# Properties

 Label 1050.3.q.b.199.3 Level $1050$ Weight $3$ Character 1050.199 Analytic conductor $28.610$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.q (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$28.6104277578$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{6})$$ Coefficient field: 16.0.22986704741655040229376.1 Defining polynomial: $$x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561$$ x^16 - 31*x^12 + 880*x^8 - 2511*x^4 + 6561 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 199.3 Root $$0.596002 + 2.22431i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.199 Dual form 1050.3.q.b.649.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(-1.73205 - 3.00000i) q^{12} +21.3906 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(10.4937 - 18.1757i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-20.8728 + 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} -10.6592i q^{22} +(-4.83250 + 2.79005i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} -5.19615 q^{27} +(-6.22374 + 12.5405i) q^{28} +9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(4.89898 + 2.82843i) q^{32} +(6.52741 + 11.3058i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(19.3960 - 11.1983i) q^{37} +(17.0426 - 29.5187i) q^{38} +(18.5248 - 32.0860i) q^{39} -51.0827i q^{41} +(-1.07820 - 17.1125i) q^{42} -34.7656i q^{43} +(7.53720 + 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(-38.8246 - 67.2462i) q^{47} -6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(21.3906 - 37.0497i) q^{52} +(43.1262 + 24.8989i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +41.7457i q^{57} +(-12.2061 + 7.04720i) q^{58} +(-72.9362 - 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} -9.30925 q^{62} +(11.6228 + 17.4903i) q^{63} -8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(-57.6618 - 33.2911i) q^{67} +(-20.9874 - 36.3513i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(7.34847 - 4.24264i) q^{72} +(43.8283 - 75.9128i) q^{73} +(-15.8368 + 27.4301i) q^{74} +48.2038i q^{76} +(23.4548 - 47.2603i) q^{77} +52.3962i q^{78} +(49.3730 + 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(36.1209 + 62.5632i) q^{82} +26.9448 q^{83} +(13.4209 + 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(8.63103 - 14.9494i) q^{87} +(-18.4623 - 10.6592i) q^{88} +(-12.0453 + 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} +11.1602i q^{92} +(9.87395 - 5.70073i) q^{93} +(95.1005 + 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} -3.69132 q^{97} +(-55.1890 + 41.9067i) q^{98} +22.6116 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + 16 q^{4} - 24 q^{9}+O(q^{10})$$ 16 * q + 16 * q^4 - 24 * q^9 $$16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100})$$ 16 * q + 16 * q^4 - 24 * q^9 - 8 * q^11 + 32 * q^14 - 32 * q^16 - 144 * q^19 - 144 * q^26 + 48 * q^29 + 192 * q^31 - 96 * q^36 + 24 * q^39 + 16 * q^44 + 64 * q^46 + 528 * q^49 + 48 * q^51 + 80 * q^56 - 624 * q^59 - 408 * q^61 - 128 * q^64 - 72 * q^66 - 128 * q^71 + 32 * q^74 + 288 * q^79 - 72 * q^81 + 352 * q^86 + 672 * q^89 - 592 * q^91 - 72 * q^94 + 48 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.22474 + 0.707107i −0.612372 + 0.353553i
$$3$$ 0.866025 1.50000i 0.288675 0.500000i
$$4$$ 1.00000 1.73205i 0.250000 0.433013i
$$5$$ 0 0
$$6$$ 2.44949i 0.408248i
$$7$$ −6.98615 + 0.440173i −0.998021 + 0.0628819i
$$8$$ 2.82843i 0.353553i
$$9$$ −1.50000 2.59808i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ −3.76860 + 6.52741i −0.342600 + 0.593401i −0.984915 0.173040i $$-0.944641\pi$$
0.642315 + 0.766441i $$0.277974\pi$$
$$12$$ −1.73205 3.00000i −0.144338 0.250000i
$$13$$ 21.3906 1.64543 0.822717 0.568451i $$-0.192457\pi$$
0.822717 + 0.568451i $$0.192457\pi$$
$$14$$ 8.24500 5.47905i 0.588928 0.391361i
$$15$$ 0 0
$$16$$ −2.00000 3.46410i −0.125000 0.216506i
$$17$$ 10.4937 18.1757i 0.617278 1.06916i −0.372703 0.927951i $$-0.621569\pi$$
0.989980 0.141205i $$-0.0450978\pi$$
$$18$$ 3.67423 + 2.12132i 0.204124 + 0.117851i
$$19$$ −20.8728 + 12.0509i −1.09857 + 0.634260i −0.935845 0.352411i $$-0.885362\pi$$
−0.162726 + 0.986671i $$0.552029\pi$$
$$20$$ 0 0
$$21$$ −5.38992 + 10.8604i −0.256663 + 0.517163i
$$22$$ 10.6592i 0.484510i
$$23$$ −4.83250 + 2.79005i −0.210109 + 0.121306i −0.601362 0.798977i $$-0.705375\pi$$
0.391253 + 0.920283i $$0.372042\pi$$
$$24$$ 4.24264 + 2.44949i 0.176777 + 0.102062i
$$25$$ 0 0
$$26$$ −26.1981 + 15.1255i −1.00762 + 0.581749i
$$27$$ −5.19615 −0.192450
$$28$$ −6.22374 + 12.5405i −0.222277 + 0.447876i
$$29$$ 9.96625 0.343664 0.171832 0.985126i $$-0.445031\pi$$
0.171832 + 0.985126i $$0.445031\pi$$
$$30$$ 0 0
$$31$$ 5.70073 + 3.29132i 0.183894 + 0.106171i 0.589121 0.808045i $$-0.299474\pi$$
−0.405227 + 0.914216i $$0.632807\pi$$
$$32$$ 4.89898 + 2.82843i 0.153093 + 0.0883883i
$$33$$ 6.52741 + 11.3058i 0.197800 + 0.342600i
$$34$$ 29.6807i 0.872962i
$$35$$ 0 0
$$36$$ −6.00000 −0.166667
$$37$$ 19.3960 11.1983i 0.524216 0.302656i −0.214442 0.976737i $$-0.568793\pi$$
0.738658 + 0.674080i $$0.235460\pi$$
$$38$$ 17.0426 29.5187i 0.448490 0.776807i
$$39$$ 18.5248 32.0860i 0.474996 0.822717i
$$40$$ 0 0
$$41$$ 51.0827i 1.24592i −0.782254 0.622959i $$-0.785930\pi$$
0.782254 0.622959i $$-0.214070\pi$$
$$42$$ −1.07820 17.1125i −0.0256714 0.407440i
$$43$$ 34.7656i 0.808503i −0.914648 0.404252i $$-0.867532\pi$$
0.914648 0.404252i $$-0.132468\pi$$
$$44$$ 7.53720 + 13.0548i 0.171300 + 0.296700i
$$45$$ 0 0
$$46$$ 3.94572 6.83419i 0.0857766 0.148569i
$$47$$ −38.8246 67.2462i −0.826056 1.43077i −0.901110 0.433591i $$-0.857246\pi$$
0.0750536 0.997179i $$-0.476087\pi$$
$$48$$ −6.92820 −0.144338
$$49$$ 48.6125 6.15023i 0.992092 0.125515i
$$50$$ 0 0
$$51$$ −18.1757 31.4812i −0.356385 0.617278i
$$52$$ 21.3906 37.0497i 0.411359 0.712494i
$$53$$ 43.1262 + 24.8989i 0.813703 + 0.469791i 0.848240 0.529612i $$-0.177662\pi$$
−0.0345374 + 0.999403i $$0.510996\pi$$
$$54$$ 6.36396 3.67423i 0.117851 0.0680414i
$$55$$ 0 0
$$56$$ −1.24500 19.7598i −0.0222321 0.352854i
$$57$$ 41.7457i 0.732381i
$$58$$ −12.2061 + 7.04720i −0.210450 + 0.121504i
$$59$$ −72.9362 42.1098i −1.23621 0.713725i −0.267890 0.963449i $$-0.586327\pi$$
−0.968317 + 0.249725i $$0.919660\pi$$
$$60$$ 0 0
$$61$$ −72.4404 + 41.8235i −1.18755 + 0.685631i −0.957749 0.287607i $$-0.907140\pi$$
−0.229799 + 0.973238i $$0.573807\pi$$
$$62$$ −9.30925 −0.150149
$$63$$ 11.6228 + 17.4903i 0.184489 + 0.277624i
$$64$$ −8.00000 −0.125000
$$65$$ 0 0
$$66$$ −15.9888 9.23115i −0.242255 0.139866i
$$67$$ −57.6618 33.2911i −0.860625 0.496882i 0.00359682 0.999994i $$-0.498855\pi$$
−0.864221 + 0.503112i $$0.832188\pi$$
$$68$$ −20.9874 36.3513i −0.308639 0.534578i
$$69$$ 9.66501i 0.140073i
$$70$$ 0 0
$$71$$ −68.1049 −0.959224 −0.479612 0.877481i $$-0.659223\pi$$
−0.479612 + 0.877481i $$0.659223\pi$$
$$72$$ 7.34847 4.24264i 0.102062 0.0589256i
$$73$$ 43.8283 75.9128i 0.600387 1.03990i −0.392375 0.919805i $$-0.628346\pi$$
0.992762 0.120096i $$-0.0383202\pi$$
$$74$$ −15.8368 + 27.4301i −0.214010 + 0.370677i
$$75$$ 0 0
$$76$$ 48.2038i 0.634260i
$$77$$ 23.4548 47.2603i 0.304608 0.613770i
$$78$$ 52.3962i 0.671746i
$$79$$ 49.3730 + 85.5165i 0.624974 + 1.08249i 0.988546 + 0.150921i $$0.0482238\pi$$
−0.363572 + 0.931566i $$0.618443\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.0555556 + 0.0962250i
$$82$$ 36.1209 + 62.5632i 0.440499 + 0.762966i
$$83$$ 26.9448 0.324636 0.162318 0.986739i $$-0.448103\pi$$
0.162318 + 0.986739i $$0.448103\pi$$
$$84$$ 13.4209 + 20.1960i 0.159772 + 0.240429i
$$85$$ 0 0
$$86$$ 24.5830 + 42.5790i 0.285849 + 0.495105i
$$87$$ 8.63103 14.9494i 0.0992072 0.171832i
$$88$$ −18.4623 10.6592i −0.209799 0.121127i
$$89$$ −12.0453 + 6.95436i −0.135341 + 0.0781389i −0.566142 0.824308i $$-0.691564\pi$$
0.430801 + 0.902447i $$0.358231\pi$$
$$90$$ 0 0
$$91$$ −149.438 + 9.41559i −1.64218 + 0.103468i
$$92$$ 11.1602i 0.121306i
$$93$$ 9.87395 5.70073i 0.106171 0.0612981i
$$94$$ 95.1005 + 54.9063i 1.01171 + 0.584110i
$$95$$ 0 0
$$96$$ 8.48528 4.89898i 0.0883883 0.0510310i
$$97$$ −3.69132 −0.0380549 −0.0190274 0.999819i $$-0.506057\pi$$
−0.0190274 + 0.999819i $$0.506057\pi$$
$$98$$ −55.1890 + 41.9067i −0.563153 + 0.427619i
$$99$$ 22.6116 0.228400
$$100$$ 0 0
$$101$$ −158.170 91.3195i −1.56604 0.904154i −0.996624 0.0821041i $$-0.973836\pi$$
−0.569416 0.822049i $$-0.692831\pi$$
$$102$$ 44.5211 + 25.7043i 0.436481 + 0.252003i
$$103$$ −45.5253 78.8521i −0.441993 0.765555i 0.555844 0.831287i $$-0.312395\pi$$
−0.997837 + 0.0657318i $$0.979062\pi$$
$$104$$ 60.5019i 0.581749i
$$105$$ 0 0
$$106$$ −70.4249 −0.664385
$$107$$ −44.6318 + 25.7682i −0.417120 + 0.240824i −0.693844 0.720125i $$-0.744084\pi$$
0.276724 + 0.960949i $$0.410751\pi$$
$$108$$ −5.19615 + 9.00000i −0.0481125 + 0.0833333i
$$109$$ 19.1807 33.2219i 0.175970 0.304788i −0.764527 0.644592i $$-0.777027\pi$$
0.940496 + 0.339804i $$0.110361\pi$$
$$110$$ 0 0
$$111$$ 38.7920i 0.349477i
$$112$$ 15.4971 + 23.3204i 0.138367 + 0.208218i
$$113$$ 198.558i 1.75715i −0.477608 0.878573i $$-0.658496\pi$$
0.477608 0.878573i $$-0.341504\pi$$
$$114$$ −29.5187 51.1278i −0.258936 0.448490i
$$115$$ 0 0
$$116$$ 9.96625 17.2621i 0.0859160 0.148811i
$$117$$ −32.0860 55.5745i −0.274239 0.474996i
$$118$$ 119.104 1.00936
$$119$$ −65.3102 + 131.597i −0.548825 + 1.10586i
$$120$$ 0 0
$$121$$ 32.0953 + 55.5907i 0.265250 + 0.459427i
$$122$$ 59.1474 102.446i 0.484814 0.839723i
$$123$$ −76.6240 44.2389i −0.622959 0.359666i
$$124$$ 11.4015 6.58263i 0.0919472 0.0530857i
$$125$$ 0 0
$$126$$ −26.6025 13.2026i −0.211131 0.104782i
$$127$$ 74.1132i 0.583569i 0.956484 + 0.291784i $$0.0942490\pi$$
−0.956484 + 0.291784i $$0.905751\pi$$
$$128$$ 9.79796 5.65685i 0.0765466 0.0441942i
$$129$$ −52.1485 30.1079i −0.404252 0.233395i
$$130$$ 0 0
$$131$$ 17.3500 10.0170i 0.132443 0.0764657i −0.432315 0.901723i $$-0.642303\pi$$
0.564757 + 0.825257i $$0.308970\pi$$
$$132$$ 26.1096 0.197800
$$133$$ 140.516 93.3773i 1.05651 0.702085i
$$134$$ 94.1614 0.702697
$$135$$ 0 0
$$136$$ 51.4085 + 29.6807i 0.378004 + 0.218241i
$$137$$ −74.6259 43.0853i −0.544715 0.314491i 0.202273 0.979329i $$-0.435167\pi$$
−0.746988 + 0.664838i $$0.768501\pi$$
$$138$$ −6.83419 11.8372i −0.0495231 0.0857766i
$$139$$ 232.502i 1.67268i −0.548213 0.836339i $$-0.684692\pi$$
0.548213 0.836339i $$-0.315308\pi$$
$$140$$ 0 0
$$141$$ −134.492 −0.953847
$$142$$ 83.4111 48.1574i 0.587402 0.339137i
$$143$$ −80.6128 + 139.625i −0.563726 + 0.976402i
$$144$$ −6.00000 + 10.3923i −0.0416667 + 0.0721688i
$$145$$ 0 0
$$146$$ 123.965i 0.849076i
$$147$$ 32.8743 78.2450i 0.223635 0.532279i
$$148$$ 44.7931i 0.302656i
$$149$$ −109.963 190.462i −0.738008 1.27827i −0.953391 0.301738i $$-0.902433\pi$$
0.215383 0.976530i $$-0.430900\pi$$
$$150$$ 0 0
$$151$$ 130.461 225.965i 0.863980 1.49646i −0.00407633 0.999992i $$-0.501298\pi$$
0.868056 0.496466i $$-0.165369\pi$$
$$152$$ −34.0852 59.0373i −0.224245 0.388403i
$$153$$ −62.9623 −0.411518
$$154$$ 4.69190 + 74.4668i 0.0304669 + 0.483551i
$$155$$ 0 0
$$156$$ −37.0497 64.1719i −0.237498 0.411359i
$$157$$ −57.0954 + 98.8921i −0.363665 + 0.629886i −0.988561 0.150822i $$-0.951808\pi$$
0.624896 + 0.780708i $$0.285141\pi$$
$$158$$ −120.939 69.8239i −0.765434 0.441923i
$$159$$ 74.6968 43.1262i 0.469791 0.271234i
$$160$$ 0 0
$$161$$ 32.5325 21.6188i 0.202065 0.134278i
$$162$$ 12.7279i 0.0785674i
$$163$$ 42.1894 24.3581i 0.258831 0.149436i −0.364970 0.931019i $$-0.618921\pi$$
0.623801 + 0.781583i $$0.285588\pi$$
$$164$$ −88.4777 51.0827i −0.539498 0.311480i
$$165$$ 0 0
$$166$$ −33.0005 + 19.0528i −0.198798 + 0.114776i
$$167$$ 49.6127 0.297082 0.148541 0.988906i $$-0.452542\pi$$
0.148541 + 0.988906i $$0.452542\pi$$
$$168$$ −30.7179 15.2450i −0.182845 0.0907440i
$$169$$ 288.560 1.70745
$$170$$ 0 0
$$171$$ 62.6185 + 36.1528i 0.366190 + 0.211420i
$$172$$ −60.2159 34.7656i −0.350092 0.202126i
$$173$$ −117.670 203.811i −0.680176 1.17810i −0.974927 0.222525i $$-0.928570\pi$$
0.294751 0.955574i $$-0.404763\pi$$
$$174$$ 24.4122i 0.140300i
$$175$$ 0 0
$$176$$ 30.1488 0.171300
$$177$$ −126.329 + 72.9362i −0.713725 + 0.412069i
$$178$$ 9.83495 17.0346i 0.0552525 0.0957002i
$$179$$ −22.1049 + 38.2868i −0.123491 + 0.213893i −0.921142 0.389226i $$-0.872742\pi$$
0.797651 + 0.603119i $$0.206076\pi$$
$$180$$ 0 0
$$181$$ 117.049i 0.646679i 0.946283 + 0.323340i $$0.104806\pi$$
−0.946283 + 0.323340i $$0.895194\pi$$
$$182$$ 176.366 117.200i 0.969043 0.643958i
$$183$$ 144.881i 0.791699i
$$184$$ −7.89145 13.6684i −0.0428883 0.0742847i
$$185$$ 0 0
$$186$$ −8.06204 + 13.9639i −0.0433443 + 0.0750746i
$$187$$ 79.0933 + 136.994i 0.422959 + 0.732586i
$$188$$ −155.299 −0.826056
$$189$$ 36.3011 2.28721i 0.192069 0.0121016i
$$190$$ 0 0
$$191$$ −117.156 202.920i −0.613383 1.06241i −0.990666 0.136313i $$-0.956475\pi$$
0.377283 0.926098i $$-0.376858\pi$$
$$192$$ −6.92820 + 12.0000i −0.0360844 + 0.0625000i
$$193$$ 16.9438 + 9.78252i 0.0877918 + 0.0506866i 0.543253 0.839569i $$-0.317192\pi$$
−0.455461 + 0.890256i $$0.650526\pi$$
$$194$$ 4.52093 2.61016i 0.0233037 0.0134544i
$$195$$ 0 0
$$196$$ 37.9600 90.3495i 0.193673 0.460967i
$$197$$ 179.443i 0.910877i 0.890267 + 0.455438i $$0.150517\pi$$
−0.890267 + 0.455438i $$0.849483\pi$$
$$198$$ −27.6934 + 15.9888i −0.139866 + 0.0807516i
$$199$$ 221.630 + 127.958i 1.11372 + 0.643006i 0.939790 0.341753i $$-0.111021\pi$$
0.173928 + 0.984758i $$0.444354\pi$$
$$200$$ 0 0
$$201$$ −99.8732 + 57.6618i −0.496882 + 0.286875i
$$202$$ 258.291 1.27867
$$203$$ −69.6257 + 4.38688i −0.342984 + 0.0216102i
$$204$$ −72.7026 −0.356385
$$205$$ 0 0
$$206$$ 111.514 + 64.3825i 0.541329 + 0.312536i
$$207$$ 14.4975 + 8.37014i 0.0700363 + 0.0404355i
$$208$$ −42.7813 74.0994i −0.205679 0.356247i
$$209$$ 181.661i 0.869190i
$$210$$ 0 0
$$211$$ 196.891 0.933132 0.466566 0.884486i $$-0.345491\pi$$
0.466566 + 0.884486i $$0.345491\pi$$
$$212$$ 86.2525 49.7979i 0.406851 0.234896i
$$213$$ −58.9806 + 102.157i −0.276904 + 0.479612i
$$214$$ 36.4417 63.1189i 0.170288 0.294948i
$$215$$ 0 0
$$216$$ 14.6969i 0.0680414i
$$217$$ −41.2749 20.4843i −0.190207 0.0943977i
$$218$$ 54.2512i 0.248859i
$$219$$ −75.9128 131.485i −0.346634 0.600387i
$$220$$ 0 0
$$221$$ 224.467 388.789i 1.01569 1.75923i
$$222$$ 27.4301 + 47.5103i 0.123559 + 0.214010i
$$223$$ 431.015 1.93280 0.966401 0.257039i $$-0.0827470\pi$$
0.966401 + 0.257039i $$0.0827470\pi$$
$$224$$ −35.4700 17.6034i −0.158348 0.0785866i
$$225$$ 0 0
$$226$$ 140.401 + 243.182i 0.621245 + 1.07603i
$$227$$ 87.5479 151.637i 0.385673 0.668006i −0.606189 0.795321i $$-0.707302\pi$$
0.991862 + 0.127315i $$0.0406358\pi$$
$$228$$ 72.3057 + 41.7457i 0.317130 + 0.183095i
$$229$$ −29.0717 + 16.7846i −0.126951 + 0.0732951i −0.562131 0.827048i $$-0.690018\pi$$
0.435180 + 0.900344i $$0.356685\pi$$
$$230$$ 0 0
$$231$$ −50.5779 76.1108i −0.218952 0.329484i
$$232$$ 28.1888i 0.121504i
$$233$$ −134.159 + 77.4567i −0.575790 + 0.332432i −0.759458 0.650556i $$-0.774536\pi$$
0.183669 + 0.982988i $$0.441203\pi$$
$$234$$ 78.5942 + 45.3764i 0.335873 + 0.193916i
$$235$$ 0 0
$$236$$ −145.872 + 84.2195i −0.618104 + 0.356862i
$$237$$ 171.033 0.721658
$$238$$ −13.0647 207.354i −0.0548935 0.871235i
$$239$$ −316.591 −1.32465 −0.662325 0.749217i $$-0.730430\pi$$
−0.662325 + 0.749217i $$0.730430\pi$$
$$240$$ 0 0
$$241$$ 202.219 + 116.751i 0.839084 + 0.484446i 0.856953 0.515395i $$-0.172355\pi$$
−0.0178685 + 0.999840i $$0.505688\pi$$
$$242$$ −78.6171 45.3896i −0.324864 0.187560i
$$243$$ 7.79423 + 13.5000i 0.0320750 + 0.0555556i
$$244$$ 167.294i 0.685631i
$$245$$ 0 0
$$246$$ 125.126 0.508644
$$247$$ −446.484 + 257.777i −1.80763 + 1.04363i
$$248$$ −9.30925 + 16.1241i −0.0375373 + 0.0650165i
$$249$$ 23.3349 40.4172i 0.0937143 0.162318i
$$250$$ 0 0
$$251$$ 56.6879i 0.225848i −0.993604 0.112924i $$-0.963978\pi$$
0.993604 0.112924i $$-0.0360217\pi$$
$$252$$ 41.9169 2.64104i 0.166337 0.0104803i
$$253$$ 42.0583i 0.166238i
$$254$$ −52.4060 90.7698i −0.206323 0.357361i
$$255$$ 0 0
$$256$$ −8.00000 + 13.8564i −0.0312500 + 0.0541266i
$$257$$ −145.219 251.528i −0.565056 0.978706i −0.997044 0.0768270i $$-0.975521\pi$$
0.431988 0.901879i $$-0.357812\pi$$
$$258$$ 85.1581 0.330070
$$259$$ −130.574 + 86.7704i −0.504147 + 0.335021i
$$260$$ 0 0
$$261$$ −14.9494 25.8931i −0.0572773 0.0992072i
$$262$$ −14.1662 + 24.5366i −0.0540694 + 0.0936510i
$$263$$ 385.031 + 222.298i 1.46399 + 0.845238i 0.999193 0.0401768i $$-0.0127921\pi$$
0.464802 + 0.885415i $$0.346125\pi$$
$$264$$ −31.9776 + 18.4623i −0.121127 + 0.0699329i
$$265$$ 0 0
$$266$$ −106.069 + 213.723i −0.398755 + 0.803471i
$$267$$ 24.0906i 0.0902270i
$$268$$ −115.324 + 66.5822i −0.430312 + 0.248441i
$$269$$ 144.956 + 83.6902i 0.538869 + 0.311116i 0.744620 0.667488i $$-0.232631\pi$$
−0.205752 + 0.978604i $$0.565964\pi$$
$$270$$ 0 0
$$271$$ 2.24099 1.29384i 0.00826933 0.00477430i −0.495860 0.868403i $$-0.665147\pi$$
0.504129 + 0.863628i $$0.331814\pi$$
$$272$$ −83.9498 −0.308639
$$273$$ −115.294 + 232.311i −0.422322 + 0.850957i
$$274$$ 121.864 0.444758
$$275$$ 0 0
$$276$$ 16.7403 + 9.66501i 0.0606532 + 0.0350181i
$$277$$ −440.903 254.556i −1.59171 0.918973i −0.993014 0.117996i $$-0.962353\pi$$
−0.598694 0.800978i $$-0.704314\pi$$
$$278$$ 164.404 + 284.756i 0.591381 + 1.02430i
$$279$$ 19.7479i 0.0707810i
$$280$$ 0 0
$$281$$ 210.688 0.749779 0.374890 0.927069i $$-0.377681\pi$$
0.374890 + 0.927069i $$0.377681\pi$$
$$282$$ 164.719 95.1005i 0.584110 0.337236i
$$283$$ −19.7433 + 34.1964i −0.0697643 + 0.120835i −0.898797 0.438364i $$-0.855558\pi$$
0.829033 + 0.559199i $$0.188891\pi$$
$$284$$ −68.1049 + 117.961i −0.239806 + 0.415356i
$$285$$ 0 0
$$286$$ 228.007i 0.797229i
$$287$$ 22.4852 + 356.871i 0.0783457 + 1.24345i
$$288$$ 16.9706i 0.0589256i
$$289$$ −75.7363 131.179i −0.262063 0.453907i
$$290$$ 0 0
$$291$$ −3.19678 + 5.53698i −0.0109855 + 0.0190274i
$$292$$ −87.6565 151.826i −0.300194 0.519951i
$$293$$ 89.6023 0.305810 0.152905 0.988241i $$-0.451137\pi$$
0.152905 + 0.988241i $$0.451137\pi$$
$$294$$ 15.0649 + 119.076i 0.0512412 + 0.405020i
$$295$$ 0 0
$$296$$ 31.6735 + 54.8602i 0.107005 + 0.185338i
$$297$$ 19.5822 33.9174i 0.0659334 0.114200i
$$298$$ 269.354 + 155.511i 0.903871 + 0.521850i
$$299$$ −103.370 + 59.6809i −0.345720 + 0.199602i
$$300$$ 0 0
$$301$$ 15.3029 + 242.878i 0.0508402 + 0.806903i
$$302$$ 368.999i 1.22185i
$$303$$ −273.959 + 158.170i −0.904154 + 0.522013i
$$304$$ 83.4914 + 48.2038i 0.274643 + 0.158565i
$$305$$ 0 0
$$306$$ 77.1128 44.5211i 0.252003 0.145494i
$$307$$ −470.478 −1.53250 −0.766251 0.642542i $$-0.777880\pi$$
−0.766251 + 0.642542i $$0.777880\pi$$
$$308$$ −58.4024 87.8852i −0.189618 0.285341i
$$309$$ −157.704 −0.510370
$$310$$ 0 0
$$311$$ 217.631 + 125.649i 0.699778 + 0.404017i 0.807265 0.590189i $$-0.200947\pi$$
−0.107487 + 0.994207i $$0.534280\pi$$
$$312$$ 90.7528 + 52.3962i 0.290874 + 0.167936i
$$313$$ −194.231 336.417i −0.620545 1.07482i −0.989384 0.145322i $$-0.953578\pi$$
0.368839 0.929493i $$-0.379755\pi$$
$$314$$ 161.490i 0.514300i
$$315$$ 0 0
$$316$$ 197.492 0.624974
$$317$$ −129.366 + 74.6898i −0.408096 + 0.235614i −0.689971 0.723837i $$-0.742377\pi$$
0.281875 + 0.959451i $$0.409044\pi$$
$$318$$ −60.9897 + 105.637i −0.191792 + 0.332193i
$$319$$ −37.5588 + 65.0538i −0.117739 + 0.203930i
$$320$$ 0 0
$$321$$ 89.2636i 0.278080i
$$322$$ −24.5572 + 49.4815i −0.0762645 + 0.153669i
$$323$$ 505.837i 1.56606i
$$324$$ 9.00000 + 15.5885i 0.0277778 + 0.0481125i
$$325$$ 0 0
$$326$$ −34.4475 + 59.6648i −0.105667 + 0.183021i
$$327$$ −33.2219 57.5420i −0.101596 0.175970i
$$328$$ 144.484 0.440499
$$329$$ 300.835 + 452.702i 0.914391 + 1.37600i
$$330$$ 0 0
$$331$$ 235.465 + 407.838i 0.711375 + 1.23214i 0.964341 + 0.264663i $$0.0852607\pi$$
−0.252966 + 0.967475i $$0.581406\pi$$
$$332$$ 26.9448 46.6697i 0.0811590 0.140571i
$$333$$ −58.1880 33.5948i −0.174739 0.100885i
$$334$$ −60.7628 + 35.0814i −0.181925 + 0.105034i
$$335$$ 0 0
$$336$$ 48.4014 3.04961i 0.144052 0.00907622i
$$337$$ 532.478i 1.58005i 0.613072 + 0.790027i $$0.289934\pi$$
−0.613072 + 0.790027i $$0.710066\pi$$
$$338$$ −353.412 + 204.042i −1.04560 + 0.603676i
$$339$$ −297.836 171.956i −0.878573 0.507244i
$$340$$ 0 0
$$341$$ −42.9675 + 24.8073i −0.126004 + 0.0727487i
$$342$$ −102.256 −0.298993
$$343$$ −336.907 + 64.3643i −0.982236 + 0.187651i
$$344$$ 98.3321 0.285849
$$345$$ 0 0
$$346$$ 288.232 + 166.411i 0.833042 + 0.480957i
$$347$$ 389.385 + 224.812i 1.12215 + 0.647872i 0.941948 0.335758i $$-0.108992\pi$$
0.180199 + 0.983630i $$0.442326\pi$$
$$348$$ −17.2621 29.8988i −0.0496036 0.0859160i
$$349$$ 330.676i 0.947495i 0.880661 + 0.473747i $$0.157099\pi$$
−0.880661 + 0.473747i $$0.842901\pi$$
$$350$$ 0 0
$$351$$ −111.149 −0.316664
$$352$$ −36.9246 + 21.3184i −0.104899 + 0.0605637i
$$353$$ −135.686 + 235.014i −0.384379 + 0.665763i −0.991683 0.128706i $$-0.958918\pi$$
0.607304 + 0.794469i $$0.292251\pi$$
$$354$$ 103.147 178.657i 0.291377 0.504680i
$$355$$ 0 0
$$356$$ 27.8174i 0.0781389i
$$357$$ 140.835 + 211.932i 0.394496 + 0.593646i
$$358$$ 62.5221i 0.174643i
$$359$$ −3.79200 6.56794i −0.0105627 0.0182951i 0.860696 0.509120i $$-0.170029\pi$$
−0.871258 + 0.490825i $$0.836696\pi$$
$$360$$ 0 0
$$361$$ 109.950 190.440i 0.304572 0.527534i
$$362$$ −82.7661 143.355i −0.228636 0.396009i
$$363$$ 111.181 0.306285
$$364$$ −133.130 + 268.250i −0.365741 + 0.736951i
$$365$$ 0 0
$$366$$ −102.446 177.442i −0.279908 0.484814i
$$367$$ 265.706 460.216i 0.723995 1.25400i −0.235392 0.971901i $$-0.575637\pi$$
0.959386 0.282095i $$-0.0910293\pi$$
$$368$$ 19.3300 + 11.1602i 0.0525272 + 0.0303266i
$$369$$ −132.717 + 76.6240i −0.359666 + 0.207653i
$$370$$ 0 0
$$371$$ −312.246 154.965i −0.841634 0.417695i
$$372$$ 22.8029i 0.0612981i
$$373$$ 497.937 287.484i 1.33495 0.770734i 0.348897 0.937161i $$-0.386556\pi$$
0.986054 + 0.166427i $$0.0532229\pi$$
$$374$$ −193.738 111.855i −0.518016 0.299077i
$$375$$ 0 0
$$376$$ 190.201 109.813i 0.505854 0.292055i
$$377$$ 213.185 0.565476
$$378$$ −42.8423 + 28.4700i −0.113339 + 0.0753174i
$$379$$ −627.464 −1.65558 −0.827789 0.561040i $$-0.810402\pi$$
−0.827789 + 0.561040i $$0.810402\pi$$
$$380$$ 0 0
$$381$$ 111.170 + 64.1839i 0.291784 + 0.168462i
$$382$$ 286.973 + 165.684i 0.751238 + 0.433727i
$$383$$ 33.3056 + 57.6870i 0.0869597 + 0.150619i 0.906225 0.422797i $$-0.138952\pi$$
−0.819265 + 0.573415i $$0.805618\pi$$
$$384$$ 19.5959i 0.0510310i
$$385$$ 0 0
$$386$$ −27.6691 −0.0716817
$$387$$ −90.3238 + 52.1485i −0.233395 + 0.134751i
$$388$$ −3.69132 + 6.39356i −0.00951372 + 0.0164782i
$$389$$ 274.525 475.491i 0.705719 1.22234i −0.260713 0.965416i $$-0.583957\pi$$
0.966431 0.256925i $$-0.0827092\pi$$
$$390$$ 0 0
$$391$$ 117.112i 0.299519i
$$392$$ 17.3955 + 137.497i 0.0443762 + 0.350757i
$$393$$ 34.7000i 0.0882950i
$$394$$ −126.885 219.772i −0.322044 0.557796i
$$395$$ 0 0
$$396$$ 22.6116 39.1644i 0.0571000 0.0989001i
$$397$$ 259.283 + 449.091i 0.653106 + 1.13121i 0.982365 + 0.186973i $$0.0598676\pi$$
−0.329259 + 0.944240i $$0.606799\pi$$
$$398$$ −361.920 −0.909347
$$399$$ −18.3753 291.642i −0.0460535 0.730931i
$$400$$ 0 0
$$401$$ 238.149 + 412.486i 0.593888 + 1.02864i 0.993703 + 0.112048i $$0.0357411\pi$$
−0.399815 + 0.916596i $$0.630926\pi$$
$$402$$ 81.5462 141.242i 0.202851 0.351349i
$$403$$ 121.942 + 70.4033i 0.302586 + 0.174698i
$$404$$ −316.340 + 182.639i −0.783020 + 0.452077i
$$405$$ 0 0
$$406$$ 82.1717 54.6056i 0.202393 0.134497i
$$407$$ 168.807i 0.414760i
$$408$$ 89.0422 51.4085i 0.218241 0.126001i
$$409$$ 93.2552 + 53.8409i 0.228008 + 0.131640i 0.609653 0.792669i $$-0.291309\pi$$
−0.381645 + 0.924309i $$0.624642\pi$$
$$410$$ 0 0
$$411$$ −129.256 + 74.6259i −0.314491 + 0.181572i
$$412$$ −182.101 −0.441993
$$413$$ 528.079 + 262.080i 1.27864 + 0.634577i
$$414$$ −23.6743 −0.0571844
$$415$$ 0 0
$$416$$ 104.792 + 60.5019i 0.251905 + 0.145437i
$$417$$ −348.753 201.353i −0.836339 0.482861i
$$418$$ 128.454 + 222.488i 0.307305 + 0.532268i
$$419$$ 323.811i 0.772818i −0.922328 0.386409i $$-0.873715\pi$$
0.922328 0.386409i $$-0.126285\pi$$
$$420$$ 0 0
$$421$$ −238.957 −0.567595 −0.283797 0.958884i $$-0.591594\pi$$
−0.283797 + 0.958884i $$0.591594\pi$$
$$422$$ −241.141 + 139.223i −0.571424 + 0.329912i
$$423$$ −116.474 + 201.739i −0.275352 + 0.476924i
$$424$$ −70.4249 + 121.979i −0.166096 + 0.287687i
$$425$$ 0 0
$$426$$ 166.822i 0.391601i
$$427$$ 487.670 324.071i 1.14208 0.758950i
$$428$$ 103.073i 0.240824i
$$429$$ 139.625 + 241.838i 0.325467 + 0.563726i
$$430$$ 0 0
$$431$$ 95.8960 166.097i 0.222497 0.385375i −0.733069 0.680154i $$-0.761913\pi$$
0.955565 + 0.294779i $$0.0952461\pi$$
$$432$$ 10.3923 + 18.0000i 0.0240563 + 0.0416667i
$$433$$ 122.083 0.281946 0.140973 0.990013i $$-0.454977\pi$$
0.140973 + 0.990013i $$0.454977\pi$$
$$434$$ 65.0358 4.09768i 0.149852 0.00944166i
$$435$$ 0 0
$$436$$ −38.3614 66.4438i −0.0879848 0.152394i
$$437$$ 67.2454 116.472i 0.153880 0.266527i
$$438$$ 185.948 + 107.357i 0.424538 + 0.245107i
$$439$$ 217.656 125.664i 0.495800 0.286250i −0.231177 0.972912i $$-0.574258\pi$$
0.726978 + 0.686661i $$0.240924\pi$$
$$440$$ 0 0
$$441$$ −88.8975 117.074i −0.201582 0.265473i
$$442$$ 634.890i 1.43640i
$$443$$ −95.0802 + 54.8946i −0.214628 + 0.123916i −0.603460 0.797393i $$-0.706212\pi$$
0.388832 + 0.921309i $$0.372879\pi$$
$$444$$ −67.1897 38.7920i −0.151328 0.0873693i
$$445$$ 0 0
$$446$$ −527.883 + 304.773i −1.18359 + 0.683349i
$$447$$ −380.924 −0.852178
$$448$$ 55.8892 3.52139i 0.124753 0.00786024i
$$449$$ −806.490 −1.79619 −0.898095 0.439801i $$-0.855049\pi$$
−0.898095 + 0.439801i $$0.855049\pi$$
$$450$$ 0 0
$$451$$ 333.437 + 192.510i 0.739329 + 0.426852i
$$452$$ −343.912 198.558i −0.760867 0.439287i
$$453$$ −225.965 391.383i −0.498819 0.863980i
$$454$$ 247.623i 0.545425i
$$455$$ 0 0
$$456$$ −118.075 −0.258936
$$457$$ −668.964 + 386.226i −1.46382 + 0.845135i −0.999185 0.0403698i $$-0.987146\pi$$
−0.464631 + 0.885504i $$0.653813\pi$$
$$458$$ 23.7370 41.1137i 0.0518275 0.0897678i
$$459$$ −54.5270 + 94.4435i −0.118795 + 0.205759i
$$460$$ 0 0
$$461$$ 793.611i 1.72150i −0.509029 0.860749i $$-0.669995\pi$$
0.509029 0.860749i $$-0.330005\pi$$
$$462$$ 115.764 + 57.4523i 0.250570 + 0.124356i
$$463$$ 274.227i 0.592284i 0.955144 + 0.296142i $$0.0957001\pi$$
−0.955144 + 0.296142i $$0.904300\pi$$
$$464$$ −19.9325 34.5241i −0.0429580 0.0744054i
$$465$$ 0 0
$$466$$ 109.540 189.730i 0.235065 0.407145i
$$467$$ 198.815 + 344.357i 0.425727 + 0.737381i 0.996488 0.0837354i $$-0.0266851\pi$$
−0.570761 + 0.821116i $$0.693352\pi$$
$$468$$ −128.344 −0.274239
$$469$$ 417.488 + 207.195i 0.890166 + 0.441781i
$$470$$ 0 0
$$471$$ 98.8921 + 171.286i 0.209962 + 0.363665i
$$472$$ 119.104 206.295i 0.252340 0.437065i
$$473$$ 226.930 + 131.018i 0.479766 + 0.276993i
$$474$$ −209.472 + 120.939i −0.441923 + 0.255145i
$$475$$ 0 0
$$476$$ 162.622 + 244.717i 0.341643 + 0.514112i
$$477$$ 149.394i 0.313194i
$$478$$ 387.743 223.864i 0.811179 0.468334i
$$479$$ 165.573 + 95.5938i 0.345665 + 0.199570i 0.662774 0.748819i $$-0.269379\pi$$
−0.317110 + 0.948389i $$0.602712\pi$$
$$480$$ 0 0
$$481$$ 414.893 239.538i 0.862563 0.498001i
$$482$$ −330.223 −0.685110
$$483$$ −4.25428 67.5212i −0.00880803 0.139795i
$$484$$ 128.381 0.265250
$$485$$ 0 0
$$486$$ −19.0919 11.0227i −0.0392837 0.0226805i
$$487$$ 164.561 + 95.0092i 0.337907 + 0.195091i 0.659346 0.751840i $$-0.270833\pi$$
−0.321439 + 0.946930i $$0.604167\pi$$
$$488$$ −118.295 204.892i −0.242407 0.419862i
$$489$$ 84.3788i 0.172554i
$$490$$ 0 0
$$491$$ −211.384 −0.430517 −0.215258 0.976557i $$-0.569059\pi$$
−0.215258 + 0.976557i $$0.569059\pi$$
$$492$$ −153.248 + 88.4777i −0.311480 + 0.179833i
$$493$$ 104.583 181.143i 0.212136 0.367430i
$$494$$ 364.552 631.423i 0.737960 1.27818i
$$495$$ 0 0
$$496$$ 26.3305i 0.0530857i
$$497$$ 475.791 29.9779i 0.957325 0.0603178i
$$498$$ 66.0010i 0.132532i
$$499$$ −126.864 219.734i −0.254236 0.440349i 0.710452 0.703746i $$-0.248491\pi$$
−0.964688 + 0.263396i $$0.915157\pi$$
$$500$$ 0 0
$$501$$ 42.9658 74.4190i 0.0857601 0.148541i
$$502$$ 40.0844 + 69.4282i 0.0798494 + 0.138303i
$$503$$ −217.815 −0.433033 −0.216516 0.976279i $$-0.569469\pi$$
−0.216516 + 0.976279i $$0.569469\pi$$
$$504$$ −49.4700 + 32.8743i −0.0981547 + 0.0652268i
$$505$$ 0 0
$$506$$ 29.7397 + 51.5107i 0.0587741 + 0.101800i
$$507$$ 249.900 432.839i 0.492899 0.853727i
$$508$$ 128.368 + 74.1132i 0.252693 + 0.145892i
$$509$$ 24.6582 14.2364i 0.0484444 0.0279694i −0.475582 0.879671i $$-0.657763\pi$$
0.524027 + 0.851702i $$0.324429\pi$$
$$510$$ 0 0
$$511$$ −272.776 + 549.630i −0.533808 + 1.07560i
$$512$$ 22.6274i 0.0441942i
$$513$$ 108.458 62.6185i 0.211420 0.122063i
$$514$$ 355.714 + 205.371i 0.692050 + 0.399555i
$$515$$ 0 0
$$516$$ −104.297 + 60.2159i −0.202126 + 0.116697i
$$517$$ 585.258 1.13203
$$518$$ 98.5640 198.601i 0.190278 0.383400i
$$519$$ −407.622 −0.785399
$$520$$ 0 0
$$521$$ 671.401 + 387.634i 1.28868 + 0.744019i 0.978418 0.206633i $$-0.0662507\pi$$
0.310260 + 0.950652i $$0.399584\pi$$
$$522$$ 36.6184 + 21.1416i 0.0701501 + 0.0405012i
$$523$$ 51.2334 + 88.7388i 0.0979605 + 0.169673i 0.910840 0.412759i $$-0.135435\pi$$
−0.812880 + 0.582431i $$0.802101\pi$$
$$524$$ 40.0681i 0.0764657i
$$525$$ 0 0
$$526$$ −628.752 −1.19535
$$527$$ 119.644 69.0763i 0.227028 0.131075i
$$528$$ 26.1096 45.2232i 0.0494501 0.0856500i
$$529$$ −248.931 + 431.162i −0.470570 + 0.815050i
$$530$$ 0 0
$$531$$ 252.659i 0.475816i
$$532$$ −21.2180 336.759i −0.0398835 0.633005i
$$533$$ 1092.69i 2.05008i
$$534$$ −17.0346 29.5049i −0.0319001 0.0552525i
$$535$$ 0 0
$$536$$ 94.1614 163.092i 0.175674 0.304277i
$$537$$ 38.2868 + 66.3147i 0.0712976 + 0.123491i
$$538$$ −236.712 −0.439984
$$539$$ −143.056 + 340.491i −0.265410 + 0.631709i
$$540$$ 0 0
$$541$$ 408.868 + 708.180i 0.755763 + 1.30902i 0.944994 + 0.327088i $$0.106067\pi$$
−0.189231 + 0.981933i $$0.560599\pi$$
$$542$$ −1.82976 + 3.16924i −0.00337594 + 0.00584730i
$$543$$ 175.573 + 101.367i 0.323340 + 0.186680i
$$544$$ 102.817 59.3614i 0.189002 0.109120i
$$545$$ 0 0
$$546$$ −23.0634 366.047i −0.0422406 0.670416i
$$547$$ 204.209i 0.373325i −0.982424 0.186662i $$-0.940233\pi$$
0.982424 0.186662i $$-0.0597670\pi$$
$$548$$ −149.252 + 86.1706i −0.272357 + 0.157246i
$$549$$ 217.321 + 125.471i 0.395849 + 0.228544i
$$550$$ 0 0
$$551$$ −208.024 + 120.103i −0.377539 + 0.217972i
$$552$$ −27.3368 −0.0495231
$$553$$ −382.569 575.698i −0.691806 1.04105i
$$554$$ 719.992 1.29962
$$555$$ 0 0
$$556$$ −402.706 232.502i −0.724291 0.418169i
$$557$$ −464.253 268.036i −0.833487 0.481214i 0.0215578 0.999768i $$-0.493137\pi$$
−0.855045 + 0.518553i $$0.826471\pi$$
$$558$$ 13.9639 + 24.1861i 0.0250249 + 0.0433443i
$$559$$ 743.660i 1.33034i
$$560$$ 0 0
$$561$$ 273.987 0.488391
$$562$$ −258.039 + 148.979i −0.459144 + 0.265087i
$$563$$ −494.806 + 857.029i −0.878874 + 1.52225i −0.0262960 + 0.999654i $$0.508371\pi$$
−0.852578 + 0.522600i $$0.824962\pi$$
$$564$$ −134.492 + 232.948i −0.238462 + 0.413028i
$$565$$ 0 0
$$566$$ 55.8424i 0.0986616i
$$567$$ 28.0068 56.4324i 0.0493948 0.0995281i
$$568$$ 192.630i 0.339137i
$$569$$ 248.330 + 430.120i 0.436432 + 0.755922i 0.997411 0.0719076i $$-0.0229087\pi$$
−0.560979 + 0.827830i $$0.689575\pi$$
$$570$$ 0 0
$$571$$ 71.0244 123.018i 0.124386 0.215443i −0.797107 0.603838i $$-0.793637\pi$$
0.921493 + 0.388395i $$0.126971\pi$$
$$572$$ 161.226 + 279.251i 0.281863 + 0.488201i
$$573$$ −405.841 −0.708274
$$574$$ −279.884 421.176i −0.487604 0.733757i
$$575$$ 0 0
$$576$$ 12.0000 + 20.7846i 0.0208333 + 0.0360844i
$$577$$ 189.689 328.551i 0.328751 0.569413i −0.653514 0.756915i $$-0.726706\pi$$
0.982264 + 0.187502i $$0.0600391\pi$$
$$578$$ 185.515 + 107.107i 0.320961 + 0.185307i
$$579$$ 29.3476 16.9438i 0.0506866 0.0292639i
$$580$$ 0 0
$$581$$ −188.240 + 11.8604i −0.323993 + 0.0204137i
$$582$$ 9.04185i 0.0155358i
$$583$$ −325.051 + 187.668i −0.557549 + 0.321901i
$$584$$ 214.714 + 123.965i 0.367661 + 0.212269i
$$585$$ 0 0
$$586$$ −109.740 + 63.3584i −0.187269 + 0.108120i
$$587$$ 234.204 0.398984 0.199492 0.979899i $$-0.436071\pi$$
0.199492 + 0.979899i $$0.436071\pi$$
$$588$$ −102.650 135.185i −0.174575 0.229906i
$$589$$ −158.654 −0.269361
$$590$$ 0 0
$$591$$ 269.164 + 155.402i 0.455438 + 0.262948i
$$592$$ −77.5840 44.7931i −0.131054 0.0756641i
$$593$$ 286.272 + 495.838i 0.482753 + 0.836152i 0.999804 0.0198023i $$-0.00630369\pi$$
−0.517051 + 0.855954i $$0.672970\pi$$
$$594$$ 55.3869i 0.0932439i
$$595$$ 0 0
$$596$$ −439.853 −0.738008
$$597$$ 383.874 221.630i 0.643006 0.371239i
$$598$$ 84.4016 146.188i 0.141140 0.244461i
$$599$$ 46.7105 80.9049i 0.0779807 0.135067i −0.824398 0.566011i $$-0.808486\pi$$
0.902379 + 0.430944i $$0.141819\pi$$
$$600$$ 0 0
$$601$$ 167.140i 0.278103i 0.990285 + 0.139051i $$0.0444053\pi$$
−0.990285 + 0.139051i $$0.955595\pi$$
$$602$$ −190.483 286.643i −0.316417 0.476151i
$$603$$ 199.746i 0.331255i
$$604$$ −260.922 451.930i −0.431990 0.748229i
$$605$$ 0 0
$$606$$ 223.686 387.436i 0.369119 0.639333i
$$607$$ −459.572 796.002i −0.757120 1.31137i −0.944314 0.329047i $$-0.893273\pi$$
0.187194 0.982323i $$-0.440061\pi$$
$$608$$ −136.341 −0.224245
$$609$$ −53.7173 + 108.238i −0.0882058 + 0.177730i
$$610$$ 0 0
$$611$$ −830.484 1438.44i −1.35922 2.35424i
$$612$$ −62.9623 + 109.054i −0.102880 + 0.178193i
$$613$$ −675.011 389.718i −1.10116 0.635755i −0.164635 0.986355i $$-0.552644\pi$$
−0.936525 + 0.350600i $$0.885978\pi$$
$$614$$ 576.215 332.678i 0.938462 0.541821i
$$615$$ 0 0
$$616$$ 133.672 + 66.3402i 0.217000 + 0.107695i
$$617$$ 510.821i 0.827911i 0.910297 + 0.413956i $$0.135853\pi$$
−0.910297 + 0.413956i $$0.864147\pi$$
$$618$$ 193.148 111.514i 0.312536 0.180443i
$$619$$ 808.792 + 466.956i 1.30661 + 0.754372i 0.981529 0.191314i $$-0.0612749\pi$$
0.325082 + 0.945686i $$0.394608\pi$$
$$620$$ 0 0
$$621$$ 25.1104 14.4975i 0.0404355 0.0233454i
$$622$$ −355.390 −0.571367
$$623$$ 81.0892 53.8862i 0.130159 0.0864947i
$$624$$ −148.199 −0.237498
$$625$$ 0 0
$$626$$ 475.766 + 274.684i 0.760009 + 0.438792i
$$627$$ −272.491 157.323i −0.434595 0.250914i
$$628$$ 114.191 + 197.784i 0.181832 + 0.314943i
$$629$$ 470.047i 0.747292i
$$630$$ 0 0
$$631$$ −614.861 −0.974423 −0.487212 0.873284i $$-0.661986\pi$$
−0.487212 + 0.873284i $$0.661986\pi$$
$$632$$ −241.877 + 139.648i −0.382717 + 0.220962i
$$633$$ 170.512 295.336i 0.269372 0.466566i
$$634$$ 105.627 182.952i 0.166605 0.288568i
$$635$$ 0 0
$$636$$ 172.505i 0.271234i
$$637$$ 1039.85 131.557i 1.63242 0.206526i
$$638$$ 106.232i 0.166508i
$$639$$ 102.157 + 176.942i 0.159871 + 0.276904i
$$640$$ 0 0
$$641$$ 94.1724 163.111i 0.146915 0.254464i −0.783171 0.621807i $$-0.786399\pi$$
0.930086 + 0.367343i $$0.119732\pi$$
$$642$$ −63.1189 109.325i −0.0983161 0.170288i
$$643$$ 23.8831 0.0371432 0.0185716 0.999828i $$-0.494088\pi$$
0.0185716 + 0.999828i $$0.494088\pi$$
$$644$$ −4.91242 77.9667i −0.00762798 0.121066i
$$645$$ 0 0
$$646$$ −357.681 619.521i −0.553685 0.959011i
$$647$$ 542.667 939.928i 0.838744 1.45275i −0.0522010 0.998637i $$-0.516624\pi$$
0.890945 0.454111i $$-0.150043\pi$$
$$648$$ −22.0454 12.7279i −0.0340207 0.0196419i
$$649$$ 549.735 317.390i 0.847049 0.489044i
$$650$$ 0 0
$$651$$ −66.4715 + 44.1724i −0.102107 + 0.0678531i
$$652$$ 97.4323i 0.149436i
$$653$$ 550.536 317.852i 0.843087 0.486756i −0.0152254 0.999884i $$-0.504847\pi$$
0.858312 + 0.513128i $$0.171513\pi$$
$$654$$ 81.3767 + 46.9829i 0.124429 + 0.0718393i
$$655$$ 0 0
$$656$$ −176.955 + 102.165i −0.269749 + 0.155740i
$$657$$ −262.970 −0.400258
$$658$$ −688.555 341.723i −1.04644 0.519336i
$$659$$ 888.955 1.34895 0.674473 0.738300i $$-0.264371\pi$$
0.674473 + 0.738300i $$0.264371\pi$$
$$660$$ 0 0
$$661$$ −656.362 378.951i −0.992983 0.573299i −0.0868187 0.996224i $$-0.527670\pi$$
−0.906165 + 0.422925i $$0.861003\pi$$
$$662$$ −576.770 332.998i −0.871253 0.503018i
$$663$$ −388.789 673.402i −0.586409 1.01569i
$$664$$ 76.2114i 0.114776i
$$665$$ 0 0
$$666$$ 95.0206 0.142674
$$667$$ −48.1620 + 27.8063i −0.0722068 + 0.0416886i
$$668$$ 49.6127 85.9316i 0.0742704 0.128640i
$$669$$ 373.270 646.522i 0.557952 0.966401i
$$670$$ 0 0
$$671$$ 630.464i 0.939589i
$$672$$ −57.1230 + 37.9600i −0.0850045 + 0.0564881i
$$673$$ 936.839i 1.39203i −0.718026 0.696017i $$-0.754954\pi$$
0.718026 0.696017i $$-0.245046\pi$$
$$674$$ −376.519 652.150i −0.558634 0.967582i
$$675$$ 0 0
$$676$$ 288.560 499.800i 0.426863 0.739349i
$$677$$ 123.589 + 214.062i 0.182554 + 0.316192i 0.942749 0.333502i $$-0.108230\pi$$
−0.760196 + 0.649694i $$0.774897\pi$$
$$678$$ 486.365 0.717352
$$679$$ 25.7881 1.62482i 0.0379795 0.00239296i
$$680$$ 0 0
$$681$$ −151.637 262.644i −0.222669 0.385673i
$$682$$ 35.0828 60.7652i 0.0514411 0.0890986i
$$683$$ −607.755 350.887i −0.889831 0.513744i −0.0159438 0.999873i $$-0.505075\pi$$
−0.873887 + 0.486129i $$0.838409\pi$$
$$684$$ 125.237 72.3057i 0.183095 0.105710i
$$685$$ 0 0
$$686$$ 367.112 317.059i 0.535149 0.462185i
$$687$$ 58.1435i 0.0846339i
$$688$$ −120.432 + 69.5313i −0.175046 + 0.101063i
$$689$$ 922.498 + 532.604i 1.33889 + 0.773011i
$$690$$ 0 0
$$691$$ −530.850 + 306.486i −0.768234 + 0.443540i −0.832244 0.554409i $$-0.812944\pi$$
0.0640104 + 0.997949i $$0.479611\pi$$
$$692$$ −470.682 −0.680176
$$693$$ −157.968 + 9.95302i −0.227948 + 0.0143622i
$$694$$ −635.863 −0.916230
$$695$$ 0 0
$$696$$ 42.2832 + 24.4122i 0.0607518 + 0.0350750i
$$697$$ −928.461 536.047i −1.33208 0.769078i
$$698$$ −233.823 404.993i −0.334990 0.580220i
$$699$$ 268.318i 0.383860i
$$700$$ 0 0
$$701$$ 161.307 0.230110 0.115055 0.993359i $$-0.463296\pi$$
0.115055 + 0.993359i $$0.463296\pi$$
$$702$$ 136.129 78.5942i 0.193916 0.111958i
$$703$$ −269.900 + 467.480i −0.383926 + 0.664979i
$$704$$ 30.1488 52.2193i 0.0428250 0.0741751i
$$705$$ 0 0
$$706$$ 383.777i 0.543593i
$$707$$ 1145.20 + 568.349i 1.61980 + 0.803889i
$$708$$ 291.745i 0.412069i
$$709$$ 285.175 + 493.938i 0.402222 + 0.696669i 0.993994 0.109436i $$-0.0349046\pi$$
−0.591772 + 0.806106i $$0.701571\pi$$
$$710$$ 0 0
$$711$$ 148.119 256.549i 0.208325 0.360829i
$$712$$ −19.6699 34.0693i −0.0276263 0.0478501i
$$713$$ −36.7317 −0.0515171
$$714$$ −322.345 159.977i −0.451464 0.224057i
$$715$$ 0 0
$$716$$ 44.2098 + 76.5736i 0.0617455 + 0.106946i
$$717$$ −274.176 + 474.887i −0.382393 + 0.662325i
$$718$$ 9.28847 + 5.36270i 0.0129366 + 0.00746894i
$$719$$ −431.817 + 249.310i −0.600580 + 0.346745i −0.769270 0.638924i $$-0.779380\pi$$
0.168690 + 0.985669i $$0.446046\pi$$
$$720$$ 0 0
$$721$$ 352.755 + 530.834i 0.489258 + 0.736246i
$$722$$ 310.987i 0.430730i
$$723$$ 350.254 202.219i 0.484446 0.279695i
$$724$$ 202.735 + 117.049i 0.280020 + 0.161670i
$$725$$ 0 0
$$726$$ −136.169 + 78.6171i −0.187560 + 0.108288i
$$727$$ 1058.79 1.45638 0.728190 0.685375i $$-0.240362\pi$$
0.728190 + 0.685375i $$0.240362\pi$$
$$728$$ −26.6313 422.675i −0.0365815 0.580597i
$$729$$ 27.0000 0.0370370
$$730$$ 0 0
$$731$$ −631.888 364.821i −0.864416 0.499071i
$$732$$ 250.941 + 144.881i 0.342816 + 0.197925i
$$733$$ −7.56721 13.1068i −0.0103236 0.0178810i 0.860817 0.508914i $$-0.169953\pi$$
−0.871141 + 0.491033i $$0.836620\pi$$
$$734$$ 751.530i 1.02388i
$$735$$ 0 0
$$736$$ −31.5658 −0.0428883
$$737$$ 434.609 250.922i 0.589700 0.340463i
$$738$$ 108.363 187.690i 0.146833 0.254322i
$$739$$ −81.3819 + 140.958i −0.110124 + 0.190741i −0.915820 0.401588i $$-0.868458\pi$$
0.805696 + 0.592329i $$0.201792\pi$$
$$740$$ 0 0
$$741$$ 892.967i 1.20508i
$$742$$ 491.998 30.9991i 0.663071 0.0417778i
$$743$$ 338.071i 0.455009i −0.973777 0.227504i $$-0.926943\pi$$
0.973777 0.227504i $$-0.0730566\pi$$
$$744$$ 16.1241 + 27.9277i 0.0216722 + 0.0375373i
$$745$$ 0 0
$$746$$ −406.564 + 704.189i −0.544991 + 0.943953i
$$747$$ −40.4172 70.0046i −0.0541060 0.0937143i
$$748$$ 316.373 0.422959
$$749$$ 300.462 199.666i 0.401151 0.266577i
$$750$$ 0 0
$$751$$ −239.087 414.111i −0.318359 0.551413i 0.661787 0.749692i $$-0.269798\pi$$
−0.980146 + 0.198279i $$0.936465\pi$$
$$752$$ −155.299 + 268.985i −0.206514 + 0.357693i
$$753$$ −85.0319 49.0932i −0.112924 0.0651968i
$$754$$ −261.097 + 150.744i −0.346282 + 0.199926i
$$755$$ 0 0
$$756$$ 32.3395 65.1625i 0.0427771 0.0861938i
$$757$$ 397.788i 0.525479i −0.964867 0.262739i $$-0.915374\pi$$
0.964867 0.262739i $$-0.0846260\pi$$
$$758$$ 768.483 443.684i 1.01383 0.585335i
$$759$$ −63.0874 36.4236i −0.0831192 0.0479889i
$$760$$ 0 0
$$761$$ −1264.02 + 729.785i −1.66100 + 0.958981i −0.688767 + 0.724983i $$0.741848\pi$$
−0.972237 + 0.233998i $$0.924819\pi$$
$$762$$ −181.540 −0.238241
$$763$$ −119.376 + 240.536i −0.156456 + 0.315250i
$$764$$ −468.625 −0.613383
$$765$$ 0 0
$$766$$ −81.5817 47.1012i −0.106503 0.0614898i
$$767$$ −1560.15 900.755i −2.03410 1.17439i
$$768$$ 13.8564 + 24.0000i 0.0180422 + 0.0312500i
$$769$$ 2.10093i 0.00273203i 0.999999 + 0.00136602i $$0.000434817\pi$$
−0.999999 + 0.00136602i $$0.999565\pi$$
$$770$$ 0 0
$$771$$ −503.055 −0.652471
$$772$$ 33.8876 19.5650i 0.0438959 0.0253433i
$$773$$ 226.305 391.972i 0.292762 0.507079i −0.681700 0.731632i $$-0.738759\pi$$
0.974462 + 0.224553i $$0.0720923\pi$$
$$774$$ 73.7491 127.737i 0.0952830 0.165035i
$$775$$ 0 0
$$776$$ 10.4406i 0.0134544i
$$777$$ 17.0752 + 271.007i 0.0219758 + 0.348786i
$$778$$ 776.473i 0.998037i
$$779$$ 615.594 + 1066.24i 0.790236 + 1.36873i
$$780$$ 0 0
$$781$$ 256.660 444.548i 0.328630 0.569204i