Properties

 Label 392.3.k.j.275.3 Level 392 Weight 3 Character 392.275 Analytic conductor 10.681 Analytic rank 0 Dimension 8 CM no Inner twists 4

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$392 = 2^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 392.k (of order $$6$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$10.6812263629$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.796594176.2 Defining polynomial: $$x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 83 x^{4} - 104 x^{3} + 22 x^{2} + 24 x + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 56) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 275.3 Root $$-0.207107 - 0.0981308i$$ of defining polynomial Character $$\chi$$ $$=$$ 392.275 Dual form 392.3.k.j.67.3

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.26663 + 1.54779i) q^{2} +(1.70711 + 2.95680i) q^{3} +(-0.791288 + 3.92095i) q^{4} +(1.34221 + 0.774923i) q^{5} +(-2.41421 + 6.38741i) q^{6} +(-7.07107 + 3.74166i) q^{8} +(-1.32843 + 2.30090i) q^{9} +O(q^{10})$$ $$q+(1.26663 + 1.54779i) q^{2} +(1.70711 + 2.95680i) q^{3} +(-0.791288 + 3.92095i) q^{4} +(1.34221 + 0.774923i) q^{5} +(-2.41421 + 6.38741i) q^{6} +(-7.07107 + 3.74166i) q^{8} +(-1.32843 + 2.30090i) q^{9} +(0.500665 + 3.05899i) q^{10} +(2.24264 + 3.88437i) q^{11} +(-12.9443 + 4.35381i) q^{12} +1.54985i q^{13} +5.29150i q^{15} +(-14.7477 - 6.20520i) q^{16} +(11.8284 + 20.4874i) q^{17} +(-5.24394 + 0.858275i) q^{18} +(-12.4350 + 21.5381i) q^{19} +(-4.10051 + 4.64954i) q^{20} +(-3.17157 + 8.39119i) q^{22} +(-30.5055 - 17.6124i) q^{23} +(-23.1344 - 14.5203i) q^{24} +(-11.2990 - 19.5704i) q^{25} +(-2.39883 + 1.96308i) q^{26} +21.6569 q^{27} -22.4499i q^{29} +(-8.19012 + 6.70239i) q^{30} +(40.4569 - 23.3578i) q^{31} +(-9.07561 - 30.6860i) q^{32} +(-7.65685 + 13.2621i) q^{33} +(-16.7279 + 44.2579i) q^{34} +(-7.97056 - 7.02938i) q^{36} +(50.7340 + 29.2913i) q^{37} +(-49.0870 + 8.03407i) q^{38} +(-4.58258 + 2.64575i) q^{39} +(-12.3903 - 0.457458i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(-17.0050 + 5.71963i) q^{44} +(-3.56604 + 2.05886i) q^{45} +(-11.3791 - 69.5245i) q^{46} +(-31.2918 - 18.0663i) q^{47} +(-6.82843 - 54.1990i) q^{48} +(15.9792 - 42.2769i) q^{50} +(-40.3848 + 69.9485i) q^{51} +(-6.07687 - 1.22637i) q^{52} +(84.7102 - 48.9075i) q^{53} +(27.4313 + 33.5202i) q^{54} +6.95149i q^{55} -84.9117 q^{57} +(34.7477 - 28.4358i) q^{58} +(30.7782 + 53.3094i) q^{59} +(-20.7477 - 4.18710i) q^{60} +(-32.6340 - 18.8412i) q^{61} +(87.3970 + 33.0329i) q^{62} +(36.0000 - 52.9150i) q^{64} +(-1.20101 + 2.08021i) q^{65} +(-30.2253 + 4.94697i) q^{66} +(16.6863 + 28.9015i) q^{67} +(-89.6899 + 30.1672i) q^{68} -120.265i q^{69} +102.199i q^{71} +(0.784207 - 21.2404i) q^{72} +(34.6569 + 60.0274i) q^{73} +(18.9246 + 115.627i) q^{74} +(38.5772 - 66.8176i) q^{75} +(-74.6102 - 65.8000i) q^{76} +(-9.89949 - 3.74166i) q^{78} +(-33.5156 - 19.3503i) q^{79} +(-14.9859 - 19.7570i) q^{80} +(48.9264 + 84.7430i) q^{81} +(34.1618 + 41.7447i) q^{82} -3.61522 q^{83} +36.6645i q^{85} +(-21.7501 - 26.5779i) q^{86} +(66.3799 - 38.3245i) q^{87} +(-30.3918 - 19.0754i) q^{88} +(22.0294 - 38.1561i) q^{89} +(-7.70354 - 2.91166i) q^{90} +(93.1960 - 105.674i) q^{92} +(138.129 + 79.7486i) q^{93} +(-11.6724 - 71.3164i) q^{94} +(-33.3807 + 19.2724i) q^{95} +(75.2393 - 79.2191i) q^{96} -96.1076 q^{97} -11.9167 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} + O(q^{10})$$ $$8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} - 28q^{10} - 16q^{11} - 24q^{12} - 8q^{16} + 72q^{17} - 16q^{18} + 8q^{19} - 112q^{20} - 48q^{22} - 40q^{24} + 68q^{25} + 28q^{26} + 128q^{27} - 16q^{33} - 32q^{34} + 72q^{36} - 76q^{38} + 56q^{40} + 80q^{41} - 160q^{43} + 48q^{44} - 224q^{46} - 32q^{48} + 224q^{50} - 176q^{51} - 56q^{52} - 16q^{54} - 272q^{57} + 168q^{58} + 184q^{59} - 56q^{60} + 224q^{62} + 288q^{64} - 168q^{65} - 32q^{66} + 224q^{67} - 216q^{68} + 160q^{72} + 232q^{73} + 280q^{74} + 88q^{75} + 48q^{76} - 336q^{80} + 52q^{81} - 48q^{82} - 176q^{83} - 8q^{86} - 240q^{88} + 312q^{89} - 616q^{90} + 112q^{92} - 112q^{94} + 176q^{96} + 272q^{97} - 480q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$295$$ $$297$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.26663 + 1.54779i 0.633316 + 0.773893i
$$3$$ 1.70711 + 2.95680i 0.569036 + 0.985599i 0.996662 + 0.0816428i $$0.0260167\pi$$
−0.427626 + 0.903956i $$0.640650\pi$$
$$4$$ −0.791288 + 3.92095i −0.197822 + 0.980238i
$$5$$ 1.34221 + 0.774923i 0.268441 + 0.154985i 0.628179 0.778069i $$-0.283801\pi$$
−0.359738 + 0.933053i $$0.617134\pi$$
$$6$$ −2.41421 + 6.38741i −0.402369 + 1.06457i
$$7$$ 0 0
$$8$$ −7.07107 + 3.74166i −0.883883 + 0.467707i
$$9$$ −1.32843 + 2.30090i −0.147603 + 0.255656i
$$10$$ 0.500665 + 3.05899i 0.0500665 + 0.305899i
$$11$$ 2.24264 + 3.88437i 0.203876 + 0.353124i 0.949774 0.312936i $$-0.101313\pi$$
−0.745898 + 0.666060i $$0.767979\pi$$
$$12$$ −12.9443 + 4.35381i −1.07869 + 0.362817i
$$13$$ 1.54985i 0.119219i 0.998222 + 0.0596094i $$0.0189855\pi$$
−0.998222 + 0.0596094i $$0.981014\pi$$
$$14$$ 0 0
$$15$$ 5.29150i 0.352767i
$$16$$ −14.7477 6.20520i −0.921733 0.387825i
$$17$$ 11.8284 + 20.4874i 0.695790 + 1.20514i 0.969914 + 0.243449i $$0.0782788\pi$$
−0.274124 + 0.961694i $$0.588388\pi$$
$$18$$ −5.24394 + 0.858275i −0.291330 + 0.0476820i
$$19$$ −12.4350 + 21.5381i −0.654475 + 1.13358i 0.327550 + 0.944834i $$0.393777\pi$$
−0.982025 + 0.188750i $$0.939556\pi$$
$$20$$ −4.10051 + 4.64954i −0.205025 + 0.232477i
$$21$$ 0 0
$$22$$ −3.17157 + 8.39119i −0.144162 + 0.381418i
$$23$$ −30.5055 17.6124i −1.32633 0.765756i −0.341598 0.939846i $$-0.610968\pi$$
−0.984730 + 0.174090i $$0.944301\pi$$
$$24$$ −23.1344 14.5203i −0.963933 0.605012i
$$25$$ −11.2990 19.5704i −0.451960 0.782817i
$$26$$ −2.39883 + 1.96308i −0.0922627 + 0.0755032i
$$27$$ 21.6569 0.802106
$$28$$ 0 0
$$29$$ 22.4499i 0.774136i −0.922051 0.387068i $$-0.873488\pi$$
0.922051 0.387068i $$-0.126512\pi$$
$$30$$ −8.19012 + 6.70239i −0.273004 + 0.223413i
$$31$$ 40.4569 23.3578i 1.30506 0.753478i 0.323795 0.946127i $$-0.395041\pi$$
0.981268 + 0.192649i $$0.0617079\pi$$
$$32$$ −9.07561 30.6860i −0.283613 0.958939i
$$33$$ −7.65685 + 13.2621i −0.232026 + 0.401881i
$$34$$ −16.7279 + 44.2579i −0.491998 + 1.30170i
$$35$$ 0 0
$$36$$ −7.97056 7.02938i −0.221405 0.195260i
$$37$$ 50.7340 + 29.2913i 1.37119 + 0.791657i 0.991078 0.133284i $$-0.0425523\pi$$
0.380111 + 0.924941i $$0.375886\pi$$
$$38$$ −49.0870 + 8.03407i −1.29176 + 0.211423i
$$39$$ −4.58258 + 2.64575i −0.117502 + 0.0678398i
$$40$$ −12.3903 0.457458i −0.309758 0.0114364i
$$41$$ 26.9706 0.657819 0.328909 0.944362i $$-0.393319\pi$$
0.328909 + 0.944362i $$0.393319\pi$$
$$42$$ 0 0
$$43$$ −17.1716 −0.399339 −0.199669 0.979863i $$-0.563987\pi$$
−0.199669 + 0.979863i $$0.563987\pi$$
$$44$$ −17.0050 + 5.71963i −0.386477 + 0.129992i
$$45$$ −3.56604 + 2.05886i −0.0792454 + 0.0457524i
$$46$$ −11.3791 69.5245i −0.247371 1.51140i
$$47$$ −31.2918 18.0663i −0.665783 0.384390i 0.128694 0.991684i $$-0.458921\pi$$
−0.794477 + 0.607295i $$0.792255\pi$$
$$48$$ −6.82843 54.1990i −0.142259 1.12915i
$$49$$ 0 0
$$50$$ 15.9792 42.2769i 0.319584 0.845539i
$$51$$ −40.3848 + 69.9485i −0.791858 + 1.37154i
$$52$$ −6.07687 1.22637i −0.116863 0.0235841i
$$53$$ 84.7102 48.9075i 1.59831 0.922782i 0.606492 0.795090i $$-0.292576\pi$$
0.991814 0.127693i $$-0.0407571\pi$$
$$54$$ 27.4313 + 33.5202i 0.507986 + 0.620744i
$$55$$ 6.95149i 0.126391i
$$56$$ 0 0
$$57$$ −84.9117 −1.48968
$$58$$ 34.7477 28.4358i 0.599099 0.490273i
$$59$$ 30.7782 + 53.3094i 0.521664 + 0.903549i 0.999682 + 0.0251987i $$0.00802186\pi$$
−0.478018 + 0.878350i $$0.658645\pi$$
$$60$$ −20.7477 4.18710i −0.345795 0.0697850i
$$61$$ −32.6340 18.8412i −0.534983 0.308873i 0.208060 0.978116i $$-0.433285\pi$$
−0.743043 + 0.669243i $$0.766618\pi$$
$$62$$ 87.3970 + 33.0329i 1.40963 + 0.532790i
$$63$$ 0 0
$$64$$ 36.0000 52.9150i 0.562500 0.826797i
$$65$$ −1.20101 + 2.08021i −0.0184771 + 0.0320032i
$$66$$ −30.2253 + 4.94697i −0.457958 + 0.0749541i
$$67$$ 16.6863 + 28.9015i 0.249049 + 0.431366i 0.963262 0.268563i $$-0.0865486\pi$$
−0.714213 + 0.699928i $$0.753215\pi$$
$$68$$ −89.6899 + 30.1672i −1.31897 + 0.443636i
$$69$$ 120.265i 1.74297i
$$70$$ 0 0
$$71$$ 102.199i 1.43942i 0.694277 + 0.719708i $$0.255724\pi$$
−0.694277 + 0.719708i $$0.744276\pi$$
$$72$$ 0.784207 21.2404i 0.0108918 0.295005i
$$73$$ 34.6569 + 60.0274i 0.474751 + 0.822294i 0.999582 0.0289132i $$-0.00920463\pi$$
−0.524830 + 0.851207i $$0.675871\pi$$
$$74$$ 18.9246 + 115.627i 0.255738 + 1.56252i
$$75$$ 38.5772 66.8176i 0.514362 0.890901i
$$76$$ −74.6102 65.8000i −0.981713 0.865789i
$$77$$ 0 0
$$78$$ −9.89949 3.74166i −0.126917 0.0479700i
$$79$$ −33.5156 19.3503i −0.424248 0.244940i 0.272645 0.962115i $$-0.412102\pi$$
−0.696893 + 0.717175i $$0.745435\pi$$
$$80$$ −14.9859 19.7570i −0.187324 0.246963i
$$81$$ 48.9264 + 84.7430i 0.604030 + 1.04621i
$$82$$ 34.1618 + 41.7447i 0.416607 + 0.509081i
$$83$$ −3.61522 −0.0435569 −0.0217785 0.999763i $$-0.506933\pi$$
−0.0217785 + 0.999763i $$0.506933\pi$$
$$84$$ 0 0
$$85$$ 36.6645i 0.431347i
$$86$$ −21.7501 26.5779i −0.252908 0.309046i
$$87$$ 66.3799 38.3245i 0.762987 0.440511i
$$88$$ −30.3918 19.0754i −0.345362 0.216766i
$$89$$ 22.0294 38.1561i 0.247522 0.428720i −0.715316 0.698801i $$-0.753717\pi$$
0.962838 + 0.270081i $$0.0870505\pi$$
$$90$$ −7.70354 2.91166i −0.0855948 0.0323518i
$$91$$ 0 0
$$92$$ 93.1960 105.674i 1.01300 1.14863i
$$93$$ 138.129 + 79.7486i 1.48525 + 0.857512i
$$94$$ −11.6724 71.3164i −0.124174 0.758685i
$$95$$ −33.3807 + 19.2724i −0.351376 + 0.202867i
$$96$$ 75.2393 79.2191i 0.783743 0.825199i
$$97$$ −96.1076 −0.990800 −0.495400 0.868665i $$-0.664979\pi$$
−0.495400 + 0.868665i $$0.664979\pi$$
$$98$$ 0 0
$$99$$ −11.9167 −0.120371
$$100$$ 85.6754 28.8170i 0.856754 0.288170i
$$101$$ −16.9881 + 9.80808i −0.168199 + 0.0971097i −0.581736 0.813377i $$-0.697626\pi$$
0.413537 + 0.910487i $$0.364293\pi$$
$$102$$ −159.418 + 26.0920i −1.56292 + 0.255803i
$$103$$ 37.3120 + 21.5421i 0.362252 + 0.209146i 0.670068 0.742300i $$-0.266265\pi$$
−0.307816 + 0.951446i $$0.599598\pi$$
$$104$$ −5.79899 10.9591i −0.0557595 0.105376i
$$105$$ 0 0
$$106$$ 182.995 + 69.1656i 1.72637 + 0.652506i
$$107$$ −7.79899 + 13.5082i −0.0728878 + 0.126245i −0.900166 0.435547i $$-0.856555\pi$$
0.827278 + 0.561793i $$0.189888\pi$$
$$108$$ −17.1368 + 84.9155i −0.158674 + 0.786254i
$$109$$ 3.33576 1.92590i 0.0306033 0.0176688i −0.484620 0.874725i $$-0.661042\pi$$
0.515224 + 0.857056i $$0.327709\pi$$
$$110$$ −10.7594 + 8.80498i −0.0978130 + 0.0800453i
$$111$$ 200.013i 1.80192i
$$112$$ 0 0
$$113$$ −13.7746 −0.121899 −0.0609496 0.998141i $$-0.519413\pi$$
−0.0609496 + 0.998141i $$0.519413\pi$$
$$114$$ −107.552 131.425i −0.943437 1.15285i
$$115$$ −27.2965 47.2789i −0.237361 0.411121i
$$116$$ 88.0252 + 17.7644i 0.758838 + 0.153141i
$$117$$ −3.56604 2.05886i −0.0304790 0.0175971i
$$118$$ −43.5269 + 115.161i −0.368872 + 0.975944i
$$119$$ 0 0
$$120$$ −19.7990 37.4166i −0.164992 0.311805i
$$121$$ 50.4411 87.3666i 0.416869 0.722038i
$$122$$ −12.1730 74.3754i −0.0997789 0.609634i
$$123$$ 46.0416 + 79.7464i 0.374322 + 0.648345i
$$124$$ 59.5718 + 177.112i 0.480418 + 1.42833i
$$125$$ 73.7695i 0.590156i
$$126$$ 0 0
$$127$$ 125.025i 0.984445i 0.870469 + 0.492223i $$0.163815\pi$$
−0.870469 + 0.492223i $$0.836185\pi$$
$$128$$ 127.500 11.3035i 0.996093 0.0883088i
$$129$$ −29.3137 50.7728i −0.227238 0.393588i
$$130$$ −4.74096 + 0.775953i −0.0364689 + 0.00596887i
$$131$$ 50.1751 86.9059i 0.383016 0.663404i −0.608475 0.793573i $$-0.708219\pi$$
0.991492 + 0.130169i $$0.0415519\pi$$
$$132$$ −45.9411 40.5163i −0.348039 0.306941i
$$133$$ 0 0
$$134$$ −23.5980 + 62.4344i −0.176104 + 0.465928i
$$135$$ 29.0679 + 16.7824i 0.215318 + 0.124314i
$$136$$ −160.297 100.610i −1.17865 0.739780i
$$137$$ −28.6569 49.6351i −0.209174 0.362300i 0.742280 0.670089i $$-0.233744\pi$$
−0.951455 + 0.307789i $$0.900411\pi$$
$$138$$ 186.144 152.331i 1.34887 1.10385i
$$139$$ 183.664 1.32132 0.660662 0.750684i $$-0.270276\pi$$
0.660662 + 0.750684i $$0.270276\pi$$
$$140$$ 0 0
$$141$$ 123.365i 0.874926i
$$142$$ −158.182 + 129.448i −1.11395 + 0.911605i
$$143$$ −6.02017 + 3.47575i −0.0420991 + 0.0243059i
$$144$$ 33.8689 25.6899i 0.235200 0.178402i
$$145$$ 17.3970 30.1324i 0.119979 0.207810i
$$146$$ −49.0122 + 129.674i −0.335700 + 0.888179i
$$147$$ 0 0
$$148$$ −154.995 + 175.748i −1.04726 + 1.18748i
$$149$$ −166.545 96.1549i −1.11775 0.645335i −0.176927 0.984224i $$-0.556616\pi$$
−0.940826 + 0.338889i $$0.889949\pi$$
$$150$$ 152.282 24.9241i 1.01522 0.166161i
$$151$$ −99.3791 + 57.3765i −0.658140 + 0.379977i −0.791568 0.611081i $$-0.790735\pi$$
0.133428 + 0.991058i $$0.457401\pi$$
$$152$$ 7.34073 198.825i 0.0482943 1.30806i
$$153$$ −62.8528 −0.410803
$$154$$ 0 0
$$155$$ 72.4020 0.467110
$$156$$ −6.74773 20.0616i −0.0432547 0.128600i
$$157$$ 183.724 106.073i 1.17022 0.675625i 0.216486 0.976286i $$-0.430540\pi$$
0.953731 + 0.300661i $$0.0972071\pi$$
$$158$$ −12.5019 76.3847i −0.0791259 0.483447i
$$159$$ 289.219 + 166.981i 1.81899 + 1.05019i
$$160$$ 11.5980 48.2199i 0.0724874 0.301374i
$$161$$ 0 0
$$162$$ −69.1924 + 183.066i −0.427114 + 1.13004i
$$163$$ 120.267 208.309i 0.737835 1.27797i −0.215634 0.976474i $$-0.569182\pi$$
0.953469 0.301493i $$-0.0974849\pi$$
$$164$$ −21.3415 + 105.750i −0.130131 + 0.644819i
$$165$$ −20.5541 + 11.8669i −0.124571 + 0.0719208i
$$166$$ −4.57916 5.59560i −0.0275853 0.0337084i
$$167$$ 212.101i 1.27006i 0.772486 + 0.635032i $$0.219013\pi$$
−0.772486 + 0.635032i $$0.780987\pi$$
$$168$$ 0 0
$$169$$ 166.598 0.985787
$$170$$ −56.7488 + 46.4404i −0.333816 + 0.273179i
$$171$$ −33.0381 57.2236i −0.193205 0.334641i
$$172$$ 13.5877 67.3289i 0.0789980 0.391447i
$$173$$ −157.801 91.1065i −0.912145 0.526627i −0.0310245 0.999519i $$-0.509877\pi$$
−0.881121 + 0.472891i $$0.843210\pi$$
$$174$$ 143.397 + 54.1990i 0.824121 + 0.311488i
$$175$$ 0 0
$$176$$ −8.97056 71.2016i −0.0509691 0.404555i
$$177$$ −105.083 + 182.010i −0.593691 + 1.02830i
$$178$$ 86.9607 14.2329i 0.488543 0.0799599i
$$179$$ −28.6030 49.5419i −0.159793 0.276770i 0.775001 0.631960i $$-0.217749\pi$$
−0.934794 + 0.355190i $$0.884416\pi$$
$$180$$ −5.25091 15.6114i −0.0291717 0.0867302i
$$181$$ 326.212i 1.80228i −0.433533 0.901138i $$-0.642733\pi$$
0.433533 0.901138i $$-0.357267\pi$$
$$182$$ 0 0
$$183$$ 128.656i 0.703039i
$$184$$ 281.606 + 10.3971i 1.53047 + 0.0565058i
$$185$$ 45.3970 + 78.6299i 0.245389 + 0.425026i
$$186$$ 51.5243 + 314.806i 0.277012 + 1.69250i
$$187$$ −53.0538 + 91.8919i −0.283710 + 0.491401i
$$188$$ 95.5980 108.398i 0.508500 0.576585i
$$189$$ 0 0
$$190$$ −72.1106 27.2552i −0.379530 0.143449i
$$191$$ −84.0589 48.5314i −0.440099 0.254091i 0.263541 0.964648i $$-0.415110\pi$$
−0.703639 + 0.710557i $$0.748443\pi$$
$$192$$ 217.915 + 16.1130i 1.13497 + 0.0839221i
$$193$$ −78.6518 136.229i −0.407522 0.705849i 0.587089 0.809522i $$-0.300274\pi$$
−0.994611 + 0.103673i $$0.966940\pi$$
$$194$$ −121.733 148.754i −0.627490 0.766774i
$$195$$ −8.20101 −0.0420565
$$196$$ 0 0
$$197$$ 124.117i 0.630034i −0.949086 0.315017i $$-0.897990\pi$$
0.949086 0.315017i $$-0.102010\pi$$
$$198$$ −15.0941 18.4446i −0.0762329 0.0931544i
$$199$$ −156.729 + 90.4874i −0.787581 + 0.454710i −0.839110 0.543961i $$-0.816924\pi$$
0.0515289 + 0.998672i $$0.483591\pi$$
$$200$$ 153.122 + 96.1069i 0.765609 + 0.480534i
$$201$$ −56.9706 + 98.6759i −0.283436 + 0.490925i
$$202$$ −36.6985 13.8707i −0.181676 0.0686669i
$$203$$ 0 0
$$204$$ −242.309 213.696i −1.18779 1.04753i
$$205$$ 36.2000 + 20.9001i 0.176586 + 0.101952i
$$206$$ 13.9180 + 85.0368i 0.0675630 + 0.412800i
$$207$$ 81.0488 46.7935i 0.391540 0.226056i
$$208$$ 9.61710 22.8567i 0.0462361 0.109888i
$$209$$ −111.549 −0.533728
$$210$$ 0 0
$$211$$ 164.049 0.777482 0.388741 0.921347i $$-0.372910\pi$$
0.388741 + 0.921347i $$0.372910\pi$$
$$212$$ 124.734 + 370.844i 0.588366 + 1.74927i
$$213$$ −302.180 + 174.464i −1.41869 + 0.819079i
$$214$$ −30.7863 + 5.03880i −0.143861 + 0.0235458i
$$215$$ −23.0478 13.3066i −0.107199 0.0618913i
$$216$$ −153.137 + 81.0325i −0.708968 + 0.375151i
$$217$$ 0 0
$$218$$ 7.20606 + 2.72363i 0.0330553 + 0.0124937i
$$219$$ −118.326 + 204.946i −0.540301 + 0.935829i
$$220$$ −27.2565 5.50063i −0.123893 0.0250029i
$$221$$ −31.7524 + 18.3322i −0.143676 + 0.0829513i
$$222$$ −309.578 + 253.343i −1.39450 + 1.14119i
$$223$$ 10.5830i 0.0474574i −0.999718 0.0237287i $$-0.992446\pi$$
0.999718 0.0237287i $$-0.00755379\pi$$
$$224$$ 0 0
$$225$$ 60.0395 0.266842
$$226$$ −17.4474 21.3201i −0.0772007 0.0943369i
$$227$$ 52.9031 + 91.6308i 0.233053 + 0.403660i 0.958705 0.284402i $$-0.0917951\pi$$
−0.725652 + 0.688062i $$0.758462\pi$$
$$228$$ 67.1896 332.935i 0.294691 1.46024i
$$229$$ 64.8469 + 37.4394i 0.283174 + 0.163491i 0.634860 0.772628i $$-0.281058\pi$$
−0.351685 + 0.936118i $$0.614391\pi$$
$$230$$ 38.6030 102.134i 0.167839 0.444061i
$$231$$ 0 0
$$232$$ 84.0000 + 158.745i 0.362069 + 0.684246i
$$233$$ 209.569 362.983i 0.899436 1.55787i 0.0712190 0.997461i $$-0.477311\pi$$
0.828217 0.560408i $$-0.189356\pi$$
$$234$$ −1.33019 8.12729i −0.00568459 0.0347320i
$$235$$ −28.0000 48.4974i −0.119149 0.206372i
$$236$$ −233.378 + 78.4967i −0.988889 + 0.332613i
$$237$$ 132.132i 0.557518i
$$238$$ 0 0
$$239$$ 148.318i 0.620577i −0.950642 0.310288i $$-0.899574\pi$$
0.950642 0.310288i $$-0.100426\pi$$
$$240$$ 32.8348 78.0376i 0.136812 0.325157i
$$241$$ −229.936 398.261i −0.954092 1.65254i −0.736433 0.676510i $$-0.763492\pi$$
−0.217658 0.976025i $$-0.569842\pi$$
$$242$$ 199.115 32.5892i 0.822790 0.134666i
$$243$$ −69.5894 + 120.532i −0.286376 + 0.496018i
$$244$$ 99.6985 113.047i 0.408600 0.463309i
$$245$$ 0 0
$$246$$ −65.1127 + 172.272i −0.264686 + 0.700293i
$$247$$ −33.3807 19.2724i −0.135145 0.0780258i
$$248$$ −198.677 + 316.541i −0.801116 + 1.27637i
$$249$$ −6.17157 10.6895i −0.0247854 0.0429296i
$$250$$ 114.179 93.4388i 0.456718 0.373755i
$$251$$ −124.919 −0.497685 −0.248842 0.968544i $$-0.580050\pi$$
−0.248842 + 0.968544i $$0.580050\pi$$
$$252$$ 0 0
$$253$$ 157.993i 0.624478i
$$254$$ −193.511 + 158.360i −0.761856 + 0.623465i
$$255$$ −108.409 + 62.5902i −0.425135 + 0.245452i
$$256$$ 178.991 + 183.025i 0.699183 + 0.714943i
$$257$$ −213.676 + 370.098i −0.831425 + 1.44007i 0.0654835 + 0.997854i $$0.479141\pi$$
−0.896908 + 0.442216i $$0.854192\pi$$
$$258$$ 41.4558 109.682i 0.160682 0.425123i
$$259$$ 0 0
$$260$$ −7.20606 6.35515i −0.0277156 0.0244429i
$$261$$ 51.6552 + 29.8231i 0.197912 + 0.114265i
$$262$$ 198.065 32.4173i 0.755974 0.123730i
$$263$$ −223.109 + 128.812i −0.848322 + 0.489779i −0.860084 0.510152i $$-0.829589\pi$$
0.0117625 + 0.999931i $$0.496256\pi$$
$$264$$ 4.52005 122.426i 0.0171214 0.463736i
$$265$$ 151.598 0.572068
$$266$$ 0 0
$$267$$ 150.426 0.563395
$$268$$ −126.525 + 42.5567i −0.472108 + 0.158794i
$$269$$ −186.408 + 107.623i −0.692968 + 0.400085i −0.804723 0.593650i $$-0.797686\pi$$
0.111755 + 0.993736i $$0.464353\pi$$
$$270$$ 10.8428 + 66.2481i 0.0401586 + 0.245363i
$$271$$ −327.833 189.275i −1.20972 0.698431i −0.247020 0.969010i $$-0.579451\pi$$
−0.962698 + 0.270580i $$0.912785\pi$$
$$272$$ −47.3137 375.541i −0.173947 1.38067i
$$273$$ 0 0
$$274$$ 40.5269 107.224i 0.147908 0.391329i
$$275$$ 50.6791 87.7789i 0.184288 0.319196i
$$276$$ 471.553 + 95.1641i 1.70852 + 0.344798i
$$277$$ 144.149 83.2243i 0.520393 0.300449i −0.216703 0.976238i $$-0.569530\pi$$
0.737095 + 0.675789i $$0.236197\pi$$
$$278$$ 232.635 + 284.273i 0.836815 + 1.02256i
$$279$$ 124.117i 0.444863i
$$280$$ 0 0
$$281$$ −421.765 −1.50094 −0.750471 0.660904i $$-0.770173\pi$$
−0.750471 + 0.660904i $$0.770173\pi$$
$$282$$ 190.942 156.257i 0.677099 0.554104i
$$283$$ −172.719 299.159i −0.610316 1.05710i −0.991187 0.132470i $$-0.957709\pi$$
0.380872 0.924628i $$-0.375624\pi$$
$$284$$ −400.716 80.8685i −1.41097 0.284748i
$$285$$ −113.969 65.8000i −0.399891 0.230877i
$$286$$ −13.0051 4.91545i −0.0454722 0.0171869i
$$287$$ 0 0
$$288$$ 82.6619 + 19.8821i 0.287021 + 0.0690350i
$$289$$ −135.323 + 234.387i −0.468247 + 0.811028i
$$290$$ 68.6741 11.2399i 0.236807 0.0387583i
$$291$$ −164.066 284.171i −0.563801 0.976532i
$$292$$ −262.788 + 88.3889i −0.899960 + 0.302702i
$$293$$ 511.038i 1.74416i 0.489365 + 0.872079i $$0.337229\pi$$
−0.489365 + 0.872079i $$0.662771\pi$$
$$294$$ 0 0
$$295$$ 95.4028i 0.323399i
$$296$$ −468.342 17.2914i −1.58224 0.0584170i
$$297$$ 48.5685 + 84.1232i 0.163530 + 0.283243i
$$298$$ −62.1241 379.569i −0.208470 1.27372i
$$299$$ 27.2965 47.2789i 0.0912925 0.158123i
$$300$$ 231.463 + 204.131i 0.771543 + 0.680437i
$$301$$ 0 0
$$302$$ −214.683 81.1427i −0.710872 0.268684i
$$303$$ −58.0010 33.4869i −0.191422 0.110518i
$$304$$ 317.037 240.476i 1.04288 0.791040i
$$305$$ −29.2010 50.5776i −0.0957410 0.165828i
$$306$$ −79.6114 97.2828i −0.260168 0.317917i
$$307$$ −223.331 −0.727462 −0.363731 0.931504i $$-0.618497\pi$$
−0.363731 + 0.931504i $$0.618497\pi$$
$$308$$ 0 0
$$309$$ 147.098i 0.476047i
$$310$$ 91.7067 + 112.063i 0.295828 + 0.361493i
$$311$$ −10.7376 + 6.19938i −0.0345262 + 0.0199337i −0.517164 0.855886i $$-0.673012\pi$$
0.482638 + 0.875820i $$0.339679\pi$$
$$312$$ 22.5042 35.8547i 0.0721289 0.114919i
$$313$$ 205.024 355.113i 0.655030 1.13455i −0.326856 0.945074i $$-0.605989\pi$$
0.981886 0.189471i $$-0.0606774\pi$$
$$314$$ 396.889 + 150.010i 1.26398 + 0.477739i
$$315$$ 0 0
$$316$$ 102.392 116.102i 0.324025 0.367410i
$$317$$ −112.857 65.1580i −0.356016 0.205546i 0.311316 0.950306i $$-0.399230\pi$$
−0.667332 + 0.744761i $$0.732564\pi$$
$$318$$ 107.883 + 659.152i 0.339256 + 2.07280i
$$319$$ 87.2038 50.3472i 0.273366 0.157828i
$$320$$ 89.3244 43.1256i 0.279139 0.134768i
$$321$$ −53.2548 −0.165903
$$322$$ 0 0
$$323$$ −588.347 −1.82151
$$324$$ −370.988 + 124.782i −1.14503 + 0.385130i
$$325$$ 30.3311 17.5117i 0.0933266 0.0538821i
$$326$$ 474.751 77.7026i 1.45629 0.238351i
$$327$$ 11.3890 + 6.57544i 0.0348287 + 0.0201084i
$$328$$ −190.711 + 100.915i −0.581435 + 0.307666i
$$329$$ 0 0
$$330$$ −44.4020 16.7824i −0.134552 0.0508557i
$$331$$ −107.130 + 185.555i −0.323655 + 0.560588i −0.981239 0.192794i $$-0.938245\pi$$
0.657584 + 0.753381i $$0.271579\pi$$
$$332$$ 2.86068 14.1751i 0.00861651 0.0426961i
$$333$$ −134.793 + 77.8227i −0.404783 + 0.233702i
$$334$$ −328.287 + 268.653i −0.982894 + 0.804352i
$$335$$ 51.7223i 0.154395i
$$336$$ 0 0
$$337$$ 164.049 0.486792 0.243396 0.969927i $$-0.421739\pi$$
0.243396 + 0.969927i $$0.421739\pi$$
$$338$$ 211.018 + 257.858i 0.624314 + 0.762894i
$$339$$ −23.5147 40.7287i −0.0693650 0.120144i
$$340$$ −143.760 29.0121i −0.422822 0.0853298i
$$341$$ 181.461 + 104.766i 0.532143 + 0.307233i
$$342$$ 46.7229 123.617i 0.136617 0.361454i
$$343$$ 0 0
$$344$$ 121.421 64.2501i 0.352969 0.186774i
$$345$$ 93.1960 161.420i 0.270133 0.467884i
$$346$$ −58.8625 359.641i −0.170123 1.03942i
$$347$$ 54.8457 + 94.9955i 0.158057 + 0.273762i 0.934168 0.356834i $$-0.116144\pi$$
−0.776111 + 0.630596i $$0.782810\pi$$
$$348$$ 97.7427 + 290.598i 0.280870 + 0.835052i
$$349$$ 463.479i 1.32802i 0.747723 + 0.664010i $$0.231147\pi$$
−0.747723 + 0.664010i $$0.768853\pi$$
$$350$$ 0 0
$$351$$ 33.5648i 0.0956261i
$$352$$ 98.8425 104.071i 0.280803 0.295656i
$$353$$ 39.0488 + 67.6345i 0.110620 + 0.191599i 0.916020 0.401132i $$-0.131383\pi$$
−0.805401 + 0.592731i $$0.798050\pi$$
$$354$$ −414.814 + 67.8926i −1.17179 + 0.191787i
$$355$$ −79.1960 + 137.171i −0.223087 + 0.386398i
$$356$$ 132.177 + 116.569i 0.371283 + 0.327441i
$$357$$ 0 0
$$358$$ 40.4508 107.023i 0.112991 0.298946i
$$359$$ −316.198 182.557i −0.880774 0.508515i −0.00986020 0.999951i $$-0.503139\pi$$
−0.870913 + 0.491437i $$0.836472\pi$$
$$360$$ 17.5122 27.9012i 0.0486450 0.0775034i
$$361$$ −128.760 223.019i −0.356676 0.617780i
$$362$$ 504.906 413.190i 1.39477 1.14141i
$$363$$ 344.434 0.948853
$$364$$ 0 0
$$365$$ 107.426i 0.294316i
$$366$$ 199.132 162.960i 0.544077 0.445245i
$$367$$ 191.165 110.369i 0.520887 0.300734i −0.216411 0.976302i $$-0.569435\pi$$
0.737297 + 0.675568i $$0.236102\pi$$
$$368$$ 340.599 + 449.036i 0.925541 + 1.22021i
$$369$$ −35.8284 + 62.0567i −0.0970960 + 0.168175i
$$370$$ −64.2010 + 169.860i −0.173516 + 0.459081i
$$371$$ 0 0
$$372$$ −421.990 + 478.492i −1.13438 + 1.28627i
$$373$$ 217.852 + 125.777i 0.584052 + 0.337203i 0.762742 0.646703i $$-0.223853\pi$$
−0.178690 + 0.983905i $$0.557186\pi$$
$$374$$ −209.429 + 34.2772i −0.559970 + 0.0916503i
$$375$$ 218.121 125.932i 0.581657 0.335820i
$$376$$ 288.864 + 10.6650i 0.768256 + 0.0283645i
$$377$$ 34.7939 0.0922916
$$378$$ 0 0
$$379$$ 286.024 0.754682 0.377341 0.926074i $$-0.376839\pi$$
0.377341 + 0.926074i $$0.376839\pi$$
$$380$$ −49.1523 146.134i −0.129348 0.384564i
$$381$$ −369.672 + 213.430i −0.970268 + 0.560184i
$$382$$ −31.3554 191.577i −0.0820821 0.501509i
$$383$$ 92.5727 + 53.4468i 0.241704 + 0.139548i 0.615960 0.787778i $$-0.288768\pi$$
−0.374256 + 0.927326i $$0.622102\pi$$
$$384$$ 251.078 + 357.695i 0.653850 + 0.931497i
$$385$$ 0 0
$$386$$ 111.230 294.288i 0.288162 0.762404i
$$387$$ 22.8112 39.5101i 0.0589436 0.102093i
$$388$$ 76.0488 376.833i 0.196002 0.971220i
$$389$$ −66.8405 + 38.5904i −0.171826 + 0.0992040i −0.583447 0.812151i $$-0.698296\pi$$
0.411620 + 0.911355i $$0.364963\pi$$
$$390$$ −10.3877 12.6934i −0.0266350 0.0325472i
$$391$$ 833.307i 2.13122i
$$392$$ 0 0
$$393$$ 342.617 0.871800
$$394$$ 192.106 157.210i 0.487579 0.399010i
$$395$$ −29.9899 51.9440i −0.0759238 0.131504i
$$396$$ 9.42957 46.7250i 0.0238120 0.117992i
$$397$$ 569.424 + 328.757i 1.43432 + 0.828103i 0.997446 0.0714218i $$-0.0227536\pi$$
0.436870 + 0.899525i $$0.356087\pi$$
$$398$$ −338.573 127.968i −0.850685 0.321529i
$$399$$ 0 0
$$400$$ 45.1960 + 358.732i 0.112990 + 0.896830i
$$401$$ −159.397 + 276.084i −0.397499 + 0.688488i −0.993417 0.114557i $$-0.963455\pi$$
0.595918 + 0.803045i $$0.296788\pi$$
$$402$$ −224.890 + 36.8078i −0.559428 + 0.0915616i
$$403$$ 36.2010 + 62.7020i 0.0898288 + 0.155588i
$$404$$ −25.0145 74.3705i −0.0619172 0.184085i
$$405$$ 151.657i 0.374461i
$$406$$ 0 0
$$407$$ 262.759i 0.645600i
$$408$$ 23.8402 645.716i 0.0584319 1.58264i
$$409$$ 72.6325 + 125.803i 0.177585 + 0.307587i 0.941053 0.338259i $$-0.109838\pi$$
−0.763468 + 0.645846i $$0.776505\pi$$
$$410$$ 13.5032 + 82.5027i 0.0329347 + 0.201226i
$$411$$ 97.8406 169.465i 0.238055 0.412323i
$$412$$ −113.990 + 129.252i −0.276675 + 0.313719i
$$413$$ 0 0
$$414$$ 175.085 + 66.1760i 0.422911 + 0.159846i
$$415$$ −4.85237 2.80152i −0.0116925 0.00675065i
$$416$$ 47.5586 14.0658i 0.114324 0.0338120i
$$417$$ 313.534 + 543.057i 0.751880 + 1.30229i
$$418$$ −141.292 172.654i −0.338019 0.413049i
$$419$$ −707.012 −1.68738 −0.843690 0.536831i $$-0.819621\pi$$
−0.843690 + 0.536831i $$0.819621\pi$$
$$420$$ 0 0
$$421$$ 121.989i 0.289761i 0.989449 + 0.144880i $$0.0462798\pi$$
−0.989449 + 0.144880i $$0.953720\pi$$
$$422$$ 207.789 + 253.913i 0.492392 + 0.601688i
$$423$$ 83.1377 47.9996i 0.196543 0.113474i
$$424$$ −415.997 + 662.784i −0.981124 + 1.56317i
$$425$$ 267.299 462.975i 0.628938 1.08935i
$$426$$ −652.784 246.729i −1.53236 0.579176i
$$427$$ 0 0
$$428$$ −46.7939 41.2684i −0.109332 0.0964214i
$$429$$ −20.5541 11.8669i −0.0479118 0.0276619i
$$430$$ −8.59720 52.5277i −0.0199935 0.122157i
$$431$$ −509.969 + 294.431i −1.18322 + 0.683133i −0.956758 0.290886i $$-0.906050\pi$$
−0.226464 + 0.974020i $$0.572717\pi$$
$$432$$ −319.389 134.385i −0.739327 0.311077i
$$433$$ −137.696 −0.318004 −0.159002 0.987278i $$-0.550828\pi$$
−0.159002 + 0.987278i $$0.550828\pi$$
$$434$$ 0 0
$$435$$ 118.794 0.273090
$$436$$ 4.91182 + 14.6033i 0.0112656 + 0.0334938i
$$437$$ 758.675 438.021i 1.73610 1.00234i
$$438$$ −467.089 + 76.4485i −1.06641 + 0.174540i
$$439$$ −381.522 220.272i −0.869070 0.501758i −0.00203069 0.999998i $$-0.500646\pi$$
−0.867039 + 0.498240i $$0.833980\pi$$
$$440$$ −26.0101 49.1545i −0.0591139 0.111715i
$$441$$ 0 0
$$442$$ −68.5929 25.9257i −0.155188 0.0586554i
$$443$$ 243.529 421.805i 0.549727 0.952155i −0.448566 0.893750i $$-0.648065\pi$$
0.998293 0.0584052i $$-0.0186015\pi$$
$$444$$ −784.243 158.268i −1.76631 0.356460i
$$445$$ 59.1361 34.1422i 0.132890 0.0767241i
$$446$$ 16.3802 13.4048i 0.0367270 0.0300555i
$$447$$ 656.587i 1.46887i
$$448$$ 0 0
$$449$$ 264.039 0.588059 0.294030 0.955796i $$-0.405004\pi$$
0.294030 + 0.955796i $$0.405004\pi$$
$$450$$ 76.0480 + 92.9284i 0.168996 + 0.206508i
$$451$$ 60.4853 + 104.764i 0.134114 + 0.232292i
$$452$$ 10.8997 54.0096i 0.0241143 0.119490i
$$453$$ −339.301 195.896i −0.749010 0.432441i
$$454$$ −74.8162 + 197.945i −0.164793 + 0.436003i
$$455$$ 0 0
$$456$$ 600.416 317.710i 1.31670 0.696733i
$$457$$ 257.161 445.417i 0.562717 0.974654i −0.434542 0.900652i $$-0.643090\pi$$
0.997258 0.0740019i $$-0.0235771\pi$$
$$458$$ 24.1890 + 147.791i 0.0528144 + 0.322688i
$$459$$ 256.167 + 443.693i 0.558097 + 0.966652i
$$460$$ 206.978 69.6169i 0.449951 0.151341i
$$461$$ 202.224i 0.438664i 0.975650 + 0.219332i $$0.0703878\pi$$
−0.975650 + 0.219332i $$0.929612\pi$$
$$462$$ 0 0
$$463$$ 722.653i 1.56081i −0.625277 0.780403i $$-0.715014\pi$$
0.625277 0.780403i $$-0.284986\pi$$
$$464$$ −139.306 + 331.086i −0.300229 + 0.713547i
$$465$$ 123.598 + 214.078i 0.265802 + 0.460383i
$$466$$ 827.267 135.399i 1.77525 0.290555i
$$467$$ −173.641 + 300.755i −0.371822 + 0.644015i −0.989846 0.142144i $$-0.954600\pi$$
0.618023 + 0.786160i $$0.287934\pi$$
$$468$$ 10.8944 12.3531i 0.0232787 0.0263956i
$$469$$ 0 0
$$470$$ 39.5980 104.766i 0.0842510 0.222907i
$$471$$ 627.273 + 362.156i 1.33179 + 0.768910i
$$472$$ −417.100 261.793i −0.883686 0.554646i
$$473$$ −38.5097 66.7007i −0.0814158 0.141016i
$$474$$ 204.512 167.362i 0.431460 0.353085i
$$475$$ 562.013 1.18319
$$476$$ 0 0
$$477$$ 259.880i 0.544822i
$$478$$ 229.564 187.864i 0.480260 0.393021i
$$479$$ −25.2716 + 14.5906i −0.0527591 + 0.0304605i −0.526148 0.850393i $$-0.676364\pi$$
0.473388 + 0.880854i $$0.343031\pi$$
$$480$$ 162.375 48.0236i 0.338282 0.100049i
$$481$$ −45.3970 + 78.6299i −0.0943804 + 0.163472i
$$482$$ 325.179 860.342i 0.674645 1.78494i
$$483$$ 0 0
$$484$$ 302.647 + 266.909i 0.625303 + 0.551466i
$$485$$ −128.996 74.4760i −0.265972 0.153559i
$$486$$ −274.702 + 44.9606i −0.565231 + 0.0925114i
$$487$$ 607.640 350.821i 1.24772 0.720372i 0.277067 0.960851i $$-0.410638\pi$$
0.970654 + 0.240478i $$0.0773043\pi$$
$$488$$ 301.255 + 11.1225i 0.617325 + 0.0227920i
$$489$$ 821.235 1.67942
$$490$$ 0 0
$$491$$ −59.9512 −0.122100 −0.0610501 0.998135i $$-0.519445\pi$$
−0.0610501 + 0.998135i $$0.519445\pi$$
$$492$$ −349.114 + 117.425i −0.709582 + 0.238668i
$$493$$ 459.942 265.548i 0.932945 0.538636i
$$494$$ −12.4516 76.0772i −0.0252056 0.154003i
$$495$$ −15.9947 9.23455i −0.0323125 0.0186557i
$$496$$ −741.588 + 93.4313i −1.49514 + 0.188370i
$$497$$ 0 0
$$498$$ 8.72792 23.0919i 0.0175259 0.0463693i
$$499$$ 42.1421 72.9923i 0.0844532 0.146277i −0.820705 0.571352i $$-0.806419\pi$$
0.905158 + 0.425075i $$0.139752\pi$$
$$500$$ 289.247 + 58.3729i 0.578493 + 0.116746i
$$501$$ −627.138 + 362.079i −1.25177 + 0.722712i
$$502$$ −158.226 193.348i −0.315192 0.385155i
$$503$$ 409.987i 0.815083i −0.913187 0.407542i $$-0.866386\pi$$
0.913187 0.407542i $$-0.133614\pi$$
$$504$$ 0 0
$$505$$ −30.4020 −0.0602020
$$506$$ 244.539 200.119i 0.483280 0.395492i
$$507$$ 284.401 + 492.596i 0.560948 + 0.971590i
$$508$$ −490.215 98.9304i −0.964991 0.194745i
$$509$$ 413.123 + 238.516i 0.811636 + 0.468598i 0.847524 0.530758i $$-0.178093\pi$$
−0.0358878 + 0.999356i $$0.511426\pi$$
$$510$$ −234.191 88.5158i −0.459198 0.173560i
$$511$$ 0 0
$$512$$ −56.5685 + 508.865i −0.110485 + 0.993878i
$$513$$ −269.304 + 466.448i −0.524958 + 0.909254i
$$514$$ −843.482 + 138.053i −1.64102 + 0.268585i
$$515$$ 33.3869 + 57.8278i 0.0648289 + 0.112287i
$$516$$ 222.273 74.7617i 0.430762 0.144887i
$$517$$ 162.065i 0.313472i
$$518$$ 0 0
$$519$$ 622.114i 1.19868i
$$520$$ 0.708989 19.2031i 0.00136344 0.0369290i
$$521$$ 105.437 + 182.621i 0.202373 + 0.350521i 0.949293 0.314394i $$-0.101801\pi$$
−0.746919 + 0.664915i $$0.768468\pi$$
$$522$$ 19.2682 + 117.726i 0.0369123 + 0.225529i
$$523$$ 255.783 443.030i 0.489069 0.847093i −0.510852 0.859669i $$-0.670670\pi$$
0.999921 + 0.0125761i $$0.00400319\pi$$
$$524$$ 301.051 + 265.502i 0.574525 + 0.506683i
$$525$$ 0 0
$$526$$ −481.970 182.167i −0.916292 0.346326i
$$527$$ 957.084 + 552.573i 1.81610 + 1.04852i
$$528$$ 195.215 148.073i 0.369725 0.280441i
$$529$$ 355.892 + 616.423i 0.672764 + 1.16526i
$$530$$ 192.019 + 234.641i 0.362300 + 0.442720i
$$531$$ −163.546 −0.307997
$$532$$ 0 0
$$533$$ 41.8002i 0.0784244i
$$534$$ 190.535 + 232.828i 0.356807 + 0.436007i
$$535$$ −20.9357 + 12.0872i −0.0391321 + 0.0225929i
$$536$$ −226.129 141.930i −0.421883 0.264795i
$$537$$ 97.6569 169.147i 0.181856 0.314984i
$$538$$ −402.688 152.202i −0.748491 0.282903i
$$539$$ 0 0
$$540$$ −88.8040 + 100.694i −0.164452 + 0.186471i
$$541$$ −296.542 171.208i −0.548136 0.316466i 0.200234 0.979748i $$-0.435830\pi$$
−0.748370 + 0.663282i $$0.769163\pi$$
$$542$$ −122.287 747.157i −0.225622 1.37852i
$$543$$ 964.542 556.878i 1.77632 1.02556i
$$544$$ 521.328 548.904i 0.958324 1.00901i
$$545$$ 5.96970 0.0109536
$$546$$ 0 0
$$547$$ −441.976 −0.807999 −0.404000 0.914759i $$-0.632380\pi$$
−0.404000 + 0.914759i $$0.632380\pi$$
$$548$$ 217.293 73.0865i 0.396520 0.133369i
$$549$$ 86.7038 50.0584i 0.157930 0.0911811i
$$550$$ 200.055 32.7430i 0.363736 0.0595327i
$$551$$ 483.529 + 279.166i 0.877548 + 0.506653i
$$552$$ 449.990 + 850.401i 0.815199 + 1.54058i
$$553$$ 0 0
$$554$$ 311.397 + 117.697i 0.562088 + 0.212449i
$$555$$ −154.995 + 268.459i −0.279270 + 0.483710i
$$556$$ −145.331 + 720.138i −0.261387 + 1.29521i
$$557$$ 316.714 182.855i 0.568607 0.328285i −0.187986 0.982172i $$-0.560196\pi$$
0.756593 + 0.653886i $$0.226863\pi$$
$$558$$ −192.106 + 157.210i −0.344276 + 0.281739i
$$559$$ 26.6133i 0.0476087i
$$560$$ 0 0
$$561$$ −362.274 −0.645765
$$562$$ −534.220 652.802i −0.950570 1.16157i
$$563$$ 403.194 + 698.353i 0.716154 + 1.24041i 0.962513 + 0.271236i $$0.0874323\pi$$
−0.246359 + 0.969179i $$0.579234\pi$$
$$564$$ 483.706 + 97.6169i 0.857636 + 0.173080i
$$565$$ −18.4883 10.6743i −0.0327227 0.0188925i
$$566$$ 244.262 646.256i 0.431558 1.14180i
$$567$$ 0 0
$$568$$ −382.392 722.653i −0.673225 1.27228i
$$569$$ −111.446 + 193.030i −0.195862 + 0.339244i −0.947183 0.320694i $$-0.896084\pi$$
0.751320 + 0.659938i $$0.229417\pi$$
$$570$$ −42.5123 259.744i −0.0745830 0.455691i
$$571$$ −286.541 496.304i −0.501823 0.869184i −0.999998 0.00210683i $$-0.999329\pi$$
0.498174 0.867077i $$-0.334004\pi$$
$$572$$ −8.86455 26.3551i −0.0154975 0.0460754i
$$573$$ 331.393i 0.578348i
$$574$$ 0 0
$$575$$ 796.008i 1.38436i
$$576$$ 73.9290 + 153.126i 0.128349 + 0.265844i
$$577$$ −361.950 626.916i −0.627297 1.08651i −0.988092 0.153865i $$-0.950828\pi$$
0.360795 0.932645i $$-0.382505\pi$$
$$578$$ −534.186 + 87.4302i −0.924197 + 0.151263i
$$579$$ 268.534 465.115i 0.463789 0.803307i
$$580$$ 104.382 + 92.0561i 0.179969 + 0.158717i
$$581$$ 0 0
$$582$$ 232.024 613.879i 0.398667 1.05477i
$$583$$ 379.949 + 219.364i 0.651714 + 0.376267i
$$584$$ −469.663 294.784i −0.804218 0.504767i
$$585$$ −3.19091 5.52682i −0.00545455 0.00944755i
$$586$$ −790.978 + 647.297i −1.34979 + 1.10460i
$$587$$ −21.1198 −0.0359793 −0.0179896 0.999838i $$-0.505727\pi$$
−0.0179896 + 0.999838i $$0.505727\pi$$
$$588$$ 0 0
$$589$$ 1161.82i 1.97253i
$$590$$ −147.663 + 120.840i −0.250277 + 0.204814i
$$591$$ 366.988 211.880i 0.620960 0.358512i
$$592$$ −566.453 746.795i −0.956846 1.26148i
$$593$$ −64.3726 + 111.497i −0.108554 + 0.188021i −0.915185 0.403035i $$-0.867955\pi$$
0.806631 + 0.591056i $$0.201289\pi$$
$$594$$ −68.6863 + 181.727i −0.115633 + 0.305937i
$$595$$ 0 0
$$596$$ 508.804 576.930i 0.853698 0.968003i
$$597$$ −535.105 308.943i −0.896324 0.517493i
$$598$$ 107.752 17.6358i 0.180188 0.0294913i
$$599$$ −280.705 + 162.065i −0.468623 + 0.270559i −0.715663 0.698446i $$-0.753875\pi$$
0.247040 + 0.969005i $$0.420542\pi$$
$$600$$ −22.7731 + 616.814i −0.0379552 + 1.02802i
$$601$$ 721.862 1.20110 0.600551 0.799587i $$-0.294948\pi$$
0.600551 + 0.799587i $$0.294948\pi$$
$$602$$ 0 0
$$603$$ −88.6661 −0.147042
$$604$$ −146.333 435.062i −0.242273 0.720301i
$$605$$ 135.405 78.1759i 0.223809 0.129216i
$$606$$ −21.6353 132.189i −0.0357019 0.218133i
$$607$$ −611.413 353.000i −1.00727 0.581548i −0.0968795 0.995296i $$-0.530886\pi$$
−0.910391 + 0.413748i $$0.864219\pi$$
$$608$$ 773.775 + 186.110i 1.27266 + 0.306103i
$$609$$ 0 0
$$610$$ 41.2965 109.260i 0.0676991 0.179115i
$$611$$ 28.0000 48.4974i 0.0458265 0.0793739i
$$612$$ 49.7347 246.443i 0.0812658 0.402684i
$$613$$ −18.9026 + 10.9134i −0.0308363 + 0.0178033i −0.515339 0.856986i $$-0.672334\pi$$
0.484503 + 0.874790i $$0.339001\pi$$
$$614$$ −282.878 345.669i −0.460713 0.562978i
$$615$$ 142.715i 0.232057i
$$616$$ 0 0
$$617$$ −699.578 −1.13384 −0.566919 0.823774i $$-0.691865\pi$$
−0.566919 + 0.823774i $$0.691865\pi$$
$$618$$ −227.677 + 186.320i −0.368409 + 0.301488i
$$619$$ 48.0990 + 83.3100i 0.0777044 + 0.134588i 0.902259 0.431194i $$-0.141908\pi$$
−0.824555 + 0.565782i $$0.808574\pi$$
$$620$$ −57.2908 + 283.885i −0.0924046 + 0.457879i
$$621$$ −660.654 381.429i −1.06386 0.614217i
$$622$$ −23.1960 8.76725i −0.0372925 0.0140953i
$$623$$ 0 0
$$624$$ 84.0000 10.5830i 0.134615 0.0169599i
$$625$$ −225.309 + 390.247i −0.360495 + 0.624395i
$$626$$ 809.329 132.463i 1.29286 0.211602i
$$627$$ −190.426 329.828i −0.303710 0.526042i
$$628$$ 270.529 + 804.308i 0.430779 + 1.28074i
$$629$$ 1385.88i 2.20331i
$$630$$ 0 0
$$631$$ 269.399i 0.426940i −0.976950 0.213470i $$-0.931523\pi$$
0.976950 0.213470i $$-0.0684766\pi$$
$$632$$ 309.393 + 11.4230i 0.489546 + 0.0180743i
$$633$$ 280.049 + 485.059i 0.442415 + 0.766285i
$$634$$ −42.0975 257.210i −0.0663999 0.405694i
$$635$$ −96.8843 + 167.809i −0.152574 + 0.264266i
$$636$$ −883.578 + 1001.88i −1.38927 + 1.57529i
$$637$$ 0 0
$$638$$ 188.382 + 71.2016i 0.295269 + 0.111601i
$$639$$ −235.149 135.763i −0.367995 0.212462i
$$640$$ 179.890 + 83.6309i 0.281079 + 0.130673i
$$641$$ −317.907 550.630i −0.495954 0.859018i 0.504035 0.863683i $$-0.331848\pi$$
−0.999989 + 0.00466541i $$0.998515\pi$$
$$642$$ −67.4543 82.4271i −0.105069 0.128391i
$$643$$ −1281.70 −1.99332 −0.996658 0.0816828i $$-0.973971\pi$$
−0.996658 + 0.0816828i $$0.973971\pi$$
$$644$$ 0 0
$$645$$ 90.8634i 0.140874i
$$646$$ −745.219 910.636i −1.15359 1.40965i
$$647$$ −225.826 + 130.381i −0.349035 + 0.201516i −0.664260 0.747501i $$-0.731253\pi$$
0.315225 + 0.949017i $$0.397920\pi$$
$$648$$ −663.041 416.158i −1.02321 0.642219i
$$649$$ −138.049 + 239.107i −0.212710 + 0.368424i
$$650$$ 65.5227 + 24.7653i 0.100804 + 0.0381004i
$$651$$ 0 0
$$652$$ 721.602 + 636.393i 1.10675 + 0.976063i
$$653$$ −944.471 545.291i −1.44636 0.835055i −0.448095 0.893986i $$-0.647897\pi$$
−0.998262 + 0.0589313i $$0.981231\pi$$
$$654$$ 4.24828 + 25.9564i 0.00649585 + 0.0396887i
$$655$$ 134.691 77.7637i 0.205635 0.118723i
$$656$$ −397.754 167.358i −0.606333 0.255119i
$$657$$ −184.156 −0.280299
$$658$$ 0 0
$$659$$ −362.780 −0.550500 −0.275250 0.961373i $$-0.588761\pi$$
−0.275250 + 0.961373i $$0.588761\pi$$
$$660$$ −30.2655 89.9820i −0.0458567 0.136336i
$$661$$ 102.047 58.9169i 0.154383 0.0891330i −0.420818 0.907145i $$-0.638257\pi$$
0.575201 + 0.818012i $$0.304924\pi$$
$$662$$ −422.893 + 69.2149i −0.638811 + 0.104554i
$$663$$ −108.409 62.5902i −0.163513 0.0944045i
$$664$$ 25.5635 13.5269i 0.0384992 0.0203719i
$$665$$ 0 0
$$666$$ −291.186 110.058i −0.437216 0.165252i
$$667$$ −395.397 + 684.848i −0.592799 + 1.02676i
$$668$$ −831.637 167.833i −1.24496 0.251247i
$$669$$ 31.2918 18.0663i 0.0467740 0.0270050i
$$670$$ −80.0552 + 65.5132i −0.119485 + 0.0977808i
$$671$$ 169.017i 0.251888i
$$672$$ 0 0
$$673$$ −6.56854 −0.00976009 −0.00488005 0.999988i $$-0.501553\pi$$
−0.00488005 + 0.999988i $$0.501553\pi$$
$$674$$ 207.789 + 253.913i 0.308293 + 0.376725i
$$675$$ −244.701 423.834i −0.362519 0.627902i
$$676$$ −131.827 + 653.223i −0.195010 + 0.966306i
$$677$$ −108.942 62.8978i −0.160919 0.0929066i 0.417378 0.908733i $$-0.362949\pi$$
−0.578297 + 0.815826i $$0.696282\pi$$
$$678$$ 33.2548 87.9840i 0.0490484 0.129770i
$$679$$ 0 0
$$680$$ −137.186 259.257i −0.201744 0.381260i
$$681$$ −180.622 + 312.847i −0.265231 + 0.459394i
$$682$$ 67.6879 + 413.563i 0.0992491 + 0.606397i
$$683$$ 276.887 + 479.583i 0.405399 + 0.702171i 0.994368 0.105984i $$-0.0337994\pi$$
−0.588969 + 0.808156i $$0.700466\pi$$
$$684$$ 250.514 84.2603i 0.366248 0.123188i
$$685$$ 88.8274i 0.129675i
$$686$$ 0 0
$$687$$ 255.652i 0.372128i
$$688$$ 253.242 + 106.553i 0.368084 + 0.154874i
$$689$$ 75.7990 + 131.288i 0.110013 + 0.190548i
$$690$$ 367.889 60.2124i 0.533172 0.0872644i
$$691$$ −523.413 + 906.577i −0.757471 + 1.31198i 0.186665 + 0.982424i $$0.440232\pi$$
−0.944136 + 0.329555i $$0.893101\pi$$
$$692$$ 482.090 546.639i 0.696662 0.789941i
$$693$$ 0 0
$$694$$ −77.5635 + 205.214i −0.111763 + 0.295697i
$$695$$ 246.515 + 142.325i 0.354698 + 0.204785i
$$696$$ −325.980 + 519.366i −0.468362 + 0.746215i
$$697$$ 319.019 + 552.558i 0.457703 + 0.792766i
$$698$$ −717.367 + 587.058i −1.02775 + 0.841057i
$$699$$ 1431.02 2.04724
$$700$$ 0 0
$$701$$ 625.993i 0.893000i 0.894784 + 0.446500i $$0.147330\pi$$
−0.894784 + 0.446500i $$0.852670\pi$$
$$702$$ −51.9511 + 42.5142i −0.0740044 + 0.0605615i
$$703$$ −1261.76 + 728.476i −1.79482 + 1.03624i
$$704$$ 286.276 + 21.1678i 0.406643 + 0.0300680i
$$705$$ 95.5980 165.581i 0.135600 0.234866i
$$706$$ −55.2233 + 146.107i −0.0782200 + 0.206951i
$$707$$ 0 0
$$708$$ −630.500 556.048i −0.890536 0.785379i
$$709$$ 513.979 + 296.746i 0.724935 + 0.418541i 0.816566 0.577252i $$-0.195875\pi$$
−0.0916314 + 0.995793i $$0.529208\pi$$
$$710$$ −312.624 + 51.1672i −0.440316 + 0.0720665i
$$711$$ 89.0461 51.4108i 0.125241 0.0723077i
$$712$$ −13.0046 + 352.231i −0.0182649 + 0.494706i
$$713$$ −1645.55 −2.30792
$$714$$ 0 0
$$715$$ −10.7737 −0.0150682
$$716$$ 216.885 72.9492i 0.302912 0.101884i
$$717$$ 438.546 253.194i 0.611640 0.353130i
$$718$$ −117.947 720.639i −0.164272 1.00368i
$$719$$ 529.578 + 305.752i 0.736549 + 0.425247i 0.820813 0.571197i $$-0.193521\pi$$
−0.0842645 + 0.996443i $$0.526854\pi$$
$$720$$ 65.3667 8.23543i 0.0907870 0.0114381i
$$721$$ 0 0
$$722$$ 182.094 481.775i 0.252208 0.667279i
$$723$$ 785.051 1359.75i 1.08582 1.88070i
$$724$$ 1279.06 + 258.127i 1.76666 + 0.356530i
$$725$$ −439.355 + 253.662i −0.606007 + 0.349878i
$$726$$ 436.270 + 533.110i 0.600924 + 0.734311i
$$727$$ 944.144i 1.29868i 0.760496 + 0.649342i $$0.224956\pi$$
−0.760496 + 0.649342i $$0.775044\pi$$
$$728$$ 0 0
$$729$$ 405.489 0.556227
$$730$$ −166.272 + 136.069i −0.227770 + 0.186395i
$$731$$ −203.113 351.802i −0.277856 0.481261i
$$732$$ 504.454 + 101.804i 0.689145 + 0.139076i
$$733$$ 189.014 + 109.127i 0.257863 + 0.148878i 0.623360 0.781935i $$-0.285767\pi$$
−0.365496 + 0.930813i $$0.619101\pi$$
$$734$$ 412.965 + 156.086i 0.562622 + 0.212651i
$$735$$ 0 0
$$736$$ −263.598 + 1095.94i −0.358149 + 1.48905i
$$737$$ −74.8427 + 129.631i −0.101550 + 0.175891i
$$738$$ −141.432 + 23.1482i −0.191642 + 0.0313661i
$$739$$ 3.64971 + 6.32149i 0.00493872 + 0.00855411i 0.868484 0.495717i $$-0.165095\pi$$
−0.863545 + 0.504271i $$0.831761\pi$$
$$740$$ −344.226 + 115.780i −0.465170 + 0.156460i
$$741$$ 131.600i 0.177598i
$$742$$ 0 0
$$743$$ 106.867i 0.143832i 0.997411 + 0.0719159i $$0.0229113\pi$$
−0.997411 + 0.0719159i $$0.977089\pi$$
$$744$$ −1275.11 47.0778i −1.71386 0.0632766i
$$745$$ −149.025 258.119i −0.200034 0.346469i
$$746$$ 81.2623 + 496.500i 0.108931 + 0.665550i
$$747$$ 4.80256 8.31828i 0.00642913 0.0111356i
$$748$$ −318.323 280.734i −0.425565 0.375313i
$$749$$ 0 0
$$750$$ 471.196 + 178.095i 0.628261 + 0.237460i
$$751$$ 110.387 + 63.7317i 0.146986 + 0.0848624i 0.571689 0.820470i $$-0.306288\pi$$
−0.424703 + 0.905333i $$0.639622\pi$$
$$752$$ 349.378 + 460.609i 0.464598 + 0.612512i
$$753$$ −213.250 369.359i −0.283200 0.490517i
$$754$$ 44.0711 + 53.8536i 0.0584497 + 0.0714239i
$$755$$ −177.849 −0.235562
$$756$$ 0 0
$$757$$ 704.275i 0.930350i −0.885219 0.465175i $$-0.845991\pi$$
0.885219 0.465175i $$-0.154009\pi$$
$$758$$ 362.288 + 442.705i 0.477952 + 0.584043i
$$759$$ 467.153 269.711i 0.615485 0.355350i
$$760$$ 163.927 261.175i 0.215693 0.343652i
$$761$$ −501.465 + 868.563i −0.658955 + 1.14134i 0.321931 + 0.946763i $$0.395668\pi$$
−0.980886 + 0.194581i $$0.937665\pi$$
$$762$$ −798.583 301.836i −1.04801 0.396110i
$$763$$ 0 0
$$764$$ 256.804 291.188i 0.336131 0.381137i
$$765$$ −84.3614 48.7061i −0.110276 0.0636681i
$$766$$ 34.5311 + 210.980i 0.0450798 + 0.275431i
$$767$$ −82.6213 + 47.7014i −0.107720 + 0.0621922i
$$768$$ −235.612 + 841.683i −0.306786 + 1.09594i
$$769$$ 646.950 0.841288 0.420644 0.907226i $$-0.361804\pi$$
0.420644 + 0.907226i $$0.361804\pi$$
$$770$$ 0 0
$$771$$ −1459.07 −1.89244
$$772$$ 596.383 200.594i 0.772517 0.259836i
$$773$$ −488.668 + 282.132i −0.632170 + 0.364984i −0.781592 0.623790i $$-0.785592\pi$$
0.149422 + 0.988774i $$0.452259\pi$$
$$774$$ 90.0466 14.7379i 0.116339 0.0190413i
$$775$$ −914.245 527.840i −1.17967 0.681083i
$$776$$ 679.584 359.602i 0.875752 0.463404i
$$777$$ 0 0
$$778$$ −144.392 54.5750i −0.185594 0.0701478i
$$779$$ −335.380 + 580.895i −0.430526 + 0.745693i
$$780$$ 6.48936