# Properties

 Label 1050.3.q.b.199.5 Level $1050$ Weight $3$ Character 1050.199 Analytic conductor $28.610$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Related objects

## 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 199.5 Root $$-2.22431 + 0.596002i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.199 Dual form 1050.3.q.b.649.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.647280 - 1.12112i) q^{11} +(1.73205 + 3.00000i) q^{12} +3.22960 q^{13} +(-4.24500 + 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(15.1826 - 26.2970i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-28.9470 + 16.7125i) q^{19} +(-0.974040 - 12.0852i) q^{21} -1.83078i q^{22} +(30.9462 - 17.8668i) q^{23} +(4.24264 + 2.44949i) q^{24} +(3.95544 - 2.28367i) q^{26} +5.19615 q^{27} +(1.12472 + 13.9547i) q^{28} +32.8033 q^{29} +(39.5125 + 22.8125i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(1.12112 + 1.94184i) q^{33} -42.9428i q^{34} -6.00000 q^{36} +(34.6873 - 20.0267i) q^{37} +(-23.6351 + 40.9372i) q^{38} +(-2.79692 + 4.84440i) q^{39} +42.2993i q^{41} +(-9.73845 - 14.1125i) q^{42} +55.4597i q^{43} +(-1.29456 - 2.24224i) q^{44} +(25.2675 - 43.7646i) q^{46} +(-30.3745 - 52.6102i) q^{47} +6.92820 q^{48} +(17.3875 - 45.8113i) q^{49} +(26.2970 + 45.5477i) q^{51} +(3.22960 - 5.59383i) q^{52} +(47.3438 + 27.3340i) q^{53} +(6.36396 - 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} -57.8939i q^{57} +(40.1757 - 23.1954i) q^{58} +(-11.4277 - 6.59780i) q^{59} +(34.1684 - 19.7271i) q^{61} +64.5236 q^{62} +(18.9713 + 9.00500i) q^{63} -8.00000 q^{64} +(2.74618 + 1.58551i) q^{66} +(34.7163 + 20.0434i) q^{67} +(-30.3651 - 52.5940i) q^{68} +61.8924i q^{69} +46.4480 q^{71} +(-7.34847 + 4.24264i) q^{72} +(68.2001 - 118.126i) q^{73} +(28.3220 - 49.0552i) q^{74} +66.8501i q^{76} +(0.728012 + 9.03263i) q^{77} +7.91088i q^{78} +(-21.1511 - 36.6348i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(29.9101 + 51.8059i) q^{82} +1.53725 q^{83} +(-21.9062 - 10.3981i) q^{84} +(39.2160 + 67.9240i) q^{86} +(-28.4085 + 49.2050i) q^{87} +(-3.17101 - 1.83078i) q^{88} +(30.2844 - 17.4847i) q^{89} +(-18.6070 + 12.8400i) q^{91} -71.4672i q^{92} +(-68.4376 + 39.5125i) q^{93} +(-74.4020 - 42.9560i) q^{94} +(8.48528 - 4.89898i) q^{96} -150.516 q^{97} +(-11.0982 - 68.4020i) q^{98} -3.88368 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
$$7$$ −5.76140 + 3.97571i −0.823057 + 0.567958i
$$8$$ 2.82843i 0.353553i
$$9$$ −1.50000 2.59808i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 0.647280 1.12112i 0.0588436 0.101920i −0.835103 0.550094i $$-0.814592\pi$$
0.893947 + 0.448174i $$0.147925\pi$$
$$12$$ 1.73205 + 3.00000i 0.144338 + 0.250000i
$$13$$ 3.22960 0.248431 0.124215 0.992255i $$-0.460359\pi$$
0.124215 + 0.992255i $$0.460359\pi$$
$$14$$ −4.24500 + 8.94315i −0.303214 + 0.638797i
$$15$$ 0 0
$$16$$ −2.00000 3.46410i −0.125000 0.216506i
$$17$$ 15.1826 26.2970i 0.893092 1.54688i 0.0569439 0.998377i $$-0.481864\pi$$
0.836148 0.548504i $$-0.184802\pi$$
$$18$$ −3.67423 2.12132i −0.204124 0.117851i
$$19$$ −28.9470 + 16.7125i −1.52352 + 0.879607i −0.523912 + 0.851773i $$0.675528\pi$$
−0.999613 + 0.0278345i $$0.991139\pi$$
$$20$$ 0 0
$$21$$ −0.974040 12.0852i −0.0463829 0.575484i
$$22$$ 1.83078i 0.0832175i
$$23$$ 30.9462 17.8668i 1.34549 0.776818i 0.357881 0.933767i $$-0.383499\pi$$
0.987607 + 0.156950i $$0.0501660\pi$$
$$24$$ 4.24264 + 2.44949i 0.176777 + 0.102062i
$$25$$ 0 0
$$26$$ 3.95544 2.28367i 0.152132 0.0878336i
$$27$$ 5.19615 0.192450
$$28$$ 1.12472 + 13.9547i 0.0401687 + 0.498384i
$$29$$ 32.8033 1.13115 0.565574 0.824697i $$-0.308655\pi$$
0.565574 + 0.824697i $$0.308655\pi$$
$$30$$ 0 0
$$31$$ 39.5125 + 22.8125i 1.27460 + 0.735888i 0.975849 0.218444i $$-0.0700981\pi$$
0.298747 + 0.954332i $$0.403431\pi$$
$$32$$ −4.89898 2.82843i −0.153093 0.0883883i
$$33$$ 1.12112 + 1.94184i 0.0339734 + 0.0588436i
$$34$$ 42.9428i 1.26302i
$$35$$ 0 0
$$36$$ −6.00000 −0.166667
$$37$$ 34.6873 20.0267i 0.937494 0.541262i 0.0483201 0.998832i $$-0.484613\pi$$
0.889174 + 0.457570i $$0.151280\pi$$
$$38$$ −23.6351 + 40.9372i −0.621976 + 1.07729i
$$39$$ −2.79692 + 4.84440i −0.0717158 + 0.124215i
$$40$$ 0 0
$$41$$ 42.2993i 1.03169i 0.856682 + 0.515845i $$0.172522\pi$$
−0.856682 + 0.515845i $$0.827478\pi$$
$$42$$ −9.73845 14.1125i −0.231868 0.336012i
$$43$$ 55.4597i 1.28976i 0.764283 + 0.644881i $$0.223093\pi$$
−0.764283 + 0.644881i $$0.776907\pi$$
$$44$$ −1.29456 2.24224i −0.0294218 0.0509601i
$$45$$ 0 0
$$46$$ 25.2675 43.7646i 0.549293 0.951403i
$$47$$ −30.3745 52.6102i −0.646266 1.11937i −0.984008 0.178127i $$-0.942996\pi$$
0.337741 0.941239i $$-0.390337\pi$$
$$48$$ 6.92820 0.144338
$$49$$ 17.3875 45.8113i 0.354847 0.934924i
$$50$$ 0 0
$$51$$ 26.2970 + 45.5477i 0.515627 + 0.893092i
$$52$$ 3.22960 5.59383i 0.0621077 0.107574i
$$53$$ 47.3438 + 27.3340i 0.893280 + 0.515735i 0.875014 0.484098i $$-0.160852\pi$$
0.0182660 + 0.999833i $$0.494185\pi$$
$$54$$ 6.36396 3.67423i 0.117851 0.0680414i
$$55$$ 0 0
$$56$$ 11.2450 + 16.2957i 0.200804 + 0.290995i
$$57$$ 57.8939i 1.01568i
$$58$$ 40.1757 23.1954i 0.692684 0.399921i
$$59$$ −11.4277 6.59780i −0.193690 0.111827i 0.400019 0.916507i $$-0.369004\pi$$
−0.593709 + 0.804680i $$0.702337\pi$$
$$60$$ 0 0
$$61$$ 34.1684 19.7271i 0.560137 0.323395i −0.193064 0.981186i $$-0.561842\pi$$
0.753200 + 0.657791i $$0.228509\pi$$
$$62$$ 64.5236 1.04070
$$63$$ 18.9713 + 9.00500i 0.301132 + 0.142937i
$$64$$ −8.00000 −0.125000
$$65$$ 0 0
$$66$$ 2.74618 + 1.58551i 0.0416087 + 0.0240228i
$$67$$ 34.7163 + 20.0434i 0.518153 + 0.299156i 0.736179 0.676787i $$-0.236628\pi$$
−0.218026 + 0.975943i $$0.569962\pi$$
$$68$$ −30.3651 52.5940i −0.446546 0.773440i
$$69$$ 61.8924i 0.896992i
$$70$$ 0 0
$$71$$ 46.4480 0.654198 0.327099 0.944990i $$-0.393929\pi$$
0.327099 + 0.944990i $$0.393929\pi$$
$$72$$ −7.34847 + 4.24264i −0.102062 + 0.0589256i
$$73$$ 68.2001 118.126i 0.934247 1.61816i 0.158277 0.987395i $$-0.449406\pi$$
0.775970 0.630769i $$-0.217261\pi$$
$$74$$ 28.3220 49.0552i 0.382730 0.662908i
$$75$$ 0 0
$$76$$ 66.8501i 0.879607i
$$77$$ 0.728012 + 9.03263i 0.00945470 + 0.117307i
$$78$$ 7.91088i 0.101422i
$$79$$ −21.1511 36.6348i −0.267736 0.463732i 0.700541 0.713612i $$-0.252942\pi$$
−0.968277 + 0.249880i $$0.919609\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.0555556 + 0.0962250i
$$82$$ 29.9101 + 51.8059i 0.364758 + 0.631779i
$$83$$ 1.53725 0.0185211 0.00926054 0.999957i $$-0.497052\pi$$
0.00926054 + 0.999957i $$0.497052\pi$$
$$84$$ −21.9062 10.3981i −0.260788 0.123787i
$$85$$ 0 0
$$86$$ 39.2160 + 67.9240i 0.456000 + 0.789814i
$$87$$ −28.4085 + 49.2050i −0.326534 + 0.565574i
$$88$$ −3.17101 1.83078i −0.0360342 0.0208044i
$$89$$ 30.2844 17.4847i 0.340274 0.196457i −0.320119 0.947377i $$-0.603723\pi$$
0.660393 + 0.750920i $$0.270390\pi$$
$$90$$ 0 0
$$91$$ −18.6070 + 12.8400i −0.204473 + 0.141098i
$$92$$ 71.4672i 0.776818i
$$93$$ −68.4376 + 39.5125i −0.735888 + 0.424865i
$$94$$ −74.4020 42.9560i −0.791511 0.456979i
$$95$$ 0 0
$$96$$ 8.48528 4.89898i 0.0883883 0.0510310i
$$97$$ −150.516 −1.55172 −0.775858 0.630907i $$-0.782683\pi$$
−0.775858 + 0.630907i $$0.782683\pi$$
$$98$$ −11.0982 68.4020i −0.113247 0.697979i
$$99$$ −3.88368 −0.0392291
$$100$$ 0 0
$$101$$ 103.806 + 59.9325i 1.02778 + 0.593391i 0.916349 0.400381i $$-0.131122\pi$$
0.111434 + 0.993772i $$0.464456\pi$$
$$102$$ 64.4142 + 37.1895i 0.631511 + 0.364603i
$$103$$ 49.8245 + 86.2986i 0.483733 + 0.837851i 0.999825 0.0186825i $$-0.00594715\pi$$
−0.516092 + 0.856533i $$0.672614\pi$$
$$104$$ 9.13469i 0.0878336i
$$105$$ 0 0
$$106$$ 77.3122 0.729360
$$107$$ 40.6950 23.4953i 0.380327 0.219582i −0.297634 0.954680i $$-0.596197\pi$$
0.677961 + 0.735098i $$0.262864\pi$$
$$108$$ 5.19615 9.00000i 0.0481125 0.0833333i
$$109$$ −29.0802 + 50.3683i −0.266791 + 0.462095i −0.968031 0.250830i $$-0.919297\pi$$
0.701241 + 0.712925i $$0.252630\pi$$
$$110$$ 0 0
$$111$$ 69.3746i 0.624996i
$$112$$ 25.2951 + 12.0067i 0.225849 + 0.107202i
$$113$$ 211.102i 1.86816i −0.357068 0.934078i $$-0.616224\pi$$
0.357068 0.934078i $$-0.383776\pi$$
$$114$$ −40.9372 70.9053i −0.359098 0.621976i
$$115$$ 0 0
$$116$$ 32.8033 56.8170i 0.282787 0.489802i
$$117$$ −4.84440 8.39075i −0.0414052 0.0717158i
$$118$$ −18.6614 −0.158148
$$119$$ 17.0762 + 211.869i 0.143498 + 1.78041i
$$120$$ 0 0
$$121$$ 59.6621 + 103.338i 0.493075 + 0.854031i
$$122$$ 27.8983 48.3213i 0.228675 0.396077i
$$123$$ −63.4490 36.6323i −0.515845 0.297823i
$$124$$ 79.0250 45.6251i 0.637298 0.367944i
$$125$$ 0 0
$$126$$ 29.6025 2.38590i 0.234940 0.0189357i
$$127$$ 90.2615i 0.710720i −0.934729 0.355360i $$-0.884358\pi$$
0.934729 0.355360i $$-0.115642\pi$$
$$128$$ −9.79796 + 5.65685i −0.0765466 + 0.0441942i
$$129$$ −83.1896 48.0296i −0.644881 0.372322i
$$130$$ 0 0
$$131$$ −174.806 + 100.924i −1.33440 + 0.770414i −0.985970 0.166923i $$-0.946617\pi$$
−0.348426 + 0.937336i $$0.613284\pi$$
$$132$$ 4.48449 0.0339734
$$133$$ 100.331 211.372i 0.754368 1.58927i
$$134$$ 56.6914 0.423070
$$135$$ 0 0
$$136$$ −74.3791 42.9428i −0.546905 0.315756i
$$137$$ −0.00352554 0.00203547i −2.57339e−5 1.48575e-5i 0.499987 0.866033i $$-0.333338\pi$$
−0.500013 + 0.866018i $$0.666671\pi$$
$$138$$ 43.7646 + 75.8024i 0.317134 + 0.549293i
$$139$$ 115.950i 0.834169i −0.908868 0.417085i $$-0.863052\pi$$
0.908868 0.417085i $$-0.136948\pi$$
$$140$$ 0 0
$$141$$ 105.220 0.746244
$$142$$ 56.8870 32.8437i 0.400613 0.231294i
$$143$$ 2.09046 3.62078i 0.0146186 0.0253201i
$$144$$ −6.00000 + 10.3923i −0.0416667 + 0.0721688i
$$145$$ 0 0
$$146$$ 192.899i 1.32123i
$$147$$ 53.6589 + 65.7550i 0.365027 + 0.447313i
$$148$$ 80.1068i 0.541262i
$$149$$ −2.59675 4.49770i −0.0174278 0.0301859i 0.857180 0.515017i $$-0.172214\pi$$
−0.874608 + 0.484831i $$0.838881\pi$$
$$150$$ 0 0
$$151$$ 80.3710 139.207i 0.532258 0.921899i −0.467032 0.884240i $$-0.654677\pi$$
0.999291 0.0376583i $$-0.0119898\pi$$
$$152$$ 47.2702 + 81.8744i 0.310988 + 0.538647i
$$153$$ −91.0954 −0.595395
$$154$$ 7.27866 + 10.5479i 0.0472640 + 0.0684928i
$$155$$ 0 0
$$156$$ 5.59383 + 9.68881i 0.0358579 + 0.0621077i
$$157$$ −47.6157 + 82.4728i −0.303285 + 0.525305i −0.976878 0.213798i $$-0.931417\pi$$
0.673593 + 0.739102i $$0.264750\pi$$
$$158$$ −51.8095 29.9122i −0.327908 0.189318i
$$159$$ −82.0019 + 47.3438i −0.515735 + 0.297760i
$$160$$ 0 0
$$161$$ −107.260 + 225.971i −0.666214 + 1.40355i
$$162$$ 12.7279i 0.0785674i
$$163$$ 213.473 123.249i 1.30965 0.756128i 0.327615 0.944811i $$-0.393755\pi$$
0.982038 + 0.188683i $$0.0604218\pi$$
$$164$$ 73.2645 + 42.2993i 0.446735 + 0.257923i
$$165$$ 0 0
$$166$$ 1.88274 1.08700i 0.0113418 0.00654819i
$$167$$ −14.9445 −0.0894879 −0.0447439 0.998998i $$-0.514247\pi$$
−0.0447439 + 0.998998i $$0.514247\pi$$
$$168$$ −34.1820 + 2.75500i −0.203464 + 0.0163988i
$$169$$ −158.570 −0.938282
$$170$$ 0 0
$$171$$ 86.8409 + 50.1376i 0.507841 + 0.293202i
$$172$$ 96.0591 + 55.4597i 0.558483 + 0.322440i
$$173$$ 83.8331 + 145.203i 0.484584 + 0.839325i 0.999843 0.0177099i $$-0.00563752\pi$$
−0.515259 + 0.857035i $$0.672304\pi$$
$$174$$ 80.3513i 0.461789i
$$175$$ 0 0
$$176$$ −5.17824 −0.0294218
$$177$$ 19.7934 11.4277i 0.111827 0.0645635i
$$178$$ 24.7271 42.8286i 0.138916 0.240610i
$$179$$ 33.4724 57.9759i 0.186997 0.323888i −0.757251 0.653124i $$-0.773458\pi$$
0.944248 + 0.329236i $$0.106791\pi$$
$$180$$ 0 0
$$181$$ 24.9109i 0.137629i −0.997629 0.0688146i $$-0.978078\pi$$
0.997629 0.0688146i $$-0.0219217\pi$$
$$182$$ −13.7097 + 28.8828i −0.0753278 + 0.158697i
$$183$$ 68.3367i 0.373425i
$$184$$ −50.5350 87.5291i −0.274647 0.475702i
$$185$$ 0 0
$$186$$ −55.8791 + 96.7854i −0.300425 + 0.520352i
$$187$$ −19.6547 34.0430i −0.105106 0.182048i
$$188$$ −121.498 −0.646266
$$189$$ −29.9371 + 20.6584i −0.158397 + 0.109304i
$$190$$ 0 0
$$191$$ 6.80231 + 11.7819i 0.0356142 + 0.0616856i 0.883283 0.468840i $$-0.155328\pi$$
−0.847669 + 0.530526i $$0.821995\pi$$
$$192$$ 6.92820 12.0000i 0.0360844 0.0625000i
$$193$$ 157.978 + 91.2089i 0.818541 + 0.472585i 0.849913 0.526923i $$-0.176654\pi$$
−0.0313718 + 0.999508i $$0.509988\pi$$
$$194$$ −184.344 + 106.431i −0.950228 + 0.548615i
$$195$$ 0 0
$$196$$ −61.9600 75.9273i −0.316122 0.387384i
$$197$$ 286.679i 1.45522i −0.685989 0.727612i $$-0.740630\pi$$
0.685989 0.727612i $$-0.259370\pi$$
$$198$$ −4.75652 + 2.74618i −0.0240228 + 0.0138696i
$$199$$ 2.74117 + 1.58262i 0.0137747 + 0.00795285i 0.506872 0.862022i $$-0.330802\pi$$
−0.493097 + 0.869974i $$0.664135\pi$$
$$200$$ 0 0
$$201$$ −60.1303 + 34.7163i −0.299156 + 0.172718i
$$202$$ 169.515 0.839181
$$203$$ −188.993 + 130.416i −0.931000 + 0.642445i
$$204$$ 105.188 0.515627
$$205$$ 0 0
$$206$$ 122.045 + 70.4625i 0.592450 + 0.342051i
$$207$$ −92.8387 53.6004i −0.448496 0.258939i
$$208$$ −6.45920 11.1877i −0.0310539 0.0537869i
$$209$$ 43.2708i 0.207037i
$$210$$ 0 0
$$211$$ −179.324 −0.849878 −0.424939 0.905222i $$-0.639705\pi$$
−0.424939 + 0.905222i $$0.639705\pi$$
$$212$$ 94.6877 54.6679i 0.446640 0.257868i
$$213$$ −40.2252 + 69.6720i −0.188851 + 0.327099i
$$214$$ 33.2273 57.5514i 0.155268 0.268932i
$$215$$ 0 0
$$216$$ 14.6969i 0.0680414i
$$217$$ −318.343 + 25.6578i −1.46702 + 0.118239i
$$218$$ 82.2512i 0.377299i
$$219$$ 118.126 + 204.600i 0.539388 + 0.934247i
$$220$$ 0 0
$$221$$ 49.0336 84.9288i 0.221872 0.384293i
$$222$$ 49.0552 + 84.9661i 0.220969 + 0.382730i
$$223$$ −71.3345 −0.319886 −0.159943 0.987126i $$-0.551131\pi$$
−0.159943 + 0.987126i $$0.551131\pi$$
$$224$$ 39.4700 3.18120i 0.176205 0.0142018i
$$225$$ 0 0
$$226$$ −149.271 258.546i −0.660493 1.14401i
$$227$$ −71.2698 + 123.443i −0.313964 + 0.543802i −0.979217 0.202817i $$-0.934990\pi$$
0.665253 + 0.746618i $$0.268324\pi$$
$$228$$ −100.275 57.8939i −0.439804 0.253921i
$$229$$ −109.001 + 62.9320i −0.475989 + 0.274812i −0.718743 0.695276i $$-0.755282\pi$$
0.242755 + 0.970088i $$0.421949\pi$$
$$230$$ 0 0
$$231$$ −14.1794 6.73047i −0.0613828 0.0291362i
$$232$$ 92.7817i 0.399921i
$$233$$ 142.258 82.1326i 0.610549 0.352500i −0.162631 0.986687i $$-0.551998\pi$$
0.773180 + 0.634186i $$0.218665\pi$$
$$234$$ −11.8663 6.85102i −0.0507108 0.0292779i
$$235$$ 0 0
$$236$$ −22.8555 + 13.1956i −0.0968452 + 0.0559136i
$$237$$ 73.2697 0.309155
$$238$$ 170.728 + 247.411i 0.717344 + 1.03954i
$$239$$ 50.4246 0.210982 0.105491 0.994420i $$-0.466359\pi$$
0.105491 + 0.994420i $$0.466359\pi$$
$$240$$ 0 0
$$241$$ −169.006 97.5757i −0.701270 0.404879i 0.106550 0.994307i $$-0.466020\pi$$
−0.807820 + 0.589429i $$0.799353\pi$$
$$242$$ 146.142 + 84.3749i 0.603891 + 0.348657i
$$243$$ −7.79423 13.5000i −0.0320750 0.0555556i
$$244$$ 78.9084i 0.323395i
$$245$$ 0 0
$$246$$ −103.612 −0.421186
$$247$$ −93.4872 + 53.9748i −0.378491 + 0.218522i
$$248$$ 64.5236 111.758i 0.260176 0.450638i
$$249$$ −1.33130 + 2.30587i −0.00534657 + 0.00926054i
$$250$$ 0 0
$$251$$ 328.725i 1.30966i 0.755775 + 0.654832i $$0.227260\pi$$
−0.755775 + 0.654832i $$0.772740\pi$$
$$252$$ 34.5684 23.8542i 0.137176 0.0946597i
$$253$$ 46.2593i 0.182843i
$$254$$ −63.8245 110.547i −0.251278 0.435225i
$$255$$ 0 0
$$256$$ −8.00000 + 13.8564i −0.0312500 + 0.0541266i
$$257$$ 201.596 + 349.175i 0.784420 + 1.35866i 0.929345 + 0.369213i $$0.120373\pi$$
−0.144924 + 0.989443i $$0.546294\pi$$
$$258$$ −135.848 −0.526543
$$259$$ −120.227 + 253.288i −0.464197 + 0.977947i
$$260$$ 0 0
$$261$$ −49.2050 85.2255i −0.188525 0.326534i
$$262$$ −142.728 + 247.213i −0.544765 + 0.943560i
$$263$$ −431.240 248.977i −1.63970 0.946679i −0.980937 0.194326i $$-0.937748\pi$$
−0.658759 0.752354i $$-0.728919\pi$$
$$264$$ 5.49235 3.17101i 0.0208044 0.0120114i
$$265$$ 0 0
$$266$$ −26.5830 329.822i −0.0999360 1.23993i
$$267$$ 60.5688i 0.226849i
$$268$$ 69.4325 40.0869i 0.259077 0.149578i
$$269$$ 155.357 + 89.6952i 0.577534 + 0.333439i 0.760153 0.649745i $$-0.225124\pi$$
−0.182619 + 0.983184i $$0.558457\pi$$
$$270$$ 0 0
$$271$$ −126.057 + 72.7792i −0.465156 + 0.268558i −0.714210 0.699932i $$-0.753214\pi$$
0.249054 + 0.968490i $$0.419880\pi$$
$$272$$ −121.461 −0.446546
$$273$$ −3.14576 39.0303i −0.0115229 0.142968i
$$274$$ −0.00575719 −2.10116e−5
$$275$$ 0 0
$$276$$ 107.201 + 61.8924i 0.388409 + 0.224248i
$$277$$ −185.057 106.843i −0.668076 0.385714i 0.127271 0.991868i $$-0.459378\pi$$
−0.795347 + 0.606154i $$0.792712\pi$$
$$278$$ −81.9887 142.009i −0.294923 0.510822i
$$279$$ 136.875i 0.490592i
$$280$$ 0 0
$$281$$ −349.479 −1.24370 −0.621849 0.783137i $$-0.713618\pi$$
−0.621849 + 0.783137i $$0.713618\pi$$
$$282$$ 128.868 74.4020i 0.456979 0.263837i
$$283$$ 47.1253 81.6234i 0.166521 0.288422i −0.770674 0.637230i $$-0.780080\pi$$
0.937194 + 0.348808i $$0.113413\pi$$
$$284$$ 46.4480 80.4503i 0.163549 0.283276i
$$285$$ 0 0
$$286$$ 5.91271i 0.0206738i
$$287$$ −168.170 243.703i −0.585957 0.849140i
$$288$$ 16.9706i 0.0589256i
$$289$$ −316.521 548.230i −1.09523 1.89699i
$$290$$ 0 0
$$291$$ 130.351 225.775i 0.447942 0.775858i
$$292$$ −136.400 236.252i −0.467124 0.809082i
$$293$$ −195.931 −0.668707 −0.334354 0.942448i $$-0.608518\pi$$
−0.334354 + 0.942448i $$0.608518\pi$$
$$294$$ 112.214 + 42.5905i 0.381681 + 0.144866i
$$295$$ 0 0
$$296$$ −56.6441 98.1104i −0.191365 0.331454i
$$297$$ 3.36337 5.82552i 0.0113245 0.0196145i
$$298$$ −6.36070 3.67235i −0.0213446 0.0123233i
$$299$$ 99.9440 57.7027i 0.334261 0.192986i
$$300$$ 0 0
$$301$$ −220.492 319.526i −0.732531 1.06155i
$$302$$ 227.324i 0.752727i
$$303$$ −179.797 + 103.806i −0.593391 + 0.342594i
$$304$$ 115.788 + 66.8501i 0.380881 + 0.219902i
$$305$$ 0 0
$$306$$ −111.569 + 64.4142i −0.364603 + 0.210504i
$$307$$ −452.419 −1.47368 −0.736839 0.676069i $$-0.763682\pi$$
−0.736839 + 0.676069i $$0.763682\pi$$
$$308$$ 16.3730 + 7.77168i 0.0531590 + 0.0252327i
$$309$$ −172.597 −0.558567
$$310$$ 0 0
$$311$$ −56.8889 32.8448i −0.182922 0.105610i 0.405743 0.913987i $$-0.367013\pi$$
−0.588665 + 0.808377i $$0.700346\pi$$
$$312$$ 13.7020 + 7.91088i 0.0439168 + 0.0253554i
$$313$$ 177.290 + 307.075i 0.566422 + 0.981071i 0.996916 + 0.0784776i $$0.0250059\pi$$
−0.430494 + 0.902593i $$0.641661\pi$$
$$314$$ 134.678i 0.428909i
$$315$$ 0 0
$$316$$ −84.6045 −0.267736
$$317$$ −116.792 + 67.4299i −0.368429 + 0.212713i −0.672772 0.739850i $$-0.734896\pi$$
0.304343 + 0.952563i $$0.401563\pi$$
$$318$$ −66.9543 + 115.968i −0.210548 + 0.364680i
$$319$$ 21.2329 36.7765i 0.0665609 0.115287i
$$320$$ 0 0
$$321$$ 81.3900i 0.253551i
$$322$$ 28.4190 + 352.601i 0.0882576 + 1.09504i
$$323$$ 1014.96i 3.14228i
$$324$$ 9.00000 + 15.5885i 0.0277778 + 0.0481125i
$$325$$ 0 0
$$326$$ 174.300 301.897i 0.534664 0.926064i
$$327$$ −50.3683 87.2405i −0.154032 0.266791i
$$328$$ 119.641 0.364758
$$329$$ 384.162 + 182.348i 1.16767 + 0.554250i
$$330$$ 0 0
$$331$$ 90.2612 + 156.337i 0.272692 + 0.472317i 0.969550 0.244892i $$-0.0787525\pi$$
−0.696858 + 0.717209i $$0.745419\pi$$
$$332$$ 1.53725 2.66259i 0.00463027 0.00801986i
$$333$$ −104.062 60.0801i −0.312498 0.180421i
$$334$$ −18.3032 + 10.5673i −0.0547999 + 0.0316387i
$$335$$ 0 0
$$336$$ −39.9162 + 27.5445i −0.118798 + 0.0819777i
$$337$$ 5.84677i 0.0173495i 0.999962 + 0.00867473i $$0.00276129\pi$$
−0.999962 + 0.00867473i $$0.997239\pi$$
$$338$$ −194.207 + 112.126i −0.574578 + 0.331733i
$$339$$ 316.653 + 182.819i 0.934078 + 0.539290i
$$340$$ 0 0
$$341$$ 51.1513 29.5322i 0.150004 0.0866047i
$$342$$ 141.811 0.414651
$$343$$ 81.9559 + 333.065i 0.238938 + 0.971035i
$$344$$ 156.864 0.456000
$$345$$ 0 0
$$346$$ 205.348 + 118.558i 0.593492 + 0.342653i
$$347$$ 339.718 + 196.136i 0.979014 + 0.565234i 0.901972 0.431794i $$-0.142119\pi$$
0.0770414 + 0.997028i $$0.475453\pi$$
$$348$$ 56.8170 + 98.4099i 0.163267 + 0.282787i
$$349$$ 230.853i 0.661471i −0.943724 0.330735i $$-0.892703\pi$$
0.943724 0.330735i $$-0.107297\pi$$
$$350$$ 0 0
$$351$$ 16.7815 0.0478106
$$352$$ −6.34202 + 3.66157i −0.0180171 + 0.0104022i
$$353$$ 62.8188 108.805i 0.177957 0.308230i −0.763224 0.646134i $$-0.776385\pi$$
0.941181 + 0.337904i $$0.109718\pi$$
$$354$$ 16.1613 27.9921i 0.0456533 0.0790738i
$$355$$ 0 0
$$356$$ 69.9388i 0.196457i
$$357$$ −332.592 157.870i −0.931630 0.442212i
$$358$$ 94.6743i 0.264453i
$$359$$ 215.984 + 374.096i 0.601628 + 1.04205i 0.992575 + 0.121637i $$0.0388143\pi$$
−0.390947 + 0.920413i $$0.627852\pi$$
$$360$$ 0 0
$$361$$ 378.118 654.919i 1.04742 1.81418i
$$362$$ −17.6147 30.5095i −0.0486593 0.0842803i
$$363$$ −206.675 −0.569354
$$364$$ 3.63241 + 45.0683i 0.00997916 + 0.123814i
$$365$$ 0 0
$$366$$ 48.3213 + 83.6950i 0.132026 + 0.228675i
$$367$$ −236.049 + 408.849i −0.643185 + 1.11403i 0.341532 + 0.939870i $$0.389054\pi$$
−0.984717 + 0.174159i $$0.944279\pi$$
$$368$$ −123.785 71.4672i −0.336372 0.194204i
$$369$$ 109.897 63.4490i 0.297823 0.171948i
$$370$$ 0 0
$$371$$ −381.439 + 30.7432i −1.02814 + 0.0828658i
$$372$$ 158.050i 0.424865i
$$373$$ 75.7963 43.7610i 0.203207 0.117322i −0.394943 0.918705i $$-0.629236\pi$$
0.598151 + 0.801384i $$0.295902\pi$$
$$374$$ −48.1441 27.7960i −0.128728 0.0743209i
$$375$$ 0 0
$$376$$ −148.804 + 85.9121i −0.395756 + 0.228490i
$$377$$ 105.942 0.281012
$$378$$ −22.0577 + 46.4700i −0.0583536 + 0.122936i
$$379$$ 359.658 0.948965 0.474483 0.880265i $$-0.342635\pi$$
0.474483 + 0.880265i $$0.342635\pi$$
$$380$$ 0 0
$$381$$ 135.392 + 78.1687i 0.355360 + 0.205167i
$$382$$ 16.6622 + 9.61992i 0.0436183 + 0.0251830i
$$383$$ 242.085 + 419.304i 0.632077 + 1.09479i 0.987126 + 0.159942i $$0.0511306\pi$$
−0.355050 + 0.934847i $$0.615536\pi$$
$$384$$ 19.5959i 0.0510310i
$$385$$ 0 0
$$386$$ 257.978 0.668336
$$387$$ 144.089 83.1896i 0.372322 0.214960i
$$388$$ −150.516 + 260.702i −0.387929 + 0.671913i
$$389$$ −179.791 + 311.407i −0.462188 + 0.800533i −0.999070 0.0431246i $$-0.986269\pi$$
0.536882 + 0.843657i $$0.319602\pi$$
$$390$$ 0 0
$$391$$ 1085.06i 2.77508i
$$392$$ −129.574 49.1793i −0.330546 0.125457i
$$393$$ 349.612i 0.889597i
$$394$$ −202.713 351.109i −0.514499 0.891139i
$$395$$ 0 0
$$396$$ −3.88368 + 6.72673i −0.00980727 + 0.0169867i
$$397$$ −90.6969 157.092i −0.228456 0.395697i 0.728895 0.684626i $$-0.240034\pi$$
−0.957351 + 0.288929i $$0.906701\pi$$
$$398$$ 4.47632 0.0112470
$$399$$ 230.169 + 333.550i 0.576865 + 0.835965i
$$400$$ 0 0
$$401$$ 132.742 + 229.916i 0.331027 + 0.573355i 0.982713 0.185133i $$-0.0592716\pi$$
−0.651687 + 0.758488i $$0.725938\pi$$
$$402$$ −49.0962 + 85.0371i −0.122130 + 0.211535i
$$403$$ 127.610 + 73.6754i 0.316649 + 0.182817i
$$404$$ 207.612 119.865i 0.513891 0.296695i
$$405$$ 0 0
$$406$$ −139.250 + 293.365i −0.342980 + 0.722574i
$$407$$ 51.8516i 0.127399i
$$408$$ 128.828 74.3791i 0.315756 0.182302i
$$409$$ 492.567 + 284.384i 1.20432 + 0.695315i 0.961513 0.274759i $$-0.0885981\pi$$
0.242808 + 0.970074i $$0.421931\pi$$
$$410$$ 0 0
$$411$$ 0.00610642 0.00352554i 1.48575e−5 8.57797e-6i
$$412$$ 199.298 0.483733
$$413$$ 92.0707 7.42071i 0.222931 0.0179678i
$$414$$ −151.605 −0.366195
$$415$$ 0 0
$$416$$ −15.8218 9.13469i −0.0380331 0.0219584i
$$417$$ 173.924 + 100.415i 0.417085 + 0.240804i
$$418$$ 30.5970 + 52.9956i 0.0731987 + 0.126784i
$$419$$ 556.041i 1.32707i −0.748146 0.663534i $$-0.769056\pi$$
0.748146 0.663534i $$-0.230944\pi$$
$$420$$ 0 0
$$421$$ −476.267 −1.13128 −0.565638 0.824654i $$-0.691370\pi$$
−0.565638 + 0.824654i $$0.691370\pi$$
$$422$$ −219.627 + 126.801i −0.520442 + 0.300477i
$$423$$ −91.1235 + 157.831i −0.215422 + 0.373122i
$$424$$ 77.3122 133.909i 0.182340 0.315822i
$$425$$ 0 0
$$426$$ 113.774i 0.267075i
$$427$$ −118.428 + 249.499i −0.277350 + 0.584307i
$$428$$ 93.9810i 0.219582i
$$429$$ 3.62078 + 6.27137i 0.00844004 + 0.0146186i
$$430$$ 0 0
$$431$$ −229.808 + 398.039i −0.533196 + 0.923523i 0.466052 + 0.884757i $$0.345676\pi$$
−0.999248 + 0.0387660i $$0.987657\pi$$
$$432$$ −10.3923 18.0000i −0.0240563 0.0416667i
$$433$$ 65.9185 0.152237 0.0761183 0.997099i $$-0.475747\pi$$
0.0761183 + 0.997099i $$0.475747\pi$$
$$434$$ −371.746 + 256.527i −0.856559 + 0.591076i
$$435$$ 0 0
$$436$$ 58.1604 + 100.737i 0.133395 + 0.231047i
$$437$$ −597.199 + 1034.38i −1.36659 + 2.36700i
$$438$$ 289.348 + 167.055i 0.660613 + 0.381405i
$$439$$ 307.619 177.604i 0.700727 0.404565i −0.106891 0.994271i $$-0.534090\pi$$
0.807618 + 0.589706i $$0.200756\pi$$
$$440$$ 0 0
$$441$$ −145.102 + 23.5429i −0.329031 + 0.0533852i
$$442$$ 138.688i 0.313774i
$$443$$ −656.650 + 379.117i −1.48228 + 0.855795i −0.999798 0.0201113i $$-0.993598\pi$$
−0.482482 + 0.875906i $$0.660265\pi$$
$$444$$ 120.160 + 69.3746i 0.270631 + 0.156249i
$$445$$ 0 0
$$446$$ −87.3666 + 50.4411i −0.195889 + 0.113097i
$$447$$ 8.99539 0.0201239
$$448$$ 46.0912 31.8057i 0.102882 0.0709948i
$$449$$ −668.104 −1.48798 −0.743992 0.668189i $$-0.767070\pi$$
−0.743992 + 0.668189i $$0.767070\pi$$
$$450$$ 0 0
$$451$$ 47.4227 + 27.3795i 0.105150 + 0.0607084i
$$452$$ −365.639 211.102i −0.808936 0.467039i
$$453$$ 139.207 + 241.113i 0.307300 + 0.532258i
$$454$$ 201.581i 0.444012i
$$455$$ 0 0
$$456$$ −163.749 −0.359098
$$457$$ 645.475 372.665i 1.41242 0.815460i 0.416802 0.908997i $$-0.363151\pi$$
0.995616 + 0.0935379i $$0.0298176\pi$$
$$458$$ −88.9993 + 154.151i −0.194322 + 0.336575i
$$459$$ 78.8909 136.643i 0.171876 0.297697i
$$460$$ 0 0
$$461$$ 592.937i 1.28620i −0.765783 0.643099i $$-0.777648\pi$$
0.765783 0.643099i $$-0.222352\pi$$
$$462$$ −22.1253 + 1.78326i −0.0478903 + 0.00385987i
$$463$$ 529.829i 1.14434i −0.820136 0.572169i $$-0.806102\pi$$
0.820136 0.572169i $$-0.193898\pi$$
$$464$$ −65.6066 113.634i −0.141394 0.244901i
$$465$$ 0 0
$$466$$ 116.153 201.183i 0.249255 0.431723i
$$467$$ 83.6375 + 144.864i 0.179095 + 0.310202i 0.941571 0.336815i $$-0.109350\pi$$
−0.762476 + 0.647017i $$0.776016\pi$$
$$468$$ −19.3776 −0.0414052
$$469$$ −279.701 + 22.5434i −0.596378 + 0.0480669i
$$470$$ 0 0
$$471$$ −82.4728 142.847i −0.175102 0.303285i
$$472$$ −18.6614 + 32.3225i −0.0395369 + 0.0684799i
$$473$$ 62.1771 + 35.8980i 0.131453 + 0.0758943i
$$474$$ 89.7367 51.8095i 0.189318 0.109303i
$$475$$ 0 0
$$476$$ 384.044 + 182.292i 0.806815 + 0.382966i
$$477$$ 164.004i 0.343824i
$$478$$ 61.7573 35.6556i 0.129199 0.0745933i
$$479$$ −221.195 127.707i −0.461785 0.266612i 0.251009 0.967985i $$-0.419237\pi$$
−0.712795 + 0.701373i $$0.752571\pi$$
$$480$$ 0 0
$$481$$ 112.026 64.6783i 0.232902 0.134466i
$$482$$ −275.986 −0.572585
$$483$$ −246.066 356.587i −0.509454 0.738276i
$$484$$ 238.648 0.493075
$$485$$ 0 0
$$486$$ −19.0919 11.0227i −0.0392837 0.0226805i
$$487$$ 525.531 + 303.415i 1.07912 + 0.623030i 0.930659 0.365889i $$-0.119235\pi$$
0.148460 + 0.988918i $$0.452568\pi$$
$$488$$ −55.7967 96.6427i −0.114337 0.198038i
$$489$$ 426.947i 0.873102i
$$490$$ 0 0
$$491$$ 707.855 1.44166 0.720830 0.693112i $$-0.243761\pi$$
0.720830 + 0.693112i $$0.243761\pi$$
$$492$$ −126.898 + 73.2645i −0.257923 + 0.148912i
$$493$$ 498.038 862.628i 1.01022 1.74975i
$$494$$ −76.3319 + 132.211i −0.154518 + 0.267633i
$$495$$ 0 0
$$496$$ 182.500i 0.367944i
$$497$$ −267.606 + 184.664i −0.538442 + 0.371557i
$$498$$ 3.76548i 0.00756120i
$$499$$ 330.115 + 571.776i 0.661553 + 1.14584i 0.980208 + 0.197972i $$0.0634357\pi$$
−0.318655 + 0.947871i $$0.603231\pi$$
$$500$$ 0 0
$$501$$ 12.9423 22.4167i 0.0258329 0.0447439i
$$502$$ 232.444 + 402.605i 0.463036 + 0.802002i
$$503$$ 254.083 0.505136 0.252568 0.967579i $$-0.418725\pi$$
0.252568 + 0.967579i $$0.418725\pi$$
$$504$$ 25.4700 53.6589i 0.0505357 0.106466i
$$505$$ 0 0
$$506$$ −32.7103 56.6559i −0.0646448 0.111968i
$$507$$ 137.325 237.855i 0.270859 0.469141i
$$508$$ −156.337 90.2615i −0.307751 0.177680i
$$509$$ −222.003 + 128.174i −0.436156 + 0.251815i −0.701966 0.712211i $$-0.747694\pi$$
0.265810 + 0.964026i $$0.414361\pi$$
$$510$$ 0 0
$$511$$ 76.7063 + 951.715i 0.150110 + 1.86246i
$$512$$ 22.6274i 0.0441942i
$$513$$ −150.413 + 86.8409i −0.293202 + 0.169280i
$$514$$ 493.807 + 285.100i 0.960715 + 0.554669i
$$515$$ 0 0
$$516$$ −166.379 + 96.0591i −0.322440 + 0.186161i
$$517$$ −78.6433 −0.152115
$$518$$ 31.8545 + 395.227i 0.0614952 + 0.762986i
$$519$$ −290.406 −0.559550
$$520$$ 0 0
$$521$$ 164.700 + 95.0898i 0.316124 + 0.182514i 0.649663 0.760222i $$-0.274910\pi$$
−0.333540 + 0.942736i $$0.608243\pi$$
$$522$$ −120.527 69.5863i −0.230895 0.133307i
$$523$$ −173.610 300.701i −0.331950 0.574954i 0.650944 0.759126i $$-0.274373\pi$$
−0.982894 + 0.184171i $$0.941040\pi$$
$$524$$ 403.697i 0.770414i
$$525$$ 0 0
$$526$$ −704.212 −1.33881
$$527$$ 1199.80 692.706i 2.27666 1.31443i
$$528$$ 4.48449 7.76736i 0.00849335 0.0147109i
$$529$$ 373.946 647.693i 0.706891 1.22437i
$$530$$ 0 0
$$531$$ 39.5868i 0.0745515i
$$532$$ −265.777 385.151i −0.499580 0.723967i
$$533$$ 136.610i 0.256304i
$$534$$ 42.8286 + 74.1813i 0.0802033 + 0.138916i
$$535$$ 0 0
$$536$$ 56.6914 98.1924i 0.105768 0.183195i
$$537$$ 57.9759 + 100.417i 0.107963 + 0.186997i
$$538$$ 253.696 0.471554
$$539$$ −40.1055 49.1462i −0.0744072 0.0911804i
$$540$$ 0 0
$$541$$ −216.672 375.287i −0.400503 0.693691i 0.593284 0.804993i $$-0.297831\pi$$
−0.993787 + 0.111302i $$0.964498\pi$$
$$542$$ −102.925 + 178.272i −0.189899 + 0.328915i
$$543$$ 37.3663 + 21.5735i 0.0688146 + 0.0397301i
$$544$$ −148.758 + 85.8856i −0.273452 + 0.157878i
$$545$$ 0 0
$$546$$ −31.4513 45.5777i −0.0576032 0.0834757i
$$547$$ 718.061i 1.31272i −0.754446 0.656362i $$-0.772094\pi$$
0.754446 0.656362i $$-0.227906\pi$$
$$548$$ −0.00705109 + 0.00407095i −1.28670e−5 + 7.42874e-6i
$$549$$ −102.505 59.1813i −0.186712 0.107798i
$$550$$ 0 0
$$551$$ −949.556 + 548.226i −1.72333 + 0.994966i
$$552$$ 175.058 0.317134
$$553$$ 267.510 + 126.977i 0.483742 + 0.229615i
$$554$$ −302.197 −0.545482
$$555$$ 0 0
$$556$$ −200.830 115.950i −0.361206 0.208542i
$$557$$ 858.396 + 495.595i 1.54111 + 0.889758i 0.998769 + 0.0495971i $$0.0157937\pi$$
0.542337 + 0.840161i $$0.317540\pi$$
$$558$$ −96.7854 167.637i −0.173451 0.300425i
$$559$$ 179.113i 0.320417i
$$560$$ 0 0
$$561$$ 68.0860 0.121365
$$562$$ −428.023 + 247.119i −0.761606 + 0.439713i
$$563$$ 290.108 502.481i 0.515289 0.892506i −0.484554 0.874762i $$-0.661018\pi$$
0.999843 0.0177449i $$-0.00564868\pi$$
$$564$$ 105.220 182.247i 0.186561 0.323133i
$$565$$ 0 0
$$566$$ 133.291i 0.235496i
$$567$$ −5.06126 62.7964i −0.00892639 0.110752i
$$568$$ 131.375i 0.231294i
$$569$$ −106.770 184.931i −0.187645 0.325010i 0.756820 0.653624i $$-0.226752\pi$$
−0.944465 + 0.328613i $$0.893419\pi$$
$$570$$ 0 0
$$571$$ 378.751 656.016i 0.663311 1.14889i −0.316429 0.948616i $$-0.602484\pi$$
0.979740 0.200273i $$-0.0641828\pi$$
$$572$$ −4.18091 7.24156i −0.00730929 0.0126601i
$$573$$ −23.5639 −0.0411237
$$574$$ −378.289 179.560i −0.659040 0.312823i
$$575$$ 0 0
$$576$$ 12.0000 + 20.7846i 0.0208333 + 0.0360844i
$$577$$ −90.7836 + 157.242i −0.157337 + 0.272516i −0.933908 0.357514i $$-0.883624\pi$$
0.776570 + 0.630031i $$0.216958\pi$$
$$578$$ −775.314 447.628i −1.34137 0.774442i
$$579$$ −273.627 + 157.978i −0.472585 + 0.272847i
$$580$$ 0 0
$$581$$ −8.85671 + 6.11165i −0.0152439 + 0.0105192i
$$582$$ 368.689i 0.633486i
$$583$$ 61.2894 35.3855i 0.105128 0.0606955i
$$584$$ −334.111 192.899i −0.572107 0.330306i
$$585$$ 0 0
$$586$$ −239.966 + 138.544i −0.409498 + 0.236424i
$$587$$ 156.397 0.266434 0.133217 0.991087i $$-0.457469\pi$$
0.133217 + 0.991087i $$0.457469\pi$$
$$588$$ 167.550 27.1850i 0.284949 0.0462329i
$$589$$ −1525.02 −2.58917
$$590$$ 0 0
$$591$$ 430.019 + 248.271i 0.727612 + 0.420087i
$$592$$ −138.749 80.1068i −0.234373 0.135316i
$$593$$ −105.889 183.404i −0.178564 0.309282i 0.762825 0.646605i $$-0.223812\pi$$
−0.941389 + 0.337323i $$0.890479\pi$$
$$594$$ 9.51303i 0.0160152i
$$595$$ 0 0
$$596$$ −10.3870 −0.0174278
$$597$$ −4.74785 + 2.74117i −0.00795285 + 0.00459158i
$$598$$ 81.6039 141.342i 0.136461 0.236358i
$$599$$ 264.528 458.175i 0.441616 0.764901i −0.556194 0.831053i $$-0.687739\pi$$
0.997810 + 0.0661519i $$0.0210722\pi$$
$$600$$ 0 0
$$601$$ 899.473i 1.49663i 0.663345 + 0.748314i $$0.269136\pi$$
−0.663345 + 0.748314i $$0.730864\pi$$
$$602$$ −495.985 235.427i −0.823895 0.391074i
$$603$$ 120.261i 0.199437i
$$604$$ −160.742 278.413i −0.266129 0.460949i
$$605$$ 0 0
$$606$$ −146.804 + 254.272i −0.242251 + 0.419591i
$$607$$ −268.038 464.255i −0.441578 0.764835i 0.556229 0.831029i $$-0.312248\pi$$
−0.997807 + 0.0661939i $$0.978914\pi$$
$$608$$ 189.081 0.310988
$$609$$ −31.9517 396.433i −0.0524659 0.650958i
$$610$$ 0 0
$$611$$ −98.0976 169.910i −0.160552 0.278085i
$$612$$ −91.0954 + 157.782i −0.148849 + 0.257813i
$$613$$ −717.977 414.524i −1.17125 0.676222i −0.217276 0.976110i $$-0.569717\pi$$
−0.953974 + 0.299888i $$0.903051\pi$$
$$614$$ −554.098 + 319.908i −0.902439 + 0.521024i
$$615$$ 0 0
$$616$$ 25.5481 2.05913i 0.0414742 0.00334274i
$$617$$ 404.320i 0.655300i −0.944799 0.327650i $$-0.893743\pi$$
0.944799 0.327650i $$-0.106257\pi$$
$$618$$ −211.388 + 122.045i −0.342051 + 0.197483i
$$619$$ 346.662 + 200.145i 0.560036 + 0.323337i 0.753160 0.657838i $$-0.228529\pi$$
−0.193124 + 0.981174i $$0.561862\pi$$
$$620$$ 0 0
$$621$$ 160.801 92.8387i 0.258939 0.149499i
$$622$$ −92.8991 −0.149355
$$623$$ −104.966 + 221.138i −0.168485 + 0.354957i
$$624$$ 22.3753 0.0358579
$$625$$ 0 0
$$626$$ 434.270 + 250.726i 0.693722 + 0.400521i
$$627$$ −64.9061 37.4736i −0.103519 0.0597665i
$$628$$ 95.2314 + 164.946i 0.151642 + 0.262652i
$$629$$ 1216.23i 1.93359i
$$630$$ 0 0
$$631$$ 334.639 0.530331 0.265165 0.964203i $$-0.414573\pi$$
0.265165 + 0.964203i $$0.414573\pi$$
$$632$$ −103.619 + 59.8244i −0.163954 + 0.0946589i
$$633$$ 155.299 268.987i 0.245339 0.424939i
$$634$$ −95.3603 + 165.169i −0.150411 + 0.260519i
$$635$$ 0 0
$$636$$ 189.375i 0.297760i
$$637$$ 56.1547 147.952i 0.0881550 0.232264i
$$638$$ 60.0558i 0.0941313i
$$639$$ −69.6720 120.676i −0.109033 0.188851i
$$640$$ 0 0
$$641$$ 36.0084 62.3683i 0.0561753 0.0972984i −0.836570 0.547860i $$-0.815443\pi$$
0.892746 + 0.450561i $$0.148776\pi$$
$$642$$ 57.5514 + 99.6819i 0.0896439 + 0.155268i
$$643$$ −1254.20 −1.95054 −0.975269 0.221020i $$-0.929061\pi$$
−0.975269 + 0.221020i $$0.929061\pi$$
$$644$$ 284.133 + 411.751i 0.441200 + 0.639366i
$$645$$ 0 0
$$646$$ 717.683 + 1243.06i 1.11096 + 1.92425i
$$647$$ 73.1699 126.734i 0.113091 0.195879i −0.803924 0.594732i $$-0.797258\pi$$
0.917015 + 0.398853i $$0.130591\pi$$
$$648$$ 22.0454 + 12.7279i 0.0340207 + 0.0196419i
$$649$$ −14.7939 + 8.54125i −0.0227949 + 0.0131606i
$$650$$ 0 0
$$651$$ 237.207 499.735i 0.364373 0.767642i
$$652$$ 492.996i 0.756128i
$$653$$ 687.082 396.687i 1.05219 0.607484i 0.128930 0.991654i $$-0.458846\pi$$
0.923262 + 0.384170i $$0.125512\pi$$
$$654$$ −123.377 71.2316i −0.188649 0.108917i
$$655$$ 0 0
$$656$$ 146.529 84.5986i 0.223368 0.128961i
$$657$$ −409.200 −0.622832
$$658$$ 599.441 48.3137i 0.911004 0.0734251i
$$659$$ −35.5649 −0.0539680 −0.0269840 0.999636i $$-0.508590\pi$$
−0.0269840 + 0.999636i $$0.508590\pi$$
$$660$$ 0 0
$$661$$ 193.509 + 111.723i 0.292752 + 0.169021i 0.639182 0.769055i $$-0.279273\pi$$
−0.346430 + 0.938076i $$0.612606\pi$$
$$662$$ 221.094 + 127.649i 0.333979 + 0.192823i
$$663$$ 84.9288 + 147.101i 0.128098 + 0.221872i
$$664$$ 4.34800i 0.00654819i
$$665$$ 0 0
$$666$$ −169.932 −0.255154
$$667$$ 1015.14 586.090i 1.52195 0.878696i
$$668$$ −14.9445 + 25.8846i −0.0223720 + 0.0387494i
$$669$$ 61.7775 107.002i 0.0923431 0.159943i
$$670$$ 0 0
$$671$$ 51.0759i 0.0761190i
$$672$$ −29.4102 + 61.9600i −0.0437652 + 0.0922024i
$$673$$ 216.920i 0.322318i 0.986928 + 0.161159i $$0.0515232\pi$$
−0.986928 + 0.161159i $$0.948477\pi$$
$$674$$ 4.13429 + 7.16080i 0.00613396 + 0.0106243i
$$675$$ 0 0
$$676$$ −158.570 + 274.651i −0.234571 + 0.406288i
$$677$$ −23.4825 40.6729i −0.0346861 0.0600781i 0.848161 0.529738i $$-0.177710\pi$$
−0.882847 + 0.469660i $$0.844376\pi$$
$$678$$ 517.091 0.762672
$$679$$ 867.186 598.410i 1.27715 0.881310i
$$680$$ 0 0
$$681$$ −123.443 213.809i −0.181267 0.313964i
$$682$$ 41.7648 72.3388i 0.0612388 0.106069i
$$683$$ −51.1993 29.5599i −0.0749623 0.0432795i 0.462050 0.886854i $$-0.347114\pi$$
−0.537013 + 0.843574i $$0.680447\pi$$
$$684$$ 173.682 100.275i 0.253921 0.146601i
$$685$$ 0 0
$$686$$ 335.888 + 349.968i 0.489632 + 0.510157i
$$687$$ 218.003i 0.317326i
$$688$$ 192.118 110.919i 0.279242 0.161220i
$$689$$ 152.902 + 88.2779i 0.221918 + 0.128125i
$$690$$ 0 0
$$691$$ 916.389 529.078i 1.32618 0.765669i 0.341472 0.939892i $$-0.389075\pi$$
0.984706 + 0.174222i $$0.0557412\pi$$
$$692$$ 335.332 0.484584
$$693$$ 22.3754 15.4404i 0.0322878 0.0222805i
$$694$$ 554.757 0.799361
$$695$$ 0 0
$$696$$ 139.173 + 80.3513i 0.199961 + 0.115447i
$$697$$ 1112.34 + 642.212i 1.59590 + 0.921395i
$$698$$ −163.238 282.736i −0.233865 0.405066i
$$699$$ 284.516i 0.407032i
$$700$$ 0 0
$$701$$ −394.358 −0.562565 −0.281283 0.959625i $$-0.590760\pi$$
−0.281283 + 0.959625i $$0.590760\pi$$
$$702$$ 20.5531 11.8663i 0.0292779 0.0169036i
$$703$$ −669.394 + 1159.42i −0.952197 + 1.64925i
$$704$$ −5.17824 + 8.96898i −0.00735546 + 0.0127400i
$$705$$ 0 0
$$706$$ 177.678i 0.251669i
$$707$$ −836.342 + 67.4075i −1.18295 + 0.0953430i
$$708$$ 45.7109i 0.0645635i
$$709$$ −20.7217 35.8911i −0.0292267 0.0506221i 0.851042 0.525097i $$-0.175971\pi$$
−0.880269 + 0.474475i $$0.842638\pi$$
$$710$$ 0 0
$$711$$ −63.4534 + 109.905i −0.0892453 + 0.154577i
$$712$$ −49.4542 85.6572i −0.0694581 0.120305i
$$713$$ 1630.35 2.28660
$$714$$ −518.971 + 41.8280i −0.726850 + 0.0585826i
$$715$$ 0 0
$$716$$ −66.9449 115.952i −0.0934984 0.161944i
$$717$$ −43.6690 + 75.6369i −0.0609051 + 0.105491i
$$718$$ 529.052 + 305.448i 0.736841 + 0.425415i
$$719$$ −556.327 + 321.195i −0.773751 + 0.446725i −0.834211 0.551445i $$-0.814077\pi$$
0.0604602 + 0.998171i $$0.480743\pi$$
$$720$$ 0 0
$$721$$ −630.157 299.113i −0.874004 0.414859i
$$722$$ 1069.48i 1.48127i
$$723$$ 292.727 169.006i 0.404879 0.233757i
$$724$$ −43.1469 24.9109i −0.0595952 0.0344073i
$$725$$ 0 0
$$726$$ −253.125 + 146.142i −0.348657 + 0.201297i
$$727$$ 979.168 1.34686 0.673431 0.739250i $$-0.264820\pi$$
0.673431 + 0.739250i $$0.264820\pi$$
$$728$$ 36.3169 + 52.6286i 0.0498858 + 0.0722921i
$$729$$ 27.0000 0.0370370
$$730$$ 0 0
$$731$$ 1458.42 + 842.021i 1.99511 + 1.15188i
$$732$$ 118.363 + 68.3367i 0.161698 + 0.0933562i
$$733$$ −618.862 1071.90i −0.844286 1.46235i −0.886240 0.463227i $$-0.846692\pi$$
0.0419537 0.999120i $$-0.486642\pi$$
$$734$$ 667.647i 0.909601i
$$735$$ 0 0
$$736$$ −202.140 −0.274647
$$737$$ 44.9423 25.9474i 0.0609800 0.0352068i
$$738$$ 89.7304 155.418i 0.121586 0.210593i
$$739$$ −477.274 + 826.662i −0.645837 + 1.11862i 0.338271 + 0.941049i $$0.390158\pi$$
−0.984108 + 0.177574i $$0.943175\pi$$
$$740$$ 0 0
$$741$$ 186.974i 0.252327i
$$742$$ −445.426 + 307.370i −0.600305 + 0.414246i
$$743$$ 401.194i 0.539964i 0.962865 + 0.269982i $$0.0870178\pi$$
−0.962865 + 0.269982i $$0.912982\pi$$
$$744$$ 111.758 + 193.571i 0.150213 + 0.260176i
$$745$$ 0 0
$$746$$ 61.8874 107.192i 0.0829590 0.143689i
$$747$$ −2.30587 3.99389i −0.00308685 0.00534657i
$$748$$ −78.6190 −0.105106
$$749$$ −141.050 + 297.157i −0.188318 + 0.396738i
$$750$$ 0 0
$$751$$ 420.870 + 728.968i 0.560412 + 0.970662i 0.997460 + 0.0712243i $$0.0226906\pi$$
−0.437048 + 0.899438i $$0.643976\pi$$
$$752$$ −121.498 + 210.441i −0.161567 + 0.279841i
$$753$$ −493.088 284.685i −0.654832 0.378067i
$$754$$ 129.751 74.9120i 0.172084 0.0993528i
$$755$$ 0 0
$$756$$ 5.84424 + 72.5110i 0.00773048 + 0.0959140i
$$757$$ 1287.18i 1.70037i 0.526487 + 0.850183i $$0.323509\pi$$
−0.526487 + 0.850183i $$0.676491\pi$$
$$758$$ 440.489 254.317i 0.581120 0.335510i
$$759$$ 69.3890 + 40.0617i 0.0914216 + 0.0527823i
$$760$$ 0 0
$$761$$ −1237.18 + 714.288i −1.62573 + 0.938618i −0.640387 + 0.768052i $$0.721226\pi$$
−0.985346 + 0.170565i $$0.945441\pi$$
$$762$$ 221.095 0.290150
$$763$$ −32.7072 405.807i −0.0428666 0.531857i
$$764$$ 27.2092 0.0356142
$$765$$ 0 0
$$766$$ 592.986 + 342.361i 0.774133 + 0.446946i
$$767$$ −36.9070 21.3083i −0.0481187 0.0277813i
$$768$$ −13.8564 24.0000i −0.0180422 0.0312500i
$$769$$ 1030.04i 1.33945i −0.742608 0.669726i $$-0.766411\pi$$
0.742608 0.669726i $$-0.233589\pi$$
$$770$$ 0 0
$$771$$ −698.349 −0.905771
$$772$$ 315.957 182.418i 0.409271 0.236293i
$$773$$ 374.310 648.324i 0.484231 0.838712i −0.515605 0.856826i $$-0.672433\pi$$
0.999836 + 0.0181142i $$0.00576625\pi$$
$$774$$ 117.648 203.772i 0.152000 0.263271i
$$775$$ 0 0
$$776$$ 425.725i 0.548615i
$$777$$ −275.813 399.695i −0.354972 0.514408i
$$778$$ 508.526i 0.653632i
$$779$$ −706.929 1224.44i −0.907482 1.57181i
$$780$$ 0 0
$$781$$ 30.0649 52.0739i 0.0384954 0.0666759i