Properties

 Label 392.3.k.l.275.6 Level 392 Weight 3 Character 392.275 Analytic conductor 10.681 Analytic rank 0 Dimension 12 CM no Inner twists 4

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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: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 56) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 275.6 Root $$0.907369 - 0.0534805i$$ of defining polynomial Character $$\chi$$ $$=$$ 392.275 Dual form 392.3.k.l.67.6

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.98615 + 0.234945i) q^{2} +(2.66613 + 4.61787i) q^{3} +(3.88960 + 0.933271i) q^{4} +(1.86796 + 1.07847i) q^{5} +(4.21039 + 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +(-9.71647 + 16.8294i) q^{9} +O(q^{10})$$ $$q+(1.98615 + 0.234945i) q^{2} +(2.66613 + 4.61787i) q^{3} +(3.88960 + 0.933271i) q^{4} +(1.86796 + 1.07847i) q^{5} +(4.21039 + 9.79818i) q^{6} +(7.50608 + 2.76746i) q^{8} +(-9.71647 + 16.8294i) q^{9} +(3.45667 + 2.58086i) q^{10} +(-2.62956 - 4.55453i) q^{11} +(6.06045 + 20.4499i) q^{12} -21.4116i q^{13} +11.5013i q^{15} +(14.2580 + 7.26011i) q^{16} +(0.463429 + 0.802683i) q^{17} +(-23.2524 + 31.1430i) q^{18} +(-2.96505 + 5.13561i) q^{19} +(6.25911 + 5.93812i) q^{20} +(-4.15264 - 9.66378i) q^{22} +(-7.52507 - 4.34460i) q^{23} +(7.23239 + 42.0405i) q^{24} +(-10.1738 - 17.6216i) q^{25} +(5.03053 - 42.5266i) q^{26} -55.6311 q^{27} -9.42223i q^{29} +(-2.70217 + 22.8434i) q^{30} +(29.8813 - 17.2520i) q^{31} +(26.6129 + 17.7695i) q^{32} +(14.0215 - 24.2859i) q^{33} +(0.731855 + 1.70313i) q^{34} +(-53.4996 + 56.3916i) q^{36} +(11.0853 + 6.40011i) q^{37} +(-7.09562 + 9.50349i) q^{38} +(98.8758 - 57.0860i) q^{39} +(11.0364 + 13.2645i) q^{40} -43.1339 q^{41} -41.7382 q^{43} +(-5.97732 - 20.1694i) q^{44} +(-36.2999 + 20.9578i) q^{45} +(-13.9252 - 10.3970i) q^{46} +(39.8357 + 22.9991i) q^{47} +(4.48745 + 85.1980i) q^{48} +(-16.0667 - 37.3894i) q^{50} +(-2.47112 + 4.28011i) q^{51} +(19.9828 - 83.2825i) q^{52} +(-64.5031 + 37.2409i) q^{53} +(-110.492 - 13.0702i) q^{54} -11.3436i q^{55} -31.6208 q^{57} +(2.21370 - 18.7140i) q^{58} +(26.8367 + 46.4825i) q^{59} +(-10.7338 + 44.7355i) q^{60} +(-24.0893 - 13.9080i) q^{61} +(63.4020 - 27.2446i) q^{62} +(48.6823 + 41.5455i) q^{64} +(23.0916 - 39.9959i) q^{65} +(33.5546 - 44.9412i) q^{66} +(39.2453 + 67.9749i) q^{67} +(1.05343 + 3.55462i) q^{68} -46.3330i q^{69} -74.5100i q^{71} +(-119.507 + 99.4329i) q^{72} +(16.8020 + 29.1020i) q^{73} +(20.5134 + 15.3160i) q^{74} +(54.2494 - 93.9627i) q^{75} +(-16.3258 + 17.2083i) q^{76} +(209.794 - 90.1511i) q^{78} +(26.1642 + 15.1059i) q^{79} +(18.8036 + 28.9384i) q^{80} +(-60.8713 - 105.432i) q^{81} +(-85.6705 - 10.1341i) q^{82} +72.9274 q^{83} +1.99917i q^{85} +(-82.8984 - 9.80616i) q^{86} +(43.5106 - 25.1209i) q^{87} +(-7.13318 - 41.4638i) q^{88} +(-27.4198 + 47.4925i) q^{89} +(-77.0211 + 33.0968i) q^{90} +(-25.2148 - 23.9217i) q^{92} +(159.335 + 91.9919i) q^{93} +(73.7162 + 55.0390i) q^{94} +(-11.0772 + 6.39541i) q^{95} +(-11.1040 + 170.270i) q^{96} +53.7125 q^{97} +102.200 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q + 2q^{2} + 6q^{3} - 4q^{4} + 56q^{6} + 8q^{8} - 40q^{9} + O(q^{10})$$ $$12q + 2q^{2} + 6q^{3} - 4q^{4} + 56q^{6} + 8q^{8} - 40q^{9} + 6q^{10} + 30q^{11} - 32q^{12} + 16q^{16} - 30q^{17} - 16q^{18} - 78q^{19} - 48q^{20} + 24q^{22} + 76q^{24} - 92q^{25} + 128q^{26} - 156q^{27} - 16q^{30} + 112q^{32} + 78q^{33} - 76q^{34} - 248q^{36} - 80q^{38} - 44q^{40} + 232q^{41} - 200q^{43} + 132q^{44} - 156q^{46} - 176q^{48} + 48q^{50} + 10q^{51} - 132q^{52} + 36q^{54} + 332q^{57} + 4q^{58} + 110q^{59} + 84q^{60} + 96q^{62} - 160q^{64} - 32q^{65} + 138q^{66} + 434q^{67} - 96q^{68} - 328q^{72} - 102q^{73} - 34q^{74} + 60q^{75} + 168q^{76} + 720q^{78} + 256q^{80} - 82q^{81} + 24q^{82} + 536q^{83} + 240q^{86} - 204q^{88} - 214q^{89} - 440q^{90} + 160q^{92} + 16q^{94} - 48q^{96} + 152q^{97} + 504q^{99} + O(q^{100})$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.98615 + 0.234945i 0.993076 + 0.117472i
$$3$$ 2.66613 + 4.61787i 0.888709 + 1.53929i 0.841403 + 0.540409i $$0.181730\pi$$
0.0473064 + 0.998880i $$0.484936\pi$$
$$4$$ 3.88960 + 0.933271i 0.972401 + 0.233318i
$$5$$ 1.86796 + 1.07847i 0.373592 + 0.215693i 0.675026 0.737794i $$-0.264132\pi$$
−0.301435 + 0.953487i $$0.597466\pi$$
$$6$$ 4.21039 + 9.79818i 0.701732 + 1.63303i
$$7$$ 0 0
$$8$$ 7.50608 + 2.76746i 0.938259 + 0.345932i
$$9$$ −9.71647 + 16.8294i −1.07961 + 1.86993i
$$10$$ 3.45667 + 2.58086i 0.345667 + 0.258086i
$$11$$ −2.62956 4.55453i −0.239051 0.414048i 0.721392 0.692527i $$-0.243503\pi$$
−0.960442 + 0.278480i $$0.910170\pi$$
$$12$$ 6.06045 + 20.4499i 0.505038 + 1.70416i
$$13$$ 21.4116i 1.64704i −0.567285 0.823522i $$-0.692006\pi$$
0.567285 0.823522i $$-0.307994\pi$$
$$14$$ 0 0
$$15$$ 11.5013i 0.766754i
$$16$$ 14.2580 + 7.26011i 0.891126 + 0.453757i
$$17$$ 0.463429 + 0.802683i 0.0272606 + 0.0472167i 0.879334 0.476206i $$-0.157988\pi$$
−0.852073 + 0.523423i $$0.824655\pi$$
$$18$$ −23.2524 + 31.1430i −1.29180 + 1.73016i
$$19$$ −2.96505 + 5.13561i −0.156055 + 0.270295i −0.933443 0.358726i $$-0.883211\pi$$
0.777388 + 0.629022i $$0.216544\pi$$
$$20$$ 6.25911 + 5.93812i 0.312956 + 0.296906i
$$21$$ 0 0
$$22$$ −4.15264 9.66378i −0.188756 0.439263i
$$23$$ −7.52507 4.34460i −0.327177 0.188896i 0.327410 0.944882i $$-0.393824\pi$$
−0.654587 + 0.755987i $$0.727157\pi$$
$$24$$ 7.23239 + 42.0405i 0.301350 + 1.75169i
$$25$$ −10.1738 17.6216i −0.406953 0.704863i
$$26$$ 5.03053 42.5266i 0.193482 1.63564i
$$27$$ −55.6311 −2.06041
$$28$$ 0 0
$$29$$ 9.42223i 0.324904i −0.986716 0.162452i $$-0.948060\pi$$
0.986716 0.162452i $$-0.0519403\pi$$
$$30$$ −2.70217 + 22.8434i −0.0900723 + 0.761445i
$$31$$ 29.8813 17.2520i 0.963912 0.556515i 0.0665375 0.997784i $$-0.478805\pi$$
0.897375 + 0.441269i $$0.145471\pi$$
$$32$$ 26.6129 + 17.7695i 0.831652 + 0.555298i
$$33$$ 14.0215 24.2859i 0.424893 0.735936i
$$34$$ 0.731855 + 1.70313i 0.0215252 + 0.0500921i
$$35$$ 0 0
$$36$$ −53.4996 + 56.3916i −1.48610 + 1.56643i
$$37$$ 11.0853 + 6.40011i 0.299603 + 0.172976i 0.642265 0.766483i $$-0.277995\pi$$
−0.342662 + 0.939459i $$0.611328\pi$$
$$38$$ −7.09562 + 9.50349i −0.186727 + 0.250092i
$$39$$ 98.8758 57.0860i 2.53528 1.46374i
$$40$$ 11.0364 + 13.2645i 0.275911 + 0.331614i
$$41$$ −43.1339 −1.05205 −0.526023 0.850470i $$-0.676317\pi$$
−0.526023 + 0.850470i $$0.676317\pi$$
$$42$$ 0 0
$$43$$ −41.7382 −0.970656 −0.485328 0.874332i $$-0.661300\pi$$
−0.485328 + 0.874332i $$0.661300\pi$$
$$44$$ −5.97732 20.1694i −0.135848 0.458395i
$$45$$ −36.2999 + 20.9578i −0.806665 + 0.465728i
$$46$$ −13.9252 10.3970i −0.302721 0.226022i
$$47$$ 39.8357 + 22.9991i 0.847567 + 0.489343i 0.859829 0.510582i $$-0.170570\pi$$
−0.0122620 + 0.999925i $$0.503903\pi$$
$$48$$ 4.48745 + 85.1980i 0.0934885 + 1.77496i
$$49$$ 0 0
$$50$$ −16.0667 37.3894i −0.321333 0.747788i
$$51$$ −2.47112 + 4.28011i −0.0484534 + 0.0839238i
$$52$$ 19.9828 83.2825i 0.384285 1.60159i
$$53$$ −64.5031 + 37.2409i −1.21704 + 0.702658i −0.964284 0.264872i $$-0.914670\pi$$
−0.252756 + 0.967530i $$0.581337\pi$$
$$54$$ −110.492 13.0702i −2.04614 0.242041i
$$55$$ 11.3436i 0.206246i
$$56$$ 0 0
$$57$$ −31.6208 −0.554751
$$58$$ 2.21370 18.7140i 0.0381672 0.322655i
$$59$$ 26.8367 + 46.4825i 0.454860 + 0.787840i 0.998680 0.0513617i $$-0.0163561\pi$$
−0.543821 + 0.839201i $$0.683023\pi$$
$$60$$ −10.7338 + 44.7355i −0.178897 + 0.745592i
$$61$$ −24.0893 13.9080i −0.394907 0.228000i 0.289377 0.957215i $$-0.406552\pi$$
−0.684284 + 0.729215i $$0.739885\pi$$
$$62$$ 63.4020 27.2446i 1.02261 0.439429i
$$63$$ 0 0
$$64$$ 48.6823 + 41.5455i 0.760661 + 0.649149i
$$65$$ 23.0916 39.9959i 0.355256 0.615322i
$$66$$ 33.5546 44.9412i 0.508403 0.680927i
$$67$$ 39.2453 + 67.9749i 0.585751 + 1.01455i 0.994781 + 0.102030i $$0.0325338\pi$$
−0.409030 + 0.912521i $$0.634133\pi$$
$$68$$ 1.05343 + 3.55462i 0.0154917 + 0.0522739i
$$69$$ 46.3330i 0.671493i
$$70$$ 0 0
$$71$$ 74.5100i 1.04944i −0.851276 0.524719i $$-0.824171\pi$$
0.851276 0.524719i $$-0.175829\pi$$
$$72$$ −119.507 + 99.4329i −1.65982 + 1.38101i
$$73$$ 16.8020 + 29.1020i 0.230165 + 0.398657i 0.957857 0.287247i $$-0.0927401\pi$$
−0.727692 + 0.685904i $$0.759407\pi$$
$$74$$ 20.5134 + 15.3160i 0.277209 + 0.206973i
$$75$$ 54.2494 93.9627i 0.723325 1.25284i
$$76$$ −16.3258 + 17.2083i −0.214813 + 0.226425i
$$77$$ 0 0
$$78$$ 209.794 90.1511i 2.68967 1.15578i
$$79$$ 26.1642 + 15.1059i 0.331192 + 0.191214i 0.656370 0.754439i $$-0.272091\pi$$
−0.325178 + 0.945653i $$0.605424\pi$$
$$80$$ 18.8036 + 28.9384i 0.235045 + 0.361730i
$$81$$ −60.8713 105.432i −0.751497 1.30163i
$$82$$ −85.6705 10.1341i −1.04476 0.123586i
$$83$$ 72.9274 0.878644 0.439322 0.898330i $$-0.355219\pi$$
0.439322 + 0.898330i $$0.355219\pi$$
$$84$$ 0 0
$$85$$ 1.99917i 0.0235197i
$$86$$ −82.8984 9.80616i −0.963935 0.114025i
$$87$$ 43.5106 25.1209i 0.500122 0.288745i
$$88$$ −7.13318 41.4638i −0.0810589 0.471180i
$$89$$ −27.4198 + 47.4925i −0.308088 + 0.533624i −0.977944 0.208867i $$-0.933022\pi$$
0.669856 + 0.742491i $$0.266356\pi$$
$$90$$ −77.0211 + 33.0968i −0.855790 + 0.367743i
$$91$$ 0 0
$$92$$ −25.2148 23.9217i −0.274074 0.260018i
$$93$$ 159.335 + 91.9919i 1.71328 + 0.989160i
$$94$$ 73.7162 + 55.0390i 0.784215 + 0.585521i
$$95$$ −11.0772 + 6.39541i −0.116602 + 0.0673201i
$$96$$ −11.1040 + 170.270i −0.115667 + 1.77365i
$$97$$ 53.7125 0.553738 0.276869 0.960908i $$-0.410703\pi$$
0.276869 + 0.960908i $$0.410703\pi$$
$$98$$ 0 0
$$99$$ 102.200 1.03232
$$100$$ −23.1264 78.0359i −0.231264 0.780359i
$$101$$ −78.2037 + 45.1509i −0.774294 + 0.447039i −0.834404 0.551153i $$-0.814188\pi$$
0.0601103 + 0.998192i $$0.480855\pi$$
$$102$$ −5.91362 + 7.92038i −0.0579766 + 0.0776508i
$$103$$ −97.6980 56.4060i −0.948525 0.547631i −0.0559023 0.998436i $$-0.517804\pi$$
−0.892622 + 0.450805i $$0.851137\pi$$
$$104$$ 59.2556 160.717i 0.569766 1.54535i
$$105$$ 0 0
$$106$$ −136.863 + 58.8114i −1.29116 + 0.554825i
$$107$$ 71.9950 124.699i 0.672851 1.16541i −0.304241 0.952595i $$-0.598403\pi$$
0.977092 0.212817i $$-0.0682637\pi$$
$$108$$ −216.383 51.9189i −2.00354 0.480730i
$$109$$ 57.7477 33.3406i 0.529795 0.305877i −0.211138 0.977456i $$-0.567717\pi$$
0.740933 + 0.671579i $$0.234384\pi$$
$$110$$ 2.66511 22.5300i 0.0242282 0.204818i
$$111$$ 68.2540i 0.614901i
$$112$$ 0 0
$$113$$ 7.16467 0.0634042 0.0317021 0.999497i $$-0.489907\pi$$
0.0317021 + 0.999497i $$0.489907\pi$$
$$114$$ −62.8037 7.42913i −0.550910 0.0651678i
$$115$$ −9.37101 16.2311i −0.0814870 0.141140i
$$116$$ 8.79349 36.6487i 0.0758060 0.315937i
$$117$$ 360.344 + 208.045i 3.07986 + 1.77816i
$$118$$ 42.3810 + 98.6266i 0.359161 + 0.835818i
$$119$$ 0 0
$$120$$ −31.8294 + 86.3297i −0.265245 + 0.719414i
$$121$$ 46.6709 80.8363i 0.385710 0.668069i
$$122$$ −44.5775 33.2830i −0.365389 0.272812i
$$123$$ −115.000 199.187i −0.934963 1.61940i
$$124$$ 132.327 39.2159i 1.06715 0.316258i
$$125$$ 97.8118i 0.782494i
$$126$$ 0 0
$$127$$ 131.492i 1.03537i −0.855572 0.517684i $$-0.826794\pi$$
0.855572 0.517684i $$-0.173206\pi$$
$$128$$ 86.9296 + 93.9534i 0.679138 + 0.734011i
$$129$$ −111.279 192.742i −0.862631 1.49412i
$$130$$ 55.2604 74.0127i 0.425080 0.569329i
$$131$$ −4.38060 + 7.58742i −0.0334397 + 0.0579193i −0.882261 0.470761i $$-0.843980\pi$$
0.848821 + 0.528680i $$0.177313\pi$$
$$132$$ 77.2032 81.3766i 0.584873 0.616489i
$$133$$ 0 0
$$134$$ 61.9769 + 144.229i 0.462514 + 1.07634i
$$135$$ −103.916 59.9962i −0.769752 0.444416i
$$136$$ 1.25714 + 7.30752i 0.00924370 + 0.0537318i
$$137$$ 118.420 + 205.110i 0.864381 + 1.49715i 0.867660 + 0.497158i $$0.165623\pi$$
−0.00327850 + 0.999995i $$0.501044\pi$$
$$138$$ 10.8857 92.0244i 0.0788818 0.666844i
$$139$$ −172.122 −1.23828 −0.619142 0.785279i $$-0.712520\pi$$
−0.619142 + 0.785279i $$0.712520\pi$$
$$140$$ 0 0
$$141$$ 245.274i 1.73954i
$$142$$ 17.5057 147.988i 0.123280 1.04217i
$$143$$ −97.5195 + 56.3029i −0.681955 + 0.393727i
$$144$$ −260.721 + 169.411i −1.81056 + 1.17647i
$$145$$ 10.1616 17.6003i 0.0700797 0.121382i
$$146$$ 26.5341 + 61.7485i 0.181740 + 0.422935i
$$147$$ 0 0
$$148$$ 37.1444 + 35.2395i 0.250976 + 0.238105i
$$149$$ −199.798 115.354i −1.34093 0.774186i −0.353985 0.935251i $$-0.615174\pi$$
−0.986944 + 0.161066i $$0.948507\pi$$
$$150$$ 129.824 173.879i 0.865491 1.15919i
$$151$$ −128.077 + 73.9452i −0.848190 + 0.489703i −0.860040 0.510227i $$-0.829561\pi$$
0.0118494 + 0.999930i $$0.496228\pi$$
$$152$$ −36.4685 + 30.3427i −0.239924 + 0.199623i
$$153$$ −18.0116 −0.117723
$$154$$ 0 0
$$155$$ 74.4227 0.480146
$$156$$ 437.864 129.764i 2.80682 0.831819i
$$157$$ −99.4450 + 57.4146i −0.633407 + 0.365698i −0.782070 0.623190i $$-0.785836\pi$$
0.148663 + 0.988888i $$0.452503\pi$$
$$158$$ 48.4170 + 36.1498i 0.306437 + 0.228796i
$$159$$ −343.947 198.578i −2.16319 1.24892i
$$160$$ 30.5479 + 61.8938i 0.190924 + 0.386836i
$$161$$ 0 0
$$162$$ −96.1289 223.706i −0.593388 1.38090i
$$163$$ −24.6545 + 42.7029i −0.151255 + 0.261981i −0.931689 0.363257i $$-0.881665\pi$$
0.780434 + 0.625238i $$0.214998\pi$$
$$164$$ −167.774 40.2556i −1.02301 0.245461i
$$165$$ 52.3830 30.2433i 0.317473 0.183293i
$$166$$ 144.845 + 17.1339i 0.872560 + 0.103216i
$$167$$ 241.457i 1.44585i −0.690926 0.722926i $$-0.742797\pi$$
0.690926 0.722926i $$-0.257203\pi$$
$$168$$ 0 0
$$169$$ −289.455 −1.71275
$$170$$ −0.469695 + 3.97066i −0.00276291 + 0.0233568i
$$171$$ −57.6196 99.8001i −0.336957 0.583626i
$$172$$ −162.345 38.9531i −0.943867 0.226471i
$$173$$ 47.1300 + 27.2105i 0.272428 + 0.157286i 0.629990 0.776603i $$-0.283059\pi$$
−0.357563 + 0.933889i $$0.616392\pi$$
$$174$$ 92.3207 39.6713i 0.530579 0.227996i
$$175$$ 0 0
$$176$$ −4.42590 84.0293i −0.0251471 0.477439i
$$177$$ −143.100 + 247.857i −0.808475 + 1.40032i
$$178$$ −65.6180 + 87.8852i −0.368641 + 0.493737i
$$179$$ 63.5100 + 110.003i 0.354805 + 0.614540i 0.987084 0.160200i $$-0.0512141\pi$$
−0.632280 + 0.774740i $$0.717881\pi$$
$$180$$ −160.751 + 47.6397i −0.893064 + 0.264665i
$$181$$ 212.704i 1.17516i 0.809165 + 0.587581i $$0.199920\pi$$
−0.809165 + 0.587581i $$0.800080\pi$$
$$182$$ 0 0
$$183$$ 148.322i 0.810502i
$$184$$ −44.4602 53.4362i −0.241632 0.290414i
$$185$$ 13.8046 + 23.9103i 0.0746194 + 0.129245i
$$186$$ 294.850 + 220.145i 1.58521 + 1.18357i
$$187$$ 2.43723 4.22140i 0.0130333 0.0225743i
$$188$$ 133.480 + 126.635i 0.710002 + 0.673590i
$$189$$ 0 0
$$190$$ −23.5035 + 10.0997i −0.123703 + 0.0531565i
$$191$$ −35.1041 20.2674i −0.183791 0.106112i 0.405282 0.914192i $$-0.367174\pi$$
−0.589073 + 0.808080i $$0.700507\pi$$
$$192$$ −62.0584 + 335.574i −0.323221 + 1.74778i
$$193$$ −141.153 244.485i −0.731364 1.26676i −0.956300 0.292387i $$-0.905551\pi$$
0.224936 0.974374i $$-0.427783\pi$$
$$194$$ 106.681 + 12.6195i 0.549904 + 0.0650488i
$$195$$ 246.261 1.26288
$$196$$ 0 0
$$197$$ 261.806i 1.32896i 0.747304 + 0.664482i $$0.231348\pi$$
−0.747304 + 0.664482i $$0.768652\pi$$
$$198$$ 202.985 + 24.0113i 1.02518 + 0.121269i
$$199$$ 278.968 161.062i 1.40185 0.809357i 0.407265 0.913310i $$-0.366482\pi$$
0.994582 + 0.103953i $$0.0331492\pi$$
$$200$$ −27.5985 160.425i −0.137992 0.802123i
$$201$$ −209.266 + 362.460i −1.04113 + 1.80328i
$$202$$ −165.932 + 71.3031i −0.821448 + 0.352986i
$$203$$ 0 0
$$204$$ −13.6062 + 14.3417i −0.0666970 + 0.0703025i
$$205$$ −80.5723 46.5184i −0.393036 0.226919i
$$206$$ −180.791 134.984i −0.877626 0.655265i
$$207$$ 146.234 84.4283i 0.706445 0.407866i
$$208$$ 155.450 305.286i 0.747357 1.46772i
$$209$$ 31.1870 0.149220
$$210$$ 0 0
$$211$$ 169.792 0.804702 0.402351 0.915485i $$-0.368193\pi$$
0.402351 + 0.915485i $$0.368193\pi$$
$$212$$ −285.647 + 84.6533i −1.34739 + 0.399308i
$$213$$ 344.077 198.653i 1.61539 0.932644i
$$214$$ 172.290 230.756i 0.805096 1.07830i
$$215$$ −77.9652 45.0133i −0.362629 0.209364i
$$216$$ −417.571 153.957i −1.93320 0.712763i
$$217$$ 0 0
$$218$$ 122.529 52.6521i 0.562059 0.241523i
$$219$$ −89.5927 + 155.179i −0.409099 + 0.708581i
$$220$$ 10.5866 44.1219i 0.0481210 0.200554i
$$221$$ 17.1867 9.92275i 0.0777679 0.0448993i
$$222$$ −16.0359 + 135.563i −0.0722338 + 0.610643i
$$223$$ 45.4626i 0.203868i 0.994791 + 0.101934i $$0.0325031\pi$$
−0.994791 + 0.101934i $$0.967497\pi$$
$$224$$ 0 0
$$225$$ 395.414 1.75740
$$226$$ 14.2301 + 1.68330i 0.0629652 + 0.00744823i
$$227$$ 92.5653 + 160.328i 0.407777 + 0.706290i 0.994640 0.103396i $$-0.0329708\pi$$
−0.586864 + 0.809686i $$0.699637\pi$$
$$228$$ −122.992 29.5108i −0.539440 0.129433i
$$229$$ −160.173 92.4759i −0.699445 0.403825i 0.107695 0.994184i $$-0.465653\pi$$
−0.807141 + 0.590359i $$0.798986\pi$$
$$230$$ −14.7988 34.4390i −0.0643428 0.149735i
$$231$$ 0 0
$$232$$ 26.0756 70.7239i 0.112395 0.304845i
$$233$$ −48.3504 + 83.7453i −0.207512 + 0.359422i −0.950930 0.309405i $$-0.899870\pi$$
0.743418 + 0.668827i $$0.233203\pi$$
$$234$$ 666.819 + 497.869i 2.84966 + 2.12765i
$$235$$ 49.6076 + 85.9228i 0.211096 + 0.365629i
$$236$$ 61.0033 + 205.845i 0.258489 + 0.872223i
$$237$$ 161.097i 0.679734i
$$238$$ 0 0
$$239$$ 163.185i 0.682782i −0.939921 0.341391i $$-0.889102\pi$$
0.939921 0.341391i $$-0.110898\pi$$
$$240$$ −83.5008 + 163.986i −0.347920 + 0.683274i
$$241$$ 102.745 + 177.960i 0.426330 + 0.738424i 0.996544 0.0830718i $$-0.0264731\pi$$
−0.570214 + 0.821496i $$0.693140\pi$$
$$242$$ 111.687 149.588i 0.461519 0.618133i
$$243$$ 74.2413 128.590i 0.305520 0.529176i
$$244$$ −80.7180 76.5784i −0.330812 0.313846i
$$245$$ 0 0
$$246$$ −181.611 422.634i −0.738254 1.71802i
$$247$$ 109.962 + 63.4863i 0.445188 + 0.257030i
$$248$$ 272.035 46.7993i 1.09692 0.188707i
$$249$$ 194.434 + 336.769i 0.780859 + 1.35249i
$$250$$ 22.9803 194.269i 0.0919214 0.777077i
$$251$$ 159.299 0.634658 0.317329 0.948316i $$-0.397214\pi$$
0.317329 + 0.948316i $$0.397214\pi$$
$$252$$ 0 0
$$253$$ 45.6975i 0.180622i
$$254$$ 30.8932 261.162i 0.121627 1.02820i
$$255$$ −9.23191 + 5.33005i −0.0362036 + 0.0209021i
$$256$$ 150.582 + 207.029i 0.588210 + 0.808708i
$$257$$ 107.889 186.868i 0.419800 0.727114i −0.576119 0.817366i $$-0.695434\pi$$
0.995919 + 0.0902512i $$0.0287670\pi$$
$$258$$ −175.734 408.959i −0.681140 1.58511i
$$259$$ 0 0
$$260$$ 127.144 134.017i 0.489017 0.515452i
$$261$$ 158.571 + 91.5507i 0.607550 + 0.350769i
$$262$$ −10.4832 + 14.0406i −0.0400121 + 0.0535900i
$$263$$ −285.059 + 164.579i −1.08387 + 0.625775i −0.931939 0.362616i $$-0.881884\pi$$
−0.151935 + 0.988391i $$0.548550\pi$$
$$264$$ 172.456 143.488i 0.653244 0.543515i
$$265$$ −160.652 −0.606234
$$266$$ 0 0
$$267$$ −292.419 −1.09520
$$268$$ 89.2097 + 301.022i 0.332872 + 1.12322i
$$269$$ −253.803 + 146.533i −0.943507 + 0.544734i −0.891058 0.453889i $$-0.850036\pi$$
−0.0524492 + 0.998624i $$0.516703\pi$$
$$270$$ −192.298 143.576i −0.712216 0.531764i
$$271$$ −23.2529 13.4251i −0.0858042 0.0495391i 0.456484 0.889732i $$-0.349109\pi$$
−0.542288 + 0.840193i $$0.682442\pi$$
$$272$$ 0.780014 + 14.8092i 0.00286770 + 0.0544456i
$$273$$ 0 0
$$274$$ 187.011 + 435.202i 0.682523 + 1.58833i
$$275$$ −53.5053 + 92.6739i −0.194565 + 0.336996i
$$276$$ 43.2413 180.217i 0.156671 0.652960i
$$277$$ −289.925 + 167.389i −1.04666 + 0.604291i −0.921713 0.387872i $$-0.873210\pi$$
−0.124949 + 0.992163i $$0.539877\pi$$
$$278$$ −341.860 40.4390i −1.22971 0.145464i
$$279$$ 670.513i 2.40327i
$$280$$ 0 0
$$281$$ −123.357 −0.438994 −0.219497 0.975613i $$-0.570442\pi$$
−0.219497 + 0.975613i $$0.570442\pi$$
$$282$$ −57.6259 + 487.152i −0.204347 + 1.72749i
$$283$$ −0.309453 0.535988i −0.00109347 0.00189395i 0.865478 0.500947i $$-0.167015\pi$$
−0.866572 + 0.499053i $$0.833681\pi$$
$$284$$ 69.5381 289.814i 0.244852 1.02047i
$$285$$ −59.0663 34.1019i −0.207250 0.119656i
$$286$$ −206.917 + 88.9145i −0.723485 + 0.310890i
$$287$$ 0 0
$$288$$ −557.634 + 275.222i −1.93623 + 0.955631i
$$289$$ 144.070 249.537i 0.498514 0.863451i
$$290$$ 24.3175 32.5695i 0.0838534 0.112309i
$$291$$ 143.204 + 248.037i 0.492112 + 0.852362i
$$292$$ 38.1932 + 128.876i 0.130799 + 0.441356i
$$293$$ 28.2794i 0.0965169i 0.998835 + 0.0482584i $$0.0153671\pi$$
−0.998835 + 0.0482584i $$0.984633\pi$$
$$294$$ 0 0
$$295$$ 115.770i 0.392440i
$$296$$ 65.4951 + 78.7178i 0.221267 + 0.265939i
$$297$$ 146.285 + 253.373i 0.492542 + 0.853108i
$$298$$ −369.728 276.051i −1.24070 0.926347i
$$299$$ −93.0247 + 161.123i −0.311119 + 0.538874i
$$300$$ 298.701 314.848i 0.995671 1.04949i
$$301$$ 0 0
$$302$$ −271.753 + 116.775i −0.899844 + 0.386674i
$$303$$ −417.002 240.756i −1.37624 0.794575i
$$304$$ −79.5608 + 51.6971i −0.261713 + 0.170056i
$$305$$ −29.9986 51.9591i −0.0983560 0.170358i
$$306$$ −35.7738 4.23172i −0.116908 0.0138292i
$$307$$ −400.893 −1.30584 −0.652921 0.757426i $$-0.726457\pi$$
−0.652921 + 0.757426i $$0.726457\pi$$
$$308$$ 0 0
$$309$$ 601.542i 1.94674i
$$310$$ 147.815 + 17.4852i 0.476822 + 0.0564039i
$$311$$ −140.492 + 81.1132i −0.451743 + 0.260814i −0.708566 0.705644i $$-0.750658\pi$$
0.256823 + 0.966459i $$0.417324\pi$$
$$312$$ 900.152 154.857i 2.88510 0.496336i
$$313$$ −133.123 + 230.576i −0.425313 + 0.736664i −0.996450 0.0841913i $$-0.973169\pi$$
0.571137 + 0.820855i $$0.306503\pi$$
$$314$$ −211.002 + 90.6700i −0.671981 + 0.288758i
$$315$$ 0 0
$$316$$ 87.6704 + 83.1742i 0.277438 + 0.263210i
$$317$$ 374.864 + 216.428i 1.18254 + 0.682737i 0.956600 0.291405i $$-0.0941228\pi$$
0.225936 + 0.974142i $$0.427456\pi$$
$$318$$ −636.476 475.214i −2.00150 1.49438i
$$319$$ −42.9138 + 24.7763i −0.134526 + 0.0776686i
$$320$$ 46.1311 + 130.108i 0.144160 + 0.406586i
$$321$$ 767.792 2.39187
$$322$$ 0 0
$$323$$ −5.49636 −0.0170166
$$324$$ −138.368 466.898i −0.427062 1.44104i
$$325$$ −377.305 + 217.837i −1.16094 + 0.670269i
$$326$$ −59.0005 + 79.0220i −0.180983 + 0.242399i
$$327$$ 307.925 + 177.781i 0.941668 + 0.543672i
$$328$$ −323.766 119.371i −0.987092 0.363937i
$$329$$ 0 0
$$330$$ 111.146 47.7608i 0.336807 0.144730i
$$331$$ −40.6264 + 70.3671i −0.122738 + 0.212589i −0.920847 0.389925i $$-0.872501\pi$$
0.798108 + 0.602514i $$0.205834\pi$$
$$332$$ 283.659 + 68.0611i 0.854394 + 0.205003i
$$333$$ −215.420 + 124.373i −0.646907 + 0.373492i
$$334$$ 56.7290 479.571i 0.169847 1.43584i
$$335$$ 169.299i 0.505370i
$$336$$ 0 0
$$337$$ −69.4941 −0.206214 −0.103107 0.994670i $$-0.532878\pi$$
−0.103107 + 0.994670i $$0.532878\pi$$
$$338$$ −574.902 68.0059i −1.70089 0.201201i
$$339$$ 19.1019 + 33.0855i 0.0563479 + 0.0975974i
$$340$$ −1.86577 + 7.77598i −0.00548756 + 0.0228705i
$$341$$ −157.149 90.7300i −0.460848 0.266071i
$$342$$ −90.9938 211.756i −0.266064 0.619168i
$$343$$ 0 0
$$344$$ −313.290 115.509i −0.910727 0.335781i
$$345$$ 49.9686 86.5481i 0.144836 0.250864i
$$346$$ 87.2145 + 65.1172i 0.252065 + 0.188200i
$$347$$ 174.677 + 302.549i 0.503391 + 0.871899i 0.999992 + 0.00392020i $$0.00124784\pi$$
−0.496601 + 0.867979i $$0.665419\pi$$
$$348$$ 192.683 57.1029i 0.553688 0.164089i
$$349$$ 165.836i 0.475174i −0.971366 0.237587i $$-0.923643\pi$$
0.971366 0.237587i $$-0.0763566\pi$$
$$350$$ 0 0
$$351$$ 1191.15i 3.39358i
$$352$$ 10.9517 167.935i 0.0311129 0.477088i
$$353$$ −235.858 408.519i −0.668154 1.15728i −0.978420 0.206627i $$-0.933751\pi$$
0.310266 0.950650i $$-0.399582\pi$$
$$354$$ −342.451 + 458.661i −0.967377 + 1.29565i
$$355$$ 80.3566 139.182i 0.226356 0.392061i
$$356$$ −150.976 + 159.137i −0.424089 + 0.447014i
$$357$$ 0 0
$$358$$ 100.296 + 233.403i 0.280157 + 0.651964i
$$359$$ 568.967 + 328.493i 1.58487 + 0.915022i 0.994134 + 0.108154i $$0.0344939\pi$$
0.590731 + 0.806869i $$0.298839\pi$$
$$360$$ −330.470 + 56.8520i −0.917971 + 0.157922i
$$361$$ 162.917 + 282.180i 0.451294 + 0.781663i
$$362$$ −49.9737 + 422.463i −0.138049 + 1.16703i
$$363$$ 497.722 1.37113
$$364$$ 0 0
$$365$$ 72.4817i 0.198580i
$$366$$ 34.8474 294.590i 0.0952115 0.804890i
$$367$$ 307.850 177.737i 0.838829 0.484298i −0.0180371 0.999837i $$-0.505742\pi$$
0.856866 + 0.515539i $$0.172408\pi$$
$$368$$ −75.7502 116.578i −0.205843 0.316788i
$$369$$ 419.109 725.918i 1.13580 1.96726i
$$370$$ 21.8004 + 50.7327i 0.0589201 + 0.137116i
$$371$$ 0 0
$$372$$ 533.895 + 506.514i 1.43520 + 1.36160i
$$373$$ −273.662 157.999i −0.733680 0.423590i 0.0860872 0.996288i $$-0.472564\pi$$
−0.819767 + 0.572698i $$0.805897\pi$$
$$374$$ 5.83250 7.81173i 0.0155949 0.0208870i
$$375$$ 451.682 260.779i 1.20449 0.695410i
$$376$$ 235.360 + 282.877i 0.625958 + 0.752332i
$$377$$ −201.745 −0.535132
$$378$$ 0 0
$$379$$ −178.404 −0.470723 −0.235361 0.971908i $$-0.575627\pi$$
−0.235361 + 0.971908i $$0.575627\pi$$
$$380$$ −49.0544 + 14.5376i −0.129091 + 0.0382568i
$$381$$ 607.211 350.574i 1.59373 0.920140i
$$382$$ −64.9604 48.5016i −0.170053 0.126968i
$$383$$ 604.832 + 349.200i 1.57920 + 0.911750i 0.994972 + 0.100158i $$0.0319349\pi$$
0.584225 + 0.811591i $$0.301398\pi$$
$$384$$ −202.099 + 651.921i −0.526299 + 1.69771i
$$385$$ 0 0
$$386$$ −222.912 518.747i −0.577491 1.34390i
$$387$$ 405.548 702.430i 1.04793 1.81506i
$$388$$ 208.920 + 50.1284i 0.538455 + 0.129197i
$$389$$ −151.865 + 87.6790i −0.390397 + 0.225396i −0.682332 0.731042i $$-0.739034\pi$$
0.291935 + 0.956438i $$0.405701\pi$$
$$390$$ 489.112 + 57.8577i 1.25413 + 0.148353i
$$391$$ 8.05366i 0.0205976i
$$392$$ 0 0
$$393$$ −46.7170 −0.118873
$$394$$ −61.5099 + 519.987i −0.156117 + 1.31976i
$$395$$ 32.5824 + 56.4344i 0.0824871 + 0.142872i
$$396$$ 397.517 + 95.3803i 1.00383 + 0.240859i
$$397$$ −334.033 192.854i −0.841393 0.485778i 0.0163447 0.999866i $$-0.494797\pi$$
−0.857737 + 0.514088i $$0.828130\pi$$
$$398$$ 591.913 254.352i 1.48722 0.639075i
$$399$$ 0 0
$$400$$ −17.1239 325.112i −0.0428098 0.812779i
$$401$$ −263.548 + 456.479i −0.657228 + 1.13835i 0.324103 + 0.946022i $$0.394938\pi$$
−0.981330 + 0.192330i $$0.938396\pi$$
$$402$$ −500.792 + 670.734i −1.24575 + 1.66849i
$$403$$ −369.392 639.805i −0.916605 1.58761i
$$404$$ −346.319 + 102.634i −0.857226 + 0.254044i
$$405$$ 262.590i 0.648371i
$$406$$ 0 0
$$407$$ 67.3178i 0.165400i
$$408$$ −30.3935 + 25.2881i −0.0744938 + 0.0619807i
$$409$$ −211.872 366.973i −0.518025 0.897245i −0.999781 0.0209399i $$-0.993334\pi$$
0.481756 0.876305i $$-0.339999\pi$$
$$410$$ −149.100 111.323i −0.363658 0.271519i
$$411$$ −631.447 + 1093.70i −1.53637 + 2.66107i
$$412$$ −327.364 310.576i −0.794574 0.753824i
$$413$$ 0 0
$$414$$ 310.279 133.331i 0.749467 0.322055i
$$415$$ 136.225 + 78.6498i 0.328254 + 0.189517i
$$416$$ 380.473 569.823i 0.914599 1.36977i
$$417$$ −458.898 794.834i −1.10047 1.90608i
$$418$$ 61.9422 + 7.32723i 0.148187 + 0.0175292i
$$419$$ −295.598 −0.705485 −0.352742 0.935721i $$-0.614751\pi$$
−0.352742 + 0.935721i $$0.614751\pi$$
$$420$$ 0 0
$$421$$ 126.260i 0.299904i −0.988693 0.149952i $$-0.952088\pi$$
0.988693 0.149952i $$-0.0479119\pi$$
$$422$$ 337.233 + 39.8917i 0.799131 + 0.0945302i
$$423$$ −774.124 + 446.941i −1.83008 + 1.05660i
$$424$$ −587.228 + 101.023i −1.38497 + 0.238262i
$$425$$ 9.42970 16.3327i 0.0221875 0.0384299i
$$426$$ 730.063 313.716i 1.71376 0.736424i
$$427$$ 0 0
$$428$$ 396.410 417.839i 0.926192 0.976259i
$$429$$ −519.999 300.221i −1.21212 0.699817i
$$430$$ −144.275 107.721i −0.335524 0.250513i
$$431$$ 220.198 127.131i 0.510900 0.294968i −0.222303 0.974978i $$-0.571358\pi$$
0.733204 + 0.680009i $$0.238024\pi$$
$$432$$ −793.188 403.887i −1.83608 0.934925i
$$433$$ −546.301 −1.26167 −0.630833 0.775919i $$-0.717287\pi$$
−0.630833 + 0.775919i $$0.717287\pi$$
$$434$$ 0 0
$$435$$ 108.368 0.249122
$$436$$ 255.731 75.7876i 0.586540 0.173825i
$$437$$ 44.6244 25.7639i 0.102115 0.0589563i
$$438$$ −214.403 + 287.160i −0.489505 + 0.655617i
$$439$$ 236.715 + 136.667i 0.539214 + 0.311315i 0.744760 0.667332i $$-0.232564\pi$$
−0.205546 + 0.978647i $$0.565897\pi$$
$$440$$ 31.3928 85.1456i 0.0713473 0.193513i
$$441$$ 0 0
$$442$$ 36.4667 15.6702i 0.0825039 0.0354529i
$$443$$ −237.385 + 411.163i −0.535858 + 0.928133i 0.463263 + 0.886221i $$0.346678\pi$$
−0.999121 + 0.0419124i $$0.986655\pi$$
$$444$$ −63.6995 + 265.481i −0.143467 + 0.597930i
$$445$$ −102.438 + 59.1427i −0.230198 + 0.132905i
$$446$$ −10.6812 + 90.2957i −0.0239489 + 0.202457i
$$447$$ 1230.19i 2.75210i
$$448$$ 0 0
$$449$$ 782.101 1.74187 0.870936 0.491396i $$-0.163513\pi$$
0.870936 + 0.491396i $$0.163513\pi$$
$$450$$ 785.353 + 92.9004i 1.74523 + 0.206445i
$$451$$ 113.423 + 196.454i 0.251492 + 0.435597i
$$452$$ 27.8677 + 6.68658i 0.0616542 + 0.0147933i
$$453$$ −682.938 394.294i −1.50759 0.870407i
$$454$$ 146.181 + 340.183i 0.321984 + 0.749302i
$$455$$ 0 0
$$456$$ −237.348 87.5092i −0.520500 0.191906i
$$457$$ 94.7793 164.163i 0.207395 0.359218i −0.743498 0.668738i $$-0.766835\pi$$
0.950893 + 0.309520i $$0.100168\pi$$
$$458$$ −296.401 221.303i −0.647164 0.483194i
$$459$$ −25.7811 44.6541i −0.0561679 0.0972857i
$$460$$ −21.3015 71.8781i −0.0463076 0.156257i
$$461$$ 202.533i 0.439335i 0.975575 + 0.219667i $$0.0704972\pi$$
−0.975575 + 0.219667i $$0.929503\pi$$
$$462$$ 0 0
$$463$$ 652.927i 1.41021i −0.709103 0.705105i $$-0.750900\pi$$
0.709103 0.705105i $$-0.249100\pi$$
$$464$$ 68.4064 134.342i 0.147428 0.289531i
$$465$$ 198.420 + 343.674i 0.426710 + 0.739084i
$$466$$ −115.707 + 154.971i −0.248298 + 0.332556i
$$467$$ 272.725 472.373i 0.583993 1.01150i −0.411008 0.911632i $$-0.634823\pi$$
0.995000 0.0998730i $$-0.0318437\pi$$
$$468$$ 1207.43 + 1145.51i 2.57998 + 2.44767i
$$469$$ 0 0
$$470$$ 78.3411 + 182.311i 0.166683 + 0.387895i
$$471$$ −530.266 306.149i −1.12583 0.649998i
$$472$$ 72.7998 + 423.171i 0.154237 + 0.896549i
$$473$$ 109.753 + 190.098i 0.232036 + 0.401898i
$$474$$ −37.8489 + 319.963i −0.0798499 + 0.675028i
$$475$$ 120.663 0.254028
$$476$$ 0 0
$$477$$ 1447.40i 3.03438i
$$478$$ 38.3394 324.110i 0.0802079 0.678054i
$$479$$ 94.3079 54.4487i 0.196885 0.113672i −0.398317 0.917248i $$-0.630405\pi$$
0.595202 + 0.803576i $$0.297072\pi$$
$$480$$ −204.373 + 306.083i −0.425777 + 0.637672i
$$481$$ 137.036 237.354i 0.284899 0.493459i
$$482$$ 162.257 + 377.596i 0.336633 + 0.783394i
$$483$$ 0 0
$$484$$ 256.973 270.865i 0.530937 0.559637i
$$485$$ 100.333 + 57.9272i 0.206872 + 0.119437i
$$486$$ 177.666 237.956i 0.365568 0.489622i
$$487$$ 371.831 214.677i 0.763513 0.440814i −0.0670428 0.997750i $$-0.521356\pi$$
0.830556 + 0.556936i $$0.188023\pi$$
$$488$$ −142.327 171.061i −0.291653 0.350534i
$$489$$ −262.929 −0.537686
$$490$$ 0 0
$$491$$ 453.887 0.924413 0.462206 0.886772i $$-0.347058\pi$$
0.462206 + 0.886772i $$0.347058\pi$$
$$492$$ −261.411 882.083i −0.531323 1.79285i
$$493$$ 7.56306 4.36654i 0.0153409 0.00885707i
$$494$$ 203.485 + 151.928i 0.411912 + 0.307547i
$$495$$ 190.905 + 110.219i 0.385667 + 0.222665i
$$496$$ 551.299 29.0374i 1.11149 0.0585431i
$$497$$ 0 0
$$498$$ 307.053 + 714.556i 0.616572 + 1.43485i
$$499$$ −166.698 + 288.730i −0.334064 + 0.578617i −0.983305 0.181967i $$-0.941754\pi$$
0.649240 + 0.760583i $$0.275087\pi$$
$$500$$ 91.2849 380.449i 0.182570 0.760898i
$$501$$ 1115.02 643.755i 2.22558 1.28494i
$$502$$ 316.392 + 37.4265i 0.630264 + 0.0745547i
$$503$$ 580.170i 1.15342i −0.816949 0.576710i $$-0.804336\pi$$
0.816949 0.576710i $$-0.195664\pi$$
$$504$$ 0 0
$$505$$ −194.775 −0.385693
$$506$$ −10.7364 + 90.7621i −0.0212181 + 0.179372i
$$507$$ −771.724 1336.67i −1.52214 2.63642i
$$508$$ 122.717 511.450i 0.241570 1.00679i
$$509$$ 266.271 + 153.732i 0.523126 + 0.302027i 0.738213 0.674568i $$-0.235670\pi$$
−0.215087 + 0.976595i $$0.569003\pi$$
$$510$$ −19.5882 + 8.41730i −0.0384083 + 0.0165045i
$$511$$ 0 0
$$512$$ 250.438 + 446.570i 0.489136 + 0.872207i
$$513$$ 164.949 285.700i 0.321538 0.556919i
$$514$$ 258.187 345.801i 0.502309 0.672765i
$$515$$ −121.664 210.728i −0.236241 0.409181i
$$516$$ −252.952 853.542i −0.490218 1.65415i
$$517$$ 241.910i 0.467911i
$$518$$ 0 0
$$519$$ 290.187i 0.559127i
$$520$$ 284.015 236.307i 0.546182 0.454437i
$$521$$ 360.480 + 624.369i 0.691899 + 1.19840i 0.971215 + 0.238205i $$0.0765591\pi$$
−0.279316 + 0.960199i $$0.590108\pi$$
$$522$$ 293.436 + 219.089i 0.562138 + 0.419711i
$$523$$ −134.988 + 233.807i −0.258104 + 0.447049i −0.965734 0.259534i $$-0.916431\pi$$
0.707630 + 0.706583i $$0.249764\pi$$
$$524$$ −24.1199 + 25.4238i −0.0460304 + 0.0485186i
$$525$$ 0 0
$$526$$ −604.837 + 259.905i −1.14988 + 0.494117i
$$527$$ 27.6957 + 15.9901i 0.0525536 + 0.0303418i
$$528$$ 376.236 244.471i 0.712569 0.463013i
$$529$$ −226.749 392.741i −0.428637 0.742421i
$$530$$ −319.080 37.7443i −0.602037 0.0712157i
$$531$$ −1043.03 −1.96428
$$532$$ 0 0
$$533$$ 923.564i 1.73277i
$$534$$ −580.788 68.7022i −1.08762 0.128656i
$$535$$ 268.967 155.288i 0.502743 0.290259i
$$536$$ 106.461 + 618.835i 0.198621 + 1.15454i
$$537$$ −338.652 + 586.562i −0.630636 + 1.09229i
$$538$$ −538.520 + 231.408i −1.00097 + 0.430127i
$$539$$ 0 0
$$540$$ −348.201 330.344i −0.644817 0.611748i
$$541$$ −785.695 453.621i −1.45230 0.838486i −0.453689 0.891160i $$-0.649892\pi$$
−0.998612 + 0.0526734i $$0.983226\pi$$
$$542$$ −43.0297 32.1274i −0.0793907 0.0592757i
$$543$$ −982.241 + 567.097i −1.80891 + 1.04438i
$$544$$ −1.93012 + 29.5966i −0.00354801 + 0.0544055i
$$545$$ 143.827 0.263903
$$546$$ 0 0
$$547$$ −557.327 −1.01888 −0.509439 0.860506i $$-0.670147\pi$$
−0.509439 + 0.860506i $$0.670147\pi$$
$$548$$ 269.185 + 908.314i 0.491213 + 1.65751i
$$549$$ 468.127 270.273i 0.852690 0.492301i
$$550$$ −128.043 + 171.494i −0.232805 + 0.311807i
$$551$$ 48.3889 + 27.9374i 0.0878202 + 0.0507030i
$$552$$ 128.225 347.779i 0.232291 0.630035i
$$553$$ 0 0
$$554$$ −615.163 + 264.343i −1.11040 + 0.477153i
$$555$$ −73.6096 + 127.496i −0.132630 + 0.229722i
$$556$$ −669.484 160.636i −1.20411 0.288914i
$$557$$ 741.896 428.334i 1.33195 0.769002i 0.346352 0.938105i $$-0.387420\pi$$
0.985598 + 0.169103i $$0.0540869\pi$$
$$558$$ −157.533 + 1331.74i −0.282318 + 2.38663i
$$559$$ 893.680i 1.59871i
$$560$$ 0 0
$$561$$ 25.9918 0.0463313
$$562$$ −245.006 28.9821i −0.435954 0.0515696i
$$563$$ 6.84436 + 11.8548i 0.0121569 + 0.0210564i 0.872040 0.489435i $$-0.162797\pi$$
−0.859883 + 0.510491i $$0.829464\pi$$
$$564$$ −228.908 + 954.020i −0.405865 + 1.69152i
$$565$$ 13.3833 + 7.72686i 0.0236873 + 0.0136759i
$$566$$ −0.488693 1.13726i −0.000863416 0.00200929i
$$567$$ 0 0
$$568$$ 206.204 559.278i 0.363034 0.984644i
$$569$$ 545.991 945.684i 0.959563 1.66201i 0.235999 0.971753i $$-0.424164\pi$$
0.723563 0.690258i $$-0.242503\pi$$
$$570$$ −109.303 81.6090i −0.191759 0.143174i
$$571$$ −359.549 622.757i −0.629683 1.09064i −0.987615 0.156895i $$-0.949852\pi$$
0.357932 0.933747i $$-0.383482\pi$$
$$572$$ −431.858 + 127.984i −0.754997 + 0.223748i
$$573$$ 216.142i 0.377210i
$$574$$ 0 0
$$575$$ 176.805i 0.307486i
$$576$$ −1172.21 + 415.620i −2.03508 + 0.721562i
$$577$$ −515.560 892.976i −0.893518 1.54762i −0.835628 0.549296i $$-0.814896\pi$$
−0.0578905 0.998323i $$-0.518437\pi$$
$$578$$ 344.773 461.771i 0.596494 0.798911i
$$579$$ 752.665 1303.65i 1.29994 2.25156i
$$580$$ 55.9503 58.9748i 0.0964660 0.101681i
$$581$$ 0 0
$$582$$ 226.151 + 526.285i 0.388575 + 0.904270i
$$583$$ 339.229 + 195.854i 0.581868 + 0.335942i
$$584$$ 45.5788 + 264.941i 0.0780459 + 0.453666i
$$585$$ 448.738 + 777.238i 0.767074 + 1.32861i
$$586$$ −6.64410 + 56.1673i −0.0113381 + 0.0958486i
$$587$$ 671.907 1.14464 0.572322 0.820029i $$-0.306043\pi$$
0.572322 + 0.820029i $$0.306043\pi$$
$$588$$ 0 0
$$589$$ 204.612i 0.347388i
$$590$$ −27.1995 + 229.937i −0.0461009 + 0.389723i
$$591$$ −1208.99 + 698.008i −2.04566 + 1.18106i
$$592$$ 111.589 + 171.733i 0.188495 + 0.290090i
$$593$$ 176.999 306.572i 0.298481 0.516984i −0.677308 0.735700i $$-0.736853\pi$$
0.975789 + 0.218716i $$0.0701867\pi$$
$$594$$ 231.016 + 537.606i 0.388915 + 0.905061i
$$595$$ 0 0
$$596$$ −669.480 635.146i −1.12329 1.06568i
$$597$$ 1487.53 + 858.824i 2.49167 + 1.43857i
$$598$$ −222.616 + 298.160i −0.372268 + 0.498595i
$$599$$ −983.923 + 568.068i −1.64261 + 0.948361i −0.662708 + 0.748878i $$0.730593\pi$$
−0.979901 + 0.199484i $$0.936074\pi$$
$$600$$ 667.238 555.158i 1.11206 0.925264i
$$601$$ 6.80783 0.0113275 0.00566375 0.999984i $$-0.498197\pi$$
0.00566375 + 0.999984i $$0.498197\pi$$
$$602$$ 0 0
$$603$$ −1525.30 −2.52953
$$604$$ −567.179 + 168.087i −0.939037 + 0.278290i
$$605$$ 174.358 100.666i 0.288196 0.166390i
$$606$$ −771.665 576.151i −1.27337 0.950744i
$$607$$ −386.628 223.220i −0.636948 0.367742i 0.146490 0.989212i $$-0.453202\pi$$
−0.783438 + 0.621470i $$0.786536\pi$$
$$608$$ −170.166 + 83.9859i −0.279878 + 0.138135i
$$609$$ 0 0
$$610$$ −47.3743 110.247i −0.0776627 0.180732i
$$611$$ 492.447 852.944i 0.805970 1.39598i
$$612$$ −70.0579 16.8097i −0.114474 0.0274668i
$$613$$ 555.650 320.805i 0.906443 0.523335i 0.0271583 0.999631i $$-0.491354\pi$$
0.879285 + 0.476296i $$0.158021\pi$$
$$614$$ −796.235 94.1877i −1.29680 0.153400i
$$615$$ 496.096i 0.806661i
$$616$$ 0 0
$$617$$ −502.890 −0.815057 −0.407528 0.913193i $$-0.633609\pi$$
−0.407528 + 0.913193i $$0.633609\pi$$
$$618$$ 141.329 1194.75i 0.228688 1.93326i
$$619$$ 216.495 + 374.980i 0.349749 + 0.605783i 0.986205 0.165530i $$-0.0529336\pi$$
−0.636456 + 0.771313i $$0.719600\pi$$
$$620$$ 289.475 + 69.4565i 0.466894 + 0.112027i
$$621$$ 418.627 + 241.695i 0.674118 + 0.389202i
$$622$$ −298.096 + 128.095i −0.479254 + 0.205941i
$$623$$ 0 0
$$624$$ 1824.22 96.0833i 2.92343 0.153980i
$$625$$ −148.859 + 257.831i −0.238174 + 0.412530i
$$626$$ −318.575 + 426.682i −0.508906 + 0.681601i
$$627$$ 83.1486 + 144.018i 0.132613 + 0.229693i
$$628$$ −440.385 + 130.511i −0.701250 + 0.207820i
$$629$$ 11.8640i 0.0188617i
$$630$$ 0 0
$$631$$ 238.957i 0.378695i 0.981910 + 0.189348i $$0.0606373\pi$$
−0.981910 + 0.189348i $$0.939363\pi$$
$$632$$ 154.585 + 185.794i 0.244597 + 0.293978i
$$633$$ 452.687 + 784.078i 0.715146 + 1.23867i
$$634$$ 693.688 + 517.930i 1.09414 + 0.816925i
$$635$$ 141.809 245.621i 0.223322 0.386805i
$$636$$ −1152.49 1093.38i −1.81209 1.71916i
$$637$$ 0 0
$$638$$ −91.0543 + 39.1271i −0.142718 + 0.0613277i
$$639$$ 1253.96 + 723.974i 1.96238 + 1.13298i
$$640$$ 61.0554 + 269.252i 0.0953991 + 0.420706i
$$641$$ 3.98065 + 6.89469i 0.00621006 + 0.0107561i 0.869114 0.494612i $$-0.164690\pi$$
−0.862904 + 0.505368i $$0.831357\pi$$
$$642$$ 1524.95 + 180.388i 2.37531 + 0.280979i
$$643$$ 584.919 0.909672 0.454836 0.890575i $$-0.349698\pi$$
0.454836 + 0.890575i $$0.349698\pi$$
$$644$$ 0 0
$$645$$ 480.044i 0.744255i
$$646$$ −10.9166 1.29134i −0.0168988 0.00199898i
$$647$$ 290.707 167.840i 0.449316 0.259413i −0.258225 0.966085i $$-0.583138\pi$$
0.707541 + 0.706672i $$0.249804\pi$$
$$648$$ −165.125 959.840i −0.254823 1.48123i
$$649$$ 141.137 244.457i 0.217469 0.376667i
$$650$$ −800.566 + 344.012i −1.23164 + 0.529250i
$$651$$ 0 0
$$652$$ −135.750 + 143.088i −0.208205 + 0.219460i
$$653$$ 42.0252 + 24.2632i 0.0643571 + 0.0371566i 0.531833 0.846849i $$-0.321503\pi$$
−0.467476 + 0.884006i $$0.654837\pi$$
$$654$$ 569.818 + 425.445i 0.871281 + 0.650528i
$$655$$ −16.3656 + 9.44866i −0.0249856 + 0.0144254i
$$656$$ −615.003 313.157i −0.937505 0.477373i
$$657$$ −653.026 −0.993951
$$658$$ 0 0
$$659$$ 1224.65 1.85835 0.929176 0.369638i $$-0.120518\pi$$
0.929176 + 0.369638i $$0.120518\pi$$
$$660$$ 231.974 68.7470i 0.351476 0.104162i
$$661$$ −725.765 + 419.021i −1.09798 + 0.633919i −0.935690 0.352823i $$-0.885222\pi$$
−0.162291 + 0.986743i $$0.551888\pi$$
$$662$$ −97.2226 + 130.215i −0.146862 + 0.196699i
$$663$$ 91.6439 + 52.9106i 0.138226 + 0.0798049i
$$664$$ 547.399 + 201.824i 0.824396 + 0.303951i
$$665$$ 0 0
$$666$$ −457.078 + 196.412i −0.686303 + 0.294912i
$$667$$ −40.9358 + 70.9029i −0.0613730 + 0.106301i
$$668$$ 225.345 939.172i 0.337343 1.40595i
$$669$$ −209.940 + 121.209i −0.313812 + 0.181180i
$$670$$ −39.7759 + 336.254i −0.0593670 + 0.501871i
$$671$$ 146.287i 0.218014i
$$672$$ 0 0
$$673$$ 147.714 0.219486 0.109743 0.993960i $$-0.464997\pi$$
0.109743 + 0.993960i $$0.464997\pi$$
$$674$$ −138.026 16.3273i −0.204786 0.0242244i
$$675$$ 565.980 + 980.307i 0.838490 + 1.45231i
$$676$$ −1125.87 270.140i −1.66548 0.399616i
$$677$$ 725.024 + 418.593i 1.07094 + 0.618305i 0.928437 0.371490i $$-0.121153\pi$$
0.142499 + 0.989795i $$0.454486\pi$$
$$678$$ 30.1661 + 70.2007i 0.0444927 + 0.103541i
$$679$$ 0 0
$$680$$ −5.53263 + 15.0059i −0.00813622 + 0.0220676i
$$681$$ −493.582 + 854.909i −0.724790 + 1.25537i
$$682$$ −290.805 217.125i −0.426401 0.318365i
$$683$$ 32.2189 + 55.8047i 0.0471725 + 0.0817053i 0.888648 0.458591i $$-0.151646\pi$$
−0.841475 + 0.540296i $$0.818312\pi$$
$$684$$ −130.977 441.957i −0.191486 0.646136i
$$685$$ 510.849i 0.745765i
$$686$$ 0 0
$$687$$ 986.210i 1.43553i
$$688$$ −595.104 303.024i −0.864976 0.440442i
$$689$$ 797.385 + 1381.11i 1.15731 + 2.00452i
$$690$$ 119.579 160.158i 0.173303 0.232113i
$$691$$ −263.374 + 456.177i −0.381149 + 0.660169i −0.991227 0.132172i $$-0.957805\pi$$
0.610078 + 0.792341i $$0.291138\pi$$
$$692$$ 157.922 + 149.823i 0.228211 + 0.216508i
$$693$$ 0 0
$$694$$ 275.852 + 641.948i 0.397482 + 0.924997i
$$695$$ −321.516 185.627i −0.462613 0.267090i
$$696$$ 396.115 68.1452i 0.569130 0.0979098i
$$697$$ −19.9895 34.6229i −0.0286794 0.0496741i
$$698$$ 38.9622 329.375i 0.0558198 0.471884i
$$699$$ −515.633 −0.737672
$$700$$ 0 0
$$701$$ 695.486i 0.992134i 0.868284 + 0.496067i $$0.165223\pi$$
−0.868284 + 0.496067i $$0.834777\pi$$
$$702$$ −279.854 + 2365.80i −0.398652 + 3.37009i
$$703$$ −65.7370 + 37.9532i −0.0935092 + 0.0539875i
$$704$$ 61.2072 330.971i 0.0869420 0.470130i
$$705$$ −264.520 + 458.162i −0.375206 + 0.649876i
$$706$$ −372.471 866.794i −0.527580 1.22775i
$$707$$ 0 0
$$708$$ −787.920 + 830.513i −1.11288 + 1.17304i
$$709$$ −803.161 463.705i −1.13281 0.654027i −0.188168 0.982137i $$-0.560255\pi$$
−0.944640 + 0.328110i $$0.893588\pi$$
$$710$$ 192.300 257.557i 0.270846 0.362756i
$$711$$ −508.447 + 293.552i −0.715115 + 0.412872i
$$712$$ −337.249 + 280.599i −0.473664 + 0.394100i
$$713$$ −299.812 −0.420493
$$714$$ 0 0
$$715$$ −242.883 −0.339697
$$716$$ 144.366 + 487.138i 0.201629 + 0.680361i
$$717$$ 753.566 435.071i 1.05100 0.606794i
$$718$$ 1052.88 + 786.113i 1.46640 + 1.09486i
$$719$$ 1150.37 + 664.169i 1.59996 + 0.923739i 0.991493 + 0.130163i $$0.0415501\pi$$
0.608471 + 0.793576i $$0.291783\pi$$
$$720$$ −669.720 + 35.2747i −0.930167 + 0.0489927i
$$721$$ 0 0
$$722$$ 257.281 + 598.730i 0.356345 + 0.829266i
$$723$$ −547.865 + 948.929i −0.757766 + 1.31249i
$$724$$ −198.511 + 827.335i −0.274186 + 1.14273i
$$725$$ −166.034 + 95.8600i −0.229013 + 0.132221i
$$726$$ 988.551 + 116.937i 1.36164 + 0.161070i
$$727$$ 539.401i 0.741954i −0.928642 0.370977i $$-0.879023\pi$$
0.928642 0.370977i $$-0.120977\pi$$
$$728$$ 0 0
$$729$$ −303.936 −0.416922
$$730$$ −17.0292 + 143.960i −0.0233277 + 0.197205i
$$731$$ −19.3427 33.5026i −0.0264606 0.0458311i
$$732$$ 138.425 576.913i 0.189105 0.788133i
$$733$$ 382.859 + 221.044i 0.522318 + 0.301561i 0.737883 0.674929i $$-0.235826\pi$$
−0.215564 + 0.976490i $$0.569159\pi$$
$$734$$ 653.196 280.686i 0.889913 0.382406i
$$735$$ 0 0
$$736$$ −123.062 249.339i −0.167204 0.338776i
$$737$$ 206.396 357.488i 0.280048 0.485058i
$$738$$ 1002.96 1343.32i 1.35903 1.82021i
$$739$$ 574.116 + 994.398i 0.776882 + 1.34560i 0.933730 + 0.357977i $$0.116533\pi$$
−0.156848 + 0.987623i $$0.550133\pi$$
$$740$$ 31.3796 + 105.885i 0.0424049 + 0.143088i
$$741$$ 677.050i 0.913698i
$$742$$ 0 0
$$743$$ 588.688i 0.792313i 0.918183 + 0.396156i $$0.129656\pi$$
−0.918183 + 0.396156i $$0.870344\pi$$
$$744$$ 941.394 + 1131.45i 1.26531 + 1.52077i
$$745$$ −248.810 430.952i −0.333973 0.578459i
$$746$$ −506.414 378.106i −0.678840 0.506844i
$$747$$ −708.597 + 1227.33i −0.948590 + 1.64301i
$$748$$ 13.4196 14.1450i 0.0179406 0.0189104i
$$749$$ 0 0
$$750$$ 958.378 411.826i 1.27784 0.549101i
$$751$$ 708.754 + 409.199i 0.943747 + 0.544873i 0.891133 0.453742i $$-0.149911\pi$$
0.0526140 + 0.998615i $$0.483245\pi$$
$$752$$ 401.001 + 617.133i 0.533246 + 0.820656i
$$753$$ 424.712 + 735.622i 0.564026 + 0.976922i
$$754$$ −400.695 47.3988i −0.531426 0.0628631i
$$755$$ −318.989 −0.422503
$$756$$ 0 0
$$757$$ 105.101i 0.138838i −0.997588 0.0694192i $$-0.977885\pi$$
0.997588 0.0694192i $$-0.0221146\pi$$
$$758$$ −354.337 41.9150i −0.467464 0.0552969i
$$759$$ −211.025 + 121.835i −0.278030 + 0.160521i
$$760$$ −100.845 + 17.3488i −0.132691 + 0.0228274i
$$761$$ 507.117 878.352i 0.666382 1.15421i −0.312527 0.949909i $$-0.601175\pi$$
0.978909 0.204299i $$-0.0654913\pi$$
$$762$$ 1288.38 553.631i 1.69079 0.726550i
$$763$$ 0 0
$$764$$ −117.626 111.594i −0.153961 0.146065i
$$765$$ −33.6449 19.4249i −0.0439803 0.0253920i
$$766$$ 1119.25 + 835.667i 1.46116 + 1.09095i
$$767$$ 995.264 574.616i 1.29761 0.749173i
$$768$$ −554.564 + 1247.33i −0.722089 + 1.62413i
$$769$$ 1183.99 1.53964 0.769822 0.638258i $$-0.220345\pi$$
0.769822 + 0.638258i $$0.220345\pi$$
$$770$$ 0 0
$$771$$ 1150.58 1.49232
$$772$$ −320.860 1082.68i −0.415621 1.40244i
$$773$$ 280.862 162.156i 0.363340 0.209774i −0.307205 0.951643i $$-0.599394\pi$$
0.670545 + 0.741869i $$0.266060\pi$$
$$774$$ 970.512 1299.85i 1.25389 1.67939i
$$775$$ −608.014 351.037i −0.784534 0.452951i
$$776$$ 403.170 + 148.647i 0.519550 + 0.191556i
$$777$$ 0 0