# Properties

 Label 98.4.c.a.79.1 Level $98$ Weight $4$ Character 98.79 Analytic conductor $5.782$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$98 = 2 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 98.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.78218718056$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 14) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 79.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 98.79 Dual form 98.4.c.a.67.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00000 + 1.73205i) q^{2} +(-2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.50000 + 7.79423i) q^{5} +10.0000 q^{6} +8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+(-1.00000 + 1.73205i) q^{2} +(-2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.50000 + 7.79423i) q^{5} +10.0000 q^{6} +8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(-9.00000 - 15.5885i) q^{10} +(28.5000 + 49.3634i) q^{11} +(-10.0000 + 17.3205i) q^{12} +70.0000 q^{13} +45.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(25.5000 + 44.1673i) q^{17} +(2.00000 + 3.46410i) q^{18} +(2.50000 - 4.33013i) q^{19} +36.0000 q^{20} -114.000 q^{22} +(-34.5000 + 59.7558i) q^{23} +(-20.0000 - 34.6410i) q^{24} +(22.0000 + 38.1051i) q^{25} +(-70.0000 + 121.244i) q^{26} -145.000 q^{27} +114.000 q^{29} +(-45.0000 + 77.9423i) q^{30} +(11.5000 + 19.9186i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(142.500 - 246.817i) q^{33} -102.000 q^{34} -8.00000 q^{36} +(126.500 - 219.104i) q^{37} +(5.00000 + 8.66025i) q^{38} +(-175.000 - 303.109i) q^{39} +(-36.0000 + 62.3538i) q^{40} +42.0000 q^{41} -124.000 q^{43} +(114.000 - 197.454i) q^{44} +(9.00000 + 15.5885i) q^{45} +(-69.0000 - 119.512i) q^{46} +(100.500 - 174.071i) q^{47} +80.0000 q^{48} -88.0000 q^{50} +(127.500 - 220.836i) q^{51} +(-140.000 - 242.487i) q^{52} +(196.500 + 340.348i) q^{53} +(145.000 - 251.147i) q^{54} -513.000 q^{55} -25.0000 q^{57} +(-114.000 + 197.454i) q^{58} +(109.500 + 189.660i) q^{59} +(-90.0000 - 155.885i) q^{60} +(-354.500 + 614.012i) q^{61} -46.0000 q^{62} +64.0000 q^{64} +(-315.000 + 545.596i) q^{65} +(285.000 + 493.634i) q^{66} +(-209.500 - 362.865i) q^{67} +(102.000 - 176.669i) q^{68} +345.000 q^{69} -96.0000 q^{71} +(8.00000 - 13.8564i) q^{72} +(-156.500 - 271.066i) q^{73} +(253.000 + 438.209i) q^{74} +(110.000 - 190.526i) q^{75} -20.0000 q^{76} +700.000 q^{78} +(-230.500 + 399.238i) q^{79} +(-72.0000 - 124.708i) q^{80} +(335.500 + 581.103i) q^{81} +(-42.0000 + 72.7461i) q^{82} +588.000 q^{83} -459.000 q^{85} +(124.000 - 214.774i) q^{86} +(-285.000 - 493.634i) q^{87} +(228.000 + 394.908i) q^{88} +(-508.500 + 880.748i) q^{89} -36.0000 q^{90} +276.000 q^{92} +(57.5000 - 99.5929i) q^{93} +(201.000 + 348.142i) q^{94} +(22.5000 + 38.9711i) q^{95} +(-80.0000 + 138.564i) q^{96} +1834.00 q^{97} +114.000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{2} - 5 q^{3} - 4 q^{4} - 9 q^{5} + 20 q^{6} + 16 q^{8} + 2 q^{9}+O(q^{10})$$ 2 * q - 2 * q^2 - 5 * q^3 - 4 * q^4 - 9 * q^5 + 20 * q^6 + 16 * q^8 + 2 * q^9 $$2 q - 2 q^{2} - 5 q^{3} - 4 q^{4} - 9 q^{5} + 20 q^{6} + 16 q^{8} + 2 q^{9} - 18 q^{10} + 57 q^{11} - 20 q^{12} + 140 q^{13} + 90 q^{15} - 16 q^{16} + 51 q^{17} + 4 q^{18} + 5 q^{19} + 72 q^{20} - 228 q^{22} - 69 q^{23} - 40 q^{24} + 44 q^{25} - 140 q^{26} - 290 q^{27} + 228 q^{29} - 90 q^{30} + 23 q^{31} - 32 q^{32} + 285 q^{33} - 204 q^{34} - 16 q^{36} + 253 q^{37} + 10 q^{38} - 350 q^{39} - 72 q^{40} + 84 q^{41} - 248 q^{43} + 228 q^{44} + 18 q^{45} - 138 q^{46} + 201 q^{47} + 160 q^{48} - 176 q^{50} + 255 q^{51} - 280 q^{52} + 393 q^{53} + 290 q^{54} - 1026 q^{55} - 50 q^{57} - 228 q^{58} + 219 q^{59} - 180 q^{60} - 709 q^{61} - 92 q^{62} + 128 q^{64} - 630 q^{65} + 570 q^{66} - 419 q^{67} + 204 q^{68} + 690 q^{69} - 192 q^{71} + 16 q^{72} - 313 q^{73} + 506 q^{74} + 220 q^{75} - 40 q^{76} + 1400 q^{78} - 461 q^{79} - 144 q^{80} + 671 q^{81} - 84 q^{82} + 1176 q^{83} - 918 q^{85} + 248 q^{86} - 570 q^{87} + 456 q^{88} - 1017 q^{89} - 72 q^{90} + 552 q^{92} + 115 q^{93} + 402 q^{94} + 45 q^{95} - 160 q^{96} + 3668 q^{97} + 228 q^{99}+O(q^{100})$$ 2 * q - 2 * q^2 - 5 * q^3 - 4 * q^4 - 9 * q^5 + 20 * q^6 + 16 * q^8 + 2 * q^9 - 18 * q^10 + 57 * q^11 - 20 * q^12 + 140 * q^13 + 90 * q^15 - 16 * q^16 + 51 * q^17 + 4 * q^18 + 5 * q^19 + 72 * q^20 - 228 * q^22 - 69 * q^23 - 40 * q^24 + 44 * q^25 - 140 * q^26 - 290 * q^27 + 228 * q^29 - 90 * q^30 + 23 * q^31 - 32 * q^32 + 285 * q^33 - 204 * q^34 - 16 * q^36 + 253 * q^37 + 10 * q^38 - 350 * q^39 - 72 * q^40 + 84 * q^41 - 248 * q^43 + 228 * q^44 + 18 * q^45 - 138 * q^46 + 201 * q^47 + 160 * q^48 - 176 * q^50 + 255 * q^51 - 280 * q^52 + 393 * q^53 + 290 * q^54 - 1026 * q^55 - 50 * q^57 - 228 * q^58 + 219 * q^59 - 180 * q^60 - 709 * q^61 - 92 * q^62 + 128 * q^64 - 630 * q^65 + 570 * q^66 - 419 * q^67 + 204 * q^68 + 690 * q^69 - 192 * q^71 + 16 * q^72 - 313 * q^73 + 506 * q^74 + 220 * q^75 - 40 * q^76 + 1400 * q^78 - 461 * q^79 - 144 * q^80 + 671 * q^81 - 84 * q^82 + 1176 * q^83 - 918 * q^85 + 248 * q^86 - 570 * q^87 + 456 * q^88 - 1017 * q^89 - 72 * q^90 + 552 * q^92 + 115 * q^93 + 402 * q^94 + 45 * q^95 - 160 * q^96 + 3668 * q^97 + 228 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 + 1.73205i −0.353553 + 0.612372i
$$3$$ −2.50000 4.33013i −0.481125 0.833333i 0.518640 0.854993i $$-0.326438\pi$$
−0.999765 + 0.0216593i $$0.993105\pi$$
$$4$$ −2.00000 3.46410i −0.250000 0.433013i
$$5$$ −4.50000 + 7.79423i −0.402492 + 0.697137i −0.994026 0.109143i $$-0.965189\pi$$
0.591534 + 0.806280i $$0.298523\pi$$
$$6$$ 10.0000 0.680414
$$7$$ 0 0
$$8$$ 8.00000 0.353553
$$9$$ 1.00000 1.73205i 0.0370370 0.0641500i
$$10$$ −9.00000 15.5885i −0.284605 0.492950i
$$11$$ 28.5000 + 49.3634i 0.781188 + 1.35306i 0.931250 + 0.364381i $$0.118720\pi$$
−0.150061 + 0.988677i $$0.547947\pi$$
$$12$$ −10.0000 + 17.3205i −0.240563 + 0.416667i
$$13$$ 70.0000 1.49342 0.746712 0.665148i $$-0.231631\pi$$
0.746712 + 0.665148i $$0.231631\pi$$
$$14$$ 0 0
$$15$$ 45.0000 0.774597
$$16$$ −8.00000 + 13.8564i −0.125000 + 0.216506i
$$17$$ 25.5000 + 44.1673i 0.363803 + 0.630126i 0.988583 0.150675i $$-0.0481447\pi$$
−0.624780 + 0.780801i $$0.714811\pi$$
$$18$$ 2.00000 + 3.46410i 0.0261891 + 0.0453609i
$$19$$ 2.50000 4.33013i 0.0301863 0.0522842i −0.850538 0.525914i $$-0.823723\pi$$
0.880724 + 0.473630i $$0.157057\pi$$
$$20$$ 36.0000 0.402492
$$21$$ 0 0
$$22$$ −114.000 −1.10477
$$23$$ −34.5000 + 59.7558i −0.312772 + 0.541736i −0.978961 0.204046i $$-0.934591\pi$$
0.666190 + 0.745782i $$0.267924\pi$$
$$24$$ −20.0000 34.6410i −0.170103 0.294628i
$$25$$ 22.0000 + 38.1051i 0.176000 + 0.304841i
$$26$$ −70.0000 + 121.244i −0.528005 + 0.914531i
$$27$$ −145.000 −1.03353
$$28$$ 0 0
$$29$$ 114.000 0.729975 0.364987 0.931012i $$-0.381073\pi$$
0.364987 + 0.931012i $$0.381073\pi$$
$$30$$ −45.0000 + 77.9423i −0.273861 + 0.474342i
$$31$$ 11.5000 + 19.9186i 0.0666278 + 0.115403i 0.897415 0.441188i $$-0.145443\pi$$
−0.830787 + 0.556590i $$0.812109\pi$$
$$32$$ −16.0000 27.7128i −0.0883883 0.153093i
$$33$$ 142.500 246.817i 0.751699 1.30198i
$$34$$ −102.000 −0.514496
$$35$$ 0 0
$$36$$ −8.00000 −0.0370370
$$37$$ 126.500 219.104i 0.562067 0.973528i −0.435249 0.900310i $$-0.643340\pi$$
0.997316 0.0732182i $$-0.0233270\pi$$
$$38$$ 5.00000 + 8.66025i 0.0213449 + 0.0369705i
$$39$$ −175.000 303.109i −0.718524 1.24452i
$$40$$ −36.0000 + 62.3538i −0.142302 + 0.246475i
$$41$$ 42.0000 0.159983 0.0799914 0.996796i $$-0.474511\pi$$
0.0799914 + 0.996796i $$0.474511\pi$$
$$42$$ 0 0
$$43$$ −124.000 −0.439763 −0.219882 0.975527i $$-0.570567\pi$$
−0.219882 + 0.975527i $$0.570567\pi$$
$$44$$ 114.000 197.454i 0.390594 0.676529i
$$45$$ 9.00000 + 15.5885i 0.0298142 + 0.0516398i
$$46$$ −69.0000 119.512i −0.221163 0.383065i
$$47$$ 100.500 174.071i 0.311903 0.540231i −0.666871 0.745173i $$-0.732367\pi$$
0.978774 + 0.204941i $$0.0657003\pi$$
$$48$$ 80.0000 0.240563
$$49$$ 0 0
$$50$$ −88.0000 −0.248902
$$51$$ 127.500 220.836i 0.350070 0.606339i
$$52$$ −140.000 242.487i −0.373356 0.646671i
$$53$$ 196.500 + 340.348i 0.509271 + 0.882083i 0.999942 + 0.0107383i $$0.00341816\pi$$
−0.490672 + 0.871345i $$0.663249\pi$$
$$54$$ 145.000 251.147i 0.365407 0.632904i
$$55$$ −513.000 −1.25769
$$56$$ 0 0
$$57$$ −25.0000 −0.0580935
$$58$$ −114.000 + 197.454i −0.258085 + 0.447016i
$$59$$ 109.500 + 189.660i 0.241622 + 0.418501i 0.961176 0.275935i $$-0.0889873\pi$$
−0.719555 + 0.694436i $$0.755654\pi$$
$$60$$ −90.0000 155.885i −0.193649 0.335410i
$$61$$ −354.500 + 614.012i −0.744083 + 1.28879i 0.206539 + 0.978438i $$0.433780\pi$$
−0.950622 + 0.310351i $$0.899553\pi$$
$$62$$ −46.0000 −0.0942259
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −315.000 + 545.596i −0.601091 + 1.04112i
$$66$$ 285.000 + 493.634i 0.531531 + 0.920639i
$$67$$ −209.500 362.865i −0.382007 0.661656i 0.609342 0.792908i $$-0.291434\pi$$
−0.991349 + 0.131251i $$0.958100\pi$$
$$68$$ 102.000 176.669i 0.181902 0.315063i
$$69$$ 345.000 0.601929
$$70$$ 0 0
$$71$$ −96.0000 −0.160466 −0.0802331 0.996776i $$-0.525566\pi$$
−0.0802331 + 0.996776i $$0.525566\pi$$
$$72$$ 8.00000 13.8564i 0.0130946 0.0226805i
$$73$$ −156.500 271.066i −0.250917 0.434601i 0.712862 0.701305i $$-0.247399\pi$$
−0.963779 + 0.266704i $$0.914065\pi$$
$$74$$ 253.000 + 438.209i 0.397441 + 0.688388i
$$75$$ 110.000 190.526i 0.169356 0.293333i
$$76$$ −20.0000 −0.0301863
$$77$$ 0 0
$$78$$ 700.000 1.01615
$$79$$ −230.500 + 399.238i −0.328269 + 0.568579i −0.982169 0.188003i $$-0.939799\pi$$
0.653899 + 0.756582i $$0.273132\pi$$
$$80$$ −72.0000 124.708i −0.100623 0.174284i
$$81$$ 335.500 + 581.103i 0.460219 + 0.797124i
$$82$$ −42.0000 + 72.7461i −0.0565625 + 0.0979691i
$$83$$ 588.000 0.777607 0.388804 0.921321i $$-0.372888\pi$$
0.388804 + 0.921321i $$0.372888\pi$$
$$84$$ 0 0
$$85$$ −459.000 −0.585712
$$86$$ 124.000 214.774i 0.155480 0.269299i
$$87$$ −285.000 493.634i −0.351209 0.608312i
$$88$$ 228.000 + 394.908i 0.276192 + 0.478378i
$$89$$ −508.500 + 880.748i −0.605628 + 1.04898i 0.386324 + 0.922363i $$0.373745\pi$$
−0.991952 + 0.126615i $$0.959589\pi$$
$$90$$ −36.0000 −0.0421637
$$91$$ 0 0
$$92$$ 276.000 0.312772
$$93$$ 57.5000 99.5929i 0.0641126 0.111046i
$$94$$ 201.000 + 348.142i 0.220549 + 0.382001i
$$95$$ 22.5000 + 38.9711i 0.0242995 + 0.0420879i
$$96$$ −80.0000 + 138.564i −0.0850517 + 0.147314i
$$97$$ 1834.00 1.91974 0.959868 0.280451i $$-0.0904839\pi$$
0.959868 + 0.280451i $$0.0904839\pi$$
$$98$$ 0 0
$$99$$ 114.000 0.115732
$$100$$ 88.0000 152.420i 0.0880000 0.152420i
$$101$$ −142.500 246.817i −0.140389 0.243161i 0.787254 0.616629i $$-0.211502\pi$$
−0.927643 + 0.373468i $$0.878169\pi$$
$$102$$ 255.000 + 441.673i 0.247537 + 0.428746i
$$103$$ −249.500 + 432.147i −0.238679 + 0.413405i −0.960336 0.278847i $$-0.910048\pi$$
0.721656 + 0.692252i $$0.243381\pi$$
$$104$$ 560.000 0.528005
$$105$$ 0 0
$$106$$ −786.000 −0.720218
$$107$$ 553.500 958.690i 0.500083 0.866169i −0.499917 0.866073i $$-0.666636\pi$$
1.00000 9.56665e-5i $$-3.04516e-5\pi$$
$$108$$ 290.000 + 502.295i 0.258382 + 0.447531i
$$109$$ −461.500 799.341i −0.405538 0.702413i 0.588846 0.808246i $$-0.299583\pi$$
−0.994384 + 0.105832i $$0.966249\pi$$
$$110$$ 513.000 888.542i 0.444660 0.770174i
$$111$$ −1265.00 −1.08170
$$112$$ 0 0
$$113$$ 1542.00 1.28371 0.641855 0.766826i $$-0.278165\pi$$
0.641855 + 0.766826i $$0.278165\pi$$
$$114$$ 25.0000 43.3013i 0.0205392 0.0355749i
$$115$$ −310.500 537.802i −0.251776 0.436089i
$$116$$ −228.000 394.908i −0.182494 0.316088i
$$117$$ 70.0000 121.244i 0.0553120 0.0958032i
$$118$$ −438.000 −0.341705
$$119$$ 0 0
$$120$$ 360.000 0.273861
$$121$$ −959.000 + 1661.04i −0.720511 + 1.24796i
$$122$$ −709.000 1228.02i −0.526146 0.911312i
$$123$$ −105.000 181.865i −0.0769718 0.133319i
$$124$$ 46.0000 79.6743i 0.0333139 0.0577013i
$$125$$ −1521.00 −1.08834
$$126$$ 0 0
$$127$$ −2056.00 −1.43654 −0.718270 0.695765i $$-0.755066\pi$$
−0.718270 + 0.695765i $$0.755066\pi$$
$$128$$ −64.0000 + 110.851i −0.0441942 + 0.0765466i
$$129$$ 310.000 + 536.936i 0.211581 + 0.366469i
$$130$$ −630.000 1091.19i −0.425036 0.736184i
$$131$$ 1024.50 1774.49i 0.683290 1.18349i −0.290681 0.956820i $$-0.593882\pi$$
0.973971 0.226673i $$-0.0727848\pi$$
$$132$$ −1140.00 −0.751699
$$133$$ 0 0
$$134$$ 838.000 0.540240
$$135$$ 652.500 1130.16i 0.415987 0.720511i
$$136$$ 204.000 + 353.338i 0.128624 + 0.222783i
$$137$$ 70.5000 + 122.110i 0.0439651 + 0.0761498i 0.887171 0.461442i $$-0.152668\pi$$
−0.843205 + 0.537591i $$0.819334\pi$$
$$138$$ −345.000 + 597.558i −0.212814 + 0.368605i
$$139$$ −1484.00 −0.905548 −0.452774 0.891625i $$-0.649566\pi$$
−0.452774 + 0.891625i $$0.649566\pi$$
$$140$$ 0 0
$$141$$ −1005.00 −0.600257
$$142$$ 96.0000 166.277i 0.0567334 0.0982651i
$$143$$ 1995.00 + 3455.44i 1.16665 + 2.02069i
$$144$$ 16.0000 + 27.7128i 0.00925926 + 0.0160375i
$$145$$ −513.000 + 888.542i −0.293809 + 0.508892i
$$146$$ 626.000 0.354850
$$147$$ 0 0
$$148$$ −1012.00 −0.562067
$$149$$ 28.5000 49.3634i 0.0156699 0.0271410i −0.858084 0.513509i $$-0.828345\pi$$
0.873754 + 0.486368i $$0.161679\pi$$
$$150$$ 220.000 + 381.051i 0.119753 + 0.207418i
$$151$$ −419.500 726.595i −0.226082 0.391586i 0.730561 0.682847i $$-0.239258\pi$$
−0.956644 + 0.291261i $$0.905925\pi$$
$$152$$ 20.0000 34.6410i 0.0106725 0.0184852i
$$153$$ 102.000 0.0538968
$$154$$ 0 0
$$155$$ −207.000 −0.107269
$$156$$ −700.000 + 1212.44i −0.359262 + 0.622260i
$$157$$ −1416.50 2453.45i −0.720057 1.24718i −0.960976 0.276631i $$-0.910782\pi$$
0.240919 0.970545i $$-0.422551\pi$$
$$158$$ −461.000 798.475i −0.232121 0.402046i
$$159$$ 982.500 1701.74i 0.490046 0.848785i
$$160$$ 288.000 0.142302
$$161$$ 0 0
$$162$$ −1342.00 −0.650849
$$163$$ 1155.50 2001.38i 0.555250 0.961721i −0.442634 0.896702i $$-0.645956\pi$$
0.997884 0.0650188i $$-0.0207107\pi$$
$$164$$ −84.0000 145.492i −0.0399957 0.0692746i
$$165$$ 1282.50 + 2221.36i 0.605106 + 1.04807i
$$166$$ −588.000 + 1018.45i −0.274926 + 0.476185i
$$167$$ −1260.00 −0.583843 −0.291921 0.956442i $$-0.594295\pi$$
−0.291921 + 0.956442i $$0.594295\pi$$
$$168$$ 0 0
$$169$$ 2703.00 1.23031
$$170$$ 459.000 795.011i 0.207081 0.358674i
$$171$$ −5.00000 8.66025i −0.00223602 0.00387290i
$$172$$ 248.000 + 429.549i 0.109941 + 0.190423i
$$173$$ 1633.50 2829.30i 0.717877 1.24340i −0.243962 0.969785i $$-0.578447\pi$$
0.961839 0.273615i $$-0.0882193\pi$$
$$174$$ 1140.00 0.496685
$$175$$ 0 0
$$176$$ −912.000 −0.390594
$$177$$ 547.500 948.298i 0.232501 0.402703i
$$178$$ −1017.00 1761.50i −0.428244 0.741740i
$$179$$ −643.500 1114.57i −0.268701 0.465403i 0.699826 0.714314i $$-0.253261\pi$$
−0.968527 + 0.248910i $$0.919928\pi$$
$$180$$ 36.0000 62.3538i 0.0149071 0.0258199i
$$181$$ 2674.00 1.09810 0.549052 0.835788i $$-0.314989\pi$$
0.549052 + 0.835788i $$0.314989\pi$$
$$182$$ 0 0
$$183$$ 3545.00 1.43199
$$184$$ −276.000 + 478.046i −0.110581 + 0.191533i
$$185$$ 1138.50 + 1971.94i 0.452455 + 0.783675i
$$186$$ 115.000 + 199.186i 0.0453345 + 0.0785216i
$$187$$ −1453.50 + 2517.54i −0.568398 + 0.984494i
$$188$$ −804.000 −0.311903
$$189$$ 0 0
$$190$$ −90.0000 −0.0343647
$$191$$ −2092.50 + 3624.32i −0.792712 + 1.37302i 0.131570 + 0.991307i $$0.457998\pi$$
−0.924282 + 0.381711i $$0.875335\pi$$
$$192$$ −160.000 277.128i −0.0601407 0.104167i
$$193$$ 42.5000 + 73.6122i 0.0158509 + 0.0274545i 0.873842 0.486210i $$-0.161621\pi$$
−0.857991 + 0.513664i $$0.828288\pi$$
$$194$$ −1834.00 + 3176.58i −0.678730 + 1.17559i
$$195$$ 3150.00 1.15680
$$196$$ 0 0
$$197$$ −390.000 −0.141047 −0.0705237 0.997510i $$-0.522467\pi$$
−0.0705237 + 0.997510i $$0.522467\pi$$
$$198$$ −114.000 + 197.454i −0.0409173 + 0.0708709i
$$199$$ −1416.50 2453.45i −0.504588 0.873972i −0.999986 0.00530596i $$-0.998311\pi$$
0.495398 0.868666i $$-0.335022\pi$$
$$200$$ 176.000 + 304.841i 0.0622254 + 0.107778i
$$201$$ −1047.50 + 1814.32i −0.367587 + 0.636679i
$$202$$ 570.000 0.198540
$$203$$ 0 0
$$204$$ −1020.00 −0.350070
$$205$$ −189.000 + 327.358i −0.0643919 + 0.111530i
$$206$$ −499.000 864.293i −0.168772 0.292321i
$$207$$ 69.0000 + 119.512i 0.0231683 + 0.0401286i
$$208$$ −560.000 + 969.948i −0.186678 + 0.323336i
$$209$$ 285.000 0.0943247
$$210$$ 0 0
$$211$$ −124.000 −0.0404574 −0.0202287 0.999795i $$-0.506439\pi$$
−0.0202287 + 0.999795i $$0.506439\pi$$
$$212$$ 786.000 1361.39i 0.254635 0.441041i
$$213$$ 240.000 + 415.692i 0.0772044 + 0.133722i
$$214$$ 1107.00 + 1917.38i 0.353612 + 0.612474i
$$215$$ 558.000 966.484i 0.177001 0.306575i
$$216$$ −1160.00 −0.365407
$$217$$ 0 0
$$218$$ 1846.00 0.573518
$$219$$ −782.500 + 1355.33i −0.241445 + 0.418195i
$$220$$ 1026.00 + 1777.08i 0.314422 + 0.544595i
$$221$$ 1785.00 + 3091.71i 0.543313 + 0.941045i
$$222$$ 1265.00 2191.04i 0.382438 0.662402i
$$223$$ −56.0000 −0.0168163 −0.00840816 0.999965i $$-0.502676\pi$$
−0.00840816 + 0.999965i $$0.502676\pi$$
$$224$$ 0 0
$$225$$ 88.0000 0.0260741
$$226$$ −1542.00 + 2670.82i −0.453860 + 0.786108i
$$227$$ −1528.50 2647.44i −0.446917 0.774083i 0.551267 0.834329i $$-0.314145\pi$$
−0.998184 + 0.0602465i $$0.980811\pi$$
$$228$$ 50.0000 + 86.6025i 0.0145234 + 0.0251552i
$$229$$ −480.500 + 832.250i −0.138656 + 0.240160i −0.926988 0.375090i $$-0.877612\pi$$
0.788332 + 0.615250i $$0.210945\pi$$
$$230$$ 1242.00 0.356065
$$231$$ 0 0
$$232$$ 912.000 0.258085
$$233$$ 1414.50 2449.99i 0.397712 0.688858i −0.595731 0.803184i $$-0.703138\pi$$
0.993443 + 0.114326i $$0.0364709\pi$$
$$234$$ 140.000 + 242.487i 0.0391115 + 0.0677431i
$$235$$ 904.500 + 1566.64i 0.251077 + 0.434878i
$$236$$ 438.000 758.638i 0.120811 0.209251i
$$237$$ 2305.00 0.631755
$$238$$ 0 0
$$239$$ −3540.00 −0.958090 −0.479045 0.877790i $$-0.659017\pi$$
−0.479045 + 0.877790i $$0.659017\pi$$
$$240$$ −360.000 + 623.538i −0.0968246 + 0.167705i
$$241$$ 2615.50 + 4530.18i 0.699084 + 1.21085i 0.968785 + 0.247904i $$0.0797419\pi$$
−0.269701 + 0.962944i $$0.586925\pi$$
$$242$$ −1918.00 3322.07i −0.509478 0.882442i
$$243$$ −280.000 + 484.974i −0.0739177 + 0.128029i
$$244$$ 2836.00 0.744083
$$245$$ 0 0
$$246$$ 420.000 0.108855
$$247$$ 175.000 303.109i 0.0450809 0.0780824i
$$248$$ 92.0000 + 159.349i 0.0235565 + 0.0408010i
$$249$$ −1470.00 2546.11i −0.374126 0.648006i
$$250$$ 1521.00 2634.45i 0.384786 0.666469i
$$251$$ −5040.00 −1.26742 −0.633709 0.773571i $$-0.718468\pi$$
−0.633709 + 0.773571i $$0.718468\pi$$
$$252$$ 0 0
$$253$$ −3933.00 −0.977334
$$254$$ 2056.00 3561.10i 0.507893 0.879697i
$$255$$ 1147.50 + 1987.53i 0.281801 + 0.488094i
$$256$$ −128.000 221.703i −0.0312500 0.0541266i
$$257$$ −718.500 + 1244.48i −0.174392 + 0.302056i −0.939951 0.341310i $$-0.889129\pi$$
0.765559 + 0.643366i $$0.222463\pi$$
$$258$$ −1240.00 −0.299221
$$259$$ 0 0
$$260$$ 2520.00 0.601091
$$261$$ 114.000 197.454i 0.0270361 0.0468279i
$$262$$ 2049.00 + 3548.97i 0.483159 + 0.836856i
$$263$$ 1162.50 + 2013.51i 0.272558 + 0.472085i 0.969516 0.245027i $$-0.0787969\pi$$
−0.696958 + 0.717112i $$0.745464\pi$$
$$264$$ 1140.00 1974.54i 0.265766 0.460320i
$$265$$ −3537.00 −0.819910
$$266$$ 0 0
$$267$$ 5085.00 1.16553
$$268$$ −838.000 + 1451.46i −0.191004 + 0.330828i
$$269$$ −1192.50 2065.47i −0.270290 0.468156i 0.698646 0.715467i $$-0.253786\pi$$
−0.968936 + 0.247311i $$0.920453\pi$$
$$270$$ 1305.00 + 2260.33i 0.294147 + 0.509478i
$$271$$ −165.500 + 286.654i −0.0370975 + 0.0642547i −0.883978 0.467528i $$-0.845145\pi$$
0.846881 + 0.531783i $$0.178478\pi$$
$$272$$ −816.000 −0.181902
$$273$$ 0 0
$$274$$ −282.000 −0.0621761
$$275$$ −1254.00 + 2171.99i −0.274978 + 0.476276i
$$276$$ −690.000 1195.12i −0.150482 0.260643i
$$277$$ −2435.50 4218.41i −0.528285 0.915017i −0.999456 0.0329750i $$-0.989502\pi$$
0.471171 0.882042i $$-0.343831\pi$$
$$278$$ 1484.00 2570.36i 0.320160 0.554533i
$$279$$ 46.0000 0.00987078
$$280$$ 0 0
$$281$$ −7026.00 −1.49159 −0.745794 0.666177i $$-0.767930\pi$$
−0.745794 + 0.666177i $$0.767930\pi$$
$$282$$ 1005.00 1740.71i 0.212223 0.367581i
$$283$$ −2676.50 4635.83i −0.562196 0.973752i −0.997305 0.0733738i $$-0.976623\pi$$
0.435109 0.900378i $$-0.356710\pi$$
$$284$$ 192.000 + 332.554i 0.0401166 + 0.0694839i
$$285$$ 112.500 194.856i 0.0233822 0.0404991i
$$286$$ −7980.00 −1.64989
$$287$$ 0 0
$$288$$ −64.0000 −0.0130946
$$289$$ 1156.00 2002.25i 0.235294 0.407541i
$$290$$ −1026.00 1777.08i −0.207754 0.359841i
$$291$$ −4585.00 7941.45i −0.923634 1.59978i
$$292$$ −626.000 + 1084.26i −0.125458 + 0.217300i
$$293$$ −4158.00 −0.829054 −0.414527 0.910037i $$-0.636053\pi$$
−0.414527 + 0.910037i $$0.636053\pi$$
$$294$$ 0 0
$$295$$ −1971.00 −0.389004
$$296$$ 1012.00 1752.84i 0.198721 0.344194i
$$297$$ −4132.50 7157.70i −0.807380 1.39842i
$$298$$ 57.0000 + 98.7269i 0.0110803 + 0.0191916i
$$299$$ −2415.00 + 4182.90i −0.467101 + 0.809042i
$$300$$ −880.000 −0.169356
$$301$$ 0 0
$$302$$ 1678.00 0.319729
$$303$$ −712.500 + 1234.09i −0.135089 + 0.233982i
$$304$$ 40.0000 + 69.2820i 0.00754657 + 0.0130710i
$$305$$ −3190.50 5526.11i −0.598975 1.03746i
$$306$$ −102.000 + 176.669i −0.0190554 + 0.0330049i
$$307$$ 9604.00 1.78544 0.892719 0.450615i $$-0.148795\pi$$
0.892719 + 0.450615i $$0.148795\pi$$
$$308$$ 0 0
$$309$$ 2495.00 0.459338
$$310$$ 207.000 358.535i 0.0379252 0.0656884i
$$311$$ 5065.50 + 8773.70i 0.923595 + 1.59971i 0.793805 + 0.608173i $$0.208097\pi$$
0.129791 + 0.991541i $$0.458570\pi$$
$$312$$ −1400.00 2424.87i −0.254037 0.440004i
$$313$$ 5399.50 9352.21i 0.975073 1.68888i 0.295378 0.955380i $$-0.404554\pi$$
0.679695 0.733495i $$-0.262112\pi$$
$$314$$ 5666.00 1.01831
$$315$$ 0 0
$$316$$ 1844.00 0.328269
$$317$$ −265.500 + 459.859i −0.0470409 + 0.0814772i −0.888587 0.458708i $$-0.848312\pi$$
0.841546 + 0.540185i $$0.181646\pi$$
$$318$$ 1965.00 + 3403.48i 0.346515 + 0.600181i
$$319$$ 3249.00 + 5627.43i 0.570248 + 0.987698i
$$320$$ −288.000 + 498.831i −0.0503115 + 0.0871421i
$$321$$ −5535.00 −0.962410
$$322$$ 0 0
$$323$$ 255.000 0.0439275
$$324$$ 1342.00 2324.41i 0.230110 0.398562i
$$325$$ 1540.00 + 2667.36i 0.262843 + 0.455257i
$$326$$ 2311.00 + 4002.77i 0.392621 + 0.680040i
$$327$$ −2307.50 + 3996.71i −0.390229 + 0.675897i
$$328$$ 336.000 0.0565625
$$329$$ 0 0
$$330$$ −5130.00 −0.855749
$$331$$ 3507.50 6075.17i 0.582446 1.00883i −0.412743 0.910848i $$-0.635429\pi$$
0.995189 0.0979784i $$-0.0312376\pi$$
$$332$$ −1176.00 2036.89i −0.194402 0.336714i
$$333$$ −253.000 438.209i −0.0416346 0.0721132i
$$334$$ 1260.00 2182.38i 0.206420 0.357529i
$$335$$ 3771.00 0.615020
$$336$$ 0 0
$$337$$ 8990.00 1.45316 0.726582 0.687079i $$-0.241108\pi$$
0.726582 + 0.687079i $$0.241108\pi$$
$$338$$ −2703.00 + 4681.73i −0.434982 + 0.753410i
$$339$$ −3855.00 6677.06i −0.617625 1.06976i
$$340$$ 918.000 + 1590.02i 0.146428 + 0.253621i
$$341$$ −655.500 + 1135.36i −0.104098 + 0.180303i
$$342$$ 20.0000 0.00316221
$$343$$ 0 0
$$344$$ −992.000 −0.155480
$$345$$ −1552.50 + 2689.01i −0.242272 + 0.419627i
$$346$$ 3267.00 + 5658.61i 0.507616 + 0.879216i
$$347$$ 4354.50 + 7542.22i 0.673665 + 1.16682i 0.976857 + 0.213893i $$0.0686143\pi$$
−0.303192 + 0.952929i $$0.598052\pi$$
$$348$$ −1140.00 + 1974.54i −0.175605 + 0.304156i
$$349$$ −6482.00 −0.994193 −0.497097 0.867695i $$-0.665601\pi$$
−0.497097 + 0.867695i $$0.665601\pi$$
$$350$$ 0 0
$$351$$ −10150.0 −1.54350
$$352$$ 912.000 1579.63i 0.138096 0.239189i
$$353$$ −1066.50 1847.23i −0.160805 0.278522i 0.774353 0.632754i $$-0.218076\pi$$
−0.935158 + 0.354232i $$0.884742\pi$$
$$354$$ 1095.00 + 1896.60i 0.164403 + 0.284754i
$$355$$ 432.000 748.246i 0.0645864 0.111867i
$$356$$ 4068.00 0.605628
$$357$$ 0 0
$$358$$ 2574.00 0.380000
$$359$$ −1924.50 + 3333.33i −0.282928 + 0.490046i −0.972105 0.234548i $$-0.924639\pi$$
0.689176 + 0.724594i $$0.257972\pi$$
$$360$$ 72.0000 + 124.708i 0.0105409 + 0.0182574i
$$361$$ 3417.00 + 5918.42i 0.498178 + 0.862869i
$$362$$ −2674.00 + 4631.50i −0.388238 + 0.672449i
$$363$$ 9590.00 1.38662
$$364$$ 0 0
$$365$$ 2817.00 0.403969
$$366$$ −3545.00 + 6140.12i −0.506284 + 0.876910i
$$367$$ 3245.50 + 5621.37i 0.461618 + 0.799545i 0.999042 0.0437668i $$-0.0139358\pi$$
−0.537424 + 0.843312i $$0.680603\pi$$
$$368$$ −552.000 956.092i −0.0781929 0.135434i
$$369$$ 42.0000 72.7461i 0.00592529 0.0102629i
$$370$$ −4554.00 −0.639868
$$371$$ 0 0
$$372$$ −460.000 −0.0641126
$$373$$ −461.500 + 799.341i −0.0640632 + 0.110961i −0.896278 0.443493i $$-0.853739\pi$$
0.832215 + 0.554453i $$0.187073\pi$$
$$374$$ −2907.00 5035.07i −0.401918 0.696143i
$$375$$ 3802.50 + 6586.12i 0.523627 + 0.906949i
$$376$$ 804.000 1392.57i 0.110274 0.191001i
$$377$$ 7980.00 1.09016
$$378$$ 0 0
$$379$$ 6344.00 0.859814 0.429907 0.902873i $$-0.358546\pi$$
0.429907 + 0.902873i $$0.358546\pi$$
$$380$$ 90.0000 155.885i 0.0121497 0.0210440i
$$381$$ 5140.00 + 8902.74i 0.691155 + 1.19712i
$$382$$ −4185.00 7248.63i −0.560532 0.970870i
$$383$$ −2503.50 + 4336.19i −0.334002 + 0.578509i −0.983293 0.182032i $$-0.941733\pi$$
0.649290 + 0.760541i $$0.275066\pi$$
$$384$$ 640.000 0.0850517
$$385$$ 0 0
$$386$$ −170.000 −0.0224165
$$387$$ −124.000 + 214.774i −0.0162875 + 0.0282108i
$$388$$ −3668.00 6353.16i −0.479934 0.831270i
$$389$$ −6145.50 10644.3i −0.801001 1.38737i −0.918958 0.394355i $$-0.870968\pi$$
0.117958 0.993019i $$-0.462365\pi$$
$$390$$ −3150.00 + 5455.96i −0.408991 + 0.708393i
$$391$$ −3519.00 −0.455150
$$392$$ 0 0
$$393$$ −10245.0 −1.31499
$$394$$ 390.000 675.500i 0.0498678 0.0863736i
$$395$$ −2074.50 3593.14i −0.264252 0.457697i
$$396$$ −228.000 394.908i −0.0289329 0.0501133i
$$397$$ 443.500 768.165i 0.0560671 0.0971110i −0.836630 0.547769i $$-0.815477\pi$$
0.892697 + 0.450658i $$0.148811\pi$$
$$398$$ 5666.00 0.713595
$$399$$ 0 0
$$400$$ −704.000 −0.0880000
$$401$$ −5977.50 + 10353.3i −0.744394 + 1.28933i 0.206083 + 0.978535i $$0.433928\pi$$
−0.950477 + 0.310794i $$0.899405\pi$$
$$402$$ −2095.00 3628.65i −0.259923 0.450200i
$$403$$ 805.000 + 1394.30i 0.0995035 + 0.172345i
$$404$$ −570.000 + 987.269i −0.0701945 + 0.121580i
$$405$$ −6039.00 −0.740939
$$406$$ 0 0
$$407$$ 14421.0 1.75632
$$408$$ 1020.00 1766.69i 0.123768 0.214373i
$$409$$ −1710.50 2962.67i −0.206794 0.358178i 0.743909 0.668281i $$-0.232970\pi$$
−0.950703 + 0.310103i $$0.899636\pi$$
$$410$$ −378.000 654.715i −0.0455319 0.0788636i
$$411$$ 352.500 610.548i 0.0423055 0.0732752i
$$412$$ 1996.00 0.238679
$$413$$ 0 0
$$414$$ −276.000 −0.0327649
$$415$$ −2646.00 + 4583.01i −0.312981 + 0.542099i
$$416$$ −1120.00 1939.90i −0.132001 0.228633i
$$417$$ 3710.00 + 6425.91i 0.435682 + 0.754624i
$$418$$ −285.000 + 493.634i −0.0333488 + 0.0577618i
$$419$$ 5460.00 0.636607 0.318304 0.947989i $$-0.396887\pi$$
0.318304 + 0.947989i $$0.396887\pi$$
$$420$$ 0 0
$$421$$ 7730.00 0.894863 0.447431 0.894318i $$-0.352339\pi$$
0.447431 + 0.894318i $$0.352339\pi$$
$$422$$ 124.000 214.774i 0.0143039 0.0247750i
$$423$$ −201.000 348.142i −0.0231039 0.0400171i
$$424$$ 1572.00 + 2722.78i 0.180054 + 0.311863i
$$425$$ −1122.00 + 1943.36i −0.128059 + 0.221804i
$$426$$ −960.000 −0.109183
$$427$$ 0 0
$$428$$ −4428.00 −0.500083
$$429$$ 9975.00 17277.2i 1.12260 1.94441i
$$430$$ 1116.00 + 1932.97i 0.125159 + 0.216781i
$$431$$ 5656.50 + 9797.35i 0.632167 + 1.09495i 0.987108 + 0.160057i $$0.0511677\pi$$
−0.354941 + 0.934889i $$0.615499\pi$$
$$432$$ 1160.00 2009.18i 0.129191 0.223765i
$$433$$ −4214.00 −0.467695 −0.233847 0.972273i $$-0.575132\pi$$
−0.233847 + 0.972273i $$0.575132\pi$$
$$434$$ 0 0
$$435$$ 5130.00 0.565436
$$436$$ −1846.00 + 3197.37i −0.202769 + 0.351207i
$$437$$ 172.500 + 298.779i 0.0188828 + 0.0327060i
$$438$$ −1565.00 2710.66i −0.170727 0.295708i
$$439$$ 8276.50 14335.3i 0.899808 1.55851i 0.0720696 0.997400i $$-0.477040\pi$$
0.827739 0.561114i $$-0.189627\pi$$
$$440$$ −4104.00 −0.444660
$$441$$ 0 0
$$442$$ −7140.00 −0.768360
$$443$$ 8197.50 14198.5i 0.879176 1.52278i 0.0269294 0.999637i $$-0.491427\pi$$
0.852247 0.523140i $$-0.175240\pi$$
$$444$$ 2530.00 + 4382.09i 0.270425 + 0.468389i
$$445$$ −4576.50 7926.73i −0.487521 0.844411i
$$446$$ 56.0000 96.9948i 0.00594546 0.0102978i
$$447$$ −285.000 −0.0301567
$$448$$ 0 0
$$449$$ −15090.0 −1.58606 −0.793030 0.609182i $$-0.791498\pi$$
−0.793030 + 0.609182i $$0.791498\pi$$
$$450$$ −88.0000 + 152.420i −0.00921858 + 0.0159670i
$$451$$ 1197.00 + 2073.26i 0.124977 + 0.216466i
$$452$$ −3084.00 5341.64i −0.320927 0.555862i
$$453$$ −2097.50 + 3632.98i −0.217548 + 0.376804i
$$454$$ 6114.00 0.632036
$$455$$ 0 0
$$456$$ −200.000 −0.0205392
$$457$$ 7392.50 12804.2i 0.756688 1.31062i −0.187842 0.982199i $$-0.560149\pi$$
0.944531 0.328423i $$-0.106517\pi$$
$$458$$ −961.000 1664.50i −0.0980449 0.169819i
$$459$$ −3697.50 6404.26i −0.376001 0.651253i
$$460$$ −1242.00 + 2151.21i −0.125888 + 0.218045i
$$461$$ −2898.00 −0.292784 −0.146392 0.989227i $$-0.546766\pi$$
−0.146392 + 0.989227i $$0.546766\pi$$
$$462$$ 0 0
$$463$$ 464.000 0.0465743 0.0232872 0.999729i $$-0.492587\pi$$
0.0232872 + 0.999729i $$0.492587\pi$$
$$464$$ −912.000 + 1579.63i −0.0912468 + 0.158044i
$$465$$ 517.500 + 896.336i 0.0516097 + 0.0893905i
$$466$$ 2829.00 + 4899.97i 0.281225 + 0.487096i
$$467$$ 2116.50 3665.89i 0.209721 0.363248i −0.741905 0.670505i $$-0.766078\pi$$
0.951627 + 0.307256i $$0.0994109\pi$$
$$468$$ −560.000 −0.0553120
$$469$$ 0 0
$$470$$ −3618.00 −0.355076
$$471$$ −7082.50 + 12267.2i −0.692876 + 1.20010i
$$472$$ 876.000 + 1517.28i 0.0854262 + 0.147963i
$$473$$ −3534.00 6121.07i −0.343538 0.595025i
$$474$$ −2305.00 + 3992.38i −0.223359 + 0.386869i
$$475$$ 220.000 0.0212511
$$476$$ 0 0
$$477$$ 786.000 0.0754475
$$478$$ 3540.00 6131.46i 0.338736 0.586708i
$$479$$ 1369.50 + 2372.04i 0.130635 + 0.226266i 0.923921 0.382582i $$-0.124965\pi$$
−0.793287 + 0.608848i $$0.791632\pi$$
$$480$$ −720.000 1247.08i −0.0684653 0.118585i
$$481$$ 8855.00 15337.3i 0.839404 1.45389i
$$482$$ −10462.0 −0.988654
$$483$$ 0 0
$$484$$ 7672.00 0.720511
$$485$$ −8253.00 + 14294.6i −0.772679 + 1.33832i
$$486$$ −560.000 969.948i −0.0522677 0.0905304i
$$487$$ −8525.50 14766.6i −0.793280 1.37400i −0.923926 0.382572i $$-0.875038\pi$$
0.130646 0.991429i $$-0.458295\pi$$
$$488$$ −2836.00 + 4912.10i −0.263073 + 0.455656i
$$489$$ −11555.0 −1.06858
$$490$$ 0 0
$$491$$ −4296.00 −0.394859 −0.197429 0.980317i $$-0.563259\pi$$
−0.197429 + 0.980317i $$0.563259\pi$$
$$492$$ −420.000 + 727.461i −0.0384859 + 0.0666595i
$$493$$ 2907.00 + 5035.07i 0.265567 + 0.459976i
$$494$$ 350.000 + 606.218i 0.0318770 + 0.0552126i
$$495$$ −513.000 + 888.542i −0.0465811 + 0.0806808i
$$496$$ −368.000 −0.0333139
$$497$$ 0 0
$$498$$ 5880.00 0.529095
$$499$$ −1700.50 + 2945.35i −0.152555 + 0.264233i −0.932166 0.362031i $$-0.882083\pi$$
0.779611 + 0.626264i $$0.215417\pi$$
$$500$$ 3042.00 + 5268.90i 0.272085 + 0.471265i
$$501$$ 3150.00 + 5455.96i 0.280901 + 0.486536i
$$502$$ 5040.00 8729.54i 0.448100 0.776132i
$$503$$ −16800.0 −1.48921 −0.744607 0.667503i $$-0.767363\pi$$
−0.744607 + 0.667503i $$0.767363\pi$$
$$504$$ 0 0
$$505$$ 2565.00 0.226022
$$506$$ 3933.00 6812.16i 0.345540 0.598493i
$$507$$ −6757.50 11704.3i −0.591935 1.02526i
$$508$$ 4112.00 + 7122.19i 0.359135 + 0.622040i
$$509$$ 919.500 1592.62i 0.0800710 0.138687i −0.823209 0.567738i $$-0.807819\pi$$
0.903280 + 0.429051i $$0.141152\pi$$
$$510$$ −4590.00 −0.398527
$$511$$ 0 0
$$512$$ 512.000 0.0441942
$$513$$ −362.500 + 627.868i −0.0311984 + 0.0540372i
$$514$$ −1437.00 2488.96i −0.123314 0.213586i
$$515$$ −2245.50 3889.32i −0.192133 0.332784i
$$516$$ 1240.00 2147.74i 0.105791 0.183235i
$$517$$ 11457.0 0.974620
$$518$$ 0 0
$$519$$ −16335.0 −1.38155
$$520$$ −2520.00 + 4364.77i −0.212518 + 0.368092i
$$521$$ 151.500 + 262.406i 0.0127396 + 0.0220656i 0.872325 0.488927i $$-0.162611\pi$$
−0.859585 + 0.510992i $$0.829278\pi$$
$$522$$ 228.000 + 394.908i 0.0191174 + 0.0331123i
$$523$$ −10833.5 + 18764.2i −0.905767 + 1.56883i −0.0858815 + 0.996305i $$0.527371\pi$$
−0.819885 + 0.572528i $$0.805963\pi$$
$$524$$ −8196.00 −0.683290
$$525$$ 0 0
$$526$$ −4650.00 −0.385456
$$527$$ −586.500 + 1015.85i −0.0484788 + 0.0839678i
$$528$$ 2280.00 + 3949.08i 0.187925 + 0.325495i
$$529$$ 3703.00 + 6413.78i 0.304348 + 0.527146i
$$530$$ 3537.00 6126.26i 0.289882 0.502090i
$$531$$ 438.000 0.0357958
$$532$$ 0 0
$$533$$ 2940.00 0.238922
$$534$$ −5085.00 + 8807.48i −0.412078 + 0.713739i
$$535$$ 4981.50 + 8628.21i 0.402559 + 0.697253i
$$536$$ −1676.00 2902.92i −0.135060 0.233931i
$$537$$ −3217.50 + 5572.87i −0.258557 + 0.447835i
$$538$$ 4770.00 0.382248
$$539$$ 0 0
$$540$$ −5220.00 −0.415987
$$541$$ −2519.50 + 4363.90i −0.200225 + 0.346800i −0.948601 0.316475i $$-0.897501\pi$$
0.748376 + 0.663275i $$0.230834\pi$$
$$542$$ −331.000 573.309i −0.0262319 0.0454349i
$$543$$ −6685.00 11578.8i −0.528326 0.915087i
$$544$$ 816.000 1413.35i 0.0643120 0.111392i
$$545$$ 8307.00 0.652904
$$546$$ 0 0
$$547$$ −2392.00 −0.186974 −0.0934868 0.995621i $$-0.529801\pi$$
−0.0934868 + 0.995621i $$0.529801\pi$$
$$548$$ 282.000 488.438i 0.0219826 0.0380749i
$$549$$ 709.000 + 1228.02i 0.0551173 + 0.0954659i
$$550$$ −2508.00 4343.98i −0.194439 0.336778i
$$551$$ 285.000 493.634i 0.0220352 0.0381661i
$$552$$ 2760.00 0.212814
$$553$$ 0 0
$$554$$ 9742.00 0.747108
$$555$$ 5692.50 9859.70i 0.435375 0.754092i
$$556$$ 2968.00 + 5140.73i 0.226387 + 0.392114i
$$557$$ 11074.5 + 19181.6i 0.842445 + 1.45916i 0.887822 + 0.460187i $$0.152218\pi$$
−0.0453775 + 0.998970i $$0.514449\pi$$
$$558$$ −46.0000 + 79.6743i −0.00348985 + 0.00604459i
$$559$$ −8680.00 −0.656753
$$560$$ 0 0
$$561$$ 14535.0 1.09388
$$562$$ 7026.00 12169.4i 0.527356 0.913407i
$$563$$ −4174.50 7230.45i −0.312494 0.541256i 0.666408 0.745588i $$-0.267831\pi$$
−0.978902 + 0.204332i $$0.934498\pi$$
$$564$$ 2010.00 + 3481.42i 0.150064 + 0.259919i
$$565$$ −6939.00 + 12018.7i −0.516683 + 0.894921i
$$566$$ 10706.0 0.795065
$$567$$ 0 0
$$568$$ −768.000 −0.0567334
$$569$$ 7672.50 13289.2i 0.565286 0.979105i −0.431737 0.902000i $$-0.642099\pi$$
0.997023 0.0771050i $$-0.0245677\pi$$
$$570$$ 225.000 + 389.711i 0.0165337 + 0.0286372i
$$571$$ 5796.50 + 10039.8i 0.424827 + 0.735821i 0.996404 0.0847268i $$-0.0270017\pi$$
−0.571578 + 0.820548i $$0.693668\pi$$
$$572$$ 7980.00 13821.8i 0.583323 1.01034i
$$573$$ 20925.0 1.52557
$$574$$ 0 0
$$575$$ −3036.00 −0.220191
$$576$$ 64.0000 110.851i 0.00462963 0.00801875i
$$577$$ −7296.50 12637.9i −0.526442 0.911825i −0.999525 0.0308071i $$-0.990192\pi$$
0.473083 0.881018i $$-0.343141\pi$$
$$578$$ 2312.00 + 4004.50i 0.166378 + 0.288175i
$$579$$ 212.500 368.061i 0.0152525 0.0264181i
$$580$$ 4104.00 0.293809
$$581$$ 0 0
$$582$$ 18340.0 1.30622
$$583$$ −11200.5 + 19399.8i −0.795673 + 1.37815i
$$584$$ −1252.00 2168.53i −0.0887125 0.153655i
$$585$$ 630.000 + 1091.19i 0.0445253 + 0.0771201i
$$586$$ 4158.00 7201.87i 0.293115 0.507690i
$$587$$ 15372.0 1.08087 0.540435 0.841386i $$-0.318260\pi$$
0.540435 + 0.841386i $$0.318260\pi$$
$$588$$ 0 0
$$589$$ 115.000 0.00804498
$$590$$ 1971.00 3413.87i 0.137534 0.238215i
$$591$$ 975.000 + 1688.75i 0.0678615 + 0.117540i
$$592$$ 2024.00 + 3505.67i 0.140517 + 0.243382i
$$593$$ −7186.50 + 12447.4i −0.497663 + 0.861978i −0.999996 0.00269639i $$-0.999142\pi$$
0.502333 + 0.864674i $$0.332475\pi$$
$$594$$ 16530.0 1.14181
$$595$$ 0 0
$$596$$ −228.000 −0.0156699
$$597$$ −7082.50 + 12267.2i −0.485540 + 0.840980i
$$598$$ −4830.00 8365.81i −0.330290 0.572079i
$$599$$ −1273.50 2205.77i −0.0868678 0.150459i 0.819318 0.573340i $$-0.194352\pi$$
−0.906186 + 0.422880i $$0.861019\pi$$
$$600$$ 880.000 1524.20i 0.0598764 0.103709i
$$601$$ 7042.00 0.477952 0.238976 0.971025i $$-0.423188\pi$$
0.238976 + 0.971025i $$0.423188\pi$$
$$602$$ 0 0
$$603$$ −838.000 −0.0565937
$$604$$ −1678.00 + 2906.38i −0.113041 + 0.195793i
$$605$$ −8631.00 14949.3i −0.580000 1.00459i
$$606$$ −1425.00 2468.17i −0.0955226 0.165450i
$$607$$ −11295.5 + 19564.4i −0.755305 + 1.30823i 0.189917 + 0.981800i $$0.439178\pi$$
−0.945223 + 0.326427i $$0.894155\pi$$
$$608$$ −160.000 −0.0106725
$$609$$ 0 0
$$610$$ 12762.0 0.847079
$$611$$ 7035.00 12185.0i 0.465803 0.806794i
$$612$$ −204.000 353.338i −0.0134742 0.0233380i
$$613$$ 4242.50 + 7348.23i 0.279532 + 0.484163i 0.971268 0.237987i $$-0.0764874\pi$$
−0.691737 + 0.722150i $$0.743154\pi$$
$$614$$ −9604.00 + 16634.6i −0.631247 + 1.09335i
$$615$$ 1890.00 0.123922
$$616$$ 0 0
$$617$$ −18282.0 −1.19288 −0.596439 0.802658i $$-0.703418\pi$$
−0.596439 + 0.802658i $$0.703418\pi$$
$$618$$ −2495.00 + 4321.47i −0.162401 + 0.281286i
$$619$$ 1145.50 + 1984.06i 0.0743805 + 0.128831i 0.900817 0.434200i $$-0.142969\pi$$
−0.826436 + 0.563030i $$0.809635\pi$$
$$620$$ 414.000 + 717.069i 0.0268172 + 0.0464487i
$$621$$ 5002.50 8664.58i 0.323258 0.559900i
$$622$$ −20262.0 −1.30616
$$623$$ 0 0
$$624$$ 5600.00 0.359262
$$625$$ 4094.50 7091.88i 0.262048 0.453880i
$$626$$ 10799.0 + 18704.4i 0.689481 + 1.19422i
$$627$$ −712.500 1234.09i −0.0453820 0.0786039i
$$628$$ −5666.00 + 9813.80i −0.360029 + 0.623588i
$$629$$ 12903.0 0.817927
$$630$$ 0 0
$$631$$ −6928.00 −0.437083 −0.218541 0.975828i $$-0.570130\pi$$
−0.218541 + 0.975828i $$0.570130\pi$$
$$632$$ −1844.00 + 3193.90i −0.116061 + 0.201023i
$$633$$ 310.000 + 536.936i 0.0194651 + 0.0337145i
$$634$$ −531.000 919.719i −0.0332629 0.0576131i
$$635$$ 9252.00 16024.9i 0.578196 1.00146i
$$636$$ −7860.00 −0.490046
$$637$$ 0 0
$$638$$ −12996.0 −0.806452
$$639$$ −96.0000 + 166.277i −0.00594319 + 0.0102939i
$$640$$ −576.000 997.661i −0.0355756 0.0616188i
$$641$$ −12487.5 21629.0i −0.769464 1.33275i −0.937854 0.347031i $$-0.887190\pi$$
0.168390 0.985721i $$-0.446143\pi$$
$$642$$ 5535.00 9586.90i 0.340263 0.589353i
$$643$$ −9548.00 −0.585593 −0.292797 0.956175i $$-0.594586\pi$$
−0.292797 + 0.956175i $$0.594586\pi$$
$$644$$ 0 0
$$645$$ −5580.00 −0.340639
$$646$$ −255.000 + 441.673i −0.0155307 + 0.0269000i
$$647$$ 5065.50 + 8773.70i 0.307798 + 0.533122i 0.977880 0.209165i $$-0.0670745\pi$$
−0.670082 + 0.742287i $$0.733741\pi$$
$$648$$ 2684.00 + 4648.82i 0.162712 + 0.281826i
$$649$$ −6241.50 + 10810.6i −0.377504 + 0.653857i
$$650$$ −6160.00 −0.371716
$$651$$ 0 0
$$652$$ −9244.00 −0.555250
$$653$$ −8329.50 + 14427.1i −0.499171 + 0.864589i −1.00000 0.000957229i $$-0.999695\pi$$
0.500829 + 0.865546i $$0.333029\pi$$
$$654$$ −4615.00 7993.41i −0.275934 0.477932i
$$655$$ 9220.50 + 15970.4i 0.550038 + 0.952693i
$$656$$ −336.000 + 581.969i −0.0199979 + 0.0346373i
$$657$$ −626.000 −0.0371729
$$658$$ 0 0
$$659$$ 29556.0 1.74710 0.873550 0.486735i $$-0.161812\pi$$
0.873550 + 0.486735i $$0.161812\pi$$
$$660$$ 5130.00 8885.42i 0.302553 0.524037i
$$661$$ 95.5000 + 165.411i 0.00561955 + 0.00973334i 0.868822 0.495125i $$-0.164878\pi$$
−0.863202 + 0.504859i $$0.831545\pi$$
$$662$$ 7015.00 + 12150.3i 0.411852 + 0.713348i
$$663$$ 8925.00 15458.6i 0.522803 0.905521i
$$664$$ 4704.00 0.274926
$$665$$ 0 0
$$666$$ 1012.00 0.0588802
$$667$$ −3933.00 + 6812.16i −0.228315 + 0.395454i
$$668$$ 2520.00 + 4364.77i 0.145961 + 0.252811i
$$669$$ 140.000 + 242.487i 0.00809075 + 0.0140136i
$$670$$ −3771.00 + 6531.56i −0.217442 + 0.376621i
$$671$$ −40413.0 −2.32508
$$672$$ 0 0
$$673$$ 2606.00 0.149263 0.0746314 0.997211i $$-0.476222\pi$$
0.0746314 + 0.997211i $$0.476222\pi$$
$$674$$ −8990.00 + 15571.1i −0.513771 + 0.889878i
$$675$$ −3190.00 5525.24i −0.181901 0.315062i
$$676$$ −5406.00 9363.47i −0.307579 0.532742i
$$677$$ −2104.50 + 3645.10i −0.119472 + 0.206931i −0.919559 0.392953i $$-0.871453\pi$$
0.800087 + 0.599885i $$0.204787\pi$$
$$678$$ 15420.0 0.873454
$$679$$ 0 0
$$680$$ −3672.00 −0.207081
$$681$$ −7642.50 + 13237.2i −0.430046 + 0.744861i
$$682$$ −1311.00 2270.72i −0.0736082 0.127493i
$$683$$ −12151.5 21047.0i −0.680768 1.17912i −0.974747 0.223312i $$-0.928313\pi$$
0.293979 0.955812i $$-0.405020\pi$$
$$684$$ −20.0000 + 34.6410i −0.00111801 + 0.00193645i
$$685$$ −1269.00 −0.0707825
$$686$$ 0 0
$$687$$ 4805.00 0.266845
$$688$$ 992.000 1718.19i 0.0549704 0.0952116i
$$689$$ 13755.0 + 23824.4i 0.760557 + 1.31732i
$$690$$ −3105.00 5378.02i −0.171312 0.296721i
$$691$$ 7520.50 13025.9i 0.414028 0.717117i −0.581298 0.813691i $$-0.697455\pi$$
0.995326 + 0.0965734i $$0.0307882\pi$$
$$692$$ −13068.0 −0.717877
$$693$$ 0 0
$$694$$ −17418.0 −0.952706
$$695$$ 6678.00 11566.6i 0.364476 0.631291i
$$696$$ −2280.00 3949.08i −0.124171 0.215071i
$$697$$ 1071.00 + 1855.03i 0.0582023 + 0.100809i
$$698$$ 6482.00 11227.2i 0.351500 0.608817i
$$699$$ −14145.0 −0.765398
$$700$$ 0 0
$$701$$ 24726.0 1.33222 0.666111 0.745852i $$-0.267958\pi$$
0.666111 + 0.745852i $$0.267958\pi$$
$$702$$ 10150.0 17580.3i 0.545708 0.945194i
$$703$$ −632.500 1095.52i −0.0339334 0.0587744i
$$704$$ 1824.00 + 3159.26i 0.0976486 + 0.169132i
$$705$$ 4522.50 7833.20i 0.241599 0.418462i
$$706$$ 4266.00 0.227412
$$707$$ 0 0
$$708$$ −4380.00 −0.232501
$$709$$ 2478.50 4292.89i 0.131286 0.227395i −0.792886 0.609370i $$-0.791423\pi$$
0.924173 + 0.381975i $$0.124756\pi$$
$$710$$ 864.000 + 1496.49i 0.0456695 + 0.0791019i
$$711$$ 461.000 + 798.475i 0.0243162 + 0.0421170i
$$712$$ −4068.00 + 7045.98i −0.214122 + 0.370870i
$$713$$ −1587.00 −0.0833571
$$714$$ 0 0
$$715$$ −35910.0 −1.87826
$$716$$ −2574.00 + 4458.30i −0.134350 + 0.232702i
$$717$$ 8850.00 + 15328.6i 0.460961 + 0.798409i
$$718$$ −3849.00 6666.66i −0.200060 0.346515i
$$719$$ 13834.5 23962.1i 0.717580 1.24288i −0.244376 0.969680i $$-0.578583\pi$$
0.961956 0.273204i $$-0.0880834\pi$$
$$720$$ −288.000 −0.0149071
$$721$$ 0 0
$$722$$ −13668.0 −0.704529
$$723$$ 13077.5 22650.9i 0.672694 1.16514i
$$724$$ −5348.00 9263.01i −0.274526 0.475493i
$$725$$ 2508.00 + 4343.98i 0.128476 + 0.222526i
$$726$$ −9590.00 + 16610.4i −0.490246 + 0.849130i
$$727$$ 13888.0 0.708497 0.354249 0.935151i $$-0.384737\pi$$
0.354249 + 0.935151i $$0.384737\pi$$
$$728$$ 0 0
$$729$$ 20917.0 1.06269
$$730$$ −2817.00 + 4879.19i −0.142824 + 0.247379i
$$731$$ −3162.00 5476.74i −0.159987 0.277106i
$$732$$ −7090.00 12280.2i −0.357997 0.620069i
$$733$$ 7121.50 12334.8i 0.358852 0.621550i −0.628917 0.777472i $$-0.716502\pi$$
0.987769 + 0.155922i $$0.0498349\pi$$
$$734$$ −12982.0 −0.652826
$$735$$ 0 0
$$736$$ 2208.00 0.110581
$$737$$ 11941.5 20683.3i 0.596840 1.03376i
$$738$$ 84.0000 + 145.492i 0.00418981 + 0.00725697i
$$739$$ −18479.5 32007.4i −0.919864 1.59325i −0.799620 0.600507i $$-0.794966\pi$$
−0.120244 0.992744i $$-0.538368\pi$$
$$740$$ 4554.00 7887.76i 0.226228 0.391838i
$$741$$ −1750.00 −0.0867582
$$742$$ 0 0
$$743$$ −12528.0 −0.618584 −0.309292 0.950967i $$-0.600092\pi$$
−0.309292 + 0.950967i $$0.600092\pi$$
$$744$$ 460.000 796.743i 0.0226672 0.0392608i
$$745$$ 256.500 + 444.271i 0.0126140 + 0.0218481i
$$746$$ −923.000 1598.68i −0.0452995 0.0784610i
$$747$$ 588.000 1018.45i 0.0288003 0.0498835i
$$748$$ 11628.0 0.568398
$$749$$ 0 0
$$750$$ −15210.0 −0.740521
$$751$$ 8883.50 15386.7i 0.431643 0.747627i −0.565372 0.824836i $$-0.691268\pi$$
0.997015 + 0.0772090i $$0.0246009\pi$$
$$752$$ 1608.00 + 2785.14i 0.0779757 + 0.135058i
$$753$$ 12600.0 + 21823.8i 0.609787 + 1.05618i
$$754$$ −7980.00 + 13821.8i −0.385430 + 0.667585i
$$755$$ 7551.00 0.363985
$$756$$ 0 0
$$757$$ −28726.0 −1.37921 −0.689606 0.724184i $$-0.742216\pi$$
−0.689606 + 0.724184i $$0.742216\pi$$
$$758$$ −6344.00 + 10988.1i −0.303990 + 0.526526i
$$759$$ 9832.50 + 17030.4i 0.470220 + 0.814445i
$$760$$ 180.000 + 311.769i 0.00859117 + 0.0148803i
$$761$$ −13234.5 + 22922.8i −0.630421 + 1.09192i 0.357045 + 0.934087i $$0.383784\pi$$
−0.987466 + 0.157834i $$0.949549\pi$$
$$762$$ −20560.0 −0.977441
$$763$$ 0 0
$$764$$ 16740.0 0.792712
$$765$$ −459.000 + 795.011i −0.0216930 + 0.0375735i
$$766$$ −5007.00 8672.38i −0.236175 0.409068i
$$767$$ 7665.00 + 13276.2i 0.360844 + 0.625000i
$$768$$ −640.000 + 1108.51i −0.0300703 + 0.0520833i
$$769$$ −5054.00 −0.236999 −0.118499 0.992954i $$-0.537808\pi$$
−0.118499 + 0.992954i $$0.537808\pi$$
$$770$$ 0 0
$$771$$ 7185.00 0.335618
$$772$$ 170.000 294.449i 0.00792543 0.0137273i
$$773$$ −17782.5 30800.2i −0.827415 1.43313i −0.900059 0.435767i $$-0.856477\pi$$
0.0726439 0.997358i $$-0.476856\pi$$
$$774$$ −248.000 429.549i −0.0115170 0.0199481i
$$775$$ −506.000 + 876.418i −0.0234530 + 0.0406217i
$$776$$ 14672.0 0.678730