $$0.597056\pi$$
$$618$$ 0 0
$$619$$ −32.3397 −1.29984 −0.649920 0.760002i $$-0.725198\pi$$
−0.649920 + 0.760002i $$0.725198\pi$$
$$620$$ 0 0
$$621$$ −15.0054 −0.602146
$$622$$ 0 0
$$623$$ 10.8511 0.434739
$$624$$ 0 0
$$625$$ −28.0511 −1.12204
$$626$$ 0 0
$$627$$ −57.7693 −2.30708
$$628$$ 0 0
$$629$$ 13.5092 0.538647
$$630$$ 0 0
$$631$$ 15.3840 0.612426 0.306213 0.951963i $$-0.400938\pi$$
0.306213 + 0.951963i $$0.400938\pi$$
$$632$$ 0 0
$$633$$ −63.0346 −2.50540
$$634$$ 0 0
$$635$$ −9.82377 −0.389844
$$636$$ 0 0
$$637$$ 3.38206 0.134002
$$638$$ 0 0
$$639$$ 110.559 4.37366
$$640$$ 0 0
$$641$$ 37.0193 1.46217 0.731087 0.682284i $$-0.239013\pi$$
0.731087 + 0.682284i $$0.239013\pi$$
$$642$$ 0 0
$$643$$ −24.7183 −0.974796 −0.487398 0.873180i $$-0.662054\pi$$
−0.487398 + 0.873180i $$0.662054\pi$$
$$644$$ 0 0
$$645$$ 78.4988 3.09089
$$646$$ 0 0
$$647$$ 20.3207 0.798887 0.399444 0.916758i $$-0.369203\pi$$
0.399444 + 0.916758i $$0.369203\pi$$
$$648$$ 0 0
$$649$$ 7.94124 0.311721
$$650$$ 0 0
$$651$$ 22.7065 0.889938
$$652$$ 0 0
$$653$$ −13.7950 −0.539839 −0.269919 0.962883i $$-0.586997\pi$$
−0.269919 + 0.962883i $$0.586997\pi$$
$$654$$ 0 0
$$655$$ −42.9453 −1.67801
$$656$$ 0 0
$$657$$ −100.623 −3.92566
$$658$$ 0 0
$$659$$ −39.4316 −1.53604 −0.768019 0.640427i $$-0.778757\pi$$
−0.768019 + 0.640427i $$0.778757\pi$$
$$660$$ 0 0
$$661$$ 38.9211 1.51385 0.756927 0.653499i $$-0.226700\pi$$
0.756927 + 0.653499i $$0.226700\pi$$
$$662$$ 0 0
$$663$$ 29.0680 1.12891
$$664$$ 0 0
$$665$$ 10.3458 0.401192
$$666$$ 0 0
$$667$$ −4.00190 −0.154954
$$668$$ 0 0
$$669$$ −8.76865 −0.339016
$$670$$ 0 0
$$671$$ −5.95329 −0.229824
$$672$$ 0 0
$$673$$ −43.7150 −1.68509 −0.842544 0.538627i $$-0.818943\pi$$
−0.842544 + 0.538627i $$0.818943\pi$$
$$674$$ 0 0
$$675$$ −64.3513 −2.47688
$$676$$ 0 0
$$677$$ 16.6777 0.640977 0.320489 0.947252i $$-0.396153\pi$$
0.320489 + 0.947252i $$0.396153\pi$$
$$678$$ 0 0
$$679$$ −3.23476 −0.124139
$$680$$ 0 0
$$681$$ −26.9234 −1.03171
$$682$$ 0 0
$$683$$ −48.7312 −1.86465 −0.932324 0.361625i $$-0.882222\pi$$
−0.932324 + 0.361625i $$0.882222\pi$$
$$684$$ 0 0
$$685$$ −8.14502 −0.311205
$$686$$ 0 0
$$687$$ −85.4504 −3.26014
$$688$$ 0 0
$$689$$ −39.9759 −1.52296
$$690$$ 0 0
$$691$$ 41.7882 1.58970 0.794849 0.606807i $$-0.207550\pi$$
0.794849 + 0.606807i $$0.207550\pi$$
$$692$$ 0 0
$$693$$ −39.7498 −1.50997
$$694$$ 0 0
$$695$$ 18.9968 0.720591
$$696$$ 0 0
$$697$$ 15.5588 0.589331
$$698$$ 0 0
$$699$$ −3.83450 −0.145034
$$700$$ 0 0
$$701$$ −28.1499 −1.06321 −0.531604 0.846993i $$-0.678410\pi$$
−0.531604 + 0.846993i $$0.678410\pi$$
$$702$$ 0 0
$$703$$ 17.3775 0.655406
$$704$$ 0 0
$$705$$ −94.7831 −3.56974
$$706$$ 0 0
$$707$$ −8.32672 −0.313159
$$708$$ 0 0
$$709$$ 22.1680 0.832536 0.416268 0.909242i $$-0.363338\pi$$
0.416268 + 0.909242i $$0.363338\pi$$
$$710$$ 0 0
$$711$$ −109.848 −4.11961
$$712$$ 0 0
$$713$$ −6.97185 −0.261098
$$714$$ 0 0
$$715$$ 53.8593 2.01422
$$716$$ 0 0
$$717$$ 18.1379 0.677374
$$718$$ 0 0
$$719$$ 22.2623 0.830243 0.415122 0.909766i $$-0.363739\pi$$
0.415122 + 0.909766i $$0.363739\pi$$
$$720$$ 0 0
$$721$$ −0.418345 −0.0155800
$$722$$ 0 0
$$723$$ −26.4628 −0.984161
$$724$$ 0 0
$$725$$ −17.1623 −0.637392
$$726$$ 0 0
$$727$$ 21.6618 0.803392 0.401696 0.915773i $$-0.368421\pi$$
0.401696 + 0.915773i $$0.368421\pi$$
$$728$$ 0 0
$$729$$ 51.5497 1.90925
$$730$$ 0 0
$$731$$ −20.8698 −0.771897
$$732$$ 0 0
$$733$$ −4.50596 −0.166431 −0.0832156 0.996532i $$-0.526519\pi$$
−0.0832156 + 0.996532i $$0.526519\pi$$
$$734$$ 0 0
$$735$$ 9.92604 0.366127
$$736$$ 0 0
$$737$$ −46.0179 −1.69509
$$738$$ 0 0
$$739$$ 15.7692 0.580079 0.290040 0.957015i $$-0.406331\pi$$
0.290040 + 0.957015i $$0.406331\pi$$
$$740$$ 0 0
$$741$$ 37.3916 1.37361
$$742$$ 0 0
$$743$$ −30.8619 −1.13222 −0.566108 0.824331i $$-0.691551\pi$$
−0.566108 + 0.824331i $$0.691551\pi$$
$$744$$ 0 0
$$745$$ 17.0113 0.623245
$$746$$ 0 0
$$747$$ 5.27790 0.193108
$$748$$ 0 0
$$749$$ 11.9084 0.435123
$$750$$ 0 0
$$751$$ −38.1808 −1.39324 −0.696618 0.717442i $$-0.745313\pi$$
−0.696618 + 0.717442i $$0.745313\pi$$
$$752$$ 0 0
$$753$$ 9.07179 0.330594
$$754$$ 0 0
$$755$$ −36.0621 −1.31243
$$756$$ 0 0
$$757$$ −15.6733 −0.569655 −0.284828 0.958579i $$-0.591936\pi$$
−0.284828 + 0.958579i $$0.591936\pi$$
$$758$$ 0 0
$$759$$ 17.0180 0.617713
$$760$$ 0 0
$$761$$ 41.8363 1.51657 0.758283 0.651926i $$-0.226039\pi$$
0.758283 + 0.651926i $$0.226039\pi$$
$$762$$ 0 0
$$763$$ 17.9154 0.648581
$$764$$ 0 0
$$765$$ 61.1835 2.21210
$$766$$ 0 0
$$767$$ −5.14003 −0.185596
$$768$$ 0 0
$$769$$ 5.39928 0.194703 0.0973515 0.995250i $$-0.468963\pi$$
0.0973515 + 0.995250i $$0.468963\pi$$
$$770$$ 0 0
$$771$$ 78.5397 2.82854
$$772$$ 0 0
$$773$$ 37.1956 1.33783 0.668917 0.743337i $$-0.266758\pi$$
0.668917 + 0.743337i $$0.266758\pi$$
$$774$$ 0 0
$$775$$ −29.8991 −1.07401
$$776$$ 0 0
$$777$$ 16.6725 0.598123
$$778$$ 0 0
$$779$$ 20.0140 0.717077
$$780$$ 0 0
$$781$$ −75.9399 −2.71734
$$782$$ 0 0
$$783$$ 60.0501 2.14602
$$784$$ 0 0
$$785$$ −52.7301 −1.88202
$$786$$ 0 0
$$787$$ 38.9942 1.38999 0.694997 0.719013i $$-0.255406\pi$$
0.694997 + 0.719013i $$0.255406\pi$$
$$788$$ 0 0
$$789$$ 11.1029 0.395273
$$790$$ 0 0
$$791$$ −12.6375 −0.449338
$$792$$ 0 0
$$793$$ 3.85331 0.136835
$$794$$ 0 0
$$795$$ −117.326 −4.16111
$$796$$ 0 0
$$797$$ 25.8311 0.914986 0.457493 0.889213i $$-0.348747\pi$$
0.457493 + 0.889213i $$0.348747\pi$$
$$798$$ 0 0
$$799$$ 25.1991 0.891482
$$800$$ 0 0
$$801$$ 82.5473 2.91667
$$802$$ 0 0
$$803$$ 69.1147 2.43901
$$804$$ 0 0
$$805$$ −3.04771 −0.107418
$$806$$ 0 0
$$807$$ −17.2303 −0.606537
$$808$$ 0 0
$$809$$ 26.7612 0.940875 0.470437 0.882433i $$-0.344096\pi$$
0.470437 + 0.882433i $$0.344096\pi$$
$$810$$ 0 0
$$811$$ −30.3856 −1.06698 −0.533492 0.845805i $$-0.679120\pi$$
−0.533492 + 0.845805i $$0.679120\pi$$
$$812$$ 0 0
$$813$$ 52.8286 1.85278
$$814$$ 0 0
$$815$$ 43.6469 1.52888
$$816$$ 0 0
$$817$$ −26.8458 −0.939217
$$818$$ 0 0
$$819$$ 25.7283 0.899021
$$820$$ 0 0
$$821$$ −16.5069 −0.576095 −0.288048 0.957616i $$-0.593006\pi$$
−0.288048 + 0.957616i $$0.593006\pi$$
$$822$$ 0 0
$$823$$ 19.9562 0.695631 0.347816 0.937563i $$-0.386924\pi$$
0.347816 + 0.937563i $$0.386924\pi$$
$$824$$ 0 0
$$825$$ 72.9822 2.54091
$$826$$ 0 0
$$827$$ 36.8443 1.28120 0.640601 0.767874i $$-0.278685\pi$$
0.640601 + 0.767874i $$0.278685\pi$$
$$828$$ 0 0
$$829$$ 5.80916 0.201760 0.100880 0.994899i $$-0.467834\pi$$
0.100880 + 0.994899i $$0.467834\pi$$
$$830$$ 0 0
$$831$$ 72.3714 2.51054
$$832$$ 0 0
$$833$$ −2.63895 −0.0914341
$$834$$ 0 0
$$835$$ 19.1505 0.662732
$$836$$ 0 0
$$837$$ 104.615 3.61604
$$838$$ 0 0
$$839$$ 12.2733 0.423722 0.211861 0.977300i $$-0.432048\pi$$
0.211861 + 0.977300i $$0.432048\pi$$
$$840$$ 0 0
$$841$$ −12.9848 −0.447752
$$842$$ 0 0
$$843$$ 18.7259 0.644954
$$844$$ 0 0
$$845$$ 4.75942 0.163729
$$846$$ 0 0
$$847$$ 16.3030 0.560177
$$848$$ 0 0
$$849$$ −45.6316 −1.56607
$$850$$ 0 0
$$851$$ −5.11916 −0.175483
$$852$$ 0 0
$$853$$ −13.2560 −0.453878 −0.226939 0.973909i $$-0.572872\pi$$
−0.226939 + 0.973909i $$0.572872\pi$$
$$854$$ 0 0
$$855$$ 78.7034 2.69160
$$856$$ 0 0
$$857$$ −19.1066 −0.652670 −0.326335 0.945254i $$-0.605814\pi$$
−0.326335 + 0.945254i $$0.605814\pi$$
$$858$$ 0 0
$$859$$ 46.1878 1.57591 0.787953 0.615735i $$-0.211141\pi$$
0.787953 + 0.615735i $$0.211141\pi$$
$$860$$ 0 0
$$861$$ 19.2020 0.654404
$$862$$ 0 0
$$863$$ −11.5341 −0.392625 −0.196313 0.980541i $$-0.562897\pi$$
−0.196313 + 0.980541i $$0.562897\pi$$
$$864$$ 0 0
$$865$$ 7.94048 0.269984
$$866$$ 0 0
$$867$$ 32.6859 1.11007
$$868$$ 0 0
$$869$$ 75.4512 2.55951
$$870$$ 0 0
$$871$$ 29.7854 1.00924
$$872$$ 0 0
$$873$$ −24.6077 −0.832846
$$874$$ 0 0
$$875$$ 2.16832 0.0733026
$$876$$ 0 0
$$877$$ −16.9695 −0.573020 −0.286510 0.958077i $$-0.592495\pi$$
−0.286510 + 0.958077i $$0.592495\pi$$
$$878$$ 0 0
$$879$$ −51.3336 −1.73144
$$880$$ 0 0
$$881$$ 11.4505 0.385775 0.192888 0.981221i $$-0.438215\pi$$
0.192888 + 0.981221i $$0.438215\pi$$
$$882$$ 0 0
$$883$$ −17.3634 −0.584325 −0.292162 0.956369i $$-0.594375\pi$$
−0.292162 + 0.956369i $$0.594375\pi$$
$$884$$ 0 0
$$885$$ −15.0855 −0.507093
$$886$$ 0 0
$$887$$ −22.7378 −0.763460 −0.381730 0.924274i $$-0.624672\pi$$
−0.381730 + 0.924274i $$0.624672\pi$$
$$888$$ 0 0
$$889$$ 3.22333 0.108107
$$890$$ 0 0
$$891$$ −136.112 −4.55992
$$892$$ 0 0
$$893$$ 32.4149 1.08472
$$894$$ 0 0
$$895$$ 76.9064 2.57070
$$896$$ 0 0
$$897$$ −11.0150 −0.367780
$$898$$ 0 0
$$899$$ 27.9006 0.930539
$$900$$ 0 0
$$901$$ 31.1923 1.03917
$$902$$ 0 0
$$903$$ −25.7567 −0.857128
$$904$$ 0 0
$$905$$ 4.15966 0.138272
$$906$$ 0 0
$$907$$ 41.5359 1.37918 0.689588 0.724202i $$-0.257792\pi$$
0.689588 + 0.724202i $$0.257792\pi$$
$$908$$ 0 0
$$909$$ −63.3438 −2.10098
$$910$$ 0 0
$$911$$ −2.92749 −0.0969921 −0.0484961 0.998823i $$-0.515443\pi$$
−0.0484961 + 0.998823i $$0.515443\pi$$
$$912$$ 0 0
$$913$$ −3.62523 −0.119978
$$914$$ 0 0
$$915$$ 11.3091 0.373867
$$916$$ 0 0
$$917$$ 14.0910 0.465326
$$918$$ 0 0
$$919$$ −13.9648 −0.460658 −0.230329 0.973113i $$-0.573980\pi$$
−0.230329 + 0.973113i $$0.573980\pi$$
$$920$$ 0 0
$$921$$ 37.4358 1.23355
$$922$$ 0 0
$$923$$ 49.1527 1.61788
$$924$$ 0 0
$$925$$ −21.9537 −0.721834
$$926$$ 0 0
$$927$$ −3.18247 −0.104526
$$928$$ 0 0
$$929$$ −23.3541 −0.766222 −0.383111 0.923702i $$-0.625147\pi$$
−0.383111 + 0.923702i $$0.625147\pi$$
$$930$$ 0 0
$$931$$ −3.39461 −0.111254
$$932$$ 0 0
$$933$$ 14.3663 0.470331
$$934$$ 0 0
$$935$$ −42.0252 −1.37437
$$936$$ 0 0
$$937$$ 11.1156 0.363130 0.181565 0.983379i $$-0.441884\pi$$
0.181565 + 0.983379i $$0.441884\pi$$
$$938$$ 0 0
$$939$$ 20.1977 0.659127
$$940$$ 0 0
$$941$$ 5.13868 0.167516 0.0837580 0.996486i $$-0.473308\pi$$
0.0837580 + 0.996486i $$0.473308\pi$$
$$942$$ 0 0
$$943$$ −5.89583 −0.191995
$$944$$ 0 0
$$945$$ 45.7321 1.48767
$$946$$ 0 0
$$947$$ −29.4147 −0.955851 −0.477925 0.878400i $$-0.658611\pi$$
−0.477925 + 0.878400i $$0.658611\pi$$
$$948$$ 0 0
$$949$$ −44.7350 −1.45216
$$950$$ 0 0
$$951$$ 30.9655 1.00412
$$952$$ 0 0
$$953$$ −5.67396 −0.183797 −0.0918987 0.995768i $$-0.529294\pi$$
−0.0918987 + 0.995768i $$0.529294\pi$$
$$954$$ 0 0
$$955$$ −67.4967 −2.18414
$$956$$ 0 0
$$957$$ −68.1041 −2.20149
$$958$$ 0 0
$$959$$ 2.67250 0.0862997
$$960$$ 0 0
$$961$$ 17.6067 0.567959
$$962$$ 0 0
$$963$$ 90.5905 2.91924
$$964$$ 0 0
$$965$$ −55.9723 −1.80181
$$966$$ 0 0
$$967$$ 0.898731 0.0289013 0.0144506 0.999896i $$-0.495400\pi$$
0.0144506 + 0.999896i $$0.495400\pi$$
$$968$$ 0 0
$$969$$ −29.1758 −0.937262
$$970$$ 0 0
$$971$$ −34.2084 −1.09780 −0.548899 0.835889i $$-0.684953\pi$$
−0.548899 + 0.835889i $$0.684953\pi$$
$$972$$ 0 0
$$973$$ −6.23315 −0.199825
$$974$$ 0 0
$$975$$ −47.2382 −1.51283
$$976$$ 0 0
$$977$$ 8.19697 0.262244 0.131122 0.991366i $$-0.458142\pi$$
0.131122 + 0.991366i $$0.458142\pi$$
$$978$$ 0 0
$$979$$ −56.6994 −1.81212
$$980$$ 0 0
$$981$$ 136.288 4.35133
$$982$$ 0 0
$$983$$ 1.12997 0.0360406 0.0180203 0.999838i $$-0.494264\pi$$
0.0180203 + 0.999838i $$0.494264\pi$$
$$984$$ 0 0
$$985$$ 3.28637 0.104712
$$986$$ 0 0
$$987$$ 31.0998 0.989917
$$988$$ 0 0
$$989$$ 7.90838 0.251472
$$990$$ 0 0
$$991$$ −14.6766 −0.466218 −0.233109 0.972451i $$-0.574890\pi$$
−0.233109 + 0.972451i $$0.574890\pi$$
$$992$$ 0 0
$$993$$ 32.5973 1.03444
$$994$$ 0 0
$$995$$ −16.9250 −0.536558
$$996$$ 0 0
$$997$$ −1.64207 −0.0520049 −0.0260024 0.999662i $$-0.508278\pi$$
−0.0260024 + 0.999662i $$0.508278\pi$$
$$998$$ 0 0
$$999$$ 76.8151 2.43032
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 2576.2.a.bb.1.1 5
4.3 odd 2 644.2.a.d.1.5 5
12.11 even 2 5796.2.a.t.1.4 5
28.27 even 2 4508.2.a.f.1.1 5

By twisted newform
Twist Min Dim Char Parity Ord Type
644.2.a.d.1.5 5 4.3 odd 2
2576.2.a.bb.1.1 5 1.1 even 1 trivial
4508.2.a.f.1.1 5 28.27 even 2
5796.2.a.t.1.4 5 12.11 even 2