Properties

Label 177.11.c.a.58.1
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.1
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.100

$q$-expansion

\(f(q)\) \(=\) \(q-63.4704i q^{2} -140.296 q^{3} -3004.49 q^{4} -5840.70 q^{5} +8904.65i q^{6} +20957.7 q^{7} +125703. i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-63.4704i q^{2} -140.296 q^{3} -3004.49 q^{4} -5840.70 q^{5} +8904.65i q^{6} +20957.7 q^{7} +125703. i q^{8} +19683.0 q^{9} +370712. i q^{10} +183897. i q^{11} +421519. q^{12} +55809.3i q^{13} -1.33019e6i q^{14} +819427. q^{15} +4.90180e6 q^{16} -2.25099e6 q^{17} -1.24929e6i q^{18} +54241.4 q^{19} +1.75483e7 q^{20} -2.94028e6 q^{21} +1.16720e7 q^{22} +8.37467e6i q^{23} -1.76356e7i q^{24} +2.43481e7 q^{25} +3.54224e6 q^{26} -2.76145e6 q^{27} -6.29672e7 q^{28} -1.62454e7 q^{29} -5.20094e7i q^{30} +1.95114e6i q^{31} -1.82400e8i q^{32} -2.58000e7i q^{33} +1.42871e8i q^{34} -1.22408e8 q^{35} -5.91374e7 q^{36} +1.62653e7i q^{37} -3.44273e6i q^{38} -7.82982e6i q^{39} -7.34192e8i q^{40} -7.41830e7 q^{41} +1.86621e8i q^{42} +2.14172e8i q^{43} -5.52517e8i q^{44} -1.14962e8 q^{45} +5.31543e8 q^{46} +3.95183e7i q^{47} -6.87704e8 q^{48} +1.56749e8 q^{49} -1.54539e9i q^{50} +3.15805e8 q^{51} -1.67679e8i q^{52} +5.95662e8 q^{53} +1.75270e8i q^{54} -1.07409e9i q^{55} +2.63444e9i q^{56} -7.60986e6 q^{57} +1.03110e9i q^{58} +(-137790. + 7.14924e8i) q^{59} -2.46196e9 q^{60} -2.70096e8i q^{61} +1.23840e8 q^{62} +4.12510e8 q^{63} -6.55754e9 q^{64} -3.25965e8i q^{65} -1.63754e9 q^{66} -1.14991e9i q^{67} +6.76308e9 q^{68} -1.17493e9i q^{69} +7.76925e9i q^{70} +1.55702e9 q^{71} +2.47421e9i q^{72} -2.37906e9i q^{73} +1.03237e9 q^{74} -3.41595e9 q^{75} -1.62968e8 q^{76} +3.85406e9i q^{77} -4.96962e8 q^{78} +6.62017e8 q^{79} -2.86299e10 q^{80} +3.87420e8 q^{81} +4.70842e9i q^{82} +6.82031e9i q^{83} +8.83405e9 q^{84} +1.31474e10 q^{85} +1.35936e10 q^{86} +2.27916e9 q^{87} -2.31164e10 q^{88} -5.62841e9i q^{89} +7.29672e9i q^{90} +1.16963e9i q^{91} -2.51616e10i q^{92} -2.73737e8i q^{93} +2.50824e9 q^{94} -3.16808e8 q^{95} +2.55900e10i q^{96} +1.89903e9i q^{97} -9.94893e9i q^{98} +3.61965e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 63.4704i 1.98345i −0.128379 0.991725i \(-0.540977\pi\)
0.128379 0.991725i \(-0.459023\pi\)
\(3\) −140.296 −0.577350
\(4\) −3004.49 −2.93408
\(5\) −5840.70 −1.86902 −0.934512 0.355932i \(-0.884164\pi\)
−0.934512 + 0.355932i \(0.884164\pi\)
\(6\) 8904.65i 1.14515i
\(7\) 20957.7 1.24696 0.623481 0.781839i \(-0.285718\pi\)
0.623481 + 0.781839i \(0.285718\pi\)
\(8\) 125703.i 3.83614i
\(9\) 19683.0 0.333333
\(10\) 370712.i 3.70712i
\(11\) 183897.i 1.14186i 0.821000 + 0.570928i \(0.193416\pi\)
−0.821000 + 0.570928i \(0.806584\pi\)
\(12\) 421519. 1.69399
\(13\) 55809.3i 0.150311i 0.997172 + 0.0751553i \(0.0239452\pi\)
−0.997172 + 0.0751553i \(0.976055\pi\)
\(14\) 1.33019e6i 2.47329i
\(15\) 819427. 1.07908
\(16\) 4.90180e6 4.67472
\(17\) −2.25099e6 −1.58536 −0.792682 0.609636i \(-0.791316\pi\)
−0.792682 + 0.609636i \(0.791316\pi\)
\(18\) 1.24929e6i 0.661150i
\(19\) 54241.4 0.0219060 0.0109530 0.999940i \(-0.496513\pi\)
0.0109530 + 0.999940i \(0.496513\pi\)
\(20\) 1.75483e7 5.48386
\(21\) −2.94028e6 −0.719933
\(22\) 1.16720e7 2.26481
\(23\) 8.37467e6i 1.30115i 0.759441 + 0.650576i \(0.225473\pi\)
−0.759441 + 0.650576i \(0.774527\pi\)
\(24\) 1.76356e7i 2.21480i
\(25\) 2.43481e7 2.49325
\(26\) 3.54224e6 0.298134
\(27\) −2.76145e6 −0.192450
\(28\) −6.29672e7 −3.65868
\(29\) −1.62454e7 −0.792027 −0.396014 0.918245i \(-0.629607\pi\)
−0.396014 + 0.918245i \(0.629607\pi\)
\(30\) 5.20094e7i 2.14030i
\(31\) 1.95114e6i 0.0681522i 0.999419 + 0.0340761i \(0.0108489\pi\)
−0.999419 + 0.0340761i \(0.989151\pi\)
\(32\) 1.82400e8i 5.43594i
\(33\) 2.58000e7i 0.659251i
\(34\) 1.42871e8i 3.14449i
\(35\) −1.22408e8 −2.33060
\(36\) −5.91374e7 −0.978025
\(37\) 1.62653e7i 0.234560i 0.993099 + 0.117280i \(0.0374175\pi\)
−0.993099 + 0.117280i \(0.962583\pi\)
\(38\) 3.44273e6i 0.0434495i
\(39\) 7.82982e6i 0.0867818i
\(40\) 7.34192e8i 7.16984i
\(41\) −7.41830e7 −0.640302 −0.320151 0.947366i \(-0.603734\pi\)
−0.320151 + 0.947366i \(0.603734\pi\)
\(42\) 1.86621e8i 1.42795i
\(43\) 2.14172e8i 1.45687i 0.685117 + 0.728433i \(0.259751\pi\)
−0.685117 + 0.728433i \(0.740249\pi\)
\(44\) 5.52517e8i 3.35029i
\(45\) −1.14962e8 −0.623008
\(46\) 5.31543e8 2.58077
\(47\) 3.95183e7i 0.172309i 0.996282 + 0.0861547i \(0.0274579\pi\)
−0.996282 + 0.0861547i \(0.972542\pi\)
\(48\) −6.87704e8 −2.69895
\(49\) 1.56749e8 0.554913
\(50\) 1.54539e9i 4.94524i
\(51\) 3.15805e8 0.915310
\(52\) 1.67679e8i 0.441022i
\(53\) 5.95662e8 1.42436 0.712182 0.701995i \(-0.247707\pi\)
0.712182 + 0.701995i \(0.247707\pi\)
\(54\) 1.75270e8i 0.381715i
\(55\) 1.07409e9i 2.13416i
\(56\) 2.63444e9i 4.78352i
\(57\) −7.60986e6 −0.0126474
\(58\) 1.03110e9i 1.57095i
\(59\) −137790. + 7.14924e8i −0.000192734 + 1.00000i
\(60\) −2.46196e9 −3.16611
\(61\) 2.70096e8i 0.319793i −0.987134 0.159896i \(-0.948884\pi\)
0.987134 0.159896i \(-0.0511160\pi\)
\(62\) 1.23840e8 0.135176
\(63\) 4.12510e8 0.415654
\(64\) −6.55754e9 −6.10719
\(65\) 3.25965e8i 0.280934i
\(66\) −1.63754e9 −1.30759
\(67\) 1.14991e9i 0.851707i −0.904792 0.425853i \(-0.859974\pi\)
0.904792 0.425853i \(-0.140026\pi\)
\(68\) 6.76308e9 4.65158
\(69\) 1.17493e9i 0.751221i
\(70\) 7.76925e9i 4.62263i
\(71\) 1.55702e9 0.862981 0.431491 0.902117i \(-0.357988\pi\)
0.431491 + 0.902117i \(0.357988\pi\)
\(72\) 2.47421e9i 1.27871i
\(73\) 2.37906e9i 1.14760i −0.818994 0.573802i \(-0.805468\pi\)
0.818994 0.573802i \(-0.194532\pi\)
\(74\) 1.03237e9 0.465238
\(75\) −3.41595e9 −1.43948
\(76\) −1.62968e8 −0.0642738
\(77\) 3.85406e9i 1.42385i
\(78\) −4.96962e8 −0.172127
\(79\) 6.62017e8 0.215146 0.107573 0.994197i \(-0.465692\pi\)
0.107573 + 0.994197i \(0.465692\pi\)
\(80\) −2.86299e10 −8.73717
\(81\) 3.87420e8 0.111111
\(82\) 4.70842e9i 1.27001i
\(83\) 6.82031e9i 1.73146i 0.500507 + 0.865732i \(0.333147\pi\)
−0.500507 + 0.865732i \(0.666853\pi\)
\(84\) 8.83405e9 2.11234
\(85\) 1.31474e10 2.96308
\(86\) 1.35936e10 2.88962
\(87\) 2.27916e9 0.457277
\(88\) −2.31164e10 −4.38032
\(89\) 5.62841e9i 1.00794i −0.863721 0.503971i \(-0.831872\pi\)
0.863721 0.503971i \(-0.168128\pi\)
\(90\) 7.29672e9i 1.23571i
\(91\) 1.16963e9i 0.187431i
\(92\) 2.51616e10i 3.81768i
\(93\) 2.73737e8i 0.0393477i
\(94\) 2.50824e9 0.341767
\(95\) −3.16808e8 −0.0409428
\(96\) 2.55900e10i 3.13844i
\(97\) 1.89903e9i 0.221143i 0.993868 + 0.110572i \(0.0352681\pi\)
−0.993868 + 0.110572i \(0.964732\pi\)
\(98\) 9.94893e9i 1.10064i
\(99\) 3.61965e9i 0.380619i
\(100\) −7.31538e10 −7.31538
\(101\) 4.43475e9i 0.421952i −0.977491 0.210976i \(-0.932336\pi\)
0.977491 0.210976i \(-0.0676641\pi\)
\(102\) 2.00443e10i 1.81547i
\(103\) 1.25631e10i 1.08370i 0.840475 + 0.541851i \(0.182276\pi\)
−0.840475 + 0.541851i \(0.817724\pi\)
\(104\) −7.01537e9 −0.576613
\(105\) 1.71733e10 1.34557
\(106\) 3.78069e10i 2.82515i
\(107\) 3.56452e9 0.254145 0.127073 0.991893i \(-0.459442\pi\)
0.127073 + 0.991893i \(0.459442\pi\)
\(108\) 8.29675e9 0.564663
\(109\) 7.75157e9i 0.503799i 0.967753 + 0.251899i \(0.0810552\pi\)
−0.967753 + 0.251899i \(0.918945\pi\)
\(110\) −6.81728e10 −4.23299
\(111\) 2.28196e9i 0.135423i
\(112\) 1.02730e11 5.82920
\(113\) 2.55116e10i 1.38467i 0.721577 + 0.692334i \(0.243418\pi\)
−0.721577 + 0.692334i \(0.756582\pi\)
\(114\) 4.83001e8i 0.0250856i
\(115\) 4.89139e10i 2.43189i
\(116\) 4.88091e10 2.32387
\(117\) 1.09849e9i 0.0501035i
\(118\) 4.53765e10 + 8.74559e6i 1.98345 + 0.000382278i
\(119\) −4.71755e10 −1.97689
\(120\) 1.03004e11i 4.13951i
\(121\) −7.88070e9 −0.303835
\(122\) −1.71431e10 −0.634293
\(123\) 1.04076e10 0.369679
\(124\) 5.86218e9i 0.199964i
\(125\) −8.51721e10 −2.79092
\(126\) 2.61822e10i 0.824429i
\(127\) 3.90746e10 1.18270 0.591351 0.806414i \(-0.298595\pi\)
0.591351 + 0.806414i \(0.298595\pi\)
\(128\) 2.29433e11i 6.67737i
\(129\) 3.00475e10i 0.841122i
\(130\) −2.06891e10 −0.557219
\(131\) 2.22871e10i 0.577693i −0.957375 0.288847i \(-0.906728\pi\)
0.957375 0.288847i \(-0.0932717\pi\)
\(132\) 7.75160e10i 1.93429i
\(133\) 1.13677e9 0.0273159
\(134\) −7.29853e10 −1.68932
\(135\) 1.61288e10 0.359694
\(136\) 2.82955e11i 6.08168i
\(137\) 1.26596e10 0.262311 0.131155 0.991362i \(-0.458131\pi\)
0.131155 + 0.991362i \(0.458131\pi\)
\(138\) −7.45735e10 −1.49001
\(139\) −7.67885e10 −1.47986 −0.739932 0.672681i \(-0.765142\pi\)
−0.739932 + 0.672681i \(0.765142\pi\)
\(140\) 3.67772e11 6.83816
\(141\) 5.54427e9i 0.0994829i
\(142\) 9.88244e10i 1.71168i
\(143\) −1.02632e10 −0.171633
\(144\) 9.64822e10 1.55824
\(145\) 9.48844e10 1.48032
\(146\) −1.51000e11 −2.27622
\(147\) −2.19913e10 −0.320379
\(148\) 4.88690e10i 0.688216i
\(149\) 3.94754e10i 0.537521i 0.963207 + 0.268760i \(0.0866140\pi\)
−0.963207 + 0.268760i \(0.913386\pi\)
\(150\) 2.16812e11i 2.85513i
\(151\) 1.80185e10i 0.229527i 0.993393 + 0.114763i \(0.0366110\pi\)
−0.993393 + 0.114763i \(0.963389\pi\)
\(152\) 6.81829e9i 0.0840345i
\(153\) −4.43062e10 −0.528454
\(154\) 2.44618e11 2.82414
\(155\) 1.13960e10i 0.127378i
\(156\) 2.35246e10i 0.254624i
\(157\) 1.64815e11i 1.72782i 0.503645 + 0.863911i \(0.331992\pi\)
−0.503645 + 0.863911i \(0.668008\pi\)
\(158\) 4.20185e10i 0.426732i
\(159\) −8.35691e10 −0.822357
\(160\) 1.06534e12i 10.1599i
\(161\) 1.75514e11i 1.62249i
\(162\) 2.45897e10i 0.220383i
\(163\) −6.49298e10 −0.564295 −0.282147 0.959371i \(-0.591047\pi\)
−0.282147 + 0.959371i \(0.591047\pi\)
\(164\) 2.22882e11 1.87869
\(165\) 1.50690e11i 1.23216i
\(166\) 4.32888e11 3.43427
\(167\) −1.16113e11 −0.893916 −0.446958 0.894555i \(-0.647493\pi\)
−0.446958 + 0.894555i \(0.647493\pi\)
\(168\) 3.69601e11i 2.76177i
\(169\) 1.34744e11 0.977407
\(170\) 8.34468e11i 5.87713i
\(171\) 1.06763e9 0.00730200
\(172\) 6.43477e11i 4.27456i
\(173\) 2.85927e11i 1.84512i 0.385852 + 0.922561i \(0.373908\pi\)
−0.385852 + 0.922561i \(0.626092\pi\)
\(174\) 1.44659e11i 0.906986i
\(175\) 5.10281e11 3.10899
\(176\) 9.01427e11i 5.33786i
\(177\) 1.93314e7 1.00301e11i 0.000111275 0.577350i
\(178\) −3.57237e11 −1.99920
\(179\) 5.43921e10i 0.295986i −0.988988 0.147993i \(-0.952719\pi\)
0.988988 0.147993i \(-0.0472813\pi\)
\(180\) 3.45404e11 1.82795
\(181\) −1.48809e11 −0.766016 −0.383008 0.923745i \(-0.625112\pi\)
−0.383008 + 0.923745i \(0.625112\pi\)
\(182\) 7.42371e10 0.371761
\(183\) 3.78934e10i 0.184632i
\(184\) −1.05272e12 −4.99141
\(185\) 9.50008e10i 0.438398i
\(186\) −1.73742e10 −0.0780441
\(187\) 4.13950e11i 1.81026i
\(188\) 1.18733e11i 0.505569i
\(189\) −5.78736e10 −0.239978
\(190\) 2.01079e10i 0.0812081i
\(191\) 3.61209e10i 0.142099i −0.997473 0.0710497i \(-0.977365\pi\)
0.997473 0.0710497i \(-0.0226349\pi\)
\(192\) 9.19998e11 3.52599
\(193\) 3.48242e11 1.30045 0.650226 0.759741i \(-0.274674\pi\)
0.650226 + 0.759741i \(0.274674\pi\)
\(194\) 1.20532e11 0.438626
\(195\) 4.57316e10i 0.162197i
\(196\) −4.70951e11 −1.62816
\(197\) −3.92258e11 −1.32203 −0.661014 0.750373i \(-0.729874\pi\)
−0.661014 + 0.750373i \(0.729874\pi\)
\(198\) 2.29740e11 0.754938
\(199\) −3.08718e11 −0.989228 −0.494614 0.869113i \(-0.664691\pi\)
−0.494614 + 0.869113i \(0.664691\pi\)
\(200\) 3.06063e12i 9.56446i
\(201\) 1.61328e11i 0.491733i
\(202\) −2.81476e11 −0.836920
\(203\) −3.40466e11 −0.987627
\(204\) −9.48834e11 −2.68559
\(205\) 4.33281e11 1.19674
\(206\) 7.97383e11 2.14947
\(207\) 1.64839e11i 0.433718i
\(208\) 2.73566e11i 0.702660i
\(209\) 9.97484e9i 0.0250135i
\(210\) 1.09000e12i 2.66888i
\(211\) 3.20677e11i 0.766754i −0.923592 0.383377i \(-0.874761\pi\)
0.923592 0.383377i \(-0.125239\pi\)
\(212\) −1.78966e12 −4.17919
\(213\) −2.18443e11 −0.498242
\(214\) 2.26242e11i 0.504085i
\(215\) 1.25091e12i 2.72292i
\(216\) 3.47122e11i 0.738266i
\(217\) 4.08913e10i 0.0849831i
\(218\) 4.91995e11 0.999260
\(219\) 3.33774e11i 0.662569i
\(220\) 3.22709e12i 6.26177i
\(221\) 1.25626e11i 0.238297i
\(222\) −1.44837e11 −0.268605
\(223\) 2.51695e10 0.0456405 0.0228202 0.999740i \(-0.492735\pi\)
0.0228202 + 0.999740i \(0.492735\pi\)
\(224\) 3.82268e12i 6.77840i
\(225\) 4.79245e11 0.831083
\(226\) 1.61923e12 2.74642
\(227\) 6.00998e11i 0.997111i 0.866858 + 0.498556i \(0.166136\pi\)
−0.866858 + 0.498556i \(0.833864\pi\)
\(228\) 2.28638e10 0.0371085
\(229\) 7.01238e10i 0.111349i −0.998449 0.0556747i \(-0.982269\pi\)
0.998449 0.0556747i \(-0.0177310\pi\)
\(230\) −3.10459e12 −4.82352
\(231\) 5.40709e11i 0.822060i
\(232\) 2.04209e12i 3.03833i
\(233\) 1.94015e11i 0.282524i 0.989972 + 0.141262i \(0.0451160\pi\)
−0.989972 + 0.141262i \(0.954884\pi\)
\(234\) 6.97218e10 0.0993778
\(235\) 2.30815e11i 0.322051i
\(236\) 4.13989e8 2.14798e12i 0.000565495 2.93408i
\(237\) −9.28784e10 −0.124215
\(238\) 2.99425e12i 3.92106i
\(239\) −7.58340e11 −0.972465 −0.486233 0.873829i \(-0.661629\pi\)
−0.486233 + 0.873829i \(0.661629\pi\)
\(240\) 4.01667e12 5.04441
\(241\) −2.40298e11 −0.295574 −0.147787 0.989019i \(-0.547215\pi\)
−0.147787 + 0.989019i \(0.547215\pi\)
\(242\) 5.00191e11i 0.602642i
\(243\) −5.43536e10 −0.0641500
\(244\) 8.11500e11i 0.938295i
\(245\) −9.15524e11 −1.03714
\(246\) 6.60574e11i 0.733239i
\(247\) 3.02717e9i 0.00329270i
\(248\) −2.45263e11 −0.261441
\(249\) 9.56863e11i 0.999662i
\(250\) 5.40591e12i 5.53565i
\(251\) −1.40436e11 −0.140965 −0.0704825 0.997513i \(-0.522454\pi\)
−0.0704825 + 0.997513i \(0.522454\pi\)
\(252\) −1.23938e12 −1.21956
\(253\) −1.54008e12 −1.48573
\(254\) 2.48008e12i 2.34583i
\(255\) −1.84452e12 −1.71074
\(256\) 7.84726e12 7.13704
\(257\) −1.16156e12 −1.03604 −0.518019 0.855369i \(-0.673331\pi\)
−0.518019 + 0.855369i \(0.673331\pi\)
\(258\) −1.90712e12 −1.66832
\(259\) 3.40883e11i 0.292487i
\(260\) 9.79360e11i 0.824281i
\(261\) −3.19758e11 −0.264009
\(262\) −1.41457e12 −1.14583
\(263\) −1.88757e10 −0.0150011 −0.00750055 0.999972i \(-0.502388\pi\)
−0.00750055 + 0.999972i \(0.502388\pi\)
\(264\) 3.24313e12 2.52898
\(265\) −3.47908e12 −2.66217
\(266\) 7.21515e10i 0.0541798i
\(267\) 7.89644e11i 0.581936i
\(268\) 3.45490e12i 2.49897i
\(269\) 1.76049e12i 1.24989i −0.780668 0.624946i \(-0.785121\pi\)
0.780668 0.624946i \(-0.214879\pi\)
\(270\) 1.02370e12i 0.713435i
\(271\) −3.04638e11 −0.208419 −0.104210 0.994555i \(-0.533231\pi\)
−0.104210 + 0.994555i \(0.533231\pi\)
\(272\) −1.10339e13 −7.41113
\(273\) 1.64095e11i 0.108214i
\(274\) 8.03508e11i 0.520280i
\(275\) 4.47755e12i 2.84693i
\(276\) 3.53008e12i 2.20414i
\(277\) 2.34538e12 1.43818 0.719091 0.694916i \(-0.244558\pi\)
0.719091 + 0.694916i \(0.244558\pi\)
\(278\) 4.87380e12i 2.93524i
\(279\) 3.84043e10i 0.0227174i
\(280\) 1.53870e13i 8.94051i
\(281\) 9.95023e11 0.567939 0.283969 0.958833i \(-0.408349\pi\)
0.283969 + 0.958833i \(0.408349\pi\)
\(282\) −3.51897e11 −0.197319
\(283\) 2.65918e12i 1.46493i −0.680806 0.732464i \(-0.738370\pi\)
0.680806 0.732464i \(-0.261630\pi\)
\(284\) −4.67804e12 −2.53205
\(285\) 4.44469e10 0.0236384
\(286\) 6.51407e11i 0.340426i
\(287\) −1.55470e12 −0.798432
\(288\) 3.59017e12i 1.81198i
\(289\) 3.05096e12 1.51338
\(290\) 6.02235e12i 2.93614i
\(291\) 2.66427e11i 0.127677i
\(292\) 7.14788e12i 3.36716i
\(293\) 1.26058e12 0.583758 0.291879 0.956455i \(-0.405720\pi\)
0.291879 + 0.956455i \(0.405720\pi\)
\(294\) 1.39580e12i 0.635456i
\(295\) 8.04790e8 4.17566e12i 0.000360224 1.86902i
\(296\) −2.04459e12 −0.899805
\(297\) 5.07822e11i 0.219750i
\(298\) 2.50552e12 1.06615
\(299\) −4.67384e11 −0.195577
\(300\) 1.02632e13 4.22354
\(301\) 4.48854e12i 1.81666i
\(302\) 1.14364e12 0.455255
\(303\) 6.22179e11i 0.243614i
\(304\) 2.65881e11 0.102404
\(305\) 1.57755e12i 0.597700i
\(306\) 2.81213e12i 1.04816i
\(307\) −2.99927e12 −1.09983 −0.549913 0.835222i \(-0.685339\pi\)
−0.549913 + 0.835222i \(0.685339\pi\)
\(308\) 1.15795e13i 4.17768i
\(309\) 1.76255e12i 0.625675i
\(310\) −7.23310e11 −0.252648
\(311\) 1.87385e12 0.644070 0.322035 0.946728i \(-0.395633\pi\)
0.322035 + 0.946728i \(0.395633\pi\)
\(312\) 9.84230e11 0.332907
\(313\) 5.09208e11i 0.169501i −0.996402 0.0847507i \(-0.972991\pi\)
0.996402 0.0847507i \(-0.0270094\pi\)
\(314\) 1.04609e13 3.42705
\(315\) −2.40935e12 −0.776867
\(316\) −1.98903e12 −0.631255
\(317\) 7.06424e11 0.220683 0.110342 0.993894i \(-0.464806\pi\)
0.110342 + 0.993894i \(0.464806\pi\)
\(318\) 5.30417e12i 1.63110i
\(319\) 2.98748e12i 0.904381i
\(320\) 3.83006e13 11.4145
\(321\) −5.00089e11 −0.146731
\(322\) 1.11399e13 3.21812
\(323\) −1.22097e11 −0.0347290
\(324\) −1.16400e12 −0.326008
\(325\) 1.35885e12i 0.374762i
\(326\) 4.12112e12i 1.11925i
\(327\) 1.08751e12i 0.290868i
\(328\) 9.32500e12i 2.45629i
\(329\) 8.28212e11i 0.214863i
\(330\) 9.56437e12 2.44392
\(331\) −1.03489e12 −0.260468 −0.130234 0.991483i \(-0.541573\pi\)
−0.130234 + 0.991483i \(0.541573\pi\)
\(332\) 2.04916e13i 5.08025i
\(333\) 3.20150e11i 0.0781866i
\(334\) 7.36971e12i 1.77304i
\(335\) 6.71628e12i 1.59186i
\(336\) −1.44127e13 −3.36549
\(337\) 7.07662e12i 1.62808i −0.580807 0.814041i \(-0.697263\pi\)
0.580807 0.814041i \(-0.302737\pi\)
\(338\) 8.55225e12i 1.93864i
\(339\) 3.57918e12i 0.799439i
\(340\) −3.95011e13 −8.69391
\(341\) −3.58809e11 −0.0778199
\(342\) 6.77632e10i 0.0144832i
\(343\) −2.63493e12 −0.555007
\(344\) −2.69220e13 −5.58875
\(345\) 6.86243e12i 1.40405i
\(346\) 1.81479e13 3.65971
\(347\) 5.98851e12i 1.19034i 0.803600 + 0.595170i \(0.202915\pi\)
−0.803600 + 0.595170i \(0.797085\pi\)
\(348\) −6.84773e12 −1.34169
\(349\) 3.89345e12i 0.751981i 0.926623 + 0.375991i \(0.122698\pi\)
−0.926623 + 0.375991i \(0.877302\pi\)
\(350\) 3.23877e13i 6.16652i
\(351\) 1.54114e11i 0.0289273i
\(352\) 3.35428e13 6.20706
\(353\) 2.56602e12i 0.468152i −0.972218 0.234076i \(-0.924793\pi\)
0.972218 0.234076i \(-0.0752065\pi\)
\(354\) −6.36615e12 1.22697e9i −1.14515 0.000220708i
\(355\) −9.09406e12 −1.61293
\(356\) 1.69105e13i 2.95738i
\(357\) 6.61854e12 1.14136
\(358\) −3.45229e12 −0.587073
\(359\) 4.72954e12 0.793134 0.396567 0.918006i \(-0.370202\pi\)
0.396567 + 0.918006i \(0.370202\pi\)
\(360\) 1.44511e13i 2.38995i
\(361\) −6.12812e12 −0.999520
\(362\) 9.44500e12i 1.51935i
\(363\) 1.10563e12 0.175419
\(364\) 3.51415e12i 0.549938i
\(365\) 1.38954e13i 2.14490i
\(366\) 2.40511e12 0.366209
\(367\) 3.31765e12i 0.498311i 0.968463 + 0.249155i \(0.0801530\pi\)
−0.968463 + 0.249155i \(0.919847\pi\)
\(368\) 4.10509e13i 6.08253i
\(369\) −1.46014e12 −0.213434
\(370\) −6.02974e12 −0.869541
\(371\) 1.24837e13 1.77613
\(372\) 8.22441e11i 0.115449i
\(373\) −4.54427e12 −0.629391 −0.314695 0.949193i \(-0.601902\pi\)
−0.314695 + 0.949193i \(0.601902\pi\)
\(374\) −2.62736e13 −3.59055
\(375\) 1.19493e13 1.61134
\(376\) −4.96756e12 −0.661004
\(377\) 9.06643e11i 0.119050i
\(378\) 3.67326e12i 0.475984i
\(379\) −1.16208e13 −1.48607 −0.743036 0.669252i \(-0.766615\pi\)
−0.743036 + 0.669252i \(0.766615\pi\)
\(380\) 9.51847e11 0.120129
\(381\) −5.48201e12 −0.682834
\(382\) −2.29261e12 −0.281847
\(383\) −8.53173e12 −1.03524 −0.517622 0.855609i \(-0.673183\pi\)
−0.517622 + 0.855609i \(0.673183\pi\)
\(384\) 3.21885e13i 3.85518i
\(385\) 2.25104e13i 2.66121i
\(386\) 2.21031e13i 2.57938i
\(387\) 4.21554e12i 0.485622i
\(388\) 5.70563e12i 0.648851i
\(389\) −8.89190e12 −0.998266 −0.499133 0.866525i \(-0.666348\pi\)
−0.499133 + 0.866525i \(0.666348\pi\)
\(390\) 2.90261e12 0.321710
\(391\) 1.88513e13i 2.06280i
\(392\) 1.97038e13i 2.12872i
\(393\) 3.12679e12i 0.333531i
\(394\) 2.48968e13i 2.62218i
\(395\) −3.86664e12 −0.402113
\(396\) 1.08752e13i 1.11676i
\(397\) 6.74847e12i 0.684309i 0.939644 + 0.342155i \(0.111157\pi\)
−0.939644 + 0.342155i \(0.888843\pi\)
\(398\) 1.95945e13i 1.96209i
\(399\) −1.59485e11 −0.0157709
\(400\) 1.19350e14 11.6553
\(401\) 1.84643e12i 0.178079i −0.996028 0.0890393i \(-0.971620\pi\)
0.996028 0.0890393i \(-0.0283797\pi\)
\(402\) 1.02396e13 0.975328
\(403\) −1.08892e11 −0.0102440
\(404\) 1.33242e13i 1.23804i
\(405\) −2.26281e12 −0.207669
\(406\) 2.16095e13i 1.95891i
\(407\) −2.99114e12 −0.267834
\(408\) 3.96976e13i 3.51126i
\(409\) 2.04755e13i 1.78903i 0.447039 + 0.894515i \(0.352479\pi\)
−0.447039 + 0.894515i \(0.647521\pi\)
\(410\) 2.75005e13i 2.37367i
\(411\) −1.77609e12 −0.151445
\(412\) 3.77457e13i 3.17966i
\(413\) −2.88776e9 + 1.49832e13i −0.000240331 + 1.24696i
\(414\) 1.04624e13 0.860257
\(415\) 3.98354e13i 3.23615i
\(416\) 1.01796e13 0.817079
\(417\) 1.07731e13 0.854400
\(418\) 6.33107e11 0.0496130
\(419\) 2.40803e12i 0.186463i −0.995644 0.0932313i \(-0.970280\pi\)
0.995644 0.0932313i \(-0.0297196\pi\)
\(420\) −5.15971e13 −3.94801
\(421\) 1.89761e13i 1.43482i 0.696653 + 0.717408i \(0.254672\pi\)
−0.696653 + 0.717408i \(0.745328\pi\)
\(422\) −2.03535e13 −1.52082
\(423\) 7.77839e11i 0.0574365i
\(424\) 7.48764e13i 5.46406i
\(425\) −5.48074e13 −3.95271
\(426\) 1.38647e13i 0.988239i
\(427\) 5.66058e12i 0.398769i
\(428\) −1.07096e13 −0.745682
\(429\) 1.43988e12 0.0990924
\(430\) −7.93959e13 −5.40077
\(431\) 6.83772e12i 0.459753i −0.973220 0.229877i \(-0.926168\pi\)
0.973220 0.229877i \(-0.0738323\pi\)
\(432\) −1.35361e13 −0.899651
\(433\) −8.12277e12 −0.533660 −0.266830 0.963744i \(-0.585976\pi\)
−0.266830 + 0.963744i \(0.585976\pi\)
\(434\) 2.59539e12 0.168560
\(435\) −1.33119e13 −0.854662
\(436\) 2.32895e13i 1.47818i
\(437\) 4.54254e11i 0.0285030i
\(438\) 2.11847e13 1.31417
\(439\) −1.54335e13 −0.946549 −0.473274 0.880915i \(-0.656928\pi\)
−0.473274 + 0.880915i \(0.656928\pi\)
\(440\) 1.35016e14 8.18693
\(441\) 3.08529e12 0.184971
\(442\) −7.97354e12 −0.472650
\(443\) 8.81273e12i 0.516525i −0.966075 0.258263i \(-0.916850\pi\)
0.966075 0.258263i \(-0.0831500\pi\)
\(444\) 6.85613e12i 0.397342i
\(445\) 3.28738e13i 1.88387i
\(446\) 1.59752e12i 0.0905256i
\(447\) 5.53824e12i 0.310338i
\(448\) −1.37431e14 −7.61543
\(449\) −2.17822e13 −1.19363 −0.596816 0.802378i \(-0.703568\pi\)
−0.596816 + 0.802378i \(0.703568\pi\)
\(450\) 3.04178e13i 1.64841i
\(451\) 1.36420e13i 0.731133i
\(452\) 7.66495e13i 4.06272i
\(453\) 2.52792e12i 0.132517i
\(454\) 3.81456e13 1.97772
\(455\) 6.83147e12i 0.350314i
\(456\) 9.56580e11i 0.0485173i
\(457\) 2.13151e13i 1.06932i 0.845068 + 0.534659i \(0.179560\pi\)
−0.845068 + 0.534659i \(0.820440\pi\)
\(458\) −4.45079e12 −0.220856
\(459\) 6.21599e12 0.305103
\(460\) 1.46961e14i 7.13534i
\(461\) 3.42266e13 1.64384 0.821920 0.569603i \(-0.192903\pi\)
0.821920 + 0.569603i \(0.192903\pi\)
\(462\) −3.43190e13 −1.63052
\(463\) 3.60218e13i 1.69302i −0.532377 0.846508i \(-0.678701\pi\)
0.532377 0.846508i \(-0.321299\pi\)
\(464\) −7.96316e13 −3.70251
\(465\) 1.59882e12i 0.0735417i
\(466\) 1.23142e13 0.560372
\(467\) 5.76659e12i 0.259618i 0.991539 + 0.129809i \(0.0414364\pi\)
−0.991539 + 0.129809i \(0.958564\pi\)
\(468\) 3.30042e12i 0.147007i
\(469\) 2.40995e13i 1.06205i
\(470\) −1.46499e13 −0.638771
\(471\) 2.31229e13i 0.997558i
\(472\) −8.98679e13 1.73206e10i −3.83614 0.000739354i
\(473\) −3.93855e13 −1.66353
\(474\) 5.89503e12i 0.246374i
\(475\) 1.32068e12 0.0546171
\(476\) 1.41739e14 5.80034
\(477\) 1.17244e13 0.474788
\(478\) 4.81321e13i 1.92884i
\(479\) 7.47303e12 0.296360 0.148180 0.988960i \(-0.452659\pi\)
0.148180 + 0.988960i \(0.452659\pi\)
\(480\) 1.49463e14i 5.86582i
\(481\) −9.07755e11 −0.0352568
\(482\) 1.52518e13i 0.586256i
\(483\) 2.46239e13i 0.936743i
\(484\) 2.36775e13 0.891475
\(485\) 1.10917e13i 0.413322i
\(486\) 3.44984e12i 0.127238i
\(487\) 1.50255e13 0.548510 0.274255 0.961657i \(-0.411569\pi\)
0.274255 + 0.961657i \(0.411569\pi\)
\(488\) 3.39517e13 1.22677
\(489\) 9.10940e12 0.325796
\(490\) 5.81087e13i 2.05713i
\(491\) 1.44317e13 0.505718 0.252859 0.967503i \(-0.418629\pi\)
0.252859 + 0.967503i \(0.418629\pi\)
\(492\) −3.12695e13 −1.08467
\(493\) 3.65682e13 1.25565
\(494\) 1.92136e11 0.00653091
\(495\) 2.11413e13i 0.711385i
\(496\) 9.56409e12i 0.318592i
\(497\) 3.26314e13 1.07610
\(498\) −6.07325e13 −1.98278
\(499\) 1.90084e13 0.614387 0.307194 0.951647i \(-0.400610\pi\)
0.307194 + 0.951647i \(0.400610\pi\)
\(500\) 2.55899e14 8.18877
\(501\) 1.62901e13 0.516103
\(502\) 8.91356e12i 0.279597i
\(503\) 5.04714e13i 1.56749i −0.621081 0.783746i \(-0.713306\pi\)
0.621081 0.783746i \(-0.286694\pi\)
\(504\) 5.18536e13i 1.59451i
\(505\) 2.59021e13i 0.788638i
\(506\) 9.77493e13i 2.94687i
\(507\) −1.89040e13 −0.564306
\(508\) −1.17399e14 −3.47014
\(509\) 1.15054e13i 0.336755i 0.985723 + 0.168378i \(0.0538528\pi\)
−0.985723 + 0.168378i \(0.946147\pi\)
\(510\) 1.17073e14i 3.39316i
\(511\) 4.98597e13i 1.43102i
\(512\) 2.63130e14i 7.47860i
\(513\) −1.49785e11 −0.00421581
\(514\) 7.37247e13i 2.05493i
\(515\) 7.33771e13i 2.02546i
\(516\) 9.02774e13i 2.46792i
\(517\) −7.26730e12 −0.196753
\(518\) 2.16360e13 0.580134
\(519\) 4.01145e13i 1.06528i
\(520\) 4.09747e13 1.07770
\(521\) 4.75369e13 1.23835 0.619173 0.785255i \(-0.287468\pi\)
0.619173 + 0.785255i \(0.287468\pi\)
\(522\) 2.02952e13i 0.523649i
\(523\) 6.54008e13 1.67138 0.835688 0.549204i \(-0.185069\pi\)
0.835688 + 0.549204i \(0.185069\pi\)
\(524\) 6.69614e13i 1.69499i
\(525\) −7.15904e13 −1.79497
\(526\) 1.19805e12i 0.0297539i
\(527\) 4.39199e12i 0.108046i
\(528\) 1.26467e14i 3.08181i
\(529\) −2.87085e13 −0.692999
\(530\) 2.20819e14i 5.28028i
\(531\) −2.71212e9 + 1.40719e13i −6.42446e−5 + 0.333333i
\(532\) −3.41543e12 −0.0801470
\(533\) 4.14010e12i 0.0962442i
\(534\) 5.01190e13 1.15424
\(535\) −2.08193e13 −0.475004
\(536\) 1.44547e14 3.26727
\(537\) 7.63100e12i 0.170887i
\(538\) −1.11739e14 −2.47910
\(539\) 2.88257e13i 0.633630i
\(540\) −4.84588e13 −1.05537
\(541\) 6.22173e13i 1.34253i −0.741216 0.671266i \(-0.765751\pi\)
0.741216 0.671266i \(-0.234249\pi\)
\(542\) 1.93355e13i 0.413389i
\(543\) 2.08774e13 0.442259
\(544\) 4.10580e14i 8.61794i
\(545\) 4.52746e13i 0.941612i
\(546\) −1.04152e13 −0.214636
\(547\) 4.77479e13 0.975029 0.487514 0.873115i \(-0.337904\pi\)
0.487514 + 0.873115i \(0.337904\pi\)
\(548\) −3.80356e13 −0.769639
\(549\) 5.31629e12i 0.106598i
\(550\) 2.84192e14 5.64675
\(551\) −8.81173e11 −0.0173501
\(552\) 1.47692e14 2.88179
\(553\) 1.38743e13 0.268279
\(554\) 1.48862e14i 2.85256i
\(555\) 1.33282e13i 0.253109i
\(556\) 2.30710e14 4.34203
\(557\) −3.04354e13 −0.567679 −0.283840 0.958872i \(-0.591608\pi\)
−0.283840 + 0.958872i \(0.591608\pi\)
\(558\) 2.43753e12 0.0450588
\(559\) −1.19528e13 −0.218982
\(560\) −6.00017e14 −10.8949
\(561\) 5.80756e13i 1.04515i
\(562\) 6.31545e13i 1.12648i
\(563\) 6.02785e13i 1.06566i −0.846221 0.532832i \(-0.821128\pi\)
0.846221 0.532832i \(-0.178872\pi\)
\(564\) 1.66577e13i 0.291890i
\(565\) 1.49006e14i 2.58798i
\(566\) −1.68779e14 −2.90561
\(567\) 8.11943e12 0.138551
\(568\) 1.95721e14i 3.31052i
\(569\) 4.35597e13i 0.730338i −0.930941 0.365169i \(-0.881011\pi\)
0.930941 0.365169i \(-0.118989\pi\)
\(570\) 2.82106e12i 0.0468855i
\(571\) 3.20890e13i 0.528659i −0.964432 0.264329i \(-0.914849\pi\)
0.964432 0.264329i \(-0.0851506\pi\)
\(572\) 3.08356e13 0.503584
\(573\) 5.06762e12i 0.0820411i
\(574\) 9.86777e13i 1.58365i
\(575\) 2.03908e14i 3.24410i
\(576\) −1.29072e14 −2.03573
\(577\) 5.85741e13 0.915855 0.457927 0.888990i \(-0.348592\pi\)
0.457927 + 0.888990i \(0.348592\pi\)
\(578\) 1.93646e14i 3.00171i
\(579\) −4.88570e13 −0.750817
\(580\) −2.85080e14 −4.34336
\(581\) 1.42938e14i 2.15907i
\(582\) −1.69102e13 −0.253241
\(583\) 1.09541e14i 1.62642i
\(584\) 2.99055e14 4.40237
\(585\) 6.41597e12i 0.0936447i
\(586\) 8.00097e13i 1.15786i
\(587\) 5.30355e13i 0.760985i 0.924784 + 0.380493i \(0.124246\pi\)
−0.924784 + 0.380493i \(0.875754\pi\)
\(588\) 6.60727e13 0.940016
\(589\) 1.05833e11i 0.00149294i
\(590\) −2.65031e14 5.10803e10i −3.70712 0.000714486i
\(591\) 5.50323e13 0.763273
\(592\) 7.97293e13i 1.09650i
\(593\) 2.02817e13 0.276586 0.138293 0.990391i \(-0.455838\pi\)
0.138293 + 0.990391i \(0.455838\pi\)
\(594\) −3.22317e13 −0.435864
\(595\) 2.75538e14 3.69485
\(596\) 1.18604e14i 1.57713i
\(597\) 4.33119e13 0.571131
\(598\) 2.96650e13i 0.387917i
\(599\) 5.40889e13 0.701414 0.350707 0.936485i \(-0.385941\pi\)
0.350707 + 0.936485i \(0.385941\pi\)
\(600\) 4.29394e14i 5.52204i
\(601\) 6.20264e13i 0.791050i 0.918455 + 0.395525i \(0.129437\pi\)
−0.918455 + 0.395525i \(0.870563\pi\)
\(602\) 2.84890e14 3.60325
\(603\) 2.26337e13i 0.283902i
\(604\) 5.41364e13i 0.673449i
\(605\) 4.60288e13 0.567875
\(606\) 3.94899e13 0.483196
\(607\) 1.23049e12 0.0149326 0.00746629 0.999972i \(-0.497623\pi\)
0.00746629 + 0.999972i \(0.497623\pi\)
\(608\) 9.89362e12i 0.119080i
\(609\) 4.77660e13 0.570207
\(610\) 1.00128e14 1.18551
\(611\) −2.20549e12 −0.0258999
\(612\) 1.33118e14 1.55053
\(613\) 7.83342e13i 0.905001i −0.891764 0.452500i \(-0.850532\pi\)
0.891764 0.452500i \(-0.149468\pi\)
\(614\) 1.90365e14i 2.18145i
\(615\) −6.07876e13 −0.690938
\(616\) −4.84465e14 −5.46209
\(617\) 1.06587e14 1.19200 0.596002 0.802983i \(-0.296755\pi\)
0.596002 + 0.802983i \(0.296755\pi\)
\(618\) −1.11870e14 −1.24100
\(619\) −9.84942e13 −1.08382 −0.541910 0.840436i \(-0.682299\pi\)
−0.541910 + 0.840436i \(0.682299\pi\)
\(620\) 3.42392e13i 0.373737i
\(621\) 2.31262e13i 0.250407i
\(622\) 1.18934e14i 1.27748i
\(623\) 1.17958e14i 1.25686i
\(624\) 3.83802e13i 0.405681i
\(625\) 2.59690e14 2.72305
\(626\) −3.23196e13 −0.336198
\(627\) 1.39943e12i 0.0144415i
\(628\) 4.95186e14i 5.06956i
\(629\) 3.66130e13i 0.371863i
\(630\) 1.52922e14i 1.54088i
\(631\) −9.27400e13 −0.927086 −0.463543 0.886074i \(-0.653422\pi\)
−0.463543 + 0.886074i \(0.653422\pi\)
\(632\) 8.32173e13i 0.825332i
\(633\) 4.49898e13i 0.442686i
\(634\) 4.48370e13i 0.437714i
\(635\) −2.28223e14 −2.21050
\(636\) 2.51083e14 2.41286
\(637\) 8.74805e12i 0.0834092i
\(638\) −1.89616e14 −1.79379
\(639\) 3.06467e13 0.287660
\(640\) 1.34005e15i 12.4802i
\(641\) −9.66091e13 −0.892746 −0.446373 0.894847i \(-0.647284\pi\)
−0.446373 + 0.894847i \(0.647284\pi\)
\(642\) 3.17408e13i 0.291034i
\(643\) −5.58926e13 −0.508510 −0.254255 0.967137i \(-0.581830\pi\)
−0.254255 + 0.967137i \(0.581830\pi\)
\(644\) 5.27329e14i 4.76050i
\(645\) 1.75498e14i 1.57208i
\(646\) 7.74954e12i 0.0688832i
\(647\) −1.06933e14 −0.943168 −0.471584 0.881821i \(-0.656318\pi\)
−0.471584 + 0.881821i \(0.656318\pi\)
\(648\) 4.86998e13i 0.426238i
\(649\) −1.31472e14 2.53392e10i −1.14186 0.000220074i
\(650\) 8.62469e13 0.743321
\(651\) 5.73689e12i 0.0490650i
\(652\) 1.95081e14 1.65568
\(653\) −1.12908e14 −0.950956 −0.475478 0.879728i \(-0.657725\pi\)
−0.475478 + 0.879728i \(0.657725\pi\)
\(654\) −6.90250e13 −0.576923
\(655\) 1.30172e14i 1.07972i
\(656\) −3.63630e14 −2.99323
\(657\) 4.68271e13i 0.382535i
\(658\) 5.25670e13 0.426171
\(659\) 1.35675e14i 1.09162i −0.837909 0.545810i \(-0.816222\pi\)
0.837909 0.545810i \(-0.183778\pi\)
\(660\) 4.52748e14i 3.61524i
\(661\) 1.55289e14 1.23065 0.615323 0.788275i \(-0.289025\pi\)
0.615323 + 0.788275i \(0.289025\pi\)
\(662\) 6.56849e13i 0.516625i
\(663\) 1.76248e13i 0.137581i
\(664\) −8.57331e14 −6.64214
\(665\) −6.63956e12 −0.0510541
\(666\) 2.03201e13 0.155079
\(667\) 1.36050e14i 1.03055i
\(668\) 3.48859e14 2.62282
\(669\) −3.53118e12 −0.0263505
\(670\) 4.26285e14 3.15738
\(671\) 4.96698e13 0.365157
\(672\) 5.36307e14i 3.91351i
\(673\) 1.74921e14i 1.26697i −0.773756 0.633484i \(-0.781624\pi\)
0.773756 0.633484i \(-0.218376\pi\)
\(674\) −4.49156e14 −3.22922
\(675\) −6.72362e13 −0.479826
\(676\) −4.04837e14 −2.86778
\(677\) −4.86161e13 −0.341851 −0.170925 0.985284i \(-0.554676\pi\)
−0.170925 + 0.985284i \(0.554676\pi\)
\(678\) −2.27172e14 −1.58565
\(679\) 3.97993e13i 0.275757i
\(680\) 1.65266e15i 11.3668i
\(681\) 8.43176e13i 0.575682i
\(682\) 2.27737e13i 0.154352i
\(683\) 1.55046e13i 0.104317i −0.998639 0.0521586i \(-0.983390\pi\)
0.998639 0.0521586i \(-0.0166101\pi\)
\(684\) −3.20770e12 −0.0214246
\(685\) −7.39407e13 −0.490265
\(686\) 1.67240e14i 1.10083i
\(687\) 9.83810e12i 0.0642876i
\(688\) 1.04983e15i 6.81045i
\(689\) 3.32435e13i 0.214097i
\(690\) 4.35561e14 2.78486
\(691\) 2.79217e14i 1.77236i 0.463343 + 0.886179i \(0.346650\pi\)
−0.463343 + 0.886179i \(0.653350\pi\)
\(692\) 8.59066e14i 5.41373i
\(693\) 7.58594e13i 0.474617i
\(694\) 3.80093e14 2.36098
\(695\) 4.48498e14 2.76590
\(696\) 2.86497e14i 1.75418i
\(697\) 1.66985e14 1.01511
\(698\) 2.47119e14 1.49152
\(699\) 2.72195e13i 0.163115i
\(700\) −1.53313e15 −9.12200
\(701\) 1.49605e14i 0.883804i 0.897063 + 0.441902i \(0.145696\pi\)
−0.897063 + 0.441902i \(0.854304\pi\)
\(702\) −9.78170e12 −0.0573758
\(703\) 8.82253e11i 0.00513827i
\(704\) 1.20591e15i 6.97353i
\(705\) 3.23824e13i 0.185936i
\(706\) −1.62867e14 −0.928557
\(707\) 9.29421e13i 0.526157i
\(708\) −5.80810e10 + 3.01354e14i −0.000326489 + 1.69399i
\(709\) 1.49929e14 0.836865 0.418433 0.908248i \(-0.362580\pi\)
0.418433 + 0.908248i \(0.362580\pi\)
\(710\) 5.77204e14i 3.19917i
\(711\) 1.30305e13 0.0717154
\(712\) 7.07506e14 3.86661
\(713\) −1.63401e13 −0.0886764
\(714\) 4.20082e14i 2.26382i
\(715\) 5.99440e13 0.320786
\(716\) 1.63421e14i 0.868444i
\(717\) 1.06392e14 0.561453
\(718\) 3.00186e14i 1.57314i
\(719\) 1.55523e13i 0.0809375i −0.999181 0.0404687i \(-0.987115\pi\)
0.999181 0.0404687i \(-0.0128851\pi\)
\(720\) −5.63523e14 −2.91239
\(721\) 2.63293e14i 1.35133i
\(722\) 3.88955e14i 1.98250i
\(723\) 3.37129e13 0.170650
\(724\) 4.47097e14 2.24755
\(725\) −3.95545e14 −1.97472
\(726\) 7.01749e13i 0.347935i
\(727\) −2.54365e14 −1.25252 −0.626261 0.779613i \(-0.715416\pi\)
−0.626261 + 0.779613i \(0.715416\pi\)
\(728\) −1.47026e14 −0.719014
\(729\) 7.62560e12 0.0370370
\(730\) 8.81947e14 4.25430
\(731\) 4.82098e14i 2.30966i
\(732\) 1.13850e14i 0.541725i
\(733\) −1.27430e14 −0.602216 −0.301108 0.953590i \(-0.597356\pi\)
−0.301108 + 0.953590i \(0.597356\pi\)
\(734\) 2.10573e14 0.988375
\(735\) 1.28444e14 0.598796
\(736\) 1.52754e15 7.07298
\(737\) 2.11465e14 0.972527
\(738\) 9.26759e13i 0.423336i
\(739\) 3.32416e14i 1.50820i −0.656758 0.754102i \(-0.728073\pi\)
0.656758 0.754102i \(-0.271927\pi\)
\(740\) 2.85429e14i 1.28629i
\(741\) 4.24701e11i 0.00190104i
\(742\) 7.92346e14i 3.52286i
\(743\) −2.55056e14 −1.12639 −0.563197 0.826322i \(-0.690429\pi\)
−0.563197 + 0.826322i \(0.690429\pi\)
\(744\) 3.44095e13 0.150943
\(745\) 2.30564e14i 1.00464i
\(746\) 2.88427e14i 1.24836i
\(747\) 1.34244e14i 0.577155i
\(748\) 1.24371e15i 5.31143i
\(749\) 7.47041e13 0.316910
\(750\) 7.58428e14i 3.19601i
\(751\) 3.85398e14i 1.61328i 0.591043 + 0.806640i \(0.298716\pi\)
−0.591043 + 0.806640i \(0.701284\pi\)
\(752\) 1.93711e14i 0.805499i
\(753\) 1.97027e13 0.0813861
\(754\) −5.75450e13 −0.236130
\(755\) 1.05241e14i 0.428991i
\(756\) 1.73881e14 0.704113
\(757\) 1.20459e14 0.484574 0.242287 0.970205i \(-0.422102\pi\)
0.242287 + 0.970205i \(0.422102\pi\)
\(758\) 7.37577e14i 2.94755i
\(759\) 2.16067e14 0.857786
\(760\) 3.98236e13i 0.157063i
\(761\) −7.56048e13 −0.296228 −0.148114 0.988970i \(-0.547320\pi\)
−0.148114 + 0.988970i \(0.547320\pi\)
\(762\) 3.47945e14i 1.35437i
\(763\) 1.62455e14i 0.628217i
\(764\) 1.08525e14i 0.416930i
\(765\) 2.58779e14 0.987694
\(766\) 5.41512e14i 2.05336i
\(767\) −3.98994e13 7.68996e9i −0.150311 2.89699e-5i
\(768\) −1.10094e15 −4.12057
\(769\) 2.33655e13i 0.0868848i 0.999056 + 0.0434424i \(0.0138325\pi\)
−0.999056 + 0.0434424i \(0.986168\pi\)
\(770\) −1.42874e15 −5.27838
\(771\) 1.62962e14 0.598157
\(772\) −1.04629e15 −3.81563
\(773\) 3.39985e14i 1.23186i −0.787800 0.615931i \(-0.788780\pi\)
0.787800 0.615931i \(-0.211220\pi\)
\(774\) 2.67562e14 0.963207
\(775\) 4.75066e13i 0.169920i
\(776\) −2.38713e14 −0.848337
\(777\) 4.78246e13i 0.168867i
\(778\) 5.64372e14i 1.98001i
\(779\) −4.02379e12 −0.0140265