# Properties

 Label 392.3.k.l.275.2 Level 392 Weight 3 Character 392.275 Analytic conductor 10.681 Analytic rank 0 Dimension 12 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: $$12$$ 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 275.2 Root $$-0.407369 - 0.812545i$$ of defining polynomial Character $$\chi$$ $$=$$ 392.275 Dual form 392.3.k.l.67.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.19654 - 1.60259i) q^{2} +(2.66613 + 4.61787i) q^{3} +(-1.13656 + 3.83513i) q^{4} +(-1.86796 - 1.07847i) q^{5} +(4.21039 - 9.79818i) q^{6} +(7.50608 - 2.76746i) q^{8} +(-9.71647 + 16.8294i) q^{9} +O(q^{10})$$ $$q+(-1.19654 - 1.60259i) q^{2} +(2.66613 + 4.61787i) q^{3} +(-1.13656 + 3.83513i) 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} +(0.506759 + 4.28400i) q^{10} +(-2.62956 - 4.55453i) q^{11} +(-20.7403 + 4.97644i) q^{12} +21.4116i q^{13} -11.5013i q^{15} +(-13.4164 - 8.71774i) q^{16} +(0.463429 + 0.802683i) q^{17} +(38.5968 - 4.56566i) 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} +(32.7919 + 27.2837i) q^{24} +(-10.1738 - 17.6216i) q^{25} +(34.3139 - 25.6199i) q^{26} -55.6311 q^{27} +9.42223i q^{29} +(-18.4318 + 13.7618i) q^{30} +(-29.8813 + 17.2520i) q^{31} +(2.08243 + 31.9322i) 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} +(11.7781 - 1.39324i) q^{38} +(-98.8758 + 57.0860i) q^{39} +(-17.0056 - 2.92555i) q^{40} -43.1339 q^{41} -41.7382 q^{43} +(20.4559 - 4.90818i) q^{44} +(36.2999 - 20.9578i) q^{45} +(-2.04148 - 17.2581i) 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} +(-82.1161 - 24.3356i) q^{52} +(64.5031 - 37.2409i) q^{53} +(66.5650 + 89.1536i) q^{54} +11.3436i q^{55} -31.6208 q^{57} +(15.0999 - 11.2741i) q^{58} +(26.8367 + 46.4825i) q^{59} +(44.1090 + 13.0720i) 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} +(-55.6975 + 6.58853i) q^{66} +(39.2453 + 67.9749i) q^{67} +(-3.60511 + 0.865011i) q^{68} +46.3330i q^{69} +74.5100i q^{71} +(-26.3578 + 153.213i) q^{72} +(16.8020 + 29.1020i) q^{73} +(3.00734 + 25.4232i) 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} +(15.6596 + 30.7536i) q^{80} +(-60.8713 - 105.432i) q^{81} +(51.6116 + 69.1258i) q^{82} +72.9274 q^{83} -1.99917i q^{85} +(49.9416 + 66.8891i) q^{86} +(-43.5106 + 25.1209i) q^{87} +(-32.3421 - 26.9094i) 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} +(10.8070 + 91.3596i) q^{94} +(11.0772 - 6.39541i) q^{95} +(-141.907 + 94.7516i) 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.19654 1.60259i −0.598272 0.801293i
$$3$$ 2.66613 + 4.61787i 0.888709 + 1.53929i 0.841403 + 0.540409i $$0.181730\pi$$
0.0473064 + 0.998880i $$0.484936\pi$$
$$4$$ −1.13656 + 3.83513i −0.284141 + 0.958782i
$$5$$ −1.86796 1.07847i −0.373592 0.215693i 0.301435 0.953487i $$-0.402534\pi$$
−0.675026 + 0.737794i $$0.735868\pi$$
$$6$$ 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
$$10$$ 0.506759 + 4.28400i 0.0506759 + 0.428400i
$$11$$ −2.62956 4.55453i −0.239051 0.414048i 0.721392 0.692527i $$-0.243503\pi$$
−0.960442 + 0.278480i $$0.910170\pi$$
$$12$$ −20.7403 + 4.97644i −1.72836 + 0.414703i
$$13$$ 21.4116i 1.64704i 0.567285 + 0.823522i $$0.307994\pi$$
−0.567285 + 0.823522i $$0.692006\pi$$
$$14$$ 0 0
$$15$$ 11.5013i 0.766754i
$$16$$ −13.4164 8.71774i −0.838528 0.544859i
$$17$$ 0.463429 + 0.802683i 0.0272606 + 0.0472167i 0.879334 0.476206i $$-0.157988\pi$$
−0.852073 + 0.523423i $$0.824655\pi$$
$$18$$ 38.5968 4.56566i 2.14426 0.253648i
$$19$$ −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 0.654587 0.755987i $$-0.272843\pi$$
−0.327410 + 0.944882i $$0.606176\pi$$
$$24$$ 32.7919 + 27.2837i 1.36633 + 1.13682i
$$25$$ −10.1738 17.6216i −0.406953 0.704863i
$$26$$ 34.3139 25.6199i 1.31976 0.985380i
$$27$$ −55.6311 −2.06041
$$28$$ 0 0
$$29$$ 9.42223i 0.324904i 0.986716 + 0.162452i $$0.0519403\pi$$
−0.986716 + 0.162452i $$0.948060\pi$$
$$30$$ −18.4318 + 13.7618i −0.614395 + 0.458728i
$$31$$ −29.8813 + 17.2520i −0.963912 + 0.556515i −0.897375 0.441269i $$-0.854529\pi$$
−0.0665375 + 0.997784i $$0.521195\pi$$
$$32$$ 2.08243 + 31.9322i 0.0650759 + 0.997880i
$$33$$ 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 0.342662 0.939459i $$-0.388672\pi$$
−0.642265 + 0.766483i $$0.722005\pi$$
$$38$$ 11.7781 1.39324i 0.309949 0.0366643i
$$39$$ −98.8758 + 57.0860i −2.53528 + 1.46374i
$$40$$ −17.0056 2.92555i −0.425141 0.0731387i
$$41$$ −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 $$0.661300\pi$$
$$44$$ 20.4559 4.90818i 0.464906 0.111550i
$$45$$ 36.2999 20.9578i 0.806665 0.465728i
$$46$$ −2.04148 17.2581i −0.0443800 0.375175i
$$47$$ −39.8357 22.9991i −0.847567 0.489343i 0.0122620 0.999925i $$-0.496097\pi$$
−0.859829 + 0.510582i $$0.829430\pi$$
$$48$$ 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
$$52$$ −82.1161 24.3356i −1.57916 0.467993i
$$53$$ 64.5031 37.2409i 1.21704 0.702658i 0.252756 0.967530i $$-0.418663\pi$$
0.964284 + 0.264872i $$0.0853297\pi$$
$$54$$ 66.5650 + 89.1536i 1.23269 + 1.65099i
$$55$$ 11.3436i 0.206246i
$$56$$ 0 0
$$57$$ −31.6208 −0.554751
$$58$$ 15.0999 11.2741i 0.260344 0.194381i
$$59$$ 26.8367 + 46.4825i 0.454860 + 0.787840i 0.998680 0.0513617i $$-0.0163561\pi$$
−0.543821 + 0.839201i $$0.683023\pi$$
$$60$$ 44.1090 + 13.0720i 0.735150 + 0.217866i
$$61$$ 24.0893 + 13.9080i 0.394907 + 0.228000i 0.684284 0.729215i $$-0.260115\pi$$
−0.289377 + 0.957215i $$0.593448\pi$$
$$62$$ 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
$$66$$ −55.6975 + 6.58853i −0.843902 + 0.0998262i
$$67$$ 39.2453 + 67.9749i 0.585751 + 1.01455i 0.994781 + 0.102030i $$0.0325338\pi$$
−0.409030 + 0.912521i $$0.634133\pi$$
$$68$$ −3.60511 + 0.865011i −0.0530164 + 0.0127207i
$$69$$ 46.3330i 0.671493i
$$70$$ 0 0
$$71$$ 74.5100i 1.04944i 0.851276 + 0.524719i $$0.175829\pi$$
−0.851276 + 0.524719i $$0.824171\pi$$
$$72$$ −26.3578 + 153.213i −0.366081 + 2.12796i
$$73$$ 16.8020 + 29.1020i 0.230165 + 0.398657i 0.957857 0.287247i $$-0.0927401\pi$$
−0.727692 + 0.685904i $$0.759407\pi$$
$$74$$ 3.00734 + 25.4232i 0.0406397 + 0.343556i
$$75$$ 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 0.325178 0.945653i $$-0.394576\pi$$
−0.656370 + 0.754439i $$0.727909\pi$$
$$80$$ 15.6596 + 30.7536i 0.195745 + 0.384420i
$$81$$ −60.8713 105.432i −0.751497 1.30163i
$$82$$ 51.6116 + 69.1258i 0.629410 + 0.842997i
$$83$$ 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
$$86$$ 49.9416 + 66.8891i 0.580716 + 0.777780i
$$87$$ −43.5106 + 25.1209i −0.500122 + 0.288745i
$$88$$ −32.3421 26.9094i −0.367524 0.305789i
$$89$$ −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
$$94$$ 10.8070 + 91.3596i 0.114969 + 0.971910i
$$95$$ 11.0772 6.39541i 0.116602 0.0673201i
$$96$$ −141.907 + 94.7516i −1.47819 + 0.986996i
$$97$$ 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
$$100$$ 79.1442 18.9899i 0.791442 0.189899i
$$101$$ 78.2037 45.1509i 0.774294 0.447039i −0.0601103 0.998192i $$-0.519145\pi$$
0.834404 + 0.551153i $$0.185812\pi$$
$$102$$ 9.81606 1.16115i 0.0962358 0.0113839i
$$103$$ 97.6980 + 56.4060i 0.948525 + 0.547631i 0.892622 0.450805i $$-0.148863\pi$$
0.0559023 + 0.998436i $$0.482196\pi$$
$$104$$ 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 $$-0.0682637\pi$$
$$108$$ 63.2283 213.352i 0.585447 1.97548i
$$109$$ −57.7477 + 33.3406i −0.529795 + 0.305877i −0.740933 0.671579i $$-0.765616\pi$$
0.211138 + 0.977456i $$0.432283\pi$$
$$110$$ 18.1790 13.5731i 0.165264 0.123391i
$$111$$ 68.2540i 0.614901i
$$112$$ 0 0
$$113$$ 7.16467 0.0634042 0.0317021 0.999497i $$-0.489907\pi$$
0.0317021 + 0.999497i $$0.489907\pi$$
$$114$$ 37.8357 + 50.6750i 0.331892 + 0.444518i
$$115$$ −9.37101 16.2311i −0.0814870 0.141140i
$$116$$ −36.1355 10.7090i −0.311513 0.0923187i
$$117$$ −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
$$122$$ −6.53521 55.2468i −0.0535673 0.452842i
$$123$$ −115.000 199.187i −0.934963 1.61940i
$$124$$ −32.2015 134.207i −0.259690 1.08231i
$$125$$ 97.8118i 0.782494i
$$126$$ 0 0
$$127$$ 131.492i 1.03537i 0.855572 + 0.517684i $$0.173206\pi$$
−0.855572 + 0.517684i $$0.826794\pi$$
$$128$$ −124.831 28.3066i −0.975241 0.221145i
$$129$$ −111.279 192.742i −0.862631 1.49412i
$$130$$ −91.7271 + 10.8505i −0.705593 + 0.0834655i
$$131$$ −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
$$136$$ 5.69993 + 4.74248i 0.0419113 + 0.0348712i
$$137$$ 118.420 + 205.110i 0.864381 + 1.49715i 0.867660 + 0.497158i $$0.165623\pi$$
−0.00327850 + 0.999995i $$0.501044\pi$$
$$138$$ 74.2526 55.4395i 0.538063 0.401735i
$$139$$ −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
$$142$$ 119.409 89.1545i 0.840907 0.627849i
$$143$$ 97.5195 56.3029i 0.681955 0.393727i
$$144$$ 277.075 141.085i 1.92413 0.979758i
$$145$$ 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 0.986944 0.161066i $$-0.0514931\pi$$
0.353985 + 0.935251i $$0.384826\pi$$
$$150$$ −215.495 + 25.4912i −1.43663 + 0.169941i
$$151$$ 128.077 73.9452i 0.848190 0.489703i −0.0118494 0.999930i $$-0.503772\pi$$
0.860040 + 0.510227i $$0.170439\pi$$
$$152$$ −8.04327 + 46.7540i −0.0529163 + 0.307592i
$$153$$ −18.0116 −0.117723
$$154$$ 0 0
$$155$$ 74.4227 0.480146
$$156$$ −106.553 444.083i −0.683034 2.84669i
$$157$$ 99.4450 57.4146i 0.633407 0.365698i −0.148663 0.988888i $$-0.547497\pi$$
0.782070 + 0.623190i $$0.214164\pi$$
$$158$$ 7.09810 + 60.0052i 0.0449247 + 0.379780i
$$159$$ 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 $$0.214998\pi$$
$$164$$ 49.0245 165.424i 0.298930 1.00868i
$$165$$ −52.3830 + 30.2433i −0.317473 + 0.183293i
$$166$$ −87.2609 116.872i −0.525668 0.704051i
$$167$$ 241.457i 1.44585i 0.690926 + 0.722926i $$0.257203\pi$$
−0.690926 + 0.722926i $$0.742797\pi$$
$$168$$ 0 0
$$169$$ −289.455 −1.71275
$$170$$ −3.20385 + 2.39210i −0.0188461 + 0.0140712i
$$171$$ −57.6196 99.8001i −0.336957 0.583626i
$$172$$ 47.4382 160.071i 0.275803 0.930648i
$$173$$ −47.1300 27.2105i −0.272428 0.157286i 0.357563 0.933889i $$-0.383608\pi$$
−0.629990 + 0.776603i $$0.716941\pi$$
$$174$$ 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
$$178$$ 108.920 12.8843i 0.611909 0.0723836i
$$179$$ 63.5100 + 110.003i 0.354805 + 0.614540i 0.987084 0.160200i $$-0.0512141\pi$$
−0.632280 + 0.774740i $$0.717881\pi$$
$$180$$ 39.1186 + 163.035i 0.217325 + 0.905748i
$$181$$ 212.704i 1.17516i −0.809165 0.587581i $$-0.800080\pi$$
0.809165 0.587581i $$-0.199920\pi$$
$$182$$ 0 0
$$183$$ 148.322i 0.810502i
$$184$$ 68.5072 + 11.7856i 0.372322 + 0.0640520i
$$185$$ 13.8046 + 23.9103i 0.0746194 + 0.129245i
$$186$$ 43.2260 + 365.420i 0.232398 + 1.96462i
$$187$$ 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 0.589073 0.808080i $$-0.299493\pi$$
−0.405282 + 0.914192i $$0.632826\pi$$
$$192$$ 321.645 + 114.043i 1.67523 + 0.593974i
$$193$$ −141.153 244.485i −0.731364 1.26676i −0.956300 0.292387i $$-0.905551\pi$$
0.224936 0.974374i $$-0.427783\pi$$
$$194$$ −64.2694 86.0790i −0.331286 0.443706i
$$195$$ 246.261 1.26288
$$196$$ 0 0
$$197$$ 261.806i 1.32896i −0.747304 0.664482i $$-0.768652\pi$$
0.747304 0.664482i $$-0.231348\pi$$
$$198$$ −122.287 163.784i −0.617610 0.827193i
$$199$$ −278.968 + 161.062i −1.40185 + 0.809357i −0.994582 0.103953i $$-0.966851\pi$$
−0.407265 + 0.913310i $$0.633518\pi$$
$$200$$ −125.132 104.113i −0.625662 0.520566i
$$201$$ −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
$$206$$ −26.5046 224.062i −0.128663 1.08768i
$$207$$ −146.234 + 84.4283i −0.706445 + 0.407866i
$$208$$ 186.661 287.267i 0.897406 1.38109i
$$209$$ 31.1870 0.149220
$$210$$ 0 0
$$211$$ 169.792 0.804702 0.402351 0.915485i $$-0.368193\pi$$
0.402351 + 0.915485i $$0.368193\pi$$
$$212$$ 69.5117 + 289.704i 0.327885 + 1.36653i
$$213$$ −344.077 + 198.653i −1.61539 + 0.932644i
$$214$$ −285.986 + 33.8297i −1.33638 + 0.158083i
$$215$$ 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
$$220$$ −43.5040 12.8927i −0.197745 0.0586031i
$$221$$ −17.1867 + 9.92275i −0.0777679 + 0.0448993i
$$222$$ −109.383 + 81.6689i −0.492716 + 0.367878i
$$223$$ 45.4626i 0.203868i −0.994791 0.101934i $$-0.967497\pi$$
0.994791 0.101934i $$-0.0325031\pi$$
$$224$$ 0 0
$$225$$ 395.414 1.75740
$$226$$ −8.57285 11.4820i −0.0379329 0.0508053i
$$227$$ 92.5653 + 160.328i 0.407777 + 0.706290i 0.994640 0.103396i $$-0.0329708\pi$$
−0.586864 + 0.809686i $$0.699637\pi$$
$$228$$ 35.9391 121.270i 0.157627 0.531885i
$$229$$ 160.173 + 92.4759i 0.699445 + 0.403825i 0.807141 0.590359i $$-0.201014\pi$$
−0.107695 + 0.994184i $$0.534347\pi$$
$$230$$ −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 $$0.233203\pi$$
$$234$$ 97.7580 + 826.417i 0.417769 + 3.53170i
$$235$$ 49.6076 + 85.9228i 0.211096 + 0.365629i
$$236$$ −208.768 + 50.0919i −0.884611 + 0.212254i
$$237$$ 161.097i 0.679734i
$$238$$ 0 0
$$239$$ 163.185i 0.682782i 0.939921 + 0.341391i $$0.110898\pi$$
−0.939921 + 0.341391i $$0.889102\pi$$
$$240$$ −100.266 + 154.307i −0.417773 + 0.642945i
$$241$$ 102.745 + 177.960i 0.426330 + 0.738424i 0.996544 0.0830718i $$-0.0264731\pi$$
−0.570214 + 0.821496i $$0.693140\pi$$
$$242$$ −185.391 + 21.9301i −0.766078 + 0.0906204i
$$243$$ 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
$$248$$ −176.547 + 212.190i −0.711883 + 0.855604i
$$249$$ 194.434 + 336.769i 0.780859 + 1.35249i
$$250$$ 156.752 117.036i 0.627007 0.468145i
$$251$$ 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
$$254$$ 210.727 157.336i 0.829633 0.619431i
$$255$$ 9.23191 5.33005i 0.0362036 0.0209021i
$$256$$ 104.002 + 233.922i 0.406257 + 0.913759i
$$257$$ 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
$$262$$ 17.4011 2.05840i 0.0664163 0.00785647i
$$263$$ 285.059 164.579i 1.08387 0.625775i 0.151935 0.988391i $$-0.451450\pi$$
0.931939 + 0.362616i $$0.118116\pi$$
$$264$$ 38.0360 221.096i 0.144076 0.837483i
$$265$$ −160.652 −0.606234
$$266$$ 0 0
$$267$$ −292.419 −1.09520
$$268$$ −305.298 + 73.2531i −1.13917 + 0.273332i
$$269$$ 253.803 146.533i 0.943507 0.544734i 0.0524492 0.998624i $$-0.483297\pi$$
0.891058 + 0.453889i $$0.149964\pi$$
$$270$$ −28.1916 238.323i −0.104413 0.882679i
$$271$$ 23.2529 + 13.4251i 0.0858042 + 0.0495391i 0.542288 0.840193i $$-0.317558\pi$$
−0.456484 + 0.889732i $$0.650891\pi$$
$$272$$ 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
$$276$$ −177.693 52.6605i −0.643816 0.190799i
$$277$$ 289.925 167.389i 1.04666 0.604291i 0.124949 0.992163i $$-0.460123\pi$$
0.921713 + 0.387872i $$0.126790\pi$$
$$278$$ 205.951 + 275.840i 0.740831 + 0.992229i
$$279$$ 670.513i 2.40327i
$$280$$ 0 0
$$281$$ −123.357 −0.438994 −0.219497 0.975613i $$-0.570442\pi$$
−0.219497 + 0.975613i $$0.570442\pi$$
$$282$$ −393.073 + 293.482i −1.39388 + 1.04072i
$$283$$ −0.309453 0.535988i −0.00109347 0.00189395i 0.865478 0.500947i $$-0.167015\pi$$
−0.866572 + 0.499053i $$0.833681\pi$$
$$284$$ −285.756 84.6855i −1.00618 0.298188i
$$285$$ 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
$$290$$ −40.3648 + 4.77480i −0.139189 + 0.0164648i
$$291$$ 143.204 + 248.037i 0.492112 + 0.852362i
$$292$$ −130.707 + 31.3617i −0.447625 + 0.107403i
$$293$$ 28.2794i 0.0965169i −0.998835 0.0482584i $$-0.984633\pi$$
0.998835 0.0482584i $$-0.0153671\pi$$
$$294$$ 0 0
$$295$$ 115.770i 0.392440i
$$296$$ −100.919 17.3615i −0.340943 0.0586538i
$$297$$ 146.285 + 253.373i 0.492542 + 0.853108i
$$298$$ −54.2034 458.220i −0.181891 1.53765i
$$299$$ −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
$$304$$ 84.5514 43.0531i 0.278130 0.141622i
$$305$$ −29.9986 51.9591i −0.0983560 0.170358i
$$306$$ 21.5517 + 28.8651i 0.0704303 + 0.0943305i
$$307$$ −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
$$310$$ −89.0500 119.269i −0.287258 0.384738i
$$311$$ 140.492 81.1132i 0.451743 0.260814i −0.256823 0.966459i $$-0.582676\pi$$
0.708566 + 0.705644i $$0.249342\pi$$
$$312$$ −584.186 + 702.126i −1.87239 + 2.25040i
$$313$$ −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 −0.225936 0.974142i $$-0.572544\pi$$
−0.956600 + 0.291405i $$0.905877\pi$$
$$318$$ −93.3096 788.812i −0.293426 2.48054i
$$319$$ 42.9138 24.7763i 0.134526 0.0776686i
$$320$$ −135.742 + 25.1030i −0.424194 + 0.0784470i
$$321$$ 767.792 2.39187
$$322$$ 0 0
$$323$$ −5.49636 −0.0170166
$$324$$ 473.530 113.619i 1.46151 0.350675i
$$325$$ 377.305 217.837i 1.16094 0.670269i
$$326$$ 97.9353 11.5849i 0.300415 0.0355365i
$$327$$ −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 $$0.205834\pi$$
$$332$$ −82.8867 + 279.686i −0.249659 + 0.842428i
$$333$$ 215.420 124.373i 0.646907 0.373492i
$$334$$ 386.956 288.914i 1.15855 0.865012i
$$335$$ 169.299i 0.505370i
$$336$$ 0 0
$$337$$ −69.4941 −0.206214 −0.103107 0.994670i $$-0.532878\pi$$
−0.103107 + 0.994670i $$0.532878\pi$$
$$338$$ 346.346 + 463.877i 1.02469 + 1.37242i
$$339$$ 19.1019 + 33.0855i 0.0563479 + 0.0975974i
$$340$$ 7.66708 + 2.27219i 0.0225502 + 0.00668291i
$$341$$ 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
$$346$$ 12.7859 + 108.089i 0.0369536 + 0.312395i
$$347$$ 174.677 + 302.549i 0.503391 + 0.871899i 0.999992 + 0.00392020i $$0.00124784\pi$$
−0.496601 + 0.867979i $$0.665419\pi$$
$$348$$ −46.8891 195.420i −0.134739 0.561552i
$$349$$ 165.836i 0.475174i 0.971366 + 0.237587i $$0.0763566\pi$$
−0.971366 + 0.237587i $$0.923643\pi$$
$$350$$ 0 0
$$351$$ 1191.15i 3.39358i
$$352$$ 139.960 93.4519i 0.397614 0.265488i
$$353$$ −235.858 408.519i −0.668154 1.15728i −0.978420 0.206627i $$-0.933751\pi$$
0.310266 0.950650i $$-0.399582\pi$$
$$354$$ 568.437 67.2412i 1.60576 0.189947i
$$355$$ 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 $$-0.965506\pi$$
−0.590731 0.806869i $$1.29884\pi$$
$$360$$ 214.470 257.769i 0.595750 0.716025i
$$361$$ 162.917 + 282.180i 0.451294 + 0.781663i
$$362$$ −340.877 + 254.510i −0.941649 + 0.703067i
$$363$$ 497.722 1.37113
$$364$$ 0 0
$$365$$ 72.4817i 0.198580i
$$366$$ 237.699 177.474i 0.649450 0.484901i
$$367$$ −307.850 + 177.737i −0.838829 + 0.484298i −0.856866 0.515539i $$-0.827592\pi$$
0.0180371 + 0.999837i $$0.494258\pi$$
$$368$$ −63.0845 123.891i −0.171425 0.336659i
$$369$$ 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 0.819767 0.572698i $$-0.194103\pi$$
−0.0860872 + 0.996288i $$0.527436\pi$$
$$374$$ −9.68141 + 1.14523i −0.0258861 + 0.00306210i
$$375$$ −451.682 + 260.779i −1.20449 + 0.695410i
$$376$$ −362.659 62.3896i −0.964518 0.165930i
$$377$$ −201.745 −0.535132
$$378$$ 0 0
$$379$$ −178.404 −0.470723 −0.235361 0.971908i $$-0.575627\pi$$
−0.235361 + 0.971908i $$0.575627\pi$$
$$380$$ 11.9373 + 49.7512i 0.0314140 + 0.130924i
$$381$$ −607.211 + 350.574i −1.59373 + 0.920140i
$$382$$ −9.52341 80.5082i −0.0249304 0.210754i
$$383$$ −604.832 349.200i −1.57920 0.911750i −0.994972 0.100158i $$-0.968065\pi$$
−0.584225 0.811591i $$1.30140\pi$$
$$384$$ −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
$$388$$ −61.0478 + 205.995i −0.157340 + 0.530914i
$$389$$ 151.865 87.6790i 0.390397 0.225396i −0.291935 0.956438i $$-0.594299\pi$$
0.682332 + 0.731042i $$0.260966\pi$$
$$390$$ −294.662 394.655i −0.755544 1.01193i
$$391$$ 8.05366i 0.0205976i
$$392$$ 0 0
$$393$$ −46.7170 −0.118873
$$394$$ −419.567 + 313.263i −1.06489 + 0.795083i
$$395$$ 32.5824 + 56.4344i 0.0824871 + 0.142872i
$$396$$ −116.157 + 391.950i −0.293325 + 0.989773i
$$397$$ 334.033 + 192.854i 0.841393 + 0.485778i 0.857737 0.514088i $$-0.171870\pi$$
−0.0163447 + 0.999866i $$0.505203\pi$$
$$398$$ 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 $$0.938396\pi$$
$$402$$ 831.269 98.3319i 2.06783 0.244607i
$$403$$ −369.392 639.805i −0.916605 1.58761i
$$404$$ 84.2761 + 351.238i 0.208604 + 0.869402i
$$405$$ 262.590i 0.648371i
$$406$$ 0 0
$$407$$ 67.3178i 0.165400i
$$408$$ −6.70340 + 38.9656i −0.0164299 + 0.0955039i
$$409$$ −211.872 366.973i −0.518025 0.897245i −0.999781 0.0209399i $$-0.993334\pi$$
0.481756 0.876305i $$-0.339999\pi$$
$$410$$ −21.8585 184.785i −0.0533134 0.450696i
$$411$$ −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
$$416$$ −683.718 + 44.5881i −1.64355 + 0.107183i
$$417$$ −458.898 794.834i −1.10047 1.90608i
$$418$$ −37.3167 49.9799i −0.0892743 0.119569i
$$419$$ −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 $$0.0479119\pi$$
−0.988693 + 0.149952i $$0.952088\pi$$
$$422$$ −203.164 272.107i −0.481431 0.644802i
$$423$$ 774.124 446.941i 1.83008 1.05660i
$$424$$ 381.102 458.043i 0.898827 1.08029i
$$425$$ 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
$$430$$ −21.1512 178.806i −0.0491889 0.415829i
$$431$$ −220.198 + 127.131i −0.510900 + 0.294968i −0.733204 0.680009i $$-0.761976\pi$$
0.222303 + 0.974978i $$0.428642\pi$$
$$432$$ 746.371 + 484.977i 1.72771 + 1.12263i
$$433$$ −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
$$436$$ −62.2317 259.364i −0.142733 0.594871i
$$437$$ −44.6244 + 25.7639i −0.102115 + 0.0589563i
$$438$$ 355.890 42.0987i 0.812534 0.0961156i
$$439$$ −236.715 136.667i −0.539214 0.311315i 0.205546 0.978647i $$-0.434103\pi$$
−0.744760 + 0.667332i $$0.767436\pi$$
$$440$$ 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 $$0.986655\pi$$
$$444$$ 261.763 + 77.5751i 0.589556 + 0.174719i
$$445$$ 102.438 59.1427i 0.230198 0.132905i
$$446$$ −72.8578 + 54.3981i −0.163358 + 0.121969i
$$447$$ 1230.19i 2.75210i
$$448$$ 0 0
$$449$$ 782.101 1.74187 0.870936 0.491396i $$-0.163513\pi$$
0.870936 + 0.491396i $$0.163513\pi$$
$$450$$ −473.131 633.686i −1.05140 1.40819i
$$451$$ 113.423 + 196.454i 0.251492 + 0.435597i
$$452$$ −8.14311 + 27.4774i −0.0180157 + 0.0607908i
$$453$$ 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 $$0.100168\pi$$
$$458$$ −43.4534 367.343i −0.0948765 0.802058i
$$459$$ −25.7811 44.6541i −0.0561679 0.0972857i
$$460$$ 72.8990 17.4914i 0.158476 0.0380247i
$$461$$ 202.533i 0.439335i −0.975575 0.219667i $$-0.929503\pi$$
0.975575 0.219667i $$-0.0704972\pi$$
$$462$$ 0 0
$$463$$ 652.927i 1.41021i 0.709103 + 0.705105i $$0.249100\pi$$
−0.709103 + 0.705105i $$0.750900\pi$$
$$464$$ 82.1406 126.413i 0.177027 0.272441i
$$465$$ 198.420 + 343.674i 0.426710 + 0.739084i
$$466$$ 192.062 22.7193i 0.412151 0.0487539i
$$467$$ 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
$$472$$ 330.077 + 274.632i 0.699316 + 0.581847i
$$473$$ 109.753 + 190.098i 0.232036 + 0.401898i
$$474$$ −258.172 + 192.760i −0.544666 + 0.406666i
$$475$$ 120.663 0.254028
$$476$$ 0 0
$$477$$ 1447.40i 3.03438i
$$478$$ 261.518 195.258i 0.547108 0.408489i
$$479$$ −94.3079 + 54.4487i −0.196885 + 0.113672i −0.595202 0.803576i $$-0.702928\pi$$
0.398317 + 0.917248i $$0.369595\pi$$
$$480$$ 367.262 23.9507i 0.765129 0.0498972i
$$481$$ 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
$$486$$ −294.909 + 34.8852i −0.606809 + 0.0717802i
$$487$$ −371.831 + 214.677i −0.763513 + 0.440814i −0.830556 0.556936i $$-0.811977\pi$$
0.0670428 + 0.997750i $$0.478644\pi$$
$$488$$ 219.306 + 37.7281i 0.449398 + 0.0773117i
$$489$$ −262.929 −0.537686
$$490$$ 0 0
$$491$$ 453.887 0.924413 0.462206 0.886772i $$-0.347058\pi$$
0.462206 + 0.886772i $$0.347058\pi$$
$$492$$ 894.612 214.653i 1.81832 0.436287i
$$493$$ −7.56306 + 4.36654i −0.0153409 + 0.00885707i
$$494$$ 29.8315 + 252.187i 0.0603877 + 0.510500i
$$495$$ −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 $$0.275087\pi$$
$$500$$ −375.121 111.169i −0.750242 0.222339i
$$501$$ −1115.02 + 643.755i −2.22558 + 1.28494i
$$502$$ −190.608 255.291i −0.379698 0.508547i
$$503$$ 580.170i 1.15342i 0.816949 + 0.576710i $$0.195664\pi$$
−0.816949 + 0.576710i $$0.804336\pi$$
$$504$$ 0 0
$$505$$ −194.775 −0.385693
$$506$$ −73.2341 + 54.6790i −0.144731 + 0.108061i
$$507$$ −771.724 1336.67i −1.52214 2.63642i
$$508$$ −504.288 149.449i −0.992692 0.294190i
$$509$$ −266.271 153.732i −0.523126 0.302027i 0.215087 0.976595i $$-0.430997\pi$$
−0.738213 + 0.674568i $$0.764330\pi$$
$$510$$ −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
$$514$$ −428.566 + 50.6956i −0.833786 + 0.0986296i
$$515$$ −121.664 210.728i −0.236241 0.409181i
$$516$$ 865.665 207.708i 1.67765 0.402534i
$$517$$ 241.910i 0.467911i
$$518$$ 0 0
$$519$$ 290.187i 0.559127i
$$520$$ 62.6406 364.118i 0.120463 0.700226i
$$521$$ 360.480 + 624.369i 0.691899 + 1.19840i 0.971215 + 0.238205i $$0.0765591\pi$$
−0.279316 + 0.960199i $$0.590108\pi$$
$$522$$ 43.0187 + 363.667i 0.0824113 + 0.696681i
$$523$$ −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
$$528$$ −399.836 + 203.595i −0.757266 + 0.385596i
$$529$$ −226.749 392.741i −0.428637 0.742421i
$$530$$ 192.227 + 257.459i 0.362693 + 0.485771i
$$531$$ −1043.03 −1.96428
$$532$$ 0 0
$$533$$ 923.564i 1.73277i
$$534$$ 349.892 + 468.626i 0.655229 + 0.877578i
$$535$$ −268.967 + 155.288i −0.502743 + 0.290259i
$$536$$ 482.696 + 401.615i 0.900553 + 0.749282i
$$537$$ −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 0.998612 0.0526734i $$-0.0167742\pi$$
0.453689 + 0.891160i $$0.350108\pi$$
$$542$$ −6.30831 53.3286i −0.0116389 0.0983922i
$$543$$ 982.241 567.097i 1.80891 1.04438i
$$544$$ −24.6664 + 16.4698i −0.0453426 + 0.0302754i
$$545$$ 143.827 0.263903
$$546$$ 0 0
$$547$$ −557.327 −1.01888 −0.509439 0.860506i $$-0.670147\pi$$
−0.509439 + 0.860506i $$0.670147\pi$$
$$548$$ −921.215 + 221.036i −1.68105 + 0.403351i
$$549$$ −468.127 + 270.273i −0.852690 + 0.492301i
$$550$$ 212.539 25.1415i 0.386435 0.0457119i
$$551$$ −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
$$556$$ 195.627 660.108i 0.351847 1.18725i
$$557$$ −741.896 + 428.334i −1.33195 + 0.769002i −0.985598 0.169103i $$-0.945913\pi$$
−0.346352 + 0.938105i $$0.612580\pi$$
$$558$$ −1074.55 + 802.298i −1.92572 + 1.43781i
$$559$$ 893.680i 1.59871i
$$560$$ 0 0
$$561$$ 25.9918 0.0463313
$$562$$ 147.602 + 197.691i 0.262638 + 0.351763i
$$563$$ 6.84436 + 11.8548i 0.0121569 + 0.0210564i 0.872040 0.489435i $$-0.162797\pi$$
−0.859883 + 0.510491i $$0.829464\pi$$
$$564$$ 940.659 + 278.770i 1.66784 + 0.494273i
$$565$$ −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 $$-0.242503\pi$$
$$570$$ −16.0241 135.463i −0.0281125 0.237655i
$$571$$ −359.549 622.757i −0.629683 1.09064i −0.987615 0.156895i $$-0.949852\pi$$
0.357932 0.933747i $$-0.383482\pi$$
$$572$$ 105.092 + 437.992i 0.183727 + 0.765720i
$$573$$ 216.142i 0.377210i
$$574$$ 0 0
$$575$$ 176.805i 0.307486i
$$576$$ 226.166 + 1222.97i 0.392650 + 2.12321i
$$577$$ −515.560 892.976i −0.893518 1.54762i −0.835628 0.549296i $$-0.814896\pi$$
−0.0578905 0.998323i $$-0.518437\pi$$
$$578$$ −572.292 + 67.6971i −0.990124 + 0.117123i
$$579$$ 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
$$584$$ 206.656 + 171.943i 0.353863 + 0.294423i
$$585$$ 448.738 + 777.238i 0.767074 + 1.32861i
$$586$$ −45.3202 + 33.8376i −0.0773383 + 0.0577434i
$$587$$ 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
$$590$$ −185.531 + 138.524i −0.314460 + 0.234786i
$$591$$ 1208.99 698.008i 2.04566 1.18106i
$$592$$ 92.9309 + 182.506i 0.156978 + 0.308286i
$$593$$ 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
$$598$$ 369.522 43.7113i 0.617930 0.0730958i
$$599$$ 983.923 568.068i 1.64261 0.948361i 0.662708 0.748878i $$-0.269407\pi$$
0.979901 0.199484i $$-0.0639265\pi$$
$$600$$ 147.162 855.424i 0.245270 1.42571i
$$601$$ 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
$$604$$ 138.022 + 575.234i 0.228513 + 0.952375i
$$605$$ −174.358 + 100.666i −0.288196 + 0.166390i
$$606$$ −113.129 956.357i −0.186681 1.57815i
$$607$$ 386.628 + 223.220i 0.636948 + 0.367742i 0.783438 0.621470i $$-0.213464\pi$$
−0.146490 + 0.989212i $$0.546798\pi$$
$$608$$ −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
$$612$$ 20.4713 69.0768i 0.0334499 0.112871i
$$613$$ −555.650 + 320.805i −0.906443 + 0.523335i −0.879285 0.476296i $$-0.841979\pi$$
−0.0271583 + 0.999631i $$0.508646\pi$$
$$614$$ 479.687 + 642.466i 0.781249 + 1.04636i
$$615$$ 496.096i 0.806661i
$$616$$ 0 0
$$617$$ −502.890 −0.815057 −0.407528 0.913193i $$-0.633609\pi$$
−0.407528 + 0.913193i $$0.633609\pi$$
$$618$$ 964.023 719.772i 1.55991 1.16468i
$$619$$ 216.495 + 374.980i 0.349749 + 0.605783i 0.986205 0.165530i $$-0.0529336\pi$$
−0.636456 + 0.771313i $$0.719600\pi$$
$$620$$ −84.5861 + 285.421i −0.136429 + 0.460356i
$$621$$ −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
$$626$$ 528.805 62.5530i 0.844736 0.0999250i
$$627$$ 83.1486 + 144.018i 0.132613 + 0.229693i
$$628$$ 107.167 + 446.640i 0.170648 + 0.711210i
$$629$$ 11.8640i 0.0188617i
$$630$$ 0 0
$$631$$ 238.957i 0.378695i −0.981910 0.189348i $$-0.939363\pi$$
0.981910 0.189348i $$-0.0606373\pi$$
$$632$$ −238.195 40.9777i −0.376891 0.0648381i
$$633$$ 452.687 + 784.078i 0.715146 + 1.23867i
$$634$$ 101.697 + 859.717i 0.160405 + 1.35602i
$$635$$ 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
$$640$$ 202.651 + 187.501i 0.316642 + 0.292971i
$$641$$ 3.98065 + 6.89469i 0.00621006 + 0.0107561i 0.869114 0.494612i $$-0.164690\pi$$
−0.862904 + 0.505368i $$0.831357\pi$$
$$642$$ −918.696 1230.45i −1.43099 1.91659i
$$643$$ 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
$$646$$ 6.57664 + 8.80839i 0.0101806 + 0.0136353i
$$647$$ −290.707 + 167.840i −0.449316 + 0.259413i −0.707541 0.706672i $$-0.750196\pi$$
0.258225 + 0.966085i $$0.416862\pi$$
$$648$$ −748.683 622.923i −1.15538 0.961300i
$$649$$ 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 0.467476 0.884006i $$-0.345163\pi$$
−0.531833 + 0.846849i $$0.678497\pi$$
$$654$$ 83.5372 + 706.199i 0.127733 + 1.07982i
$$655$$ 16.3656 9.44866i 0.0249856 0.0144254i
$$656$$ 578.703 + 376.030i 0.882170 + 0.573217i
$$657$$ −653.026 −0.993951
$$658$$ 0 0
$$659$$ 1224.65 1.85835 0.929176 0.369638i $$-0.120518\pi$$
0.929176 + 0.369638i $$0.120518\pi$$
$$660$$ −56.4505 235.269i −0.0855311 0.356468i
$$661$$ 725.765 419.021i 1.09798 0.633919i 0.162291 0.986743i $$-0.448112\pi$$
0.935690 + 0.352823i $$0.114778\pi$$
$$662$$ 161.381 19.0899i 0.243777 0.0288367i
$$663$$ −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
$$668$$ −926.019 274.432i −1.38626 0.410826i
$$669$$ 209.940 121.209i 0.313812 0.181180i
$$670$$ −271.316 + 202.574i −0.404950 + 0.302349i
$$671$$ 146.287i 0.218014i
$$672$$ 0 0
$$673$$ 147.714 0.219486 0.109743 0.993960i $$-0.464997\pi$$
0.109743 + 0.993960i $$0.464997\pi$$
$$674$$ 83.1528 + 111.370i 0.123372 + 0.165238i
$$675$$ 565.980 + 980.307i 0.838490 + 1.45231i
$$676$$ 328.984 1110.10i 0.486663 1.64216i
$$677$$ −725.024 418.593i −1.07094 0.618305i −0.142499 0.989795i $$-0.545514\pi$$
−0.928437 + 0.371490i $$0.878847\pi$$
$$678$$ 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
$$682$$ −42.6331 360.407i −0.0625118 0.528457i
$$683$$ 32.2189 + 55.8047i 0.0471725 + 0.0817053i 0.888648 0.458591i $$-0.151646\pi$$
−0.841475 + 0.540296i $$0.818312\pi$$
$$684$$ 448.235 107.549i 0.655314 0.157236i
$$685$$ 510.849i 0.745765i
$$686$$ 0 0
$$687$$ 986.210i 1.43553i
$$688$$ 559.978 + 363.863i 0.813922 + 0.528871i
$$689$$ 797.385 + 1381.11i 1.15731 + 2.00452i
$$690$$ −198.490 + 23.4797i −0.287667 + 0.0340285i
$$691$$ −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
$$696$$ −257.073 + 308.973i −0.369358 + 0.443926i
$$697$$ −19.9895 34.6229i −0.0286794 0.0496741i
$$698$$ 265.766 198.430i 0.380754 0.284284i
$$699$$ −515.633 −0.737672
$$700$$ 0 0
$$701$$ 695.486i 0.992134i −0.868284 0.496067i $$-0.834777\pi$$
0.868284 0.496067i $$-0.165223\pi$$
$$702$$ −1908.92 + 1425.26i −2.71926 + 2.03029i
$$703$$ 65.7370 37.9532i 0.0935092 0.0539875i
$$704$$ −317.233 112.479i −0.450615 0.159771i
$$705$$ −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 0.944640 0.328110i $$-0.106412\pi$$
0.188168 + 0.982137i $$0.439745\pi$$
$$710$$ −319.201 + 37.7587i −0.449578 + 0.0531812i
$$711$$ 508.447 293.552i 0.715115 0.412872i
$$712$$ −74.3816 + 432.366i −0.104469 + 0.607255i
$$713$$ −299.812 −0.420493
$$714$$ 0 0
$$715$$ −242.883 −0.339697
$$716$$ −494.057 + 118.544i −0.690024 + 0.165564i
$$717$$ −753.566 + 435.071i −1.05100 + 0.606794i
$$718$$ 154.355 + 1304.87i 0.214979 + 1.81737i
$$719$$ −1150.37 664.169i −1.59996 0.923739i −0.991493 0.130163i $$-0.958450\pi$$
−0.608471 0.793576i $$1.29178\pi$$
$$720$$ −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
$$724$$ 815.749 + 241.752i 1.12673 + 0.333912i
$$725$$ 166.034 95.8600i 0.229013 0.132221i
$$726$$ −595.546 797.642i −0.820311 1.09868i
$$727$$ 539.401i 0.741954i 0.928642 + 0.370977i $$0.120977\pi$$
−0.928642 + 0.370977i $$0.879023\pi$$
$$728$$ 0 0
$$729$$ −303.936 −0.416922
$$730$$ −116.158 + 86.7276i −0.159121 + 0.118805i
$$731$$ −19.3427 33.5026i −0.0264606 0.0458311i
$$732$$ −568.834 168.577i −0.777095 0.230297i
$$733$$ −382.859 221.044i −0.522318 0.301561i 0.215564 0.976490i $$-0.430841\pi$$
−0.737883 + 0.674929i $$0.764174\pi$$
$$734$$ 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
$$738$$ −1664.83 + 196.935i −2.25587 + 0.266849i
$$739$$ 574.116 + 994.398i 0.776882 + 1.34560i 0.933730 + 0.357977i $$0.116533\pi$$
−0.156848 + 0.987623i $$0.550133\pi$$
$$740$$ −107.389 + 25.7669i −0.145120 + 0.0348201i
$$741$$ 677.050i 0.913698i
$$742$$ 0 0
$$743$$ 588.688i 0.792313i −0.918183 0.396156i $$-0.870344\pi$$
0.918183 0.396156i $$-0.129656\pi$$
$$744$$ −1450.56 249.546i −1.94968 0.335411i
$$745$$ −248.810 430.952i −0.333973 0.578459i
$$746$$ −74.2420 627.621i −0.0995202 0.841314i
$$747$$ −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 −0.0526140 0.998615i $$-0.516755\pi$$
−0.891133 + 0.453742i $$0.850089\pi$$
$$752$$ 333.952 + 655.844i 0.444086 + 0.872133i
$$753$$ 424.712 + 735.622i 0.564026 + 0.976922i
$$754$$ 241.396 + 323.313i 0.320154 + 0.428797i
$$755$$ −318.989 −0.422503
$$756$$ 0 0
$$757$$ 105.101i 0.138838i 0.997588 + 0.0694192i $$0.0221146\pi$$
−0.997588 + 0.0694192i $$0.977885\pi$$
$$758$$ 213.468 + 285.908i 0.281620 + 0.377187i
$$759$$ 211.025 121.835i 0.278030 0.160521i
$$760$$ 65.4471 78.6600i 0.0861146 0.103500i
$$761$$ 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
$$766$$ 164.085 + 1387.13i 0.214211 + 1.81087i
$$767$$ −995.264 + 574.616i −1.29761 + 0.749173i
$$768$$ −802.940 + 1103.93i −1.04549 + 1.43741i
$$769$$ 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
$$772$$ 1098.06 263.469i 1.42236 0.341281i
$$773$$ −280.862 + 162.156i −0.363340 + 0.209774i −0.670545 0.741869i $$-0.733940\pi$$
0.307205 + 0.951643i $$0.400606\pi$$
$$774$$ −1610.96 + 190.563i −2.08134 + 0.246205i
$$775$$ 608.014 + 351.037i 0.784534 + 0.452951i
$$776$$ 403.170 148.647i 0.519550 0.191556i
$$777$$ 0 0