Properties

 Label 138.8.a.h.1.1 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 1.1 Root $$33.2734$$ of defining polynomial Character $$\chi$$ $$=$$ 138.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -427.795 q^{5} +216.000 q^{6} +345.429 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$$ $$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -427.795 q^{5} +216.000 q^{6} +345.429 q^{7} +512.000 q^{8} +729.000 q^{9} -3422.36 q^{10} +2181.54 q^{11} +1728.00 q^{12} -2610.39 q^{13} +2763.43 q^{14} -11550.5 q^{15} +4096.00 q^{16} +37979.0 q^{17} +5832.00 q^{18} -26348.1 q^{19} -27378.9 q^{20} +9326.57 q^{21} +17452.3 q^{22} -12167.0 q^{23} +13824.0 q^{24} +104884. q^{25} -20883.1 q^{26} +19683.0 q^{27} +22107.4 q^{28} +250851. q^{29} -92403.8 q^{30} +179145. q^{31} +32768.0 q^{32} +58901.7 q^{33} +303832. q^{34} -147773. q^{35} +46656.0 q^{36} +434281. q^{37} -210785. q^{38} -70480.6 q^{39} -219031. q^{40} -200429. q^{41} +74612.6 q^{42} +841346. q^{43} +139619. q^{44} -311863. q^{45} -97336.0 q^{46} -200025. q^{47} +110592. q^{48} -704222. q^{49} +839072. q^{50} +1.02543e6 q^{51} -167065. q^{52} -1.62417e6 q^{53} +157464. q^{54} -933254. q^{55} +176859. q^{56} -711399. q^{57} +2.00681e6 q^{58} -2.18662e6 q^{59} -739231. q^{60} +2.54771e6 q^{61} +1.43316e6 q^{62} +251817. q^{63} +262144. q^{64} +1.11671e6 q^{65} +471213. q^{66} +4.66306e6 q^{67} +2.43066e6 q^{68} -328509. q^{69} -1.18218e6 q^{70} +4.02892e6 q^{71} +373248. q^{72} -2.58030e6 q^{73} +3.47425e6 q^{74} +2.83187e6 q^{75} -1.68628e6 q^{76} +753568. q^{77} -563845. q^{78} +1.22032e6 q^{79} -1.75225e6 q^{80} +531441. q^{81} -1.60343e6 q^{82} -2.16585e6 q^{83} +596901. q^{84} -1.62473e7 q^{85} +6.73077e6 q^{86} +6.77298e6 q^{87} +1.11695e6 q^{88} +1.19998e6 q^{89} -2.49490e6 q^{90} -901704. q^{91} -778688. q^{92} +4.83690e6 q^{93} -1.60020e6 q^{94} +1.12716e7 q^{95} +884736. q^{96} +8.97814e6 q^{97} -5.63378e6 q^{98} +1.59035e6 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10})$$ 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
$$5$$ −427.795 −1.53053 −0.765264 0.643717i $$-0.777391\pi$$
−0.765264 + 0.643717i $$0.777391\pi$$
$$6$$ 216.000 0.408248
$$7$$ 345.429 0.380641 0.190320 0.981722i $$-0.439047\pi$$
0.190320 + 0.981722i $$0.439047\pi$$
$$8$$ 512.000 0.353553
$$9$$ 729.000 0.333333
$$10$$ −3422.36 −1.08225
$$11$$ 2181.54 0.494185 0.247092 0.968992i $$-0.420525\pi$$
0.247092 + 0.968992i $$0.420525\pi$$
$$12$$ 1728.00 0.288675
$$13$$ −2610.39 −0.329537 −0.164768 0.986332i $$-0.552688\pi$$
−0.164768 + 0.986332i $$0.552688\pi$$
$$14$$ 2763.43 0.269154
$$15$$ −11550.5 −0.883651
$$16$$ 4096.00 0.250000
$$17$$ 37979.0 1.87488 0.937438 0.348152i $$-0.113191\pi$$
0.937438 + 0.348152i $$0.113191\pi$$
$$18$$ 5832.00 0.235702
$$19$$ −26348.1 −0.881276 −0.440638 0.897685i $$-0.645248\pi$$
−0.440638 + 0.897685i $$0.645248\pi$$
$$20$$ −27378.9 −0.765264
$$21$$ 9326.57 0.219763
$$22$$ 17452.3 0.349442
$$23$$ −12167.0 −0.208514
$$24$$ 13824.0 0.204124
$$25$$ 104884. 1.34251
$$26$$ −20883.1 −0.233018
$$27$$ 19683.0 0.192450
$$28$$ 22107.4 0.190320
$$29$$ 250851. 1.90995 0.954977 0.296679i $$-0.0958793\pi$$
0.954977 + 0.296679i $$0.0958793\pi$$
$$30$$ −92403.8 −0.624835
$$31$$ 179145. 1.08003 0.540017 0.841654i $$-0.318418\pi$$
0.540017 + 0.841654i $$0.318418\pi$$
$$32$$ 32768.0 0.176777
$$33$$ 58901.7 0.285318
$$34$$ 303832. 1.32574
$$35$$ −147773. −0.582581
$$36$$ 46656.0 0.166667
$$37$$ 434281. 1.40950 0.704749 0.709456i $$-0.251059\pi$$
0.704749 + 0.709456i $$0.251059\pi$$
$$38$$ −210785. −0.623157
$$39$$ −70480.6 −0.190258
$$40$$ −219031. −0.541123
$$41$$ −200429. −0.454168 −0.227084 0.973875i $$-0.572919\pi$$
−0.227084 + 0.973875i $$0.572919\pi$$
$$42$$ 74612.6 0.155396
$$43$$ 841346. 1.61375 0.806873 0.590725i $$-0.201158\pi$$
0.806873 + 0.590725i $$0.201158\pi$$
$$44$$ 139619. 0.247092
$$45$$ −311863. −0.510176
$$46$$ −97336.0 −0.147442
$$47$$ −200025. −0.281024 −0.140512 0.990079i $$-0.544875\pi$$
−0.140512 + 0.990079i $$0.544875\pi$$
$$48$$ 110592. 0.144338
$$49$$ −704222. −0.855113
$$50$$ 839072. 0.949301
$$51$$ 1.02543e6 1.08246
$$52$$ −167065. −0.164768
$$53$$ −1.62417e6 −1.49853 −0.749266 0.662269i $$-0.769593\pi$$
−0.749266 + 0.662269i $$0.769593\pi$$
$$54$$ 157464. 0.136083
$$55$$ −933254. −0.756364
$$56$$ 176859. 0.134577
$$57$$ −711399. −0.508805
$$58$$ 2.00681e6 1.35054
$$59$$ −2.18662e6 −1.38609 −0.693044 0.720895i $$-0.743731\pi$$
−0.693044 + 0.720895i $$0.743731\pi$$
$$60$$ −739231. −0.441825
$$61$$ 2.54771e6 1.43713 0.718564 0.695460i $$-0.244800\pi$$
0.718564 + 0.695460i $$0.244800\pi$$
$$62$$ 1.43316e6 0.763700
$$63$$ 251817. 0.126880
$$64$$ 262144. 0.125000
$$65$$ 1.11671e6 0.504365
$$66$$ 471213. 0.201750
$$67$$ 4.66306e6 1.89413 0.947063 0.321048i $$-0.104035\pi$$
0.947063 + 0.321048i $$0.104035\pi$$
$$68$$ 2.43066e6 0.937438
$$69$$ −328509. −0.120386
$$70$$ −1.18218e6 −0.411947
$$71$$ 4.02892e6 1.33593 0.667966 0.744192i $$-0.267165\pi$$
0.667966 + 0.744192i $$0.267165\pi$$
$$72$$ 373248. 0.117851
$$73$$ −2.58030e6 −0.776319 −0.388160 0.921592i $$-0.626889\pi$$
−0.388160 + 0.921592i $$0.626889\pi$$
$$74$$ 3.47425e6 0.996666
$$75$$ 2.83187e6 0.775101
$$76$$ −1.68628e6 −0.440638
$$77$$ 753568. 0.188107
$$78$$ −563845. −0.134533
$$79$$ 1.22032e6 0.278471 0.139236 0.990259i $$-0.455535\pi$$
0.139236 + 0.990259i $$0.455535\pi$$
$$80$$ −1.75225e6 −0.382632
$$81$$ 531441. 0.111111
$$82$$ −1.60343e6 −0.321145
$$83$$ −2.16585e6 −0.415771 −0.207886 0.978153i $$-0.566658\pi$$
−0.207886 + 0.978153i $$0.566658\pi$$
$$84$$ 596901. 0.109881
$$85$$ −1.62473e7 −2.86955
$$86$$ 6.73077e6 1.14109
$$87$$ 6.77298e6 1.10271
$$88$$ 1.11695e6 0.174721
$$89$$ 1.19998e6 0.180430 0.0902148 0.995922i $$-0.471245\pi$$
0.0902148 + 0.995922i $$0.471245\pi$$
$$90$$ −2.49490e6 −0.360749
$$91$$ −901704. −0.125435
$$92$$ −778688. −0.104257
$$93$$ 4.83690e6 0.623558
$$94$$ −1.60020e6 −0.198714
$$95$$ 1.12716e7 1.34882
$$96$$ 884736. 0.102062
$$97$$ 8.97814e6 0.998815 0.499408 0.866367i $$-0.333551\pi$$
0.499408 + 0.866367i $$0.333551\pi$$
$$98$$ −5.63378e6 −0.604656
$$99$$ 1.59035e6 0.164728
$$100$$ 6.71257e6 0.671257
$$101$$ −9.74940e6 −0.941571 −0.470785 0.882248i $$-0.656029\pi$$
−0.470785 + 0.882248i $$0.656029\pi$$
$$102$$ 8.20347e6 0.765415
$$103$$ −1.50223e7 −1.35459 −0.677294 0.735713i $$-0.736847\pi$$
−0.677294 + 0.735713i $$0.736847\pi$$
$$104$$ −1.33652e6 −0.116509
$$105$$ −3.98987e6 −0.336353
$$106$$ −1.29934e7 −1.05962
$$107$$ −1.75798e7 −1.38730 −0.693650 0.720312i $$-0.743999\pi$$
−0.693650 + 0.720312i $$0.743999\pi$$
$$108$$ 1.25971e6 0.0962250
$$109$$ 1.64602e7 1.21742 0.608711 0.793392i $$-0.291687\pi$$
0.608711 + 0.793392i $$0.291687\pi$$
$$110$$ −7.46604e6 −0.534830
$$111$$ 1.17256e7 0.813775
$$112$$ 1.41488e6 0.0951602
$$113$$ 1.70487e6 0.111152 0.0555761 0.998454i $$-0.482300\pi$$
0.0555761 + 0.998454i $$0.482300\pi$$
$$114$$ −5.69120e6 −0.359780
$$115$$ 5.20499e6 0.319137
$$116$$ 1.60545e7 0.954977
$$117$$ −1.90298e6 −0.109846
$$118$$ −1.74929e7 −0.980112
$$119$$ 1.31190e7 0.713654
$$120$$ −5.91384e6 −0.312418
$$121$$ −1.47280e7 −0.755781
$$122$$ 2.03817e7 1.01620
$$123$$ −5.41157e6 −0.262214
$$124$$ 1.14653e7 0.540017
$$125$$ −1.14474e7 −0.524228
$$126$$ 2.01454e6 0.0897179
$$127$$ 1.90880e7 0.826889 0.413444 0.910529i $$-0.364326\pi$$
0.413444 + 0.910529i $$0.364326\pi$$
$$128$$ 2.09715e6 0.0883883
$$129$$ 2.27163e7 0.931696
$$130$$ 8.93371e6 0.356640
$$131$$ 3.31709e6 0.128916 0.0644582 0.997920i $$-0.479468\pi$$
0.0644582 + 0.997920i $$0.479468\pi$$
$$132$$ 3.76971e6 0.142659
$$133$$ −9.10140e6 −0.335450
$$134$$ 3.73045e7 1.33935
$$135$$ −8.42030e6 −0.294550
$$136$$ 1.94453e7 0.662869
$$137$$ −5.17700e7 −1.72011 −0.860055 0.510202i $$-0.829571\pi$$
−0.860055 + 0.510202i $$0.829571\pi$$
$$138$$ −2.62807e6 −0.0851257
$$139$$ −1.27587e7 −0.402954 −0.201477 0.979493i $$-0.564574\pi$$
−0.201477 + 0.979493i $$0.564574\pi$$
$$140$$ −9.45746e6 −0.291291
$$141$$ −5.40069e6 −0.162249
$$142$$ 3.22314e7 0.944647
$$143$$ −5.69468e6 −0.162852
$$144$$ 2.98598e6 0.0833333
$$145$$ −1.07313e8 −2.92324
$$146$$ −2.06424e7 −0.548941
$$147$$ −1.90140e7 −0.493700
$$148$$ 2.77940e7 0.704749
$$149$$ −4.76667e7 −1.18049 −0.590246 0.807223i $$-0.700969\pi$$
−0.590246 + 0.807223i $$0.700969\pi$$
$$150$$ 2.26549e7 0.548079
$$151$$ 4.87918e7 1.15326 0.576631 0.817005i $$-0.304367\pi$$
0.576631 + 0.817005i $$0.304367\pi$$
$$152$$ −1.34902e7 −0.311578
$$153$$ 2.76867e7 0.624959
$$154$$ 6.02854e6 0.133012
$$155$$ −7.66372e7 −1.65302
$$156$$ −4.51076e6 −0.0951291
$$157$$ 1.52646e7 0.314801 0.157401 0.987535i $$-0.449689\pi$$
0.157401 + 0.987535i $$0.449689\pi$$
$$158$$ 9.76259e6 0.196909
$$159$$ −4.38526e7 −0.865178
$$160$$ −1.40180e7 −0.270562
$$161$$ −4.20283e6 −0.0793691
$$162$$ 4.25153e6 0.0785674
$$163$$ −7.21694e7 −1.30526 −0.652629 0.757678i $$-0.726334\pi$$
−0.652629 + 0.757678i $$0.726334\pi$$
$$164$$ −1.28274e7 −0.227084
$$165$$ −2.51979e7 −0.436687
$$166$$ −1.73268e7 −0.293995
$$167$$ 3.34621e7 0.555962 0.277981 0.960587i $$-0.410335\pi$$
0.277981 + 0.960587i $$0.410335\pi$$
$$168$$ 4.77521e6 0.0776979
$$169$$ −5.59344e7 −0.891405
$$170$$ −1.29978e8 −2.02908
$$171$$ −1.92078e7 −0.293759
$$172$$ 5.38461e7 0.806873
$$173$$ −4.16573e7 −0.611688 −0.305844 0.952082i $$-0.598939\pi$$
−0.305844 + 0.952082i $$0.598939\pi$$
$$174$$ 5.41838e7 0.779736
$$175$$ 3.62299e7 0.511016
$$176$$ 8.93560e6 0.123546
$$177$$ −5.90387e7 −0.800258
$$178$$ 9.59982e6 0.127583
$$179$$ −6.94962e7 −0.905682 −0.452841 0.891591i $$-0.649589\pi$$
−0.452841 + 0.891591i $$0.649589\pi$$
$$180$$ −1.99592e7 −0.255088
$$181$$ 3.54533e7 0.444408 0.222204 0.975000i $$-0.428675\pi$$
0.222204 + 0.975000i $$0.428675\pi$$
$$182$$ −7.21363e6 −0.0886960
$$183$$ 6.87882e7 0.829727
$$184$$ −6.22950e6 −0.0737210
$$185$$ −1.85783e8 −2.15728
$$186$$ 3.86952e7 0.440922
$$187$$ 8.28529e7 0.926536
$$188$$ −1.28016e7 −0.140512
$$189$$ 6.79907e6 0.0732543
$$190$$ 9.01729e7 0.953758
$$191$$ 5.59759e7 0.581279 0.290639 0.956833i $$-0.406132\pi$$
0.290639 + 0.956833i $$0.406132\pi$$
$$192$$ 7.07789e6 0.0721688
$$193$$ 8.02723e7 0.803740 0.401870 0.915697i $$-0.368360\pi$$
0.401870 + 0.915697i $$0.368360\pi$$
$$194$$ 7.18251e7 0.706269
$$195$$ 3.01513e7 0.291195
$$196$$ −4.50702e7 −0.427556
$$197$$ 3.52484e7 0.328479 0.164240 0.986420i $$-0.447483\pi$$
0.164240 + 0.986420i $$0.447483\pi$$
$$198$$ 1.27228e7 0.116481
$$199$$ 4.36909e7 0.393012 0.196506 0.980503i $$-0.437041\pi$$
0.196506 + 0.980503i $$0.437041\pi$$
$$200$$ 5.37006e7 0.474651
$$201$$ 1.25903e8 1.09357
$$202$$ −7.79952e7 −0.665791
$$203$$ 8.66511e7 0.727006
$$204$$ 6.56278e7 0.541230
$$205$$ 8.57425e7 0.695116
$$206$$ −1.20179e8 −0.957838
$$207$$ −8.86974e6 −0.0695048
$$208$$ −1.06922e7 −0.0823842
$$209$$ −5.74796e7 −0.435514
$$210$$ −3.19189e7 −0.237838
$$211$$ −1.86224e8 −1.36473 −0.682365 0.731012i $$-0.739048\pi$$
−0.682365 + 0.731012i $$0.739048\pi$$
$$212$$ −1.03947e8 −0.749266
$$213$$ 1.08781e8 0.771301
$$214$$ −1.40638e8 −0.980970
$$215$$ −3.59924e8 −2.46988
$$216$$ 1.00777e7 0.0680414
$$217$$ 6.18817e7 0.411105
$$218$$ 1.31681e8 0.860848
$$219$$ −6.96681e7 −0.448208
$$220$$ −5.97283e7 −0.378182
$$221$$ −9.91401e7 −0.617841
$$222$$ 9.38047e7 0.575425
$$223$$ 4.97859e7 0.300635 0.150317 0.988638i $$-0.451970\pi$$
0.150317 + 0.988638i $$0.451970\pi$$
$$224$$ 1.13190e7 0.0672884
$$225$$ 7.64604e7 0.447505
$$226$$ 1.36390e7 0.0785964
$$227$$ 1.75842e8 0.997773 0.498886 0.866667i $$-0.333743\pi$$
0.498886 + 0.866667i $$0.333743\pi$$
$$228$$ −4.55296e7 −0.254403
$$229$$ 4.00032e7 0.220125 0.110063 0.993925i $$-0.464895\pi$$
0.110063 + 0.993925i $$0.464895\pi$$
$$230$$ 4.16399e7 0.225664
$$231$$ 2.03463e7 0.108604
$$232$$ 1.28436e8 0.675271
$$233$$ 1.16608e8 0.603923 0.301962 0.953320i $$-0.402359\pi$$
0.301962 + 0.953320i $$0.402359\pi$$
$$234$$ −1.52238e7 −0.0776726
$$235$$ 8.55700e7 0.430114
$$236$$ −1.39944e8 −0.693044
$$237$$ 3.29487e7 0.160775
$$238$$ 1.04952e8 0.504630
$$239$$ −7.54954e7 −0.357707 −0.178854 0.983876i $$-0.557239\pi$$
−0.178854 + 0.983876i $$0.557239\pi$$
$$240$$ −4.73108e7 −0.220913
$$241$$ 4.32182e8 1.98887 0.994436 0.105346i $$-0.0335949\pi$$
0.994436 + 0.105346i $$0.0335949\pi$$
$$242$$ −1.17824e8 −0.534418
$$243$$ 1.43489e7 0.0641500
$$244$$ 1.63053e8 0.718564
$$245$$ 3.01263e8 1.30877
$$246$$ −4.32926e7 −0.185413
$$247$$ 6.87789e7 0.290413
$$248$$ 9.17220e7 0.381850
$$249$$ −5.84779e7 −0.240046
$$250$$ −9.15789e7 −0.370685
$$251$$ −1.77661e8 −0.709141 −0.354571 0.935029i $$-0.615373\pi$$
−0.354571 + 0.935029i $$0.615373\pi$$
$$252$$ 1.61163e7 0.0634401
$$253$$ −2.65428e7 −0.103045
$$254$$ 1.52704e8 0.584699
$$255$$ −4.38676e8 −1.65674
$$256$$ 1.67772e7 0.0625000
$$257$$ −3.32079e8 −1.22033 −0.610163 0.792276i $$-0.708896\pi$$
−0.610163 + 0.792276i $$0.708896\pi$$
$$258$$ 1.81731e8 0.658809
$$259$$ 1.50013e8 0.536513
$$260$$ 7.14697e7 0.252183
$$261$$ 1.82870e8 0.636651
$$262$$ 2.65368e7 0.0911577
$$263$$ 3.55827e8 1.20613 0.603064 0.797693i $$-0.293946\pi$$
0.603064 + 0.797693i $$0.293946\pi$$
$$264$$ 3.01577e7 0.100875
$$265$$ 6.94812e8 2.29354
$$266$$ −7.28112e7 −0.237199
$$267$$ 3.23994e7 0.104171
$$268$$ 2.98436e8 0.947063
$$269$$ 2.51996e6 0.00789332 0.00394666 0.999992i $$-0.498744\pi$$
0.00394666 + 0.999992i $$0.498744\pi$$
$$270$$ −6.73624e7 −0.208278
$$271$$ −4.75682e7 −0.145186 −0.0725929 0.997362i $$-0.523127\pi$$
−0.0725929 + 0.997362i $$0.523127\pi$$
$$272$$ 1.55562e8 0.468719
$$273$$ −2.43460e7 −0.0724200
$$274$$ −4.14160e8 −1.21630
$$275$$ 2.28809e8 0.663451
$$276$$ −2.10246e7 −0.0601929
$$277$$ −6.57962e7 −0.186004 −0.0930018 0.995666i $$-0.529646\pi$$
−0.0930018 + 0.995666i $$0.529646\pi$$
$$278$$ −1.02070e8 −0.284932
$$279$$ 1.30596e8 0.360012
$$280$$ −7.56597e7 −0.205973
$$281$$ 1.33552e8 0.359069 0.179535 0.983752i $$-0.442541\pi$$
0.179535 + 0.983752i $$0.442541\pi$$
$$282$$ −4.32055e7 −0.114727
$$283$$ −1.61478e8 −0.423508 −0.211754 0.977323i $$-0.567917\pi$$
−0.211754 + 0.977323i $$0.567917\pi$$
$$284$$ 2.57851e8 0.667966
$$285$$ 3.04333e8 0.778740
$$286$$ −4.55575e7 −0.115154
$$287$$ −6.92338e7 −0.172875
$$288$$ 2.38879e7 0.0589256
$$289$$ 1.03207e9 2.51516
$$290$$ −8.58504e8 −2.06704
$$291$$ 2.42410e8 0.576666
$$292$$ −1.65139e8 −0.388160
$$293$$ −1.53715e8 −0.357009 −0.178505 0.983939i $$-0.557126\pi$$
−0.178505 + 0.983939i $$0.557126\pi$$
$$294$$ −1.52112e8 −0.349098
$$295$$ 9.35425e8 2.12145
$$296$$ 2.22352e8 0.498333
$$297$$ 4.29393e7 0.0951059
$$298$$ −3.81333e8 −0.834734
$$299$$ 3.17606e7 0.0687132
$$300$$ 1.81239e8 0.387551
$$301$$ 2.90625e8 0.614257
$$302$$ 3.90335e8 0.815479
$$303$$ −2.63234e8 −0.543616
$$304$$ −1.07922e8 −0.220319
$$305$$ −1.08990e9 −2.19957
$$306$$ 2.21494e8 0.441913
$$307$$ −4.52238e8 −0.892037 −0.446019 0.895024i $$-0.647159\pi$$
−0.446019 + 0.895024i $$0.647159\pi$$
$$308$$ 4.82283e7 0.0940534
$$309$$ −4.05603e8 −0.782071
$$310$$ −6.13098e8 −1.16886
$$311$$ 7.24988e8 1.36669 0.683344 0.730096i $$-0.260525\pi$$
0.683344 + 0.730096i $$0.260525\pi$$
$$312$$ −3.60861e7 −0.0672664
$$313$$ −5.66818e8 −1.04481 −0.522407 0.852696i $$-0.674966\pi$$
−0.522407 + 0.852696i $$0.674966\pi$$
$$314$$ 1.22117e8 0.222598
$$315$$ −1.07726e8 −0.194194
$$316$$ 7.81007e7 0.139236
$$317$$ −9.63349e8 −1.69854 −0.849271 0.527958i $$-0.822958\pi$$
−0.849271 + 0.527958i $$0.822958\pi$$
$$318$$ −3.50821e8 −0.611773
$$319$$ 5.47243e8 0.943871
$$320$$ −1.12144e8 −0.191316
$$321$$ −4.74654e8 −0.800958
$$322$$ −3.36226e7 −0.0561224
$$323$$ −1.00068e9 −1.65228
$$324$$ 3.40122e7 0.0555556
$$325$$ −2.73788e8 −0.442408
$$326$$ −5.77355e8 −0.922957
$$327$$ 4.44424e8 0.702879
$$328$$ −1.02619e8 −0.160573
$$329$$ −6.90945e7 −0.106969
$$330$$ −2.01583e8 −0.308784
$$331$$ −4.26221e8 −0.646006 −0.323003 0.946398i $$-0.604692\pi$$
−0.323003 + 0.946398i $$0.604692\pi$$
$$332$$ −1.38614e8 −0.207886
$$333$$ 3.16591e8 0.469833
$$334$$ 2.67697e8 0.393125
$$335$$ −1.99483e9 −2.89901
$$336$$ 3.82016e7 0.0549407
$$337$$ −2.41775e8 −0.344118 −0.172059 0.985087i $$-0.555042\pi$$
−0.172059 + 0.985087i $$0.555042\pi$$
$$338$$ −4.47475e8 −0.630319
$$339$$ 4.60316e7 0.0641737
$$340$$ −1.03982e9 −1.43477
$$341$$ 3.90812e8 0.533737
$$342$$ −1.53662e8 −0.207719
$$343$$ −5.27734e8 −0.706131
$$344$$ 4.30769e8 0.570545
$$345$$ 1.40535e8 0.184254
$$346$$ −3.33258e8 −0.432528
$$347$$ 1.34412e9 1.72697 0.863484 0.504375i $$-0.168277\pi$$
0.863484 + 0.504375i $$0.168277\pi$$
$$348$$ 4.33471e8 0.551356
$$349$$ 3.27029e8 0.411811 0.205905 0.978572i $$-0.433986\pi$$
0.205905 + 0.978572i $$0.433986\pi$$
$$350$$ 2.89839e8 0.361343
$$351$$ −5.13803e7 −0.0634194
$$352$$ 7.14848e7 0.0873604
$$353$$ 1.52857e9 1.84958 0.924789 0.380480i $$-0.124241\pi$$
0.924789 + 0.380480i $$0.124241\pi$$
$$354$$ −4.72309e8 −0.565868
$$355$$ −1.72355e9 −2.04468
$$356$$ 7.67985e7 0.0902148
$$357$$ 3.54214e8 0.412028
$$358$$ −5.55970e8 −0.640414
$$359$$ −4.65294e7 −0.0530759 −0.0265379 0.999648i $$-0.508448\pi$$
−0.0265379 + 0.999648i $$0.508448\pi$$
$$360$$ −1.59674e8 −0.180374
$$361$$ −1.99648e8 −0.223352
$$362$$ 2.83627e8 0.314244
$$363$$ −3.97657e8 −0.436351
$$364$$ −5.77091e7 −0.0627176
$$365$$ 1.10384e9 1.18818
$$366$$ 5.50306e8 0.586705
$$367$$ 4.58322e8 0.483993 0.241997 0.970277i $$-0.422198\pi$$
0.241997 + 0.970277i $$0.422198\pi$$
$$368$$ −4.98360e7 −0.0521286
$$369$$ −1.46112e8 −0.151389
$$370$$ −1.48627e9 −1.52543
$$371$$ −5.61035e8 −0.570402
$$372$$ 3.09562e8 0.311779
$$373$$ 7.39771e8 0.738102 0.369051 0.929409i $$-0.379683\pi$$
0.369051 + 0.929409i $$0.379683\pi$$
$$374$$ 6.62823e8 0.655160
$$375$$ −3.09079e8 −0.302663
$$376$$ −1.02413e8 −0.0993568
$$377$$ −6.54820e8 −0.629400
$$378$$ 5.43926e7 0.0517986
$$379$$ 3.93984e8 0.371742 0.185871 0.982574i $$-0.440489\pi$$
0.185871 + 0.982574i $$0.440489\pi$$
$$380$$ 7.21383e8 0.674409
$$381$$ 5.15376e8 0.477404
$$382$$ 4.47807e8 0.411026
$$383$$ 1.33816e9 1.21706 0.608530 0.793531i $$-0.291760\pi$$
0.608530 + 0.793531i $$0.291760\pi$$
$$384$$ 5.66231e7 0.0510310
$$385$$ −3.22373e8 −0.287903
$$386$$ 6.42179e8 0.568330
$$387$$ 6.13341e8 0.537915
$$388$$ 5.74601e8 0.499408
$$389$$ −1.71698e9 −1.47891 −0.739455 0.673206i $$-0.764917\pi$$
−0.739455 + 0.673206i $$0.764917\pi$$
$$390$$ 2.41210e8 0.205906
$$391$$ −4.62091e8 −0.390939
$$392$$ −3.60562e8 −0.302328
$$393$$ 8.95615e7 0.0744299
$$394$$ 2.81987e8 0.232270
$$395$$ −5.22049e8 −0.426208
$$396$$ 1.01782e8 0.0823642
$$397$$ −9.91563e7 −0.0795341 −0.0397671 0.999209i $$-0.512662\pi$$
−0.0397671 + 0.999209i $$0.512662\pi$$
$$398$$ 3.49528e8 0.277901
$$399$$ −2.45738e8 −0.193672
$$400$$ 4.29605e8 0.335629
$$401$$ 1.41606e9 1.09667 0.548334 0.836259i $$-0.315262\pi$$
0.548334 + 0.836259i $$0.315262\pi$$
$$402$$ 1.00722e9 0.773274
$$403$$ −4.67638e8 −0.355911
$$404$$ −6.23961e8 −0.470785
$$405$$ −2.27348e8 −0.170059
$$406$$ 6.93209e8 0.514071
$$407$$ 9.47403e8 0.696553
$$408$$ 5.25022e8 0.382707
$$409$$ −1.39619e9 −1.00905 −0.504524 0.863397i $$-0.668332\pi$$
−0.504524 + 0.863397i $$0.668332\pi$$
$$410$$ 6.85940e8 0.491521
$$411$$ −1.39779e9 −0.993106
$$412$$ −9.61429e8 −0.677294
$$413$$ −7.55320e8 −0.527601
$$414$$ −7.09579e7 −0.0491473
$$415$$ 9.26540e8 0.636350
$$416$$ −8.55373e7 −0.0582544
$$417$$ −3.44486e8 −0.232646
$$418$$ −4.59837e8 −0.307955
$$419$$ −9.81338e8 −0.651733 −0.325866 0.945416i $$-0.605656\pi$$
−0.325866 + 0.945416i $$0.605656\pi$$
$$420$$ −2.55351e8 −0.168177
$$421$$ −1.16824e9 −0.763037 −0.381518 0.924361i $$-0.624599\pi$$
−0.381518 + 0.924361i $$0.624599\pi$$
$$422$$ −1.48979e9 −0.965010
$$423$$ −1.45819e8 −0.0936745
$$424$$ −8.31575e8 −0.529811
$$425$$ 3.98339e9 2.51705
$$426$$ 8.70247e8 0.545392
$$427$$ 8.80052e8 0.547030
$$428$$ −1.12511e9 −0.693650
$$429$$ −1.53756e8 −0.0940227
$$430$$ −2.87939e9 −1.74647
$$431$$ 1.91210e9 1.15037 0.575187 0.818022i $$-0.304929\pi$$
0.575187 + 0.818022i $$0.304929\pi$$
$$432$$ 8.06216e7 0.0481125
$$433$$ 1.67730e9 0.992894 0.496447 0.868067i $$-0.334638\pi$$
0.496447 + 0.868067i $$0.334638\pi$$
$$434$$ 4.95053e8 0.290695
$$435$$ −2.89745e9 −1.68773
$$436$$ 1.05345e9 0.608711
$$437$$ 3.20578e8 0.183759
$$438$$ −5.57345e8 −0.316931
$$439$$ −1.78469e8 −0.100679 −0.0503393 0.998732i $$-0.516030\pi$$
−0.0503393 + 0.998732i $$0.516030\pi$$
$$440$$ −4.77826e8 −0.267415
$$441$$ −5.13378e8 −0.285038
$$442$$ −7.93121e8 −0.436879
$$443$$ 1.00078e7 0.00546921 0.00273461 0.999996i $$-0.499130\pi$$
0.00273461 + 0.999996i $$0.499130\pi$$
$$444$$ 7.50437e8 0.406887
$$445$$ −5.13345e8 −0.276153
$$446$$ 3.98287e8 0.212581
$$447$$ −1.28700e9 −0.681557
$$448$$ 9.05520e7 0.0475801
$$449$$ 2.38685e9 1.24441 0.622203 0.782856i $$-0.286238\pi$$
0.622203 + 0.782856i $$0.286238\pi$$
$$450$$ 6.11683e8 0.316434
$$451$$ −4.37244e8 −0.224443
$$452$$ 1.09112e8 0.0555761
$$453$$ 1.31738e9 0.665836
$$454$$ 1.40673e9 0.705532
$$455$$ 3.85745e8 0.191982
$$456$$ −3.64237e8 −0.179890
$$457$$ 1.40659e9 0.689385 0.344692 0.938716i $$-0.387983\pi$$
0.344692 + 0.938716i $$0.387983\pi$$
$$458$$ 3.20025e8 0.155652
$$459$$ 7.47541e8 0.360820
$$460$$ 3.33119e8 0.159569
$$461$$ −8.75198e8 −0.416057 −0.208029 0.978123i $$-0.566705\pi$$
−0.208029 + 0.978123i $$0.566705\pi$$
$$462$$ 1.62771e8 0.0767943
$$463$$ −8.95572e8 −0.419341 −0.209670 0.977772i $$-0.567239\pi$$
−0.209670 + 0.977772i $$0.567239\pi$$
$$464$$ 1.02749e9 0.477489
$$465$$ −2.06921e9 −0.954373
$$466$$ 9.32862e8 0.427038
$$467$$ −2.18071e9 −0.990807 −0.495403 0.868663i $$-0.664980\pi$$
−0.495403 + 0.868663i $$0.664980\pi$$
$$468$$ −1.21790e8 −0.0549228
$$469$$ 1.61075e9 0.720981
$$470$$ 6.84560e8 0.304137
$$471$$ 4.12144e8 0.181751
$$472$$ −1.11955e9 −0.490056
$$473$$ 1.83543e9 0.797489
$$474$$ 2.63590e8 0.113685
$$475$$ −2.76350e9 −1.18313
$$476$$ 8.39619e8 0.356827
$$477$$ −1.18402e9 −0.499510
$$478$$ −6.03963e8 −0.252937
$$479$$ 1.86608e9 0.775812 0.387906 0.921699i $$-0.373199\pi$$
0.387906 + 0.921699i $$0.373199\pi$$
$$480$$ −3.78486e8 −0.156209
$$481$$ −1.13364e9 −0.464482
$$482$$ 3.45745e9 1.40634
$$483$$ −1.13476e8 −0.0458237
$$484$$ −9.42594e8 −0.377891
$$485$$ −3.84081e9 −1.52871
$$486$$ 1.14791e8 0.0453609
$$487$$ −9.54001e8 −0.374281 −0.187140 0.982333i $$-0.559922\pi$$
−0.187140 + 0.982333i $$0.559922\pi$$
$$488$$ 1.30443e9 0.508102
$$489$$ −1.94857e9 −0.753591
$$490$$ 2.41010e9 0.925443
$$491$$ 1.21183e9 0.462017 0.231008 0.972952i $$-0.425798\pi$$
0.231008 + 0.972952i $$0.425798\pi$$
$$492$$ −3.46341e8 −0.131107
$$493$$ 9.52708e9 3.58093
$$494$$ 5.50232e8 0.205353
$$495$$ −6.80343e8 −0.252121
$$496$$ 7.33776e8 0.270009
$$497$$ 1.39170e9 0.508510
$$498$$ −4.67823e8 −0.169738
$$499$$ −1.17097e9 −0.421884 −0.210942 0.977499i $$-0.567653\pi$$
−0.210942 + 0.977499i $$0.567653\pi$$
$$500$$ −7.32631e8 −0.262114
$$501$$ 9.03476e8 0.320985
$$502$$ −1.42128e9 −0.501439
$$503$$ −3.36243e9 −1.17806 −0.589028 0.808113i $$-0.700489\pi$$
−0.589028 + 0.808113i $$0.700489\pi$$
$$504$$ 1.28931e8 0.0448589
$$505$$ 4.17075e9 1.44110
$$506$$ −2.12343e8 −0.0728636
$$507$$ −1.51023e9 −0.514653
$$508$$ 1.22163e9 0.413444
$$509$$ −3.89948e9 −1.31067 −0.655336 0.755337i $$-0.727473\pi$$
−0.655336 + 0.755337i $$0.727473\pi$$
$$510$$ −3.50941e9 −1.17149
$$511$$ −8.91310e8 −0.295499
$$512$$ 1.34218e8 0.0441942
$$513$$ −5.18610e8 −0.169602
$$514$$ −2.65663e9 −0.862900
$$515$$ 6.42648e9 2.07323
$$516$$ 1.45385e9 0.465848
$$517$$ −4.36364e8 −0.138878
$$518$$ 1.20010e9 0.379372
$$519$$ −1.12475e9 −0.353158
$$520$$ 5.71758e8 0.178320
$$521$$ −4.08573e9 −1.26572 −0.632860 0.774266i $$-0.718119\pi$$
−0.632860 + 0.774266i $$0.718119\pi$$
$$522$$ 1.46296e9 0.450181
$$523$$ −6.17299e9 −1.88686 −0.943430 0.331571i $$-0.892421\pi$$
−0.943430 + 0.331571i $$0.892421\pi$$
$$524$$ 2.12294e8 0.0644582
$$525$$ 9.78208e8 0.295035
$$526$$ 2.84661e9 0.852861
$$527$$ 6.80374e9 2.02493
$$528$$ 2.41261e8 0.0713295
$$529$$ 1.48036e8 0.0434783
$$530$$ 5.55850e9 1.62178
$$531$$ −1.59404e9 −0.462029
$$532$$ −5.82489e8 −0.167725
$$533$$ 5.23197e8 0.149665
$$534$$ 2.59195e8 0.0736601
$$535$$ 7.52056e9 2.12330
$$536$$ 2.38748e9 0.669675
$$537$$ −1.87640e9 −0.522896
$$538$$ 2.01596e7 0.00558142
$$539$$ −1.53629e9 −0.422584
$$540$$ −5.38899e8 −0.147275
$$541$$ 6.18398e9 1.67910 0.839552 0.543280i $$-0.182818\pi$$
0.839552 + 0.543280i $$0.182818\pi$$
$$542$$ −3.80546e8 −0.102662
$$543$$ 9.57240e8 0.256579
$$544$$ 1.24450e9 0.331434
$$545$$ −7.04158e9 −1.86330
$$546$$ −1.94768e8 −0.0512087
$$547$$ −3.11011e9 −0.812494 −0.406247 0.913763i $$-0.633163\pi$$
−0.406247 + 0.913763i $$0.633163\pi$$
$$548$$ −3.31328e9 −0.860055
$$549$$ 1.85728e9 0.479043
$$550$$ 1.83047e9 0.469130
$$551$$ −6.60946e9 −1.68320
$$552$$ −1.68197e8 −0.0425628
$$553$$ 4.21535e8 0.105997
$$554$$ −5.26369e8 −0.131524
$$555$$ −5.01615e9 −1.24550
$$556$$ −8.16559e8 −0.201477
$$557$$ 5.56754e9 1.36512 0.682559 0.730831i $$-0.260867\pi$$
0.682559 + 0.730831i $$0.260867\pi$$
$$558$$ 1.04477e9 0.254567
$$559$$ −2.19624e9 −0.531789
$$560$$ −6.05277e8 −0.145645
$$561$$ 2.23703e9 0.534936
$$562$$ 1.06842e9 0.253900
$$563$$ −6.88023e9 −1.62489 −0.812445 0.583038i $$-0.801864\pi$$
−0.812445 + 0.583038i $$0.801864\pi$$
$$564$$ −3.45644e8 −0.0811245
$$565$$ −7.29337e8 −0.170121
$$566$$ −1.29182e9 −0.299465
$$567$$ 1.83575e8 0.0422934
$$568$$ 2.06281e9 0.472323
$$569$$ 8.40627e9 1.91298 0.956490 0.291765i $$-0.0942425\pi$$
0.956490 + 0.291765i $$0.0942425\pi$$
$$570$$ 2.43467e9 0.550653
$$571$$ −5.25925e8 −0.118222 −0.0591109 0.998251i $$-0.518827\pi$$
−0.0591109 + 0.998251i $$0.518827\pi$$
$$572$$ −3.64460e8 −0.0814261
$$573$$ 1.51135e9 0.335602
$$574$$ −5.53870e8 −0.122241
$$575$$ −1.27612e9 −0.279934
$$576$$ 1.91103e8 0.0416667
$$577$$ −1.66741e9 −0.361349 −0.180674 0.983543i $$-0.557828\pi$$
−0.180674 + 0.983543i $$0.557828\pi$$
$$578$$ 8.25654e9 1.77849
$$579$$ 2.16735e9 0.464039
$$580$$ −6.86803e9 −1.46162
$$581$$ −7.48146e8 −0.158259
$$582$$ 1.93928e9 0.407765
$$583$$ −3.54320e9 −0.740552
$$584$$ −1.32111e9 −0.274470
$$585$$ 8.14084e8 0.168122
$$586$$ −1.22972e9 −0.252444
$$587$$ −1.24841e9 −0.254756 −0.127378 0.991854i $$-0.540656\pi$$
−0.127378 + 0.991854i $$0.540656\pi$$
$$588$$ −1.21690e9 −0.246850
$$589$$ −4.72012e9 −0.951809
$$590$$ 7.48340e9 1.50009
$$591$$ 9.51707e8 0.189648
$$592$$ 1.77881e9 0.352375
$$593$$ −2.61091e9 −0.514163 −0.257081 0.966390i $$-0.582761\pi$$
−0.257081 + 0.966390i $$0.582761\pi$$
$$594$$ 3.43515e8 0.0672501
$$595$$ −5.61227e9 −1.09227
$$596$$ −3.05067e9 −0.590246
$$597$$ 1.17966e9 0.226905
$$598$$ 2.54085e8 0.0485876
$$599$$ −6.36475e9 −1.21001 −0.605003 0.796223i $$-0.706828\pi$$
−0.605003 + 0.796223i $$0.706828\pi$$
$$600$$ 1.44992e9 0.274040
$$601$$ −1.44570e9 −0.271656 −0.135828 0.990732i $$-0.543369\pi$$
−0.135828 + 0.990732i $$0.543369\pi$$
$$602$$ 2.32500e9 0.434345
$$603$$ 3.39937e9 0.631375
$$604$$ 3.12268e9 0.576631
$$605$$ 6.30059e9 1.15674
$$606$$ −2.10587e9 −0.384395
$$607$$ −4.03112e9 −0.731586 −0.365793 0.930696i $$-0.619202\pi$$
−0.365793 + 0.930696i $$0.619202\pi$$
$$608$$ −8.63375e8 −0.155789
$$609$$ 2.33958e9 0.419737
$$610$$ −8.71919e9 −1.55533
$$611$$ 5.22145e8 0.0926076
$$612$$ 1.77195e9 0.312479
$$613$$ 2.16682e9 0.379936 0.189968 0.981790i $$-0.439162\pi$$
0.189968 + 0.981790i $$0.439162\pi$$
$$614$$ −3.61791e9 −0.630766
$$615$$ 2.31505e9 0.401325
$$616$$ 3.85827e8 0.0665058
$$617$$ −3.74148e9 −0.641276 −0.320638 0.947202i $$-0.603897\pi$$
−0.320638 + 0.947202i $$0.603897\pi$$
$$618$$ −3.24482e9 −0.553008
$$619$$ 1.01384e10 1.71811 0.859054 0.511885i $$-0.171053\pi$$
0.859054 + 0.511885i $$0.171053\pi$$
$$620$$ −4.90478e9 −0.826511
$$621$$ −2.39483e8 −0.0401286
$$622$$ 5.79990e9 0.966394
$$623$$ 4.14506e8 0.0686789
$$624$$ −2.88688e8 −0.0475645
$$625$$ −3.29693e9 −0.540169
$$626$$ −4.53455e9 −0.738795
$$627$$ −1.55195e9 −0.251444
$$628$$ 9.76934e8 0.157401
$$629$$ 1.64936e10 2.64264
$$630$$ −8.61811e8 −0.137316
$$631$$ 8.21596e9 1.30183 0.650917 0.759149i $$-0.274385\pi$$
0.650917 + 0.759149i $$0.274385\pi$$
$$632$$ 6.24806e8 0.0984544
$$633$$ −5.02804e9 −0.787927
$$634$$ −7.70679e9 −1.20105
$$635$$ −8.16575e9 −1.26558
$$636$$ −2.80657e9 −0.432589
$$637$$ 1.83830e9 0.281791
$$638$$ 4.37794e9 0.667417
$$639$$ 2.93708e9 0.445311
$$640$$ −8.97152e8 −0.135281
$$641$$ 8.20911e8 0.123110 0.0615549 0.998104i $$-0.480394\pi$$
0.0615549 + 0.998104i $$0.480394\pi$$
$$642$$ −3.79724e9 −0.566363
$$643$$ 5.92103e9 0.878333 0.439166 0.898406i $$-0.355274\pi$$
0.439166 + 0.898406i $$0.355274\pi$$
$$644$$ −2.68981e8 −0.0396845
$$645$$ −9.71795e9 −1.42599
$$646$$ −8.00541e9 −1.16834
$$647$$ −1.09657e10 −1.59174 −0.795870 0.605468i $$-0.792986\pi$$
−0.795870 + 0.605468i $$0.792986\pi$$
$$648$$ 2.72098e8 0.0392837
$$649$$ −4.77020e9 −0.684984
$$650$$ −2.19031e9 −0.312830
$$651$$ 1.67080e9 0.237352
$$652$$ −4.61884e9 −0.652629
$$653$$ −6.73255e9 −0.946201 −0.473101 0.881008i $$-0.656865\pi$$
−0.473101 + 0.881008i $$0.656865\pi$$
$$654$$ 3.55539e9 0.497011
$$655$$ −1.41904e9 −0.197310
$$656$$ −8.20956e8 −0.113542
$$657$$ −1.88104e9 −0.258773
$$658$$ −5.52756e8 −0.0756385
$$659$$ −1.25637e10 −1.71009 −0.855043 0.518557i $$-0.826469\pi$$
−0.855043 + 0.518557i $$0.826469\pi$$
$$660$$ −1.61266e9 −0.218343
$$661$$ 7.27312e9 0.979526 0.489763 0.871856i $$-0.337083\pi$$
0.489763 + 0.871856i $$0.337083\pi$$
$$662$$ −3.40977e9 −0.456796
$$663$$ −2.67678e9 −0.356711
$$664$$ −1.10891e9 −0.146997
$$665$$ 3.89354e9 0.513415
$$666$$ 2.53273e9 0.332222
$$667$$ −3.05210e9 −0.398253
$$668$$ 2.14157e9 0.277981
$$669$$ 1.34422e9 0.173572
$$670$$ −1.59587e10 −2.04991
$$671$$ 5.55794e9 0.710207
$$672$$ 3.05613e8 0.0388490
$$673$$ −2.38576e9 −0.301699 −0.150849 0.988557i $$-0.548201\pi$$
−0.150849 + 0.988557i $$0.548201\pi$$
$$674$$ −1.93420e9 −0.243328
$$675$$ 2.06443e9 0.258367
$$676$$ −3.57980e9 −0.445703
$$677$$ −1.25080e10 −1.54928 −0.774639 0.632404i $$-0.782068\pi$$
−0.774639 + 0.632404i $$0.782068\pi$$
$$678$$ 3.68253e8 0.0453777
$$679$$ 3.10131e9 0.380190
$$680$$ −8.31859e9 −1.01454
$$681$$ 4.74773e9 0.576064
$$682$$ 3.12649e9 0.377409
$$683$$ −6.33284e9 −0.760548 −0.380274 0.924874i $$-0.624170\pi$$
−0.380274 + 0.924874i $$0.624170\pi$$
$$684$$ −1.22930e9 −0.146879
$$685$$ 2.21470e10 2.63267
$$686$$ −4.22187e9 −0.499310
$$687$$ 1.08009e9 0.127089
$$688$$ 3.44615e9 0.403436
$$689$$ 4.23972e9 0.493821
$$690$$ 1.12428e9 0.130287
$$691$$ −2.30362e9 −0.265606 −0.132803 0.991142i $$-0.542398\pi$$
−0.132803 + 0.991142i $$0.542398\pi$$
$$692$$ −2.66607e9 −0.305844
$$693$$ 5.49351e8 0.0627023
$$694$$ 1.07530e10 1.22115
$$695$$ 5.45813e9 0.616733
$$696$$ 3.46777e9 0.389868
$$697$$ −7.61208e9 −0.851508
$$698$$ 2.61624e9 0.291194
$$699$$ 3.14841e9 0.348675
$$700$$ 2.31871e9 0.255508
$$701$$ −5.07693e9 −0.556657 −0.278329 0.960486i $$-0.589780\pi$$
−0.278329 + 0.960486i $$0.589780\pi$$
$$702$$ −4.11043e8 −0.0448443
$$703$$ −1.14425e10 −1.24216
$$704$$ 5.71879e8 0.0617731
$$705$$ 2.31039e9 0.248327
$$706$$ 1.22285e10 1.30785
$$707$$ −3.36772e9 −0.358400
$$708$$ −3.77848e9 −0.400129
$$709$$ 8.96481e8 0.0944669 0.0472334 0.998884i $$-0.484960\pi$$
0.0472334 + 0.998884i $$0.484960\pi$$
$$710$$ −1.37884e10 −1.44581
$$711$$ 8.89616e8 0.0928237
$$712$$ 6.14388e8 0.0637915
$$713$$ −2.17965e9 −0.225203
$$714$$ 2.83371e9 0.291348
$$715$$ 2.43616e9 0.249250
$$716$$ −4.44776e9 −0.452841
$$717$$ −2.03838e9 −0.206522
$$718$$ −3.72235e8 −0.0375303
$$719$$ −4.13828e9 −0.415210 −0.207605 0.978213i $$-0.566567\pi$$
−0.207605 + 0.978213i $$0.566567\pi$$
$$720$$ −1.27739e9 −0.127544
$$721$$ −5.18914e9 −0.515611
$$722$$ −1.59718e9 −0.157934
$$723$$ 1.16689e10 1.14828
$$724$$ 2.26901e9 0.222204
$$725$$ 2.63103e10 2.56414
$$726$$ −3.18126e9 −0.308546
$$727$$ 1.34281e10 1.29611 0.648057 0.761591i $$-0.275582\pi$$
0.648057 + 0.761591i $$0.275582\pi$$
$$728$$ −4.61672e8 −0.0443480
$$729$$ 3.87420e8 0.0370370
$$730$$ 8.83073e9 0.840169
$$731$$ 3.19535e10 3.02557
$$732$$ 4.40244e9 0.414863
$$733$$ 2.59875e8 0.0243725 0.0121863 0.999926i $$-0.496121\pi$$
0.0121863 + 0.999926i $$0.496121\pi$$
$$734$$ 3.66658e9 0.342235
$$735$$ 8.13410e9 0.755621
$$736$$ −3.98688e8 −0.0368605
$$737$$ 1.01727e10 0.936049
$$738$$ −1.16890e9 −0.107048
$$739$$ −1.08950e10 −0.993056 −0.496528 0.868021i $$-0.665392\pi$$
−0.496528 + 0.868021i $$0.665392\pi$$
$$740$$ −1.18901e10 −1.07864
$$741$$ 1.85703e9 0.167670
$$742$$ −4.48828e9 −0.403335
$$743$$ −1.77102e10 −1.58403 −0.792014 0.610503i $$-0.790967\pi$$
−0.792014 + 0.610503i $$0.790967\pi$$
$$744$$ 2.47649e9 0.220461
$$745$$ 2.03916e10 1.80678
$$746$$ 5.91817e9 0.521917
$$747$$ −1.57890e9 −0.138590
$$748$$ 5.30259e9 0.463268
$$749$$ −6.07256e9 −0.528063
$$750$$ −2.47263e9 −0.214015
$$751$$ −2.21088e10 −1.90470 −0.952348 0.305013i $$-0.901339\pi$$
−0.952348 + 0.305013i $$0.901339\pi$$
$$752$$ −8.19304e8 −0.0702559
$$753$$ −4.79683e9 −0.409423
$$754$$ −5.23856e9 −0.445053
$$755$$ −2.08729e10 −1.76510
$$756$$ 4.35141e8 0.0366272
$$757$$ −1.59200e10 −1.33385 −0.666925 0.745125i $$-0.732390\pi$$
−0.666925 + 0.745125i $$0.732390\pi$$
$$758$$ 3.15188e9 0.262861
$$759$$ −7.16657e8 −0.0594929
$$760$$ 5.77106e9 0.476879
$$761$$ −6.68228e7 −0.00549640 −0.00274820 0.999996i $$-0.500875\pi$$
−0.00274820 + 0.999996i $$0.500875\pi$$
$$762$$ 4.12301e9 0.337576
$$763$$ 5.68581e9 0.463400
$$764$$ 3.58246e9 0.290639
$$765$$ −1.18442e10 −0.956517
$$766$$ 1.07053e10 0.860591
$$767$$ 5.70793e9 0.456767
$$768$$ 4.52985e8 0.0360844
$$769$$ −6.62635e9 −0.525451 −0.262726 0.964871i $$-0.584621\pi$$
−0.262726 + 0.964871i $$0.584621\pi$$
$$770$$ −2.57898e9 −0.203578
$$771$$ −8.96613e9 −0.704555
$$772$$ 5.13743e9 0.401870
$$773$$ −3.61939e9 −0.281843 −0.140922 0.990021i $$-0.545007\pi$$
−0.140922 + 0.990021i $$0.545007\pi$$
$$774$$ 4.90673e9 0.380363
$$775$$ 1.87894e10 1.44996
$$776$$ 4.59681e9 0.353135
$$777$$ 4.05035e9 0.309756
$$778$$ −1.37359e10 −1.04575
$$779$$ 5.28092e9 0.400247
$$780$$ 1.92968e9 0.145598
$$781$$ 8.78926e9 0.660197
$$782$$ −3.69673e9 −0.276435
$$783$$ 4.93750e9 0.367571
$$784$$ −2.88449e9 −0.213778
$$785$$ −6.53012e9 −0.481812
$$786$$ 7.16492e8 0.0526299
$$787$$ 1.01537e10 0.742525 0.371263 0.928528i $$-0.378925\pi$$
0.371263 + 0.928528i $$0.378925\pi$$
$$788$$ 2.25590e9 0.164240
$$789$$ 9.60732e9 0.696358
$$790$$ −4.17639e9 −0.301374
$$791$$ 5.88912e8 0.0423090
$$792$$ 8.14257e8 0.0582403
$$793$$ −6.65052e9 −0.473587
$$794$$ −7.93250e8 −0.0562391
$$795$$ 1.87599e10 1.32418
$$796$$ 2.79622e9 0.196506
$$797$$ 1.25904e10 0.880916 0.440458 0.897773i $$-0.354816\pi$$
0.440458 + 0.897773i $$0.354816\pi$$
$$798$$ −1.96590e9 −0.136947
$$799$$ −7.59677e9 −0.526884
$$800$$ 3.43684e9 0.237325
$$801$$ 8.74783e8 0.0601432
$$802$$ 1.13285e10 0.775461
$$803$$ −5.62904e9 −0.383645
$$804$$ 8.05776e9 0.546787
$$805$$ 1.79795e9 0.121477
$$806$$ −3.74110e9 −0.251667
$$807$$ 6.80388e7 0.00455721
$$808$$ −4.99169e9 −0.332896
$$809$$ 2.20668e10 1.46528 0.732638 0.680618i $$-0.238289\pi$$
0.732638 + 0.680618i $$0.238289\pi$$
$$810$$ −1.81878e9 −0.120250
$$811$$ 7.09047e9 0.466769 0.233384 0.972385i $$-0.425020\pi$$
0.233384 + 0.972385i $$0.425020\pi$$
$$812$$ 5.54567e9 0.363503
$$813$$ −1.28434e9 −0.0838231
$$814$$ 7.57922e9 0.492537
$$815$$ 3.08737e10 1.99773
$$816$$ 4.20018e9 0.270615
$$817$$ −2.21679e10 −1.42216
$$818$$ −1.11695e10 −0.713505
$$819$$ −6.57342e8 −0.0418117
$$820$$ 5.48752e9 0.347558
$$821$$ 3.26295e9 0.205783 0.102891 0.994693i $$-0.467191\pi$$
0.102891 + 0.994693i $$0.467191\pi$$
$$822$$ −1.11823e10 −0.702232
$$823$$ 4.72161e9 0.295250 0.147625 0.989043i $$-0.452837\pi$$
0.147625 + 0.989043i $$0.452837\pi$$
$$824$$ −7.69143e9 −0.478919
$$825$$ 6.17784e9 0.383043
$$826$$ −6.04256e9 −0.373071
$$827$$ 1.78452e10 1.09712 0.548558 0.836112i $$-0.315177\pi$$
0.548558 + 0.836112i $$0.315177\pi$$
$$828$$ −5.67664e8 −0.0347524
$$829$$ −2.93379e10 −1.78850 −0.894248 0.447572i $$-0.852289\pi$$
−0.894248 + 0.447572i $$0.852289\pi$$
$$830$$ 7.41232e9 0.449967
$$831$$ −1.77650e9 −0.107389
$$832$$ −6.84299e8 −0.0411921
$$833$$ −2.67457e10 −1.60323
$$834$$ −2.75589e9 −0.164505
$$835$$ −1.43149e10 −0.850916
$$836$$ −3.67869e9 −0.217757
$$837$$ 3.52610e9 0.207853
$$838$$ −7.85070e9 −0.460845
$$839$$ −1.90554e9 −0.111391 −0.0556957 0.998448i $$-0.517738\pi$$
−0.0556957 + 0.998448i $$0.517738\pi$$
$$840$$ −2.04281e9 −0.118919
$$841$$ 4.56764e10 2.64793
$$842$$ −9.34594e9 −0.539549
$$843$$ 3.60590e9 0.207309
$$844$$ −1.19183e10 −0.682365
$$845$$ 2.39285e10 1.36432
$$846$$ −1.16655e9 −0.0662379
$$847$$ −5.08749e9 −0.287681
$$848$$ −6.65260e9 −0.374633
$$849$$ −4.35991e9 −0.244512
$$850$$ 3.18671e10 1.77982
$$851$$ −5.28390e9 −0.293901
$$852$$ 6.96197e9 0.385650
$$853$$ 1.63652e8 0.00902818 0.00451409 0.999990i $$-0.498563\pi$$
0.00451409 + 0.999990i $$0.498563\pi$$
$$854$$ 7.04042e9 0.386808
$$855$$ 8.21700e9 0.449606
$$856$$ −9.00085e9 −0.490485
$$857$$ −6.70099e9 −0.363669 −0.181834 0.983329i $$-0.558203\pi$$
−0.181834 + 0.983329i $$0.558203\pi$$
$$858$$ −1.23005e9 −0.0664841
$$859$$ 1.52632e10 0.821620 0.410810 0.911721i $$-0.365246\pi$$
0.410810 + 0.911721i $$0.365246\pi$$
$$860$$ −2.30351e10 −1.23494
$$861$$ −1.86931e9 −0.0998092
$$862$$ 1.52968e10 0.813437
$$863$$ −1.65285e9 −0.0875376 −0.0437688 0.999042i $$-0.513936\pi$$
−0.0437688 + 0.999042i $$0.513936\pi$$
$$864$$ 6.44973e8 0.0340207
$$865$$ 1.78208e10 0.936205
$$866$$ 1.34184e10 0.702082
$$867$$ 2.78658e10 1.45213
$$868$$ 3.96043e9 0.205553
$$869$$ 2.66219e9 0.137616
$$870$$ −2.31796e10 −1.19341
$$871$$ −1.21724e10 −0.624184
$$872$$ 8.42760e9 0.430424
$$873$$ 6.54506e9 0.332938
$$874$$ 2.56462e9 0.129937
$$875$$ −3.95425e9 −0.199543
$$876$$ −4.45876e9 −0.224104
$$877$$ −1.13923e10 −0.570313 −0.285156 0.958481i $$-0.592045\pi$$
−0.285156 + 0.958481i $$0.592045\pi$$
$$878$$ −1.42775e9 −0.0711905
$$879$$ −4.15030e9 −0.206119
$$880$$ −3.82261e9 −0.189091
$$881$$ −1.15694e10 −0.570024 −0.285012 0.958524i $$-0.591998\pi$$
−0.285012 + 0.958524i $$0.591998\pi$$
$$882$$ −4.10702e9 −0.201552
$$883$$ −2.51966e10 −1.23163 −0.615814 0.787892i $$-0.711173\pi$$
−0.615814 + 0.787892i $$0.711173\pi$$
$$884$$ −6.34497e9 −0.308920
$$885$$ 2.52565e10 1.22482
$$886$$ 8.00622e7 0.00386732
$$887$$ −3.78563e10 −1.82140 −0.910700 0.413069i $$-0.864457\pi$$
−0.910700 + 0.413069i $$0.864457\pi$$
$$888$$ 6.00350e9 0.287713
$$889$$ 6.59354e9 0.314747
$$890$$ −4.10676e9 −0.195269
$$891$$ 1.15936e9 0.0549094
$$892$$ 3.18630e9 0.150317
$$893$$ 5.27030e9 0.247659
$$894$$ −1.02960e10 −0.481934
$$895$$ 2.97302e10 1.38617
$$896$$ 7.24416e8 0.0336442
$$897$$ 8.57537e8 0.0396716
$$898$$ 1.90948e10 0.879928
$$899$$ 4.49386e10 2.06282
$$900$$ 4.89347e9 0.223752
$$901$$ −6.16844e10 −2.80956
$$902$$ −3.49795e9 −0.158705
$$903$$ 7.84687e9 0.354641
$$904$$ 8.72895e8 0.0392982
$$905$$ −1.51668e10 −0.680179
$$906$$ 1.05390e10 0.470817
$$907$$ −9.07644e9 −0.403915 −0.201957 0.979394i $$-0.564730\pi$$
−0.201957 + 0.979394i $$0.564730\pi$$
$$908$$ 1.12539e10 0.498886
$$909$$ −7.10731e9 −0.313857
$$910$$ 3.08596e9 0.135752
$$911$$ −3.63398e10 −1.59246 −0.796229 0.604995i $$-0.793175\pi$$
−0.796229 + 0.604995i $$0.793175\pi$$
$$912$$ −2.91389e9 −0.127201
$$913$$ −4.72489e9 −0.205468
$$914$$ 1.12527e10 0.487469
$$915$$ −2.94273e10 −1.26992
$$916$$ 2.56020e9 0.110063
$$917$$ 1.14582e9 0.0490708
$$918$$ 5.98033e9 0.255138
$$919$$ 2.16445e10 0.919904 0.459952 0.887944i $$-0.347867\pi$$
0.459952 + 0.887944i $$0.347867\pi$$
$$920$$ 2.66495e9 0.112832
$$921$$ −1.22104e10 −0.515018
$$922$$ −7.00158e9 −0.294197
$$923$$ −1.05171e10 −0.440239
$$924$$ 1.30216e9 0.0543018
$$925$$ 4.55491e10 1.89227
$$926$$ −7.16458e9 −0.296519
$$927$$ −1.09513e10 −0.451529
$$928$$ 8.21989e9 0.337635
$$929$$ 7.00431e9 0.286623 0.143311 0.989678i $$-0.454225\pi$$
0.143311 + 0.989678i $$0.454225\pi$$
$$930$$ −1.65536e10 −0.674844
$$931$$ 1.85549e10 0.753591
$$932$$ 7.46289e9 0.301962
$$933$$ 1.95747e10 0.789058
$$934$$ −1.74457e10 −0.700606
$$935$$ −3.54441e10 −1.41809
$$936$$ −9.74324e8 −0.0388363
$$937$$ −3.16263e10 −1.25591 −0.627957 0.778248i $$-0.716109\pi$$
−0.627957 + 0.778248i $$0.716109\pi$$
$$938$$ 1.28860e10 0.509811
$$939$$ −1.53041e10 −0.603223
$$940$$ 5.47648e9 0.215057
$$941$$ −2.31615e10 −0.906155 −0.453077 0.891471i $$-0.649674\pi$$
−0.453077 + 0.891471i $$0.649674\pi$$
$$942$$ 3.29715e9 0.128517
$$943$$ 2.43861e9 0.0947005
$$944$$ −8.95639e9 −0.346522
$$945$$ −2.90861e9 −0.112118
$$946$$ 1.46835e10 0.563910
$$947$$ 1.11874e10 0.428060 0.214030 0.976827i $$-0.431341\pi$$
0.214030 + 0.976827i $$0.431341\pi$$
$$948$$ 2.10872e9 0.0803877
$$949$$ 6.73560e9 0.255826
$$950$$ −2.21080e10 −0.836597
$$951$$ −2.60104e10 −0.980653
$$952$$ 6.71695e9 0.252315
$$953$$ −1.85383e10 −0.693817 −0.346908 0.937899i $$-0.612768\pi$$
−0.346908 + 0.937899i $$0.612768\pi$$
$$954$$ −9.47216e9 −0.353207
$$955$$ −2.39463e10 −0.889663
$$956$$ −4.83170e9 −0.178854
$$957$$ 1.47755e10 0.544944
$$958$$ 1.49287e10 0.548582
$$959$$ −1.78828e10 −0.654743
$$960$$ −3.02789e9 −0.110456
$$961$$ 4.58016e9 0.166475
$$962$$ −9.06915e9 −0.328438
$$963$$ −1.28157e10 −0.462433
$$964$$ 2.76596e10 0.994436
$$965$$ −3.43401e10 −1.23015
$$966$$ −9.07811e8 −0.0324023
$$967$$ −7.91753e9 −0.281577 −0.140788 0.990040i $$-0.544964\pi$$
−0.140788 + 0.990040i $$0.544964\pi$$
$$968$$ −7.54076e9 −0.267209
$$969$$ −2.70183e10 −0.953947
$$970$$ −3.07265e10 −1.08096
$$971$$ −3.25866e10 −1.14228 −0.571139 0.820853i $$-0.693498\pi$$
−0.571139 + 0.820853i $$0.693498\pi$$
$$972$$ 9.18330e8 0.0320750
$$973$$ −4.40723e9 −0.153381
$$974$$ −7.63201e9 −0.264656
$$975$$ −7.39228e9 −0.255424
$$976$$ 1.04354e10 0.359282
$$977$$ 6.25658e9 0.214638 0.107319 0.994225i $$-0.465773\pi$$
0.107319 + 0.994225i $$0.465773\pi$$
$$978$$ −1.55886e10 −0.532869
$$979$$ 2.61780e9 0.0891656
$$980$$ 1.92808e10 0.654387
$$981$$ 1.19995e10 0.405807
$$982$$ 9.69467e9 0.326695
$$983$$ 8.04489e9 0.270136 0.135068 0.990836i $$-0.456875\pi$$
0.135068 + 0.990836i $$0.456875\pi$$
$$984$$ −2.77073e9 −0.0927066
$$985$$ −1.50791e10 −0.502746
$$986$$ 7.62166e10 2.53210
$$987$$ −1.86555e9 −0.0617586
$$988$$ 4.40185e9 0.145207
$$989$$ −1.02367e10 −0.336489
$$990$$ −5.44274e9 −0.178277
$$991$$ −3.99983e10 −1.30552 −0.652761 0.757564i $$-0.726389\pi$$
−0.652761 + 0.757564i $$0.726389\pi$$
$$992$$ 5.87021e9 0.190925
$$993$$ −1.15080e10 −0.372972
$$994$$ 1.11336e10 0.359571
$$995$$ −1.86908e10 −0.601515
$$996$$ −3.74258e9 −0.120023
$$997$$ 3.00799e10 0.961267 0.480633 0.876922i $$-0.340407\pi$$
0.480633 + 0.876922i $$0.340407\pi$$
$$998$$ −9.36774e9 −0.298317
$$999$$ 8.54795e9 0.271258
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.1.1 4
3.2 odd 2 414.8.a.i.1.4 4

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