# Properties

 Label 6.11.b.a.5.1 Level $6$ Weight $11$ Character 6.5 Analytic conductor $3.812$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$6 = 2 \cdot 3$$ Weight: $$k$$ $$=$$ $$11$$ Character orbit: $$[\chi]$$ $$=$$ 6.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.81214351604$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{85})$$ Defining polynomial: $$x^{4} - 2 x^{3} - 37 x^{2} + 38 x + 531$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{11}\cdot 3^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 5.1 Root $$-4.10977 + 1.41421i$$ of defining polynomial Character $$\chi$$ $$=$$ 6.5 Dual form 6.11.b.a.5.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-22.6274i q^{2} +(-200.269 + 137.627i) q^{3} -512.000 q^{4} +3630.47i q^{5} +(3114.15 + 4531.57i) q^{6} -23226.5 q^{7} +11585.2i q^{8} +(21166.4 - 55125.0i) q^{9} +O(q^{10})$$ $$q-22.6274i q^{2} +(-200.269 + 137.627i) q^{3} -512.000 q^{4} +3630.47i q^{5} +(3114.15 + 4531.57i) q^{6} -23226.5 q^{7} +11585.2i q^{8} +(21166.4 - 55125.0i) q^{9} +82148.2 q^{10} -62442.7i q^{11} +(102538. - 70465.2i) q^{12} -170161. q^{13} +525556. i q^{14} +(-499653. - 727072. i) q^{15} +262144. q^{16} +2.66626e6i q^{17} +(-1.24734e6 - 478941. i) q^{18} +766825. q^{19} -1.85880e6i q^{20} +(4.65156e6 - 3.19661e6i) q^{21} -1.41292e6 q^{22} -1.40327e6i q^{23} +(-1.59445e6 - 2.32016e6i) q^{24} -3.41471e6 q^{25} +3.85029e6i q^{26} +(3.34774e6 + 1.39529e7i) q^{27} +1.18920e7 q^{28} -4.83245e6i q^{29} +(-1.64518e7 + 1.13058e7i) q^{30} -4.18297e7 q^{31} -5.93164e6i q^{32} +(8.59382e6 + 1.25053e7i) q^{33} +6.03306e7 q^{34} -8.43233e7i q^{35} +(-1.08372e7 + 2.82240e7i) q^{36} +5.01619e7 q^{37} -1.73513e7i q^{38} +(3.40779e7 - 2.34188e7i) q^{39} -4.20599e7 q^{40} +1.49239e8i q^{41} +(-7.23310e7 - 1.05253e8i) q^{42} -1.98719e8 q^{43} +3.19706e7i q^{44} +(2.00130e8 + 7.68440e7i) q^{45} -3.17523e7 q^{46} +1.55059e8i q^{47} +(-5.24993e7 + 3.60782e7i) q^{48} +2.56996e8 q^{49} +7.72661e7i q^{50} +(-3.66951e8 - 5.33970e8i) q^{51} +8.71222e7 q^{52} -4.21541e7i q^{53} +(3.15718e8 - 7.57507e7i) q^{54} +2.26696e8 q^{55} -2.69085e8i q^{56} +(-1.53571e8 + 1.05536e8i) q^{57} -1.09346e8 q^{58} -2.92026e8i q^{59} +(2.55822e8 + 3.72261e8i) q^{60} -5.30727e8 q^{61} +9.46499e8i q^{62} +(-4.91622e8 + 1.28036e9i) q^{63} -1.34218e8 q^{64} -6.17764e8i q^{65} +(2.82963e8 - 1.94456e8i) q^{66} +5.22093e8 q^{67} -1.36513e9i q^{68} +(1.93128e8 + 2.81031e8i) q^{69} -1.90802e9 q^{70} -5.71364e8i q^{71} +(6.38636e8 + 2.45218e8i) q^{72} +2.18588e9 q^{73} -1.13503e9i q^{74} +(6.83861e8 - 4.69958e8i) q^{75} -3.92615e8 q^{76} +1.45033e9i q^{77} +(-5.29906e8 - 7.71095e8i) q^{78} +1.96592e9 q^{79} +9.51707e8i q^{80} +(-2.59075e9 - 2.33360e9i) q^{81} +3.37689e9 q^{82} +2.18558e9i q^{83} +(-2.38160e9 + 1.63666e9i) q^{84} -9.67979e9 q^{85} +4.49650e9i q^{86} +(6.65078e8 + 9.67791e8i) q^{87} +7.23413e8 q^{88} +2.38742e8i q^{89} +(1.73878e9 - 4.52842e9i) q^{90} +3.95224e9 q^{91} +7.18473e8i q^{92} +(8.37720e9 - 5.75692e9i) q^{93} +3.50858e9 q^{94} +2.78394e9i q^{95} +(8.16356e8 + 1.18792e9i) q^{96} -8.84112e9 q^{97} -5.81517e9i q^{98} +(-3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9} + O(q^{10})$$ $$4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9} - 53760 q^{10} - 43008 q^{12} + 275240 q^{13} - 1180800 q^{15} + 1048576 q^{16} - 2907648 q^{18} - 1568728 q^{19} + 9628008 q^{21} + 7730688 q^{22} - 2752512 q^{24} - 33732380 q^{25} + 34619508 q^{27} + 23097344 q^{28} - 85731840 q^{30} - 21785848 q^{31} + 25974144 q^{33} + 151087104 q^{34} - 81414144 q^{36} - 71014168 q^{37} + 217287240 q^{39} + 27525120 q^{40} - 145233408 q^{42} - 470688664 q^{43} + 312318720 q^{45} + 188814336 q^{46} + 22020096 q^{48} - 50058420 q^{49} - 708576768 q^{51} - 140922880 q^{52} + 481662720 q^{54} + 2701359360 q^{55} - 1058753208 q^{57} - 1564177920 q^{58} + 604569600 q^{60} - 1184038744 q^{61} - 905007096 q^{63} - 536870912 q^{64} + 3123445248 q^{66} - 297365848 q^{67} + 596268288 q^{69} - 3962250240 q^{70} + 1488715776 q^{72} + 6534269000 q^{73} - 5150031180 q^{75} + 803188736 q^{76} - 1322135040 q^{78} + 199282568 q^{79} + 1458964548 q^{81} + 8378668032 q^{82} - 4929540096 q^{84} - 12880512000 q^{85} + 210268800 q^{87} - 3958112256 q^{88} - 9243763200 q^{90} + 8317232080 q^{91} + 31744468392 q^{93} + 8505477120 q^{94} + 1409286144 q^{96} - 39176355064 q^{97} - 2626912512 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$\chi(n)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 22.6274i 0.707107i
$$3$$ −200.269 + 137.627i −0.824153 + 0.566368i
$$4$$ −512.000 −0.500000
$$5$$ 3630.47i 1.16175i 0.813992 + 0.580876i $$0.197290\pi$$
−0.813992 + 0.580876i $$0.802710\pi$$
$$6$$ 3114.15 + 4531.57i 0.400483 + 0.582764i
$$7$$ −23226.5 −1.38196 −0.690978 0.722876i $$-0.742820\pi$$
−0.690978 + 0.722876i $$0.742820\pi$$
$$8$$ 11585.2i 0.353553i
$$9$$ 21166.4 55125.0i 0.358455 0.933547i
$$10$$ 82148.2 0.821482
$$11$$ 62442.7i 0.387720i −0.981029 0.193860i $$-0.937899\pi$$
0.981029 0.193860i $$-0.0621007\pi$$
$$12$$ 102538. 70465.2i 0.412076 0.283184i
$$13$$ −170161. −0.458292 −0.229146 0.973392i $$-0.573593\pi$$
−0.229146 + 0.973392i $$0.573593\pi$$
$$14$$ 525556.i 0.977190i
$$15$$ −499653. 727072.i −0.657979 0.957460i
$$16$$ 262144. 0.250000
$$17$$ 2.66626e6i 1.87784i 0.344139 + 0.938919i $$0.388171\pi$$
−0.344139 + 0.938919i $$0.611829\pi$$
$$18$$ −1.24734e6 478941.i −0.660117 0.253466i
$$19$$ 766825. 0.309691 0.154845 0.987939i $$-0.450512\pi$$
0.154845 + 0.987939i $$0.450512\pi$$
$$20$$ 1.85880e6i 0.580876i
$$21$$ 4.65156e6 3.19661e6i 1.13894 0.782695i
$$22$$ −1.41292e6 −0.274159
$$23$$ 1.40327e6i 0.218022i −0.994041 0.109011i $$-0.965232\pi$$
0.994041 0.109011i $$-0.0347684\pi$$
$$24$$ −1.59445e6 2.32016e6i −0.200241 0.291382i
$$25$$ −3.41471e6 −0.349667
$$26$$ 3.85029e6i 0.324061i
$$27$$ 3.34774e6 + 1.39529e7i 0.233310 + 0.972402i
$$28$$ 1.18920e7 0.690978
$$29$$ 4.83245e6i 0.235601i −0.993037 0.117801i $$-0.962416\pi$$
0.993037 0.117801i $$-0.0375844\pi$$
$$30$$ −1.64518e7 + 1.13058e7i −0.677027 + 0.465261i
$$31$$ −4.18297e7 −1.46109 −0.730544 0.682865i $$-0.760734\pi$$
−0.730544 + 0.682865i $$0.760734\pi$$
$$32$$ 5.93164e6i 0.176777i
$$33$$ 8.59382e6 + 1.25053e7i 0.219592 + 0.319540i
$$34$$ 6.03306e7 1.32783
$$35$$ 8.43233e7i 1.60549i
$$36$$ −1.08372e7 + 2.82240e7i −0.179227 + 0.466774i
$$37$$ 5.01619e7 0.723378 0.361689 0.932299i $$-0.382200\pi$$
0.361689 + 0.932299i $$0.382200\pi$$
$$38$$ 1.73513e7i 0.218985i
$$39$$ 3.40779e7 2.34188e7i 0.377702 0.259562i
$$40$$ −4.20599e7 −0.410741
$$41$$ 1.49239e8i 1.28814i 0.764967 + 0.644069i $$0.222755\pi$$
−0.764967 + 0.644069i $$0.777245\pi$$
$$42$$ −7.23310e7 1.05253e8i −0.553449 0.805354i
$$43$$ −1.98719e8 −1.35175 −0.675876 0.737015i $$-0.736235\pi$$
−0.675876 + 0.737015i $$0.736235\pi$$
$$44$$ 3.19706e7i 0.193860i
$$45$$ 2.00130e8 + 7.68440e7i 1.08455 + 0.416435i
$$46$$ −3.17523e7 −0.154165
$$47$$ 1.55059e8i 0.676093i 0.941129 + 0.338047i $$0.109766\pi$$
−0.941129 + 0.338047i $$0.890234\pi$$
$$48$$ −5.24993e7 + 3.60782e7i −0.206038 + 0.141592i
$$49$$ 2.56996e8 0.909802
$$50$$ 7.72661e7i 0.247252i
$$51$$ −3.66951e8 5.33970e8i −1.06355 1.54762i
$$52$$ 8.71222e7 0.229146
$$53$$ 4.21541e7i 0.100800i −0.998729 0.0503999i $$-0.983950\pi$$
0.998729 0.0503999i $$-0.0160496\pi$$
$$54$$ 3.15718e8 7.57507e7i 0.687592 0.164975i
$$55$$ 2.26696e8 0.450434
$$56$$ 2.69085e8i 0.488595i
$$57$$ −1.53571e8 + 1.05536e8i −0.255233 + 0.175399i
$$58$$ −1.09346e8 −0.166595
$$59$$ 2.92026e8i 0.408471i −0.978922 0.204236i $$-0.934529\pi$$
0.978922 0.204236i $$-0.0654708\pi$$
$$60$$ 2.55822e8 + 3.72261e8i 0.328989 + 0.478730i
$$61$$ −5.30727e8 −0.628379 −0.314190 0.949360i $$-0.601733\pi$$
−0.314190 + 0.949360i $$0.601733\pi$$
$$62$$ 9.46499e8i 1.03315i
$$63$$ −4.91622e8 + 1.28036e9i −0.495369 + 1.29012i
$$64$$ −1.34218e8 −0.125000
$$65$$ 6.17764e8i 0.532421i
$$66$$ 2.82963e8 1.94456e8i 0.225949 0.155275i
$$67$$ 5.22093e8 0.386700 0.193350 0.981130i $$-0.438065\pi$$
0.193350 + 0.981130i $$0.438065\pi$$
$$68$$ 1.36513e9i 0.938919i
$$69$$ 1.93128e8 + 2.81031e8i 0.123481 + 0.179684i
$$70$$ −1.90802e9 −1.13525
$$71$$ 5.71364e8i 0.316681i −0.987385 0.158340i $$-0.949386\pi$$
0.987385 0.158340i $$-0.0506143\pi$$
$$72$$ 6.38636e8 + 2.45218e8i 0.330059 + 0.126733i
$$73$$ 2.18588e9 1.05441 0.527207 0.849737i $$-0.323239\pi$$
0.527207 + 0.849737i $$0.323239\pi$$
$$74$$ 1.13503e9i 0.511506i
$$75$$ 6.83861e8 4.69958e8i 0.288179 0.198040i
$$76$$ −3.92615e8 −0.154845
$$77$$ 1.45033e9i 0.535812i
$$78$$ −5.29906e8 7.71095e8i −0.183538 0.267076i
$$79$$ 1.96592e9 0.638897 0.319449 0.947604i $$-0.396502\pi$$
0.319449 + 0.947604i $$0.396502\pi$$
$$80$$ 9.51707e8i 0.290438i
$$81$$ −2.59075e9 2.33360e9i −0.743020 0.669269i
$$82$$ 3.37689e9 0.910851
$$83$$ 2.18558e9i 0.554850i 0.960747 + 0.277425i $$0.0894810\pi$$
−0.960747 + 0.277425i $$0.910519\pi$$
$$84$$ −2.38160e9 + 1.63666e9i −0.569471 + 0.391348i
$$85$$ −9.67979e9 −2.18158
$$86$$ 4.49650e9i 0.955833i
$$87$$ 6.65078e8 + 9.67791e8i 0.133437 + 0.194171i
$$88$$ 7.23413e8 0.137080
$$89$$ 2.38742e8i 0.0427542i 0.999771 + 0.0213771i $$0.00680506\pi$$
−0.999771 + 0.0213771i $$0.993195\pi$$
$$90$$ 1.73878e9 4.52842e9i 0.294464 0.766892i
$$91$$ 3.95224e9 0.633339
$$92$$ 7.18473e8i 0.109011i
$$93$$ 8.37720e9 5.75692e9i 1.20416 0.827514i
$$94$$ 3.50858e9 0.478070
$$95$$ 2.78394e9i 0.359784i
$$96$$ 8.16356e8 + 1.18792e9i 0.100121 + 0.145691i
$$97$$ −8.84112e9 −1.02955 −0.514776 0.857324i $$-0.672125\pi$$
−0.514776 + 0.857324i $$0.672125\pi$$
$$98$$ 5.81517e9i 0.643327i
$$99$$ −3.44215e9 1.32169e9i −0.361955 0.138980i
$$100$$ 1.74833e9 0.174833
$$101$$ 1.67928e10i 1.59778i −0.601477 0.798890i $$-0.705421\pi$$
0.601477 0.798890i $$-0.294579\pi$$
$$102$$ −1.20824e10 + 8.30314e9i −1.09434 + 0.752041i
$$103$$ 8.36865e9 0.721887 0.360944 0.932588i $$-0.382455\pi$$
0.360944 + 0.932588i $$0.382455\pi$$
$$104$$ 1.97135e9i 0.162031i
$$105$$ 1.16052e10 + 1.68873e10i 0.909297 + 1.32317i
$$106$$ −9.53837e8 −0.0712763
$$107$$ 1.43555e10i 1.02353i 0.859126 + 0.511764i $$0.171008\pi$$
−0.859126 + 0.511764i $$0.828992\pi$$
$$108$$ −1.71404e9 7.14389e9i −0.116655 0.486201i
$$109$$ −4.72564e9 −0.307134 −0.153567 0.988138i $$-0.549076\pi$$
−0.153567 + 0.988138i $$0.549076\pi$$
$$110$$ 5.12956e9i 0.318505i
$$111$$ −1.00459e10 + 6.90365e9i −0.596174 + 0.409698i
$$112$$ −6.08870e9 −0.345489
$$113$$ 1.32158e10i 0.717303i 0.933472 + 0.358651i $$0.116763\pi$$
−0.933472 + 0.358651i $$0.883237\pi$$
$$114$$ 2.38801e9 + 3.47492e9i 0.124026 + 0.180477i
$$115$$ 5.09452e9 0.253288
$$116$$ 2.47422e9i 0.117801i
$$117$$ −3.60169e9 + 9.38011e9i −0.164277 + 0.427837i
$$118$$ −6.60779e9 −0.288833
$$119$$ 6.19280e10i 2.59509i
$$120$$ 8.42330e9 5.78859e9i 0.338513 0.232631i
$$121$$ 2.20383e10 0.849673
$$122$$ 1.20090e10i 0.444331i
$$123$$ −2.05393e10 2.98879e10i −0.729560 1.06162i
$$124$$ 2.14168e10 0.730544
$$125$$ 2.30568e10i 0.755526i
$$126$$ 2.89713e10 + 1.11241e10i 0.912253 + 0.350279i
$$127$$ −3.17814e10 −0.961953 −0.480976 0.876733i $$-0.659718\pi$$
−0.480976 + 0.876733i $$0.659718\pi$$
$$128$$ 3.03700e9i 0.0883883i
$$129$$ 3.97973e10 2.73492e10i 1.11405 0.765589i
$$130$$ −1.39784e10 −0.376479
$$131$$ 5.01094e10i 1.29886i 0.760421 + 0.649430i $$0.224993\pi$$
−0.760421 + 0.649430i $$0.775007\pi$$
$$132$$ −4.40004e9 6.40273e9i −0.109796 0.159770i
$$133$$ −1.78107e10 −0.427979
$$134$$ 1.18136e10i 0.273438i
$$135$$ −5.06557e10 + 1.21539e10i −1.12969 + 0.271048i
$$136$$ −3.08893e10 −0.663916
$$137$$ 2.74744e10i 0.569279i 0.958635 + 0.284639i $$0.0918738\pi$$
−0.958635 + 0.284639i $$0.908126\pi$$
$$138$$ 6.35900e9 4.36999e9i 0.127056 0.0873142i
$$139$$ 6.32488e10 1.21893 0.609464 0.792814i $$-0.291385\pi$$
0.609464 + 0.792814i $$0.291385\pi$$
$$140$$ 4.31735e10i 0.802745i
$$141$$ −2.13403e10 3.10534e10i −0.382917 0.557204i
$$142$$ −1.29285e10 −0.223927
$$143$$ 1.06253e10i 0.177689i
$$144$$ 5.54864e9 1.44507e10i 0.0896137 0.233387i
$$145$$ 1.75441e10 0.273710
$$146$$ 4.94607e10i 0.745583i
$$147$$ −5.14684e10 + 3.53697e10i −0.749815 + 0.515282i
$$148$$ −2.56829e10 −0.361689
$$149$$ 3.38479e10i 0.460893i −0.973085 0.230446i $$-0.925981\pi$$
0.973085 0.230446i $$-0.0740186\pi$$
$$150$$ −1.06339e10 1.54740e10i −0.140035 0.203773i
$$151$$ 1.22386e11 1.55901 0.779503 0.626399i $$-0.215472\pi$$
0.779503 + 0.626399i $$0.215472\pi$$
$$152$$ 8.88385e9i 0.109492i
$$153$$ 1.46978e11 + 5.64351e10i 1.75305 + 0.673120i
$$154$$ 3.28171e10 0.378876
$$155$$ 1.51862e11i 1.69742i
$$156$$ −1.74479e10 + 1.19904e10i −0.188851 + 0.129781i
$$157$$ −1.58971e11 −1.66656 −0.833279 0.552853i $$-0.813539\pi$$
−0.833279 + 0.552853i $$0.813539\pi$$
$$158$$ 4.44838e10i 0.451769i
$$159$$ 5.80155e9 + 8.44215e9i 0.0570898 + 0.0830745i
$$160$$ 2.15347e10 0.205371
$$161$$ 3.25930e10i 0.301297i
$$162$$ −5.28033e10 + 5.86220e10i −0.473245 + 0.525395i
$$163$$ −9.20831e10 −0.800280 −0.400140 0.916454i $$-0.631038\pi$$
−0.400140 + 0.916454i $$0.631038\pi$$
$$164$$ 7.64102e10i 0.644069i
$$165$$ −4.54003e10 + 3.11996e10i −0.371226 + 0.255111i
$$166$$ 4.94540e10 0.392338
$$167$$ 2.12416e11i 1.63533i 0.575697 + 0.817663i $$0.304731\pi$$
−0.575697 + 0.817663i $$0.695269\pi$$
$$168$$ 3.70334e10 + 5.38894e10i 0.276725 + 0.402677i
$$169$$ −1.08904e11 −0.789968
$$170$$ 2.19029e11i 1.54261i
$$171$$ 1.62309e10 4.22713e10i 0.111010 0.289111i
$$172$$ 1.01744e11 0.675876
$$173$$ 3.04132e11i 1.96260i −0.192482 0.981300i $$-0.561654\pi$$
0.192482 0.981300i $$-0.438346\pi$$
$$174$$ 2.18986e10 1.50490e10i 0.137300 0.0943542i
$$175$$ 7.93119e10 0.483224
$$176$$ 1.63690e10i 0.0969300i
$$177$$ 4.01908e10 + 5.84837e10i 0.231345 + 0.336642i
$$178$$ 5.40212e9 0.0302318
$$179$$ 7.07114e9i 0.0384791i −0.999815 0.0192395i $$-0.993875\pi$$
0.999815 0.0192395i $$-0.00612451\pi$$
$$180$$ −1.02467e11 3.93442e10i −0.542275 0.208218i
$$181$$ −1.27309e11 −0.655337 −0.327669 0.944793i $$-0.606263\pi$$
−0.327669 + 0.944793i $$0.606263\pi$$
$$182$$ 8.94290e10i 0.447838i
$$183$$ 1.06288e11 7.30425e10i 0.517880 0.355894i
$$184$$ 1.62572e10 0.0770825
$$185$$ 1.82111e11i 0.840386i
$$186$$ −1.30264e11 1.89554e11i −0.585141 0.851470i
$$187$$ 1.66488e11 0.728075
$$188$$ 7.93900e10i 0.338047i
$$189$$ −7.77563e10 3.24078e11i −0.322424 1.34382i
$$190$$ 6.29934e10 0.254406
$$191$$ 2.06460e11i 0.812209i 0.913827 + 0.406105i $$0.133113\pi$$
−0.913827 + 0.406105i $$0.866887\pi$$
$$192$$ 2.68797e10 1.84720e10i 0.103019 0.0707960i
$$193$$ 3.11606e11 1.16364 0.581821 0.813317i $$-0.302340\pi$$
0.581821 + 0.813317i $$0.302340\pi$$
$$194$$ 2.00052e11i 0.728004i
$$195$$ 8.50212e10 + 1.23719e11i 0.301546 + 0.438796i
$$196$$ −1.31582e11 −0.454901
$$197$$ 1.51694e11i 0.511255i 0.966775 + 0.255628i $$0.0822821\pi$$
−0.966775 + 0.255628i $$0.917718\pi$$
$$198$$ −2.99063e10 + 7.78870e10i −0.0982737 + 0.255941i
$$199$$ −1.11692e11 −0.357895 −0.178947 0.983859i $$-0.557269\pi$$
−0.178947 + 0.983859i $$0.557269\pi$$
$$200$$ 3.95603e10i 0.123626i
$$201$$ −1.04559e11 + 7.18543e10i −0.318700 + 0.219014i
$$202$$ −3.79978e11 −1.12980
$$203$$ 1.12241e11i 0.325591i
$$204$$ 1.87879e11 + 2.73392e11i 0.531773 + 0.773812i
$$205$$ −5.41807e11 −1.49650
$$206$$ 1.89361e11i 0.510451i
$$207$$ −7.73551e10 2.97021e10i −0.203534 0.0781512i
$$208$$ −4.46066e10 −0.114573
$$209$$ 4.78826e10i 0.120073i
$$210$$ 3.82117e11 2.62596e11i 0.935621 0.642970i
$$211$$ 1.53066e11 0.365987 0.182994 0.983114i $$-0.441421\pi$$
0.182994 + 0.983114i $$0.441421\pi$$
$$212$$ 2.15829e10i 0.0503999i
$$213$$ 7.86354e10 + 1.14427e11i 0.179358 + 0.260993i
$$214$$ 3.24828e11 0.723744
$$215$$ 7.21444e11i 1.57040i
$$216$$ −1.61648e11 + 3.87843e10i −0.343796 + 0.0824874i
$$217$$ 9.71560e11 2.01916
$$218$$ 1.06929e11i 0.217177i
$$219$$ −4.37763e11 + 3.00836e11i −0.868998 + 0.597186i
$$220$$ −1.16069e11 −0.225217
$$221$$ 4.53693e11i 0.860598i
$$222$$ 1.56212e11 + 2.27312e11i 0.289700 + 0.421559i
$$223$$ −6.05759e11 −1.09844 −0.549219 0.835678i $$-0.685075\pi$$
−0.549219 + 0.835678i $$0.685075\pi$$
$$224$$ 1.37771e11i 0.244298i
$$225$$ −7.22772e10 + 1.88236e11i −0.125340 + 0.326430i
$$226$$ 2.99040e11 0.507210
$$227$$ 6.70588e11i 1.11257i −0.830992 0.556284i $$-0.812227\pi$$
0.830992 0.556284i $$-0.187773\pi$$
$$228$$ 7.86286e10 5.40345e10i 0.127616 0.0876995i
$$229$$ 3.53356e11 0.561094 0.280547 0.959840i $$-0.409484\pi$$
0.280547 + 0.959840i $$0.409484\pi$$
$$230$$ 1.15276e11i 0.179102i
$$231$$ −1.99605e11 2.90456e11i −0.303467 0.441591i
$$232$$ 5.59851e10 0.0832976
$$233$$ 1.12390e12i 1.63662i 0.574779 + 0.818309i $$0.305088\pi$$
−0.574779 + 0.818309i $$0.694912\pi$$
$$234$$ 2.12248e11 + 8.14969e10i 0.302527 + 0.116161i
$$235$$ −5.62936e11 −0.785452
$$236$$ 1.49517e11i 0.204236i
$$237$$ −3.93714e11 + 2.70565e11i −0.526549 + 0.361851i
$$238$$ −1.40127e12 −1.83500
$$239$$ 2.64603e11i 0.339317i 0.985503 + 0.169658i $$0.0542665\pi$$
−0.985503 + 0.169658i $$0.945734\pi$$
$$240$$ −1.30981e11 1.90597e11i −0.164495 0.239365i
$$241$$ 8.86768e11 1.09075 0.545375 0.838192i $$-0.316387\pi$$
0.545375 + 0.838192i $$0.316387\pi$$
$$242$$ 4.98671e11i 0.600810i
$$243$$ 8.40014e11 + 1.10789e11i 0.991414 + 0.130757i
$$244$$ 2.71732e11 0.314190
$$245$$ 9.33019e11i 1.05696i
$$246$$ −6.76286e11 + 4.64752e11i −0.750680 + 0.515877i
$$247$$ −1.30483e11 −0.141929
$$248$$ 4.84607e11i 0.516573i
$$249$$ −3.00795e11 4.37704e11i −0.314249 0.457281i
$$250$$ 5.21716e11 0.534237
$$251$$ 8.59494e11i 0.862729i 0.902178 + 0.431364i $$0.141968\pi$$
−0.902178 + 0.431364i $$0.858032\pi$$
$$252$$ 2.51710e11 6.55546e11i 0.247684 0.645060i
$$253$$ −8.76237e10 −0.0845316
$$254$$ 7.19130e11i 0.680203i
$$255$$ 1.93856e12 1.33220e12i 1.79796 1.23558i
$$256$$ 6.87195e10 0.0625000
$$257$$ 2.17900e12i 1.94353i −0.235954 0.971764i $$-0.575821\pi$$
0.235954 0.971764i $$-0.424179\pi$$
$$258$$ −6.18841e11 9.00510e11i −0.541353 0.787753i
$$259$$ −1.16509e12 −0.999677
$$260$$ 3.16295e11i 0.266211i
$$261$$ −2.66389e11 1.02286e11i −0.219945 0.0844524i
$$262$$ 1.13385e12 0.918433
$$263$$ 1.37942e12i 1.09627i 0.836391 + 0.548134i $$0.184661\pi$$
−0.836391 + 0.548134i $$0.815339\pi$$
$$264$$ −1.44877e11 + 9.95615e10i −0.112975 + 0.0776375i
$$265$$ 1.53039e11 0.117104
$$266$$ 4.03010e11i 0.302627i
$$267$$ −3.28574e10 4.78126e10i −0.0242146 0.0352360i
$$268$$ −2.67312e11 −0.193350
$$269$$ 1.18129e12i 0.838680i −0.907829 0.419340i $$-0.862262\pi$$
0.907829 0.419340i $$-0.137738\pi$$
$$270$$ 2.75011e11 + 1.14621e12i 0.191660 + 0.798812i
$$271$$ −1.42251e12 −0.973213 −0.486606 0.873621i $$-0.661765\pi$$
−0.486606 + 0.873621i $$0.661765\pi$$
$$272$$ 6.98944e11i 0.469459i
$$273$$ −7.91511e11 + 5.43937e11i −0.521968 + 0.358703i
$$274$$ 6.21674e11 0.402541
$$275$$ 2.13224e11i 0.135573i
$$276$$ −9.88815e10 1.43888e11i −0.0617404 0.0898418i
$$277$$ 5.29960e11 0.324971 0.162485 0.986711i $$-0.448049\pi$$
0.162485 + 0.986711i $$0.448049\pi$$
$$278$$ 1.43116e12i 0.861913i
$$279$$ −8.85385e11 + 2.30587e12i −0.523734 + 1.36400i
$$280$$ 9.76905e11 0.567626
$$281$$ 2.28441e12i 1.30389i 0.758265 + 0.651946i $$0.226047\pi$$
−0.758265 + 0.651946i $$0.773953\pi$$
$$282$$ −7.02659e11 + 4.82876e11i −0.394003 + 0.270764i
$$283$$ 2.31274e12 1.27408 0.637038 0.770833i $$-0.280160\pi$$
0.637038 + 0.770833i $$0.280160\pi$$
$$284$$ 2.92539e11i 0.158340i
$$285$$ −3.83146e11 5.57537e11i −0.203770 0.296517i
$$286$$ 2.40423e11 0.125645
$$287$$ 3.46630e12i 1.78015i
$$288$$ −3.26982e11 1.25551e11i −0.165029 0.0633665i
$$289$$ −5.09295e12 −2.52627
$$290$$ 3.96978e11i 0.193542i
$$291$$ 1.77060e12 1.21678e12i 0.848509 0.583106i
$$292$$ −1.11917e12 −0.527207
$$293$$ 1.05989e12i 0.490822i −0.969419 0.245411i $$-0.921077\pi$$
0.969419 0.245411i $$-0.0789229\pi$$
$$294$$ 8.00326e11 + 1.16460e12i 0.364360 + 0.530199i
$$295$$ 1.06019e12 0.474542
$$296$$ 5.81138e11i 0.255753i
$$297$$ 8.71257e11 2.09042e11i 0.377020 0.0904588i
$$298$$ −7.65890e11 −0.325900
$$299$$ 2.38781e11i 0.0999179i
$$300$$ −3.50137e11 + 2.40618e11i −0.144089 + 0.0990200i
$$301$$ 4.61555e12 1.86806
$$302$$ 2.76928e12i 1.10238i
$$303$$ 2.31115e12 + 3.36308e12i 0.904931 + 1.31681i
$$304$$ 2.01019e11 0.0774227
$$305$$ 1.92679e12i 0.730020i
$$306$$ 1.27698e12 3.32573e12i 0.475968 1.23959i
$$307$$ 6.89209e11 0.252731 0.126366 0.991984i $$-0.459669\pi$$
0.126366 + 0.991984i $$0.459669\pi$$
$$308$$ 7.42567e11i 0.267906i
$$309$$ −1.67598e12 + 1.15176e12i −0.594945 + 0.408854i
$$310$$ −3.43624e12 −1.20026
$$311$$ 1.95674e12i 0.672559i 0.941762 + 0.336280i $$0.109169\pi$$
−0.941762 + 0.336280i $$0.890831\pi$$
$$312$$ 2.71312e11 + 3.94801e11i 0.0917690 + 0.133538i
$$313$$ −2.48821e11 −0.0828256 −0.0414128 0.999142i $$-0.513186\pi$$
−0.0414128 + 0.999142i $$0.513186\pi$$
$$314$$ 3.59711e12i 1.17843i
$$315$$ −4.64832e12 1.78482e12i −1.49880 0.575495i
$$316$$ −1.00655e12 −0.319449
$$317$$ 4.63675e12i 1.44850i 0.689539 + 0.724249i $$0.257813\pi$$
−0.689539 + 0.724249i $$0.742187\pi$$
$$318$$ 1.91024e11 1.31274e11i 0.0587425 0.0403686i
$$319$$ −3.01751e11 −0.0913473
$$320$$ 4.87274e11i 0.145219i
$$321$$ −1.97571e12 2.87497e12i −0.579694 0.843544i
$$322$$ 7.37496e11 0.213049
$$323$$ 2.04456e12i 0.581549i
$$324$$ 1.32646e12 + 1.19480e12i 0.371510 + 0.334634i
$$325$$ 5.81050e11 0.160249
$$326$$ 2.08360e12i 0.565883i
$$327$$ 9.46400e11 6.50378e11i 0.253125 0.173951i
$$328$$ −1.72897e12 −0.455426
$$329$$ 3.60147e12i 0.934331i
$$330$$ 7.05967e11 + 1.02729e12i 0.180391 + 0.262497i
$$331$$ −1.41443e12 −0.355994 −0.177997 0.984031i $$-0.556962\pi$$
−0.177997 + 0.984031i $$0.556962\pi$$
$$332$$ 1.11902e12i 0.277425i
$$333$$ 1.06175e12 2.76518e12i 0.259298 0.675308i
$$334$$ 4.80642e12 1.15635
$$335$$ 1.89545e12i 0.449249i
$$336$$ 1.21938e12 8.37971e11i 0.284736 0.195674i
$$337$$ 8.67755e11 0.199640 0.0998201 0.995006i $$-0.468173\pi$$
0.0998201 + 0.995006i $$0.468173\pi$$
$$338$$ 2.46421e12i 0.558592i
$$339$$ −1.81886e12 2.64672e12i −0.406257 0.591167i
$$340$$ 4.95605e12 1.09079
$$341$$ 2.61196e12i 0.566493i
$$342$$ −9.56490e11 3.67264e11i −0.204432 0.0784961i
$$343$$ 5.91785e11 0.124650
$$344$$ 2.30221e12i 0.477917i
$$345$$ −1.02028e12 + 7.01146e11i −0.208748 + 0.143454i
$$346$$ −6.88173e12 −1.38777
$$347$$ 5.20712e12i 1.03502i −0.855676 0.517512i $$-0.826858\pi$$
0.855676 0.517512i $$-0.173142\pi$$
$$348$$ −3.40520e11 4.95509e11i −0.0667185 0.0970857i
$$349$$ 1.11953e12 0.216226 0.108113 0.994139i $$-0.465519\pi$$
0.108113 + 0.994139i $$0.465519\pi$$
$$350$$ 1.79462e12i 0.341691i
$$351$$ −5.69653e11 2.37424e12i −0.106924 0.445644i
$$352$$ −3.70388e11 −0.0685398
$$353$$ 3.73952e12i 0.682248i −0.940018 0.341124i $$-0.889192\pi$$
0.940018 0.341124i $$-0.110808\pi$$
$$354$$ 1.32334e12 9.09413e11i 0.238042 0.163586i
$$355$$ 2.07432e12 0.367904
$$356$$ 1.22236e11i 0.0213771i
$$357$$ 8.52299e12 + 1.24023e13i 1.46977 + 2.13875i
$$358$$ −1.60002e11 −0.0272088
$$359$$ 3.54489e12i 0.594471i −0.954804 0.297235i $$-0.903935\pi$$
0.954804 0.297235i $$-0.0960646\pi$$
$$360$$ −8.90257e11 + 2.31855e12i −0.147232 + 0.383446i
$$361$$ −5.54305e12 −0.904092
$$362$$ 2.88066e12i 0.463393i
$$363$$ −4.41360e12 + 3.03308e12i −0.700260 + 0.481228i
$$364$$ −2.02355e12 −0.316670
$$365$$ 7.93577e12i 1.22497i
$$366$$ −1.65276e12 2.40503e12i −0.251655 0.366197i
$$367$$ −1.01161e13 −1.51944 −0.759722 0.650248i $$-0.774665\pi$$
−0.759722 + 0.650248i $$0.774665\pi$$
$$368$$ 3.67858e11i 0.0545056i
$$369$$ 8.22679e12 + 3.15885e12i 1.20254 + 0.461739i
$$370$$ 4.12071e12 0.594242
$$371$$ 9.79093e11i 0.139301i
$$372$$ −4.28913e12 + 2.94754e12i −0.602080 + 0.413757i
$$373$$ 3.81055e12 0.527769 0.263885 0.964554i $$-0.414996\pi$$
0.263885 + 0.964554i $$0.414996\pi$$
$$374$$ 3.76720e12i 0.514827i
$$375$$ −3.17325e12 4.61757e12i −0.427906 0.622669i
$$376$$ −1.79639e12 −0.239035
$$377$$ 8.22293e11i 0.107974i
$$378$$ −7.33304e12 + 1.75943e12i −0.950222 + 0.227988i
$$379$$ 1.11052e13 1.42014 0.710069 0.704132i $$-0.248664\pi$$
0.710069 + 0.704132i $$0.248664\pi$$
$$380$$ 1.42538e12i 0.179892i
$$381$$ 6.36482e12 4.37399e12i 0.792796 0.544819i
$$382$$ 4.67165e12 0.574319
$$383$$ 4.29169e12i 0.520756i −0.965507 0.260378i $$-0.916153\pi$$
0.965507 0.260378i $$-0.0838472\pi$$
$$384$$ −4.17974e11 6.08217e11i −0.0500603 0.0728455i
$$385$$ −5.26537e12 −0.622480
$$386$$ 7.05084e12i 0.822820i
$$387$$ −4.20617e12 + 1.09544e13i −0.484542 + 1.26192i
$$388$$ 4.52665e12 0.514776
$$389$$ 1.50554e13i 1.69023i −0.534588 0.845113i $$-0.679533\pi$$
0.534588 0.845113i $$-0.320467\pi$$
$$390$$ 2.79944e12 1.92381e12i 0.310276 0.213225i
$$391$$ 3.74148e12 0.409411
$$392$$ 2.97736e12i 0.321663i
$$393$$ −6.89642e12 1.00354e13i −0.735633 1.07046i
$$394$$ 3.43245e12 0.361512
$$395$$ 7.13723e12i 0.742240i
$$396$$ 1.76238e12 + 6.76703e11i 0.180977 + 0.0694900i
$$397$$ −1.11669e13 −1.13235 −0.566174 0.824286i $$-0.691577\pi$$
−0.566174 + 0.824286i $$0.691577\pi$$
$$398$$ 2.52729e12i 0.253070i
$$399$$ 3.56693e12 2.45124e12i 0.352720 0.242394i
$$400$$ −8.95146e11 −0.0874166
$$401$$ 1.15685e13i 1.11572i 0.829935 + 0.557861i $$0.188378\pi$$
−0.829935 + 0.557861i $$0.811622\pi$$
$$402$$ 1.62588e12 + 2.36590e12i 0.154867 + 0.225355i
$$403$$ 7.11777e12 0.669605
$$404$$ 8.59793e12i 0.798890i
$$405$$ 8.47206e12 9.40565e12i 0.777524 0.863205i
$$406$$ 2.53973e12 0.230227
$$407$$ 3.13224e12i 0.280468i
$$408$$ 6.18616e12 4.25121e12i 0.547168 0.376021i
$$409$$ −1.07411e13 −0.938498 −0.469249 0.883066i $$-0.655475\pi$$
−0.469249 + 0.883066i $$0.655475\pi$$
$$410$$ 1.22597e13i 1.05818i
$$411$$ −3.78123e12 5.50227e12i −0.322421 0.469172i
$$412$$ −4.28475e12 −0.360944
$$413$$ 6.78275e12i 0.564489i
$$414$$ −6.72082e11 + 1.75035e12i −0.0552612 + 0.143920i
$$415$$ −7.93468e12 −0.644598
$$416$$ 1.00933e12i 0.0810153i
$$417$$ −1.26668e13 + 8.70477e12i −1.00458 + 0.690362i
$$418$$ −1.08346e12 −0.0849047
$$419$$ 8.81717e12i 0.682746i 0.939928 + 0.341373i $$0.110892\pi$$
−0.939928 + 0.341373i $$0.889108\pi$$
$$420$$ −5.94186e12 8.64632e12i −0.454649 0.661584i
$$421$$ −5.69741e12 −0.430792 −0.215396 0.976527i $$-0.569104\pi$$
−0.215396 + 0.976527i $$0.569104\pi$$
$$422$$ 3.46348e12i 0.258792i
$$423$$ 8.54761e12 + 3.28203e12i 0.631165 + 0.242349i
$$424$$ 4.88365e11 0.0356381
$$425$$ 9.10451e12i 0.656617i
$$426$$ 2.58918e12 1.77932e12i 0.184550 0.126825i
$$427$$ 1.23269e13 0.868392
$$428$$ 7.35003e12i 0.511764i
$$429$$ −1.46233e12 2.12792e12i −0.100637 0.146443i
$$430$$ −1.63244e13 −1.11044
$$431$$ 1.80323e13i 1.21245i 0.795293 + 0.606226i $$0.207317\pi$$
−0.795293 + 0.606226i $$0.792683\pi$$
$$432$$ 8.77590e11 + 3.65767e12i 0.0583274 + 0.243101i
$$433$$ 2.06339e13 1.35563 0.677816 0.735232i $$-0.262927\pi$$
0.677816 + 0.735232i $$0.262927\pi$$
$$434$$ 2.19839e13i 1.42776i
$$435$$ −3.51354e12 + 2.41455e12i −0.225579 + 0.155021i
$$436$$ 2.41953e12 0.153567
$$437$$ 1.07606e12i 0.0675195i
$$438$$ 6.80715e12 + 9.90545e12i 0.422275 + 0.614474i
$$439$$ 1.95313e13 1.19787 0.598935 0.800798i $$-0.295591\pi$$
0.598935 + 0.800798i $$0.295591\pi$$
$$440$$ 2.62633e12i 0.159253i
$$441$$ 5.43969e12 1.41669e13i 0.326123 0.849343i
$$442$$ −1.02659e13 −0.608535
$$443$$ 2.97469e13i 1.74351i −0.489946 0.871753i $$-0.662984\pi$$
0.489946 0.871753i $$-0.337016\pi$$
$$444$$ 5.14349e12 3.53467e12i 0.298087 0.204849i
$$445$$ −8.66747e11 −0.0496698
$$446$$ 1.37068e13i 0.776713i
$$447$$ 4.65839e12 + 6.77868e12i 0.261035 + 0.379846i
$$448$$ 3.11741e12 0.172744
$$449$$ 1.37505e13i 0.753509i −0.926313 0.376754i $$-0.877040\pi$$
0.926313 0.376754i $$-0.122960\pi$$
$$450$$ 4.25930e12 + 1.63545e12i 0.230821 + 0.0886285i
$$451$$ 9.31887e12 0.499437
$$452$$ 6.76651e12i 0.358651i
$$453$$ −2.45102e13 + 1.68437e13i −1.28486 + 0.882971i
$$454$$ −1.51737e13 −0.786704
$$455$$ 1.43485e13i 0.735783i
$$456$$ −1.22266e12 1.77916e12i −0.0620129 0.0902383i
$$457$$ 4.10224e11 0.0205798 0.0102899 0.999947i $$-0.496725\pi$$
0.0102899 + 0.999947i $$0.496725\pi$$
$$458$$ 7.99554e12i 0.396753i
$$459$$ −3.72021e13 + 8.92594e12i −1.82601 + 0.438118i
$$460$$ −2.60840e12 −0.126644
$$461$$ 2.10914e11i 0.0101298i −0.999987 0.00506490i $$-0.998388\pi$$
0.999987 0.00506490i $$-0.00161221\pi$$
$$462$$ −6.57226e12 + 4.51654e12i −0.312252 + 0.214583i
$$463$$ −1.96738e13 −0.924660 −0.462330 0.886708i $$-0.652987\pi$$
−0.462330 + 0.886708i $$0.652987\pi$$
$$464$$ 1.26680e12i 0.0589003i
$$465$$ 2.09003e13 + 3.04132e13i 0.961365 + 1.39893i
$$466$$ 2.54309e13 1.15726
$$467$$ 1.21902e13i 0.548815i −0.961614 0.274407i $$-0.911518\pi$$
0.961614 0.274407i $$-0.0884817\pi$$
$$468$$ 1.84406e12 4.80261e12i 0.0821385 0.213919i
$$469$$ −1.21264e13 −0.534402
$$470$$ 1.27378e13i 0.555399i
$$471$$ 3.18370e13 2.18788e13i 1.37350 0.943885i
$$472$$ 3.38319e12 0.144416
$$473$$ 1.24085e13i 0.524101i
$$474$$ 6.12218e12 + 8.90872e12i 0.255867 + 0.372326i
$$475$$ −2.61849e12 −0.108289
$$476$$ 3.17071e13i 1.29754i
$$477$$ −2.32374e12 8.92250e11i −0.0941014 0.0361322i
$$478$$ 5.98729e12 0.239933
$$479$$ 5.00886e12i 0.198637i 0.995056 + 0.0993187i $$0.0316663\pi$$
−0.995056 + 0.0993187i $$0.968334\pi$$
$$480$$ −4.31273e12 + 2.96376e12i −0.169257 + 0.116315i
$$481$$ −8.53558e12 −0.331518
$$482$$ 2.00653e13i 0.771276i
$$483$$ −4.48569e12 6.52737e12i −0.170645 0.248315i
$$484$$ −1.12836e13 −0.424837
$$485$$ 3.20975e13i 1.19608i
$$486$$ 2.50686e12 1.90074e13i 0.0924590 0.701036i
$$487$$ −4.17000e13 −1.52227 −0.761134 0.648595i $$-0.775357\pi$$
−0.761134 + 0.648595i $$0.775357\pi$$
$$488$$ 6.14859e12i 0.222166i
$$489$$ 1.84414e13 1.26732e13i 0.659553 0.453253i
$$490$$ 2.11118e13 0.747386
$$491$$ 2.10340e12i 0.0737081i −0.999321 0.0368540i $$-0.988266\pi$$
0.999321 0.0368540i $$-0.0117337\pi$$
$$492$$ 1.05161e13 + 1.53026e13i 0.364780 + 0.530811i
$$493$$ 1.28846e13 0.442421
$$494$$ 2.95250e12i 0.100359i
$$495$$ 4.79835e12 1.24966e13i 0.161460 0.420501i
$$496$$ −1.09654e13 −0.365272
$$497$$ 1.32708e13i 0.437639i
$$498$$ −9.90410e12 + 6.80622e12i −0.323347 + 0.222208i
$$499$$ 2.74482e13 0.887179 0.443589 0.896230i $$-0.353705\pi$$
0.443589 + 0.896230i $$0.353705\pi$$
$$500$$ 1.18051e13i 0.377763i
$$501$$ −2.92342e13 4.25403e13i −0.926197 1.34776i
$$502$$ 1.94481e13 0.610041
$$503$$ 2.26985e13i 0.704949i 0.935822 + 0.352474i $$0.114660\pi$$
−0.935822 + 0.352474i $$0.885340\pi$$
$$504$$ −1.48333e13 5.69556e12i −0.456127 0.175139i
$$505$$ 6.09659e13 1.85622
$$506$$ 1.98270e12i 0.0597729i
$$507$$ 2.18101e13 1.49882e13i 0.651055 0.447413i
$$508$$ 1.62721e13 0.480976
$$509$$ 4.21460e13i 1.23358i 0.787127 + 0.616791i $$0.211567\pi$$
−0.787127 + 0.616791i $$0.788433\pi$$
$$510$$ −3.01443e13 4.38647e13i −0.873685 1.27135i
$$511$$ −5.07703e13 −1.45715
$$512$$ 1.55494e12i 0.0441942i
$$513$$ 2.56713e12 + 1.06994e13i 0.0722539 + 0.301144i
$$514$$ −4.93051e13 −1.37428
$$515$$ 3.03822e13i 0.838653i
$$516$$ −2.03762e13 + 1.40028e13i −0.557025 + 0.382795i
$$517$$ 9.68227e12 0.262135
$$518$$ 2.63629e13i 0.706878i
$$519$$ 4.18569e13 + 6.09083e13i 1.11155 + 1.61748i
$$520$$ 7.15694e12 0.188239
$$521$$ 6.54420e13i 1.70478i 0.522907 + 0.852390i $$0.324848\pi$$
−0.522907 + 0.852390i $$0.675152\pi$$
$$522$$ −2.31446e12 + 6.02770e12i −0.0597169 + 0.155525i
$$523$$ −6.14531e13 −1.57049 −0.785245 0.619185i $$-0.787463\pi$$
−0.785245 + 0.619185i $$0.787463\pi$$
$$524$$ 2.56560e13i 0.649430i
$$525$$ −1.58837e13 + 1.09155e13i −0.398250 + 0.273682i
$$526$$ 3.12126e13 0.775178
$$527$$ 1.11529e14i 2.74369i
$$528$$ 2.25282e12 + 3.27820e12i 0.0548980 + 0.0798851i
$$529$$ 3.94574e13 0.952466
$$530$$ 3.46288e12i 0.0828053i
$$531$$ −1.60979e13 6.18114e12i −0.381327 0.146418i
$$532$$ 9.11907e12 0.213990
$$533$$ 2.53946e13i 0.590343i
$$534$$ −1.08188e12 + 7.43479e11i −0.0249156 + 0.0171223i
$$535$$ −5.21173e13 −1.18909
$$536$$ 6.04857e12i 0.136719i
$$537$$ 9.73183e11 + 1.41613e12i 0.0217933 + 0.0317126i
$$538$$ −2.67296e13 −0.593036
$$539$$ 1.60475e13i 0.352748i
$$540$$ 2.59357e13 6.22278e12i 0.564845 0.135524i
$$541$$ 1.50207e13 0.324118 0.162059 0.986781i $$-0.448187\pi$$
0.162059 + 0.986781i $$0.448187\pi$$
$$542$$ 3.21877e13i 0.688166i
$$543$$ 2.54960e13 1.75211e13i 0.540098 0.371162i
$$544$$ 1.58153e13 0.331958
$$545$$ 1.71563e13i 0.356814i
$$546$$ 1.23079e13 + 1.79099e13i 0.253641 + 0.369087i
$$547$$ 7.15097e13 1.46025 0.730127 0.683312i $$-0.239461\pi$$
0.730127 + 0.683312i $$0.239461\pi$$
$$548$$ 1.40669e13i 0.284639i
$$549$$ −1.12336e13 + 2.92563e13i −0.225245 + 0.586621i
$$550$$ 4.82470e12 0.0958644
$$551$$ 3.70565e12i 0.0729636i
$$552$$ −3.25581e12 + 2.23743e12i −0.0635278 + 0.0436571i
$$553$$ −4.56616e13 −0.882928
$$554$$ 1.19916e13i 0.229789i
$$555$$ −2.50635e13 3.64713e13i −0.475967 0.692606i
$$556$$ −3.23834e13 −0.609464
$$557$$ 7.34107e13i 1.36925i −0.728895 0.684626i $$-0.759966\pi$$
0.728895 0.684626i $$-0.240034\pi$$
$$558$$ 5.21758e13 + 2.00340e13i 0.964490 + 0.370336i
$$559$$ 3.38141e13 0.619497
$$560$$ 2.21048e13i 0.401372i
$$561$$ −3.33425e13 + 2.29134e13i −0.600045 + 0.412358i
$$562$$ 5.16902e13 0.921991
$$563$$ 4.77347e13i 0.843902i 0.906619 + 0.421951i $$0.138655\pi$$
−0.906619 + 0.421951i $$0.861345\pi$$
$$564$$ 1.09262e13 + 1.58994e13i 0.191459 + 0.278602i
$$565$$ −4.79797e13 −0.833327
$$566$$ 5.23314e13i 0.900907i
$$567$$ 6.01742e13 + 5.42013e13i 1.02682 + 0.924900i
$$568$$ 6.61939e12 0.111963
$$569$$ 1.90951e13i 0.320156i 0.987104 + 0.160078i $$0.0511745\pi$$
−0.987104 + 0.160078i $$0.948825\pi$$
$$570$$ −1.26156e13 + 8.66961e12i −0.209669 + 0.144087i
$$571$$ −2.09448e13 −0.345060 −0.172530 0.985004i $$-0.555194\pi$$
−0.172530 + 0.985004i $$0.555194\pi$$
$$572$$ 5.44014e12i 0.0888444i
$$573$$ −2.84145e13 4.13475e13i −0.460009 0.669385i
$$574$$ −7.84334e13 −1.25876
$$575$$ 4.79175e12i 0.0762351i
$$576$$ −2.84091e12 + 7.39876e12i −0.0448069 + 0.116693i
$$577$$ 3.56688e13 0.557711 0.278855 0.960333i $$-0.410045\pi$$
0.278855 + 0.960333i $$0.410045\pi$$
$$578$$ 1.15240e14i 1.78635i
$$579$$ −6.24051e13 + 4.28856e13i −0.959019 + 0.659050i
$$580$$ −8.98258e12 −0.136855
$$581$$ 5.07634e13i 0.766778i
$$582$$ −2.75326e13 4.00642e13i −0.412318 0.599986i
$$583$$ −2.63221e12 −0.0390821
$$584$$ 2.53239e13i 0.372792i
$$585$$ −3.40542e13 1.30758e13i −0.497040 0.190849i
$$586$$ −2.39826e13 −0.347064
$$587$$ 1.29418e14i 1.85697i 0.371375 + 0.928483i $$0.378886\pi$$
−0.371375 + 0.928483i $$0.621114\pi$$
$$588$$ 2.63518e13 1.81093e13i 0.374908 0.257641i
$$589$$ −3.20761e13 −0.452486
$$590$$ 2.39894e13i 0.335552i
$$591$$ −2.08773e13 3.03797e13i −0.289559 0.421352i
$$592$$ 1.31496e13 0.180845
$$593$$ 3.96596e13i 0.540848i −0.962741 0.270424i $$-0.912836\pi$$
0.962741 0.270424i $$-0.0871639\pi$$
$$594$$ −4.73007e12 1.97143e13i −0.0639640 0.266593i
$$595$$ 2.24828e14 3.01485
$$596$$ 1.73301e13i 0.230446i
$$597$$ 2.23684e13 1.53718e13i 0.294960 0.202700i
$$598$$ 5.40299e12 0.0706526
$$599$$ 4.57555e13i 0.593347i 0.954979 + 0.296674i $$0.0958774\pi$$
−0.954979 + 0.296674i $$0.904123\pi$$
$$600$$ 5.44458e12 + 7.92270e12i 0.0700177 + 0.101887i
$$601$$ 1.06033e14 1.35229 0.676143 0.736770i $$-0.263650\pi$$
0.676143 + 0.736770i $$0.263650\pi$$
$$602$$ 1.04438e14i 1.32092i
$$603$$ 1.10508e13 2.87804e13i 0.138614 0.361003i
$$604$$ −6.26617e13 −0.779503
$$605$$ 8.00096e13i 0.987109i
$$606$$ 7.60979e13 5.22954e13i 0.931128 0.639883i
$$607$$ −9.55067e13 −1.15902 −0.579509 0.814966i $$-0.696756\pi$$
−0.579509 + 0.814966i $$0.696756\pi$$
$$608$$ 4.54853e12i 0.0547461i
$$609$$ −1.54475e13 2.24784e13i −0.184404 0.268336i
$$610$$ −4.35983e13 −0.516202
$$611$$ 2.63849e13i 0.309848i
$$612$$ −7.52526e13 2.88948e13i −0.876525 0.336560i
$$613$$ −5.18411e13 −0.598924 −0.299462 0.954108i $$-0.596807\pi$$
−0.299462 + 0.954108i $$0.596807\pi$$
$$614$$ 1.55950e13i 0.178708i
$$615$$ 1.08507e14 7.45675e13i 1.23334 0.847567i
$$616$$ −1.68024e13 −0.189438
$$617$$ 8.05443e13i 0.900760i −0.892837 0.450380i $$-0.851289\pi$$
0.892837 0.450380i $$-0.148711\pi$$
$$618$$ 2.60612e13 + 3.79231e13i 0.289103 + 0.420690i
$$619$$ −5.14946e13 −0.566642 −0.283321 0.959025i $$-0.591436\pi$$
−0.283321 + 0.959025i $$0.591436\pi$$
$$620$$ 7.77532e13i 0.848711i
$$621$$ 1.95797e13 4.69777e12i 0.212005 0.0508667i
$$622$$ 4.42759e13 0.475571
$$623$$ 5.54515e12i 0.0590844i
$$624$$ 8.93332e12 6.13909e12i 0.0944256 0.0648905i
$$625$$ −1.17054e14 −1.22740
$$626$$ 5.63017e12i 0.0585665i
$$627$$ 6.58996e12 + 9.58941e12i 0.0680057 + 0.0989587i
$$628$$ 8.13933e13 0.833279
$$629$$ 1.33745e14i 1.35839i
$$630$$ −4.03859e13 + 1.05180e14i −0.406937 + 1.05981i
$$631$$ −1.02922e13 −0.102887 −0.0514435 0.998676i $$-0.516382\pi$$
−0.0514435 + 0.998676i $$0.516382\pi$$
$$632$$ 2.27757e13i 0.225884i
$$633$$ −3.06543e13 + 2.10660e13i −0.301629 + 0.207283i
$$634$$ 1.04918e14 1.02424
$$635$$ 1.15381e14i 1.11755i
$$636$$ −2.97040e12 4.32238e12i −0.0285449 0.0415372i
$$637$$ −4.37307e13 −0.416955
$$638$$ 6.82785e12i 0.0645923i
$$639$$ −3.14965e13 1.20937e13i −0.295636 0.113516i
$$640$$ −1.10257e13 −0.102685
$$641$$ 4.62451e13i 0.427342i 0.976906 + 0.213671i $$0.0685420\pi$$
−0.976906 + 0.213671i $$0.931458\pi$$
$$642$$ −6.50531e13 + 4.47053e13i −0.596476 + 0.409906i
$$643$$ 2.73102e13 0.248468 0.124234 0.992253i $$-0.460353\pi$$
0.124234 + 0.992253i $$0.460353\pi$$
$$644$$ 1.66876e13i 0.150649i
$$645$$ 9.92905e13 + 1.44483e14i 0.889424 + 1.29425i
$$646$$ 4.62630e13 0.411217
$$647$$ 1.34984e13i 0.119059i −0.998227 0.0595293i $$-0.981040\pi$$
0.998227 0.0595293i $$-0.0189600\pi$$
$$648$$ 2.70353e13 3.00145e13i 0.236622 0.262697i
$$649$$ −1.82349e13 −0.158372
$$650$$ 1.31476e13i 0.113313i
$$651$$ −1.94573e14 + 1.33713e14i −1.66410 + 1.14359i
$$652$$ 4.71466e13 0.400140
$$653$$ 8.41840e13i 0.709029i −0.935051 0.354514i $$-0.884646\pi$$
0.935051 0.354514i $$-0.115354\pi$$
$$654$$ −1.47164e13 2.14146e13i −0.123002 0.178987i
$$655$$ −1.81921e14 −1.50895
$$656$$ 3.91220e13i 0.322034i
$$657$$ 4.62671e13 1.20496e14i 0.377960 0.984345i
$$658$$ −8.14920e13 −0.660672
$$659$$ 1.65464e14i 1.33130i −0.746264 0.665650i $$-0.768154\pi$$
0.746264 0.665650i $$-0.231846\pi$$
$$660$$ 2.32449e13 1.59742e13i 0.185613 0.127556i
$$661$$ 2.01681e14 1.59830 0.799148 0.601135i $$-0.205284\pi$$
0.799148 + 0.601135i $$0.205284\pi$$
$$662$$ 3.20050e13i 0.251726i
$$663$$ 6.24405e13 + 9.08606e13i 0.487415 + 0.709264i
$$664$$ −2.53204e13 −0.196169
$$665$$ 6.46612e13i 0.497205i
$$666$$ −6.25688e13 2.40246e13i −0.477515 0.183352i
$$667$$ −6.78122e12 −0.0513664
$$668$$ 1.08757e14i 0.817663i
$$669$$ 1.21315e14 8.33691e13i 0.905281 0.622120i
$$670$$ 4.28890e13 0.317667
$$671$$ 3.31400e13i 0.243635i
$$672$$ −1.89611e13 2.75914e13i −0.138362 0.201338i
$$673$$ 6.04368e12 0.0437750 0.0218875 0.999760i $$-0.493032\pi$$
0.0218875 + 0.999760i $$0.493032\pi$$
$$674$$ 1.96351e13i 0.141167i
$$675$$ −1.14316e13 4.76452e13i −0.0815806 0.340017i
$$676$$ 5.57588e13 0.394984
$$677$$ 1.21474e14i 0.854164i 0.904213 + 0.427082i $$0.140458\pi$$
−0.904213 + 0.427082i $$0.859542\pi$$
$$678$$ −5.98885e13 + 4.11561e13i −0.418018 + 0.287267i
$$679$$ 2.05349e14 1.42280
$$680$$ 1.12143e14i 0.771305i
$$681$$ 9.22913e13 + 1.34298e14i 0.630123 + 0.916926i
$$682$$ 5.91019e13 0.400571
$$683$$ 1.51629e14i 1.02019i −0.860119 0.510094i $$-0.829611\pi$$
0.860119 0.510094i $$-0.170389\pi$$
$$684$$ −8.31024e12 + 2.16429e13i −0.0555051 + 0.144556i
$$685$$ −9.97450e13 −0.661360
$$686$$ 1.33906e13i 0.0881410i
$$687$$ −7.07663e13 + 4.86315e13i −0.462427 + 0.317785i
$$688$$ −5.20930e13 −0.337938
$$689$$ 7.17296e12i 0.0461958i
$$690$$ 1.58651e13 + 2.30862e13i 0.101437 + 0.147607i
$$691$$ 6.62249e13 0.420369 0.210185 0.977662i $$-0.432593\pi$$
0.210185 + 0.977662i $$0.432593\pi$$
$$692$$ 1.55716e14i 0.981300i
$$693$$ 7.99493e13 + 3.06982e13i 0.500205 + 0.192064i
$$694$$ −1.17824e14 −0.731873
$$695$$ 2.29623e14i 1.41609i
$$696$$ −1.12121e13 + 7.70509e12i −0.0686500 + 0.0471771i
$$697$$ −3.97909e14 −2.41891
$$698$$ 2.53321e13i 0.152895i
$$699$$ −1.54679e14 2.25082e14i −0.926928 1.34882i
$$700$$ −4.06077e13 −0.241612
$$701$$ 5.78990e13i 0.342043i 0.985267 + 0.171022i $$0.0547068\pi$$
−0.985267 + 0.171022i $$0.945293\pi$$
$$702$$ −5.37228e13 + 1.28898e13i −0.315118 + 0.0756066i
$$703$$ 3.84654e13 0.224024
$$704$$ 8.38091e12i 0.0484650i
$$705$$ 1.12739e14 7.74754e13i 0.647332 0.444855i
$$706$$ −8.46157e13 −0.482422
$$707$$ 3.90039e14i 2.20806i
$$708$$ −2.05777e13 2.99437e13i −0.115672 0.168321i
$$709$$ 2.70077e14 1.50750 0.753750 0.657162i $$-0.228243\pi$$
0.753750 + 0.657162i $$0.228243\pi$$
$$710$$ 4.69366e13i 0.260148i
$$711$$ 4.16115e13 1.08372e14i 0.229016 0.596441i
$$712$$ −2.76588e12 −0.0151159
$$713$$ 5.86983e13i 0.318550i
$$714$$ 2.80631e14 1.92853e14i 1.51232 1.03929i
$$715$$ −3.85748e13 −0.206430
$$716$$ 3.62043e12i 0.0192395i
$$717$$ −3.64166e13 5.29918e13i −0.192178 0.279649i
$$718$$ −8.02117e13 −0.420354
$$719$$ 1.48102e14i 0.770755i −0.922759 0.385377i $$-0.874071\pi$$
0.922759 0.385377i $$-0.125929\pi$$
$$720$$ 5.24629e13 + 2.01442e13i 0.271137 + 0.104109i
$$721$$ −1.94375e14 −0.997616
$$722$$ 1.25425e14i 0.639289i
$$723$$ −1.77592e14 + 1.22044e14i −0.898944 + 0.617765i
$$724$$ 6.51820e13 0.327669
$$725$$ 1.65014e13i 0.0823819i
$$726$$ 6.86307e13 + 9.98683e13i 0.340279 + 0.495159i
$$727$$ 5.21602e13 0.256842 0.128421 0.991720i $$-0.459009\pi$$
0.128421 + 0.991720i $$0.459009\pi$$
$$728$$ 4.57876e13i 0.223919i
$$729$$ −1.83476e14 + 9.34214e13i −0.891133 + 0.453742i
$$730$$ 1.79566e14 0.866183
$$731$$ 5.29837e14i 2.53837i
$$732$$ −5.44195e13 + 3.73978e13i −0.258940 + 0.177947i
$$733$$ 3.21782e14 1.52069 0.760346 0.649518i $$-0.225029\pi$$
0.760346 + 0.649518i $$0.225029\pi$$
$$734$$ 2.28902e14i 1.07441i
$$735$$ −1.28409e14 1.86855e14i −0.598630 0.871099i
$$736$$ −8.32367e12 −0.0385413
$$737$$ 3.26009e13i 0.149931i
$$738$$ 7.14765e13 1.86151e14i 0.326499 0.850322i
$$739$$ 1.66542e14 0.755617 0.377809 0.925884i $$-0.376678\pi$$
0.377809 + 0.925884i $$0.376678\pi$$
$$740$$ 9.32411e13i 0.420193i
$$741$$ 2.61318e13 1.79581e13i 0.116971 0.0803839i
$$742$$ 2.21543e13 0.0985007
$$743$$ 1.13631e14i 0.501825i 0.968010 + 0.250912i $$0.0807306\pi$$
−0.968010 + 0.250912i $$0.919269\pi$$
$$744$$ 6.66953e13 + 9.70519e13i 0.292570 + 0.425735i
$$745$$ 1.22884e14 0.535443
$$746$$ 8.62230e13i 0.373189i
$$747$$ 1.20480e14 + 4.62608e13i 0.517979 + 0.198889i
$$748$$ −8.52421e13 −0.364037
$$749$$ 3.33429e14i 1.41447i
$$750$$ −1.04484e14 + 7.18025e13i −0.440293 + 0.302575i
$$751$$ −1.64956e14 −0.690508 −0.345254 0.938509i $$-0.612207\pi$$
−0.345254 + 0.938509i $$0.612207\pi$$
$$752$$ 4.06477e13i 0.169023i
$$753$$ −1.18290e14 1.72130e14i −0.488622 0.711020i
$$754$$ 1.86064e13 0.0763493
$$755$$ 4.44320e14i 1.81118i
$$756$$ 3.98112e13 + 1.65928e14i 0.161212 + 0.671909i
$$757$$ −2.67990e14 −1.07805 −0.539026 0.842289i $$-0.681207\pi$$
−0.539026 + 0.842289i $$0.681207\pi$$
$$758$$ 2.51282e14i 1.00419i
$$759$$ 1.75483e13 1.20594e13i 0.0696669 0.0478760i
$$760$$ −3.22526e13 −0.127203
$$761$$ 1.29795e14i 0.508550i −0.967132 0.254275i $$-0.918163\pi$$
0.967132 0.254275i $$-0.0818368\pi$$
$$762$$ −9.89720e13 1.44020e14i −0.385245 0.560591i
$$763$$ 1.09760e14 0.424446
$$764$$ 1.05707e14i 0.406105i
$$765$$ −2.04886e14 + 5.33599e14i −0.781998 + 2.03661i
$$766$$ −9.71099e13 −0.368230
$$767$$ 4.96913e13i 0.187199i
$$768$$ −1.37624e13 + 9.45768e12i −0.0515095 + 0.0353980i
$$769$$ −2.19185e14 −0.815041