# Properties

 Label 5290.2.a.q.1.3 Level $5290$ Weight $2$ Character 5290.1 Self dual yes Analytic conductor $42.241$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5290 = 2 \cdot 5 \cdot 23^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5290.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$42.2408626693$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.1509.1 Defining polynomial: $$x^{3} - x^{2} - 7x + 4$$ x^3 - x^2 - 7*x + 4 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.3 Root $$-2.47735$$ of defining polynomial Character $$\chi$$ $$=$$ 5290.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.47735 q^{6} +2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.47735 q^{6} +2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +1.00000 q^{10} +4.47735 q^{11} +2.47735 q^{12} +0.137275 q^{13} +2.13727 q^{14} +2.47735 q^{15} +1.00000 q^{16} +1.52265 q^{17} +3.13727 q^{18} +5.09198 q^{19} +1.00000 q^{20} +5.29478 q^{21} +4.47735 q^{22} +2.47735 q^{24} +1.00000 q^{25} +0.137275 q^{26} +0.340078 q^{27} +2.13727 q^{28} -7.22925 q^{29} +2.47735 q^{30} -2.81743 q^{31} +1.00000 q^{32} +11.0920 q^{33} +1.52265 q^{34} +2.13727 q^{35} +3.13727 q^{36} -11.9094 q^{37} +5.09198 q^{38} +0.340078 q^{39} +1.00000 q^{40} +4.47735 q^{41} +5.29478 q^{42} -7.22925 q^{43} +4.47735 q^{44} +3.13727 q^{45} -4.68016 q^{47} +2.47735 q^{48} -2.43206 q^{49} +1.00000 q^{50} +3.77213 q^{51} +0.137275 q^{52} +1.72545 q^{53} +0.340078 q^{54} +4.47735 q^{55} +2.13727 q^{56} +12.6146 q^{57} -7.22925 q^{58} -13.2293 q^{59} +2.47735 q^{60} +9.15751 q^{61} -2.81743 q^{62} +6.70522 q^{63} +1.00000 q^{64} +0.137275 q^{65} +11.0920 q^{66} +2.95470 q^{67} +1.52265 q^{68} +2.13727 q^{70} -1.52265 q^{71} +3.13727 q^{72} -15.2293 q^{73} -11.9094 q^{74} +2.47735 q^{75} +5.09198 q^{76} +9.56933 q^{77} +0.340078 q^{78} +4.68016 q^{79} +1.00000 q^{80} -8.56933 q^{81} +4.47735 q^{82} -16.1840 q^{83} +5.29478 q^{84} +1.52265 q^{85} -7.22925 q^{86} -17.9094 q^{87} +4.47735 q^{88} +4.27455 q^{89} +3.13727 q^{90} +0.293394 q^{91} -6.97977 q^{93} -4.68016 q^{94} +5.09198 q^{95} +2.47735 q^{96} -19.4321 q^{97} -2.43206 q^{98} +14.0467 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10})$$ 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9 $$3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} - q^{15} + 3 q^{16} + 13 q^{17} + 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} - 5 q^{38} - 4 q^{39} + 3 q^{40} + 5 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} - 19 q^{51} - 3 q^{52} + 12 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 26 q^{57} + 2 q^{58} - 16 q^{59} - q^{60} + 9 q^{61} + 5 q^{62} + 42 q^{63} + 3 q^{64} - 3 q^{65} + 13 q^{66} - 8 q^{67} + 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} - 2 q^{74} - q^{75} - 5 q^{76} - 4 q^{78} + 4 q^{79} + 3 q^{80} + 3 q^{81} + 5 q^{82} - 8 q^{83} - 6 q^{84} + 13 q^{85} + 2 q^{86} - 20 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{90} + 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} - 33 q^{97} + 18 q^{98} + 5 q^{99}+O(q^{100})$$ 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^10 + 5 * q^11 - q^12 - 3 * q^13 + 3 * q^14 - q^15 + 3 * q^16 + 13 * q^17 + 6 * q^18 - 5 * q^19 + 3 * q^20 - 6 * q^21 + 5 * q^22 - q^24 + 3 * q^25 - 3 * q^26 - 4 * q^27 + 3 * q^28 + 2 * q^29 - q^30 + 5 * q^31 + 3 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 + 6 * q^36 - 2 * q^37 - 5 * q^38 - 4 * q^39 + 3 * q^40 + 5 * q^41 - 6 * q^42 + 2 * q^43 + 5 * q^44 + 6 * q^45 - 4 * q^47 - q^48 + 18 * q^49 + 3 * q^50 - 19 * q^51 - 3 * q^52 + 12 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 26 * q^57 + 2 * q^58 - 16 * q^59 - q^60 + 9 * q^61 + 5 * q^62 + 42 * q^63 + 3 * q^64 - 3 * q^65 + 13 * q^66 - 8 * q^67 + 13 * q^68 + 3 * q^70 - 13 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 - q^75 - 5 * q^76 - 4 * q^78 + 4 * q^79 + 3 * q^80 + 3 * q^81 + 5 * q^82 - 8 * q^83 - 6 * q^84 + 13 * q^85 + 2 * q^86 - 20 * q^87 + 5 * q^88 + 6 * q^89 + 6 * q^90 + 33 * q^91 - 36 * q^93 - 4 * q^94 - 5 * q^95 - q^96 - 33 * q^97 + 18 * q^98 + 5 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 2.47735 1.43030 0.715150 0.698971i $$-0.246358\pi$$
0.715150 + 0.698971i $$0.246358\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 1.00000 0.447214
$$6$$ 2.47735 1.01137
$$7$$ 2.13727 0.807814 0.403907 0.914800i $$-0.367652\pi$$
0.403907 + 0.914800i $$0.367652\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 3.13727 1.04576
$$10$$ 1.00000 0.316228
$$11$$ 4.47735 1.34997 0.674986 0.737830i $$-0.264150\pi$$
0.674986 + 0.737830i $$0.264150\pi$$
$$12$$ 2.47735 0.715150
$$13$$ 0.137275 0.0380731 0.0190366 0.999819i $$-0.493940\pi$$
0.0190366 + 0.999819i $$0.493940\pi$$
$$14$$ 2.13727 0.571211
$$15$$ 2.47735 0.639650
$$16$$ 1.00000 0.250000
$$17$$ 1.52265 0.369296 0.184648 0.982805i $$-0.440885\pi$$
0.184648 + 0.982805i $$0.440885\pi$$
$$18$$ 3.13727 0.739463
$$19$$ 5.09198 1.16818 0.584090 0.811689i $$-0.301451\pi$$
0.584090 + 0.811689i $$0.301451\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 5.29478 1.15542
$$22$$ 4.47735 0.954575
$$23$$ 0 0
$$24$$ 2.47735 0.505687
$$25$$ 1.00000 0.200000
$$26$$ 0.137275 0.0269218
$$27$$ 0.340078 0.0654480
$$28$$ 2.13727 0.403907
$$29$$ −7.22925 −1.34244 −0.671219 0.741259i $$-0.734229\pi$$
−0.671219 + 0.741259i $$0.734229\pi$$
$$30$$ 2.47735 0.452301
$$31$$ −2.81743 −0.506025 −0.253013 0.967463i $$-0.581421\pi$$
−0.253013 + 0.967463i $$0.581421\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 11.0920 1.93087
$$34$$ 1.52265 0.261132
$$35$$ 2.13727 0.361265
$$36$$ 3.13727 0.522879
$$37$$ −11.9094 −1.95789 −0.978947 0.204113i $$-0.934569\pi$$
−0.978947 + 0.204113i $$0.934569\pi$$
$$38$$ 5.09198 0.826028
$$39$$ 0.340078 0.0544560
$$40$$ 1.00000 0.158114
$$41$$ 4.47735 0.699245 0.349622 0.936891i $$-0.386310\pi$$
0.349622 + 0.936891i $$0.386310\pi$$
$$42$$ 5.29478 0.817003
$$43$$ −7.22925 −1.10245 −0.551225 0.834356i $$-0.685840\pi$$
−0.551225 + 0.834356i $$0.685840\pi$$
$$44$$ 4.47735 0.674986
$$45$$ 3.13727 0.467677
$$46$$ 0 0
$$47$$ −4.68016 −0.682671 −0.341335 0.939942i $$-0.610879\pi$$
−0.341335 + 0.939942i $$0.610879\pi$$
$$48$$ 2.47735 0.357575
$$49$$ −2.43206 −0.347437
$$50$$ 1.00000 0.141421
$$51$$ 3.77213 0.528205
$$52$$ 0.137275 0.0190366
$$53$$ 1.72545 0.237009 0.118504 0.992954i $$-0.462190\pi$$
0.118504 + 0.992954i $$0.462190\pi$$
$$54$$ 0.340078 0.0462787
$$55$$ 4.47735 0.603726
$$56$$ 2.13727 0.285605
$$57$$ 12.6146 1.67085
$$58$$ −7.22925 −0.949248
$$59$$ −13.2293 −1.72230 −0.861151 0.508349i $$-0.830256\pi$$
−0.861151 + 0.508349i $$0.830256\pi$$
$$60$$ 2.47735 0.319825
$$61$$ 9.15751 1.17250 0.586249 0.810131i $$-0.300604\pi$$
0.586249 + 0.810131i $$0.300604\pi$$
$$62$$ −2.81743 −0.357814
$$63$$ 6.70522 0.844778
$$64$$ 1.00000 0.125000
$$65$$ 0.137275 0.0170268
$$66$$ 11.0920 1.36533
$$67$$ 2.95470 0.360975 0.180487 0.983577i $$-0.442233\pi$$
0.180487 + 0.983577i $$0.442233\pi$$
$$68$$ 1.52265 0.184648
$$69$$ 0 0
$$70$$ 2.13727 0.255453
$$71$$ −1.52265 −0.180705 −0.0903525 0.995910i $$-0.528799\pi$$
−0.0903525 + 0.995910i $$0.528799\pi$$
$$72$$ 3.13727 0.369731
$$73$$ −15.2293 −1.78245 −0.891225 0.453562i $$-0.850153\pi$$
−0.891225 + 0.453562i $$0.850153\pi$$
$$74$$ −11.9094 −1.38444
$$75$$ 2.47735 0.286060
$$76$$ 5.09198 0.584090
$$77$$ 9.56933 1.09053
$$78$$ 0.340078 0.0385062
$$79$$ 4.68016 0.526559 0.263279 0.964720i $$-0.415196\pi$$
0.263279 + 0.964720i $$0.415196\pi$$
$$80$$ 1.00000 0.111803
$$81$$ −8.56933 −0.952148
$$82$$ 4.47735 0.494441
$$83$$ −16.1840 −1.77642 −0.888210 0.459437i $$-0.848051\pi$$
−0.888210 + 0.459437i $$0.848051\pi$$
$$84$$ 5.29478 0.577708
$$85$$ 1.52265 0.165154
$$86$$ −7.22925 −0.779551
$$87$$ −17.9094 −1.92009
$$88$$ 4.47735 0.477287
$$89$$ 4.27455 0.453101 0.226551 0.973999i $$-0.427255\pi$$
0.226551 + 0.973999i $$0.427255\pi$$
$$90$$ 3.13727 0.330698
$$91$$ 0.293394 0.0307560
$$92$$ 0 0
$$93$$ −6.97977 −0.723768
$$94$$ −4.68016 −0.482721
$$95$$ 5.09198 0.522426
$$96$$ 2.47735 0.252844
$$97$$ −19.4321 −1.97303 −0.986513 0.163682i $$-0.947663\pi$$
−0.986513 + 0.163682i $$0.947663\pi$$
$$98$$ −2.43206 −0.245675
$$99$$ 14.0467 1.41174
$$100$$ 1.00000 0.100000
$$101$$ −11.9094 −1.18503 −0.592515 0.805559i $$-0.701865\pi$$
−0.592515 + 0.805559i $$0.701865\pi$$
$$102$$ 3.77213 0.373497
$$103$$ 12.1122 1.19345 0.596726 0.802445i $$-0.296468\pi$$
0.596726 + 0.802445i $$0.296468\pi$$
$$104$$ 0.137275 0.0134609
$$105$$ 5.29478 0.516718
$$106$$ 1.72545 0.167591
$$107$$ 6.00000 0.580042 0.290021 0.957020i $$-0.406338\pi$$
0.290021 + 0.957020i $$0.406338\pi$$
$$108$$ 0.340078 0.0327240
$$109$$ 6.90802 0.661668 0.330834 0.943689i $$-0.392670\pi$$
0.330834 + 0.943689i $$0.392670\pi$$
$$110$$ 4.47735 0.426899
$$111$$ −29.5038 −2.80038
$$112$$ 2.13727 0.201953
$$113$$ 13.2293 1.24450 0.622252 0.782817i $$-0.286218\pi$$
0.622252 + 0.782817i $$0.286218\pi$$
$$114$$ 12.6146 1.18147
$$115$$ 0 0
$$116$$ −7.22925 −0.671219
$$117$$ 0.430668 0.0398153
$$118$$ −13.2293 −1.21785
$$119$$ 3.25432 0.298323
$$120$$ 2.47735 0.226150
$$121$$ 9.04668 0.822426
$$122$$ 9.15751 0.829082
$$123$$ 11.0920 1.00013
$$124$$ −2.81743 −0.253013
$$125$$ 1.00000 0.0894427
$$126$$ 6.70522 0.597348
$$127$$ 20.0934 1.78300 0.891499 0.453023i $$-0.149654\pi$$
0.891499 + 0.453023i $$0.149654\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −17.9094 −1.57684
$$130$$ 0.137275 0.0120398
$$131$$ 5.90941 0.516307 0.258154 0.966104i $$-0.416886\pi$$
0.258154 + 0.966104i $$0.416886\pi$$
$$132$$ 11.0920 0.965433
$$133$$ 10.8830 0.943672
$$134$$ 2.95470 0.255248
$$135$$ 0.340078 0.0292692
$$136$$ 1.52265 0.130566
$$137$$ −12.3212 −1.05267 −0.526337 0.850276i $$-0.676435\pi$$
−0.526337 + 0.850276i $$0.676435\pi$$
$$138$$ 0 0
$$139$$ 16.9547 1.43808 0.719040 0.694969i $$-0.244582\pi$$
0.719040 + 0.694969i $$0.244582\pi$$
$$140$$ 2.13727 0.180633
$$141$$ −11.5944 −0.976424
$$142$$ −1.52265 −0.127778
$$143$$ 0.614627 0.0513977
$$144$$ 3.13727 0.261440
$$145$$ −7.22925 −0.600357
$$146$$ −15.2293 −1.26038
$$147$$ −6.02506 −0.496939
$$148$$ −11.9094 −0.978947
$$149$$ 17.0920 1.40023 0.700115 0.714030i $$-0.253132\pi$$
0.700115 + 0.714030i $$0.253132\pi$$
$$150$$ 2.47735 0.202275
$$151$$ 18.4774 1.50367 0.751833 0.659354i $$-0.229170\pi$$
0.751833 + 0.659354i $$0.229170\pi$$
$$152$$ 5.09198 0.413014
$$153$$ 4.77696 0.386195
$$154$$ 9.56933 0.771119
$$155$$ −2.81743 −0.226301
$$156$$ 0.340078 0.0272280
$$157$$ −14.9547 −1.19352 −0.596758 0.802422i $$-0.703545\pi$$
−0.596758 + 0.802422i $$0.703545\pi$$
$$158$$ 4.68016 0.372333
$$159$$ 4.27455 0.338994
$$160$$ 1.00000 0.0790569
$$161$$ 0 0
$$162$$ −8.56933 −0.673270
$$163$$ −11.3665 −0.890295 −0.445148 0.895457i $$-0.646849\pi$$
−0.445148 + 0.895457i $$0.646849\pi$$
$$164$$ 4.47735 0.349622
$$165$$ 11.0920 0.863509
$$166$$ −16.1840 −1.25612
$$167$$ 10.1840 0.788058 0.394029 0.919098i $$-0.371081\pi$$
0.394029 + 0.919098i $$0.371081\pi$$
$$168$$ 5.29478 0.408501
$$169$$ −12.9812 −0.998550
$$170$$ 1.52265 0.116782
$$171$$ 15.9749 1.22163
$$172$$ −7.22925 −0.551225
$$173$$ 4.47735 0.340407 0.170203 0.985409i $$-0.445558\pi$$
0.170203 + 0.985409i $$0.445558\pi$$
$$174$$ −17.9094 −1.35771
$$175$$ 2.13727 0.161563
$$176$$ 4.47735 0.337493
$$177$$ −32.7735 −2.46341
$$178$$ 4.27455 0.320391
$$179$$ −7.72545 −0.577427 −0.288714 0.957415i $$-0.593228\pi$$
−0.288714 + 0.957415i $$0.593228\pi$$
$$180$$ 3.13727 0.233839
$$181$$ 9.36653 0.696209 0.348104 0.937456i $$-0.386826\pi$$
0.348104 + 0.937456i $$0.386826\pi$$
$$182$$ 0.293394 0.0217478
$$183$$ 22.6864 1.67702
$$184$$ 0 0
$$185$$ −11.9094 −0.875597
$$186$$ −6.97977 −0.511781
$$187$$ 6.81743 0.498540
$$188$$ −4.68016 −0.341335
$$189$$ 0.726839 0.0528698
$$190$$ 5.09198 0.369411
$$191$$ 16.2745 1.17759 0.588793 0.808284i $$-0.299604\pi$$
0.588793 + 0.808284i $$0.299604\pi$$
$$192$$ 2.47735 0.178788
$$193$$ −6.95470 −0.500611 −0.250305 0.968167i $$-0.580531\pi$$
−0.250305 + 0.968167i $$0.580531\pi$$
$$194$$ −19.4321 −1.39514
$$195$$ 0.340078 0.0243535
$$196$$ −2.43206 −0.173718
$$197$$ 1.43206 0.102030 0.0510149 0.998698i $$-0.483754\pi$$
0.0510149 + 0.998698i $$0.483754\pi$$
$$198$$ 14.0467 0.998254
$$199$$ −5.90941 −0.418907 −0.209453 0.977819i $$-0.567168\pi$$
−0.209453 + 0.977819i $$0.567168\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 7.31984 0.516302
$$202$$ −11.9094 −0.837943
$$203$$ −15.4509 −1.08444
$$204$$ 3.77213 0.264102
$$205$$ 4.47735 0.312712
$$206$$ 12.1122 0.843898
$$207$$ 0 0
$$208$$ 0.137275 0.00951828
$$209$$ 22.7986 1.57701
$$210$$ 5.29478 0.365375
$$211$$ 17.6349 1.21403 0.607017 0.794689i $$-0.292366\pi$$
0.607017 + 0.794689i $$0.292366\pi$$
$$212$$ 1.72545 0.118504
$$213$$ −3.77213 −0.258462
$$214$$ 6.00000 0.410152
$$215$$ −7.22925 −0.493031
$$216$$ 0.340078 0.0231394
$$217$$ −6.02162 −0.408774
$$218$$ 6.90802 0.467870
$$219$$ −37.7282 −2.54944
$$220$$ 4.47735 0.301863
$$221$$ 0.209021 0.0140603
$$222$$ −29.5038 −1.98017
$$223$$ 13.5038 0.904282 0.452141 0.891947i $$-0.350660\pi$$
0.452141 + 0.891947i $$0.350660\pi$$
$$224$$ 2.13727 0.142803
$$225$$ 3.13727 0.209152
$$226$$ 13.2293 0.879997
$$227$$ −19.6349 −1.30321 −0.651606 0.758558i $$-0.725904\pi$$
−0.651606 + 0.758558i $$0.725904\pi$$
$$228$$ 12.6146 0.835424
$$229$$ 0.0905906 0.00598640 0.00299320 0.999996i $$-0.499047\pi$$
0.00299320 + 0.999996i $$0.499047\pi$$
$$230$$ 0 0
$$231$$ 23.7066 1.55978
$$232$$ −7.22925 −0.474624
$$233$$ −2.95470 −0.193569 −0.0967846 0.995305i $$-0.530856\pi$$
−0.0967846 + 0.995305i $$0.530856\pi$$
$$234$$ 0.430668 0.0281537
$$235$$ −4.68016 −0.305300
$$236$$ −13.2293 −0.861151
$$237$$ 11.5944 0.753137
$$238$$ 3.25432 0.210946
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 2.47735 0.159912
$$241$$ 5.90941 0.380659 0.190329 0.981720i $$-0.439044\pi$$
0.190329 + 0.981720i $$0.439044\pi$$
$$242$$ 9.04668 0.581543
$$243$$ −22.2495 −1.42731
$$244$$ 9.15751 0.586249
$$245$$ −2.43206 −0.155378
$$246$$ 11.0920 0.707199
$$247$$ 0.699000 0.0444763
$$248$$ −2.81743 −0.178907
$$249$$ −40.0934 −2.54081
$$250$$ 1.00000 0.0632456
$$251$$ −19.5505 −1.23402 −0.617008 0.786957i $$-0.711655\pi$$
−0.617008 + 0.786957i $$0.711655\pi$$
$$252$$ 6.70522 0.422389
$$253$$ 0 0
$$254$$ 20.0934 1.26077
$$255$$ 3.77213 0.236220
$$256$$ 1.00000 0.0625000
$$257$$ 29.4132 1.83475 0.917373 0.398029i $$-0.130306\pi$$
0.917373 + 0.398029i $$0.130306\pi$$
$$258$$ −17.9094 −1.11499
$$259$$ −25.4537 −1.58161
$$260$$ 0.137275 0.00851341
$$261$$ −22.6802 −1.40387
$$262$$ 5.90941 0.365085
$$263$$ 5.79720 0.357470 0.178735 0.983897i $$-0.442799\pi$$
0.178735 + 0.983897i $$0.442799\pi$$
$$264$$ 11.0920 0.682664
$$265$$ 1.72545 0.105994
$$266$$ 10.8830 0.667277
$$267$$ 10.5896 0.648071
$$268$$ 2.95470 0.180487
$$269$$ 8.86411 0.540455 0.270227 0.962797i $$-0.412901\pi$$
0.270227 + 0.962797i $$0.412901\pi$$
$$270$$ 0.340078 0.0206965
$$271$$ 21.0014 1.27574 0.637872 0.770143i $$-0.279815\pi$$
0.637872 + 0.770143i $$0.279815\pi$$
$$272$$ 1.52265 0.0923241
$$273$$ 0.726839 0.0439903
$$274$$ −12.3212 −0.744353
$$275$$ 4.47735 0.269995
$$276$$ 0 0
$$277$$ −22.3679 −1.34396 −0.671979 0.740570i $$-0.734555\pi$$
−0.671979 + 0.740570i $$0.734555\pi$$
$$278$$ 16.9547 1.01688
$$279$$ −8.83905 −0.529180
$$280$$ 2.13727 0.127727
$$281$$ −10.5896 −0.631720 −0.315860 0.948806i $$-0.602293\pi$$
−0.315860 + 0.948806i $$0.602293\pi$$
$$282$$ −11.5944 −0.690436
$$283$$ −7.22925 −0.429735 −0.214867 0.976643i $$-0.568932\pi$$
−0.214867 + 0.976643i $$0.568932\pi$$
$$284$$ −1.52265 −0.0903525
$$285$$ 12.6146 0.747226
$$286$$ 0.614627 0.0363437
$$287$$ 9.56933 0.564860
$$288$$ 3.13727 0.184866
$$289$$ −14.6815 −0.863620
$$290$$ −7.22925 −0.424516
$$291$$ −48.1401 −2.82202
$$292$$ −15.2293 −0.891225
$$293$$ 17.8188 1.04099 0.520493 0.853866i $$-0.325748\pi$$
0.520493 + 0.853866i $$0.325748\pi$$
$$294$$ −6.02506 −0.351389
$$295$$ −13.2293 −0.770237
$$296$$ −11.9094 −0.692220
$$297$$ 1.52265 0.0883530
$$298$$ 17.0920 0.990112
$$299$$ 0 0
$$300$$ 2.47735 0.143030
$$301$$ −15.4509 −0.890575
$$302$$ 18.4774 1.06325
$$303$$ −29.5038 −1.69495
$$304$$ 5.09198 0.292045
$$305$$ 9.15751 0.524357
$$306$$ 4.77696 0.273081
$$307$$ 17.3415 0.989730 0.494865 0.868970i $$-0.335218\pi$$
0.494865 + 0.868970i $$0.335218\pi$$
$$308$$ 9.56933 0.545263
$$309$$ 30.0062 1.70699
$$310$$ −2.81743 −0.160019
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 0.340078 0.0192531
$$313$$ 12.3212 0.696437 0.348219 0.937413i $$-0.386787\pi$$
0.348219 + 0.937413i $$0.386787\pi$$
$$314$$ −14.9547 −0.843943
$$315$$ 6.70522 0.377796
$$316$$ 4.68016 0.263279
$$317$$ −21.7721 −1.22284 −0.611422 0.791304i $$-0.709402\pi$$
−0.611422 + 0.791304i $$0.709402\pi$$
$$318$$ 4.27455 0.239705
$$319$$ −32.3679 −1.81226
$$320$$ 1.00000 0.0559017
$$321$$ 14.8641 0.829634
$$322$$ 0 0
$$323$$ 7.75329 0.431405
$$324$$ −8.56933 −0.476074
$$325$$ 0.137275 0.00761463
$$326$$ −11.3665 −0.629534
$$327$$ 17.1136 0.946384
$$328$$ 4.47735 0.247220
$$329$$ −10.0028 −0.551471
$$330$$ 11.0920 0.610593
$$331$$ −0.274549 −0.0150906 −0.00754530 0.999972i $$-0.502402\pi$$
−0.00754530 + 0.999972i $$0.502402\pi$$
$$332$$ −16.1840 −0.888210
$$333$$ −37.3631 −2.04748
$$334$$ 10.1840 0.557241
$$335$$ 2.95470 0.161433
$$336$$ 5.29478 0.288854
$$337$$ 20.0467 1.09201 0.546006 0.837781i $$-0.316147\pi$$
0.546006 + 0.837781i $$0.316147\pi$$
$$338$$ −12.9812 −0.706082
$$339$$ 32.7735 1.78001
$$340$$ 1.52265 0.0825772
$$341$$ −12.6146 −0.683120
$$342$$ 15.9749 0.863826
$$343$$ −20.1589 −1.08848
$$344$$ −7.22925 −0.389775
$$345$$ 0 0
$$346$$ 4.47735 0.240704
$$347$$ 1.11704 0.0599659 0.0299830 0.999550i $$-0.490455\pi$$
0.0299830 + 0.999550i $$0.490455\pi$$
$$348$$ −17.9094 −0.960045
$$349$$ −28.7331 −1.53805 −0.769023 0.639222i $$-0.779257\pi$$
−0.769023 + 0.639222i $$0.779257\pi$$
$$350$$ 2.13727 0.114242
$$351$$ 0.0466840 0.00249181
$$352$$ 4.47735 0.238644
$$353$$ −6.82365 −0.363186 −0.181593 0.983374i $$-0.558125\pi$$
−0.181593 + 0.983374i $$0.558125\pi$$
$$354$$ −32.7735 −1.74189
$$355$$ −1.52265 −0.0808137
$$356$$ 4.27455 0.226551
$$357$$ 8.06209 0.426691
$$358$$ −7.72545 −0.408303
$$359$$ 22.5896 1.19223 0.596116 0.802898i $$-0.296710\pi$$
0.596116 + 0.802898i $$0.296710\pi$$
$$360$$ 3.13727 0.165349
$$361$$ 6.92825 0.364645
$$362$$ 9.36653 0.492294
$$363$$ 22.4118 1.17632
$$364$$ 0.293394 0.0153780
$$365$$ −15.2293 −0.797136
$$366$$ 22.6864 1.18584
$$367$$ 32.3679 1.68959 0.844796 0.535089i $$-0.179722\pi$$
0.844796 + 0.535089i $$0.179722\pi$$
$$368$$ 0 0
$$369$$ 14.0467 0.731241
$$370$$ −11.9094 −0.619141
$$371$$ 3.68776 0.191459
$$372$$ −6.97977 −0.361884
$$373$$ −13.7255 −0.710677 −0.355338 0.934738i $$-0.615634\pi$$
−0.355338 + 0.934738i $$0.615634\pi$$
$$374$$ 6.81743 0.352521
$$375$$ 2.47735 0.127930
$$376$$ −4.68016 −0.241361
$$377$$ −0.992393 −0.0511109
$$378$$ 0.726839 0.0373846
$$379$$ −28.4774 −1.46278 −0.731392 0.681958i $$-0.761129\pi$$
−0.731392 + 0.681958i $$0.761129\pi$$
$$380$$ 5.09198 0.261213
$$381$$ 49.7784 2.55022
$$382$$ 16.2745 0.832678
$$383$$ 9.36031 0.478290 0.239145 0.970984i $$-0.423133\pi$$
0.239145 + 0.970984i $$0.423133\pi$$
$$384$$ 2.47735 0.126422
$$385$$ 9.56933 0.487698
$$386$$ −6.95470 −0.353985
$$387$$ −22.6802 −1.15290
$$388$$ −19.4321 −0.986513
$$389$$ 30.1122 1.52675 0.763375 0.645956i $$-0.223541\pi$$
0.763375 + 0.645956i $$0.223541\pi$$
$$390$$ 0.340078 0.0172205
$$391$$ 0 0
$$392$$ −2.43206 −0.122837
$$393$$ 14.6397 0.738475
$$394$$ 1.43206 0.0721460
$$395$$ 4.68016 0.235484
$$396$$ 14.0467 0.705872
$$397$$ 12.8830 0.646577 0.323289 0.946300i $$-0.395212\pi$$
0.323289 + 0.946300i $$0.395212\pi$$
$$398$$ −5.90941 −0.296212
$$399$$ 26.9609 1.34973
$$400$$ 1.00000 0.0500000
$$401$$ −22.0028 −1.09877 −0.549383 0.835571i $$-0.685137\pi$$
−0.549383 + 0.835571i $$0.685137\pi$$
$$402$$ 7.31984 0.365081
$$403$$ −0.386762 −0.0192660
$$404$$ −11.9094 −0.592515
$$405$$ −8.56933 −0.425814
$$406$$ −15.4509 −0.766815
$$407$$ −53.3226 −2.64310
$$408$$ 3.77213 0.186748
$$409$$ −13.7721 −0.680988 −0.340494 0.940247i $$-0.610594\pi$$
−0.340494 + 0.940247i $$0.610594\pi$$
$$410$$ 4.47735 0.221121
$$411$$ −30.5240 −1.50564
$$412$$ 12.1122 0.596726
$$413$$ −28.2745 −1.39130
$$414$$ 0 0
$$415$$ −16.1840 −0.794439
$$416$$ 0.137275 0.00673044
$$417$$ 42.0028 2.05688
$$418$$ 22.7986 1.11512
$$419$$ 1.31984 0.0644786 0.0322393 0.999480i $$-0.489736\pi$$
0.0322393 + 0.999480i $$0.489736\pi$$
$$420$$ 5.29478 0.258359
$$421$$ −25.4599 −1.24084 −0.620420 0.784270i $$-0.713038\pi$$
−0.620420 + 0.784270i $$0.713038\pi$$
$$422$$ 17.6349 0.858452
$$423$$ −14.6829 −0.713909
$$424$$ 1.72545 0.0837953
$$425$$ 1.52265 0.0738593
$$426$$ −3.77213 −0.182761
$$427$$ 19.5721 0.947161
$$428$$ 6.00000 0.290021
$$429$$ 1.52265 0.0735141
$$430$$ −7.22925 −0.348626
$$431$$ 29.9094 1.44069 0.720343 0.693618i $$-0.243985\pi$$
0.720343 + 0.693618i $$0.243985\pi$$
$$432$$ 0.340078 0.0163620
$$433$$ −3.77213 −0.181277 −0.0906386 0.995884i $$-0.528891\pi$$
−0.0906386 + 0.995884i $$0.528891\pi$$
$$434$$ −6.02162 −0.289047
$$435$$ −17.9094 −0.858690
$$436$$ 6.90802 0.330834
$$437$$ 0 0
$$438$$ −37.7282 −1.80272
$$439$$ 1.99378 0.0951580 0.0475790 0.998867i $$-0.484849\pi$$
0.0475790 + 0.998867i $$0.484849\pi$$
$$440$$ 4.47735 0.213449
$$441$$ −7.63003 −0.363335
$$442$$ 0.209021 0.00994211
$$443$$ 12.7268 0.604670 0.302335 0.953202i $$-0.402234\pi$$
0.302335 + 0.953202i $$0.402234\pi$$
$$444$$ −29.5038 −1.40019
$$445$$ 4.27455 0.202633
$$446$$ 13.5038 0.639424
$$447$$ 42.3429 2.00275
$$448$$ 2.13727 0.100977
$$449$$ −35.4070 −1.67096 −0.835480 0.549521i $$-0.814810\pi$$
−0.835480 + 0.549521i $$0.814810\pi$$
$$450$$ 3.13727 0.147893
$$451$$ 20.0467 0.943961
$$452$$ 13.2293 0.622252
$$453$$ 45.7749 2.15069
$$454$$ −19.6349 −0.921510
$$455$$ 0.293394 0.0137545
$$456$$ 12.6146 0.590734
$$457$$ 7.31984 0.342408 0.171204 0.985236i $$-0.445234\pi$$
0.171204 + 0.985236i $$0.445234\pi$$
$$458$$ 0.0905906 0.00423302
$$459$$ 0.517818 0.0241697
$$460$$ 0 0
$$461$$ 22.2745 1.03743 0.518715 0.854947i $$-0.326411\pi$$
0.518715 + 0.854947i $$0.326411\pi$$
$$462$$ 23.7066 1.10293
$$463$$ 8.82365 0.410070 0.205035 0.978755i $$-0.434269\pi$$
0.205035 + 0.978755i $$0.434269\pi$$
$$464$$ −7.22925 −0.335610
$$465$$ −6.97977 −0.323679
$$466$$ −2.95470 −0.136874
$$467$$ −16.1840 −0.748904 −0.374452 0.927246i $$-0.622169\pi$$
−0.374452 + 0.927246i $$0.622169\pi$$
$$468$$ 0.430668 0.0199076
$$469$$ 6.31502 0.291600
$$470$$ −4.68016 −0.215879
$$471$$ −37.0481 −1.70709
$$472$$ −13.2293 −0.608926
$$473$$ −32.3679 −1.48828
$$474$$ 11.5944 0.532548
$$475$$ 5.09198 0.233636
$$476$$ 3.25432 0.149161
$$477$$ 5.41321 0.247854
$$478$$ 12.0000 0.548867
$$479$$ −10.3651 −0.473595 −0.236798 0.971559i $$-0.576098\pi$$
−0.236798 + 0.971559i $$0.576098\pi$$
$$480$$ 2.47735 0.113075
$$481$$ −1.63486 −0.0745432
$$482$$ 5.90941 0.269166
$$483$$ 0 0
$$484$$ 9.04668 0.411213
$$485$$ −19.4321 −0.882364
$$486$$ −22.2495 −1.00926
$$487$$ −8.27455 −0.374956 −0.187478 0.982269i $$-0.560031\pi$$
−0.187478 + 0.982269i $$0.560031\pi$$
$$488$$ 9.15751 0.414541
$$489$$ −28.1589 −1.27339
$$490$$ −2.43206 −0.109869
$$491$$ −16.2745 −0.734460 −0.367230 0.930130i $$-0.619694\pi$$
−0.367230 + 0.930130i $$0.619694\pi$$
$$492$$ 11.0920 0.500065
$$493$$ −11.0076 −0.495758
$$494$$ 0.699000 0.0314495
$$495$$ 14.0467 0.631351
$$496$$ −2.81743 −0.126506
$$497$$ −3.25432 −0.145976
$$498$$ −40.0934 −1.79663
$$499$$ 23.1387 1.03583 0.517914 0.855432i $$-0.326709\pi$$
0.517914 + 0.855432i $$0.326709\pi$$
$$500$$ 1.00000 0.0447214
$$501$$ 25.2293 1.12716
$$502$$ −19.5505 −0.872581
$$503$$ −25.1324 −1.12060 −0.560300 0.828290i $$-0.689314\pi$$
−0.560300 + 0.828290i $$0.689314\pi$$
$$504$$ 6.70522 0.298674
$$505$$ −11.9094 −0.529962
$$506$$ 0 0
$$507$$ −32.1589 −1.42823
$$508$$ 20.0934 0.891499
$$509$$ −23.3226 −1.03376 −0.516879 0.856059i $$-0.672906\pi$$
−0.516879 + 0.856059i $$0.672906\pi$$
$$510$$ 3.77213 0.167033
$$511$$ −32.5491 −1.43989
$$512$$ 1.00000 0.0441942
$$513$$ 1.73167 0.0764550
$$514$$ 29.4132 1.29736
$$515$$ 12.1122 0.533728
$$516$$ −17.9094 −0.788418
$$517$$ −20.9547 −0.921587
$$518$$ −25.4537 −1.11837
$$519$$ 11.0920 0.486884
$$520$$ 0.137275 0.00601989
$$521$$ 40.4990 1.77429 0.887146 0.461489i $$-0.152684\pi$$
0.887146 + 0.461489i $$0.152684\pi$$
$$522$$ −22.6802 −0.992683
$$523$$ 1.72545 0.0754487 0.0377243 0.999288i $$-0.487989\pi$$
0.0377243 + 0.999288i $$0.487989\pi$$
$$524$$ 5.90941 0.258154
$$525$$ 5.29478 0.231083
$$526$$ 5.79720 0.252770
$$527$$ −4.28995 −0.186873
$$528$$ 11.0920 0.482716
$$529$$ 0 0
$$530$$ 1.72545 0.0749488
$$531$$ −41.5038 −1.80111
$$532$$ 10.8830 0.471836
$$533$$ 0.614627 0.0266225
$$534$$ 10.5896 0.458255
$$535$$ 6.00000 0.259403
$$536$$ 2.95470 0.127624
$$537$$ −19.1387 −0.825894
$$538$$ 8.86411 0.382159
$$539$$ −10.8892 −0.469030
$$540$$ 0.340078 0.0146346
$$541$$ 9.31984 0.400691 0.200346 0.979725i $$-0.435793\pi$$
0.200346 + 0.979725i $$0.435793\pi$$
$$542$$ 21.0014 0.902087
$$543$$ 23.2042 0.995787
$$544$$ 1.52265 0.0652830
$$545$$ 6.90802 0.295907
$$546$$ 0.726839 0.0311059
$$547$$ −22.5429 −0.963864 −0.481932 0.876209i $$-0.660065\pi$$
−0.481932 + 0.876209i $$0.660065\pi$$
$$548$$ −12.3212 −0.526337
$$549$$ 28.7296 1.22615
$$550$$ 4.47735 0.190915
$$551$$ −36.8112 −1.56821
$$552$$ 0 0
$$553$$ 10.0028 0.425361
$$554$$ −22.3679 −0.950322
$$555$$ −29.5038 −1.25237
$$556$$ 16.9547 0.719040
$$557$$ −20.2773 −0.859178 −0.429589 0.903025i $$-0.641342\pi$$
−0.429589 + 0.903025i $$0.641342\pi$$
$$558$$ −8.83905 −0.374187
$$559$$ −0.992393 −0.0419738
$$560$$ 2.13727 0.0903163
$$561$$ 16.8892 0.713062
$$562$$ −10.5896 −0.446694
$$563$$ 23.7282 1.00003 0.500013 0.866018i $$-0.333329\pi$$
0.500013 + 0.866018i $$0.333329\pi$$
$$564$$ −11.5944 −0.488212
$$565$$ 13.2293 0.556559
$$566$$ −7.22925 −0.303868
$$567$$ −18.3150 −0.769158
$$568$$ −1.52265 −0.0638889
$$569$$ −35.4132 −1.48460 −0.742300 0.670068i $$-0.766265\pi$$
−0.742300 + 0.670068i $$0.766265\pi$$
$$570$$ 12.6146 0.528369
$$571$$ 36.8453 1.54193 0.770963 0.636880i $$-0.219775\pi$$
0.770963 + 0.636880i $$0.219775\pi$$
$$572$$ 0.614627 0.0256988
$$573$$ 40.3178 1.68430
$$574$$ 9.56933 0.399416
$$575$$ 0 0
$$576$$ 3.13727 0.130720
$$577$$ 15.6349 0.650888 0.325444 0.945561i $$-0.394486\pi$$
0.325444 + 0.945561i $$0.394486\pi$$
$$578$$ −14.6815 −0.610672
$$579$$ −17.2293 −0.716023
$$580$$ −7.22925 −0.300178
$$581$$ −34.5896 −1.43502
$$582$$ −48.1401 −1.99547
$$583$$ 7.72545 0.319955
$$584$$ −15.2293 −0.630191
$$585$$ 0.430668 0.0178059
$$586$$ 17.8188 0.736089
$$587$$ 19.0265 0.785306 0.392653 0.919687i $$-0.371557\pi$$
0.392653 + 0.919687i $$0.371557\pi$$
$$588$$ −6.02506 −0.248469
$$589$$ −14.3463 −0.591129
$$590$$ −13.2293 −0.544640
$$591$$ 3.54771 0.145933
$$592$$ −11.9094 −0.489474
$$593$$ 32.4585 1.33291 0.666456 0.745545i $$-0.267811\pi$$
0.666456 + 0.745545i $$0.267811\pi$$
$$594$$ 1.52265 0.0624750
$$595$$ 3.25432 0.133414
$$596$$ 17.0920 0.700115
$$597$$ −14.6397 −0.599163
$$598$$ 0 0
$$599$$ −28.3868 −1.15985 −0.579926 0.814669i $$-0.696918\pi$$
−0.579926 + 0.814669i $$0.696918\pi$$
$$600$$ 2.47735 0.101137
$$601$$ −16.4118 −0.669452 −0.334726 0.942315i $$-0.608644\pi$$
−0.334726 + 0.942315i $$0.608644\pi$$
$$602$$ −15.4509 −0.629732
$$603$$ 9.26972 0.377492
$$604$$ 18.4774 0.751833
$$605$$ 9.04668 0.367800
$$606$$ −29.5038 −1.19851
$$607$$ −38.1840 −1.54984 −0.774920 0.632060i $$-0.782210\pi$$
−0.774920 + 0.632060i $$0.782210\pi$$
$$608$$ 5.09198 0.206507
$$609$$ −38.2773 −1.55108
$$610$$ 9.15751 0.370777
$$611$$ −0.642467 −0.0259914
$$612$$ 4.77696 0.193097
$$613$$ −7.22925 −0.291987 −0.145993 0.989286i $$-0.546638\pi$$
−0.145993 + 0.989286i $$0.546638\pi$$
$$614$$ 17.3415 0.699845
$$615$$ 11.0920 0.447272
$$616$$ 9.56933 0.385559
$$617$$ 15.9812 0.643377 0.321689 0.946846i $$-0.395750\pi$$
0.321689 + 0.946846i $$0.395750\pi$$
$$618$$ 30.0062 1.20703
$$619$$ −47.0014 −1.88915 −0.944573 0.328302i $$-0.893523\pi$$
−0.944573 + 0.328302i $$0.893523\pi$$
$$620$$ −2.81743 −0.113151
$$621$$ 0 0
$$622$$ 12.0000 0.481156
$$623$$ 9.13589 0.366022
$$624$$ 0.340078 0.0136140
$$625$$ 1.00000 0.0400000
$$626$$ 12.3212 0.492456
$$627$$ 56.4801 2.25560
$$628$$ −14.9547 −0.596758
$$629$$ −18.1338 −0.723043
$$630$$ 6.70522 0.267142
$$631$$ 5.50380 0.219103 0.109551 0.993981i $$-0.465059\pi$$
0.109551 + 0.993981i $$0.465059\pi$$
$$632$$ 4.68016 0.186167
$$633$$ 43.6878 1.73643
$$634$$ −21.7721 −0.864682
$$635$$ 20.0934 0.797381
$$636$$ 4.27455 0.169497
$$637$$ −0.333860 −0.0132280
$$638$$ −32.3679 −1.28146
$$639$$ −4.77696 −0.188974
$$640$$ 1.00000 0.0395285
$$641$$ −26.0529 −1.02903 −0.514514 0.857482i $$-0.672028\pi$$
−0.514514 + 0.857482i $$0.672028\pi$$
$$642$$ 14.8641 0.586640
$$643$$ −2.14349 −0.0845311 −0.0422655 0.999106i $$-0.513458\pi$$
−0.0422655 + 0.999106i $$0.513458\pi$$
$$644$$ 0 0
$$645$$ −17.9094 −0.705182
$$646$$ 7.75329 0.305049
$$647$$ 3.85651 0.151615 0.0758075 0.997122i $$-0.475847\pi$$
0.0758075 + 0.997122i $$0.475847\pi$$
$$648$$ −8.56933 −0.336635
$$649$$ −59.2320 −2.32506
$$650$$ 0.137275 0.00538436
$$651$$ −14.9177 −0.584670
$$652$$ −11.3665 −0.445148
$$653$$ 5.67877 0.222227 0.111114 0.993808i $$-0.464558\pi$$
0.111114 + 0.993808i $$0.464558\pi$$
$$654$$ 17.1136 0.669195
$$655$$ 5.90941 0.230900
$$656$$ 4.47735 0.174811
$$657$$ −47.7784 −1.86401
$$658$$ −10.0028 −0.389949
$$659$$ 30.2369 1.17786 0.588930 0.808184i $$-0.299549\pi$$
0.588930 + 0.808184i $$0.299549\pi$$
$$660$$ 11.0920 0.431755
$$661$$ 20.1651 0.784332 0.392166 0.919894i $$-0.371726\pi$$
0.392166 + 0.919894i $$0.371726\pi$$
$$662$$ −0.274549 −0.0106707
$$663$$ 0.517818 0.0201104
$$664$$ −16.1840 −0.628059
$$665$$ 10.8830 0.422023
$$666$$ −37.3631 −1.44779
$$667$$ 0 0
$$668$$ 10.1840 0.394029
$$669$$ 33.4537 1.29339
$$670$$ 2.95470 0.114150
$$671$$ 41.0014 1.58284
$$672$$ 5.29478 0.204251
$$673$$ 22.2244 0.856689 0.428344 0.903616i $$-0.359097\pi$$
0.428344 + 0.903616i $$0.359097\pi$$
$$674$$ 20.0467 0.772169
$$675$$ 0.340078 0.0130896
$$676$$ −12.9812 −0.499275
$$677$$ 8.04047 0.309020 0.154510 0.987991i $$-0.450620\pi$$
0.154510 + 0.987991i $$0.450620\pi$$
$$678$$ 32.7735 1.25866
$$679$$ −41.5316 −1.59384
$$680$$ 1.52265 0.0583909
$$681$$ −48.6425 −1.86398
$$682$$ −12.6146 −0.483039
$$683$$ 2.72406 0.104233 0.0521167 0.998641i $$-0.483403\pi$$
0.0521167 + 0.998641i $$0.483403\pi$$
$$684$$ 15.9749 0.610817
$$685$$ −12.3212 −0.470770
$$686$$ −20.1589 −0.769670
$$687$$ 0.224425 0.00856234
$$688$$ −7.22925 −0.275613
$$689$$ 0.236861 0.00902367
$$690$$ 0 0
$$691$$ 26.9952 1.02694 0.513472 0.858106i $$-0.328359\pi$$
0.513472 + 0.858106i $$0.328359\pi$$
$$692$$ 4.47735 0.170203
$$693$$ 30.0216 1.14043
$$694$$ 1.11704 0.0424023
$$695$$ 16.9547 0.643129
$$696$$ −17.9094 −0.678854
$$697$$ 6.81743 0.258229
$$698$$ −28.7331 −1.08756
$$699$$ −7.31984 −0.276862
$$700$$ 2.13727 0.0807814
$$701$$ 2.63347 0.0994648 0.0497324 0.998763i $$-0.484163\pi$$
0.0497324 + 0.998763i $$0.484163\pi$$
$$702$$ 0.0466840 0.00176198
$$703$$ −60.6425 −2.28717
$$704$$ 4.47735 0.168747
$$705$$ −11.5944 −0.436670
$$706$$ −6.82365 −0.256811
$$707$$ −25.4537 −0.957284
$$708$$ −32.7735 −1.23170
$$709$$ 43.7595 1.64342 0.821711 0.569904i $$-0.193020\pi$$
0.821711 + 0.569904i $$0.193020\pi$$
$$710$$ −1.52265 −0.0571439
$$711$$ 14.6829 0.550653
$$712$$ 4.27455 0.160196
$$713$$ 0 0
$$714$$ 8.06209 0.301716
$$715$$ 0.614627 0.0229857
$$716$$ −7.72545 −0.288714
$$717$$ 29.7282 1.11022
$$718$$ 22.5896 0.843035
$$719$$ −32.4523 −1.21027 −0.605133 0.796124i $$-0.706880\pi$$
−0.605133 + 0.796124i $$0.706880\pi$$
$$720$$ 3.13727 0.116919
$$721$$ 25.8871 0.964087
$$722$$ 6.92825 0.257843
$$723$$ 14.6397 0.544456
$$724$$ 9.36653 0.348104
$$725$$ −7.22925 −0.268488
$$726$$ 22.4118 0.831781
$$727$$ 41.2104 1.52841 0.764205 0.644974i $$-0.223132\pi$$
0.764205 + 0.644974i $$0.223132\pi$$
$$728$$ 0.293394 0.0108739
$$729$$ −29.4118 −1.08933
$$730$$ −15.2293 −0.563660
$$731$$ −11.0076 −0.407131
$$732$$ 22.6864 0.838512
$$733$$ 37.5443 1.38673 0.693365 0.720587i $$-0.256128\pi$$
0.693365 + 0.720587i $$0.256128\pi$$
$$734$$ 32.3679 1.19472
$$735$$ −6.02506 −0.222238
$$736$$ 0 0
$$737$$ 13.2293 0.487306
$$738$$ 14.0467 0.517066
$$739$$ 14.4962 0.533251 0.266626 0.963800i $$-0.414091\pi$$
0.266626 + 0.963800i $$0.414091\pi$$
$$740$$ −11.9094 −0.437799
$$741$$ 1.73167 0.0636144
$$742$$ 3.68776 0.135382
$$743$$ 34.5052 1.26587 0.632936 0.774204i $$-0.281849\pi$$
0.632936 + 0.774204i $$0.281849\pi$$
$$744$$ −6.97977 −0.255891
$$745$$ 17.0920 0.626202
$$746$$ −13.7255 −0.502524
$$747$$ −50.7735 −1.85771
$$748$$ 6.81743 0.249270
$$749$$ 12.8236 0.468566
$$750$$ 2.47735 0.0904601
$$751$$ 22.1840 0.809504 0.404752 0.914426i $$-0.367358\pi$$
0.404752 + 0.914426i $$0.367358\pi$$
$$752$$ −4.68016 −0.170668
$$753$$ −48.4334 −1.76501
$$754$$ −0.992393 −0.0361408
$$755$$ 18.4774 0.672460
$$756$$ 0.726839 0.0264349
$$757$$ −1.72545 −0.0627126 −0.0313563 0.999508i $$-0.509983\pi$$
−0.0313563 + 0.999508i $$0.509983\pi$$
$$758$$ −28.4774 −1.03434
$$759$$ 0 0
$$760$$ 5.09198 0.184706
$$761$$ −39.6815 −1.43845 −0.719227 0.694775i $$-0.755504\pi$$
−0.719227 + 0.694775i $$0.755504\pi$$
$$762$$ 49.7784 1.80328
$$763$$ 14.7643 0.534505
$$764$$ 16.2745 0.588793
$$765$$ 4.77696 0.172711
$$766$$ 9.36031 0.338202
$$767$$ −1.81604 −0.0655735
$$768$$ 2.47735 0.0893938
$$769$$ −5.90941 −0.213099 −0.106549 0.994307i $$-0.533980\pi$$
−0.106549 + 0.994307i $$0.533980\pi$$
$$770$$ 9.56933 0.344855
$$771$$ 72.8669 2.62424
$$772$$ −6.95470 −0.250305
$$773$$ −12.3150 −0.442940 −0.221470 0.975167i $$-0.571086\pi$$
−0.221470 + 0.975167i $$0.571086\pi$$
$$774$$ −22.6802 −0.815221
$$775$$ −2.81743 −0.101205
$$776$$ −19.4321 −0.697570
$$777$$ −63.0577 −2.26218
$$778$$ 30.1122 1.07958
$$779$$ 22.7986 0.816844
$$780$$ 0.340078 0.0121767
$$781$$ −6.81743 −0.243947
$$782$$ 0 0
$$783$$ −2.45851 −0.0878599
$$784$$ −2.43206 −0.0868592
$$785$$ −14.9547 −0.533756
$$786$$ 14.6397 0.522180
$$787$$ −9.85651 −0.351347 −0.175673 0.984449i $$-0.556210\pi$$
−0.175673 + 0.984449i $$0.556210\pi$$
$$788$$ 1.43206 0.0510149
$$789$$ 14.3617 0.511290
$$790$$ 4.68016 0.166512
$$791$$ 28.2745 1.00533
$$792$$ 14.0467 0.499127
$$793$$ 1.25709 0.0446407
$$794$$ 12.8830 0.457199
$$795$$ 4.27455 0.151603
$$796$$ −5.90941 −0.209453
$$797$$ 19.8160 0.701920 0.350960 0.936390i $$-0.385855\pi$$
0.350960 + 0.936390i $$0.385855\pi$$
$$798$$ 26.9609 0.954406
$$799$$ −7.12623 −0.252108
$$800$$ 1.00000 0.0353553
$$801$$ 13.4104 0.473834
$$802$$ −22.0028 −0.776945
$$803$$ −68.1867 −2.40626
$$804$$ 7.31984 0.258151
$$805$$ 0 0
$$806$$ −0.386762 −0.0136231
$$807$$ 21.9595 0.773012
$$808$$ −11.9094 −0.418972
$$809$$ −7.11704 −0.250222 −0.125111 0.992143i $$-0.539929\pi$$
−0.125111 + 0.992143i $$0.539929\pi$$
$$810$$ −8.56933 −0.301096
$$811$$ −35.5066 −1.24680 −0.623402 0.781901i $$-0.714250\pi$$
−0.623402 + 0.781901i $$0.714250\pi$$
$$812$$ −15.4509 −0.542220
$$813$$ 52.0278 1.82470
$$814$$ −53.3226 −1.86896
$$815$$ −11.3665 −0.398152
$$816$$ 3.77213 0.132051
$$817$$ −36.8112 −1.28786
$$818$$ −13.7721 −0.481531
$$819$$ 0.920456 0.0321634
$$820$$ 4.47735 0.156356
$$821$$ 36.3150 1.26740 0.633701 0.773578i $$-0.281535\pi$$
0.633701 + 0.773578i $$0.281535\pi$$
$$822$$ −30.5240 −1.06465
$$823$$ 18.0405 0.628851 0.314426 0.949282i $$-0.398188\pi$$
0.314426 + 0.949282i $$0.398188\pi$$
$$824$$ 12.1122 0.421949
$$825$$ 11.0920 0.386173
$$826$$ −28.2745 −0.983797
$$827$$ −52.0028 −1.80831 −0.904157 0.427201i $$-0.859500\pi$$
−0.904157 + 0.427201i $$0.859500\pi$$
$$828$$ 0 0
$$829$$ −9.00761 −0.312847 −0.156424 0.987690i $$-0.549996\pi$$
−0.156424 + 0.987690i $$0.549996\pi$$
$$830$$ −16.1840 −0.561753
$$831$$ −55.4132 −1.92226
$$832$$ 0.137275 0.00475914
$$833$$ −3.70317 −0.128307
$$834$$ 42.0028 1.45444
$$835$$ 10.1840 0.352430
$$836$$ 22.7986 0.788506
$$837$$ −0.958145 −0.0331183
$$838$$ 1.31984 0.0455933
$$839$$ 49.8717 1.72176 0.860882 0.508805i $$-0.169913\pi$$
0.860882 + 0.508805i $$0.169913\pi$$
$$840$$ 5.29478 0.182687
$$841$$ 23.2621 0.802142
$$842$$ −25.4599 −0.877406
$$843$$ −26.2341 −0.903550
$$844$$ 17.6349 0.607017
$$845$$ −12.9812 −0.446565
$$846$$ −14.6829 −0.504810
$$847$$ 19.3352 0.664367
$$848$$ 1.72545 0.0592522
$$849$$ −17.9094 −0.614649
$$850$$ 1.52265 0.0522264
$$851$$ 0 0
$$852$$ −3.77213 −0.129231
$$853$$ −14.5958 −0.499750 −0.249875 0.968278i $$-0.580390\pi$$
−0.249875 + 0.968278i $$0.580390\pi$$
$$854$$ 19.5721 0.669744
$$855$$ 15.9749 0.546331
$$856$$ 6.00000 0.205076
$$857$$ 37.1387 1.26863 0.634316 0.773074i $$-0.281282\pi$$
0.634316 + 0.773074i $$0.281282\pi$$
$$858$$ 1.52265 0.0519823
$$859$$ −14.0028 −0.477769 −0.238884 0.971048i $$-0.576782\pi$$
−0.238884 + 0.971048i $$0.576782\pi$$
$$860$$ −7.22925 −0.246516
$$861$$ 23.7066 0.807919
$$862$$ 29.9094 1.01872
$$863$$ −12.1812 −0.414652 −0.207326 0.978272i $$-0.566476\pi$$
−0.207326 + 0.978272i $$0.566476\pi$$
$$864$$ 0.340078 0.0115697
$$865$$ 4.47735 0.152235
$$866$$ −3.77213 −0.128182
$$867$$ −36.3714 −1.23524
$$868$$ −6.02162 −0.204387
$$869$$ 20.9547 0.710840
$$870$$ −17.9094 −0.607186
$$871$$ 0.405606 0.0137434
$$872$$ 6.90802 0.233935
$$873$$ −60.9637 −2.06331
$$874$$ 0 0
$$875$$ 2.13727 0.0722531
$$876$$ −37.7282 −1.27472
$$877$$ 28.4397 0.960339 0.480170 0.877176i $$-0.340575\pi$$
0.480170 + 0.877176i $$0.340575\pi$$
$$878$$ 1.99378 0.0672869
$$879$$ 44.1435 1.48892
$$880$$ 4.47735 0.150932
$$881$$ 35.0076 1.17944 0.589718 0.807609i $$-0.299239\pi$$
0.589718 + 0.807609i $$0.299239\pi$$
$$882$$ −7.63003 −0.256917
$$883$$ 12.4647 0.419471 0.209736 0.977758i $$-0.432740\pi$$
0.209736 + 0.977758i $$0.432740\pi$$
$$884$$ 0.209021 0.00703013
$$885$$ −32.7735 −1.10167
$$886$$ 12.7268 0.427567
$$887$$ 1.04807 0.0351908 0.0175954 0.999845i $$-0.494399\pi$$
0.0175954 + 0.999845i $$0.494399\pi$$
$$888$$ −29.5038 −0.990083
$$889$$ 42.9450 1.44033
$$890$$ 4.27455 0.143283
$$891$$ −38.3679 −1.28537
$$892$$ 13.5038 0.452141
$$893$$ −23.8313 −0.797483
$$894$$ 42.3429 1.41616
$$895$$ −7.72545 −0.258233
$$896$$ 2.13727 0.0714013
$$897$$ 0 0
$$898$$ −35.4070 −1.18155
$$899$$ 20.3679 0.679308
$$900$$ 3.13727 0.104576
$$901$$ 2.62725 0.0875265
$$902$$ 20.0467 0.667482
$$903$$ −38.2773 −1.27379
$$904$$ 13.2293 0.439998
$$905$$ 9.36653 0.311354
$$906$$ 45.7749 1.52077
$$907$$ 22.9170 0.760947 0.380474 0.924792i $$-0.375761\pi$$
0.380474 + 0.924792i $$0.375761\pi$$
$$908$$ −19.6349 −0.651606
$$909$$ −37.3631 −1.23926
$$910$$ 0.293394 0.00972590
$$911$$ 36.0000 1.19273 0.596367 0.802712i $$-0.296610\pi$$
0.596367 + 0.802712i $$0.296610\pi$$
$$912$$ 12.6146 0.417712
$$913$$ −72.4613 −2.39812
$$914$$ 7.31984 0.242119
$$915$$ 22.6864 0.749988
$$916$$ 0.0905906 0.00299320
$$917$$ 12.6300 0.417080
$$918$$ 0.517818 0.0170906
$$919$$ −47.2320 −1.55804 −0.779020 0.626998i $$-0.784283\pi$$
−0.779020 + 0.626998i $$0.784283\pi$$
$$920$$ 0 0
$$921$$ 42.9609 1.41561
$$922$$ 22.2745 0.733573
$$923$$ −0.209021 −0.00688001
$$924$$ 23.7066 0.779890
$$925$$ −11.9094 −0.391579
$$926$$ 8.82365 0.289963
$$927$$ 37.9993 1.24806
$$928$$ −7.22925 −0.237312
$$929$$ −18.0000 −0.590561 −0.295280 0.955411i $$-0.595413\pi$$
−0.295280 + 0.955411i $$0.595413\pi$$
$$930$$ −6.97977 −0.228876
$$931$$ −12.3840 −0.405869
$$932$$ −2.95470 −0.0967846
$$933$$ 29.7282 0.973258
$$934$$ −16.1840 −0.529555
$$935$$ 6.81743 0.222954
$$936$$ 0.430668 0.0140768
$$937$$ −38.9609 −1.27280 −0.636399 0.771360i $$-0.719577\pi$$
−0.636399 + 0.771360i $$0.719577\pi$$
$$938$$ 6.31502 0.206193
$$939$$ 30.5240 0.996114
$$940$$ −4.68016 −0.152650
$$941$$ −3.65370 −0.119107 −0.0595537 0.998225i $$-0.518968\pi$$
−0.0595537 + 0.998225i $$0.518968\pi$$
$$942$$ −37.0481 −1.20709
$$943$$ 0 0
$$944$$ −13.2293 −0.430576
$$945$$ 0.726839 0.0236441
$$946$$ −32.3679 −1.05237
$$947$$ −43.4599 −1.41226 −0.706128 0.708084i $$-0.749560\pi$$
−0.706128 + 0.708084i $$0.749560\pi$$
$$948$$ 11.5944 0.376568
$$949$$ −2.09059 −0.0678634
$$950$$ 5.09198 0.165206
$$951$$ −53.9372 −1.74904
$$952$$ 3.25432 0.105473
$$953$$ 10.2962 0.333526 0.166763 0.985997i $$-0.446669\pi$$
0.166763 + 0.985997i $$0.446669\pi$$
$$954$$ 5.41321 0.175259
$$955$$ 16.2745 0.526632
$$956$$ 12.0000 0.388108
$$957$$ −80.1867 −2.59207
$$958$$ −10.3651 −0.334882
$$959$$ −26.3339 −0.850365
$$960$$ 2.47735 0.0799562
$$961$$ −23.0621 −0.743938
$$962$$ −1.63486 −0.0527100
$$963$$ 18.8236 0.606584
$$964$$ 5.90941 0.190329
$$965$$ −6.95470 −0.223880
$$966$$ 0 0
$$967$$ −24.6802 −0.793660 −0.396830 0.917892i $$-0.629890\pi$$
−0.396830 + 0.917892i $$0.629890\pi$$
$$968$$ 9.04668 0.290771
$$969$$ 19.2076 0.617038
$$970$$ −19.4321 −0.623926
$$971$$ 57.9812 1.86070 0.930352 0.366668i $$-0.119501\pi$$
0.930352 + 0.366668i $$0.119501\pi$$
$$972$$ −22.2495 −0.713653
$$973$$ 36.2369 1.16170
$$974$$ −8.27455 −0.265134
$$975$$ 0.340078 0.0108912
$$976$$ 9.15751 0.293125
$$977$$ 13.1324 0.420144 0.210072 0.977686i $$-0.432630\pi$$
0.210072 + 0.977686i $$0.432630\pi$$
$$978$$ −28.1589 −0.900422
$$979$$ 19.1387 0.611674
$$980$$ −2.43206 −0.0776892
$$981$$ 21.6724 0.691945
$$982$$ −16.2745 −0.519342
$$983$$ 30.2028 0.963320 0.481660 0.876358i $$-0.340034\pi$$
0.481660 + 0.876358i $$0.340034\pi$$
$$984$$ 11.0920 0.353599
$$985$$ 1.43206 0.0456291
$$986$$ −11.0076 −0.350554
$$987$$ −24.7804 −0.788769
$$988$$ 0.699000 0.0222381
$$989$$ 0 0
$$990$$ 14.0467 0.446433
$$991$$ −24.5679 −0.780426 −0.390213 0.920725i $$-0.627599\pi$$
−0.390213 + 0.920725i $$0.627599\pi$$
$$992$$ −2.81743 −0.0894535
$$993$$ −0.680155 −0.0215841
$$994$$ −3.25432 −0.103221
$$995$$ −5.90941 −0.187341
$$996$$ −40.0934 −1.27041
$$997$$ −21.8188 −0.691009 −0.345504 0.938417i $$-0.612292\pi$$
−0.345504 + 0.938417i $$0.612292\pi$$
$$998$$ 23.1387 0.732442
$$999$$ −4.05012 −0.128140
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 5290.2.a.q.1.3 yes 3
23.22 odd 2 5290.2.a.p.1.3 3

By twisted newform
Twist Min Dim Char Parity Ord Type
5290.2.a.p.1.3 3 23.22 odd 2
5290.2.a.q.1.3 yes 3 1.1 even 1 trivial