Properties

Label 21.30.c.a.20.6
Level $21$
Weight $30$
Character 21.20
Analytic conductor $111.884$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(111.883889004\)
Analytic rank: \(0\)
Dimension: \(76\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.6
Character \(\chi\) \(=\) 21.20
Dual form 21.30.c.a.20.5

$q$-expansion

\(f(q)\) \(=\) \(q+38457.7i q^{2} +(8.27750e6 + 336727. i) q^{3} -9.42122e8 q^{4} -2.26488e10 q^{5} +(-1.29498e10 + 3.18333e11i) q^{6} +(6.92104e11 + 1.65557e12i) q^{7} -1.55850e13i q^{8} +(6.84036e13 + 5.57452e12i) q^{9} +O(q^{10})\) \(q+38457.7i q^{2} +(8.27750e6 + 336727. i) q^{3} -9.42122e8 q^{4} -2.26488e10 q^{5} +(-1.29498e10 + 3.18333e11i) q^{6} +(6.92104e11 + 1.65557e12i) q^{7} -1.55850e13i q^{8} +(6.84036e13 + 5.57452e12i) q^{9} -8.71020e14i q^{10} -2.70292e14i q^{11} +(-7.79842e15 - 3.17238e14i) q^{12} +4.56446e15i q^{13} +(-6.36692e16 + 2.66167e16i) q^{14} +(-1.87475e17 - 7.62647e15i) q^{15} +9.35660e16 q^{16} +1.12100e18 q^{17} +(-2.14383e17 + 2.63064e18i) q^{18} -5.21426e18i q^{19} +2.13379e19 q^{20} +(5.17141e18 + 1.39370e19i) q^{21} +1.03948e19 q^{22} -7.10335e19i q^{23} +(5.24791e18 - 1.29005e20i) q^{24} +3.26704e20 q^{25} -1.75539e20 q^{26} +(5.64334e20 + 6.91765e19i) q^{27} +(-6.52046e20 - 1.55975e21i) q^{28} +4.93987e20i q^{29} +(2.93296e20 - 7.20987e21i) q^{30} -4.68274e21i q^{31} -4.76882e21i q^{32} +(9.10148e19 - 2.23734e21i) q^{33} +4.31110e22i q^{34} +(-1.56753e22 - 3.74966e22i) q^{35} +(-6.44446e22 - 5.25188e21i) q^{36} +8.67228e22 q^{37} +2.00528e23 q^{38} +(-1.53698e21 + 3.77823e22i) q^{39} +3.52982e23i q^{40} +7.90557e22 q^{41} +(-5.35984e23 + 1.98881e23i) q^{42} -3.53714e23 q^{43} +2.54648e23i q^{44} +(-1.54926e24 - 1.26256e23i) q^{45} +2.73178e24 q^{46} -1.01420e24 q^{47} +(7.74492e23 + 3.15062e22i) q^{48} +(-2.26189e24 + 2.29165e24i) q^{49} +1.25643e25i q^{50} +(9.27906e24 + 3.77471e23i) q^{51} -4.30028e24i q^{52} -1.01570e25i q^{53} +(-2.66037e24 + 2.17030e25i) q^{54} +6.12180e24i q^{55} +(2.58020e25 - 1.07865e25i) q^{56} +(1.75578e24 - 4.31611e25i) q^{57} -1.89976e25 q^{58} -4.20416e25 q^{59} +(1.76625e26 + 7.18507e24i) q^{60} -1.70909e25i q^{61} +1.80087e26 q^{62} +(3.81134e25 + 1.17105e26i) q^{63} +2.33631e26 q^{64} -1.03380e26i q^{65} +(8.60431e25 + 3.50022e24i) q^{66} +3.45672e26 q^{67} -1.05612e27 q^{68} +(2.39189e25 - 5.87980e26i) q^{69} +(1.44203e27 - 6.02837e26i) q^{70} +5.62685e26i q^{71} +(8.68791e25 - 1.06607e27i) q^{72} +1.75673e27i q^{73} +3.33516e27i q^{74} +(2.70429e27 + 1.10010e26i) q^{75} +4.91247e27i q^{76} +(4.47487e26 - 1.87070e26i) q^{77} +(-1.45302e27 - 5.91086e25i) q^{78} +3.30282e27 q^{79} -2.11916e27 q^{80} +(4.64798e27 + 7.62635e26i) q^{81} +3.04030e27i q^{82} -1.10330e27 q^{83} +(-4.87211e27 - 1.31304e28i) q^{84} -2.53893e28 q^{85} -1.36030e28i q^{86} +(-1.66339e26 + 4.08898e27i) q^{87} -4.21251e27 q^{88} +1.29438e28 q^{89} +(4.85552e27 - 5.95809e28i) q^{90} +(-7.55676e27 + 3.15908e27i) q^{91} +6.69222e28i q^{92} +(1.57681e27 - 3.87614e28i) q^{93} -3.90039e28i q^{94} +1.18097e29i q^{95} +(1.60579e27 - 3.94739e28i) q^{96} +1.79904e28i q^{97} +(-8.81314e28 - 8.69871e28i) q^{98} +(1.50675e27 - 1.84890e28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} + O(q^{10}) \) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} - 116668222909200048q^{15} + 4964525139713333892q^{16} + 1542346202347854996q^{18} + 33840646982361357348q^{21} - 9870996616978150672q^{22} + \)\(32\!\cdots\!12\)\(q^{25} - \)\(31\!\cdots\!64\)\(q^{28} + \)\(51\!\cdots\!44\)\(q^{30} - \)\(85\!\cdots\!52\)\(q^{36} - \)\(17\!\cdots\!76\)\(q^{37} + \)\(38\!\cdots\!96\)\(q^{39} + \)\(80\!\cdots\!56\)\(q^{42} + \)\(23\!\cdots\!20\)\(q^{43} - \)\(10\!\cdots\!00\)\(q^{46} - \)\(51\!\cdots\!40\)\(q^{49} - \)\(96\!\cdots\!00\)\(q^{51} + \)\(20\!\cdots\!48\)\(q^{57} - \)\(40\!\cdots\!72\)\(q^{58} - \)\(16\!\cdots\!96\)\(q^{60} - \)\(36\!\cdots\!84\)\(q^{63} - \)\(16\!\cdots\!28\)\(q^{64} + \)\(48\!\cdots\!64\)\(q^{67} - \)\(65\!\cdots\!20\)\(q^{70} + \)\(19\!\cdots\!24\)\(q^{72} - \)\(80\!\cdots\!36\)\(q^{78} - \)\(11\!\cdots\!52\)\(q^{79} + \)\(18\!\cdots\!32\)\(q^{81} - \)\(72\!\cdots\!52\)\(q^{84} + \)\(14\!\cdots\!48\)\(q^{85} - \)\(16\!\cdots\!84\)\(q^{88} + \)\(44\!\cdots\!40\)\(q^{91} + \)\(22\!\cdots\!32\)\(q^{93} - \)\(23\!\cdots\!24\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

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 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 38457.7i 1.65977i 0.557934 + 0.829885i \(0.311594\pi\)
−0.557934 + 0.829885i \(0.688406\pi\)
\(3\) 8.27750e6 + 336727.i 0.999174 + 0.0406462i
\(4\) −9.42122e8 −1.75484
\(5\) −2.26488e10 −1.65951 −0.829756 0.558127i \(-0.811520\pi\)
−0.829756 + 0.558127i \(0.811520\pi\)
\(6\) −1.29498e10 + 3.18333e11i −0.0674634 + 1.65840i
\(7\) 6.92104e11 + 1.65557e12i 0.385700 + 0.922624i
\(8\) 1.55850e13i 1.25286i
\(9\) 6.84036e13 + 5.57452e12i 0.996696 + 0.0812253i
\(10\) 8.71020e14i 2.75441i
\(11\) 2.70292e14i 0.214605i −0.994226 0.107302i \(-0.965779\pi\)
0.994226 0.107302i \(-0.0342213\pi\)
\(12\) −7.79842e15 3.17238e14i −1.75339 0.0713276i
\(13\) 4.56446e15i 0.321522i 0.986993 + 0.160761i \(0.0513948\pi\)
−0.986993 + 0.160761i \(0.948605\pi\)
\(14\) −6.36692e16 + 2.66167e16i −1.53134 + 0.640174i
\(15\) −1.87475e17 7.62647e15i −1.65814 0.0674529i
\(16\) 9.35660e16 0.324622
\(17\) 1.12100e18 1.61471 0.807357 0.590063i \(-0.200897\pi\)
0.807357 + 0.590063i \(0.200897\pi\)
\(18\) −2.14383e17 + 2.63064e18i −0.134815 + 1.65429i
\(19\) 5.21426e18i 1.49715i −0.663049 0.748576i \(-0.730738\pi\)
0.663049 0.748576i \(-0.269262\pi\)
\(20\) 2.13379e19 2.91218
\(21\) 5.17141e18 + 1.39370e19i 0.347880 + 0.937539i
\(22\) 1.03948e19 0.356195
\(23\) 7.10335e19i 1.27764i −0.769355 0.638821i \(-0.779422\pi\)
0.769355 0.638821i \(-0.220578\pi\)
\(24\) 5.24791e18 1.29005e20i 0.0509241 1.25183i
\(25\) 3.26704e20 1.75398
\(26\) −1.75539e20 −0.533653
\(27\) 5.64334e20 + 6.91765e19i 0.992571 + 0.121670i
\(28\) −6.52046e20 1.55975e21i −0.676842 1.61906i
\(29\) 4.93987e20i 0.308280i 0.988049 + 0.154140i \(0.0492606\pi\)
−0.988049 + 0.154140i \(0.950739\pi\)
\(30\) 2.93296e20 7.20987e21i 0.111956 2.75213i
\(31\) 4.68274e21i 1.11111i −0.831481 0.555553i \(-0.812506\pi\)
0.831481 0.555553i \(-0.187494\pi\)
\(32\) 4.76882e21i 0.714062i
\(33\) 9.10148e19 2.23734e21i 0.00872288 0.214428i
\(34\) 4.31110e22i 2.68006i
\(35\) −1.56753e22 3.74966e22i −0.640074 1.53111i
\(36\) −6.44446e22 5.25188e21i −1.74904 0.142537i
\(37\) 8.67228e22 1.58201 0.791003 0.611812i \(-0.209559\pi\)
0.791003 + 0.611812i \(0.209559\pi\)
\(38\) 2.00528e23 2.48493
\(39\) −1.53698e21 + 3.77823e22i −0.0130687 + 0.321256i
\(40\) 3.52982e23i 2.07914i
\(41\) 7.90557e22 0.325512 0.162756 0.986666i \(-0.447962\pi\)
0.162756 + 0.986666i \(0.447962\pi\)
\(42\) −5.35984e23 + 1.98881e23i −1.55610 + 0.577401i
\(43\) −3.53714e23 −0.730061 −0.365031 0.930995i \(-0.618942\pi\)
−0.365031 + 0.930995i \(0.618942\pi\)
\(44\) 2.54648e23i 0.376597i
\(45\) −1.54926e24 1.26256e23i −1.65403 0.134794i
\(46\) 2.73178e24 2.12059
\(47\) −1.01420e24 −0.576375 −0.288188 0.957574i \(-0.593053\pi\)
−0.288188 + 0.957574i \(0.593053\pi\)
\(48\) 7.74492e23 + 3.15062e22i 0.324354 + 0.0131947i
\(49\) −2.26189e24 + 2.29165e24i −0.702471 + 0.711712i
\(50\) 1.25643e25i 2.91120i
\(51\) 9.27906e24 + 3.77471e23i 1.61338 + 0.0656320i
\(52\) 4.30028e24i 0.564220i
\(53\) 1.01570e25i 1.01103i −0.862818 0.505514i \(-0.831303\pi\)
0.862818 0.505514i \(-0.168697\pi\)
\(54\) −2.66037e24 + 2.17030e25i −0.201944 + 1.64744i
\(55\) 6.12180e24i 0.356139i
\(56\) 2.58020e25 1.07865e25i 1.15592 0.483228i
\(57\) 1.75578e24 4.31611e25i 0.0608535 1.49591i
\(58\) −1.89976e25 −0.511674
\(59\) −4.20416e25 −0.883741 −0.441870 0.897079i \(-0.645685\pi\)
−0.441870 + 0.897079i \(0.645685\pi\)
\(60\) 1.76625e26 + 7.18507e24i 2.90977 + 0.118369i
\(61\) 1.70909e25i 0.221556i −0.993845 0.110778i \(-0.964666\pi\)
0.993845 0.110778i \(-0.0353342\pi\)
\(62\) 1.80087e26 1.84418
\(63\) 3.81134e25 + 1.17105e26i 0.309485 + 0.950904i
\(64\) 2.33631e26 1.50980
\(65\) 1.03380e26i 0.533569i
\(66\) 8.60431e25 + 3.50022e24i 0.355901 + 0.0144780i
\(67\) 3.45672e26 1.14969 0.574843 0.818264i \(-0.305063\pi\)
0.574843 + 0.818264i \(0.305063\pi\)
\(68\) −1.05612e27 −2.83356
\(69\) 2.39189e25 5.87980e26i 0.0519314 1.27659i
\(70\) 1.44203e27 6.02837e26i 2.54128 1.06238i
\(71\) 5.62685e26i 0.807270i 0.914920 + 0.403635i \(0.132254\pi\)
−0.914920 + 0.403635i \(0.867746\pi\)
\(72\) 8.68791e25 1.06607e27i 0.101764 1.24872i
\(73\) 1.75673e27i 1.68470i 0.538931 + 0.842350i \(0.318828\pi\)
−0.538931 + 0.842350i \(0.681172\pi\)
\(74\) 3.33516e27i 2.62577i
\(75\) 2.70429e27 + 1.10010e26i 1.75253 + 0.0712926i
\(76\) 4.91247e27i 2.62726i
\(77\) 4.47487e26 1.87070e26i 0.198000 0.0827731i
\(78\) −1.45302e27 5.91086e25i −0.533212 0.0216910i
\(79\) 3.30282e27 1.00761 0.503804 0.863818i \(-0.331933\pi\)
0.503804 + 0.863818i \(0.331933\pi\)
\(80\) −2.11916e27 −0.538714
\(81\) 4.64798e27 + 7.62635e26i 0.986805 + 0.161914i
\(82\) 3.04030e27i 0.540276i
\(83\) −1.10330e27 −0.164460 −0.0822300 0.996613i \(-0.526204\pi\)
−0.0822300 + 0.996613i \(0.526204\pi\)
\(84\) −4.87211e27 1.31304e28i −0.610474 1.64523i
\(85\) −2.53893e28 −2.67964
\(86\) 1.36030e28i 1.21173i
\(87\) −1.66339e26 + 4.08898e27i −0.0125304 + 0.308025i
\(88\) −4.21251e27 −0.268870
\(89\) 1.29438e28 0.701304 0.350652 0.936506i \(-0.385960\pi\)
0.350652 + 0.936506i \(0.385960\pi\)
\(90\) 4.85552e27 5.95809e28i 0.223728 2.74531i
\(91\) −7.55676e27 + 3.15908e27i −0.296644 + 0.124011i
\(92\) 6.69222e28i 2.24206i
\(93\) 1.57681e27 3.87614e28i 0.0451623 1.11019i
\(94\) 3.90039e28i 0.956651i
\(95\) 1.18097e29i 2.48454i
\(96\) 1.60579e27 3.94739e28i 0.0290239 0.713472i
\(97\) 1.79904e28i 0.279802i 0.990165 + 0.139901i \(0.0446785\pi\)
−0.990165 + 0.139901i \(0.955322\pi\)
\(98\) −8.81314e28 8.69871e28i −1.18128 1.16594i
\(99\) 1.50675e27 1.84890e28i 0.0174313 0.213896i
\(100\) −3.07795e29 −3.07795
\(101\) −2.73147e28 −0.236449 −0.118224 0.992987i \(-0.537720\pi\)
−0.118224 + 0.992987i \(0.537720\pi\)
\(102\) −1.45167e28 + 3.56851e29i −0.108934 + 2.67784i
\(103\) 2.71089e29i 1.76592i 0.469445 + 0.882961i \(0.344454\pi\)
−0.469445 + 0.882961i \(0.655546\pi\)
\(104\) 7.11372e28 0.402822
\(105\) −1.17126e29 3.15656e29i −0.577311 1.55586i
\(106\) 3.90613e29 1.67808
\(107\) 2.14216e29i 0.803131i −0.915830 0.401565i \(-0.868466\pi\)
0.915830 0.401565i \(-0.131534\pi\)
\(108\) −5.31671e29 6.51727e28i −1.74180 0.213511i
\(109\) −2.60574e29 −0.746872 −0.373436 0.927656i \(-0.621820\pi\)
−0.373436 + 0.927656i \(0.621820\pi\)
\(110\) −2.35430e29 −0.591110
\(111\) 7.17848e29 + 2.92019e28i 1.58070 + 0.0643026i
\(112\) 6.47574e28 + 1.54905e29i 0.125207 + 0.299504i
\(113\) 8.14445e28i 0.138428i −0.997602 0.0692141i \(-0.977951\pi\)
0.997602 0.0692141i \(-0.0220492\pi\)
\(114\) 1.65987e30 + 6.75234e28i 2.48287 + 0.101003i
\(115\) 1.60882e30i 2.12026i
\(116\) 4.65396e29i 0.540981i
\(117\) −2.54447e28 + 3.12225e29i −0.0261157 + 0.320460i
\(118\) 1.61682e30i 1.46681i
\(119\) 7.75847e29 + 1.85589e30i 0.622795 + 1.48977i
\(120\) −1.18859e29 + 2.92181e30i −0.0845090 + 2.07742i
\(121\) 1.51325e30 0.953945
\(122\) 6.57277e29 0.367732
\(123\) 6.54384e29 + 2.66202e28i 0.325243 + 0.0132308i
\(124\) 4.41172e30i 1.94981i
\(125\) −3.18078e30 −1.25123
\(126\) −4.50358e30 + 1.46575e30i −1.57828 + 0.513675i
\(127\) 3.70027e29 0.115632 0.0578161 0.998327i \(-0.481586\pi\)
0.0578161 + 0.998327i \(0.481586\pi\)
\(128\) 6.42465e30i 1.79186i
\(129\) −2.92787e30 1.19105e29i −0.729458 0.0296742i
\(130\) 3.97574e30 0.885603
\(131\) −7.07561e30 −1.41036 −0.705180 0.709028i \(-0.749134\pi\)
−0.705180 + 0.709028i \(0.749134\pi\)
\(132\) −8.57471e28 + 2.10785e30i −0.0153073 + 0.376286i
\(133\) 8.63255e30 3.60881e30i 1.38131 0.577451i
\(134\) 1.32937e31i 1.90821i
\(135\) −1.27815e31 1.56676e30i −1.64718 0.201913i
\(136\) 1.74708e31i 2.02301i
\(137\) 1.49881e31i 1.56062i −0.625390 0.780312i \(-0.715060\pi\)
0.625390 0.780312i \(-0.284940\pi\)
\(138\) 2.26123e31 + 9.19866e29i 2.11884 + 0.0861942i
\(139\) 9.27965e30i 0.783100i −0.920157 0.391550i \(-0.871939\pi\)
0.920157 0.391550i \(-0.128061\pi\)
\(140\) 1.47681e31 + 3.53264e31i 1.12323 + 2.68684i
\(141\) −8.39506e30 3.41510e29i −0.575899 0.0234275i
\(142\) −2.16395e31 −1.33988
\(143\) 1.23374e30 0.0690002
\(144\) 6.40025e30 + 5.21585e29i 0.323550 + 0.0263675i
\(145\) 1.11882e31i 0.511593i
\(146\) −6.75596e31 −2.79622
\(147\) −1.94945e31 + 1.82075e31i −0.730819 + 0.682571i
\(148\) −8.17035e31 −2.77617
\(149\) 1.95223e31i 0.601632i −0.953682 0.300816i \(-0.902741\pi\)
0.953682 0.300816i \(-0.0972590\pi\)
\(150\) −4.23073e30 + 1.04001e32i −0.118329 + 2.90879i
\(151\) 1.81054e31 0.459878 0.229939 0.973205i \(-0.426147\pi\)
0.229939 + 0.973205i \(0.426147\pi\)
\(152\) −8.12644e31 −1.87572
\(153\) 7.66803e31 + 6.24903e30i 1.60938 + 0.131156i
\(154\) 7.19429e30 + 1.72093e31i 0.137384 + 0.328634i
\(155\) 1.06059e32i 1.84389i
\(156\) 1.44802e30 3.55956e31i 0.0229334 0.563753i
\(157\) 9.75167e31i 1.40778i −0.710310 0.703889i \(-0.751445\pi\)
0.710310 0.703889i \(-0.248555\pi\)
\(158\) 1.27019e32i 1.67240i
\(159\) 3.42013e30 8.40742e31i 0.0410945 1.01019i
\(160\) 1.08008e32i 1.18499i
\(161\) 1.17601e32 4.91625e31i 1.17878 0.492787i
\(162\) −2.93292e31 + 1.78750e32i −0.268740 + 1.63787i
\(163\) 1.73117e32 1.45084 0.725418 0.688309i \(-0.241647\pi\)
0.725418 + 0.688309i \(0.241647\pi\)
\(164\) −7.44802e31 −0.571222
\(165\) −2.06138e30 + 5.06732e31i −0.0144757 + 0.355845i
\(166\) 4.24303e31i 0.272966i
\(167\) −7.62933e30 −0.0449881 −0.0224941 0.999747i \(-0.507161\pi\)
−0.0224941 + 0.999747i \(0.507161\pi\)
\(168\) 2.17208e32 8.05966e31i 1.17461 0.435845i
\(169\) 1.80704e32 0.896624
\(170\) 9.76413e32i 4.44758i
\(171\) 2.90670e31 3.56674e32i 0.121607 1.49220i
\(172\) 3.33242e32 1.28114
\(173\) −2.34259e31 −0.0827997 −0.0413998 0.999143i \(-0.513182\pi\)
−0.0413998 + 0.999143i \(0.513182\pi\)
\(174\) −1.57253e32 6.39701e30i −0.511251 0.0207976i
\(175\) 2.26113e32 + 5.40879e32i 0.676509 + 1.61826i
\(176\) 2.52902e31i 0.0696655i
\(177\) −3.47999e32 1.41565e31i −0.883010 0.0359207i
\(178\) 4.97788e32i 1.16400i
\(179\) 3.98140e32i 0.858356i −0.903220 0.429178i \(-0.858803\pi\)
0.903220 0.429178i \(-0.141197\pi\)
\(180\) 1.45959e33 + 1.18949e32i 2.90255 + 0.236542i
\(181\) 2.29515e32i 0.421183i 0.977574 + 0.210592i \(0.0675390\pi\)
−0.977574 + 0.210592i \(0.932461\pi\)
\(182\) −1.21491e32 2.90616e32i −0.205830 0.492361i
\(183\) 5.75498e30 1.41470e32i 0.00900541 0.221373i
\(184\) −1.10706e33 −1.60071
\(185\) −1.96417e33 −2.62536
\(186\) 1.49067e33 + 6.06404e31i 1.84266 + 0.0749591i
\(187\) 3.02997e32i 0.346526i
\(188\) 9.55502e32 1.01145
\(189\) 2.76051e32 + 9.82169e32i 0.270579 + 0.962698i
\(190\) −4.54173e33 −4.12377
\(191\) 2.83099e32i 0.238207i 0.992882 + 0.119103i \(0.0380020\pi\)
−0.992882 + 0.119103i \(0.961998\pi\)
\(192\) 1.93388e33 + 7.86698e31i 1.50855 + 0.0613677i
\(193\) 4.55989e32 0.329893 0.164947 0.986303i \(-0.447255\pi\)
0.164947 + 0.986303i \(0.447255\pi\)
\(194\) −6.91870e32 −0.464408
\(195\) 3.48107e31 8.55724e32i 0.0216876 0.533128i
\(196\) 2.13098e33 2.15901e33i 1.23272 1.24894i
\(197\) 2.52192e33i 1.35510i −0.735476 0.677551i \(-0.763041\pi\)
0.735476 0.677551i \(-0.236959\pi\)
\(198\) 7.11043e32 + 5.79461e31i 0.355018 + 0.0289320i
\(199\) 2.83707e32i 0.131674i −0.997830 0.0658370i \(-0.979028\pi\)
0.997830 0.0658370i \(-0.0209717\pi\)
\(200\) 5.09169e33i 2.19749i
\(201\) 2.86130e33 + 1.16397e32i 1.14874 + 0.0467304i
\(202\) 1.05046e33i 0.392451i
\(203\) −8.17828e32 + 3.41891e32i −0.284426 + 0.118903i
\(204\) −8.74201e33 3.55624e32i −2.83122 0.115174i
\(205\) −1.79052e33 −0.540191
\(206\) −1.04254e34 −2.93103
\(207\) 3.95978e32 4.85895e33i 0.103777 1.27342i
\(208\) 4.27078e32i 0.104373i
\(209\) −1.40937e33 −0.321296
\(210\) 1.21394e34 4.50441e33i 2.58237 0.958204i
\(211\) 3.05740e33 0.607095 0.303547 0.952816i \(-0.401829\pi\)
0.303547 + 0.952816i \(0.401829\pi\)
\(212\) 9.56910e33i 1.77419i
\(213\) −1.89471e32 + 4.65762e33i −0.0328125 + 0.806603i
\(214\) 8.23823e33 1.33301
\(215\) 8.01119e33 1.21155
\(216\) 1.07812e33 8.79516e33i 0.152436 1.24355i
\(217\) 7.75259e33 3.24094e33i 1.02513 0.428554i
\(218\) 1.00211e34i 1.23964i
\(219\) −5.91538e32 + 1.45413e34i −0.0684767 + 1.68331i
\(220\) 5.76748e33i 0.624967i
\(221\) 5.11675e33i 0.519166i
\(222\) −1.12304e33 + 2.76068e34i −0.106728 + 2.62360i
\(223\) 1.40921e34i 1.25475i 0.778719 + 0.627373i \(0.215870\pi\)
−0.778719 + 0.627373i \(0.784130\pi\)
\(224\) 7.89509e33 3.30052e33i 0.658811 0.275414i
\(225\) 2.23477e34 + 1.82122e33i 1.74818 + 0.142467i
\(226\) 3.13217e33 0.229759
\(227\) −2.52431e34 −1.73687 −0.868435 0.495803i \(-0.834874\pi\)
−0.868435 + 0.495803i \(0.834874\pi\)
\(228\) −1.65416e33 + 4.06630e34i −0.106788 + 2.62509i
\(229\) 2.67628e34i 1.62150i −0.585391 0.810751i \(-0.699059\pi\)
0.585391 0.810751i \(-0.300941\pi\)
\(230\) −6.18716e34 −3.51915
\(231\) 3.76706e33 1.39779e33i 0.201200 0.0746568i
\(232\) 7.69881e33 0.386231
\(233\) 6.46876e33i 0.304902i −0.988311 0.152451i \(-0.951283\pi\)
0.988311 0.152451i \(-0.0487166\pi\)
\(234\) −1.20075e34 9.78543e32i −0.531890 0.0433461i
\(235\) 2.29705e34 0.956501
\(236\) 3.96083e34 1.55082
\(237\) 2.73390e34 + 1.11215e33i 1.00677 + 0.0409554i
\(238\) −7.13731e34 + 2.98373e34i −2.47268 + 1.03370i
\(239\) 9.92111e33i 0.323438i 0.986837 + 0.161719i \(0.0517038\pi\)
−0.986837 + 0.161719i \(0.948296\pi\)
\(240\) −1.75413e34 7.13578e32i −0.538269 0.0218967i
\(241\) 3.90029e34i 1.12681i 0.826181 + 0.563404i \(0.190509\pi\)
−0.826181 + 0.563404i \(0.809491\pi\)
\(242\) 5.81961e34i 1.58333i
\(243\) 3.82168e34 + 7.87781e33i 0.979408 + 0.201890i
\(244\) 1.61017e34i 0.388795i
\(245\) 5.12291e34 5.19031e34i 1.16576 1.18109i
\(246\) −1.02375e33 + 2.51661e34i −0.0219602 + 0.539829i
\(247\) 2.38003e34 0.481367
\(248\) −7.29807e34 −1.39206
\(249\) −9.13254e33 3.71510e32i −0.164324 0.00668468i
\(250\) 1.22325e35i 2.07676i
\(251\) −7.00461e33 −0.112232 −0.0561158 0.998424i \(-0.517872\pi\)
−0.0561158 + 0.998424i \(0.517872\pi\)
\(252\) −3.59075e34 1.10327e35i −0.543097 1.66868i
\(253\) −1.91998e34 −0.274188
\(254\) 1.42304e34i 0.191923i
\(255\) −2.10160e35 8.54926e33i −2.67742 0.108917i
\(256\) −1.21648e35 −1.46428
\(257\) 3.49331e34 0.397380 0.198690 0.980062i \(-0.436331\pi\)
0.198690 + 0.980062i \(0.436331\pi\)
\(258\) 4.58051e33 1.12599e35i 0.0492524 1.21073i
\(259\) 6.00212e34 + 1.43575e35i 0.610180 + 1.45960i
\(260\) 9.73962e34i 0.936329i
\(261\) −2.75374e33 + 3.37905e34i −0.0250401 + 0.307261i
\(262\) 2.72112e35i 2.34088i
\(263\) 1.42561e34i 0.116049i 0.998315 + 0.0580245i \(0.0184802\pi\)
−0.998315 + 0.0580245i \(0.981520\pi\)
\(264\) −3.48691e34 1.41847e33i −0.268648 0.0109286i
\(265\) 2.30043e35i 1.67781i
\(266\) 1.38787e35 + 3.31988e35i 0.958437 + 2.29265i
\(267\) 1.07142e35 + 4.35853e33i 0.700725 + 0.0285054i
\(268\) −3.25665e35 −2.01751
\(269\) −4.00535e34 −0.235089 −0.117545 0.993068i \(-0.537502\pi\)
−0.117545 + 0.993068i \(0.537502\pi\)
\(270\) 6.02541e34 4.91546e35i 0.335129 2.73394i
\(271\) 7.49708e34i 0.395219i 0.980281 + 0.197609i \(0.0633178\pi\)
−0.980281 + 0.197609i \(0.936682\pi\)
\(272\) 1.04887e35 0.524172
\(273\) −6.36148e34 + 2.36047e34i −0.301439 + 0.111851i
\(274\) 5.76408e35 2.59028
\(275\) 8.83055e34i 0.376412i
\(276\) −2.25345e34 + 5.53949e35i −0.0911312 + 2.24021i
\(277\) 3.47843e35 1.33483 0.667416 0.744685i \(-0.267400\pi\)
0.667416 + 0.744685i \(0.267400\pi\)
\(278\) 3.56874e35 1.29977
\(279\) 2.61041e34 3.20317e35i 0.0902500 1.10744i
\(280\) −5.84385e35 + 2.44300e35i −1.91826 + 0.801923i
\(281\) 3.09052e35i 0.963363i −0.876346 0.481682i \(-0.840026\pi\)
0.876346 0.481682i \(-0.159974\pi\)
\(282\) 1.31337e34 3.22854e35i 0.0388843 0.955861i
\(283\) 1.61227e35i 0.453455i 0.973958 + 0.226727i \(0.0728026\pi\)
−0.973958 + 0.226727i \(0.927197\pi\)
\(284\) 5.30118e35i 1.41663i
\(285\) −3.97664e34 + 9.77546e35i −0.100987 + 2.48249i
\(286\) 4.74467e34i 0.114525i
\(287\) 5.47148e34 + 1.30882e35i 0.125550 + 0.300326i
\(288\) 2.65839e34 3.26204e35i 0.0579999 0.711703i
\(289\) 7.74669e35 1.60730
\(290\) 4.30273e35 0.849128
\(291\) −6.05787e33 + 1.48916e35i −0.0113729 + 0.279571i
\(292\) 1.65505e36i 2.95638i
\(293\) 6.93789e35 1.17936 0.589681 0.807636i \(-0.299254\pi\)
0.589681 + 0.807636i \(0.299254\pi\)
\(294\) −7.00217e35 7.49711e35i −1.13291 1.21299i
\(295\) 9.52191e35 1.46658
\(296\) 1.35158e36i 1.98203i
\(297\) 1.86979e34 1.52535e35i 0.0261110 0.213011i
\(298\) 7.50784e35 0.998571
\(299\) 3.24229e35 0.410790
\(300\) −2.54777e36 1.03643e35i −3.07540 0.125107i
\(301\) −2.44807e35 5.85596e35i −0.281585 0.673572i
\(302\) 6.96293e35i 0.763293i
\(303\) −2.26098e35 9.19762e33i −0.236253 0.00961075i
\(304\) 4.87877e35i 0.486008i
\(305\) 3.87089e35i 0.367674i
\(306\) −2.40323e35 + 2.94895e36i −0.217688 + 2.67120i
\(307\) 7.37793e35i 0.637424i −0.947852 0.318712i \(-0.896750\pi\)
0.947852 0.318712i \(-0.103250\pi\)
\(308\) −4.21587e35 + 1.76243e35i −0.347458 + 0.145254i
\(309\) −9.12830e34 + 2.24394e36i −0.0717781 + 1.76446i
\(310\) −4.07876e36 −3.06044
\(311\) 1.68006e36 1.20309 0.601545 0.798839i \(-0.294552\pi\)
0.601545 + 0.798839i \(0.294552\pi\)
\(312\) 5.88838e35 + 2.39539e34i 0.402489 + 0.0163732i
\(313\) 1.99981e36i 1.30496i −0.757807 0.652479i \(-0.773729\pi\)
0.757807 0.652479i \(-0.226271\pi\)
\(314\) 3.75027e36 2.33659
\(315\) −8.63223e35 2.65228e36i −0.513594 1.57804i
\(316\) −3.11166e36 −1.76819
\(317\) 1.51211e36i 0.820776i 0.911911 + 0.410388i \(0.134607\pi\)
−0.911911 + 0.410388i \(0.865393\pi\)
\(318\) 3.23330e36 + 1.31530e35i 1.67669 + 0.0682075i
\(319\) 1.33521e35 0.0661583
\(320\) −5.29145e36 −2.50553
\(321\) 7.21323e34 1.77317e36i 0.0326442 0.802467i
\(322\) 1.89068e36 + 4.52265e36i 0.817913 + 1.95651i
\(323\) 5.84518e36i 2.41747i
\(324\) −4.37896e36 7.18495e35i −1.73168 0.284133i
\(325\) 1.49123e36i 0.563942i
\(326\) 6.65766e36i 2.40805i
\(327\) −2.15690e36 8.77422e34i −0.746255 0.0303575i
\(328\) 1.23209e36i 0.407822i
\(329\) −7.01933e35 1.67908e36i −0.222308 0.531778i
\(330\) −1.94877e36 7.92757e34i −0.590621 0.0240264i
\(331\) 3.80003e36 1.10225 0.551126 0.834422i \(-0.314198\pi\)
0.551126 + 0.834422i \(0.314198\pi\)
\(332\) 1.03944e36 0.288601
\(333\) 5.93215e36 + 4.83438e35i 1.57678 + 0.128499i
\(334\) 2.93406e35i 0.0746700i
\(335\) −7.82905e36 −1.90792
\(336\) 4.83868e35 + 1.30403e36i 0.112930 + 0.304346i
\(337\) −7.28308e36 −1.62810 −0.814051 0.580793i \(-0.802743\pi\)
−0.814051 + 0.580793i \(0.802743\pi\)
\(338\) 6.94945e36i 1.48819i
\(339\) 2.74246e34 6.74157e35i 0.00562658 0.138314i
\(340\) 2.39198e37 4.70233
\(341\) −1.26571e36 −0.238449
\(342\) 1.37169e37 + 1.11785e36i 2.47672 + 0.201839i
\(343\) −5.35944e36 2.15865e36i −0.927586 0.373609i
\(344\) 5.51264e36i 0.914665i
\(345\) −5.41735e35 + 1.33170e37i −0.0861807 + 2.11851i
\(346\) 9.00908e35i 0.137428i
\(347\) 4.70220e36i 0.687898i −0.938988 0.343949i \(-0.888235\pi\)
0.938988 0.343949i \(-0.111765\pi\)
\(348\) 1.56712e35 3.85232e36i 0.0219888 0.540534i
\(349\) 8.47899e36i 1.14124i 0.821216 + 0.570618i \(0.193296\pi\)
−0.821216 + 0.570618i \(0.806704\pi\)
\(350\) −2.08010e37 + 8.69578e36i −2.68594 + 1.12285i
\(351\) −3.15753e35 + 2.57588e36i −0.0391196 + 0.319133i
\(352\) −1.28897e36 −0.153241
\(353\) 1.15005e37 1.31215 0.656076 0.754695i \(-0.272215\pi\)
0.656076 + 0.754695i \(0.272215\pi\)
\(354\) 5.44428e35 1.33832e37i 0.0596202 1.46559i
\(355\) 1.27441e37i 1.33967i
\(356\) −1.21946e37 −1.23068
\(357\) 5.79715e36 + 1.56234e37i 0.561727 + 1.51386i
\(358\) 1.53116e37 1.42467
\(359\) 1.99530e37i 1.78295i 0.453068 + 0.891476i \(0.350329\pi\)
−0.453068 + 0.891476i \(0.649671\pi\)
\(360\) −1.96771e36 + 2.41453e37i −0.168878 + 2.07227i
\(361\) −1.50587e37 −1.24146
\(362\) −8.82660e36 −0.699068
\(363\) 1.25259e37 + 5.09553e35i 0.953156 + 0.0387743i
\(364\) 7.11939e36 2.97624e36i 0.520563 0.217620i
\(365\) 3.97877e37i 2.79578i
\(366\) 5.44061e36 + 2.21323e35i 0.367428 + 0.0149469i
\(367\) 3.61576e35i 0.0234716i −0.999931 0.0117358i \(-0.996264\pi\)
0.999931 0.0117358i \(-0.00373570\pi\)
\(368\) 6.64632e36i 0.414751i
\(369\) 5.40770e36 + 4.40698e35i 0.324437 + 0.0264398i
\(370\) 7.55373e37i 4.35749i
\(371\) 1.68155e37 7.02967e36i 0.932800 0.389954i
\(372\) −1.48555e36 + 3.65180e37i −0.0792526 + 1.94820i
\(373\) −3.55697e37 −1.82516 −0.912582 0.408894i \(-0.865915\pi\)
−0.912582 + 0.408894i \(0.865915\pi\)
\(374\) 1.16526e37 0.575153
\(375\) −2.63289e37 1.07106e36i −1.25020 0.0508579i
\(376\) 1.58064e37i 0.722118i
\(377\) −2.25478e36 −0.0991187
\(378\) −3.77719e37 + 1.06163e37i −1.59786 + 0.449099i
\(379\) 2.05886e37 0.838219 0.419110 0.907936i \(-0.362342\pi\)
0.419110 + 0.907936i \(0.362342\pi\)
\(380\) 1.11262e38i 4.35997i
\(381\) 3.06290e36 + 1.24598e35i 0.115537 + 0.00470002i
\(382\) −1.08873e37 −0.395369
\(383\) −1.21324e37 −0.424193 −0.212096 0.977249i \(-0.568029\pi\)
−0.212096 + 0.977249i \(0.568029\pi\)
\(384\) −2.16336e36 + 5.31800e37i −0.0728325 + 1.79038i
\(385\) −1.01350e37 + 4.23692e36i −0.328583 + 0.137363i
\(386\) 1.75363e37i 0.547547i
\(387\) −2.41953e37 1.97179e36i −0.727649 0.0592994i
\(388\) 1.69492e37i 0.491008i
\(389\) 5.01531e37i 1.39968i 0.714300 + 0.699840i \(0.246745\pi\)
−0.714300 + 0.699840i \(0.753255\pi\)
\(390\) 3.29092e37 + 1.33874e36i 0.884871 + 0.0359964i
\(391\) 7.96284e37i 2.06303i
\(392\) 3.57154e37 + 3.52516e37i 0.891676 + 0.880098i
\(393\) −5.85684e37 2.38255e36i −1.40920 0.0573258i
\(394\) 9.69874e37 2.24916
\(395\) −7.48048e37 −1.67214
\(396\) −1.41954e36 + 1.74189e37i −0.0305892 + 0.375353i
\(397\) 4.76288e37i 0.989481i 0.869041 + 0.494741i \(0.164737\pi\)
−0.869041 + 0.494741i \(0.835263\pi\)
\(398\) 1.09107e37 0.218549
\(399\) 7.26711e37 2.69651e37i 1.40364 0.520829i
\(400\) 3.05683e37 0.569380
\(401\) 1.04863e37i 0.188377i −0.995554 0.0941885i \(-0.969974\pi\)
0.995554 0.0941885i \(-0.0300256\pi\)
\(402\) −4.47636e36 + 1.10039e38i −0.0775617 + 1.90664i
\(403\) 2.13742e37 0.357245
\(404\) 2.57338e37 0.414930
\(405\) −1.05271e38 1.72728e37i −1.63761 0.268698i
\(406\) −1.31483e37 3.14518e37i −0.197353 0.472082i
\(407\) 2.34405e37i 0.339506i
\(408\) 5.88289e36 1.44614e38i 0.0822278 2.02134i
\(409\) 9.82064e37i 1.32480i 0.749148 + 0.662402i \(0.230463\pi\)
−0.749148 + 0.662402i \(0.769537\pi\)
\(410\) 6.88591e37i 0.896594i
\(411\) 5.04691e36 1.24064e38i 0.0634335 1.55934i
\(412\) 2.55399e38i 3.09891i
\(413\) −2.90971e37 6.96026e37i −0.340859 0.815360i
\(414\) 1.86864e38 + 1.52284e37i 2.11359 + 0.172246i
\(415\) 2.49884e37 0.272923
\(416\) 2.17671e37 0.229587
\(417\) 3.12471e36 7.68123e37i 0.0318301 0.782453i
\(418\) 5.42013e37i 0.533278i
\(419\) 1.19025e38 1.13119 0.565593 0.824685i \(-0.308647\pi\)
0.565593 + 0.824685i \(0.308647\pi\)
\(420\) 1.10347e38 + 2.97387e38i 1.01309 + 2.73028i
\(421\) 8.78733e37 0.779411 0.389706 0.920939i \(-0.372577\pi\)
0.389706 + 0.920939i \(0.372577\pi\)
\(422\) 1.17580e38i 1.00764i
\(423\) −6.93751e37 5.65369e36i −0.574471 0.0468163i
\(424\) −1.58296e38 −1.26668
\(425\) 3.66234e38 2.83217
\(426\) −1.79121e38 7.28663e36i −1.33878 0.0544612i
\(427\) 2.82952e37 1.18287e37i 0.204413 0.0854541i
\(428\) 2.01817e38i 1.40937i
\(429\) 1.02123e37 + 4.15433e35i 0.0689432 + 0.00280460i
\(430\) 3.08092e38i 2.01089i
\(431\) 7.39165e37i 0.466467i 0.972421 + 0.233234i \(0.0749307\pi\)
−0.972421 + 0.233234i \(0.925069\pi\)
\(432\) 5.28024e37 + 6.47256e36i 0.322210 + 0.0394968i
\(433\) 4.84871e37i 0.286122i −0.989714 0.143061i \(-0.954305\pi\)
0.989714 0.143061i \(-0.0456946\pi\)
\(434\) 1.24639e38 + 2.98147e38i 0.711301 + 1.70149i
\(435\) 3.76738e36 9.26105e37i 0.0207943 0.511171i
\(436\) 2.45492e38 1.31064
\(437\) −3.70387e38 −1.91282
\(438\) −5.59225e38 2.27492e37i −2.79390 0.113656i
\(439\) 1.46341e37i 0.0707342i −0.999374 0.0353671i \(-0.988740\pi\)
0.999374 0.0353671i \(-0.0112601\pi\)
\(440\) 9.54084e37 0.446193
\(441\) −1.67496e38 + 1.44148e38i −0.757959 + 0.652302i
\(442\) −1.96778e38 −0.861697
\(443\) 3.47079e38i 1.47087i 0.677596 + 0.735434i \(0.263022\pi\)
−0.677596 + 0.735434i \(0.736978\pi\)
\(444\) −6.76301e38 2.75118e37i −2.77387 0.112841i
\(445\) −2.93161e38 −1.16382
\(446\) −5.41950e38 −2.08259
\(447\) 6.57371e36 1.61596e38i 0.0244541 0.601135i
\(448\) 1.61697e38 + 3.86791e38i 0.582331 + 1.39298i
\(449\) 4.82451e38i 1.68221i −0.540868 0.841107i \(-0.681904\pi\)
0.540868 0.841107i \(-0.318096\pi\)
\(450\) −7.00398e37 + 8.59441e38i −0.236463 + 2.90158i
\(451\) 2.13681e37i 0.0698565i
\(452\) 7.67307e37i 0.242919i
\(453\) 1.49868e38 + 6.09659e36i 0.459498 + 0.0186923i
\(454\) 9.70790e38i 2.88281i
\(455\) 1.71152e38 7.15494e37i 0.492284 0.205798i
\(456\) −6.72666e38 2.73640e37i −1.87417 0.0762410i
\(457\) 2.40631e38 0.649482 0.324741 0.945803i \(-0.394723\pi\)
0.324741 + 0.945803i \(0.394723\pi\)
\(458\) 1.02924e39 2.69132
\(459\) 6.32617e38 + 7.75467e37i 1.60272 + 0.196462i
\(460\) 1.51571e39i 3.72072i
\(461\) 6.18821e37 0.147198 0.0735989 0.997288i \(-0.476552\pi\)
0.0735989 + 0.997288i \(0.476552\pi\)
\(462\) 5.37559e37 + 1.44872e38i 0.123913 + 0.333947i
\(463\) −1.28888e38 −0.287932 −0.143966 0.989583i \(-0.545986\pi\)
−0.143966 + 0.989583i \(0.545986\pi\)
\(464\) 4.62204e37i 0.100074i
\(465\) −3.57128e37 + 8.77899e38i −0.0749473 + 1.84237i
\(466\) 2.48774e38 0.506068
\(467\) −1.69432e38 −0.334118 −0.167059 0.985947i \(-0.553427\pi\)
−0.167059 + 0.985947i \(0.553427\pi\)
\(468\) 2.39720e37 2.94155e38i 0.0458289 0.562355i
\(469\) 2.39241e38 + 5.72282e38i 0.443434 + 1.06073i
\(470\) 8.83391e38i 1.58757i
\(471\) 3.28365e37 8.07194e38i 0.0572209 1.40661i
\(472\) 6.55219e38i 1.10720i
\(473\) 9.56061e37i 0.156675i
\(474\) −4.27706e37 + 1.05140e39i −0.0679767 + 1.67102i
\(475\) 1.70352e39i 2.62597i
\(476\) −7.30943e38 1.74847e39i −1.09291 2.61432i
\(477\) 5.66202e37 6.94773e38i 0.0821211 1.00769i
\(478\) −3.81543e38 −0.536833
\(479\) 8.24390e38 1.12530 0.562649 0.826696i \(-0.309782\pi\)
0.562649 + 0.826696i \(0.309782\pi\)
\(480\) −3.63693e37 + 8.94036e38i −0.0481655 + 1.18401i
\(481\) 3.95843e38i 0.508650i
\(482\) −1.49996e39 −1.87024
\(483\) 9.89993e38 3.67344e38i 1.19784 0.444467i
\(484\) −1.42567e39 −1.67402
\(485\) 4.07462e38i 0.464335i
\(486\) −3.02962e38 + 1.46973e39i −0.335091 + 1.62559i
\(487\) 1.14817e39 1.23264 0.616321 0.787495i \(-0.288622\pi\)
0.616321 + 0.787495i \(0.288622\pi\)
\(488\) −2.66363e38 −0.277578
\(489\) 1.43297e39 + 5.82931e37i 1.44964 + 0.0589710i
\(490\) 1.99607e39 + 1.97015e39i 1.96035 + 1.93489i
\(491\) 6.04572e38i 0.576456i 0.957562 + 0.288228i \(0.0930661\pi\)
−0.957562 + 0.288228i \(0.906934\pi\)
\(492\) −6.16509e38 2.50795e37i −0.570750 0.0232180i
\(493\) 5.53759e38i 0.497783i
\(494\) 9.15304e38i 0.798959i
\(495\) −3.41261e37 + 4.18753e38i −0.0289275 + 0.354962i
\(496\) 4.38145e38i 0.360690i
\(497\) −9.31562e38 + 3.89436e38i −0.744807 + 0.311364i
\(498\) 1.42874e37 3.51216e38i 0.0110950 0.272740i
\(499\) 1.45576e39 1.09807 0.549037 0.835798i \(-0.314995\pi\)
0.549037 + 0.835798i \(0.314995\pi\)
\(500\) 2.99668e39 2.19571
\(501\) −6.31518e37 2.56901e36i −0.0449509 0.00182860i
\(502\) 2.69381e38i 0.186279i
\(503\) −1.23391e39 −0.828985 −0.414493 0.910053i \(-0.636041\pi\)
−0.414493 + 0.910053i \(0.636041\pi\)
\(504\) 1.82508e39 5.93999e38i 1.19135 0.387742i
\(505\) 6.18646e38 0.392390
\(506\) 7.38380e38i 0.455090i
\(507\) 1.49578e39 + 6.08479e37i 0.895883 + 0.0364444i
\(508\) −3.48610e38 −0.202916
\(509\) −2.01483e39 −1.13981 −0.569903 0.821712i \(-0.693019\pi\)
−0.569903 + 0.821712i \(0.693019\pi\)
\(510\) 3.28785e38 8.08225e39i 0.180777 4.44391i
\(511\) −2.90838e39 + 1.21584e39i −1.55434 + 0.649789i
\(512\) 1.22908e39i 0.638507i
\(513\) 3.60704e38 2.94258e39i 0.182158 1.48603i
\(514\) 1.34344e39i 0.659560i
\(515\) 6.13984e39i 2.93057i
\(516\) 2.75841e39 + 1.12212e38i 1.28008 + 0.0520735i
\(517\) 2.74131e38i 0.123693i
\(518\) −5.52157e39 + 2.30828e39i −2.42260 + 1.01276i
\(519\) −1.93908e38 7.88816e36i −0.0827312 0.00336549i
\(520\) −1.61117e39 −0.668488
\(521\) 1.92698e39 0.777555 0.388777 0.921332i \(-0.372898\pi\)
0.388777 + 0.921332i \(0.372898\pi\)
\(522\) −1.29950e39 1.05903e38i −0.509983 0.0415608i
\(523\) 2.09948e39i 0.801378i −0.916214 0.400689i \(-0.868771\pi\)
0.916214 0.400689i \(-0.131229\pi\)
\(524\) 6.66609e39 2.47496
\(525\) 1.68952e39 + 4.55327e39i 0.610174 + 1.64442i
\(526\) −5.48255e38 −0.192615
\(527\) 5.24935e39i 1.79412i
\(528\) 8.51589e36 2.09339e38i 0.00283164 0.0696079i
\(529\) −1.95470e39 −0.632371
\(530\) −8.84692e39 −2.78479
\(531\) −2.87580e39 2.34362e38i −0.880820 0.0717821i
\(532\) −8.13292e39 + 3.39994e39i −2.42397 + 1.01333i
\(533\) 3.60847e38i 0.104659i
\(534\) −1.67619e38 + 4.12044e39i −0.0473124 + 1.16304i
\(535\) 4.85173e39i 1.33280i
\(536\) 5.38730e39i 1.44040i
\(537\) 1.34065e38 3.29561e39i 0.0348889 0.857646i
\(538\) 1.54037e39i 0.390194i
\(539\) 6.19414e38 + 6.11371e38i 0.152737 + 0.150754i
\(540\) 1.20417e40 + 1.47608e39i 2.89054 + 0.354325i
\(541\) −2.26614e39 −0.529574 −0.264787 0.964307i \(-0.585302\pi\)
−0.264787 + 0.964307i \(0.585302\pi\)
\(542\) −2.88320e39 −0.655973
\(543\) −7.72839e37 + 1.89981e39i −0.0171195 + 0.420835i
\(544\) 5.34584e39i 1.15301i
\(545\) 5.90168e39 1.23944
\(546\) −9.07782e38 2.44648e39i −0.185647 0.500320i
\(547\) 2.35298e39 0.468600 0.234300 0.972164i \(-0.424720\pi\)
0.234300 + 0.972164i \(0.424720\pi\)
\(548\) 1.41206e40i 2.73865i
\(549\) 9.52737e37 1.16908e39i 0.0179959 0.220824i
\(550\) 3.39602e39 0.624758
\(551\) 2.57578e39 0.461541
\(552\) −9.16368e39 3.72777e38i −1.59939 0.0650628i
\(553\) 2.28589e39 + 5.46803e39i 0.388634 + 0.929643i
\(554\) 1.33772e40i 2.21551i
\(555\) −1.62584e40 6.61389e38i −2.62319 0.106711i
\(556\) 8.74257e39i 1.37421i
\(557\) 7.49881e39i 1.14840i 0.818716 + 0.574198i \(0.194686\pi\)
−0.818716 + 0.574198i \(0.805314\pi\)
\(558\) 1.23186e40 + 1.00390e39i 1.83809 + 0.149794i
\(559\) 1.61451e39i 0.234731i
\(560\) −1.46668e39 3.50840e39i −0.207782 0.497031i
\(561\) 1.02027e38 2.50806e39i 0.0140850 0.346239i
\(562\) 1.18854e40 1.59896
\(563\) 8.01663e39 1.05104 0.525521 0.850781i \(-0.323870\pi\)
0.525521 + 0.850781i \(0.323870\pi\)
\(564\) 7.90917e39 + 3.21744e38i 1.01061 + 0.0411115i
\(565\) 1.84462e39i 0.229723i
\(566\) −6.20041e39 −0.752631
\(567\) 1.95429e39 + 8.22286e39i 0.231225 + 0.972900i
\(568\) 8.76946e39 1.01140
\(569\) 1.59640e40i 1.79480i −0.441223 0.897398i \(-0.645455\pi\)
0.441223 0.897398i \(-0.354545\pi\)
\(570\) −3.75942e40 1.52932e39i −4.12036 0.167616i
\(571\) 4.55261e39 0.486449 0.243224 0.969970i \(-0.421795\pi\)
0.243224 + 0.969970i \(0.421795\pi\)
\(572\) −1.16233e39 −0.121084
\(573\) −9.53271e37 + 2.34335e39i −0.00968221 + 0.238010i
\(574\) −5.03342e39 + 2.10420e39i −0.498472 + 0.208384i
\(575\) 2.32069e40i 2.24096i
\(576\) 1.59812e40 + 1.30238e39i 1.50481 + 0.122634i
\(577\) 9.87344e39i 0.906608i −0.891356 0.453304i \(-0.850245\pi\)
0.891356 0.453304i \(-0.149755\pi\)
\(578\) 2.97920e40i 2.66775i
\(579\) 3.77445e39 + 1.53544e38i 0.329620 + 0.0134089i
\(580\) 1.05407e40i 0.897764i
\(581\) −7.63596e38 1.82658e39i −0.0634322 0.151735i
\(582\) −5.72695e39 2.32972e38i −0.464024 0.0188764i
\(583\) −2.74535e39 −0.216972
\(584\) 2.73786e40 2.11069
\(585\) 5.76291e38 7.07153e39i 0.0433393 0.531806i
\(586\) 2.66815e40i 1.95747i
\(587\) −1.31675e40 −0.942431 −0.471216 0.882018i \(-0.656185\pi\)
−0.471216 + 0.882018i \(0.656185\pi\)
\(588\) 1.83662e40 1.71537e40i 1.28247 1.19780i
\(589\) −2.44171e40 −1.66349
\(590\) 3.66191e40i 2.43418i
\(591\) 8.49201e38 2.08752e40i 0.0550798 1.35398i
\(592\) 8.11430e39 0.513554
\(593\) 8.54716e39 0.527872 0.263936 0.964540i \(-0.414979\pi\)
0.263936 + 0.964540i \(0.414979\pi\)
\(594\) 5.86614e39 + 7.19076e38i 0.353549 + 0.0433383i
\(595\) −1.75720e40 4.20336e40i −1.03354 2.47230i
\(596\) 1.83924e40i 1.05577i
\(597\) 9.55318e37 2.34838e39i 0.00535205 0.131565i
\(598\) 1.24691e40i 0.681818i
\(599\) 2.56471e40i 1.36883i 0.729093 + 0.684414i \(0.239942\pi\)
−0.729093 + 0.684414i \(0.760058\pi\)
\(600\) 1.71451e39 4.21464e40i 0.0893196 2.19567i
\(601\) 2.37314e40i 1.20682i −0.797430 0.603411i \(-0.793808\pi\)
0.797430 0.603411i \(-0.206192\pi\)
\(602\) 2.25207e40 9.41470e39i 1.11798 0.467366i
\(603\) 2.36452e40 + 1.92695e39i 1.14589 + 0.0933835i
\(604\) −1.70575e40 −0.807013
\(605\) −3.42733e40 −1.58308
\(606\) 3.53719e38 8.69520e39i 0.0159517 0.392127i
\(607\) 3.00569e40i 1.32345i 0.749745 + 0.661727i \(0.230176\pi\)
−0.749745 + 0.661727i \(0.769824\pi\)
\(608\) −2.48659e40 −1.06906
\(609\) −6.88470e39 + 2.55461e39i −0.289024 + 0.107244i
\(610\) −1.48865e40 −0.610255
\(611\) 4.62928e39i 0.185317i
\(612\) −7.22423e40 5.88735e39i −2.82420 0.230157i
\(613\) 1.43309e40 0.547137 0.273568 0.961853i \(-0.411796\pi\)
0.273568 + 0.961853i \(0.411796\pi\)
\(614\) 2.83738e40 1.05798
\(615\) −1.48210e40 6.02916e38i −0.539745 0.0219567i
\(616\) −2.91550e39 6.97409e39i −0.103703 0.248066i
\(617\) 5.04374e40i 1.75234i −0.482004 0.876169i \(-0.660091\pi\)
0.482004 0.876169i \(-0.339909\pi\)
\(618\) −8.62966e40 3.51053e39i −2.92861 0.119135i
\(619\) 2.74656e40i 0.910489i 0.890367 + 0.455244i \(0.150448\pi\)
−0.890367 + 0.455244i \(0.849552\pi\)
\(620\) 9.99201e40i 3.23574i
\(621\) 4.91384e39 4.00866e40i 0.155451 1.26815i
\(622\) 6.46111e40i 1.99685i
\(623\) 8.95845e39 + 2.14293e40i 0.270493 + 0.647040i
\(624\) −1.43809e38 + 3.53514e39i −0.00424238 + 0.104287i
\(625\) 1.11875e40 0.322459
\(626\) 7.69082e40 2.16593
\(627\) −1.16661e40 4.74575e38i −0.321030 0.0130595i
\(628\) 9.18727e40i 2.47042i
\(629\) 9.72161e40 2.55449
\(630\) 1.02001e41 3.31976e40i 2.61918 0.852449i
\(631\) −5.69393e40 −1.42885 −0.714424 0.699713i \(-0.753311\pi\)
−0.714424 + 0.699713i \(0.753311\pi\)
\(632\) 5.14745e40i 1.26239i
\(633\) 2.53076e40 + 1.02951e39i 0.606593 + 0.0246761i
\(634\) −5.81523e40 −1.36230
\(635\) −8.38066e39 −0.191893
\(636\) −3.22218e39 + 7.92082e40i −0.0721143 + 1.77273i
\(637\) −1.04601e40 1.03243e40i −0.228831 0.225860i
\(638\) 5.13491e39i 0.109808i
\(639\) −3.13670e39 + 3.84897e40i −0.0655708 + 0.804603i
\(640\) 1.45511e41i 2.97362i
\(641\) 5.17757e40i 1.03439i −0.855867 0.517195i \(-0.826976\pi\)
0.855867 0.517195i \(-0.173024\pi\)
\(642\) 6.81920e40 + 2.77404e39i 1.33191 + 0.0541820i
\(643\) 3.73349e40i 0.712946i 0.934306 + 0.356473i \(0.116021\pi\)
−0.934306 + 0.356473i \(0.883979\pi\)
\(644\) −1.10794e41 + 4.63171e40i −2.06858 + 0.864762i
\(645\) 6.63127e40 + 2.69759e39i 1.21054 + 0.0492447i
\(646\) 2.24792e41 4.01245
\(647\) −3.84820e40 −0.671654 −0.335827 0.941924i \(-0.609016\pi\)
−0.335827 + 0.941924i \(0.609016\pi\)
\(648\) 1.18857e40 7.24389e40i 0.202855 1.23633i
\(649\) 1.13635e40i 0.189655i
\(650\) −5.73491e40 −0.936015
\(651\) 6.52634e40 2.42164e40i 1.04171 0.386532i
\(652\) −1.63097e41 −2.54598
\(653\) 1.14977e40i 0.175538i 0.996141 + 0.0877688i \(0.0279737\pi\)
−0.996141 + 0.0877688i \(0.972026\pi\)
\(654\) 3.37436e39 8.29493e40i 0.0503865 1.23861i
\(655\) 1.60254e41 2.34051
\(656\) 7.39692e39 0.105668
\(657\) −9.79291e39 + 1.20166e41i −0.136840 + 1.67913i
\(658\) 6.45734e40 2.69947e40i 0.882630 0.368980i
\(659\) 1.40806e41i 1.88271i −0.337417 0.941355i \(-0.609553\pi\)
0.337417 0.941355i \(-0.390447\pi\)
\(660\) 1.94207e39 4.77403e40i 0.0254026 0.624451i
\(661\) 2.80928e40i 0.359479i −0.983714 0.179739i \(-0.942475\pi\)
0.983714 0.179739i \(-0.0575254\pi\)
\(662\) 1.46140e41i 1.82949i
\(663\) −1.72295e39 + 4.23539e40i −0.0211021 + 0.518737i
\(664\) 1.71949e40i 0.206045i
\(665\) −1.95517e41 + 8.17352e40i −2.29230 + 0.958287i
\(666\) −1.85919e40 + 2.28137e41i −0.213279 + 2.61709i
\(667\) 3.50896e40 0.393871
\(668\) 7.18777e39 0.0789469
\(669\) −4.74520e39 + 1.16648e41i −0.0510007 + 1.25371i
\(670\) 3.01087e41i 3.16670i
\(671\) −4.61955e39 −0.0475470
\(672\) 6.64630e40 2.46615e40i 0.669461 0.248408i
\(673\) 5.75574e40 0.567391 0.283696 0.958914i \(-0.408439\pi\)
0.283696 + 0.958914i \(0.408439\pi\)
\(674\) 2.80090e41i 2.70228i
\(675\) 1.84370e41 + 2.26002e40i 1.74095 + 0.213407i
\(676\) −1.70245e41 −1.57343
\(677\) −1.35604e41 −1.22669 −0.613346 0.789814i \(-0.710177\pi\)
−0.613346 + 0.789814i \(0.710177\pi\)
\(678\) 2.59265e40 + 1.05469e39i 0.229569 + 0.00933884i
\(679\) −2.97843e40 + 1.24512e40i −0.258152 + 0.107920i
\(680\) 3.95693e41i 3.35721i
\(681\) −2.08950e41 8.50004e39i −1.73543 0.0705972i
\(682\) 4.86762e40i 0.395771i
\(683\) 1.77966e41i 1.41657i 0.705927 + 0.708285i \(0.250531\pi\)
−0.705927 + 0.708285i \(0.749469\pi\)
\(684\) −2.73847e40 + 3.36031e41i −0.213400 + 2.61858i
\(685\) 3.39463e41i 2.58987i
\(686\) 8.30167e40 2.06111e41i 0.620106 1.53958i
\(687\) 9.01178e39 2.21529e41i 0.0659079 1.62016i
\(688\) −3.30956e40 −0.236994
\(689\) 4.63610e40 0.325068
\(690\) −5.12142e41 2.08339e40i −3.51624 0.143040i
\(691\) 3.43405e40i 0.230874i 0.993315 + 0.115437i \(0.0368269\pi\)
−0.993315 + 0.115437i \(0.963173\pi\)
\(692\) 2.20701e40 0.145300
\(693\) 3.16525e40 1.03018e40i 0.204069 0.0664170i
\(694\) 1.80836e41 1.14175
\(695\) 2.10173e41i 1.29956i
\(696\) 6.37269e40 + 2.59240e39i 0.385912 + 0.0156988i
\(697\) 8.86214e40 0.525609
\(698\) −3.26082e41 −1.89419
\(699\) 2.17821e39 5.35452e40i 0.0123931 0.304650i
\(700\) −2.13026e41 5.09575e41i −1.18716 2.83979i
\(701\) 1.75246e40i 0.0956615i 0.998855 + 0.0478307i \(0.0152308\pi\)
−0.998855 + 0.0478307i \(0.984769\pi\)
\(702\) −9.90623e40 1.21431e40i −0.529688 0.0649296i
\(703\) 4.52195e41i 2.36850i
\(704\) 6.31485e40i 0.324011i
\(705\) 1.90138e41 + 7.73478e39i 0.955711 + 0.0388782i
\(706\) 4.42283e41i 2.17787i
\(707\) −1.89046e40 4.52214e40i −0.0911983 0.218153i
\(708\) 3.27858e41 + 1.33372e40i 1.54954 + 0.0630351i
\(709\) 2.33578e41 1.08159 0.540793 0.841156i \(-0.318124\pi\)
0.540793 + 0.841156i \(0.318124\pi\)
\(710\) 4.90110e41 2.22355
\(711\) 2.25924e41 + 1.84116e40i 1.00428 + 0.0818432i
\(712\) 2.01729e41i 0.878637i
\(713\) −3.32632e41 −1.41960
\(714\) −6.00838e41 + 2.22945e41i −2.51266 + 0.932338i
\(715\) −2.79427e40 −0.114507
\(716\) 3.75097e41i 1.50628i
\(717\) −3.34071e39 + 8.21220e40i −0.0131465 + 0.323170i
\(718\) −7.67348e41 −2.95929
\(719\) −8.57988e40 −0.324274 −0.162137 0.986768i \(-0.551839\pi\)
−0.162137 + 0.986768i \(0.551839\pi\)
\(720\) −1.44958e41 1.18133e40i −0.536934 0.0437572i
\(721\) −4.48805e41 + 1.87622e41i −1.62928 + 0.681117i
\(722\) 5.79123e41i 2.06054i
\(723\) −1.31334e40 + 3.22847e41i −0.0458005 + 1.12588i
\(724\) 2.16231e41i 0.739109i
\(725\) 1.61387e41i 0.540715i
\(726\) −1.95962e40 + 4.81718e41i −0.0643564 + 1.58202i
\(727\) 5.74080e41i 1.84809i −0.382283 0.924045i \(-0.624862\pi\)
0.382283 0.924045i \(-0.375138\pi\)
\(728\) 4.92343e40 + 1.17772e41i 0.155369 + 0.371654i
\(729\) 3.13687e41 + 7.80772e40i 0.970393 + 0.241532i
\(730\) 1.53014e42 4.64035
\(731\) −3.96513e41 −1.17884
\(732\) −5.42190e39 + 1.33282e41i −0.0158030 + 0.388474i
\(733\) 2.25888e41i 0.645484i 0.946487 + 0.322742i \(0.104605\pi\)
−0.946487 + 0.322742i \(0.895395\pi\)
\(734\) 1.39054e40 0.0389574
\(735\) 4.41526e41 4.12377e41i 1.21280 1.13273i
\(736\) −3.38746e41 −0.912316
\(737\) 9.34324e40i 0.246728i
\(738\) −1.69482e40 + 2.07967e41i −0.0438841 + 0.538491i
\(739\) 4.92269e41 1.24985 0.624925 0.780685i \(-0.285129\pi\)
0.624925 + 0.780685i \(0.285129\pi\)
\(740\) 1.85049e42 4.60708
\(741\) 1.97007e41 + 8.01421e39i 0.480969 + 0.0195658i
\(742\) 2.70345e41 + 6.46686e41i 0.647234 + 1.54823i
\(743\) 1.40196e41i 0.329152i 0.986364 + 0.164576i \(0.0526256\pi\)
−0.986364 + 0.164576i \(0.947374\pi\)
\(744\) −6.04098e41 2.45746e40i −1.39091 0.0565821i
\(745\) 4.42158e41i 0.998415i
\(746\) 1.36793e42i 3.02935i
\(747\) −7.54695e40 6.15035e39i −0.163917 0.0133583i
\(748\) 2.85460e41i 0.608097i
\(749\) 3.54648e41 1.48259e41i 0.740988 0.309768i
\(750\) 4.11903e40 1.01255e42i 0.0844125 2.07504i
\(751\) −5.68191e41 −1.14213 −0.571064 0.820905i \(-0.693469\pi\)
−0.571064 + 0.820905i \(0.693469\pi\)
\(752\) −9.48948e40 −0.187104
\(753\) −5.79807e40 2.35865e39i −0.112139 0.00456179i
\(754\) 8.67138e40i