Properties

Label 177.11.c.a.58.14
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 58.14
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.87

$q$-expansion

\(f(q)\) \(=\) \(q-50.8045i q^{2} -140.296 q^{3} -1557.09 q^{4} +737.455 q^{5} +7127.67i q^{6} -21294.5 q^{7} +27083.5i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-50.8045i q^{2} -140.296 q^{3} -1557.09 q^{4} +737.455 q^{5} +7127.67i q^{6} -21294.5 q^{7} +27083.5i q^{8} +19683.0 q^{9} -37466.0i q^{10} +265503. i q^{11} +218454. q^{12} +470017. i q^{13} +1.08186e6i q^{14} -103462. q^{15} -218501. q^{16} -1.88282e6 q^{17} -999984. i q^{18} -4.41356e6 q^{19} -1.14829e6 q^{20} +2.98754e6 q^{21} +1.34887e7 q^{22} +1.07346e7i q^{23} -3.79971e6i q^{24} -9.22178e6 q^{25} +2.38790e7 q^{26} -2.76145e6 q^{27} +3.31576e7 q^{28} +1.25709e7 q^{29} +5.25634e6i q^{30} -4.28985e7i q^{31} +3.88343e7i q^{32} -3.72490e7i q^{33} +9.56558e7i q^{34} -1.57038e7 q^{35} -3.06483e7 q^{36} +2.69313e7i q^{37} +2.24228e8i q^{38} -6.59416e7i q^{39} +1.99729e7i q^{40} +4.52994e6 q^{41} -1.51780e8i q^{42} -1.84390e8i q^{43} -4.13412e8i q^{44} +1.45153e7 q^{45} +5.45366e8 q^{46} +1.36961e8i q^{47} +3.06549e7 q^{48} +1.70982e8 q^{49} +4.68508e8i q^{50} +2.64153e8 q^{51} -7.31860e8i q^{52} -4.28407e7 q^{53} +1.40294e8i q^{54} +1.95796e8i q^{55} -5.76730e8i q^{56} +6.19205e8 q^{57} -6.38655e8i q^{58} +(6.78517e8 - 2.25236e8i) q^{59} +1.61100e8 q^{60} +4.89796e8i q^{61} -2.17943e9 q^{62} -4.19140e8 q^{63} +1.74921e9 q^{64} +3.46617e8i q^{65} -1.89242e9 q^{66} +8.12593e8i q^{67} +2.93173e9 q^{68} -1.50603e9i q^{69} +7.97821e8i q^{70} -2.09745e9 q^{71} +5.33084e8i q^{72} -3.96104e9i q^{73} +1.36823e9 q^{74} +1.29378e9 q^{75} +6.87232e9 q^{76} -5.65376e9i q^{77} -3.35012e9 q^{78} -2.20220e9 q^{79} -1.61135e8 q^{80} +3.87420e8 q^{81} -2.30141e8i q^{82} -2.68481e9i q^{83} -4.65188e9 q^{84} -1.38850e9 q^{85} -9.36785e9 q^{86} -1.76364e9 q^{87} -7.19074e9 q^{88} -3.26412e9i q^{89} -7.37444e8i q^{90} -1.00088e10i q^{91} -1.67148e10i q^{92} +6.01849e9i q^{93} +6.95822e9 q^{94} -3.25480e9 q^{95} -5.44831e9i q^{96} +1.33057e10i q^{97} -8.68665e9i q^{98} +5.22589e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 50.8045i 1.58764i −0.608153 0.793820i \(-0.708089\pi\)
0.608153 0.793820i \(-0.291911\pi\)
\(3\) −140.296 −0.577350
\(4\) −1557.09 −1.52060
\(5\) 737.455 0.235986 0.117993 0.993014i \(-0.462354\pi\)
0.117993 + 0.993014i \(0.462354\pi\)
\(6\) 7127.67i 0.916624i
\(7\) −21294.5 −1.26700 −0.633502 0.773741i \(-0.718383\pi\)
−0.633502 + 0.773741i \(0.718383\pi\)
\(8\) 27083.5i 0.826522i
\(9\) 19683.0 0.333333
\(10\) 37466.0i 0.374660i
\(11\) 265503.i 1.64856i 0.566180 + 0.824282i \(0.308421\pi\)
−0.566180 + 0.824282i \(0.691579\pi\)
\(12\) 218454. 0.877918
\(13\) 470017.i 1.26589i 0.774196 + 0.632946i \(0.218155\pi\)
−0.774196 + 0.632946i \(0.781845\pi\)
\(14\) 1.08186e6i 2.01155i
\(15\) −103462. −0.136246
\(16\) −218501. −0.208379
\(17\) −1.88282e6 −1.32606 −0.663032 0.748591i \(-0.730731\pi\)
−0.663032 + 0.748591i \(0.730731\pi\)
\(18\) 999984.i 0.529213i
\(19\) −4.41356e6 −1.78246 −0.891232 0.453547i \(-0.850158\pi\)
−0.891232 + 0.453547i \(0.850158\pi\)
\(20\) −1.14829e6 −0.358839
\(21\) 2.98754e6 0.731505
\(22\) 1.34887e7 2.61732
\(23\) 1.07346e7i 1.66781i 0.551906 + 0.833907i \(0.313901\pi\)
−0.551906 + 0.833907i \(0.686099\pi\)
\(24\) 3.79971e6i 0.477193i
\(25\) −9.22178e6 −0.944311
\(26\) 2.38790e7 2.00978
\(27\) −2.76145e6 −0.192450
\(28\) 3.31576e7 1.92660
\(29\) 1.25709e7 0.612879 0.306440 0.951890i \(-0.400862\pi\)
0.306440 + 0.951890i \(0.400862\pi\)
\(30\) 5.25634e6i 0.216310i
\(31\) 4.28985e7i 1.49842i −0.662333 0.749209i \(-0.730434\pi\)
0.662333 0.749209i \(-0.269566\pi\)
\(32\) 3.88343e7i 1.15735i
\(33\) 3.72490e7i 0.951798i
\(34\) 9.56558e7i 2.10531i
\(35\) −1.57038e7 −0.298995
\(36\) −3.06483e7 −0.506866
\(37\) 2.69313e7i 0.388372i 0.980965 + 0.194186i \(0.0622066\pi\)
−0.980965 + 0.194186i \(0.937793\pi\)
\(38\) 2.24228e8i 2.82991i
\(39\) 6.59416e7i 0.730863i
\(40\) 1.99729e7i 0.195047i
\(41\) 4.52994e6 0.0390997 0.0195499 0.999809i \(-0.493777\pi\)
0.0195499 + 0.999809i \(0.493777\pi\)
\(42\) 1.51780e8i 1.16137i
\(43\) 1.84390e8i 1.25428i −0.778905 0.627142i \(-0.784225\pi\)
0.778905 0.627142i \(-0.215775\pi\)
\(44\) 4.13412e8i 2.50680i
\(45\) 1.45153e7 0.0786619
\(46\) 5.45366e8 2.64789
\(47\) 1.36961e8i 0.597183i 0.954381 + 0.298591i \(0.0965168\pi\)
−0.954381 + 0.298591i \(0.903483\pi\)
\(48\) 3.06549e7 0.120308
\(49\) 1.70982e8 0.605299
\(50\) 4.68508e8i 1.49922i
\(51\) 2.64153e8 0.765604
\(52\) 7.31860e8i 1.92491i
\(53\) −4.28407e7 −0.102442 −0.0512209 0.998687i \(-0.516311\pi\)
−0.0512209 + 0.998687i \(0.516311\pi\)
\(54\) 1.40294e8i 0.305541i
\(55\) 1.95796e8i 0.389037i
\(56\) 5.76730e8i 1.04721i
\(57\) 6.19205e8 1.02911
\(58\) 6.38655e8i 0.973031i
\(59\) 6.78517e8 2.25236e8i 0.949076 0.315048i
\(60\) 1.61100e8 0.207176
\(61\) 4.89796e8i 0.579917i 0.957039 + 0.289959i \(0.0936415\pi\)
−0.957039 + 0.289959i \(0.906358\pi\)
\(62\) −2.17943e9 −2.37895
\(63\) −4.19140e8 −0.422335
\(64\) 1.74921e9 1.62908
\(65\) 3.46617e8i 0.298732i
\(66\) −1.89242e9 −1.51111
\(67\) 8.12593e8i 0.601865i 0.953645 + 0.300933i \(0.0972979\pi\)
−0.953645 + 0.300933i \(0.902702\pi\)
\(68\) 2.93173e9 2.01641
\(69\) 1.50603e9i 0.962912i
\(70\) 7.97821e8i 0.474696i
\(71\) −2.09745e9 −1.16252 −0.581259 0.813719i \(-0.697440\pi\)
−0.581259 + 0.813719i \(0.697440\pi\)
\(72\) 5.33084e8i 0.275507i
\(73\) 3.96104e9i 1.91071i −0.295461 0.955355i \(-0.595473\pi\)
0.295461 0.955355i \(-0.404527\pi\)
\(74\) 1.36823e9 0.616595
\(75\) 1.29378e9 0.545198
\(76\) 6.87232e9 2.71041
\(77\) 5.65376e9i 2.08874i
\(78\) −3.35012e9 −1.16035
\(79\) −2.20220e9 −0.715683 −0.357841 0.933782i \(-0.616487\pi\)
−0.357841 + 0.933782i \(0.616487\pi\)
\(80\) −1.61135e8 −0.0491745
\(81\) 3.87420e8 0.111111
\(82\) 2.30141e8i 0.0620762i
\(83\) 2.68481e9i 0.681589i −0.940138 0.340794i \(-0.889304\pi\)
0.940138 0.340794i \(-0.110696\pi\)
\(84\) −4.65188e9 −1.11233
\(85\) −1.38850e9 −0.312932
\(86\) −9.36785e9 −1.99135
\(87\) −1.76364e9 −0.353846
\(88\) −7.19074e9 −1.36257
\(89\) 3.26412e9i 0.584542i −0.956335 0.292271i \(-0.905589\pi\)
0.956335 0.292271i \(-0.0944110\pi\)
\(90\) 7.37444e8i 0.124887i
\(91\) 1.00088e10i 1.60389i
\(92\) 1.67148e10i 2.53607i
\(93\) 6.01849e9i 0.865112i
\(94\) 6.95822e9 0.948111
\(95\) −3.25480e9 −0.420636
\(96\) 5.44831e9i 0.668198i
\(97\) 1.33057e10i 1.54946i 0.632295 + 0.774728i \(0.282113\pi\)
−0.632295 + 0.774728i \(0.717887\pi\)
\(98\) 8.68665e9i 0.960997i
\(99\) 5.22589e9i 0.549521i
\(100\) 1.43592e10 1.43592
\(101\) 9.24528e9i 0.879656i 0.898082 + 0.439828i \(0.144961\pi\)
−0.898082 + 0.439828i \(0.855039\pi\)
\(102\) 1.34201e10i 1.21550i
\(103\) 1.21978e10i 1.05220i −0.850424 0.526098i \(-0.823655\pi\)
0.850424 0.526098i \(-0.176345\pi\)
\(104\) −1.27297e10 −1.04629
\(105\) 2.20318e9 0.172625
\(106\) 2.17650e9i 0.162641i
\(107\) −1.87753e10 −1.33866 −0.669328 0.742967i \(-0.733418\pi\)
−0.669328 + 0.742967i \(0.733418\pi\)
\(108\) 4.29983e9 0.292639
\(109\) 4.37724e9i 0.284490i 0.989831 + 0.142245i \(0.0454322\pi\)
−0.989831 + 0.142245i \(0.954568\pi\)
\(110\) 9.94733e9 0.617651
\(111\) 3.77835e9i 0.224227i
\(112\) 4.65289e9 0.264017
\(113\) 9.12797e8i 0.0495430i 0.999693 + 0.0247715i \(0.00788582\pi\)
−0.999693 + 0.0247715i \(0.992114\pi\)
\(114\) 3.14584e10i 1.63385i
\(115\) 7.91630e9i 0.393580i
\(116\) −1.95740e10 −0.931943
\(117\) 9.25134e9i 0.421964i
\(118\) −1.14430e10 3.44717e10i −0.500183 1.50679i
\(119\) 4.00938e10 1.68013
\(120\) 2.80211e9i 0.112611i
\(121\) −4.45543e10 −1.71776
\(122\) 2.48838e10 0.920699
\(123\) −6.35534e8 −0.0225742
\(124\) 6.67969e10i 2.27849i
\(125\) −1.40024e10 −0.458830
\(126\) 2.12942e10i 0.670515i
\(127\) 2.76027e10 0.835474 0.417737 0.908568i \(-0.362823\pi\)
0.417737 + 0.908568i \(0.362823\pi\)
\(128\) 4.91014e10i 1.42904i
\(129\) 2.58692e10i 0.724161i
\(130\) 1.76097e10 0.474279
\(131\) 1.39688e10i 0.362079i 0.983476 + 0.181039i \(0.0579461\pi\)
−0.983476 + 0.181039i \(0.942054\pi\)
\(132\) 5.80001e10i 1.44730i
\(133\) 9.39847e10 2.25839
\(134\) 4.12834e10 0.955545
\(135\) −2.03644e9 −0.0454155
\(136\) 5.09934e10i 1.09602i
\(137\) −1.40192e10 −0.290483 −0.145241 0.989396i \(-0.546396\pi\)
−0.145241 + 0.989396i \(0.546396\pi\)
\(138\) −7.65128e10 −1.52876
\(139\) −5.80410e10 −1.11856 −0.559282 0.828978i \(-0.688923\pi\)
−0.559282 + 0.828978i \(0.688923\pi\)
\(140\) 2.44522e10 0.454651
\(141\) 1.92151e10i 0.344784i
\(142\) 1.06560e11i 1.84566i
\(143\) −1.24791e11 −2.08690
\(144\) −4.30076e9 −0.0694598
\(145\) 9.27044e9 0.144631
\(146\) −2.01238e11 −3.03352
\(147\) −2.39881e10 −0.349470
\(148\) 4.19345e10i 0.590558i
\(149\) 1.28271e11i 1.74661i 0.487170 + 0.873307i \(0.338029\pi\)
−0.487170 + 0.873307i \(0.661971\pi\)
\(150\) 6.57298e10i 0.865578i
\(151\) 4.39180e10i 0.559445i 0.960081 + 0.279722i \(0.0902425\pi\)
−0.960081 + 0.279722i \(0.909758\pi\)
\(152\) 1.19535e11i 1.47325i
\(153\) −3.70596e10 −0.442022
\(154\) −2.87236e11 −3.31616
\(155\) 3.16357e10i 0.353605i
\(156\) 1.02677e11i 1.11135i
\(157\) 4.40831e9i 0.0462141i −0.999733 0.0231070i \(-0.992644\pi\)
0.999733 0.0231070i \(-0.00735585\pi\)
\(158\) 1.11881e11i 1.13625i
\(159\) 6.01038e9 0.0591448
\(160\) 2.86386e10i 0.273119i
\(161\) 2.28589e11i 2.11313i
\(162\) 1.96827e10i 0.176404i
\(163\) 9.45102e10 0.821374 0.410687 0.911776i \(-0.365289\pi\)
0.410687 + 0.911776i \(0.365289\pi\)
\(164\) −7.05354e9 −0.0594550
\(165\) 2.74695e10i 0.224611i
\(166\) −1.36400e11 −1.08212
\(167\) 3.78770e10 0.291604 0.145802 0.989314i \(-0.453424\pi\)
0.145802 + 0.989314i \(0.453424\pi\)
\(168\) 8.09130e10i 0.604605i
\(169\) −8.30574e10 −0.602483
\(170\) 7.05418e10i 0.496824i
\(171\) −8.68721e10 −0.594155
\(172\) 2.87113e11i 1.90726i
\(173\) 2.01673e11i 1.30142i 0.759326 + 0.650710i \(0.225529\pi\)
−0.759326 + 0.650710i \(0.774471\pi\)
\(174\) 8.96009e10i 0.561780i
\(175\) 1.96374e11 1.19645
\(176\) 5.80127e10i 0.343526i
\(177\) −9.51933e10 + 3.15997e10i −0.547949 + 0.181893i
\(178\) −1.65832e11 −0.928042
\(179\) 2.07742e10i 0.113047i −0.998401 0.0565236i \(-0.981998\pi\)
0.998401 0.0565236i \(-0.0180016\pi\)
\(180\) −2.26017e10 −0.119613
\(181\) −8.19283e10 −0.421737 −0.210868 0.977514i \(-0.567629\pi\)
−0.210868 + 0.977514i \(0.567629\pi\)
\(182\) −5.08491e11 −2.54640
\(183\) 6.87164e10i 0.334815i
\(184\) −2.90731e11 −1.37848
\(185\) 1.98606e10i 0.0916503i
\(186\) 3.05766e11 1.37349
\(187\) 4.99894e11i 2.18610i
\(188\) 2.13261e11i 0.908075i
\(189\) 5.88038e10 0.243835
\(190\) 1.65358e11i 0.667819i
\(191\) 7.73059e9i 0.0304121i −0.999884 0.0152060i \(-0.995160\pi\)
0.999884 0.0152060i \(-0.00484042\pi\)
\(192\) −2.45408e11 −0.940550
\(193\) 1.50108e11 0.560553 0.280276 0.959919i \(-0.409574\pi\)
0.280276 + 0.959919i \(0.409574\pi\)
\(194\) 6.75989e11 2.45998
\(195\) 4.86290e10i 0.172473i
\(196\) −2.66235e11 −0.920417
\(197\) 4.73540e11 1.59597 0.797986 0.602676i \(-0.205899\pi\)
0.797986 + 0.602676i \(0.205899\pi\)
\(198\) 2.65499e11 0.872441
\(199\) −4.86539e10 −0.155902 −0.0779511 0.996957i \(-0.524838\pi\)
−0.0779511 + 0.996957i \(0.524838\pi\)
\(200\) 2.49758e11i 0.780494i
\(201\) 1.14004e11i 0.347487i
\(202\) 4.69701e11 1.39658
\(203\) −2.67690e11 −0.776520
\(204\) −4.11310e11 −1.16418
\(205\) 3.34063e9 0.00922697
\(206\) −6.19704e11 −1.67051
\(207\) 2.11289e11i 0.555938i
\(208\) 1.02699e11i 0.263786i
\(209\) 1.17181e12i 2.93851i
\(210\) 1.11931e11i 0.274066i
\(211\) 4.12413e10i 0.0986099i 0.998784 + 0.0493050i \(0.0157006\pi\)
−0.998784 + 0.0493050i \(0.984299\pi\)
\(212\) 6.67069e10 0.155773
\(213\) 2.94264e11 0.671180
\(214\) 9.53871e11i 2.12530i
\(215\) 1.35980e11i 0.295993i
\(216\) 7.47896e10i 0.159064i
\(217\) 9.13503e11i 1.89850i
\(218\) 2.22383e11 0.451668
\(219\) 5.55718e11i 1.10315i
\(220\) 3.04873e11i 0.591570i
\(221\) 8.84958e11i 1.67865i
\(222\) −1.91957e11 −0.355991
\(223\) −1.00117e12 −1.81545 −0.907723 0.419570i \(-0.862181\pi\)
−0.907723 + 0.419570i \(0.862181\pi\)
\(224\) 8.26959e11i 1.46637i
\(225\) −1.81512e11 −0.314770
\(226\) 4.63742e10 0.0786564
\(227\) 7.87897e10i 0.130719i −0.997862 0.0653597i \(-0.979181\pi\)
0.997862 0.0653597i \(-0.0208195\pi\)
\(228\) −9.64160e11 −1.56486
\(229\) 5.49767e10i 0.0872975i −0.999047 0.0436487i \(-0.986102\pi\)
0.999047 0.0436487i \(-0.0138982\pi\)
\(230\) 4.02183e11 0.624863
\(231\) 7.93200e11i 1.20593i
\(232\) 3.40462e11i 0.506558i
\(233\) 2.97509e11i 0.433232i −0.976257 0.216616i \(-0.930498\pi\)
0.976257 0.216616i \(-0.0695020\pi\)
\(234\) 4.70009e11 0.669927
\(235\) 1.01003e11i 0.140927i
\(236\) −1.05651e12 + 3.50713e11i −1.44316 + 0.479062i
\(237\) 3.08960e11 0.413200
\(238\) 2.03694e12i 2.66744i
\(239\) 1.29232e12 1.65722 0.828611 0.559825i \(-0.189132\pi\)
0.828611 + 0.559825i \(0.189132\pi\)
\(240\) 2.26066e10 0.0283909
\(241\) −7.85630e10 −0.0966347 −0.0483173 0.998832i \(-0.515386\pi\)
−0.0483173 + 0.998832i \(0.515386\pi\)
\(242\) 2.26356e12i 2.72718i
\(243\) −5.43536e10 −0.0641500
\(244\) 7.62657e11i 0.881821i
\(245\) 1.26092e11 0.142842
\(246\) 3.22879e10i 0.0358397i
\(247\) 2.07445e12i 2.25641i
\(248\) 1.16184e12 1.23848
\(249\) 3.76668e11i 0.393516i
\(250\) 7.11383e11i 0.728456i
\(251\) 1.77996e12 1.78665 0.893327 0.449407i \(-0.148365\pi\)
0.893327 + 0.449407i \(0.148365\pi\)
\(252\) 6.52640e11 0.642201
\(253\) −2.85007e12 −2.74950
\(254\) 1.40234e12i 1.32643i
\(255\) 1.94801e11 0.180672
\(256\) −7.03376e11 −0.639717
\(257\) 1.30368e12 1.16280 0.581401 0.813617i \(-0.302505\pi\)
0.581401 + 0.813617i \(0.302505\pi\)
\(258\) 1.31427e12 1.14971
\(259\) 5.73489e11i 0.492069i
\(260\) 5.39714e11i 0.454252i
\(261\) 2.47432e11 0.204293
\(262\) 7.09678e11 0.574850
\(263\) −1.34743e12 −1.07085 −0.535424 0.844583i \(-0.679848\pi\)
−0.535424 + 0.844583i \(0.679848\pi\)
\(264\) 1.00883e12 0.786682
\(265\) −3.15931e10 −0.0241748
\(266\) 4.77484e12i 3.58551i
\(267\) 4.57943e11i 0.337486i
\(268\) 1.26528e12i 0.915195i
\(269\) 2.05438e12i 1.45854i −0.684226 0.729270i \(-0.739860\pi\)
0.684226 0.729270i \(-0.260140\pi\)
\(270\) 1.03460e11i 0.0721034i
\(271\) −2.88296e12 −1.97239 −0.986195 0.165590i \(-0.947047\pi\)
−0.986195 + 0.165590i \(0.947047\pi\)
\(272\) 4.11399e11 0.276324
\(273\) 1.40419e12i 0.926007i
\(274\) 7.12238e11i 0.461182i
\(275\) 2.44841e12i 1.55676i
\(276\) 2.34502e12i 1.46420i
\(277\) −1.28054e12 −0.785227 −0.392614 0.919704i \(-0.628429\pi\)
−0.392614 + 0.919704i \(0.628429\pi\)
\(278\) 2.94874e12i 1.77588i
\(279\) 8.44370e11i 0.499473i
\(280\) 4.25313e11i 0.247126i
\(281\) 1.63468e12 0.933044 0.466522 0.884510i \(-0.345507\pi\)
0.466522 + 0.884510i \(0.345507\pi\)
\(282\) −9.76212e11 −0.547392
\(283\) 2.29521e12i 1.26442i −0.774799 0.632208i \(-0.782149\pi\)
0.774799 0.632208i \(-0.217851\pi\)
\(284\) 3.26592e12 1.76772
\(285\) 4.56636e11 0.242854
\(286\) 6.33993e12i 3.31325i
\(287\) −9.64631e10 −0.0495395
\(288\) 7.64376e11i 0.385784i
\(289\) 1.52903e12 0.758447
\(290\) 4.70980e11i 0.229621i
\(291\) 1.86674e12i 0.894579i
\(292\) 6.16770e12i 2.90542i
\(293\) −1.27557e12 −0.590701 −0.295351 0.955389i \(-0.595436\pi\)
−0.295351 + 0.955389i \(0.595436\pi\)
\(294\) 1.21870e12i 0.554832i
\(295\) 5.00376e11 1.66101e11i 0.223968 0.0743469i
\(296\) −7.29392e11 −0.320998
\(297\) 7.33172e11i 0.317266i
\(298\) 6.51674e12 2.77299
\(299\) −5.04545e12 −2.11127
\(300\) −2.01454e12 −0.829027
\(301\) 3.92650e12i 1.58918i
\(302\) 2.23123e12 0.888197
\(303\) 1.29708e12i 0.507870i
\(304\) 9.64369e11 0.371429
\(305\) 3.61203e11i 0.136852i
\(306\) 1.88279e12i 0.701771i
\(307\) 3.69241e12 1.35400 0.677000 0.735983i \(-0.263280\pi\)
0.677000 + 0.735983i \(0.263280\pi\)
\(308\) 8.80342e12i 3.17613i
\(309\) 1.71131e12i 0.607485i
\(310\) −1.60723e12 −0.561398
\(311\) 2.89941e11 0.0996568 0.0498284 0.998758i \(-0.484133\pi\)
0.0498284 + 0.998758i \(0.484133\pi\)
\(312\) 1.78593e12 0.604075
\(313\) 1.31084e12i 0.436342i 0.975911 + 0.218171i \(0.0700091\pi\)
−0.975911 + 0.218171i \(0.929991\pi\)
\(314\) −2.23962e11 −0.0733713
\(315\) −3.09097e11 −0.0996649
\(316\) 3.42902e12 1.08827
\(317\) −2.03370e11 −0.0635316 −0.0317658 0.999495i \(-0.510113\pi\)
−0.0317658 + 0.999495i \(0.510113\pi\)
\(318\) 3.05354e11i 0.0939006i
\(319\) 3.33760e12i 1.01037i
\(320\) 1.28997e12 0.384440
\(321\) 2.63411e12 0.772873
\(322\) −1.16133e13 −3.35488
\(323\) 8.30995e12 2.36366
\(324\) −6.03250e11 −0.168955
\(325\) 4.33440e12i 1.19540i
\(326\) 4.80154e12i 1.30405i
\(327\) 6.14109e11i 0.164251i
\(328\) 1.22687e11i 0.0323168i
\(329\) 2.91652e12i 0.756633i
\(330\) −1.39557e12 −0.356601
\(331\) −4.34702e12 −1.09409 −0.547043 0.837105i \(-0.684246\pi\)
−0.547043 + 0.837105i \(0.684246\pi\)
\(332\) 4.18049e12i 1.03642i
\(333\) 5.30088e11i 0.129457i
\(334\) 1.92432e12i 0.462961i
\(335\) 5.99251e11i 0.142032i
\(336\) −6.52782e11 −0.152430
\(337\) 1.60227e12i 0.368626i 0.982868 + 0.184313i \(0.0590060\pi\)
−0.982868 + 0.184313i \(0.940994\pi\)
\(338\) 4.21969e12i 0.956526i
\(339\) 1.28062e11i 0.0286036i
\(340\) 2.16202e12 0.475844
\(341\) 1.13897e13 2.47024
\(342\) 4.41349e12i 0.943304i
\(343\) 2.37420e12 0.500088
\(344\) 4.99393e12 1.03669
\(345\) 1.11063e12i 0.227234i
\(346\) 1.02459e13 2.06619
\(347\) 2.33249e12i 0.463630i −0.972760 0.231815i \(-0.925534\pi\)
0.972760 0.231815i \(-0.0744664\pi\)
\(348\) 2.74615e12 0.538057
\(349\) 1.84957e12i 0.357227i 0.983919 + 0.178613i \(0.0571611\pi\)
−0.983919 + 0.178613i \(0.942839\pi\)
\(350\) 9.97665e12i 1.89952i
\(351\) 1.29793e12i 0.243621i
\(352\) −1.03106e13 −1.90797
\(353\) 8.17195e12i 1.49091i 0.666555 + 0.745456i \(0.267768\pi\)
−0.666555 + 0.745456i \(0.732232\pi\)
\(354\) 1.60541e12 + 4.83625e12i 0.288781 + 0.869945i
\(355\) −1.54677e12 −0.274337
\(356\) 5.08254e12i 0.888854i
\(357\) −5.62501e12 −0.970023
\(358\) −1.05542e12 −0.179478
\(359\) −1.10519e13 −1.85338 −0.926692 0.375821i \(-0.877361\pi\)
−0.926692 + 0.375821i \(0.877361\pi\)
\(360\) 3.93126e11i 0.0650158i
\(361\) 1.33484e13 2.17718
\(362\) 4.16232e12i 0.669566i
\(363\) 6.25079e12 0.991750
\(364\) 1.55846e13i 2.43887i
\(365\) 2.92109e12i 0.450900i
\(366\) −3.49110e12 −0.531566
\(367\) 1.43915e12i 0.216161i −0.994142 0.108080i \(-0.965530\pi\)
0.994142 0.108080i \(-0.0344704\pi\)
\(368\) 2.34553e12i 0.347538i
\(369\) 8.91629e10 0.0130332
\(370\) 1.00901e12 0.145508
\(371\) 9.12273e11 0.129794
\(372\) 9.37134e12i 1.31549i
\(373\) 7.89849e12 1.09396 0.546978 0.837147i \(-0.315778\pi\)
0.546978 + 0.837147i \(0.315778\pi\)
\(374\) −2.53969e13 −3.47074
\(375\) 1.96448e12 0.264905
\(376\) −3.70938e12 −0.493585
\(377\) 5.90851e12i 0.775839i
\(378\) 2.98749e12i 0.387122i
\(379\) 1.41936e12 0.181508 0.0907539 0.995873i \(-0.471072\pi\)
0.0907539 + 0.995873i \(0.471072\pi\)
\(380\) 5.06803e12 0.639619
\(381\) −3.87255e12 −0.482361
\(382\) −3.92749e11 −0.0482834
\(383\) −1.32733e13 −1.61059 −0.805293 0.592877i \(-0.797992\pi\)
−0.805293 + 0.592877i \(0.797992\pi\)
\(384\) 6.88873e12i 0.825056i
\(385\) 4.16939e12i 0.492912i
\(386\) 7.62614e12i 0.889956i
\(387\) 3.62935e12i 0.418094i
\(388\) 2.07182e13i 2.35610i
\(389\) 1.36976e13 1.53778 0.768892 0.639379i \(-0.220808\pi\)
0.768892 + 0.639379i \(0.220808\pi\)
\(390\) −2.47057e12 −0.273825
\(391\) 2.02114e13i 2.21163i
\(392\) 4.63079e12i 0.500293i
\(393\) 1.95977e12i 0.209046i
\(394\) 2.40579e13i 2.53383i
\(395\) −1.62402e12 −0.168891
\(396\) 8.13720e12i 0.835601i
\(397\) 1.94529e13i 1.97257i 0.165064 + 0.986283i \(0.447217\pi\)
−0.165064 + 0.986283i \(0.552783\pi\)
\(398\) 2.47183e12i 0.247516i
\(399\) −1.31857e13 −1.30388
\(400\) 2.01497e12 0.196775
\(401\) 8.82993e12i 0.851600i 0.904817 + 0.425800i \(0.140007\pi\)
−0.904817 + 0.425800i \(0.859993\pi\)
\(402\) −5.79190e12 −0.551684
\(403\) 2.01630e13 1.89684
\(404\) 1.43958e13i 1.33760i
\(405\) 2.85705e11 0.0262206
\(406\) 1.35999e13i 1.23283i
\(407\) −7.15032e12 −0.640256
\(408\) 7.15417e12i 0.632788i
\(409\) 1.47875e13i 1.29205i −0.763317 0.646024i \(-0.776430\pi\)
0.763317 0.646024i \(-0.223570\pi\)
\(410\) 1.69719e11i 0.0146491i
\(411\) 1.96684e12 0.167710
\(412\) 1.89932e13i 1.59997i
\(413\) −1.44487e13 + 4.79629e12i −1.20248 + 0.399168i
\(414\) 1.07344e13 0.882629
\(415\) 1.97992e12i 0.160845i
\(416\) −1.82528e13 −1.46508
\(417\) 8.14292e12 0.645803
\(418\) −5.95333e13 −4.66529
\(419\) 4.70785e12i 0.364546i −0.983248 0.182273i \(-0.941654\pi\)
0.983248 0.182273i \(-0.0583455\pi\)
\(420\) −3.43055e12 −0.262493
\(421\) 1.07219e13i 0.810705i −0.914160 0.405352i \(-0.867149\pi\)
0.914160 0.405352i \(-0.132851\pi\)
\(422\) 2.09524e12 0.156557
\(423\) 2.69580e12i 0.199061i
\(424\) 1.16028e12i 0.0846704i
\(425\) 1.73630e13 1.25222
\(426\) 1.49499e13i 1.06559i
\(427\) 1.04300e13i 0.734757i
\(428\) 2.92349e13 2.03556
\(429\) 1.75077e13 1.20487
\(430\) −6.90837e12 −0.469930
\(431\) 3.83070e12i 0.257568i 0.991673 + 0.128784i \(0.0411074\pi\)
−0.991673 + 0.128784i \(0.958893\pi\)
\(432\) 6.03381e11 0.0401026
\(433\) −1.83002e13 −1.20231 −0.601155 0.799132i \(-0.705293\pi\)
−0.601155 + 0.799132i \(0.705293\pi\)
\(434\) 4.64100e13 3.01414
\(435\) −1.30061e12 −0.0835026
\(436\) 6.81576e12i 0.432596i
\(437\) 4.73779e13i 2.97282i
\(438\) 2.82330e13 1.75140
\(439\) 1.76364e12 0.108165 0.0540826 0.998536i \(-0.482777\pi\)
0.0540826 + 0.998536i \(0.482777\pi\)
\(440\) −5.30285e12 −0.321548
\(441\) 3.36544e12 0.201766
\(442\) −4.49598e13 −2.66510
\(443\) 1.89410e13i 1.11016i 0.831799 + 0.555078i \(0.187311\pi\)
−0.831799 + 0.555078i \(0.812689\pi\)
\(444\) 5.88324e12i 0.340959i
\(445\) 2.40714e12i 0.137944i
\(446\) 5.08639e13i 2.88227i
\(447\) 1.79959e13i 1.00841i
\(448\) −3.72486e13 −2.06405
\(449\) 3.00893e13 1.64884 0.824422 0.565975i \(-0.191500\pi\)
0.824422 + 0.565975i \(0.191500\pi\)
\(450\) 9.22164e12i 0.499742i
\(451\) 1.20271e12i 0.0644584i
\(452\) 1.42131e12i 0.0753350i
\(453\) 6.16152e12i 0.322996i
\(454\) −4.00287e12 −0.207535
\(455\) 7.38104e12i 0.378495i
\(456\) 1.67702e13i 0.850579i
\(457\) 1.19194e13i 0.597959i −0.954259 0.298980i \(-0.903354\pi\)
0.954259 0.298980i \(-0.0966463\pi\)
\(458\) −2.79306e12 −0.138597
\(459\) 5.19932e12 0.255201
\(460\) 1.23264e13i 0.598477i
\(461\) 1.70479e13 0.818781 0.409390 0.912359i \(-0.365741\pi\)
0.409390 + 0.912359i \(0.365741\pi\)
\(462\) 4.02981e13 1.91459
\(463\) 9.18157e12i 0.431531i −0.976445 0.215765i \(-0.930775\pi\)
0.976445 0.215765i \(-0.0692246\pi\)
\(464\) −2.74675e12 −0.127711
\(465\) 4.43836e12i 0.204154i
\(466\) −1.51148e13 −0.687816
\(467\) 1.00375e13i 0.451901i 0.974139 + 0.225951i \(0.0725488\pi\)
−0.974139 + 0.225951i \(0.927451\pi\)
\(468\) 1.44052e13i 0.641638i
\(469\) 1.73038e13i 0.762566i
\(470\) 5.13138e12 0.223741
\(471\) 6.18469e11i 0.0266817i
\(472\) 6.10017e12 + 1.83766e13i 0.260395 + 0.784432i
\(473\) 4.89561e13 2.06777
\(474\) 1.56965e13i 0.656012i
\(475\) 4.07009e13 1.68320
\(476\) −6.24298e13 −2.55480
\(477\) −8.43234e11 −0.0341473
\(478\) 6.56556e13i 2.63107i
\(479\) −7.90833e12 −0.313622 −0.156811 0.987629i \(-0.550121\pi\)
−0.156811 + 0.987629i \(0.550121\pi\)
\(480\) 4.01788e12i 0.157685i
\(481\) −1.26582e13 −0.491637
\(482\) 3.99135e12i 0.153421i
\(483\) 3.20701e13i 1.22001i
\(484\) 6.93751e13 2.61202
\(485\) 9.81236e12i 0.365649i
\(486\) 2.76140e12i 0.101847i
\(487\) −5.02388e13 −1.83398 −0.916990 0.398910i \(-0.869389\pi\)
−0.916990 + 0.398910i \(0.869389\pi\)
\(488\) −1.32654e13 −0.479314
\(489\) −1.32594e13 −0.474220
\(490\) 6.40602e12i 0.226781i
\(491\) −2.51290e13 −0.880578 −0.440289 0.897856i \(-0.645124\pi\)
−0.440289 + 0.897856i \(0.645124\pi\)
\(492\) 9.89585e11 0.0343263
\(493\) −2.36687e13 −0.812717
\(494\) −1.05391e14 −3.58236
\(495\) 3.85386e12i 0.129679i
\(496\) 9.37338e12i 0.312239i
\(497\) 4.46642e13 1.47291
\(498\) 1.91364e13 0.624761
\(499\) −2.88039e13 −0.930996 −0.465498 0.885049i \(-0.654125\pi\)
−0.465498 + 0.885049i \(0.654125\pi\)
\(500\) 2.18030e13 0.697695
\(501\) −5.31399e12 −0.168357
\(502\) 9.04296e13i 2.83656i
\(503\) 3.68002e13i 1.14290i 0.820635 + 0.571452i \(0.193620\pi\)
−0.820635 + 0.571452i \(0.806380\pi\)
\(504\) 1.13518e13i 0.349069i
\(505\) 6.81798e12i 0.207586i
\(506\) 1.44796e14i 4.36521i
\(507\) 1.16526e13 0.347844
\(508\) −4.29800e13 −1.27042
\(509\) 2.32005e13i 0.679059i −0.940595 0.339530i \(-0.889732\pi\)
0.940595 0.339530i \(-0.110268\pi\)
\(510\) 9.89675e12i 0.286841i
\(511\) 8.43485e13i 2.42088i
\(512\) 1.45452e13i 0.413398i
\(513\) 1.21878e13 0.343036
\(514\) 6.62328e13i 1.84611i
\(515\) 8.99536e12i 0.248303i
\(516\) 4.02808e13i 1.10116i
\(517\) −3.63635e13 −0.984493
\(518\) −2.91358e13 −0.781228
\(519\) 2.82940e13i 0.751376i
\(520\) −9.38758e12 −0.246909
\(521\) −5.31516e13 −1.38461 −0.692305 0.721605i \(-0.743405\pi\)
−0.692305 + 0.721605i \(0.743405\pi\)
\(522\) 1.25707e13i 0.324344i
\(523\) 4.18890e13 1.07051 0.535256 0.844690i \(-0.320215\pi\)
0.535256 + 0.844690i \(0.320215\pi\)
\(524\) 2.17507e13i 0.550576i
\(525\) −2.75505e13 −0.690768
\(526\) 6.84555e13i 1.70012i
\(527\) 8.07702e13i 1.98700i
\(528\) 8.13896e12i 0.198335i
\(529\) −7.38055e13 −1.78160
\(530\) 1.60507e12i 0.0383809i
\(531\) 1.33553e13 4.43332e12i 0.316359 0.105016i
\(532\) −1.46343e14 −3.43410
\(533\) 2.12915e12i 0.0494960i
\(534\) 2.32656e13 0.535805
\(535\) −1.38460e13 −0.315904
\(536\) −2.20079e13 −0.497455
\(537\) 2.91454e12i 0.0652678i
\(538\) −1.04371e14 −2.31564
\(539\) 4.53962e13i 0.997874i
\(540\) 3.17093e12 0.0690587
\(541\) 3.34393e13i 0.721557i 0.932652 + 0.360778i \(0.117489\pi\)
−0.932652 + 0.360778i \(0.882511\pi\)
\(542\) 1.46467e14i 3.13144i
\(543\) 1.14942e13 0.243490
\(544\) 7.31181e13i 1.53473i
\(545\) 3.22802e12i 0.0671357i
\(546\) 7.13393e13 1.47016
\(547\) 2.71848e13 0.555124 0.277562 0.960708i \(-0.410474\pi\)
0.277562 + 0.960708i \(0.410474\pi\)
\(548\) 2.18292e13 0.441707
\(549\) 9.64065e12i 0.193306i
\(550\) −1.24390e14 −2.47157
\(551\) −5.54822e13 −1.09244
\(552\) 4.07884e13 0.795868
\(553\) 4.68948e13 0.906773
\(554\) 6.50573e13i 1.24666i
\(555\) 2.78637e12i 0.0529143i
\(556\) 9.03752e13 1.70089
\(557\) 2.55587e13 0.476720 0.238360 0.971177i \(-0.423390\pi\)
0.238360 + 0.971177i \(0.423390\pi\)
\(558\) −4.28978e13 −0.792983
\(559\) 8.66665e13 1.58779
\(560\) 3.43130e12 0.0623043
\(561\) 7.01333e13i 1.26215i
\(562\) 8.30492e13i 1.48134i
\(563\) 6.99852e13i 1.23727i −0.785679 0.618635i \(-0.787686\pi\)
0.785679 0.618635i \(-0.212314\pi\)
\(564\) 2.99197e13i 0.524277i
\(565\) 6.73147e11i 0.0116914i
\(566\) −1.16607e14 −2.00744
\(567\) −8.24994e12 −0.140778
\(568\) 5.68062e13i 0.960846i
\(569\) 3.54639e13i 0.594600i −0.954784 0.297300i \(-0.903914\pi\)
0.954784 0.297300i \(-0.0960861\pi\)
\(570\) 2.31992e13i 0.385565i
\(571\) 3.19129e13i 0.525757i 0.964829 + 0.262879i \(0.0846719\pi\)
−0.964829 + 0.262879i \(0.915328\pi\)
\(572\) 1.94311e14 3.17334
\(573\) 1.08457e12i 0.0175584i
\(574\) 4.90075e12i 0.0786508i
\(575\) 9.89923e13i 1.57493i
\(576\) 3.44297e13 0.543027
\(577\) 7.85901e13 1.22882 0.614411 0.788986i \(-0.289394\pi\)
0.614411 + 0.788986i \(0.289394\pi\)
\(578\) 7.76813e13i 1.20414i
\(579\) −2.10595e13 −0.323635
\(580\) −1.44349e13 −0.219925
\(581\) 5.71717e13i 0.863576i
\(582\) −9.48386e13 −1.42027
\(583\) 1.13743e13i 0.168882i
\(584\) 1.07279e14 1.57924
\(585\) 6.82245e12i 0.0995775i
\(586\) 6.48049e13i 0.937820i
\(587\) 3.43134e13i 0.492349i 0.969226 + 0.246174i \(0.0791736\pi\)
−0.969226 + 0.246174i \(0.920826\pi\)
\(588\) 3.73517e13 0.531403
\(589\) 1.89335e14i 2.67088i
\(590\) −8.43869e12 2.54213e13i −0.118036 0.355581i
\(591\) −6.64358e13 −0.921435
\(592\) 5.88452e12i 0.0809287i
\(593\) −3.65885e13 −0.498967 −0.249483 0.968379i \(-0.580261\pi\)
−0.249483 + 0.968379i \(0.580261\pi\)
\(594\) −3.72484e13 −0.503704
\(595\) 2.95674e13 0.396486
\(596\) 1.99730e14i 2.65590i
\(597\) 6.82595e12 0.0900101
\(598\) 2.56331e14i 3.35194i
\(599\) 1.08094e14 1.40174 0.700870 0.713289i \(-0.252795\pi\)
0.700870 + 0.713289i \(0.252795\pi\)
\(600\) 3.50401e13i 0.450618i
\(601\) 1.29552e14i 1.65223i −0.563499 0.826117i \(-0.690545\pi\)
0.563499 0.826117i \(-0.309455\pi\)
\(602\) 1.99484e14 2.52305
\(603\) 1.59943e13i 0.200622i
\(604\) 6.83843e13i 0.850691i
\(605\) −3.28568e13 −0.405367
\(606\) −6.58973e13 −0.806314
\(607\) −8.69381e13 −1.05503 −0.527517 0.849544i \(-0.676877\pi\)
−0.527517 + 0.849544i \(0.676877\pi\)
\(608\) 1.71398e14i 2.06294i
\(609\) 3.75559e13 0.448324
\(610\) 1.83507e13 0.217272
\(611\) −6.43739e13 −0.755969
\(612\) 5.77052e13 0.672137
\(613\) 1.13794e14i 1.31467i 0.753598 + 0.657336i \(0.228317\pi\)
−0.753598 + 0.657336i \(0.771683\pi\)
\(614\) 1.87591e14i 2.14966i
\(615\) −4.68678e11 −0.00532720
\(616\) 1.53123e14 1.72639
\(617\) −2.54094e13 −0.284163 −0.142082 0.989855i \(-0.545380\pi\)
−0.142082 + 0.989855i \(0.545380\pi\)
\(618\) 8.69421e13 0.964468
\(619\) 1.45010e14 1.59567 0.797837 0.602873i \(-0.205977\pi\)
0.797837 + 0.602873i \(0.205977\pi\)
\(620\) 4.92597e13i 0.537692i
\(621\) 2.96431e13i 0.320971i
\(622\) 1.47303e13i 0.158219i
\(623\) 6.95079e13i 0.740617i
\(624\) 1.44083e13i 0.152297i
\(625\) 7.97304e13 0.836034
\(626\) 6.65964e13 0.692754
\(627\) 1.64401e14i 1.69655i
\(628\) 6.86415e12i 0.0702730i
\(629\) 5.07068e13i 0.515007i
\(630\) 1.57035e13i 0.158232i
\(631\) 9.63252e13 0.962927 0.481463 0.876466i \(-0.340105\pi\)
0.481463 + 0.876466i \(0.340105\pi\)
\(632\) 5.96432e13i 0.591528i
\(633\) 5.78600e12i 0.0569325i
\(634\) 1.03321e13i 0.100865i
\(635\) 2.03558e13 0.197160
\(636\) −9.35873e12 −0.0899355
\(637\) 8.03644e13i 0.766243i
\(638\) 1.69565e14 1.60410
\(639\) −4.12841e13 −0.387506
\(640\) 3.62101e13i 0.337233i
\(641\) 9.08204e13 0.839253 0.419627 0.907697i \(-0.362161\pi\)
0.419627 + 0.907697i \(0.362161\pi\)
\(642\) 1.33824e14i 1.22704i
\(643\) 5.76101e13 0.524136 0.262068 0.965049i \(-0.415596\pi\)
0.262068 + 0.965049i \(0.415596\pi\)
\(644\) 3.55934e14i 3.21322i
\(645\) 1.90774e13i 0.170892i
\(646\) 4.22182e14i 3.75265i
\(647\) 6.00411e13 0.529575 0.264788 0.964307i \(-0.414698\pi\)
0.264788 + 0.964307i \(0.414698\pi\)
\(648\) 1.04927e13i 0.0918358i
\(649\) 5.98007e13 + 1.80148e14i 0.519377 + 1.56461i
\(650\) −2.20207e14 −1.89786
\(651\) 1.28161e14i 1.09610i
\(652\) −1.47161e14 −1.24898
\(653\) 1.80413e14 1.51950 0.759751 0.650215i \(-0.225321\pi\)
0.759751 + 0.650215i \(0.225321\pi\)
\(654\) −3.11995e13 −0.260771
\(655\) 1.03014e13i 0.0854454i
\(656\) −9.89800e11 −0.00814757
\(657\) 7.79651e13i 0.636903i
\(658\) −1.48172e14 −1.20126
\(659\) 2.13417e14i 1.71712i −0.512709 0.858562i \(-0.671358\pi\)
0.512709 0.858562i \(-0.328642\pi\)
\(660\) 4.27725e13i 0.341543i
\(661\) −1.04672e14 −0.829510 −0.414755 0.909933i \(-0.636133\pi\)
−0.414755 + 0.909933i \(0.636133\pi\)
\(662\) 2.20848e14i 1.73701i
\(663\) 1.24156e14i 0.969172i
\(664\) 7.27139e13 0.563348
\(665\) 6.93095e13 0.532948
\(666\) 2.69308e13 0.205532
\(667\) 1.34943e14i 1.02217i
\(668\) −5.89780e13 −0.443412
\(669\) 1.40460e14 1.04815
\(670\) 3.04446e13 0.225495
\(671\) −1.30042e14 −0.956030
\(672\) 1.16019e14i 0.846610i
\(673\) 3.77116e13i 0.273149i 0.990630 + 0.136574i \(0.0436093\pi\)
−0.990630 + 0.136574i \(0.956391\pi\)
\(674\) 8.14025e13 0.585245
\(675\) 2.54655e13 0.181733
\(676\) 1.29328e14 0.916135
\(677\) −1.41601e14 −0.995687 −0.497844 0.867267i \(-0.665875\pi\)
−0.497844 + 0.867267i \(0.665875\pi\)
\(678\) −6.50611e12 −0.0454123
\(679\) 2.83339e14i 1.96317i
\(680\) 3.76053e13i 0.258645i
\(681\) 1.10539e13i 0.0754709i
\(682\) 5.78645e14i 3.92185i
\(683\) 2.66011e11i 0.00178977i −1.00000 0.000894883i \(-0.999715\pi\)
1.00000 0.000894883i \(-0.000284850\pi\)
\(684\) 1.35268e14 0.903471
\(685\) −1.03385e13 −0.0685498
\(686\) 1.20620e14i 0.793959i
\(687\) 7.71302e12i 0.0504012i
\(688\) 4.02895e13i 0.261367i
\(689\) 2.01359e13i 0.129680i
\(690\) −5.64248e13 −0.360765
\(691\) 1.09596e14i 0.695672i 0.937555 + 0.347836i \(0.113083\pi\)
−0.937555 + 0.347836i \(0.886917\pi\)
\(692\) 3.14024e14i 1.97894i
\(693\) 1.11283e14i 0.696245i
\(694\) −1.18501e14 −0.736077
\(695\) −4.28026e13 −0.263965
\(696\) 4.77656e13i 0.292461i
\(697\) −8.52908e12 −0.0518488
\(698\) 9.39664e13 0.567147
\(699\) 4.17394e13i 0.250127i
\(700\) −3.05772e14 −1.81931
\(701\) 1.21445e14i 0.717444i −0.933444 0.358722i \(-0.883213\pi\)
0.933444 0.358722i \(-0.116787\pi\)
\(702\) −6.59405e13 −0.386782
\(703\) 1.18863e14i 0.692260i
\(704\) 4.64420e14i 2.68564i
\(705\) 1.41703e13i 0.0813640i
\(706\) 4.15171e14 2.36703
\(707\) 1.96874e14i 1.11453i
\(708\) 1.48225e14 4.92037e13i 0.833210 0.276587i
\(709\) 3.72063e13 0.207676 0.103838 0.994594i \(-0.466888\pi\)
0.103838 + 0.994594i \(0.466888\pi\)
\(710\) 7.85830e13i 0.435549i
\(711\) −4.33458e13 −0.238561
\(712\) 8.84037e13 0.483137
\(713\) 4.60499e14 2.49908
\(714\) 2.85775e14i 1.54005i
\(715\) −9.20276e13 −0.492479
\(716\) 3.23474e13i 0.171899i
\(717\) −1.81307e14 −0.956797
\(718\) 5.61487e14i 2.94251i
\(719\) 1.17385e14i 0.610899i 0.952208 + 0.305449i \(0.0988067\pi\)
−0.952208 + 0.305449i \(0.901193\pi\)
\(720\) −3.17162e12 −0.0163915
\(721\) 2.59747e14i 1.33314i
\(722\) 6.78160e14i 3.45658i
\(723\) 1.10221e13 0.0557921
\(724\) 1.27570e14 0.641292
\(725\) −1.15926e14 −0.578748
\(726\) 3.17568e14i 1.57454i
\(727\) −2.78503e14 −1.37138 −0.685689 0.727894i \(-0.740499\pi\)
−0.685689 + 0.727894i \(0.740499\pi\)
\(728\) 2.71073e14 1.32565
\(729\) 7.62560e12 0.0370370
\(730\) −1.48404e14 −0.715867
\(731\) 3.47174e14i 1.66326i
\(732\) 1.06998e14i 0.509119i
\(733\) −1.01510e14 −0.479720 −0.239860 0.970807i \(-0.577102\pi\)
−0.239860 + 0.970807i \(0.577102\pi\)
\(734\) −7.31155e13 −0.343186
\(735\) −1.76902e13 −0.0824698
\(736\) −4.16872e14 −1.93025
\(737\) −2.15746e14 −0.992213
\(738\) 4.52987e12i 0.0206921i
\(739\) 2.86584e14i 1.30026i −0.759824 0.650129i \(-0.774715\pi\)
0.759824 0.650129i \(-0.225285\pi\)
\(740\) 3.09248e13i 0.139363i
\(741\) 2.91037e14i 1.30274i
\(742\) 4.63475e13i 0.206066i
\(743\) −7.90605e13 −0.349153 −0.174576 0.984644i \(-0.555856\pi\)
−0.174576 + 0.984644i \(0.555856\pi\)
\(744\) −1.63002e14 −0.715035
\(745\) 9.45941e13i 0.412176i
\(746\) 4.01279e14i 1.73681i
\(747\) 5.28450e13i 0.227196i
\(748\) 7.78382e14i 3.32418i
\(749\) 3.99812e14 1.69608
\(750\) 9.98042e13i 0.420574i
\(751\) 3.25139e13i 0.136104i 0.997682 + 0.0680518i \(0.0216783\pi\)
−0.997682 + 0.0680518i \(0.978322\pi\)
\(752\) 2.99262e13i 0.124440i
\(753\) −2.49721e14 −1.03153
\(754\) 3.00179e14 1.23175
\(755\) 3.23875e13i 0.132021i
\(756\) −9.15629e13 −0.370775
\(757\) 6.85566e13 0.275785 0.137892 0.990447i \(-0.455967\pi\)
0.137892 + 0.990447i \(0.455967\pi\)
\(758\) 7.21096e13i 0.288169i
\(759\) 3.99854e14 1.58742
\(760\) 8.81514e13i 0.347665i
\(761\) −2.11057e14 −0.826947 −0.413473 0.910516i \(-0.635684\pi\)
−0.413473 + 0.910516i \(0.635684\pi\)
\(762\) 1.96743e14i 0.765816i
\(763\) 9.32112e13i 0.360451i
\(764\) 1.20372e13i 0.0462445i
\(765\) −2.73298e13 −0.104311
\(766\) 6.74341e14i 2.55703i
\(767\) 1.05865e14 + 3.18915e14i 0.398817 + 1.20143i
\(768\) 9.86810e13 0.369341
\(769\) 1.83509e14i 0.682380i 0.939994 + 0.341190i \(0.110830\pi\)
−0.939994 + 0.341190i \(0.889170\pi\)
\(770\) −2.11824e14 −0.782566
\(771\) −1.82901e14 −0.671344
\(772\) −2.33732e14 −0.852376
\(773\) 2.04840e14i 0.742195i −0.928594 0.371098i \(-0.878982\pi\)
0.928594 0.371098i \(-0.121018\pi\)
\(774\) −1.84387e14 −0.663783
\(775\) 3.95600e14i 1.41497i
\(776\) −3.60365e14 −1.28066
\(777\) 8.04582e13i 0.284096i
\(778\) 6.95897e14i 2.44145i
\(779\) −1.99932e13 −0.0696939