Properties

Label 69.7.d.a.22.4
Level $69$
Weight $7$
Character 69.22
Analytic conductor $15.874$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.4
Character \(\chi\) \(=\) 69.22
Dual form 69.7.d.a.22.3

$q$-expansion

\(f(q)\) \(=\) \(q-13.6749 q^{2} -15.5885 q^{3} +123.003 q^{4} +37.2861i q^{5} +213.170 q^{6} +322.993i q^{7} -806.853 q^{8} +243.000 q^{9} +O(q^{10})\) \(q-13.6749 q^{2} -15.5885 q^{3} +123.003 q^{4} +37.2861i q^{5} +213.170 q^{6} +322.993i q^{7} -806.853 q^{8} +243.000 q^{9} -509.883i q^{10} -2211.16i q^{11} -1917.42 q^{12} -449.620 q^{13} -4416.89i q^{14} -581.232i q^{15} +3161.46 q^{16} -5356.12i q^{17} -3323.00 q^{18} +2647.39i q^{19} +4586.28i q^{20} -5034.96i q^{21} +30237.4i q^{22} +(-4323.93 + 11372.8i) q^{23} +12577.6 q^{24} +14234.7 q^{25} +6148.50 q^{26} -3788.00 q^{27} +39729.0i q^{28} +3292.80 q^{29} +7948.29i q^{30} +21814.2 q^{31} +8405.97 q^{32} +34468.6i q^{33} +73244.3i q^{34} -12043.1 q^{35} +29889.6 q^{36} +36999.4i q^{37} -36202.8i q^{38} +7008.88 q^{39} -30084.4i q^{40} -84193.7 q^{41} +68852.6i q^{42} +23651.2i q^{43} -271978. i q^{44} +9060.51i q^{45} +(59129.3 - 155521. i) q^{46} +65868.0 q^{47} -49282.3 q^{48} +13324.4 q^{49} -194659. q^{50} +83493.6i q^{51} -55304.3 q^{52} +183208. i q^{53} +51800.4 q^{54} +82445.5 q^{55} -260608. i q^{56} -41268.8i q^{57} -45028.6 q^{58} +283187. q^{59} -71493.0i q^{60} +36008.5i q^{61} -298307. q^{62} +78487.3i q^{63} -317284. q^{64} -16764.5i q^{65} -471354. i q^{66} +154256. i q^{67} -658816. i q^{68} +(67403.4 - 177284. i) q^{69} +164689. q^{70} -415789. q^{71} -196065. q^{72} -44631.0 q^{73} -505963. i q^{74} -221898. q^{75} +325636. i q^{76} +714190. q^{77} -95845.6 q^{78} +751803. i q^{79} +117878. i q^{80} +59049.0 q^{81} +1.15134e6 q^{82} +988237. i q^{83} -619313. i q^{84} +199709. q^{85} -323427. i q^{86} -51329.6 q^{87} +1.78408e6i q^{88} +410195. i q^{89} -123902. i q^{90} -145224. i q^{91} +(-531854. + 1.39888e6i) q^{92} -340050. q^{93} -900737. q^{94} -98710.9 q^{95} -131036. q^{96} +1.20225e6i q^{97} -182210. q^{98} -537312. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + O(q^{10}) \) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + 384q^{13} + 29544q^{16} - 4860q^{18} + 29336q^{23} - 39204q^{24} - 61272q^{25} + 10088q^{26} + 64672q^{29} + 9696q^{31} - 319620q^{32} - 225744q^{35} + 198288q^{36} - 11664q^{39} + 135280q^{41} + 233232q^{46} - 74336q^{47} + 552096q^{48} - 722136q^{49} + 619324q^{50} + 1059720q^{52} - 78732q^{54} - 1019328q^{55} - 694344q^{58} + 1057648q^{59} - 488776q^{62} - 273888q^{64} - 23328q^{69} + 2785512q^{70} - 255392q^{71} - 228420q^{72} - 322560q^{73} - 365472q^{75} - 1002960q^{77} - 171072q^{78} + 1417176q^{81} - 5732712q^{82} - 2704704q^{85} + 611712q^{87} - 1611444q^{92} + 2484432q^{93} - 147720q^{94} - 1672656q^{95} - 1818612q^{96} + 9104212q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −13.6749 −1.70936 −0.854680 0.519154i \(-0.826247\pi\)
−0.854680 + 0.519154i \(0.826247\pi\)
\(3\) −15.5885 −0.577350
\(4\) 123.003 1.92191
\(5\) 37.2861i 0.298289i 0.988815 + 0.149144i \(0.0476519\pi\)
−0.988815 + 0.149144i \(0.952348\pi\)
\(6\) 213.170 0.986900
\(7\) 322.993i 0.941671i 0.882221 + 0.470835i \(0.156047\pi\)
−0.882221 + 0.470835i \(0.843953\pi\)
\(8\) −806.853 −1.57588
\(9\) 243.000 0.333333
\(10\) 509.883i 0.509883i
\(11\) 2211.16i 1.66128i −0.556811 0.830639i \(-0.687975\pi\)
0.556811 0.830639i \(-0.312025\pi\)
\(12\) −1917.42 −1.10962
\(13\) −449.620 −0.204652 −0.102326 0.994751i \(-0.532628\pi\)
−0.102326 + 0.994751i \(0.532628\pi\)
\(14\) 4416.89i 1.60966i
\(15\) 581.232i 0.172217i
\(16\) 3161.46 0.771841
\(17\) 5356.12i 1.09019i −0.838373 0.545096i \(-0.816493\pi\)
0.838373 0.545096i \(-0.183507\pi\)
\(18\) −3323.00 −0.569787
\(19\) 2647.39i 0.385974i 0.981201 + 0.192987i \(0.0618175\pi\)
−0.981201 + 0.192987i \(0.938183\pi\)
\(20\) 4586.28i 0.573285i
\(21\) 5034.96i 0.543674i
\(22\) 30237.4i 2.83972i
\(23\) −4323.93 + 11372.8i −0.355382 + 0.934721i
\(24\) 12577.6 0.909837
\(25\) 14234.7 0.911024
\(26\) 6148.50 0.349823
\(27\) −3788.00 −0.192450
\(28\) 39729.0i 1.80981i
\(29\) 3292.80 0.135012 0.0675058 0.997719i \(-0.478496\pi\)
0.0675058 + 0.997719i \(0.478496\pi\)
\(30\) 7948.29i 0.294381i
\(31\) 21814.2 0.732243 0.366121 0.930567i \(-0.380686\pi\)
0.366121 + 0.930567i \(0.380686\pi\)
\(32\) 8405.97 0.256530
\(33\) 34468.6i 0.959139i
\(34\) 73244.3i 1.86353i
\(35\) −12043.1 −0.280890
\(36\) 29889.6 0.640638
\(37\) 36999.4i 0.730449i 0.930920 + 0.365224i \(0.119008\pi\)
−0.930920 + 0.365224i \(0.880992\pi\)
\(38\) 36202.8i 0.659768i
\(39\) 7008.88 0.118156
\(40\) 30084.4i 0.470068i
\(41\) −84193.7 −1.22160 −0.610799 0.791786i \(-0.709152\pi\)
−0.610799 + 0.791786i \(0.709152\pi\)
\(42\) 68852.6i 0.929335i
\(43\) 23651.2i 0.297473i 0.988877 + 0.148736i \(0.0475206\pi\)
−0.988877 + 0.148736i \(0.952479\pi\)
\(44\) 271978.i 3.19283i
\(45\) 9060.51i 0.0994295i
\(46\) 59129.3 155521.i 0.607476 1.59778i
\(47\) 65868.0 0.634426 0.317213 0.948354i \(-0.397253\pi\)
0.317213 + 0.948354i \(0.397253\pi\)
\(48\) −49282.3 −0.445623
\(49\) 13324.4 0.113256
\(50\) −194659. −1.55727
\(51\) 83493.6i 0.629423i
\(52\) −55304.3 −0.393323
\(53\) 183208.i 1.23060i 0.788294 + 0.615299i \(0.210965\pi\)
−0.788294 + 0.615299i \(0.789035\pi\)
\(54\) 51800.4 0.328967
\(55\) 82445.5 0.495540
\(56\) 260608.i 1.48396i
\(57\) 41268.8i 0.222842i
\(58\) −45028.6 −0.230783
\(59\) 283187. 1.37885 0.689426 0.724357i \(-0.257863\pi\)
0.689426 + 0.724357i \(0.257863\pi\)
\(60\) 71493.0i 0.330986i
\(61\) 36008.5i 0.158641i 0.996849 + 0.0793204i \(0.0252750\pi\)
−0.996849 + 0.0793204i \(0.974725\pi\)
\(62\) −298307. −1.25167
\(63\) 78487.3i 0.313890i
\(64\) −317284. −1.21034
\(65\) 16764.5i 0.0610452i
\(66\) 471354.i 1.63952i
\(67\) 154256.i 0.512883i 0.966560 + 0.256442i \(0.0825502\pi\)
−0.966560 + 0.256442i \(0.917450\pi\)
\(68\) 658816.i 2.09526i
\(69\) 67403.4 177284.i 0.205180 0.539662i
\(70\) 164689. 0.480142
\(71\) −415789. −1.16171 −0.580856 0.814007i \(-0.697282\pi\)
−0.580856 + 0.814007i \(0.697282\pi\)
\(72\) −196065. −0.525295
\(73\) −44631.0 −0.114728 −0.0573638 0.998353i \(-0.518269\pi\)
−0.0573638 + 0.998353i \(0.518269\pi\)
\(74\) 505963.i 1.24860i
\(75\) −221898. −0.525980
\(76\) 325636.i 0.741808i
\(77\) 714190. 1.56438
\(78\) −95845.6 −0.201971
\(79\) 751803.i 1.52483i 0.647086 + 0.762417i \(0.275988\pi\)
−0.647086 + 0.762417i \(0.724012\pi\)
\(80\) 117878.i 0.230231i
\(81\) 59049.0 0.111111
\(82\) 1.15134e6 2.08815
\(83\) 988237.i 1.72833i 0.503208 + 0.864166i \(0.332153\pi\)
−0.503208 + 0.864166i \(0.667847\pi\)
\(84\) 619313.i 1.04489i
\(85\) 199709. 0.325192
\(86\) 323427.i 0.508488i
\(87\) −51329.6 −0.0779490
\(88\) 1.78408e6i 2.61798i
\(89\) 410195.i 0.581863i 0.956744 + 0.290932i \(0.0939652\pi\)
−0.956744 + 0.290932i \(0.906035\pi\)
\(90\) 123902.i 0.169961i
\(91\) 145224.i 0.192714i
\(92\) −531854. + 1.39888e6i −0.683014 + 1.79645i
\(93\) −340050. −0.422760
\(94\) −900737. −1.08446
\(95\) −98710.9 −0.115132
\(96\) −131036. −0.148108
\(97\) 1.20225e6i 1.31728i 0.752458 + 0.658640i \(0.228868\pi\)
−0.752458 + 0.658640i \(0.771132\pi\)
\(98\) −182210. −0.193595
\(99\) 537312.i 0.553759i
\(100\) 1.75091e6 1.75091
\(101\) 1.05470e6 1.02368 0.511841 0.859080i \(-0.328964\pi\)
0.511841 + 0.859080i \(0.328964\pi\)
\(102\) 1.14177e6i 1.07591i
\(103\) 1.03009e6i 0.942675i −0.881953 0.471338i \(-0.843771\pi\)
0.881953 0.471338i \(-0.156229\pi\)
\(104\) 362777. 0.322507
\(105\) 187734. 0.162172
\(106\) 2.50534e6i 2.10353i
\(107\) 1.68790e6i 1.37783i 0.724842 + 0.688915i \(0.241913\pi\)
−0.724842 + 0.688915i \(0.758087\pi\)
\(108\) −465933. −0.369873
\(109\) 1.83556e6i 1.41739i −0.705515 0.708695i \(-0.749284\pi\)
0.705515 0.708695i \(-0.250716\pi\)
\(110\) −1.12743e6 −0.847057
\(111\) 576764.i 0.421725i
\(112\) 1.02113e6i 0.726820i
\(113\) 949159.i 0.657815i −0.944362 0.328908i \(-0.893320\pi\)
0.944362 0.328908i \(-0.106680\pi\)
\(114\) 564346.i 0.380917i
\(115\) −424045. 161222.i −0.278817 0.106006i
\(116\) 405022. 0.259481
\(117\) −109258. −0.0682172
\(118\) −3.87255e6 −2.35695
\(119\) 1.72999e6 1.02660
\(120\) 468969.i 0.271394i
\(121\) −3.11767e6 −1.75985
\(122\) 492412.i 0.271175i
\(123\) 1.31245e6 0.705290
\(124\) 2.68321e6 1.40731
\(125\) 1.11335e6i 0.570037i
\(126\) 1.07331e6i 0.536552i
\(127\) 1.28898e6 0.629267 0.314634 0.949213i \(-0.398118\pi\)
0.314634 + 0.949213i \(0.398118\pi\)
\(128\) 3.80084e6 1.81238
\(129\) 368685.i 0.171746i
\(130\) 229253.i 0.104348i
\(131\) −4.14126e6 −1.84213 −0.921063 0.389415i \(-0.872677\pi\)
−0.921063 + 0.389415i \(0.872677\pi\)
\(132\) 4.23972e6i 1.84338i
\(133\) −855090. −0.363460
\(134\) 2.10944e6i 0.876703i
\(135\) 141239.i 0.0574057i
\(136\) 4.32160e6i 1.71802i
\(137\) 1.53664e6i 0.597599i 0.954316 + 0.298800i \(0.0965862\pi\)
−0.954316 + 0.298800i \(0.903414\pi\)
\(138\) −921734. + 2.42433e6i −0.350726 + 0.922476i
\(139\) 2.86467e6 1.06667 0.533334 0.845904i \(-0.320939\pi\)
0.533334 + 0.845904i \(0.320939\pi\)
\(140\) −1.48134e6 −0.539846
\(141\) −1.02678e6 −0.366286
\(142\) 5.68587e6 1.98578
\(143\) 994181.i 0.339983i
\(144\) 768235. 0.257280
\(145\) 122775.i 0.0402724i
\(146\) 610324. 0.196111
\(147\) −207707. −0.0653882
\(148\) 4.55102e6i 1.40386i
\(149\) 2.26609e6i 0.685043i −0.939510 0.342522i \(-0.888719\pi\)
0.939510 0.342522i \(-0.111281\pi\)
\(150\) 3.03443e6 0.899089
\(151\) 1.59103e6 0.462112 0.231056 0.972941i \(-0.425782\pi\)
0.231056 + 0.972941i \(0.425782\pi\)
\(152\) 2.13606e6i 0.608250i
\(153\) 1.30154e6i 0.363398i
\(154\) −9.76647e6 −2.67409
\(155\) 813367.i 0.218420i
\(156\) 862109. 0.227085
\(157\) 2.27500e6i 0.587872i −0.955825 0.293936i \(-0.905035\pi\)
0.955825 0.293936i \(-0.0949652\pi\)
\(158\) 1.02808e7i 2.60649i
\(159\) 2.85592e6i 0.710486i
\(160\) 313426.i 0.0765199i
\(161\) −3.67332e6 1.39660e6i −0.880200 0.334653i
\(162\) −807488. −0.189929
\(163\) 7.17414e6 1.65656 0.828280 0.560314i \(-0.189320\pi\)
0.828280 + 0.560314i \(0.189320\pi\)
\(164\) −1.03560e7 −2.34781
\(165\) −1.28520e6 −0.286100
\(166\) 1.35140e7i 2.95434i
\(167\) 3.11636e6 0.669112 0.334556 0.942376i \(-0.391414\pi\)
0.334556 + 0.942376i \(0.391414\pi\)
\(168\) 4.06248e6i 0.856767i
\(169\) −4.62465e6 −0.958118
\(170\) −2.73099e6 −0.555870
\(171\) 643317.i 0.128658i
\(172\) 2.90915e6i 0.571717i
\(173\) 7.18746e6 1.38815 0.694077 0.719901i \(-0.255813\pi\)
0.694077 + 0.719901i \(0.255813\pi\)
\(174\) 701927. 0.133243
\(175\) 4.59773e6i 0.857885i
\(176\) 6.99050e6i 1.28224i
\(177\) −4.41445e6 −0.796080
\(178\) 5.60938e6i 0.994614i
\(179\) −2.51654e6 −0.438777 −0.219389 0.975638i \(-0.570406\pi\)
−0.219389 + 0.975638i \(0.570406\pi\)
\(180\) 1.11447e6i 0.191095i
\(181\) 5.09223e6i 0.858761i 0.903124 + 0.429380i \(0.141268\pi\)
−0.903124 + 0.429380i \(0.858732\pi\)
\(182\) 1.98592e6i 0.329419i
\(183\) 561316.i 0.0915914i
\(184\) 3.48878e6 9.17614e6i 0.560041 1.47301i
\(185\) −1.37956e6 −0.217884
\(186\) 4.65015e6 0.722650
\(187\) −1.18432e7 −1.81111
\(188\) 8.10193e6 1.21931
\(189\) 1.22350e6i 0.181225i
\(190\) 1.34986e6 0.196801
\(191\) 1.03443e7i 1.48457i 0.670083 + 0.742286i \(0.266258\pi\)
−0.670083 + 0.742286i \(0.733742\pi\)
\(192\) 4.94597e6 0.698792
\(193\) −375366. −0.0522136 −0.0261068 0.999659i \(-0.508311\pi\)
−0.0261068 + 0.999659i \(0.508311\pi\)
\(194\) 1.64406e7i 2.25171i
\(195\) 261333.i 0.0352445i
\(196\) 1.63894e6 0.217668
\(197\) 1.02944e7 1.34649 0.673246 0.739418i \(-0.264899\pi\)
0.673246 + 0.739418i \(0.264899\pi\)
\(198\) 7.34768e6i 0.946575i
\(199\) 609008.i 0.0772795i −0.999253 0.0386397i \(-0.987698\pi\)
0.999253 0.0386397i \(-0.0123025\pi\)
\(200\) −1.14853e7 −1.43567
\(201\) 2.40462e6i 0.296113i
\(202\) −1.44229e7 −1.74984
\(203\) 1.06355e6i 0.127136i
\(204\) 1.02699e7i 1.20970i
\(205\) 3.13925e6i 0.364389i
\(206\) 1.40863e7i 1.61137i
\(207\) −1.05072e6 + 2.76358e6i −0.118461 + 0.311574i
\(208\) −1.42145e6 −0.157958
\(209\) 5.85381e6 0.641210
\(210\) −2.56724e6 −0.277210
\(211\) 1.63949e7 1.74527 0.872634 0.488375i \(-0.162410\pi\)
0.872634 + 0.488375i \(0.162410\pi\)
\(212\) 2.25350e7i 2.36510i
\(213\) 6.48151e6 0.670714
\(214\) 2.30819e7i 2.35521i
\(215\) −881859. −0.0887327
\(216\) 3.05635e6 0.303279
\(217\) 7.04585e6i 0.689532i
\(218\) 2.51011e7i 2.42283i
\(219\) 695728. 0.0662380
\(220\) 1.01410e7 0.952386
\(221\) 2.40821e6i 0.223110i
\(222\) 7.88718e6i 0.720880i
\(223\) −5.00948e6 −0.451729 −0.225865 0.974159i \(-0.572521\pi\)
−0.225865 + 0.974159i \(0.572521\pi\)
\(224\) 2.71507e6i 0.241567i
\(225\) 3.45904e6 0.303675
\(226\) 1.29796e7i 1.12444i
\(227\) 1.80090e7i 1.53962i 0.638276 + 0.769808i \(0.279648\pi\)
−0.638276 + 0.769808i \(0.720352\pi\)
\(228\) 5.07616e6i 0.428283i
\(229\) 1.75626e7i 1.46245i −0.682135 0.731227i \(-0.738948\pi\)
0.682135 0.731227i \(-0.261052\pi\)
\(230\) 5.79877e6 + 2.20470e6i 0.476598 + 0.181203i
\(231\) −1.11331e7 −0.903194
\(232\) −2.65680e6 −0.212763
\(233\) −9.02808e6 −0.713720 −0.356860 0.934158i \(-0.616153\pi\)
−0.356860 + 0.934158i \(0.616153\pi\)
\(234\) 1.49408e6 0.116608
\(235\) 2.45596e6i 0.189242i
\(236\) 3.48327e7 2.65003
\(237\) 1.17194e7i 0.880364i
\(238\) −2.36574e7 −1.75483
\(239\) −3.96922e6 −0.290744 −0.145372 0.989377i \(-0.546438\pi\)
−0.145372 + 0.989377i \(0.546438\pi\)
\(240\) 1.83754e6i 0.132924i
\(241\) 629815.i 0.0449948i −0.999747 0.0224974i \(-0.992838\pi\)
0.999747 0.0224974i \(-0.00716175\pi\)
\(242\) 4.26338e7 3.00821
\(243\) −920483. −0.0641500
\(244\) 4.42913e6i 0.304894i
\(245\) 496816.i 0.0337829i
\(246\) −1.79476e7 −1.20559
\(247\) 1.19032e6i 0.0789901i
\(248\) −1.76009e7 −1.15393
\(249\) 1.54051e7i 0.997852i
\(250\) 1.52250e7i 0.974398i
\(251\) 1.95221e7i 1.23454i 0.786750 + 0.617271i \(0.211762\pi\)
−0.786750 + 0.617271i \(0.788238\pi\)
\(252\) 9.65414e6i 0.603270i
\(253\) 2.51470e7 + 9.56091e6i 1.55283 + 0.590388i
\(254\) −1.76267e7 −1.07564
\(255\) −3.11315e6 −0.187750
\(256\) −3.16699e7 −1.88767
\(257\) −2.29451e7 −1.35173 −0.675865 0.737026i \(-0.736230\pi\)
−0.675865 + 0.737026i \(0.736230\pi\)
\(258\) 5.04173e6i 0.293576i
\(259\) −1.19506e7 −0.687842
\(260\) 2.06208e6i 0.117324i
\(261\) 800150. 0.0450039
\(262\) 5.66313e7 3.14886
\(263\) 1.91287e7i 1.05152i −0.850633 0.525760i \(-0.823781\pi\)
0.850633 0.525760i \(-0.176219\pi\)
\(264\) 2.78111e7i 1.51149i
\(265\) −6.83109e6 −0.367073
\(266\) 1.16933e7 0.621285
\(267\) 6.39431e6i 0.335939i
\(268\) 1.89739e7i 0.985718i
\(269\) 1.19114e6 0.0611938 0.0305969 0.999532i \(-0.490259\pi\)
0.0305969 + 0.999532i \(0.490259\pi\)
\(270\) 1.93143e6i 0.0981270i
\(271\) −2.17557e6 −0.109311 −0.0546555 0.998505i \(-0.517406\pi\)
−0.0546555 + 0.998505i \(0.517406\pi\)
\(272\) 1.69332e7i 0.841455i
\(273\) 2.26382e6i 0.111264i
\(274\) 2.10134e7i 1.02151i
\(275\) 3.14753e7i 1.51346i
\(276\) 8.29079e6 2.18063e7i 0.394338 1.03718i
\(277\) −1.09170e7 −0.513644 −0.256822 0.966459i \(-0.582675\pi\)
−0.256822 + 0.966459i \(0.582675\pi\)
\(278\) −3.91740e7 −1.82332
\(279\) 5.30086e6 0.244081
\(280\) 9.71705e6 0.442650
\(281\) 3.02627e7i 1.36392i −0.731389 0.681960i \(-0.761128\pi\)
0.731389 0.681960i \(-0.238872\pi\)
\(282\) 1.40411e7 0.626115
\(283\) 1.25781e7i 0.554952i 0.960733 + 0.277476i \(0.0894979\pi\)
−0.960733 + 0.277476i \(0.910502\pi\)
\(284\) −5.11431e7 −2.23271
\(285\) 1.53875e6 0.0664712
\(286\) 1.35953e7i 0.581154i
\(287\) 2.71940e7i 1.15034i
\(288\) 2.04265e6 0.0855100
\(289\) −4.55042e6 −0.188520
\(290\) 1.67894e6i 0.0688401i
\(291\) 1.87412e7i 0.760532i
\(292\) −5.48972e6 −0.220497
\(293\) 3.33132e7i 1.32438i −0.749334 0.662192i \(-0.769626\pi\)
0.749334 0.662192i \(-0.230374\pi\)
\(294\) 2.84037e6 0.111772
\(295\) 1.05589e7i 0.411295i
\(296\) 2.98531e7i 1.15110i
\(297\) 8.37587e6i 0.319713i
\(298\) 3.09885e7i 1.17099i
\(299\) 1.94412e6 5.11341e6i 0.0727295 0.191292i
\(300\) −2.72940e7 −1.01089
\(301\) −7.63916e6 −0.280121
\(302\) −2.17571e7 −0.789915
\(303\) −1.64411e7 −0.591023
\(304\) 8.36963e6i 0.297910i
\(305\) −1.34261e6 −0.0473208
\(306\) 1.77984e7i 0.621178i
\(307\) −1.60265e7 −0.553889 −0.276944 0.960886i \(-0.589322\pi\)
−0.276944 + 0.960886i \(0.589322\pi\)
\(308\) 8.78472e7 3.00660
\(309\) 1.60575e7i 0.544254i
\(310\) 1.11227e7i 0.373358i
\(311\) 5.76398e7 1.91620 0.958101 0.286431i \(-0.0924690\pi\)
0.958101 + 0.286431i \(0.0924690\pi\)
\(312\) −5.65513e6 −0.186200
\(313\) 2.12438e7i 0.692785i 0.938090 + 0.346393i \(0.112594\pi\)
−0.938090 + 0.346393i \(0.887406\pi\)
\(314\) 3.11104e7i 1.00489i
\(315\) −2.92648e6 −0.0936299
\(316\) 9.24737e7i 2.93060i
\(317\) −1.49707e7 −0.469963 −0.234982 0.972000i \(-0.575503\pi\)
−0.234982 + 0.972000i \(0.575503\pi\)
\(318\) 3.90544e7i 1.21448i
\(319\) 7.28091e6i 0.224292i
\(320\) 1.18303e7i 0.361032i
\(321\) 2.63118e7i 0.795491i
\(322\) 5.02323e7 + 1.90983e7i 1.50458 + 0.572042i
\(323\) 1.41797e7 0.420786
\(324\) 7.26318e6 0.213546
\(325\) −6.40022e6 −0.186442
\(326\) −9.81056e7 −2.83166
\(327\) 2.86136e7i 0.818331i
\(328\) 6.79320e7 1.92510
\(329\) 2.12749e7i 0.597420i
\(330\) 1.75749e7 0.489049
\(331\) 7.01864e7 1.93539 0.967696 0.252118i \(-0.0811272\pi\)
0.967696 + 0.252118i \(0.0811272\pi\)
\(332\) 1.21556e8i 3.32170i
\(333\) 8.99086e6i 0.243483i
\(334\) −4.26159e7 −1.14375
\(335\) −5.75161e6 −0.152987
\(336\) 1.59178e7i 0.419630i
\(337\) 5.70254e7i 1.48997i −0.667079 0.744987i \(-0.732456\pi\)
0.667079 0.744987i \(-0.267544\pi\)
\(338\) 6.32416e7 1.63777
\(339\) 1.47959e7i 0.379790i
\(340\) 2.45647e7 0.624991
\(341\) 4.82348e7i 1.21646i
\(342\) 8.79728e6i 0.219923i
\(343\) 4.23035e7i 1.04832i
\(344\) 1.90830e7i 0.468782i
\(345\) 6.61021e6 + 2.51321e6i 0.160975 + 0.0612028i
\(346\) −9.82878e7 −2.37285
\(347\) −4.93406e7 −1.18091 −0.590454 0.807071i \(-0.701051\pi\)
−0.590454 + 0.807071i \(0.701051\pi\)
\(348\) −6.31367e6 −0.149811
\(349\) −4.04362e7 −0.951248 −0.475624 0.879649i \(-0.657778\pi\)
−0.475624 + 0.879649i \(0.657778\pi\)
\(350\) 6.28734e7i 1.46643i
\(351\) 1.70316e6 0.0393852
\(352\) 1.85870e7i 0.426168i
\(353\) −7.10708e7 −1.61572 −0.807862 0.589371i \(-0.799375\pi\)
−0.807862 + 0.589371i \(0.799375\pi\)
\(354\) 6.03671e7 1.36079
\(355\) 1.55031e7i 0.346525i
\(356\) 5.04551e7i 1.11829i
\(357\) −2.69679e7 −0.592709
\(358\) 3.44134e7 0.750029
\(359\) 9.17063e7i 1.98206i −0.133654 0.991028i \(-0.542671\pi\)
0.133654 0.991028i \(-0.457329\pi\)
\(360\) 7.31050e6i 0.156689i
\(361\) 4.00372e7 0.851024
\(362\) 6.96357e7i 1.46793i
\(363\) 4.85997e7 1.01605
\(364\) 1.78629e7i 0.370381i
\(365\) 1.66411e6i 0.0342219i
\(366\) 7.67594e6i 0.156563i
\(367\) 5.00464e7i 1.01245i 0.862401 + 0.506226i \(0.168960\pi\)
−0.862401 + 0.506226i \(0.831040\pi\)
\(368\) −1.36699e7 + 3.59545e7i −0.274298 + 0.721456i
\(369\) −2.04591e7 −0.407199
\(370\) 1.88654e7 0.372443
\(371\) −5.91748e7 −1.15882
\(372\) −4.18270e7 −0.812509
\(373\) 4.27907e7i 0.824560i 0.911057 + 0.412280i \(0.135268\pi\)
−0.911057 + 0.412280i \(0.864732\pi\)
\(374\) 1.61955e8 3.09585
\(375\) 1.73555e7i 0.329111i
\(376\) −5.31458e7 −0.999782
\(377\) −1.48051e6 −0.0276303
\(378\) 1.67312e7i 0.309778i
\(379\) 5.51532e7i 1.01310i 0.862210 + 0.506551i \(0.169080\pi\)
−0.862210 + 0.506551i \(0.830920\pi\)
\(380\) −1.21417e7 −0.221273
\(381\) −2.00932e7 −0.363308
\(382\) 1.41457e8i 2.53767i
\(383\) 7.95541e7i 1.41601i 0.706208 + 0.708005i \(0.250404\pi\)
−0.706208 + 0.708005i \(0.749596\pi\)
\(384\) −5.92493e7 −1.04638
\(385\) 2.66293e7i 0.466636i
\(386\) 5.13309e6 0.0892519
\(387\) 5.74723e6i 0.0991575i
\(388\) 1.47879e8i 2.53170i
\(389\) 5.54580e7i 0.942140i −0.882096 0.471070i \(-0.843868\pi\)
0.882096 0.471070i \(-0.156132\pi\)
\(390\) 3.57370e6i 0.0602455i
\(391\) 6.09138e7 + 2.31595e7i 1.01903 + 0.387435i
\(392\) −1.07509e7 −0.178478
\(393\) 6.45559e7 1.06355
\(394\) −1.40775e8 −2.30164
\(395\) −2.80318e7 −0.454841
\(396\) 6.60908e7i 1.06428i
\(397\) 2.45447e7 0.392271 0.196136 0.980577i \(-0.437161\pi\)
0.196136 + 0.980577i \(0.437161\pi\)
\(398\) 8.32812e6i 0.132098i
\(399\) 1.33295e7 0.209844
\(400\) 4.50026e7 0.703166
\(401\) 5.32006e7i 0.825056i −0.910945 0.412528i \(-0.864646\pi\)
0.910945 0.412528i \(-0.135354\pi\)
\(402\) 3.28829e7i 0.506165i
\(403\) −9.80811e6 −0.149855
\(404\) 1.29731e8 1.96743
\(405\) 2.20171e6i 0.0331432i
\(406\) 1.45439e7i 0.217322i
\(407\) 8.18117e7 1.21348
\(408\) 6.73671e7i 0.991898i
\(409\) 1.24784e8 1.82385 0.911924 0.410360i \(-0.134597\pi\)
0.911924 + 0.410360i \(0.134597\pi\)
\(410\) 4.29289e7i 0.622872i
\(411\) 2.39538e7i 0.345024i
\(412\) 1.26703e8i 1.81174i
\(413\) 9.14675e7i 1.29842i
\(414\) 1.43684e7 3.77916e7i 0.202492 0.532592i
\(415\) −3.68475e7 −0.515541
\(416\) −3.77949e6 −0.0524993
\(417\) −4.46557e7 −0.615842
\(418\) −8.00502e7 −1.09606
\(419\) 1.38099e8i 1.87737i 0.344775 + 0.938685i \(0.387955\pi\)
−0.344775 + 0.938685i \(0.612045\pi\)
\(420\) 2.30918e7 0.311680
\(421\) 1.35095e8i 1.81048i 0.424905 + 0.905238i \(0.360307\pi\)
−0.424905 + 0.905238i \(0.639693\pi\)
\(422\) −2.24199e8 −2.98329
\(423\) 1.60059e7 0.211475
\(424\) 1.47822e8i 1.93928i
\(425\) 7.62430e7i 0.993192i
\(426\) −8.86340e7 −1.14649
\(427\) −1.16305e7 −0.149388
\(428\) 2.07616e8i 2.64807i
\(429\) 1.54978e7i 0.196289i
\(430\) 1.20593e7 0.151676
\(431\) 1.04449e8i 1.30459i 0.757966 + 0.652294i \(0.226193\pi\)
−0.757966 + 0.652294i \(0.773807\pi\)
\(432\) −1.19756e7 −0.148541
\(433\) 7.45093e7i 0.917797i 0.888489 + 0.458899i \(0.151756\pi\)
−0.888489 + 0.458899i \(0.848244\pi\)
\(434\) 9.63512e7i 1.17866i
\(435\) 1.91388e6i 0.0232513i
\(436\) 2.25779e8i 2.72410i
\(437\) −3.01081e7 1.14471e7i −0.360778 0.137168i
\(438\) −9.51400e6 −0.113225
\(439\) 7.03400e7 0.831397 0.415699 0.909502i \(-0.363537\pi\)
0.415699 + 0.909502i \(0.363537\pi\)
\(440\) −6.65214e7 −0.780914
\(441\) 3.23784e6 0.0377519
\(442\) 3.29321e7i 0.381375i
\(443\) 4.84579e7 0.557383 0.278691 0.960381i \(-0.410099\pi\)
0.278691 + 0.960381i \(0.410099\pi\)
\(444\) 7.09434e7i 0.810519i
\(445\) −1.52946e7 −0.173563
\(446\) 6.85041e7 0.772168
\(447\) 3.53248e7i 0.395510i
\(448\) 1.02481e8i 1.13975i
\(449\) 5.38849e7 0.595289 0.297644 0.954677i \(-0.403799\pi\)
0.297644 + 0.954677i \(0.403799\pi\)
\(450\) −4.73020e7 −0.519090
\(451\) 1.86166e8i 2.02941i
\(452\) 1.16749e8i 1.26426i
\(453\) −2.48017e7 −0.266800
\(454\) 2.46271e8i 2.63176i
\(455\) 5.41483e6 0.0574845
\(456\) 3.32978e7i 0.351173i
\(457\) 1.72326e8i 1.80552i −0.430141 0.902762i \(-0.641536\pi\)
0.430141 0.902762i \(-0.358464\pi\)
\(458\) 2.40166e8i 2.49986i
\(459\) 2.02889e7i 0.209808i
\(460\) −5.21586e7 1.98308e7i −0.535862 0.203735i
\(461\) 1.09790e8 1.12063 0.560315 0.828280i \(-0.310680\pi\)
0.560315 + 0.828280i \(0.310680\pi\)
\(462\) 1.52244e8 1.54388
\(463\) −8.40623e7 −0.846951 −0.423475 0.905908i \(-0.639190\pi\)
−0.423475 + 0.905908i \(0.639190\pi\)
\(464\) 1.04100e7 0.104207
\(465\) 1.26791e7i 0.126105i
\(466\) 1.23458e8 1.22000
\(467\) 9.26107e7i 0.909307i −0.890668 0.454654i \(-0.849763\pi\)
0.890668 0.454654i \(-0.150237\pi\)
\(468\) −1.34390e7 −0.131108
\(469\) −4.98237e7 −0.482967
\(470\) 3.35849e7i 0.323483i
\(471\) 3.54638e7i 0.339408i
\(472\) −2.28490e8 −2.17291
\(473\) 5.22965e7 0.494185
\(474\) 1.60262e8i 1.50486i
\(475\) 3.76850e7i 0.351631i
\(476\) 2.12793e8 1.97304
\(477\) 4.45195e7i 0.410199i
\(478\) 5.42786e7 0.496987
\(479\) 4.47728e7i 0.407387i 0.979035 + 0.203694i \(0.0652946\pi\)
−0.979035 + 0.203694i \(0.934705\pi\)
\(480\) 4.88582e6i 0.0441788i
\(481\) 1.66357e7i 0.149487i
\(482\) 8.61266e6i 0.0769123i
\(483\) 5.72614e7 + 2.17708e7i 0.508184 + 0.193212i
\(484\) −3.83482e8 −3.38227
\(485\) −4.48270e7 −0.392930
\(486\) 1.25875e7 0.109656
\(487\) 3.68023e7 0.318631 0.159316 0.987228i \(-0.449071\pi\)
0.159316 + 0.987228i \(0.449071\pi\)
\(488\) 2.90535e7i 0.250000i
\(489\) −1.11834e8 −0.956416
\(490\) 6.79390e6i 0.0577472i
\(491\) −1.41972e8 −1.19938 −0.599691 0.800232i \(-0.704710\pi\)
−0.599691 + 0.800232i \(0.704710\pi\)
\(492\) 1.61435e8 1.35551
\(493\) 1.76366e7i 0.147189i
\(494\) 1.62775e7i 0.135023i
\(495\) 2.00343e7 0.165180
\(496\) 6.89648e7 0.565175
\(497\) 1.34297e8i 1.09395i
\(498\) 2.10663e8i 1.70569i
\(499\) −4.54773e7 −0.366010 −0.183005 0.983112i \(-0.558583\pi\)
−0.183005 + 0.983112i \(0.558583\pi\)
\(500\) 1.36945e8i 1.09556i
\(501\) −4.85793e7 −0.386312
\(502\) 2.66963e8i 2.11028i
\(503\) 6.18309e7i 0.485850i 0.970045 + 0.242925i \(0.0781068\pi\)
−0.970045 + 0.242925i \(0.921893\pi\)
\(504\) 6.33277e7i 0.494655i
\(505\) 3.93256e7i 0.305352i
\(506\) −3.43882e8 1.30744e8i −2.65435 1.00919i
\(507\) 7.20912e7 0.553170
\(508\) 1.58548e8 1.20940
\(509\) −2.87994e7 −0.218389 −0.109194 0.994020i \(-0.534827\pi\)
−0.109194 + 0.994020i \(0.534827\pi\)
\(510\) 4.25719e7 0.320932
\(511\) 1.44155e7i 0.108036i
\(512\) 1.89828e8 1.41433
\(513\) 1.00283e7i 0.0742807i
\(514\) 3.13771e8 2.31059
\(515\) 3.84079e7 0.281189
\(516\) 4.53492e7i 0.330081i
\(517\) 1.45645e8i 1.05396i
\(518\) 1.63423e8 1.17577
\(519\) −1.12041e8 −0.801451
\(520\) 1.35265e7i 0.0962002i
\(521\) 8.76991e7i 0.620129i −0.950716 0.310064i \(-0.899649\pi\)
0.950716 0.310064i \(-0.100351\pi\)
\(522\) −1.09420e7 −0.0769278
\(523\) 2.05677e7i 0.143774i 0.997413 + 0.0718871i \(0.0229021\pi\)
−0.997413 + 0.0718871i \(0.977098\pi\)
\(524\) −5.09386e8 −3.54041
\(525\) 7.16715e7i 0.495300i
\(526\) 2.61582e8i 1.79743i
\(527\) 1.16840e8i 0.798285i
\(528\) 1.08971e8i 0.740303i
\(529\) −1.10643e8 9.83500e7i −0.747407 0.664366i
\(530\) 9.34144e7 0.627460
\(531\) 6.88145e7 0.459617
\(532\) −1.05178e8 −0.698539
\(533\) 3.78551e7 0.250002
\(534\) 8.74415e7i 0.574241i
\(535\) −6.29352e7 −0.410991
\(536\) 1.24462e8i 0.808245i
\(537\) 3.92289e7 0.253328
\(538\) −1.62888e7 −0.104602
\(539\) 2.94625e7i 0.188149i
\(540\) 1.73728e7i 0.110329i
\(541\) 1.59395e8 1.00666 0.503329 0.864095i \(-0.332108\pi\)
0.503329 + 0.864095i \(0.332108\pi\)
\(542\) 2.97506e7 0.186852
\(543\) 7.93800e7i 0.495806i
\(544\) 4.50234e7i 0.279667i
\(545\) 6.84409e7 0.422791
\(546\) 3.09575e7i 0.190190i
\(547\) −2.45660e7 −0.150097 −0.0750486 0.997180i \(-0.523911\pi\)
−0.0750486 + 0.997180i \(0.523911\pi\)
\(548\) 1.89010e8i 1.14853i
\(549\) 8.75006e6i 0.0528803i
\(550\) 4.30422e8i 2.58706i
\(551\) 8.71733e6i 0.0521109i
\(552\) −5.43846e7 + 1.43042e8i −0.323340 + 0.850444i
\(553\) −2.42827e8 −1.43589
\(554\) 1.49288e8 0.878003
\(555\) 2.15053e7 0.125796
\(556\) 3.52361e8 2.05005
\(557\) 4.07722e7i 0.235938i −0.993017 0.117969i \(-0.962362\pi\)
0.993017 0.117969i \(-0.0376384\pi\)
\(558\) −7.24887e7 −0.417222
\(559\) 1.06340e7i 0.0608782i
\(560\) −3.80739e7 −0.216802
\(561\) 1.84618e8 1.04565
\(562\) 4.13839e8i 2.33143i
\(563\) 1.75318e8i 0.982429i 0.871039 + 0.491215i \(0.163447\pi\)
−0.871039 + 0.491215i \(0.836553\pi\)
\(564\) −1.26297e8 −0.703970
\(565\) 3.53904e7 0.196219
\(566\) 1.72004e8i 0.948613i
\(567\) 1.90724e7i 0.104630i
\(568\) 3.35481e8 1.83072
\(569\) 9.94027e7i 0.539587i −0.962918 0.269793i \(-0.913045\pi\)
0.962918 0.269793i \(-0.0869554\pi\)
\(570\) −2.10422e7 −0.113623
\(571\) 1.33988e7i 0.0719712i 0.999352 + 0.0359856i \(0.0114571\pi\)
−0.999352 + 0.0359856i \(0.988543\pi\)
\(572\) 1.22287e8i 0.653419i
\(573\) 1.61252e8i 0.857118i
\(574\) 3.71875e8i 1.96635i
\(575\) −6.15501e7 + 1.61888e8i −0.323761 + 0.851553i
\(576\) −7.71001e7 −0.403448
\(577\) −5.21549e7 −0.271499 −0.135749 0.990743i \(-0.543344\pi\)
−0.135749 + 0.990743i \(0.543344\pi\)
\(578\) 6.22264e7 0.322249
\(579\) 5.85138e6 0.0301455
\(580\) 1.51017e7i 0.0774001i
\(581\) −3.19194e8 −1.62752
\(582\) 2.56283e8i 1.30002i
\(583\) 4.05102e8 2.04436
\(584\) 3.60106e7 0.180797
\(585\) 4.07378e6i 0.0203484i
\(586\) 4.55555e8i 2.26385i
\(587\) 2.48417e8 1.22820 0.614098 0.789230i \(-0.289520\pi\)
0.614098 + 0.789230i \(0.289520\pi\)
\(588\) −2.55485e7 −0.125671
\(589\) 5.77509e7i 0.282626i
\(590\) 1.44392e8i 0.703052i
\(591\) −1.60474e8 −0.777398
\(592\) 1.16972e8i 0.563790i
\(593\) −3.98370e8 −1.91039 −0.955197 0.295971i \(-0.904357\pi\)
−0.955197 + 0.295971i \(0.904357\pi\)
\(594\) 1.14539e8i 0.546505i
\(595\) 6.45045e7i 0.306224i
\(596\) 2.78735e8i 1.31659i
\(597\) 9.49350e6i 0.0446173i
\(598\) −2.65857e7 + 6.99253e7i −0.124321 + 0.326987i
\(599\) 2.13213e8 0.992050 0.496025 0.868308i \(-0.334792\pi\)
0.496025 + 0.868308i \(0.334792\pi\)
\(600\) 1.79039e8 0.828884
\(601\) 5.00614e6 0.0230611 0.0115305 0.999934i \(-0.496330\pi\)
0.0115305 + 0.999934i \(0.496330\pi\)
\(602\) 1.04465e8 0.478828
\(603\) 3.74843e7i 0.170961i
\(604\) 1.95700e8 0.888139
\(605\) 1.16246e8i 0.524942i
\(606\) 2.24831e8 1.01027
\(607\) −2.11822e8 −0.947122 −0.473561 0.880761i \(-0.657032\pi\)
−0.473561 + 0.880761i \(0.657032\pi\)
\(608\) 2.22539e7i 0.0990138i
\(609\) 1.65791e7i 0.0734023i
\(610\) 1.83601e7 0.0808883
\(611\) −2.96155e7 −0.129836
\(612\) 1.60092e8i 0.698419i
\(613\) 2.61252e8i 1.13417i −0.823660 0.567084i \(-0.808071\pi\)
0.823660 0.567084i \(-0.191929\pi\)
\(614\) 2.19160e8 0.946796
\(615\) 4.89361e7i 0.210380i
\(616\) −5.76246e8 −2.46528
\(617\) 592013.i 0.00252044i 0.999999 + 0.00126022i \(0.000401140\pi\)
−0.999999 + 0.00126022i \(0.999599\pi\)
\(618\) 2.19584e8i 0.930326i
\(619\) 1.03326e8i 0.435652i −0.975988 0.217826i \(-0.930104\pi\)
0.975988 0.217826i \(-0.0698965\pi\)
\(620\) 1.00046e8i 0.419784i
\(621\) 1.63790e7 4.30799e7i 0.0683933 0.179887i
\(622\) −7.88218e8 −3.27548
\(623\) −1.32490e8 −0.547924
\(624\) 2.21583e7 0.0911974
\(625\) 1.80905e8 0.740989
\(626\) 2.90506e8i 1.18422i
\(627\) −9.12519e7 −0.370203
\(628\) 2.79831e8i 1.12984i
\(629\) 1.98173e8 0.796330
\(630\) 4.00193e7 0.160047
\(631\) 2.30118e8i 0.915930i −0.888970 0.457965i \(-0.848578\pi\)
0.888970 0.457965i \(-0.151422\pi\)
\(632\) 6.06594e8i 2.40296i
\(633\) −2.55572e8 −1.00763
\(634\) 2.04723e8 0.803337
\(635\) 4.80610e7i 0.187703i
\(636\) 3.51286e8i 1.36549i
\(637\) −5.99092e6 −0.0231780
\(638\) 9.95656e7i 0.383396i
\(639\) −1.01037e8 −0.387237
\(640\) 1.41719e8i 0.540613i
\(641\) 1.68567e8i 0.640026i 0.947413 + 0.320013i \(0.103687\pi\)
−0.947413 + 0.320013i \(0.896313\pi\)
\(642\) 3.59811e8i 1.35978i
\(643\) 4.56236e8i 1.71615i −0.513521 0.858077i \(-0.671659\pi\)
0.513521 0.858077i \(-0.328341\pi\)
\(644\) −4.51828e8 1.71785e8i −1.69167 0.643174i
\(645\) 1.37468e7 0.0512298
\(646\) −1.93906e8 −0.719274
\(647\) 1.41351e8 0.521897 0.260949 0.965353i \(-0.415965\pi\)
0.260949 + 0.965353i \(0.415965\pi\)
\(648\) −4.76439e7 −0.175098
\(649\) 6.26172e8i 2.29066i
\(650\) 8.75223e7 0.318698
\(651\) 1.09834e8i 0.398101i
\(652\) 8.82438e8 3.18377
\(653\) 6.26888e7 0.225139 0.112569 0.993644i \(-0.464092\pi\)
0.112569 + 0.993644i \(0.464092\pi\)
\(654\) 3.91288e8i 1.39882i
\(655\) 1.54411e8i 0.549485i
\(656\) −2.66175e8 −0.942879
\(657\) −1.08453e7 −0.0382425
\(658\) 2.90932e8i 1.02121i
\(659\) 4.33761e8i 1.51563i 0.652468 + 0.757816i \(0.273734\pi\)
−0.652468 + 0.757816i \(0.726266\pi\)
\(660\) −1.58083e8 −0.549860
\(661\) 1.04892e8i 0.363192i −0.983373 0.181596i \(-0.941874\pi\)
0.983373 0.181596i \(-0.0581264\pi\)
\(662\) −9.59791e8 −3.30828
\(663\) 3.75404e7i 0.128812i
\(664\) 7.97362e8i 2.72365i
\(665\) 3.18829e7i 0.108416i
\(666\) 1.22949e8i 0.416200i
\(667\) −1.42378e7 + 3.74482e7i −0.0479807 + 0.126198i
\(668\) 3.83321e8 1.28598
\(669\) 7.80901e7 0.260806
\(670\) 7.86527e7 0.261510
\(671\) 7.96205e7 0.263547
\(672\) 4.23238e7i 0.139469i
\(673\) −3.60124e8 −1.18143 −0.590713 0.806882i \(-0.701153\pi\)
−0.590713 + 0.806882i \(0.701153\pi\)
\(674\) 7.79816e8i 2.54690i
\(675\) −5.39212e7 −0.175327
\(676\) −5.68844e8 −1.84142
\(677\) 2.26507e8i 0.729987i 0.931010 + 0.364994i \(0.118929\pi\)
−0.931010 + 0.364994i \(0.881071\pi\)
\(678\) 2.02333e8i 0.649198i
\(679\) −3.88317e8 −1.24044
\(680\) −1.61135e8 −0.512465
\(681\) 2.80733e8i 0.888898i
\(682\) 6.59605e8i 2.07937i
\(683\) 4.40752e8 1.38335 0.691674 0.722209i \(-0.256873\pi\)
0.691674 + 0.722209i \(0.256873\pi\)
\(684\) 7.91296e7i 0.247269i
\(685\) −5.72952e7 −0.178257
\(686\) 5.78496e8i 1.79196i
\(687\) 2.73774e8i 0.844348i
\(688\) 7.47722e7i 0.229602i
\(689\) 8.23737e7i 0.251844i
\(690\) −9.03939e7 3.43678e7i −0.275164 0.104618i
\(691\) −1.00558e8 −0.304776 −0.152388 0.988321i \(-0.548696\pi\)
−0.152388 + 0.988321i \(0.548696\pi\)
\(692\) 8.84076e8 2.66791
\(693\) 1.73548e8 0.521459
\(694\) 6.74728e8 2.01860
\(695\) 1.06812e8i 0.318175i
\(696\) 4.14155e7 0.122839
\(697\) 4.50951e8i 1.33178i
\(698\) 5.52960e8 1.62603
\(699\) 1.40734e8 0.412066
\(700\) 5.65532e8i 1.64878i
\(701\) 1.87714e8i 0.544933i 0.962165 + 0.272466i \(0.0878393\pi\)
−0.962165 + 0.272466i \(0.912161\pi\)
\(702\) −2.32905e7 −0.0673235
\(703\) −9.79520e7 −0.281934
\(704\) 7.01567e8i 2.01072i
\(705\) 3.82846e7i 0.109259i
\(706\) 9.71886e8 2.76186
\(707\) 3.40661e8i 0.963971i
\(708\) −5.42988e8 −1.53000
\(709\) 4.15837e8i 1.16677i 0.812196 + 0.583384i \(0.198272\pi\)
−0.812196 + 0.583384i \(0.801728\pi\)
\(710\) 2.12004e8i 0.592337i
\(711\) 1.82688e8i 0.508278i
\(712\) 3.30967e8i 0.916949i
\(713\) −9.43233e7 + 2.48088e8i −0.260226 + 0.684443i
\(714\) 3.68782e8 1.01315
\(715\) −3.70691e7 −0.101413
\(716\) −3.09540e8 −0.843293
\(717\) 6.18740e7 0.167861
\(718\) 1.25407e9i 3.38805i
\(719\) −4.55072e7 −0.122432 −0.0612158 0.998125i \(-0.519498\pi\)
−0.0612158 + 0.998125i \(0.519498\pi\)
\(720\) 2.86445e7i 0.0767438i
\(721\) 3.32711e8 0.887690
\(722\) −5.47504e8 −1.45471
\(723\) 9.81785e6i 0.0259778i
\(724\) 6.26357e8i 1.65046i
\(725\) 4.68721e7 0.122999
\(726\) −6.64596e8 −1.73679
\(727\) 2.63013e8i 0.684502i −0.939609 0.342251i \(-0.888811\pi\)
0.939609 0.342251i \(-0.111189\pi\)
\(728\) 1.17174e8i 0.303696i
\(729\) 1.43489e7 0.0370370
\(730\) 2.27566e7i 0.0584976i
\(731\) 1.26678e8 0.324302
\(732\) 6.90433e7i 0.176031i
\(733\) 3.66525e8i 0.930662i −0.885137 0.465331i \(-0.845935\pi\)
0.885137 0.465331i \(-0.154065\pi\)
\(734\) 6.84379e8i 1.73065i
\(735\) 7.74459e6i 0.0195046i
\(736\) −3.63468e7 + 9.55991e7i −0.0911661 + 0.239784i
\(737\) 3.41086e8 0.852042
\(738\) 2.79776e8 0.696050
\(739\) −2.84036e8 −0.703785 −0.351892 0.936040i \(-0.614462\pi\)
−0.351892 + 0.936040i \(0.614462\pi\)
\(740\) −1.69690e8 −0.418755
\(741\) 1.85552e7i 0.0456050i
\(742\) 8.09209e8 1.98084
\(743\) 4.52986e8i 1.10438i −0.833718 0.552190i \(-0.813792\pi\)
0.833718 0.552190i \(-0.186208\pi\)
\(744\) 2.74371e8 0.666222
\(745\) 8.44935e7 0.204341
\(746\) 5.85157e8i 1.40947i
\(747\) 2.40142e8i 0.576110i
\(748\) −1.45675e9 −3.48080
\(749\) −5.45180e8 −1.29746
\(750\) 2.37334e8i 0.562569i
\(751\) 2.97297e8i 0.701893i 0.936396 + 0.350946i \(0.114140\pi\)
−0.936396 + 0.350946i \(0.885860\pi\)
\(752\) 2.08239e8 0.489676
\(753\) 3.04320e8i 0.712764i
\(754\) 2.02458e7 0.0472302
\(755\) 5.93232e7i 0.137843i
\(756\) 1.50493e8i 0.348298i
\(757\) 1.73511e8i 0.399982i 0.979798 + 0.199991i \(0.0640912\pi\)
−0.979798 + 0.199991i \(0.935909\pi\)
\(758\) 7.54214e8i 1.73176i
\(759\) −3.92003e8 1.49040e8i −0.896528 0.340861i
\(760\) 7.96452e7 0.181434
\(761\) −9.85680e7 −0.223657 −0.111828 0.993728i \(-0.535671\pi\)
−0.111828 + 0.993728i \(0.535671\pi\)
\(762\) 2.74772e8 0.621024
\(763\) 5.92874e8 1.33472
\(764\) 1.27238e9i 2.85322i
\(765\) 4.85292e7 0.108397
\(766\) 1.08789e9i 2.42047i
\(767\) −1.27326e8 −0.282184
\(768\) 4.93685e8 1.08985
\(769\) 1.01130e8i 0.222382i 0.993799 + 0.111191i \(0.0354665\pi\)
−0.993799 + 0.111191i \(0.964533\pi\)
\(770\) 3.64153e8i 0.797649i
\(771\) 3.57678e8 0.780421
\(772\) −4.61710e7 −0.100350
\(773\) 7.09878e8i 1.53690i 0.639910 + 0.768449i \(0.278971\pi\)
−0.639910 + 0.768449i \(0.721029\pi\)
\(774\) 7.85927e7i 0.169496i
\(775\) 3.10520e8 0.667090
\(776\) 9.70036e8i 2.07588i
\(777\) 1.86291e8 0.397126
\(778\) 7.58382e8i 1.61046i
\(779\) 2.22894e8i 0.471504i
\(780\) 3.21447e7i 0.0677369i
\(781\) 9.19377e8i 1.92993i
\(782\) −8.32989e8 3.16703e8i −1.74188 0.662266i
\(783\) −1.24731e7 −0.0259830
\(784\) 4.21246e7 0.0874154