# Properties

 Label 363.3.b.m.122.2 Level $363$ Weight $3$ Character 363.122 Analytic conductor $9.891$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$363 = 3 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 363.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.89103359628$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ Defining polynomial: $$x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331$$ x^8 + 29*x^6 + 282*x^4 + 1061*x^2 + 1331 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 33) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 122.2 Root $$-3.06025i$$ of defining polynomial Character $$\chi$$ $$=$$ 363.122 Dual form 363.3.b.m.122.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.06025i q^{2} +(0.126437 - 2.99733i) q^{3} -5.36516 q^{4} -6.63932i q^{5} +(-9.17261 - 0.386930i) q^{6} -3.06298 q^{7} +4.17774i q^{8} +(-8.96803 - 0.757950i) q^{9} +O(q^{10})$$ $$q-3.06025i q^{2} +(0.126437 - 2.99733i) q^{3} -5.36516 q^{4} -6.63932i q^{5} +(-9.17261 - 0.386930i) q^{6} -3.06298 q^{7} +4.17774i q^{8} +(-8.96803 - 0.757950i) q^{9} -20.3180 q^{10} +(-0.678356 + 16.0812i) q^{12} +16.2447 q^{13} +9.37349i q^{14} +(-19.9003 - 0.839458i) q^{15} -8.67570 q^{16} +0.805648i q^{17} +(-2.31952 + 27.4444i) q^{18} +20.7018 q^{19} +35.6210i q^{20} +(-0.387274 + 9.18076i) q^{21} -27.3224i q^{23} +(12.5221 + 0.528222i) q^{24} -19.0806 q^{25} -49.7128i q^{26} +(-3.40572 + 26.7843i) q^{27} +16.4334 q^{28} +3.78268i q^{29} +(-2.56896 + 60.8999i) q^{30} -20.7800 q^{31} +43.2608i q^{32} +2.46549 q^{34} +20.3361i q^{35} +(48.1149 + 4.06652i) q^{36} +38.5536 q^{37} -63.3527i q^{38} +(2.05393 - 48.6907i) q^{39} +27.7373 q^{40} +13.3726i q^{41} +(28.0955 + 1.18516i) q^{42} +43.4125 q^{43} +(-5.03227 + 59.5416i) q^{45} -83.6135 q^{46} -19.8903i q^{47} +(-1.09693 + 26.0040i) q^{48} -39.6182 q^{49} +58.3915i q^{50} +(2.41480 + 0.101864i) q^{51} -87.1552 q^{52} +17.6754i q^{53} +(81.9669 + 10.4224i) q^{54} -12.7963i q^{56} +(2.61748 - 62.0502i) q^{57} +11.5760 q^{58} -43.5255i q^{59} +(106.768 + 4.50383i) q^{60} +10.6547 q^{61} +63.5921i q^{62} +(27.4689 + 2.32158i) q^{63} +97.6863 q^{64} -107.854i q^{65} +72.2963 q^{67} -4.32243i q^{68} +(-81.8944 - 3.45457i) q^{69} +62.2336 q^{70} -2.56990i q^{71} +(3.16651 - 37.4660i) q^{72} -45.4788 q^{73} -117.984i q^{74} +(-2.41250 + 57.1910i) q^{75} -111.068 q^{76} +(-149.006 - 6.28555i) q^{78} -98.2423 q^{79} +57.6008i q^{80} +(79.8510 + 13.5946i) q^{81} +40.9237 q^{82} +31.9006i q^{83} +(2.07779 - 49.2563i) q^{84} +5.34895 q^{85} -132.853i q^{86} +(11.3380 + 0.478272i) q^{87} -18.5409i q^{89} +(182.213 + 15.4000i) q^{90} -49.7570 q^{91} +146.589i q^{92} +(-2.62737 + 62.2846i) q^{93} -60.8693 q^{94} -137.446i q^{95} +(129.667 + 5.46978i) q^{96} -63.3019 q^{97} +121.242i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 5 q^{3} - 26 q^{4} + q^{6} + 28 q^{7} + 11 q^{9}+O(q^{10})$$ 8 * q + 5 * q^3 - 26 * q^4 + q^6 + 28 * q^7 + 11 * q^9 $$8 q + 5 q^{3} - 26 q^{4} + q^{6} + 28 q^{7} + 11 q^{9} - 6 q^{10} + 53 q^{12} + 44 q^{13} - 54 q^{15} - 14 q^{16} + q^{18} + 68 q^{19} - 6 q^{21} + 33 q^{24} + 42 q^{25} - 25 q^{27} - 118 q^{28} + 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} + 38 q^{39} + 58 q^{40} + 174 q^{42} - 78 q^{43} - 36 q^{45} - 286 q^{46} - 285 q^{48} - 140 q^{49} + 58 q^{51} - 102 q^{52} + 523 q^{54} - 22 q^{57} - 68 q^{58} + 262 q^{60} + 22 q^{61} + 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} + 489 q^{72} - 378 q^{73} - 33 q^{75} - 450 q^{76} - 246 q^{78} - 252 q^{79} + 11 q^{81} - 200 q^{82} + 450 q^{84} - 156 q^{85} + 66 q^{87} + 598 q^{90} - 148 q^{91} + 380 q^{93} - 460 q^{94} + 399 q^{96} - 324 q^{97}+O(q^{100})$$ 8 * q + 5 * q^3 - 26 * q^4 + q^6 + 28 * q^7 + 11 * q^9 - 6 * q^10 + 53 * q^12 + 44 * q^13 - 54 * q^15 - 14 * q^16 + q^18 + 68 * q^19 - 6 * q^21 + 33 * q^24 + 42 * q^25 - 25 * q^27 - 118 * q^28 + 10 * q^30 + 2 * q^31 - 66 * q^34 - 7 * q^36 + 140 * q^37 + 38 * q^39 + 58 * q^40 + 174 * q^42 - 78 * q^43 - 36 * q^45 - 286 * q^46 - 285 * q^48 - 140 * q^49 + 58 * q^51 - 102 * q^52 + 523 * q^54 - 22 * q^57 - 68 * q^58 + 262 * q^60 + 22 * q^61 + 246 * q^63 - 52 * q^64 + 184 * q^67 - 176 * q^69 + 374 * q^70 + 489 * q^72 - 378 * q^73 - 33 * q^75 - 450 * q^76 - 246 * q^78 - 252 * q^79 + 11 * q^81 - 200 * q^82 + 450 * q^84 - 156 * q^85 + 66 * q^87 + 598 * q^90 - 148 * q^91 + 380 * q^93 - 460 * q^94 + 399 * q^96 - 324 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$$.

 $$n$$ $$122$$ $$244$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 3.06025i 1.53013i −0.643955 0.765064i $$-0.722707\pi$$
0.643955 0.765064i $$-0.277293\pi$$
$$3$$ 0.126437 2.99733i 0.0421458 0.999111i
$$4$$ −5.36516 −1.34129
$$5$$ 6.63932i 1.32786i −0.747793 0.663932i $$-0.768886\pi$$
0.747793 0.663932i $$-0.231114\pi$$
$$6$$ −9.17261 0.386930i −1.52877 0.0644884i
$$7$$ −3.06298 −0.437568 −0.218784 0.975773i $$-0.570209\pi$$
−0.218784 + 0.975773i $$0.570209\pi$$
$$8$$ 4.17774i 0.522217i
$$9$$ −8.96803 0.757950i −0.996447 0.0842166i
$$10$$ −20.3180 −2.03180
$$11$$ 0 0
$$12$$ −0.678356 + 16.0812i −0.0565297 + 1.34010i
$$13$$ 16.2447 1.24959 0.624795 0.780789i $$-0.285183\pi$$
0.624795 + 0.780789i $$0.285183\pi$$
$$14$$ 9.37349i 0.669535i
$$15$$ −19.9003 0.839458i −1.32668 0.0559639i
$$16$$ −8.67570 −0.542231
$$17$$ 0.805648i 0.0473910i 0.999719 + 0.0236955i $$0.00754322\pi$$
−0.999719 + 0.0236955i $$0.992457\pi$$
$$18$$ −2.31952 + 27.4444i −0.128862 + 1.52469i
$$19$$ 20.7018 1.08957 0.544784 0.838577i $$-0.316612\pi$$
0.544784 + 0.838577i $$0.316612\pi$$
$$20$$ 35.6210i 1.78105i
$$21$$ −0.387274 + 9.18076i −0.0184416 + 0.437179i
$$22$$ 0 0
$$23$$ 27.3224i 1.18793i −0.804491 0.593965i $$-0.797562\pi$$
0.804491 0.593965i $$-0.202438\pi$$
$$24$$ 12.5221 + 0.528222i 0.521753 + 0.0220092i
$$25$$ −19.0806 −0.763224
$$26$$ 49.7128i 1.91203i
$$27$$ −3.40572 + 26.7843i −0.126138 + 0.992013i
$$28$$ 16.4334 0.586906
$$29$$ 3.78268i 0.130437i 0.997871 + 0.0652187i $$0.0207745\pi$$
−0.997871 + 0.0652187i $$0.979226\pi$$
$$30$$ −2.56896 + 60.8999i −0.0856318 + 2.03000i
$$31$$ −20.7800 −0.670323 −0.335161 0.942161i $$-0.608791\pi$$
−0.335161 + 0.942161i $$0.608791\pi$$
$$32$$ 43.2608i 1.35190i
$$33$$ 0 0
$$34$$ 2.46549 0.0725143
$$35$$ 20.3361i 0.581031i
$$36$$ 48.1149 + 4.06652i 1.33652 + 0.112959i
$$37$$ 38.5536 1.04199 0.520995 0.853560i $$-0.325561\pi$$
0.520995 + 0.853560i $$0.325561\pi$$
$$38$$ 63.3527i 1.66718i
$$39$$ 2.05393 48.6907i 0.0526649 1.24848i
$$40$$ 27.7373 0.693433
$$41$$ 13.3726i 0.326162i 0.986613 + 0.163081i $$0.0521432\pi$$
−0.986613 + 0.163081i $$0.947857\pi$$
$$42$$ 28.0955 + 1.18516i 0.668940 + 0.0282181i
$$43$$ 43.4125 1.00959 0.504797 0.863238i $$-0.331567\pi$$
0.504797 + 0.863238i $$0.331567\pi$$
$$44$$ 0 0
$$45$$ −5.03227 + 59.5416i −0.111828 + 1.32315i
$$46$$ −83.6135 −1.81768
$$47$$ 19.8903i 0.423198i −0.977357 0.211599i $$-0.932133\pi$$
0.977357 0.211599i $$-0.0678670\pi$$
$$48$$ −1.09693 + 26.0040i −0.0228528 + 0.541750i
$$49$$ −39.6182 −0.808534
$$50$$ 58.3915i 1.16783i
$$51$$ 2.41480 + 0.101864i 0.0473489 + 0.00199733i
$$52$$ −87.1552 −1.67606
$$53$$ 17.6754i 0.333499i 0.985999 + 0.166750i $$0.0533271\pi$$
−0.985999 + 0.166750i $$0.946673\pi$$
$$54$$ 81.9669 + 10.4224i 1.51791 + 0.193007i
$$55$$ 0 0
$$56$$ 12.7963i 0.228505i
$$57$$ 2.61748 62.0502i 0.0459207 1.08860i
$$58$$ 11.5760 0.199586
$$59$$ 43.5255i 0.737721i −0.929485 0.368860i $$-0.879748\pi$$
0.929485 0.368860i $$-0.120252\pi$$
$$60$$ 106.768 + 4.50383i 1.77947 + 0.0750638i
$$61$$ 10.6547 0.174668 0.0873339 0.996179i $$-0.472165\pi$$
0.0873339 + 0.996179i $$0.472165\pi$$
$$62$$ 63.5921i 1.02568i
$$63$$ 27.4689 + 2.32158i 0.436014 + 0.0368505i
$$64$$ 97.6863 1.52635
$$65$$ 107.854i 1.65929i
$$66$$ 0 0
$$67$$ 72.2963 1.07905 0.539525 0.841970i $$-0.318604\pi$$
0.539525 + 0.841970i $$0.318604\pi$$
$$68$$ 4.32243i 0.0635651i
$$69$$ −81.8944 3.45457i −1.18687 0.0500662i
$$70$$ 62.2336 0.889052
$$71$$ 2.56990i 0.0361957i −0.999836 0.0180979i $$-0.994239\pi$$
0.999836 0.0180979i $$-0.00576105\pi$$
$$72$$ 3.16651 37.4660i 0.0439793 0.520362i
$$73$$ −45.4788 −0.622997 −0.311499 0.950247i $$-0.600831\pi$$
−0.311499 + 0.950247i $$0.600831\pi$$
$$74$$ 117.984i 1.59438i
$$75$$ −2.41250 + 57.1910i −0.0321667 + 0.762546i
$$76$$ −111.068 −1.46143
$$77$$ 0 0
$$78$$ −149.006 6.28555i −1.91033 0.0805840i
$$79$$ −98.2423 −1.24357 −0.621786 0.783187i $$-0.713593\pi$$
−0.621786 + 0.783187i $$0.713593\pi$$
$$80$$ 57.6008i 0.720010i
$$81$$ 79.8510 + 13.5946i 0.985815 + 0.167835i
$$82$$ 40.9237 0.499069
$$83$$ 31.9006i 0.384345i 0.981361 + 0.192172i $$0.0615533\pi$$
−0.981361 + 0.192172i $$0.938447\pi$$
$$84$$ 2.07779 49.2563i 0.0247356 0.586384i
$$85$$ 5.34895 0.0629289
$$86$$ 132.853i 1.54481i
$$87$$ 11.3380 + 0.478272i 0.130321 + 0.00549738i
$$88$$ 0 0
$$89$$ 18.5409i 0.208325i −0.994560 0.104162i $$-0.966784\pi$$
0.994560 0.104162i $$-0.0332161\pi$$
$$90$$ 182.213 + 15.4000i 2.02458 + 0.171112i
$$91$$ −49.7570 −0.546780
$$92$$ 146.589i 1.59336i
$$93$$ −2.62737 + 62.2846i −0.0282513 + 0.669727i
$$94$$ −60.8693 −0.647546
$$95$$ 137.446i 1.44680i
$$96$$ 129.667 + 5.46978i 1.35070 + 0.0569769i
$$97$$ −63.3019 −0.652597 −0.326298 0.945267i $$-0.605801\pi$$
−0.326298 + 0.945267i $$0.605801\pi$$
$$98$$ 121.242i 1.23716i
$$99$$ 0 0
$$100$$ 102.371 1.02371
$$101$$ 150.359i 1.48870i 0.667790 + 0.744350i $$0.267241\pi$$
−0.667790 + 0.744350i $$0.732759\pi$$
$$102$$ 0.311729 7.38989i 0.00305617 0.0724499i
$$103$$ −149.767 −1.45405 −0.727026 0.686610i $$-0.759098\pi$$
−0.727026 + 0.686610i $$0.759098\pi$$
$$104$$ 67.8659i 0.652557i
$$105$$ 60.9541 + 2.57124i 0.580515 + 0.0244880i
$$106$$ 54.0914 0.510296
$$107$$ 20.7515i 0.193939i 0.995287 + 0.0969696i $$0.0309150\pi$$
−0.995287 + 0.0969696i $$0.969085\pi$$
$$108$$ 18.2722 143.702i 0.169187 1.33058i
$$109$$ −105.794 −0.970583 −0.485291 0.874352i $$-0.661286\pi$$
−0.485291 + 0.874352i $$0.661286\pi$$
$$110$$ 0 0
$$111$$ 4.87462 115.558i 0.0439155 1.04106i
$$112$$ 26.5735 0.237263
$$113$$ 132.769i 1.17495i −0.809244 0.587473i $$-0.800123\pi$$
0.809244 0.587473i $$-0.199877\pi$$
$$114$$ −189.889 8.01015i −1.66570 0.0702644i
$$115$$ −181.402 −1.57741
$$116$$ 20.2947i 0.174954i
$$117$$ −145.683 12.3126i −1.24515 0.105236i
$$118$$ −133.199 −1.12881
$$119$$ 2.46768i 0.0207368i
$$120$$ 3.50703 83.1381i 0.0292253 0.692817i
$$121$$ 0 0
$$122$$ 32.6062i 0.267264i
$$123$$ 40.0823 + 1.69080i 0.325872 + 0.0137463i
$$124$$ 111.488 0.899097
$$125$$ 39.3007i 0.314406i
$$126$$ 7.10463 84.0617i 0.0563860 0.667156i
$$127$$ −146.655 −1.15477 −0.577384 0.816473i $$-0.695926\pi$$
−0.577384 + 0.816473i $$0.695926\pi$$
$$128$$ 125.902i 0.983607i
$$129$$ 5.48896 130.122i 0.0425501 1.00870i
$$130$$ −330.059 −2.53892
$$131$$ 149.467i 1.14097i −0.821309 0.570484i $$-0.806756\pi$$
0.821309 0.570484i $$-0.193244\pi$$
$$132$$ 0 0
$$133$$ −63.4091 −0.476760
$$134$$ 221.245i 1.65108i
$$135$$ 177.830 + 22.6117i 1.31726 + 0.167494i
$$136$$ −3.36578 −0.0247484
$$137$$ 152.207i 1.11100i 0.831517 + 0.555500i $$0.187473\pi$$
−0.831517 + 0.555500i $$0.812527\pi$$
$$138$$ −10.5719 + 250.618i −0.0766077 + 1.81607i
$$139$$ 111.836 0.804573 0.402286 0.915514i $$-0.368216\pi$$
0.402286 + 0.915514i $$0.368216\pi$$
$$140$$ 109.106i 0.779331i
$$141$$ −59.6178 2.51487i −0.422822 0.0178360i
$$142$$ −7.86454 −0.0553841
$$143$$ 0 0
$$144$$ 77.8039 + 6.57574i 0.540305 + 0.0456649i
$$145$$ 25.1145 0.173203
$$146$$ 139.177i 0.953265i
$$147$$ −5.00921 + 118.749i −0.0340763 + 0.807816i
$$148$$ −206.846 −1.39761
$$149$$ 259.695i 1.74292i −0.490465 0.871461i $$-0.663173\pi$$
0.490465 0.871461i $$-0.336827\pi$$
$$150$$ 175.019 + 7.38287i 1.16679 + 0.0492191i
$$151$$ 88.0177 0.582899 0.291449 0.956586i $$-0.405863\pi$$
0.291449 + 0.956586i $$0.405863\pi$$
$$152$$ 86.4866i 0.568991i
$$153$$ 0.610640 7.22507i 0.00399111 0.0472227i
$$154$$ 0 0
$$155$$ 137.965i 0.890098i
$$156$$ −11.0197 + 261.233i −0.0706389 + 1.67457i
$$157$$ −7.65530 −0.0487598 −0.0243799 0.999703i $$-0.507761\pi$$
−0.0243799 + 0.999703i $$0.507761\pi$$
$$158$$ 300.646i 1.90282i
$$159$$ 52.9792 + 2.23484i 0.333203 + 0.0140556i
$$160$$ 287.222 1.79514
$$161$$ 83.6879i 0.519800i
$$162$$ 41.6030 244.364i 0.256809 1.50842i
$$163$$ 262.547 1.61072 0.805359 0.592788i $$-0.201973\pi$$
0.805359 + 0.592788i $$0.201973\pi$$
$$164$$ 71.7464i 0.437478i
$$165$$ 0 0
$$166$$ 97.6240 0.588096
$$167$$ 160.006i 0.958122i −0.877782 0.479061i $$-0.840977\pi$$
0.877782 0.479061i $$-0.159023\pi$$
$$168$$ −38.3548 1.61793i −0.228302 0.00963054i
$$169$$ 94.8889 0.561473
$$170$$ 16.3692i 0.0962892i
$$171$$ −185.654 15.6909i −1.08570 0.0917597i
$$172$$ −232.915 −1.35416
$$173$$ 165.524i 0.956785i 0.878146 + 0.478392i $$0.158780\pi$$
−0.878146 + 0.478392i $$0.841220\pi$$
$$174$$ 1.46363 34.6971i 0.00841169 0.199408i
$$175$$ 58.4435 0.333963
$$176$$ 0 0
$$177$$ −130.461 5.50325i −0.737065 0.0310918i
$$178$$ −56.7398 −0.318763
$$179$$ 58.5371i 0.327023i −0.986541 0.163511i $$-0.947718\pi$$
0.986541 0.163511i $$-0.0522820\pi$$
$$180$$ 26.9989 319.450i 0.149994 1.77472i
$$181$$ 284.678 1.57281 0.786403 0.617713i $$-0.211941\pi$$
0.786403 + 0.617713i $$0.211941\pi$$
$$182$$ 152.269i 0.836643i
$$183$$ 1.34716 31.9358i 0.00736151 0.174513i
$$184$$ 114.146 0.620357
$$185$$ 255.970i 1.38362i
$$186$$ 190.607 + 8.04041i 1.02477 + 0.0432280i
$$187$$ 0 0
$$188$$ 106.715i 0.567631i
$$189$$ 10.4316 82.0398i 0.0551939 0.434073i
$$190$$ −420.619 −2.21379
$$191$$ 137.443i 0.719595i −0.933031 0.359797i $$-0.882846\pi$$
0.933031 0.359797i $$-0.117154\pi$$
$$192$$ 12.3512 292.798i 0.0643291 1.52499i
$$193$$ 298.094 1.54453 0.772265 0.635300i $$-0.219124\pi$$
0.772265 + 0.635300i $$0.219124\pi$$
$$194$$ 193.720i 0.998556i
$$195$$ −323.273 13.6367i −1.65781 0.0699318i
$$196$$ 212.558 1.08448
$$197$$ 58.1375i 0.295114i 0.989054 + 0.147557i $$0.0471410\pi$$
−0.989054 + 0.147557i $$0.952859\pi$$
$$198$$ 0 0
$$199$$ −125.049 −0.628385 −0.314193 0.949359i $$-0.601734\pi$$
−0.314193 + 0.949359i $$0.601734\pi$$
$$200$$ 79.7138i 0.398569i
$$201$$ 9.14095 216.696i 0.0454774 1.07809i
$$202$$ 460.136 2.27790
$$203$$ 11.5863i 0.0570752i
$$204$$ −12.9558 0.546516i −0.0635086 0.00267900i
$$205$$ 88.7853 0.433099
$$206$$ 458.326i 2.22489i
$$207$$ −20.7090 + 245.028i −0.100043 + 1.18371i
$$208$$ −140.934 −0.677566
$$209$$ 0 0
$$210$$ 7.86865 186.535i 0.0374698 0.888262i
$$211$$ −48.3927 −0.229349 −0.114675 0.993403i $$-0.536583\pi$$
−0.114675 + 0.993403i $$0.536583\pi$$
$$212$$ 94.8316i 0.447319i
$$213$$ −7.70284 0.324931i −0.0361636 0.00152550i
$$214$$ 63.5048 0.296752
$$215$$ 288.230i 1.34060i
$$216$$ −111.898 14.2282i −0.518046 0.0658713i
$$217$$ 63.6486 0.293312
$$218$$ 323.755i 1.48512i
$$219$$ −5.75021 + 136.315i −0.0262567 + 0.622444i
$$220$$ 0 0
$$221$$ 13.0875i 0.0592193i
$$222$$ −353.637 14.9176i −1.59296 0.0671962i
$$223$$ 211.716 0.949401 0.474701 0.880147i $$-0.342556\pi$$
0.474701 + 0.880147i $$0.342556\pi$$
$$224$$ 132.507i 0.591548i
$$225$$ 171.115 + 14.4621i 0.760513 + 0.0642762i
$$226$$ −406.307 −1.79782
$$227$$ 121.385i 0.534736i −0.963594 0.267368i $$-0.913846\pi$$
0.963594 0.267368i $$-0.0861540\pi$$
$$228$$ −14.0432 + 332.909i −0.0615929 + 1.46013i
$$229$$ 322.944 1.41023 0.705117 0.709091i $$-0.250894\pi$$
0.705117 + 0.709091i $$0.250894\pi$$
$$230$$ 555.137i 2.41364i
$$231$$ 0 0
$$232$$ −15.8030 −0.0681166
$$233$$ 402.409i 1.72708i 0.504282 + 0.863539i $$0.331757\pi$$
−0.504282 + 0.863539i $$0.668243\pi$$
$$234$$ −37.6798 + 445.826i −0.161025 + 1.90524i
$$235$$ −132.058 −0.561949
$$236$$ 233.521i 0.989497i
$$237$$ −12.4215 + 294.465i −0.0524113 + 1.24247i
$$238$$ −7.55173 −0.0317299
$$239$$ 0.321443i 0.00134495i −1.00000 0.000672476i $$-0.999786\pi$$
1.00000 0.000672476i $$-0.000214056\pi$$
$$240$$ 172.649 + 7.28289i 0.719370 + 0.0303454i
$$241$$ 290.799 1.20664 0.603318 0.797500i $$-0.293845\pi$$
0.603318 + 0.797500i $$0.293845\pi$$
$$242$$ 0 0
$$243$$ 50.8438 237.621i 0.209234 0.977866i
$$244$$ −57.1643 −0.234280
$$245$$ 263.038i 1.07362i
$$246$$ 5.17428 122.662i 0.0210337 0.498626i
$$247$$ 336.293 1.36151
$$248$$ 86.8133i 0.350054i
$$249$$ 95.6168 + 4.03343i 0.384003 + 0.0161985i
$$250$$ −120.270 −0.481081
$$251$$ 112.621i 0.448691i 0.974510 + 0.224345i $$0.0720244\pi$$
−0.974510 + 0.224345i $$0.927976\pi$$
$$252$$ −147.375 12.4557i −0.584821 0.0494272i
$$253$$ 0 0
$$254$$ 448.803i 1.76694i
$$255$$ 0.676307 16.0326i 0.00265219 0.0628730i
$$256$$ 5.45390 0.0213043
$$257$$ 196.568i 0.764858i −0.923985 0.382429i $$-0.875088\pi$$
0.923985 0.382429i $$-0.124912\pi$$
$$258$$ −398.206 16.7976i −1.54343 0.0651071i
$$259$$ −118.089 −0.455942
$$260$$ 578.651i 2.22558i
$$261$$ 2.86708 33.9232i 0.0109850 0.129974i
$$262$$ −457.407 −1.74583
$$263$$ 378.327i 1.43850i −0.694749 0.719252i $$-0.744485\pi$$
0.694749 0.719252i $$-0.255515\pi$$
$$264$$ 0 0
$$265$$ 117.353 0.442842
$$266$$ 194.048i 0.729503i
$$267$$ −55.5732 2.34426i −0.208139 0.00877999i
$$268$$ −387.881 −1.44732
$$269$$ 201.154i 0.747785i −0.927472 0.373892i $$-0.878023\pi$$
0.927472 0.373892i $$-0.121977\pi$$
$$270$$ 69.1975 544.205i 0.256287 2.01557i
$$271$$ 80.2146 0.295995 0.147997 0.988988i $$-0.452717\pi$$
0.147997 + 0.988988i $$0.452717\pi$$
$$272$$ 6.98956i 0.0256969i
$$273$$ −6.29114 + 149.138i −0.0230445 + 0.546294i
$$274$$ 465.792 1.69997
$$275$$ 0 0
$$276$$ 439.376 + 18.5343i 1.59194 + 0.0671533i
$$277$$ 218.915 0.790306 0.395153 0.918615i $$-0.370692\pi$$
0.395153 + 0.918615i $$0.370692\pi$$
$$278$$ 342.245i 1.23110i
$$279$$ 186.356 + 15.7502i 0.667941 + 0.0564523i
$$280$$ −84.9588 −0.303424
$$281$$ 496.437i 1.76668i 0.468733 + 0.883340i $$0.344711\pi$$
−0.468733 + 0.883340i $$0.655289\pi$$
$$282$$ −7.69615 + 182.446i −0.0272913 + 0.646971i
$$283$$ −307.702 −1.08729 −0.543643 0.839317i $$-0.682955\pi$$
−0.543643 + 0.839317i $$0.682955\pi$$
$$284$$ 13.7879i 0.0485490i
$$285$$ −411.971 17.3783i −1.44551 0.0609764i
$$286$$ 0 0
$$287$$ 40.9601i 0.142718i
$$288$$ 32.7895 387.964i 0.113852 1.34710i
$$289$$ 288.351 0.997754
$$290$$ 76.8566i 0.265023i
$$291$$ −8.00372 + 189.737i −0.0275042 + 0.652017i
$$292$$ 244.001 0.835620
$$293$$ 339.698i 1.15938i 0.814837 + 0.579690i $$0.196826\pi$$
−0.814837 + 0.579690i $$0.803174\pi$$
$$294$$ 363.402 + 15.3295i 1.23606 + 0.0521411i
$$295$$ −288.980 −0.979593
$$296$$ 161.067i 0.544145i
$$297$$ 0 0
$$298$$ −794.734 −2.66689
$$299$$ 443.843i 1.48442i
$$300$$ 12.9435 306.839i 0.0431448 1.02280i
$$301$$ −132.972 −0.441766
$$302$$ 269.357i 0.891909i
$$303$$ 450.675 + 19.0109i 1.48738 + 0.0627424i
$$304$$ −179.603 −0.590798
$$305$$ 70.7402i 0.231935i
$$306$$ −22.1106 1.86871i −0.0722567 0.00610691i
$$307$$ −396.129 −1.29032 −0.645161 0.764047i $$-0.723210\pi$$
−0.645161 + 0.764047i $$0.723210\pi$$
$$308$$ 0 0
$$309$$ −18.9362 + 448.903i −0.0612821 + 1.45276i
$$310$$ 422.208 1.36196
$$311$$ 87.0358i 0.279858i 0.990162 + 0.139929i $$0.0446874\pi$$
−0.990162 + 0.139929i $$0.955313\pi$$
$$312$$ 203.417 + 8.58078i 0.651977 + 0.0275025i
$$313$$ −598.914 −1.91346 −0.956731 0.290973i $$-0.906021\pi$$
−0.956731 + 0.290973i $$0.906021\pi$$
$$314$$ 23.4272i 0.0746088i
$$315$$ 15.4137 182.375i 0.0489325 0.578967i
$$316$$ 527.085 1.66799
$$317$$ 2.45490i 0.00774416i 0.999993 + 0.00387208i $$0.00123252\pi$$
−0.999993 + 0.00387208i $$0.998767\pi$$
$$318$$ 6.83917 162.130i 0.0215068 0.509843i
$$319$$ 0 0
$$320$$ 648.571i 2.02678i
$$321$$ 62.1992 + 2.62376i 0.193767 + 0.00817371i
$$322$$ 256.106 0.795361
$$323$$ 16.6783i 0.0516357i
$$324$$ −428.413 72.9373i −1.32226 0.225115i
$$325$$ −309.958 −0.953717
$$326$$ 803.461i 2.46460i
$$327$$ −13.3762 + 317.099i −0.0409059 + 0.969720i
$$328$$ −55.8674 −0.170327
$$329$$ 60.9235i 0.185178i
$$330$$ 0 0
$$331$$ 368.074 1.11200 0.556002 0.831181i $$-0.312335\pi$$
0.556002 + 0.831181i $$0.312335\pi$$
$$332$$ 171.152i 0.515518i
$$333$$ −345.750 29.2217i −1.03829 0.0877529i
$$334$$ −489.660 −1.46605
$$335$$ 479.999i 1.43283i
$$336$$ 3.35988 79.6496i 0.00999963 0.237052i
$$337$$ 591.880 1.75632 0.878160 0.478368i $$-0.158771\pi$$
0.878160 + 0.478368i $$0.158771\pi$$
$$338$$ 290.384i 0.859125i
$$339$$ −397.953 16.7869i −1.17390 0.0495190i
$$340$$ −28.6980 −0.0844059
$$341$$ 0 0
$$342$$ −48.0182 + 568.149i −0.140404 + 1.66125i
$$343$$ 271.435 0.791357
$$344$$ 181.366i 0.527227i
$$345$$ −22.9360 + 543.723i −0.0664812 + 1.57601i
$$346$$ 506.545 1.46400
$$347$$ 294.601i 0.848994i −0.905429 0.424497i $$-0.860451\pi$$
0.905429 0.424497i $$-0.139549\pi$$
$$348$$ −60.8300 2.56601i −0.174799 0.00737358i
$$349$$ 412.008 1.18054 0.590269 0.807206i $$-0.299021\pi$$
0.590269 + 0.807206i $$0.299021\pi$$
$$350$$ 178.852i 0.511005i
$$351$$ −55.3248 + 435.102i −0.157620 + 1.23961i
$$352$$ 0 0
$$353$$ 135.577i 0.384070i 0.981388 + 0.192035i $$0.0615086\pi$$
−0.981388 + 0.192035i $$0.938491\pi$$
$$354$$ −16.8413 + 399.242i −0.0475744 + 1.12780i
$$355$$ −17.0624 −0.0480630
$$356$$ 99.4748i 0.279424i
$$357$$ −7.39646 0.312007i −0.0207184 0.000873968i
$$358$$ −179.138 −0.500386
$$359$$ 278.775i 0.776533i −0.921547 0.388267i $$-0.873074\pi$$
0.921547 0.388267i $$-0.126926\pi$$
$$360$$ −248.749 21.0235i −0.690970 0.0583986i
$$361$$ 67.5639 0.187158
$$362$$ 871.187i 2.40659i
$$363$$ 0 0
$$364$$ 266.954 0.733391
$$365$$ 301.948i 0.827256i
$$366$$ −97.7317 4.12264i −0.267026 0.0112640i
$$367$$ −176.388 −0.480620 −0.240310 0.970696i $$-0.577249\pi$$
−0.240310 + 0.970696i $$0.577249\pi$$
$$368$$ 237.041i 0.644133i
$$369$$ 10.1358 119.926i 0.0274683 0.325003i
$$370$$ −783.333 −2.11712
$$371$$ 54.1395i 0.145929i
$$372$$ 14.0962 334.167i 0.0378931 0.898298i
$$373$$ 163.109 0.437289 0.218645 0.975805i $$-0.429836\pi$$
0.218645 + 0.975805i $$0.429836\pi$$
$$374$$ 0 0
$$375$$ −117.797 4.96908i −0.314126 0.0132509i
$$376$$ 83.0964 0.221001
$$377$$ 61.4484i 0.162993i
$$378$$ −251.063 31.9235i −0.664187 0.0844537i
$$379$$ 53.2306 0.140450 0.0702250 0.997531i $$-0.477628\pi$$
0.0702250 + 0.997531i $$0.477628\pi$$
$$380$$ 737.419i 1.94058i
$$381$$ −18.5427 + 439.575i −0.0486685 + 1.15374i
$$382$$ −420.609 −1.10107
$$383$$ 89.6653i 0.234113i −0.993125 0.117057i $$-0.962654\pi$$
0.993125 0.117057i $$-0.0373459\pi$$
$$384$$ −377.369 15.9187i −0.982733 0.0414549i
$$385$$ 0 0
$$386$$ 912.245i 2.36333i
$$387$$ −389.325 32.9045i −1.00601 0.0850246i
$$388$$ 339.625 0.875322
$$389$$ 269.601i 0.693062i −0.938038 0.346531i $$-0.887360\pi$$
0.938038 0.346531i $$-0.112640\pi$$
$$390$$ −41.7318 + 989.298i −0.107005 + 2.53666i
$$391$$ 22.0122 0.0562972
$$392$$ 165.514i 0.422230i
$$393$$ −448.002 18.8982i −1.13995 0.0480870i
$$394$$ 177.916 0.451562
$$395$$ 652.262i 1.65130i
$$396$$ 0 0
$$397$$ 211.490 0.532720 0.266360 0.963874i $$-0.414179\pi$$
0.266360 + 0.963874i $$0.414179\pi$$
$$398$$ 382.681i 0.961509i
$$399$$ −8.01727 + 190.058i −0.0200934 + 0.476336i
$$400$$ 165.538 0.413844
$$401$$ 449.798i 1.12169i 0.827920 + 0.560846i $$0.189524\pi$$
−0.827920 + 0.560846i $$0.810476\pi$$
$$402$$ −663.146 27.9736i −1.64962 0.0695861i
$$403$$ −337.564 −0.837628
$$404$$ 806.698i 1.99678i
$$405$$ 90.2591 530.157i 0.222862 1.30903i
$$406$$ −35.4569 −0.0873323
$$407$$ 0 0
$$408$$ −0.425560 + 10.0884i −0.00104304 + 0.0247264i
$$409$$ −154.294 −0.377247 −0.188623 0.982049i $$-0.560403\pi$$
−0.188623 + 0.982049i $$0.560403\pi$$
$$410$$ 271.706i 0.662697i
$$411$$ 456.215 + 19.2446i 1.11001 + 0.0468239i
$$412$$ 803.526 1.95031
$$413$$ 133.318i 0.322803i
$$414$$ 749.848 + 63.3748i 1.81123 + 0.153079i
$$415$$ 211.798 0.510358
$$416$$ 702.757i 1.68932i
$$417$$ 14.1402 335.209i 0.0339093 0.803858i
$$418$$ 0 0
$$419$$ 755.530i 1.80317i −0.432599 0.901587i $$-0.642403\pi$$
0.432599 0.901587i $$-0.357597\pi$$
$$420$$ −327.028 13.7951i −0.778639 0.0328455i
$$421$$ −436.890 −1.03774 −0.518872 0.854852i $$-0.673648\pi$$
−0.518872 + 0.854852i $$0.673648\pi$$
$$422$$ 148.094i 0.350933i
$$423$$ −15.0758 + 178.377i −0.0356403 + 0.421694i
$$424$$ −73.8433 −0.174159
$$425$$ 15.3722i 0.0361700i
$$426$$ −0.994371 + 23.5727i −0.00233420 + 0.0553349i
$$427$$ −32.6352 −0.0764290
$$428$$ 111.335i 0.260129i
$$429$$ 0 0
$$430$$ −882.057 −2.05129
$$431$$ 9.73407i 0.0225849i −0.999936 0.0112924i $$-0.996405\pi$$
0.999936 0.0112924i $$-0.00359457\pi$$
$$432$$ 29.5470 232.373i 0.0683959 0.537900i
$$433$$ −59.2747 −0.136893 −0.0684466 0.997655i $$-0.521804\pi$$
−0.0684466 + 0.997655i $$0.521804\pi$$
$$434$$ 194.781i 0.448804i
$$435$$ 3.17540 75.2764i 0.00729978 0.173049i
$$436$$ 567.599 1.30183
$$437$$ 565.622i 1.29433i
$$438$$ 417.159 + 17.5971i 0.952418 + 0.0401761i
$$439$$ 444.724 1.01304 0.506519 0.862229i $$-0.330932\pi$$
0.506519 + 0.862229i $$0.330932\pi$$
$$440$$ 0 0
$$441$$ 355.297 + 30.0286i 0.805662 + 0.0680920i
$$442$$ 40.0510 0.0906131
$$443$$ 535.351i 1.20847i 0.796807 + 0.604234i $$0.206521\pi$$
−0.796807 + 0.604234i $$0.793479\pi$$
$$444$$ −26.1531 + 619.988i −0.0589034 + 1.39637i
$$445$$ −123.099 −0.276627
$$446$$ 647.906i 1.45270i
$$447$$ −778.394 32.8352i −1.74137 0.0734568i
$$448$$ −299.211 −0.667881
$$449$$ 769.414i 1.71362i −0.515635 0.856809i $$-0.672444\pi$$
0.515635 0.856809i $$-0.327556\pi$$
$$450$$ 44.2578 523.657i 0.0983508 1.16368i
$$451$$ 0 0
$$452$$ 712.327i 1.57594i
$$453$$ 11.1287 263.818i 0.0245667 0.582381i
$$454$$ −371.470 −0.818215
$$455$$ 330.353i 0.726050i
$$456$$ 259.229 + 10.9351i 0.568485 + 0.0239805i
$$457$$ 169.655 0.371236 0.185618 0.982622i $$-0.440571\pi$$
0.185618 + 0.982622i $$0.440571\pi$$
$$458$$ 988.290i 2.15784i
$$459$$ −21.5787 2.74381i −0.0470125 0.00597780i
$$460$$ 973.252 2.11577
$$461$$ 266.355i 0.577777i 0.957363 + 0.288888i $$0.0932857\pi$$
−0.957363 + 0.288888i $$0.906714\pi$$
$$462$$ 0 0
$$463$$ −704.848 −1.52235 −0.761175 0.648547i $$-0.775377\pi$$
−0.761175 + 0.648547i $$0.775377\pi$$
$$464$$ 32.8174i 0.0707272i
$$465$$ 413.528 + 17.4439i 0.889307 + 0.0375138i
$$466$$ 1231.47 2.64265
$$467$$ 675.178i 1.44578i −0.690965 0.722888i $$-0.742814\pi$$
0.690965 0.722888i $$-0.257186\pi$$
$$468$$ 781.610 + 66.0592i 1.67011 + 0.141152i
$$469$$ −221.442 −0.472158
$$470$$ 404.131i 0.859854i
$$471$$ −0.967915 + 22.9455i −0.00205502 + 0.0487165i
$$472$$ 181.838 0.385250
$$473$$ 0 0
$$474$$ 901.138 + 38.0129i 1.90113 + 0.0801960i
$$475$$ −395.003 −0.831585
$$476$$ 13.2395i 0.0278141i
$$477$$ 13.3971 158.514i 0.0280862 0.332314i
$$478$$ −0.983699 −0.00205795
$$479$$ 699.807i 1.46098i 0.682926 + 0.730488i $$0.260707\pi$$
−0.682926 + 0.730488i $$0.739293\pi$$
$$480$$ 36.3156 860.902i 0.0756575 1.79355i
$$481$$ 626.291 1.30206
$$482$$ 889.920i 1.84631i
$$483$$ 250.841 + 10.5813i 0.519339 + 0.0219074i
$$484$$ 0 0
$$485$$ 420.282i 0.866560i
$$486$$ −727.182 155.595i −1.49626 0.320154i
$$487$$ −653.347 −1.34157 −0.670787 0.741650i $$-0.734044\pi$$
−0.670787 + 0.741650i $$0.734044\pi$$
$$488$$ 44.5127i 0.0912145i
$$489$$ 33.1957 786.941i 0.0678849 1.60929i
$$490$$ 804.963 1.64278
$$491$$ 61.8372i 0.125941i 0.998015 + 0.0629707i $$0.0200575\pi$$
−0.998015 + 0.0629707i $$0.979943\pi$$
$$492$$ −215.048 9.07141i −0.437089 0.0184378i
$$493$$ −3.04751 −0.00618156
$$494$$ 1029.14i 2.08329i
$$495$$ 0 0
$$496$$ 180.281 0.363470
$$497$$ 7.87154i 0.0158381i
$$498$$ 12.3433 292.612i 0.0247858 0.587574i
$$499$$ 329.993 0.661309 0.330654 0.943752i $$-0.392731\pi$$
0.330654 + 0.943752i $$0.392731\pi$$
$$500$$ 210.855i 0.421709i
$$501$$ −479.592 20.2308i −0.957270 0.0403808i
$$502$$ 344.650 0.686554
$$503$$ 347.179i 0.690217i −0.938563 0.345109i $$-0.887842\pi$$
0.938563 0.345109i $$-0.112158\pi$$
$$504$$ −9.69895 + 114.758i −0.0192440 + 0.227694i
$$505$$ 998.280 1.97679
$$506$$ 0 0
$$507$$ 11.9975 284.414i 0.0236637 0.560974i
$$508$$ 786.830 1.54888
$$509$$ 856.194i 1.68211i −0.540950 0.841055i $$-0.681935\pi$$
0.540950 0.841055i $$-0.318065\pi$$
$$510$$ −49.0639 2.06967i −0.0962036 0.00405818i
$$511$$ 139.300 0.272604
$$512$$ 520.297i 1.01621i
$$513$$ −70.5045 + 554.484i −0.137436 + 1.08086i
$$514$$ −601.549 −1.17033
$$515$$ 994.354i 1.93078i
$$516$$ −29.4492 + 698.125i −0.0570720 + 1.35295i
$$517$$ 0 0
$$518$$ 361.382i 0.697649i
$$519$$ 496.130 + 20.9284i 0.955935 + 0.0403244i
$$520$$ 450.584 0.866507
$$521$$ 712.659i 1.36787i 0.729544 + 0.683934i $$0.239732\pi$$
−0.729544 + 0.683934i $$0.760268\pi$$
$$522$$ −103.814 8.77400i −0.198877 0.0168084i
$$523$$ 503.925 0.963527 0.481764 0.876301i $$-0.339996\pi$$
0.481764 + 0.876301i $$0.339996\pi$$
$$524$$ 801.914i 1.53037i
$$525$$ 7.38943 175.175i 0.0140751 0.333666i
$$526$$ −1157.78 −2.20109
$$527$$ 16.7414i 0.0317673i
$$528$$ 0 0
$$529$$ −217.513 −0.411179
$$530$$ 359.130i 0.677604i
$$531$$ −32.9901 + 390.338i −0.0621283 + 0.735100i
$$532$$ 340.200 0.639473
$$533$$ 217.234i 0.407568i
$$534$$ −7.17403 + 170.068i −0.0134345 + 0.318480i
$$535$$ 137.776 0.257525
$$536$$ 302.035i 0.563498i
$$537$$ −175.455 7.40127i −0.326732 0.0137826i
$$538$$ −615.583 −1.14421
$$539$$ 0 0
$$540$$ −954.086 121.315i −1.76683 0.224658i
$$541$$ −586.637 −1.08436 −0.542179 0.840263i $$-0.682400\pi$$
−0.542179 + 0.840263i $$0.682400\pi$$
$$542$$ 245.477i 0.452910i
$$543$$ 35.9939 853.275i 0.0662871 1.57141i
$$544$$ −34.8530 −0.0640679
$$545$$ 702.397i 1.28880i
$$546$$ 456.401 + 19.2525i 0.835900 + 0.0352610i
$$547$$ 688.847 1.25932 0.629659 0.776872i $$-0.283195\pi$$
0.629659 + 0.776872i $$0.283195\pi$$
$$548$$ 816.614i 1.49017i
$$549$$ −95.5519 8.07575i −0.174047 0.0147099i
$$550$$ 0 0
$$551$$ 78.3083i 0.142120i
$$552$$ 14.4323 342.133i 0.0261454 0.619806i
$$553$$ 300.914 0.544148
$$554$$ 669.935i 1.20927i
$$555$$ −767.228 32.3642i −1.38239 0.0583138i
$$556$$ −600.016 −1.07917
$$557$$ 618.806i 1.11096i 0.831529 + 0.555481i $$0.187466\pi$$
−0.831529 + 0.555481i $$0.812534\pi$$
$$558$$ 48.1996 570.296i 0.0863792 1.02204i
$$559$$ 705.222 1.26158
$$560$$ 176.430i 0.315053i
$$561$$ 0 0
$$562$$ 1519.22 2.70325
$$563$$ 569.270i 1.01114i −0.862787 0.505568i $$-0.831283\pi$$
0.862787 0.505568i $$-0.168717\pi$$
$$564$$ 319.859 + 13.4927i 0.567126 + 0.0239232i
$$565$$ −881.496 −1.56017
$$566$$ 941.645i 1.66368i
$$567$$ −244.582 41.6400i −0.431361 0.0734392i
$$568$$ 10.7364 0.0189020
$$569$$ 901.528i 1.58441i 0.610256 + 0.792204i $$0.291066\pi$$
−0.610256 + 0.792204i $$0.708934\pi$$
$$570$$ −53.1820 + 1260.74i −0.0933017 + 2.21182i
$$571$$ −804.182 −1.40837 −0.704187 0.710014i $$-0.748688\pi$$
−0.704187 + 0.710014i $$0.748688\pi$$
$$572$$ 0 0
$$573$$ −411.961 17.3779i −0.718955 0.0303279i
$$574$$ −125.348 −0.218377
$$575$$ 521.328i 0.906658i
$$576$$ −876.053 74.0413i −1.52093 0.128544i
$$577$$ −787.100 −1.36412 −0.682062 0.731294i $$-0.738917\pi$$
−0.682062 + 0.731294i $$0.738917\pi$$
$$578$$ 882.427i 1.52669i
$$579$$ 37.6902 893.489i 0.0650954 1.54316i
$$580$$ −134.743 −0.232316
$$581$$ 97.7108i 0.168177i
$$582$$ 580.643 + 24.4934i 0.997669 + 0.0420849i
$$583$$ 0 0
$$584$$ 189.998i 0.325340i
$$585$$ −81.7475 + 967.233i −0.139739 + 1.65339i
$$586$$ 1039.56 1.77400
$$587$$ 182.527i 0.310948i 0.987840 + 0.155474i $$0.0496906\pi$$
−0.987840 + 0.155474i $$0.950309\pi$$
$$588$$ 26.8752 637.107i 0.0457062 1.08352i
$$589$$ −430.183 −0.730362
$$590$$ 884.352i 1.49890i
$$591$$ 174.258 + 7.35075i 0.294852 + 0.0124378i
$$592$$ −334.480 −0.565000
$$593$$ 685.071i 1.15526i 0.816297 + 0.577632i $$0.196023\pi$$
−0.816297 + 0.577632i $$0.803977\pi$$
$$594$$ 0 0
$$595$$ −16.3837 −0.0275357
$$596$$ 1393.31i 2.33776i
$$597$$ −15.8108 + 374.813i −0.0264838 + 0.627827i
$$598$$ −1358.27 −2.27136
$$599$$ 360.876i 0.602463i 0.953551 + 0.301232i $$0.0973978\pi$$
−0.953551 + 0.301232i $$0.902602\pi$$
$$600$$ −238.929 10.0788i −0.398215 0.0167980i
$$601$$ −419.487 −0.697982 −0.348991 0.937126i $$-0.613476\pi$$
−0.348991 + 0.937126i $$0.613476\pi$$
$$602$$ 406.927i 0.675958i
$$603$$ −648.355 54.7970i −1.07522 0.0908739i
$$604$$ −472.229 −0.781836
$$605$$ 0 0
$$606$$ 58.1783 1379.18i 0.0960039 2.27588i
$$607$$ 1007.72 1.66017 0.830084 0.557639i $$-0.188293\pi$$
0.830084 + 0.557639i $$0.188293\pi$$
$$608$$ 895.576i 1.47299i
$$609$$ −34.7279 1.46494i −0.0570245 0.00240548i
$$610$$ −216.483 −0.354890
$$611$$ 323.111i 0.528823i
$$612$$ −3.27618 + 38.7636i −0.00535324 + 0.0633393i
$$613$$ −552.248 −0.900893 −0.450447 0.892803i $$-0.648735\pi$$
−0.450447 + 0.892803i $$0.648735\pi$$
$$614$$ 1212.26i 1.97436i
$$615$$ 11.2258 266.119i 0.0182533 0.432714i
$$616$$ 0 0
$$617$$ 675.556i 1.09490i 0.836837 + 0.547452i $$0.184402\pi$$
−0.836837 + 0.547452i $$0.815598\pi$$
$$618$$ 1373.76 + 57.9495i 2.22291 + 0.0937695i
$$619$$ −269.119 −0.434765 −0.217382 0.976087i $$-0.569752\pi$$
−0.217382 + 0.976087i $$0.569752\pi$$
$$620$$ 740.205i 1.19388i
$$621$$ 731.813 + 93.0525i 1.17844 + 0.149843i
$$622$$ 266.352 0.428218
$$623$$ 56.7903i 0.0911562i
$$624$$ −17.8193 + 422.426i −0.0285565 + 0.676964i
$$625$$ −737.946 −1.18071
$$626$$ 1832.83i 2.92784i
$$627$$ 0 0
$$628$$ 41.0719 0.0654011
$$629$$ 31.0606i 0.0493810i
$$630$$ −558.113 47.1699i −0.885893 0.0748729i
$$631$$ 93.3489 0.147938 0.0739690 0.997261i $$-0.476433\pi$$
0.0739690 + 0.997261i $$0.476433\pi$$
$$632$$ 410.430i 0.649415i
$$633$$ −6.11864 + 145.049i −0.00966609 + 0.229145i
$$634$$ 7.51261 0.0118495
$$635$$ 973.693i 1.53337i
$$636$$ −284.242 11.9902i −0.446921 0.0188526i
$$637$$ −643.584 −1.01034
$$638$$ 0 0
$$639$$ −1.94785 + 23.0469i −0.00304828 + 0.0360672i
$$640$$ −835.902 −1.30610
$$641$$ 14.7703i 0.0230425i 0.999934 + 0.0115213i $$0.00366741\pi$$
−0.999934 + 0.0115213i $$0.996333\pi$$
$$642$$ 8.02938 190.345i 0.0125068 0.296488i
$$643$$ −436.040 −0.678133 −0.339067 0.940762i $$-0.610111\pi$$
−0.339067 + 0.940762i $$0.610111\pi$$
$$644$$ 448.999i 0.697203i
$$645$$ −863.921 36.4430i −1.33941 0.0565008i
$$646$$ 51.0400 0.0790092
$$647$$ 314.372i 0.485892i 0.970040 + 0.242946i $$0.0781137\pi$$
−0.970040 + 0.242946i $$0.921886\pi$$
$$648$$ −56.7948 + 333.596i −0.0876462 + 0.514809i
$$649$$ 0 0
$$650$$ 948.550i 1.45931i
$$651$$ 8.04756 190.776i 0.0123618 0.293051i
$$652$$ −1408.61 −2.16044
$$653$$ 191.919i 0.293904i 0.989144 + 0.146952i $$0.0469463\pi$$
−0.989144 + 0.146952i $$0.953054\pi$$
$$654$$ 970.402 + 40.9347i 1.48380 + 0.0625913i
$$655$$ −992.359 −1.51505
$$656$$ 116.017i 0.176855i
$$657$$ 407.855 + 34.4706i 0.620784 + 0.0524667i
$$658$$ 186.441 0.283346
$$659$$ 127.678i 0.193745i −0.995297 0.0968724i $$-0.969116\pi$$
0.995297 0.0968724i $$-0.0308839\pi$$
$$660$$ 0 0
$$661$$ 580.599 0.878364 0.439182 0.898398i $$-0.355268\pi$$
0.439182 + 0.898398i $$0.355268\pi$$
$$662$$ 1126.40i 1.70151i
$$663$$ 39.2275 + 1.65474i 0.0591667 + 0.00249584i
$$664$$ −133.272 −0.200711
$$665$$ 420.993i 0.633073i
$$666$$ −89.4259 + 1058.08i −0.134273 + 1.58871i
$$667$$ 103.352 0.154950
$$668$$ 858.459i 1.28512i
$$669$$ 26.7689 634.585i 0.0400132 0.948558i
$$670$$ −1468.92 −2.19241
$$671$$ 0 0
$$672$$ −397.167 16.7538i −0.591023 0.0249313i
$$673$$ −546.461 −0.811977 −0.405989 0.913878i $$-0.633073\pi$$
−0.405989 + 0.913878i $$0.633073\pi$$
$$674$$ 1811.30i 2.68739i
$$675$$ 64.9832 511.062i 0.0962715 0.757128i
$$676$$ −509.094 −0.753098
$$677$$ 29.1664i 0.0430819i −0.999768 0.0215409i $$-0.993143\pi$$
0.999768 0.0215409i $$-0.00685722\pi$$
$$678$$ −51.3723 + 1217.84i −0.0757704 + 1.79622i
$$679$$ 193.892 0.285556
$$680$$ 22.3465i 0.0328625i
$$681$$ −363.832 15.3476i −0.534261 0.0225369i
$$682$$ 0 0
$$683$$ 82.4506i 0.120718i 0.998177 + 0.0603592i $$0.0192246\pi$$
−0.998177 + 0.0603592i $$0.980775\pi$$
$$684$$ 996.064 + 84.1842i 1.45623 + 0.123076i
$$685$$ 1010.55 1.47526
$$686$$ 830.661i 1.21088i
$$687$$ 40.8321 967.970i 0.0594354 1.40898i
$$688$$ −376.634 −0.547433
$$689$$ 287.132i 0.416737i
$$690$$ 1663.93 + 70.1900i 2.41149 + 0.101725i
$$691$$ 967.715 1.40046 0.700228 0.713919i $$-0.253082\pi$$
0.700228 + 0.713919i $$0.253082\pi$$
$$692$$ 888.061i 1.28333i
$$693$$ 0 0
$$694$$ −901.554 −1.29907
$$695$$ 742.513i 1.06836i
$$696$$ −1.99809 + 47.3670i −0.00287083 + 0.0680561i
$$697$$ −10.7736 −0.0154572
$$698$$ 1260.85i 1.80638i
$$699$$ 1206.16 + 50.8795i 1.72554 + 0.0727890i
$$700$$ −313.558 −0.447941
$$701$$ 314.100i 0.448075i −0.974581 0.224037i $$-0.928076\pi$$
0.974581 0.224037i $$-0.0719237\pi$$
$$702$$ 1331.52 + 169.308i 1.89676 + 0.241179i
$$703$$ 798.129 1.13532
$$704$$ 0 0
$$705$$ −16.6971 + 395.822i −0.0236838 + 0.561450i
$$706$$ 414.899 0.587675
$$707$$ 460.545i 0.651408i
$$708$$ 699.941 + 29.5258i 0.988618 + 0.0417031i
$$709$$ 327.352 0.461709 0.230855 0.972988i $$-0.425848\pi$$
0.230855 + 0.972988i $$0.425848\pi$$
$$710$$ 52.2152i 0.0735426i
$$711$$ 881.039 + 74.4627i 1.23916 + 0.104730i
$$712$$ 77.4589 0.108791
$$713$$ 567.759i 0.796297i
$$714$$ −0.954820 + 22.6351i −0.00133728 + 0.0317018i
$$715$$ 0 0
$$716$$ 314.061i 0.438632i
$$717$$ −0.963473 0.0406424i −0.00134376 5.66840e-5i
$$718$$ −853.124 −1.18820
$$719$$ 1106.21i 1.53853i 0.638928 + 0.769266i $$0.279378\pi$$
−0.638928 + 0.769266i $$0.720622\pi$$
$$720$$ 43.6585 516.565i 0.0606368 0.717452i
$$721$$ 458.734 0.636247
$$722$$ 206.763i 0.286375i
$$723$$ 36.7679 871.623i 0.0508546 1.20556i
$$724$$ −1527.34 −2.10959
$$725$$ 72.1759i 0.0995530i
$$726$$ 0 0
$$727$$ 577.040 0.793727 0.396864 0.917878i $$-0.370099\pi$$
0.396864 + 0.917878i $$0.370099\pi$$
$$728$$ 207.872i 0.285538i
$$729$$ −705.802 182.440i −0.968178 0.250261i
$$730$$ 924.039 1.26581
$$731$$ 34.9752i 0.0478457i
$$732$$ −7.22770 + 171.341i −0.00987391 + 0.234072i
$$733$$ 619.302 0.844886 0.422443 0.906389i $$-0.361173\pi$$
0.422443 + 0.906389i $$0.361173\pi$$
$$734$$ 539.791i 0.735410i
$$735$$ 788.412 + 33.2578i 1.07267 + 0.0452487i
$$736$$ 1181.99 1.60596
$$737$$ 0 0
$$738$$ −367.005 31.0181i −0.497297 0.0420299i
$$739$$ −1119.31 −1.51462 −0.757311 0.653055i $$-0.773487\pi$$
−0.757311 + 0.653055i $$0.773487\pi$$
$$740$$ 1373.32i 1.85584i
$$741$$ 42.5200 1007.98i 0.0573819 1.36030i
$$742$$ −165.681 −0.223289
$$743$$ 1148.58i 1.54586i −0.634489 0.772932i $$-0.718790\pi$$
0.634489 0.772932i $$-0.281210\pi$$
$$744$$ −260.209 10.9764i −0.349743 0.0147533i
$$745$$ −1724.20 −2.31436
$$746$$ 499.155i 0.669108i
$$747$$ 24.1791 286.086i 0.0323682 0.382979i
$$748$$ 0 0
$$749$$ 63.5613i 0.0848616i
$$750$$ −15.2066 + 360.490i −0.0202755 + 0.480654i
$$751$$ −273.658 −0.364391 −0.182196 0.983262i $$-0.558320\pi$$
−0.182196 + 0.983262i $$0.558320\pi$$
$$752$$ 172.562i 0.229471i
$$753$$ 337.564 + 14.2395i 0.448292 + 0.0189104i
$$754$$ 188.048 0.249400
$$755$$ 584.378i 0.774011i
$$756$$ −55.9674 + 440.157i −0.0740310 + 0.582218i
$$757$$ −558.006 −0.737128 −0.368564 0.929602i $$-0.620150\pi$$
−0.368564 + 0.929602i $$0.620150\pi$$
$$758$$ 162.899i 0.214906i
$$759$$ 0 0
$$760$$ 574.212 0.755543
$$761$$ 421.755i 0.554211i 0.960839 + 0.277106i $$0.0893752\pi$$
−0.960839 + 0.277106i $$0.910625\pi$$
$$762$$ 1345.21 + 56.7454i 1.76537 + 0.0744691i
$$763$$ 324.043 0.424696
$$764$$ 737.401i 0.965185i
$$765$$ −47.9696 4.05424i −0.0627053 0.00529966i
$$766$$ −274.399 −0.358223
$$767$$ 707.057i 0.921847i
$$768$$ 0.689576 16.3472i 0.000897886 0.0212854i
$$769$$ −108.997 −0.141738 −0.0708692 0.997486i $$-0.522577\pi$$
−0.0708692 + 0.997486i $$0.522577\pi$$
$$770$$ 0 0
$$771$$ −589.181 24.8536i −0.764178 0.0322355i
$$772$$ −1599.32 −2.07166
$$773$$ 1031.61i 1.33456i 0.744808 + 0.667279i $$0.232541\pi$$
−0.744808 + 0.667279i $$0.767459\pi$$
$$774$$ −100.696 + 1191.43i −0.130098 + 1.53932i
$$775$$ 396.495 0.511607
$$776$$ 264.459i 0.340797i
$$777$$ −14.9308 + 353.952i −0.0192160 + 0.455536i
$$778$$ −825.048 −1.06047
$$779$$ 276.838i 0.355376i
$$780$$ 1734.41 + 73.1631i 2.22360 + 0.0937988i
$$781$$ 0 0
$$782$$ 67.3630i 0.0861420i