# Properties

 Label 4598.2.a.cd.1.8 Level $4598$ Weight $2$ Character 4598.1 Self dual yes Analytic conductor $36.715$ Analytic rank $0$ Dimension $10$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4598 = 2 \cdot 11^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4598.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$36.7152148494$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ Defining polynomial: $$x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44$$ x^10 - 2*x^9 - 19*x^8 + 36*x^7 + 118*x^6 - 220*x^5 - 270*x^4 + 512*x^3 + 176*x^2 - 392*x + 44 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 418) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.8 Root $$2.10092$$ of defining polynomial Character $$\chi$$ $$=$$ 4598.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} +2.10092 q^{6} +3.09995 q^{7} +1.00000 q^{8} +1.41386 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} +2.10092 q^{6} +3.09995 q^{7} +1.00000 q^{8} +1.41386 q^{9} +2.46005 q^{10} +2.10092 q^{12} +3.97832 q^{13} +3.09995 q^{14} +5.16836 q^{15} +1.00000 q^{16} +2.14576 q^{17} +1.41386 q^{18} +1.00000 q^{19} +2.46005 q^{20} +6.51275 q^{21} -2.55940 q^{23} +2.10092 q^{24} +1.05183 q^{25} +3.97832 q^{26} -3.33234 q^{27} +3.09995 q^{28} -6.50365 q^{29} +5.16836 q^{30} +1.48635 q^{31} +1.00000 q^{32} +2.14576 q^{34} +7.62603 q^{35} +1.41386 q^{36} -1.74921 q^{37} +1.00000 q^{38} +8.35814 q^{39} +2.46005 q^{40} -5.48529 q^{41} +6.51275 q^{42} -4.59472 q^{43} +3.47817 q^{45} -2.55940 q^{46} -3.40634 q^{47} +2.10092 q^{48} +2.60971 q^{49} +1.05183 q^{50} +4.50808 q^{51} +3.97832 q^{52} -11.7609 q^{53} -3.33234 q^{54} +3.09995 q^{56} +2.10092 q^{57} -6.50365 q^{58} -6.65028 q^{59} +5.16836 q^{60} +6.34059 q^{61} +1.48635 q^{62} +4.38291 q^{63} +1.00000 q^{64} +9.78686 q^{65} +14.1154 q^{67} +2.14576 q^{68} -5.37710 q^{69} +7.62603 q^{70} -15.9696 q^{71} +1.41386 q^{72} +3.17623 q^{73} -1.74921 q^{74} +2.20981 q^{75} +1.00000 q^{76} +8.35814 q^{78} -7.25669 q^{79} +2.46005 q^{80} -11.2426 q^{81} -5.48529 q^{82} -11.2166 q^{83} +6.51275 q^{84} +5.27868 q^{85} -4.59472 q^{86} -13.6636 q^{87} -4.63686 q^{89} +3.47817 q^{90} +12.3326 q^{91} -2.55940 q^{92} +3.12270 q^{93} -3.40634 q^{94} +2.46005 q^{95} +2.10092 q^{96} -5.47081 q^{97} +2.60971 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10})$$ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 $$10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100})$$ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * q^98

## 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
$$3$$ 2.10092 1.21297 0.606483 0.795096i $$-0.292580\pi$$
0.606483 + 0.795096i $$0.292580\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 2.46005 1.10017 0.550083 0.835110i $$-0.314596\pi$$
0.550083 + 0.835110i $$0.314596\pi$$
$$6$$ 2.10092 0.857697
$$7$$ 3.09995 1.17167 0.585836 0.810430i $$-0.300766\pi$$
0.585836 + 0.810430i $$0.300766\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.41386 0.471288
$$10$$ 2.46005 0.777935
$$11$$ 0 0
$$12$$ 2.10092 0.606483
$$13$$ 3.97832 1.10339 0.551694 0.834047i $$-0.313982\pi$$
0.551694 + 0.834047i $$0.313982\pi$$
$$14$$ 3.09995 0.828497
$$15$$ 5.16836 1.33447
$$16$$ 1.00000 0.250000
$$17$$ 2.14576 0.520424 0.260212 0.965551i $$-0.416208\pi$$
0.260212 + 0.965551i $$0.416208\pi$$
$$18$$ 1.41386 0.333251
$$19$$ 1.00000 0.229416
$$20$$ 2.46005 0.550083
$$21$$ 6.51275 1.42120
$$22$$ 0 0
$$23$$ −2.55940 −0.533672 −0.266836 0.963742i $$-0.585978\pi$$
−0.266836 + 0.963742i $$0.585978\pi$$
$$24$$ 2.10092 0.428848
$$25$$ 1.05183 0.210366
$$26$$ 3.97832 0.780213
$$27$$ −3.33234 −0.641310
$$28$$ 3.09995 0.585836
$$29$$ −6.50365 −1.20770 −0.603849 0.797099i $$-0.706367\pi$$
−0.603849 + 0.797099i $$0.706367\pi$$
$$30$$ 5.16836 0.943609
$$31$$ 1.48635 0.266956 0.133478 0.991052i $$-0.457385\pi$$
0.133478 + 0.991052i $$0.457385\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 2.14576 0.367995
$$35$$ 7.62603 1.28903
$$36$$ 1.41386 0.235644
$$37$$ −1.74921 −0.287569 −0.143784 0.989609i $$-0.545927\pi$$
−0.143784 + 0.989609i $$0.545927\pi$$
$$38$$ 1.00000 0.162221
$$39$$ 8.35814 1.33837
$$40$$ 2.46005 0.388968
$$41$$ −5.48529 −0.856659 −0.428329 0.903623i $$-0.640898\pi$$
−0.428329 + 0.903623i $$0.640898\pi$$
$$42$$ 6.51275 1.00494
$$43$$ −4.59472 −0.700689 −0.350344 0.936621i $$-0.613935\pi$$
−0.350344 + 0.936621i $$0.613935\pi$$
$$44$$ 0 0
$$45$$ 3.47817 0.518495
$$46$$ −2.55940 −0.377363
$$47$$ −3.40634 −0.496866 −0.248433 0.968649i $$-0.579916\pi$$
−0.248433 + 0.968649i $$0.579916\pi$$
$$48$$ 2.10092 0.303242
$$49$$ 2.60971 0.372815
$$50$$ 1.05183 0.148751
$$51$$ 4.50808 0.631257
$$52$$ 3.97832 0.551694
$$53$$ −11.7609 −1.61548 −0.807742 0.589536i $$-0.799311\pi$$
−0.807742 + 0.589536i $$0.799311\pi$$
$$54$$ −3.33234 −0.453475
$$55$$ 0 0
$$56$$ 3.09995 0.414249
$$57$$ 2.10092 0.278274
$$58$$ −6.50365 −0.853971
$$59$$ −6.65028 −0.865793 −0.432896 0.901444i $$-0.642508\pi$$
−0.432896 + 0.901444i $$0.642508\pi$$
$$60$$ 5.16836 0.667233
$$61$$ 6.34059 0.811829 0.405915 0.913911i $$-0.366953\pi$$
0.405915 + 0.913911i $$0.366953\pi$$
$$62$$ 1.48635 0.188766
$$63$$ 4.38291 0.552195
$$64$$ 1.00000 0.125000
$$65$$ 9.78686 1.21391
$$66$$ 0 0
$$67$$ 14.1154 1.72447 0.862236 0.506506i $$-0.169063\pi$$
0.862236 + 0.506506i $$0.169063\pi$$
$$68$$ 2.14576 0.260212
$$69$$ −5.37710 −0.647326
$$70$$ 7.62603 0.911485
$$71$$ −15.9696 −1.89524 −0.947619 0.319404i $$-0.896517\pi$$
−0.947619 + 0.319404i $$0.896517\pi$$
$$72$$ 1.41386 0.166626
$$73$$ 3.17623 0.371749 0.185875 0.982573i $$-0.440488\pi$$
0.185875 + 0.982573i $$0.440488\pi$$
$$74$$ −1.74921 −0.203342
$$75$$ 2.20981 0.255167
$$76$$ 1.00000 0.114708
$$77$$ 0 0
$$78$$ 8.35814 0.946373
$$79$$ −7.25669 −0.816442 −0.408221 0.912883i $$-0.633851\pi$$
−0.408221 + 0.912883i $$0.633851\pi$$
$$80$$ 2.46005 0.275042
$$81$$ −11.2426 −1.24918
$$82$$ −5.48529 −0.605749
$$83$$ −11.2166 −1.23118 −0.615588 0.788068i $$-0.711082\pi$$
−0.615588 + 0.788068i $$0.711082\pi$$
$$84$$ 6.51275 0.710600
$$85$$ 5.27868 0.572553
$$86$$ −4.59472 −0.495462
$$87$$ −13.6636 −1.46490
$$88$$ 0 0
$$89$$ −4.63686 −0.491506 −0.245753 0.969332i $$-0.579035\pi$$
−0.245753 + 0.969332i $$0.579035\pi$$
$$90$$ 3.47817 0.366632
$$91$$ 12.3326 1.29281
$$92$$ −2.55940 −0.266836
$$93$$ 3.12270 0.323809
$$94$$ −3.40634 −0.351338
$$95$$ 2.46005 0.252395
$$96$$ 2.10092 0.214424
$$97$$ −5.47081 −0.555477 −0.277738 0.960657i $$-0.589585\pi$$
−0.277738 + 0.960657i $$0.589585\pi$$
$$98$$ 2.60971 0.263620
$$99$$ 0 0
$$100$$ 1.05183 0.105183
$$101$$ 5.80492 0.577611 0.288806 0.957388i $$-0.406742\pi$$
0.288806 + 0.957388i $$0.406742\pi$$
$$102$$ 4.50808 0.446366
$$103$$ −9.56301 −0.942271 −0.471136 0.882061i $$-0.656156\pi$$
−0.471136 + 0.882061i $$0.656156\pi$$
$$104$$ 3.97832 0.390107
$$105$$ 16.0217 1.56356
$$106$$ −11.7609 −1.14232
$$107$$ 14.5663 1.40818 0.704090 0.710111i $$-0.251355\pi$$
0.704090 + 0.710111i $$0.251355\pi$$
$$108$$ −3.33234 −0.320655
$$109$$ 3.38080 0.323822 0.161911 0.986805i $$-0.448234\pi$$
0.161911 + 0.986805i $$0.448234\pi$$
$$110$$ 0 0
$$111$$ −3.67496 −0.348811
$$112$$ 3.09995 0.292918
$$113$$ 11.3668 1.06930 0.534650 0.845074i $$-0.320444\pi$$
0.534650 + 0.845074i $$0.320444\pi$$
$$114$$ 2.10092 0.196769
$$115$$ −6.29625 −0.587128
$$116$$ −6.50365 −0.603849
$$117$$ 5.62481 0.520014
$$118$$ −6.65028 −0.612208
$$119$$ 6.65177 0.609766
$$120$$ 5.16836 0.471805
$$121$$ 0 0
$$122$$ 6.34059 0.574050
$$123$$ −11.5242 −1.03910
$$124$$ 1.48635 0.133478
$$125$$ −9.71268 −0.868729
$$126$$ 4.38291 0.390461
$$127$$ 13.3466 1.18432 0.592160 0.805820i $$-0.298275\pi$$
0.592160 + 0.805820i $$0.298275\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −9.65314 −0.849912
$$130$$ 9.78686 0.858364
$$131$$ 4.58757 0.400818 0.200409 0.979712i $$-0.435773\pi$$
0.200409 + 0.979712i $$0.435773\pi$$
$$132$$ 0 0
$$133$$ 3.09995 0.268800
$$134$$ 14.1154 1.21939
$$135$$ −8.19772 −0.705548
$$136$$ 2.14576 0.183998
$$137$$ −13.6371 −1.16509 −0.582546 0.812798i $$-0.697943\pi$$
−0.582546 + 0.812798i $$0.697943\pi$$
$$138$$ −5.37710 −0.457729
$$139$$ 5.78982 0.491086 0.245543 0.969386i $$-0.421034\pi$$
0.245543 + 0.969386i $$0.421034\pi$$
$$140$$ 7.62603 0.644517
$$141$$ −7.15646 −0.602682
$$142$$ −15.9696 −1.34014
$$143$$ 0 0
$$144$$ 1.41386 0.117822
$$145$$ −15.9993 −1.32867
$$146$$ 3.17623 0.262866
$$147$$ 5.48278 0.452212
$$148$$ −1.74921 −0.143784
$$149$$ 10.3503 0.847926 0.423963 0.905679i $$-0.360639\pi$$
0.423963 + 0.905679i $$0.360639\pi$$
$$150$$ 2.20981 0.180430
$$151$$ 12.1731 0.990632 0.495316 0.868713i $$-0.335052\pi$$
0.495316 + 0.868713i $$0.335052\pi$$
$$152$$ 1.00000 0.0811107
$$153$$ 3.03382 0.245270
$$154$$ 0 0
$$155$$ 3.65649 0.293696
$$156$$ 8.35814 0.669186
$$157$$ 3.72389 0.297199 0.148599 0.988897i $$-0.452524\pi$$
0.148599 + 0.988897i $$0.452524\pi$$
$$158$$ −7.25669 −0.577312
$$159$$ −24.7087 −1.95953
$$160$$ 2.46005 0.194484
$$161$$ −7.93402 −0.625289
$$162$$ −11.2426 −0.883301
$$163$$ −19.8920 −1.55806 −0.779032 0.626984i $$-0.784289\pi$$
−0.779032 + 0.626984i $$0.784289\pi$$
$$164$$ −5.48529 −0.428329
$$165$$ 0 0
$$166$$ −11.2166 −0.870573
$$167$$ 21.9867 1.70138 0.850690 0.525667i $$-0.176184\pi$$
0.850690 + 0.525667i $$0.176184\pi$$
$$168$$ 6.51275 0.502470
$$169$$ 2.82705 0.217465
$$170$$ 5.27868 0.404856
$$171$$ 1.41386 0.108121
$$172$$ −4.59472 −0.350344
$$173$$ 25.4819 1.93735 0.968675 0.248333i $$-0.0798828\pi$$
0.968675 + 0.248333i $$0.0798828\pi$$
$$174$$ −13.6636 −1.03584
$$175$$ 3.26062 0.246480
$$176$$ 0 0
$$177$$ −13.9717 −1.05018
$$178$$ −4.63686 −0.347547
$$179$$ 22.7884 1.70329 0.851643 0.524122i $$-0.175607\pi$$
0.851643 + 0.524122i $$0.175607\pi$$
$$180$$ 3.47817 0.259248
$$181$$ −1.54547 −0.114874 −0.0574368 0.998349i $$-0.518293\pi$$
−0.0574368 + 0.998349i $$0.518293\pi$$
$$182$$ 12.3326 0.914154
$$183$$ 13.3211 0.984722
$$184$$ −2.55940 −0.188682
$$185$$ −4.30315 −0.316374
$$186$$ 3.12270 0.228967
$$187$$ 0 0
$$188$$ −3.40634 −0.248433
$$189$$ −10.3301 −0.751405
$$190$$ 2.46005 0.178471
$$191$$ 7.14404 0.516925 0.258462 0.966021i $$-0.416784\pi$$
0.258462 + 0.966021i $$0.416784\pi$$
$$192$$ 2.10092 0.151621
$$193$$ 12.0980 0.870833 0.435417 0.900229i $$-0.356601\pi$$
0.435417 + 0.900229i $$0.356601\pi$$
$$194$$ −5.47081 −0.392781
$$195$$ 20.5614 1.47243
$$196$$ 2.60971 0.186408
$$197$$ −18.2516 −1.30037 −0.650186 0.759775i $$-0.725309\pi$$
−0.650186 + 0.759775i $$0.725309\pi$$
$$198$$ 0 0
$$199$$ 23.9705 1.69923 0.849613 0.527406i $$-0.176835\pi$$
0.849613 + 0.527406i $$0.176835\pi$$
$$200$$ 1.05183 0.0743756
$$201$$ 29.6554 2.09173
$$202$$ 5.80492 0.408433
$$203$$ −20.1610 −1.41503
$$204$$ 4.50808 0.315629
$$205$$ −13.4941 −0.942467
$$206$$ −9.56301 −0.666286
$$207$$ −3.61865 −0.251513
$$208$$ 3.97832 0.275847
$$209$$ 0 0
$$210$$ 16.0217 1.10560
$$211$$ −20.7466 −1.42826 −0.714129 0.700015i $$-0.753177\pi$$
−0.714129 + 0.700015i $$0.753177\pi$$
$$212$$ −11.7609 −0.807742
$$213$$ −33.5508 −2.29886
$$214$$ 14.5663 0.995734
$$215$$ −11.3032 −0.770874
$$216$$ −3.33234 −0.226737
$$217$$ 4.60761 0.312785
$$218$$ 3.38080 0.228977
$$219$$ 6.67300 0.450920
$$220$$ 0 0
$$221$$ 8.53654 0.574230
$$222$$ −3.67496 −0.246647
$$223$$ 28.3845 1.90077 0.950384 0.311080i $$-0.100691\pi$$
0.950384 + 0.311080i $$0.100691\pi$$
$$224$$ 3.09995 0.207124
$$225$$ 1.48715 0.0991430
$$226$$ 11.3668 0.756109
$$227$$ 8.50634 0.564585 0.282293 0.959328i $$-0.408905\pi$$
0.282293 + 0.959328i $$0.408905\pi$$
$$228$$ 2.10092 0.139137
$$229$$ −1.70730 −0.112822 −0.0564109 0.998408i $$-0.517966\pi$$
−0.0564109 + 0.998408i $$0.517966\pi$$
$$230$$ −6.29625 −0.415162
$$231$$ 0 0
$$232$$ −6.50365 −0.426986
$$233$$ −9.95632 −0.652260 −0.326130 0.945325i $$-0.605745\pi$$
−0.326130 + 0.945325i $$0.605745\pi$$
$$234$$ 5.62481 0.367705
$$235$$ −8.37977 −0.546636
$$236$$ −6.65028 −0.432896
$$237$$ −15.2457 −0.990317
$$238$$ 6.65177 0.431170
$$239$$ −16.2786 −1.05297 −0.526487 0.850183i $$-0.676491\pi$$
−0.526487 + 0.850183i $$0.676491\pi$$
$$240$$ 5.16836 0.333616
$$241$$ 5.95144 0.383366 0.191683 0.981457i $$-0.438605\pi$$
0.191683 + 0.981457i $$0.438605\pi$$
$$242$$ 0 0
$$243$$ −13.6227 −0.873899
$$244$$ 6.34059 0.405915
$$245$$ 6.42000 0.410159
$$246$$ −11.5242 −0.734753
$$247$$ 3.97832 0.253135
$$248$$ 1.48635 0.0943832
$$249$$ −23.5651 −1.49338
$$250$$ −9.71268 −0.614284
$$251$$ −21.0594 −1.32926 −0.664630 0.747173i $$-0.731411\pi$$
−0.664630 + 0.747173i $$0.731411\pi$$
$$252$$ 4.38291 0.276098
$$253$$ 0 0
$$254$$ 13.3466 0.837441
$$255$$ 11.0901 0.694488
$$256$$ 1.00000 0.0625000
$$257$$ 1.27738 0.0796811 0.0398405 0.999206i $$-0.487315\pi$$
0.0398405 + 0.999206i $$0.487315\pi$$
$$258$$ −9.65314 −0.600978
$$259$$ −5.42248 −0.336936
$$260$$ 9.78686 0.606955
$$261$$ −9.19528 −0.569174
$$262$$ 4.58757 0.283421
$$263$$ −8.85896 −0.546267 −0.273134 0.961976i $$-0.588060\pi$$
−0.273134 + 0.961976i $$0.588060\pi$$
$$264$$ 0 0
$$265$$ −28.9324 −1.77730
$$266$$ 3.09995 0.190070
$$267$$ −9.74167 −0.596181
$$268$$ 14.1154 0.862236
$$269$$ 26.0234 1.58667 0.793337 0.608783i $$-0.208342\pi$$
0.793337 + 0.608783i $$0.208342\pi$$
$$270$$ −8.19772 −0.498897
$$271$$ −17.0826 −1.03770 −0.518848 0.854867i $$-0.673639\pi$$
−0.518848 + 0.854867i $$0.673639\pi$$
$$272$$ 2.14576 0.130106
$$273$$ 25.9098 1.56813
$$274$$ −13.6371 −0.823845
$$275$$ 0 0
$$276$$ −5.37710 −0.323663
$$277$$ −8.49406 −0.510359 −0.255179 0.966894i $$-0.582135\pi$$
−0.255179 + 0.966894i $$0.582135\pi$$
$$278$$ 5.78982 0.347251
$$279$$ 2.10150 0.125813
$$280$$ 7.62603 0.455742
$$281$$ −29.4238 −1.75527 −0.877637 0.479325i $$-0.840881\pi$$
−0.877637 + 0.479325i $$0.840881\pi$$
$$282$$ −7.15646 −0.426161
$$283$$ 17.0589 1.01405 0.507024 0.861932i $$-0.330745\pi$$
0.507024 + 0.861932i $$0.330745\pi$$
$$284$$ −15.9696 −0.947619
$$285$$ 5.16836 0.306147
$$286$$ 0 0
$$287$$ −17.0041 −1.00372
$$288$$ 1.41386 0.0833128
$$289$$ −12.3957 −0.729159
$$290$$ −15.9993 −0.939510
$$291$$ −11.4937 −0.673775
$$292$$ 3.17623 0.185875
$$293$$ −20.5142 −1.19845 −0.599227 0.800579i $$-0.704525\pi$$
−0.599227 + 0.800579i $$0.704525\pi$$
$$294$$ 5.48278 0.319762
$$295$$ −16.3600 −0.952516
$$296$$ −1.74921 −0.101671
$$297$$ 0 0
$$298$$ 10.3503 0.599575
$$299$$ −10.1821 −0.588847
$$300$$ 2.20981 0.127584
$$301$$ −14.2434 −0.820977
$$302$$ 12.1731 0.700483
$$303$$ 12.1957 0.700623
$$304$$ 1.00000 0.0573539
$$305$$ 15.5982 0.893147
$$306$$ 3.03382 0.173432
$$307$$ −5.64603 −0.322236 −0.161118 0.986935i $$-0.551510\pi$$
−0.161118 + 0.986935i $$0.551510\pi$$
$$308$$ 0 0
$$309$$ −20.0911 −1.14294
$$310$$ 3.65649 0.207674
$$311$$ 8.41613 0.477235 0.238617 0.971114i $$-0.423306\pi$$
0.238617 + 0.971114i $$0.423306\pi$$
$$312$$ 8.35814 0.473186
$$313$$ 31.3766 1.77351 0.886756 0.462239i $$-0.152954\pi$$
0.886756 + 0.462239i $$0.152954\pi$$
$$314$$ 3.72389 0.210151
$$315$$ 10.7822 0.607507
$$316$$ −7.25669 −0.408221
$$317$$ 7.20289 0.404555 0.202277 0.979328i $$-0.435166\pi$$
0.202277 + 0.979328i $$0.435166\pi$$
$$318$$ −24.7087 −1.38560
$$319$$ 0 0
$$320$$ 2.46005 0.137521
$$321$$ 30.6027 1.70808
$$322$$ −7.93402 −0.442146
$$323$$ 2.14576 0.119393
$$324$$ −11.2426 −0.624588
$$325$$ 4.18452 0.232115
$$326$$ −19.8920 −1.10172
$$327$$ 7.10279 0.392785
$$328$$ −5.48529 −0.302875
$$329$$ −10.5595 −0.582164
$$330$$ 0 0
$$331$$ 20.4083 1.12174 0.560870 0.827904i $$-0.310467\pi$$
0.560870 + 0.827904i $$0.310467\pi$$
$$332$$ −11.2166 −0.615588
$$333$$ −2.47315 −0.135528
$$334$$ 21.9867 1.20306
$$335$$ 34.7246 1.89721
$$336$$ 6.51275 0.355300
$$337$$ 32.1119 1.74925 0.874623 0.484803i $$-0.161109\pi$$
0.874623 + 0.484803i $$0.161109\pi$$
$$338$$ 2.82705 0.153771
$$339$$ 23.8807 1.29702
$$340$$ 5.27868 0.286277
$$341$$ 0 0
$$342$$ 1.41386 0.0764530
$$343$$ −13.6097 −0.734855
$$344$$ −4.59472 −0.247731
$$345$$ −13.2279 −0.712167
$$346$$ 25.4819 1.36991
$$347$$ −1.12968 −0.0606444 −0.0303222 0.999540i $$-0.509653\pi$$
−0.0303222 + 0.999540i $$0.509653\pi$$
$$348$$ −13.6636 −0.732448
$$349$$ 21.1559 1.13245 0.566225 0.824251i $$-0.308403\pi$$
0.566225 + 0.824251i $$0.308403\pi$$
$$350$$ 3.26062 0.174288
$$351$$ −13.2571 −0.707614
$$352$$ 0 0
$$353$$ −0.0272714 −0.00145151 −0.000725755 1.00000i $$-0.500231\pi$$
−0.000725755 1.00000i $$0.500231\pi$$
$$354$$ −13.9717 −0.742588
$$355$$ −39.2858 −2.08508
$$356$$ −4.63686 −0.245753
$$357$$ 13.9748 0.739626
$$358$$ 22.7884 1.20441
$$359$$ −15.1154 −0.797758 −0.398879 0.917004i $$-0.630601\pi$$
−0.398879 + 0.917004i $$0.630601\pi$$
$$360$$ 3.47817 0.183316
$$361$$ 1.00000 0.0526316
$$362$$ −1.54547 −0.0812279
$$363$$ 0 0
$$364$$ 12.3326 0.646404
$$365$$ 7.81367 0.408986
$$366$$ 13.3211 0.696304
$$367$$ 21.4714 1.12080 0.560399 0.828223i $$-0.310648\pi$$
0.560399 + 0.828223i $$0.310648\pi$$
$$368$$ −2.55940 −0.133418
$$369$$ −7.75546 −0.403733
$$370$$ −4.30315 −0.223710
$$371$$ −36.4582 −1.89282
$$372$$ 3.12270 0.161904
$$373$$ 18.3417 0.949697 0.474848 0.880068i $$-0.342503\pi$$
0.474848 + 0.880068i $$0.342503\pi$$
$$374$$ 0 0
$$375$$ −20.4056 −1.05374
$$376$$ −3.40634 −0.175669
$$377$$ −25.8736 −1.33256
$$378$$ −10.3301 −0.531323
$$379$$ 12.3232 0.633003 0.316501 0.948592i $$-0.397492\pi$$
0.316501 + 0.948592i $$0.397492\pi$$
$$380$$ 2.46005 0.126198
$$381$$ 28.0402 1.43654
$$382$$ 7.14404 0.365521
$$383$$ 28.7507 1.46909 0.734546 0.678558i $$-0.237395\pi$$
0.734546 + 0.678558i $$0.237395\pi$$
$$384$$ 2.10092 0.107212
$$385$$ 0 0
$$386$$ 12.0980 0.615772
$$387$$ −6.49631 −0.330226
$$388$$ −5.47081 −0.277738
$$389$$ 2.72988 0.138410 0.0692052 0.997602i $$-0.477954\pi$$
0.0692052 + 0.997602i $$0.477954\pi$$
$$390$$ 20.5614 1.04117
$$391$$ −5.49187 −0.277736
$$392$$ 2.60971 0.131810
$$393$$ 9.63812 0.486179
$$394$$ −18.2516 −0.919502
$$395$$ −17.8518 −0.898222
$$396$$ 0 0
$$397$$ 7.21330 0.362025 0.181013 0.983481i $$-0.442062\pi$$
0.181013 + 0.983481i $$0.442062\pi$$
$$398$$ 23.9705 1.20153
$$399$$ 6.51275 0.326045
$$400$$ 1.05183 0.0525915
$$401$$ −1.18981 −0.0594164 −0.0297082 0.999559i $$-0.509458\pi$$
−0.0297082 + 0.999559i $$0.509458\pi$$
$$402$$ 29.6554 1.47908
$$403$$ 5.91317 0.294556
$$404$$ 5.80492 0.288806
$$405$$ −27.6573 −1.37430
$$406$$ −20.1610 −1.00057
$$407$$ 0 0
$$408$$ 4.50808 0.223183
$$409$$ −11.7792 −0.582442 −0.291221 0.956656i $$-0.594061\pi$$
−0.291221 + 0.956656i $$0.594061\pi$$
$$410$$ −13.4941 −0.666425
$$411$$ −28.6504 −1.41322
$$412$$ −9.56301 −0.471136
$$413$$ −20.6156 −1.01443
$$414$$ −3.61865 −0.177847
$$415$$ −27.5932 −1.35450
$$416$$ 3.97832 0.195053
$$417$$ 12.1640 0.595672
$$418$$ 0 0
$$419$$ 20.0798 0.980963 0.490482 0.871452i $$-0.336821\pi$$
0.490482 + 0.871452i $$0.336821\pi$$
$$420$$ 16.0217 0.781778
$$421$$ 0.885182 0.0431412 0.0215706 0.999767i $$-0.493133\pi$$
0.0215706 + 0.999767i $$0.493133\pi$$
$$422$$ −20.7466 −1.00993
$$423$$ −4.81611 −0.234167
$$424$$ −11.7609 −0.571160
$$425$$ 2.25698 0.109480
$$426$$ −33.5508 −1.62554
$$427$$ 19.6555 0.951198
$$428$$ 14.5663 0.704090
$$429$$ 0 0
$$430$$ −11.3032 −0.545090
$$431$$ 20.3046 0.978038 0.489019 0.872273i $$-0.337355\pi$$
0.489019 + 0.872273i $$0.337355\pi$$
$$432$$ −3.33234 −0.160327
$$433$$ −36.1713 −1.73828 −0.869140 0.494566i $$-0.835327\pi$$
−0.869140 + 0.494566i $$0.835327\pi$$
$$434$$ 4.60761 0.221172
$$435$$ −33.6132 −1.61163
$$436$$ 3.38080 0.161911
$$437$$ −2.55940 −0.122433
$$438$$ 6.67300 0.318848
$$439$$ −21.4914 −1.02573 −0.512864 0.858470i $$-0.671416\pi$$
−0.512864 + 0.858470i $$0.671416\pi$$
$$440$$ 0 0
$$441$$ 3.68977 0.175703
$$442$$ 8.53654 0.406042
$$443$$ −24.5995 −1.16876 −0.584379 0.811481i $$-0.698662\pi$$
−0.584379 + 0.811481i $$0.698662\pi$$
$$444$$ −3.67496 −0.174406
$$445$$ −11.4069 −0.540739
$$446$$ 28.3845 1.34405
$$447$$ 21.7451 1.02851
$$448$$ 3.09995 0.146459
$$449$$ 35.2701 1.66450 0.832251 0.554400i $$-0.187052\pi$$
0.832251 + 0.554400i $$0.187052\pi$$
$$450$$ 1.48715 0.0701047
$$451$$ 0 0
$$452$$ 11.3668 0.534650
$$453$$ 25.5747 1.20160
$$454$$ 8.50634 0.399222
$$455$$ 30.3388 1.42230
$$456$$ 2.10092 0.0983846
$$457$$ 7.37055 0.344780 0.172390 0.985029i $$-0.444851\pi$$
0.172390 + 0.985029i $$0.444851\pi$$
$$458$$ −1.70730 −0.0797770
$$459$$ −7.15042 −0.333753
$$460$$ −6.29625 −0.293564
$$461$$ 36.4875 1.69939 0.849696 0.527272i $$-0.176785\pi$$
0.849696 + 0.527272i $$0.176785\pi$$
$$462$$ 0 0
$$463$$ −16.2208 −0.753844 −0.376922 0.926245i $$-0.623018\pi$$
−0.376922 + 0.926245i $$0.623018\pi$$
$$464$$ −6.50365 −0.301924
$$465$$ 7.68199 0.356244
$$466$$ −9.95632 −0.461217
$$467$$ 4.27354 0.197756 0.0988779 0.995100i $$-0.468475\pi$$
0.0988779 + 0.995100i $$0.468475\pi$$
$$468$$ 5.62481 0.260007
$$469$$ 43.7571 2.02052
$$470$$ −8.37977 −0.386530
$$471$$ 7.82359 0.360492
$$472$$ −6.65028 −0.306104
$$473$$ 0 0
$$474$$ −15.2457 −0.700260
$$475$$ 1.05183 0.0482613
$$476$$ 6.65177 0.304883
$$477$$ −16.6283 −0.761359
$$478$$ −16.2786 −0.744564
$$479$$ 39.1936 1.79080 0.895402 0.445260i $$-0.146889\pi$$
0.895402 + 0.445260i $$0.146889\pi$$
$$480$$ 5.16836 0.235902
$$481$$ −6.95893 −0.317300
$$482$$ 5.95144 0.271081
$$483$$ −16.6687 −0.758454
$$484$$ 0 0
$$485$$ −13.4585 −0.611117
$$486$$ −13.6227 −0.617940
$$487$$ 3.27438 0.148376 0.0741882 0.997244i $$-0.476363\pi$$
0.0741882 + 0.997244i $$0.476363\pi$$
$$488$$ 6.34059 0.287025
$$489$$ −41.7916 −1.88988
$$490$$ 6.42000 0.290026
$$491$$ −40.6503 −1.83452 −0.917260 0.398288i $$-0.869604\pi$$
−0.917260 + 0.398288i $$0.869604\pi$$
$$492$$ −11.5242 −0.519549
$$493$$ −13.9553 −0.628515
$$494$$ 3.97832 0.178993
$$495$$ 0 0
$$496$$ 1.48635 0.0667390
$$497$$ −49.5049 −2.22060
$$498$$ −23.5651 −1.05598
$$499$$ −14.1445 −0.633195 −0.316598 0.948560i $$-0.602540\pi$$
−0.316598 + 0.948560i $$0.602540\pi$$
$$500$$ −9.71268 −0.434364
$$501$$ 46.1923 2.06372
$$502$$ −21.0594 −0.939928
$$503$$ 27.7402 1.23688 0.618438 0.785834i $$-0.287766\pi$$
0.618438 + 0.785834i $$0.287766\pi$$
$$504$$ 4.38291 0.195230
$$505$$ 14.2804 0.635468
$$506$$ 0 0
$$507$$ 5.93940 0.263778
$$508$$ 13.3466 0.592160
$$509$$ 4.86817 0.215778 0.107889 0.994163i $$-0.465591\pi$$
0.107889 + 0.994163i $$0.465591\pi$$
$$510$$ 11.0901 0.491077
$$511$$ 9.84616 0.435568
$$512$$ 1.00000 0.0441942
$$513$$ −3.33234 −0.147127
$$514$$ 1.27738 0.0563430
$$515$$ −23.5254 −1.03666
$$516$$ −9.65314 −0.424956
$$517$$ 0 0
$$518$$ −5.42248 −0.238250
$$519$$ 53.5353 2.34994
$$520$$ 9.78686 0.429182
$$521$$ 18.6548 0.817281 0.408641 0.912695i $$-0.366003\pi$$
0.408641 + 0.912695i $$0.366003\pi$$
$$522$$ −9.19528 −0.402466
$$523$$ 8.39239 0.366974 0.183487 0.983022i $$-0.441262\pi$$
0.183487 + 0.983022i $$0.441262\pi$$
$$524$$ 4.58757 0.200409
$$525$$ 6.85031 0.298972
$$526$$ −8.85896 −0.386269
$$527$$ 3.18935 0.138930
$$528$$ 0 0
$$529$$ −16.4495 −0.715194
$$530$$ −28.9324 −1.25674
$$531$$ −9.40259 −0.408038
$$532$$ 3.09995 0.134400
$$533$$ −21.8223 −0.945227
$$534$$ −9.74167 −0.421563
$$535$$ 35.8338 1.54923
$$536$$ 14.1154 0.609693
$$537$$ 47.8766 2.06603
$$538$$ 26.0234 1.12195
$$539$$ 0 0
$$540$$ −8.19772 −0.352774
$$541$$ 32.0199 1.37664 0.688322 0.725405i $$-0.258347\pi$$
0.688322 + 0.725405i $$0.258347\pi$$
$$542$$ −17.0826 −0.733762
$$543$$ −3.24690 −0.139338
$$544$$ 2.14576 0.0919989
$$545$$ 8.31693 0.356258
$$546$$ 25.9098 1.10884
$$547$$ −25.7176 −1.09961 −0.549803 0.835295i $$-0.685297\pi$$
−0.549803 + 0.835295i $$0.685297\pi$$
$$548$$ −13.6371 −0.582546
$$549$$ 8.96474 0.382606
$$550$$ 0 0
$$551$$ −6.50365 −0.277065
$$552$$ −5.37710 −0.228864
$$553$$ −22.4954 −0.956602
$$554$$ −8.49406 −0.360878
$$555$$ −9.04057 −0.383751
$$556$$ 5.78982 0.245543
$$557$$ −37.3111 −1.58092 −0.790461 0.612512i $$-0.790159\pi$$
−0.790461 + 0.612512i $$0.790159\pi$$
$$558$$ 2.10150 0.0889634
$$559$$ −18.2793 −0.773131
$$560$$ 7.62603 0.322259
$$561$$ 0 0
$$562$$ −29.4238 −1.24117
$$563$$ −0.758990 −0.0319876 −0.0159938 0.999872i $$-0.505091\pi$$
−0.0159938 + 0.999872i $$0.505091\pi$$
$$564$$ −7.15646 −0.301341
$$565$$ 27.9629 1.17641
$$566$$ 17.0589 0.717041
$$567$$ −34.8515 −1.46362
$$568$$ −15.9696 −0.670068
$$569$$ 31.2487 1.31001 0.655007 0.755623i $$-0.272666\pi$$
0.655007 + 0.755623i $$0.272666\pi$$
$$570$$ 5.16836 0.216479
$$571$$ 20.5848 0.861445 0.430723 0.902484i $$-0.358259\pi$$
0.430723 + 0.902484i $$0.358259\pi$$
$$572$$ 0 0
$$573$$ 15.0091 0.627012
$$574$$ −17.0041 −0.709739
$$575$$ −2.69206 −0.112267
$$576$$ 1.41386 0.0589110
$$577$$ 12.5133 0.520934 0.260467 0.965483i $$-0.416124\pi$$
0.260467 + 0.965483i $$0.416124\pi$$
$$578$$ −12.3957 −0.515593
$$579$$ 25.4169 1.05629
$$580$$ −15.9993 −0.664334
$$581$$ −34.7708 −1.44254
$$582$$ −11.4937 −0.476431
$$583$$ 0 0
$$584$$ 3.17623 0.131433
$$585$$ 13.8373 0.572102
$$586$$ −20.5142 −0.847435
$$587$$ 12.0214 0.496178 0.248089 0.968737i $$-0.420197\pi$$
0.248089 + 0.968737i $$0.420197\pi$$
$$588$$ 5.48278 0.226106
$$589$$ 1.48635 0.0612439
$$590$$ −16.3600 −0.673531
$$591$$ −38.3451 −1.57731
$$592$$ −1.74921 −0.0718922
$$593$$ 33.2839 1.36680 0.683402 0.730042i $$-0.260500\pi$$
0.683402 + 0.730042i $$0.260500\pi$$
$$594$$ 0 0
$$595$$ 16.3637 0.670844
$$596$$ 10.3503 0.423963
$$597$$ 50.3602 2.06110
$$598$$ −10.1821 −0.416378
$$599$$ −14.8580 −0.607081 −0.303541 0.952819i $$-0.598169\pi$$
−0.303541 + 0.952819i $$0.598169\pi$$
$$600$$ 2.20981 0.0902152
$$601$$ −30.9531 −1.26260 −0.631301 0.775538i $$-0.717479\pi$$
−0.631301 + 0.775538i $$0.717479\pi$$
$$602$$ −14.2434 −0.580518
$$603$$ 19.9573 0.812724
$$604$$ 12.1731 0.495316
$$605$$ 0 0
$$606$$ 12.1957 0.495415
$$607$$ −29.4283 −1.19446 −0.597229 0.802071i $$-0.703732\pi$$
−0.597229 + 0.802071i $$0.703732\pi$$
$$608$$ 1.00000 0.0405554
$$609$$ −42.3567 −1.71638
$$610$$ 15.5982 0.631551
$$611$$ −13.5515 −0.548236
$$612$$ 3.03382 0.122635
$$613$$ −21.5787 −0.871554 −0.435777 0.900055i $$-0.643526\pi$$
−0.435777 + 0.900055i $$0.643526\pi$$
$$614$$ −5.64603 −0.227855
$$615$$ −28.3500 −1.14318
$$616$$ 0 0
$$617$$ −21.8270 −0.878721 −0.439360 0.898311i $$-0.644795\pi$$
−0.439360 + 0.898311i $$0.644795\pi$$
$$618$$ −20.0911 −0.808183
$$619$$ 41.5379 1.66955 0.834775 0.550592i $$-0.185598\pi$$
0.834775 + 0.550592i $$0.185598\pi$$
$$620$$ 3.65649 0.146848
$$621$$ 8.52881 0.342249
$$622$$ 8.41613 0.337456
$$623$$ −14.3740 −0.575884
$$624$$ 8.35814 0.334593
$$625$$ −29.1528 −1.16611
$$626$$ 31.3766 1.25406
$$627$$ 0 0
$$628$$ 3.72389 0.148599
$$629$$ −3.75340 −0.149658
$$630$$ 10.7822 0.429572
$$631$$ 1.40462 0.0559171 0.0279585 0.999609i $$-0.491099\pi$$
0.0279585 + 0.999609i $$0.491099\pi$$
$$632$$ −7.25669 −0.288656
$$633$$ −43.5870 −1.73243
$$634$$ 7.20289 0.286063
$$635$$ 32.8333 1.30295
$$636$$ −24.7087 −0.979765
$$637$$ 10.3822 0.411360
$$638$$ 0 0
$$639$$ −22.5788 −0.893203
$$640$$ 2.46005 0.0972419
$$641$$ −12.6801 −0.500832 −0.250416 0.968138i $$-0.580567\pi$$
−0.250416 + 0.968138i $$0.580567\pi$$
$$642$$ 30.6027 1.20779
$$643$$ 4.42309 0.174429 0.0872147 0.996190i $$-0.472203\pi$$
0.0872147 + 0.996190i $$0.472203\pi$$
$$644$$ −7.93402 −0.312644
$$645$$ −23.7472 −0.935044
$$646$$ 2.14576 0.0844239
$$647$$ −24.5901 −0.966736 −0.483368 0.875417i $$-0.660587\pi$$
−0.483368 + 0.875417i $$0.660587\pi$$
$$648$$ −11.2426 −0.441650
$$649$$ 0 0
$$650$$ 4.18452 0.164130
$$651$$ 9.68022 0.379398
$$652$$ −19.8920 −0.779032
$$653$$ 19.5368 0.764533 0.382267 0.924052i $$-0.375144\pi$$
0.382267 + 0.924052i $$0.375144\pi$$
$$654$$ 7.10279 0.277741
$$655$$ 11.2856 0.440967
$$656$$ −5.48529 −0.214165
$$657$$ 4.49076 0.175201
$$658$$ −10.5595 −0.411652
$$659$$ −35.3980 −1.37891 −0.689456 0.724328i $$-0.742150\pi$$
−0.689456 + 0.724328i $$0.742150\pi$$
$$660$$ 0 0
$$661$$ −26.3898 −1.02644 −0.513222 0.858256i $$-0.671548\pi$$
−0.513222 + 0.858256i $$0.671548\pi$$
$$662$$ 20.4083 0.793190
$$663$$ 17.9346 0.696522
$$664$$ −11.2166 −0.435287
$$665$$ 7.62603 0.295725
$$666$$ −2.47315 −0.0958326
$$667$$ 16.6455 0.644514
$$668$$ 21.9867 0.850690
$$669$$ 59.6336 2.30557
$$670$$ 34.7246 1.34153
$$671$$ 0 0
$$672$$ 6.51275 0.251235
$$673$$ 4.02795 0.155266 0.0776331 0.996982i $$-0.475264\pi$$
0.0776331 + 0.996982i $$0.475264\pi$$
$$674$$ 32.1119 1.23690
$$675$$ −3.50506 −0.134910
$$676$$ 2.82705 0.108733
$$677$$ −21.6069 −0.830419 −0.415210 0.909726i $$-0.636292\pi$$
−0.415210 + 0.909726i $$0.636292\pi$$
$$678$$ 23.8807 0.917135
$$679$$ −16.9593 −0.650837
$$680$$ 5.27868 0.202428
$$681$$ 17.8711 0.684823
$$682$$ 0 0
$$683$$ 3.73163 0.142787 0.0713935 0.997448i $$-0.477255\pi$$
0.0713935 + 0.997448i $$0.477255\pi$$
$$684$$ 1.41386 0.0540605
$$685$$ −33.5478 −1.28180
$$686$$ −13.6097 −0.519621
$$687$$ −3.58691 −0.136849
$$688$$ −4.59472 −0.175172
$$689$$ −46.7887 −1.78251
$$690$$ −13.2279 −0.503578
$$691$$ 42.4147 1.61353 0.806765 0.590872i $$-0.201216\pi$$
0.806765 + 0.590872i $$0.201216\pi$$
$$692$$ 25.4819 0.968675
$$693$$ 0 0
$$694$$ −1.12968 −0.0428820
$$695$$ 14.2432 0.540277
$$696$$ −13.6636 −0.517919
$$697$$ −11.7701 −0.445826
$$698$$ 21.1559 0.800763
$$699$$ −20.9174 −0.791170
$$700$$ 3.26062 0.123240
$$701$$ 51.9082 1.96054 0.980272 0.197654i $$-0.0633322\pi$$
0.980272 + 0.197654i $$0.0633322\pi$$
$$702$$ −13.2571 −0.500358
$$703$$ −1.74921 −0.0659728
$$704$$ 0 0
$$705$$ −17.6052 −0.663051
$$706$$ −0.0272714 −0.00102637
$$707$$ 17.9950 0.676771
$$708$$ −13.9717 −0.525089
$$709$$ −42.1161 −1.58170 −0.790852 0.612008i $$-0.790362\pi$$
−0.790852 + 0.612008i $$0.790362\pi$$
$$710$$ −39.2858 −1.47437
$$711$$ −10.2600 −0.384779
$$712$$ −4.63686 −0.173774
$$713$$ −3.80416 −0.142467
$$714$$ 13.9748 0.522995
$$715$$ 0 0
$$716$$ 22.7884 0.851643
$$717$$ −34.2000 −1.27722
$$718$$ −15.1154 −0.564100
$$719$$ −6.37162 −0.237621 −0.118811 0.992917i $$-0.537908\pi$$
−0.118811 + 0.992917i $$0.537908\pi$$
$$720$$ 3.47817 0.129624
$$721$$ −29.6449 −1.10403
$$722$$ 1.00000 0.0372161
$$723$$ 12.5035 0.465010
$$724$$ −1.54547 −0.0574368
$$725$$ −6.84074 −0.254059
$$726$$ 0 0
$$727$$ −36.8358 −1.36616 −0.683082 0.730342i $$-0.739361\pi$$
−0.683082 + 0.730342i $$0.739361\pi$$
$$728$$ 12.3326 0.457077
$$729$$ 5.10748 0.189166
$$730$$ 7.81367 0.289197
$$731$$ −9.85919 −0.364655
$$732$$ 13.3211 0.492361
$$733$$ 7.23710 0.267308 0.133654 0.991028i $$-0.457329\pi$$
0.133654 + 0.991028i $$0.457329\pi$$
$$734$$ 21.4714 0.792524
$$735$$ 13.4879 0.497509
$$736$$ −2.55940 −0.0943408
$$737$$ 0 0
$$738$$ −7.75546 −0.285482
$$739$$ −19.6497 −0.722825 −0.361413 0.932406i $$-0.617705\pi$$
−0.361413 + 0.932406i $$0.617705\pi$$
$$740$$ −4.30315 −0.158187
$$741$$ 8.35814 0.307044
$$742$$ −36.4582 −1.33842
$$743$$ −7.72331 −0.283341 −0.141670 0.989914i $$-0.545247\pi$$
−0.141670 + 0.989914i $$0.545247\pi$$
$$744$$ 3.12270 0.114484
$$745$$ 25.4621 0.932860
$$746$$ 18.3417 0.671537
$$747$$ −15.8587 −0.580239
$$748$$ 0 0
$$749$$ 45.1549 1.64992
$$750$$ −20.4056 −0.745106
$$751$$ −45.4390 −1.65809 −0.829046 0.559181i $$-0.811116\pi$$
−0.829046 + 0.559181i $$0.811116\pi$$
$$752$$ −3.40634 −0.124217
$$753$$ −44.2442 −1.61235
$$754$$ −25.8736 −0.942261
$$755$$ 29.9464 1.08986
$$756$$ −10.3301 −0.375702
$$757$$ −0.394649 −0.0143438 −0.00717189 0.999974i $$-0.502283\pi$$
−0.00717189 + 0.999974i $$0.502283\pi$$
$$758$$ 12.3232 0.447601
$$759$$ 0 0
$$760$$ 2.46005 0.0892353
$$761$$ −37.5003 −1.35938 −0.679692 0.733498i $$-0.737886\pi$$
−0.679692 + 0.733498i $$0.737886\pi$$
$$762$$ 28.0402 1.01579
$$763$$ 10.4803 0.379413
$$764$$ 7.14404 0.258462
$$765$$ 7.46334 0.269838
$$766$$ 28.7507 1.03881
$$767$$ −26.4570 −0.955305
$$768$$ 2.10092 0.0758104
$$769$$ −0.388213 −0.0139993 −0.00699965 0.999976i $$-0.502228\pi$$
−0.00699965 + 0.999976i $$0.502228\pi$$
$$770$$ 0 0
$$771$$ 2.68368 0.0966505
$$772$$ 12.0980 0.435417
$$773$$ −32.5057 −1.16915 −0.584574 0.811341i $$-0.698738\pi$$
−0.584574 + 0.811341i $$0.698738\pi$$
$$774$$ −6.49631 −0.233505
$$775$$ 1.56339 0.0561585
$$776$$ −5.47081 −0.196391
$$777$$ −11.3922 −0.408693
$$778$$ 2.72988 0.0978709
$$779$$ −5.48529 −0.196531
$$780$$ 20.5614 0.736216
$$781$$ 0 0
$$782$$ −5.49187 −0.196389
$$783$$ 21.6724 0.774508
$$784$$ 2.60971 0.0932038
$$785$$ 9.16094 0.326968
$$786$$ 9.63812 0.343781
$$787$$ 11.8225 0.421425 0.210713 0.977548i $$-0.432422\pi$$
0.210713 + 0.977548i $$0.432422\pi$$
$$788$$ −18.2516 −0.650186
$$789$$ −18.6120 −0.662604
$$790$$ −17.8518 −0.635139
$$791$$ 35.2366 1.25287
$$792$$ 0 0
$$793$$ 25.2249 0.895763
$$794$$ 7.21330 0.255991
$$795$$ −60.7846 −2.15581
$$796$$ 23.9705 0.849613
$$797$$ 27.4045 0.970719 0.485359 0.874315i $$-0.338689\pi$$
0.485359 + 0.874315i $$0.338689\pi$$
$$798$$ 6.51275 0.230549
$$799$$ −7.30921 −0.258581
$$800$$ 1.05183 0.0371878
$$801$$ −6.55589 −0.231641
$$802$$ −1.18981 −0.0420137
$$803$$ 0 0
$$804$$ 29.6554 1.04586
$$805$$ −19.5181 −0.687922
$$806$$ 5.91317 0.208283
$$807$$ 54.6731 1.92458
$$808$$ 5.80492 0.204216
$$809$$ −9.23218 −0.324586 −0.162293 0.986743i $$-0.551889\pi$$
−0.162293 + 0.986743i $$0.551889\pi$$
$$810$$ −27.6573 −0.971778
$$811$$ 28.3825 0.996646 0.498323 0.866992i $$-0.333949\pi$$
0.498323 + 0.866992i $$0.333949\pi$$
$$812$$ −20.1610 −0.707513
$$813$$ −35.8892 −1.25869
$$814$$ 0 0
$$815$$ −48.9353 −1.71413
$$816$$ 4.50808 0.157814
$$817$$ −4.59472 −0.160749
$$818$$ −11.7792 −0.411849
$$819$$ 17.4366 0.609285
$$820$$ −13.4941 −0.471233
$$821$$ −29.3170 −1.02317 −0.511584 0.859233i $$-0.670941\pi$$
−0.511584 + 0.859233i $$0.670941\pi$$
$$822$$ −28.6504 −0.999296
$$823$$ −19.1547 −0.667692 −0.333846 0.942628i $$-0.608347\pi$$
−0.333846 + 0.942628i $$0.608347\pi$$
$$824$$ −9.56301 −0.333143
$$825$$ 0 0
$$826$$ −20.6156 −0.717307
$$827$$ 19.0633 0.662896 0.331448 0.943473i $$-0.392463\pi$$
0.331448 + 0.943473i $$0.392463\pi$$
$$828$$ −3.61865 −0.125757
$$829$$ −3.45420 −0.119969 −0.0599847 0.998199i $$-0.519105\pi$$
−0.0599847 + 0.998199i $$0.519105\pi$$
$$830$$ −27.5932 −0.957775
$$831$$ −17.8453 −0.619048
$$832$$ 3.97832 0.137923
$$833$$ 5.59981 0.194022
$$834$$ 12.1640 0.421203
$$835$$ 54.0883 1.87180
$$836$$ 0 0
$$837$$ −4.95302 −0.171202
$$838$$ 20.0798 0.693646
$$839$$ 16.7961 0.579865 0.289932 0.957047i $$-0.406367\pi$$
0.289932 + 0.957047i $$0.406367\pi$$
$$840$$ 16.0217 0.552800
$$841$$ 13.2975 0.458533
$$842$$ 0.885182 0.0305054
$$843$$ −61.8170 −2.12909
$$844$$ −20.7466 −0.714129
$$845$$ 6.95466 0.239248
$$846$$ −4.81611 −0.165581
$$847$$ 0 0
$$848$$ −11.7609 −0.403871
$$849$$ 35.8395 1.23001
$$850$$ 2.25698 0.0774138
$$851$$ 4.47694 0.153467
$$852$$ −33.5508 −1.14943
$$853$$ 5.53724 0.189592 0.0947958 0.995497i $$-0.469780\pi$$
0.0947958 + 0.995497i $$0.469780\pi$$
$$854$$ 19.6555 0.672598
$$855$$ 3.47817 0.118951
$$856$$ 14.5663 0.497867
$$857$$ −26.5793 −0.907932 −0.453966 0.891019i $$-0.649991\pi$$
−0.453966 + 0.891019i $$0.649991\pi$$
$$858$$ 0 0
$$859$$ 19.7426 0.673610 0.336805 0.941574i $$-0.390654\pi$$
0.336805 + 0.941574i $$0.390654\pi$$
$$860$$ −11.3032 −0.385437
$$861$$ −35.7243 −1.21748
$$862$$ 20.3046 0.691577
$$863$$ −22.8417 −0.777539 −0.388770 0.921335i $$-0.627100\pi$$
−0.388770 + 0.921335i $$0.627100\pi$$
$$864$$ −3.33234 −0.113369
$$865$$ 62.6866 2.13141
$$866$$ −36.1713 −1.22915
$$867$$ −26.0424 −0.884445
$$868$$ 4.60761 0.156392
$$869$$ 0 0
$$870$$ −33.6132 −1.13959
$$871$$ 56.1557 1.90276
$$872$$ 3.38080 0.114488
$$873$$ −7.73499 −0.261790
$$874$$ −2.55940 −0.0865730
$$875$$ −30.1089 −1.01787
$$876$$ 6.67300 0.225460
$$877$$ −39.1209 −1.32102 −0.660510 0.750817i $$-0.729660\pi$$
−0.660510 + 0.750817i $$0.729660\pi$$
$$878$$ −21.4914 −0.725300
$$879$$ −43.0987 −1.45368
$$880$$ 0 0
$$881$$ 39.7517 1.33927 0.669635 0.742691i $$-0.266451\pi$$
0.669635 + 0.742691i $$0.266451\pi$$
$$882$$ 3.68977 0.124241
$$883$$ −24.1017 −0.811088 −0.405544 0.914075i $$-0.632918\pi$$
−0.405544 + 0.914075i $$0.632918\pi$$
$$884$$ 8.53654 0.287115
$$885$$ −34.3710 −1.15537
$$886$$ −24.5995 −0.826437
$$887$$ 40.9484 1.37491 0.687457 0.726225i $$-0.258727\pi$$
0.687457 + 0.726225i $$0.258727\pi$$
$$888$$ −3.67496 −0.123323
$$889$$ 41.3739 1.38764
$$890$$ −11.4069 −0.382360
$$891$$ 0 0
$$892$$ 28.3845 0.950384
$$893$$ −3.40634 −0.113989
$$894$$ 21.7451 0.727264
$$895$$ 56.0606 1.87390
$$896$$ 3.09995 0.103562
$$897$$ −21.3918 −0.714252
$$898$$ 35.2701 1.17698
$$899$$ −9.66669 −0.322402
$$900$$ 1.48715 0.0495715
$$901$$ −25.2361 −0.840737
$$902$$ 0 0
$$903$$ −29.9243 −0.995818
$$904$$ 11.3668 0.378054
$$905$$ −3.80192 −0.126380
$$906$$ 25.5747 0.849662
$$907$$ −54.8992 −1.82290 −0.911449 0.411413i $$-0.865035\pi$$
−0.911449 + 0.411413i $$0.865035\pi$$
$$908$$ 8.50634 0.282293
$$909$$ 8.20737 0.272221
$$910$$ 30.3388 1.00572
$$911$$ 46.8459 1.55207 0.776037 0.630687i $$-0.217227\pi$$
0.776037 + 0.630687i $$0.217227\pi$$
$$912$$ 2.10092 0.0695684
$$913$$ 0 0
$$914$$ 7.37055 0.243796
$$915$$ 32.7705 1.08336
$$916$$ −1.70730 −0.0564109
$$917$$ 14.2213 0.469627
$$918$$ −7.15042 −0.235999
$$919$$ 1.76516 0.0582272 0.0291136 0.999576i $$-0.490732\pi$$
0.0291136 + 0.999576i $$0.490732\pi$$
$$920$$ −6.29625 −0.207581
$$921$$ −11.8619 −0.390861
$$922$$ 36.4875 1.20165
$$923$$ −63.5320 −2.09118
$$924$$ 0 0
$$925$$ −1.83988 −0.0604947
$$926$$ −16.2208 −0.533048
$$927$$ −13.5208 −0.444081
$$928$$ −6.50365 −0.213493
$$929$$ −28.8886 −0.947805 −0.473902 0.880577i $$-0.657155\pi$$
−0.473902 + 0.880577i $$0.657155\pi$$
$$930$$ 7.68199 0.251902
$$931$$ 2.60971 0.0855297
$$932$$ −9.95632 −0.326130
$$933$$ 17.6816 0.578870
$$934$$ 4.27354 0.139835
$$935$$ 0 0
$$936$$ 5.62481 0.183853
$$937$$ −25.1445 −0.821436 −0.410718 0.911762i $$-0.634722\pi$$
−0.410718 + 0.911762i $$0.634722\pi$$
$$938$$ 43.7571 1.42872
$$939$$ 65.9198 2.15121
$$940$$ −8.37977 −0.273318
$$941$$ 0.744662 0.0242753 0.0121376 0.999926i $$-0.496136\pi$$
0.0121376 + 0.999926i $$0.496136\pi$$
$$942$$ 7.82359 0.254906
$$943$$ 14.0391 0.457175
$$944$$ −6.65028 −0.216448
$$945$$ −25.4125 −0.826670
$$946$$ 0 0
$$947$$ 54.6088 1.77455 0.887273 0.461244i $$-0.152597\pi$$
0.887273 + 0.461244i $$0.152597\pi$$
$$948$$ −15.2457 −0.495158
$$949$$ 12.6361 0.410184
$$950$$ 1.05183 0.0341259
$$951$$ 15.1327 0.490712
$$952$$ 6.65177 0.215585
$$953$$ −29.4684 −0.954574 −0.477287 0.878747i $$-0.658380\pi$$
−0.477287 + 0.878747i $$0.658380\pi$$
$$954$$ −16.6283 −0.538362
$$955$$ 17.5747 0.568703
$$956$$ −16.2786 −0.526487
$$957$$ 0 0
$$958$$ 39.1936 1.26629
$$959$$ −42.2742 −1.36511
$$960$$ 5.16836 0.166808
$$961$$ −28.7908 −0.928734
$$962$$ −6.95893 −0.224365
$$963$$ 20.5948 0.663659
$$964$$ 5.95144 0.191683
$$965$$ 29.7616 0.958061
$$966$$ −16.6687 −0.536308
$$967$$ 30.8647 0.992541 0.496271 0.868168i $$-0.334702\pi$$
0.496271 + 0.868168i $$0.334702\pi$$
$$968$$ 0 0
$$969$$ 4.50808 0.144820
$$970$$ −13.4585 −0.432125
$$971$$ −10.8297 −0.347541 −0.173771 0.984786i $$-0.555595\pi$$
−0.173771 + 0.984786i $$0.555595\pi$$
$$972$$ −13.6227 −0.436949
$$973$$ 17.9482 0.575392
$$974$$ 3.27438 0.104918
$$975$$ 8.79134 0.281548
$$976$$ 6.34059 0.202957
$$977$$ 5.53214 0.176989 0.0884945 0.996077i $$-0.471794\pi$$
0.0884945 + 0.996077i $$0.471794\pi$$
$$978$$ −41.7916 −1.33635
$$979$$ 0 0
$$980$$ 6.42000 0.205079
$$981$$ 4.77999 0.152613
$$982$$ −40.6503 −1.29720
$$983$$ 22.2474 0.709583 0.354791 0.934945i $$-0.384552\pi$$
0.354791 + 0.934945i $$0.384552\pi$$
$$984$$ −11.5242 −0.367377
$$985$$ −44.8998 −1.43063
$$986$$ −13.9553 −0.444427
$$987$$ −22.1847 −0.706146
$$988$$ 3.97832 0.126567
$$989$$ 11.7597 0.373938
$$990$$ 0 0
$$991$$ −8.28887 −0.263305 −0.131652 0.991296i $$-0.542028\pi$$
−0.131652 + 0.991296i $$0.542028\pi$$
$$992$$ 1.48635 0.0471916
$$993$$ 42.8761 1.36063
$$994$$ −49.5049 −1.57020
$$995$$ 58.9686 1.86943
$$996$$ −23.5651 −0.746688
$$997$$ 27.5534 0.872624 0.436312 0.899795i $$-0.356284\pi$$
0.436312 + 0.899795i $$0.356284\pi$$
$$998$$ −14.1445 −0.447736
$$999$$ 5.82898 0.184421
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 4598.2.a.cd.1.8 10
11.7 odd 10 418.2.f.h.115.2 20
11.8 odd 10 418.2.f.h.229.2 yes 20
11.10 odd 2 4598.2.a.cc.1.8 10

By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.h.115.2 20 11.7 odd 10
418.2.f.h.229.2 yes 20 11.8 odd 10
4598.2.a.cc.1.8 10 11.10 odd 2
4598.2.a.cd.1.8 10 1.1 even 1 trivial