# Properties

 Label 150.11.b.a.149.2 Level $150$ Weight $11$ Character 150.149 Analytic conductor $95.304$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$11$$ Character orbit: $$[\chi]$$ $$=$$ 150.b (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$95.3035879011$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.3421020160000.10 Defining polynomial: $$x^{8} + 967 x^{4} + 194481$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{26}\cdot 3^{8}$$ Twist minimal: no (minimal twist has level 6) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 149.2 Root $$-3.61315 + 3.61315i$$ of defining polynomial Character $$\chi$$ $$=$$ 150.149 Dual form 150.11.b.a.149.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-22.6274 q^{2} +(-137.627 + 200.269i) q^{3} +512.000 q^{4} +(3114.15 - 4531.57i) q^{6} -23226.5i q^{7} -11585.2 q^{8} +(-21166.4 - 55125.0i) q^{9} +O(q^{10})$$ $$q-22.6274 q^{2} +(-137.627 + 200.269i) q^{3} +512.000 q^{4} +(3114.15 - 4531.57i) q^{6} -23226.5i q^{7} -11585.2 q^{8} +(-21166.4 - 55125.0i) q^{9} +62442.7i q^{11} +(-70465.2 + 102538. i) q^{12} +170161. i q^{13} +525556. i q^{14} +262144. q^{16} +2.66626e6 q^{17} +(478941. + 1.24734e6i) q^{18} -766825. q^{19} +(4.65156e6 + 3.19661e6i) q^{21} -1.41292e6i q^{22} +1.40327e6 q^{23} +(1.59445e6 - 2.32016e6i) q^{24} -3.85029e6i q^{26} +(1.39529e7 + 3.34774e6i) q^{27} -1.18920e7i q^{28} -4.83245e6i q^{29} -4.18297e7 q^{31} -5.93164e6 q^{32} +(-1.25053e7 - 8.59382e6i) q^{33} -6.03306e7 q^{34} +(-1.08372e7 - 2.82240e7i) q^{36} +5.01619e7i q^{37} +1.73513e7 q^{38} +(-3.40779e7 - 2.34188e7i) q^{39} -1.49239e8i q^{41} +(-1.05253e8 - 7.23310e7i) q^{42} +1.98719e8i q^{43} +3.19706e7i q^{44} -3.17523e7 q^{46} +1.55059e8 q^{47} +(-3.60782e7 + 5.24993e7i) q^{48} -2.56996e8 q^{49} +(-3.66951e8 + 5.33970e8i) q^{51} +8.71222e7i q^{52} +4.21541e7 q^{53} +(-3.15718e8 - 7.57507e7i) q^{54} +2.69085e8i q^{56} +(1.05536e8 - 1.53571e8i) q^{57} +1.09346e8i q^{58} -2.92026e8i q^{59} -5.30727e8 q^{61} +9.46499e8 q^{62} +(-1.28036e9 + 4.91622e8i) q^{63} +1.34218e8 q^{64} +(2.82963e8 + 1.94456e8i) q^{66} +5.22093e8i q^{67} +1.36513e9 q^{68} +(-1.93128e8 + 2.81031e8i) q^{69} +5.71364e8i q^{71} +(2.45218e8 + 6.38636e8i) q^{72} -2.18588e9i q^{73} -1.13503e9i q^{74} -3.92615e8 q^{76} +1.45033e9 q^{77} +(7.71095e8 + 5.29906e8i) q^{78} -1.96592e9 q^{79} +(-2.59075e9 + 2.33360e9i) q^{81} +3.37689e9i q^{82} -2.18558e9 q^{83} +(2.38160e9 + 1.63666e9i) q^{84} -4.49650e9i q^{86} +(9.67791e8 + 6.65078e8i) q^{87} -7.23413e8i q^{88} +2.38742e8i q^{89} +3.95224e9 q^{91} +7.18473e8 q^{92} +(5.75692e9 - 8.37720e9i) q^{93} -3.50858e9 q^{94} +(8.16356e8 - 1.18792e9i) q^{96} -8.84112e9i q^{97} +5.81517e9 q^{98} +(3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + O(q^{10})$$ $$8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + 2097152 q^{16} + 3137456 q^{19} + 19256016 q^{21} + 5505024 q^{24} - 43571696 q^{31} - 302174208 q^{34} - 162828288 q^{36} - 434574480 q^{39} + 377628672 q^{46} + 100116840 q^{49} - 1417153536 q^{51} - 963325440 q^{54} - 2368077488 q^{61} + 1073741824 q^{64} + 6246890496 q^{66} - 1192536576 q^{69} + 1606377472 q^{76} - 398565136 q^{79} + 2917929096 q^{81} + 9859080192 q^{84} + 16634464160 q^{91} - 17010954240 q^{94} + 2818572288 q^{96} + 5253825024 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −22.6274 −0.707107
$$3$$ −137.627 + 200.269i −0.566368 + 0.824153i
$$4$$ 512.000 0.500000
$$5$$ 0 0
$$6$$ 3114.15 4531.57i 0.400483 0.582764i
$$7$$ 23226.5i 1.38196i −0.722876 0.690978i $$-0.757180\pi$$
0.722876 0.690978i $$-0.242820\pi$$
$$8$$ −11585.2 −0.353553
$$9$$ −21166.4 55125.0i −0.358455 0.933547i
$$10$$ 0 0
$$11$$ 62442.7i 0.387720i 0.981029 + 0.193860i $$0.0621007\pi$$
−0.981029 + 0.193860i $$0.937899\pi$$
$$12$$ −70465.2 + 102538.i −0.283184 + 0.412076i
$$13$$ 170161.i 0.458292i 0.973392 + 0.229146i $$0.0735933\pi$$
−0.973392 + 0.229146i $$0.926407\pi$$
$$14$$ 525556.i 0.977190i
$$15$$ 0 0
$$16$$ 262144. 0.250000
$$17$$ 2.66626e6 1.87784 0.938919 0.344139i $$-0.111829\pi$$
0.938919 + 0.344139i $$0.111829\pi$$
$$18$$ 478941. + 1.24734e6i 0.253466 + 0.660117i
$$19$$ −766825. −0.309691 −0.154845 0.987939i $$-0.549488\pi$$
−0.154845 + 0.987939i $$0.549488\pi$$
$$20$$ 0 0
$$21$$ 4.65156e6 + 3.19661e6i 1.13894 + 0.782695i
$$22$$ 1.41292e6i 0.274159i
$$23$$ 1.40327e6 0.218022 0.109011 0.994041i $$-0.465232\pi$$
0.109011 + 0.994041i $$0.465232\pi$$
$$24$$ 1.59445e6 2.32016e6i 0.200241 0.291382i
$$25$$ 0 0
$$26$$ 3.85029e6i 0.324061i
$$27$$ 1.39529e7 + 3.34774e6i 0.972402 + 0.233310i
$$28$$ 1.18920e7i 0.690978i
$$29$$ 4.83245e6i 0.235601i −0.993037 0.117801i $$-0.962416\pi$$
0.993037 0.117801i $$-0.0375844\pi$$
$$30$$ 0 0
$$31$$ −4.18297e7 −1.46109 −0.730544 0.682865i $$-0.760734\pi$$
−0.730544 + 0.682865i $$0.760734\pi$$
$$32$$ −5.93164e6 −0.176777
$$33$$ −1.25053e7 8.59382e6i −0.319540 0.219592i
$$34$$ −6.03306e7 −1.32783
$$35$$ 0 0
$$36$$ −1.08372e7 2.82240e7i −0.179227 0.466774i
$$37$$ 5.01619e7i 0.723378i 0.932299 + 0.361689i $$0.117800\pi$$
−0.932299 + 0.361689i $$0.882200\pi$$
$$38$$ 1.73513e7 0.218985
$$39$$ −3.40779e7 2.34188e7i −0.377702 0.259562i
$$40$$ 0 0
$$41$$ 1.49239e8i 1.28814i −0.764967 0.644069i $$-0.777245\pi$$
0.764967 0.644069i $$-0.222755\pi$$
$$42$$ −1.05253e8 7.23310e7i −0.805354 0.553449i
$$43$$ 1.98719e8i 1.35175i 0.737015 + 0.675876i $$0.236235\pi$$
−0.737015 + 0.675876i $$0.763765\pi$$
$$44$$ 3.19706e7i 0.193860i
$$45$$ 0 0
$$46$$ −3.17523e7 −0.154165
$$47$$ 1.55059e8 0.676093 0.338047 0.941129i $$-0.390234\pi$$
0.338047 + 0.941129i $$0.390234\pi$$
$$48$$ −3.60782e7 + 5.24993e7i −0.141592 + 0.206038i
$$49$$ −2.56996e8 −0.909802
$$50$$ 0 0
$$51$$ −3.66951e8 + 5.33970e8i −1.06355 + 1.54762i
$$52$$ 8.71222e7i 0.229146i
$$53$$ 4.21541e7 0.100800 0.0503999 0.998729i $$-0.483950\pi$$
0.0503999 + 0.998729i $$0.483950\pi$$
$$54$$ −3.15718e8 7.57507e7i −0.687592 0.164975i
$$55$$ 0 0
$$56$$ 2.69085e8i 0.488595i
$$57$$ 1.05536e8 1.53571e8i 0.175399 0.255233i
$$58$$ 1.09346e8i 0.166595i
$$59$$ 2.92026e8i 0.408471i −0.978922 0.204236i $$-0.934529\pi$$
0.978922 0.204236i $$-0.0654708\pi$$
$$60$$ 0 0
$$61$$ −5.30727e8 −0.628379 −0.314190 0.949360i $$-0.601733\pi$$
−0.314190 + 0.949360i $$0.601733\pi$$
$$62$$ 9.46499e8 1.03315
$$63$$ −1.28036e9 + 4.91622e8i −1.29012 + 0.495369i
$$64$$ 1.34218e8 0.125000
$$65$$ 0 0
$$66$$ 2.82963e8 + 1.94456e8i 0.225949 + 0.155275i
$$67$$ 5.22093e8i 0.386700i 0.981130 + 0.193350i $$0.0619353\pi$$
−0.981130 + 0.193350i $$0.938065\pi$$
$$68$$ 1.36513e9 0.938919
$$69$$ −1.93128e8 + 2.81031e8i −0.123481 + 0.179684i
$$70$$ 0 0
$$71$$ 5.71364e8i 0.316681i 0.987385 + 0.158340i $$0.0506143\pi$$
−0.987385 + 0.158340i $$0.949386\pi$$
$$72$$ 2.45218e8 + 6.38636e8i 0.126733 + 0.330059i
$$73$$ 2.18588e9i 1.05441i −0.849737 0.527207i $$-0.823239\pi$$
0.849737 0.527207i $$-0.176761\pi$$
$$74$$ 1.13503e9i 0.511506i
$$75$$ 0 0
$$76$$ −3.92615e8 −0.154845
$$77$$ 1.45033e9 0.535812
$$78$$ 7.71095e8 + 5.29906e8i 0.267076 + 0.183538i
$$79$$ −1.96592e9 −0.638897 −0.319449 0.947604i $$-0.603498\pi$$
−0.319449 + 0.947604i $$0.603498\pi$$
$$80$$ 0 0
$$81$$ −2.59075e9 + 2.33360e9i −0.743020 + 0.669269i
$$82$$ 3.37689e9i 0.910851i
$$83$$ −2.18558e9 −0.554850 −0.277425 0.960747i $$-0.589481\pi$$
−0.277425 + 0.960747i $$0.589481\pi$$
$$84$$ 2.38160e9 + 1.63666e9i 0.569471 + 0.391348i
$$85$$ 0 0
$$86$$ 4.49650e9i 0.955833i
$$87$$ 9.67791e8 + 6.65078e8i 0.194171 + 0.133437i
$$88$$ 7.23413e8i 0.137080i
$$89$$ 2.38742e8i 0.0427542i 0.999771 + 0.0213771i $$0.00680506\pi$$
−0.999771 + 0.0213771i $$0.993195\pi$$
$$90$$ 0 0
$$91$$ 3.95224e9 0.633339
$$92$$ 7.18473e8 0.109011
$$93$$ 5.75692e9 8.37720e9i 0.827514 1.20416i
$$94$$ −3.50858e9 −0.478070
$$95$$ 0 0
$$96$$ 8.16356e8 1.18792e9i 0.100121 0.145691i
$$97$$ 8.84112e9i 1.02955i −0.857324 0.514776i $$-0.827875\pi$$
0.857324 0.514776i $$-0.172125\pi$$
$$98$$ 5.81517e9 0.643327
$$99$$ 3.44215e9 1.32169e9i 0.361955 0.138980i
$$100$$ 0 0
$$101$$ 1.67928e10i 1.59778i 0.601477 + 0.798890i $$0.294579\pi$$
−0.601477 + 0.798890i $$0.705421\pi$$
$$102$$ 8.30314e9 1.20824e10i 0.752041 1.09434i
$$103$$ 8.36865e9i 0.721887i −0.932588 0.360944i $$-0.882455\pi$$
0.932588 0.360944i $$-0.117545\pi$$
$$104$$ 1.97135e9i 0.162031i
$$105$$ 0 0
$$106$$ −9.53837e8 −0.0712763
$$107$$ 1.43555e10 1.02353 0.511764 0.859126i $$-0.328992\pi$$
0.511764 + 0.859126i $$0.328992\pi$$
$$108$$ 7.14389e9 + 1.71404e9i 0.486201 + 0.116655i
$$109$$ 4.72564e9 0.307134 0.153567 0.988138i $$-0.450924\pi$$
0.153567 + 0.988138i $$0.450924\pi$$
$$110$$ 0 0
$$111$$ −1.00459e10 6.90365e9i −0.596174 0.409698i
$$112$$ 6.08870e9i 0.345489i
$$113$$ −1.32158e10 −0.717303 −0.358651 0.933472i $$-0.616763\pi$$
−0.358651 + 0.933472i $$0.616763\pi$$
$$114$$ −2.38801e9 + 3.47492e9i −0.124026 + 0.180477i
$$115$$ 0 0
$$116$$ 2.47422e9i 0.117801i
$$117$$ 9.38011e9 3.60169e9i 0.427837 0.164277i
$$118$$ 6.60779e9i 0.288833i
$$119$$ 6.19280e10i 2.59509i
$$120$$ 0 0
$$121$$ 2.20383e10 0.849673
$$122$$ 1.20090e10 0.444331
$$123$$ 2.98879e10 + 2.05393e10i 1.06162 + 0.729560i
$$124$$ −2.14168e10 −0.730544
$$125$$ 0 0
$$126$$ 2.89713e10 1.11241e10i 0.912253 0.350279i
$$127$$ 3.17814e10i 0.961953i −0.876733 0.480976i $$-0.840282\pi$$
0.876733 0.480976i $$-0.159718\pi$$
$$128$$ −3.03700e9 −0.0883883
$$129$$ −3.97973e10 2.73492e10i −1.11405 0.765589i
$$130$$ 0 0
$$131$$ 5.01094e10i 1.29886i −0.760421 0.649430i $$-0.775007\pi$$
0.760421 0.649430i $$-0.224993\pi$$
$$132$$ −6.40273e9 4.40004e9i −0.159770 0.109796i
$$133$$ 1.78107e10i 0.427979i
$$134$$ 1.18136e10i 0.273438i
$$135$$ 0 0
$$136$$ −3.08893e10 −0.663916
$$137$$ 2.74744e10 0.569279 0.284639 0.958635i $$-0.408126\pi$$
0.284639 + 0.958635i $$0.408126\pi$$
$$138$$ 4.36999e9 6.35900e9i 0.0873142 0.127056i
$$139$$ −6.32488e10 −1.21893 −0.609464 0.792814i $$-0.708615\pi$$
−0.609464 + 0.792814i $$0.708615\pi$$
$$140$$ 0 0
$$141$$ −2.13403e10 + 3.10534e10i −0.382917 + 0.557204i
$$142$$ 1.29285e10i 0.223927i
$$143$$ −1.06253e10 −0.177689
$$144$$ −5.54864e9 1.44507e10i −0.0896137 0.233387i
$$145$$ 0 0
$$146$$ 4.94607e10i 0.745583i
$$147$$ 3.53697e10 5.14684e10i 0.515282 0.749815i
$$148$$ 2.56829e10i 0.361689i
$$149$$ 3.38479e10i 0.460893i −0.973085 0.230446i $$-0.925981\pi$$
0.973085 0.230446i $$-0.0740186\pi$$
$$150$$ 0 0
$$151$$ 1.22386e11 1.55901 0.779503 0.626399i $$-0.215472\pi$$
0.779503 + 0.626399i $$0.215472\pi$$
$$152$$ 8.88385e9 0.109492
$$153$$ −5.64351e10 1.46978e11i −0.673120 1.75305i
$$154$$ −3.28171e10 −0.378876
$$155$$ 0 0
$$156$$ −1.74479e10 1.19904e10i −0.188851 0.129781i
$$157$$ 1.58971e11i 1.66656i −0.552853 0.833279i $$-0.686461\pi$$
0.552853 0.833279i $$-0.313539\pi$$
$$158$$ 4.44838e10 0.451769
$$159$$ −5.80155e9 + 8.44215e9i −0.0570898 + 0.0830745i
$$160$$ 0 0
$$161$$ 3.25930e10i 0.301297i
$$162$$ 5.86220e10 5.28033e10i 0.525395 0.473245i
$$163$$ 9.20831e10i 0.800280i 0.916454 + 0.400140i $$0.131038\pi$$
−0.916454 + 0.400140i $$0.868962\pi$$
$$164$$ 7.64102e10i 0.644069i
$$165$$ 0 0
$$166$$ 4.94540e10 0.392338
$$167$$ 2.12416e11 1.63533 0.817663 0.575697i $$-0.195269\pi$$
0.817663 + 0.575697i $$0.195269\pi$$
$$168$$ −5.38894e10 3.70334e10i −0.402677 0.276725i
$$169$$ 1.08904e11 0.789968
$$170$$ 0 0
$$171$$ 1.62309e10 + 4.22713e10i 0.111010 + 0.289111i
$$172$$ 1.01744e11i 0.675876i
$$173$$ 3.04132e11 1.96260 0.981300 0.192482i $$-0.0616538\pi$$
0.981300 + 0.192482i $$0.0616538\pi$$
$$174$$ −2.18986e10 1.50490e10i −0.137300 0.0943542i
$$175$$ 0 0
$$176$$ 1.63690e10i 0.0969300i
$$177$$ 5.84837e10 + 4.01908e10i 0.336642 + 0.231345i
$$178$$ 5.40212e9i 0.0302318i
$$179$$ 7.07114e9i 0.0384791i −0.999815 0.0192395i $$-0.993875\pi$$
0.999815 0.0192395i $$-0.00612451\pi$$
$$180$$ 0 0
$$181$$ −1.27309e11 −0.655337 −0.327669 0.944793i $$-0.606263\pi$$
−0.327669 + 0.944793i $$0.606263\pi$$
$$182$$ −8.94290e10 −0.447838
$$183$$ 7.30425e10 1.06288e11i 0.355894 0.517880i
$$184$$ −1.62572e10 −0.0770825
$$185$$ 0 0
$$186$$ −1.30264e11 + 1.89554e11i −0.585141 + 0.851470i
$$187$$ 1.66488e11i 0.728075i
$$188$$ 7.93900e10 0.338047
$$189$$ 7.77563e10 3.24078e11i 0.322424 1.34382i
$$190$$ 0 0
$$191$$ 2.06460e11i 0.812209i −0.913827 0.406105i $$-0.866887\pi$$
0.913827 0.406105i $$-0.133113\pi$$
$$192$$ −1.84720e10 + 2.68797e10i −0.0707960 + 0.103019i
$$193$$ 3.11606e11i 1.16364i −0.813317 0.581821i $$-0.802340\pi$$
0.813317 0.581821i $$-0.197660\pi$$
$$194$$ 2.00052e11i 0.728004i
$$195$$ 0 0
$$196$$ −1.31582e11 −0.454901
$$197$$ 1.51694e11 0.511255 0.255628 0.966775i $$-0.417718\pi$$
0.255628 + 0.966775i $$0.417718\pi$$
$$198$$ −7.78870e10 + 2.99063e10i −0.255941 + 0.0982737i
$$199$$ 1.11692e11 0.357895 0.178947 0.983859i $$-0.442731\pi$$
0.178947 + 0.983859i $$0.442731\pi$$
$$200$$ 0 0
$$201$$ −1.04559e11 7.18543e10i −0.318700 0.219014i
$$202$$ 3.79978e11i 1.12980i
$$203$$ −1.12241e11 −0.325591
$$204$$ −1.87879e11 + 2.73392e11i −0.531773 + 0.773812i
$$205$$ 0 0
$$206$$ 1.89361e11i 0.510451i
$$207$$ −2.97021e10 7.73551e10i −0.0781512 0.203534i
$$208$$ 4.46066e10i 0.114573i
$$209$$ 4.78826e10i 0.120073i
$$210$$ 0 0
$$211$$ 1.53066e11 0.365987 0.182994 0.983114i $$-0.441421\pi$$
0.182994 + 0.983114i $$0.441421\pi$$
$$212$$ 2.15829e10 0.0503999
$$213$$ −1.14427e11 7.86354e10i −0.260993 0.179358i
$$214$$ −3.24828e11 −0.723744
$$215$$ 0 0
$$216$$ −1.61648e11 3.87843e10i −0.343796 0.0824874i
$$217$$ 9.71560e11i 2.01916i
$$218$$ −1.06929e11 −0.217177
$$219$$ 4.37763e11 + 3.00836e11i 0.868998 + 0.597186i
$$220$$ 0 0
$$221$$ 4.53693e11i 0.860598i
$$222$$ 2.27312e11 + 1.56212e11i 0.421559 + 0.289700i
$$223$$ 6.05759e11i 1.09844i 0.835678 + 0.549219i $$0.185075\pi$$
−0.835678 + 0.549219i $$0.814925\pi$$
$$224$$ 1.37771e11i 0.244298i
$$225$$ 0 0
$$226$$ 2.99040e11 0.507210
$$227$$ −6.70588e11 −1.11257 −0.556284 0.830992i $$-0.687773\pi$$
−0.556284 + 0.830992i $$0.687773\pi$$
$$228$$ 5.40345e10 7.86286e10i 0.0876995 0.127616i
$$229$$ −3.53356e11 −0.561094 −0.280547 0.959840i $$-0.590516\pi$$
−0.280547 + 0.959840i $$0.590516\pi$$
$$230$$ 0 0
$$231$$ −1.99605e11 + 2.90456e11i −0.303467 + 0.441591i
$$232$$ 5.59851e10i 0.0832976i
$$233$$ −1.12390e12 −1.63662 −0.818309 0.574779i $$-0.805088\pi$$
−0.818309 + 0.574779i $$0.805088\pi$$
$$234$$ −2.12248e11 + 8.14969e10i −0.302527 + 0.116161i
$$235$$ 0 0
$$236$$ 1.49517e11i 0.204236i
$$237$$ 2.70565e11 3.93714e11i 0.361851 0.526549i
$$238$$ 1.40127e12i 1.83500i
$$239$$ 2.64603e11i 0.339317i 0.985503 + 0.169658i $$0.0542665\pi$$
−0.985503 + 0.169658i $$0.945734\pi$$
$$240$$ 0 0
$$241$$ 8.86768e11 1.09075 0.545375 0.838192i $$-0.316387\pi$$
0.545375 + 0.838192i $$0.316387\pi$$
$$242$$ −4.98671e11 −0.600810
$$243$$ −1.10789e11 8.40014e11i −0.130757 0.991414i
$$244$$ −2.71732e11 −0.314190
$$245$$ 0 0
$$246$$ −6.76286e11 4.64752e11i −0.750680 0.515877i
$$247$$ 1.30483e11i 0.141929i
$$248$$ 4.84607e11 0.516573
$$249$$ 3.00795e11 4.37704e11i 0.314249 0.457281i
$$250$$ 0 0
$$251$$ 8.59494e11i 0.862729i −0.902178 0.431364i $$-0.858032\pi$$
0.902178 0.431364i $$-0.141968\pi$$
$$252$$ −6.55546e11 + 2.51710e11i −0.645060 + 0.247684i
$$253$$ 8.76237e10i 0.0845316i
$$254$$ 7.19130e11i 0.680203i
$$255$$ 0 0
$$256$$ 6.87195e10 0.0625000
$$257$$ −2.17900e12 −1.94353 −0.971764 0.235954i $$-0.924179\pi$$
−0.971764 + 0.235954i $$0.924179\pi$$
$$258$$ 9.00510e11 + 6.18841e11i 0.787753 + 0.541353i
$$259$$ 1.16509e12 0.999677
$$260$$ 0 0
$$261$$ −2.66389e11 + 1.02286e11i −0.219945 + 0.0844524i
$$262$$ 1.13385e12i 0.918433i
$$263$$ −1.37942e12 −1.09627 −0.548134 0.836391i $$-0.684661\pi$$
−0.548134 + 0.836391i $$0.684661\pi$$
$$264$$ 1.44877e11 + 9.95615e10i 0.112975 + 0.0776375i
$$265$$ 0 0
$$266$$ 4.03010e11i 0.302627i
$$267$$ −4.78126e10 3.28574e10i −0.0352360 0.0242146i
$$268$$ 2.67312e11i 0.193350i
$$269$$ 1.18129e12i 0.838680i −0.907829 0.419340i $$-0.862262\pi$$
0.907829 0.419340i $$-0.137738\pi$$
$$270$$ 0 0
$$271$$ −1.42251e12 −0.973213 −0.486606 0.873621i $$-0.661765\pi$$
−0.486606 + 0.873621i $$0.661765\pi$$
$$272$$ 6.98944e11 0.469459
$$273$$ −5.43937e11 + 7.91511e11i −0.358703 + 0.521968i
$$274$$ −6.21674e11 −0.402541
$$275$$ 0 0
$$276$$ −9.88815e10 + 1.43888e11i −0.0617404 + 0.0898418i
$$277$$ 5.29960e11i 0.324971i 0.986711 + 0.162485i $$0.0519510\pi$$
−0.986711 + 0.162485i $$0.948049\pi$$
$$278$$ 1.43116e12 0.861913
$$279$$ 8.85385e11 + 2.30587e12i 0.523734 + 1.36400i
$$280$$ 0 0
$$281$$ 2.28441e12i 1.30389i −0.758265 0.651946i $$-0.773953\pi$$
0.758265 0.651946i $$-0.226047\pi$$
$$282$$ 4.82876e11 7.02659e11i 0.270764 0.394003i
$$283$$ 2.31274e12i 1.27408i −0.770833 0.637038i $$-0.780160\pi$$
0.770833 0.637038i $$-0.219840\pi$$
$$284$$ 2.92539e11i 0.158340i
$$285$$ 0 0
$$286$$ 2.40423e11 0.125645
$$287$$ −3.46630e12 −1.78015
$$288$$ 1.25551e11 + 3.26982e11i 0.0633665 + 0.165029i
$$289$$ 5.09295e12 2.52627
$$290$$ 0 0
$$291$$ 1.77060e12 + 1.21678e12i 0.848509 + 0.583106i
$$292$$ 1.11917e12i 0.527207i
$$293$$ 1.05989e12 0.490822 0.245411 0.969419i $$-0.421077\pi$$
0.245411 + 0.969419i $$0.421077\pi$$
$$294$$ −8.00326e11 + 1.16460e12i −0.364360 + 0.530199i
$$295$$ 0 0
$$296$$ 5.81138e11i 0.255753i
$$297$$ −2.09042e11 + 8.71257e11i −0.0904588 + 0.377020i
$$298$$ 7.65890e11i 0.325900i
$$299$$ 2.38781e11i 0.0999179i
$$300$$ 0 0
$$301$$ 4.61555e12 1.86806
$$302$$ −2.76928e12 −1.10238
$$303$$ −3.36308e12 2.31115e12i −1.31681 0.904931i
$$304$$ −2.01019e11 −0.0774227
$$305$$ 0 0
$$306$$ 1.27698e12 + 3.32573e12i 0.475968 + 1.23959i
$$307$$ 6.89209e11i 0.252731i 0.991984 + 0.126366i $$0.0403313\pi$$
−0.991984 + 0.126366i $$0.959669\pi$$
$$308$$ 7.42567e11 0.267906
$$309$$ 1.67598e12 + 1.15176e12i 0.594945 + 0.408854i
$$310$$ 0 0
$$311$$ 1.95674e12i 0.672559i −0.941762 0.336280i $$-0.890831\pi$$
0.941762 0.336280i $$-0.109169\pi$$
$$312$$ 3.94801e11 + 2.71312e11i 0.133538 + 0.0917690i
$$313$$ 2.48821e11i 0.0828256i 0.999142 + 0.0414128i $$0.0131859\pi$$
−0.999142 + 0.0414128i $$0.986814\pi$$
$$314$$ 3.59711e12i 1.17843i
$$315$$ 0 0
$$316$$ −1.00655e12 −0.319449
$$317$$ 4.63675e12 1.44850 0.724249 0.689539i $$-0.242187\pi$$
0.724249 + 0.689539i $$0.242187\pi$$
$$318$$ 1.31274e11 1.91024e11i 0.0403686 0.0587425i
$$319$$ 3.01751e11 0.0913473
$$320$$ 0 0
$$321$$ −1.97571e12 + 2.87497e12i −0.579694 + 0.843544i
$$322$$ 7.37496e11i 0.213049i
$$323$$ −2.04456e12 −0.581549
$$324$$ −1.32646e12 + 1.19480e12i −0.371510 + 0.334634i
$$325$$ 0 0
$$326$$ 2.08360e12i 0.565883i
$$327$$ −6.50378e11 + 9.46400e11i −0.173951 + 0.253125i
$$328$$ 1.72897e12i 0.455426i
$$329$$ 3.60147e12i 0.934331i
$$330$$ 0 0
$$331$$ −1.41443e12 −0.355994 −0.177997 0.984031i $$-0.556962\pi$$
−0.177997 + 0.984031i $$0.556962\pi$$
$$332$$ −1.11902e12 −0.277425
$$333$$ 2.76518e12 1.06175e12i 0.675308 0.259298i
$$334$$ −4.80642e12 −1.15635
$$335$$ 0 0
$$336$$ 1.21938e12 + 8.37971e11i 0.284736 + 0.195674i
$$337$$ 8.67755e11i 0.199640i 0.995006 + 0.0998201i $$0.0318267\pi$$
−0.995006 + 0.0998201i $$0.968173\pi$$
$$338$$ −2.46421e12 −0.558592
$$339$$ 1.81886e12 2.64672e12i 0.406257 0.591167i
$$340$$ 0 0
$$341$$ 2.61196e12i 0.566493i
$$342$$ −3.67264e11 9.56490e11i −0.0784961 0.204432i
$$343$$ 5.91785e11i 0.124650i
$$344$$ 2.30221e12i 0.477917i
$$345$$ 0 0
$$346$$ −6.88173e12 −1.38777
$$347$$ −5.20712e12 −1.03502 −0.517512 0.855676i $$-0.673142\pi$$
−0.517512 + 0.855676i $$0.673142\pi$$
$$348$$ 4.95509e11 + 3.40520e11i 0.0970857 + 0.0667185i
$$349$$ −1.11953e12 −0.216226 −0.108113 0.994139i $$-0.534481\pi$$
−0.108113 + 0.994139i $$0.534481\pi$$
$$350$$ 0 0
$$351$$ −5.69653e11 + 2.37424e12i −0.106924 + 0.445644i
$$352$$ 3.70388e11i 0.0685398i
$$353$$ 3.73952e12 0.682248 0.341124 0.940018i $$-0.389192\pi$$
0.341124 + 0.940018i $$0.389192\pi$$
$$354$$ −1.32334e12 9.09413e11i −0.238042 0.163586i
$$355$$ 0 0
$$356$$ 1.22236e11i 0.0213771i
$$357$$ 1.24023e13 + 8.52299e12i 2.13875 + 1.46977i
$$358$$ 1.60002e11i 0.0272088i
$$359$$ 3.54489e12i 0.594471i −0.954804 0.297235i $$-0.903935\pi$$
0.954804 0.297235i $$-0.0960646\pi$$
$$360$$ 0 0
$$361$$ −5.54305e12 −0.904092
$$362$$ 2.88066e12 0.463393
$$363$$ −3.03308e12 + 4.41360e12i −0.481228 + 0.700260i
$$364$$ 2.02355e12 0.316670
$$365$$ 0 0
$$366$$ −1.65276e12 + 2.40503e12i −0.251655 + 0.366197i
$$367$$ 1.01161e13i 1.51944i −0.650248 0.759722i $$-0.725335\pi$$
0.650248 0.759722i $$-0.274665\pi$$
$$368$$ 3.67858e11 0.0545056
$$369$$ −8.22679e12 + 3.15885e12i −1.20254 + 0.461739i
$$370$$ 0 0
$$371$$ 9.79093e11i 0.139301i
$$372$$ 2.94754e12 4.28913e12i 0.413757 0.602080i
$$373$$ 3.81055e12i 0.527769i −0.964554 0.263885i $$-0.914996\pi$$
0.964554 0.263885i $$-0.0850038\pi$$
$$374$$ 3.76720e12i 0.514827i
$$375$$ 0 0
$$376$$ −1.79639e12 −0.239035
$$377$$ 8.22293e11 0.107974
$$378$$ −1.75943e12 + 7.33304e12i −0.227988 + 0.950222i
$$379$$ −1.11052e13 −1.42014 −0.710069 0.704132i $$-0.751336\pi$$
−0.710069 + 0.704132i $$0.751336\pi$$
$$380$$ 0 0
$$381$$ 6.36482e12 + 4.37399e12i 0.792796 + 0.544819i
$$382$$ 4.67165e12i 0.574319i
$$383$$ 4.29169e12 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$384$$ 4.17974e11 6.08217e11i 0.0500603 0.0728455i
$$385$$ 0 0
$$386$$ 7.05084e12i 0.822820i
$$387$$ 1.09544e13 4.20617e12i 1.26192 0.484542i
$$388$$ 4.52665e12i 0.514776i
$$389$$ 1.50554e13i 1.69023i −0.534588 0.845113i $$-0.679533\pi$$
0.534588 0.845113i $$-0.320467\pi$$
$$390$$ 0 0
$$391$$ 3.74148e12 0.409411
$$392$$ 2.97736e12 0.321663
$$393$$ 1.00354e13 + 6.89642e12i 1.07046 + 0.735633i
$$394$$ −3.43245e12 −0.361512
$$395$$ 0 0
$$396$$ 1.76238e12 6.76703e11i 0.180977 0.0694900i
$$397$$ 1.11669e13i 1.13235i −0.824286 0.566174i $$-0.808423\pi$$
0.824286 0.566174i $$-0.191577\pi$$
$$398$$ −2.52729e12 −0.253070
$$399$$ −3.56693e12 2.45124e12i −0.352720 0.242394i
$$400$$ 0 0
$$401$$ 1.15685e13i 1.11572i −0.829935 0.557861i $$-0.811622\pi$$
0.829935 0.557861i $$-0.188378\pi$$
$$402$$ 2.36590e12 + 1.62588e12i 0.225355 + 0.154867i
$$403$$ 7.11777e12i 0.669605i
$$404$$ 8.59793e12i 0.798890i
$$405$$ 0 0
$$406$$ 2.53973e12 0.230227
$$407$$ −3.13224e12 −0.280468
$$408$$ 4.25121e12 6.18616e12i 0.376021 0.547168i
$$409$$ 1.07411e13 0.938498 0.469249 0.883066i $$-0.344525\pi$$
0.469249 + 0.883066i $$0.344525\pi$$
$$410$$ 0 0
$$411$$ −3.78123e12 + 5.50227e12i −0.322421 + 0.469172i
$$412$$ 4.28475e12i 0.360944i
$$413$$ −6.78275e12 −0.564489
$$414$$ 6.72082e11 + 1.75035e12i 0.0552612 + 0.143920i
$$415$$ 0 0
$$416$$ 1.00933e12i 0.0810153i
$$417$$ 8.70477e12 1.26668e13i 0.690362 1.00458i
$$418$$ 1.08346e12i 0.0849047i
$$419$$ 8.81717e12i 0.682746i 0.939928 + 0.341373i $$0.110892\pi$$
−0.939928 + 0.341373i $$0.889108\pi$$
$$420$$ 0 0
$$421$$ −5.69741e12 −0.430792 −0.215396 0.976527i $$-0.569104\pi$$
−0.215396 + 0.976527i $$0.569104\pi$$
$$422$$ −3.46348e12 −0.258792
$$423$$ −3.28203e12 8.54761e12i −0.242349 0.631165i
$$424$$ −4.88365e11 −0.0356381
$$425$$ 0 0
$$426$$ 2.58918e12 + 1.77932e12i 0.184550 + 0.126825i
$$427$$ 1.23269e13i 0.868392i
$$428$$ 7.35003e12 0.511764
$$429$$ 1.46233e12 2.12792e12i 0.100637 0.146443i
$$430$$ 0 0
$$431$$ 1.80323e13i 1.21245i −0.795293 0.606226i $$-0.792683\pi$$
0.795293 0.606226i $$-0.207317\pi$$
$$432$$ 3.65767e12 + 8.77590e11i 0.243101 + 0.0583274i
$$433$$ 2.06339e13i 1.35563i −0.735232 0.677816i $$-0.762927\pi$$
0.735232 0.677816i $$-0.237073\pi$$
$$434$$ 2.19839e13i 1.42776i
$$435$$ 0 0
$$436$$ 2.41953e12 0.153567
$$437$$ −1.07606e12 −0.0675195
$$438$$ −9.90545e12 6.80715e12i −0.614474 0.422275i
$$439$$ −1.95313e13 −1.19787 −0.598935 0.800798i $$-0.704409\pi$$
−0.598935 + 0.800798i $$0.704409\pi$$
$$440$$ 0 0
$$441$$ 5.43969e12 + 1.41669e13i 0.326123 + 0.849343i
$$442$$ 1.02659e13i 0.608535i
$$443$$ 2.97469e13 1.74351 0.871753 0.489946i $$-0.162984\pi$$
0.871753 + 0.489946i $$0.162984\pi$$
$$444$$ −5.14349e12 3.53467e12i −0.298087 0.204849i
$$445$$ 0 0
$$446$$ 1.37068e13i 0.776713i
$$447$$ 6.77868e12 + 4.65839e12i 0.379846 + 0.261035i
$$448$$ 3.11741e12i 0.172744i
$$449$$ 1.37505e13i 0.753509i −0.926313 0.376754i $$-0.877040\pi$$
0.926313 0.376754i $$-0.122960\pi$$
$$450$$ 0 0
$$451$$ 9.31887e12 0.499437
$$452$$ −6.76651e12 −0.358651
$$453$$ −1.68437e13 + 2.45102e13i −0.882971 + 1.28486i
$$454$$ 1.51737e13 0.786704
$$455$$ 0 0
$$456$$ −1.22266e12 + 1.77916e12i −0.0620129 + 0.0902383i
$$457$$ 4.10224e11i 0.0205798i 0.999947 + 0.0102899i $$0.00327543\pi$$
−0.999947 + 0.0102899i $$0.996725\pi$$
$$458$$ 7.99554e12 0.396753
$$459$$ 3.72021e13 + 8.92594e12i 1.82601 + 0.438118i
$$460$$ 0 0
$$461$$ 2.10914e11i 0.0101298i 0.999987 + 0.00506490i $$0.00161221\pi$$
−0.999987 + 0.00506490i $$0.998388\pi$$
$$462$$ 4.51654e12 6.57226e12i 0.214583 0.312252i
$$463$$ 1.96738e13i 0.924660i 0.886708 + 0.462330i $$0.152987\pi$$
−0.886708 + 0.462330i $$0.847013\pi$$
$$464$$ 1.26680e12i 0.0589003i
$$465$$ 0 0
$$466$$ 2.54309e13 1.15726
$$467$$ −1.21902e13 −0.548815 −0.274407 0.961614i $$-0.588482\pi$$
−0.274407 + 0.961614i $$0.588482\pi$$
$$468$$ 4.80261e12 1.84406e12i 0.213919 0.0821385i
$$469$$ 1.21264e13 0.534402
$$470$$ 0 0
$$471$$ 3.18370e13 + 2.18788e13i 1.37350 + 0.943885i
$$472$$ 3.38319e12i 0.144416i
$$473$$ −1.24085e13 −0.524101
$$474$$ −6.12218e12 + 8.90872e12i −0.255867 + 0.372326i
$$475$$ 0 0
$$476$$ 3.17071e13i 1.29754i
$$477$$ −8.92250e11 2.32374e12i −0.0361322 0.0941014i
$$478$$ 5.98729e12i 0.239933i
$$479$$ 5.00886e12i 0.198637i 0.995056 + 0.0993187i $$0.0316663\pi$$
−0.995056 + 0.0993187i $$0.968334\pi$$
$$480$$ 0 0
$$481$$ −8.53558e12 −0.331518
$$482$$ −2.00653e13 −0.771276
$$483$$ 6.52737e12 + 4.48569e12i 0.248315 + 0.170645i
$$484$$ 1.12836e13 0.424837
$$485$$ 0 0
$$486$$ 2.50686e12 + 1.90074e13i 0.0924590 + 0.701036i
$$487$$ 4.17000e13i 1.52227i −0.648595 0.761134i $$-0.724643\pi$$
0.648595 0.761134i $$-0.275357\pi$$
$$488$$ 6.14859e12 0.222166
$$489$$ −1.84414e13 1.26732e13i −0.659553 0.453253i
$$490$$ 0 0
$$491$$ 2.10340e12i 0.0737081i 0.999321 + 0.0368540i $$0.0117337\pi$$
−0.999321 + 0.0368540i $$0.988266\pi$$
$$492$$ 1.53026e13 + 1.05161e13i 0.530811 + 0.364780i
$$493$$ 1.28846e13i 0.442421i
$$494$$ 2.95250e12i 0.100359i
$$495$$ 0 0
$$496$$ −1.09654e13 −0.365272
$$497$$ 1.32708e13 0.437639
$$498$$ −6.80622e12 + 9.90410e12i −0.222208 + 0.323347i
$$499$$ −2.74482e13 −0.887179 −0.443589 0.896230i $$-0.646295\pi$$
−0.443589 + 0.896230i $$0.646295\pi$$
$$500$$ 0 0
$$501$$ −2.92342e13 + 4.25403e13i −0.926197 + 1.34776i
$$502$$ 1.94481e13i 0.610041i
$$503$$ −2.26985e13 −0.704949 −0.352474 0.935822i $$-0.614660\pi$$
−0.352474 + 0.935822i $$0.614660\pi$$
$$504$$ 1.48333e13 5.69556e12i 0.456127 0.175139i
$$505$$ 0 0
$$506$$ 1.98270e12i 0.0597729i
$$507$$ −1.49882e13 + 2.18101e13i −0.447413 + 0.651055i
$$508$$ 1.62721e13i 0.480976i
$$509$$ 4.21460e13i 1.23358i 0.787127 + 0.616791i $$0.211567\pi$$
−0.787127 + 0.616791i $$0.788433\pi$$
$$510$$ 0 0
$$511$$ −5.07703e13 −1.45715
$$512$$ −1.55494e12 −0.0441942
$$513$$ −1.06994e13 2.56713e12i −0.301144 0.0722539i
$$514$$ 4.93051e13 1.37428
$$515$$ 0 0
$$516$$ −2.03762e13 1.40028e13i −0.557025 0.382795i
$$517$$ 9.68227e12i 0.262135i
$$518$$ −2.63629e13 −0.706878
$$519$$ −4.18569e13 + 6.09083e13i −1.11155 + 1.61748i
$$520$$ 0 0
$$521$$ 6.54420e13i 1.70478i −0.522907 0.852390i $$-0.675152\pi$$
0.522907 0.852390i $$-0.324848\pi$$
$$522$$ 6.02770e12 2.31446e12i 0.155525 0.0597169i
$$523$$ 6.14531e13i 1.57049i 0.619185 + 0.785245i $$0.287463\pi$$
−0.619185 + 0.785245i $$0.712537\pi$$
$$524$$ 2.56560e13i 0.649430i
$$525$$ 0 0
$$526$$ 3.12126e13 0.775178
$$527$$ −1.11529e14 −2.74369
$$528$$ −3.27820e12 2.25282e12i −0.0798851 0.0548980i
$$529$$ −3.94574e13 −0.952466
$$530$$ 0 0
$$531$$ −1.60979e13 + 6.18114e12i −0.381327 + 0.146418i
$$532$$ 9.11907e12i 0.213990i
$$533$$ 2.53946e13 0.590343
$$534$$ 1.08188e12 + 7.43479e11i 0.0249156 + 0.0171223i
$$535$$ 0 0
$$536$$ 6.04857e12i 0.136719i
$$537$$ 1.41613e12 + 9.73183e11i 0.0317126 + 0.0217933i
$$538$$ 2.67296e13i 0.593036i
$$539$$ 1.60475e13i 0.352748i
$$540$$ 0 0
$$541$$ 1.50207e13 0.324118 0.162059 0.986781i $$-0.448187\pi$$
0.162059 + 0.986781i $$0.448187\pi$$
$$542$$ 3.21877e13 0.688166
$$543$$ 1.75211e13 2.54960e13i 0.371162 0.540098i
$$544$$ −1.58153e13 −0.331958
$$545$$ 0 0
$$546$$ 1.23079e13 1.79099e13i 0.253641 0.369087i
$$547$$ 7.15097e13i 1.46025i 0.683312 + 0.730127i $$0.260539\pi$$
−0.683312 + 0.730127i $$0.739461\pi$$
$$548$$ 1.40669e13 0.284639
$$549$$ 1.12336e13 + 2.92563e13i 0.225245 + 0.586621i
$$550$$ 0 0
$$551$$ 3.70565e12i 0.0729636i
$$552$$ 2.23743e12 3.25581e12i 0.0436571 0.0635278i
$$553$$ 4.56616e13i 0.882928i
$$554$$ 1.19916e13i 0.229789i
$$555$$ 0 0
$$556$$ −3.23834e13 −0.609464
$$557$$ −7.34107e13 −1.36925 −0.684626 0.728895i $$-0.740034\pi$$
−0.684626 + 0.728895i $$0.740034\pi$$
$$558$$ −2.00340e13 5.21758e13i −0.370336 0.964490i
$$559$$ −3.38141e13 −0.619497
$$560$$ 0 0
$$561$$ −3.33425e13 2.29134e13i −0.600045 0.412358i
$$562$$ 5.16902e13i 0.921991i
$$563$$ −4.77347e13 −0.843902 −0.421951 0.906619i $$-0.638655\pi$$
−0.421951 + 0.906619i $$0.638655\pi$$
$$564$$ −1.09262e13 + 1.58994e13i −0.191459 + 0.278602i
$$565$$ 0 0
$$566$$ 5.23314e13i 0.900907i
$$567$$ 5.42013e13 + 6.01742e13i 0.924900 + 1.02682i
$$568$$ 6.61939e12i 0.111963i
$$569$$ 1.90951e13i 0.320156i 0.987104 + 0.160078i $$0.0511745\pi$$
−0.987104 + 0.160078i $$0.948825\pi$$
$$570$$ 0 0
$$571$$ −2.09448e13 −0.345060 −0.172530 0.985004i $$-0.555194\pi$$
−0.172530 + 0.985004i $$0.555194\pi$$
$$572$$ −5.44014e12 −0.0888444
$$573$$ 4.13475e13 + 2.84145e13i 0.669385 + 0.460009i
$$574$$ 7.84334e13 1.25876
$$575$$ 0 0
$$576$$ −2.84091e12 7.39876e12i −0.0448069 0.116693i
$$577$$ 3.56688e13i 0.557711i 0.960333 + 0.278855i $$0.0899550\pi$$
−0.960333 + 0.278855i $$0.910045\pi$$
$$578$$ −1.15240e14 −1.78635
$$579$$ 6.24051e13 + 4.28856e13i 0.959019 + 0.659050i
$$580$$ 0 0
$$581$$ 5.07634e13i 0.766778i
$$582$$ −4.00642e13 2.75326e13i −0.599986 0.412318i
$$583$$ 2.63221e12i 0.0390821i
$$584$$ 2.53239e13i 0.372792i
$$585$$ 0 0
$$586$$ −2.39826e13 −0.347064
$$587$$ 1.29418e14 1.85697 0.928483 0.371375i $$-0.121114\pi$$
0.928483 + 0.371375i $$0.121114\pi$$
$$588$$ 1.81093e13 2.63518e13i 0.257641 0.374908i
$$589$$ 3.20761e13 0.452486
$$590$$ 0 0
$$591$$ −2.08773e13 + 3.03797e13i −0.289559 + 0.421352i
$$592$$ 1.31496e13i 0.180845i
$$593$$ 3.96596e13 0.540848 0.270424 0.962741i $$-0.412836\pi$$
0.270424 + 0.962741i $$0.412836\pi$$
$$594$$ 4.73007e12 1.97143e13i 0.0639640 0.266593i
$$595$$ 0 0
$$596$$ 1.73301e13i 0.230446i
$$597$$ −1.53718e13 + 2.23684e13i −0.202700 + 0.294960i
$$598$$ 5.40299e12i 0.0706526i
$$599$$ 4.57555e13i 0.593347i 0.954979 + 0.296674i $$0.0958774\pi$$
−0.954979 + 0.296674i $$0.904123\pi$$
$$600$$ 0 0
$$601$$ 1.06033e14 1.35229 0.676143 0.736770i $$-0.263650\pi$$
0.676143 + 0.736770i $$0.263650\pi$$
$$602$$ −1.04438e14 −1.32092
$$603$$ 2.87804e13 1.10508e13i 0.361003 0.138614i
$$604$$ 6.26617e13 0.779503
$$605$$ 0 0
$$606$$ 7.60979e13 + 5.22954e13i 0.931128 + 0.639883i
$$607$$ 9.55067e13i 1.15902i −0.814966 0.579509i $$-0.803244\pi$$
0.814966 0.579509i $$-0.196756\pi$$
$$608$$ 4.54853e12 0.0547461
$$609$$ 1.54475e13 2.24784e13i 0.184404 0.268336i
$$610$$ 0 0
$$611$$ 2.63849e13i 0.309848i
$$612$$ −2.88948e13 7.52526e13i −0.336560 0.876525i
$$613$$ 5.18411e13i 0.598924i 0.954108 + 0.299462i $$0.0968072\pi$$
−0.954108 + 0.299462i $$0.903193\pi$$
$$614$$ 1.55950e13i 0.178708i
$$615$$ 0 0
$$616$$ −1.68024e13 −0.189438
$$617$$ −8.05443e13 −0.900760 −0.450380 0.892837i $$-0.648711\pi$$
−0.450380 + 0.892837i $$0.648711\pi$$
$$618$$ −3.79231e13 2.60612e13i −0.420690 0.289103i
$$619$$ 5.14946e13 0.566642 0.283321 0.959025i $$-0.408564\pi$$
0.283321 + 0.959025i $$0.408564\pi$$
$$620$$ 0 0
$$621$$ 1.95797e13 + 4.69777e12i 0.212005 + 0.0508667i
$$622$$ 4.42759e13i 0.475571i
$$623$$ 5.54515e12 0.0590844
$$624$$ −8.93332e12 6.13909e12i −0.0944256 0.0648905i
$$625$$ 0 0
$$626$$ 5.63017e12i 0.0585665i
$$627$$ 9.58941e12 + 6.58996e12i 0.0989587 + 0.0680057i
$$628$$ 8.13933e13i 0.833279i
$$629$$ 1.33745e14i 1.35839i
$$630$$ 0 0
$$631$$ −1.02922e13 −0.102887 −0.0514435 0.998676i $$-0.516382\pi$$
−0.0514435 + 0.998676i $$0.516382\pi$$
$$632$$ 2.27757e13 0.225884
$$633$$ −2.10660e13 + 3.06543e13i −0.207283 + 0.301629i
$$634$$ −1.04918e14 −1.02424
$$635$$ 0 0
$$636$$ −2.97040e12 + 4.32238e12i −0.0285449 + 0.0415372i
$$637$$ 4.37307e13i 0.416955i
$$638$$ −6.82785e12 −0.0645923
$$639$$ 3.14965e13 1.20937e13i 0.295636 0.113516i
$$640$$ 0 0
$$641$$ 4.62451e13i 0.427342i −0.976906 0.213671i $$-0.931458\pi$$
0.976906 0.213671i $$-0.0685420\pi$$
$$642$$ 4.47053e13 6.50531e13i 0.409906 0.596476i
$$643$$ 2.73102e13i 0.248468i −0.992253 0.124234i $$-0.960353\pi$$
0.992253 0.124234i $$-0.0396474\pi$$
$$644$$ 1.66876e13i 0.150649i
$$645$$ 0 0
$$646$$ 4.62630e13 0.411217
$$647$$ −1.34984e13 −0.119059 −0.0595293 0.998227i $$-0.518960\pi$$
−0.0595293 + 0.998227i $$0.518960\pi$$
$$648$$ 3.00145e13 2.70353e13i 0.262697 0.236622i
$$649$$ 1.82349e13 0.158372
$$650$$ 0 0
$$651$$ −1.94573e14 1.33713e14i −1.66410 1.14359i
$$652$$ 4.71466e13i 0.400140i
$$653$$ 8.41840e13 0.709029 0.354514 0.935051i $$-0.384646\pi$$
0.354514 + 0.935051i $$0.384646\pi$$
$$654$$ 1.47164e13 2.14146e13i 0.123002 0.178987i
$$655$$ 0 0
$$656$$ 3.91220e13i 0.322034i
$$657$$ −1.20496e14 + 4.62671e13i −0.984345 + 0.377960i
$$658$$ 8.14920e13i 0.660672i
$$659$$ 1.65464e14i 1.33130i −0.746264 0.665650i $$-0.768154\pi$$
0.746264 0.665650i $$-0.231846\pi$$
$$660$$ 0 0
$$661$$ 2.01681e14 1.59830 0.799148 0.601135i $$-0.205284\pi$$
0.799148 + 0.601135i $$0.205284\pi$$
$$662$$ 3.20050e13 0.251726
$$663$$ −9.08606e13 6.24405e13i −0.709264 0.487415i
$$664$$ 2.53204e13 0.196169
$$665$$ 0 0
$$666$$ −6.25688e13 + 2.40246e13i −0.477515 + 0.183352i
$$667$$ 6.78122e12i 0.0513664i
$$668$$ 1.08757e14 0.817663
$$669$$ −1.21315e14 8.33691e13i −0.905281 0.622120i
$$670$$ 0 0
$$671$$ 3.31400e13i 0.243635i
$$672$$ −2.75914e13 1.89611e13i −0.201338 0.138362i
$$673$$ 6.04368e12i 0.0437750i −0.999760 0.0218875i $$-0.993032\pi$$
0.999760 0.0218875i $$-0.00696757\pi$$
$$674$$ 1.96351e13i 0.141167i
$$675$$ 0 0
$$676$$ 5.57588e13 0.394984
$$677$$ 1.21474e14 0.854164 0.427082 0.904213i $$-0.359542\pi$$
0.427082 + 0.904213i $$0.359542\pi$$
$$678$$ −4.11561e13 + 5.98885e13i −0.287267 + 0.418018i
$$679$$ −2.05349e14 −1.42280
$$680$$ 0 0
$$681$$ 9.22913e13 1.34298e14i 0.630123 0.916926i
$$682$$ 5.91019e13i 0.400571i
$$683$$ 1.51629e14 1.02019 0.510094 0.860119i $$-0.329611\pi$$
0.510094 + 0.860119i $$0.329611\pi$$
$$684$$ 8.31024e12 + 2.16429e13i 0.0555051 + 0.144556i
$$685$$ 0 0
$$686$$ 1.33906e13i 0.0881410i
$$687$$ 4.86315e13 7.07663e13i 0.317785 0.462427i
$$688$$ 5.20930e13i 0.337938i
$$689$$ 7.17296e12i 0.0461958i
$$690$$ 0 0
$$691$$ 6.62249e13 0.420369 0.210185 0.977662i $$-0.432593\pi$$
0.210185 + 0.977662i $$0.432593\pi$$
$$692$$ 1.55716e14 0.981300
$$693$$ −3.06982e13 7.99493e13i −0.192064 0.500205i
$$694$$ 1.17824e14 0.731873
$$695$$ 0 0
$$696$$ −1.12121e13 7.70509e12i −0.0686500 0.0471771i
$$697$$ 3.97909e14i 2.41891i
$$698$$ 2.53321e13 0.152895
$$699$$ 1.54679e14 2.25082e14i 0.926928 1.34882i
$$700$$ 0 0
$$701$$ 5.78990e13i 0.342043i −0.985267 0.171022i $$-0.945293\pi$$
0.985267 0.171022i $$-0.0547068\pi$$
$$702$$ 1.28898e13 5.37228e13i 0.0756066 0.315118i
$$703$$ 3.84654e13i 0.224024i
$$704$$ 8.38091e12i 0.0484650i
$$705$$ 0 0
$$706$$ −8.46157e13 −0.482422
$$707$$ 3.90039e14 2.20806
$$708$$ 2.99437e13 + 2.05777e13i 0.168321 + 0.115672i
$$709$$ −2.70077e14 −1.50750 −0.753750 0.657162i $$-0.771757\pi$$
−0.753750 + 0.657162i $$0.771757\pi$$
$$710$$ 0 0
$$711$$ 4.16115e13 + 1.08372e14i 0.229016 + 0.596441i
$$712$$ 2.76588e12i 0.0151159i
$$713$$ −5.86983e13 −0.318550
$$714$$ −2.80631e14 1.92853e14i −1.51232 1.03929i
$$715$$ 0 0
$$716$$ 3.62043e12i 0.0192395i
$$717$$ −5.29918e13 3.64166e13i −0.279649 0.192178i
$$718$$ 8.02117e13i 0.420354i
$$719$$ 1.48102e14i 0.770755i −0.922759 0.385377i $$-0.874071\pi$$
0.922759 0.385377i $$-0.125929\pi$$
$$720$$ 0 0
$$721$$ −1.94375e14 −0.997616
$$722$$ 1.25425e14 0.639289
$$723$$ −1.22044e14 + 1.77592e14i −0.617765 + 0.898944i
$$724$$ −6.51820e13 −0.327669
$$725$$ 0 0
$$726$$ 6.86307e13 9.98683e13i 0.340279 0.495159i
$$727$$ 5.21602e13i 0.256842i 0.991720 + 0.128421i $$0.0409910\pi$$
−0.991720 + 0.128421i $$0.959009\pi$$
$$728$$ −4.57876e13 −0.223919
$$729$$ 1.83476e14 + 9.34214e13i 0.891133 + 0.453742i
$$730$$ 0 0
$$731$$ 5.29837e14i 2.53837i
$$732$$ 3.73978e13 5.44195e13i 0.177947 0.258940i
$$733$$ 3.21782e14i 1.52069i −0.649518 0.760346i $$-0.725029\pi$$
0.649518 0.760346i $$-0.274971\pi$$
$$734$$ 2.28902e14i 1.07441i
$$735$$ 0 0
$$736$$ −8.32367e12 −0.0385413
$$737$$ −3.26009e13 −0.149931
$$738$$ 1.86151e14 7.14765e13i 0.850322 0.326499i
$$739$$ −1.66542e14 −0.755617 −0.377809 0.925884i $$-0.623322\pi$$
−0.377809 + 0.925884i $$0.623322\pi$$
$$740$$ 0 0
$$741$$ 2.61318e13 + 1.79581e13i 0.116971 + 0.0803839i
$$742$$ 2.21543e13i 0.0985007i
$$743$$ −1.13631e14 −0.501825 −0.250912 0.968010i $$-0.580731\pi$$
−0.250912 + 0.968010i $$0.580731\pi$$
$$744$$ −6.66953e13 + 9.70519e13i −0.292570 + 0.425735i
$$745$$ 0 0
$$746$$ 8.62230e13i 0.373189i
$$747$$ 4.62608e13 + 1.20480e14i 0.198889 + 0.517979i
$$748$$ 8.52421e13i 0.364037i
$$749$$ 3.33429e14i 1.41447i
$$750$$ 0 0
$$751$$ −1.64956e14 −0.690508 −0.345254 0.938509i $$-0.612207\pi$$
−0.345254 + 0.938509i $$0.612207\pi$$
$$752$$ 4.06477e13 0.169023
$$753$$ 1.72130e14 + 1.18290e14i 0.711020 + 0.488622i
$$754$$ −1.86064e13 −0.0763493
$$755$$ 0 0
$$756$$ 3.98112e13 1.65928e14i 0.161212 0.671909i
$$757$$ 2.67990e14i 1.07805i −0.842289 0.539026i $$-0.818793\pi$$
0.842289 0.539026i $$-0.181207\pi$$
$$758$$ 2.51282e14 1.00419
$$759$$ −1.75483e13 1.20594e13i −0.0696669 0.0478760i
$$760$$ 0 0
$$761$$ 1.29795e14i 0.508550i 0.967132 + 0.254275i $$0.0818368\pi$$
−0.967132 + 0.254275i $$0.918163\pi$$
$$762$$ −1.44020e14 9.89720e13i −0.560591 0.385245i
$$763$$ 1.09760e14i 0.424446i
$$764$$ 1.05707e14i 0.406105i
$$765$$ 0 0
$$766$$ −9.71099e13 −0.368230
$$767$$ 4.96913e13 0.187199
$$768$$ −9.45768e12 + 1.37624e13i −0.0353980 + 0.0515095i
$$769$$ 2.19185e14 0.815041 0.407521 0.913196i $$-0.366393\pi$$
0.407521 + 0.913196i $$0.366393\pi$$
$$770$$ 0 0
$$771$$ 2.99890e14 4.36386e14i 1.10075 1.60176i
$$772$$ 1.59542e14i 0.581821i
$$773$$ −4.05042e14 −1.46758 −0.733792 0.679374i $$-0.762251\pi$$
−0.733792 + 0.679374i $$0.762251\pi$$
$$774$$ −2.47870e14 + 9.51747e13i −0.892315 + 0.342623i
$$775$$ 0