Properties

Label 21.7.f.a.19.2
Level $21$
Weight $7$
Character 21.19
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 21.f (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83113575602\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 212 x^{6} + 473 x^{5} + 39800 x^{4} + 36821 x^{3} + 985651 x^{2} - 601290 x + 21068100\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(2.26350 - 3.92050i\) of defining polynomial
Character \(\chi\) \(=\) 21.19
Dual form 21.7.f.a.10.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.76350 + 4.78652i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(16.7261 + 28.9705i) q^{4} +(-57.9943 - 33.4830i) q^{5} -86.1574i q^{6} +(-240.457 - 244.600i) q^{7} -538.619 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})\) \(q+(-2.76350 + 4.78652i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(16.7261 + 28.9705i) q^{4} +(-57.9943 - 33.4830i) q^{5} -86.1574i q^{6} +(-240.457 - 244.600i) q^{7} -538.619 q^{8} +(121.500 - 210.444i) q^{9} +(320.535 - 185.061i) q^{10} +(-862.868 - 1494.53i) q^{11} +(-451.605 - 260.734i) q^{12} +2807.43i q^{13} +(1835.29 - 475.002i) q^{14} +1043.90 q^{15} +(418.002 - 724.000i) q^{16} +(-5323.58 + 3073.57i) q^{17} +(671.531 + 1163.13i) q^{18} +(7737.30 + 4467.13i) q^{19} -2240.17i q^{20} +(5152.64 + 1427.92i) q^{21} +9538.15 q^{22} +(-4950.64 + 8574.76i) q^{23} +(7271.35 - 4198.12i) q^{24} +(-5570.27 - 9648.00i) q^{25} +(-13437.8 - 7758.32i) q^{26} +3788.00i q^{27} +(3064.27 - 11057.4i) q^{28} -13610.4 q^{29} +(-2884.81 + 4996.64i) q^{30} +(-21833.0 + 12605.3i) q^{31} +(-14925.5 - 25851.7i) q^{32} +(23297.4 + 13450.8i) q^{33} -33975.2i q^{34} +(5755.21 + 22236.7i) q^{35} +8128.90 q^{36} +(-11366.4 + 19687.1i) q^{37} +(-42764.1 + 24689.9i) q^{38} +(-21881.7 - 37900.2i) q^{39} +(31236.8 + 18034.6i) q^{40} -37897.2i q^{41} +(-21074.1 + 20717.2i) q^{42} +73646.2 q^{43} +(28864.9 - 49995.4i) q^{44} +(-14092.6 + 8136.38i) q^{45} +(-27362.2 - 47392.7i) q^{46} +(120523. + 69583.9i) q^{47} +13032.0i q^{48} +(-2009.47 + 117632. i) q^{49} +61573.8 q^{50} +(47912.2 - 82986.3i) q^{51} +(-81332.5 + 46957.3i) q^{52} +(8258.79 + 14304.7i) q^{53} +(-18131.3 - 10468.1i) q^{54} +115566. i q^{55} +(129515. + 131746. i) q^{56} -139271. q^{57} +(37612.3 - 65146.4i) q^{58} +(-61989.7 + 35789.8i) q^{59} +(17460.4 + 30242.2i) q^{60} +(-228557. - 131958. i) q^{61} -139339. i q^{62} +(-80690.3 + 20883.9i) q^{63} +218491. q^{64} +(94001.1 - 162815. i) q^{65} +(-128765. + 74342.5i) q^{66} +(-274333. - 475159. i) q^{67} +(-178086. - 102818. i) q^{68} -154346. i q^{69} +(-122341. - 33903.6i) q^{70} +465655. q^{71} +(-65442.2 + 113349. i) q^{72} +(-289020. + 166866. i) q^{73} +(-62821.9 - 108811. i) q^{74} +(150397. + 86832.0i) q^{75} +298871. i q^{76} +(-158080. + 570429. i) q^{77} +241881. q^{78} +(205012. - 355091. i) q^{79} +(-48483.5 + 27991.9i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(181396. + 104729. i) q^{82} +71948.9i q^{83} +(44816.2 + 173158. i) q^{84} +411649. q^{85} +(-203521. + 352509. i) q^{86} +(183740. - 106082. i) q^{87} +(464757. + 804983. i) q^{88} +(-141505. - 81698.0i) q^{89} -89939.6i q^{90} +(686697. - 675066. i) q^{91} -331220. q^{92} +(196497. - 340342. i) q^{93} +(-666130. + 384590. i) q^{94} +(-299146. - 518137. i) q^{95} +(402989. + 232666. i) q^{96} +651914. i q^{97} +(-557494. - 334694. i) q^{98} -419354. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 5q^{2} - 108q^{3} - 173q^{4} - 294q^{5} - 656q^{7} + 3326q^{8} + 972q^{9} + O(q^{10}) \) \( 8q - 5q^{2} - 108q^{3} - 173q^{4} - 294q^{5} - 656q^{7} + 3326q^{8} + 972q^{9} - 3411q^{10} - 314q^{11} + 4671q^{12} - 5360q^{14} + 5292q^{15} - 12721q^{16} - 5532q^{17} + 1215q^{18} - 18234q^{19} + 9342q^{21} + 86106q^{22} + 3928q^{23} - 44901q^{24} - 17038q^{25} + 12366q^{26} + 85037q^{28} - 8300q^{29} + 30699q^{30} - 89508q^{31} - 186207q^{32} + 8478q^{33} - 25860q^{35} - 84078q^{36} + 64706q^{37} - 77136q^{38} + 29106q^{39} + 221823q^{40} + 173583q^{42} + 45740q^{43} + 92529q^{44} - 71442q^{45} - 111504q^{46} + 483276q^{47} - 310684q^{49} + 967216q^{50} + 49788q^{51} - 1673988q^{52} - 540974q^{53} - 32805q^{54} - 241885q^{56} + 328212q^{57} + 539799q^{58} - 181770q^{59} - 146367q^{60} + 418224q^{61} - 92826q^{63} + 2378626q^{64} - 414204q^{65} - 1162431q^{66} - 1158902q^{67} - 821250q^{68} + 1087917q^{70} + 1442344q^{71} + 404109q^{72} - 378666q^{73} - 432940q^{74} + 460026q^{75} + 1065994q^{77} - 222588q^{78} + 611452q^{79} - 2094945q^{80} - 236196q^{81} - 1561266q^{82} - 1579716q^{84} - 275112q^{85} + 816224q^{86} + 112050q^{87} - 366441q^{88} - 989196q^{89} + 304446q^{91} + 678720q^{92} + 805572q^{93} - 716148q^{94} - 591792q^{95} + 5027589q^{96} + 3509629q^{98} - 152604q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76350 + 4.78652i −0.345438 + 0.598316i −0.985433 0.170063i \(-0.945603\pi\)
0.639996 + 0.768379i \(0.278936\pi\)
\(3\) −13.5000 + 7.79423i −0.500000 + 0.288675i
\(4\) 16.7261 + 28.9705i 0.261346 + 0.452664i
\(5\) −57.9943 33.4830i −0.463955 0.267864i 0.249751 0.968310i \(-0.419651\pi\)
−0.713706 + 0.700446i \(0.752985\pi\)
\(6\) 86.1574i 0.398877i
\(7\) −240.457 244.600i −0.701042 0.713120i
\(8\) −538.619 −1.05199
\(9\) 121.500 210.444i 0.166667 0.288675i
\(10\) 320.535 185.061i 0.320535 0.185061i
\(11\) −862.868 1494.53i −0.648285 1.12286i −0.983532 0.180733i \(-0.942153\pi\)
0.335247 0.942130i \(-0.391180\pi\)
\(12\) −451.605 260.734i −0.261346 0.150888i
\(13\) 2807.43i 1.27785i 0.769271 + 0.638923i \(0.220620\pi\)
−0.769271 + 0.638923i \(0.779380\pi\)
\(14\) 1835.29 475.002i 0.668837 0.173106i
\(15\) 1043.90 0.309303
\(16\) 418.002 724.000i 0.102051 0.176758i
\(17\) −5323.58 + 3073.57i −1.08357 + 0.625599i −0.931857 0.362826i \(-0.881812\pi\)
−0.151712 + 0.988425i \(0.548479\pi\)
\(18\) 671.531 + 1163.13i 0.115146 + 0.199439i
\(19\) 7737.30 + 4467.13i 1.12805 + 0.651281i 0.943444 0.331532i \(-0.107565\pi\)
0.184607 + 0.982812i \(0.440899\pi\)
\(20\) 2240.17i 0.280021i
\(21\) 5152.64 + 1427.92i 0.556381 + 0.154187i
\(22\) 9538.15 0.895769
\(23\) −4950.64 + 8574.76i −0.406891 + 0.704755i −0.994540 0.104361i \(-0.966720\pi\)
0.587649 + 0.809116i \(0.300054\pi\)
\(24\) 7271.35 4198.12i 0.525995 0.303683i
\(25\) −5570.27 9648.00i −0.356497 0.617472i
\(26\) −13437.8 7758.32i −0.764555 0.441416i
\(27\) 3788.00i 0.192450i
\(28\) 3064.27 11057.4i 0.139589 0.503707i
\(29\) −13610.4 −0.558054 −0.279027 0.960283i \(-0.590012\pi\)
−0.279027 + 0.960283i \(0.590012\pi\)
\(30\) −2884.81 + 4996.64i −0.106845 + 0.185061i
\(31\) −21833.0 + 12605.3i −0.732871 + 0.423123i −0.819472 0.573120i \(-0.805733\pi\)
0.0866007 + 0.996243i \(0.472400\pi\)
\(32\) −14925.5 25851.7i −0.455490 0.788932i
\(33\) 23297.4 + 13450.8i 0.648285 + 0.374288i
\(34\) 33975.2i 0.864422i
\(35\) 5755.21 + 22236.7i 0.134232 + 0.518639i
\(36\) 8128.90 0.174230
\(37\) −11366.4 + 19687.1i −0.224397 + 0.388666i −0.956138 0.292916i \(-0.905374\pi\)
0.731742 + 0.681582i \(0.238708\pi\)
\(38\) −42764.1 + 24689.9i −0.779343 + 0.449954i
\(39\) −21881.7 37900.2i −0.368882 0.638923i
\(40\) 31236.8 + 18034.6i 0.488075 + 0.281790i
\(41\) 37897.2i 0.549865i −0.961464 0.274932i \(-0.911345\pi\)
0.961464 0.274932i \(-0.0886554\pi\)
\(42\) −21074.1 + 20717.2i −0.284447 + 0.279630i
\(43\) 73646.2 0.926286 0.463143 0.886284i \(-0.346722\pi\)
0.463143 + 0.886284i \(0.346722\pi\)
\(44\) 28864.9 49995.4i 0.338853 0.586911i
\(45\) −14092.6 + 8136.38i −0.154652 + 0.0892881i
\(46\) −27362.2 47392.7i −0.281111 0.486898i
\(47\) 120523. + 69583.9i 1.16085 + 0.670216i 0.951507 0.307626i \(-0.0995346\pi\)
0.209342 + 0.977843i \(0.432868\pi\)
\(48\) 13032.0i 0.117839i
\(49\) −2009.47 + 117632.i −0.0170802 + 0.999854i
\(50\) 61573.8 0.492591
\(51\) 47912.2 82986.3i 0.361190 0.625599i
\(52\) −81332.5 + 46957.3i −0.578434 + 0.333959i
\(53\) 8258.79 + 14304.7i 0.0554739 + 0.0960837i 0.892429 0.451188i \(-0.149000\pi\)
−0.836955 + 0.547272i \(0.815666\pi\)
\(54\) −18131.3 10468.1i −0.115146 0.0664795i
\(55\) 115566.i 0.694610i
\(56\) 129515. + 131746.i 0.737489 + 0.750195i
\(57\) −139271. −0.752034
\(58\) 37612.3 65146.4i 0.192773 0.333892i
\(59\) −61989.7 + 35789.8i −0.301831 + 0.174262i −0.643265 0.765644i \(-0.722421\pi\)
0.341434 + 0.939906i \(0.389087\pi\)
\(60\) 17460.4 + 30242.2i 0.0808350 + 0.140010i
\(61\) −228557. 131958.i −1.00695 0.581360i −0.0966496 0.995318i \(-0.530813\pi\)
−0.910296 + 0.413958i \(0.864146\pi\)
\(62\) 139339.i 0.584651i
\(63\) −80690.3 + 20883.9i −0.322700 + 0.0835201i
\(64\) 218491. 0.833476
\(65\) 94001.1 162815.i 0.342289 0.592862i
\(66\) −128765. + 74342.5i −0.447884 + 0.258586i
\(67\) −274333. 475159.i −0.912125 1.57985i −0.811057 0.584967i \(-0.801107\pi\)
−0.101068 0.994880i \(-0.532226\pi\)
\(68\) −178086. 102818.i −0.566372 0.326995i
\(69\) 154346.i 0.469837i
\(70\) −122341. 33903.6i −0.356679 0.0988443i
\(71\) 465655. 1.30103 0.650517 0.759491i \(-0.274552\pi\)
0.650517 + 0.759491i \(0.274552\pi\)
\(72\) −65442.2 + 113349.i −0.175332 + 0.303683i
\(73\) −289020. + 166866.i −0.742950 + 0.428942i −0.823141 0.567837i \(-0.807780\pi\)
0.0801910 + 0.996780i \(0.474447\pi\)
\(74\) −62821.9 108811.i −0.155030 0.268520i
\(75\) 150397. + 86832.0i 0.356497 + 0.205824i
\(76\) 298871.i 0.680837i
\(77\) −158080. + 570429.i −0.346261 + 1.24948i
\(78\) 241881. 0.509703
\(79\) 205012. 355091.i 0.415813 0.720209i −0.579700 0.814830i \(-0.696830\pi\)
0.995513 + 0.0946203i \(0.0301637\pi\)
\(80\) −48483.5 + 27991.9i −0.0946942 + 0.0546717i
\(81\) −29524.5 51137.9i −0.0555556 0.0962250i
\(82\) 181396. + 104729.i 0.328993 + 0.189944i
\(83\) 71948.9i 0.125832i 0.998019 + 0.0629158i \(0.0200400\pi\)
−0.998019 + 0.0629158i \(0.979960\pi\)
\(84\) 44816.2 + 173158.i 0.0756131 + 0.292150i
\(85\) 411649. 0.670302
\(86\) −203521. + 352509.i −0.319974 + 0.554211i
\(87\) 183740. 106082.i 0.279027 0.161096i
\(88\) 464757. + 804983.i 0.681990 + 1.18124i
\(89\) −141505. 81698.0i −0.200725 0.115889i 0.396269 0.918135i \(-0.370305\pi\)
−0.596994 + 0.802246i \(0.703638\pi\)
\(90\) 89939.6i 0.123374i
\(91\) 686697. 675066.i 0.911257 0.895823i
\(92\) −331220. −0.425357
\(93\) 196497. 340342.i 0.244290 0.423123i
\(94\) −666130. + 384590.i −0.802002 + 0.463036i
\(95\) −299146. 518137.i −0.348910 0.604329i
\(96\) 402989. + 232666.i 0.455490 + 0.262977i
\(97\) 651914.i 0.714291i 0.934049 + 0.357146i \(0.116250\pi\)
−0.934049 + 0.357146i \(0.883750\pi\)
\(98\) −557494. 334694.i −0.592328 0.355607i
\(99\) −419354. −0.432190
\(100\) 186338. 322747.i 0.186338 0.322747i
\(101\) 883850. 510291.i 0.857856 0.495283i −0.00543765 0.999985i \(-0.501731\pi\)
0.863294 + 0.504702i \(0.168398\pi\)
\(102\) 264811. + 458666.i 0.249537 + 0.432211i
\(103\) 363147. + 209663.i 0.332331 + 0.191871i 0.656875 0.753999i \(-0.271878\pi\)
−0.324545 + 0.945870i \(0.605211\pi\)
\(104\) 1.51213e6i 1.34428i
\(105\) −251013. 255338.i −0.216834 0.220570i
\(106\) −91292.8 −0.0766512
\(107\) −1.10621e6 + 1.91600e6i −0.902993 + 1.56403i −0.0794039 + 0.996843i \(0.525302\pi\)
−0.823589 + 0.567187i \(0.808032\pi\)
\(108\) −109740. + 63358.5i −0.0871152 + 0.0502960i
\(109\) −382955. 663297.i −0.295711 0.512187i 0.679439 0.733732i \(-0.262223\pi\)
−0.975150 + 0.221545i \(0.928890\pi\)
\(110\) −553158. 319366.i −0.415596 0.239944i
\(111\) 354368.i 0.259111i
\(112\) −277602. + 71847.9i −0.197592 + 0.0511399i
\(113\) −2.66096e6 −1.84418 −0.922090 0.386976i \(-0.873520\pi\)
−0.922090 + 0.386976i \(0.873520\pi\)
\(114\) 384877. 666626.i 0.259781 0.449954i
\(115\) 574218. 331525.i 0.377558 0.217983i
\(116\) −227649. 394299.i −0.145845 0.252611i
\(117\) 590806. + 341102.i 0.368882 + 0.212974i
\(118\) 395620.i 0.240787i
\(119\) 2.03189e6 + 563085.i 1.20575 + 0.334144i
\(120\) −562263. −0.325384
\(121\) −603302. + 1.04495e6i −0.340548 + 0.589847i
\(122\) 1.26324e6 729331.i 0.695674 0.401647i
\(123\) 295380. + 511612.i 0.158732 + 0.274932i
\(124\) −730361. 421674.i −0.383065 0.221163i
\(125\) 1.79238e6i 0.917700i
\(126\) 123026. 443939.i 0.0615015 0.221928i
\(127\) −1.11648e6 −0.545055 −0.272527 0.962148i \(-0.587859\pi\)
−0.272527 + 0.962148i \(0.587859\pi\)
\(128\) 351433. 608699.i 0.167576 0.290250i
\(129\) −994224. + 574015.i −0.463143 + 0.267396i
\(130\) 519544. + 899877.i 0.236479 + 0.409594i
\(131\) 247826. + 143083.i 0.110239 + 0.0636463i 0.554106 0.832446i \(-0.313060\pi\)
−0.443867 + 0.896093i \(0.646394\pi\)
\(132\) 899918.i 0.391274i
\(133\) −767830. 2.96670e6i −0.326370 1.26101i
\(134\) 3.03248e6 1.26033
\(135\) 126834. 219682.i 0.0515505 0.0892881i
\(136\) 2.86738e6 1.65548e6i 1.13990 0.658124i
\(137\) 1.86697e6 + 3.23368e6i 0.726063 + 1.25758i 0.958535 + 0.284975i \(0.0919854\pi\)
−0.232472 + 0.972603i \(0.574681\pi\)
\(138\) 738779. + 426534.i 0.281111 + 0.162299i
\(139\) 618216.i 0.230195i 0.993354 + 0.115097i \(0.0367180\pi\)
−0.993354 + 0.115097i \(0.963282\pi\)
\(140\) −547945. + 538664.i −0.199688 + 0.196306i
\(141\) −2.16941e6 −0.773899
\(142\) −1.28684e6 + 2.22887e6i −0.449426 + 0.778429i
\(143\) 4.19579e6 2.42244e6i 1.43485 0.828408i
\(144\) −101574. 175932.i −0.0340171 0.0589193i
\(145\) 789324. + 455716.i 0.258911 + 0.149483i
\(146\) 1.84454e6i 0.592691i
\(147\) −889722. 1.60369e6i −0.280093 0.504858i
\(148\) −760461. −0.234580
\(149\) −1.86160e6 + 3.22438e6i −0.562765 + 0.974737i 0.434489 + 0.900677i \(0.356929\pi\)
−0.997254 + 0.0740601i \(0.976404\pi\)
\(150\) −831247. + 479920.i −0.246295 + 0.142199i
\(151\) 1.27599e6 + 2.21009e6i 0.370611 + 0.641917i 0.989660 0.143436i \(-0.0458151\pi\)
−0.619049 + 0.785352i \(0.712482\pi\)
\(152\) −4.16746e6 2.40608e6i −1.18670 0.685140i
\(153\) 1.49375e6i 0.417066i
\(154\) −2.29352e6 2.33303e6i −0.627972 0.638791i
\(155\) 1.68825e6 0.453358
\(156\) 731993. 1.26785e6i 0.192811 0.333959i
\(157\) −5.87057e6 + 3.38938e6i −1.51699 + 0.875832i −0.517186 + 0.855873i \(0.673020\pi\)
−0.999801 + 0.0199592i \(0.993646\pi\)
\(158\) 1.13310e6 + 1.96259e6i 0.287275 + 0.497575i
\(159\) −222987. 128742.i −0.0554739 0.0320279i
\(160\) 1.99900e6i 0.488038i
\(161\) 3.28781e6 850937.i 0.787823 0.203901i
\(162\) 326364. 0.0767639
\(163\) 4.13571e6 7.16325e6i 0.954964 1.65405i 0.220513 0.975384i \(-0.429227\pi\)
0.734451 0.678662i \(-0.237440\pi\)
\(164\) 1.09790e6 633874.i 0.248904 0.143705i
\(165\) −900746. 1.56014e6i −0.200517 0.347305i
\(166\) −344385. 198831.i −0.0752871 0.0434670i
\(167\) 2.59960e6i 0.558158i −0.960268 0.279079i \(-0.909971\pi\)
0.960268 0.279079i \(-0.0900291\pi\)
\(168\) −2.77531e6 769106.i −0.585307 0.162203i
\(169\) −3.05483e6 −0.632888
\(170\) −1.13759e6 + 1.97037e6i −0.231548 + 0.401052i
\(171\) 1.88016e6 1.08551e6i 0.376017 0.217094i
\(172\) 1.23182e6 + 2.13357e6i 0.242081 + 0.419296i
\(173\) −7.10612e6 4.10272e6i −1.37244 0.792380i −0.381208 0.924489i \(-0.624492\pi\)
−0.991235 + 0.132109i \(0.957825\pi\)
\(174\) 1.17263e6i 0.222595i
\(175\) −1.02049e6 + 3.68242e6i −0.190412 + 0.687099i
\(176\) −1.44272e6 −0.264633
\(177\) 557907. 966324.i 0.100610 0.174262i
\(178\) 782099. 451545.i 0.138676 0.0800647i
\(179\) −4.09401e6 7.09104e6i −0.713822 1.23638i −0.963412 0.268025i \(-0.913629\pi\)
0.249590 0.968352i \(-0.419704\pi\)
\(180\) −471430. 272180.i −0.0808350 0.0466701i
\(181\) 3.25606e6i 0.549106i −0.961572 0.274553i \(-0.911470\pi\)
0.961572 0.274553i \(-0.0885298\pi\)
\(182\) 1.33353e6 + 5.15244e6i 0.221202 + 0.854670i
\(183\) 4.11403e6 0.671297
\(184\) 2.66651e6 4.61853e6i 0.428045 0.741395i
\(185\) 1.31837e6 761161.i 0.208220 0.120216i
\(186\) 1.08604e6 + 1.88107e6i 0.168774 + 0.292325i
\(187\) 9.18709e6 + 5.30417e6i 1.40492 + 0.811133i
\(188\) 4.65547e6i 0.700633i
\(189\) 926544. 910851.i 0.137240 0.134916i
\(190\) 3.30677e6 0.482106
\(191\) −4.30425e6 + 7.45518e6i −0.617728 + 1.06994i 0.372171 + 0.928164i \(0.378614\pi\)
−0.989899 + 0.141773i \(0.954720\pi\)
\(192\) −2.94963e6 + 1.70297e6i −0.416738 + 0.240604i
\(193\) 89943.0 + 155786.i 0.0125111 + 0.0216699i 0.872213 0.489126i \(-0.162684\pi\)
−0.859702 + 0.510796i \(0.829351\pi\)
\(194\) −3.12040e6 1.80157e6i −0.427372 0.246743i
\(195\) 2.93067e6i 0.395241i
\(196\) −3.44146e6 + 1.90931e6i −0.457062 + 0.253576i
\(197\) 2.69333e6 0.352283 0.176141 0.984365i \(-0.443638\pi\)
0.176141 + 0.984365i \(0.443638\pi\)
\(198\) 1.15888e6 2.00725e6i 0.149295 0.258586i
\(199\) 5.23271e6 3.02111e6i 0.663999 0.383360i −0.129800 0.991540i \(-0.541434\pi\)
0.793799 + 0.608180i \(0.208100\pi\)
\(200\) 3.00025e6 + 5.19659e6i 0.375032 + 0.649574i
\(201\) 7.40700e6 + 4.27643e6i 0.912125 + 0.526616i
\(202\) 5.64076e6i 0.684358i
\(203\) 3.27271e6 + 3.32910e6i 0.391219 + 0.397959i
\(204\) 3.20554e6 0.377581
\(205\) −1.26891e6 + 2.19782e6i −0.147289 + 0.255112i
\(206\) −2.00711e6 + 1.15881e6i −0.229599 + 0.132559i
\(207\) 1.20301e6 + 2.08367e6i 0.135630 + 0.234918i
\(208\) 2.03258e6 + 1.17351e6i 0.225869 + 0.130406i
\(209\) 1.54182e7i 1.68886i
\(210\) 1.91585e6 495854.i 0.206873 0.0535422i
\(211\) −1.38113e7 −1.47024 −0.735118 0.677939i \(-0.762873\pi\)
−0.735118 + 0.677939i \(0.762873\pi\)
\(212\) −276275. + 478523.i −0.0289958 + 0.0502221i
\(213\) −6.28634e6 + 3.62942e6i −0.650517 + 0.375576i
\(214\) −6.11400e6 1.05898e7i −0.623855 1.08055i
\(215\) −4.27106e6 2.46590e6i −0.429755 0.248119i
\(216\) 2.04029e6i 0.202456i
\(217\) 8.33314e6 + 2.30932e6i 0.815511 + 0.225998i
\(218\) 4.23318e6 0.408599
\(219\) 2.60118e6 4.50538e6i 0.247650 0.428942i
\(220\) −3.34800e6 + 1.93297e6i −0.314425 + 0.181533i
\(221\) −8.62881e6 1.49455e7i −0.799419 1.38463i
\(222\) 1.69619e6 + 979297.i 0.155030 + 0.0895067i
\(223\) 9.81400e6i 0.884976i −0.896774 0.442488i \(-0.854096\pi\)
0.896774 0.442488i \(-0.145904\pi\)
\(224\) −2.73439e6 + 9.86702e6i −0.243286 + 0.877894i
\(225\) −2.70715e6 −0.237665
\(226\) 7.35357e6 1.27368e7i 0.637049 1.10340i
\(227\) −1.26217e7 + 7.28715e6i −1.07905 + 0.622989i −0.930639 0.365938i \(-0.880748\pi\)
−0.148408 + 0.988926i \(0.547415\pi\)
\(228\) −2.32947e6 4.03476e6i −0.196541 0.340419i
\(229\) 1.27292e7 + 7.34923e6i 1.05998 + 0.611978i 0.925426 0.378929i \(-0.123708\pi\)
0.134551 + 0.990907i \(0.457041\pi\)
\(230\) 3.66468e6i 0.301198i
\(231\) −2.31198e6 8.93290e6i −0.187563 0.724697i
\(232\) 7.33080e6 0.587067
\(233\) −2.87597e6 + 4.98133e6i −0.227362 + 0.393802i −0.957025 0.290004i \(-0.906343\pi\)
0.729664 + 0.683806i \(0.239677\pi\)
\(234\) −3.26539e6 + 1.88527e6i −0.254852 + 0.147139i
\(235\) −4.65976e6 8.07094e6i −0.359054 0.621900i
\(236\) −2.07369e6 1.19725e6i −0.157764 0.0910853i
\(237\) 6.39164e6i 0.480140i
\(238\) −8.31035e6 + 8.16960e6i −0.616436 + 0.605996i
\(239\) 1.60167e7 1.17322 0.586610 0.809869i \(-0.300462\pi\)
0.586610 + 0.809869i \(0.300462\pi\)
\(240\) 436351. 755782.i 0.0315647 0.0546717i
\(241\) −2.23613e7 + 1.29103e7i −1.59752 + 0.922327i −0.605553 + 0.795805i \(0.707048\pi\)
−0.991964 + 0.126522i \(0.959618\pi\)
\(242\) −3.33445e6 5.77544e6i −0.235276 0.407510i
\(243\) 797162. + 460241.i 0.0555556 + 0.0320750i
\(244\) 8.82856e6i 0.607744i
\(245\) 4.05521e6 6.75469e6i 0.275750 0.459312i
\(246\) −3.26513e6 −0.219328
\(247\) −1.25411e7 + 2.17219e7i −0.832236 + 1.44147i
\(248\) 1.17596e7 6.78943e6i 0.770973 0.445121i
\(249\) −560786. 971311.i −0.0363245 0.0629158i
\(250\) −8.57929e6 4.95325e6i −0.549074 0.317008i
\(251\) 9.51912e6i 0.601971i 0.953629 + 0.300985i \(0.0973156\pi\)
−0.953629 + 0.300985i \(0.902684\pi\)
\(252\) −1.95465e6 1.98833e6i −0.122143 0.124247i
\(253\) 1.70870e7 1.05513
\(254\) 3.08539e6 5.34406e6i 0.188282 0.326115i
\(255\) −5.55727e6 + 3.20849e6i −0.335151 + 0.193500i
\(256\) 8.93408e6 + 1.54743e7i 0.532512 + 0.922339i
\(257\) 1.93872e7 + 1.11932e7i 1.14213 + 0.659408i 0.946957 0.321361i \(-0.104140\pi\)
0.195171 + 0.980769i \(0.437474\pi\)
\(258\) 6.34517e6i 0.369474i
\(259\) 7.54860e6 1.95370e6i 0.434477 0.112450i
\(260\) 6.28910e6 0.357823
\(261\) −1.65366e6 + 2.86422e6i −0.0930089 + 0.161096i
\(262\) −1.36974e6 + 790818.i −0.0761612 + 0.0439717i
\(263\) −5.24659e6 9.08736e6i −0.288410 0.499540i 0.685021 0.728524i \(-0.259793\pi\)
−0.973430 + 0.228983i \(0.926460\pi\)
\(264\) −1.25484e7 7.24484e6i −0.681990 0.393747i
\(265\) 1.10612e6i 0.0594380i
\(266\) 1.63221e7 + 4.52324e6i 0.867223 + 0.240328i
\(267\) 2.54709e6 0.133817
\(268\) 9.17707e6 1.58951e7i 0.476760 0.825772i
\(269\) 2.33663e7 1.34905e7i 1.20042 0.693063i 0.239772 0.970829i \(-0.422927\pi\)
0.960649 + 0.277766i \(0.0895941\pi\)
\(270\) 701009. + 1.21418e6i 0.0356150 + 0.0616869i
\(271\) −1.09955e6 634826.i −0.0552468 0.0318968i 0.472122 0.881533i \(-0.343488\pi\)
−0.527369 + 0.849636i \(0.676821\pi\)
\(272\) 5.13903e6i 0.255373i
\(273\) −4.00878e6 + 1.44657e7i −0.197027 + 0.710969i
\(274\) −2.06374e7 −1.00324
\(275\) −9.61282e6 + 1.66499e7i −0.462224 + 0.800596i
\(276\) 4.47147e6 2.58160e6i 0.212678 0.122790i
\(277\) 3.35016e6 + 5.80265e6i 0.157626 + 0.273016i 0.934012 0.357242i \(-0.116283\pi\)
−0.776386 + 0.630257i \(0.782949\pi\)
\(278\) −2.95911e6 1.70844e6i −0.137729 0.0795180i
\(279\) 6.12616e6i 0.282082i
\(280\) −3.09986e6 1.19771e7i −0.141211 0.545603i
\(281\) −321000. −0.0144673 −0.00723363 0.999974i \(-0.502303\pi\)
−0.00723363 + 0.999974i \(0.502303\pi\)
\(282\) 5.99517e6 1.03839e7i 0.267334 0.463036i
\(283\) 2.77311e6 1.60105e6i 0.122351 0.0706394i −0.437575 0.899182i \(-0.644163\pi\)
0.559926 + 0.828542i \(0.310829\pi\)
\(284\) 7.78860e6 + 1.34902e7i 0.340020 + 0.588931i
\(285\) 8.07695e6 + 4.66323e6i 0.348910 + 0.201443i
\(286\) 2.67776e7i 1.14465i
\(287\) −9.26967e6 + 9.11267e6i −0.392119 + 0.385478i
\(288\) −7.25380e6 −0.303660
\(289\) 6.82485e6 1.18210e7i 0.282748 0.489734i
\(290\) −4.36260e6 + 2.51875e6i −0.178876 + 0.103274i
\(291\) −5.08117e6 8.80084e6i −0.206198 0.357146i
\(292\) −9.66837e6 5.58204e6i −0.388333 0.224204i
\(293\) 2.67440e6i 0.106322i 0.998586 + 0.0531610i \(0.0169297\pi\)
−0.998586 + 0.0531610i \(0.983070\pi\)
\(294\) 1.01349e7 + 173131.i 0.398819 + 0.00681290i
\(295\) 4.79340e6 0.186714
\(296\) 6.12214e6 1.06039e7i 0.236063 0.408873i
\(297\) 5.66128e6 3.26854e6i 0.216095 0.124763i
\(298\) −1.02891e7 1.78212e7i −0.388800 0.673422i
\(299\) −2.40730e7 1.38986e7i −0.900568 0.519943i
\(300\) 5.80945e6i 0.215165i
\(301\) −1.77088e7 1.80139e7i −0.649365 0.660553i
\(302\) −1.41048e7 −0.512092
\(303\) −7.95465e6 + 1.37779e7i −0.285952 + 0.495283i
\(304\) 6.46841e6 3.73454e6i 0.230238 0.132928i
\(305\) 8.83669e6 + 1.53056e7i 0.311451 + 0.539449i
\(306\) −7.14989e6 4.12799e6i −0.249537 0.144070i
\(307\) 1.98765e7i 0.686950i −0.939162 0.343475i \(-0.888396\pi\)
0.939162 0.343475i \(-0.111604\pi\)
\(308\) −1.91697e7 + 4.96142e6i −0.656088 + 0.169806i
\(309\) −6.53664e6 −0.221554
\(310\) −4.66548e6 + 8.08085e6i −0.156607 + 0.271251i
\(311\) −1.36580e7 + 7.88548e6i −0.454054 + 0.262148i −0.709541 0.704664i \(-0.751098\pi\)
0.255487 + 0.966813i \(0.417764\pi\)
\(312\) 1.17859e7 + 2.04138e7i 0.388060 + 0.672140i
\(313\) −9.13939e6 5.27663e6i −0.298047 0.172077i 0.343518 0.939146i \(-0.388381\pi\)
−0.641565 + 0.767069i \(0.721715\pi\)
\(314\) 3.74662e7i 1.21018i
\(315\) 5.37883e6 + 1.49060e6i 0.172090 + 0.0476904i
\(316\) 1.37162e7 0.434684
\(317\) 1.61613e7 2.79923e7i 0.507341 0.878740i −0.492623 0.870243i \(-0.663962\pi\)
0.999964 0.00849733i \(-0.00270482\pi\)
\(318\) 1.23245e6 711557.i 0.0383256 0.0221273i
\(319\) 1.17440e7 + 2.03411e7i 0.361778 + 0.626618i
\(320\) −1.26712e7 7.31574e6i −0.386695 0.223259i
\(321\) 3.44881e7i 1.04269i
\(322\) −5.01282e6 + 1.80887e7i −0.150146 + 0.541802i
\(323\) −5.49201e7 −1.62976
\(324\) 987661. 1.71068e6i 0.0290384 0.0502960i
\(325\) 2.70860e7 1.56381e7i 0.789033 0.455549i
\(326\) 2.28581e7 + 3.95913e7i 0.659761 + 1.14274i
\(327\) 1.03398e7 + 5.96968e6i 0.295711 + 0.170729i
\(328\) 2.04122e7i 0.578452i
\(329\) −1.19604e7 4.62119e7i −0.335859 1.29767i
\(330\) 9.95685e6 0.277064
\(331\) −1.00165e7 + 1.73490e7i −0.276205 + 0.478400i −0.970438 0.241349i \(-0.922410\pi\)
0.694234 + 0.719750i \(0.255743\pi\)
\(332\) −2.08440e6 + 1.20343e6i −0.0569595 + 0.0328856i
\(333\) 2.76203e6 + 4.78397e6i 0.0747989 + 0.129555i
\(334\) 1.24430e7 + 7.18400e6i 0.333955 + 0.192809i
\(335\) 3.67421e7i 0.977303i
\(336\) 3.18763e6 3.13364e6i 0.0840331 0.0826098i
\(337\) −3.66702e6 −0.0958128 −0.0479064 0.998852i \(-0.515255\pi\)
−0.0479064 + 0.998852i \(0.515255\pi\)
\(338\) 8.44203e6 1.46220e7i 0.218623 0.378667i
\(339\) 3.59230e7 2.07401e7i 0.922090 0.532369i
\(340\) 6.88530e6 + 1.19257e7i 0.175181 + 0.303422i
\(341\) 3.76779e7 + 2.17534e7i 0.950219 + 0.548609i
\(342\) 1.19993e7i 0.299969i
\(343\) 2.92560e7 2.77939e7i 0.724990 0.688760i
\(344\) −3.96672e7 −0.974443
\(345\) −5.16796e6 + 8.95117e6i −0.125853 + 0.217983i
\(346\) 3.92756e7 2.26758e7i 0.948187 0.547436i
\(347\) −3.22802e6 5.59109e6i −0.0772587 0.133816i 0.824808 0.565414i \(-0.191283\pi\)
−0.902066 + 0.431598i \(0.857950\pi\)
\(348\) 6.14652e6 + 3.54869e6i 0.145845 + 0.0842036i
\(349\) 4.01536e7i 0.944600i 0.881438 + 0.472300i \(0.156576\pi\)
−0.881438 + 0.472300i \(0.843424\pi\)
\(350\) −1.48059e7 1.50610e7i −0.345327 0.351276i
\(351\) −1.06345e7 −0.245921
\(352\) −2.57575e7 + 4.46133e7i −0.590575 + 1.02291i
\(353\) 7.02915e6 4.05828e6i 0.159801 0.0922610i −0.417967 0.908462i \(-0.637257\pi\)
0.577768 + 0.816201i \(0.303924\pi\)
\(354\) 3.08356e6 + 5.34087e6i 0.0695091 + 0.120393i
\(355\) −2.70053e7 1.55915e7i −0.603621 0.348501i
\(356\) 5.46596e6i 0.121148i
\(357\) −3.18193e7 + 8.23535e6i −0.699336 + 0.181000i
\(358\) 4.52552e7 0.986324
\(359\) −1.84586e7 + 3.19712e7i −0.398946 + 0.690996i −0.993596 0.112989i \(-0.963957\pi\)
0.594650 + 0.803985i \(0.297291\pi\)
\(360\) 7.59055e6 4.38241e6i 0.162692 0.0939302i
\(361\) 1.63876e7 + 2.83842e7i 0.348333 + 0.603330i
\(362\) 1.55852e7 + 8.99811e6i 0.328539 + 0.189682i
\(363\) 1.88091e7i 0.393231i
\(364\) 3.10428e7 + 8.60270e6i 0.643660 + 0.178374i
\(365\) 2.23487e7 0.459593
\(366\) −1.13691e7 + 1.96919e7i −0.231891 + 0.401647i
\(367\) 1.70742e7 9.85777e6i 0.345415 0.199425i −0.317249 0.948342i \(-0.602759\pi\)
0.662664 + 0.748917i \(0.269426\pi\)
\(368\) 4.13875e6 + 7.16853e6i 0.0830474 + 0.143842i
\(369\) −7.97525e6 4.60451e6i −0.158732 0.0916441i
\(370\) 8.41387e6i 0.166108i
\(371\) 1.51303e6 5.45976e6i 0.0296296 0.106918i
\(372\) 1.31465e7 0.255377
\(373\) −5.21653e6 + 9.03530e6i −0.100521 + 0.174107i −0.911899 0.410414i \(-0.865384\pi\)
0.811379 + 0.584521i \(0.198718\pi\)
\(374\) −5.07770e7 + 2.93161e7i −0.970627 + 0.560392i
\(375\) −1.39702e7 2.41972e7i −0.264917 0.458850i
\(376\) −6.49158e7 3.74792e7i −1.22120 0.705061i
\(377\) 3.82101e7i 0.713106i
\(378\) 1.79931e6 + 6.95207e6i 0.0333142 + 0.128718i
\(379\) −5.26018e7 −0.966235 −0.483118 0.875556i \(-0.660496\pi\)
−0.483118 + 0.875556i \(0.660496\pi\)
\(380\) 1.00071e7 1.73328e7i 0.182372 0.315878i
\(381\) 1.50725e7 8.70210e6i 0.272527 0.157344i
\(382\) −2.37896e7 4.12048e7i −0.426773 0.739193i
\(383\) 6.36846e7 + 3.67683e7i 1.13354 + 0.654451i 0.944823 0.327580i \(-0.106233\pi\)
0.188719 + 0.982031i \(0.439566\pi\)
\(384\) 1.09566e7i 0.193500i
\(385\) 2.82674e7 2.77886e7i 0.495340 0.486951i
\(386\) −994230. −0.0172872
\(387\) 8.94802e6 1.54984e7i 0.154381 0.267396i
\(388\) −1.88863e7 + 1.09040e7i −0.323334 + 0.186677i
\(389\) −8.60695e6 1.49077e7i −0.146218 0.253257i 0.783609 0.621255i \(-0.213377\pi\)
−0.929827 + 0.367998i \(0.880043\pi\)
\(390\) −1.40277e7 8.09890e6i −0.236479 0.136531i
\(391\) 6.08645e7i 1.01820i
\(392\) 1.08234e6 6.33587e7i 0.0179682 1.05184i
\(393\) −4.46088e6 −0.0734924
\(394\) −7.44303e6 + 1.28917e7i −0.121692 + 0.210776i
\(395\) −2.37791e7 + 1.37289e7i −0.385837 + 0.222763i
\(396\) −7.01416e6 1.21489e7i −0.112951 0.195637i
\(397\) −5.31024e7 3.06587e7i −0.848678 0.489984i 0.0115267 0.999934i \(-0.496331\pi\)
−0.860205 + 0.509949i \(0.829664\pi\)
\(398\) 3.33953e7i 0.529708i
\(399\) 3.34888e7 + 3.40658e7i 0.527207 + 0.536290i
\(400\) −9.31354e6 −0.145524
\(401\) 2.30735e7 3.99645e7i 0.357833 0.619785i −0.629765 0.776785i \(-0.716849\pi\)
0.987599 + 0.157000i \(0.0501823\pi\)
\(402\) −4.09385e7 + 2.36359e7i −0.630165 + 0.363826i
\(403\) −3.53883e7 6.12944e7i −0.540686 0.936495i
\(404\) 2.95668e7 + 1.70704e7i 0.448394 + 0.258880i
\(405\) 3.95428e6i 0.0595254i
\(406\) −2.49790e7 + 6.46496e6i −0.373247 + 0.0966023i
\(407\) 3.92307e7 0.581892
\(408\) −2.58064e7 + 4.46980e7i −0.379968 + 0.658124i
\(409\) −5.25613e7 + 3.03463e7i −0.768239 + 0.443543i −0.832246 0.554406i \(-0.812945\pi\)
0.0640071 + 0.997949i \(0.479612\pi\)
\(410\) −7.01329e6 1.21474e7i −0.101758 0.176251i
\(411\) −5.04081e7 2.91031e7i −0.726063 0.419193i
\(412\) 1.40274e7i 0.200579i
\(413\) 2.36601e7 + 6.55677e6i 0.335866 + 0.0930765i
\(414\) −1.32980e7 −0.187407
\(415\) 2.40907e6 4.17263e6i 0.0337058 0.0583802i
\(416\) 7.25768e7 4.19022e7i 1.00813 0.582046i
\(417\) −4.81852e6 8.34592e6i −0.0664516 0.115097i
\(418\) 7.37995e7 + 4.26082e7i 1.01047 + 0.583397i
\(419\) 1.17371e8i 1.59558i 0.602939 + 0.797788i \(0.293996\pi\)
−0.602939 + 0.797788i \(0.706004\pi\)
\(420\) 3.19878e6 1.15428e7i 0.0431754 0.155798i
\(421\) −1.28510e7 −0.172222 −0.0861111 0.996286i \(-0.527444\pi\)
−0.0861111 + 0.996286i \(0.527444\pi\)
\(422\) 3.81676e7 6.61081e7i 0.507875 0.879666i
\(423\) 2.92870e7 1.69089e7i 0.386950 0.223405i
\(424\) −4.44834e6 7.70475e6i −0.0583580 0.101079i
\(425\) 5.93075e7 + 3.42412e7i 0.772579 + 0.446049i
\(426\) 4.01196e7i 0.518953i
\(427\) 2.26815e7 + 8.76354e7i 0.291331 + 1.12563i
\(428\) −7.40101e7 −0.943973
\(429\) −3.77621e7 + 6.54058e7i −0.478282 + 0.828408i
\(430\) 2.36062e7 1.36290e7i 0.296907 0.171419i
\(431\) 5.69282e7 + 9.86026e7i 0.711043 + 1.23156i 0.964466 + 0.264207i \(0.0851102\pi\)
−0.253423 + 0.967356i \(0.581556\pi\)
\(432\) 2.74251e6 + 1.58339e6i 0.0340171 + 0.0196398i
\(433\) 2.76112e7i 0.340111i 0.985434 + 0.170056i \(0.0543947\pi\)
−0.985434 + 0.170056i \(0.945605\pi\)
\(434\) −3.40822e7 + 3.35050e7i −0.416926 + 0.409865i
\(435\) −1.42078e7 −0.172608
\(436\) 1.28107e7 2.21888e7i 0.154566 0.267716i
\(437\) −7.66092e7 + 4.42303e7i −0.917987 + 0.530000i
\(438\) 1.43767e7 + 2.49012e7i 0.171095 + 0.296346i
\(439\) 6.22452e7 + 3.59373e7i 0.735720 + 0.424768i 0.820511 0.571631i \(-0.193689\pi\)
−0.0847914 + 0.996399i \(0.527022\pi\)
\(440\) 6.22459e7i 0.730723i
\(441\) 2.45108e7 + 1.47151e7i 0.285786 + 0.171573i
\(442\) 9.53829e7 1.10460
\(443\) 4.75145e7 8.22975e7i 0.546531 0.946620i −0.451978 0.892029i \(-0.649281\pi\)
0.998509 0.0545904i \(-0.0173853\pi\)
\(444\) 1.02662e7 5.92721e6i 0.117290 0.0677175i
\(445\) 5.47099e6 + 9.47603e6i 0.0620849 + 0.107534i
\(446\) 4.69750e7 + 2.71210e7i 0.529495 + 0.305704i
\(447\) 5.80389e7i 0.649825i
\(448\) −5.25377e7 5.34429e7i −0.584302 0.594369i
\(449\) 1.15401e8 1.27488 0.637440 0.770500i \(-0.279993\pi\)
0.637440 + 0.770500i \(0.279993\pi\)
\(450\) 7.48122e6 1.29579e7i 0.0820984 0.142199i
\(451\) −5.66386e7 + 3.27003e7i −0.617423 + 0.356469i
\(452\) −4.45076e7 7.70894e7i −0.481968 0.834794i
\(453\) −3.44518e7 1.98908e7i −0.370611 0.213972i
\(454\) 8.05522e7i 0.860815i
\(455\) −6.24278e7 + 1.61573e7i −0.662741 + 0.171528i
\(456\) 7.50142e7 0.791132
\(457\) −4.58763e6 + 7.94601e6i −0.0480662 + 0.0832531i −0.889058 0.457796i \(-0.848639\pi\)
0.840991 + 0.541049i \(0.181973\pi\)
\(458\) −7.03546e7 + 4.06192e7i −0.732311 + 0.422800i
\(459\) −1.16427e7 2.01657e7i −0.120397 0.208533i
\(460\) 1.92089e7 + 1.10903e7i 0.197346 + 0.113938i
\(461\) 5.79354e7i 0.591346i 0.955289 + 0.295673i \(0.0955438\pi\)
−0.955289 + 0.295673i \(0.904456\pi\)
\(462\) 4.91467e7 + 1.36197e7i 0.498389 + 0.138116i
\(463\) 6.51781e7 0.656687 0.328344 0.944558i \(-0.393510\pi\)
0.328344 + 0.944558i \(0.393510\pi\)
\(464\) −5.68916e6 + 9.85391e6i −0.0569500 + 0.0986404i
\(465\) −2.27914e7 + 1.31586e7i −0.226679 + 0.130873i
\(466\) −1.58955e7 2.75318e7i −0.157079 0.272068i
\(467\) −1.46749e8 8.47258e7i −1.44087 0.831888i −0.442965 0.896539i \(-0.646073\pi\)
−0.997908 + 0.0646508i \(0.979407\pi\)
\(468\) 2.28213e7i 0.222640i
\(469\) −5.02586e7 + 1.81358e8i −0.487182 + 1.75799i
\(470\) 5.15090e7 0.496123
\(471\) 5.28352e7 9.15132e7i 0.505662 0.875832i
\(472\) 3.33888e7 1.92770e7i 0.317523 0.183322i
\(473\) −6.35470e7 1.10067e8i −0.600498 1.04009i
\(474\) −3.05938e7 1.76633e7i −0.287275 0.165858i
\(475\) 9.95326e7i 0.928719i
\(476\) 1.76728e7 + 6.82830e7i 0.163864 + 0.633129i
\(477\) 4.01377e6 0.0369826
\(478\) −4.42622e7 + 7.66644e7i −0.405275 + 0.701956i
\(479\) −7.92689e7 + 4.57659e7i −0.721268 + 0.416424i −0.815219 0.579153i \(-0.803383\pi\)
0.0939514 + 0.995577i \(0.470050\pi\)
\(480\) −1.55807e7 2.69866e7i −0.140885 0.244019i
\(481\) −5.52701e7 3.19102e7i −0.496656 0.286744i
\(482\) 1.42710e8i 1.27443i
\(483\) −3.77530e7 + 3.71136e7i −0.335050 + 0.329375i
\(484\) −4.03636e7 −0.356003
\(485\) 2.18281e7 3.78073e7i 0.191333 0.331399i
\(486\) −4.40591e6 + 2.54376e6i −0.0383820 + 0.0221598i
\(487\) 6.56199e7 + 1.13657e8i 0.568131 + 0.984032i 0.996751 + 0.0805467i \(0.0256666\pi\)
−0.428620 + 0.903485i \(0.641000\pi\)
\(488\) 1.23105e8 + 7.10749e7i 1.05930 + 0.611585i
\(489\) 1.28939e8i 1.10270i
\(490\) 2.11249e7 + 3.80770e7i 0.179559 + 0.323649i
\(491\) −8.81776e7 −0.744927 −0.372463 0.928047i \(-0.621487\pi\)
−0.372463 + 0.928047i \(0.621487\pi\)
\(492\) −9.88111e6 + 1.71146e7i −0.0829680 + 0.143705i
\(493\) 7.24558e7 4.18324e7i 0.604690 0.349118i
\(494\) −6.93149e7 1.20057e8i −0.574971 0.995879i
\(495\) 2.43201e7 + 1.40412e7i 0.200517 + 0.115768i
\(496\) 2.10761e7i 0.172721i
\(497\) −1.11970e8 1.13899e8i −0.912080 0.927794i
\(498\) 6.19894e6 0.0501914
\(499\) 1.14235e8 1.97862e8i 0.919389 1.59243i 0.119043 0.992889i \(-0.462017\pi\)
0.800346 0.599539i \(-0.204649\pi\)
\(500\) −5.19262e7 + 2.99796e7i −0.415410 + 0.239837i
\(501\) 2.02619e7 + 3.50946e7i 0.161126 + 0.279079i
\(502\) −4.55635e7 2.63061e7i −0.360169 0.207943i
\(503\) 2.07735e8i 1.63232i 0.577824 + 0.816161i \(0.303902\pi\)
−0.577824 + 0.816161i \(0.696098\pi\)
\(504\) 4.34613e7 1.12485e7i 0.339477 0.0878623i
\(505\) −6.83444e7 −0.530675
\(506\) −4.72199e7 + 8.17873e7i −0.364480 + 0.631298i
\(507\) 4.12402e7 2.38100e7i 0.316444 0.182699i
\(508\) −1.86744e7 3.23450e7i −0.142448 0.246727i
\(509\) −4.74960e7 2.74218e7i −0.360167 0.207942i 0.308987 0.951066i \(-0.400010\pi\)
−0.669154 + 0.743124i \(0.733343\pi\)
\(510\) 3.54667e7i 0.267368i
\(511\) 1.10312e8 + 3.05702e7i 0.826726 + 0.229106i
\(512\) −5.37739e7 −0.400647
\(513\) −1.69215e7 + 2.93089e7i −0.125339 + 0.217094i
\(514\) −1.07153e8 + 6.18647e7i −0.789068 + 0.455569i
\(515\) −1.40403e7 2.43185e7i −0.102791 0.178039i
\(516\) −3.32590e7 1.92021e7i −0.242081 0.139765i
\(517\) 2.40167e8i 1.73797i
\(518\) −1.15091e7 + 4.15306e7i −0.0828044 + 0.298799i
\(519\) 1.27910e8 0.914962
\(520\) −5.06308e7 + 8.76951e7i −0.360085 + 0.623685i
\(521\) −2.47035e7 + 1.42626e7i −0.174681 + 0.100852i −0.584791 0.811184i \(-0.698824\pi\)
0.410110 + 0.912036i \(0.365490\pi\)
\(522\) −9.13978e6 1.58306e7i −0.0642576 0.111297i
\(523\) −9.32394e7 5.38318e7i −0.651770 0.376300i 0.137364 0.990521i \(-0.456137\pi\)
−0.789134 + 0.614221i \(0.789470\pi\)
\(524\) 9.57287e6i 0.0665347i
\(525\) −1.49251e7 5.76666e7i −0.103143 0.398517i
\(526\) 5.79958e7 0.398510
\(527\) 7.74863e7 1.34210e8i 0.529411 0.916966i
\(528\) 1.94767e7 1.12449e7i 0.132317 0.0763930i
\(529\) 2.50003e7 + 4.33018e7i 0.168880 + 0.292509i
\(530\) 5.29446e6 + 3.05676e6i 0.0355627 + 0.0205321i
\(531\) 1.73938e7i 0.116175i
\(532\) 7.31040e7 7.18658e7i 0.485519 0.477296i
\(533\) 1.06394e8 0.702642
\(534\) −7.03889e6 + 1.21917e7i −0.0462253 + 0.0800647i
\(535\) 1.28307e8 7.40782e7i 0.837895 0.483759i
\(536\) 1.47761e8 + 2.55930e8i 0.959546 + 1.66198i
\(537\) 1.10538e8 + 6.38193e7i 0.713822 + 0.412125i
\(538\) 1.49125e8i 0.957640i
\(539\) 1.77538e8 9.84975e7i 1.13377 0.629012i
\(540\) 8.48574e6 0.0538900
\(541\) −2.77877e7 + 4.81297e7i −0.175493 + 0.303963i −0.940332 0.340259i \(-0.889485\pi\)
0.764839 + 0.644222i \(0.222819\pi\)
\(542\) 6.07722e6 3.50868e6i 0.0381686 0.0220367i
\(543\) 2.53784e7 + 4.39567e7i 0.158513 + 0.274553i
\(544\) 1.58914e8 + 9.17491e7i 0.987110 + 0.569908i
\(545\) 5.12900e7i 0.316842i
\(546\) −5.81620e7 5.91640e7i −0.357323 0.363479i
\(547\) 5.44170e7 0.332485 0.166243 0.986085i \(-0.446837\pi\)
0.166243 + 0.986085i \(0.446837\pi\)
\(548\) −6.24542e7 + 1.08174e8i −0.379507 + 0.657325i
\(549\) −5.55395e7 + 3.20657e7i −0.335648 + 0.193787i
\(550\) −5.31301e7 9.20240e7i −0.319339 0.553112i
\(551\) −1.05308e8 6.07993e7i −0.629513 0.363449i
\(552\) 8.31335e7i 0.494264i
\(553\) −1.36152e8 + 3.52384e7i −0.805098 + 0.208372i
\(554\) −3.70327e7 −0.217799
\(555\) −1.18653e7 + 2.05513e7i −0.0694066 + 0.120216i
\(556\) −1.79100e7 + 1.03404e7i −0.104201 + 0.0601605i
\(557\) −6.26135e6 1.08450e7i −0.0362329 0.0627571i 0.847340 0.531050i \(-0.178202\pi\)
−0.883573 + 0.468293i \(0.844869\pi\)
\(558\) −2.93230e7 1.69296e7i −0.168774 0.0974418i
\(559\) 2.06756e8i 1.18365i
\(560\) 1.85050e7 + 5.12819e6i 0.105372 + 0.0292012i
\(561\) −1.65368e8 −0.936616
\(562\) 887085. 1.53648e6i 0.00499754 0.00865599i
\(563\) 1.50742e8 8.70310e7i 0.844713 0.487695i −0.0141502 0.999900i \(-0.504504\pi\)
0.858864 + 0.512204i \(0.171171\pi\)
\(564\) −3.62858e7 6.28489e7i −0.202255 0.350316i
\(565\) 1.54321e8 + 8.90971e7i 0.855616 + 0.493990i
\(566\) 1.76981e7i 0.0976060i
\(567\) −5.40896e6 + 1.95182e7i −0.0296732 + 0.107076i
\(568\) −2.50810e8 −1.36868
\(569\) −2.37803e7 + 4.11886e7i −0.129086 + 0.223584i −0.923323 0.384025i \(-0.874538\pi\)
0.794237 + 0.607609i \(0.207871\pi\)
\(570\) −4.46413e7 + 2.57737e7i −0.241053 + 0.139172i
\(571\) −8.27707e7 1.43363e8i −0.444599 0.770068i 0.553425 0.832899i \(-0.313320\pi\)
−0.998024 + 0.0628311i \(0.979987\pi\)
\(572\) 1.40358e8 + 8.10360e7i 0.749981 + 0.433002i
\(573\) 1.34193e8i 0.713291i
\(574\) −1.80013e7 6.95523e7i −0.0951848 0.367770i
\(575\) 1.10306e8 0.580222
\(576\) 2.65466e7 4.59801e7i 0.138913 0.240604i
\(577\) −4.44692e7 + 2.56743e7i −0.231490 + 0.133651i −0.611259 0.791431i \(-0.709337\pi\)
0.379769 + 0.925081i \(0.376003\pi\)
\(578\) 3.77210e7 + 6.53346e7i 0.195344 + 0.338345i
\(579\) −2.42846e6 1.40207e6i −0.0125111 0.00722328i
\(580\) 3.04895e7i 0.156267i
\(581\) 1.75987e7 1.73007e7i 0.0897331 0.0882133i
\(582\) 5.61673e7 0.284914
\(583\) 1.42525e7 2.46861e7i 0.0719259 0.124579i
\(584\) 1.55672e8 8.98771e7i 0.781576 0.451243i
\(585\) −2.28423e7 3.95640e7i −0.114096 0.197621i
\(586\) −1.28011e7 7.39070e6i −0.0636141 0.0367276i
\(587\) 2.37624e8i 1.17483i −0.809285 0.587416i \(-0.800145\pi\)
0.809285 0.587416i \(-0.199855\pi\)
\(588\) 3.15782e7 5.25992e7i 0.155330 0.258730i
\(589\) −2.25238e8 −1.10229
\(590\) −1.32466e7 + 2.29437e7i −0.0644982 + 0.111714i
\(591\) −3.63600e7 + 2.09925e7i −0.176141 + 0.101695i
\(592\) 9.50232e6 + 1.64585e7i 0.0457999 + 0.0793278i
\(593\) −3.20624e8 1.85112e8i −1.53756 0.887711i −0.998981 0.0451361i \(-0.985628\pi\)
−0.538579 0.842575i \(-0.681039\pi\)
\(594\) 3.61305e7i 0.172391i
\(595\) −9.89842e7 1.00690e8i −0.469910 0.478006i
\(596\) −1.24549e8 −0.588305
\(597\) −4.70944e7 + 8.15699e7i −0.221333 + 0.383360i
\(598\) 1.33052e8 7.68173e7i 0.622180 0.359216i
\(599\) 1.87938e7 + 3.25519e7i 0.0874451 + 0.151459i 0.906430 0.422355i \(-0.138796\pi\)
−0.818985 + 0.573814i \(0.805463\pi\)
\(600\) −8.10068e7 4.67693e7i −0.375032 0.216525i
\(601\) 2.67605e7i 0.123274i −0.998099 0.0616369i \(-0.980368\pi\)
0.998099 0.0616369i \(-0.0196321\pi\)
\(602\) 1.35162e8 3.49821e7i 0.619534 0.160346i
\(603\) −1.33326e8 −0.608083
\(604\) −4.26849e7 + 7.39324e7i −0.193715 + 0.335524i
\(605\) 6.99761e7 4.04007e7i 0.315998 0.182441i
\(606\) −4.39654e7 7.61503e7i −0.197557 0.342179i
\(607\) 6.69071e7 + 3.86288e7i 0.299162 + 0.172721i 0.642066 0.766649i \(-0.278077\pi\)
−0.342905 + 0.939370i \(0.611411\pi\)
\(608\) 2.66697e8i 1.18661i
\(609\) −7.01294e7 1.94345e7i −0.310490 0.0860444i
\(610\) −9.76808e7 −0.430348
\(611\) −1.95352e8 + 3.38359e8i −0.856433 + 1.48338i
\(612\) −4.32748e7 + 2.49847e7i −0.188791 + 0.108998i
\(613\) 1.76486e8 + 3.05682e8i 0.766174 + 1.32705i 0.939623 + 0.342210i \(0.111175\pi\)
−0.173449 + 0.984843i \(0.555491\pi\)
\(614\) 9.51394e7 + 5.49288e7i 0.411013 + 0.237298i
\(615\) 3.95608e7i 0.170075i
\(616\) 8.51446e7 3.07244e8i 0.364263 1.31444i
\(617\) 1.82109e8 0.775310 0.387655 0.921805i \(-0.373285\pi\)
0.387655 + 0.921805i \(0.373285\pi\)
\(618\) 1.80640e7 3.12878e7i 0.0765330 0.132559i
\(619\) 8.43335e7 4.86900e7i 0.355573 0.205290i −0.311564 0.950225i \(-0.600853\pi\)
0.667137 + 0.744935i \(0.267520\pi\)
\(620\) 2.82379e7 + 4.89094e7i 0.118483 + 0.205219i
\(621\) −3.24811e7 1.87530e7i −0.135630 0.0783062i
\(622\) 8.71661e7i 0.362223i
\(623\) 1.40426e7 + 5.42570e7i 0.0580742 + 0.224384i
\(624\) −3.65864e7 −0.150579
\(625\) −2.70211e7 + 4.68019e7i −0.110678 + 0.191701i
\(626\) 5.05134e7 2.91639e7i 0.205913 0.118884i
\(627\) 1.20173e8 + 2.08145e8i 0.487533 + 0.844431i
\(628\) −1.96384e8 1.13382e8i −0.792916 0.457790i
\(629\) 1.39741e8i 0.561529i
\(630\) −2.19992e7 + 2.16266e7i −0.0879804 + 0.0864903i
\(631\) −1.37285e8 −0.546430 −0.273215 0.961953i \(-0.588087\pi\)
−0.273215 + 0.961953i \(0.588087\pi\)
\(632\) −1.10423e8 + 1.91259e8i −0.437431 + 0.757653i
\(633\) 1.86453e8 1.07648e8i 0.735118 0.424421i
\(634\) 8.93238e7 + 1.54713e8i 0.350509 + 0.607100i
\(635\) 6.47495e7 + 3.73832e7i 0.252881 + 0.146001i
\(636\) 8.61341e6i 0.0334814i
\(637\) −3.30243e8 5.64143e6i −1.27766 0.0218258i
\(638\) −1.29818e8 −0.499887
\(639\) 5.65770e7 9.79943e7i 0.216839 0.375576i
\(640\) −4.07622e7 + 2.35341e7i −0.155495 + 0.0897753i
\(641\) 1.04673e8 + 1.81298e8i 0.397428 + 0.688366i 0.993408 0.114633i \(-0.0365693\pi\)
−0.595979 + 0.803000i \(0.703236\pi\)
\(642\) 1.65078e8 + 9.53078e7i 0.623855 + 0.360183i
\(643\) 3.49818e8i 1.31586i 0.753079 + 0.657930i \(0.228568\pi\)
−0.753079 + 0.657930i \(0.771432\pi\)
\(644\) 7.96443e7 + 8.10165e7i 0.298193 + 0.303330i
\(645\) 7.68791e7 0.286503
\(646\) 1.51772e8 2.62877e8i 0.562981 0.975112i
\(647\) 3.20197e8 1.84866e8i 1.18224 0.682566i 0.225707 0.974195i \(-0.427531\pi\)
0.956531 + 0.291630i \(0.0941974\pi\)
\(648\) 1.59025e7 + 2.75439e7i 0.0584439 + 0.101228i
\(649\) 1.06978e8 + 6.17637e7i 0.391345 + 0.225943i
\(650\) 1.72864e8i 0.629454i
\(651\) −1.30497e8 + 3.37747e7i −0.472995 + 0.122419i
\(652\) 2.76697e8 0.998303
\(653\) 1.97623e7 3.42293e7i 0.0709737 0.122930i −0.828355 0.560204i \(-0.810723\pi\)
0.899328 + 0.437274i \(0.144056\pi\)
\(654\) −5.71480e7 + 3.29944e7i −0.204300 + 0.117952i
\(655\) −9.58169e6 1.65960e7i −0.0340971 0.0590580i
\(656\) −2.74376e7 1.58411e7i −0.0971929 0.0561144i
\(657\) 8.10968e7i 0.285962i
\(658\) 2.54247e8 + 7.04579e7i 0.892437 + 0.247316i
\(659\) −3.29124e8 −1.15002 −0.575008 0.818148i \(-0.695001\pi\)
−0.575008 + 0.818148i \(0.695001\pi\)
\(660\) 3.01320e7 5.21901e7i 0.104808 0.181533i
\(661\) −1.39292e8 + 8.04205e7i −0.482306 + 0.278460i −0.721377 0.692543i \(-0.756491\pi\)
0.239071 + 0.971002i \(0.423157\pi\)
\(662\) −5.53611e7 9.58882e7i −0.190823 0.330515i
\(663\) 2.32978e8 + 1.34510e8i 0.799419 + 0.461545i
\(664\) 3.87530e7i 0.132374i
\(665\) −5.48044e7 + 1.97761e8i −0.186359 + 0.672474i
\(666\) −3.05315e7 −0.103353
\(667\) 6.73800e7 1.16706e8i 0.227067 0.393291i
\(668\) 7.53117e7 4.34812e7i 0.252658 0.145872i
\(669\) 7.64926e7 + 1.32489e8i 0.255471 + 0.442488i
\(670\) −1.75867e8 1.01537e8i −0.584735 0.337597i
\(671\) 4.55448e8i 1.50755i
\(672\) −3.99916e7 1.54517e8i −0.131783 0.509177i
\(673\) 5.32162e8 1.74582 0.872908 0.487886i \(-0.162232\pi\)
0.872908 + 0.487886i \(0.162232\pi\)
\(674\) 1.01338e7 1.75523e7i 0.0330974 0.0573263i
\(675\) 3.65466e7 2.11002e7i 0.118832 0.0686080i
\(676\) −5.10955e7 8.84999e7i −0.165403 0.286486i
\(677\) −4.68878e8 2.70707e8i −1.51110 0.872435i −0.999916 0.0129645i \(-0.995873\pi\)
−0.511186 0.859470i \(-0.670794\pi\)
\(678\) 2.29262e8i 0.735601i
\(679\) 1.59458e8 1.56758e8i 0.509375 0.500748i
\(680\) −2.21722e8 −0.705151
\(681\) 1.13595e8 1.96753e8i 0.359683 0.622989i
\(682\) −2.08246e8 + 1.20231e8i −0.656483 + 0.379021i
\(683\) −1.24469e8 2.15587e8i −0.390662 0.676646i 0.601875 0.798590i \(-0.294420\pi\)
−0.992537 + 0.121944i \(0.961087\pi\)
\(684\) 6.28957e7 + 3.63129e7i 0.196541 + 0.113473i
\(685\) 2.50047e8i 0.777946i
\(686\) 5.21875e7 + 2.16843e8i 0.161657 + 0.671696i
\(687\) −2.29126e8 −0.706651
\(688\) 3.07843e7 5.33199e7i 0.0945286 0.163728i
\(689\) −4.01592e7 + 2.31860e7i −0.122780 + 0.0708871i
\(690\) −2.85633e7 4.94731e7i −0.0869484 0.150599i
\(691\) 8.00565e7 + 4.62206e7i 0.242640 + 0.140088i 0.616390 0.787441i \(-0.288595\pi\)
−0.373749 + 0.927530i \(0.621928\pi\)
\(692\) 2.74491e8i 0.828341i
\(693\) 1.00837e8 + 1.02574e8i 0.302984 + 0.308204i
\(694\) 3.56825e7 0.106752
\(695\) 2.06997e7 3.58530e7i 0.0616610 0.106800i
\(696\) −9.89658e7 + 5.71379e7i −0.293533 + 0.169472i
\(697\) 1.16480e8 + 2.01749e8i 0.343995 + 0.595816i
\(698\) −1.92196e8 1.10964e8i −0.565169 0.326300i
\(699\) 8.96640e7i 0.262535i
\(700\) −1.23750e8 + 3.20286e7i −0.360788 + 0.0933778i
\(701\) 5.38435e8 1.56307 0.781537 0.623859i \(-0.214436\pi\)
0.781537 + 0.623859i \(0.214436\pi\)
\(702\) 2.93885e7 5.09024e7i 0.0849505 0.147139i
\(703\) −1.75890e8 + 1.01550e8i −0.506262 + 0.292290i
\(704\) −1.88529e8 3.26541e8i −0.540331 0.935880i
\(705\) 1.25813e8 + 7.26384e7i 0.359054 + 0.207300i
\(706\) 4.48603e7i 0.127482i
\(707\) −3.37346e8 9.34866e7i −0.954590 0.264540i
\(708\) 3.73265e7 0.105176
\(709\) −3.53455e7 + 6.12202e7i −0.0991735 + 0.171773i −0.911343 0.411648i \(-0.864953\pi\)
0.812169 + 0.583422i \(0.198287\pi\)
\(710\) 1.49258e8 8.61744e7i 0.417027 0.240771i
\(711\) −4.98179e7 8.62872e7i −0.138604 0.240070i
\(712\) 7.62173e7 + 4.40041e7i 0.211161 + 0.121914i
\(713\) 2.49616e8i 0.688660i
\(714\) 4.85140e7 1.75062e8i 0.133282 0.480948i
\(715\) −3.24442e8 −0.887604
\(716\) 1.36954e8 2.37211e8i 0.373109 0.646243i
\(717\) −2.16226e8 + 1.24838e8i −0.586610 + 0.338680i
\(718\) −1.02021e8 1.76705e8i −0.275622 0.477392i
\(719\) −3.38940e8 1.95687e8i −0.911876 0.526472i −0.0308415 0.999524i \(-0.509819\pi\)
−0.881034 + 0.473053i \(0.843152\pi\)
\(720\) 1.36041e7i 0.0364478i
\(721\) −3.60378e7 1.39241e8i −0.0961506 0.371501i
\(722\) −1.81149e8 −0.481309
\(723\) 2.01252e8 3.48578e8i 0.532506 0.922327i
\(724\) 9.43295e7 5.44612e7i 0.248560 0.143506i
\(725\) 7.58135e7 + 1.31313e8i 0.198945 + 0.344582i
\(726\) 9.00302e7 + 5.19789e7i 0.235276 + 0.135837i
\(727\) 4.83550e8i 1.25846i 0.777221 + 0.629228i \(0.216629\pi\)
−0.777221 + 0.629228i \(0.783371\pi\)
\(728\) −3.69868e8 + 3.63603e8i −0.958633 + 0.942397i
\(729\) −1.43489e7 −0.0370370
\(730\) −6.17607e7 + 1.06973e8i −0.158761 + 0.274982i
\(731\) −3.92061e8 + 2.26357e8i −1.00369 + 0.579484i
\(732\) 6.88118e7 + 1.19186e8i 0.175441 + 0.303872i
\(733\) −2.76711e8 1.59759e8i −0.702611 0.405653i 0.105708 0.994397i \(-0.466289\pi\)
−0.808319 + 0.588745i \(0.799622\pi\)
\(734\) 1.08968e8i 0.275556i
\(735\) −2.09768e6 + 1.22796e8i −0.00528295 + 0.309258i
\(736\) 2.95563e8 0.741339
\(737\) −4.73427e8 + 8.20000e8i −1.18263 + 2.04838i
\(738\) 4.40792e7 2.54491e7i 0.109664 0.0633146i
\(739\) −1.76757e8 3.06151e8i −0.437968 0.758582i 0.559565 0.828787i \(-0.310968\pi\)
−0.997533 + 0.0702042i \(0.977635\pi\)
\(740\) 4.41024e7 + 2.54625e7i 0.108835 + 0.0628357i
\(741\) 3.90994e8i 0.960983i
\(742\) 2.19520e7 + 2.23302e7i 0.0537357 + 0.0546615i
\(743\) 4.63396e8 1.12976 0.564880 0.825173i \(-0.308923\pi\)
0.564880 + 0.825173i \(0.308923\pi\)
\(744\) −1.05837e8 + 1.83315e8i −0.256991 + 0.445121i
\(745\) 2.15924e8 1.24664e8i 0.522195 0.301489i
\(746\) −2.88318e7 4.99381e7i −0.0694472 0.120286i
\(747\) 1.51412e7 + 8.74179e6i 0.0363245 + 0.0209719i
\(748\) 3.54873e8i 0.847945i
\(749\) 7.34650e8 1.90139e8i 1.74838 0.452508i
\(750\) 1.54427e8 0.366050
\(751\) 1.48510e7 2.57226e7i 0.0350618 0.0607289i −0.847962 0.530057i \(-0.822171\pi\)
0.883024 + 0.469328i \(0.155504\pi\)
\(752\) 1.00757e8 5.81724e7i 0.236932 0.136793i
\(753\) −7.41942e7 1.28508e8i −0.173774 0.300985i
\(754\) 1.82894e8 + 1.05594e8i 0.426662 + 0.246334i
\(755\) 1.70897e8i 0.397093i
\(756\) 4.18853e7 + 1.16074e7i 0.0969385 + 0.0268640i
\(757\) 7.11235e8 1.63955 0.819776 0.572684i \(-0.194098\pi\)
0.819776 + 0.572684i \(0.194098\pi\)
\(758\) 1.45365e8 2.51780e8i 0.333774 0.578113i
\(759\) −2.30674e8 + 1.33180e8i −0.527563 + 0.304588i
\(760\) 1.61126e8 + 2.79078e8i 0.367049 + 0.635748i
\(761\) 3.18255e8 + 1.83745e8i 0.722140 + 0.416928i 0.815540 0.578701i \(-0.196440\pi\)
−0.0933998 + 0.995629i \(0.529773\pi\)
\(762\) 9.61931e7i 0.217410i
\(763\) −7.01583e7 + 2.53166e8i −0.157945 + 0.569942i
\(764\) −2.87974e8 −0.645763
\(765\) 5.00154e7