# Properties

 Label 1050.3.q.b.199.1 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 199.1 Root $$-1.25838 + 0.337183i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.199 Dual form 1050.3.q.b.649.1

## $q$-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} +(2.76860 - 4.79536i) q^{11} +(1.73205 + 3.00000i) q^{12} +3.50434 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.06994 + 7.04933i) q^{17} +(3.67423 + 2.12132i) q^{18} +(15.3628 - 8.86974i) q^{19} +(5.38992 - 10.8604i) q^{21} +7.83078i q^{22} +(10.3316 - 5.96495i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-4.29192 + 2.47794i) q^{26} +5.19615 q^{27} +(-6.22374 + 12.5405i) q^{28} +8.52374 q^{29} +(-6.68072 - 3.85711i) q^{31} +(4.89898 + 2.82843i) q^{32} +(4.79536 + 8.30580i) q^{33} -11.5115i q^{34} -6.00000 q^{36} +(-24.2950 + 14.0267i) q^{37} +(-12.5437 + 21.7263i) q^{38} +(-3.03484 + 5.25650i) q^{39} -3.14207i q^{41} +(1.07820 + 17.1125i) q^{42} +43.1943i q^{43} +(-5.53720 - 9.59071i) q^{44} +(-8.43572 + 14.6111i) q^{46} +(9.35524 + 16.2037i) q^{47} +6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-7.04933 - 12.2098i) q^{51} +(3.50434 - 6.06969i) q^{52} +(2.44037 + 1.40895i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +30.7257i q^{57} +(-10.4394 + 6.02720i) q^{58} +(26.1612 + 15.1042i) q^{59} +(-41.0095 + 23.6769i) q^{61} +10.9096 q^{62} +(11.6228 + 17.4903i) q^{63} -8.00000 q^{64} +(-11.7462 - 6.78166i) q^{66} +(-5.70032 - 3.29108i) q^{67} +(8.13987 + 14.0987i) q^{68} +20.6632i q^{69} -97.7751 q^{71} +(7.34847 - 4.24264i) q^{72} +(-30.5806 + 52.9672i) q^{73} +(19.8368 - 34.3583i) q^{74} -35.4790i q^{76} +(-17.2311 + 34.7197i) q^{77} -8.58383i q^{78} +(61.5670 + 106.637i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.22178 + 3.84823i) q^{82} +89.5815 q^{83} +(-13.4209 - 20.1960i) q^{84} +(-30.5430 - 52.9020i) q^{86} +(-7.38178 + 12.7856i) q^{87} +(13.5633 + 7.83078i) q^{88} +(102.290 - 59.0573i) q^{89} +(-24.4818 + 1.54251i) q^{91} -23.8598i q^{92} +(11.5713 - 6.68072i) q^{93} +(-22.9156 - 13.2303i) q^{94} +(-8.48528 + 4.89898i) q^{96} -65.1965 q^{97} +(-55.1890 + 41.9067i) q^{98} -16.6116 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
$$11$$ 2.76860 4.79536i 0.251691 0.435942i −0.712301 0.701875i $$-0.752347\pi$$
0.963991 + 0.265933i $$0.0856800\pi$$
$$12$$ 1.73205 + 3.00000i 0.144338 + 0.250000i
$$13$$ 3.50434 0.269564 0.134782 0.990875i $$-0.456967\pi$$
0.134782 + 0.990875i $$0.456967\pi$$
$$14$$ 8.24500 5.47905i 0.588928 0.391361i
$$15$$ 0 0
$$16$$ −2.00000 3.46410i −0.125000 0.216506i
$$17$$ −4.06994 + 7.04933i −0.239408 + 0.414667i −0.960545 0.278126i $$-0.910287\pi$$
0.721137 + 0.692793i $$0.243620\pi$$
$$18$$ 3.67423 + 2.12132i 0.204124 + 0.117851i
$$19$$ 15.3628 8.86974i 0.808571 0.466828i −0.0378887 0.999282i $$-0.512063\pi$$
0.846459 + 0.532454i $$0.178730\pi$$
$$20$$ 0 0
$$21$$ 5.38992 10.8604i 0.256663 0.517163i
$$22$$ 7.83078i 0.355945i
$$23$$ 10.3316 5.96495i 0.449200 0.259346i −0.258292 0.966067i $$-0.583160\pi$$
0.707492 + 0.706721i $$0.249826\pi$$
$$24$$ −4.24264 2.44949i −0.176777 0.102062i
$$25$$ 0 0
$$26$$ −4.29192 + 2.47794i −0.165074 + 0.0953054i
$$27$$ 5.19615 0.192450
$$28$$ −6.22374 + 12.5405i −0.222277 + 0.447876i
$$29$$ 8.52374 0.293922 0.146961 0.989142i $$-0.453051\pi$$
0.146961 + 0.989142i $$0.453051\pi$$
$$30$$ 0 0
$$31$$ −6.68072 3.85711i −0.215507 0.124423i 0.388361 0.921507i $$-0.373041\pi$$
−0.603868 + 0.797084i $$0.706375\pi$$
$$32$$ 4.89898 + 2.82843i 0.153093 + 0.0883883i
$$33$$ 4.79536 + 8.30580i 0.145314 + 0.251691i
$$34$$ 11.5115i 0.338574i
$$35$$ 0 0
$$36$$ −6.00000 −0.166667
$$37$$ −24.2950 + 14.0267i −0.656621 + 0.379100i −0.790988 0.611831i $$-0.790433\pi$$
0.134367 + 0.990932i $$0.457100\pi$$
$$38$$ −12.5437 + 21.7263i −0.330098 + 0.571746i
$$39$$ −3.03484 + 5.25650i −0.0778165 + 0.134782i
$$40$$ 0 0
$$41$$ 3.14207i 0.0766358i −0.999266 0.0383179i $$-0.987800\pi$$
0.999266 0.0383179i $$-0.0121999\pi$$
$$42$$ 1.07820 + 17.1125i 0.0256714 + 0.407440i
$$43$$ 43.1943i 1.00452i 0.864717 + 0.502260i $$0.167498\pi$$
−0.864717 + 0.502260i $$0.832502\pi$$
$$44$$ −5.53720 9.59071i −0.125845 0.217971i
$$45$$ 0 0
$$46$$ −8.43572 + 14.6111i −0.183385 + 0.317632i
$$47$$ 9.35524 + 16.2037i 0.199048 + 0.344761i 0.948220 0.317615i $$-0.102882\pi$$
−0.749172 + 0.662375i $$0.769548\pi$$
$$48$$ 6.92820 0.144338
$$49$$ 48.6125 6.15023i 0.992092 0.125515i
$$50$$ 0 0
$$51$$ −7.04933 12.2098i −0.138222 0.239408i
$$52$$ 3.50434 6.06969i 0.0673911 0.116725i
$$53$$ 2.44037 + 1.40895i 0.0460448 + 0.0265840i 0.522846 0.852427i $$-0.324870\pi$$
−0.476801 + 0.879011i $$0.658204\pi$$
$$54$$ −6.36396 + 3.67423i −0.117851 + 0.0680414i
$$55$$ 0 0
$$56$$ −1.24500 19.7598i −0.0222321 0.352854i
$$57$$ 30.7257i 0.539047i
$$58$$ −10.4394 + 6.02720i −0.179990 + 0.103917i
$$59$$ 26.1612 + 15.1042i 0.443411 + 0.256003i 0.705043 0.709164i $$-0.250928\pi$$
−0.261633 + 0.965168i $$0.584261\pi$$
$$60$$ 0 0
$$61$$ −41.0095 + 23.6769i −0.672288 + 0.388145i −0.796943 0.604055i $$-0.793551\pi$$
0.124655 + 0.992200i $$0.460218\pi$$
$$62$$ 10.9096 0.175961
$$63$$ 11.6228 + 17.4903i 0.184489 + 0.277624i
$$64$$ −8.00000 −0.125000
$$65$$ 0 0
$$66$$ −11.7462 6.78166i −0.177972 0.102752i
$$67$$ −5.70032 3.29108i −0.0850794 0.0491206i 0.456857 0.889540i $$-0.348975\pi$$
−0.541936 + 0.840420i $$0.682309\pi$$
$$68$$ 8.13987 + 14.0987i 0.119704 + 0.207333i
$$69$$ 20.6632i 0.299467i
$$70$$ 0 0
$$71$$ −97.7751 −1.37711 −0.688557 0.725182i $$-0.741755\pi$$
−0.688557 + 0.725182i $$0.741755\pi$$
$$72$$ 7.34847 4.24264i 0.102062 0.0589256i
$$73$$ −30.5806 + 52.9672i −0.418913 + 0.725578i −0.995830 0.0912244i $$-0.970922\pi$$
0.576918 + 0.816802i $$0.304255\pi$$
$$74$$ 19.8368 34.3583i 0.268064 0.464301i
$$75$$ 0 0
$$76$$ 35.4790i 0.466828i
$$77$$ −17.2311 + 34.7197i −0.223780 + 0.450906i
$$78$$ 8.58383i 0.110049i
$$79$$ 61.5670 + 106.637i 0.779329 + 1.34984i 0.932329 + 0.361612i $$0.117773\pi$$
−0.152999 + 0.988226i $$0.548893\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.0555556 + 0.0962250i
$$82$$ 2.22178 + 3.84823i 0.0270948 + 0.0469296i
$$83$$ 89.5815 1.07930 0.539648 0.841891i $$-0.318557\pi$$
0.539648 + 0.841891i $$0.318557\pi$$
$$84$$ −13.4209 20.1960i −0.159772 0.240429i
$$85$$ 0 0
$$86$$ −30.5430 52.9020i −0.355151 0.615140i
$$87$$ −7.38178 + 12.7856i −0.0848480 + 0.146961i
$$88$$ 13.5633 + 7.83078i 0.154129 + 0.0889862i
$$89$$ 102.290 59.0573i 1.14933 0.663566i 0.200606 0.979672i $$-0.435709\pi$$
0.948724 + 0.316107i $$0.102376\pi$$
$$90$$ 0 0
$$91$$ −24.4818 + 1.54251i −0.269031 + 0.0169507i
$$92$$ 23.8598i 0.259346i
$$93$$ 11.5713 6.68072i 0.124423 0.0718357i
$$94$$ −22.9156 13.2303i −0.243783 0.140748i
$$95$$ 0 0
$$96$$ −8.48528 + 4.89898i −0.0883883 + 0.0510310i
$$97$$ −65.1965 −0.672128 −0.336064 0.941839i $$-0.609096\pi$$
−0.336064 + 0.941839i $$0.609096\pi$$
$$98$$ −55.1890 + 41.9067i −0.563153 + 0.427619i
$$99$$ −16.6116 −0.167794
$$100$$ 0 0
$$101$$ −120.895 69.7987i −1.19698 0.691076i −0.237099 0.971486i $$-0.576196\pi$$
−0.959881 + 0.280409i $$0.909530\pi$$
$$102$$ 17.2673 + 9.96926i 0.169287 + 0.0977379i
$$103$$ 87.2421 + 151.108i 0.847011 + 1.46707i 0.883863 + 0.467746i $$0.154934\pi$$
−0.0368520 + 0.999321i $$0.511733\pi$$
$$104$$ 9.91176i 0.0953054i
$$105$$ 0 0
$$106$$ −3.98511 −0.0375954
$$107$$ −52.3741 + 30.2382i −0.489477 + 0.282600i −0.724358 0.689424i $$-0.757864\pi$$
0.234880 + 0.972024i $$0.424530\pi$$
$$108$$ 5.19615 9.00000i 0.0481125 0.0833333i
$$109$$ −50.4057 + 87.3052i −0.462437 + 0.800965i −0.999082 0.0428435i $$-0.986358\pi$$
0.536644 + 0.843808i $$0.319692\pi$$
$$110$$ 0 0
$$111$$ 48.5899i 0.437747i
$$112$$ 15.4971 + 23.3204i 0.138367 + 0.208218i
$$113$$ 74.1876i 0.656527i −0.944586 0.328264i $$-0.893537\pi$$
0.944586 0.328264i $$-0.106463\pi$$
$$114$$ −21.7263 37.6311i −0.190582 0.330098i
$$115$$ 0 0
$$116$$ 8.52374 14.7636i 0.0734805 0.127272i
$$117$$ −5.25650 9.10453i −0.0449274 0.0778165i
$$118$$ −42.7211 −0.362043
$$119$$ 25.3302 51.0392i 0.212859 0.428901i
$$120$$ 0 0
$$121$$ 45.1697 + 78.2362i 0.373303 + 0.646580i
$$122$$ 33.4842 57.9963i 0.274460 0.475379i
$$123$$ 4.71310 + 2.72111i 0.0383179 + 0.0221228i
$$124$$ −13.3614 + 7.71423i −0.107754 + 0.0622115i
$$125$$ 0 0
$$126$$ −26.6025 13.2026i −0.211131 0.104782i
$$127$$ 151.093i 1.18971i 0.803833 + 0.594855i $$0.202791\pi$$
−0.803833 + 0.594855i $$0.797209\pi$$
$$128$$ 9.79796 5.65685i 0.0765466 0.0441942i
$$129$$ −64.7915 37.4074i −0.502260 0.289980i
$$130$$ 0 0
$$131$$ −186.820 + 107.861i −1.42611 + 0.823363i −0.996811 0.0798009i $$-0.974572\pi$$
−0.429296 + 0.903164i $$0.641238\pi$$
$$132$$ 19.1814 0.145314
$$133$$ −103.423 + 68.7276i −0.777615 + 0.516749i
$$134$$ 9.30859 0.0694671
$$135$$ 0 0
$$136$$ −19.9385 11.5115i −0.146607 0.0846435i
$$137$$ −115.736 66.8203i −0.844789 0.487739i 0.0141000 0.999901i $$-0.495512\pi$$
−0.858889 + 0.512161i $$0.828845\pi$$
$$138$$ −14.6111 25.3072i −0.105877 0.183385i
$$139$$ 193.762i 1.39397i 0.717085 + 0.696986i $$0.245476\pi$$
−0.717085 + 0.696986i $$0.754524\pi$$
$$140$$ 0 0
$$141$$ −32.4075 −0.229840
$$142$$ 119.750 69.1374i 0.843306 0.486883i
$$143$$ 9.70210 16.8045i 0.0678469 0.117514i
$$144$$ −6.00000 + 10.3923i −0.0416667 + 0.0721688i
$$145$$ 0 0
$$146$$ 86.4950i 0.592432i
$$147$$ −32.8743 + 78.2450i −0.223635 + 0.532279i
$$148$$ 56.1068i 0.379100i
$$149$$ 33.0032 + 57.1632i 0.221498 + 0.383646i 0.955263 0.295758i $$-0.0955721\pi$$
−0.733765 + 0.679403i $$0.762239\pi$$
$$150$$ 0 0
$$151$$ −17.4410 + 30.2087i −0.115503 + 0.200057i −0.917981 0.396625i $$-0.870181\pi$$
0.802478 + 0.596682i $$0.203515\pi$$
$$152$$ 25.0874 + 43.4527i 0.165049 + 0.285873i
$$153$$ 24.4196 0.159605
$$154$$ −3.44690 54.7070i −0.0223825 0.355240i
$$155$$ 0 0
$$156$$ 6.06969 + 10.5130i 0.0389082 + 0.0673911i
$$157$$ 26.7503 46.3329i 0.170384 0.295114i −0.768170 0.640246i $$-0.778832\pi$$
0.938554 + 0.345132i $$0.112166\pi$$
$$158$$ −150.808 87.0689i −0.954480 0.551069i
$$159$$ −4.22685 + 2.44037i −0.0265840 + 0.0153483i
$$160$$ 0 0
$$161$$ −69.5525 + 46.2197i −0.432003 + 0.287079i
$$162$$ 12.7279i 0.0785674i
$$163$$ −178.387 + 102.992i −1.09440 + 0.631852i −0.934744 0.355321i $$-0.884372\pi$$
−0.159655 + 0.987173i $$0.551038\pi$$
$$164$$ −5.44222 3.14207i −0.0331843 0.0191589i
$$165$$ 0 0
$$166$$ −109.714 + 63.3437i −0.660931 + 0.381589i
$$167$$ −137.945 −0.826020 −0.413010 0.910727i $$-0.635523\pi$$
−0.413010 + 0.910727i $$0.635523\pi$$
$$168$$ 30.7179 + 15.2450i 0.182845 + 0.0907440i
$$169$$ −156.720 −0.927335
$$170$$ 0 0
$$171$$ −46.0885 26.6092i −0.269524 0.155609i
$$172$$ 74.8148 + 43.1943i 0.434970 + 0.251130i
$$173$$ −110.283 191.016i −0.637475 1.10414i −0.985985 0.166834i $$-0.946646\pi$$
0.348510 0.937305i $$-0.386688\pi$$
$$174$$ 20.8788i 0.119993i
$$175$$ 0 0
$$176$$ −22.1488 −0.125845
$$177$$ −45.3126 + 26.1612i −0.256003 + 0.147804i
$$178$$ −83.5197 + 144.660i −0.469212 + 0.812699i
$$179$$ −36.6501 + 63.4798i −0.204749 + 0.354636i −0.950053 0.312089i $$-0.898971\pi$$
0.745304 + 0.666725i $$0.232305\pi$$
$$180$$ 0 0
$$181$$ 61.4619i 0.339568i 0.985481 + 0.169784i $$0.0543071\pi$$
−0.985481 + 0.169784i $$0.945693\pi$$
$$182$$ 28.8932 19.2004i 0.158754 0.105497i
$$183$$ 82.0191i 0.448192i
$$184$$ 16.8714 + 29.2222i 0.0916926 + 0.158816i
$$185$$ 0 0
$$186$$ −9.44796 + 16.3643i −0.0507955 + 0.0879804i
$$187$$ 22.5360 + 39.0336i 0.120514 + 0.208736i
$$188$$ 37.4210 0.199048
$$189$$ −36.3011 + 2.28721i −0.192069 + 0.0121016i
$$190$$ 0 0
$$191$$ 179.931 + 311.650i 0.942048 + 1.63168i 0.761556 + 0.648099i $$0.224436\pi$$
0.180492 + 0.983577i $$0.442231\pi$$
$$192$$ 6.92820 12.0000i 0.0360844 0.0625000i
$$193$$ −121.023 69.8724i −0.627060 0.362033i 0.152552 0.988295i $$-0.451251\pi$$
−0.779613 + 0.626262i $$0.784584\pi$$
$$194$$ 79.8490 46.1009i 0.411593 0.237633i
$$195$$ 0 0
$$196$$ 37.9600 90.3495i 0.193673 0.460967i
$$197$$ 248.343i 1.26062i 0.776342 + 0.630311i $$0.217073\pi$$
−0.776342 + 0.630311i $$0.782927\pi$$
$$198$$ 20.3450 11.7462i 0.102752 0.0593241i
$$199$$ 106.170 + 61.2973i 0.533518 + 0.308026i 0.742448 0.669904i $$-0.233665\pi$$
−0.208930 + 0.977931i $$0.566998\pi$$
$$200$$ 0 0
$$201$$ 9.87325 5.70032i 0.0491206 0.0283598i
$$202$$ 197.421 0.977329
$$203$$ −59.5481 + 3.75192i −0.293341 + 0.0184824i
$$204$$ −28.1973 −0.138222
$$205$$ 0 0
$$206$$ −213.699 123.379i −1.03737 0.598927i
$$207$$ −30.9948 17.8949i −0.149733 0.0864486i
$$208$$ −7.00867 12.1394i −0.0336955 0.0583624i
$$209$$ 98.2271i 0.469986i
$$210$$ 0 0
$$211$$ 352.829 1.67218 0.836088 0.548596i $$-0.184837\pi$$
0.836088 + 0.548596i $$0.184837\pi$$
$$212$$ 4.88074 2.81790i 0.0230224 0.0132920i
$$213$$ 84.6757 146.663i 0.397538 0.688557i
$$214$$ 42.7632 74.0681i 0.199828 0.346113i
$$215$$ 0 0
$$216$$ 14.6969i 0.0680414i
$$217$$ 48.3703 + 24.0057i 0.222904 + 0.110625i
$$218$$ 142.569i 0.653985i
$$219$$ −52.9672 91.7418i −0.241859 0.418913i
$$220$$ 0 0
$$221$$ −14.2624 + 24.7032i −0.0645358 + 0.111779i
$$222$$ 34.3583 + 59.5103i 0.154767 + 0.268064i
$$223$$ −61.7420 −0.276870 −0.138435 0.990372i $$-0.544207\pi$$
−0.138435 + 0.990372i $$0.544207\pi$$
$$224$$ −35.4700 17.6034i −0.158348 0.0785866i
$$225$$ 0 0
$$226$$ 52.4586 + 90.8609i 0.232118 + 0.402039i
$$227$$ 104.762 181.452i 0.461505 0.799350i −0.537531 0.843244i $$-0.680643\pi$$
0.999036 + 0.0438940i $$0.0139764\pi$$
$$228$$ 53.2184 + 30.7257i 0.233414 + 0.134762i
$$229$$ 93.3568 53.8996i 0.407671 0.235369i −0.282117 0.959380i $$-0.591037\pi$$
0.689789 + 0.724011i $$0.257703\pi$$
$$230$$ 0 0
$$231$$ −37.1571 55.9148i −0.160853 0.242055i
$$232$$ 24.1088i 0.103917i
$$233$$ 283.057 163.423i 1.21484 0.701387i 0.251029 0.967980i $$-0.419231\pi$$
0.963809 + 0.266592i $$0.0858978\pi$$
$$234$$ 12.8758 + 7.43382i 0.0550246 + 0.0317685i
$$235$$ 0 0
$$236$$ 52.3224 30.2084i 0.221705 0.128002i
$$237$$ −213.274 −0.899892
$$238$$ 5.06706 + 80.4211i 0.0212902 + 0.337904i
$$239$$ 9.20117 0.0384986 0.0192493 0.999815i $$-0.493872\pi$$
0.0192493 + 0.999815i $$0.493872\pi$$
$$240$$ 0 0
$$241$$ 278.156 + 160.593i 1.15417 + 0.666362i 0.949900 0.312553i $$-0.101184\pi$$
0.204272 + 0.978914i $$0.434517\pi$$
$$242$$ −110.643 63.8796i −0.457201 0.263965i
$$243$$ −7.79423 13.5000i −0.0320750 0.0555556i
$$244$$ 94.7075i 0.388145i
$$245$$ 0 0
$$246$$ −7.69646 −0.0312864
$$247$$ 53.8365 31.0825i 0.217962 0.125840i
$$248$$ 10.9096 18.8959i 0.0439902 0.0761932i
$$249$$ −77.5799 + 134.372i −0.311566 + 0.539648i
$$250$$ 0 0
$$251$$ 19.2394i 0.0766511i −0.999265 0.0383255i $$-0.987798\pi$$
0.999265 0.0383255i $$-0.0122024\pi$$
$$252$$ 41.9169 2.64104i 0.166337 0.0104803i
$$253$$ 66.0583i 0.261100i
$$254$$ −106.839 185.051i −0.420626 0.728546i
$$255$$ 0 0
$$256$$ −8.00000 + 13.8564i −0.0312500 + 0.0541266i
$$257$$ 64.7109 + 112.083i 0.251793 + 0.436119i 0.964020 0.265831i $$-0.0856464\pi$$
−0.712226 + 0.701950i $$0.752313\pi$$
$$258$$ 105.804 0.410093
$$259$$ 163.554 108.687i 0.631483 0.419640i
$$260$$ 0 0
$$261$$ −12.7856 22.1453i −0.0489870 0.0848480i
$$262$$ 152.538 264.203i 0.582206 1.00841i
$$263$$ 144.561 + 83.4625i 0.549663 + 0.317348i 0.748986 0.662586i $$-0.230541\pi$$
−0.199323 + 0.979934i $$0.563874\pi$$
$$264$$ −23.4924 + 13.5633i −0.0889862 + 0.0513762i
$$265$$ 0 0
$$266$$ 78.0688 157.305i 0.293492 0.591371i
$$267$$ 204.581i 0.766220i
$$268$$ −11.4006 + 6.58217i −0.0425397 + 0.0245603i
$$269$$ −181.081 104.547i −0.673162 0.388650i 0.124112 0.992268i $$-0.460392\pi$$
−0.797274 + 0.603618i $$0.793725\pi$$
$$270$$ 0 0
$$271$$ 123.029 71.0308i 0.453981 0.262106i −0.255529 0.966801i $$-0.582250\pi$$
0.709510 + 0.704695i $$0.248916\pi$$
$$272$$ 32.5595 0.119704
$$273$$ 18.8881 38.0586i 0.0691871 0.139409i
$$274$$ 188.996 0.689768
$$275$$ 0 0
$$276$$ 35.7897 + 20.6632i 0.129673 + 0.0748667i
$$277$$ −386.179 222.961i −1.39415 0.804912i −0.400377 0.916350i $$-0.631121\pi$$
−0.993771 + 0.111438i $$0.964454\pi$$
$$278$$ −137.010 237.309i −0.492843 0.853630i
$$279$$ 23.1427i 0.0829487i
$$280$$ 0 0
$$281$$ 482.012 1.71534 0.857672 0.514196i $$-0.171910\pi$$
0.857672 + 0.514196i $$0.171910\pi$$
$$282$$ 39.6909 22.9156i 0.140748 0.0812609i
$$283$$ −108.257 + 187.506i −0.382533 + 0.662566i −0.991424 0.130688i $$-0.958281\pi$$
0.608891 + 0.793254i $$0.291615\pi$$
$$284$$ −97.7751 + 169.351i −0.344278 + 0.596308i
$$285$$ 0 0
$$286$$ 27.4417i 0.0959500i
$$287$$ 1.38305 + 21.9509i 0.00481900 + 0.0764841i
$$288$$ 16.9706i 0.0589256i
$$289$$ 111.371 + 192.901i 0.385368 + 0.667476i
$$290$$ 0 0
$$291$$ 56.4618 97.7947i 0.194027 0.336064i
$$292$$ 61.1612 + 105.934i 0.209456 + 0.362789i
$$293$$ 383.704 1.30957 0.654786 0.755815i $$-0.272759\pi$$
0.654786 + 0.755815i $$0.272759\pi$$
$$294$$ −15.0649 119.076i −0.0512412 0.405020i
$$295$$ 0 0
$$296$$ −39.6735 68.7166i −0.134032 0.232151i
$$297$$ 14.3861 24.9174i 0.0484379 0.0838970i
$$298$$ −80.8410 46.6736i −0.271278 0.156623i
$$299$$ 36.2054 20.9032i 0.121088 0.0699104i
$$300$$ 0 0
$$301$$ −19.0130 301.762i −0.0631661 1.00253i
$$302$$ 49.3305i 0.163346i
$$303$$ 209.396 120.895i 0.691076 0.398993i
$$304$$ −61.4514 35.4790i −0.202143 0.116707i
$$305$$ 0 0
$$306$$ −29.9078 + 17.2673i −0.0977379 + 0.0564290i
$$307$$ −21.1264 −0.0688155 −0.0344078 0.999408i $$-0.510954\pi$$
−0.0344078 + 0.999408i $$0.510954\pi$$
$$308$$ 42.9053 + 64.5648i 0.139303 + 0.209626i
$$309$$ −302.216 −0.978044
$$310$$ 0 0
$$311$$ 75.0288 + 43.3179i 0.241250 + 0.139286i 0.615751 0.787941i $$-0.288853\pi$$
−0.374501 + 0.927226i $$0.622186\pi$$
$$312$$ −14.8676 8.58383i −0.0476527 0.0275123i
$$313$$ 1.41903 + 2.45782i 0.00453363 + 0.00785247i 0.868283 0.496069i $$-0.165224\pi$$
−0.863750 + 0.503921i $$0.831890\pi$$
$$314$$ 75.6613i 0.240960i
$$315$$ 0 0
$$316$$ 246.268 0.779329
$$317$$ 268.338 154.925i 0.846493 0.488723i −0.0129730 0.999916i $$-0.504130\pi$$
0.859466 + 0.511193i $$0.170796\pi$$
$$318$$ 3.45121 5.97767i 0.0108529 0.0187977i
$$319$$ 23.5988 40.8744i 0.0739776 0.128133i
$$320$$ 0 0
$$321$$ 104.748i 0.326318i
$$322$$ 52.5018 105.788i 0.163049 0.328535i
$$323$$ 144.397i 0.447050i
$$324$$ 9.00000 + 15.5885i 0.0277778 + 0.0481125i
$$325$$ 0 0
$$326$$ 145.652 252.278i 0.446787 0.773857i
$$327$$ −87.3052 151.217i −0.266988 0.462437i
$$328$$ 8.88711 0.0270948
$$329$$ −72.4895 109.084i −0.220333 0.331562i
$$330$$ 0 0
$$331$$ 208.295 + 360.777i 0.629289 + 1.08996i 0.987695 + 0.156394i $$0.0499871\pi$$
−0.358406 + 0.933566i $$0.616680\pi$$
$$332$$ 89.5815 155.160i 0.269824 0.467349i
$$333$$ 72.8849 + 42.0801i 0.218874 + 0.126367i
$$334$$ 168.948 97.5421i 0.505832 0.292042i
$$335$$ 0 0
$$336$$ −48.4014 + 3.04961i −0.144052 + 0.00907622i
$$337$$ 155.491i 0.461399i −0.973025 0.230699i $$-0.925899\pi$$
0.973025 0.230699i $$-0.0741014\pi$$
$$338$$ 191.942 110.818i 0.567874 0.327862i
$$339$$ 111.281 + 64.2483i 0.328264 + 0.189523i
$$340$$ 0 0
$$341$$ −36.9925 + 21.3576i −0.108482 + 0.0626323i
$$342$$ 75.2622 0.220065
$$343$$ −336.907 + 64.3643i −0.982236 + 0.187651i
$$344$$ −122.172 −0.355151
$$345$$ 0 0
$$346$$ 270.138 + 155.964i 0.780744 + 0.450763i
$$347$$ −443.844 256.253i −1.27909 0.738482i −0.302408 0.953179i $$-0.597790\pi$$
−0.976681 + 0.214697i $$0.931124\pi$$
$$348$$ 14.7636 + 25.5712i 0.0424240 + 0.0734805i
$$349$$ 269.185i 0.771305i 0.922644 + 0.385652i $$0.126024\pi$$
−0.922644 + 0.385652i $$0.873976\pi$$
$$350$$ 0 0
$$351$$ 18.2091 0.0518777
$$352$$ 27.1266 15.6616i 0.0770643 0.0444931i
$$353$$ 293.231 507.890i 0.830682 1.43878i −0.0668166 0.997765i $$-0.521284\pi$$
0.897498 0.441018i $$-0.145382\pi$$
$$354$$ 36.9976 64.0816i 0.104513 0.181022i
$$355$$ 0 0
$$356$$ 236.229i 0.663566i
$$357$$ 54.6221 + 82.1966i 0.153003 + 0.230242i
$$358$$ 103.662i 0.289559i
$$359$$ 44.4221 + 76.9413i 0.123738 + 0.214321i 0.921239 0.388997i $$-0.127178\pi$$
−0.797501 + 0.603318i $$0.793845\pi$$
$$360$$ 0 0
$$361$$ −23.1554 + 40.1064i −0.0641424 + 0.111098i
$$362$$ −43.4601 75.2751i −0.120056 0.207942i
$$363$$ −156.472 −0.431054
$$364$$ −21.8101 + 43.9462i −0.0599178 + 0.120731i
$$365$$ 0 0
$$366$$ 57.9963 + 100.452i 0.158460 + 0.274460i
$$367$$ 353.019 611.446i 0.961904 1.66607i 0.244191 0.969727i $$-0.421478\pi$$
0.717713 0.696339i $$-0.245189\pi$$
$$368$$ −41.3264 23.8598i −0.112300 0.0648365i
$$369$$ −8.16333 + 4.71310i −0.0221228 + 0.0127726i
$$370$$ 0 0
$$371$$ −17.6690 8.76894i −0.0476253 0.0236360i
$$372$$ 26.7229i 0.0718357i
$$373$$ −44.3770 + 25.6211i −0.118973 + 0.0686892i −0.558306 0.829635i $$-0.688548\pi$$
0.439332 + 0.898325i $$0.355215\pi$$
$$374$$ −55.2018 31.8708i −0.147598 0.0852160i
$$375$$ 0 0
$$376$$ −45.8311 + 26.4606i −0.121891 + 0.0703740i
$$377$$ 29.8701 0.0792309
$$378$$ 42.8423 28.4700i 0.113339 0.0753174i
$$379$$ 194.724 0.513784 0.256892 0.966440i $$-0.417302\pi$$
0.256892 + 0.966440i $$0.417302\pi$$
$$380$$ 0 0
$$381$$ −226.640 130.851i −0.594855 0.343440i
$$382$$ −440.740 254.461i −1.15377 0.666129i
$$383$$ 262.540 + 454.732i 0.685482 + 1.18729i 0.973285 + 0.229600i $$0.0737418\pi$$
−0.287803 + 0.957690i $$0.592925\pi$$
$$384$$ 19.5959i 0.0510310i
$$385$$ 0 0
$$386$$ 197.629 0.511993
$$387$$ 112.222 64.7915i 0.289980 0.167420i
$$388$$ −65.1965 + 112.924i −0.168032 + 0.291040i
$$389$$ −201.765 + 349.467i −0.518675 + 0.898372i 0.481089 + 0.876672i $$0.340241\pi$$
−0.999765 + 0.0217005i $$0.993092\pi$$
$$390$$ 0 0
$$391$$ 97.1079i 0.248358i
$$392$$ 17.3955 + 137.497i 0.0443762 + 0.350757i
$$393$$ 373.640i 0.950738i
$$394$$ −175.605 304.156i −0.445697 0.771971i
$$395$$ 0 0
$$396$$ −16.6116 + 28.7721i −0.0419485 + 0.0726569i
$$397$$ 80.5960 + 139.596i 0.203013 + 0.351628i 0.949498 0.313774i $$-0.101593\pi$$
−0.746485 + 0.665402i $$0.768260\pi$$
$$398$$ −173.375 −0.435615
$$399$$ −13.5246 214.654i −0.0338963 0.537980i
$$400$$ 0 0
$$401$$ 212.506 + 368.071i 0.529940 + 0.917883i 0.999390 + 0.0349237i $$0.0111188\pi$$
−0.469450 + 0.882959i $$0.655548\pi$$
$$402$$ −8.06147 + 13.9629i −0.0200534 + 0.0347335i
$$403$$ −23.4115 13.5166i −0.0580930 0.0335400i
$$404$$ −241.790 + 139.597i −0.598490 + 0.345538i
$$405$$ 0 0
$$406$$ 70.2782 46.7020i 0.173099 0.115030i
$$407$$ 155.337i 0.381664i
$$408$$ 34.5345 19.9385i 0.0846435 0.0488689i
$$409$$ −373.605 215.701i −0.913460 0.527386i −0.0319171 0.999491i $$-0.510161\pi$$
−0.881543 + 0.472104i $$0.843495\pi$$
$$410$$ 0 0
$$411$$ 200.461 115.736i 0.487739 0.281596i
$$412$$ 348.969 0.847011
$$413$$ −189.415 94.0046i −0.458631 0.227614i
$$414$$ 50.6143 0.122257
$$415$$ 0 0
$$416$$ 17.1677 + 9.91176i 0.0412684 + 0.0238263i
$$417$$ −290.643 167.803i −0.696986 0.402405i
$$418$$ 69.4570 + 120.303i 0.166165 + 0.287806i
$$419$$ 585.412i 1.39716i −0.715530 0.698582i $$-0.753815\pi$$
0.715530 0.698582i $$-0.246185\pi$$
$$420$$ 0 0
$$421$$ 400.267 0.950754 0.475377 0.879782i $$-0.342312\pi$$
0.475377 + 0.879782i $$0.342312\pi$$
$$422$$ −432.126 + 249.488i −1.02399 + 0.591203i
$$423$$ 28.0657 48.6112i 0.0663492 0.114920i
$$424$$ −3.98511 + 6.90241i −0.00939885 + 0.0162793i
$$425$$ 0 0
$$426$$ 239.499i 0.562204i
$$427$$ 276.077 183.461i 0.646550 0.429652i
$$428$$ 120.953i 0.282600i
$$429$$ 16.8045 + 29.1063i 0.0391714 + 0.0678469i
$$430$$ 0 0
$$431$$ −197.631 + 342.307i −0.458541 + 0.794216i −0.998884 0.0472289i $$-0.984961\pi$$
0.540344 + 0.841445i $$0.318294\pi$$
$$432$$ −10.3923 18.0000i −0.0240563 0.0416667i
$$433$$ 2.39222 0.00552477 0.00276238 0.999996i $$-0.499121\pi$$
0.00276238 + 0.999996i $$0.499121\pi$$
$$434$$ −76.2158 + 4.80210i −0.175613 + 0.0110647i
$$435$$ 0 0
$$436$$ 100.811 + 174.610i 0.231219 + 0.400482i
$$437$$ 105.815 183.277i 0.242140 0.419399i
$$438$$ 129.743 + 74.9069i 0.296216 + 0.171020i
$$439$$ 350.264 202.225i 0.797867 0.460649i −0.0448578 0.998993i $$-0.514283\pi$$
0.842725 + 0.538345i $$0.180950\pi$$
$$440$$ 0 0
$$441$$ −88.8975 117.074i −0.201582 0.265473i
$$442$$ 40.3402i 0.0912674i
$$443$$ 252.889 146.005i 0.570855 0.329583i −0.186636 0.982429i $$-0.559758\pi$$
0.757491 + 0.652846i $$0.226425\pi$$
$$444$$ −84.1603 48.5899i −0.189550 0.109437i
$$445$$ 0 0
$$446$$ 75.6182 43.6582i 0.169547 0.0978883i
$$447$$ −114.326 −0.255764
$$448$$ 55.8892 3.52139i 0.124753 0.00786024i
$$449$$ −125.680 −0.279911 −0.139956 0.990158i $$-0.544696\pi$$
−0.139956 + 0.990158i $$0.544696\pi$$
$$450$$ 0 0
$$451$$ −15.0673 8.69913i −0.0334087 0.0192885i
$$452$$ −128.497 74.1876i −0.284285 0.164132i
$$453$$ −30.2087 52.3229i −0.0666858 0.115503i
$$454$$ 296.310i 0.652666i
$$455$$ 0 0
$$456$$ −86.9054 −0.190582
$$457$$ −74.4808 + 43.0015i −0.162978 + 0.0940952i −0.579270 0.815135i $$-0.696662\pi$$
0.416293 + 0.909231i $$0.363329\pi$$
$$458$$ −76.2255 + 132.026i −0.166431 + 0.288267i
$$459$$ −21.1480 + 36.6294i −0.0460741 + 0.0798027i
$$460$$ 0 0
$$461$$ 131.449i 0.285138i −0.989785 0.142569i $$-0.954464\pi$$
0.989785 0.142569i $$-0.0455362\pi$$
$$462$$ 85.0456 + 42.2073i 0.184081 + 0.0913578i
$$463$$ 73.9873i 0.159800i 0.996803 + 0.0798999i $$0.0254601\pi$$
−0.996803 + 0.0798999i $$0.974540\pi$$
$$464$$ −17.0475 29.5271i −0.0367403 0.0636360i
$$465$$ 0 0
$$466$$ −231.115 + 400.303i −0.495956 + 0.859020i
$$467$$ 223.453 + 387.032i 0.478486 + 0.828762i 0.999696 0.0246667i $$-0.00785244\pi$$
−0.521210 + 0.853429i $$0.674519\pi$$
$$468$$ −21.0260 −0.0449274
$$469$$ 41.2719 + 20.4829i 0.0879999 + 0.0436735i
$$470$$ 0 0
$$471$$ 46.3329 + 80.2509i 0.0983713 + 0.170384i
$$472$$ −42.7211 + 73.9951i −0.0905108 + 0.156769i
$$473$$ 207.132 + 119.588i 0.437912 + 0.252828i
$$474$$ 261.207 150.808i 0.551069 0.318160i
$$475$$ 0 0
$$476$$ −63.0722 94.9124i −0.132505 0.199396i
$$477$$ 8.45370i 0.0177226i
$$478$$ −11.2691 + 6.50621i −0.0235755 + 0.0136113i
$$479$$ −513.818 296.653i −1.07269 0.619318i −0.143775 0.989610i $$-0.545924\pi$$
−0.928915 + 0.370293i $$0.879257\pi$$
$$480$$ 0 0
$$481$$ −85.1377 + 49.1543i −0.177002 + 0.102192i
$$482$$ −454.226 −0.942378
$$483$$ −9.09539 144.356i −0.0188310 0.298874i
$$484$$ 180.679 0.373303
$$485$$ 0 0
$$486$$ 19.0919 + 11.0227i 0.0392837 + 0.0226805i
$$487$$ −709.744 409.771i −1.45738 0.841418i −0.458498 0.888696i $$-0.651612\pi$$
−0.998882 + 0.0472773i $$0.984946\pi$$
$$488$$ −66.9683 115.993i −0.137230 0.237690i
$$489$$ 356.774i 0.729600i
$$490$$ 0 0
$$491$$ 554.724 1.12978 0.564892 0.825165i $$-0.308918\pi$$
0.564892 + 0.825165i $$0.308918\pi$$
$$492$$ 9.42620 5.44222i 0.0191589 0.0110614i
$$493$$ −34.6911 + 60.0867i −0.0703673 + 0.121880i
$$494$$ −43.9574 + 76.1364i −0.0889825 + 0.154122i
$$495$$ 0 0
$$496$$ 30.8569i 0.0622115i
$$497$$ 683.071 43.0380i 1.37439 0.0865955i
$$498$$ 219.429i 0.440620i
$$499$$ 317.394 + 549.742i 0.636060 + 1.10169i 0.986290 + 0.165024i $$0.0527701\pi$$
−0.350230 + 0.936664i $$0.613897\pi$$
$$500$$ 0 0
$$501$$ 119.464 206.918i 0.238451 0.413010i
$$502$$ 13.6043 + 23.5634i 0.0271003 + 0.0469390i
$$503$$ −120.116 −0.238800 −0.119400 0.992846i $$-0.538097\pi$$
−0.119400 + 0.992846i $$0.538097\pi$$
$$504$$ −49.4700 + 32.8743i −0.0981547 + 0.0652268i
$$505$$ 0 0
$$506$$ 46.7103 + 80.9046i 0.0923128 + 0.159890i
$$507$$ 135.723 235.079i 0.267699 0.463668i
$$508$$ 261.701 + 151.093i 0.515160 + 0.297428i
$$509$$ −51.1082 + 29.5073i −0.100409 + 0.0579712i −0.549364 0.835583i $$-0.685130\pi$$
0.448955 + 0.893555i $$0.351796\pi$$
$$510$$ 0 0
$$511$$ 190.326 383.497i 0.372458 0.750484i
$$512$$ 22.6274i 0.0441942i
$$513$$ 79.8277 46.0885i 0.155609 0.0898412i
$$514$$ −158.509 91.5150i −0.308383 0.178045i
$$515$$ 0 0
$$516$$ −129.583 + 74.8148i −0.251130 + 0.144990i
$$517$$ 103.604 0.200394
$$518$$ −123.459 + 248.764i −0.238338 + 0.480239i
$$519$$ 382.032 0.736093
$$520$$ 0 0
$$521$$ −841.241 485.691i −1.61467 0.932228i −0.988269 0.152725i $$-0.951195\pi$$
−0.626398 0.779504i $$-0.715471\pi$$
$$522$$ 31.3182 + 18.0816i 0.0599966 + 0.0346391i
$$523$$ 345.682 + 598.739i 0.660960 + 1.14482i 0.980364 + 0.197197i $$0.0631840\pi$$
−0.319404 + 0.947619i $$0.603483\pi$$
$$524$$ 431.442i 0.823363i
$$525$$ 0 0
$$526$$ −236.068 −0.448798
$$527$$ 54.3802 31.3964i 0.103188 0.0595757i
$$528$$ 19.1814 33.2232i 0.0363285 0.0629227i
$$529$$ −193.339 + 334.872i −0.365479 + 0.633029i
$$530$$ 0 0
$$531$$ 90.6251i 0.170669i
$$532$$ 15.6169 + 247.861i 0.0293551 + 0.465905i
$$533$$ 11.0109i 0.0206583i
$$534$$ −144.660 250.559i −0.270900 0.469212i
$$535$$ 0 0
$$536$$ 9.30859 16.1229i 0.0173668 0.0300801i
$$537$$ −63.4798 109.950i −0.118212 0.204749i
$$538$$ 295.703 0.549635
$$539$$ 105.096 250.142i 0.194983 0.464085i
$$540$$ 0 0
$$541$$ −270.888 469.192i −0.500717 0.867267i −1.00000 0.000828025i $$-0.999736\pi$$
0.499283 0.866439i $$-0.333597\pi$$
$$542$$ −100.453 + 173.989i −0.185337 + 0.321013i
$$543$$ −92.1928 53.2275i −0.169784 0.0980249i
$$544$$ −39.8771 + 23.0230i −0.0733034 + 0.0423217i
$$545$$ 0 0
$$546$$ 3.77837 + 59.9679i 0.00692010 + 0.109831i
$$547$$ 318.491i 0.582251i 0.956685 + 0.291126i $$0.0940297\pi$$
−0.956685 + 0.291126i $$0.905970\pi$$
$$548$$ −231.472 + 133.641i −0.422395 + 0.243870i
$$549$$ 123.029 + 71.0306i 0.224096 + 0.129382i
$$550$$ 0 0
$$551$$ 130.949 75.6034i 0.237657 0.137211i
$$552$$ −58.4444 −0.105877
$$553$$ −477.055 717.883i −0.862667 1.29816i
$$554$$ 630.628 1.13832
$$555$$ 0 0
$$556$$ 335.606 + 193.762i 0.603607 + 0.348493i
$$557$$ 499.660 + 288.479i 0.897055 + 0.517915i 0.876244 0.481869i $$-0.160042\pi$$
0.0208114 + 0.999783i $$0.493375\pi$$
$$558$$ −16.3643 28.3439i −0.0293268 0.0507955i
$$559$$ 151.367i 0.270783i
$$560$$ 0 0
$$561$$ −78.0672 −0.139157
$$562$$ −590.342 + 340.834i −1.05043 + 0.606466i
$$563$$ −177.985 + 308.279i −0.316137 + 0.547565i −0.979678 0.200574i $$-0.935719\pi$$
0.663542 + 0.748139i $$0.269053\pi$$
$$564$$ −32.4075 + 56.1314i −0.0574601 + 0.0995238i
$$565$$ 0 0
$$566$$ 306.196i 0.540983i
$$567$$ 28.0068 56.4324i 0.0493948 0.0995281i
$$568$$ 276.550i 0.486883i
$$569$$ −186.085 322.308i −0.327038 0.566447i 0.654885 0.755729i $$-0.272717\pi$$
−0.981923 + 0.189282i $$0.939384\pi$$
$$570$$ 0 0
$$571$$ 82.9355 143.649i 0.145246 0.251574i −0.784219 0.620485i $$-0.786936\pi$$
0.929465 + 0.368911i $$0.120269\pi$$
$$572$$ −19.4042 33.6091i −0.0339234 0.0587571i
$$573$$ −623.300 −1.08778
$$574$$ −17.2155 25.9063i −0.0299922 0.0451330i
$$575$$ 0 0
$$576$$ 12.0000 + 20.7846i 0.0208333 + 0.0360844i
$$577$$ 8.06639 13.9714i 0.0139799 0.0242139i −0.858951 0.512058i $$-0.828883\pi$$
0.872931 + 0.487844i $$0.162217\pi$$
$$578$$ −272.803 157.503i −0.471977 0.272496i
$$579$$ 209.617 121.023i 0.362033 0.209020i
$$580$$ 0 0
$$581$$ −625.830 + 39.4314i −1.07716 + 0.0678681i
$$582$$ 159.698i 0.274395i
$$583$$ 13.5128 7.80164i 0.0231781 0.0133819i
$$584$$ −149.814 86.4950i −0.256530 0.148108i
$$585$$ 0 0
$$586$$ −469.940 + 271.320i −0.801945 + 0.463003i
$$587$$ 204.516 0.348409 0.174205 0.984709i $$-0.444265\pi$$
0.174205 + 0.984709i $$0.444265\pi$$
$$588$$ 102.650 + 135.185i 0.174575 + 0.229906i
$$589$$ −136.846 −0.232337
$$590$$ 0 0
$$591$$ −372.514 215.071i −0.630311 0.363910i
$$592$$ 97.1799 + 56.1068i 0.164155 + 0.0947751i
$$593$$ −345.011 597.577i −0.581806 1.00772i −0.995265 0.0971952i $$-0.969013\pi$$
0.413459 0.910523i $$-0.364320\pi$$
$$594$$ 40.6899i 0.0685016i
$$595$$ 0 0
$$596$$ 132.013 0.221498
$$597$$ −183.892 + 106.170i −0.308026 + 0.177839i
$$598$$ −29.5616 + 51.2022i −0.0494341 + 0.0856224i
$$599$$ −477.775 + 827.531i −0.797622 + 1.38152i 0.123539 + 0.992340i $$0.460575\pi$$
−0.921161 + 0.389182i $$0.872758\pi$$
$$600$$ 0 0
$$601$$ 587.954i 0.978293i 0.872202 + 0.489146i $$0.162692\pi$$
−0.872202 + 0.489146i $$0.837308\pi$$
$$602$$ 236.664 + 356.137i 0.393130 + 0.591590i
$$603$$ 19.7465i 0.0327471i
$$604$$ 34.8820 + 60.4173i 0.0577516 + 0.100029i
$$605$$ 0 0
$$606$$ −170.971 + 296.131i −0.282131 + 0.488665i
$$607$$ 259.483 + 449.438i 0.427485 + 0.740425i 0.996649 0.0817986i $$-0.0260664\pi$$
−0.569164 + 0.822224i $$0.692733\pi$$
$$608$$ 100.350 0.165049
$$609$$ 45.9423 92.5714i 0.0754389 0.152006i
$$610$$ 0 0
$$611$$ 32.7839 + 56.7834i 0.0536561 + 0.0929351i
$$612$$ 24.4196 42.2960i 0.0399013 0.0691111i
$$613$$ 110.465 + 63.7771i 0.180204 + 0.104041i 0.587389 0.809305i $$-0.300156\pi$$
−0.407184 + 0.913346i $$0.633489\pi$$
$$614$$ 25.8744 14.9386i 0.0421407 0.0243300i
$$615$$ 0 0
$$616$$ −98.2022 48.7368i −0.159419 0.0791182i
$$617$$ 486.581i 0.788624i 0.918977 + 0.394312i $$0.129017\pi$$
−0.918977 + 0.394312i $$0.870983\pi$$
$$618$$ 370.137 213.699i 0.598927 0.345791i
$$619$$ −370.662 214.002i −0.598808 0.345722i 0.169765 0.985485i $$-0.445699\pi$$
−0.768572 + 0.639763i $$0.779033\pi$$
$$620$$ 0 0
$$621$$ 53.6846 30.9948i 0.0864486 0.0499111i
$$622$$ −122.522 −0.196980
$$623$$ −688.620 + 457.609i −1.10533 + 0.734524i
$$624$$ 24.2787 0.0389082
$$625$$ 0 0
$$626$$ −3.47589 2.00680i −0.00555254 0.00320576i
$$627$$ 147.341 + 85.0671i 0.234993 + 0.135673i
$$628$$ −53.5006 92.6658i −0.0851921 0.147557i
$$629$$ 228.351i 0.363038i
$$630$$ 0 0
$$631$$ −64.4987 −0.102217 −0.0511083 0.998693i $$-0.516275\pi$$
−0.0511083 + 0.998693i $$0.516275\pi$$
$$632$$ −301.616 + 174.138i −0.477240 + 0.275535i
$$633$$ −305.559 + 529.244i −0.482716 + 0.836088i
$$634$$ −219.097 + 379.488i −0.345579 + 0.598561i
$$635$$ 0 0
$$636$$ 9.76149i 0.0153483i
$$637$$ 170.354 21.5525i 0.267432 0.0338343i
$$638$$ 66.7476i 0.104620i
$$639$$ 146.663 + 254.027i 0.229519 + 0.397538i
$$640$$ 0 0
$$641$$ −352.662 + 610.829i −0.550175 + 0.952932i 0.448086 + 0.893990i $$0.352106\pi$$
−0.998261 + 0.0589413i $$0.981228\pi$$
$$642$$ 74.0681 + 128.290i 0.115371 + 0.199828i
$$643$$ −1092.83 −1.69958 −0.849788 0.527124i $$-0.823270\pi$$
−0.849788 + 0.527124i $$0.823270\pi$$
$$644$$ 10.5025 + 166.688i 0.0163082 + 0.258833i
$$645$$ 0 0
$$646$$ −102.104 176.850i −0.158056 0.273761i
$$647$$ 257.546 446.083i 0.398062 0.689463i −0.595425 0.803411i $$-0.703016\pi$$
0.993487 + 0.113948i $$0.0363496\pi$$
$$648$$ −22.0454 12.7279i −0.0340207 0.0196419i
$$649$$ 144.860 83.6349i 0.223205 0.128867i
$$650$$ 0 0
$$651$$ −77.8984 + 51.7659i −0.119660 + 0.0795175i
$$652$$ 411.967i 0.631852i
$$653$$ 681.245 393.317i 1.04325 0.602323i 0.122501 0.992468i $$-0.460909\pi$$
0.920753 + 0.390145i $$0.127575\pi$$
$$654$$ 213.853 + 123.468i 0.326993 + 0.188789i
$$655$$ 0 0
$$656$$ −10.8844 + 6.28413i −0.0165921 + 0.00957947i
$$657$$ 183.484 0.279275
$$658$$ 165.915 + 82.3420i 0.252151 + 0.125140i
$$659$$ 819.425 1.24344 0.621719 0.783241i $$-0.286435\pi$$
0.621719 + 0.783241i $$0.286435\pi$$
$$660$$ 0 0
$$661$$ −889.453 513.526i −1.34562 0.776892i −0.357991 0.933725i $$-0.616538\pi$$
−0.987625 + 0.156833i $$0.949872\pi$$
$$662$$ −510.216 294.573i −0.770718 0.444974i
$$663$$ −24.7032 42.7873i −0.0372598 0.0645358i
$$664$$ 253.375i 0.381589i
$$665$$ 0 0
$$666$$ −119.021 −0.178710
$$667$$ 88.0639 50.8437i 0.132030 0.0762275i
$$668$$ −137.945 + 238.928i −0.206505 + 0.357677i
$$669$$ 53.4701 92.6130i 0.0799254 0.138435i
$$670$$ 0 0
$$671$$ 262.207i 0.390771i
$$672$$ 57.1230 37.9600i 0.0850045 0.0564881i
$$673$$ 669.779i 0.995213i −0.867403 0.497607i $$-0.834212\pi$$
0.867403 0.497607i $$-0.165788\pi$$
$$674$$ 109.949 + 190.437i 0.163129 + 0.282548i
$$675$$ 0 0
$$676$$ −156.720 + 271.446i −0.231834 + 0.401548i
$$677$$ 454.099 + 786.522i 0.670751 + 1.16178i 0.977691 + 0.210047i $$0.0673616\pi$$
−0.306940 + 0.951729i $$0.599305\pi$$
$$678$$ −181.722 −0.268026
$$679$$ 455.472 28.6977i 0.670798 0.0422647i
$$680$$ 0 0
$$681$$ 181.452 + 314.285i 0.266450 + 0.461505i
$$682$$ 30.2042 52.3153i 0.0442877 0.0767086i
$$683$$ 572.733 + 330.668i 0.838555 + 0.484140i 0.856773 0.515694i $$-0.172466\pi$$
−0.0182177 + 0.999834i $$0.505799\pi$$
$$684$$ −92.1770 + 53.2184i −0.134762 + 0.0778047i
$$685$$ 0 0
$$686$$ 367.112 317.059i 0.535149 0.462185i
$$687$$ 186.714i 0.271781i
$$688$$ 149.630 86.3887i 0.217485 0.125565i
$$689$$ 8.55188 + 4.93743i 0.0124120 + 0.00716608i
$$690$$ 0 0
$$691$$ −239.610 + 138.339i −0.346759 + 0.200201i −0.663257 0.748392i $$-0.730826\pi$$
0.316498 + 0.948593i $$0.397493\pi$$
$$692$$ −441.133 −0.637475
$$693$$ 116.051 7.31198i 0.167462 0.0105512i
$$694$$ 724.794 1.04437
$$695$$ 0 0
$$696$$ −36.1632 20.8788i −0.0519586 0.0299983i
$$697$$ 22.1495 + 12.7880i 0.0317783 + 0.0183472i
$$698$$ −190.343 329.683i −0.272697 0.472326i
$$699$$ 566.115i 0.809892i
$$700$$ 0 0
$$701$$ −415.967 −0.593391 −0.296696 0.954972i $$-0.595885\pi$$
−0.296696 + 0.954972i $$0.595885\pi$$
$$702$$ −22.3015 + 12.8758i −0.0317685 + 0.0183415i
$$703$$ −248.827 + 430.980i −0.353950 + 0.613059i
$$704$$ −22.1488 + 38.3629i −0.0314614 + 0.0544927i
$$705$$ 0 0
$$706$$ 829.382i 1.17476i
$$707$$ 875.313 + 434.409i 1.23807 + 0.614440i
$$708$$ 104.645i 0.147804i
$$709$$ 136.620 + 236.632i 0.192693 + 0.333755i 0.946142 0.323752i $$-0.104944\pi$$
−0.753449 + 0.657507i $$0.771611\pi$$
$$710$$ 0 0
$$711$$ 184.701 319.912i 0.259776 0.449946i
$$712$$ 167.039 + 289.321i 0.234606 + 0.406349i
$$713$$ −92.0300 −0.129074
$$714$$ −125.020 62.0462i −0.175098 0.0868994i
$$715$$ 0 0
$$716$$ 73.3002 + 126.960i 0.102375 + 0.177318i
$$717$$ −7.96845 + 13.8018i −0.0111136 + 0.0192493i
$$718$$ −108.811 62.8223i −0.151548 0.0874962i
$$719$$ −361.463 + 208.691i −0.502731 + 0.290252i −0.729840 0.683617i $$-0.760406\pi$$
0.227110 + 0.973869i $$0.427072\pi$$
$$720$$ 0 0
$$721$$ −676.000 1017.26i −0.937587 1.41090i
$$722$$ 65.4934i 0.0907111i
$$723$$ −481.779 + 278.156i −0.666362 + 0.384724i
$$724$$ 106.455 + 61.4619i 0.147037 + 0.0848921i
$$725$$ 0 0
$$726$$ 191.639 110.643i 0.263965 0.152400i
$$727$$ −357.267 −0.491426 −0.245713 0.969343i $$-0.579022\pi$$
−0.245713 + 0.969343i $$0.579022\pi$$
$$728$$ −4.36289 69.2450i −0.00599298 0.0951167i
$$729$$ 27.0000 0.0370370
$$730$$ 0 0
$$731$$ −304.491 175.798i −0.416541 0.240490i
$$732$$ −142.061 82.0191i −0.194073 0.112048i
$$733$$ 215.521 + 373.293i 0.294026 + 0.509267i 0.974758 0.223265i $$-0.0716716\pi$$
−0.680732 + 0.732532i $$0.738338\pi$$
$$734$$ 998.488i 1.36034i
$$735$$ 0 0
$$736$$ 67.4858 0.0916926
$$737$$ −31.5638 + 18.2234i −0.0428274 + 0.0247264i
$$738$$ 6.66533 11.5447i 0.00903161 0.0156432i
$$739$$ 159.512 276.282i 0.215848 0.373860i −0.737687 0.675143i $$-0.764082\pi$$
0.953535 + 0.301284i $$0.0974151\pi$$
$$740$$ 0 0
$$741$$ 107.673i 0.145308i
$$742$$ 27.8406 1.75414i 0.0375210 0.00236407i
$$743$$ 1303.33i 1.75414i 0.480360 + 0.877072i $$0.340506\pi$$
−0.480360 + 0.877072i $$0.659494\pi$$
$$744$$ 18.8959 + 32.7287i 0.0253977 + 0.0439902i
$$745$$ 0 0
$$746$$ 36.2337 62.7585i 0.0485706 0.0841267i
$$747$$ −134.372 232.740i −0.179883 0.311566i
$$748$$ 90.1442 0.120514
$$749$$ 352.583 234.302i 0.470738 0.312820i
$$750$$ 0 0
$$751$$ −614.473 1064.30i −0.818206 1.41717i −0.907003 0.421124i $$-0.861636\pi$$
0.0887971 0.996050i $$-0.471698\pi$$
$$752$$ 37.4210 64.8150i 0.0497619 0.0861901i
$$753$$ 28.8591 + 16.6618i 0.0383255 + 0.0221273i
$$754$$ −36.5832 + 21.1213i −0.0485188 + 0.0280124i
$$755$$ 0 0
$$756$$ −32.3395 + 65.1625i −0.0427771 + 0.0861938i
$$757$$ 1206.22i 1.59342i 0.604359 + 0.796712i $$0.293429\pi$$
−0.604359 + 0.796712i $$0.706571\pi$$
$$758$$ −238.487 + 137.691i −0.314627 + 0.181650i
$$759$$ 99.0874 + 57.2082i 0.130550 + 0.0753731i
$$760$$ 0 0
$$761$$ −204.456 + 118.043i −0.268667 + 0.155115i −0.628282 0.777986i $$-0.716242\pi$$
0.359614 + 0.933101i $$0.382908\pi$$
$$762$$ 370.101 0.485697
$$763$$ 313.712 632.114i 0.411156 0.828459i
$$764$$ 719.725 0.942048
$$765$$ 0 0
$$766$$ −643.088 371.287i −0.839540 0.484709i
$$767$$ 91.6777 + 52.9301i 0.119528 + 0.0690093i
$$768$$ −13.8564 24.0000i −0.0180422 0.0312500i
$$769$$ 1341.44i 1.74440i −0.489149 0.872200i $$-0.662693\pi$$
0.489149 0.872200i $$-0.337307\pi$$
$$770$$ 0 0
$$771$$ −224.165 −0.290746
$$772$$ −242.045 + 139.745i −0.313530 + 0.181017i
$$773$$ −90.0279 + 155.933i −0.116466 + 0.201724i −0.918365 0.395735i $$-0.870490\pi$$
0.801899 + 0.597460i $$0.203823\pi$$
$$774$$ −91.6290 + 158.706i −0.118384 + 0.205047i
$$775$$ 0 0
$$776$$ 184.403i 0.237633i
$$777$$ 21.3880 + 339.456i 0.0275264 + 0.436881i
$$778$$ 570.677i 0.733518i
$$779$$ −27.8693 48.2711i −0.0357758 0.0619654i
$$780$$ 0 0
$$781$$ −270.700 + 468.866i −0.346607 + 0.600341i