# Properties

 Label 14.13.d.a.5.3 Level $14$ Weight $13$ Character 14.5 Analytic conductor $12.796$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$14 = 2 \cdot 7$$ Weight: $$k$$ $$=$$ $$13$$ Character orbit: $$[\chi]$$ $$=$$ 14.d (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.7959134419$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ Defining polynomial: $$x^{16} + 527434 x^{14} - 31307480 x^{13} + 193554267483 x^{12} - 12267558721140 x^{11} + 36740634631350658 x^{10} - 2684653740993140180 x^{9} + 5051027688394458110177 x^{8} - 329042050982173184619740 x^{7} + 328571000441888143595366884 x^{6} - 20799163177686535050419379920 x^{5} + 15169931128056380497155715556632 x^{4} - 685746033739471361446313307383040 x^{3} + 159607415711477686151635843287775328 x^{2} + 6015487435743293961505549572273215360 x + 735121207672317095821497912841120438336$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{48}\cdot 3^{8}\cdot 7^{7}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 5.3 Root $$127.460 - 220.767i$$ of defining polynomial Character $$\chi$$ $$=$$ 14.5 Dual form 14.13.d.a.3.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-22.6274 + 39.1918i) q^{2} +(702.607 - 405.650i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-18305.2 - 10568.5i) q^{5} +36715.3i q^{6} +(-9080.55 + 117298. i) q^{7} +92681.9 q^{8} +(63384.0 - 109784. i) q^{9} +O(q^{10})$$ $$q+(-22.6274 + 39.1918i) q^{2} +(702.607 - 405.650i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-18305.2 - 10568.5i) q^{5} +36715.3i q^{6} +(-9080.55 + 117298. i) q^{7} +92681.9 q^{8} +(63384.0 - 109784. i) q^{9} +(828399. - 478276. i) q^{10} +(651539. + 1.12850e6i) q^{11} +(-1.43894e6 - 830772. i) q^{12} +7.09849e6i q^{13} +(-4.39166e6 - 3.01003e6i) q^{14} -1.71485e7 q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(-2.79240e7 + 1.61219e7i) q^{17} +(2.86843e6 + 4.96827e6i) q^{18} +(-2.32303e7 - 1.34120e7i) q^{19} +4.32886e7i q^{20} +(4.12019e7 + 8.60980e7i) q^{21} -5.89706e7 q^{22} +(6.22412e7 - 1.07805e8i) q^{23} +(6.51190e7 - 3.75965e7i) q^{24} +(1.01317e8 + 1.75486e8i) q^{25} +(-2.78203e8 - 1.60621e8i) q^{26} +3.28312e8i q^{27} +(2.17341e8 - 1.04008e8i) q^{28} -7.52793e8 q^{29} +(3.88026e8 - 6.72081e8i) q^{30} +(9.46508e8 - 5.46467e8i) q^{31} +(-9.49063e7 - 1.64382e8i) q^{32} +(9.15552e8 + 5.28594e8i) q^{33} -1.45919e9i q^{34} +(1.40589e9 - 2.05120e9i) q^{35} -2.59621e8 q^{36} +(-1.93585e9 + 3.35299e9i) q^{37} +(1.05129e9 - 6.06960e8i) q^{38} +(2.87951e9 + 4.98745e9i) q^{39} +(-1.69656e9 - 9.79510e8i) q^{40} -2.55800e9i q^{41} +(-4.30663e9 - 3.33395e8i) q^{42} -4.36133e9 q^{43} +(1.33435e9 - 2.31116e9i) q^{44} +(-2.32051e9 + 1.33975e9i) q^{45} +(2.81672e9 + 4.87869e9i) q^{46} +(8.04169e9 + 4.64287e9i) q^{47} +3.40284e9i q^{48} +(-1.36764e10 - 2.13026e9i) q^{49} -9.17013e9 q^{50} +(-1.30797e10 + 2.26548e10i) q^{51} +(1.25900e10 - 7.26886e9i) q^{52} +(-1.09179e8 - 1.89104e8i) q^{53} +(-1.28671e10 - 7.42884e9i) q^{54} -2.75432e10i q^{55} +(-8.41602e8 + 1.08714e10i) q^{56} -2.17624e10 q^{57} +(1.70338e10 - 2.95033e10i) q^{58} +(5.45224e10 - 3.14785e10i) q^{59} +(1.75600e10 + 3.04149e10i) q^{60} +(4.19753e10 + 2.42344e10i) q^{61} +4.94605e10i q^{62} +(1.23019e10 + 8.43172e9i) q^{63} +8.58993e9 q^{64} +(7.50205e10 - 1.29939e11i) q^{65} +(-4.14331e10 + 2.39214e10i) q^{66} +(-5.49220e10 - 9.51277e10i) q^{67} +(5.71884e10 + 3.30177e10i) q^{68} -1.00993e11i q^{69} +(4.85786e10 + 1.01513e11i) q^{70} -7.43754e10 q^{71} +(5.87455e9 - 1.01750e10i) q^{72} +(-2.26320e11 + 1.30666e11i) q^{73} +(-8.76065e10 - 1.51739e11i) q^{74} +(1.42372e11 + 8.21982e10i) q^{75} +5.49357e10i q^{76} +(-1.38287e11 + 6.61769e10i) q^{77} -2.60623e11 q^{78} +(-1.20639e11 + 2.08953e11i) q^{79} +(7.67776e10 - 4.43276e10i) q^{80} +(1.66865e11 + 2.89018e11i) q^{81} +(1.00253e11 + 5.78810e10i) q^{82} -2.09983e11i q^{83} +(1.10514e11 - 1.61241e11i) q^{84} +6.81540e11 q^{85} +(9.86855e10 - 1.70928e11i) q^{86} +(-5.28918e11 + 3.05371e11i) q^{87} +(6.03859e10 + 1.04591e11i) q^{88} +(1.79050e10 + 1.03374e10i) q^{89} -1.21260e11i q^{90} +(-8.32640e11 - 6.44582e10i) q^{91} -2.54940e11 q^{92} +(4.43349e11 - 7.67903e11i) q^{93} +(-3.63926e11 + 2.10113e11i) q^{94} +(2.83491e11 + 4.91020e11i) q^{95} +(-1.33364e11 - 7.69975e10i) q^{96} +4.74911e11i q^{97} +(3.92950e11 - 4.87800e11i) q^{98} +1.65189e11 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9} + O(q^{10})$$ $$16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9} - 2290176 q^{10} + 2072088 q^{11} - 11501568 q^{14} - 27163728 q^{15} - 33554432 q^{16} - 101561040 q^{17} - 4592640 q^{18} + 174931848 q^{19} - 323731368 q^{21} + 62776320 q^{22} + 25630560 q^{23} + 242221056 q^{24} + 521205808 q^{25} - 1434682368 q^{26} + 350863360 q^{28} + 532360944 q^{29} - 2151917568 q^{30} + 4583818344 q^{31} + 6054957720 q^{33} - 1612540440 q^{35} - 9675767808 q^{36} + 5764524040 q^{37} - 149506560 q^{38} + 10526083272 q^{39} + 4690280448 q^{40} - 12685086720 q^{42} - 66929432000 q^{43} + 4243636224 q^{44} + 57253352184 q^{45} + 7203213312 q^{46} + 18116171640 q^{47} - 9977452064 q^{49} - 99248080896 q^{50} - 23299256376 q^{51} + 8269578240 q^{52} + 39134161800 q^{53} + 105152205312 q^{54} + 3623878656 q^{56} - 328243960080 q^{57} + 29637396480 q^{58} + 201845459088 q^{59} + 27815657472 q^{60} + 336780254328 q^{61} - 389095094520 q^{63} + 137438953472 q^{64} + 158322703896 q^{65} + 268884080640 q^{66} + 107767119920 q^{67} + 207997009920 q^{68} - 6077815296 q^{70} - 1150259029344 q^{71} - 9405726720 q^{72} - 738414283320 q^{73} + 4902778368 q^{74} + 1537028640000 q^{75} - 321203352960 q^{77} - 786088888320 q^{78} + 227632064768 q^{79} - 76101451776 q^{80} - 391984178400 q^{81} - 302578053120 q^{82} - 32685686784 q^{84} + 710209696080 q^{85} - 38105192448 q^{86} + 1957017683880 q^{87} - 64282951680 q^{88} - 2485007442792 q^{89} + 1803248333904 q^{91} - 104982773760 q^{92} - 458668768680 q^{93} - 2021298693120 q^{94} - 186503862960 q^{95} - 496068722688 q^{96} - 356371660800 q^{98} + 3921180354576 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −22.6274 + 39.1918i −0.353553 + 0.612372i
$$3$$ 702.607 405.650i 0.963796 0.556448i 0.0664566 0.997789i $$-0.478831\pi$$
0.897339 + 0.441342i $$0.145497\pi$$
$$4$$ −1024.00 1773.62i −0.250000 0.433013i
$$5$$ −18305.2 10568.5i −1.17153 0.676385i −0.217492 0.976062i $$-0.569788\pi$$
−0.954041 + 0.299677i $$0.903121\pi$$
$$6$$ 36715.3i 0.786936i
$$7$$ −9080.55 + 117298.i −0.0771834 + 0.997017i
$$8$$ 92681.9 0.353553
$$9$$ 63384.0 109784.i 0.119268 0.206579i
$$10$$ 828399. 478276.i 0.828399 0.478276i
$$11$$ 651539. + 1.12850e6i 0.367777 + 0.637008i 0.989218 0.146453i $$-0.0467857\pi$$
−0.621441 + 0.783461i $$0.713452\pi$$
$$12$$ −1.43894e6 830772.i −0.481898 0.278224i
$$13$$ 7.09849e6i 1.47064i 0.677720 + 0.735320i $$0.262968\pi$$
−0.677720 + 0.735320i $$0.737032\pi$$
$$14$$ −4.39166e6 3.01003e6i −0.583257 0.399764i
$$15$$ −1.71485e7 −1.50549
$$16$$ −2.09715e6 + 3.63237e6i −0.125000 + 0.216506i
$$17$$ −2.79240e7 + 1.61219e7i −1.15687 + 0.667919i −0.950552 0.310566i $$-0.899481\pi$$
−0.206318 + 0.978485i $$0.566148\pi$$
$$18$$ 2.86843e6 + 4.96827e6i 0.0843353 + 0.146073i
$$19$$ −2.32303e7 1.34120e7i −0.493780 0.285084i 0.232361 0.972630i $$-0.425355\pi$$
−0.726141 + 0.687545i $$0.758688\pi$$
$$20$$ 4.32886e7i 0.676385i
$$21$$ 4.12019e7 + 8.60980e7i 0.480399 + 1.00387i
$$22$$ −5.89706e7 −0.520115
$$23$$ 6.22412e7 1.07805e8i 0.420447 0.728235i −0.575536 0.817776i $$-0.695207\pi$$
0.995983 + 0.0895411i $$0.0285400\pi$$
$$24$$ 6.51190e7 3.75965e7i 0.340753 0.196734i
$$25$$ 1.01317e8 + 1.75486e8i 0.414993 + 0.718789i
$$26$$ −2.78203e8 1.60621e8i −0.900579 0.519950i
$$27$$ 3.28312e8i 0.847429i
$$28$$ 2.17341e8 1.04008e8i 0.451017 0.215833i
$$29$$ −7.52793e8 −1.26557 −0.632787 0.774326i $$-0.718089\pi$$
−0.632787 + 0.774326i $$0.718089\pi$$
$$30$$ 3.88026e8 6.72081e8i 0.532272 0.921921i
$$31$$ 9.46508e8 5.46467e8i 1.06648 0.615735i 0.139265 0.990255i $$-0.455526\pi$$
0.927219 + 0.374520i $$0.122193\pi$$
$$32$$ −9.49063e7 1.64382e8i −0.0883883 0.153093i
$$33$$ 9.15552e8 + 5.28594e8i 0.708923 + 0.409297i
$$34$$ 1.45919e9i 0.944580i
$$35$$ 1.40589e9 2.05120e9i 0.764790 1.11583i
$$36$$ −2.59621e8 −0.119268
$$37$$ −1.93585e9 + 3.35299e9i −0.754503 + 1.30684i 0.191117 + 0.981567i $$0.438789\pi$$
−0.945621 + 0.325271i $$0.894544\pi$$
$$38$$ 1.05129e9 6.06960e8i 0.349156 0.201585i
$$39$$ 2.87951e9 + 4.98745e9i 0.818334 + 1.41740i
$$40$$ −1.69656e9 9.79510e8i −0.414199 0.239138i
$$41$$ 2.55800e9i 0.538516i −0.963068 0.269258i $$-0.913222\pi$$
0.963068 0.269258i $$-0.0867784\pi$$
$$42$$ −4.30663e9 3.33395e8i −0.784588 0.0607384i
$$43$$ −4.36133e9 −0.689934 −0.344967 0.938615i $$-0.612110\pi$$
−0.344967 + 0.938615i $$0.612110\pi$$
$$44$$ 1.33435e9 2.31116e9i 0.183888 0.318504i
$$45$$ −2.32051e9 + 1.33975e9i −0.279453 + 0.161342i
$$46$$ 2.81672e9 + 4.87869e9i 0.297301 + 0.514940i
$$47$$ 8.04169e9 + 4.64287e9i 0.746037 + 0.430725i 0.824260 0.566211i $$-0.191591\pi$$
−0.0782231 + 0.996936i $$0.524925\pi$$
$$48$$ 3.40284e9i 0.278224i
$$49$$ −1.36764e10 2.13026e9i −0.988085 0.153906i
$$50$$ −9.17013e9 −0.586888
$$51$$ −1.30797e10 + 2.26548e10i −0.743324 + 1.28747i
$$52$$ 1.25900e10 7.26886e9i 0.636805 0.367660i
$$53$$ −1.09179e8 1.89104e8i −0.00492590 0.00853191i 0.863552 0.504260i $$-0.168235\pi$$
−0.868478 + 0.495728i $$0.834901\pi$$
$$54$$ −1.28671e10 7.42884e9i −0.518942 0.299612i
$$55$$ 2.75432e10i 0.995034i
$$56$$ −8.41602e8 + 1.08714e10i −0.0272884 + 0.352499i
$$57$$ −2.17624e10 −0.634538
$$58$$ 1.70338e10 2.95033e10i 0.447448 0.775003i
$$59$$ 5.45224e10 3.14785e10i 1.29260 0.746280i 0.313482 0.949594i $$-0.398505\pi$$
0.979114 + 0.203314i $$0.0651712\pi$$
$$60$$ 1.75600e10 + 3.04149e10i 0.376373 + 0.651897i
$$61$$ 4.19753e10 + 2.42344e10i 0.814732 + 0.470386i 0.848596 0.529041i $$-0.177448\pi$$
−0.0338645 + 0.999426i $$0.510781\pi$$
$$62$$ 4.94605e10i 0.870780i
$$63$$ 1.23019e10 + 8.43172e9i 0.196757 + 0.134857i
$$64$$ 8.58993e9 0.125000
$$65$$ 7.50205e10 1.29939e11i 0.994718 1.72290i
$$66$$ −4.14331e10 + 2.39214e10i −0.501284 + 0.289417i
$$67$$ −5.49220e10 9.51277e10i −0.607152 1.05162i −0.991707 0.128516i $$-0.958979\pi$$
0.384556 0.923102i $$-0.374355\pi$$
$$68$$ 5.71884e10 + 3.30177e10i 0.578435 + 0.333959i
$$69$$ 1.00993e11i 0.935826i
$$70$$ 4.85786e10 + 1.01513e11i 0.412911 + 0.862843i
$$71$$ −7.43754e10 −0.580603 −0.290302 0.956935i $$-0.593756\pi$$
−0.290302 + 0.956935i $$0.593756\pi$$
$$72$$ 5.87455e9 1.01750e10i 0.0421677 0.0730366i
$$73$$ −2.26320e11 + 1.30666e11i −1.49550 + 0.863427i −0.999987 0.00517437i $$-0.998353\pi$$
−0.495512 + 0.868601i $$0.665020\pi$$
$$74$$ −8.76065e10 1.51739e11i −0.533514 0.924074i
$$75$$ 1.42372e11 + 8.21982e10i 0.799937 + 0.461844i
$$76$$ 5.49357e10i 0.285084i
$$77$$ −1.38287e11 + 6.61769e10i −0.663494 + 0.317513i
$$78$$ −2.60623e11 −1.15730
$$79$$ −1.20639e11 + 2.08953e11i −0.496279 + 0.859580i −0.999991 0.00429190i $$-0.998634\pi$$
0.503712 + 0.863871i $$0.331967\pi$$
$$80$$ 7.67776e10 4.43276e10i 0.292883 0.169096i
$$81$$ 1.66865e11 + 2.89018e11i 0.590818 + 1.02333i
$$82$$ 1.00253e11 + 5.78810e10i 0.329772 + 0.190394i
$$83$$ 2.09983e11i 0.642268i −0.947034 0.321134i $$-0.895936\pi$$
0.947034 0.321134i $$-0.104064\pi$$
$$84$$ 1.10514e11 1.61241e11i 0.314588 0.458986i
$$85$$ 6.81540e11 1.80708
$$86$$ 9.86855e10 1.70928e11i 0.243929 0.422497i
$$87$$ −5.28918e11 + 3.05371e11i −1.21975 + 0.704226i
$$88$$ 6.03859e10 + 1.04591e11i 0.130029 + 0.225216i
$$89$$ 1.79050e10 + 1.03374e10i 0.0360275 + 0.0208005i 0.517906 0.855438i $$-0.326712\pi$$
−0.481878 + 0.876238i $$0.660045\pi$$
$$90$$ 1.21260e11i 0.228173i
$$91$$ −8.32640e11 6.44582e10i −1.46625 0.113509i
$$92$$ −2.54940e11 −0.420447
$$93$$ 4.43349e11 7.67903e11i 0.685248 1.18689i
$$94$$ −3.63926e11 + 2.10113e11i −0.527528 + 0.304568i
$$95$$ 2.83491e11 + 4.91020e11i 0.385653 + 0.667971i
$$96$$ −1.33364e11 7.69975e10i −0.170377 0.0983670i
$$97$$ 4.74911e11i 0.570140i 0.958507 + 0.285070i $$0.0920169\pi$$
−0.958507 + 0.285070i $$0.907983\pi$$
$$98$$ 3.92950e11 4.87800e11i 0.443589 0.550662i
$$99$$ 1.65189e11 0.175456
$$100$$ 2.07496e11 3.59394e11i 0.207496 0.359394i
$$101$$ 9.97000e11 5.75618e11i 0.939219 0.542259i 0.0495038 0.998774i $$-0.484236\pi$$
0.889715 + 0.456515i $$0.150903\pi$$
$$102$$ −5.91921e11 1.02524e12i −0.525609 0.910382i
$$103$$ 8.21363e11 + 4.74214e11i 0.687878 + 0.397147i 0.802817 0.596226i $$-0.203334\pi$$
−0.114938 + 0.993373i $$0.536667\pi$$
$$104$$ 6.57902e11i 0.519950i
$$105$$ 1.55718e11 2.01148e12i 0.116199 1.50100i
$$106$$ 9.88179e9 0.00696628
$$107$$ 1.66978e11 2.89214e11i 0.111264 0.192715i −0.805016 0.593253i $$-0.797843\pi$$
0.916280 + 0.400538i $$0.131177\pi$$
$$108$$ 5.82300e11 3.36191e11i 0.366948 0.211857i
$$109$$ 3.67785e11 + 6.37022e11i 0.219298 + 0.379835i 0.954594 0.297911i $$-0.0962899\pi$$
−0.735295 + 0.677747i $$0.762957\pi$$
$$110$$ 1.07947e12 + 6.23231e11i 0.609332 + 0.351798i
$$111$$ 3.14111e12i 1.67937i
$$112$$ −4.07027e11 2.78976e11i −0.206213 0.141338i
$$113$$ −2.66369e12 −1.27942 −0.639709 0.768617i $$-0.720945\pi$$
−0.639709 + 0.768617i $$0.720945\pi$$
$$114$$ 4.92427e11 8.52908e11i 0.224343 0.388574i
$$115$$ −2.27868e12 + 1.31559e12i −0.985134 + 0.568768i
$$116$$ 7.70860e11 + 1.33517e12i 0.316394 + 0.548010i
$$117$$ 7.79303e11 + 4.49931e11i 0.303803 + 0.175400i
$$118$$ 2.84911e12i 1.05540i
$$119$$ −1.63751e12 3.42183e12i −0.576635 1.20497i
$$120$$ −1.58935e12 −0.532272
$$121$$ 7.20208e11 1.24744e12i 0.229481 0.397472i
$$122$$ −1.89958e12 + 1.09673e12i −0.576102 + 0.332613i
$$123$$ −1.03766e12 1.79727e12i −0.299656 0.519019i
$$124$$ −1.93845e12 1.11916e12i −0.533242 0.307867i
$$125$$ 8.77343e11i 0.229990i
$$126$$ −6.08815e11 + 2.91347e11i −0.152147 + 0.0728094i
$$127$$ −2.69168e11 −0.0641506 −0.0320753 0.999485i $$-0.510212\pi$$
−0.0320753 + 0.999485i $$0.510212\pi$$
$$128$$ −1.94368e11 + 3.36655e11i −0.0441942 + 0.0765466i
$$129$$ −3.06430e12 + 1.76917e12i −0.664956 + 0.383912i
$$130$$ 3.39504e12 + 5.88038e12i 0.703372 + 1.21828i
$$131$$ 4.16356e12 + 2.40383e12i 0.823829 + 0.475638i 0.851735 0.523972i $$-0.175551\pi$$
−0.0279059 + 0.999611i $$0.508884\pi$$
$$132$$ 2.16512e12i 0.409297i
$$133$$ 1.78415e12 2.60308e12i 0.322345 0.470304i
$$134$$ 4.97097e12 0.858642
$$135$$ 3.46976e12 6.00981e12i 0.573188 0.992791i
$$136$$ −2.58805e12 + 1.49421e12i −0.409015 + 0.236145i
$$137$$ −5.08937e12 8.81505e12i −0.769734 1.33322i −0.937707 0.347427i $$-0.887056\pi$$
0.167973 0.985792i $$-0.446278\pi$$
$$138$$ 3.95809e12 + 2.28520e12i 0.573074 + 0.330865i
$$139$$ 3.81539e11i 0.0528994i −0.999650 0.0264497i $$-0.991580\pi$$
0.999650 0.0264497i $$-0.00842018\pi$$
$$140$$ −5.07767e12 3.93084e11i −0.674367 0.0522057i
$$141$$ 7.53354e12 0.958703
$$142$$ 1.68292e12 2.91491e12i 0.205274 0.355545i
$$143$$ −8.01064e12 + 4.62495e12i −0.936809 + 0.540867i
$$144$$ 2.65852e11 + 4.60469e11i 0.0298170 + 0.0516446i
$$145$$ 1.37800e13 + 7.95590e12i 1.48266 + 0.856015i
$$146$$ 1.18265e13i 1.22107i
$$147$$ −1.04733e13 + 4.05109e12i −1.03795 + 0.401484i
$$148$$ 7.92924e12 0.754503
$$149$$ 1.01352e13 1.75546e13i 0.926218 1.60426i 0.136627 0.990623i $$-0.456374\pi$$
0.789591 0.613634i $$-0.210293\pi$$
$$150$$ −6.44300e12 + 3.71987e12i −0.565641 + 0.326573i
$$151$$ 9.98191e12 + 1.72892e13i 0.842077 + 1.45852i 0.888136 + 0.459582i $$0.152001\pi$$
−0.0460585 + 0.998939i $$0.514666\pi$$
$$152$$ −2.15303e12 1.24305e12i −0.174578 0.100793i
$$153$$ 4.08749e12i 0.318646i
$$154$$ 5.35485e11 6.91713e12i 0.0401442 0.518563i
$$155$$ −2.31014e13 −1.66589
$$156$$ 5.89723e12 1.02143e13i 0.409167 0.708698i
$$157$$ 6.85383e12 3.95706e12i 0.457652 0.264226i −0.253404 0.967360i $$-0.581550\pi$$
0.711057 + 0.703135i $$0.248217\pi$$
$$158$$ −5.45950e12 9.45613e12i −0.350922 0.607815i
$$159$$ −1.53420e11 8.85774e10i −0.00949512 0.00548201i
$$160$$ 4.01207e12i 0.239138i
$$161$$ 1.20801e13 + 8.27970e12i 0.693611 + 0.475400i
$$162$$ −1.51029e13 −0.835543
$$163$$ −1.22758e13 + 2.12623e13i −0.654521 + 1.13366i 0.327493 + 0.944854i $$0.393796\pi$$
−0.982014 + 0.188810i $$0.939537\pi$$
$$164$$ −4.53693e12 + 2.61940e12i −0.233184 + 0.134629i
$$165$$ −1.11729e13 1.93520e13i −0.553685 0.959010i
$$166$$ 8.22964e12 + 4.75138e12i 0.393307 + 0.227076i
$$167$$ 2.03607e13i 0.938629i 0.883031 + 0.469315i $$0.155499\pi$$
−0.883031 + 0.469315i $$0.844501\pi$$
$$168$$ 3.81867e12 + 7.97972e12i 0.169847 + 0.354921i
$$169$$ −2.70905e13 −1.16278
$$170$$ −1.54215e13 + 2.67108e13i −0.638899 + 1.10661i
$$171$$ −2.94486e12 + 1.70022e12i −0.117785 + 0.0680030i
$$172$$ 4.46600e12 + 7.73533e12i 0.172484 + 0.298750i
$$173$$ 1.88719e13 + 1.08957e13i 0.703945 + 0.406423i 0.808815 0.588063i $$-0.200109\pi$$
−0.104870 + 0.994486i $$0.533443\pi$$
$$174$$ 2.76390e13i 0.995926i
$$175$$ −2.15041e13 + 1.02907e13i −0.748675 + 0.358276i
$$176$$ −5.46550e12 −0.183888
$$177$$ 2.55385e13 4.42340e13i 0.830532 1.43852i
$$178$$ −8.10287e11 + 4.67819e11i −0.0254753 + 0.0147081i
$$179$$ −5.29449e12 9.17033e12i −0.160956 0.278783i 0.774256 0.632872i $$-0.218124\pi$$
−0.935212 + 0.354089i $$0.884791\pi$$
$$180$$ 4.75241e12 + 2.74381e12i 0.139727 + 0.0806712i
$$181$$ 5.35655e13i 1.52340i 0.647930 + 0.761700i $$0.275635\pi$$
−0.647930 + 0.761700i $$0.724365\pi$$
$$182$$ 2.13667e13 3.11742e13i 0.587908 0.857761i
$$183$$ 3.93229e13 1.04698
$$184$$ 5.76863e12 9.99156e12i 0.148650 0.257470i
$$185$$ 7.08722e13 4.09181e13i 1.76785 1.02067i
$$186$$ 2.00637e13 + 3.47513e13i 0.484544 + 0.839255i
$$187$$ −3.63872e13 2.10081e13i −0.850939 0.491290i
$$188$$ 1.90172e13i 0.430725i
$$189$$ −3.85103e13 2.98125e12i −0.844901 0.0654075i
$$190$$ −2.56586e13 −0.545396
$$191$$ −3.11402e13 + 5.39365e13i −0.641390 + 1.11092i 0.343733 + 0.939067i $$0.388308\pi$$
−0.985123 + 0.171852i $$0.945025\pi$$
$$192$$ 6.03535e12 3.48451e12i 0.120474 0.0695560i
$$193$$ 1.97810e13 + 3.42617e13i 0.382740 + 0.662926i 0.991453 0.130465i $$-0.0416471\pi$$
−0.608713 + 0.793391i $$0.708314\pi$$
$$194$$ −1.86126e13 1.07460e13i −0.349138 0.201575i
$$195$$ 1.21728e14i 2.21403i
$$196$$ 1.02263e13 + 2.64381e13i 0.180378 + 0.466330i
$$197$$ 2.98938e12 0.0511427 0.0255713 0.999673i $$-0.491860\pi$$
0.0255713 + 0.999673i $$0.491860\pi$$
$$198$$ −3.73779e12 + 6.47404e12i −0.0620332 + 0.107445i
$$199$$ 5.16217e13 2.98038e13i 0.831216 0.479903i −0.0230526 0.999734i $$-0.507339\pi$$
0.854269 + 0.519831i $$0.174005\pi$$
$$200$$ 9.39022e12 + 1.62643e13i 0.146722 + 0.254130i
$$201$$ −7.71771e13 4.45582e13i −1.17034 0.675697i
$$202$$ 5.20990e13i 0.766869i
$$203$$ 6.83577e12 8.83011e13i 0.0976813 1.26180i
$$204$$ 5.35746e13 0.743324
$$205$$ −2.70343e13 + 4.68248e13i −0.364244 + 0.630889i
$$206$$ −3.71706e13 + 2.14605e13i −0.486403 + 0.280825i
$$207$$ −7.89019e12 1.36662e13i −0.100292 0.173711i
$$208$$ −2.57844e13 1.48866e13i −0.318403 0.183830i
$$209$$ 3.49539e13i 0.419389i
$$210$$ 7.53103e13 + 5.16175e13i 0.878089 + 0.601841i
$$211$$ 1.29666e14 1.46937 0.734684 0.678409i $$-0.237330\pi$$
0.734684 + 0.678409i $$0.237330\pi$$
$$212$$ −2.23599e11 + 3.87286e11i −0.00246295 + 0.00426595i
$$213$$ −5.22567e13 + 3.01704e13i −0.559583 + 0.323075i
$$214$$ 7.55654e12 + 1.30883e13i 0.0786756 + 0.136270i
$$215$$ 7.98349e13 + 4.60927e13i 0.808281 + 0.466661i
$$216$$ 3.04285e13i 0.299612i
$$217$$ 5.55047e13 + 1.15986e14i 0.531583 + 1.11083i
$$218$$ −3.32881e13 −0.310134
$$219$$ −1.06009e14 + 1.83614e14i −0.960904 + 1.66433i
$$220$$ −4.88512e13 + 2.82042e13i −0.430863 + 0.248759i
$$221$$ −1.14441e14 1.98218e14i −0.982268 1.70134i
$$222$$ −1.23106e14 7.10753e13i −1.02840 0.593746i
$$223$$ 1.05020e14i 0.853972i 0.904258 + 0.426986i $$0.140425\pi$$
−0.904258 + 0.426986i $$0.859575\pi$$
$$224$$ 2.01435e13 9.63964e12i 0.159459 0.0763084i
$$225$$ 2.56874e13 0.197982
$$226$$ 6.02724e13 1.04395e14i 0.452343 0.783481i
$$227$$ 6.69859e13 3.86743e13i 0.489585 0.282662i −0.234817 0.972040i $$-0.575449\pi$$
0.724402 + 0.689378i $$0.242116\pi$$
$$228$$ 2.22847e13 + 3.85982e13i 0.158635 + 0.274763i
$$229$$ −1.53002e14 8.83360e13i −1.06093 0.612526i −0.135238 0.990813i $$-0.543180\pi$$
−0.925688 + 0.378287i $$0.876513\pi$$
$$230$$ 1.19074e14i 0.804359i
$$231$$ −7.03168e13 + 1.02593e14i −0.462793 + 0.675218i
$$232$$ −6.97703e13 −0.447448
$$233$$ −1.16414e14 + 2.01635e14i −0.727562 + 1.26017i 0.230349 + 0.973108i $$0.426013\pi$$
−0.957911 + 0.287066i $$0.907320\pi$$
$$234$$ −3.52672e13 + 2.03616e13i −0.214821 + 0.124027i
$$235$$ −9.81366e13 1.69977e14i −0.582671 1.00922i
$$236$$ −1.11662e14 6.44680e13i −0.646298 0.373140i
$$237$$ 1.95749e14i 1.10461i
$$238$$ 1.71160e14 + 1.32503e13i 0.941762 + 0.0729058i
$$239$$ 1.20020e14 0.643971 0.321986 0.946745i $$-0.395650\pi$$
0.321986 + 0.946745i $$0.395650\pi$$
$$240$$ 3.59630e13 6.22897e13i 0.188186 0.325948i
$$241$$ 4.44336e13 2.56537e13i 0.226782 0.130933i −0.382305 0.924036i $$-0.624869\pi$$
0.609087 + 0.793104i $$0.291536\pi$$
$$242$$ 3.25929e13 + 5.64526e13i 0.162267 + 0.281055i
$$243$$ 8.33779e13 + 4.81383e13i 0.404961 + 0.233804i
$$244$$ 9.92643e13i 0.470386i
$$245$$ 2.27835e14 + 1.83534e14i 1.05347 + 0.848632i
$$246$$ 9.39179e13 0.423777
$$247$$ 9.52053e13 1.64900e14i 0.419256 0.726173i
$$248$$ 8.77242e13 5.06476e13i 0.377059 0.217695i
$$249$$ −8.51799e13 1.47536e14i −0.357389 0.619016i
$$250$$ −3.43847e13 1.98520e13i −0.140840 0.0813138i
$$251$$ 1.04293e14i 0.417073i −0.978015 0.208537i $$-0.933130\pi$$
0.978015 0.208537i $$-0.0668700\pi$$
$$252$$ 2.35750e12 3.04530e13i 0.00920552 0.118912i
$$253$$ 1.62210e14 0.618522
$$254$$ 6.09057e12 1.05492e13i 0.0226807 0.0392841i
$$255$$ 4.78855e14 2.76467e14i 1.74166 1.00555i
$$256$$ −8.79609e12 1.52353e13i −0.0312500 0.0541266i
$$257$$ 2.30306e14 + 1.32967e14i 0.799295 + 0.461473i 0.843225 0.537561i $$-0.180654\pi$$
−0.0439295 + 0.999035i $$0.513988\pi$$
$$258$$ 1.60127e14i 0.542934i
$$259$$ −3.75721e14 2.57518e14i −1.24470 0.853119i
$$260$$ −3.07284e14 −0.994718
$$261$$ −4.77150e13 + 8.26449e13i −0.150943 + 0.261440i
$$262$$ −1.88421e14 + 1.08785e14i −0.582535 + 0.336327i
$$263$$ 1.98352e14 + 3.43556e14i 0.599380 + 1.03816i 0.992913 + 0.118846i $$0.0379195\pi$$
−0.393533 + 0.919311i $$0.628747\pi$$
$$264$$ 8.48551e13 + 4.89911e13i 0.250642 + 0.144708i
$$265$$ 4.61546e12i 0.0133272i
$$266$$ 6.16489e13 + 1.28825e14i 0.174035 + 0.363673i
$$267$$ 1.67735e13 0.0462975
$$268$$ −1.12480e14 + 1.94821e14i −0.303576 + 0.525809i
$$269$$ −5.98003e13 + 3.45257e13i −0.157830 + 0.0911232i −0.576835 0.816861i $$-0.695712\pi$$
0.419005 + 0.907984i $$0.362379\pi$$
$$270$$ 1.57024e14 + 2.71973e14i 0.405305 + 0.702010i
$$271$$ −6.55851e14 3.78656e14i −1.65573 0.955936i −0.974652 0.223726i $$-0.928178\pi$$
−0.681078 0.732211i $$-0.738489\pi$$
$$272$$ 1.35241e14i 0.333959i
$$273$$ −6.11166e14 + 2.92472e14i −1.47633 + 0.706493i
$$274$$ 4.60637e14 1.08857
$$275$$ −1.32023e14 + 2.28671e14i −0.305249 + 0.528707i
$$276$$ −1.79123e14 + 1.03416e14i −0.405225 + 0.233957i
$$277$$ −1.16361e14 2.01543e14i −0.257590 0.446159i 0.708006 0.706207i $$-0.249595\pi$$
−0.965596 + 0.260047i $$0.916262\pi$$
$$278$$ 1.49532e13 + 8.63325e12i 0.0323941 + 0.0187028i
$$279$$ 1.38549e14i 0.293750i
$$280$$ 1.30300e14 1.90109e14i 0.270394 0.394506i
$$281$$ −7.05866e14 −1.43379 −0.716893 0.697183i $$-0.754436\pi$$
−0.716893 + 0.697183i $$0.754436\pi$$
$$282$$ −1.70464e14 + 2.95253e14i −0.338953 + 0.587083i
$$283$$ 6.72043e14 3.88004e14i 1.30821 0.755297i 0.326414 0.945227i $$-0.394159\pi$$
0.981798 + 0.189930i $$0.0608262\pi$$
$$284$$ 7.61604e13 + 1.31914e14i 0.145151 + 0.251409i
$$285$$ 3.98365e14 + 2.29996e14i 0.743382 + 0.429192i
$$286$$ 4.18602e14i 0.764901i
$$287$$ 3.00049e14 + 2.32281e13i 0.536909 + 0.0415644i
$$288$$ −2.40622e13 −0.0421677
$$289$$ 2.28522e14 3.95813e14i 0.392231 0.679364i
$$290$$ −6.23613e14 + 3.60043e14i −1.04840 + 0.605294i
$$291$$ 1.92648e14 + 3.33676e14i 0.317253 + 0.549499i
$$292$$ 4.63504e14 + 2.67604e14i 0.747749 + 0.431713i
$$293$$ 6.68824e14i 1.05708i 0.848910 + 0.528538i $$0.177260\pi$$
−0.848910 + 0.528538i $$0.822740\pi$$
$$294$$ 7.82131e13 5.02132e14i 0.121114 0.777560i
$$295$$ −1.33072e15 −2.01909
$$296$$ −1.79418e14 + 3.10761e14i −0.266757 + 0.462037i
$$297$$ −3.70499e14 + 2.13908e14i −0.539819 + 0.311665i
$$298$$ 4.58665e14 + 7.94431e14i 0.654935 + 1.13438i
$$299$$ 7.65253e14 + 4.41819e14i 1.07097 + 0.618325i
$$300$$ 3.36684e14i 0.461844i
$$301$$ 3.96032e13 5.11575e14i 0.0532515 0.687876i
$$302$$ −9.03459e14 −1.19088
$$303$$ 4.67000e14 8.08867e14i 0.603477 1.04525i
$$304$$ 9.74351e13 5.62542e13i 0.123445 0.0712711i
$$305$$ −5.12244e14 8.87233e14i −0.636323 1.10214i
$$306$$ −1.60196e14 9.24894e13i −0.195130 0.112658i
$$307$$ 7.37934e14i 0.881429i 0.897647 + 0.440714i $$0.145275\pi$$
−0.897647 + 0.440714i $$0.854725\pi$$
$$308$$ 2.58978e14 + 1.77503e14i 0.303361 + 0.207923i
$$309$$ 7.69460e14 0.883965
$$310$$ 5.22724e14 9.05385e14i 0.588983 1.02015i
$$311$$ 4.21657e14 2.43444e14i 0.466012 0.269052i −0.248557 0.968617i $$-0.579956\pi$$
0.714569 + 0.699565i $$0.246623\pi$$
$$312$$ 2.66878e14 + 4.62247e14i 0.289325 + 0.501125i
$$313$$ 2.88228e14 + 1.66408e14i 0.306528 + 0.176974i 0.645372 0.763869i $$-0.276703\pi$$
−0.338844 + 0.940843i $$0.610036\pi$$
$$314$$ 3.58152e14i 0.373671i
$$315$$ −1.36078e14 2.84357e14i −0.139292 0.291073i
$$316$$ 4.94138e14 0.496279
$$317$$ 7.44042e14 1.28872e15i 0.733233 1.27000i −0.222261 0.974987i $$-0.571344\pi$$
0.955494 0.295010i $$-0.0953229\pi$$
$$318$$ 6.94302e12 4.00855e12i 0.00671407 0.00387637i
$$319$$ −4.90474e14 8.49526e14i −0.465449 0.806181i
$$320$$ −1.57240e14 9.07828e13i −0.146442 0.0845481i
$$321$$ 2.70938e14i 0.247651i
$$322$$ −5.97839e14 + 2.86094e14i −0.536350 + 0.256669i
$$323$$ 8.64912e14 0.761653
$$324$$ 3.41739e14 5.91909e14i 0.295409 0.511664i
$$325$$ −1.24568e15 + 7.19195e14i −1.05708 + 0.610305i
$$326$$ −5.55538e14 9.62221e14i −0.462816 0.801621i
$$327$$ 5.16817e14 + 2.98384e14i 0.422717 + 0.244056i
$$328$$ 2.37081e14i 0.190394i
$$329$$ −6.17623e14 + 9.01115e14i −0.487021 + 0.710567i
$$330$$ 1.01126e15 0.783028
$$331$$ −1.12300e14 + 1.94510e14i −0.0853912 + 0.147902i −0.905558 0.424223i $$-0.860547\pi$$
0.820167 + 0.572125i $$0.193881\pi$$
$$332$$ −3.72431e14 + 2.15023e14i −0.278110 + 0.160567i
$$333$$ 2.45404e14 + 4.25052e14i 0.179977 + 0.311728i
$$334$$ −7.97974e14 4.60710e14i −0.574791 0.331856i
$$335$$ 2.32177e15i 1.64267i
$$336$$ −3.99147e14 3.08997e13i −0.277394 0.0214743i
$$337$$ 1.02994e15 0.703124 0.351562 0.936165i $$-0.385651\pi$$
0.351562 + 0.936165i $$0.385651\pi$$
$$338$$ 6.12989e14 1.06173e15i 0.411105 0.712054i
$$339$$ −1.87153e15 + 1.08053e15i −1.23310 + 0.711930i
$$340$$ −6.97896e14 1.20879e15i −0.451770 0.782489i
$$341$$ 1.23337e15 + 7.12089e14i 0.784456 + 0.452906i
$$342$$ 1.53886e14i 0.0961707i
$$343$$ 3.74064e14 1.58487e15i 0.229711 0.973259i
$$344$$ −4.04216e14 −0.243929
$$345$$ −1.06734e15 + 1.84869e15i −0.632979 + 1.09635i
$$346$$ −8.54044e14 + 4.93083e14i −0.497764 + 0.287384i
$$347$$ 4.36316e14 + 7.55722e14i 0.249934 + 0.432898i 0.963507 0.267683i $$-0.0862579\pi$$
−0.713574 + 0.700580i $$0.752925\pi$$
$$348$$ 1.08322e15 + 6.25399e14i 0.609877 + 0.352113i
$$349$$ 2.50531e14i 0.138647i 0.997594 + 0.0693233i $$0.0220840\pi$$
−0.997594 + 0.0693233i $$0.977916\pi$$
$$350$$ 8.32698e13 1.07564e15i 0.0452980 0.585138i
$$351$$ −2.33052e15 −1.24626
$$352$$ 1.23670e14 2.14203e14i 0.0650144 0.112608i
$$353$$ −2.45457e14 + 1.41714e14i −0.126861 + 0.0732430i −0.562087 0.827078i $$-0.690002\pi$$
0.435227 + 0.900321i $$0.356668\pi$$
$$354$$ 1.15574e15 + 2.00180e15i 0.587275 + 1.01719i
$$355$$ 1.36146e15 + 7.86038e14i 0.680196 + 0.392711i
$$356$$ 4.23422e13i 0.0208005i
$$357$$ −2.53859e15 1.73995e15i −1.22626 0.840478i
$$358$$ 4.79203e14 0.227626
$$359$$ −2.96270e14 + 5.13154e14i −0.138395 + 0.239707i −0.926889 0.375335i $$-0.877528\pi$$
0.788494 + 0.615042i $$0.210861\pi$$
$$360$$ −2.15070e14 + 1.24171e14i −0.0988016 + 0.0570431i
$$361$$ −7.46892e14 1.29365e15i −0.337454 0.584487i
$$362$$ −2.09933e15 1.21205e15i −0.932888 0.538603i
$$363$$ 1.16861e15i 0.510776i
$$364$$ 7.38299e14 + 1.54279e15i 0.317412 + 0.663283i
$$365$$ 5.52378e15 2.33603
$$366$$ −8.89775e14 + 1.54113e15i −0.370163 + 0.641142i
$$367$$ −4.05423e14 + 2.34071e14i −0.165925 + 0.0957969i −0.580663 0.814144i $$-0.697207\pi$$
0.414738 + 0.909941i $$0.363873\pi$$
$$368$$ 2.61059e14 + 4.52167e14i 0.105112 + 0.182059i
$$369$$ −2.80829e14 1.62137e14i −0.111246 0.0642278i
$$370$$ 3.70348e15i 1.44344i
$$371$$ 2.31730e13 1.10894e13i 0.00888666 0.00425268i
$$372$$ −1.81596e15 −0.685248
$$373$$ 1.17094e15 2.02812e15i 0.434791 0.753081i −0.562487 0.826806i $$-0.690155\pi$$
0.997279 + 0.0737253i $$0.0234888\pi$$
$$374$$ 1.64669e15 9.50720e14i 0.601705 0.347394i
$$375$$ 3.55895e14 + 6.16428e14i 0.127978 + 0.221664i
$$376$$ 7.45320e14 + 4.30310e14i 0.263764 + 0.152284i
$$377$$ 5.34370e15i 1.86120i
$$378$$ 9.88229e14 1.44183e15i 0.338772 0.494269i
$$379$$ −4.89878e15 −1.65292 −0.826461 0.562994i $$-0.809649\pi$$
−0.826461 + 0.562994i $$0.809649\pi$$
$$380$$ 5.80589e14 1.00561e15i 0.192827 0.333986i
$$381$$ −1.89119e14 + 1.09188e14i −0.0618281 + 0.0356965i
$$382$$ −1.40925e15 2.44089e15i −0.453531 0.785539i
$$383$$ −4.07029e15 2.34998e15i −1.28953 0.744513i −0.310963 0.950422i $$-0.600652\pi$$
−0.978571 + 0.205909i $$0.933985\pi$$
$$384$$ 3.15382e14i 0.0983670i
$$385$$ 3.23076e15 + 2.50107e14i 0.992066 + 0.0768001i
$$386$$ −1.79037e15 −0.541276
$$387$$ −2.76438e14 + 4.78805e14i −0.0822872 + 0.142526i
$$388$$ 8.42311e14 4.86309e14i 0.246878 0.142535i
$$389$$ 1.04054e15 + 1.80226e15i 0.300303 + 0.520140i 0.976205 0.216852i $$-0.0695788\pi$$
−0.675901 + 0.736992i $$0.736246\pi$$
$$390$$ 4.77076e15 + 2.75440e15i 1.35581 + 0.782779i
$$391$$ 4.01379e15i 1.12330i
$$392$$ −1.26755e15 1.97437e14i −0.349341 0.0544141i
$$393$$ 3.90046e15 1.05867
$$394$$ −6.76419e13 + 1.17159e14i −0.0180817 + 0.0313184i
$$395$$ 4.41665e15 2.54995e15i 1.16281 0.671350i
$$396$$ −1.69153e14 2.92982e14i −0.0438641 0.0759748i
$$397$$ 5.98851e14 + 3.45747e14i 0.152959 + 0.0883110i 0.574526 0.818486i $$-0.305186\pi$$
−0.421567 + 0.906797i $$0.638520\pi$$
$$398$$ 2.69753e15i 0.678685i
$$399$$ 1.97614e14 2.55269e15i 0.0489758 0.632645i
$$400$$ −8.49905e14 −0.207496
$$401$$ 2.13958e15 3.70586e15i 0.514592 0.891299i −0.485265 0.874367i $$-0.661277\pi$$
0.999857 0.0169316i $$-0.00538977\pi$$
$$402$$ 3.49264e15 2.01648e15i 0.827556 0.477790i
$$403$$ 3.87909e15 + 6.71878e15i 0.905524 + 1.56841i
$$404$$ −2.04186e15 1.17887e15i −0.469610 0.271129i
$$405$$ 7.05404e15i 1.59848i
$$406$$ 3.30601e15 + 2.26593e15i 0.738155 + 0.505931i
$$407$$ −5.04512e15 −1.10996
$$408$$ −1.21226e15 + 2.09969e15i −0.262805 + 0.455191i
$$409$$ −5.93554e13 + 3.42689e13i −0.0126800 + 0.00732082i −0.506327 0.862342i $$-0.668997\pi$$
0.493647 + 0.869663i $$0.335664\pi$$
$$410$$ −1.22343e15 2.11905e15i −0.257559 0.446106i
$$411$$ −7.15166e15 4.12901e15i −1.48373 0.856633i
$$412$$ 1.94238e15i 0.397147i
$$413$$ 3.19727e15 + 6.68121e15i 0.644287 + 1.34634i
$$414$$ 7.14139e14 0.141834
$$415$$ −2.21921e15 + 3.84379e15i −0.434421 + 0.752439i
$$416$$ 1.16687e15 6.73692e14i 0.225145 0.129987i
$$417$$ −1.54772e14 2.68072e14i −0.0294357 0.0509842i
$$418$$ 1.36991e15 + 7.90916e14i 0.256823 + 0.148277i
$$419$$ 2.03797e15i 0.376628i 0.982109 + 0.188314i $$0.0603023\pi$$
−0.982109 + 0.188314i $$0.939698\pi$$
$$420$$ −3.72706e15 + 1.78358e15i −0.679002 + 0.324934i
$$421$$ −7.75234e15 −1.39232 −0.696162 0.717885i $$-0.745110\pi$$
−0.696162 + 0.717885i $$0.745110\pi$$
$$422$$ −2.93400e15 + 5.08184e15i −0.519500 + 0.899801i
$$423$$ 1.01943e15 5.88568e14i 0.177957 0.102744i
$$424$$ −1.01190e13 1.75265e13i −0.00174157 0.00301649i
$$425$$ −5.65833e15 3.26684e15i −0.960185 0.554363i
$$426$$ 2.73071e15i 0.456897i
$$427$$ −3.22381e15 + 4.70356e15i −0.531866 + 0.775996i
$$428$$ −6.83940e14 −0.111264
$$429$$ −3.75222e15 + 6.49904e15i −0.601928 + 1.04257i
$$430$$ −3.61292e15 + 2.08592e15i −0.571541 + 0.329979i
$$431$$ −3.20180e13 5.54569e13i −0.00499495 0.00865151i 0.863517 0.504320i $$-0.168257\pi$$
−0.868512 + 0.495668i $$0.834923\pi$$
$$432$$ −1.19255e15 6.88519e14i −0.183474 0.105929i
$$433$$ 3.93012e14i 0.0596319i 0.999555 + 0.0298159i $$0.00949211\pi$$
−0.999555 + 0.0298159i $$0.990508\pi$$
$$434$$ −5.80162e15 4.49129e14i −0.868183 0.0672098i
$$435$$ 1.29093e16 1.90531
$$436$$ 7.53223e14 1.30462e15i 0.109649 0.189918i
$$437$$ −2.89177e15 + 1.66956e15i −0.415217 + 0.239725i
$$438$$ −4.79744e15 8.30941e15i −0.679461 1.17686i
$$439$$ 6.94942e15 + 4.01225e15i 0.970871 + 0.560533i 0.899502 0.436917i $$-0.143930\pi$$
0.0713694 + 0.997450i $$0.477263\pi$$
$$440$$ 2.55276e15i 0.351798i
$$441$$ −1.10073e15 + 1.36643e15i −0.149641 + 0.185761i
$$442$$ 1.03581e16 1.38914
$$443$$ −7.81118e14 + 1.35294e15i −0.103346 + 0.179001i −0.913061 0.407822i $$-0.866288\pi$$
0.809715 + 0.586823i $$0.199622\pi$$
$$444$$ 5.57114e15 3.21650e15i 0.727187 0.419842i
$$445$$ −2.18503e14 3.78458e14i −0.0281382 0.0487369i
$$446$$ −4.11593e15 2.37633e15i −0.522949 0.301925i
$$447$$ 1.64453e16i 2.06157i
$$448$$ −7.80013e13 + 1.00758e15i −0.00964792 + 0.124627i
$$449$$ −2.29552e15 −0.280158 −0.140079 0.990140i $$-0.544736\pi$$
−0.140079 + 0.990140i $$0.544736\pi$$
$$450$$ −5.81240e14 + 1.00674e15i −0.0699971 + 0.121239i
$$451$$ 2.88670e15 1.66664e15i 0.343039 0.198053i
$$452$$ 2.72762e15 + 4.72437e15i 0.319855 + 0.554005i
$$453$$ 1.40267e16 + 8.09833e15i 1.62318 + 0.937144i
$$454$$ 3.50040e15i 0.399744i
$$455$$ 1.45604e16 + 9.97968e15i 1.64099 + 1.12473i
$$456$$ −2.01698e15 −0.224343
$$457$$ −3.78307e15 + 6.55247e15i −0.415286 + 0.719296i −0.995458 0.0951976i $$-0.969652\pi$$
0.580173 + 0.814493i $$0.302985\pi$$
$$458$$ 6.92410e15 3.99763e15i 0.750188 0.433121i
$$459$$ −5.29302e15 9.16777e15i −0.566014 0.980365i
$$460$$ 4.66673e15 + 2.69434e15i 0.492567 + 0.284384i
$$461$$ 3.83644e15i 0.399690i 0.979828 + 0.199845i $$0.0640439\pi$$
−0.979828 + 0.199845i $$0.935956\pi$$
$$462$$ −2.42970e15 5.07725e15i −0.249863 0.522127i
$$463$$ 4.62714e15 0.469707 0.234853 0.972031i $$-0.424539\pi$$
0.234853 + 0.972031i $$0.424539\pi$$
$$464$$ 1.57872e15 2.73443e15i 0.158197 0.274005i
$$465$$ −1.62312e16 + 9.37108e15i −1.60558 + 0.926983i
$$466$$ −5.26830e15 9.12496e15i −0.514464 0.891078i
$$467$$ −1.22742e16 7.08650e15i −1.18329 0.683173i −0.226517 0.974007i $$-0.572734\pi$$
−0.956773 + 0.290834i $$0.906067\pi$$
$$468$$ 1.84292e15i 0.175400i
$$469$$ 1.16570e16 5.57843e15i 1.09534 0.524173i
$$470$$ 8.88231e15 0.824022
$$471$$ 3.21037e15 5.56052e15i 0.294056 0.509319i
$$472$$ 5.05324e15 2.91749e15i 0.457001 0.263850i
$$473$$ −2.84157e15 4.92175e15i −0.253742 0.439494i
$$474$$ −7.67177e15 4.42930e15i −0.676434 0.390539i
$$475$$ 5.43545e15i 0.473232i
$$476$$ −4.39222e15 + 6.40827e15i −0.377609 + 0.550933i
$$477$$ −2.76809e13 −0.00235001
$$478$$ −2.71575e15 + 4.70381e15i −0.227678 + 0.394350i
$$479$$ 3.20508e15 1.85045e15i 0.265354 0.153202i −0.361421 0.932403i $$-0.617708\pi$$
0.626774 + 0.779201i $$0.284375\pi$$
$$480$$ 1.62750e15 + 2.81891e15i 0.133068 + 0.230480i
$$481$$ −2.38012e16 1.37416e16i −1.92189 1.10960i
$$482$$ 2.32191e15i 0.185167i
$$483$$ 1.18462e16 + 9.17069e14i 0.933035 + 0.0722302i
$$484$$ −2.94997e15 −0.229481
$$485$$ 5.01910e15 8.69334e15i 0.385634 0.667938i
$$486$$ −3.77325e15 + 2.17849e15i −0.286351 + 0.165325i
$$487$$ 8.57581e15 + 1.48537e16i 0.642838 + 1.11343i 0.984796 + 0.173713i $$0.0555764\pi$$
−0.341959 + 0.939715i $$0.611090\pi$$
$$488$$ 3.89035e15 + 2.24609e15i 0.288051 + 0.166306i
$$489$$ 1.99187e16i 1.45683i
$$490$$ −1.23483e16 + 4.77638e15i −0.892139 + 0.345082i
$$491$$ −1.18747e16 −0.847487 −0.423744 0.905782i $$-0.639284\pi$$
−0.423744 + 0.905782i $$0.639284\pi$$
$$492$$ −2.12512e15 + 3.68081e15i −0.149828 + 0.259510i
$$493$$ 2.10210e16 1.21365e16i 1.46410 0.845301i
$$494$$ 4.30850e15 + 7.46254e15i 0.296459 + 0.513482i
$$495$$ −3.02381e15 1.74580e15i −0.205553 0.118676i
$$496$$ 4.58410e15i 0.307867i
$$497$$ 6.75369e14 8.72409e15i 0.0448129 0.578871i
$$498$$ 7.70960e15 0.505424
$$499$$ 1.47725e15 2.55868e15i 0.0956868 0.165734i −0.814208 0.580573i $$-0.802829\pi$$
0.909895 + 0.414839i $$0.136162\pi$$
$$500$$ 1.55607e15 8.98399e14i 0.0995887 0.0574976i
$$501$$ 8.25933e15 + 1.43056e16i 0.522298 + 0.904647i
$$502$$ 4.08743e15 + 2.35988e15i 0.255404 + 0.147458i
$$503$$ 3.88753e15i 0.240030i −0.992772 0.120015i $$-0.961706\pi$$
0.992772 0.120015i $$-0.0382943\pi$$
$$504$$ 1.14017e15 + 7.81468e14i 0.0695640 + 0.0476791i
$$505$$ −2.43337e16 −1.46710
$$506$$ −3.67040e15 + 6.35732e15i −0.218681 + 0.378766i
$$507$$ −1.90340e16 + 1.09893e16i −1.12068 + 0.647026i
$$508$$ 2.75628e14 + 4.77402e14i 0.0160377 + 0.0277780i
$$509$$ −2.28834e15 1.32117e15i −0.131587 0.0759719i 0.432761 0.901509i $$-0.357539\pi$$
−0.564349 + 0.825537i $$0.690873\pi$$
$$510$$ 2.50229e16i 1.42206i
$$511$$ −1.32718e16 2.77334e16i −0.745423 1.55768i
$$512$$ 7.96131e14 0.0441942
$$513$$ 4.40333e15 7.62679e15i 0.241589 0.418444i
$$514$$ −1.04225e16 + 6.01742e15i −0.565187 + 0.326311i
$$515$$ −1.00235e16 1.73612e16i −0.537248 0.930541i
$$516$$ 6.27568e15 + 3.62327e15i 0.332478 + 0.191956i
$$517$$ 1.21001e16i 0.633642i
$$518$$ 1.85942e16 8.89820e15i 0.962496 0.460600i
$$519$$ 1.76794e16 0.904613
$$520$$ 6.95305e15 1.20430e16i 0.351686 0.609138i
$$521$$ −8.74947e15 + 5.05151e15i −0.437477 + 0.252578i −0.702527 0.711657i $$-0.747945\pi$$
0.265050 + 0.964235i $$0.414612\pi$$
$$522$$ −2.15934e15 3.74008e15i −0.106733 0.184866i
$$523$$ 2.00319e16 + 1.15654e16i 0.978843 + 0.565135i 0.901921 0.431902i $$-0.142157\pi$$
0.0769222 + 0.997037i $$0.475491\pi$$
$$524$$ 9.84610e15i 0.475638i
$$525$$ −1.09345e16 + 1.59535e16i −0.522208 + 0.761904i
$$526$$ −1.79528e16 −0.847651
$$527$$ −1.76202e16 + 3.05191e16i −0.822522 + 1.42465i
$$528$$ −3.84010e15 + 2.21708e15i −0.177231 + 0.102324i
$$529$$ 3.20938e15 + 5.55881e15i 0.146449 + 0.253657i
$$530$$ −1.80888e14 1.04436e14i −0.00816122 0.00471188i
$$531$$ 7.98093e15i 0.356030i
$$532$$ −6.44385e15 4.98846e14i −0.284234 0.0220038i
$$533$$ 1.81580e16 0.791962
$$534$$ −3.79542e14 + 6.57386e14i −0.0163686 + 0.0283513i
$$535$$ −6.11311e15 + 3.52941e15i −0.260699 + 0.150515i
$$536$$ −5.09027e15 8.81661e15i −0.214661 0.371803i
$$537$$ −7.43989e15 4.29542e15i −0.310257 0.179127i
$$538$$ 3.12491e15i 0.128868i
$$539$$ −6.50669e15 1.68217e16i −0.265355 0.686021i
$$540$$ −1.42122e16 −0.573188
$$541$$ 1.20154e16 2.08113e16i 0.479243 0.830073i −0.520474 0.853878i $$-0.674245\pi$$
0.999717 + 0.0238046i $$0.00757796\pi$$
$$542$$ 2.96804e16 1.71360e16i 1.17078 0.675949i
$$543$$ 2.17289e16 + 3.76355e16i 0.847692 + 1.46825i
$$544$$ 5.30033e15 + 3.06015e15i 0.204508 + 0.118072i
$$545$$ 1.55478e16i 0.593320i
$$546$$ 2.36660e15 3.05706e16i 0.0893242 1.15385i
$$547$$ 2.61473e16 0.976119 0.488060 0.872810i $$-0.337705\pi$$
0.488060 + 0.872810i $$0.337705\pi$$
$$548$$ −1.04230e16 + 1.80532e16i −0.384867 + 0.666609i
$$549$$ 5.32112e15 3.07215e15i 0.194343 0.112204i
$$550$$ −5.97470e15 1.03485e16i −0.215844 0.373853i
$$551$$ 1.74876e16 + 1.00965e16i 0.624916 + 0.360795i
$$552$$ 9.36019e15i 0.330865i
$$553$$ −2.34143e16 1.60481e16i −0.818711 0.561143i
$$554$$ 1.05318e16 0.364288
$$555$$ 3.31969e16 5.74987e16i 1.13590 1.96743i
$$556$$ −6.76706e14 + 3.90696e14i −0.0229061 + 0.0132248i
$$557$$ 9.52588e15 + 1.64993e16i 0.318988 + 0.552503i 0.980277 0.197628i $$-0.0633238\pi$$
−0.661289 + 0.750131i $$0.729990\pi$$
$$558$$ 5.42999e15 + 3.13501e15i 0.179885 + 0.103856i
$$559$$ 3.09588e16i 1.01464i
$$560$$ 4.50235e15 + 9.40838e15i 0.145986 + 0.305061i
$$561$$ −3.40878e16 −1.09351
$$562$$ 1.59719e16 2.76642e16i 0.506920 0.878011i
$$563$$ −1.49006e16 + 8.60286e15i −0.467900 + 0.270142i −0.715360 0.698756i $$-0.753737\pi$$
0.247460 + 0.968898i $$0.420404\pi$$
$$564$$ −7.71434e15 1.33616e16i −0.239676 0.415131i
$$565$$ 4.87593e16 + 2.81512e16i 1.49888 + 0.865379i
$$566$$ 3.51181e16i 1.06815i
$$567$$ −3.54165e16 + 1.69484e16i −1.06588 + 0.510072i
$$568$$ −6.89326e15 −0.205274
$$569$$ −1.64180e16 + 2.84368e16i −0.483779 + 0.837930i −0.999826 0.0186304i $$-0.994069\pi$$
0.516048 + 0.856560i $$0.327403\pi$$
$$570$$ −1.80279e16 + 1.04084e16i −0.525651 + 0.303484i
$$571$$ −2.21946e16 3.84422e16i −0.640369 1.10915i −0.985350 0.170543i $$-0.945448\pi$$
0.344981 0.938610i $$-0.387885\pi$$
$$572$$ 1.64058e16 + 9.47189e15i 0.468404 + 0.270433i
$$573$$ 5.05282e16i 1.42760i
$$574$$ −7.69968e15 + 1.12339e16i −0.215279 + 0.314093i
$$575$$ 2.52243e16 0.697929
$$576$$ 5.44464e14 9.43040e14i 0.0149085 0.0258223i
$$577$$ −1.53625e16 + 8.86954e15i −0.416300 + 0.240351i −0.693493 0.720463i $$-0.743929\pi$$
0.277193 + 0.960814i $$0.410596\pi$$
$$578$$ 1.03417e16 + 1.79124e16i 0.277349 + 0.480383i
$$579$$ 2.77965e16 + 1.60483e16i 0.737767 + 0.425950i
$$580$$ 3.25874e16i 0.856015i
$$581$$ 2.46307e16 + 1.90676e15i 0.640352 + 0.0495724i
$$582$$ −1.74365e16 −0.448664
$$583$$ 1.42269e14 2.46418e14i 0.00362326 0.00627568i
$$584$$ −2.09758e16 + 1.21104e16i −0.528739 + 0.305267i
$$585$$ −9.51020e15 1.64722e16i −0.237276 0.410975i
$$586$$ −2.62124e16 1.51338e16i −0.647324 0.373733i
$$587$$ 1.42997e16i 0.349542i 0.984609 + 0.174771i $$0.0559185\pi$$
−0.984609 + 0.174771i $$0.944081\pi$$
$$588$$ 1.79097e16 + 1.44273e16i 0.433336 + 0.349076i
$$589$$ −2.93169e16 −0.702145
$$590$$ 3.01108e16 5.21535e16i 0.713856 1.23644i
$$591$$ 2.10036e15 1.21264e15i 0.0492911 0.0284582i
$$592$$ −8.11954e15 1.40635e16i −0.188626 0.326710i
$$593$$ 6.69933e15 + 3.86786e15i 0.154065 + 0.0889493i 0.575050 0.818118i $$-0.304982\pi$$
−0.420986 + 0.907067i $$0.638316\pi$$
$$594$$ 1.93607e16i 0.440761i
$$595$$ −6.18875e15 + 7.99433e16i −0.139477 + 1.80169i
$$596$$ −4.15136e16 −0.926218
$$597$$ 2.41799e16 4.18807e16i 0.534082 0.925057i
$$598$$ −3.46314e16 + 1.99944e16i −0.757291 + 0.437222i
$$599$$ −1.42448e16 2.46727e16i −0.308387 0.534141i 0.669623 0.742701i $$-0.266456\pi$$
−0.978010 + 0.208560i $$0.933122\pi$$
$$600$$ 1.31953e16 + 7.61829e15i 0.282820 + 0.163286i
$$601$$ 1.25771e16i 0.266892i 0.991056 + 0.133446i $$0.0426042\pi$$
−0.991056 + 0.133446i $$0.957396\pi$$
$$602$$ 1.91534e16 + 1.31277e16i 0.402409 + 0.275811i
$$603$$ −1.39247e16 −0.289656
$$604$$ 2.04429e16 3.54082e16i 0.421039 0.729260i
$$605$$ −2.63671e16 + 1.52231e16i −0.537688 + 0.310434i
$$606$$ 2.11340e16 + 3.66051e16i 0.426723 + 0.739105i
$$607$$ −3.41643e16 1.97248e16i −0.683030 0.394348i 0.117965 0.993018i $$-0.462363\pi$$
−0.800996 + 0.598670i $$0.795696\pi$$
$$608$$ 5.09155e15i 0.100793i
$$609$$ −3.10165e16 6.48139e16i −0.607980 1.27047i
$$610$$ 4.63630e16 0.899897
$$611$$ −3.29574e16 + 5.70839e16i −0.633441 + 1.09715i
$$612$$ 7.24966e15 4.18559e15i 0.137978 0.0796615i
$$613$$ 1.23442e16 + 2.13807e16i 0.232648 + 0.402958i 0.958586 0.284802i $$-0.0919277\pi$$
−0.725939 + 0.687759i $$0.758594\pi$$
$$614$$ −2.89210e16 1.66975e16i −0.539763 0.311632i
$$615$$ 4.38659e16i 0.810730i
$$616$$ −1.28167e16 + 6.13340e15i −0.234581 + 0.112258i
$$617$$ −4.97598e16 −0.901919 −0.450959 0.892545i $$-0.648918\pi$$
−0.450959 + 0.892545i $$0.648918\pi$$
$$618$$ −1.74109e16 + 3.01566e16i −0.312529 + 0.541316i
$$619$$ −1.68034e16 + 9.70147e15i −0.298713 + 0.172462i −0.641865 0.766818i $$-0.721839\pi$$
0.343152 + 0.939280i $$0.388506\pi$$
$$620$$ 2.36558e16 + 4.09730e16i 0.416474 + 0.721353i
$$621$$ 3.53936e16 + 2.04345e16i 0.617128 + 0.356299i
$$622$$ 2.20340e16i 0.380497i
$$623$$ −1.37515e15 + 2.00635e15i −0.0235191 + 0.0343145i
$$624$$ −2.41551e16 −0.409167
$$625$$ 3.40077e16 5.89031e16i 0.570555 0.988230i
$$626$$ −1.30437e16 + 7.53079e15i −0.216748 + 0.125139i
$$627$$ −1.41791e16 2.45588e16i −0.233368 0.404206i
$$628$$ −1.40366e16 8.10406e15i −0.228826 0.132113i
$$629$$ 1.24839e17i 2.01579i
$$630$$ 1.42236e16 + 1.10111e15i 0.227492 + 0.0176111i
$$631$$ 1.89698e16 0.300530 0.150265 0.988646i $$-0.451987\pi$$
0.150265 + 0.988646i $$0.451987\pi$$
$$632$$ −1.11811e16 + 1.93662e16i −0.175461 + 0.303907i
$$633$$ 9.11041e16 5.25990e16i 1.41617 0.817627i
$$634$$ 3.36715e16 + 5.83208e16i 0.518474 + 0.898024i
$$635$$ 4.92717e15 + 2.84470e15i 0.0751546 + 0.0433905i
$$636$$ 3.62813e14i 0.00548201i
$$637$$ 1.51216e16 9.70817e16i 0.226341 1.45312i
$$638$$ 4.43926e16 0.658244
$$639$$ −4.71421e15 + 8.16526e15i −0.0692475 + 0.119940i
$$640$$ 7.11589e15 4.10836e15i 0.103550 0.0597845i
$$641$$ −2.80509e16 4.85856e16i −0.404389 0.700422i 0.589861 0.807505i $$-0.299182\pi$$
−0.994250 + 0.107083i $$0.965849\pi$$
$$642$$ 1.06186e16 + 6.13063e15i 0.151655 + 0.0875578i
$$643$$ 3.11805e15i 0.0441182i −0.999757 0.0220591i $$-0.992978\pi$$
0.999757 0.0220591i $$-0.00702220\pi$$
$$644$$ 2.31499e15 2.99040e16i 0.0324515 0.419192i
$$645$$ 7.47901e16 1.03869
$$646$$ −1.95707e16 + 3.38975e16i −0.269285 + 0.466415i
$$647$$ 6.91898e16 3.99467e16i 0.943227 0.544572i 0.0522565 0.998634i $$-0.483359\pi$$
0.890970 + 0.454061i $$0.150025\pi$$
$$648$$ 1.54653e16 + 2.67867e16i 0.208886 + 0.361801i
$$649$$ 7.10469e16 + 4.10189e16i 0.950773 + 0.548929i
$$650$$ 6.50941e16i 0.863101i
$$651$$ 8.60477e16 + 5.89769e16i 1.13045 + 0.774812i
$$652$$ 5.02816e16 0.654521
$$653$$ −6.87264e16 + 1.19038e17i −0.886430 + 1.53534i −0.0423648 + 0.999102i $$0.513489\pi$$
−0.844066 + 0.536240i $$0.819844\pi$$
$$654$$ −2.33884e16 + 1.35033e16i −0.298906 + 0.172574i
$$655$$ −5.08099e16 8.80053e16i −0.643429 1.11445i
$$656$$ 9.29163e15 + 5.36453e15i 0.116592 + 0.0673144i
$$657$$ 3.31285e16i 0.411917i
$$658$$ −2.13411e16 4.45957e16i −0.262943 0.549462i
$$659$$ −2.77636e15 −0.0338972 −0.0169486 0.999856i $$-0.505395\pi$$
−0.0169486 + 0.999856i $$0.505395\pi$$
$$660$$ −2.28821e16 + 3.96330e16i −0.276842 + 0.479505i
$$661$$ 1.34435e17 7.76164e16i 1.61178 0.930560i 0.622820 0.782365i $$-0.285987\pi$$
0.988958 0.148195i $$-0.0473463\pi$$
$$662$$ −5.08213e15 8.80251e15i −0.0603807 0.104582i
$$663$$ −1.60815e17 9.28465e16i −1.89341 1.09316i
$$664$$ 1.94617e16i 0.227076i
$$665$$ −6.01700e16 + 2.87942e16i −0.695745 + 0.332947i
$$666$$ −2.22114e16 −0.254525
$$667$$ −4.68547e16 + 8.11548e16i −0.532106 + 0.921635i
$$668$$ 3.61122e16 2.08494e16i 0.406438 0.234657i
$$669$$ 4.26015e16 + 7.37879e16i 0.475191 + 0.823054i
$$670$$ −9.09946e16 5.25358e16i −1.00593 0.580773i
$$671$$ 6.31587e16i 0.691988i
$$672$$ 1.02427e16 1.49441e16i 0.111224 0.162276i
$$673$$ 4.53293e15 0.0487852 0.0243926 0.999702i $$-0.492235\pi$$
0.0243926 + 0.999702i $$0.492235\pi$$
$$674$$ −2.33048e16 + 4.03652e16i −0.248592 + 0.430574i
$$675$$ −5.76139e16 + 3.32634e16i −0.609123 + 0.351677i
$$676$$ 2.77407e16 + 4.80483e16i 0.290695 + 0.503498i
$$677$$ −8.53907e16 4.93003e16i −0.886908 0.512057i −0.0139781 0.999902i $$-0.504450\pi$$
−0.872930 + 0.487846i $$0.837783\pi$$
$$678$$ 9.77981e16i 1.00682i
$$679$$ −5.57061e16 4.31245e15i −0.568439 0.0440053i
$$680$$ 6.31664e16 0.638899
$$681$$ 3.13765e16 5.43457e16i 0.314573 0.544857i
$$682$$ −5.58161e16 + 3.22255e16i −0.554694 + 0.320253i
$$683$$ −3.01263e16 5.21802e16i −0.296771 0.514022i 0.678625 0.734485i $$-0.262576\pi$$
−0.975395 + 0.220463i $$0.929243\pi$$
$$684$$ 6.03108e15 + 3.48205e15i 0.0588923 + 0.0340015i
$$685$$ 2.15148e17i 2.08255i
$$686$$ 5.36498e16 + 5.05217e16i 0.514782 + 0.484768i
$$687$$ −1.43334e17 −1.36336
$$688$$ 9.14636e15 1.58420e16i 0.0862418 0.149375i
$$689$$ 1.34236e15 7.75010e14i 0.0125474 0.00724422i
$$690$$ −4.83024e16 8.36622e16i −0.447584 0.775238i
$$691$$ 1.24730e15 + 7.20129e14i 0.0114578 + 0.00661518i 0.505718 0.862699i $$-0.331228\pi$$
−0.494260 + 0.869314i $$0.664561\pi$$
$$692$$ 4.46288e16i 0.406423i
$$693$$ −1.50000e15 + 1.93763e16i −0.0135423 + 0.174933i
$$694$$ −3.94909e16 −0.353460
$$695$$ −4.03230e15 + 6.98415e15i −0.0357803 + 0.0619733i
$$696$$ −4.90211e16 + 2.83023e16i −0.431248 + 0.248981i
$$697$$ 4.12400e16 + 7.14298e16i 0.359685 + 0.622992i
$$698$$ −9.81877e15 5.66887e15i −0.0849033 0.0490190i
$$699$$ 1.88894e17i 1.61940i
$$700$$ 4.02721e16 + 2.76024e16i 0.342307 + 0.234617i
$$701$$ 1.76004e17 1.48325 0.741623 0.670817i $$-0.234056\pi$$
0.741623 + 0.670817i $$0.234056\pi$$
$$702$$ 5.27336e16 9.13373e16i 0.440621 0.763177i
$$703$$ 8.99409e16 5.19274e16i 0.745118 0.430194i
$$704$$ 5.59668e15 + 9.69373e15i 0.0459721 + 0.0796260i
$$705$$ −1.37903e17 7.96183e16i −1.12315 0.648452i
$$706$$ 1.28265e16i 0.103581i
$$707$$ 5.84656e16 + 1.22173e17i 0.468149 + 0.978271i
$$708$$ −1.04606e17 −0.830532
$$709$$ −7.39721e16 + 1.28123e17i −0.582358 + 1.00867i 0.412841 + 0.910803i $$0.364537\pi$$
−0.995199 + 0.0978712i $$0.968797\pi$$
$$710$$ −6.16125e16 + 3.55720e16i −0.480971 + 0.277689i
$$711$$ 1.52932e16 + 2.64886e16i 0.118380 + 0.205041i
$$712$$ 1.65947e15 + 9.58094e14i 0.0127376 + 0.00735407i
$$713$$ 1.36051e17i 1.03553i
$$714$$ 1.25633e17 6.01215e16i 0.948235 0.453775i
$$715$$ 1.95515e17 1.46334
$$716$$ −1.08431e16 + 1.87808e16i −0.0804778 + 0.139392i
$$717$$ 8.43270e16 4.86862e16i 0.620657 0.358336i
$$718$$ −1.34076e16 2.32227e16i −0.0978601 0.169499i
$$719$$ −1.77523e16 1.02493e16i −0.128493 0.0741857i 0.434375 0.900732i $$-0.356969\pi$$
−0.562869 + 0.826546i $$0.690302\pi$$
$$720$$ 1.12386e16i 0.0806712i
$$721$$ −6.30828e16 + 9.20381e16i −0.449055 + 0.655173i
$$722$$ 6.76009e16 0.477232
$$723$$ 2.08129e16 3.60490e16i 0.145714 0.252385i
$$724$$ 9.50049e16 5.48511e16i 0.659651 0.380850i
$$725$$ −7.62704e16 1.32104e17i −0.525204 0.909680i
$$726$$ 4.58000e16 + 2.64427e16i 0.312785 + 0.180586i
$$727$$ 9.52642e15i 0.0645243i −0.999479 0.0322621i $$-0.989729\pi$$
0.999479 0.0322621i $$-0.0102711\pi$$
$$728$$ −7.71706e16 5.97411e15i −0.518398 0.0401315i
$$729$$ −9.92481e16 −0.661237
$$730$$ −1.24989e17 + 2.16487e17i −0.825913 + 1.43052i
$$731$$ 1.21786e17 7.03130e16i 0.798164 0.460820i
$$732$$ −4.02666e16 6.97438e16i −0.261745 0.453356i
$$733$$ 8.31903e16 + 4.80299e16i 0.536351 + 0.309662i 0.743599 0.668626i $$-0.233117\pi$$
−0.207248 + 0.978288i $$0.566451\pi$$
$$734$$ 2.11857e16i 0.135477i
$$735$$ 2.34529e17 + 3.65307e16i 1.48755 + 0.231704i
$$736$$ −2.36283e16 −0.148650
$$737$$ 7.15676e16 1.23959e17i 0.446593 0.773521i
$$738$$ 1.27089e16 7.33747e15i 0.0786626 0.0454159i
$$739$$ −1.14442e17 1.98220e17i −0.702618 1.21697i −0.967544 0.252702i $$-0.918681\pi$$
0.264926 0.964269i $$-0.414653\pi$$
$$740$$ −1.45146e17 8.38003e16i −0.883926 0.510335i
$$741$$ 1.54480e17i 0.933177i
$$742$$ −8.97321e13 + 1.15912e15i −0.000537681 + 0.00694549i
$$743$$ −1.73334e17 −1.03027 −0.515136 0.857109i $$-0.672258\pi$$
−0.515136 + 0.857109i $$0.672258\pi$$
$$744$$ 4.10904e16 7.11707e16i 0.242272 0.419627i
$$745$$ −3.71052e17 + 2.14227e17i −2.17019 + 1.25296i
$$746$$ 5.29906e16 + 9.17824e16i 0.307444 + 0.532508i
$$747$$ −2.30529e16 1.33096e16i −0.132679 0.0766022i
$$748$$ 8.60493e16i 0.491290i
$$749$$ 3.24079e16 + 2.22124e16i 0.183553 + 0.125807i
$$750$$ −3.22119e16 −0.180988
$$751$$ −5.91242e16 + 1.02406e17i −0.329553 + 0.570803i −0.982423 0.186667i $$-0.940231\pi$$
0.652870 + 0.757470i $$0.273565\pi$$
$$752$$ −3.37293e16 + 1.94736e16i −0.186509 + 0.107681i
$$753$$ −4.23064e16 7.32769e16i −0.232079 0.401973i
$$754$$ 2.09429e17 + 1.20914e17i 1.13975 + 0.658035i
$$755$$ 4.21976e17i 2.27827i
$$756$$ 3.41469e16 + 7.13554e16i 0.182903