# Properties

 Label 108.3.d.d.55.2 Level 108 Weight 3 Character 108.55 Analytic conductor 2.943 Analytic rank 0 Dimension 8 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 108.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.94278685509$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.207360000.1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}\cdot 3^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 55.2 Root $$0.437016 + 0.756934i$$ of $$x^{8} + 6 x^{6} + 32 x^{4} + 24 x^{2} + 16$$ Character $$\chi$$ $$=$$ 108.55 Dual form 108.3.d.d.55.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.85123 + 0.756934i) q^{2} +(2.85410 - 2.80252i) q^{4} -1.08036 q^{5} -6.01392i q^{7} +(-3.16228 + 7.34847i) q^{8} +O(q^{10})$$ $$q+(-1.85123 + 0.756934i) q^{2} +(2.85410 - 2.80252i) q^{4} -1.08036 q^{5} -6.01392i q^{7} +(-3.16228 + 7.34847i) q^{8} +(2.00000 - 0.817763i) q^{10} -17.7247i q^{11} +12.4164 q^{13} +(4.55214 + 11.1331i) q^{14} +(0.291796 - 15.9973i) q^{16} +26.3786 q^{17} -5.19615i q^{19} +(-3.08347 + 3.02774i) q^{20} +(13.4164 + 32.8124i) q^{22} -29.8356i q^{23} -23.8328 q^{25} +(-22.9856 + 9.39840i) q^{26} +(-16.8541 - 17.1643i) q^{28} -4.32145 q^{29} +44.8403i q^{31} +(11.5687 + 29.8356i) q^{32} +(-48.8328 + 19.9668i) q^{34} +6.49721i q^{35} -20.4164 q^{37} +(3.93314 + 9.61927i) q^{38} +(3.41641 - 7.93901i) q^{40} -59.2393 q^{41} -19.1491i q^{43} +(-49.6737 - 50.5880i) q^{44} +(22.5836 + 55.2326i) q^{46} +41.0631i q^{47} +12.8328 q^{49} +(44.1200 - 18.0399i) q^{50} +(35.4377 - 34.7972i) q^{52} +70.0430 q^{53} +19.1491i q^{55} +(44.1931 + 19.0177i) q^{56} +(8.00000 - 3.27105i) q^{58} +28.9521i q^{59} +18.4164 q^{61} +(-33.9411 - 83.0096i) q^{62} +(-44.0000 - 46.4758i) q^{64} -13.4142 q^{65} -94.8767i q^{67} +(75.2872 - 73.9264i) q^{68} +(-4.91796 - 12.0278i) q^{70} +83.8931i q^{71} +55.8328 q^{73} +(37.7955 - 15.4539i) q^{74} +(-14.5623 - 14.8303i) q^{76} -106.595 q^{77} +41.0410i q^{79} +(-0.315246 + 17.2829i) q^{80} +(109.666 - 44.8403i) q^{82} +35.4493i q^{83} -28.4984 q^{85} +(14.4946 + 35.4493i) q^{86} +(130.249 + 56.0503i) q^{88} +26.3786 q^{89} -74.6712i q^{91} +(-83.6148 - 85.1539i) q^{92} +(-31.0820 - 76.0172i) q^{94} +5.61373i q^{95} +76.3313 q^{97} +(-23.7565 + 9.71359i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 4q^{4} + O(q^{10})$$ $$8q - 4q^{4} + 16q^{10} - 8q^{13} + 56q^{16} + 24q^{25} - 108q^{28} - 176q^{34} - 56q^{37} - 80q^{40} + 288q^{46} - 112q^{49} + 364q^{52} + 64q^{58} + 40q^{61} - 352q^{64} - 576q^{70} + 232q^{73} - 36q^{76} + 448q^{82} + 416q^{85} + 720q^{88} + 288q^{94} - 248q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$55$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.85123 + 0.756934i −0.925615 + 0.378467i
$$3$$ 0 0
$$4$$ 2.85410 2.80252i 0.713525 0.700629i
$$5$$ −1.08036 −0.216073 −0.108036 0.994147i $$-0.534456\pi$$
−0.108036 + 0.994147i $$0.534456\pi$$
$$6$$ 0 0
$$7$$ 6.01392i 0.859131i −0.903036 0.429565i $$-0.858667\pi$$
0.903036 0.429565i $$-0.141333\pi$$
$$8$$ −3.16228 + 7.34847i −0.395285 + 0.918559i
$$9$$ 0 0
$$10$$ 2.00000 0.817763i 0.200000 0.0817763i
$$11$$ 17.7247i 1.61133i −0.592369 0.805667i $$-0.701807\pi$$
0.592369 0.805667i $$-0.298193\pi$$
$$12$$ 0 0
$$13$$ 12.4164 0.955108 0.477554 0.878602i $$-0.341523\pi$$
0.477554 + 0.878602i $$0.341523\pi$$
$$14$$ 4.55214 + 11.1331i 0.325153 + 0.795224i
$$15$$ 0 0
$$16$$ 0.291796 15.9973i 0.0182373 0.999834i
$$17$$ 26.3786 1.55168 0.775841 0.630929i $$-0.217326\pi$$
0.775841 + 0.630929i $$0.217326\pi$$
$$18$$ 0 0
$$19$$ 5.19615i 0.273482i −0.990607 0.136741i $$-0.956337\pi$$
0.990607 0.136741i $$-0.0436628\pi$$
$$20$$ −3.08347 + 3.02774i −0.154173 + 0.151387i
$$21$$ 0 0
$$22$$ 13.4164 + 32.8124i 0.609837 + 1.49147i
$$23$$ 29.8356i 1.29720i −0.761129 0.648600i $$-0.775355\pi$$
0.761129 0.648600i $$-0.224645\pi$$
$$24$$ 0 0
$$25$$ −23.8328 −0.953313
$$26$$ −22.9856 + 9.39840i −0.884062 + 0.361477i
$$27$$ 0 0
$$28$$ −16.8541 17.1643i −0.601932 0.613012i
$$29$$ −4.32145 −0.149016 −0.0745078 0.997220i $$-0.523739\pi$$
−0.0745078 + 0.997220i $$0.523739\pi$$
$$30$$ 0 0
$$31$$ 44.8403i 1.44646i 0.690607 + 0.723230i $$0.257343\pi$$
−0.690607 + 0.723230i $$0.742657\pi$$
$$32$$ 11.5687 + 29.8356i 0.361523 + 0.932363i
$$33$$ 0 0
$$34$$ −48.8328 + 19.9668i −1.43626 + 0.587260i
$$35$$ 6.49721i 0.185635i
$$36$$ 0 0
$$37$$ −20.4164 −0.551795 −0.275897 0.961187i $$-0.588975\pi$$
−0.275897 + 0.961187i $$0.588975\pi$$
$$38$$ 3.93314 + 9.61927i 0.103504 + 0.253139i
$$39$$ 0 0
$$40$$ 3.41641 7.93901i 0.0854102 0.198475i
$$41$$ −59.2393 −1.44486 −0.722431 0.691443i $$-0.756975\pi$$
−0.722431 + 0.691443i $$0.756975\pi$$
$$42$$ 0 0
$$43$$ 19.1491i 0.445328i −0.974895 0.222664i $$-0.928525\pi$$
0.974895 0.222664i $$-0.0714752\pi$$
$$44$$ −49.6737 50.5880i −1.12895 1.14973i
$$45$$ 0 0
$$46$$ 22.5836 + 55.2326i 0.490948 + 1.20071i
$$47$$ 41.0631i 0.873683i 0.899539 + 0.436841i $$0.143903\pi$$
−0.899539 + 0.436841i $$0.856097\pi$$
$$48$$ 0 0
$$49$$ 12.8328 0.261894
$$50$$ 44.1200 18.0399i 0.882400 0.360797i
$$51$$ 0 0
$$52$$ 35.4377 34.7972i 0.681494 0.669177i
$$53$$ 70.0430 1.32157 0.660783 0.750577i $$-0.270224\pi$$
0.660783 + 0.750577i $$0.270224\pi$$
$$54$$ 0 0
$$55$$ 19.1491i 0.348165i
$$56$$ 44.1931 + 19.0177i 0.789162 + 0.339601i
$$57$$ 0 0
$$58$$ 8.00000 3.27105i 0.137931 0.0563975i
$$59$$ 28.9521i 0.490714i 0.969433 + 0.245357i $$0.0789052\pi$$
−0.969433 + 0.245357i $$0.921095\pi$$
$$60$$ 0 0
$$61$$ 18.4164 0.301908 0.150954 0.988541i $$-0.451765\pi$$
0.150954 + 0.988541i $$0.451765\pi$$
$$62$$ −33.9411 83.0096i −0.547438 1.33887i
$$63$$ 0 0
$$64$$ −44.0000 46.4758i −0.687500 0.726184i
$$65$$ −13.4142 −0.206373
$$66$$ 0 0
$$67$$ 94.8767i 1.41607i −0.706177 0.708035i $$-0.749582\pi$$
0.706177 0.708035i $$-0.250418\pi$$
$$68$$ 75.2872 73.9264i 1.10716 1.08715i
$$69$$ 0 0
$$70$$ −4.91796 12.0278i −0.0702566 0.171826i
$$71$$ 83.8931i 1.18159i 0.806821 + 0.590797i $$0.201186\pi$$
−0.806821 + 0.590797i $$0.798814\pi$$
$$72$$ 0 0
$$73$$ 55.8328 0.764833 0.382417 0.923990i $$-0.375092\pi$$
0.382417 + 0.923990i $$0.375092\pi$$
$$74$$ 37.7955 15.4539i 0.510749 0.208836i
$$75$$ 0 0
$$76$$ −14.5623 14.8303i −0.191609 0.195136i
$$77$$ −106.595 −1.38435
$$78$$ 0 0
$$79$$ 41.0410i 0.519507i 0.965675 + 0.259753i $$0.0836413\pi$$
−0.965675 + 0.259753i $$0.916359\pi$$
$$80$$ −0.315246 + 17.2829i −0.00394057 + 0.216037i
$$81$$ 0 0
$$82$$ 109.666 44.8403i 1.33739 0.546833i
$$83$$ 35.4493i 0.427101i 0.976932 + 0.213550i $$0.0685027\pi$$
−0.976932 + 0.213550i $$0.931497\pi$$
$$84$$ 0 0
$$85$$ −28.4984 −0.335276
$$86$$ 14.4946 + 35.4493i 0.168542 + 0.412202i
$$87$$ 0 0
$$88$$ 130.249 + 56.0503i 1.48010 + 0.636936i
$$89$$ 26.3786 0.296389 0.148194 0.988958i $$-0.452654\pi$$
0.148194 + 0.988958i $$0.452654\pi$$
$$90$$ 0 0
$$91$$ 74.6712i 0.820563i
$$92$$ −83.6148 85.1539i −0.908857 0.925586i
$$93$$ 0 0
$$94$$ −31.0820 76.0172i −0.330660 0.808693i
$$95$$ 5.61373i 0.0590919i
$$96$$ 0 0
$$97$$ 76.3313 0.786920 0.393460 0.919342i $$-0.371278\pi$$
0.393460 + 0.919342i $$0.371278\pi$$
$$98$$ −23.7565 + 9.71359i −0.242413 + 0.0991183i
$$99$$ 0 0
$$100$$ −68.0213 + 66.7919i −0.680213 + 0.667919i
$$101$$ −72.2037 −0.714888 −0.357444 0.933935i $$-0.616352\pi$$
−0.357444 + 0.933935i $$0.616352\pi$$
$$102$$ 0 0
$$103$$ 57.9754i 0.562868i 0.959581 + 0.281434i $$0.0908101\pi$$
−0.959581 + 0.281434i $$0.909190\pi$$
$$104$$ −39.2641 + 91.2416i −0.377540 + 0.877323i
$$105$$ 0 0
$$106$$ −129.666 + 53.0179i −1.22326 + 0.500169i
$$107$$ 64.4015i 0.601883i 0.953643 + 0.300942i $$0.0973009\pi$$
−0.953643 + 0.300942i $$0.902699\pi$$
$$108$$ 0 0
$$109$$ −43.1672 −0.396029 −0.198015 0.980199i $$-0.563449\pi$$
−0.198015 + 0.980199i $$0.563449\pi$$
$$110$$ −14.4946 35.4493i −0.131769 0.322267i
$$111$$ 0 0
$$112$$ −96.2067 1.75484i −0.858988 0.0156682i
$$113$$ 81.2965 0.719438 0.359719 0.933061i $$-0.382873\pi$$
0.359719 + 0.933061i $$0.382873\pi$$
$$114$$ 0 0
$$115$$ 32.2333i 0.280290i
$$116$$ −12.3339 + 12.1109i −0.106326 + 0.104405i
$$117$$ 0 0
$$118$$ −21.9149 53.5971i −0.185719 0.454212i
$$119$$ 158.639i 1.33310i
$$120$$ 0 0
$$121$$ −193.164 −1.59640
$$122$$ −34.0930 + 13.9400i −0.279451 + 0.114262i
$$123$$ 0 0
$$124$$ 125.666 + 127.979i 1.01343 + 1.03209i
$$125$$ 52.7572 0.422057
$$126$$ 0 0
$$127$$ 191.968i 1.51156i 0.654826 + 0.755780i $$0.272742\pi$$
−0.654826 + 0.755780i $$0.727258\pi$$
$$128$$ 116.633 + 52.7323i 0.911197 + 0.411971i
$$129$$ 0 0
$$130$$ 24.8328 10.1537i 0.191022 0.0781053i
$$131$$ 141.797i 1.08242i −0.840887 0.541211i $$-0.817966\pi$$
0.840887 0.541211i $$-0.182034\pi$$
$$132$$ 0 0
$$133$$ −31.2492 −0.234957
$$134$$ 71.8154 + 175.639i 0.535936 + 1.31074i
$$135$$ 0 0
$$136$$ −83.4164 + 193.842i −0.613356 + 1.42531i
$$137$$ 87.7787 0.640720 0.320360 0.947296i $$-0.396196\pi$$
0.320360 + 0.947296i $$0.396196\pi$$
$$138$$ 0 0
$$139$$ 183.501i 1.32015i −0.751200 0.660075i $$-0.770524\pi$$
0.751200 0.660075i $$-0.229476\pi$$
$$140$$ 18.2085 + 18.5437i 0.130061 + 0.132455i
$$141$$ 0 0
$$142$$ −63.5016 155.305i −0.447194 1.09370i
$$143$$ 220.077i 1.53900i
$$144$$ 0 0
$$145$$ 4.66874 0.0321982
$$146$$ −103.359 + 42.2618i −0.707941 + 0.289464i
$$147$$ 0 0
$$148$$ −58.2705 + 57.2173i −0.393720 + 0.386604i
$$149$$ 153.950 1.03322 0.516611 0.856220i $$-0.327193\pi$$
0.516611 + 0.856220i $$0.327193\pi$$
$$150$$ 0 0
$$151$$ 185.375i 1.22765i 0.789442 + 0.613825i $$0.210370\pi$$
−0.789442 + 0.613825i $$0.789630\pi$$
$$152$$ 38.1838 + 16.4317i 0.251209 + 0.108103i
$$153$$ 0 0
$$154$$ 197.331 80.6851i 1.28137 0.523930i
$$155$$ 48.4438i 0.312540i
$$156$$ 0 0
$$157$$ 196.164 1.24945 0.624726 0.780844i $$-0.285211\pi$$
0.624726 + 0.780844i $$0.285211\pi$$
$$158$$ −31.0653 75.9764i −0.196616 0.480863i
$$159$$ 0 0
$$160$$ −12.4984 32.2333i −0.0781153 0.201458i
$$161$$ −179.429 −1.11447
$$162$$ 0 0
$$163$$ 129.325i 0.793403i −0.917948 0.396701i $$-0.870155\pi$$
0.917948 0.396701i $$-0.129845\pi$$
$$164$$ −169.075 + 166.019i −1.03095 + 1.01231i
$$165$$ 0 0
$$166$$ −26.8328 65.6249i −0.161643 0.395331i
$$167$$ 137.951i 0.826052i 0.910719 + 0.413026i $$0.135528\pi$$
−0.910719 + 0.413026i $$0.864472\pi$$
$$168$$ 0 0
$$169$$ −14.8328 −0.0877681
$$170$$ 52.7572 21.5714i 0.310336 0.126891i
$$171$$ 0 0
$$172$$ −53.6656 54.6534i −0.312009 0.317753i
$$173$$ 160.432 0.927354 0.463677 0.886004i $$-0.346530\pi$$
0.463677 + 0.886004i $$0.346530\pi$$
$$174$$ 0 0
$$175$$ 143.329i 0.819020i
$$176$$ −283.548 5.17199i −1.61107 0.0293863i
$$177$$ 0 0
$$178$$ −48.8328 + 19.9668i −0.274342 + 0.112173i
$$179$$ 201.469i 1.12552i −0.826619 0.562762i $$-0.809739\pi$$
0.826619 0.562762i $$-0.190261\pi$$
$$180$$ 0 0
$$181$$ −48.2523 −0.266587 −0.133294 0.991077i $$-0.542555\pi$$
−0.133294 + 0.991077i $$0.542555\pi$$
$$182$$ 56.5212 + 138.234i 0.310556 + 0.759525i
$$183$$ 0 0
$$184$$ 219.246 + 94.3485i 1.19155 + 0.512764i
$$185$$ 22.0571 0.119228
$$186$$ 0 0
$$187$$ 467.552i 2.50028i
$$188$$ 115.080 + 117.198i 0.612128 + 0.623395i
$$189$$ 0 0
$$190$$ −4.24922 10.3923i −0.0223643 0.0546963i
$$191$$ 147.411i 0.771786i 0.922544 + 0.385893i $$0.126107\pi$$
−0.922544 + 0.385893i $$0.873893\pi$$
$$192$$ 0 0
$$193$$ 25.1641 0.130384 0.0651919 0.997873i $$-0.479234\pi$$
0.0651919 + 0.997873i $$0.479234\pi$$
$$194$$ −141.307 + 57.7777i −0.728385 + 0.297823i
$$195$$ 0 0
$$196$$ 36.6262 35.9642i 0.186868 0.183491i
$$197$$ −385.506 −1.95688 −0.978441 0.206528i $$-0.933784\pi$$
−0.978441 + 0.206528i $$0.933784\pi$$
$$198$$ 0 0
$$199$$ 121.386i 0.609978i −0.952356 0.304989i $$-0.901347\pi$$
0.952356 0.304989i $$-0.0986528\pi$$
$$200$$ 75.3660 175.135i 0.376830 0.875674i
$$201$$ 0 0
$$202$$ 133.666 54.6534i 0.661711 0.270562i
$$203$$ 25.9888i 0.128024i
$$204$$ 0 0
$$205$$ 64.0000 0.312195
$$206$$ −43.8836 107.326i −0.213027 0.520999i
$$207$$ 0 0
$$208$$ 3.62306 198.629i 0.0174186 0.954949i
$$209$$ −92.1001 −0.440670
$$210$$ 0 0
$$211$$ 261.631i 1.23996i 0.784619 + 0.619978i $$0.212859\pi$$
−0.784619 + 0.619978i $$0.787141\pi$$
$$212$$ 199.910 196.297i 0.942971 0.925928i
$$213$$ 0 0
$$214$$ −48.7477 119.222i −0.227793 0.557112i
$$215$$ 20.6880i 0.0962231i
$$216$$ 0 0
$$217$$ 269.666 1.24270
$$218$$ 79.9124 32.6747i 0.366570 0.149884i
$$219$$ 0 0
$$220$$ 53.6656 + 54.6534i 0.243935 + 0.248425i
$$221$$ 327.527 1.48202
$$222$$ 0 0
$$223$$ 70.0542i 0.314144i 0.987587 + 0.157072i $$0.0502056\pi$$
−0.987587 + 0.157072i $$0.949794\pi$$
$$224$$ 179.429 69.5735i 0.801022 0.310596i
$$225$$ 0 0
$$226$$ −150.498 + 61.5361i −0.665922 + 0.272283i
$$227$$ 298.356i 1.31434i 0.753740 + 0.657172i $$0.228248\pi$$
−0.753740 + 0.657172i $$0.771752\pi$$
$$228$$ 0 0
$$229$$ 259.666 1.13391 0.566956 0.823748i $$-0.308121\pi$$
0.566956 + 0.823748i $$0.308121\pi$$
$$230$$ −24.3985 59.6712i −0.106080 0.259440i
$$231$$ 0 0
$$232$$ 13.6656 31.7561i 0.0589036 0.136880i
$$233$$ −7.38192 −0.0316821 −0.0158410 0.999875i $$-0.505043\pi$$
−0.0158410 + 0.999875i $$0.505043\pi$$
$$234$$ 0 0
$$235$$ 44.3630i 0.188779i
$$236$$ 81.1389 + 82.6323i 0.343809 + 0.350137i
$$237$$ 0 0
$$238$$ 120.079 + 293.676i 0.504533 + 1.23393i
$$239$$ 82.1262i 0.343624i 0.985130 + 0.171812i $$0.0549622\pi$$
−0.985130 + 0.171812i $$0.945038\pi$$
$$240$$ 0 0
$$241$$ −415.827 −1.72542 −0.862711 0.505698i $$-0.831235\pi$$
−0.862711 + 0.505698i $$0.831235\pi$$
$$242$$ 357.591 146.212i 1.47765 0.604184i
$$243$$ 0 0
$$244$$ 52.5623 51.6123i 0.215419 0.211526i
$$245$$ −13.8641 −0.0565882
$$246$$ 0 0
$$247$$ 64.5175i 0.261205i
$$248$$ −329.507 141.797i −1.32866 0.571764i
$$249$$ 0 0
$$250$$ −97.6656 + 39.9337i −0.390663 + 0.159735i
$$251$$ 140.030i 0.557890i 0.960307 + 0.278945i $$0.0899847\pi$$
−0.960307 + 0.278945i $$0.910015\pi$$
$$252$$ 0 0
$$253$$ −528.827 −2.09022
$$254$$ −145.307 355.377i −0.572075 1.39912i
$$255$$ 0 0
$$256$$ −255.830 9.33592i −0.999335 0.0364684i
$$257$$ 66.9825 0.260632 0.130316 0.991472i $$-0.458401\pi$$
0.130316 + 0.991472i $$0.458401\pi$$
$$258$$ 0 0
$$259$$ 122.783i 0.474064i
$$260$$ −38.2856 + 37.5936i −0.147252 + 0.144591i
$$261$$ 0 0
$$262$$ 107.331 + 262.500i 0.409661 + 1.00191i
$$263$$ 37.2163i 0.141507i −0.997494 0.0707534i $$-0.977460\pi$$
0.997494 0.0707534i $$-0.0225404\pi$$
$$264$$ 0 0
$$265$$ −75.6718 −0.285554
$$266$$ 57.8495 23.6536i 0.217479 0.0889233i
$$267$$ 0 0
$$268$$ −265.894 270.788i −0.992140 1.01040i
$$269$$ −279.092 −1.03752 −0.518758 0.854921i $$-0.673605\pi$$
−0.518758 + 0.854921i $$0.673605\pi$$
$$270$$ 0 0
$$271$$ 406.305i 1.49928i 0.661845 + 0.749641i $$0.269774\pi$$
−0.661845 + 0.749641i $$0.730226\pi$$
$$272$$ 7.69717 421.987i 0.0282984 1.55142i
$$273$$ 0 0
$$274$$ −162.498 + 66.4426i −0.593060 + 0.242491i
$$275$$ 422.429i 1.53611i
$$276$$ 0 0
$$277$$ 4.83282 0.0174470 0.00872349 0.999962i $$-0.497223\pi$$
0.00872349 + 0.999962i $$0.497223\pi$$
$$278$$ 138.898 + 339.702i 0.499633 + 1.22195i
$$279$$ 0 0
$$280$$ −47.7446 20.5460i −0.170516 0.0733785i
$$281$$ −4.32145 −0.0153788 −0.00768942 0.999970i $$-0.502448\pi$$
−0.00768942 + 0.999970i $$0.502448\pi$$
$$282$$ 0 0
$$283$$ 44.3630i 0.156760i −0.996924 0.0783799i $$-0.975025\pi$$
0.996924 0.0783799i $$-0.0249747\pi$$
$$284$$ 235.112 + 239.440i 0.827859 + 0.843097i
$$285$$ 0 0
$$286$$ 166.584 + 407.413i 0.582460 + 1.42452i
$$287$$ 356.260i 1.24133i
$$288$$ 0 0
$$289$$ 406.830 1.40772
$$290$$ −8.64290 + 3.53393i −0.0298031 + 0.0121860i
$$291$$ 0 0
$$292$$ 159.353 156.472i 0.545728 0.535864i
$$293$$ −388.927 −1.32740 −0.663699 0.748000i $$-0.731014\pi$$
−0.663699 + 0.748000i $$0.731014\pi$$
$$294$$ 0 0
$$295$$ 31.2788i 0.106030i
$$296$$ 64.5624 150.029i 0.218116 0.506856i
$$297$$ 0 0
$$298$$ −284.997 + 116.530i −0.956365 + 0.391040i
$$299$$ 370.451i 1.23897i
$$300$$ 0 0
$$301$$ −115.161 −0.382595
$$302$$ −140.317 343.172i −0.464625 1.13633i
$$303$$ 0 0
$$304$$ −83.1246 1.51622i −0.273436 0.00498756i
$$305$$ −19.8964 −0.0652341
$$306$$ 0 0
$$307$$ 96.6999i 0.314983i −0.987520 0.157492i $$-0.949659\pi$$
0.987520 0.157492i $$-0.0503407\pi$$
$$308$$ −304.232 + 298.733i −0.987767 + 0.969914i
$$309$$ 0 0
$$310$$ 36.6687 + 89.6805i 0.118286 + 0.289292i
$$311$$ 136.184i 0.437890i −0.975737 0.218945i $$-0.929739\pi$$
0.975737 0.218945i $$-0.0702615\pi$$
$$312$$ 0 0
$$313$$ 282.161 0.901473 0.450736 0.892657i $$-0.351161\pi$$
0.450736 + 0.892657i $$0.351161\pi$$
$$314$$ −363.145 + 148.483i −1.15651 + 0.472877i
$$315$$ 0 0
$$316$$ 115.018 + 117.135i 0.363982 + 0.370681i
$$317$$ −275.489 −0.869051 −0.434526 0.900659i $$-0.643084\pi$$
−0.434526 + 0.900659i $$0.643084\pi$$
$$318$$ 0 0
$$319$$ 76.5963i 0.240114i
$$320$$ 47.5360 + 50.2107i 0.148550 + 0.156909i
$$321$$ 0 0
$$322$$ 332.164 135.816i 1.03157 0.421788i
$$323$$ 137.067i 0.424356i
$$324$$ 0 0
$$325$$ −295.918 −0.910517
$$326$$ 97.8902 + 239.410i 0.300277 + 0.734385i
$$327$$ 0 0
$$328$$ 187.331 435.319i 0.571132 1.32719i
$$329$$ 246.950 0.750608
$$330$$ 0 0
$$331$$ 55.5221i 0.167741i −0.996477 0.0838703i $$-0.973272\pi$$
0.996477 0.0838703i $$-0.0267281\pi$$
$$332$$ 99.3474 + 101.176i 0.299239 + 0.304747i
$$333$$ 0 0
$$334$$ −104.420 255.378i −0.312633 0.764606i
$$335$$ 102.501i 0.305974i
$$336$$ 0 0
$$337$$ −430.659 −1.27792 −0.638961 0.769239i $$-0.720635\pi$$
−0.638961 + 0.769239i $$0.720635\pi$$
$$338$$ 27.4589 11.2275i 0.0812395 0.0332173i
$$339$$ 0 0
$$340$$ −81.3375 + 79.8674i −0.239228 + 0.234904i
$$341$$ 794.779 2.33073
$$342$$ 0 0
$$343$$ 371.857i 1.08413i
$$344$$ 140.716 + 60.5547i 0.409059 + 0.176031i
$$345$$ 0 0
$$346$$ −296.997 + 121.437i −0.858373 + 0.350973i
$$347$$ 135.871i 0.391559i −0.980648 0.195779i $$-0.937276\pi$$
0.980648 0.195779i $$-0.0627236\pi$$
$$348$$ 0 0
$$349$$ 288.082 0.825450 0.412725 0.910856i $$-0.364577\pi$$
0.412725 + 0.910856i $$0.364577\pi$$
$$350$$ −108.490 265.334i −0.309972 0.758097i
$$351$$ 0 0
$$352$$ 528.827 205.052i 1.50235 0.582535i
$$353$$ 198.964 0.563638 0.281819 0.959468i $$-0.409062\pi$$
0.281819 + 0.959468i $$0.409062\pi$$
$$354$$ 0 0
$$355$$ 90.6350i 0.255310i
$$356$$ 75.2872 73.9264i 0.211481 0.207659i
$$357$$ 0 0
$$358$$ 152.498 + 372.965i 0.425973 + 1.04180i
$$359$$ 324.658i 0.904339i −0.891932 0.452170i $$-0.850650\pi$$
0.891932 0.452170i $$-0.149350\pi$$
$$360$$ 0 0
$$361$$ 334.000 0.925208
$$362$$ 89.3261 36.5238i 0.246757 0.100895i
$$363$$ 0 0
$$364$$ −209.267 213.119i −0.574910 0.585493i
$$365$$ −60.3197 −0.165259
$$366$$ 0 0
$$367$$ 176.141i 0.479948i 0.970779 + 0.239974i $$0.0771390\pi$$
−0.970779 + 0.239974i $$0.922861\pi$$
$$368$$ −477.290 8.70592i −1.29699 0.0236574i
$$369$$ 0 0
$$370$$ −40.8328 + 16.6958i −0.110359 + 0.0451238i
$$371$$ 421.233i 1.13540i
$$372$$ 0 0
$$373$$ 596.580 1.59941 0.799706 0.600392i $$-0.204989\pi$$
0.799706 + 0.600392i $$0.204989\pi$$
$$374$$ 353.906 + 865.546i 0.946272 + 2.31429i
$$375$$ 0 0
$$376$$ −301.751 129.853i −0.802529 0.345353i
$$377$$ −53.6569 −0.142326
$$378$$ 0 0
$$379$$ 30.3082i 0.0799689i 0.999200 + 0.0399844i $$0.0127308\pi$$
−0.999200 + 0.0399844i $$0.987269\pi$$
$$380$$ 15.7326 + 16.0222i 0.0414015 + 0.0421636i
$$381$$ 0 0
$$382$$ −111.580 272.892i −0.292096 0.714377i
$$383$$ 707.220i 1.84653i −0.384167 0.923264i $$-0.625511\pi$$
0.384167 0.923264i $$-0.374489\pi$$
$$384$$ 0 0
$$385$$ 115.161 0.299119
$$386$$ −46.5845 + 19.0475i −0.120685 + 0.0493460i
$$387$$ 0 0
$$388$$ 217.857 213.920i 0.561488 0.551339i
$$389$$ 577.088 1.48352 0.741758 0.670668i $$-0.233992\pi$$
0.741758 + 0.670668i $$0.233992\pi$$
$$390$$ 0 0
$$391$$ 787.021i 2.01284i
$$392$$ −40.5809 + 94.3016i −0.103523 + 0.240565i
$$393$$ 0 0
$$394$$ 713.659 291.802i 1.81132 0.740615i
$$395$$ 44.3392i 0.112251i
$$396$$ 0 0
$$397$$ 26.8266 0.0675733 0.0337867 0.999429i $$-0.489243\pi$$
0.0337867 + 0.999429i $$0.489243\pi$$
$$398$$ 91.8809 + 224.713i 0.230857 + 0.564605i
$$399$$ 0 0
$$400$$ −6.95432 + 381.262i −0.0173858 + 0.953154i
$$401$$ −505.065 −1.25951 −0.629756 0.776793i $$-0.716845\pi$$
−0.629756 + 0.776793i $$0.716845\pi$$
$$402$$ 0 0
$$403$$ 556.755i 1.38153i
$$404$$ −206.077 + 202.352i −0.510091 + 0.500872i
$$405$$ 0 0
$$406$$ −19.6718 48.1113i −0.0484528 0.118501i
$$407$$ 361.874i 0.889126i
$$408$$ 0 0
$$409$$ −683.328 −1.67073 −0.835364 0.549696i $$-0.814743\pi$$
−0.835364 + 0.549696i $$0.814743\pi$$
$$410$$ −118.479 + 48.4438i −0.288972 + 0.118156i
$$411$$ 0 0
$$412$$ 162.477 + 165.468i 0.394362 + 0.401621i
$$413$$ 174.116 0.421588
$$414$$ 0 0
$$415$$ 38.2982i 0.0922847i
$$416$$ 143.642 + 370.451i 0.345294 + 0.890508i
$$417$$ 0 0
$$418$$ 170.498 69.7137i 0.407891 0.166779i
$$419$$ 306.620i 0.731791i −0.930656 0.365895i $$-0.880763\pi$$
0.930656 0.365895i $$-0.119237\pi$$
$$420$$ 0 0
$$421$$ −18.5867 −0.0441489 −0.0220745 0.999756i $$-0.507027\pi$$
−0.0220745 + 0.999756i $$0.507027\pi$$
$$422$$ −198.037 484.339i −0.469283 1.14772i
$$423$$ 0 0
$$424$$ −221.495 + 514.709i −0.522395 + 1.21394i
$$425$$ −628.676 −1.47924
$$426$$ 0 0
$$427$$ 110.755i 0.259379i
$$428$$ 180.486 + 183.808i 0.421697 + 0.429459i
$$429$$ 0 0
$$430$$ −15.6594 38.2982i −0.0364173 0.0890655i
$$431$$ 308.130i 0.714918i −0.933929 0.357459i $$-0.883643\pi$$
0.933929 0.357459i $$-0.116357\pi$$
$$432$$ 0 0
$$433$$ 174.839 0.403785 0.201893 0.979408i $$-0.435291\pi$$
0.201893 + 0.979408i $$0.435291\pi$$
$$434$$ −499.213 + 204.119i −1.15026 + 0.470320i
$$435$$ 0 0
$$436$$ −123.204 + 120.977i −0.282577 + 0.277470i
$$437$$ −155.030 −0.354761
$$438$$ 0 0
$$439$$ 480.159i 1.09376i −0.837212 0.546878i $$-0.815816\pi$$
0.837212 0.546878i $$-0.184184\pi$$
$$440$$ −140.716 60.5547i −0.319810 0.137624i
$$441$$ 0 0
$$442$$ −606.328 + 247.917i −1.37178 + 0.560897i
$$443$$ 555.962i 1.25499i 0.778619 + 0.627497i $$0.215920\pi$$
−0.778619 + 0.627497i $$0.784080\pi$$
$$444$$ 0 0
$$445$$ −28.4984 −0.0640415
$$446$$ −53.0264 129.686i −0.118893 0.290777i
$$447$$ 0 0
$$448$$ −279.502 + 264.612i −0.623887 + 0.590652i
$$449$$ 801.711 1.78555 0.892774 0.450504i $$-0.148756\pi$$
0.892774 + 0.450504i $$0.148756\pi$$
$$450$$ 0 0
$$451$$ 1050.00i 2.32816i
$$452$$ 232.028 227.835i 0.513337 0.504059i
$$453$$ 0 0
$$454$$ −225.836 552.326i −0.497436 1.21658i
$$455$$ 80.6720i 0.177301i
$$456$$ 0 0
$$457$$ −137.830 −0.301597 −0.150798 0.988565i $$-0.548184\pi$$
−0.150798 + 0.988565i $$0.548184\pi$$
$$458$$ −480.701 + 196.550i −1.04956 + 0.429148i
$$459$$ 0 0
$$460$$ 90.3344 + 91.9971i 0.196379 + 0.199994i
$$461$$ −188.341 −0.408549 −0.204274 0.978914i $$-0.565483\pi$$
−0.204274 + 0.978914i $$0.565483\pi$$
$$462$$ 0 0
$$463$$ 548.425i 1.18450i 0.805753 + 0.592251i $$0.201761\pi$$
−0.805753 + 0.592251i $$0.798239\pi$$
$$464$$ −1.26098 + 69.1317i −0.00271764 + 0.148991i
$$465$$ 0 0
$$466$$ 13.6656 5.58763i 0.0293254 0.0119906i
$$467$$ 618.597i 1.32462i 0.749231 + 0.662309i $$0.230423\pi$$
−0.749231 + 0.662309i $$0.769577\pi$$
$$468$$ 0 0
$$469$$ −570.580 −1.21659
$$470$$ 33.5799 + 82.1262i 0.0714466 + 0.174737i
$$471$$ 0 0
$$472$$ −212.754 91.5547i −0.450750 0.193972i
$$473$$ −339.411 −0.717571
$$474$$ 0 0
$$475$$ 123.839i 0.260714i
$$476$$ −444.587 452.771i −0.934007 0.951199i
$$477$$ 0 0
$$478$$ −62.1641 152.034i −0.130050 0.318064i
$$479$$ 770.425i 1.60840i −0.594357 0.804202i $$-0.702593\pi$$
0.594357 0.804202i $$-0.297407\pi$$
$$480$$ 0 0
$$481$$ −253.498 −0.527024
$$482$$ 769.791 314.753i 1.59708 0.653015i
$$483$$ 0 0
$$484$$ −551.310 + 541.346i −1.13907 + 1.11848i
$$485$$ −82.4655 −0.170032
$$486$$ 0 0
$$487$$ 549.208i 1.12774i −0.825865 0.563868i $$-0.809313\pi$$
0.825865 0.563868i $$-0.190687\pi$$
$$488$$ −58.2378 + 135.332i −0.119340 + 0.277321i
$$489$$ 0 0
$$490$$ 25.6656 10.4942i 0.0523788 0.0214168i
$$491$$ 23.0256i 0.0468952i 0.999725 + 0.0234476i $$0.00746429\pi$$
−0.999725 + 0.0234476i $$0.992536\pi$$
$$492$$ 0 0
$$493$$ −113.994 −0.231225
$$494$$ 48.8355 + 119.437i 0.0988573 + 0.241775i
$$495$$ 0 0
$$496$$ 717.325 + 13.0842i 1.44622 + 0.0263795i
$$497$$ 504.526 1.01514
$$498$$ 0 0
$$499$$ 626.809i 1.25613i 0.778160 + 0.628065i $$0.216153\pi$$
−0.778160 + 0.628065i $$0.783847\pi$$
$$500$$ 150.574 147.853i 0.301149 0.295706i
$$501$$ 0 0
$$502$$ −105.994 259.228i −0.211143 0.516391i
$$503$$ 732.896i 1.45705i 0.685019 + 0.728525i $$0.259794\pi$$
−0.685019 + 0.728525i $$0.740206\pi$$
$$504$$ 0 0
$$505$$ 78.0062 0.154468
$$506$$ 978.979 400.287i 1.93474 0.791081i
$$507$$ 0 0
$$508$$ 537.994 + 547.896i 1.05904 + 1.07854i
$$509$$ −437.363 −0.859259 −0.429630 0.903005i $$-0.641356\pi$$
−0.429630 + 0.903005i $$0.641356\pi$$
$$510$$ 0 0
$$511$$ 335.774i 0.657092i
$$512$$ 480.666 176.363i 0.938801 0.344459i
$$513$$ 0 0
$$514$$ −124.000 + 50.7013i −0.241245 + 0.0986407i
$$515$$ 62.6345i 0.121620i
$$516$$ 0 0
$$517$$ 727.830 1.40779
$$518$$ −92.9383 227.299i −0.179418 0.438801i
$$519$$ 0 0
$$520$$ 42.4195 98.5740i 0.0815760 0.189565i
$$521$$ 385.236 0.739417 0.369709 0.929148i $$-0.379458\pi$$
0.369709 + 0.929148i $$0.379458\pi$$
$$522$$ 0 0
$$523$$ 418.572i 0.800328i −0.916443 0.400164i $$-0.868953\pi$$
0.916443 0.400164i $$-0.131047\pi$$
$$524$$ −397.390 404.704i −0.758377 0.772336i
$$525$$ 0 0
$$526$$ 28.1703 + 68.8959i 0.0535557 + 0.130981i
$$527$$ 1182.82i 2.24445i
$$528$$ 0 0
$$529$$ −361.164 −0.682730
$$530$$ 140.086 57.2786i 0.264313 0.108073i
$$531$$ 0 0
$$532$$ −89.1885 + 87.5765i −0.167648 + 0.164617i
$$533$$ −735.540 −1.38000
$$534$$ 0 0
$$535$$ 69.5770i 0.130050i
$$536$$ 697.199 + 300.026i 1.30074 + 0.559751i
$$537$$ 0 0
$$538$$ 516.663 211.254i 0.960339 0.392665i
$$539$$ 227.457i 0.421999i
$$540$$ 0 0
$$541$$ −23.4257 −0.0433008 −0.0216504 0.999766i $$-0.506892\pi$$
−0.0216504 + 0.999766i $$0.506892\pi$$
$$542$$ −307.546 752.164i −0.567429 1.38776i
$$543$$ 0 0
$$544$$ 305.167 + 787.021i 0.560969 + 1.44673i
$$545$$ 46.6362 0.0855711
$$546$$ 0 0
$$547$$ 722.163i 1.32023i 0.751167 + 0.660113i $$0.229491\pi$$
−0.751167 + 0.660113i $$0.770509\pi$$
$$548$$ 250.529 246.001i 0.457170 0.448907i
$$549$$ 0 0
$$550$$ −319.751 782.013i −0.581365 1.42184i
$$551$$ 22.4549i 0.0407530i
$$552$$ 0 0
$$553$$ 246.817 0.446324
$$554$$ −8.94665 + 3.65812i −0.0161492 + 0.00660311i
$$555$$ 0 0
$$556$$ −514.264 523.730i −0.924936 0.941961i
$$557$$ 2.34135 0.00420349 0.00210175 0.999998i $$-0.499331\pi$$
0.00210175 + 0.999998i $$0.499331\pi$$
$$558$$ 0 0
$$559$$ 237.763i 0.425336i
$$560$$ 103.938 + 1.89586i 0.185604 + 0.00338547i
$$561$$ 0 0
$$562$$ 8.00000 3.27105i 0.0142349 0.00582038i
$$563$$ 359.794i 0.639066i −0.947575 0.319533i $$-0.896474\pi$$
0.947575 0.319533i $$-0.103526\pi$$
$$564$$ 0 0
$$565$$ −87.8297 −0.155451
$$566$$ 33.5799 + 82.1262i 0.0593284 + 0.145099i
$$567$$ 0 0
$$568$$ −616.486 265.293i −1.08536 0.467066i
$$569$$ −18.6354 −0.0327512 −0.0163756 0.999866i $$-0.505213\pi$$
−0.0163756 + 0.999866i $$0.505213\pi$$
$$570$$ 0 0
$$571$$ 284.528i 0.498298i −0.968465 0.249149i $$-0.919849\pi$$
0.968465 0.249149i $$-0.0801509\pi$$
$$572$$ −616.769 628.122i −1.07827 1.09811i
$$573$$ 0 0
$$574$$ −269.666 659.520i −0.469801 1.14899i
$$575$$ 711.067i 1.23664i
$$576$$ 0 0
$$577$$ 664.823 1.15221 0.576104 0.817377i $$-0.304572\pi$$
0.576104 + 0.817377i $$0.304572\pi$$
$$578$$ −753.135 + 307.943i −1.30300 + 0.532774i
$$579$$ 0 0
$$580$$ 13.3251 13.0842i 0.0229742 0.0225590i
$$581$$ 213.189 0.366935
$$582$$ 0 0
$$583$$ 1241.49i 2.12948i
$$584$$ −176.559 + 410.286i −0.302327 + 0.702544i
$$585$$ 0 0
$$586$$ 719.994 294.392i 1.22866 0.502376i
$$587$$ 754.467i 1.28529i 0.766162 + 0.642647i $$0.222164\pi$$
−0.766162 + 0.642647i $$0.777836\pi$$
$$588$$ 0 0
$$589$$ 232.997 0.395580
$$590$$ 23.6760 + 57.9043i 0.0401288 + 0.0981428i
$$591$$ 0 0
$$592$$ −5.95743 + 326.608i −0.0100632 + 0.551703i
$$593$$ −550.801 −0.928838 −0.464419 0.885615i $$-0.653737\pi$$
−0.464419 + 0.885615i $$0.653737\pi$$
$$594$$ 0 0
$$595$$ 171.387i 0.288046i
$$596$$ 439.389 431.448i 0.737230 0.723905i
$$597$$ 0 0
$$598$$ 280.407 + 685.790i 0.468908 + 1.14681i
$$599$$ 25.9888i 0.0433871i 0.999765 + 0.0216935i $$0.00690581\pi$$
−0.999765 + 0.0216935i $$0.993094\pi$$
$$600$$ 0 0
$$601$$ 186.170 0.309768 0.154884 0.987933i $$-0.450500\pi$$
0.154884 + 0.987933i $$0.450500\pi$$
$$602$$ 213.189 87.1693i 0.354135 0.144799i
$$603$$ 0 0
$$604$$ 519.517 + 529.079i 0.860127 + 0.875959i
$$605$$ 208.687 0.344938
$$606$$ 0 0
$$607$$ 99.5447i 0.163994i 0.996633 + 0.0819972i $$0.0261299\pi$$
−0.996633 + 0.0819972i $$0.973870\pi$$
$$608$$ 155.030 60.1130i 0.254984 0.0988700i
$$609$$ 0 0
$$610$$ 36.8328 15.0603i 0.0603817 0.0246890i
$$611$$ 509.856i 0.834461i
$$612$$ 0 0
$$613$$ −960.234 −1.56645 −0.783225 0.621739i $$-0.786427\pi$$
−0.783225 + 0.621739i $$0.786427\pi$$
$$614$$ 73.1954 + 179.014i 0.119211 + 0.291553i
$$615$$ 0 0
$$616$$ 337.082 783.308i 0.547211 1.27160i
$$617$$ −354.625 −0.574757 −0.287378 0.957817i $$-0.592784\pi$$
−0.287378 + 0.957817i $$0.592784\pi$$
$$618$$ 0 0
$$619$$ 360.647i 0.582629i −0.956627 0.291314i $$-0.905907\pi$$
0.956627 0.291314i $$-0.0940926\pi$$
$$620$$ −135.765 138.263i −0.218975 0.223006i
$$621$$ 0 0
$$622$$ 103.082 + 252.107i 0.165727 + 0.405317i
$$623$$ 158.639i 0.254637i
$$624$$ 0 0
$$625$$ 538.823 0.862118
$$626$$ −522.345 + 213.577i −0.834417 + 0.341178i
$$627$$ 0 0
$$628$$ 559.872 549.753i 0.891516 0.875403i
$$629$$ −538.556 −0.856210
$$630$$ 0 0
$$631$$ 82.7121i 0.131081i −0.997850 0.0655405i $$-0.979123\pi$$
0.997850 0.0655405i $$-0.0208772\pi$$
$$632$$ −301.589 129.783i −0.477197 0.205353i
$$633$$ 0 0
$$634$$ 509.994 208.527i 0.804407 0.328907i
$$635$$ 207.395i 0.326607i
$$636$$ 0 0
$$637$$ 159.337 0.250137
$$638$$ −57.9784 141.797i −0.0908752 0.222253i
$$639$$ 0 0
$$640$$ −126.006 56.9700i −0.196885 0.0890156i
$$641$$ −760.569 −1.18653 −0.593267 0.805005i $$-0.702162\pi$$
−0.593267 + 0.805005i $$0.702162\pi$$
$$642$$ 0 0
$$643$$ 787.021i 1.22398i 0.790864 + 0.611992i $$0.209631\pi$$
−0.790864 + 0.611992i $$0.790369\pi$$
$$644$$ −512.108 + 502.853i −0.795199 + 0.780827i
$$645$$ 0 0
$$646$$ 103.751 + 253.743i 0.160605 + 0.392791i
$$647$$ 978.962i 1.51308i −0.653948 0.756539i $$-0.726889\pi$$
0.653948 0.756539i $$-0.273111\pi$$
$$648$$ 0 0
$$649$$ 513.167 0.790704
$$650$$ 547.812 223.990i 0.842788 0.344601i
$$651$$ 0 0
$$652$$ −362.435 369.106i −0.555881 0.566113i
$$653$$ 939.548 1.43882 0.719409 0.694587i $$-0.244413\pi$$
0.719409 + 0.694587i $$0.244413\pi$$
$$654$$ 0 0
$$655$$ 153.193i 0.233882i
$$656$$ −17.2858 + 947.672i −0.0263503 + 1.44462i
$$657$$ 0 0
$$658$$ −457.161 + 186.925i −0.694774 + 0.284080i
$$659$$ 149.491i 0.226845i −0.993547 0.113423i $$-0.963819\pi$$
0.993547 0.113423i $$-0.0361814\pi$$
$$660$$ 0 0
$$661$$ 337.420 0.510468 0.255234 0.966879i $$-0.417847\pi$$
0.255234 + 0.966879i $$0.417847\pi$$
$$662$$ 42.0266 + 102.784i 0.0634843 + 0.155263i
$$663$$ 0 0
$$664$$ −260.498 112.101i −0.392317 0.168826i
$$665$$ 33.7605 0.0507677
$$666$$ 0 0
$$667$$ 128.933i 0.193303i
$$668$$ 386.609 + 393.725i 0.578756 + 0.589409i
$$669$$ 0 0
$$670$$ −77.5867 189.753i −0.115801 0.283214i
$$671$$ 326.425i 0.486475i
$$672$$ 0 0
$$673$$ −321.341 −0.477475 −0.238737 0.971084i $$-0.576734\pi$$
−0.238737 + 0.971084i $$0.576734\pi$$
$$674$$ 797.249 325.981i 1.18286 0.483651i
$$675$$ 0 0
$$676$$ −42.3344 + 41.5692i −0.0626248 + 0.0614929i
$$677$$ 741.841 1.09578 0.547889 0.836551i $$-0.315432\pi$$
0.547889 + 0.836551i $$0.315432\pi$$
$$678$$ 0 0
$$679$$ 459.050i 0.676067i
$$680$$ 90.1200 209.420i 0.132529 0.307971i
$$681$$ 0 0
$$682$$ −1471.32 + 601.595i −2.15736 + 0.882105i
$$683$$ 1259.02i 1.84337i −0.387938 0.921686i $$-0.626812\pi$$
0.387938 0.921686i $$-0.373188\pi$$
$$684$$ 0 0
$$685$$ −94.8328 −0.138442
$$686$$ 281.471 + 688.393i 0.410308 + 1.00349i
$$687$$ 0 0
$$688$$ −306.334 5.58763i −0.445253 0.00812155i
$$689$$ 869.682 1.26224
$$690$$ 0 0
$$691$$ 222.770i 0.322387i 0.986923 + 0.161194i $$0.0515344\pi$$
−0.986923 + 0.161194i $$0.948466\pi$$
$$692$$ 457.890 449.614i 0.661691 0.649731i
$$693$$ 0 0
$$694$$ 102.845 + 251.528i 0.148192 + 0.362432i
$$695$$ 198.248i 0.285248i
$$696$$ 0 0
$$697$$ −1562.65 −2.24197
$$698$$ −533.306 + 218.059i −0.764049 + 0.312406i
$$699$$ 0 0
$$700$$ 401.681 + 409.074i 0.573830 + 0.584392i
$$701$$ 2.34135 0.00334001 0.00167000 0.999999i $$-0.499468\pi$$
0.00167000 + 0.999999i $$0.499468\pi$$
$$702$$ 0 0
$$703$$ 106.087i 0.150906i
$$704$$ −823.768 + 779.886i −1.17013 + 1.10779i
$$705$$ 0 0
$$706$$ −368.328 + 150.603i −0.521711 + 0.213318i
$$707$$ 434.227i 0.614182i
$$708$$ 0 0
$$709$$ −495.085 −0.698287 −0.349143 0.937069i $$-0.613527\pi$$
−0.349143 + 0.937069i $$0.613527\pi$$
$$710$$ 68.6047 + 167.786i 0.0966264 + 0.236319i
$$711$$ 0 0
$$712$$ −83.4164 + 193.842i −0.117158 + 0.272250i
$$713$$ 1337.84 1.87635
$$714$$ 0 0
$$715$$ 237.763i 0.332535i
$$716$$ −564.619 575.012i −0.788574 0.803089i
$$717$$ 0 0
$$718$$ 245.745 + 601.016i 0.342263 + 0.837070i
$$719$$ 962.433i 1.33857i −0.743005 0.669286i $$-0.766600\pi$$
0.743005 0.669286i $$-0.233400\pi$$
$$720$$ 0 0
$$721$$ 348.659 0.483578
$$722$$ −618.311 + 252.816i −0.856386 + 0.350161i
$$723$$ 0 0
$$724$$ −137.717 + 135.228i −0.190217 + 0.186779i
$$725$$ 102.992 0.142058
$$726$$ 0 0
$$727$$ 544.625i 0.749141i 0.927198 + 0.374570i $$0.122210\pi$$
−0.927198 + 0.374570i $$0.877790\pi$$
$$728$$ 548.719 + 236.131i 0.753735 + 0.324356i
$$729$$ 0 0
$$730$$ 111.666 45.6580i 0.152967 0.0625453i
$$731$$ 505.126i 0.691006i
$$732$$ 0 0
$$733$$ −146.170 −0.199414 −0.0997069 0.995017i $$-0.531791\pi$$
−0.0997069 + 0.995017i $$0.531791\pi$$
$$734$$ −133.327 326.077i −0.181645 0.444247i
$$735$$ 0 0
$$736$$ 890.164 345.161i 1.20946 0.468968i
$$737$$ −1681.66 −2.28176
$$738$$ 0 0
$$739$$ 1172.87i 1.58710i 0.608505 + 0.793550i $$0.291769\pi$$
−0.608505 + 0.793550i $$0.708231\pi$$
$$740$$ 62.9533 61.8155i 0.0850720 0.0835344i
$$741$$ 0 0
$$742$$ 318.845 + 779.798i 0.429711 + 1.05094i
$$743$$ 494.837i 0.665998i −0.942927 0.332999i $$-0.891939\pi$$
0.942927 0.332999i $$-0.108061\pi$$
$$744$$ 0 0
$$745$$ −166.322 −0.223251
$$746$$ −1104.41 + 451.572i −1.48044 + 0.605324i
$$747$$ 0 0
$$748$$ −1310.32 1334.44i −1.75177 1.78401i
$$749$$ 387.305 0.517096
$$750$$ 0 0
$$751$$ 927.250i 1.23469i −0.786693 0.617344i $$-0.788209\pi$$
0.786693 0.617344i $$-0.211791\pi$$
$$752$$ 656.900 + 11.9820i 0.873537 + 0.0159336i
$$753$$ 0 0
$$754$$ 99.3313 40.6147i 0.131739 0.0538657i
$$755$$ 200.272i 0.265261i
$$756$$ 0 0
$$757$$ −757.748 −1.00099 −0.500494 0.865740i $$-0.666848\pi$$
−0.500494 + 0.865740i $$0.666848\pi$$
$$758$$ −22.9413 56.1074i −0.0302656 0.0740204i
$$759$$ 0 0
$$760$$ −41.2523 17.7522i −0.0542794 0.0233581i
$$761$$ 953.139 1.25248 0.626241 0.779629i $$-0.284592\pi$$
0.626241 + 0.779629i $$0.284592\pi$$
$$762$$ 0 0
$$763$$ 259.604i 0.340241i
$$764$$ 413.122 + 420.726i 0.540736 + 0.550689i
$$765$$ 0 0
$$766$$ 535.319 + 1309.23i 0.698850 + 1.70917i
$$767$$ 359.482i 0.468685i
$$768$$ 0 0
$$769$$ 145.675 0.189434 0.0947171 0.995504i $$-0.469805\pi$$
0.0947171 + 0.995504i $$0.469805\pi$$
$$770$$ −213.189 + 87.1693i −0.276869 + 0.113207i
$$771$$ 0 0
$$772$$ 71.8208 70.5228i 0.0930322 0.0913507i
$$773$$ 60.1391 0.0777996 0.0388998 0.999243i $$-0.487615\pi$$
0.0388998 + 0.999243i $$0.487615\pi$$
$$774$$ 0 0
$$775$$ 1068.67i 1.37893i
$$776$$ −241.381 + 560.918i −0.311058 + 0.722832i
$$777$$ 0 0
$$778$$ −1068.32 + 436.817i −1.37316 + 0.561462i
$$779$$ 307.817i 0.395143i
$$780$$ 0 0
$$781$$ 1486.98 1.90394
$$782$$ 595.723 + 1456.96i 0.761794 + 1.86312i
$$783$$ 0 0
$$784$$ 3.74457 205.291i 0.00477623 0.261851i
$$785$$ −211.928 −0.269973
$$786$$ 0 0
$$787$$ 328.312i 0.417169i 0.978004 + 0.208585i $$0.0668856\pi$$
−0.978004 + 0.208585i $$0.933114\pi$$
$$788$$ −1100.27 + 1080.39i −1.39628 + 1.37105i
$$789$$ 0 0
$$790$$ 33.5619 + 82.0821i 0.0424834 + 0.103901i
$$791$$ 488.910i 0.618091i
$$792$$ 0 0
$$793$$ 228.666 0.288355
$$794$$ −49.6622 + 20.3060i −0.0625469 +