Properties

Label 69.6.c.b.68.23
Level $69$
Weight $6$
Character 69.68
Analytic conductor $11.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0664835671\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 68.23
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.9

$q$-expansion

\(f(q)\) \(=\) \(q+5.41836i q^{2} +(3.03549 + 15.2901i) q^{3} +2.64141 q^{4} -41.1824 q^{5} +(-82.8470 + 16.4474i) q^{6} -67.8449i q^{7} +187.700i q^{8} +(-224.572 + 92.8256i) q^{9} +O(q^{10})\) \(q+5.41836i q^{2} +(3.03549 + 15.2901i) q^{3} +2.64141 q^{4} -41.1824 q^{5} +(-82.8470 + 16.4474i) q^{6} -67.8449i q^{7} +187.700i q^{8} +(-224.572 + 92.8256i) q^{9} -223.141i q^{10} -718.835 q^{11} +(8.01796 + 40.3872i) q^{12} -17.0158 q^{13} +367.608 q^{14} +(-125.009 - 629.681i) q^{15} -932.498 q^{16} +1853.18 q^{17} +(-502.962 - 1216.81i) q^{18} +1139.13i q^{19} -108.779 q^{20} +(1037.35 - 205.943i) q^{21} -3894.90i q^{22} +(-1493.34 - 2050.92i) q^{23} +(-2869.94 + 569.760i) q^{24} -1429.01 q^{25} -92.1977i q^{26} +(-2100.99 - 3151.94i) q^{27} -179.206i q^{28} +1744.71i q^{29} +(3411.84 - 677.342i) q^{30} +3913.17 q^{31} +953.777i q^{32} +(-2182.02 - 10991.0i) q^{33} +10041.2i q^{34} +2794.01i q^{35} +(-593.185 + 245.190i) q^{36} +9229.25i q^{37} -6172.22 q^{38} +(-51.6513 - 260.173i) q^{39} -7729.91i q^{40} +5011.22i q^{41} +(1115.87 + 5620.75i) q^{42} +5505.60i q^{43} -1898.73 q^{44} +(9248.39 - 3822.78i) q^{45} +(11112.6 - 8091.43i) q^{46} +20518.7i q^{47} +(-2830.59 - 14257.9i) q^{48} +12204.1 q^{49} -7742.90i q^{50} +(5625.31 + 28335.2i) q^{51} -44.9456 q^{52} -36672.8 q^{53} +(17078.3 - 11383.9i) q^{54} +29603.3 q^{55} +12734.5 q^{56} +(-17417.4 + 3457.82i) q^{57} -9453.46 q^{58} +30068.0i q^{59} +(-330.199 - 1663.24i) q^{60} +30394.4i q^{61} +21202.9i q^{62} +(6297.75 + 15236.0i) q^{63} -35007.8 q^{64} +700.751 q^{65} +(59553.3 - 11822.9i) q^{66} -42629.9i q^{67} +4895.00 q^{68} +(26825.7 - 29058.7i) q^{69} -15139.0 q^{70} -42884.6i q^{71} +(-17423.3 - 42152.0i) q^{72} +10487.2 q^{73} -50007.4 q^{74} +(-4337.75 - 21849.7i) q^{75} +3008.91i q^{76} +48769.3i q^{77} +(1409.71 - 279.865i) q^{78} +37112.3i q^{79} +38402.5 q^{80} +(41815.8 - 41692.0i) q^{81} -27152.6 q^{82} +65765.4 q^{83} +(2740.07 - 543.978i) q^{84} -76318.4 q^{85} -29831.3 q^{86} +(-26676.7 + 5296.05i) q^{87} -134925. i q^{88} -107918. q^{89} +(20713.2 + 50111.1i) q^{90} +1154.44i q^{91} +(-3944.50 - 5417.32i) q^{92} +(11878.4 + 59832.6i) q^{93} -111177. q^{94} -46912.1i q^{95} +(-14583.3 + 2895.18i) q^{96} -69228.0i q^{97} +66126.0i q^{98} +(161430. - 66726.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 408 q^{4} - 528 q^{6} - 444 q^{9} + O(q^{10}) \) \( 32 q - 408 q^{4} - 528 q^{6} - 444 q^{9} - 2484 q^{12} + 520 q^{13} + 4936 q^{16} + 7188 q^{18} + 18660 q^{24} + 36032 q^{25} - 22032 q^{27} + 6544 q^{31} - 33912 q^{36} - 63912 q^{39} + 54328 q^{46} + 88284 q^{48} - 207664 q^{49} + 46296 q^{52} - 38628 q^{54} - 139296 q^{55} - 184144 q^{58} + 486584 q^{64} - 113580 q^{69} + 37176 q^{70} - 15504 q^{72} - 93896 q^{73} + 249840 q^{75} + 368028 q^{78} - 339372 q^{81} - 23512 q^{82} + 259584 q^{85} + 509928 q^{87} + 82740 q^{93} - 562000 q^{94} + 1404 q^{96} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.41836i 0.957839i 0.877859 + 0.478920i \(0.158971\pi\)
−0.877859 + 0.478920i \(0.841029\pi\)
\(3\) 3.03549 + 15.2901i 0.194727 + 0.980858i
\(4\) 2.64141 0.0825439
\(5\) −41.1824 −0.736693 −0.368346 0.929689i \(-0.620076\pi\)
−0.368346 + 0.929689i \(0.620076\pi\)
\(6\) −82.8470 + 16.4474i −0.939504 + 0.186517i
\(7\) 67.8449i 0.523326i −0.965159 0.261663i \(-0.915729\pi\)
0.965159 0.261663i \(-0.0842709\pi\)
\(8\) 187.700i 1.03690i
\(9\) −224.572 + 92.8256i −0.924163 + 0.381998i
\(10\) 223.141i 0.705633i
\(11\) −718.835 −1.79121 −0.895607 0.444847i \(-0.853258\pi\)
−0.895607 + 0.444847i \(0.853258\pi\)
\(12\) 8.01796 + 40.3872i 0.0160735 + 0.0809638i
\(13\) −17.0158 −0.0279251 −0.0139625 0.999903i \(-0.504445\pi\)
−0.0139625 + 0.999903i \(0.504445\pi\)
\(14\) 367.608 0.501262
\(15\) −125.009 629.681i −0.143454 0.722591i
\(16\) −932.498 −0.910643
\(17\) 1853.18 1.55523 0.777616 0.628739i \(-0.216429\pi\)
0.777616 + 0.628739i \(0.216429\pi\)
\(18\) −502.962 1216.81i −0.365893 0.885200i
\(19\) 1139.13i 0.723918i 0.932194 + 0.361959i \(0.117892\pi\)
−0.932194 + 0.361959i \(0.882108\pi\)
\(20\) −108.779 −0.0608095
\(21\) 1037.35 205.943i 0.513308 0.101906i
\(22\) 3894.90i 1.71569i
\(23\) −1493.34 2050.92i −0.588624 0.808407i
\(24\) −2869.94 + 569.760i −1.01705 + 0.201913i
\(25\) −1429.01 −0.457284
\(26\) 92.1977i 0.0267477i
\(27\) −2100.99 3151.94i −0.554645 0.832087i
\(28\) 179.206i 0.0431974i
\(29\) 1744.71i 0.385237i 0.981274 + 0.192619i \(0.0616980\pi\)
−0.981274 + 0.192619i \(0.938302\pi\)
\(30\) 3411.84 677.342i 0.692126 0.137406i
\(31\) 3913.17 0.731348 0.365674 0.930743i \(-0.380838\pi\)
0.365674 + 0.930743i \(0.380838\pi\)
\(32\) 953.777i 0.164654i
\(33\) −2182.02 10991.0i −0.348797 1.75693i
\(34\) 10041.2i 1.48966i
\(35\) 2794.01i 0.385530i
\(36\) −593.185 + 245.190i −0.0762840 + 0.0315316i
\(37\) 9229.25i 1.10831i 0.832413 + 0.554156i \(0.186959\pi\)
−0.832413 + 0.554156i \(0.813041\pi\)
\(38\) −6172.22 −0.693398
\(39\) −51.6513 260.173i −0.00543776 0.0273905i
\(40\) 7729.91i 0.763879i
\(41\) 5011.22i 0.465569i 0.972528 + 0.232784i \(0.0747836\pi\)
−0.972528 + 0.232784i \(0.925216\pi\)
\(42\) 1115.87 + 5620.75i 0.0976091 + 0.491667i
\(43\) 5505.60i 0.454081i 0.973885 + 0.227041i \(0.0729050\pi\)
−0.973885 + 0.227041i \(0.927095\pi\)
\(44\) −1898.73 −0.147854
\(45\) 9248.39 3822.78i 0.680824 0.281416i
\(46\) 11112.6 8091.43i 0.774324 0.563807i
\(47\) 20518.7i 1.35489i 0.735573 + 0.677446i \(0.236913\pi\)
−0.735573 + 0.677446i \(0.763087\pi\)
\(48\) −2830.59 14257.9i −0.177327 0.893211i
\(49\) 12204.1 0.726130
\(50\) 7742.90i 0.438004i
\(51\) 5625.31 + 28335.2i 0.302846 + 1.52546i
\(52\) −44.9456 −0.00230504
\(53\) −36672.8 −1.79331 −0.896653 0.442734i \(-0.854009\pi\)
−0.896653 + 0.442734i \(0.854009\pi\)
\(54\) 17078.3 11383.9i 0.797005 0.531261i
\(55\) 29603.3 1.31957
\(56\) 12734.5 0.542638
\(57\) −17417.4 + 3457.82i −0.710061 + 0.140966i
\(58\) −9453.46 −0.368995
\(59\) 30068.0i 1.12454i 0.826955 + 0.562269i \(0.190071\pi\)
−0.826955 + 0.562269i \(0.809929\pi\)
\(60\) −330.199 1663.24i −0.0118412 0.0596455i
\(61\) 30394.4i 1.04585i 0.852379 + 0.522924i \(0.175159\pi\)
−0.852379 + 0.522924i \(0.824841\pi\)
\(62\) 21202.9i 0.700514i
\(63\) 6297.75 + 15236.0i 0.199910 + 0.483638i
\(64\) −35007.8 −1.06835
\(65\) 700.751 0.0205722
\(66\) 59553.3 11822.9i 1.68285 0.334092i
\(67\) 42629.9i 1.16019i −0.814550 0.580093i \(-0.803016\pi\)
0.814550 0.580093i \(-0.196984\pi\)
\(68\) 4895.00 0.128375
\(69\) 26825.7 29058.7i 0.678311 0.734775i
\(70\) −15139.0 −0.369276
\(71\) 42884.6i 1.00961i −0.863232 0.504807i \(-0.831564\pi\)
0.863232 0.504807i \(-0.168436\pi\)
\(72\) −17423.3 42152.0i −0.396095 0.958267i
\(73\) 10487.2 0.230330 0.115165 0.993346i \(-0.463260\pi\)
0.115165 + 0.993346i \(0.463260\pi\)
\(74\) −50007.4 −1.06158
\(75\) −4337.75 21849.7i −0.0890454 0.448530i
\(76\) 3008.91i 0.0597551i
\(77\) 48769.3i 0.937388i
\(78\) 1409.71 279.865i 0.0262357 0.00520850i
\(79\) 37112.3i 0.669037i 0.942389 + 0.334519i \(0.108574\pi\)
−0.942389 + 0.334519i \(0.891426\pi\)
\(80\) 38402.5 0.670864
\(81\) 41815.8 41692.0i 0.708154 0.706058i
\(82\) −27152.6 −0.445940
\(83\) 65765.4 1.04786 0.523929 0.851762i \(-0.324466\pi\)
0.523929 + 0.851762i \(0.324466\pi\)
\(84\) 2740.07 543.978i 0.0423705 0.00841168i
\(85\) −76318.4 −1.14573
\(86\) −29831.3 −0.434937
\(87\) −26676.7 + 5296.05i −0.377863 + 0.0750160i
\(88\) 134925.i 1.85731i
\(89\) −107918. −1.44418 −0.722088 0.691801i \(-0.756818\pi\)
−0.722088 + 0.691801i \(0.756818\pi\)
\(90\) 20713.2 + 50111.1i 0.269551 + 0.652120i
\(91\) 1154.44i 0.0146139i
\(92\) −3944.50 5417.32i −0.0485873 0.0667291i
\(93\) 11878.4 + 59832.6i 0.142413 + 0.717349i
\(94\) −111177. −1.29777
\(95\) 46912.1i 0.533306i
\(96\) −14583.3 + 2895.18i −0.161502 + 0.0320625i
\(97\) 69228.0i 0.747055i −0.927619 0.373528i \(-0.878148\pi\)
0.927619 0.373528i \(-0.121852\pi\)
\(98\) 66126.0i 0.695516i
\(99\) 161430. 66726.3i 1.65537 0.684241i
\(100\) −3774.60 −0.0377460
\(101\) 18385.9i 0.179342i 0.995971 + 0.0896709i \(0.0285815\pi\)
−0.995971 + 0.0896709i \(0.971418\pi\)
\(102\) −153530. + 30479.9i −1.46115 + 0.290077i
\(103\) 3247.41i 0.0301608i 0.999886 + 0.0150804i \(0.00480043\pi\)
−0.999886 + 0.0150804i \(0.995200\pi\)
\(104\) 3193.86i 0.0289556i
\(105\) −42720.6 + 8481.20i −0.378150 + 0.0750731i
\(106\) 198706.i 1.71770i
\(107\) 34846.8 0.294241 0.147121 0.989119i \(-0.452999\pi\)
0.147121 + 0.989119i \(0.452999\pi\)
\(108\) −5549.58 8325.55i −0.0457826 0.0686837i
\(109\) 227445.i 1.83362i 0.399318 + 0.916812i \(0.369247\pi\)
−0.399318 + 0.916812i \(0.630753\pi\)
\(110\) 160401.i 1.26394i
\(111\) −141116. + 28015.3i −1.08710 + 0.215818i
\(112\) 63265.2i 0.476563i
\(113\) 29482.7 0.217206 0.108603 0.994085i \(-0.465362\pi\)
0.108603 + 0.994085i \(0.465362\pi\)
\(114\) −18735.7 94373.6i −0.135023 0.680124i
\(115\) 61499.1 + 84462.0i 0.433635 + 0.595548i
\(116\) 4608.48i 0.0317990i
\(117\) 3821.27 1579.50i 0.0258073 0.0106673i
\(118\) −162919. −1.07713
\(119\) 125729.i 0.813894i
\(120\) 118191. 23464.1i 0.749256 0.148748i
\(121\) 355672. 2.20845
\(122\) −164688. −1.00175
\(123\) −76621.8 + 15211.5i −0.456657 + 0.0906587i
\(124\) 10336.3 0.0603684
\(125\) 187545. 1.07357
\(126\) −82554.3 + 34123.4i −0.463248 + 0.191481i
\(127\) 218296. 1.20098 0.600491 0.799631i \(-0.294972\pi\)
0.600491 + 0.799631i \(0.294972\pi\)
\(128\) 159164.i 0.858658i
\(129\) −84180.9 + 16712.2i −0.445389 + 0.0884218i
\(130\) 3796.92i 0.0197049i
\(131\) 366952.i 1.86823i −0.356971 0.934116i \(-0.616190\pi\)
0.356971 0.934116i \(-0.383810\pi\)
\(132\) −5763.59 29031.7i −0.0287911 0.145023i
\(133\) 77284.2 0.378845
\(134\) 230984. 1.11127
\(135\) 86523.9 + 129804.i 0.408603 + 0.612992i
\(136\) 347841.i 1.61263i
\(137\) 126931. 0.577786 0.288893 0.957361i \(-0.406713\pi\)
0.288893 + 0.957361i \(0.406713\pi\)
\(138\) 157451. + 145351.i 0.703796 + 0.649713i
\(139\) 147020. 0.645416 0.322708 0.946499i \(-0.395407\pi\)
0.322708 + 0.946499i \(0.395407\pi\)
\(140\) 7380.13i 0.0318232i
\(141\) −313732. + 62284.2i −1.32896 + 0.263834i
\(142\) 232364. 0.967048
\(143\) 12231.6 0.0500198
\(144\) 209413. 86559.7i 0.841582 0.347864i
\(145\) 71851.3i 0.283801i
\(146\) 56823.2i 0.220619i
\(147\) 37045.3 + 186601.i 0.141397 + 0.712230i
\(148\) 24378.2i 0.0914844i
\(149\) 193942. 0.715660 0.357830 0.933787i \(-0.383517\pi\)
0.357830 + 0.933787i \(0.383517\pi\)
\(150\) 118389. 23503.5i 0.429620 0.0852912i
\(151\) −22344.9 −0.0797510 −0.0398755 0.999205i \(-0.512696\pi\)
−0.0398755 + 0.999205i \(0.512696\pi\)
\(152\) −213814. −0.750633
\(153\) −416172. + 172023.i −1.43729 + 0.594097i
\(154\) −264249. −0.897867
\(155\) −161154. −0.538779
\(156\) −136.432 687.221i −0.000448854 0.00226092i
\(157\) 139190.i 0.450670i 0.974281 + 0.225335i \(0.0723476\pi\)
−0.974281 + 0.225335i \(0.927652\pi\)
\(158\) −201088. −0.640830
\(159\) −111320. 560729.i −0.349205 1.75898i
\(160\) 39278.8i 0.121299i
\(161\) −139145. + 101315.i −0.423060 + 0.308042i
\(162\) 225902. + 226573.i 0.676290 + 0.678298i
\(163\) −128054. −0.377507 −0.188753 0.982025i \(-0.560445\pi\)
−0.188753 + 0.982025i \(0.560445\pi\)
\(164\) 13236.7i 0.0384299i
\(165\) 89860.6 + 452636.i 0.256956 + 1.29431i
\(166\) 356340.i 1.00368i
\(167\) 183367.i 0.508781i 0.967102 + 0.254391i \(0.0818749\pi\)
−0.967102 + 0.254391i \(0.918125\pi\)
\(168\) 38655.3 + 194711.i 0.105666 + 0.532251i
\(169\) −371003. −0.999220
\(170\) 413520.i 1.09742i
\(171\) −105741. 255816.i −0.276536 0.669019i
\(172\) 14542.5i 0.0374816i
\(173\) 343548.i 0.872716i 0.899773 + 0.436358i \(0.143732\pi\)
−0.899773 + 0.436358i \(0.856268\pi\)
\(174\) −28695.9 144544.i −0.0718532 0.361932i
\(175\) 96951.2i 0.239308i
\(176\) 670312. 1.63116
\(177\) −459741. + 91271.0i −1.10301 + 0.218978i
\(178\) 584740.i 1.38329i
\(179\) 185482.i 0.432684i −0.976318 0.216342i \(-0.930587\pi\)
0.976318 0.216342i \(-0.0694125\pi\)
\(180\) 24428.8 10097.5i 0.0561979 0.0232291i
\(181\) 667226.i 1.51383i −0.653514 0.756915i \(-0.726706\pi\)
0.653514 0.756915i \(-0.273294\pi\)
\(182\) −6255.15 −0.0139978
\(183\) −464732. + 92261.8i −1.02583 + 0.203655i
\(184\) 384958. 280298.i 0.838240 0.610346i
\(185\) 380082.i 0.816485i
\(186\) −324194. + 64361.3i −0.687105 + 0.136409i
\(187\) −1.33213e6 −2.78575
\(188\) 54198.1i 0.111838i
\(189\) −213843. + 142542.i −0.435453 + 0.290260i
\(190\) 254187. 0.510821
\(191\) 280522. 0.556396 0.278198 0.960524i \(-0.410263\pi\)
0.278198 + 0.960524i \(0.410263\pi\)
\(192\) −106266. 535272.i −0.208037 1.04790i
\(193\) 561191. 1.08447 0.542235 0.840227i \(-0.317578\pi\)
0.542235 + 0.840227i \(0.317578\pi\)
\(194\) 375102. 0.715559
\(195\) 2127.12 + 10714.5i 0.00400596 + 0.0201784i
\(196\) 32235.9 0.0599376
\(197\) 111595.i 0.204870i −0.994740 0.102435i \(-0.967337\pi\)
0.994740 0.102435i \(-0.0326633\pi\)
\(198\) 361547. + 874685.i 0.655393 + 1.58558i
\(199\) 60669.5i 0.108602i −0.998525 0.0543010i \(-0.982707\pi\)
0.998525 0.0543010i \(-0.0172930\pi\)
\(200\) 268225.i 0.474159i
\(201\) 651814. 129403.i 1.13798 0.225919i
\(202\) −99621.4 −0.171781
\(203\) 118370. 0.201605
\(204\) 14858.7 + 74844.8i 0.0249981 + 0.125918i
\(205\) 206374.i 0.342981i
\(206\) −17595.6 −0.0288892
\(207\) 525739. + 321960.i 0.852795 + 0.522246i
\(208\) 15867.2 0.0254298
\(209\) 818847.i 1.29669i
\(210\) −45954.2 231476.i −0.0719080 0.362207i
\(211\) −722950. −1.11790 −0.558949 0.829202i \(-0.688795\pi\)
−0.558949 + 0.829202i \(0.688795\pi\)
\(212\) −96867.7 −0.148026
\(213\) 655708. 130176.i 0.990288 0.196599i
\(214\) 188812.i 0.281836i
\(215\) 226734.i 0.334518i
\(216\) 591618. 394356.i 0.862793 0.575113i
\(217\) 265489.i 0.382734i
\(218\) −1.23238e6 −1.75632
\(219\) 31833.7 + 160349.i 0.0448515 + 0.225921i
\(220\) 78194.4 0.108923
\(221\) −31533.4 −0.0434300
\(222\) −151797. 764615.i −0.206719 1.04126i
\(223\) −868784. −1.16990 −0.584951 0.811068i \(-0.698886\pi\)
−0.584951 + 0.811068i \(0.698886\pi\)
\(224\) 64708.9 0.0861676
\(225\) 320915. 132649.i 0.422605 0.174682i
\(226\) 159748.i 0.208048i
\(227\) 783005. 1.00856 0.504278 0.863541i \(-0.331759\pi\)
0.504278 + 0.863541i \(0.331759\pi\)
\(228\) −46006.3 + 9133.51i −0.0586112 + 0.0116359i
\(229\) 375685.i 0.473408i 0.971582 + 0.236704i \(0.0760672\pi\)
−0.971582 + 0.236704i \(0.923933\pi\)
\(230\) −457645. + 333224.i −0.570439 + 0.415353i
\(231\) −745685. + 148039.i −0.919444 + 0.182535i
\(232\) −327481. −0.399454
\(233\) 1.40334e6i 1.69345i 0.532028 + 0.846727i \(0.321430\pi\)
−0.532028 + 0.846727i \(0.678570\pi\)
\(234\) 8558.31 + 20705.0i 0.0102176 + 0.0247193i
\(235\) 845008.i 0.998139i
\(236\) 79421.6i 0.0928237i
\(237\) −567449. + 112654.i −0.656230 + 0.130279i
\(238\) 681244. 0.779579
\(239\) 262619.i 0.297394i −0.988883 0.148697i \(-0.952492\pi\)
0.988883 0.148697i \(-0.0475078\pi\)
\(240\) 116570. + 587176.i 0.130635 + 0.658022i
\(241\) 54510.1i 0.0604552i −0.999543 0.0302276i \(-0.990377\pi\)
0.999543 0.0302276i \(-0.00962322\pi\)
\(242\) 1.92716e6i 2.11534i
\(243\) 764404. + 512810.i 0.830439 + 0.557110i
\(244\) 80283.9i 0.0863284i
\(245\) −502593. −0.534935
\(246\) −82421.4 415164.i −0.0868365 0.437404i
\(247\) 19383.2i 0.0202155i
\(248\) 734500.i 0.758337i
\(249\) 199630. + 1.00556e6i 0.204046 + 1.02780i
\(250\) 1.01619e6i 1.02831i
\(251\) −720999. −0.722354 −0.361177 0.932497i \(-0.617625\pi\)
−0.361177 + 0.932497i \(0.617625\pi\)
\(252\) 16634.9 + 40244.6i 0.0165013 + 0.0399214i
\(253\) 1.07346e6 + 1.47428e6i 1.05435 + 1.44803i
\(254\) 1.18281e6i 1.15035i
\(255\) −231664. 1.16691e6i −0.223104 1.12380i
\(256\) −257843. −0.245898
\(257\) 728645.i 0.688150i −0.938942 0.344075i \(-0.888193\pi\)
0.938942 0.344075i \(-0.111807\pi\)
\(258\) −90552.7 456122.i −0.0846939 0.426611i
\(259\) 626158. 0.580008
\(260\) 1850.97 0.00169811
\(261\) −161954. 391812.i −0.147160 0.356022i
\(262\) 1.98828e6 1.78947
\(263\) −932289. −0.831116 −0.415558 0.909567i \(-0.636414\pi\)
−0.415558 + 0.909567i \(0.636414\pi\)
\(264\) 2.06301e6 409563.i 1.82176 0.361669i
\(265\) 1.51027e6 1.32112
\(266\) 418754.i 0.362873i
\(267\) −327585. 1.65008e6i −0.281220 1.41653i
\(268\) 112603.i 0.0957663i
\(269\) 1.71866e6i 1.44814i −0.689727 0.724070i \(-0.742269\pi\)
0.689727 0.724070i \(-0.257731\pi\)
\(270\) −703327. + 468818.i −0.587148 + 0.391376i
\(271\) −254210. −0.210266 −0.105133 0.994458i \(-0.533527\pi\)
−0.105133 + 0.994458i \(0.533527\pi\)
\(272\) −1.72809e6 −1.41626
\(273\) −17651.4 + 3504.28i −0.0143342 + 0.00284572i
\(274\) 687759.i 0.553426i
\(275\) 1.02722e6 0.819093
\(276\) 70857.7 76755.9i 0.0559905 0.0606512i
\(277\) −1.61758e6 −1.26668 −0.633341 0.773873i \(-0.718317\pi\)
−0.633341 + 0.773873i \(0.718317\pi\)
\(278\) 796607.i 0.618204i
\(279\) −878786. + 363242.i −0.675885 + 0.279374i
\(280\) −524435. −0.399758
\(281\) 2.17180e6 1.64080 0.820398 0.571793i \(-0.193752\pi\)
0.820398 + 0.571793i \(0.193752\pi\)
\(282\) −337478. 1.69991e6i −0.252710 1.27293i
\(283\) 836177.i 0.620629i 0.950634 + 0.310314i \(0.100434\pi\)
−0.950634 + 0.310314i \(0.899566\pi\)
\(284\) 113276.i 0.0833375i
\(285\) 717289. 142401.i 0.523097 0.103849i
\(286\) 66274.9i 0.0479109i
\(287\) 339986. 0.243644
\(288\) −88534.9 214191.i −0.0628975 0.152167i
\(289\) 2.01442e6 1.41875
\(290\) 389316. 0.271836
\(291\) 1.05850e6 210141.i 0.732755 0.145472i
\(292\) 27700.8 0.0190124
\(293\) −762605. −0.518956 −0.259478 0.965749i \(-0.583550\pi\)
−0.259478 + 0.965749i \(0.583550\pi\)
\(294\) −1.01107e6 + 200725.i −0.682202 + 0.135436i
\(295\) 1.23827e6i 0.828438i
\(296\) −1.73233e6 −1.14921
\(297\) 1.51027e6 + 2.26572e6i 0.993488 + 1.49045i
\(298\) 1.05085e6i 0.685487i
\(299\) 25410.3 + 34898.1i 0.0164374 + 0.0225748i
\(300\) −11457.8 57713.8i −0.00735015 0.0370234i
\(301\) 373527. 0.237632
\(302\) 121073.i 0.0763887i
\(303\) −281121. + 55810.2i −0.175909 + 0.0349226i
\(304\) 1.06224e6i 0.659231i
\(305\) 1.25171e6i 0.770469i
\(306\) −932080. 2.25497e6i −0.569049 1.37669i
\(307\) −2.20009e6 −1.33228 −0.666139 0.745827i \(-0.732054\pi\)
−0.666139 + 0.745827i \(0.732054\pi\)
\(308\) 128819.i 0.0773757i
\(309\) −49653.0 + 9857.47i −0.0295835 + 0.00587312i
\(310\) 873188.i 0.516064i
\(311\) 1.36064e6i 0.797702i −0.917016 0.398851i \(-0.869409\pi\)
0.917016 0.398851i \(-0.130591\pi\)
\(312\) 48834.3 9694.93i 0.0284013 0.00563843i
\(313\) 173231.i 0.0999460i 0.998751 + 0.0499730i \(0.0159135\pi\)
−0.998751 + 0.0499730i \(0.984086\pi\)
\(314\) −754181. −0.431669
\(315\) −259356. 627456.i −0.147272 0.356293i
\(316\) 98028.7i 0.0552250i
\(317\) 2.83762e6i 1.58601i 0.609214 + 0.793006i \(0.291485\pi\)
−0.609214 + 0.793006i \(0.708515\pi\)
\(318\) 3.03823e6 603171.i 1.68482 0.334482i
\(319\) 1.25416e6i 0.690042i
\(320\) 1.44171e6 0.787049
\(321\) 105777. + 532809.i 0.0572966 + 0.288609i
\(322\) −548962. 753936.i −0.295055 0.405224i
\(323\) 2.11102e6i 1.12586i
\(324\) 110452. 110125.i 0.0584538 0.0582808i
\(325\) 24315.8 0.0127697
\(326\) 693844.i 0.361591i
\(327\) −3.47765e6 + 690408.i −1.79852 + 0.357056i
\(328\) −940603. −0.482750
\(329\) 1.39209e6 0.709050
\(330\) −2.45255e6 + 486897.i −1.23974 + 0.246123i
\(331\) −22793.4 −0.0114351 −0.00571755 0.999984i \(-0.501820\pi\)
−0.00571755 + 0.999984i \(0.501820\pi\)
\(332\) 173713. 0.0864942
\(333\) −856711. 2.07263e6i −0.423373 1.02426i
\(334\) −993550. −0.487331
\(335\) 1.75560e6i 0.854700i
\(336\) −967329. + 192041.i −0.467440 + 0.0927995i
\(337\) 399386.i 0.191566i 0.995402 + 0.0957829i \(0.0305355\pi\)
−0.995402 + 0.0957829i \(0.969465\pi\)
\(338\) 2.01023e6i 0.957092i
\(339\) 89494.5 + 450792.i 0.0422958 + 0.213048i
\(340\) −201588. −0.0945729
\(341\) −2.81292e6 −1.31000
\(342\) 1.38611e6 572940.i 0.640812 0.264877i
\(343\) 1.96825e6i 0.903328i
\(344\) −1.03340e6 −0.470838
\(345\) −1.10475e6 + 1.19671e6i −0.499707 + 0.541303i
\(346\) −1.86147e6 −0.835921
\(347\) 1.58642e6i 0.707287i −0.935380 0.353644i \(-0.884943\pi\)
0.935380 0.353644i \(-0.115057\pi\)
\(348\) −70464.0 + 13989.0i −0.0311903 + 0.00619211i
\(349\) −932063. −0.409620 −0.204810 0.978802i \(-0.565658\pi\)
−0.204810 + 0.978802i \(0.565658\pi\)
\(350\) −525316. −0.229219
\(351\) 35750.1 + 53632.8i 0.0154885 + 0.0232361i
\(352\) 685608.i 0.294930i
\(353\) 1.30567e6i 0.557696i −0.960335 0.278848i \(-0.910047\pi\)
0.960335 0.278848i \(-0.0899526\pi\)
\(354\) −494539. 2.49104e6i −0.209745 1.05651i
\(355\) 1.76609e6i 0.743776i
\(356\) −285056. −0.119208
\(357\) 1.92240e6 381649.i 0.798314 0.158487i
\(358\) 1.00501e6 0.414441
\(359\) 2.20403e6 0.902569 0.451285 0.892380i \(-0.350966\pi\)
0.451285 + 0.892380i \(0.350966\pi\)
\(360\) 717534. + 1.73592e6i 0.291801 + 0.705949i
\(361\) 1.17848e6 0.475942
\(362\) 3.61527e6 1.45000
\(363\) 1.07964e6 + 5.43825e6i 0.430044 + 2.16617i
\(364\) 3049.33i 0.00120629i
\(365\) −431886. −0.169683
\(366\) −499908. 2.51808e6i −0.195068 0.982578i
\(367\) 3.53355e6i 1.36945i −0.728802 0.684725i \(-0.759922\pi\)
0.728802 0.684725i \(-0.240078\pi\)
\(368\) 1.39253e6 + 1.91248e6i 0.536026 + 0.736170i
\(369\) −465170. 1.12538e6i −0.177847 0.430261i
\(370\) 2.05942e6 0.782062
\(371\) 2.48806e6i 0.938483i
\(372\) 31375.6 + 158042.i 0.0117553 + 0.0592128i
\(373\) 4.42433e6i 1.64655i 0.567642 + 0.823275i \(0.307856\pi\)
−0.567642 + 0.823275i \(0.692144\pi\)
\(374\) 7.21796e6i 2.66830i
\(375\) 569291. + 2.86757e6i 0.209053 + 1.05302i
\(376\) −3.85134e6 −1.40489
\(377\) 29687.6i 0.0107578i
\(378\) −772342. 1.15868e6i −0.278023 0.417094i
\(379\) 4.48833e6i 1.60504i 0.596623 + 0.802522i \(0.296509\pi\)
−0.596623 + 0.802522i \(0.703491\pi\)
\(380\) 123914.i 0.0440211i
\(381\) 662635. + 3.33776e6i 0.233863 + 1.17799i
\(382\) 1.51997e6i 0.532938i
\(383\) −781954. −0.272386 −0.136193 0.990682i \(-0.543487\pi\)
−0.136193 + 0.990682i \(0.543487\pi\)
\(384\) 2.43363e6 483141.i 0.842221 0.167204i
\(385\) 2.00844e6i 0.690567i
\(386\) 3.04073e6i 1.03875i
\(387\) −511061. 1.23640e6i −0.173458 0.419645i
\(388\) 182859.i 0.0616648i
\(389\) −3.16228e6 −1.05956 −0.529780 0.848135i \(-0.677726\pi\)
−0.529780 + 0.848135i \(0.677726\pi\)
\(390\) −58055.1 + 11525.5i −0.0193277 + 0.00383706i
\(391\) −2.76742e6 3.80073e6i −0.915447 1.25726i
\(392\) 2.29070e6i 0.752926i
\(393\) 5.61071e6 1.11388e6i 1.83247 0.363795i
\(394\) 604660. 0.196232
\(395\) 1.52837e6i 0.492875i
\(396\) 426402. 176251.i 0.136641 0.0564799i
\(397\) 2.47813e6 0.789129 0.394564 0.918868i \(-0.370896\pi\)
0.394564 + 0.918868i \(0.370896\pi\)
\(398\) 328729. 0.104023
\(399\) 234596. + 1.18168e6i 0.0737713 + 0.371593i
\(400\) 1.33255e6 0.416422
\(401\) 993255. 0.308461 0.154230 0.988035i \(-0.450710\pi\)
0.154230 + 0.988035i \(0.450710\pi\)
\(402\) 701150. + 3.53176e6i 0.216394 + 1.09000i
\(403\) −66585.7 −0.0204230
\(404\) 48564.6i 0.0148036i
\(405\) −1.72207e6 + 1.71698e6i −0.521692 + 0.520148i
\(406\) 641369.i 0.193105i
\(407\) 6.63430e6i 1.98522i
\(408\) −5.31851e6 + 1.05587e6i −1.58176 + 0.314021i
\(409\) 69730.4 0.0206117 0.0103059 0.999947i \(-0.496719\pi\)
0.0103059 + 0.999947i \(0.496719\pi\)
\(410\) 1.11821e6 0.328521
\(411\) 385298. + 1.94079e6i 0.112510 + 0.566726i
\(412\) 8577.71i 0.00248959i
\(413\) 2.03996e6 0.588499
\(414\) −1.74449e6 + 2.84864e6i −0.500228 + 0.816840i
\(415\) −2.70837e6 −0.771949
\(416\) 16229.3i 0.00459797i
\(417\) 446278. + 2.24794e6i 0.125680 + 0.633061i
\(418\) 4.43681e6 1.24202
\(419\) 4.63224e6 1.28901 0.644504 0.764601i \(-0.277064\pi\)
0.644504 + 0.764601i \(0.277064\pi\)
\(420\) −112843. + 22402.3i −0.0312140 + 0.00619683i
\(421\) 355118.i 0.0976490i −0.998807 0.0488245i \(-0.984453\pi\)
0.998807 0.0488245i \(-0.0155475\pi\)
\(422\) 3.91720e6i 1.07077i
\(423\) −1.90466e6 4.60791e6i −0.517566 1.25214i
\(424\) 6.88347e6i 1.85948i
\(425\) −2.64822e6 −0.711183
\(426\) 705339. + 3.55286e6i 0.188310 + 0.948537i
\(427\) 2.06210e6 0.547319
\(428\) 92044.5 0.0242878
\(429\) 37128.8 + 187021.i 0.00974019 + 0.0490623i
\(430\) 1.22852e6 0.320415
\(431\) −1.55734e6 −0.403823 −0.201912 0.979404i \(-0.564715\pi\)
−0.201912 + 0.979404i \(0.564715\pi\)
\(432\) 1.95917e6 + 2.93918e6i 0.505084 + 0.757734i
\(433\) 5.82917e6i 1.49412i 0.664754 + 0.747062i \(0.268536\pi\)
−0.664754 + 0.747062i \(0.731464\pi\)
\(434\) 1.43851e6 0.366597
\(435\) 1.09861e6 218104.i 0.278369 0.0552637i
\(436\) 600775.i 0.151355i
\(437\) 2.33627e6 1.70110e6i 0.585221 0.426116i
\(438\) −868830. + 172486.i −0.216396 + 0.0429605i
\(439\) 2.18077e6 0.540067 0.270034 0.962851i \(-0.412965\pi\)
0.270034 + 0.962851i \(0.412965\pi\)
\(440\) 5.55653e6i 1.36827i
\(441\) −2.74069e6 + 1.13285e6i −0.671063 + 0.277381i
\(442\) 170859.i 0.0415989i
\(443\) 3.48490e6i 0.843687i −0.906669 0.421844i \(-0.861383\pi\)
0.906669 0.421844i \(-0.138617\pi\)
\(444\) −372744. + 73999.7i −0.0897332 + 0.0178145i
\(445\) 4.44434e6 1.06391
\(446\) 4.70738e6i 1.12058i
\(447\) 588710. + 2.96539e6i 0.139358 + 0.701961i
\(448\) 2.37510e6i 0.559098i
\(449\) 3.61570e6i 0.846401i 0.906036 + 0.423201i \(0.139093\pi\)
−0.906036 + 0.423201i \(0.860907\pi\)
\(450\) 718739. + 1.73883e6i 0.167317 + 0.404787i
\(451\) 3.60224e6i 0.833933i
\(452\) 77875.8 0.0179290
\(453\) −67827.8 341655.i −0.0155297 0.0782244i
\(454\) 4.24260e6i 0.966034i
\(455\) 47542.4i 0.0107660i
\(456\) −649031. 3.26923e6i −0.146168 0.736264i
\(457\) 4.19748e6i 0.940153i 0.882626 + 0.470076i \(0.155774\pi\)
−0.882626 + 0.470076i \(0.844226\pi\)
\(458\) −2.03560e6 −0.453449
\(459\) −3.89352e6 5.84112e6i −0.862603 1.29409i
\(460\) 162444. + 223098.i 0.0357939 + 0.0491588i
\(461\) 8.43215e6i 1.84793i 0.382474 + 0.923966i \(0.375072\pi\)
−0.382474 + 0.923966i \(0.624928\pi\)
\(462\) −802126. 4.04039e6i −0.174839 0.880680i
\(463\) 4.96492e6 1.07636 0.538182 0.842828i \(-0.319111\pi\)
0.538182 + 0.842828i \(0.319111\pi\)
\(464\) 1.62694e6i 0.350813i
\(465\) −489180. 2.46405e6i −0.104915 0.528466i
\(466\) −7.60380e6 −1.62206
\(467\) −4.73084e6 −1.00380 −0.501898 0.864927i \(-0.667365\pi\)
−0.501898 + 0.864927i \(0.667365\pi\)
\(468\) 10093.5 4172.11i 0.00213024 0.000880523i
\(469\) −2.89222e6 −0.607155
\(470\) 4.57855e6 0.956057
\(471\) −2.12822e6 + 422510.i −0.442043 + 0.0877575i
\(472\) −5.64374e6 −1.16604
\(473\) 3.95762e6i 0.813356i
\(474\) −610400. 3.07464e6i −0.124787 0.628563i
\(475\) 1.62783e6i 0.331036i
\(476\) 332101.i 0.0671820i
\(477\) 8.23567e6 3.40418e6i 1.65731 0.685040i
\(478\) 1.42296e6 0.284855
\(479\) 7.96225e6 1.58561 0.792807 0.609473i \(-0.208619\pi\)
0.792807 + 0.609473i \(0.208619\pi\)
\(480\) 600575. 119230.i 0.118977 0.0236202i
\(481\) 157043.i 0.0309497i
\(482\) 295355. 0.0579064
\(483\) −1.97149e6 1.81999e6i −0.384527 0.354978i
\(484\) 939475. 0.182294
\(485\) 2.85098e6i 0.550350i
\(486\) −2.77859e6 + 4.14182e6i −0.533622 + 0.795427i
\(487\) −7.38263e6 −1.41055 −0.705276 0.708933i \(-0.749177\pi\)
−0.705276 + 0.708933i \(0.749177\pi\)
\(488\) −5.70501e6 −1.08444
\(489\) −388707. 1.95796e6i −0.0735107 0.370281i
\(490\) 2.72323e6i 0.512382i
\(491\) 8.19011e6i 1.53315i −0.642152 0.766577i \(-0.721958\pi\)
0.642152 0.766577i \(-0.278042\pi\)
\(492\) −202389. + 40179.8i −0.0376942 + 0.00748332i
\(493\) 3.23326e6i 0.599133i
\(494\) 105025. 0.0193632
\(495\) −6.64807e6 + 2.74795e6i −1.21950 + 0.504075i
\(496\) −3.64902e6 −0.665997
\(497\) −2.90950e6 −0.528357
\(498\) −5.44846e6 + 1.08167e6i −0.984466 + 0.195443i
\(499\) 4.71417e6 0.847527 0.423764 0.905773i \(-0.360709\pi\)
0.423764 + 0.905773i \(0.360709\pi\)
\(500\) 495382. 0.0886167
\(501\) −2.80370e6 + 556610.i −0.499042 + 0.0990733i
\(502\) 3.90663e6i 0.691899i
\(503\) −4.20494e6 −0.741037 −0.370518 0.928825i \(-0.620820\pi\)
−0.370518 + 0.928825i \(0.620820\pi\)
\(504\) −2.85980e6 + 1.18208e6i −0.501486 + 0.207287i
\(505\) 757175.i 0.132120i
\(506\) −7.98815e6 + 5.81640e6i −1.38698 + 1.00990i
\(507\) −1.12618e6 5.67266e6i −0.194575 0.980093i
\(508\) 576608. 0.0991338
\(509\) 1.13142e7i 1.93567i 0.251595 + 0.967833i \(0.419045\pi\)
−0.251595 + 0.967833i \(0.580955\pi\)
\(510\) 6.32275e6 1.25524e6i 1.07642 0.213698i
\(511\) 711501.i 0.120538i
\(512\) 6.49034e6i 1.09419i
\(513\) 3.59047e6 2.39331e6i 0.602363 0.401518i
\(514\) 3.94806e6 0.659137
\(515\) 133736.i 0.0222193i
\(516\) −222356. + 44143.7i −0.0367641 + 0.00729868i
\(517\) 1.47495e7i 2.42690i
\(518\) 3.39275e6i 0.555555i
\(519\) −5.25287e6 + 1.04284e6i −0.856010 + 0.169941i
\(520\) 131531.i 0.0213314i
\(521\) 6.03040e6 0.973311 0.486656 0.873594i \(-0.338217\pi\)
0.486656 + 0.873594i \(0.338217\pi\)
\(522\) 2.12298e6 877523.i 0.341012 0.140956i
\(523\) 7.18045e6i 1.14788i 0.818897 + 0.573941i \(0.194586\pi\)
−0.818897 + 0.573941i \(0.805414\pi\)
\(524\) 969268.i 0.154211i
\(525\) −1.48239e6 + 294294.i −0.234727 + 0.0465998i
\(526\) 5.05148e6i 0.796075i
\(527\) 7.25181e6 1.13742
\(528\) 2.03473e6 + 1.02491e7i 0.317630 + 1.59993i
\(529\) −1.97624e6 + 6.12544e6i −0.307044 + 0.951695i
\(530\) 8.18320e6i 1.26542i
\(531\) −2.79108e6 6.75241e6i −0.429571 1.03926i
\(532\) 204139. 0.0312714
\(533\) 85270.0i 0.0130010i
\(534\) 8.94071e6 1.77497e6i 1.35681 0.269363i
\(535\) −1.43507e6 −0.216765
\(536\) 8.00162e6 1.20300
\(537\) 2.83604e6 563030.i 0.424401 0.0842551i
\(538\) 9.31234e6 1.38708
\(539\) −8.77271e6 −1.30065
\(540\) 228545. + 342866.i 0.0337277 + 0.0505988i
\(541\) −5.52819e6 −0.812063 −0.406032 0.913859i \(-0.633088\pi\)
−0.406032 + 0.913859i \(0.633088\pi\)
\(542\) 1.37740e6i 0.201401i
\(543\) 1.02019e7 2.02536e6i 1.48485 0.294783i
\(544\) 1.76752e6i 0.256075i
\(545\) 9.36673e6i 1.35082i
\(546\) −18987.4 95641.5i −0.00272574 0.0137298i
\(547\) −9.72255e6 −1.38935 −0.694675 0.719324i \(-0.744452\pi\)
−0.694675 + 0.719324i \(0.744452\pi\)
\(548\) 335277. 0.0476927
\(549\) −2.82138e6 6.82571e6i −0.399512 0.966534i
\(550\) 5.56586e6i 0.784559i
\(551\) −1.98745e6 −0.278880
\(552\) 5.45431e6 + 5.03518e6i 0.761890 + 0.703343i
\(553\) 2.51788e6 0.350125
\(554\) 8.76465e6i 1.21328i
\(555\) 5.81148e6 1.15374e6i 0.800856 0.158992i
\(556\) 388339. 0.0532751
\(557\) −7.29824e6 −0.996736 −0.498368 0.866966i \(-0.666067\pi\)
−0.498368 + 0.866966i \(0.666067\pi\)
\(558\) −1.96818e6 4.76158e6i −0.267595 0.647389i
\(559\) 93682.2i 0.0126802i
\(560\) 2.60541e6i 0.351080i
\(561\) −4.04367e6 2.03684e7i −0.542461 2.73243i
\(562\) 1.17676e7i 1.57162i
\(563\) 1.13785e7 1.51291 0.756457 0.654043i \(-0.226928\pi\)
0.756457 + 0.654043i \(0.226928\pi\)
\(564\) −828692. + 164518.i −0.109697 + 0.0217779i
\(565\) −1.21417e6 −0.160014
\(566\) −4.53070e6 −0.594463
\(567\) −2.82859e6 2.83699e6i −0.369498 0.370595i
\(568\) 8.04942e6 1.04687
\(569\) −1.31430e7 −1.70182 −0.850909 0.525313i \(-0.823948\pi\)
−0.850909 + 0.525313i \(0.823948\pi\)
\(570\) 771581. + 3.88653e6i 0.0994705 + 0.501043i
\(571\) 7.25737e6i 0.931513i −0.884913 0.465757i \(-0.845782\pi\)
0.884913 0.465757i \(-0.154218\pi\)
\(572\) 32308.5 0.00412883
\(573\) 851523. + 4.28920e6i 0.108345 + 0.545745i
\(574\) 1.84216e6i 0.233372i
\(575\) 2.13399e6 + 2.93080e6i 0.269168 + 0.369671i
\(576\) 7.86177e6 3.24962e6i 0.987334 0.408110i
\(577\) −6.61354e6 −0.826979 −0.413490 0.910509i \(-0.635690\pi\)
−0.413490 + 0.910509i \(0.635690\pi\)
\(578\) 1.09149e7i 1.35893i
\(579\) 1.70349e6 + 8.58064e6i 0.211175 + 1.06371i
\(580\) 189788.i 0.0234261i
\(581\) 4.46185e6i 0.548371i
\(582\) 1.13862e6 + 5.73533e6i 0.139338 + 0.701861i
\(583\) 2.63617e7 3.21219
\(584\) 1.96844e6i 0.238830i
\(585\) −157369. + 65047.7i −0.0190121 + 0.00785855i
\(586\) 4.13206e6i 0.497076i
\(587\) 1.11235e7i 1.33244i 0.745756 + 0.666219i \(0.232088\pi\)
−0.745756 + 0.666219i \(0.767912\pi\)
\(588\) 97851.7 + 492888.i 0.0116715 + 0.0587903i
\(589\) 4.45761e6i 0.529437i
\(590\) 6.70939e6 0.793511
\(591\) 1.70629e6 338744.i 0.200948 0.0398936i
\(592\) 8.60626e6i 1.00928i
\(593\) 1.11287e7i 1.29959i 0.760110 + 0.649795i \(0.225145\pi\)
−0.760110 + 0.649795i \(0.774855\pi\)
\(594\) −1.22765e7 + 8.18317e6i −1.42761 + 0.951602i
\(595\) 5.17781e6i 0.599590i
\(596\) 512280. 0.0590734
\(597\) 927640. 184162.i 0.106523 0.0211477i
\(598\) −189091. + 137682.i −0.0216231 + 0.0157443i
\(599\) 9.52232e6i 1.08437i 0.840261 + 0.542183i \(0.182402\pi\)
−0.840261 + 0.542183i \(0.817598\pi\)
\(600\) 4.10117e6 814194.i 0.465082 0.0923314i
\(601\) 6.82958e6 0.771272 0.385636 0.922651i \(-0.373982\pi\)
0.385636 + 0.922651i \(0.373982\pi\)
\(602\) 2.02390e6i 0.227614i
\(603\) 3.95715e6 + 9.57347e6i 0.443189 + 1.07220i
\(604\) −59022.0 −0.00658296
\(605\) −1.46474e7 −1.62695
\(606\) −302400. 1.52322e6i −0.0334503 0.168492i
\(607\) −1.59142e7 −1.75312 −0.876562 0.481290i \(-0.840169\pi\)
−0.876562 + 0.481290i \(0.840169\pi\)
\(608\) −1.08648e6 −0.119196
\(609\) 359310. + 1.80988e6i 0.0392578 + 0.197745i
\(610\) 6.78223e6 0.737985
\(611\) 349142.i 0.0378354i
\(612\) −1.09928e6 + 454382.i −0.118639 + 0.0490391i
\(613\) 508854.i 0.0546943i 0.999626 + 0.0273471i \(0.00870595\pi\)
−0.999626 + 0.0273471i \(0.991294\pi\)
\(614\) 1.19209e7i 1.27611i
\(615\) 3.15547e6 626446.i 0.336416 0.0667876i
\(616\) −9.15397e6 −0.971981
\(617\) −7.01562e6 −0.741913 −0.370957 0.928650i \(-0.620970\pi\)
−0.370957 + 0.928650i \(0.620970\pi\)
\(618\) −53411.3 269038.i −0.00562551 0.0283362i
\(619\) 7.74825e6i 0.812788i −0.913698 0.406394i \(-0.866786\pi\)
0.913698 0.406394i \(-0.133214\pi\)
\(620\) −425672. −0.0444729
\(621\) −3.32690e6 + 9.01589e6i −0.346187 + 0.938165i
\(622\) 7.37241e6 0.764071
\(623\) 7.32171e6i 0.755775i
\(624\) 48164.8 + 242610.i 0.00495185 + 0.0249430i
\(625\) −3.25789e6 −0.333608
\(626\) −938629. −0.0957322
\(627\) 1.25202e7 2.48560e6i 1.27187 0.252501i
\(628\) 367657.i 0.0372001i
\(629\) 1.71035e7i 1.72368i
\(630\) 3.39978e6 1.40528e6i 0.341271 0.141063i
\(631\) 6.56263e6i 0.656152i −0.944651 0.328076i \(-0.893600\pi\)
0.944651 0.328076i \(-0.106400\pi\)
\(632\) −6.96596e6 −0.693727
\(633\) −2.19451e6 1.10539e7i −0.217685 1.09650i
\(634\) −1.53752e7 −1.51914
\(635\) −8.98995e6 −0.884755
\(636\) −294041. 1.48111e6i −0.0288247 0.145193i
\(637\) −207662. −0.0202772
\(638\) 6.79547e6 0.660949
\(639\) 3.98079e6 + 9.63067e6i 0.385671 + 0.933048i
\(640\) 6.55476e6i 0.632567i
\(641\) 1.76495e7 1.69663 0.848316 0.529490i \(-0.177617\pi\)
0.848316 + 0.529490i \(0.177617\pi\)
\(642\) −2.88695e6 + 573138.i −0.276441 + 0.0548809i
\(643\) 1.16866e7i 1.11470i 0.830277 + 0.557351i \(0.188182\pi\)
−0.830277 + 0.557351i \(0.811818\pi\)
\(644\) −367538. + 267615.i −0.0349211 + 0.0254270i
\(645\) 3.46677e6 688248.i 0.328115 0.0651397i
\(646\) −1.14382e7 −1.07839
\(647\) 3.55429e6i 0.333805i 0.985973 + 0.166902i \(0.0533764\pi\)
−0.985973 + 0.166902i \(0.946624\pi\)
\(648\) 7.82557e6 + 7.84881e6i 0.732113 + 0.734287i
\(649\) 2.16139e7i 2.01429i
\(650\) 131752.i 0.0122313i
\(651\) 4.05933e6 805888.i 0.375407 0.0745285i
\(652\) −338243. −0.0311609
\(653\) 6.10634e6i 0.560400i −0.959942 0.280200i \(-0.909599\pi\)
0.959942 0.280200i \(-0.0904007\pi\)
\(654\) −3.74087e6 1.88431e7i −0.342002 1.72270i
\(655\) 1.51119e7i 1.37631i
\(656\) 4.67295e6i 0.423967i
\(657\) −2.35512e6 + 973478.i −0.212863 + 0.0879858i
\(658\) 7.54283e6i 0.679156i
\(659\) −1.03682e7 −0.930015 −0.465008 0.885307i \(-0.653948\pi\)
−0.465008 + 0.885307i \(0.653948\pi\)
\(660\) 237358. + 1.19560e6i 0.0212102 + 0.106838i
\(661\) 1.12713e7i 1.00339i −0.865043 0.501697i \(-0.832709\pi\)
0.865043 0.501697i \(-0.167291\pi\)
\(662\) 123503.i 0.0109530i
\(663\) −95719.2 482147.i −0.00845698 0.0425986i
\(664\) 1.23441e7i 1.08653i
\(665\) −3.18275e6 −0.279093
\(666\) 1.12302e7 4.64196e6i 0.981077 0.405524i
\(667\) 3.57827e6 2.60544e6i 0.311428 0.226760i
\(668\) 484348.i 0.0419968i
\(669\) −2.63719e6 1.32838e7i −0.227811 1.14751i
\(670\) −9.51248e6 −0.818666
\(671\) 2.18485e7i 1.87334i
\(672\) 196423. + 989403.i 0.0167791 + 0.0845181i
\(673\) 1.22876e7 1.04576 0.522878 0.852407i \(-0.324858\pi\)
0.522878 + 0.852407i \(0.324858\pi\)
\(674\) −2.16402e6 −0.183489
\(675\) 3.00234e6 + 4.50416e6i 0.253630 + 0.380500i
\(676\) −979970. −0.0824795
\(677\) 1.93499e7 1.62259 0.811293 0.584639i \(-0.198764\pi\)
0.811293 + 0.584639i \(0.198764\pi\)
\(678\) −2.44255e6 + 484913.i −0.204066 + 0.0405126i
\(679\) −4.69677e6 −0.390953
\(680\) 1.43249e7i 1.18801i
\(681\) 2.37680e6 + 1.19722e7i 0.196393 + 0.989249i
\(682\) 1.52414e7i 1.25477i
\(683\) 1.67467e7i 1.37365i −0.726822 0.686826i \(-0.759004\pi\)
0.726822 0.686826i \(-0.240996\pi\)
\(684\) −279304. 675715.i −0.0228263 0.0552234i
\(685\) −5.22733e6 −0.425651
\(686\) 1.06647e7 0.865243
\(687\) −5.74425e6 + 1.14039e6i −0.464346 + 0.0921852i
\(688\) 5.13396e6i 0.413506i
\(689\) 624017. 0.0500782
\(690\) −6.48419e6 5.98592e6i −0.518481 0.478639i
\(691\) 5.86496e6 0.467272 0.233636 0.972324i \(-0.424938\pi\)
0.233636 + 0.972324i \(0.424938\pi\)
\(692\) 907451.i 0.0720374i
\(693\) −4.52704e6 1.09522e7i −0.358081 0.866300i
\(694\) 8.59582e6 0.677467
\(695\) −6.05463e6 −0.475473
\(696\) −994066. 5.00720e6i −0.0777843 0.391807i
\(697\) 9.28669e6i 0.724068i
\(698\) 5.05025e6i 0.392351i
\(699\) −2.14572e7 + 4.25983e6i −1.66104 + 0.329761i
\(700\) 256087.i 0.0197534i
\(701\) 5.62134e6 0.432061 0.216030 0.976387i \(-0.430689\pi\)
0.216030 + 0.976387i \(0.430689\pi\)
\(702\) −290602. + 193707.i −0.0222564 + 0.0148355i
\(703\) −1.05133e7 −0.802328
\(704\) 2.51649e7 1.91365
\(705\) 1.29202e7 2.56501e6i 0.979032 0.194364i
\(706\) 7.07460e6 0.534183
\(707\) 1.24739e6 0.0938542
\(708\) −1.21436e6 + 241084.i −0.0910468 + 0.0180753i
\(709\) 2.00990e7i 1.50162i 0.660520 + 0.750809i \(0.270336\pi\)
−0.660520 + 0.750809i \(0.729664\pi\)
\(710\) −9.56931e6 −0.712418
\(711\) −3.44497e6 8.33437e6i −0.255571 0.618300i
\(712\) 2.02562e7i 1.49747i
\(713\) −5.84367e6 8.02561e6i −0.430489 0.591227i
\(714\) 2.06791e6 + 1.04163e7i 0.151805 + 0.764656i
\(715\) −503725. −0.0368492
\(716\) 489934.i 0.0357154i
\(717\) 4.01546e6 797178.i 0.291701 0.0579105i
\(718\) 1.19422e7i 0.864516i
\(719\) 2.86471e6i 0.206661i 0.994647 + 0.103330i \(0.0329499\pi\)
−0.994647 + 0.103330i \(0.967050\pi\)
\(720\) −8.62411e6 + 3.56473e6i −0.619988 + 0.256269i
\(721\) 220320. 0.0157839
\(722\) 6.38542e6i 0.455876i
\(723\) 833462. 165465.i 0.0592980 0.0117723i
\(724\) 1.76242e6i 0.124957i
\(725\) 2.49321e6i 0.176163i
\(726\) −2.94664e7 + 5.84988e6i −2.07484 + 0.411913i
\(727\) 1.23443e7i 0.866224i −0.901340 0.433112i \(-0.857415\pi\)
0.901340 0.433112i \(-0.142585\pi\)
\(728\) −216687. −0.0151532
\(729\) −5.52056e6 + 1.32444e7i −0.384737 + 0.923026i
\(730\) 2.34011e6i 0.162529i
\(731\) 1.02029e7i 0.706202i
\(732\) −1.22754e6 + 243701.i −0.0846759 + 0.0168104i
\(733\) 2.73775e7i 1.88206i −0.338322 0.941030i \(-0.609859\pi\)
0.338322 0.941030i \(-0.390141\pi\)
\(734\) 1.91460e7 1.31171
\(735\) −1.52561e6 7.68467e6i −0.104166 0.524695i
\(736\) 1.95612e6 1.42431e6i 0.133107 0.0969192i
\(737\) 3.06439e7i 2.07814i
\(738\) 6.09770e6 2.52045e6i 0.412121 0.170348i
\(739\) 1.27646e7 0.859794 0.429897 0.902878i \(-0.358550\pi\)
0.429897 + 0.902878i \(0.358550\pi\)
\(740\) 1.00395e6i 0.0673959i
\(741\) 296371. 58837.6i 0.0198285 0.00393649i
\(742\) −1.34812e7 −0.898916
\(743\) 1.30516e7 0.867346 0.433673 0.901070i \(-0.357217\pi\)
0.433673 + 0.901070i \(0.357217\pi\)
\(744\) −1.12305e7 + 2.22957e6i −0.743821 + 0.147669i
\(745\) −7.98700e6 −0.527222
\(746\) −2.39726e7 −1.57713
\(747\) −1.47690e7 + 6.10471e6i −0.968391 + 0.400280i
\(748\) −3.51870e6 −0.229947
\(749\) 2.36418e6i 0.153984i
\(750\) −1.55375e7 + 3.08462e6i −1.00862 + 0.200239i
\(751\) 1.49278e7i 0.965817i 0.875671 + 0.482909i \(0.160420\pi\)
−0.875671 + 0.482909i \(0.839580\pi\)
\(752\) 1.91336e7i 1.23382i
\(753\) −2.18859e6 1.10241e7i −0.140662 0.708527i
\(754\) 160858. 0.0103042
\(755\) 920217. 0.0587520
\(756\) −564846. + 376510.i −0.0359440 + 0.0239592i
\(757\) 8.72424e6i 0.553335i 0.960966 + 0.276667i \(0.0892300\pi\)
−0.960966 + 0.276667i \(0.910770\pi\)
\(758\) −2.43194e7 −1.53737
\(759\) −1.92833e7 + 2.08884e7i −1.21500 + 1.31614i
\(760\) 8.80538e6 0.552986
\(761\) 849979.i 0.0532043i 0.999646 + 0.0266022i \(0.00846873\pi\)
−0.999646 + 0.0266022i \(0.991531\pi\)
\(762\) −1.80852e7 + 3.59040e6i −1.12833 + 0.224004i
\(763\) 1.54310e7 0.959583
\(764\) 740973. 0.0459271
\(765\) 1.71389e7 7.08430e6i 1.05884 0.437667i
\(766\) 4.23690e6i 0.260902i
\(767\) 511631.i 0.0314028i
\(768\) −782679. 3.94243e6i −0.0478829 0.241191i
\(769\) 1.44206e7i 0.879365i −0.898153 0.439682i \(-0.855091\pi\)
0.898153 0.439682i \(-0.144909\pi\)
\(770\) 1.08824e7 0.661452
\(771\) 1.11410e7 2.21179e6i 0.674977 0.134001i
\(772\) 1.48233e6 0.0895163
\(773\) −1.08132e7 −0.650885 −0.325443 0.945562i \(-0.605513\pi\)
−0.325443 + 0.945562i \(0.605513\pi\)
\(774\) 6.69927e6 2.76911e6i 0.401953 0.166145i
\(775\) −5.59196e6 −0.334434
\(776\) 1.29941e7 0.774624
\(777\) 1.90070e6 + 9.57398e6i 0.112943 + 0.568906i
\(778\) 1.71343e7i 1.01489i