# Properties

 Label 138.8.a.h.1.4 Level $138$ Weight $8$ Character 138.1 Self dual yes Analytic conductor $43.109$ Analytic rank $0$ Dimension $4$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$138 = 2 \cdot 3 \cdot 23$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 138.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$43.1091335168$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ Defining polynomial: $$x^{4} - 2x^{3} - 8367x^{2} - 89140x + 11077220$$ x^4 - 2*x^3 - 8367*x^2 - 89140*x + 11077220 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{5}\cdot 3$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.4 Root $$-56.1267$$ of defining polynomial Character $$\chi$$ $$=$$ 138.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +366.876 q^{5} +216.000 q^{6} -561.721 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$$ $$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +366.876 q^{5} +216.000 q^{6} -561.721 q^{7} +512.000 q^{8} +729.000 q^{9} +2935.00 q^{10} -1096.20 q^{11} +1728.00 q^{12} +6925.11 q^{13} -4493.77 q^{14} +9905.64 q^{15} +4096.00 q^{16} +13654.6 q^{17} +5832.00 q^{18} +29540.8 q^{19} +23480.0 q^{20} -15166.5 q^{21} -8769.58 q^{22} -12167.0 q^{23} +13824.0 q^{24} +56472.7 q^{25} +55400.9 q^{26} +19683.0 q^{27} -35950.1 q^{28} +150266. q^{29} +79245.1 q^{30} -204841. q^{31} +32768.0 q^{32} -29597.3 q^{33} +109237. q^{34} -206082. q^{35} +46656.0 q^{36} -492163. q^{37} +236327. q^{38} +186978. q^{39} +187840. q^{40} +416521. q^{41} -121332. q^{42} +371500. q^{43} -70156.6 q^{44} +267452. q^{45} -97336.0 q^{46} +930660. q^{47} +110592. q^{48} -508013. q^{49} +451782. q^{50} +368675. q^{51} +443207. q^{52} +1.01318e6 q^{53} +157464. q^{54} -402168. q^{55} -287601. q^{56} +797602. q^{57} +1.20213e6 q^{58} -2.28957e6 q^{59} +633961. q^{60} +2.95586e6 q^{61} -1.63873e6 q^{62} -409495. q^{63} +262144. q^{64} +2.54066e6 q^{65} -236779. q^{66} -1.46138e6 q^{67} +873896. q^{68} -328509. q^{69} -1.64865e6 q^{70} -1.82588e6 q^{71} +373248. q^{72} -40352.1 q^{73} -3.93731e6 q^{74} +1.52476e6 q^{75} +1.89061e6 q^{76} +615757. q^{77} +1.49582e6 q^{78} -2.36229e6 q^{79} +1.50272e6 q^{80} +531441. q^{81} +3.33217e6 q^{82} +1.27885e6 q^{83} -970654. q^{84} +5.00955e6 q^{85} +2.97200e6 q^{86} +4.05718e6 q^{87} -561253. q^{88} +3.88462e6 q^{89} +2.13962e6 q^{90} -3.88998e6 q^{91} -778688. q^{92} -5.53072e6 q^{93} +7.44528e6 q^{94} +1.08378e7 q^{95} +884736. q^{96} -8.46502e6 q^{97} -4.06410e6 q^{98} -799128. q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10})$$ 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9 $$4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9} + 2160 q^{10} + 4120 q^{11} + 6912 q^{12} + 8036 q^{13} + 16176 q^{14} + 7290 q^{15} + 16384 q^{16} + 37182 q^{17} + 23328 q^{18} + 5702 q^{19} + 17280 q^{20} + 54594 q^{21} + 32960 q^{22} - 48668 q^{23} + 55296 q^{24} + 121480 q^{25} + 64288 q^{26} + 78732 q^{27} + 129408 q^{28} + 217716 q^{29} + 58320 q^{30} + 222852 q^{31} + 131072 q^{32} + 111240 q^{33} + 297456 q^{34} + 68440 q^{35} + 186624 q^{36} + 486428 q^{37} + 45616 q^{38} + 216972 q^{39} + 138240 q^{40} + 338336 q^{41} + 436752 q^{42} + 730974 q^{43} + 263680 q^{44} + 196830 q^{45} - 389344 q^{46} + 338248 q^{47} + 442368 q^{48} - 310552 q^{49} + 971840 q^{50} + 1003914 q^{51} + 514304 q^{52} - 375502 q^{53} + 629856 q^{54} + 424840 q^{55} + 1035264 q^{56} + 153954 q^{57} + 1741728 q^{58} + 71392 q^{59} + 466560 q^{60} + 2101164 q^{61} + 1782816 q^{62} + 1474038 q^{63} + 1048576 q^{64} + 1578780 q^{65} + 889920 q^{66} + 4337162 q^{67} + 2379648 q^{68} - 1314036 q^{69} + 547520 q^{70} + 2288016 q^{71} + 1492992 q^{72} - 1107328 q^{73} + 3891424 q^{74} + 3279960 q^{75} + 364928 q^{76} + 5826200 q^{77} + 1735776 q^{78} + 60610 q^{79} + 1105920 q^{80} + 2125764 q^{81} + 2706688 q^{82} + 1485464 q^{83} + 3494016 q^{84} - 8843820 q^{85} + 5847792 q^{86} + 5878332 q^{87} + 2109440 q^{88} + 1485090 q^{89} + 1574640 q^{90} - 2898412 q^{91} - 3114752 q^{92} + 6017004 q^{93} + 2705984 q^{94} + 8545200 q^{95} + 3538944 q^{96} + 1935444 q^{97} - 2484416 q^{98} + 3003480 q^{99}+O(q^{100})$$ 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9 + 2160 * q^10 + 4120 * q^11 + 6912 * q^12 + 8036 * q^13 + 16176 * q^14 + 7290 * q^15 + 16384 * q^16 + 37182 * q^17 + 23328 * q^18 + 5702 * q^19 + 17280 * q^20 + 54594 * q^21 + 32960 * q^22 - 48668 * q^23 + 55296 * q^24 + 121480 * q^25 + 64288 * q^26 + 78732 * q^27 + 129408 * q^28 + 217716 * q^29 + 58320 * q^30 + 222852 * q^31 + 131072 * q^32 + 111240 * q^33 + 297456 * q^34 + 68440 * q^35 + 186624 * q^36 + 486428 * q^37 + 45616 * q^38 + 216972 * q^39 + 138240 * q^40 + 338336 * q^41 + 436752 * q^42 + 730974 * q^43 + 263680 * q^44 + 196830 * q^45 - 389344 * q^46 + 338248 * q^47 + 442368 * q^48 - 310552 * q^49 + 971840 * q^50 + 1003914 * q^51 + 514304 * q^52 - 375502 * q^53 + 629856 * q^54 + 424840 * q^55 + 1035264 * q^56 + 153954 * q^57 + 1741728 * q^58 + 71392 * q^59 + 466560 * q^60 + 2101164 * q^61 + 1782816 * q^62 + 1474038 * q^63 + 1048576 * q^64 + 1578780 * q^65 + 889920 * q^66 + 4337162 * q^67 + 2379648 * q^68 - 1314036 * q^69 + 547520 * q^70 + 2288016 * q^71 + 1492992 * q^72 - 1107328 * q^73 + 3891424 * q^74 + 3279960 * q^75 + 364928 * q^76 + 5826200 * q^77 + 1735776 * q^78 + 60610 * q^79 + 1105920 * q^80 + 2125764 * q^81 + 2706688 * q^82 + 1485464 * q^83 + 3494016 * q^84 - 8843820 * q^85 + 5847792 * q^86 + 5878332 * q^87 + 2109440 * q^88 + 1485090 * q^89 + 1574640 * q^90 - 2898412 * q^91 - 3114752 * q^92 + 6017004 * q^93 + 2705984 * q^94 + 8545200 * q^95 + 3538944 * q^96 + 1935444 * q^97 - 2484416 * q^98 + 3003480 * 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 8.00000 0.707107
$$3$$ 27.0000 0.577350
$$4$$ 64.0000 0.500000
$$5$$ 366.876 1.31257 0.656287 0.754511i $$-0.272126\pi$$
0.656287 + 0.754511i $$0.272126\pi$$
$$6$$ 216.000 0.408248
$$7$$ −561.721 −0.618981 −0.309491 0.950903i $$-0.600159\pi$$
−0.309491 + 0.950903i $$0.600159\pi$$
$$8$$ 512.000 0.353553
$$9$$ 729.000 0.333333
$$10$$ 2935.00 0.928130
$$11$$ −1096.20 −0.248322 −0.124161 0.992262i $$-0.539624\pi$$
−0.124161 + 0.992262i $$0.539624\pi$$
$$12$$ 1728.00 0.288675
$$13$$ 6925.11 0.874229 0.437115 0.899406i $$-0.356000\pi$$
0.437115 + 0.899406i $$0.356000\pi$$
$$14$$ −4493.77 −0.437686
$$15$$ 9905.64 0.757815
$$16$$ 4096.00 0.250000
$$17$$ 13654.6 0.674075 0.337038 0.941491i $$-0.390575\pi$$
0.337038 + 0.941491i $$0.390575\pi$$
$$18$$ 5832.00 0.235702
$$19$$ 29540.8 0.988064 0.494032 0.869444i $$-0.335523\pi$$
0.494032 + 0.869444i $$0.335523\pi$$
$$20$$ 23480.0 0.656287
$$21$$ −15166.5 −0.357369
$$22$$ −8769.58 −0.175590
$$23$$ −12167.0 −0.208514
$$24$$ 13824.0 0.204124
$$25$$ 56472.7 0.722851
$$26$$ 55400.9 0.618173
$$27$$ 19683.0 0.192450
$$28$$ −35950.1 −0.309491
$$29$$ 150266. 1.14411 0.572054 0.820216i $$-0.306147\pi$$
0.572054 + 0.820216i $$0.306147\pi$$
$$30$$ 79245.1 0.535856
$$31$$ −204841. −1.23496 −0.617479 0.786588i $$-0.711846\pi$$
−0.617479 + 0.786588i $$0.711846\pi$$
$$32$$ 32768.0 0.176777
$$33$$ −29597.3 −0.143368
$$34$$ 109237. 0.476643
$$35$$ −206082. −0.812459
$$36$$ 46656.0 0.166667
$$37$$ −492163. −1.59736 −0.798681 0.601755i $$-0.794468\pi$$
−0.798681 + 0.601755i $$0.794468\pi$$
$$38$$ 236327. 0.698667
$$39$$ 186978. 0.504736
$$40$$ 187840. 0.464065
$$41$$ 416521. 0.943829 0.471915 0.881644i $$-0.343563\pi$$
0.471915 + 0.881644i $$0.343563\pi$$
$$42$$ −121332. −0.252698
$$43$$ 371500. 0.712557 0.356279 0.934380i $$-0.384045\pi$$
0.356279 + 0.934380i $$0.384045\pi$$
$$44$$ −70156.6 −0.124161
$$45$$ 267452. 0.437525
$$46$$ −97336.0 −0.147442
$$47$$ 930660. 1.30752 0.653760 0.756702i $$-0.273191\pi$$
0.653760 + 0.756702i $$0.273191\pi$$
$$48$$ 110592. 0.144338
$$49$$ −508013. −0.616862
$$50$$ 451782. 0.511133
$$51$$ 368675. 0.389177
$$52$$ 443207. 0.437115
$$53$$ 1.01318e6 0.934804 0.467402 0.884045i $$-0.345190\pi$$
0.467402 + 0.884045i $$0.345190\pi$$
$$54$$ 157464. 0.136083
$$55$$ −402168. −0.325940
$$56$$ −287601. −0.218843
$$57$$ 797602. 0.570459
$$58$$ 1.20213e6 0.809007
$$59$$ −2.28957e6 −1.45135 −0.725676 0.688036i $$-0.758473\pi$$
−0.725676 + 0.688036i $$0.758473\pi$$
$$60$$ 633961. 0.378908
$$61$$ 2.95586e6 1.66736 0.833681 0.552246i $$-0.186229\pi$$
0.833681 + 0.552246i $$0.186229\pi$$
$$62$$ −1.63873e6 −0.873246
$$63$$ −409495. −0.206327
$$64$$ 262144. 0.125000
$$65$$ 2.54066e6 1.14749
$$66$$ −236779. −0.101377
$$67$$ −1.46138e6 −0.593609 −0.296804 0.954938i $$-0.595921\pi$$
−0.296804 + 0.954938i $$0.595921\pi$$
$$68$$ 873896. 0.337038
$$69$$ −328509. −0.120386
$$70$$ −1.64865e6 −0.574495
$$71$$ −1.82588e6 −0.605437 −0.302718 0.953080i $$-0.597894\pi$$
−0.302718 + 0.953080i $$0.597894\pi$$
$$72$$ 373248. 0.117851
$$73$$ −40352.1 −0.0121405 −0.00607024 0.999982i $$-0.501932\pi$$
−0.00607024 + 0.999982i $$0.501932\pi$$
$$74$$ −3.93731e6 −1.12951
$$75$$ 1.52476e6 0.417338
$$76$$ 1.89061e6 0.494032
$$77$$ 615757. 0.153706
$$78$$ 1.49582e6 0.356903
$$79$$ −2.36229e6 −0.539061 −0.269531 0.962992i $$-0.586869\pi$$
−0.269531 + 0.962992i $$0.586869\pi$$
$$80$$ 1.50272e6 0.328144
$$81$$ 531441. 0.111111
$$82$$ 3.33217e6 0.667388
$$83$$ 1.27885e6 0.245497 0.122749 0.992438i $$-0.460829\pi$$
0.122749 + 0.992438i $$0.460829\pi$$
$$84$$ −970654. −0.178684
$$85$$ 5.00955e6 0.884774
$$86$$ 2.97200e6 0.503854
$$87$$ 4.05718e6 0.660551
$$88$$ −561253. −0.0877949
$$89$$ 3.88462e6 0.584095 0.292047 0.956404i $$-0.405664\pi$$
0.292047 + 0.956404i $$0.405664\pi$$
$$90$$ 2.13962e6 0.309377
$$91$$ −3.88998e6 −0.541131
$$92$$ −778688. −0.104257
$$93$$ −5.53072e6 −0.713003
$$94$$ 7.44528e6 0.924556
$$95$$ 1.08378e7 1.29691
$$96$$ 884736. 0.102062
$$97$$ −8.46502e6 −0.941731 −0.470865 0.882205i $$-0.656058\pi$$
−0.470865 + 0.882205i $$0.656058\pi$$
$$98$$ −4.06410e6 −0.436188
$$99$$ −799128. −0.0827738
$$100$$ 3.61425e6 0.361425
$$101$$ 5.79563e6 0.559727 0.279863 0.960040i $$-0.409711\pi$$
0.279863 + 0.960040i $$0.409711\pi$$
$$102$$ 2.94940e6 0.275190
$$103$$ 1.34033e6 0.120860 0.0604298 0.998172i $$-0.480753\pi$$
0.0604298 + 0.998172i $$0.480753\pi$$
$$104$$ 3.54566e6 0.309087
$$105$$ −5.56421e6 −0.469073
$$106$$ 8.10543e6 0.661006
$$107$$ −1.37815e7 −1.08756 −0.543779 0.839229i $$-0.683007\pi$$
−0.543779 + 0.839229i $$0.683007\pi$$
$$108$$ 1.25971e6 0.0962250
$$109$$ 9.40692e6 0.695752 0.347876 0.937541i $$-0.386903\pi$$
0.347876 + 0.937541i $$0.386903\pi$$
$$110$$ −3.21734e6 −0.230475
$$111$$ −1.32884e7 −0.922237
$$112$$ −2.30081e6 −0.154745
$$113$$ −776740. −0.0506409 −0.0253204 0.999679i $$-0.508061\pi$$
−0.0253204 + 0.999679i $$0.508061\pi$$
$$114$$ 6.38082e6 0.403375
$$115$$ −4.46378e6 −0.273691
$$116$$ 9.61701e6 0.572054
$$117$$ 5.04841e6 0.291410
$$118$$ −1.83166e7 −1.02626
$$119$$ −7.67008e6 −0.417240
$$120$$ 5.07169e6 0.267928
$$121$$ −1.82855e7 −0.938336
$$122$$ 2.36469e7 1.17900
$$123$$ 1.12461e7 0.544920
$$124$$ −1.31099e7 −0.617479
$$125$$ −7.94369e6 −0.363779
$$126$$ −3.27596e6 −0.145895
$$127$$ −2.02779e7 −0.878434 −0.439217 0.898381i $$-0.644744\pi$$
−0.439217 + 0.898381i $$0.644744\pi$$
$$128$$ 2.09715e6 0.0883883
$$129$$ 1.00305e7 0.411395
$$130$$ 2.03252e7 0.811398
$$131$$ −5.73353e6 −0.222829 −0.111415 0.993774i $$-0.535538\pi$$
−0.111415 + 0.993774i $$0.535538\pi$$
$$132$$ −1.89423e6 −0.0716842
$$133$$ −1.65937e7 −0.611593
$$134$$ −1.16910e7 −0.419745
$$135$$ 7.22121e6 0.252605
$$136$$ 6.99116e6 0.238322
$$137$$ −2.96971e7 −0.986716 −0.493358 0.869826i $$-0.664231\pi$$
−0.493358 + 0.869826i $$0.664231\pi$$
$$138$$ −2.62807e6 −0.0851257
$$139$$ 2.70200e7 0.853362 0.426681 0.904402i $$-0.359683\pi$$
0.426681 + 0.904402i $$0.359683\pi$$
$$140$$ −1.31892e7 −0.406229
$$141$$ 2.51278e7 0.754897
$$142$$ −1.46071e7 −0.428108
$$143$$ −7.59129e6 −0.217090
$$144$$ 2.98598e6 0.0833333
$$145$$ 5.51289e7 1.50173
$$146$$ −322816. −0.00858461
$$147$$ −1.37163e7 −0.356146
$$148$$ −3.14984e7 −0.798681
$$149$$ −1.22268e7 −0.302803 −0.151401 0.988472i $$-0.548379\pi$$
−0.151401 + 0.988472i $$0.548379\pi$$
$$150$$ 1.21981e7 0.295103
$$151$$ −7.91442e7 −1.87068 −0.935341 0.353747i $$-0.884907\pi$$
−0.935341 + 0.353747i $$0.884907\pi$$
$$152$$ 1.51249e7 0.349333
$$153$$ 9.95422e6 0.224692
$$154$$ 4.92606e6 0.108687
$$155$$ −7.51513e7 −1.62097
$$156$$ 1.19666e7 0.252368
$$157$$ −6.65855e7 −1.37319 −0.686595 0.727040i $$-0.740895\pi$$
−0.686595 + 0.727040i $$0.740895\pi$$
$$158$$ −1.88983e7 −0.381174
$$159$$ 2.73558e7 0.539709
$$160$$ 1.20218e7 0.232033
$$161$$ 6.83446e6 0.129066
$$162$$ 4.25153e6 0.0785674
$$163$$ 5.57898e7 1.00902 0.504508 0.863407i $$-0.331674\pi$$
0.504508 + 0.863407i $$0.331674\pi$$
$$164$$ 2.66573e7 0.471915
$$165$$ −1.08585e7 −0.188182
$$166$$ 1.02308e7 0.173593
$$167$$ −2.85952e7 −0.475100 −0.237550 0.971375i $$-0.576344\pi$$
−0.237550 + 0.971375i $$0.576344\pi$$
$$168$$ −7.76523e6 −0.126349
$$169$$ −1.47913e7 −0.235724
$$170$$ 4.00764e7 0.625629
$$171$$ 2.15353e7 0.329355
$$172$$ 2.37760e7 0.356279
$$173$$ −5.94429e7 −0.872847 −0.436424 0.899741i $$-0.643755\pi$$
−0.436424 + 0.899741i $$0.643755\pi$$
$$174$$ 3.24574e7 0.467080
$$175$$ −3.17219e7 −0.447431
$$176$$ −4.49002e6 −0.0620804
$$177$$ −6.18185e7 −0.837939
$$178$$ 3.10769e7 0.413017
$$179$$ −1.09127e8 −1.42216 −0.711079 0.703112i $$-0.751793\pi$$
−0.711079 + 0.703112i $$0.751793\pi$$
$$180$$ 1.71169e7 0.218762
$$181$$ −9.89431e7 −1.24025 −0.620127 0.784501i $$-0.712919\pi$$
−0.620127 + 0.784501i $$0.712919\pi$$
$$182$$ −3.11199e7 −0.382638
$$183$$ 7.98083e7 0.962652
$$184$$ −6.22950e6 −0.0737210
$$185$$ −1.80563e8 −2.09666
$$186$$ −4.42457e7 −0.504169
$$187$$ −1.49682e7 −0.167387
$$188$$ 5.95622e7 0.653760
$$189$$ −1.10564e7 −0.119123
$$190$$ 8.67025e7 0.917052
$$191$$ −6.19114e7 −0.642916 −0.321458 0.946924i $$-0.604173\pi$$
−0.321458 + 0.946924i $$0.604173\pi$$
$$192$$ 7.07789e6 0.0721688
$$193$$ 1.03484e8 1.03615 0.518076 0.855334i $$-0.326648\pi$$
0.518076 + 0.855334i $$0.326648\pi$$
$$194$$ −6.77201e7 −0.665904
$$195$$ 6.85977e7 0.662504
$$196$$ −3.25128e7 −0.308431
$$197$$ −1.11986e8 −1.04360 −0.521798 0.853069i $$-0.674739\pi$$
−0.521798 + 0.853069i $$0.674739\pi$$
$$198$$ −6.39302e6 −0.0585299
$$199$$ −1.09861e7 −0.0988228 −0.0494114 0.998779i $$-0.515735\pi$$
−0.0494114 + 0.998779i $$0.515735\pi$$
$$200$$ 2.89140e7 0.255566
$$201$$ −3.94572e7 −0.342720
$$202$$ 4.63651e7 0.395787
$$203$$ −8.44074e7 −0.708182
$$204$$ 2.35952e7 0.194589
$$205$$ 1.52811e8 1.23885
$$206$$ 1.07226e7 0.0854606
$$207$$ −8.86974e6 −0.0695048
$$208$$ 2.83653e7 0.218557
$$209$$ −3.23826e7 −0.245357
$$210$$ −4.45136e7 −0.331685
$$211$$ 7.14052e7 0.523289 0.261644 0.965164i $$-0.415735\pi$$
0.261644 + 0.965164i $$0.415735\pi$$
$$212$$ 6.48434e7 0.467402
$$213$$ −4.92988e7 −0.349549
$$214$$ −1.10252e8 −0.769019
$$215$$ 1.36294e8 0.935284
$$216$$ 1.00777e7 0.0680414
$$217$$ 1.15064e8 0.764415
$$218$$ 7.52553e7 0.491971
$$219$$ −1.08951e6 −0.00700931
$$220$$ −2.57388e7 −0.162970
$$221$$ 9.45598e7 0.589296
$$222$$ −1.06307e8 −0.652120
$$223$$ 1.21124e8 0.731415 0.365707 0.930730i $$-0.380827\pi$$
0.365707 + 0.930730i $$0.380827\pi$$
$$224$$ −1.84065e7 −0.109421
$$225$$ 4.11686e7 0.240950
$$226$$ −6.21392e6 −0.0358085
$$227$$ 3.23693e7 0.183672 0.0918360 0.995774i $$-0.470726\pi$$
0.0918360 + 0.995774i $$0.470726\pi$$
$$228$$ 5.10465e7 0.285229
$$229$$ 2.14673e8 1.18128 0.590642 0.806934i $$-0.298875\pi$$
0.590642 + 0.806934i $$0.298875\pi$$
$$230$$ −3.57102e7 −0.193528
$$231$$ 1.66254e7 0.0887424
$$232$$ 7.69361e7 0.404503
$$233$$ −2.34580e8 −1.21491 −0.607457 0.794353i $$-0.707810\pi$$
−0.607457 + 0.794353i $$0.707810\pi$$
$$234$$ 4.03873e7 0.206058
$$235$$ 3.41436e8 1.71622
$$236$$ −1.46533e8 −0.725676
$$237$$ −6.37818e7 −0.311227
$$238$$ −6.13607e7 −0.295033
$$239$$ −1.73526e8 −0.822189 −0.411095 0.911593i $$-0.634853\pi$$
−0.411095 + 0.911593i $$0.634853\pi$$
$$240$$ 4.05735e7 0.189454
$$241$$ 1.89649e8 0.872752 0.436376 0.899764i $$-0.356262\pi$$
0.436376 + 0.899764i $$0.356262\pi$$
$$242$$ −1.46284e8 −0.663504
$$243$$ 1.43489e7 0.0641500
$$244$$ 1.89175e8 0.833681
$$245$$ −1.86377e8 −0.809678
$$246$$ 8.99685e7 0.385317
$$247$$ 2.04574e8 0.863794
$$248$$ −1.04879e8 −0.436623
$$249$$ 3.45290e7 0.141738
$$250$$ −6.35495e7 −0.257230
$$251$$ 2.71105e8 1.08213 0.541064 0.840981i $$-0.318022\pi$$
0.541064 + 0.840981i $$0.318022\pi$$
$$252$$ −2.62076e7 −0.103164
$$253$$ 1.33374e7 0.0517786
$$254$$ −1.62223e8 −0.621147
$$255$$ 1.35258e8 0.510824
$$256$$ 1.67772e7 0.0625000
$$257$$ 4.36260e8 1.60317 0.801584 0.597882i $$-0.203991\pi$$
0.801584 + 0.597882i $$0.203991\pi$$
$$258$$ 8.02441e7 0.290900
$$259$$ 2.76458e8 0.988737
$$260$$ 1.62602e8 0.573745
$$261$$ 1.09544e8 0.381369
$$262$$ −4.58682e7 −0.157564
$$263$$ 1.27332e8 0.431609 0.215805 0.976437i $$-0.430763\pi$$
0.215805 + 0.976437i $$0.430763\pi$$
$$264$$ −1.51538e7 −0.0506884
$$265$$ 3.71711e8 1.22700
$$266$$ −1.32750e8 −0.432461
$$267$$ 1.04885e8 0.337227
$$268$$ −9.35281e7 −0.296804
$$269$$ 2.50990e8 0.786182 0.393091 0.919500i $$-0.371406\pi$$
0.393091 + 0.919500i $$0.371406\pi$$
$$270$$ 5.77697e7 0.178619
$$271$$ 1.19209e8 0.363844 0.181922 0.983313i $$-0.441768\pi$$
0.181922 + 0.983313i $$0.441768\pi$$
$$272$$ 5.59293e7 0.168519
$$273$$ −1.05029e8 −0.312422
$$274$$ −2.37577e8 −0.697714
$$275$$ −6.19052e7 −0.179499
$$276$$ −2.10246e7 −0.0601929
$$277$$ −2.70183e8 −0.763799 −0.381899 0.924204i $$-0.624730\pi$$
−0.381899 + 0.924204i $$0.624730\pi$$
$$278$$ 2.16160e8 0.603418
$$279$$ −1.49329e8 −0.411652
$$280$$ −1.05514e8 −0.287248
$$281$$ −6.33010e8 −1.70192 −0.850958 0.525233i $$-0.823978\pi$$
−0.850958 + 0.525233i $$0.823978\pi$$
$$282$$ 2.01022e8 0.533793
$$283$$ 6.68305e8 1.75276 0.876379 0.481622i $$-0.159952\pi$$
0.876379 + 0.481622i $$0.159952\pi$$
$$284$$ −1.16857e8 −0.302718
$$285$$ 2.92621e8 0.748770
$$286$$ −6.07303e7 −0.153506
$$287$$ −2.33969e8 −0.584213
$$288$$ 2.38879e7 0.0589256
$$289$$ −2.23890e8 −0.545623
$$290$$ 4.41031e8 1.06188
$$291$$ −2.28555e8 −0.543709
$$292$$ −2.58253e6 −0.00607024
$$293$$ 5.36402e8 1.24582 0.622908 0.782295i $$-0.285951\pi$$
0.622908 + 0.782295i $$0.285951\pi$$
$$294$$ −1.09731e8 −0.251833
$$295$$ −8.39989e8 −1.90501
$$296$$ −2.51988e8 −0.564753
$$297$$ −2.15765e7 −0.0477895
$$298$$ −9.78141e7 −0.214114
$$299$$ −8.42579e7 −0.182289
$$300$$ 9.75849e7 0.208669
$$301$$ −2.08680e8 −0.441059
$$302$$ −6.33154e8 −1.32277
$$303$$ 1.56482e8 0.323158
$$304$$ 1.20999e8 0.247016
$$305$$ 1.08443e9 2.18854
$$306$$ 7.96337e7 0.158881
$$307$$ −1.07221e8 −0.211493 −0.105746 0.994393i $$-0.533723\pi$$
−0.105746 + 0.994393i $$0.533723\pi$$
$$308$$ 3.94084e7 0.0768532
$$309$$ 3.61889e7 0.0697783
$$310$$ −6.01211e8 −1.14620
$$311$$ −9.74611e8 −1.83726 −0.918629 0.395122i $$-0.870702\pi$$
−0.918629 + 0.395122i $$0.870702\pi$$
$$312$$ 9.57328e7 0.178451
$$313$$ −6.47093e8 −1.19278 −0.596392 0.802693i $$-0.703400\pi$$
−0.596392 + 0.802693i $$0.703400\pi$$
$$314$$ −5.32684e8 −0.970992
$$315$$ −1.50234e8 −0.270820
$$316$$ −1.51186e8 −0.269531
$$317$$ 5.22962e8 0.922068 0.461034 0.887382i $$-0.347479\pi$$
0.461034 + 0.887382i $$0.347479\pi$$
$$318$$ 2.18847e8 0.381632
$$319$$ −1.64721e8 −0.284107
$$320$$ 9.61742e7 0.164072
$$321$$ −3.72100e8 −0.627902
$$322$$ 5.46757e7 0.0912638
$$323$$ 4.03369e8 0.666029
$$324$$ 3.40122e7 0.0555556
$$325$$ 3.91080e8 0.631937
$$326$$ 4.46319e8 0.713483
$$327$$ 2.53987e8 0.401693
$$328$$ 2.13259e8 0.333694
$$329$$ −5.22771e8 −0.809330
$$330$$ −8.68683e7 −0.133065
$$331$$ −1.00533e8 −0.152373 −0.0761867 0.997094i $$-0.524275\pi$$
−0.0761867 + 0.997094i $$0.524275\pi$$
$$332$$ 8.18465e7 0.122749
$$333$$ −3.58787e8 −0.532454
$$334$$ −2.28761e8 −0.335946
$$335$$ −5.36144e8 −0.779156
$$336$$ −6.21218e7 −0.0893422
$$337$$ −4.77653e8 −0.679842 −0.339921 0.940454i $$-0.610400\pi$$
−0.339921 + 0.940454i $$0.610400\pi$$
$$338$$ −1.18330e8 −0.166682
$$339$$ −2.09720e7 −0.0292375
$$340$$ 3.20611e8 0.442387
$$341$$ 2.24547e8 0.306666
$$342$$ 1.72282e8 0.232889
$$343$$ 7.47963e8 1.00081
$$344$$ 1.90208e8 0.251927
$$345$$ −1.20522e8 −0.158015
$$346$$ −4.75543e8 −0.617196
$$347$$ −9.37582e8 −1.20464 −0.602318 0.798256i $$-0.705756\pi$$
−0.602318 + 0.798256i $$0.705756\pi$$
$$348$$ 2.59659e8 0.330276
$$349$$ 9.69080e8 1.22031 0.610155 0.792282i $$-0.291107\pi$$
0.610155 + 0.792282i $$0.291107\pi$$
$$350$$ −2.53775e8 −0.316382
$$351$$ 1.36307e8 0.168245
$$352$$ −3.59202e7 −0.0438975
$$353$$ −4.61929e8 −0.558938 −0.279469 0.960155i $$-0.590158\pi$$
−0.279469 + 0.960155i $$0.590158\pi$$
$$354$$ −4.94548e8 −0.592512
$$355$$ −6.69872e8 −0.794680
$$356$$ 2.48616e8 0.292047
$$357$$ −2.07092e8 −0.240894
$$358$$ −8.73019e8 −1.00562
$$359$$ −7.75397e8 −0.884491 −0.442245 0.896894i $$-0.645818\pi$$
−0.442245 + 0.896894i $$0.645818\pi$$
$$360$$ 1.36936e8 0.154688
$$361$$ −2.12115e7 −0.0237299
$$362$$ −7.91545e8 −0.876992
$$363$$ −4.93709e8 −0.541749
$$364$$ −2.48959e8 −0.270566
$$365$$ −1.48042e7 −0.0159353
$$366$$ 6.38467e8 0.680698
$$367$$ −2.89183e8 −0.305381 −0.152690 0.988274i $$-0.548794\pi$$
−0.152690 + 0.988274i $$0.548794\pi$$
$$368$$ −4.98360e7 −0.0521286
$$369$$ 3.03644e8 0.314610
$$370$$ −1.44450e9 −1.48256
$$371$$ −5.69124e8 −0.578626
$$372$$ −3.53966e8 −0.356501
$$373$$ 6.15666e8 0.614277 0.307138 0.951665i $$-0.400629\pi$$
0.307138 + 0.951665i $$0.400629\pi$$
$$374$$ −1.19745e8 −0.118361
$$375$$ −2.14480e8 −0.210028
$$376$$ 4.76498e8 0.462278
$$377$$ 1.04061e9 1.00021
$$378$$ −8.84508e7 −0.0842327
$$379$$ 9.95325e8 0.939134 0.469567 0.882897i $$-0.344410\pi$$
0.469567 + 0.882897i $$0.344410\pi$$
$$380$$ 6.93620e8 0.648453
$$381$$ −5.47502e8 −0.507164
$$382$$ −4.95292e8 −0.454610
$$383$$ −2.09760e8 −0.190777 −0.0953887 0.995440i $$-0.530409\pi$$
−0.0953887 + 0.995440i $$0.530409\pi$$
$$384$$ 5.66231e7 0.0510310
$$385$$ 2.25906e8 0.201751
$$386$$ 8.27874e8 0.732671
$$387$$ 2.70824e8 0.237519
$$388$$ −5.41761e8 −0.470865
$$389$$ 2.53008e8 0.217927 0.108963 0.994046i $$-0.465247\pi$$
0.108963 + 0.994046i $$0.465247\pi$$
$$390$$ 5.48782e8 0.468461
$$391$$ −1.66136e8 −0.140554
$$392$$ −2.60102e8 −0.218094
$$393$$ −1.54805e8 −0.128651
$$394$$ −8.95889e8 −0.737934
$$395$$ −8.66666e8 −0.707558
$$396$$ −5.11442e7 −0.0413869
$$397$$ 1.23414e9 0.989914 0.494957 0.868917i $$-0.335184\pi$$
0.494957 + 0.868917i $$0.335184\pi$$
$$398$$ −8.78887e7 −0.0698783
$$399$$ −4.48030e8 −0.353103
$$400$$ 2.31312e8 0.180713
$$401$$ 1.41825e9 1.09837 0.549185 0.835701i $$-0.314938\pi$$
0.549185 + 0.835701i $$0.314938\pi$$
$$402$$ −3.15657e8 −0.242340
$$403$$ −1.41855e9 −1.07964
$$404$$ 3.70921e8 0.279863
$$405$$ 1.94973e8 0.145842
$$406$$ −6.75260e8 −0.500760
$$407$$ 5.39508e8 0.396659
$$408$$ 1.88761e8 0.137595
$$409$$ 8.33868e8 0.602651 0.301325 0.953521i $$-0.402571\pi$$
0.301325 + 0.953521i $$0.402571\pi$$
$$410$$ 1.22249e9 0.875996
$$411$$ −8.01822e8 −0.569681
$$412$$ 8.57810e7 0.0604298
$$413$$ 1.28610e9 0.898360
$$414$$ −7.09579e7 −0.0491473
$$415$$ 4.69180e8 0.322234
$$416$$ 2.26922e8 0.154543
$$417$$ 7.29540e8 0.492689
$$418$$ −2.59061e8 −0.173494
$$419$$ −5.56088e8 −0.369313 −0.184656 0.982803i $$-0.559117\pi$$
−0.184656 + 0.982803i $$0.559117\pi$$
$$420$$ −3.56109e8 −0.234537
$$421$$ 1.76819e9 1.15489 0.577447 0.816428i $$-0.304049\pi$$
0.577447 + 0.816428i $$0.304049\pi$$
$$422$$ 5.71242e8 0.370021
$$423$$ 6.78451e8 0.435840
$$424$$ 5.18747e8 0.330503
$$425$$ 7.71113e8 0.487256
$$426$$ −3.94391e8 −0.247168
$$427$$ −1.66037e9 −1.03207
$$428$$ −8.82014e8 −0.543779
$$429$$ −2.04965e8 −0.125337
$$430$$ 1.09036e9 0.661346
$$431$$ 1.86575e9 1.12249 0.561244 0.827650i $$-0.310323\pi$$
0.561244 + 0.827650i $$0.310323\pi$$
$$432$$ 8.06216e7 0.0481125
$$433$$ −8.86037e8 −0.524498 −0.262249 0.965000i $$-0.584464\pi$$
−0.262249 + 0.965000i $$0.584464\pi$$
$$434$$ 9.20510e8 0.540523
$$435$$ 1.48848e9 0.867023
$$436$$ 6.02043e8 0.347876
$$437$$ −3.59423e8 −0.206026
$$438$$ −8.71604e6 −0.00495633
$$439$$ −1.11162e9 −0.627094 −0.313547 0.949573i $$-0.601517\pi$$
−0.313547 + 0.949573i $$0.601517\pi$$
$$440$$ −2.05910e8 −0.115237
$$441$$ −3.70341e8 −0.205621
$$442$$ 7.56478e8 0.416695
$$443$$ 3.79851e8 0.207587 0.103794 0.994599i $$-0.466902\pi$$
0.103794 + 0.994599i $$0.466902\pi$$
$$444$$ −8.50458e8 −0.461119
$$445$$ 1.42517e9 0.766668
$$446$$ 9.68993e8 0.517188
$$447$$ −3.30123e8 −0.174823
$$448$$ −1.47252e8 −0.0773726
$$449$$ 1.04853e9 0.546664 0.273332 0.961920i $$-0.411874\pi$$
0.273332 + 0.961920i $$0.411874\pi$$
$$450$$ 3.29349e8 0.170378
$$451$$ −4.56589e8 −0.234373
$$452$$ −4.97114e7 −0.0253204
$$453$$ −2.13689e9 −1.08004
$$454$$ 2.58955e8 0.129876
$$455$$ −1.42714e9 −0.710275
$$456$$ 4.08372e8 0.201688
$$457$$ −1.49813e9 −0.734250 −0.367125 0.930172i $$-0.619658\pi$$
−0.367125 + 0.930172i $$0.619658\pi$$
$$458$$ 1.71739e9 0.835293
$$459$$ 2.68764e8 0.129726
$$460$$ −2.85682e8 −0.136845
$$461$$ 1.49236e9 0.709447 0.354723 0.934971i $$-0.384575\pi$$
0.354723 + 0.934971i $$0.384575\pi$$
$$462$$ 1.33003e8 0.0627503
$$463$$ −3.06867e9 −1.43687 −0.718433 0.695596i $$-0.755140\pi$$
−0.718433 + 0.695596i $$0.755140\pi$$
$$464$$ 6.15489e8 0.286027
$$465$$ −2.02909e9 −0.935869
$$466$$ −1.87664e9 −0.859074
$$467$$ 1.68526e9 0.765698 0.382849 0.923811i $$-0.374943\pi$$
0.382849 + 0.923811i $$0.374943\pi$$
$$468$$ 3.23098e8 0.145705
$$469$$ 8.20886e8 0.367433
$$470$$ 2.73149e9 1.21355
$$471$$ −1.79781e9 −0.792812
$$472$$ −1.17226e9 −0.513131
$$473$$ −4.07238e8 −0.176943
$$474$$ −5.10254e8 −0.220071
$$475$$ 1.66825e9 0.714223
$$476$$ −4.90885e8 −0.208620
$$477$$ 7.38607e8 0.311601
$$478$$ −1.38821e9 −0.581376
$$479$$ −2.69509e9 −1.12047 −0.560233 0.828335i $$-0.689288\pi$$
−0.560233 + 0.828335i $$0.689288\pi$$
$$480$$ 3.24588e8 0.133964
$$481$$ −3.40829e9 −1.39646
$$482$$ 1.51719e9 0.617129
$$483$$ 1.84530e8 0.0745166
$$484$$ −1.17027e9 −0.469168
$$485$$ −3.10561e9 −1.23609
$$486$$ 1.14791e8 0.0453609
$$487$$ −2.88969e9 −1.13371 −0.566853 0.823819i $$-0.691839\pi$$
−0.566853 + 0.823819i $$0.691839\pi$$
$$488$$ 1.51340e9 0.589502
$$489$$ 1.50633e9 0.582556
$$490$$ −1.49102e9 −0.572528
$$491$$ −2.94886e9 −1.12427 −0.562133 0.827047i $$-0.690019\pi$$
−0.562133 + 0.827047i $$0.690019\pi$$
$$492$$ 7.19748e8 0.272460
$$493$$ 2.05182e9 0.771215
$$494$$ 1.63659e9 0.610795
$$495$$ −2.93181e8 −0.108647
$$496$$ −8.39030e8 −0.308739
$$497$$ 1.02564e9 0.374754
$$498$$ 2.76232e8 0.100224
$$499$$ 3.10068e9 1.11713 0.558567 0.829459i $$-0.311351\pi$$
0.558567 + 0.829459i $$0.311351\pi$$
$$500$$ −5.08396e8 −0.181889
$$501$$ −7.72070e8 −0.274299
$$502$$ 2.16884e9 0.765181
$$503$$ −6.25596e8 −0.219183 −0.109591 0.993977i $$-0.534954\pi$$
−0.109591 + 0.993977i $$0.534954\pi$$
$$504$$ −2.09661e8 −0.0729476
$$505$$ 2.12628e9 0.734683
$$506$$ 1.06699e8 0.0366130
$$507$$ −3.99365e8 −0.136095
$$508$$ −1.29778e9 −0.439217
$$509$$ 4.35887e9 1.46508 0.732541 0.680723i $$-0.238334\pi$$
0.732541 + 0.680723i $$0.238334\pi$$
$$510$$ 1.08206e9 0.361207
$$511$$ 2.26666e7 0.00751472
$$512$$ 1.34218e8 0.0441942
$$513$$ 5.81452e8 0.190153
$$514$$ 3.49008e9 1.13361
$$515$$ 4.91734e8 0.158637
$$516$$ 6.41953e8 0.205698
$$517$$ −1.02019e9 −0.324685
$$518$$ 2.21167e9 0.699142
$$519$$ −1.60496e9 −0.503939
$$520$$ 1.30082e9 0.405699
$$521$$ 1.86006e9 0.576229 0.288115 0.957596i $$-0.406972\pi$$
0.288115 + 0.957596i $$0.406972\pi$$
$$522$$ 8.76350e8 0.269669
$$523$$ 1.89981e9 0.580703 0.290352 0.956920i $$-0.406228\pi$$
0.290352 + 0.956920i $$0.406228\pi$$
$$524$$ −3.66946e8 −0.111415
$$525$$ −8.56491e8 −0.258324
$$526$$ 1.01865e9 0.305194
$$527$$ −2.79703e9 −0.832454
$$528$$ −1.21231e8 −0.0358421
$$529$$ 1.48036e8 0.0434783
$$530$$ 2.97368e9 0.867620
$$531$$ −1.66910e9 −0.483784
$$532$$ −1.06200e9 −0.305796
$$533$$ 2.88446e9 0.825123
$$534$$ 8.39077e8 0.238456
$$535$$ −5.05608e9 −1.42750
$$536$$ −7.48225e8 −0.209872
$$537$$ −2.94644e9 −0.821083
$$538$$ 2.00792e9 0.555914
$$539$$ 5.56882e8 0.153180
$$540$$ 4.62158e8 0.126303
$$541$$ 6.17189e9 1.67582 0.837910 0.545808i $$-0.183777\pi$$
0.837910 + 0.545808i $$0.183777\pi$$
$$542$$ 9.53670e8 0.257277
$$543$$ −2.67147e9 −0.716061
$$544$$ 4.47435e8 0.119161
$$545$$ 3.45117e9 0.913226
$$546$$ −8.40236e8 −0.220916
$$547$$ 4.97696e9 1.30020 0.650098 0.759851i $$-0.274728\pi$$
0.650098 + 0.759851i $$0.274728\pi$$
$$548$$ −1.90061e9 −0.493358
$$549$$ 2.15483e9 0.555788
$$550$$ −4.95242e8 −0.126925
$$551$$ 4.43898e9 1.13045
$$552$$ −1.68197e8 −0.0425628
$$553$$ 1.32695e9 0.333669
$$554$$ −2.16146e9 −0.540087
$$555$$ −4.87519e9 −1.21050
$$556$$ 1.72928e9 0.426681
$$557$$ −2.16771e9 −0.531506 −0.265753 0.964041i $$-0.585621\pi$$
−0.265753 + 0.964041i $$0.585621\pi$$
$$558$$ −1.19464e9 −0.291082
$$559$$ 2.57268e9 0.622938
$$560$$ −8.44111e8 −0.203115
$$561$$ −4.04140e8 −0.0966411
$$562$$ −5.06408e9 −1.20344
$$563$$ 4.33727e9 1.02432 0.512162 0.858889i $$-0.328845\pi$$
0.512162 + 0.858889i $$0.328845\pi$$
$$564$$ 1.60818e9 0.377449
$$565$$ −2.84967e8 −0.0664699
$$566$$ 5.34644e9 1.23939
$$567$$ −2.98522e8 −0.0687757
$$568$$ −9.34852e8 −0.214054
$$569$$ −1.76759e9 −0.402243 −0.201122 0.979566i $$-0.564459\pi$$
−0.201122 + 0.979566i $$0.564459\pi$$
$$570$$ 2.34097e9 0.529460
$$571$$ 4.35096e9 0.978046 0.489023 0.872271i $$-0.337353\pi$$
0.489023 + 0.872271i $$0.337353\pi$$
$$572$$ −4.85843e8 −0.108545
$$573$$ −1.67161e9 −0.371188
$$574$$ −1.87175e9 −0.413101
$$575$$ −6.87104e8 −0.150725
$$576$$ 1.91103e8 0.0416667
$$577$$ 7.46172e9 1.61705 0.808525 0.588462i $$-0.200266\pi$$
0.808525 + 0.588462i $$0.200266\pi$$
$$578$$ −1.79112e9 −0.385813
$$579$$ 2.79407e9 0.598223
$$580$$ 3.52825e9 0.750864
$$581$$ −7.18358e8 −0.151958
$$582$$ −1.82844e9 −0.384460
$$583$$ −1.11064e9 −0.232132
$$584$$ −2.06603e7 −0.00429231
$$585$$ 1.85214e9 0.382497
$$586$$ 4.29122e9 0.880925
$$587$$ −3.27341e9 −0.667985 −0.333992 0.942576i $$-0.608396\pi$$
−0.333992 + 0.942576i $$0.608396\pi$$
$$588$$ −8.77846e8 −0.178073
$$589$$ −6.05118e9 −1.22022
$$590$$ −6.71991e9 −1.34704
$$591$$ −3.02363e9 −0.602521
$$592$$ −2.01590e9 −0.399340
$$593$$ −5.07631e9 −0.999670 −0.499835 0.866121i $$-0.666606\pi$$
−0.499835 + 0.866121i $$0.666606\pi$$
$$594$$ −1.72612e8 −0.0337923
$$595$$ −2.81397e9 −0.547658
$$596$$ −7.82513e8 −0.151401
$$597$$ −2.96624e8 −0.0570554
$$598$$ −6.74063e8 −0.128898
$$599$$ −9.57665e9 −1.82062 −0.910311 0.413926i $$-0.864157\pi$$
−0.910311 + 0.413926i $$0.864157\pi$$
$$600$$ 7.80679e8 0.147551
$$601$$ −1.02812e9 −0.193189 −0.0965945 0.995324i $$-0.530795\pi$$
−0.0965945 + 0.995324i $$0.530795\pi$$
$$602$$ −1.66944e9 −0.311876
$$603$$ −1.06534e9 −0.197870
$$604$$ −5.06523e9 −0.935341
$$605$$ −6.70851e9 −1.23164
$$606$$ 1.25186e9 0.228507
$$607$$ 2.45045e9 0.444719 0.222359 0.974965i $$-0.428624\pi$$
0.222359 + 0.974965i $$0.428624\pi$$
$$608$$ 9.67994e8 0.174667
$$609$$ −2.27900e9 −0.408869
$$610$$ 8.67548e9 1.54753
$$611$$ 6.44492e9 1.14307
$$612$$ 6.37070e8 0.112346
$$613$$ 8.90460e8 0.156136 0.0780679 0.996948i $$-0.475125\pi$$
0.0780679 + 0.996948i $$0.475125\pi$$
$$614$$ −8.57767e8 −0.149548
$$615$$ 4.12591e9 0.715248
$$616$$ 3.15268e8 0.0543434
$$617$$ 3.73214e9 0.639675 0.319838 0.947472i $$-0.396372\pi$$
0.319838 + 0.947472i $$0.396372\pi$$
$$618$$ 2.89511e8 0.0493407
$$619$$ −9.73916e9 −1.65046 −0.825228 0.564799i $$-0.808954\pi$$
−0.825228 + 0.564799i $$0.808954\pi$$
$$620$$ −4.80968e9 −0.810486
$$621$$ −2.39483e8 −0.0401286
$$622$$ −7.79689e9 −1.29914
$$623$$ −2.18207e9 −0.361544
$$624$$ 7.65862e8 0.126184
$$625$$ −7.32628e9 −1.20034
$$626$$ −5.17675e9 −0.843426
$$627$$ −8.74329e8 −0.141657
$$628$$ −4.26147e9 −0.686595
$$629$$ −6.72030e9 −1.07674
$$630$$ −1.20187e9 −0.191498
$$631$$ −8.10602e8 −0.128441 −0.0642207 0.997936i $$-0.520456\pi$$
−0.0642207 + 0.997936i $$0.520456\pi$$
$$632$$ −1.20949e9 −0.190587
$$633$$ 1.92794e9 0.302121
$$634$$ 4.18370e9 0.652001
$$635$$ −7.43946e9 −1.15301
$$636$$ 1.75077e9 0.269855
$$637$$ −3.51805e9 −0.539279
$$638$$ −1.31777e9 −0.200894
$$639$$ −1.33107e9 −0.201812
$$640$$ 7.69394e8 0.116016
$$641$$ −1.53566e9 −0.230299 −0.115150 0.993348i $$-0.536735\pi$$
−0.115150 + 0.993348i $$0.536735\pi$$
$$642$$ −2.97680e9 −0.443993
$$643$$ 9.03556e9 1.34035 0.670173 0.742205i $$-0.266220\pi$$
0.670173 + 0.742205i $$0.266220\pi$$
$$644$$ 4.37405e8 0.0645332
$$645$$ 3.67995e9 0.539986
$$646$$ 3.22695e9 0.470954
$$647$$ −6.44225e8 −0.0935132 −0.0467566 0.998906i $$-0.514889\pi$$
−0.0467566 + 0.998906i $$0.514889\pi$$
$$648$$ 2.72098e8 0.0392837
$$649$$ 2.50983e9 0.360402
$$650$$ 3.12864e9 0.446847
$$651$$ 3.10672e9 0.441335
$$652$$ 3.57055e9 0.504508
$$653$$ −3.14760e9 −0.442368 −0.221184 0.975232i $$-0.570992\pi$$
−0.221184 + 0.975232i $$0.570992\pi$$
$$654$$ 2.03189e9 0.284040
$$655$$ −2.10349e9 −0.292480
$$656$$ 1.70607e9 0.235957
$$657$$ −2.94166e7 −0.00404682
$$658$$ −4.18217e9 −0.572283
$$659$$ 1.35636e10 1.84619 0.923093 0.384577i $$-0.125653\pi$$
0.923093 + 0.384577i $$0.125653\pi$$
$$660$$ −6.94946e8 −0.0940909
$$661$$ 1.38238e10 1.86176 0.930880 0.365325i $$-0.119042\pi$$
0.930880 + 0.365325i $$0.119042\pi$$
$$662$$ −8.04261e8 −0.107744
$$663$$ 2.55311e9 0.340230
$$664$$ 6.54772e8 0.0867964
$$665$$ −6.08782e9 −0.802761
$$666$$ −2.87030e9 −0.376502
$$667$$ −1.82828e9 −0.238563
$$668$$ −1.83009e9 −0.237550
$$669$$ 3.27035e9 0.422283
$$670$$ −4.28915e9 −0.550946
$$671$$ −3.24021e9 −0.414042
$$672$$ −4.96975e8 −0.0631745
$$673$$ −3.45394e9 −0.436780 −0.218390 0.975862i $$-0.570080\pi$$
−0.218390 + 0.975862i $$0.570080\pi$$
$$674$$ −3.82123e9 −0.480721
$$675$$ 1.11155e9 0.139113
$$676$$ −9.46644e8 −0.117862
$$677$$ 6.53708e9 0.809699 0.404849 0.914383i $$-0.367324\pi$$
0.404849 + 0.914383i $$0.367324\pi$$
$$678$$ −1.67776e8 −0.0206741
$$679$$ 4.75498e9 0.582914
$$680$$ 2.56489e9 0.312815
$$681$$ 8.73971e8 0.106043
$$682$$ 1.79637e9 0.216846
$$683$$ −1.53942e10 −1.84877 −0.924386 0.381457i $$-0.875422\pi$$
−0.924386 + 0.381457i $$0.875422\pi$$
$$684$$ 1.37826e9 0.164677
$$685$$ −1.08951e10 −1.29514
$$686$$ 5.98370e9 0.707678
$$687$$ 5.79618e9 0.682014
$$688$$ 1.52167e9 0.178139
$$689$$ 7.01638e9 0.817233
$$690$$ −9.64176e8 −0.111734
$$691$$ −6.43606e9 −0.742074 −0.371037 0.928618i $$-0.620998\pi$$
−0.371037 + 0.928618i $$0.620998\pi$$
$$692$$ −3.80434e9 −0.436424
$$693$$ 4.48887e8 0.0512354
$$694$$ −7.50066e9 −0.851807
$$695$$ 9.91297e9 1.12010
$$696$$ 2.07727e9 0.233540
$$697$$ 5.68744e9 0.636212
$$698$$ 7.75264e9 0.862890
$$699$$ −6.33366e9 −0.701431
$$700$$ −2.03020e9 −0.223716
$$701$$ 3.29232e9 0.360985 0.180492 0.983576i $$-0.442231\pi$$
0.180492 + 0.983576i $$0.442231\pi$$
$$702$$ 1.09046e9 0.118968
$$703$$ −1.45389e10 −1.57829
$$704$$ −2.87362e8 −0.0310402
$$705$$ 9.21878e9 0.990858
$$706$$ −3.69543e9 −0.395229
$$707$$ −3.25553e9 −0.346460
$$708$$ −3.95639e9 −0.418969
$$709$$ −1.33790e10 −1.40981 −0.704907 0.709300i $$-0.749011\pi$$
−0.704907 + 0.709300i $$0.749011\pi$$
$$710$$ −5.35898e9 −0.561924
$$711$$ −1.72211e9 −0.179687
$$712$$ 1.98892e9 0.206509
$$713$$ 2.49231e9 0.257506
$$714$$ −1.65674e9 −0.170337
$$715$$ −2.78506e9 −0.284947
$$716$$ −6.98415e9 −0.711079
$$717$$ −4.68520e9 −0.474691
$$718$$ −6.20317e9 −0.625430
$$719$$ 9.99931e9 1.00327 0.501636 0.865079i $$-0.332732\pi$$
0.501636 + 0.865079i $$0.332732\pi$$
$$720$$ 1.09548e9 0.109381
$$721$$ −7.52890e8 −0.0748098
$$722$$ −1.69692e8 −0.0167796
$$723$$ 5.12052e9 0.503884
$$724$$ −6.33236e9 −0.620127
$$725$$ 8.48592e9 0.827020
$$726$$ −3.94967e9 −0.383074
$$727$$ 3.87514e9 0.374039 0.187019 0.982356i $$-0.440117\pi$$
0.187019 + 0.982356i $$0.440117\pi$$
$$728$$ −1.99167e9 −0.191319
$$729$$ 3.87420e8 0.0370370
$$730$$ −1.18433e8 −0.0112679
$$731$$ 5.07270e9 0.480317
$$732$$ 5.10773e9 0.481326
$$733$$ 2.03185e10 1.90559 0.952793 0.303620i $$-0.0981954\pi$$
0.952793 + 0.303620i $$0.0981954\pi$$
$$734$$ −2.31346e9 −0.215937
$$735$$ −5.03219e9 −0.467468
$$736$$ −3.98688e8 −0.0368605
$$737$$ 1.60196e9 0.147406
$$738$$ 2.42915e9 0.222463
$$739$$ 6.01270e9 0.548042 0.274021 0.961724i $$-0.411646\pi$$
0.274021 + 0.961724i $$0.411646\pi$$
$$740$$ −1.15560e10 −1.04833
$$741$$ 5.52349e9 0.498712
$$742$$ −4.55299e9 −0.409150
$$743$$ 7.10581e9 0.635554 0.317777 0.948165i $$-0.397064\pi$$
0.317777 + 0.948165i $$0.397064\pi$$
$$744$$ −2.83173e9 −0.252085
$$745$$ −4.48570e9 −0.397451
$$746$$ 4.92533e9 0.434359
$$747$$ 9.32283e8 0.0818325
$$748$$ −9.57962e8 −0.0836937
$$749$$ 7.74134e9 0.673178
$$750$$ −1.71584e9 −0.148512
$$751$$ −2.66674e9 −0.229743 −0.114871 0.993380i $$-0.536646\pi$$
−0.114871 + 0.993380i $$0.536646\pi$$
$$752$$ 3.81198e9 0.326880
$$753$$ 7.31983e9 0.624767
$$754$$ 8.32486e9 0.707257
$$755$$ −2.90361e10 −2.45541
$$756$$ −7.07607e8 −0.0595615
$$757$$ 1.21053e10 1.01424 0.507119 0.861876i $$-0.330711\pi$$
0.507119 + 0.861876i $$0.330711\pi$$
$$758$$ 7.96260e9 0.664068
$$759$$ 3.60111e8 0.0298944
$$760$$ 5.54896e9 0.458526
$$761$$ −2.97000e9 −0.244293 −0.122146 0.992512i $$-0.538978\pi$$
−0.122146 + 0.992512i $$0.538978\pi$$
$$762$$ −4.38002e9 −0.358619
$$763$$ −5.28406e9 −0.430657
$$764$$ −3.96233e9 −0.321458
$$765$$ 3.65196e9 0.294925
$$766$$ −1.67808e9 −0.134900
$$767$$ −1.58556e10 −1.26881
$$768$$ 4.52985e8 0.0360844
$$769$$ 1.95706e10 1.55190 0.775948 0.630797i $$-0.217272\pi$$
0.775948 + 0.630797i $$0.217272\pi$$
$$770$$ 1.80725e9 0.142659
$$771$$ 1.17790e10 0.925589
$$772$$ 6.62299e9 0.518076
$$773$$ −1.54223e9 −0.120094 −0.0600468 0.998196i $$-0.519125\pi$$
−0.0600468 + 0.998196i $$0.519125\pi$$
$$774$$ 2.16659e9 0.167951
$$775$$ −1.15680e10 −0.892690
$$776$$ −4.33409e9 −0.332952
$$777$$ 7.46438e9 0.570847
$$778$$ 2.02406e9 0.154098
$$779$$ 1.23044e10 0.932564
$$780$$ 4.39025e9 0.331252
$$781$$ 2.00153e9 0.150343
$$782$$ −1.32909e9 −0.0993870
$$783$$ 2.95768e9 0.220184
$$784$$ −2.08082e9 −0.154216
$$785$$ −2.44286e10 −1.80241
$$786$$ −1.23844e9 −0.0909697
$$787$$ −1.76348e10 −1.28961 −0.644805 0.764347i $$-0.723061\pi$$
−0.644805 + 0.764347i $$0.723061\pi$$
$$788$$ −7.16712e9 −0.521798
$$789$$ 3.43795e9 0.249190
$$790$$ −6.93333e9 −0.500319
$$791$$ 4.36311e8 0.0313458
$$792$$ −4.09153e8 −0.0292650
$$793$$ 2.04697e10 1.45766
$$794$$ 9.87312e9 0.699975
$$795$$ 1.00362e10 0.708408
$$796$$ −7.03110e8 −0.0494114
$$797$$ 2.10641e10 1.47380 0.736901 0.676000i $$-0.236288\pi$$
0.736901 + 0.676000i $$0.236288\pi$$
$$798$$ −3.58424e9 −0.249682
$$799$$ 1.27078e10 0.881367
$$800$$ 1.85050e9 0.127783
$$801$$ 2.83189e9 0.194698
$$802$$ 1.13460e10 0.776664
$$803$$ 4.42338e7 0.00301474
$$804$$ −2.52526e9 −0.171360
$$805$$ 2.50740e9 0.169409
$$806$$ −1.13484e10 −0.763417
$$807$$ 6.77672e9 0.453902
$$808$$ 2.96736e9 0.197893
$$809$$ −2.12308e10 −1.40977 −0.704884 0.709323i $$-0.749001\pi$$
−0.704884 + 0.709323i $$0.749001\pi$$
$$810$$ 1.55978e9 0.103126
$$811$$ 9.31477e9 0.613196 0.306598 0.951839i $$-0.400809\pi$$
0.306598 + 0.951839i $$0.400809\pi$$
$$812$$ −5.40208e9 −0.354091
$$813$$ 3.21864e9 0.210066
$$814$$ 4.31606e9 0.280480
$$815$$ 2.04679e10 1.32441
$$816$$ 1.51009e9 0.0972944
$$817$$ 1.09744e10 0.704052
$$818$$ 6.67094e9 0.426138
$$819$$ −2.83580e9 −0.180377
$$820$$ 9.77993e9 0.619423
$$821$$ −1.51846e10 −0.957642 −0.478821 0.877913i $$-0.658936\pi$$
−0.478821 + 0.877913i $$0.658936\pi$$
$$822$$ −6.41458e9 −0.402825
$$823$$ −9.38917e9 −0.587121 −0.293561 0.955940i $$-0.594840\pi$$
−0.293561 + 0.955940i $$0.594840\pi$$
$$824$$ 6.86248e8 0.0427303
$$825$$ −1.67144e9 −0.103634
$$826$$ 1.02888e10 0.635236
$$827$$ 1.40878e10 0.866114 0.433057 0.901366i $$-0.357435\pi$$
0.433057 + 0.901366i $$0.357435\pi$$
$$828$$ −5.67664e8 −0.0347524
$$829$$ 1.99910e10 1.21869 0.609345 0.792905i $$-0.291432\pi$$
0.609345 + 0.792905i $$0.291432\pi$$
$$830$$ 3.75344e9 0.227854
$$831$$ −7.29494e9 −0.440979
$$832$$ 1.81538e9 0.109279
$$833$$ −6.93672e9 −0.415812
$$834$$ 5.83632e9 0.348384
$$835$$ −1.04909e10 −0.623604
$$836$$ −2.07248e9 −0.122679
$$837$$ −4.03189e9 −0.237668
$$838$$ −4.44870e9 −0.261143
$$839$$ 2.49729e10 1.45983 0.729915 0.683538i $$-0.239560\pi$$
0.729915 + 0.683538i $$0.239560\pi$$
$$840$$ −2.84887e9 −0.165842
$$841$$ 5.32994e9 0.308984
$$842$$ 1.41455e10 0.816633
$$843$$ −1.70913e10 −0.982602
$$844$$ 4.56993e9 0.261644
$$845$$ −5.42657e9 −0.309405
$$846$$ 5.42761e9 0.308185
$$847$$ 1.02714e10 0.580813
$$848$$ 4.14998e9 0.233701
$$849$$ 1.80442e10 1.01196
$$850$$ 6.16891e9 0.344542
$$851$$ 5.98815e9 0.333073
$$852$$ −3.15513e9 −0.174775
$$853$$ 2.15537e10 1.18905 0.594526 0.804077i $$-0.297340\pi$$
0.594526 + 0.804077i $$0.297340\pi$$
$$854$$ −1.32830e10 −0.729781
$$855$$ 7.90076e9 0.432302
$$856$$ −7.05611e9 −0.384510
$$857$$ −1.83252e9 −0.0994524 −0.0497262 0.998763i $$-0.515835\pi$$
−0.0497262 + 0.998763i $$0.515835\pi$$
$$858$$ −1.63972e9 −0.0886266
$$859$$ 2.88323e10 1.55204 0.776020 0.630708i $$-0.217235\pi$$
0.776020 + 0.630708i $$0.217235\pi$$
$$860$$ 8.72284e9 0.467642
$$861$$ −6.31715e9 −0.337295
$$862$$ 1.49260e10 0.793719
$$863$$ −2.80605e10 −1.48613 −0.743067 0.669217i $$-0.766630\pi$$
−0.743067 + 0.669217i $$0.766630\pi$$
$$864$$ 6.44973e8 0.0340207
$$865$$ −2.18081e10 −1.14568
$$866$$ −7.08829e9 −0.370876
$$867$$ −6.04503e9 −0.315015
$$868$$ 7.36408e9 0.382208
$$869$$ 2.58953e9 0.133860
$$870$$ 1.19078e10 0.613078
$$871$$ −1.01202e10 −0.518950
$$872$$ 4.81634e9 0.245986
$$873$$ −6.17100e9 −0.313910
$$874$$ −2.87539e9 −0.145682
$$875$$ 4.46214e9 0.225172
$$876$$ −6.97283e7 −0.00350465
$$877$$ −1.07928e10 −0.540299 −0.270149 0.962818i $$-0.587073\pi$$
−0.270149 + 0.962818i $$0.587073\pi$$
$$878$$ −8.89300e9 −0.443422
$$879$$ 1.44829e10 0.719272
$$880$$ −1.64728e9 −0.0814851
$$881$$ −2.86597e10 −1.41207 −0.706034 0.708178i $$-0.749517\pi$$
−0.706034 + 0.708178i $$0.749517\pi$$
$$882$$ −2.96273e9 −0.145396
$$883$$ −3.47774e10 −1.69994 −0.849972 0.526828i $$-0.823381\pi$$
−0.849972 + 0.526828i $$0.823381\pi$$
$$884$$ 6.05183e9 0.294648
$$885$$ −2.26797e10 −1.09986
$$886$$ 3.03881e9 0.146786
$$887$$ 6.42202e9 0.308986 0.154493 0.987994i $$-0.450626\pi$$
0.154493 + 0.987994i $$0.450626\pi$$
$$888$$ −6.80367e9 −0.326060
$$889$$ 1.13905e10 0.543734
$$890$$ 1.14014e10 0.542116
$$891$$ −5.82564e8 −0.0275913
$$892$$ 7.75195e9 0.365707
$$893$$ 2.74925e10 1.29191
$$894$$ −2.64098e9 −0.123619
$$895$$ −4.00362e10 −1.86669
$$896$$ −1.17801e9 −0.0547107
$$897$$ −2.27496e9 −0.105245
$$898$$ 8.38827e9 0.386550
$$899$$ −3.07807e10 −1.41292
$$900$$ 2.63479e9 0.120475
$$901$$ 1.38346e10 0.630128
$$902$$ −3.65271e9 −0.165727
$$903$$ −5.63435e9 −0.254646
$$904$$ −3.97691e8 −0.0179043
$$905$$ −3.62998e10 −1.62793
$$906$$ −1.70952e10 −0.763703
$$907$$ −3.96724e10 −1.76548 −0.882740 0.469861i $$-0.844304\pi$$
−0.882740 + 0.469861i $$0.844304\pi$$
$$908$$ 2.07164e9 0.0918360
$$909$$ 4.22502e9 0.186576
$$910$$ −1.14171e10 −0.502240
$$911$$ 3.39607e10 1.48820 0.744102 0.668066i $$-0.232878\pi$$
0.744102 + 0.668066i $$0.232878\pi$$
$$912$$ 3.26698e9 0.142615
$$913$$ −1.40187e9 −0.0609623
$$914$$ −1.19851e10 −0.519193
$$915$$ 2.92797e10 1.26355
$$916$$ 1.37391e10 0.590642
$$917$$ 3.22064e9 0.137927
$$918$$ 2.15011e9 0.0917300
$$919$$ 1.98186e10 0.842304 0.421152 0.906990i $$-0.361626\pi$$
0.421152 + 0.906990i $$0.361626\pi$$
$$920$$ −2.28545e9 −0.0967642
$$921$$ −2.89496e9 −0.122105
$$922$$ 1.19389e10 0.501655
$$923$$ −1.26444e10 −0.529290
$$924$$ 1.06403e9 0.0443712
$$925$$ −2.77938e10 −1.15465
$$926$$ −2.45493e10 −1.01602
$$927$$ 9.77099e8 0.0402865
$$928$$ 4.92391e9 0.202252
$$929$$ −2.08980e10 −0.855164 −0.427582 0.903976i $$-0.640635\pi$$
−0.427582 + 0.903976i $$0.640635\pi$$
$$930$$ −1.62327e10 −0.661759
$$931$$ −1.50071e10 −0.609499
$$932$$ −1.50131e10 −0.607457
$$933$$ −2.63145e10 −1.06074
$$934$$ 1.34821e10 0.541430
$$935$$ −5.49145e9 −0.219708
$$936$$ 2.58479e9 0.103029
$$937$$ −4.61325e9 −0.183197 −0.0915986 0.995796i $$-0.529198\pi$$
−0.0915986 + 0.995796i $$0.529198\pi$$
$$938$$ 6.56709e9 0.259814
$$939$$ −1.74715e10 −0.688654
$$940$$ 2.18519e10 0.858109
$$941$$ 2.61949e10 1.02483 0.512417 0.858737i $$-0.328750\pi$$
0.512417 + 0.858737i $$0.328750\pi$$
$$942$$ −1.43825e10 −0.560603
$$943$$ −5.06781e9 −0.196802
$$944$$ −9.37810e9 −0.362838
$$945$$ −4.05631e9 −0.156358
$$946$$ −3.25790e9 −0.125118
$$947$$ −1.01216e10 −0.387278 −0.193639 0.981073i $$-0.562029\pi$$
−0.193639 + 0.981073i $$0.562029\pi$$
$$948$$ −4.08203e9 −0.155614
$$949$$ −2.79443e8 −0.0106136
$$950$$ 1.33460e10 0.505032
$$951$$ 1.41200e10 0.532356
$$952$$ −3.92708e9 −0.147517
$$953$$ −5.16517e9 −0.193312 −0.0966562 0.995318i $$-0.530815\pi$$
−0.0966562 + 0.995318i $$0.530815\pi$$
$$954$$ 5.90886e9 0.220335
$$955$$ −2.27138e10 −0.843875
$$956$$ −1.11057e10 −0.411095
$$957$$ −4.44747e9 −0.164029
$$958$$ −2.15607e10 −0.792289
$$959$$ 1.66815e10 0.610759
$$960$$ 2.59670e9 0.0947269
$$961$$ 1.44474e10 0.525119
$$962$$ −2.72663e10 −0.987446
$$963$$ −1.00467e10 −0.362519
$$964$$ 1.21375e10 0.436376
$$965$$ 3.79659e10 1.36003
$$966$$ 1.47624e9 0.0526912
$$967$$ 2.33871e10 0.831734 0.415867 0.909425i $$-0.363478\pi$$
0.415867 + 0.909425i $$0.363478\pi$$
$$968$$ −9.36219e9 −0.331752
$$969$$ 1.08910e10 0.384532
$$970$$ −2.48449e10 −0.874049
$$971$$ −4.05447e9 −0.142124 −0.0710619 0.997472i $$-0.522639\pi$$
−0.0710619 + 0.997472i $$0.522639\pi$$
$$972$$ 9.18330e8 0.0320750
$$973$$ −1.51777e10 −0.528215
$$974$$ −2.31176e10 −0.801651
$$975$$ 1.05592e10 0.364849
$$976$$ 1.21072e10 0.416841
$$977$$ 5.68903e10 1.95167 0.975837 0.218499i $$-0.0701160\pi$$
0.975837 + 0.218499i $$0.0701160\pi$$
$$978$$ 1.20506e10 0.411929
$$979$$ −4.25831e9 −0.145043
$$980$$ −1.19282e10 −0.404839
$$981$$ 6.85764e9 0.231917
$$982$$ −2.35909e10 −0.794977
$$983$$ 3.74559e10 1.25772 0.628859 0.777519i $$-0.283522\pi$$
0.628859 + 0.777519i $$0.283522\pi$$
$$984$$ 5.75799e9 0.192658
$$985$$ −4.10850e10 −1.36980
$$986$$ 1.64146e10 0.545331
$$987$$ −1.41148e10 −0.467267
$$988$$ 1.30927e10 0.431897
$$989$$ −4.52004e9 −0.148578
$$990$$ −2.34544e9 −0.0768249
$$991$$ 1.00112e8 0.00326759 0.00163379 0.999999i $$-0.499480\pi$$
0.00163379 + 0.999999i $$0.499480\pi$$
$$992$$ −6.71224e9 −0.218312
$$993$$ −2.71438e9 −0.0879729
$$994$$ 8.20509e9 0.264991
$$995$$ −4.03053e9 −0.129712
$$996$$ 2.20986e9 0.0708690
$$997$$ −3.72236e10 −1.18956 −0.594779 0.803889i $$-0.702760\pi$$
−0.594779 + 0.803889i $$0.702760\pi$$
$$998$$ 2.48055e10 0.789934
$$999$$ −9.68725e9 −0.307412
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 138.8.a.h.1.4 4
3.2 odd 2 414.8.a.i.1.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
138.8.a.h.1.4 4 1.1 even 1 trivial
414.8.a.i.1.1 4 3.2 odd 2