# Properties

 Label 49.12.c.b.18.1 Level $49$ Weight $12$ Character 49.18 Analytic conductor $37.649$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$49 = 7^{2}$$ Weight: $$k$$ $$=$$ $$12$$ Character orbit: $$[\chi]$$ $$=$$ 49.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$37.6488158474$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 18.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 49.18 Dual form 49.12.c.b.30.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(12.0000 + 20.7846i) q^{2} +(-126.000 + 218.238i) q^{3} +(736.000 - 1274.79i) q^{4} +(-2415.00 - 4182.90i) q^{5} -6048.00 q^{6} +84480.0 q^{8} +(56821.5 + 98417.7i) q^{9} +O(q^{10})$$ $$q+(12.0000 + 20.7846i) q^{2} +(-126.000 + 218.238i) q^{3} +(736.000 - 1274.79i) q^{4} +(-2415.00 - 4182.90i) q^{5} -6048.00 q^{6} +84480.0 q^{8} +(56821.5 + 98417.7i) q^{9} +(57960.0 - 100390. i) q^{10} +(-267306. + 462988. i) q^{11} +(185472. + 321247. i) q^{12} -577738. q^{13} +1.21716e6 q^{15} +(-493568. - 854885. i) q^{16} +(3.45297e6 - 5.98071e6i) q^{17} +(-1.36372e6 + 2.36203e6i) q^{18} +(-5.33071e6 - 9.23306e6i) q^{19} -7.10976e6 q^{20} -1.28307e7 q^{22} +(-9.32164e6 - 1.61455e7i) q^{23} +(-1.06445e7 + 1.84368e7i) q^{24} +(1.27496e7 - 2.20830e7i) q^{25} +(-6.93286e6 - 1.20081e7i) q^{26} -7.32791e7 q^{27} +1.28407e8 q^{29} +(1.46059e7 + 2.52982e7i) q^{30} +(2.64216e7 - 4.57635e7i) q^{31} +(9.83532e7 - 1.70353e8i) q^{32} +(-6.73611e7 - 1.16673e8i) q^{33} +1.65742e8 q^{34} +1.67282e8 q^{36} +(9.11067e7 + 1.57801e8i) q^{37} +(1.27937e8 - 2.21593e8i) q^{38} +(7.27950e7 - 1.26085e8i) q^{39} +(-2.04019e8 - 3.53372e8i) q^{40} +3.08120e8 q^{41} -1.71257e7 q^{43} +(3.93474e8 + 6.81518e8i) q^{44} +(2.74448e8 - 4.75358e8i) q^{45} +(2.23719e8 - 3.87493e8i) q^{46} +(-1.34367e9 - 2.32731e9i) q^{47} +2.48758e8 q^{48} +6.11981e8 q^{50} +(8.70148e8 + 1.50714e9i) q^{51} +(-4.25215e8 + 7.36494e8i) q^{52} +(7.98028e8 - 1.38222e9i) q^{53} +(-8.79349e8 - 1.52308e9i) q^{54} +2.58218e9 q^{55} +2.68668e9 q^{57} +(1.54088e9 + 2.66888e9i) q^{58} +(2.59460e9 - 4.49398e9i) q^{59} +(8.95830e8 - 1.55162e9i) q^{60} +(-3.47824e9 - 6.02449e9i) q^{61} +1.26824e9 q^{62} +2.69930e9 q^{64} +(1.39524e9 + 2.41662e9i) q^{65} +(1.61667e9 - 2.80015e9i) q^{66} +(7.74091e9 - 1.34077e10i) q^{67} +(-5.08277e9 - 8.80361e9i) q^{68} +4.69810e9 q^{69} +9.79149e9 q^{71} +(4.80028e9 + 8.31433e9i) q^{72} +(-7.31896e8 + 1.26768e9i) q^{73} +(-2.18656e9 + 3.78723e9i) q^{74} +(3.21290e9 + 5.56491e9i) q^{75} -1.56936e10 q^{76} +3.49416e9 q^{78} +(-1.90584e10 - 3.30102e10i) q^{79} +(-2.38393e9 + 4.12909e9i) q^{80} +(-8.32594e8 + 1.44210e9i) q^{81} +(3.69745e9 + 6.40416e9i) q^{82} -2.93351e10 q^{83} -3.33557e10 q^{85} +(-2.05508e8 - 3.55951e8i) q^{86} +(-1.61792e10 + 2.80233e10i) q^{87} +(-2.25820e10 + 3.91132e10i) q^{88} +(1.24965e10 + 2.16445e10i) q^{89} +1.31735e10 q^{90} -2.74429e10 q^{92} +(6.65824e9 + 1.15324e10i) q^{93} +(3.22482e10 - 5.58555e10i) q^{94} +(-2.57473e10 + 4.45957e10i) q^{95} +(2.47850e10 + 4.29289e10i) q^{96} +7.50136e10 q^{97} -6.07549e10 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 24q^{2} - 252q^{3} + 1472q^{4} - 4830q^{5} - 12096q^{6} + 168960q^{8} + 113643q^{9} + O(q^{10})$$ $$2q + 24q^{2} - 252q^{3} + 1472q^{4} - 4830q^{5} - 12096q^{6} + 168960q^{8} + 113643q^{9} + 115920q^{10} - 534612q^{11} + 370944q^{12} - 1155476q^{13} + 2434320q^{15} - 987136q^{16} + 6905934q^{17} - 2727432q^{18} - 10661420q^{19} - 14219520q^{20} - 25661376q^{22} - 18643272q^{23} - 21288960q^{24} + 25499225q^{25} - 13865712q^{26} - 146558160q^{27} + 256813260q^{29} + 29211840q^{30} + 52843168q^{31} + 196706304q^{32} - 134722224q^{33} + 331484832q^{34} + 334564992q^{36} + 182213314q^{37} + 255874080q^{38} + 145589976q^{39} - 408038400q^{40} + 616240884q^{41} - 34251416q^{43} + 786948864q^{44} + 548895690q^{45} + 447438528q^{46} - 2687348496q^{47} + 497516544q^{48} + 1223962800q^{50} + 1740295368q^{51} - 850430336q^{52} + 1596055698q^{53} - 1758697920q^{54} + 5164351920q^{55} + 5373355680q^{57} + 3081759120q^{58} + 5189203740q^{59} + 1791659520q^{60} - 6956478662q^{61} + 2536472064q^{62} + 5398593536q^{64} + 2790474540q^{65} + 3233333376q^{66} + 15481826884q^{67} - 10165534848q^{68} + 9396209088q^{69} + 19582970544q^{71} + 9600560640q^{72} - 1463791322q^{73} - 4373119536q^{74} + 6425804700q^{75} - 31387220480q^{76} + 6988318848q^{78} - 38116845680q^{79} - 4767866880q^{80} - 1665188361q^{81} + 7394890608q^{82} - 58670199336q^{83} - 66711322440q^{85} - 411016992q^{86} - 32358470760q^{87} - 45164021760q^{88} + 24992917110q^{89} + 26346993120q^{90} - 54885792768q^{92} + 13316478336q^{93} + 64496363904q^{94} - 51494658600q^{95} + 49569988608q^{96} + 150027137092q^{97} - 121509823032q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 12.0000 + 20.7846i 0.265165 + 0.459279i 0.967607 0.252462i $$-0.0812402\pi$$
−0.702442 + 0.711741i $$0.747907\pi$$
$$3$$ −126.000 + 218.238i −0.299367 + 0.518519i −0.975991 0.217810i $$-0.930109\pi$$
0.676624 + 0.736328i $$0.263442\pi$$
$$4$$ 736.000 1274.79i 0.359375 0.622456i
$$5$$ −2415.00 4182.90i −0.345607 0.598608i 0.639857 0.768494i $$-0.278994\pi$$
−0.985464 + 0.169886i $$0.945660\pi$$
$$6$$ −6048.00 −0.317526
$$7$$ 0 0
$$8$$ 84480.0 0.911505
$$9$$ 56821.5 + 98417.7i 0.320759 + 0.555571i
$$10$$ 57960.0 100390.i 0.183286 0.317460i
$$11$$ −267306. + 462988.i −0.500436 + 0.866781i 0.499563 + 0.866277i $$0.333494\pi$$
−1.00000 0.000504048i $$0.999840\pi$$
$$12$$ 185472. + 321247.i 0.215170 + 0.372685i
$$13$$ −577738. −0.431561 −0.215781 0.976442i $$-0.569230\pi$$
−0.215781 + 0.976442i $$0.569230\pi$$
$$14$$ 0 0
$$15$$ 1.21716e6 0.413853
$$16$$ −493568. 854885.i −0.117676 0.203820i
$$17$$ 3.45297e6 5.98071e6i 0.589825 1.02161i −0.404430 0.914569i $$-0.632530\pi$$
0.994255 0.107038i $$-0.0341367\pi$$
$$18$$ −1.36372e6 + 2.36203e6i −0.170108 + 0.294636i
$$19$$ −5.33071e6 9.23306e6i −0.493901 0.855462i 0.506074 0.862490i $$-0.331096\pi$$
−0.999975 + 0.00702781i $$0.997763\pi$$
$$20$$ −7.10976e6 −0.496810
$$21$$ 0 0
$$22$$ −1.28307e7 −0.530793
$$23$$ −9.32164e6 1.61455e7i −0.301988 0.523058i 0.674599 0.738185i $$-0.264317\pi$$
−0.976586 + 0.215127i $$0.930983\pi$$
$$24$$ −1.06445e7 + 1.84368e7i −0.272874 + 0.472632i
$$25$$ 1.27496e7 2.20830e7i 0.261112 0.452259i
$$26$$ −6.93286e6 1.20081e7i −0.114435 0.198207i
$$27$$ −7.32791e7 −0.982832
$$28$$ 0 0
$$29$$ 1.28407e8 1.16251 0.581257 0.813720i $$-0.302561\pi$$
0.581257 + 0.813720i $$0.302561\pi$$
$$30$$ 1.46059e7 + 2.52982e7i 0.109739 + 0.190074i
$$31$$ 2.64216e7 4.57635e7i 0.165756 0.287098i −0.771167 0.636632i $$-0.780327\pi$$
0.936924 + 0.349534i $$0.113660\pi$$
$$32$$ 9.83532e7 1.70353e8i 0.518159 0.897478i
$$33$$ −6.73611e7 1.16673e8i −0.299628 0.518971i
$$34$$ 1.65742e8 0.625604
$$35$$ 0 0
$$36$$ 1.67282e8 0.461091
$$37$$ 9.11067e7 + 1.57801e8i 0.215993 + 0.374112i 0.953579 0.301142i $$-0.0973677\pi$$
−0.737586 + 0.675253i $$0.764034\pi$$
$$38$$ 1.27937e8 2.21593e8i 0.261931 0.453677i
$$39$$ 7.27950e7 1.26085e8i 0.129195 0.223773i
$$40$$ −2.04019e8 3.53372e8i −0.315022 0.545634i
$$41$$ 3.08120e8 0.415345 0.207673 0.978198i $$-0.433411\pi$$
0.207673 + 0.978198i $$0.433411\pi$$
$$42$$ 0 0
$$43$$ −1.71257e7 −0.0177653 −0.00888264 0.999961i $$-0.502827\pi$$
−0.00888264 + 0.999961i $$0.502827\pi$$
$$44$$ 3.93474e8 + 6.81518e8i 0.359689 + 0.622999i
$$45$$ 2.74448e8 4.75358e8i 0.221713 0.384018i
$$46$$ 2.23719e8 3.87493e8i 0.160153 0.277393i
$$47$$ −1.34367e9 2.32731e9i −0.854586 1.48019i −0.877029 0.480438i $$-0.840478\pi$$
0.0224426 0.999748i $$-0.492856\pi$$
$$48$$ 2.48758e8 0.140913
$$49$$ 0 0
$$50$$ 6.11981e8 0.276951
$$51$$ 8.70148e8 + 1.50714e9i 0.353148 + 0.611671i
$$52$$ −4.25215e8 + 7.36494e8i −0.155092 + 0.268628i
$$53$$ 7.98028e8 1.38222e9i 0.262120 0.454006i −0.704685 0.709520i $$-0.748912\pi$$
0.966805 + 0.255515i $$0.0822449\pi$$
$$54$$ −8.79349e8 1.52308e9i −0.260613 0.451394i
$$55$$ 2.58218e9 0.691817
$$56$$ 0 0
$$57$$ 2.68668e9 0.591431
$$58$$ 1.54088e9 + 2.66888e9i 0.308258 + 0.533919i
$$59$$ 2.59460e9 4.49398e9i 0.472481 0.818362i −0.527023 0.849851i $$-0.676692\pi$$
0.999504 + 0.0314895i $$0.0100251\pi$$
$$60$$ 8.95830e8 1.55162e9i 0.148728 0.257605i
$$61$$ −3.47824e9 6.02449e9i −0.527285 0.913284i −0.999494 0.0317979i $$-0.989877\pi$$
0.472209 0.881486i $$-0.343457\pi$$
$$62$$ 1.26824e9 0.175811
$$63$$ 0 0
$$64$$ 2.69930e9 0.314240
$$65$$ 1.39524e9 + 2.41662e9i 0.149150 + 0.258336i
$$66$$ 1.61667e9 2.80015e9i 0.158902 0.275226i
$$67$$ 7.74091e9 1.34077e10i 0.700456 1.21323i −0.267851 0.963460i $$-0.586313\pi$$
0.968307 0.249765i $$-0.0803533\pi$$
$$68$$ −5.08277e9 8.80361e9i −0.423937 0.734280i
$$69$$ 4.69810e9 0.361620
$$70$$ 0 0
$$71$$ 9.79149e9 0.644062 0.322031 0.946729i $$-0.395634\pi$$
0.322031 + 0.946729i $$0.395634\pi$$
$$72$$ 4.80028e9 + 8.31433e9i 0.292373 + 0.506406i
$$73$$ −7.31896e8 + 1.26768e9i −0.0413212 + 0.0715705i −0.885946 0.463788i $$-0.846490\pi$$
0.844625 + 0.535358i $$0.179823\pi$$
$$74$$ −2.18656e9 + 3.78723e9i −0.114548 + 0.198403i
$$75$$ 3.21290e9 + 5.56491e9i 0.156337 + 0.270783i
$$76$$ −1.56936e10 −0.709983
$$77$$ 0 0
$$78$$ 3.49416e9 0.137032
$$79$$ −1.90584e10 3.30102e10i −0.696848 1.20698i −0.969554 0.244878i $$-0.921252\pi$$
0.272706 0.962097i $$-0.412081\pi$$
$$80$$ −2.38393e9 + 4.12909e9i −0.0813391 + 0.140883i
$$81$$ −8.32594e8 + 1.44210e9i −0.0265317 + 0.0459543i
$$82$$ 3.69745e9 + 6.40416e9i 0.110135 + 0.190760i
$$83$$ −2.93351e10 −0.817444 −0.408722 0.912659i $$-0.634025\pi$$
−0.408722 + 0.912659i $$0.634025\pi$$
$$84$$ 0 0
$$85$$ −3.33557e10 −0.815390
$$86$$ −2.05508e8 3.55951e8i −0.00471073 0.00815923i
$$87$$ −1.61792e10 + 2.80233e10i −0.348018 + 0.602785i
$$88$$ −2.25820e10 + 3.91132e10i −0.456150 + 0.790075i
$$89$$ 1.24965e10 + 2.16445e10i 0.237215 + 0.410868i 0.959914 0.280294i $$-0.0904321\pi$$
−0.722699 + 0.691163i $$0.757099\pi$$
$$90$$ 1.31735e10 0.235162
$$91$$ 0 0
$$92$$ −2.74429e10 −0.434107
$$93$$ 6.65824e9 + 1.15324e10i 0.0992438 + 0.171895i
$$94$$ 3.22482e10 5.58555e10i 0.453213 0.784987i
$$95$$ −2.57473e10 + 4.45957e10i −0.341391 + 0.591307i
$$96$$ 2.47850e10 + 4.29289e10i 0.310239 + 0.537351i
$$97$$ 7.50136e10 0.886942 0.443471 0.896289i $$-0.353747\pi$$
0.443471 + 0.896289i $$0.353747\pi$$
$$98$$ 0 0
$$99$$ −6.07549e10 −0.642078
$$100$$ −1.87674e10 3.25061e10i −0.187674 0.325061i
$$101$$ −4.08715e10 + 7.07915e10i −0.386948 + 0.670214i −0.992037 0.125944i $$-0.959804\pi$$
0.605089 + 0.796158i $$0.293137\pi$$
$$102$$ −2.08835e10 + 3.61714e10i −0.187285 + 0.324387i
$$103$$ 1.12878e11 + 1.95510e11i 0.959407 + 1.66174i 0.723944 + 0.689858i $$0.242327\pi$$
0.235463 + 0.971883i $$0.424339\pi$$
$$104$$ −4.88073e10 −0.393370
$$105$$ 0 0
$$106$$ 3.83053e10 0.278021
$$107$$ −4.51206e10 7.81512e10i −0.311003 0.538673i 0.667577 0.744541i $$-0.267332\pi$$
−0.978580 + 0.205868i $$0.933998\pi$$
$$108$$ −5.39334e10 + 9.34154e10i −0.353205 + 0.611769i
$$109$$ −3.67413e10 + 6.36379e10i −0.228723 + 0.396159i −0.957430 0.288666i $$-0.906788\pi$$
0.728707 + 0.684825i $$0.240122\pi$$
$$110$$ 3.09861e10 + 5.36695e10i 0.183446 + 0.317737i
$$111$$ −4.59178e10 −0.258645
$$112$$ 0 0
$$113$$ −8.51469e10 −0.434748 −0.217374 0.976088i $$-0.569749\pi$$
−0.217374 + 0.976088i $$0.569749\pi$$
$$114$$ 3.22401e10 + 5.58416e10i 0.156827 + 0.271632i
$$115$$ −4.50235e10 + 7.79830e10i −0.208738 + 0.361545i
$$116$$ 9.45073e10 1.63691e11i 0.417779 0.723614i
$$117$$ −3.28279e10 5.68597e10i −0.138427 0.239763i
$$118$$ 1.24541e11 0.501142
$$119$$ 0 0
$$120$$ 1.02826e11 0.377229
$$121$$ −2.49160e8 4.31558e8i −0.000873290 0.00151258i
$$122$$ 8.34777e10 1.44588e11i 0.279635 0.484342i
$$123$$ −3.88232e10 + 6.72437e10i −0.124341 + 0.215364i
$$124$$ −3.88926e10 6.73639e10i −0.119137 0.206352i
$$125$$ −3.59001e11 −1.05218
$$126$$ 0 0
$$127$$ −2.62717e11 −0.705615 −0.352808 0.935696i $$-0.614773\pi$$
−0.352808 + 0.935696i $$0.614773\pi$$
$$128$$ −1.69036e11 2.92778e11i −0.434834 0.753155i
$$129$$ 2.15784e9 3.73749e9i 0.00531833 0.00921163i
$$130$$ −3.34857e10 + 5.79989e10i −0.0790990 + 0.137003i
$$131$$ −3.15764e11 5.46920e11i −0.715107 1.23860i −0.962918 0.269793i $$-0.913045\pi$$
0.247811 0.968808i $$-0.420289\pi$$
$$132$$ −1.98311e11 −0.430715
$$133$$ 0 0
$$134$$ 3.71564e11 0.742946
$$135$$ 1.76969e11 + 3.06519e11i 0.339673 + 0.588331i
$$136$$ 2.91707e11 5.05251e11i 0.537629 0.931200i
$$137$$ 1.48599e11 2.57382e11i 0.263059 0.455632i −0.703994 0.710206i $$-0.748602\pi$$
0.967053 + 0.254574i $$0.0819351\pi$$
$$138$$ 5.63773e10 + 9.76483e10i 0.0958890 + 0.166085i
$$139$$ 5.96794e11 0.975535 0.487767 0.872974i $$-0.337811\pi$$
0.487767 + 0.872974i $$0.337811\pi$$
$$140$$ 0 0
$$141$$ 6.77212e11 1.02334
$$142$$ 1.17498e11 + 2.03512e11i 0.170783 + 0.295804i
$$143$$ 1.54433e11 2.67486e11i 0.215969 0.374069i
$$144$$ 5.60905e10 9.71517e10i 0.0754911 0.130754i
$$145$$ −3.10102e11 5.37112e11i −0.401773 0.695891i
$$146$$ −3.51310e10 −0.0438278
$$147$$ 0 0
$$148$$ 2.68218e11 0.310491
$$149$$ 5.57717e11 + 9.65994e11i 0.622142 + 1.07758i 0.989086 + 0.147338i $$0.0470705\pi$$
−0.366945 + 0.930243i $$0.619596\pi$$
$$150$$ −7.71097e10 + 1.33558e11i −0.0829100 + 0.143604i
$$151$$ 4.12224e11 7.13992e11i 0.427326 0.740151i −0.569308 0.822124i $$-0.692789\pi$$
0.996635 + 0.0819732i $$0.0261222\pi$$
$$152$$ −4.50338e11 7.80009e11i −0.450194 0.779758i
$$153$$ 7.84811e11 0.756767
$$154$$ 0 0
$$155$$ −2.55233e11 −0.229146
$$156$$ −1.07154e11 1.85597e11i −0.0928590 0.160837i
$$157$$ −6.57558e11 + 1.13892e12i −0.550156 + 0.952899i 0.448106 + 0.893980i $$0.352099\pi$$
−0.998263 + 0.0589187i $$0.981235\pi$$
$$158$$ 4.57402e11 7.92244e11i 0.369559 0.640096i
$$159$$ 2.01103e11 + 3.48321e11i 0.156940 + 0.271829i
$$160$$ −9.50091e11 −0.716317
$$161$$ 0 0
$$162$$ −3.99645e10 −0.0281412
$$163$$ 1.78916e11 + 3.09892e11i 0.121792 + 0.210950i 0.920474 0.390803i $$-0.127803\pi$$
−0.798682 + 0.601753i $$0.794469\pi$$
$$164$$ 2.26777e11 3.92789e11i 0.149265 0.258534i
$$165$$ −3.25354e11 + 5.63530e11i −0.207107 + 0.358720i
$$166$$ −3.52021e11 6.09719e11i −0.216758 0.375435i
$$167$$ 2.75483e12 1.64117 0.820587 0.571521i $$-0.193646\pi$$
0.820587 + 0.571521i $$0.193646\pi$$
$$168$$ 0 0
$$169$$ −1.45838e12 −0.813755
$$170$$ −4.00268e11 6.93284e11i −0.216213 0.374492i
$$171$$ 6.05798e11 1.04927e12i 0.316847 0.548795i
$$172$$ −1.26045e10 + 2.18317e10i −0.00638440 + 0.0110581i
$$173$$ 4.75194e11 + 8.23060e11i 0.233140 + 0.403811i 0.958731 0.284316i $$-0.0917666\pi$$
−0.725590 + 0.688127i $$0.758433\pi$$
$$174$$ −7.76603e11 −0.369129
$$175$$ 0 0
$$176$$ 5.27735e11 0.235557
$$177$$ 6.53840e11 + 1.13248e12i 0.282890 + 0.489981i
$$178$$ −2.99915e11 + 5.19468e11i −0.125802 + 0.217896i
$$179$$ −8.40692e11 + 1.45612e12i −0.341936 + 0.592251i −0.984792 0.173736i $$-0.944416\pi$$
0.642856 + 0.765987i $$0.277749\pi$$
$$180$$ −4.03987e11 6.99726e11i −0.159356 0.276013i
$$181$$ −9.96774e11 −0.381386 −0.190693 0.981650i $$-0.561073\pi$$
−0.190693 + 0.981650i $$0.561073\pi$$
$$182$$ 0 0
$$183$$ 1.75303e12 0.631406
$$184$$ −7.87492e11 1.36398e12i −0.275263 0.476770i
$$185$$ 4.40045e11 7.62181e11i 0.149298 0.258591i
$$186$$ −1.59798e11 + 2.76778e11i −0.0526319 + 0.0911612i
$$187$$ 1.84600e12 + 3.19736e12i 0.590340 + 1.02250i
$$188$$ −3.95578e12 −1.22847
$$189$$ 0 0
$$190$$ −1.23587e12 −0.362100
$$191$$ −1.38120e12 2.39231e12i −0.393164 0.680980i 0.599701 0.800224i $$-0.295286\pi$$
−0.992865 + 0.119244i $$0.961953\pi$$
$$192$$ −3.40111e11 + 5.89090e11i −0.0940729 + 0.162939i
$$193$$ −2.72119e12 + 4.71325e12i −0.731466 + 1.26694i 0.224790 + 0.974407i $$0.427830\pi$$
−0.956256 + 0.292530i $$0.905503\pi$$
$$194$$ 9.00163e11 + 1.55913e12i 0.235186 + 0.407354i
$$195$$ −7.03200e11 −0.178603
$$196$$ 0 0
$$197$$ −2.87609e12 −0.690619 −0.345309 0.938489i $$-0.612226\pi$$
−0.345309 + 0.938489i $$0.612226\pi$$
$$198$$ −7.29059e11 1.26277e12i −0.170257 0.294893i
$$199$$ −3.64196e11 + 6.30805e11i −0.0827262 + 0.143286i −0.904420 0.426643i $$-0.859696\pi$$
0.821694 + 0.569929i $$0.193029\pi$$
$$200$$ 1.07709e12 1.86557e12i 0.238005 0.412237i
$$201$$ 1.95071e12 + 3.37873e12i 0.419386 + 0.726399i
$$202$$ −1.96183e12 −0.410421
$$203$$ 0 0
$$204$$ 2.56171e12 0.507651
$$205$$ −7.44111e11 1.28884e12i −0.143546 0.248629i
$$206$$ −2.70906e12 + 4.69223e12i −0.508802 + 0.881272i
$$207$$ 1.05934e12 1.83483e12i 0.193730 0.335551i
$$208$$ 2.85153e11 + 4.93899e11i 0.0507843 + 0.0879610i
$$209$$ 5.69972e12 0.988665
$$210$$ 0 0
$$211$$ −6.79317e12 −1.11820 −0.559099 0.829101i $$-0.688853\pi$$
−0.559099 + 0.829101i $$0.688853\pi$$
$$212$$ −1.17470e12 2.03463e12i −0.188399 0.326317i
$$213$$ −1.23373e12 + 2.13688e12i −0.192811 + 0.333958i
$$214$$ 1.08290e12 1.87563e12i 0.164934 0.285674i
$$215$$ 4.13586e10 + 7.16352e10i 0.00613980 + 0.0106344i
$$216$$ −6.19062e12 −0.895856
$$217$$ 0 0
$$218$$ −1.76358e12 −0.242597
$$219$$ −1.84438e11 3.19455e11i −0.0247404 0.0428517i
$$220$$ 1.90048e12 3.29173e12i 0.248622 0.430625i
$$221$$ −1.99491e12 + 3.45529e12i −0.254546 + 0.440886i
$$222$$ −5.51013e11 9.54383e11i −0.0685836 0.118790i
$$223$$ 7.33486e12 0.890667 0.445333 0.895365i $$-0.353085\pi$$
0.445333 + 0.895365i $$0.353085\pi$$
$$224$$ 0 0
$$225$$ 2.89781e12 0.335016
$$226$$ −1.02176e12 1.76974e12i −0.115280 0.199671i
$$227$$ 6.79920e11 1.17766e12i 0.0748713 0.129681i −0.826159 0.563437i $$-0.809479\pi$$
0.901030 + 0.433756i $$0.142812\pi$$
$$228$$ 1.97739e12 3.42495e12i 0.212545 0.368139i
$$229$$ 5.91221e12 + 1.02402e13i 0.620375 + 1.07452i 0.989416 + 0.145108i $$0.0463530\pi$$
−0.369041 + 0.929413i $$0.620314\pi$$
$$230$$ −2.16113e12 −0.221400
$$231$$ 0 0
$$232$$ 1.08478e13 1.05964
$$233$$ 8.78168e12 + 1.52103e13i 0.837761 + 1.45104i 0.891763 + 0.452503i $$0.149469\pi$$
−0.0540024 + 0.998541i $$0.517198\pi$$
$$234$$ 7.87871e11 1.36463e12i 0.0734121 0.127153i
$$235$$ −6.48995e12 + 1.12409e13i −0.590701 + 1.02312i
$$236$$ −3.81925e12 6.61514e12i −0.339596 0.588197i
$$237$$ 9.60545e12 0.834452
$$238$$ 0 0
$$239$$ −7.13958e12 −0.592221 −0.296111 0.955154i $$-0.595690\pi$$
−0.296111 + 0.955154i $$0.595690\pi$$
$$240$$ −6.00751e11 1.04053e12i −0.0487004 0.0843516i
$$241$$ 1.15653e11 2.00318e11i 0.00916357 0.0158718i −0.861407 0.507915i $$-0.830416\pi$$
0.870571 + 0.492043i $$0.163750\pi$$
$$242$$ 5.97984e9 1.03574e10i 0.000463132 0.000802169i
$$243$$ −6.70040e12 1.16054e13i −0.507301 0.878672i
$$244$$ −1.02399e13 −0.757972
$$245$$ 0 0
$$246$$ −1.86351e12 −0.131883
$$247$$ 3.07975e12 + 5.33429e12i 0.213149 + 0.369184i
$$248$$ 2.23210e12 3.86610e12i 0.151087 0.261691i
$$249$$ 3.69622e12 6.40205e12i 0.244716 0.423860i
$$250$$ −4.30801e12 7.46170e12i −0.279002 0.483245i
$$251$$ 1.29831e13 0.822567 0.411284 0.911507i $$-0.365081\pi$$
0.411284 + 0.911507i $$0.365081\pi$$
$$252$$ 0 0
$$253$$ 9.96692e12 0.604502
$$254$$ −3.15261e12 5.46047e12i −0.187105 0.324075i
$$255$$ 4.20281e12 7.27949e12i 0.244101 0.422795i
$$256$$ 6.82094e12 1.18142e13i 0.387725 0.671560i
$$257$$ −1.19806e13 2.07510e13i −0.666571 1.15453i −0.978857 0.204546i $$-0.934428\pi$$
0.312286 0.949988i $$-0.398905\pi$$
$$258$$ 1.03576e11 0.00564095
$$259$$ 0 0
$$260$$ 4.10758e12 0.214404
$$261$$ 7.29626e12 + 1.26375e13i 0.372887 + 0.645859i
$$262$$ 7.57835e12 1.31261e13i 0.379243 0.656868i
$$263$$ 1.21369e13 2.10217e13i 0.594771 1.03017i −0.398808 0.917034i $$-0.630576\pi$$
0.993579 0.113139i $$-0.0360907\pi$$
$$264$$ −5.69067e12 9.85652e12i −0.273112 0.473045i
$$265$$ −7.70895e12 −0.362362
$$266$$ 0 0
$$267$$ −6.29822e12 −0.284057
$$268$$ −1.13946e13 1.97361e13i −0.503453 0.872006i
$$269$$ −1.29189e13 + 2.23761e13i −0.559225 + 0.968606i 0.438337 + 0.898811i $$0.355568\pi$$
−0.997561 + 0.0697949i $$0.977766\pi$$
$$270$$ −4.24726e12 + 7.35646e12i −0.180139 + 0.312010i
$$271$$ 1.88397e12 + 3.26313e12i 0.0782964 + 0.135613i 0.902515 0.430658i $$-0.141719\pi$$
−0.824219 + 0.566272i $$0.808385\pi$$
$$272$$ −6.81710e12 −0.277633
$$273$$ 0 0
$$274$$ 7.13277e12 0.279017
$$275$$ 6.81610e12 + 1.18058e13i 0.261340 + 0.452654i
$$276$$ 3.45780e12 5.98909e12i 0.129957 0.225093i
$$277$$ 8.20947e12 1.42192e13i 0.302466 0.523886i −0.674228 0.738523i $$-0.735524\pi$$
0.976694 + 0.214637i $$0.0688569\pi$$
$$278$$ 7.16152e12 + 1.24041e13i 0.258678 + 0.448043i
$$279$$ 6.00526e12 0.212671
$$280$$ 0 0
$$281$$ 2.10357e13 0.716263 0.358132 0.933671i $$-0.383414\pi$$
0.358132 + 0.933671i $$0.383414\pi$$
$$282$$ 8.12654e12 + 1.40756e13i 0.271354 + 0.469998i
$$283$$ −8.35659e12 + 1.44740e13i −0.273655 + 0.473985i −0.969795 0.243922i $$-0.921566\pi$$
0.696140 + 0.717906i $$0.254899\pi$$
$$284$$ 7.20653e12 1.24821e13i 0.231460 0.400900i
$$285$$ −6.48833e12 1.12381e13i −0.204402 0.354035i
$$286$$ 7.41278e12 0.229070
$$287$$ 0 0
$$288$$ 2.23543e13 0.664817
$$289$$ −6.71001e12 1.16221e13i −0.195788 0.339114i
$$290$$ 7.44245e12 1.28907e13i 0.213072 0.369052i
$$291$$ −9.45171e12 + 1.63708e13i −0.265521 + 0.459896i
$$292$$ 1.07735e12 + 1.86603e12i 0.0296996 + 0.0514413i
$$293$$ −2.39269e13 −0.647312 −0.323656 0.946175i $$-0.604912\pi$$
−0.323656 + 0.946175i $$0.604912\pi$$
$$294$$ 0 0
$$295$$ −2.50639e13 −0.653171
$$296$$ 7.69669e12 + 1.33311e13i 0.196879 + 0.341005i
$$297$$ 1.95879e13 3.39273e13i 0.491845 0.851900i
$$298$$ −1.33852e13 + 2.31839e13i −0.329940 + 0.571474i
$$299$$ 5.38546e12 + 9.32790e12i 0.130326 + 0.225731i
$$300$$ 9.45878e12 0.224734
$$301$$ 0 0
$$302$$ 1.97867e13 0.453248
$$303$$ −1.02996e13 1.78395e13i −0.231679 0.401280i
$$304$$ −5.26214e12 + 9.11429e12i −0.116240 + 0.201334i
$$305$$ −1.67999e13 + 2.90983e13i −0.364466 + 0.631274i
$$306$$ 9.41773e12 + 1.63120e13i 0.200668 + 0.347567i
$$307$$ 1.53111e13 0.320439 0.160219 0.987081i $$-0.448780\pi$$
0.160219 + 0.987081i $$0.448780\pi$$
$$308$$ 0 0
$$309$$ −5.68903e13 −1.14886
$$310$$ −3.06279e12 5.30491e12i −0.0607614 0.105242i
$$311$$ −2.49376e13 + 4.31932e13i −0.486040 + 0.841846i −0.999871 0.0160451i $$-0.994892\pi$$
0.513831 + 0.857891i $$0.328226\pi$$
$$312$$ 6.14972e12 1.06516e13i 0.117762 0.203970i
$$313$$ 4.97404e13 + 8.61529e13i 0.935870 + 1.62097i 0.773075 + 0.634315i $$0.218718\pi$$
0.162795 + 0.986660i $$0.447949\pi$$
$$314$$ −3.15628e13 −0.583529
$$315$$ 0 0
$$316$$ −5.61080e13 −1.00172
$$317$$ −4.16846e13 7.21999e13i −0.731392 1.26681i −0.956289 0.292425i $$-0.905538\pi$$
0.224897 0.974383i $$-0.427795\pi$$
$$318$$ −4.82647e12 + 8.35970e12i −0.0832301 + 0.144159i
$$319$$ −3.43239e13 + 5.94507e13i −0.581765 + 1.00765i
$$320$$ −6.51880e12 1.12909e13i −0.108603 0.188106i
$$321$$ 2.27408e13 0.372416
$$322$$ 0 0
$$323$$ −7.36271e13 −1.16526
$$324$$ 1.22558e12 + 2.12276e12i 0.0190697 + 0.0330297i
$$325$$ −7.36594e12 + 1.27582e13i −0.112686 + 0.195178i
$$326$$ −4.29399e12 + 7.43741e12i −0.0645899 + 0.111873i
$$327$$ −9.25882e12 1.60367e13i −0.136944 0.237194i
$$328$$ 2.60300e13 0.378589
$$329$$ 0 0
$$330$$ −1.56170e13 −0.219670
$$331$$ 3.17920e13 + 5.50654e13i 0.439809 + 0.761771i 0.997674 0.0681600i $$-0.0217128\pi$$
−0.557865 + 0.829931i $$0.688379\pi$$
$$332$$ −2.15906e13 + 3.73961e13i −0.293769 + 0.508823i
$$333$$ −1.03536e13 + 1.79330e13i −0.138564 + 0.239999i
$$334$$ 3.30580e13 + 5.72581e13i 0.435182 + 0.753758i
$$335$$ −7.47772e13 −0.968329
$$336$$ 0 0
$$337$$ 1.21001e14 1.51644 0.758221 0.651997i $$-0.226069\pi$$
0.758221 + 0.651997i $$0.226069\pi$$
$$338$$ −1.75006e13 3.03118e13i −0.215779 0.373741i
$$339$$ 1.07285e13 1.85823e13i 0.130149 0.225425i
$$340$$ −2.45498e13 + 4.25214e13i −0.293031 + 0.507544i
$$341$$ 1.41253e13 + 2.44657e13i 0.165901 + 0.287349i
$$342$$ 2.90783e13 0.336067
$$343$$ 0 0
$$344$$ −1.44678e12 −0.0161931
$$345$$ −1.13459e13 1.96517e13i −0.124978 0.216469i
$$346$$ −1.14046e13 + 1.97534e13i −0.123641 + 0.214153i
$$347$$ 7.78308e13 1.34807e14i 0.830499 1.43847i −0.0671435 0.997743i $$-0.521389\pi$$
0.897643 0.440724i $$-0.145278\pi$$
$$348$$ 2.38158e13 + 4.12502e13i 0.250138 + 0.433252i
$$349$$ −2.56430e13 −0.265112 −0.132556 0.991176i $$-0.542318\pi$$
−0.132556 + 0.991176i $$0.542318\pi$$
$$350$$ 0 0
$$351$$ 4.23361e13 0.424152
$$352$$ 5.25808e13 + 9.10726e13i 0.518612 + 0.898262i
$$353$$ −1.24549e13 + 2.15725e13i −0.120943 + 0.209479i −0.920140 0.391590i $$-0.871925\pi$$
0.799197 + 0.601069i $$0.205258\pi$$
$$354$$ −1.56922e13 + 2.71796e13i −0.150025 + 0.259851i
$$355$$ −2.36464e13 4.09568e13i −0.222592 0.385541i
$$356$$ 3.67896e13 0.340996
$$357$$ 0 0
$$358$$ −4.03532e13 −0.362678
$$359$$ −7.87921e13 1.36472e14i −0.697370 1.20788i −0.969375 0.245584i $$-0.921020\pi$$
0.272006 0.962296i $$-0.412313\pi$$
$$360$$ 2.31854e13 4.01582e13i 0.202092 0.350034i
$$361$$ 1.41219e12 2.44599e12i 0.0121228 0.0209974i
$$362$$ −1.19613e13 2.07176e13i −0.101130 0.175163i
$$363$$ 1.25577e11 0.00104574
$$364$$ 0 0
$$365$$ 7.07011e12 0.0571236
$$366$$ 2.10364e13 + 3.64361e13i 0.167427 + 0.289992i
$$367$$ 8.89506e13 1.54067e14i 0.697406 1.20794i −0.271957 0.962309i $$-0.587671\pi$$
0.969363 0.245633i $$-0.0789958\pi$$
$$368$$ −9.20172e12 + 1.59379e13i −0.0710732 + 0.123102i
$$369$$ 1.75079e13 + 3.03245e13i 0.133226 + 0.230754i
$$370$$ 2.11222e13 0.158354
$$371$$ 0 0
$$372$$ 1.96019e13 0.142663
$$373$$ 2.75809e13 + 4.77715e13i 0.197792 + 0.342586i 0.947812 0.318829i $$-0.103290\pi$$
−0.750020 + 0.661415i $$0.769956\pi$$
$$374$$ −4.43039e13 + 7.67367e13i −0.313075 + 0.542262i
$$375$$ 4.52341e13 7.83478e13i 0.314988 0.545576i
$$376$$ −1.13514e14 1.96611e14i −0.778959 1.34920i
$$377$$ −7.41854e13 −0.501696
$$378$$ 0 0
$$379$$ 1.46463e14 0.962083 0.481042 0.876698i $$-0.340259\pi$$
0.481042 + 0.876698i $$0.340259\pi$$
$$380$$ 3.79001e13 + 6.56448e13i 0.245375 + 0.425002i
$$381$$ 3.31024e13 5.73350e13i 0.211238 0.365875i
$$382$$ 3.31488e13 5.74155e13i 0.208507 0.361144i
$$383$$ −1.15725e14 2.00441e14i −0.717519 1.24278i −0.961980 0.273120i $$-0.911945\pi$$
0.244462 0.969659i $$-0.421389\pi$$
$$384$$ 8.51940e13 0.520700
$$385$$ 0 0
$$386$$ −1.30617e14 −0.775837
$$387$$ −9.73108e11 1.68547e12i −0.00569837 0.00986987i
$$388$$ 5.52100e13 9.56265e13i 0.318745 0.552082i
$$389$$ 7.49358e13 1.29793e14i 0.426547 0.738800i −0.570017 0.821633i $$-0.693063\pi$$
0.996563 + 0.0828326i $$0.0263967\pi$$
$$390$$ −8.43840e12 1.46157e13i −0.0473592 0.0820286i
$$391$$ −1.28749e14 −0.712480
$$392$$ 0 0
$$393$$ 1.59145e14 0.856317
$$394$$ −3.45131e13 5.97784e13i −0.183128 0.317187i
$$395$$ −9.20522e13 + 1.59439e14i −0.481671 + 0.834278i
$$396$$ −4.47156e13 + 7.74497e13i −0.230747 + 0.399665i
$$397$$ −1.04055e14 1.80229e14i −0.529562 0.917228i −0.999405 0.0344782i $$-0.989023\pi$$
0.469844 0.882750i $$-0.344310\pi$$
$$398$$ −1.74814e13 −0.0877443
$$399$$ 0 0
$$400$$ −2.51712e13 −0.122906
$$401$$ 6.67040e13 + 1.15535e14i 0.321261 + 0.556440i 0.980748 0.195275i $$-0.0625601\pi$$
−0.659488 + 0.751715i $$0.729227\pi$$
$$402$$ −4.68170e13 + 8.10895e13i −0.222413 + 0.385231i
$$403$$ −1.52648e13 + 2.64393e13i −0.0715339 + 0.123900i
$$404$$ 6.01628e13 + 1.04205e14i 0.278119 + 0.481716i
$$405$$ 8.04286e12 0.0366782
$$406$$ 0 0
$$407$$ −9.74134e13 −0.432364
$$408$$ 7.35101e13 + 1.27323e14i 0.321896 + 0.557541i
$$409$$ 1.03084e14 1.78546e14i 0.445361 0.771388i −0.552716 0.833369i $$-0.686409\pi$$
0.998077 + 0.0619816i $$0.0197420\pi$$
$$410$$ 1.78587e13 3.09321e13i 0.0761268 0.131856i
$$411$$ 3.74470e13 + 6.48602e13i 0.157503 + 0.272802i
$$412$$ 3.32312e14 1.37915
$$413$$ 0 0
$$414$$ 5.08483e13 0.205482
$$415$$ 7.08443e13 + 1.22706e14i 0.282514 + 0.489329i
$$416$$ −5.68224e13 + 9.84192e13i −0.223618 + 0.387317i
$$417$$ −7.51960e13 + 1.30243e14i −0.292043 + 0.505833i
$$418$$ 6.83967e13 + 1.18467e14i 0.262159 + 0.454073i
$$419$$ 7.34035e13 0.277677 0.138838 0.990315i $$-0.455663\pi$$
0.138838 + 0.990315i $$0.455663\pi$$
$$420$$ 0 0
$$421$$ 1.71112e14 0.630563 0.315282 0.948998i $$-0.397901\pi$$
0.315282 + 0.948998i $$0.397901\pi$$
$$422$$ −8.15180e13 1.41193e14i −0.296507 0.513565i
$$423$$ 1.52699e14 2.64483e14i 0.548232 0.949566i
$$424$$ 6.74174e13 1.16770e14i 0.238924 0.413828i
$$425$$ −8.80480e13 1.52504e14i −0.308021 0.533508i
$$426$$ −5.92189e13 −0.204507
$$427$$ 0 0
$$428$$ −1.32835e14 −0.447067
$$429$$ 3.89171e13 + 6.74063e13i 0.129308 + 0.223968i
$$430$$ −9.92606e11 + 1.71924e12i −0.00325612 + 0.00563977i
$$431$$ 3.58879e13 6.21597e13i 0.116231 0.201319i −0.802040 0.597270i $$-0.796252\pi$$
0.918271 + 0.395952i $$0.129585\pi$$
$$432$$ 3.61682e13 + 6.26452e13i 0.115656 + 0.200321i
$$433$$ 9.98812e13 0.315356 0.157678 0.987491i $$-0.449599\pi$$
0.157678 + 0.987491i $$0.449599\pi$$
$$434$$ 0 0
$$435$$ 1.56291e14 0.481110
$$436$$ 5.40832e13 + 9.36749e13i 0.164394 + 0.284739i
$$437$$ −9.93819e13 + 1.72134e14i −0.298304 + 0.516678i
$$438$$ 4.42650e12 7.66693e12i 0.0131206 0.0227255i
$$439$$ 1.45156e13 + 2.51418e13i 0.0424894 + 0.0735938i 0.886488 0.462752i $$-0.153138\pi$$
−0.843999 + 0.536345i $$0.819804\pi$$
$$440$$ 2.18142e14 0.630594
$$441$$ 0 0
$$442$$ −9.57557e13 −0.269987
$$443$$ −1.64185e14 2.84377e14i −0.457207 0.791906i 0.541605 0.840633i $$-0.317817\pi$$
−0.998812 + 0.0487274i $$0.984483\pi$$
$$444$$ −3.37955e13 + 5.85355e13i −0.0929506 + 0.160995i
$$445$$ 6.03579e13 1.04543e14i 0.163966 0.283998i
$$446$$ 8.80184e13 + 1.52452e14i 0.236174 + 0.409065i
$$447$$ −2.81089e14 −0.744994
$$448$$ 0 0
$$449$$ −6.12368e14 −1.58364 −0.791822 0.610752i $$-0.790867\pi$$
−0.791822 + 0.610752i $$0.790867\pi$$
$$450$$ 3.47737e13 + 6.02298e13i 0.0888346 + 0.153866i
$$451$$ −8.23624e13 + 1.42656e14i −0.207854 + 0.360014i
$$452$$ −6.26681e13 + 1.08544e14i −0.156237 + 0.270611i
$$453$$ 1.03880e14 + 1.79926e14i 0.255855 + 0.443153i
$$454$$ 3.26361e13 0.0794130
$$455$$ 0 0
$$456$$ 2.26971e14 0.539092
$$457$$ −1.51742e14 2.62824e14i −0.356095 0.616774i 0.631210 0.775612i $$-0.282559\pi$$
−0.987305 + 0.158838i $$0.949225\pi$$
$$458$$ −1.41893e14 + 2.45766e14i −0.329004 + 0.569851i
$$459$$ −2.53030e14 + 4.38261e14i −0.579699 + 1.00407i
$$460$$ 6.62746e13 + 1.14791e14i 0.150030 + 0.259860i
$$461$$ −7.29308e14 −1.63138 −0.815691 0.578487i $$-0.803643\pi$$
−0.815691 + 0.578487i $$0.803643\pi$$
$$462$$ 0 0
$$463$$ 1.22188e14 0.266891 0.133445 0.991056i $$-0.457396\pi$$
0.133445 + 0.991056i $$0.457396\pi$$
$$464$$ −6.33774e13 1.09773e14i −0.136800 0.236944i
$$465$$ 3.21593e13 5.57015e13i 0.0685986 0.118816i
$$466$$ −2.10760e14 + 3.65047e14i −0.444290 + 0.769532i
$$467$$ 3.08690e14 + 5.34667e14i 0.643103 + 1.11389i 0.984736 + 0.174053i $$0.0556864\pi$$
−0.341634 + 0.939833i $$0.610980\pi$$
$$468$$ −9.66455e13 −0.198989
$$469$$ 0 0
$$470$$ −3.11517e14 −0.626533
$$471$$ −1.65705e14 2.87009e14i −0.329397 0.570533i
$$472$$ 2.19192e14 3.79652e14i 0.430669 0.745941i
$$473$$ 4.57780e12 7.92899e12i 0.00889039 0.0153986i
$$474$$ 1.15265e14 + 1.99645e14i 0.221268 + 0.383247i
$$475$$ −2.71858e14 −0.515854
$$476$$ 0 0
$$477$$ 1.81381e14 0.336310
$$478$$ −8.56749e13 1.48393e14i −0.157036 0.271995i
$$479$$ −5.25419e14 + 9.10052e14i −0.952052 + 1.64900i −0.211076 + 0.977470i $$0.567697\pi$$
−0.740976 + 0.671532i $$0.765637\pi$$
$$480$$ 1.19712e14 2.07346e14i 0.214442 0.371424i
$$481$$ −5.26358e13 9.11678e13i −0.0932144 0.161452i
$$482$$ 5.55137e12 0.00971944
$$483$$ 0 0
$$484$$ −7.33527e11 −0.00125536
$$485$$ −1.81158e14 3.13774e14i −0.306533 0.530931i
$$486$$ 1.60810e14 2.78530e14i 0.269037 0.465986i
$$487$$ 1.09955e14 1.90448e14i 0.181889 0.315040i −0.760635 0.649180i $$-0.775112\pi$$
0.942524 + 0.334139i $$0.108446\pi$$
$$488$$ −2.93842e14 5.08949e14i −0.480623 0.832463i
$$489$$ −9.01739e13 −0.145842
$$490$$ 0 0
$$491$$ −4.83863e14 −0.765199 −0.382599 0.923914i $$-0.624971\pi$$
−0.382599 + 0.923914i $$0.624971\pi$$
$$492$$ 5.71477e13 + 9.89827e13i 0.0893698 + 0.154793i
$$493$$ 4.43384e14 7.67963e14i 0.685681 1.18763i
$$494$$ −7.39141e13 + 1.28023e14i −0.113039 + 0.195790i
$$495$$ 1.46723e14 + 2.54132e14i 0.221906 + 0.384353i
$$496$$ −5.21634e13 −0.0780219
$$497$$ 0 0
$$498$$ 1.77419e14 0.259560
$$499$$ 5.44389e13 + 9.42909e13i 0.0787691 + 0.136432i 0.902719 0.430230i $$-0.141568\pi$$
−0.823950 + 0.566663i $$0.808234\pi$$
$$500$$ −2.64225e14 + 4.57651e14i −0.378128 + 0.654937i
$$501$$ −3.47109e14 + 6.01211e14i −0.491313 + 0.850979i
$$502$$ 1.55797e14 + 2.69848e14i 0.218116 + 0.377788i
$$503$$ 5.06588e14 0.701506 0.350753 0.936468i $$-0.385926\pi$$
0.350753 + 0.936468i $$0.385926\pi$$
$$504$$ 0 0
$$505$$ 3.94818e14 0.534927
$$506$$ 1.19603e14 + 2.07158e14i 0.160293 + 0.277635i
$$507$$ 1.83756e14 3.18274e14i 0.243611 0.421947i
$$508$$ −1.93360e14 + 3.34909e14i −0.253581 + 0.439214i
$$509$$ −4.28767e13 7.42646e13i −0.0556254 0.0963461i 0.836872 0.547399i $$-0.184382\pi$$
−0.892497 + 0.451053i $$0.851049\pi$$
$$510$$ 2.01735e14 0.258908
$$511$$ 0 0
$$512$$ −3.64965e14 −0.458423
$$513$$ 3.90630e14 + 6.76590e14i 0.485422 + 0.840776i
$$514$$ 2.87534e14 4.98024e14i 0.353503 0.612284i
$$515$$ 5.45199e14 9.44312e14i 0.663155 1.14862i
$$516$$ −3.17634e12 5.50158e12i −0.00382255 0.00662086i
$$517$$ 1.43669e15 1.71066
$$518$$ 0 0
$$519$$ −2.39498e14 −0.279178
$$520$$ 1.17870e14 + 2.04156e14i 0.135951 + 0.235475i
$$521$$ −4.63787e14 + 8.03303e14i −0.529312 + 0.916795i 0.470104 + 0.882611i $$0.344216\pi$$
−0.999416 + 0.0341835i $$0.989117\pi$$
$$522$$ −1.75110e14 + 3.03300e14i −0.197753 + 0.342519i
$$523$$ 1.09093e13 + 1.88955e13i 0.0121910 + 0.0211154i 0.872057 0.489405i $$-0.162786\pi$$
−0.859866 + 0.510521i $$0.829453\pi$$
$$524$$ −9.29610e14 −1.02797
$$525$$ 0 0
$$526$$ 5.82569e14 0.630850
$$527$$ −1.82466e14 3.16040e14i −0.195534 0.338675i
$$528$$ −6.64946e13 + 1.15172e14i −0.0705179 + 0.122141i
$$529$$ 3.02619e14 5.24152e14i 0.317607 0.550112i
$$530$$ −9.25074e13 1.60227e14i −0.0960858 0.166425i
$$531$$ 5.89717e14 0.606211
$$532$$ 0 0
$$533$$ −1.78013e14 −0.179247
$$534$$ −7.55786e13 1.30906e14i −0.0753220 0.130462i
$$535$$ −2.17933e14 + 3.77470e14i −0.214969 + 0.372338i
$$536$$ 6.53952e14 1.13268e15i 0.638469 1.10586i
$$537$$ −2.11854e14 3.66943e14i −0.204729 0.354601i
$$538$$ −6.20105e14 −0.593147
$$539$$ 0 0
$$540$$ 5.20997e14 0.488280
$$541$$ 8.47633e14 + 1.46814e15i 0.786363 + 1.36202i 0.928181 + 0.372128i $$0.121372\pi$$
−0.141819 + 0.989893i $$0.545295\pi$$
$$542$$ −4.52152e13 + 7.83150e13i −0.0415230 + 0.0719199i
$$543$$ 1.25594e14 2.17534e14i 0.114174 0.197756i
$$544$$ −6.79220e14 1.17644e15i −0.611247 1.05871i
$$545$$ 3.54921e14 0.316192
$$546$$ 0 0
$$547$$ 7.52145e14 0.656706 0.328353 0.944555i $$-0.393506\pi$$
0.328353 + 0.944555i $$0.393506\pi$$
$$548$$ −2.18738e14 3.78866e14i −0.189074 0.327486i
$$549$$ 3.95278e14 6.84641e14i 0.338263 0.585888i
$$550$$ −1.63586e14 + 2.83340e14i −0.138596 + 0.240056i
$$551$$ −6.84499e14 1.18559e15i −0.574168 0.994488i
$$552$$ 3.96896e14 0.329619
$$553$$ 0 0
$$554$$ 3.94054e14 0.320813
$$555$$ 1.10891e14 + 1.92070e14i 0.0893895 + 0.154827i
$$556$$ 4.39240e14 7.60786e14i 0.350583 0.607227i
$$557$$ −9.37445e13 + 1.62370e14i −0.0740870 + 0.128323i −0.900689 0.434465i $$-0.856938\pi$$
0.826602 + 0.562787i $$0.190271\pi$$
$$558$$ 7.20631e13 + 1.24817e14i 0.0563929 + 0.0976754i
$$559$$ 9.89417e12 0.00766681
$$560$$ 0 0
$$561$$ −9.30383e14 −0.706913
$$562$$ 2.52429e14 + 4.37219e14i 0.189928 + 0.328965i
$$563$$ −1.22486e14 + 2.12151e14i −0.0912618 + 0.158070i −0.908042 0.418878i $$-0.862423\pi$$
0.816781 + 0.576949i $$0.195757\pi$$
$$564$$ 4.98428e14 8.63302e14i 0.367762 0.636983i
$$565$$ 2.05630e14 + 3.56161e14i 0.150252 + 0.260244i
$$566$$ −4.01116e14 −0.290255
$$567$$ 0 0
$$568$$ 8.27185e14 0.587066
$$569$$ −6.76213e14 1.17124e15i −0.475298 0.823240i 0.524302 0.851533i $$-0.324326\pi$$
−0.999600 + 0.0282923i $$0.990993\pi$$
$$570$$ 1.55720e14 2.69715e14i 0.108401 0.187756i
$$571$$ −7.16114e14 + 1.24035e15i −0.493723 + 0.855154i −0.999974 0.00723249i $$-0.997698\pi$$
0.506250 + 0.862387i $$0.331031\pi$$
$$572$$ −2.27325e14 3.93739e14i −0.155228 0.268862i
$$573$$ 6.96126e14 0.470801
$$574$$ 0 0
$$575$$ −4.75389e14 −0.315410
$$576$$ 1.53378e14 + 2.65659e14i 0.100795 + 0.174582i
$$577$$ 4.38830e14 7.60075e14i 0.285647 0.494754i −0.687119 0.726545i $$-0.741125\pi$$
0.972766 + 0.231790i $$0.0744583\pi$$
$$578$$ 1.61040e14 2.78930e14i 0.103832 0.179842i
$$579$$ −6.85741e14 1.18774e15i −0.437953 0.758558i
$$580$$ −9.12940e14 −0.577548
$$581$$ 0 0
$$582$$ −4.53682e14 −0.281628
$$583$$ 4.26635e14 + 7.38954e14i 0.262349 + 0.454402i
$$584$$ −6.18305e13 + 1.07094e14i −0.0376645 + 0.0652369i
$$585$$ −1.58559e14 + 2.74632e14i −0.0956827 + 0.165727i
$$586$$ −2.87122e14 4.97310e14i −0.171645 0.297297i
$$587$$ −2.43425e15 −1.44164 −0.720818 0.693124i $$-0.756234\pi$$
−0.720818 + 0.693124i $$0.756234\pi$$
$$588$$ 0 0
$$589$$ −5.63383e14 −0.327469
$$590$$ −3.00766e14 5.20942e14i −0.173198 0.299988i
$$591$$ 3.62388e14 6.27674e14i 0.206748 0.358099i
$$592$$ 8.99347e13 1.55771e14i 0.0508344 0.0880478i
$$593$$ 1.51659e14 + 2.62681e14i 0.0849313 + 0.147105i 0.905362 0.424641i $$-0.139600\pi$$
−0.820431 + 0.571746i $$0.806266\pi$$
$$594$$ 9.40221e14 0.521680
$$595$$ 0 0
$$596$$ 1.64192e15 0.894329
$$597$$ −9.17773e13 1.58963e14i −0.0495309 0.0857901i
$$598$$ −1.29251e14 + 2.23870e14i −0.0691159 + 0.119712i
$$599$$ 8.50992e14 1.47396e15i 0.450898 0.780978i −0.547544 0.836777i $$-0.684437\pi$$
0.998442 + 0.0557990i $$0.0177706\pi$$
$$600$$ 2.71426e14 + 4.70124e14i 0.142502 + 0.246820i
$$601$$ 2.33922e15 1.21692 0.608458 0.793586i $$-0.291788\pi$$
0.608458 + 0.793586i $$0.291788\pi$$
$$602$$ 0 0
$$603$$ 1.75940e15 0.898710
$$604$$ −6.06793e14 1.05100e15i −0.307141 0.531984i
$$605$$ −1.20344e12 + 2.08442e12i −0.000603630 + 0.00104552i
$$606$$ 2.47191e14 4.28147e14i 0.122866 0.212811i
$$607$$ 1.24804e15 + 2.16166e15i 0.614737 + 1.06476i 0.990431 + 0.138012i $$0.0440712\pi$$
−0.375694 + 0.926744i $$0.622595\pi$$
$$608$$ −2.09717e15 −1.02368
$$609$$ 0 0
$$610$$ −8.06395e14 −0.386575
$$611$$ 7.76292e14 + 1.34458e15i 0.368806 + 0.638791i
$$612$$ 5.77621e14 1.00047e15i 0.271963 0.471054i
$$613$$ −1.23650e15 + 2.14169e15i −0.576983 + 0.999364i 0.418840 + 0.908060i $$0.362437\pi$$
−0.995823 + 0.0913040i $$0.970897\pi$$
$$614$$ 1.83733e14 + 3.18235e14i 0.0849692 + 0.147171i
$$615$$ 3.75032e14 0.171892
$$616$$ 0 0
$$617$$ 2.43368e13 0.0109571 0.00547854 0.999985i $$-0.498256\pi$$
0.00547854 + 0.999985i $$0.498256\pi$$
$$618$$ −6.82684e14 1.18244e15i −0.304637 0.527647i
$$619$$ −2.11273e15 + 3.65935e15i −0.934425 + 1.61847i −0.158769 + 0.987316i $$0.550753\pi$$
−0.775656 + 0.631156i $$0.782581\pi$$
$$620$$ −1.87851e14 + 3.25368e14i −0.0823492 + 0.142633i
$$621$$ 6.83081e14 + 1.18313e15i 0.296803 + 0.514078i
$$622$$ −1.19700e15 −0.515523
$$623$$ 0 0
$$624$$ −1.43717e14 −0.0608126
$$625$$ 2.44448e14 + 4.23396e14i 0.102529 + 0.177585i
$$626$$ −1.19377e15 + 2.06767e15i −0.496320 + 0.859652i
$$627$$ −7.18165e14 + 1.24390e15i −0.295973 + 0.512641i
$$628$$ 9.67926e14 + 1.67650e15i 0.395425 + 0.684896i
$$629$$ 1.25835e15 0.509594
$$630$$ 0 0
$$631$$ −4.26326e15 −1.69660 −0.848302 0.529513i $$-0.822375\pi$$
−0.848302 + 0.529513i $$0.822375\pi$$
$$632$$ −1.61006e15 2.78870e15i −0.635180 1.10016i
$$633$$ 8.55939e14 1.48253e15i 0.334751 0.579807i
$$634$$ 1.00043e15 1.73280e15i 0.387879 0.671826i
$$635$$ 6.34462e14 + 1.09892e15i 0.243865 + 0.422387i
$$636$$ 5.92047e14 0.225602
$$637$$ 0 0
$$638$$ −1.64755e15 −0.617055
$$639$$ 5.56367e14 + 9.63656e14i 0.206589 + 0.357822i
$$640$$ −8.16442e14 + 1.41412e15i −0.300563 + 0.520591i
$$641$$ −5.04148e14 + 8.73210e14i −0.184009 + 0.318713i −0.943242 0.332106i $$-0.892241\pi$$
0.759233 + 0.650819i $$0.225574\pi$$
$$642$$ 2.72890e14 + 4.72659e14i 0.0987516 + 0.171043i
$$643$$ 3.03982e14 0.109066 0.0545328 0.998512i $$-0.482633\pi$$
0.0545328 + 0.998512i $$0.482633\pi$$
$$644$$ 0 0
$$645$$ −2.08447e13 −0.00735221
$$646$$ −8.83525e14 1.53031e15i −0.308987 0.535181i
$$647$$ −1.71791e15 + 2.97551e15i −0.595700 + 1.03178i 0.397747 + 0.917495i $$0.369792\pi$$
−0.993448 + 0.114288i $$0.963541\pi$$
$$648$$ −7.03376e13 + 1.21828e14i −0.0241838 + 0.0418876i
$$649$$ 1.38711e15 + 2.40254e15i 0.472894 + 0.819076i
$$650$$ −3.53565e14 −0.119521
$$651$$ 0 0
$$652$$ 5.26730e14 0.175076
$$653$$ 5.92694e14 + 1.02658e15i 0.195347 + 0.338352i 0.947014 0.321191i $$-0.104083\pi$$
−0.751667 + 0.659543i $$0.770750\pi$$
$$654$$ 2.22212e14 3.84882e14i 0.0726255 0.125791i
$$655$$ −1.52514e15 + 2.64162e15i −0.494291 + 0.856138i
$$656$$ −1.52078e14 2.63407e14i −0.0488761 0.0846559i
$$657$$ −1.66350e14 −0.0530167
$$658$$ 0 0
$$659$$ −2.26510e15 −0.709934 −0.354967 0.934879i $$-0.615508\pi$$
−0.354967 + 0.934879i $$0.615508\pi$$
$$660$$ 4.78921e14 + 8.29516e14i 0.148858 + 0.257830i
$$661$$ 2.66506e15 4.61602e15i 0.821484 1.42285i −0.0830931 0.996542i $$-0.526480\pi$$
0.904577 0.426310i $$-0.140187\pi$$
$$662$$ −7.63008e14 + 1.32157e15i −0.233244 + 0.403990i
$$663$$ −5.02717e14 8.70732e14i −0.152405 0.263973i
$$664$$ −2.47823e15 −0.745104
$$665$$ 0 0
$$666$$ −4.96974e14 −0.146969
$$667$$ −1.19696e15 2.07320e15i −0.351065 0.608062i
$$668$$ 2.02756e15 3.51183e15i 0.589797 1.02156i
$$669$$ −9.24193e14 + 1.60075e15i −0.266636 + 0.461827i
$$670$$ −8.97327e14 1.55422e15i −0.256767 0.444733i
$$671$$ 3.71902e15 1.05549
$$672$$ 0 0
$$673$$ 4.74120e15 1.32375 0.661874 0.749615i $$-0.269761\pi$$
0.661874 + 0.749615i $$0.269761\pi$$
$$674$$ 1.45202e15 + 2.51497e15i 0.402108 + 0.696471i
$$675$$ −9.34280e14 + 1.61822e15i −0.256629 + 0.444495i
$$676$$ −1.07337e15 + 1.85913e15i −0.292443 + 0.506526i
$$677$$ 7.06536e14 + 1.22376e15i 0.190940 + 0.330717i 0.945562 0.325442i $$-0.105513\pi$$
−0.754622 + 0.656160i $$0.772180\pi$$
$$678$$ 5.14968e14 0.138044
$$679$$ 0 0
$$680$$ −2.81789e15 −0.743232
$$681$$ 1.71340e14 + 2.96769e14i 0.0448280 + 0.0776443i
$$682$$ −3.39007e14 + 5.87178e14i −0.0879822 + 0.152390i
$$683$$ 1.51558e15 2.62506e15i 0.390180 0.675811i −0.602293 0.798275i $$-0.705746\pi$$
0.992473 + 0.122464i $$0.0390796\pi$$
$$684$$ −8.91734e14 1.54453e15i −0.227734 0.394446i
$$685$$ −1.43547e15 −0.363660
$$686$$ 0 0
$$687$$ −2.97975e15 −0.742879
$$688$$ 8.45270e12 + 1.46405e13i 0.00209054 + 0.00362093i
$$689$$ −4.61051e14 + 7.98564e14i −0.113121 + 0.195931i
$$690$$ 2.72302e14 4.71641e14i 0.0662798 0.114800i
$$691$$ 1.37366e15 + 2.37924e15i 0.331703 + 0.574526i 0.982846 0.184429i $$-0.0590436\pi$$
−0.651143 + 0.758955i $$0.725710\pi$$
$$692$$ 1.39897e15 0.335139
$$693$$ 0 0
$$694$$ 3.73588e15 0.880878
$$695$$ −1.44126e15 2.49633e15i −0.337151 0.583963i
$$696$$ −1.36682e15 + 2.36740e15i −0.317220 + 0.549442i
$$697$$ 1.06393e15 1.84278e15i 0.244981 0.424320i
$$698$$ −3.07716e14 5.32980e14i −0.0702984 0.121760i
$$699$$ −4.42597e15 −1.00319
$$700$$ 0 0
$$701$$ 5.72747e15 1.27795 0.638974 0.769228i $$-0.279359\pi$$
0.638974 + 0.769228i $$0.279359\pi$$
$$702$$ 5.08033e14 + 8.79940e14i 0.112470 + 0.194804i
$$703$$ 9.71326e14 1.68239e15i 0.213359 0.369549i
$$704$$ −7.21538e14 + 1.24974e15i −0.157257 + 0.272377i
$$705$$ −1.63547e15 2.83271e15i −0.353673 0.612579i
$$706$$ −5.97836e14 −0.128279
$$707$$ 0 0
$$708$$ 1.92490e15 0.406655
$$709$$ −3.49163e14 6.04768e14i −0.0731938 0.126775i 0.827106 0.562047i $$-0.189986\pi$$
−0.900299 + 0.435271i $$0.856652\pi$$
$$710$$ 5.67514e14 9.82964e14i 0.118047 0.204464i
$$711$$ 2.16586e15 3.75137e15i 0.447040 0.774297i
$$712$$ 1.05570e15 + 1.82853e15i 0.216223 + 0.374508i
$$713$$ −9.85170e14 −0.200225
$$714$$ 0 0
$$715$$ −1.49182e15 −0.298561
$$716$$ 1.23750e15 + 2.14341e15i 0.245767 + 0.425681i
$$717$$ 8.99587e14 1.55813e15i 0.177291 0.307078i
$$718$$ 1.89101e15 3.27533e15i 0.369836 0.640575i
$$719$$ −4.85489e15 8.40892e15i −0.942260 1.63204i −0.761146 0.648580i $$-0.775363\pi$$
−0.181114 0.983462i $$-0.557970\pi$$
$$720$$ −5.41835e14 −0.104361
$$721$$ 0 0
$$722$$ 6.77852e13 0.0128582
$$723$$ 2.91447e13 + 5.04801e13i 0.00548654 + 0.00950297i
$$724$$ −7.33626e14 + 1.27068e15i −0.137061 + 0.237396i
$$725$$ 1.63713e15 2.83560e15i 0.303547 0.525758i
$$726$$ 1.50692e12 + 2.61006e12i 0.000277293 + 0.000480285i
$$727$$ 2.46469e15 0.450114 0.225057 0.974346i $$-0.427743\pi$$
0.225057 + 0.974346i $$0.427743\pi$$
$$728$$ 0 0
$$729$$ 3.08202e15 0.554413
$$730$$ 8.48413e13 + 1.46950e14i 0.0151472 + 0.0262357i
$$731$$ −5.91345e13 + 1.02424e14i −0.0104784 + 0.0181491i
$$732$$ 1.29023e15 2.23475e15i 0.226912 0.393023i
$$733$$ −3.95643e15 6.85273e15i −0.690607 1.19617i −0.971639 0.236469i $$-0.924010\pi$$
0.281032 0.959698i $$-0.409323\pi$$
$$734$$ 4.26963e15 0.739711
$$735$$ 0 0
$$736$$ −3.66725e15 −0.625911
$$737$$ 4.13839e15 + 7.16789e15i 0.701067 + 1.21428i
$$738$$ −4.20189e14 + 7.27788e14i −0.0706536 + 0.122376i
$$739$$ 4.20347e15 7.28062e15i 0.701558 1.21513i −0.266362 0.963873i $$-0.585822\pi$$
0.967920 0.251260i $$-0.0808450\pi$$
$$740$$ −6.47746e14 1.12193e15i −0.107308 0.185862i
$$741$$ −1.55220e15 −0.255239
$$742$$ 0 0
$$743$$ 1.36287e15 0.220809 0.110404 0.993887i $$-0.464785\pi$$
0.110404 + 0.993887i $$0.464785\pi$$
$$744$$ 5.62488e14 + 9.74258e14i 0.0904612 + 0.156683i
$$745$$ 2.69377e15 4.66575e15i 0.430033 0.744838i
$$746$$ −6.61941e14 + 1.14652e15i −0.104895 + 0.181684i
$$747$$ −1.66686e15 2.88709e15i −0.262203 0.454148i
$$748$$ 5.43462e15 0.848614
$$749$$ 0 0
$$750$$ 2.17124e15 0.334095
$$751$$ −3.40861e15 5.90389e15i −0.520664 0.901817i −0.999711 0.0240276i $$-0.992351\pi$$
0.479047 0.877789i $$-0.340982\pi$$
$$752$$ −1.32639e15 + 2.29737e15i −0.201128 + 0.348364i
$$753$$ −1.63586e15 + 2.83340e15i −0.246249 + 0.426516i
$$754$$ −8.90225e14 1.54191e15i −0.133032 0.230419i
$$755$$ −3.98208e15 −0.590747
$$756$$ 0 0
$$757$$ −6.67049e14 −0.0975282 −0.0487641 0.998810i $$-0.515528\pi$$
−0.0487641 + 0.998810i $$0.515528\pi$$
$$758$$ 1.75756e15 + 3.04418e15i 0.255111 + 0.441865i
$$759$$ −1.25583e15 + 2.17516e15i −0.180968 + 0.313446i
$$760$$ −2.17513e15 + 3.76744e15i −0.311180 + 0.538979i
$$761$$ 3.87204e15 + 6.70657e15i 0.549951 + 0.952544i 0.998277 + 0.0586734i $$0.0186871\pi$$
−0.448326 + 0.893870i $$0.647980\pi$$
$$762$$ 1.58891e15 0.224052
$$763$$ 0 0
$$764$$ −4.06626e15 −0.565173
$$765$$ −1.89532e15 3.28279e15i −0.261544 0.453007i
$$766$$ 2.77739e15 4.81059e15i 0.380522 0.659083i