Properties

Label 8.14.b.b.5.8
Level 8
Weight 14
Character 8.5
Analytic conductor 8.578
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 8.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(8.57847431615\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{48}\cdot 3^{4} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.8
Root \(27.9424 + 31.0290i\)
Character \(\chi\) = 8.5
Dual form 8.14.b.b.5.7

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(65.8848 + 62.0580i) q^{2}\) \(-1231.41i q^{3}\) \(+(489.620 + 8177.36i) q^{4}\) \(+25270.7i q^{5}\) \(+(76418.8 - 81131.3i) q^{6}\) \(+608245. q^{7}\) \(+(-475211. + 569148. i) q^{8}\) \(+77950.5 q^{9}\) \(+O(q^{10})\) \(q\)\(+(65.8848 + 62.0580i) q^{2}\) \(-1231.41i q^{3}\) \(+(489.620 + 8177.36i) q^{4}\) \(+25270.7i q^{5}\) \(+(76418.8 - 81131.3i) q^{6}\) \(+608245. q^{7}\) \(+(-475211. + 569148. i) q^{8}\) \(+77950.5 q^{9}\) \(+(-1.56825e6 + 1.66495e6i) q^{10}\) \(+7.12288e6i q^{11}\) \(+(1.00697e7 - 602923. i) q^{12}\) \(-1.12887e7i q^{13}\) \(+(4.00741e7 + 3.77465e7i) q^{14}\) \(+3.11186e7 q^{15}\) \(+(-6.66294e7 + 8.00759e6i) q^{16}\) \(-5.09178e7 q^{17}\) \(+(5.13575e6 + 4.83745e6i) q^{18}\) \(-1.86178e8i q^{19}\) \(+(-2.06647e8 + 1.23730e7i) q^{20}\) \(-7.49000e8i q^{21}\) \(+(-4.42031e8 + 4.69289e8i) q^{22}\) \(-3.07644e8 q^{23}\) \(+(7.00855e8 + 5.85181e8i) q^{24}\) \(+5.82097e8 q^{25}\) \(+(7.00553e8 - 7.43753e8i) q^{26}\) \(-2.05926e9i q^{27}\) \(+(2.97809e8 + 4.97384e9i) q^{28}\) \(+4.74147e8i q^{29}\) \(+(2.05024e9 + 1.93115e9i) q^{30}\) \(-2.41919e9 q^{31}\) \(+(-4.88680e9 - 3.60731e9i) q^{32}\) \(+8.77119e9 q^{33}\) \(+(-3.35471e9 - 3.15985e9i) q^{34}\) \(+1.53708e10i q^{35}\) \(+(3.81661e7 + 6.37429e8i) q^{36}\) \(-1.55589e10i q^{37}\) \(+(1.15538e10 - 1.22663e10i) q^{38}\) \(-1.39010e10 q^{39}\) \(+(-1.43828e10 - 1.20089e10i) q^{40}\) \(-2.32986e10 q^{41}\) \(+(4.64814e10 - 4.93477e10i) q^{42}\) \(+6.55713e10i q^{43}\) \(+(-5.82463e10 + 3.48750e9i) q^{44}\) \(+1.96986e9i q^{45}\) \(+(-2.02691e10 - 1.90917e10i) q^{46}\) \(-6.84950e10 q^{47}\) \(+(9.86063e9 + 8.20482e10i) q^{48}\) \(+2.73073e11 q^{49}\) \(+(3.83514e10 + 3.61237e10i) q^{50}\) \(+6.27007e10i q^{51}\) \(+(9.23116e10 - 5.52716e9i) q^{52}\) \(-9.64859e10i q^{53}\) \(+(1.27793e11 - 1.35674e11i) q^{54}\) \(-1.80000e11 q^{55}\) \(+(-2.89045e11 + 3.46182e11i) q^{56}\) \(-2.29261e11 q^{57}\) \(+(-2.94246e10 + 3.12391e10i) q^{58}\) \(-3.22470e11i q^{59}\) \(+(1.52363e10 + 2.54468e11i) q^{60}\) \(-6.66785e11i q^{61}\) \(+(-1.59388e11 - 1.50130e11i) q^{62}\) \(+4.74130e10 q^{63}\) \(+(-9.81039e10 - 5.40932e11i) q^{64}\) \(+2.85273e11 q^{65}\) \(+(5.77888e11 + 5.44322e11i) q^{66}\) \(+5.91556e11i q^{67}\) \(+(-2.49303e10 - 4.16373e11i) q^{68}\) \(+3.78836e11i q^{69}\) \(+(-9.53878e11 + 1.01270e12i) q^{70}\) \(+8.43664e11 q^{71}\) \(+(-3.70430e10 + 4.43654e10i) q^{72}\) \(-7.21901e11 q^{73}\) \(+(9.65556e11 - 1.02510e12i) q^{74}\) \(-7.16800e11i q^{75}\) \(+(1.52244e12 - 9.11562e10i) q^{76}\) \(+4.33246e12i q^{77}\) \(+(-9.15866e11 - 8.62668e11i) q^{78}\) \(+5.78664e11 q^{79}\) \(+(-2.02357e11 - 1.68377e12i) q^{80}\) \(-2.41151e12 q^{81}\) \(+(-1.53502e12 - 1.44586e12i) q^{82}\) \(-1.54397e11i q^{83}\) \(+(6.12484e12 - 3.66725e11i) q^{84}\) \(-1.28673e12i q^{85}\) \(+(-4.06922e12 + 4.32015e12i) q^{86}\) \(+5.83870e11 q^{87}\) \(+(-4.05397e12 - 3.38487e12i) q^{88}\) \(+2.38527e12 q^{89}\) \(+(-1.22245e11 + 1.29784e11i) q^{90}\) \(-6.86629e12i q^{91}\) \(+(-1.50628e11 - 2.51571e12i) q^{92}\) \(+2.97901e12i q^{93}\) \(+(-4.51278e12 - 4.25066e12i) q^{94}\) \(+4.70483e12 q^{95}\) \(+(-4.44208e12 + 6.01766e12i) q^{96}\) \(-1.26695e13 q^{97}\) \(+(1.79914e13 + 1.69464e13i) q^{98}\) \(+5.55232e11i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut -\mathstrut 4542088q^{10} \) \(\mathstrut +\mathstrut 27987880q^{12} \) \(\mathstrut +\mathstrut 1408688q^{14} \) \(\mathstrut -\mathstrut 145914416q^{15} \) \(\mathstrut +\mathstrut 56624912q^{16} \) \(\mathstrut +\mathstrut 217326004q^{17} \) \(\mathstrut -\mathstrut 147615262q^{18} \) \(\mathstrut +\mathstrut 21655184q^{20} \) \(\mathstrut -\mathstrut 177987876q^{22} \) \(\mathstrut -\mathstrut 78679952q^{23} \) \(\mathstrut +\mathstrut 320199056q^{24} \) \(\mathstrut -\mathstrut 3076402574q^{25} \) \(\mathstrut +\mathstrut 3734872040q^{26} \) \(\mathstrut -\mathstrut 1653812448q^{28} \) \(\mathstrut +\mathstrut 6338232752q^{30} \) \(\mathstrut +\mathstrut 648233792q^{31} \) \(\mathstrut -\mathstrut 11298380000q^{32} \) \(\mathstrut +\mathstrut 15484079688q^{33} \) \(\mathstrut -\mathstrut 6096822724q^{34} \) \(\mathstrut +\mathstrut 4004708940q^{36} \) \(\mathstrut -\mathstrut 18764968628q^{38} \) \(\mathstrut -\mathstrut 63497510288q^{39} \) \(\mathstrut +\mathstrut 7466802592q^{40} \) \(\mathstrut +\mathstrut 59324640356q^{41} \) \(\mathstrut +\mathstrut 53897620960q^{42} \) \(\mathstrut +\mathstrut 13325704392q^{44} \) \(\mathstrut -\mathstrut 55046867440q^{46} \) \(\mathstrut -\mathstrut 10176534816q^{47} \) \(\mathstrut -\mathstrut 301841943264q^{48} \) \(\mathstrut +\mathstrut 182708552058q^{49} \) \(\mathstrut +\mathstrut 326454435302q^{50} \) \(\mathstrut -\mathstrut 53296499536q^{52} \) \(\mathstrut +\mathstrut 35449773752q^{54} \) \(\mathstrut -\mathstrut 123010753008q^{55} \) \(\mathstrut -\mathstrut 462152447680q^{56} \) \(\mathstrut -\mathstrut 511372324504q^{57} \) \(\mathstrut +\mathstrut 766482705096q^{58} \) \(\mathstrut +\mathstrut 1813082440992q^{60} \) \(\mathstrut -\mathstrut 1665308528960q^{62} \) \(\mathstrut -\mathstrut 898991123792q^{63} \) \(\mathstrut -\mathstrut 2180548996032q^{64} \) \(\mathstrut +\mathstrut 1577231990240q^{65} \) \(\mathstrut +\mathstrut 2269525079448q^{66} \) \(\mathstrut +\mathstrut 2338280915304q^{68} \) \(\mathstrut -\mathstrut 6070110714688q^{70} \) \(\mathstrut +\mathstrut 726361179984q^{71} \) \(\mathstrut -\mathstrut 3600753685960q^{72} \) \(\mathstrut -\mathstrut 633240365532q^{73} \) \(\mathstrut +\mathstrut 7528513982264q^{74} \) \(\mathstrut +\mathstrut 10338420845032q^{76} \) \(\mathstrut -\mathstrut 8252024440816q^{78} \) \(\mathstrut +\mathstrut 5445103565344q^{79} \) \(\mathstrut -\mathstrut 15406871881920q^{80} \) \(\mathstrut -\mathstrut 9674575380574q^{81} \) \(\mathstrut +\mathstrut 12273334206796q^{82} \) \(\mathstrut +\mathstrut 20362643366464q^{84} \) \(\mathstrut -\mathstrut 26794541719396q^{86} \) \(\mathstrut +\mathstrut 7632221772720q^{87} \) \(\mathstrut -\mathstrut 27677491769136q^{88} \) \(\mathstrut +\mathstrut 5506344808004q^{89} \) \(\mathstrut +\mathstrut 31454099524040q^{90} \) \(\mathstrut +\mathstrut 33971694298464q^{92} \) \(\mathstrut -\mathstrut 45356008560096q^{94} \) \(\mathstrut -\mathstrut 14214732035504q^{95} \) \(\mathstrut -\mathstrut 35398666935232q^{96} \) \(\mathstrut +\mathstrut 1361133320788q^{97} \) \(\mathstrut +\mathstrut 54325451514942q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 65.8848 + 62.0580i 0.727931 + 0.685650i
\(3\) 1231.41i 0.975247i −0.873054 0.487624i \(-0.837864\pi\)
0.873054 0.487624i \(-0.162136\pi\)
\(4\) 489.620 + 8177.36i 0.0597680 + 0.998212i
\(5\) 25270.7i 0.723288i 0.932316 + 0.361644i \(0.117784\pi\)
−0.932316 + 0.361644i \(0.882216\pi\)
\(6\) 76418.8 81131.3i 0.668678 0.709913i
\(7\) 608245. 1.95408 0.977038 0.213064i \(-0.0683442\pi\)
0.977038 + 0.213064i \(0.0683442\pi\)
\(8\) −475211. + 569148.i −0.640917 + 0.767610i
\(9\) 77950.5 0.0488925
\(10\) −1.56825e6 + 1.66495e6i −0.495923 + 0.526504i
\(11\) 7.12288e6i 1.21228i 0.795358 + 0.606140i \(0.207283\pi\)
−0.795358 + 0.606140i \(0.792717\pi\)
\(12\) 1.00697e7 602923.i 0.973504 0.0582886i
\(13\) 1.12887e7i 0.648652i −0.945945 0.324326i \(-0.894863\pi\)
0.945945 0.324326i \(-0.105137\pi\)
\(14\) 4.00741e7 + 3.77465e7i 1.42243 + 1.33981i
\(15\) 3.11186e7 0.705385
\(16\) −6.66294e7 + 8.00759e6i −0.992856 + 0.119322i
\(17\) −5.09178e7 −0.511625 −0.255812 0.966726i \(-0.582343\pi\)
−0.255812 + 0.966726i \(0.582343\pi\)
\(18\) 5.13575e6 + 4.83745e6i 0.0355904 + 0.0335232i
\(19\) 1.86178e8i 0.907881i −0.891032 0.453941i \(-0.850018\pi\)
0.891032 0.453941i \(-0.149982\pi\)
\(20\) −2.06647e8 + 1.23730e7i −0.721995 + 0.0432295i
\(21\) 7.49000e8i 1.90571i
\(22\) −4.42031e8 + 4.69289e8i −0.831200 + 0.882457i
\(23\) −3.07644e8 −0.433328 −0.216664 0.976246i \(-0.569518\pi\)
−0.216664 + 0.976246i \(0.569518\pi\)
\(24\) 7.00855e8 + 5.85181e8i 0.748610 + 0.625053i
\(25\) 5.82097e8 0.476854
\(26\) 7.00553e8 7.43753e8i 0.444748 0.472174i
\(27\) 2.05926e9i 1.02293i
\(28\) 2.97809e8 + 4.97384e9i 0.116791 + 1.95058i
\(29\) 4.74147e8i 0.148022i 0.997257 + 0.0740110i \(0.0235800\pi\)
−0.997257 + 0.0740110i \(0.976420\pi\)
\(30\) 2.05024e9 + 1.93115e9i 0.513472 + 0.483647i
\(31\) −2.41919e9 −0.489574 −0.244787 0.969577i \(-0.578718\pi\)
−0.244787 + 0.969577i \(0.578718\pi\)
\(32\) −4.88680e9 3.60731e9i −0.804544 0.593893i
\(33\) 8.77119e9 1.18227
\(34\) −3.35471e9 3.15985e9i −0.372427 0.350795i
\(35\) 1.53708e10i 1.41336i
\(36\) 3.81661e7 + 6.37429e8i 0.00292221 + 0.0488051i
\(37\) 1.55589e10i 0.996939i −0.866907 0.498470i \(-0.833896\pi\)
0.866907 0.498470i \(-0.166104\pi\)
\(38\) 1.15538e10 1.22663e10i 0.622489 0.660875i
\(39\) −1.39010e10 −0.632596
\(40\) −1.43828e10 1.20089e10i −0.555203 0.463568i
\(41\) −2.32986e10 −0.766009 −0.383005 0.923746i \(-0.625111\pi\)
−0.383005 + 0.923746i \(0.625111\pi\)
\(42\) 4.64814e10 4.93477e10i 1.30665 1.38722i
\(43\) 6.55713e10i 1.58186i 0.611905 + 0.790932i \(0.290404\pi\)
−0.611905 + 0.790932i \(0.709596\pi\)
\(44\) −5.82463e10 + 3.48750e9i −1.21011 + 0.0724556i
\(45\) 1.96986e9i 0.0353634i
\(46\) −2.02691e10 1.90917e10i −0.315433 0.297112i
\(47\) −6.84950e10 −0.926879 −0.463440 0.886129i \(-0.653385\pi\)
−0.463440 + 0.886129i \(0.653385\pi\)
\(48\) 9.86063e9 + 8.20482e10i 0.116369 + 0.968280i
\(49\) 2.73073e11 2.81842
\(50\) 3.83514e10 + 3.61237e10i 0.347117 + 0.326955i
\(51\) 6.27007e10i 0.498960i
\(52\) 9.23116e10 5.52716e9i 0.647492 0.0387686i
\(53\) 9.64859e10i 0.597958i −0.954260 0.298979i \(-0.903354\pi\)
0.954260 0.298979i \(-0.0966460\pi\)
\(54\) 1.27793e11 1.35674e11i 0.701372 0.744623i
\(55\) −1.80000e11 −0.876828
\(56\) −2.89045e11 + 3.46182e11i −1.25240 + 1.49997i
\(57\) −2.29261e11 −0.885409
\(58\) −2.94246e10 + 3.12391e10i −0.101491 + 0.107750i
\(59\) 3.22470e11i 0.995295i −0.867379 0.497647i \(-0.834197\pi\)
0.867379 0.497647i \(-0.165803\pi\)
\(60\) 1.52363e10 + 2.54468e11i 0.0421595 + 0.704124i
\(61\) 6.66785e11i 1.65707i −0.559934 0.828537i \(-0.689174\pi\)
0.559934 0.828537i \(-0.310826\pi\)
\(62\) −1.59388e11 1.50130e11i −0.356377 0.335677i
\(63\) 4.74130e10 0.0955397
\(64\) −9.81039e10 5.40932e11i −0.178450 0.983949i
\(65\) 2.85273e11 0.469162
\(66\) 5.77888e11 + 5.44322e11i 0.860614 + 0.810626i
\(67\) 5.91556e11i 0.798932i 0.916748 + 0.399466i \(0.130804\pi\)
−0.916748 + 0.399466i \(0.869196\pi\)
\(68\) −2.49303e10 4.16373e11i −0.0305788 0.510710i
\(69\) 3.78836e11i 0.422602i
\(70\) −9.53878e11 + 1.01270e12i −0.969071 + 1.02883i
\(71\) 8.43664e11 0.781610 0.390805 0.920473i \(-0.372197\pi\)
0.390805 + 0.920473i \(0.372197\pi\)
\(72\) −3.70430e10 + 4.43654e10i −0.0313361 + 0.0375304i
\(73\) −7.21901e11 −0.558315 −0.279158 0.960245i \(-0.590055\pi\)
−0.279158 + 0.960245i \(0.590055\pi\)
\(74\) 9.65556e11 1.02510e12i 0.683552 0.725703i
\(75\) 7.16800e11i 0.465050i
\(76\) 1.52244e12 9.11562e10i 0.906258 0.0542622i
\(77\) 4.33246e12i 2.36889i
\(78\) −9.15866e11 8.62668e11i −0.460486 0.433739i
\(79\) 5.78664e11 0.267824 0.133912 0.990993i \(-0.457246\pi\)
0.133912 + 0.990993i \(0.457246\pi\)
\(80\) −2.02357e11 1.68377e12i −0.0863045 0.718121i
\(81\) −2.41151e12 −0.948717
\(82\) −1.53502e12 1.44586e12i −0.557602 0.525214i
\(83\) 1.54397e11i 0.0518361i −0.999664 0.0259180i \(-0.991749\pi\)
0.999664 0.0259180i \(-0.00825089\pi\)
\(84\) 6.12484e12 3.66725e11i 1.90230 0.113900i
\(85\) 1.28673e12i 0.370052i
\(86\) −4.06922e12 + 4.32015e12i −1.08460 + 1.15149i
\(87\) 5.83870e11 0.144358
\(88\) −4.05397e12 3.38487e12i −0.930558 0.776971i
\(89\) 2.38527e12 0.508749 0.254374 0.967106i \(-0.418130\pi\)
0.254374 + 0.967106i \(0.418130\pi\)
\(90\) −1.22245e11 + 1.29784e11i −0.0242469 + 0.0257421i
\(91\) 6.86629e12i 1.26752i
\(92\) −1.50628e11 2.51571e12i −0.0258992 0.432554i
\(93\) 2.97901e12i 0.477456i
\(94\) −4.51278e12 4.25066e12i −0.674704 0.635515i
\(95\) 4.70483e12 0.656660
\(96\) −4.44208e12 + 6.01766e12i −0.579193 + 0.784629i
\(97\) −1.26695e13 −1.54435 −0.772173 0.635412i \(-0.780830\pi\)
−0.772173 + 0.635412i \(0.780830\pi\)
\(98\) 1.79914e13 + 1.69464e13i 2.05161 + 1.93245i
\(99\) 5.55232e11i 0.0592714i
\(100\) 2.85006e11 + 4.76001e12i 0.0285006 + 0.476001i
\(101\) 1.38377e13i 1.29710i −0.761170 0.648552i \(-0.775375\pi\)
0.761170 0.648552i \(-0.224625\pi\)
\(102\) −3.89108e12 + 4.13102e12i −0.342112 + 0.363209i
\(103\) 1.67913e12 0.138561 0.0692806 0.997597i \(-0.477930\pi\)
0.0692806 + 0.997597i \(0.477930\pi\)
\(104\) 6.42494e12 + 5.36451e12i 0.497912 + 0.415732i
\(105\) 1.89277e13 1.37838
\(106\) 5.98772e12 6.35695e12i 0.409990 0.435272i
\(107\) 1.44249e13i 0.929217i 0.885516 + 0.464608i \(0.153805\pi\)
−0.885516 + 0.464608i \(0.846195\pi\)
\(108\) 1.68393e13 1.00825e12i 1.02110 0.0611385i
\(109\) 4.17643e12i 0.238524i −0.992863 0.119262i \(-0.961947\pi\)
0.992863 0.119262i \(-0.0380529\pi\)
\(110\) −1.18593e13 1.11704e13i −0.638271 0.601197i
\(111\) −1.91594e13 −0.972263
\(112\) −4.05270e13 + 4.87058e12i −1.94012 + 0.233165i
\(113\) 1.63143e13 0.737156 0.368578 0.929597i \(-0.379845\pi\)
0.368578 + 0.929597i \(0.379845\pi\)
\(114\) −1.51048e13 1.42275e13i −0.644517 0.607080i
\(115\) 7.77436e12i 0.313421i
\(116\) −3.87727e12 + 2.32152e11i −0.147757 + 0.00884698i
\(117\) 8.79958e11i 0.0317142i
\(118\) 2.00119e13 2.12459e13i 0.682424 0.724506i
\(119\) −3.09705e13 −0.999753
\(120\) −1.47879e13 + 1.77111e13i −0.452094 + 0.541461i
\(121\) −1.62127e13 −0.469623
\(122\) 4.13793e13 4.39310e13i 1.13617 1.20624i
\(123\) 2.86901e13i 0.747048i
\(124\) −1.18448e12 1.97826e13i −0.0292609 0.488699i
\(125\) 4.55579e13i 1.06819i
\(126\) 3.12380e12 + 2.94235e12i 0.0695464 + 0.0655068i
\(127\) −1.28760e13 −0.272306 −0.136153 0.990688i \(-0.543474\pi\)
−0.136153 + 0.990688i \(0.543474\pi\)
\(128\) 2.71056e13 4.17273e13i 0.544745 0.838602i
\(129\) 8.07452e13 1.54271
\(130\) 1.87951e13 + 1.77034e13i 0.341518 + 0.321681i
\(131\) 7.97301e13i 1.37835i 0.724596 + 0.689174i \(0.242027\pi\)
−0.724596 + 0.689174i \(0.757973\pi\)
\(132\) 4.29454e12 + 7.17251e13i 0.0706621 + 1.18016i
\(133\) 1.13242e14i 1.77407i
\(134\) −3.67108e13 + 3.89746e13i −0.547788 + 0.581567i
\(135\) 5.20387e13 0.739873
\(136\) 2.41967e13 2.89798e13i 0.327909 0.392728i
\(137\) −1.07364e14 −1.38732 −0.693660 0.720303i \(-0.744003\pi\)
−0.693660 + 0.720303i \(0.744003\pi\)
\(138\) −2.35098e13 + 2.49595e13i −0.289757 + 0.307626i
\(139\) 1.57684e12i 0.0185435i 0.999957 + 0.00927176i \(0.00295134\pi\)
−0.999957 + 0.00927176i \(0.997049\pi\)
\(140\) −1.25692e14 + 7.52583e12i −1.41083 + 0.0844738i
\(141\) 8.43455e13i 0.903936i
\(142\) 5.55847e13 + 5.23561e13i 0.568959 + 0.535911i
\(143\) 8.04079e13 0.786348
\(144\) −5.19379e12 + 6.24195e11i −0.0485432 + 0.00583397i
\(145\) −1.19820e13 −0.107063
\(146\) −4.75623e13 4.47997e13i −0.406415 0.382809i
\(147\) 3.36266e14i 2.74865i
\(148\) 1.27231e14 7.61796e12i 0.995157 0.0595851i
\(149\) 6.35045e13i 0.475438i −0.971334 0.237719i \(-0.923600\pi\)
0.971334 0.237719i \(-0.0763998\pi\)
\(150\) 4.44832e13 4.72263e13i 0.318862 0.338525i
\(151\) −5.05899e13 −0.347307 −0.173654 0.984807i \(-0.555557\pi\)
−0.173654 + 0.984807i \(0.555557\pi\)
\(152\) 1.05963e14 + 8.84737e13i 0.696899 + 0.581877i
\(153\) −3.96906e12 −0.0250146
\(154\) −2.68863e14 + 2.85443e14i −1.62423 + 1.72439i
\(155\) 6.11345e13i 0.354104i
\(156\) −6.80621e12 1.13673e14i −0.0378090 0.631465i
\(157\) 1.02755e14i 0.547587i 0.961788 + 0.273794i \(0.0882786\pi\)
−0.961788 + 0.273794i \(0.911721\pi\)
\(158\) 3.81251e13 + 3.59107e13i 0.194958 + 0.183634i
\(159\) −1.18814e14 −0.583157
\(160\) 9.11590e13 1.23493e14i 0.429556 0.581917i
\(161\) −1.87123e14 −0.846757
\(162\) −1.58882e14 1.49653e14i −0.690601 0.650488i
\(163\) 1.15948e14i 0.484221i 0.970249 + 0.242111i \(0.0778397\pi\)
−0.970249 + 0.242111i \(0.922160\pi\)
\(164\) −1.14074e13 1.90521e14i −0.0457828 0.764640i
\(165\) 2.21654e14i 0.855124i
\(166\) 9.58158e12 1.01724e13i 0.0355414 0.0377331i
\(167\) 4.53080e14 1.61628 0.808142 0.588988i \(-0.200474\pi\)
0.808142 + 0.588988i \(0.200474\pi\)
\(168\) 4.26292e14 + 3.55933e14i 1.46284 + 1.22140i
\(169\) 1.75441e14 0.579251
\(170\) 7.98516e13 8.47757e13i 0.253726 0.269373i
\(171\) 1.45126e13i 0.0443886i
\(172\) −5.36200e14 + 3.21050e13i −1.57904 + 0.0945448i
\(173\) 2.54255e14i 0.721058i 0.932748 + 0.360529i \(0.117404\pi\)
−0.932748 + 0.360529i \(0.882596\pi\)
\(174\) 3.84682e13 + 3.62338e13i 0.105083 + 0.0989792i
\(175\) 3.54058e14 0.931809
\(176\) −5.70370e13 4.74593e14i −0.144652 1.20362i
\(177\) −3.97094e14 −0.970659
\(178\) 1.57153e14 + 1.48025e14i 0.370334 + 0.348823i
\(179\) 7.88234e14i 1.79106i 0.445000 + 0.895531i \(0.353204\pi\)
−0.445000 + 0.895531i \(0.646796\pi\)
\(180\) −1.61082e13 + 9.64482e11i −0.0353002 + 0.00211360i
\(181\) 4.57640e13i 0.0967417i −0.998829 0.0483708i \(-0.984597\pi\)
0.998829 0.0483708i \(-0.0154029\pi\)
\(182\) 4.26108e14 4.52384e14i 0.869072 0.922664i
\(183\) −8.21086e14 −1.61606
\(184\) 1.46196e14 1.75095e14i 0.277728 0.332627i
\(185\) 3.93185e14 0.721075
\(186\) −1.84872e14 + 1.96272e14i −0.327368 + 0.347555i
\(187\) 3.62681e14i 0.620232i
\(188\) −3.35365e13 5.60108e14i −0.0553977 0.925222i
\(189\) 1.25253e15i 1.99888i
\(190\) 3.09977e14 + 2.91972e14i 0.478003 + 0.450239i
\(191\) −1.01606e15 −1.51426 −0.757131 0.653263i \(-0.773400\pi\)
−0.757131 + 0.653263i \(0.773400\pi\)
\(192\) −6.66109e14 + 1.20806e14i −0.959594 + 0.174033i
\(193\) 1.86151e14 0.259265 0.129632 0.991562i \(-0.458620\pi\)
0.129632 + 0.991562i \(0.458620\pi\)
\(194\) −8.34731e14 7.86246e14i −1.12418 1.05888i
\(195\) 3.51288e14i 0.457549i
\(196\) 1.33702e14 + 2.23302e15i 0.168451 + 2.81338i
\(197\) 4.84912e14i 0.591061i 0.955333 + 0.295530i \(0.0954963\pi\)
−0.955333 + 0.295530i \(0.904504\pi\)
\(198\) −3.44565e13 + 3.65813e13i −0.0406395 + 0.0431455i
\(199\) 9.85926e14 1.12538 0.562690 0.826668i \(-0.309766\pi\)
0.562690 + 0.826668i \(0.309766\pi\)
\(200\) −2.76619e14 + 3.31300e14i −0.305624 + 0.366038i
\(201\) 7.28448e14 0.779156
\(202\) 8.58740e14 9.11695e14i 0.889360 0.944203i
\(203\) 2.88398e14i 0.289246i
\(204\) −5.12726e14 + 3.06995e13i −0.498068 + 0.0298219i
\(205\) 5.88770e14i 0.554046i
\(206\) 1.10629e14 + 1.04203e14i 0.100863 + 0.0950045i
\(207\) −2.39810e13 −0.0211865
\(208\) 9.03951e13 + 7.52158e14i 0.0773986 + 0.644018i
\(209\) 1.32612e15 1.10061
\(210\) 1.24705e15 + 1.17462e15i 1.00336 + 0.945084i
\(211\) 1.22592e14i 0.0956368i −0.998856 0.0478184i \(-0.984773\pi\)
0.998856 0.0478184i \(-0.0152269\pi\)
\(212\) 7.88999e14 4.72414e13i 0.596889 0.0357388i
\(213\) 1.03890e15i 0.762263i
\(214\) −8.95177e14 + 9.50379e14i −0.637118 + 0.676406i
\(215\) −1.65703e15 −1.14414
\(216\) 1.17202e15 + 9.78582e14i 0.785211 + 0.655613i
\(217\) −1.47146e15 −0.956666
\(218\) 2.59181e14 2.75163e14i 0.163544 0.173629i
\(219\) 8.88957e14i 0.544495i
\(220\) −8.81314e13 1.47192e15i −0.0524063 0.875261i
\(221\) 5.74795e14i 0.331866i
\(222\) −1.26232e15 1.18900e15i −0.707740 0.666632i
\(223\) −8.05170e14 −0.438436 −0.219218 0.975676i \(-0.570351\pi\)
−0.219218 + 0.975676i \(0.570351\pi\)
\(224\) −2.97237e15 2.19413e15i −1.57214 1.16051i
\(225\) 4.53747e13 0.0233146
\(226\) 1.07487e15 + 1.01243e15i 0.536599 + 0.505431i
\(227\) 5.78017e14i 0.280396i 0.990123 + 0.140198i \(0.0447740\pi\)
−0.990123 + 0.140198i \(0.955226\pi\)
\(228\) −1.12251e14 1.87475e15i −0.0529191 0.883826i
\(229\) 1.90351e15i 0.872219i 0.899894 + 0.436110i \(0.143644\pi\)
−0.899894 + 0.436110i \(0.856356\pi\)
\(230\) 4.82461e14 5.12212e14i 0.214897 0.228149i
\(231\) 5.33503e15 2.31025
\(232\) −2.69860e14 2.25320e14i −0.113623 0.0948699i
\(233\) −3.29786e15 −1.35026 −0.675132 0.737697i \(-0.735913\pi\)
−0.675132 + 0.737697i \(0.735913\pi\)
\(234\) 5.46084e13 5.79759e13i 0.0217449 0.0230858i
\(235\) 1.73091e15i 0.670401i
\(236\) 2.63695e15 1.57888e14i 0.993516 0.0594868i
\(237\) 7.12573e14i 0.261195i
\(238\) −2.04049e15 1.92197e15i −0.727752 0.685481i
\(239\) 4.02617e14 0.139735 0.0698675 0.997556i \(-0.477742\pi\)
0.0698675 + 0.997556i \(0.477742\pi\)
\(240\) −2.07341e15 + 2.49185e14i −0.700346 + 0.0841682i
\(241\) 3.60468e14 0.118510 0.0592551 0.998243i \(-0.481127\pi\)
0.0592551 + 0.998243i \(0.481127\pi\)
\(242\) −1.06817e15 1.00612e15i −0.341853 0.321997i
\(243\) 3.13557e14i 0.0976959i
\(244\) 5.45254e15 3.26471e14i 1.65411 0.0990400i
\(245\) 6.90075e15i 2.03853i
\(246\) −1.78045e15 + 1.89024e15i −0.512214 + 0.543800i
\(247\) −2.10170e15 −0.588899
\(248\) 1.14963e15 1.37688e15i 0.313777 0.375802i
\(249\) −1.90127e14 −0.0505530
\(250\) −2.82723e15 + 3.00158e15i −0.732405 + 0.777570i
\(251\) 2.41736e15i 0.610187i 0.952322 + 0.305093i \(0.0986876\pi\)
−0.952322 + 0.305093i \(0.901312\pi\)
\(252\) 2.32143e13 + 3.87713e14i 0.00571022 + 0.0953689i
\(253\) 2.19131e15i 0.525315i
\(254\) −8.48333e14 7.99058e14i −0.198220 0.186706i
\(255\) −1.58449e15 −0.360892
\(256\) 4.37536e15 1.06708e15i 0.971524 0.236940i
\(257\) 4.22633e14 0.0914952 0.0457476 0.998953i \(-0.485433\pi\)
0.0457476 + 0.998953i \(0.485433\pi\)
\(258\) 5.31988e15 + 5.01088e15i 1.12299 + 1.05776i
\(259\) 9.46365e15i 1.94810i
\(260\) 1.39675e14 + 2.33277e15i 0.0280409 + 0.468324i
\(261\) 3.69600e13i 0.00723717i
\(262\) −4.94789e15 + 5.25301e15i −0.945065 + 1.00334i
\(263\) 7.16704e15 1.33545 0.667725 0.744408i \(-0.267268\pi\)
0.667725 + 0.744408i \(0.267268\pi\)
\(264\) −4.16817e15 + 4.99211e15i −0.757739 + 0.907524i
\(265\) 2.43826e15 0.432496
\(266\) 7.02755e15 7.46091e15i 1.21639 1.29140i
\(267\) 2.93725e15i 0.496156i
\(268\) −4.83736e15 + 2.89637e14i −0.797503 + 0.0477506i
\(269\) 3.89871e14i 0.0627381i 0.999508 + 0.0313690i \(0.00998671\pi\)
−0.999508 + 0.0313690i \(0.990013\pi\)
\(270\) 3.42856e15 + 3.22942e15i 0.538577 + 0.507294i
\(271\) −2.03497e15 −0.312073 −0.156037 0.987751i \(-0.549872\pi\)
−0.156037 + 0.987751i \(0.549872\pi\)
\(272\) 3.39262e15 4.07728e14i 0.507969 0.0610482i
\(273\) −8.45523e15 −1.23614
\(274\) −7.07368e15 6.66281e15i −1.00987 0.951216i
\(275\) 4.14620e15i 0.578080i
\(276\) −3.09788e15 + 1.85485e14i −0.421847 + 0.0252581i
\(277\) 1.40387e16i 1.86728i −0.358215 0.933639i \(-0.616614\pi\)
0.358215 0.933639i \(-0.383386\pi\)
\(278\) −9.78557e13 + 1.03890e14i −0.0127144 + 0.0134984i
\(279\) −1.88577e14 −0.0239365
\(280\) −8.74824e15 7.30436e15i −1.08491 0.905848i
\(281\) 9.81872e15 1.18977 0.594886 0.803810i \(-0.297197\pi\)
0.594886 + 0.803810i \(0.297197\pi\)
\(282\) −5.23431e15 + 5.55709e15i −0.619784 + 0.658004i
\(283\) 4.93395e15i 0.570930i 0.958389 + 0.285465i \(0.0921480\pi\)
−0.958389 + 0.285465i \(0.907852\pi\)
\(284\) 4.13074e14 + 6.89894e15i 0.0467153 + 0.780213i
\(285\) 5.79358e15i 0.640406i
\(286\) 5.29766e15 + 4.98995e15i 0.572407 + 0.539159i
\(287\) −1.41712e16 −1.49684
\(288\) −3.80928e14 2.81191e14i −0.0393362 0.0290369i
\(289\) −7.31196e15 −0.738240
\(290\) −7.89433e14 7.43580e14i −0.0779343 0.0734075i
\(291\) 1.56014e16i 1.50612i
\(292\) −3.53457e14 5.90324e15i −0.0333694 0.557317i
\(293\) 5.77550e15i 0.533274i −0.963797 0.266637i \(-0.914088\pi\)
0.963797 0.266637i \(-0.0859124\pi\)
\(294\) 2.08680e16 2.21548e16i 1.88461 2.00083i
\(295\) 8.14904e15 0.719885
\(296\) 8.85534e15 + 7.39379e15i 0.765261 + 0.638956i
\(297\) 1.46678e16 1.24008
\(298\) 3.94096e15 4.18399e15i 0.325984 0.346086i
\(299\) 3.47289e15i 0.281079i
\(300\) 5.86153e15 3.50960e14i 0.464219 0.0277951i
\(301\) 3.98835e16i 3.09108i
\(302\) −3.33311e15 3.13951e15i −0.252816 0.238131i
\(303\) −1.70399e16 −1.26500
\(304\) 1.49083e15 + 1.24049e16i 0.108330 + 0.901395i
\(305\) 1.68501e16 1.19854
\(306\) −2.61501e14 2.46312e14i −0.0182089 0.0171513i
\(307\) 4.46483e15i 0.304373i −0.988352 0.152186i \(-0.951369\pi\)
0.988352 0.152186i \(-0.0486314\pi\)
\(308\) −3.54280e16 + 2.12126e15i −2.36465 + 0.141584i
\(309\) 2.06770e15i 0.135132i
\(310\) 3.79388e15 4.02783e15i 0.242791 0.257763i
\(311\) 9.38805e15 0.588346 0.294173 0.955752i \(-0.404956\pi\)
0.294173 + 0.955752i \(0.404956\pi\)
\(312\) 6.60592e15 7.91174e15i 0.405442 0.485587i
\(313\) −1.26946e16 −0.763100 −0.381550 0.924348i \(-0.624610\pi\)
−0.381550 + 0.924348i \(0.624610\pi\)
\(314\) −6.37674e15 + 6.76997e15i −0.375453 + 0.398606i
\(315\) 1.19816e15i 0.0691028i
\(316\) 2.83325e14 + 4.73194e15i 0.0160073 + 0.267346i
\(317\) 2.54168e16i 1.40681i −0.710789 0.703405i \(-0.751662\pi\)
0.710789 0.703405i \(-0.248338\pi\)
\(318\) −7.82802e15 7.37334e15i −0.424498 0.399841i
\(319\) −3.37729e15 −0.179444
\(320\) 1.36697e16 2.47915e15i 0.711679 0.129071i
\(321\) 1.77629e16 0.906216
\(322\) −1.23286e16 1.16125e16i −0.616381 0.580579i
\(323\) 9.47975e15i 0.464494i
\(324\) −1.18072e15 1.97198e16i −0.0567029 0.947021i
\(325\) 6.57111e15i 0.309312i
\(326\) −7.19550e15 + 7.63921e15i −0.332006 + 0.352480i
\(327\) −5.14290e15 −0.232620
\(328\) 1.10717e16 1.32603e16i 0.490949 0.587996i
\(329\) −4.16618e16 −1.81119
\(330\) −1.37554e16 + 1.46036e16i −0.586316 + 0.622472i
\(331\) 2.60098e16i 1.08706i −0.839389 0.543531i \(-0.817087\pi\)
0.839389 0.543531i \(-0.182913\pi\)
\(332\) 1.26256e15 7.55960e13i 0.0517434 0.00309814i
\(333\) 1.21283e15i 0.0487429i
\(334\) 2.98511e16 + 2.81172e16i 1.17654 + 1.10820i
\(335\) −1.49490e16 −0.577858
\(336\) 5.99768e15 + 4.99054e16i 0.227394 + 1.89209i
\(337\) −1.68977e16 −0.628395 −0.314197 0.949358i \(-0.601735\pi\)
−0.314197 + 0.949358i \(0.601735\pi\)
\(338\) 1.15589e16 + 1.08875e16i 0.421655 + 0.397163i
\(339\) 2.00897e16i 0.718910i
\(340\) 1.05220e16 6.30006e14i 0.369391 0.0221173i
\(341\) 1.72316e16i 0.593501i
\(342\) 9.00624e14 9.56162e14i 0.0304350 0.0323118i
\(343\) 1.07163e17 3.55332
\(344\) −3.73198e16 3.11602e16i −1.21425 1.01384i
\(345\) −9.57343e15 −0.305663
\(346\) −1.57786e16 + 1.67516e16i −0.494394 + 0.524881i
\(347\) 3.24877e16i 0.999027i −0.866306 0.499513i \(-0.833512\pi\)
0.866306 0.499513i \(-0.166488\pi\)
\(348\) 2.85874e14 + 4.77451e15i 0.00862800 + 0.144100i
\(349\) 4.20305e16i 1.24509i 0.782586 + 0.622543i \(0.213900\pi\)
−0.782586 + 0.622543i \(0.786100\pi\)
\(350\) 2.33270e16 + 2.19721e16i 0.678293 + 0.638895i
\(351\) −2.32463e16 −0.663525
\(352\) 2.56944e16 3.48081e16i 0.719965 0.975333i
\(353\) 1.92556e16 0.529691 0.264845 0.964291i \(-0.414679\pi\)
0.264845 + 0.964291i \(0.414679\pi\)
\(354\) −2.61624e16 2.46428e16i −0.706573 0.665532i
\(355\) 2.13199e16i 0.565330i
\(356\) 1.16788e15 + 1.95052e16i 0.0304069 + 0.507839i
\(357\) 3.81374e16i 0.975007i
\(358\) −4.89162e16 + 5.19327e16i −1.22804 + 1.30377i
\(359\) −1.57860e16 −0.389186 −0.194593 0.980884i \(-0.562339\pi\)
−0.194593 + 0.980884i \(0.562339\pi\)
\(360\) −1.12114e15 9.36100e14i −0.0271453 0.0226650i
\(361\) 7.39089e15 0.175752
\(362\) 2.84002e15 3.01516e15i 0.0663309 0.0704213i
\(363\) 1.99644e16i 0.457999i
\(364\) 5.61481e16 3.36187e15i 1.26525 0.0757569i
\(365\) 1.82429e16i 0.403823i
\(366\) −5.40971e16 5.09549e16i −1.17638 1.10805i
\(367\) −4.63823e16 −0.990885 −0.495442 0.868641i \(-0.664994\pi\)
−0.495442 + 0.868641i \(0.664994\pi\)
\(368\) 2.04981e16 2.46348e15i 0.430233 0.0517058i
\(369\) −1.81613e15 −0.0374521
\(370\) 2.59049e16 + 2.44002e16i 0.524893 + 0.494405i
\(371\) 5.86871e16i 1.16846i
\(372\) −2.43605e16 + 1.45858e15i −0.476603 + 0.0285366i
\(373\) 3.24323e16i 0.623548i 0.950156 + 0.311774i \(0.100923\pi\)
−0.950156 + 0.311774i \(0.899077\pi\)
\(374\) 2.25072e16 2.38952e16i 0.425262 0.451486i
\(375\) 5.61005e16 1.04175
\(376\) 3.25496e16 3.89838e16i 0.594053 0.711482i
\(377\) 5.35250e15 0.0960148
\(378\) 7.77296e16 8.25229e16i 1.37053 1.45505i
\(379\) 7.89922e16i 1.36908i 0.728975 + 0.684541i \(0.239997\pi\)
−0.728975 + 0.684541i \(0.760003\pi\)
\(380\) 2.30358e15 + 3.84731e16i 0.0392473 + 0.655486i
\(381\) 1.58556e16i 0.265565i
\(382\) −6.69427e16 6.30544e16i −1.10228 1.03825i
\(383\) −3.96583e16 −0.642010 −0.321005 0.947078i \(-0.604021\pi\)
−0.321005 + 0.947078i \(0.604021\pi\)
\(384\) −5.13835e16 3.33781e16i −0.817844 0.531261i
\(385\) −1.09484e17 −1.71339
\(386\) 1.22645e16 + 1.15522e16i 0.188727 + 0.177765i
\(387\) 5.11131e15i 0.0773413i
\(388\) −6.20326e15 1.03603e17i −0.0923025 1.54159i
\(389\) 3.70327e16i 0.541892i −0.962595 0.270946i \(-0.912663\pi\)
0.962595 0.270946i \(-0.0873365\pi\)
\(390\) 2.18002e16 2.31445e16i 0.313719 0.333064i
\(391\) 1.56645e16 0.221701
\(392\) −1.29768e17 + 1.55419e17i −1.80637 + 2.16344i
\(393\) 9.81805e16 1.34423
\(394\) −3.00926e16 + 3.19483e16i −0.405261 + 0.430252i
\(395\) 1.46232e16i 0.193714i
\(396\) −4.54033e15 + 2.71852e14i −0.0591655 + 0.00354254i
\(397\) 1.88759e16i 0.241974i −0.992654 0.120987i \(-0.961394\pi\)
0.992654 0.120987i \(-0.0386060\pi\)
\(398\) 6.49576e16 + 6.11846e16i 0.819200 + 0.771617i
\(399\) −1.39447e17 −1.73016
\(400\) −3.87848e16 + 4.66119e15i −0.473447 + 0.0568993i
\(401\) 8.64929e16 1.03882 0.519412 0.854524i \(-0.326151\pi\)
0.519412 + 0.854524i \(0.326151\pi\)
\(402\) 4.79937e16 + 4.52060e16i 0.567172 + 0.534228i
\(403\) 2.73095e16i 0.317563i
\(404\) 1.13156e17 6.77521e15i 1.29479 0.0775254i
\(405\) 6.09405e16i 0.686196i
\(406\) −1.78974e16 + 1.90011e16i −0.198322 + 0.210552i
\(407\) 1.10824e17 1.20857
\(408\) −3.56860e16 2.97961e16i −0.383007 0.319792i
\(409\) 6.70383e16 0.708144 0.354072 0.935218i \(-0.384797\pi\)
0.354072 + 0.935218i \(0.384797\pi\)
\(410\) 3.65379e16 3.87910e16i 0.379881 0.403307i
\(411\) 1.32210e17i 1.35298i
\(412\) 8.22134e14 + 1.37308e16i 0.00828153 + 0.138314i
\(413\) 1.96141e17i 1.94488i
\(414\) −1.57998e15 1.48821e15i −0.0154223 0.0145265i
\(415\) 3.90172e15 0.0374924
\(416\) −4.07218e16 + 5.51656e16i −0.385230 + 0.521869i
\(417\) 1.94174e15 0.0180845
\(418\) 8.73712e16 + 8.22963e16i 0.801166 + 0.754631i
\(419\) 4.36873e16i 0.394425i 0.980361 + 0.197212i \(0.0631889\pi\)
−0.980361 + 0.197212i \(0.936811\pi\)
\(420\) 9.26738e15 + 1.54779e17i 0.0823828 + 1.37591i
\(421\) 1.39165e17i 1.21814i 0.793116 + 0.609071i \(0.208457\pi\)
−0.793116 + 0.609071i \(0.791543\pi\)
\(422\) 7.60779e15 8.07693e15i 0.0655734 0.0696170i
\(423\) −5.33922e15 −0.0453175
\(424\) 5.49148e16 + 4.58512e16i 0.458998 + 0.383242i
\(425\) −2.96391e16 −0.243970
\(426\) 6.44718e16 6.84475e16i 0.522646 0.554875i
\(427\) 4.05569e17i 3.23805i
\(428\) −1.17957e17 + 7.06269e15i −0.927556 + 0.0555375i
\(429\) 9.90152e16i 0.766883i
\(430\) −1.09173e17 1.02832e17i −0.832858 0.784482i
\(431\) −2.36158e17 −1.77460 −0.887299 0.461195i \(-0.847421\pi\)
−0.887299 + 0.461195i \(0.847421\pi\)
\(432\) 1.64897e16 + 1.37207e17i 0.122058 + 1.01562i
\(433\) −1.55171e17 −1.13146 −0.565730 0.824590i \(-0.691406\pi\)
−0.565730 + 0.824590i \(0.691406\pi\)
\(434\) −9.69469e16 9.13158e16i −0.696387 0.655938i
\(435\) 1.47548e16i 0.104413i
\(436\) 3.41521e16 2.04486e15i 0.238098 0.0142561i
\(437\) 5.72764e16i 0.393411i
\(438\) −5.51669e16 + 5.85688e16i −0.373333 + 0.396355i
\(439\) 1.35637e17 0.904398 0.452199 0.891917i \(-0.350640\pi\)
0.452199 + 0.891917i \(0.350640\pi\)
\(440\) 8.55380e16 1.02447e17i 0.561974 0.673062i
\(441\) 2.12862e16 0.137799
\(442\) −3.56706e16 + 3.78702e16i −0.227544 + 0.241576i
\(443\) 2.37606e17i 1.49360i 0.665050 + 0.746799i \(0.268410\pi\)
−0.665050 + 0.746799i \(0.731590\pi\)
\(444\) −9.38084e15 1.56674e17i −0.0581102 0.970524i
\(445\) 6.02774e16i 0.367972i
\(446\) −5.30485e16 4.99672e16i −0.319151 0.300614i
\(447\) −7.82002e16 −0.463670
\(448\) −5.96713e16 3.29019e17i −0.348705 1.92271i
\(449\) 3.25912e17 1.87715 0.938576 0.345074i \(-0.112146\pi\)
0.938576 + 0.345074i \(0.112146\pi\)
\(450\) 2.98951e15 + 2.81586e15i 0.0169714 + 0.0159856i
\(451\) 1.65953e17i 0.928618i
\(452\) 7.98782e15 + 1.33408e17i 0.0440584 + 0.735839i
\(453\) 6.22970e16i 0.338710i
\(454\) −3.58705e16 + 3.80825e16i −0.192254 + 0.204109i
\(455\) 1.73516e17 0.916779
\(456\) 1.08947e17 1.30484e17i 0.567474 0.679648i
\(457\) −2.28623e17 −1.17399 −0.586995 0.809591i \(-0.699689\pi\)
−0.586995 + 0.809591i \(0.699689\pi\)
\(458\) −1.18128e17 + 1.25413e17i −0.598037 + 0.634916i
\(459\) 1.04853e17i 0.523356i
\(460\) 6.35737e16 3.80648e15i 0.312861 0.0187326i
\(461\) 1.78032e17i 0.863857i 0.901908 + 0.431928i \(0.142167\pi\)
−0.901908 + 0.431928i \(0.857833\pi\)
\(462\) 3.51498e17 + 3.31081e17i 1.68170 + 1.58402i
\(463\) 2.15010e17 1.01434 0.507168 0.861847i \(-0.330692\pi\)
0.507168 + 0.861847i \(0.330692\pi\)
\(464\) −3.79678e15 3.15922e16i −0.0176623 0.146965i
\(465\) −7.52817e16 −0.345339
\(466\) −2.17279e17 2.04658e17i −0.982899 0.925808i
\(467\) 9.62373e16i 0.429322i 0.976689 + 0.214661i \(0.0688647\pi\)
−0.976689 + 0.214661i \(0.931135\pi\)
\(468\) 7.19573e15 4.30845e14i 0.0316575 0.00189550i
\(469\) 3.59811e17i 1.56117i
\(470\) 1.07417e17 1.14041e17i 0.459660 0.488006i
\(471\) 1.26533e17 0.534033
\(472\) 1.83533e17 + 1.53242e17i 0.763998 + 0.637902i
\(473\) −4.67056e17 −1.91766
\(474\) 4.42208e16 4.69477e16i 0.179088 0.190132i
\(475\) 1.08373e17i 0.432927i
\(476\) −1.51638e16 2.53257e17i −0.0597533 0.997966i
\(477\) 7.52112e15i 0.0292357i
\(478\) 2.65263e16 + 2.49856e16i 0.101718 + 0.0958093i
\(479\) −1.07139e17 −0.405290 −0.202645 0.979252i \(-0.564954\pi\)
−0.202645 + 0.979252i \(0.564954\pi\)
\(480\) −1.52070e17 1.12254e17i −0.567513 0.418923i
\(481\) −1.75640e17 −0.646666
\(482\) 2.37494e16 + 2.23699e16i 0.0862674 + 0.0812566i
\(483\) 2.30425e17i 0.825798i
\(484\) −7.93804e15 1.32577e17i −0.0280684 0.468783i
\(485\) 3.20168e17i 1.11701i
\(486\) 1.94587e16 2.06587e16i 0.0669852 0.0711159i
\(487\) 2.87139e17 0.975337 0.487668 0.873029i \(-0.337848\pi\)
0.487668 + 0.873029i \(0.337848\pi\)
\(488\) 3.79500e17 + 3.16864e17i 1.27199 + 1.06205i
\(489\) 1.42780e17 0.472235
\(490\) −4.28246e17 + 4.54654e17i −1.39772 + 1.48391i
\(491\) 4.18123e17i 1.34671i −0.739319 0.673355i \(-0.764853\pi\)
0.739319 0.673355i \(-0.235147\pi\)
\(492\) −2.34609e17 + 1.40472e16i −0.745713 + 0.0446496i
\(493\) 2.41425e16i 0.0757317i
\(494\) −1.38470e17 1.30427e17i −0.428678 0.403778i
\(495\) −1.40311e16 −0.0428703
\(496\) 1.61189e17 1.93719e16i 0.486077 0.0584172i
\(497\) 5.13155e17 1.52733
\(498\) −1.25265e16 1.17989e16i −0.0367991 0.0346617i
\(499\) 2.23370e17i 0.647695i −0.946109 0.323847i \(-0.895024\pi\)
0.946109 0.323847i \(-0.104976\pi\)
\(500\) −3.72543e17 + 2.23061e16i −1.06628 + 0.0638437i
\(501\) 5.57927e17i 1.57628i
\(502\) −1.50017e17 + 1.59268e17i −0.418374 + 0.444174i
\(503\) −5.16254e17 −1.42125 −0.710626 0.703570i \(-0.751588\pi\)
−0.710626 + 0.703570i \(0.751588\pi\)
\(504\) −2.25312e16 + 2.69850e16i −0.0612331 + 0.0733372i
\(505\) 3.49688e17 0.938181
\(506\) 1.35988e17 1.44374e17i 0.360183 0.382394i
\(507\) 2.16040e17i 0.564913i
\(508\) −6.30434e15 1.05292e17i −0.0162752 0.271819i
\(509\) 7.65587e17i 1.95132i 0.219284 + 0.975661i \(0.429628\pi\)
−0.219284 + 0.975661i \(0.570372\pi\)
\(510\) −1.04394e17 9.83301e16i −0.262705 0.247446i
\(511\) −4.39093e17 −1.09099
\(512\) 3.54491e17 + 2.01221e17i 0.869661 + 0.493650i
\(513\) −3.83387e17 −0.928699
\(514\) 2.78451e16 + 2.62278e16i 0.0666022 + 0.0627337i
\(515\) 4.24327e16i 0.100220i
\(516\) 3.95344e16 + 6.60282e17i 0.0922046 + 1.53995i
\(517\) 4.87882e17i 1.12364i
\(518\) 5.87295e17 6.23511e17i 1.33571 1.41808i
\(519\) 3.13093e17 0.703210
\(520\) −1.35565e17 + 1.62362e17i −0.300694 + 0.360134i
\(521\) 1.10381e17 0.241796 0.120898 0.992665i \(-0.461423\pi\)
0.120898 + 0.992665i \(0.461423\pi\)
\(522\) −2.29366e15 + 2.43510e15i −0.00496217 + 0.00526816i
\(523\) 6.91731e15i 0.0147801i 0.999973 + 0.00739003i \(0.00235234\pi\)
−0.999973 + 0.00739003i \(0.997648\pi\)
\(524\) −6.51982e17 + 3.90374e16i −1.37588 + 0.0823812i
\(525\) 4.35991e17i 0.908744i
\(526\) 4.72199e17 + 4.44772e17i 0.972116 + 0.915651i
\(527\) 1.23180e17 0.250478
\(528\) −5.84419e17 + 7.02360e16i −1.17383 + 0.141072i
\(529\) −4.09392e17 −0.812226
\(530\) 1.60644e17 + 1.51314e17i 0.314827 + 0.296541i
\(531\) 2.51367e16i 0.0486625i
\(532\) 9.26017e17 5.54453e16i 1.77090 0.106033i
\(533\) 2.63010e17i 0.496873i
\(534\) 1.82280e17 1.93520e17i 0.340189 0.361167i
\(535\) −3.64526e17 −0.672092
\(536\) −3.36683e17 2.81114e17i −0.613268 0.512049i
\(537\) 9.70640e17 1.74673
\(538\) −2.41946e16 + 2.56866e16i −0.0430164 + 0.0456690i
\(539\) 1.94507e18i 3.41671i
\(540\) 2.54792e16 + 4.25539e17i 0.0442208 + 0.738551i
\(541\) 1.19723e17i 0.205304i −0.994717 0.102652i \(-0.967267\pi\)
0.994717 0.102652i \(-0.0327327\pi\)
\(542\) −1.34073e17 1.26286e17i −0.227168 0.213973i
\(543\) −5.63543e16 −0.0943471
\(544\) 2.48825e17 + 1.83676e17i 0.411624 + 0.303850i
\(545\) 1.05541e17 0.172522
\(546\) −5.57071e17 5.24714e17i −0.899826 0.847560i
\(547\) 6.30037e17i 1.00565i 0.864387 + 0.502827i \(0.167707\pi\)
−0.864387 + 0.502827i \(0.832293\pi\)
\(548\) −5.25677e16 8.77957e17i −0.0829173 1.38484i
\(549\) 5.19762e16i 0.0810185i
\(550\) −2.57305e17 + 2.73172e17i −0.396361 + 0.420803i
\(551\) 8.82756e16 0.134386
\(552\) −2.15614e17 1.80027e17i −0.324394 0.270853i
\(553\) 3.51969e17 0.523349
\(554\) 8.71214e17 9.24939e17i 1.28030 1.35925i
\(555\) 4.84172e17i 0.703226i
\(556\) −1.28944e16 + 7.72053e14i −0.0185104 + 0.00110831i
\(557\) 5.28413e17i 0.749747i −0.927076 0.374873i \(-0.877686\pi\)
0.927076 0.374873i \(-0.122314\pi\)
\(558\) −1.24244e16 1.17027e16i −0.0174241 0.0164121i
\(559\) 7.40214e17 1.02608
\(560\) −1.23083e17 1.02414e18i −0.168646 1.40326i
\(561\) −4.46609e17 −0.604880
\(562\) 6.46905e17 + 6.09330e17i 0.866073 + 0.815768i
\(563\) 7.95577e17i 1.05288i −0.850213 0.526439i \(-0.823527\pi\)
0.850213 0.526439i \(-0.176473\pi\)
\(564\) −6.89723e17 + 4.12972e16i −0.902320 + 0.0540265i
\(565\) 4.12274e17i 0.533177i
\(566\) −3.06191e17 + 3.25072e17i −0.391458 + 0.415598i
\(567\) −1.46679e18 −1.85387
\(568\) −4.00919e17 + 4.80170e17i −0.500948 + 0.599972i
\(569\) −1.05443e18 −1.30253 −0.651264 0.758851i \(-0.725761\pi\)
−0.651264 + 0.758851i \(0.725761\pi\)
\(570\) 3.59538e17 3.81709e17i 0.439094 0.466171i
\(571\) 2.04900e17i 0.247405i −0.992319 0.123702i \(-0.960523\pi\)
0.992319 0.123702i \(-0.0394768\pi\)
\(572\) 3.93693e16 + 6.57524e17i 0.0469984 + 0.784942i
\(573\) 1.25118e18i 1.47678i
\(574\) −9.33670e17 8.79438e17i −1.08960 1.02631i
\(575\) −1.79079e17 −0.206634
\(576\) −7.64725e15 4.21659e16i −0.00872487 0.0481077i
\(577\) 4.21685e16 0.0475714 0.0237857 0.999717i \(-0.492428\pi\)
0.0237857 + 0.999717i \(0.492428\pi\)
\(578\) −4.81747e17 4.53765e17i −0.537388 0.506175i
\(579\) 2.29229e17i 0.252847i
\(580\) −5.86663e15 9.79812e16i −0.00639892 0.106871i
\(581\) 9.39115e16i 0.101292i
\(582\) −9.68192e17 + 1.02790e18i −1.03267 + 1.09635i
\(583\) 6.87257e17 0.724892
\(584\) 3.43056e17 4.10869e17i 0.357834 0.428568i
\(585\) 2.22371e16 0.0229385
\(586\) 3.58416e17 3.80518e17i 0.365639 0.388187i
\(587\) 7.61315e17i 0.768099i −0.923313 0.384049i \(-0.874529\pi\)
0.923313 0.384049i \(-0.125471\pi\)
\(588\) 2.74976e18 1.64642e17i 2.74374 0.164281i
\(589\) 4.50399e17i 0.444475i
\(590\) 5.36898e17 + 5.05713e17i 0.524027 + 0.493589i
\(591\) 5.97125e17 0.576430
\(592\) 1.24590e17 + 1.03668e18i 0.118957 + 0.989817i
\(593\) 1.40229e18 1.32428 0.662142 0.749378i \(-0.269647\pi\)
0.662142 + 0.749378i \(0.269647\pi\)
\(594\) 9.66387e17 + 9.10255e17i 0.902691 + 0.850259i
\(595\) 7.82645e17i 0.723110i
\(596\) 5.19299e17 3.10931e16i 0.474588 0.0284160i
\(597\) 1.21408e18i 1.09752i
\(598\) −2.15521e17 + 2.28811e17i −0.192722 + 0.204606i
\(599\) −5.57093e16 −0.0492780 −0.0246390 0.999696i \(-0.507844\pi\)
−0.0246390 + 0.999696i \(0.507844\pi\)
\(600\) 4.07966e17 + 3.40632e17i 0.356977 + 0.298059i
\(601\) −1.05450e18 −0.912769 −0.456384 0.889783i \(-0.650856\pi\)
−0.456384 + 0.889783i \(0.650856\pi\)
\(602\) −2.47509e18 + 2.62771e18i −2.11940 + 2.25010i
\(603\) 4.61121e16i 0.0390618i
\(604\) −2.47698e16 4.13692e17i −0.0207579 0.346686i
\(605\) 4.09705e17i 0.339673i
\(606\) −1.12267e18 1.05746e18i −0.920832 0.867346i
\(607\) 2.20475e18 1.78910 0.894548 0.446971i \(-0.147497\pi\)
0.894548 + 0.446971i \(0.147497\pi\)
\(608\) −6.71600e17 + 9.09813e17i −0.539184 + 0.730430i
\(609\) 3.55136e17 0.282087
\(610\) 1.11017e18 + 1.04568e18i 0.872457 + 0.821781i
\(611\) 7.73219e17i 0.601222i
\(612\) −1.94333e15 3.24564e16i −0.00149507 0.0249699i
\(613\) 9.76001e17i 0.742946i 0.928444 + 0.371473i \(0.121147\pi\)
−0.928444 + 0.371473i \(0.878853\pi\)
\(614\) 2.77078e17 2.94165e17i 0.208693 0.221562i
\(615\) −7.25018e17 −0.540331
\(616\) −2.46581e18 2.05883e18i −1.81838 1.51826i
\(617\) −2.29244e18 −1.67280 −0.836402 0.548117i \(-0.815345\pi\)
−0.836402 + 0.548117i \(0.815345\pi\)
\(618\) 1.28317e17 1.36230e17i 0.0926529 0.0983665i
\(619\) 1.01339e18i 0.724084i −0.932162 0.362042i \(-0.882080\pi\)
0.932162 0.362042i \(-0.117920\pi\)
\(620\) 4.99918e17 2.99326e16i 0.353470 0.0211641i
\(621\) 6.33517e17i 0.443265i
\(622\) 6.18530e17 + 5.82603e17i 0.428276 + 0.403400i
\(623\) 1.45083e18 0.994134
\(624\) 9.26216e17 1.11314e17i 0.628076 0.0754828i
\(625\) −4.40712e17 −0.295757
\(626\) −8.36382e17 7.87802e17i −0.555484 0.523219i
\(627\) 1.63300e18i 1.07336i
\(628\) −8.40261e17 + 5.03107e16i −0.546609 + 0.0327282i
\(629\) 7.92226e17i 0.510059i
\(630\) −7.43552e16 + 7.89404e16i −0.0473803 + 0.0503021i
\(631\) −1.25814e18 −0.793485 −0.396742 0.917930i \(-0.629859\pi\)
−0.396742 + 0.917930i \(0.629859\pi\)
\(632\) −2.74988e17 + 3.29345e17i −0.171653 + 0.205585i
\(633\) −1.50961e17 −0.0932695
\(634\) 1.57731e18 1.67458e18i 0.964580 1.02406i
\(635\) 3.25385e17i 0.196956i
\(636\) −5.81735e16 9.71582e17i −0.0348541 0.582114i
\(637\) 3.08264e18i 1.82817i
\(638\) −2.22512e17 2.09588e17i −0.130623 0.123036i
\(639\) 6.57640e16 0.0382149
\(640\) 1.05448e18 + 6.84975e17i 0.606551 + 0.394008i
\(641\) −4.20462e17 −0.239414 −0.119707 0.992809i \(-0.538196\pi\)
−0.119707 + 0.992809i \(0.538196\pi\)
\(642\) 1.17031e18 + 1.10233e18i 0.659663 + 0.621347i
\(643\) 2.53475e18i 1.41437i 0.707026 + 0.707187i \(0.250036\pi\)
−0.707026 + 0.707187i \(0.749964\pi\)
\(644\) −9.16190e16 1.53017e18i −0.0506090 0.845243i
\(645\) 2.04049e18i 1.11582i
\(646\) −5.88294e17 + 6.24571e17i −0.318480 + 0.338120i
\(647\) −1.77278e18 −0.950119 −0.475059 0.879954i \(-0.657573\pi\)
−0.475059 + 0.879954i \(0.657573\pi\)
\(648\) 1.14598e18 1.37251e18i 0.608049 0.728245i
\(649\) 2.29692e18 1.20658
\(650\) 4.07790e17 4.32936e17i 0.212080 0.225158i
\(651\) 1.81197e18i 0.932986i
\(652\) −9.48148e17 + 5.67704e16i −0.483356 + 0.0289409i
\(653\) 4.81484e17i 0.243022i −0.992590 0.121511i \(-0.961226\pi\)
0.992590 0.121511i \(-0.0387740\pi\)
\(654\) −3.38839e17 3.19158e17i −0.169332 0.159496i
\(655\) −2.01483e18 −0.996944
\(656\) 1.55237e18 1.86565e17i 0.760536 0.0914020i
\(657\) −5.62726e16 −0.0272974
\(658\) −2.74488e18 2.58545e18i −1.31842 1.24184i
\(659\) 2.71767e18i 1.29253i 0.763113 + 0.646266i \(0.223670\pi\)
−0.763113 + 0.646266i \(0.776330\pi\)
\(660\) −1.81254e18 + 1.08526e17i −0.853596 + 0.0511091i
\(661\) 8.55628e17i 0.399002i 0.979898 + 0.199501i \(0.0639322\pi\)
−0.979898 + 0.199501i \(0.936068\pi\)
\(662\) 1.61411e18 1.71365e18i 0.745345 0.791307i
\(663\) 7.07808e17 0.323652
\(664\) 8.78750e16 + 7.33714e16i 0.0397899 + 0.0332226i
\(665\) 2.86169e18 1.28316
\(666\) 7.52655e16 7.99069e16i 0.0334206 0.0354815i
\(667\) 1.45869e17i 0.0641422i
\(668\) 2.21837e17 + 3.70499e18i 0.0966020 + 1.61339i
\(669\) 9.91495e17i 0.427583i
\(670\) −9.84913e17 9.27705e17i −0.420641 0.396208i
\(671\) 4.74943e18 2.00884
\(672\) −2.70187e18 + 3.66021e18i −1.13179 + 1.53323i
\(673\) 7.38036e17 0.306182 0.153091 0.988212i \(-0.451077\pi\)
0.153091 + 0.988212i \(0.451077\pi\)
\(674\) −1.11330e18 1.04863e18i −0.457428 0.430859i
\(675\) 1.19869e18i 0.487788i
\(676\) 8.58992e16 + 1.43464e18i 0.0346207 + 0.578215i
\(677\) 3.87097e17i 0.154523i 0.997011 + 0.0772615i \(0.0246176\pi\)
−0.997011 + 0.0772615i \(0.975382\pi\)
\(678\) 1.24672e18 1.32360e18i 0.492921 0.523317i
\(679\) −7.70619e18 −3.01777
\(680\) 7.32338e17 + 6.11467e17i 0.284056 + 0.237173i
\(681\) 7.11776e17 0.273456
\(682\) 1.06936e18 1.13530e18i 0.406934 0.432028i
\(683\) 3.15274e18i 1.18838i −0.804326 0.594188i \(-0.797474\pi\)
0.804326 0.594188i \(-0.202526\pi\)
\(684\) 1.18675e17 7.10567e15i 0.0443092 0.00265302i
\(685\) 2.71317e18i 1.00343i
\(686\) 7.06044e18 + 6.65034e18i 2.58657 + 2.43634i
\(687\) 2.34401e18 0.850629
\(688\) −5.25068e17 4.36898e18i −0.188752 1.57056i
\(689\) −1.08920e18 −0.387866
\(690\) −6.30744e17 5.94108e17i −0.222502 0.209578i
\(691\) 3.51153e18i 1.22712i 0.789646 + 0.613562i \(0.210264\pi\)
−0.789646 + 0.613562i \(0.789736\pi\)
\(692\) −2.07914e18 + 1.24488e17i −0.719769 + 0.0430962i
\(693\) 3.37717e17i 0.115821i
\(694\) 2.01612e18 2.14045e18i 0.684983 0.727223i
\(695\) −3.98479e16 −0.0134123
\(696\) −2.77462e17 + 3.32309e17i −0.0925216 + 0.110811i
\(697\) 1.18631e18 0.391909
\(698\) −2.60833e18 + 2.76917e18i −0.853693 + 0.906337i
\(699\) 4.06102e18i 1.31684i
\(700\) 1.73354e17 + 2.89526e18i 0.0556924 + 0.930143i
\(701\) 3.88716e18i 1.23727i −0.785678 0.618636i \(-0.787686\pi\)
0.785678 0.618636i \(-0.212314\pi\)
\(702\) −1.53158e18 1.44262e18i −0.483001 0.454946i
\(703\) −2.89673e18 −0.905102
\(704\) 3.85299e18 6.98782e17i 1.19282 0.216331i
\(705\) −2.13147e18 −0.653807
\(706\) 1.26865e18 + 1.19497e18i 0.385578 + 0.363182i
\(707\) 8.41672e18i 2.53464i
\(708\) −1.94425e17 3.24717e18i −0.0580143 0.968923i
\(709\) 5.71982e18i 1.69115i −0.533857 0.845575i \(-0.679258\pi\)
0.533857 0.845575i \(-0.320742\pi\)
\(710\) −1.32307e18 + 1.40466e18i −0.387618 + 0.411521i
\(711\) 4.51071e16 0.0130946
\(712\) −1.13351e18 + 1.35757e18i −0.326066 + 0.390520i
\(713\) 7.44248e17 0.212147
\(714\) −2.36673e18 + 2.51268e18i −0.668514 + 0.709738i
\(715\) 2.03196e18i 0.568756i
\(716\) −6.44567e18 + 3.85935e17i −1.78786 + 0.107048i
\(717\) 4.95786e17i 0.136276i
\(718\) −1.04005e18 9.79644e17i −0.283300 0.266845i
\(719\) −1.87126e17 −0.0505121 −0.0252560 0.999681i \(-0.508040\pi\)
−0.0252560 + 0.999681i \(0.508040\pi\)
\(720\) −1.57738e16 1.31251e17i −0.00421964 0.0351107i
\(721\) 1.02132e18 0.270759
\(722\) 4.86948e17 + 4.58664e17i 0.127935 + 0.120504i
\(723\) 4.43884e17i 0.115577i
\(724\) 3.74229e17 2.24070e16i 0.0965687 0.00578206i
\(725\) 2.76000e17i 0.0705849i
\(726\) −1.23895e18 + 1.31535e18i −0.314027 + 0.333392i
\(727\) 4.51258e18 1.13358 0.566789 0.823863i \(-0.308186\pi\)
0.566789 + 0.823863i \(0.308186\pi\)
\(728\) 3.90794e18 + 3.26294e18i 0.972957 + 0.812372i
\(729\) −4.23085e18 −1.04399
\(730\) 1.13212e18 1.20193e18i 0.276881 0.293955i
\(731\) 3.33874e18i 0.809320i
\(732\) −4.02020e17 6.71431e18i −0.0965885 1.61317i
\(733\) 7.21224e18i 1.71749i 0.512403 + 0.858745i \(0.328755\pi\)
−0.512403 + 0.858745i \(0.671245\pi\)
\(734\) −3.05589e18 2.87839e18i −0.721296 0.679400i
\(735\) 8.49765e18 1.98807
\(736\) 1.50339e18 + 1.10977e18i 0.348632 + 0.257351i
\(737\) −4.21358e18 −0.968529
\(738\) −1.19656e17 1.12706e17i −0.0272626 0.0256790i
\(739\) 3.50368e18i 0.791289i 0.918404 + 0.395644i \(0.129479\pi\)
−0.918404 + 0.395644i \(0.870521\pi\)
\(740\) 1.92511e17 + 3.21521e18i 0.0430972 + 0.719786i
\(741\) 2.58806e18i 0.574322i
\(742\) 3.64200e18 3.86659e18i 0.801151 0.850555i
\(743\) −5.28199e18 −1.15178 −0.575891 0.817526i \(-0.695345\pi\)
−0.575891 + 0.817526i \(0.695345\pi\)
\(744\) −1.69550e18 1.41566e18i −0.366500 0.306010i
\(745\) 1.60480e18 0.343879
\(746\) −2.01268e18 + 2.13680e18i −0.427536 + 0.453900i
\(747\) 1.20353e16i 0.00253440i
\(748\) 2.96577e18 1.77576e17i 0.619123 0.0370700i
\(749\) 8.77386e18i 1.81576i
\(750\) 3.69617e18 + 3.48149e18i 0.758323 + 0.714276i
\(751\) 3.18060e18 0.646917 0.323459 0.946242i \(-0.395154\pi\)
0.323459 + 0.946242i \(0.395154\pi\)
\(752\) 4.56378e18 5.48480e17i 0.920257 0.110597i
\(753\) 2.97677e18 0.595083
\(754\) 3.52649e17 + 3.32165e17i 0.0698922 + 0.0658325i
\(755\) 1.27844e18i 0.251203i
\(756\) 1.02424e19 6.13265e17i 1.99531 0.119469i
\(757\) 1.08578e18i 0.209710i 0.994488 + 0.104855i \(0.0334378\pi\)
−0.994488 + 0.104855i \(0.966562\pi\)
\(758\) −4.90209e18 + 5.20439e18i −0.938711 + 0.996597i
\(759\) −2.69840e18 −0.512313
\(760\) −2.23579e18 + 2.67775e18i −0.420865 + 0.504059i
\(761\) −7.22568e17 −0.134859 −0.0674293 0.997724i \(-0.521480\pi\)
−0.0674293 + 0.997724i \(0.521480\pi\)
\(762\) −9.83969e17 + 1.04465e18i −0.182085 + 0.193313i
\(763\) 2.54029e18i 0.466095i
\(764\) −4.97481e17 8.30866e18i −0.0905045 1.51156i
\(765\) 1.00301e17i 0.0180928i
\(766\) −2.61288e18 2.46111e18i −0.467339 0.440194i
\(767\) −3.64027e18 −0.645600
\(768\) −1.31402e18 5.38786e18i −0.231075 0.947477i
\(769\) 7.37979e18 1.28684