Properties

Label 21.7.f.b.19.3
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: \(x^{8} - x^{7} + 212 x^{6} - 787 x^{5} + 38792 x^{4} - 92833 x^{3} + 1563109 x^{2} + 3107772 x + 38787984\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.3
Root \(-2.30325 + 3.98935i\) of defining polynomial
Character \(\chi\) \(=\) 21.19
Dual form 21.7.f.b.10.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.80325 - 3.12332i) q^{2} +(13.5000 - 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(71.9311 + 41.5295i) q^{5} -56.2198i q^{6} +(77.0894 - 334.225i) q^{7} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})\) \(q+(1.80325 - 3.12332i) q^{2} +(13.5000 - 7.79423i) q^{3} +(25.4966 + 44.1614i) q^{4} +(71.9311 + 41.5295i) q^{5} -56.2198i q^{6} +(77.0894 - 334.225i) q^{7} +414.723 q^{8} +(121.500 - 210.444i) q^{9} +(259.420 - 149.776i) q^{10} +(221.304 + 383.310i) q^{11} +(688.408 + 397.452i) q^{12} -696.494i q^{13} +(-904.880 - 843.466i) q^{14} +1294.76 q^{15} +(-883.932 + 1531.01i) q^{16} +(-5447.24 + 3144.96i) q^{17} +(-438.190 - 758.967i) q^{18} +(-2327.56 - 1343.82i) q^{19} +4235.44i q^{20} +(-1564.32 - 5112.89i) q^{21} +1596.27 q^{22} +(-7885.31 + 13657.8i) q^{23} +(5598.76 - 3232.44i) q^{24} +(-4363.11 - 7557.12i) q^{25} +(-2175.37 - 1255.95i) q^{26} -3788.00i q^{27} +(16725.3 - 5117.22i) q^{28} -23274.5 q^{29} +(2334.78 - 4043.95i) q^{30} +(41177.0 - 23773.6i) q^{31} +(16459.0 + 28507.9i) q^{32} +(5975.21 + 3449.79i) q^{33} +22684.6i q^{34} +(19425.3 - 20839.7i) q^{35} +12391.3 q^{36} +(5079.89 - 8798.64i) q^{37} +(-8394.35 + 4846.48i) q^{38} +(-5428.63 - 9402.67i) q^{39} +(29831.5 + 17223.2i) q^{40} -38165.4i q^{41} +(-18790.0 - 4333.95i) q^{42} -151197. q^{43} +(-11285.0 + 19546.2i) q^{44} +(17479.3 - 10091.7i) q^{45} +(28438.4 + 49256.7i) q^{46} +(-43543.1 - 25139.6i) q^{47} +27558.3i q^{48} +(-105763. - 51530.4i) q^{49} -31471.1 q^{50} +(-49025.1 + 84914.0i) q^{51} +(30758.1 - 17758.2i) q^{52} +(99778.2 + 172821. i) q^{53} +(-11831.1 - 6830.70i) q^{54} +36762.6i q^{55} +(31970.7 - 138611. i) q^{56} -41896.1 q^{57} +(-41969.8 + 72693.8i) q^{58} +(335347. - 193612. i) q^{59} +(33012.0 + 57178.4i) q^{60} +(-10203.5 - 5890.98i) q^{61} -171479. i q^{62} +(-60969.3 - 56831.3i) q^{63} +5575.73 q^{64} +(28925.0 - 50099.6i) q^{65} +(21549.6 - 12441.7i) q^{66} +(192138. + 332792. i) q^{67} +(-277772. - 160372. i) q^{68} +245840. i q^{69} +(-30060.4 - 98250.6i) q^{70} +156126. q^{71} +(50388.8 - 87276.0i) q^{72} +(325227. - 187770. i) q^{73} +(-18320.6 - 31732.3i) q^{74} +(-117804. - 68014.1i) q^{75} -137051. i q^{76} +(145172. - 44416.2i) q^{77} -39156.7 q^{78} +(-16591.8 + 28737.9i) q^{79} +(-127164. + 73418.4i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(-119203. - 68821.8i) q^{82} +984986. i q^{83} +(185907. - 199444. i) q^{84} -522434. q^{85} +(-272646. + 472237. i) q^{86} +(-314206. + 181407. i) q^{87} +(91779.9 + 158967. i) q^{88} +(-227430. - 131307. i) q^{89} -72791.1i q^{90} +(-232786. - 53692.3i) q^{91} -804193. q^{92} +(370593. - 641886. i) q^{93} +(-157038. + 90666.0i) q^{94} +(-111616. - 193325. i) q^{95} +(444394. + 256571. i) q^{96} -575147. i q^{97} +(-351664. + 237411. i) q^{98} +107554. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 5q^{2} + 108q^{3} - 173q^{4} - 42q^{5} + 748q^{7} - 454q^{8} + 972q^{9} + O(q^{10}) \) \( 8q - 5q^{2} + 108q^{3} - 173q^{4} - 42q^{5} + 748q^{7} - 454q^{8} + 972q^{9} + 261q^{10} - 1070q^{11} - 4671q^{12} + 6070q^{14} - 756q^{15} + 3911q^{16} + 7212q^{17} + 1215q^{18} - 24606q^{19} + 8154q^{21} - 78q^{22} - 15224q^{23} - 6129q^{24} + 22274q^{25} - 19044q^{26} - 3415q^{28} + 32524q^{29} + 2349q^{30} + 40200q^{31} + 70203q^{32} - 28890q^{33} - 242436q^{35} - 84078q^{36} - 45670q^{37} + 503310q^{38} + 93366q^{39} - 94941q^{40} + 55161q^{42} - 445660q^{43} - 188829q^{44} - 10206q^{45} + 525804q^{46} + 82884q^{47} + 24116q^{49} - 1218884q^{50} + 64908q^{51} + 722856q^{52} - 13034q^{53} + 32805q^{54} + 127061q^{56} - 442908q^{57} - 159501q^{58} + 1810362q^{59} + 429705q^{60} - 392856q^{61} + 38394q^{63} - 1410446q^{64} - 389004q^{65} - 1053q^{66} + 384094q^{67} - 1616346q^{68} + 406005q^{70} + 225688q^{71} - 55161q^{72} + 903078q^{73} + 1185530q^{74} + 601398q^{75} - 327674q^{77} - 342792q^{78} - 559592q^{79} + 847713q^{80} - 236196q^{81} + 347634q^{82} - 879444q^{84} + 1953576q^{85} - 2302402q^{86} + 439074q^{87} + 304887q^{88} - 1770036q^{89} - 2960718q^{91} - 113064q^{92} + 361800q^{93} - 1837620q^{94} + 1160112q^{95} + 1895481q^{96} + 5732467q^{98} - 520020q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.80325 3.12332i 0.225406 0.390415i −0.731035 0.682340i \(-0.760962\pi\)
0.956441 + 0.291925i \(0.0942957\pi\)
\(3\) 13.5000 7.79423i 0.500000 0.288675i
\(4\) 25.4966 + 44.1614i 0.398384 + 0.690021i
\(5\) 71.9311 + 41.5295i 0.575449 + 0.332236i 0.759323 0.650714i \(-0.225530\pi\)
−0.183874 + 0.982950i \(0.558864\pi\)
\(6\) 56.2198i 0.260277i
\(7\) 77.0894 334.225i 0.224750 0.974416i
\(8\) 414.723 0.810006
\(9\) 121.500 210.444i 0.166667 0.288675i
\(10\) 259.420 149.776i 0.259420 0.149776i
\(11\) 221.304 + 383.310i 0.166269 + 0.287986i 0.937105 0.349047i \(-0.113495\pi\)
−0.770836 + 0.637033i \(0.780161\pi\)
\(12\) 688.408 + 397.452i 0.398384 + 0.230007i
\(13\) 696.494i 0.317020i −0.987357 0.158510i \(-0.949331\pi\)
0.987357 0.158510i \(-0.0506691\pi\)
\(14\) −904.880 843.466i −0.329767 0.307386i
\(15\) 1294.76 0.383633
\(16\) −883.932 + 1531.01i −0.215804 + 0.373783i
\(17\) −5447.24 + 3144.96i −1.10874 + 0.640131i −0.938503 0.345272i \(-0.887787\pi\)
−0.170237 + 0.985403i \(0.554453\pi\)
\(18\) −438.190 758.967i −0.0751354 0.130138i
\(19\) −2327.56 1343.82i −0.339344 0.195920i 0.320638 0.947202i \(-0.396103\pi\)
−0.659982 + 0.751281i \(0.729436\pi\)
\(20\) 4235.44i 0.529430i
\(21\) −1564.32 5112.89i −0.168915 0.552088i
\(22\) 1596.27 0.149912
\(23\) −7885.31 + 13657.8i −0.648090 + 1.12252i 0.335489 + 0.942044i \(0.391098\pi\)
−0.983579 + 0.180480i \(0.942235\pi\)
\(24\) 5598.76 3232.44i 0.405003 0.233828i
\(25\) −4363.11 7557.12i −0.279239 0.483656i
\(26\) −2175.37 1255.95i −0.123770 0.0714584i
\(27\) 3788.00i 0.192450i
\(28\) 16725.3 5117.22i 0.761905 0.233109i
\(29\) −23274.5 −0.954304 −0.477152 0.878821i \(-0.658331\pi\)
−0.477152 + 0.878821i \(0.658331\pi\)
\(30\) 2334.78 4043.95i 0.0864732 0.149776i
\(31\) 41177.0 23773.6i 1.38220 0.798012i 0.389778 0.920909i \(-0.372552\pi\)
0.992419 + 0.122897i \(0.0392185\pi\)
\(32\) 16459.0 + 28507.9i 0.502290 + 0.869991i
\(33\) 5975.21 + 3449.79i 0.166269 + 0.0959955i
\(34\) 22684.6i 0.577158i
\(35\) 19425.3 20839.7i 0.453068 0.486057i
\(36\) 12391.3 0.265589
\(37\) 5079.89 8798.64i 0.100288 0.173704i −0.811515 0.584331i \(-0.801357\pi\)
0.911803 + 0.410627i \(0.134690\pi\)
\(38\) −8394.35 + 4846.48i −0.152981 + 0.0883234i
\(39\) −5428.63 9402.67i −0.0915159 0.158510i
\(40\) 29831.5 + 17223.2i 0.466117 + 0.269113i
\(41\) 38165.4i 0.553756i −0.960905 0.276878i \(-0.910700\pi\)
0.960905 0.276878i \(-0.0892998\pi\)
\(42\) −18790.0 4333.95i −0.253618 0.0584973i
\(43\) −151197. −1.90168 −0.950841 0.309679i \(-0.899779\pi\)
−0.950841 + 0.309679i \(0.899779\pi\)
\(44\) −11285.0 + 19546.2i −0.132478 + 0.229458i
\(45\) 17479.3 10091.7i 0.191816 0.110745i
\(46\) 28438.4 + 49256.7i 0.292167 + 0.506048i
\(47\) −43543.1 25139.6i −0.419397 0.242139i 0.275422 0.961323i \(-0.411182\pi\)
−0.694819 + 0.719184i \(0.744516\pi\)
\(48\) 27558.3i 0.249189i
\(49\) −105763. 51530.4i −0.898975 0.438001i
\(50\) −31471.1 −0.251769
\(51\) −49025.1 + 84914.0i −0.369580 + 0.640131i
\(52\) 30758.1 17758.2i 0.218751 0.126296i
\(53\) 99778.2 + 172821.i 0.670206 + 1.16083i 0.977846 + 0.209328i \(0.0671275\pi\)
−0.307640 + 0.951503i \(0.599539\pi\)
\(54\) −11831.1 6830.70i −0.0751354 0.0433795i
\(55\) 36762.6i 0.220962i
\(56\) 31970.7 138611.i 0.182049 0.789283i
\(57\) −41896.1 −0.226229
\(58\) −41969.8 + 72693.8i −0.215106 + 0.372575i
\(59\) 335347. 193612.i 1.63282 0.942708i 0.649600 0.760277i \(-0.274937\pi\)
0.983219 0.182431i \(-0.0583968\pi\)
\(60\) 33012.0 + 57178.4i 0.152833 + 0.264715i
\(61\) −10203.5 5890.98i −0.0449530 0.0259536i 0.477355 0.878711i \(-0.341596\pi\)
−0.522308 + 0.852757i \(0.674929\pi\)
\(62\) 171479.i 0.719508i
\(63\) −60969.3 56831.3i −0.243831 0.227283i
\(64\) 5575.73 0.0212697
\(65\) 28925.0 50099.6i 0.105325 0.182429i
\(66\) 21549.6 12441.7i 0.0749562 0.0432760i
\(67\) 192138. + 332792.i 0.638834 + 1.10649i 0.985689 + 0.168575i \(0.0539165\pi\)
−0.346854 + 0.937919i \(0.612750\pi\)
\(68\) −277772. 160372.i −0.883408 0.510036i
\(69\) 245840.i 0.748350i
\(70\) −30060.4 98250.6i −0.0876395 0.286445i
\(71\) 156126. 0.436213 0.218107 0.975925i \(-0.430012\pi\)
0.218107 + 0.975925i \(0.430012\pi\)
\(72\) 50388.8 87276.0i 0.135001 0.233828i
\(73\) 325227. 187770.i 0.836022 0.482677i −0.0198883 0.999802i \(-0.506331\pi\)
0.855910 + 0.517125i \(0.172998\pi\)
\(74\) −18320.6 31732.3i −0.0452111 0.0783080i
\(75\) −117804. 68014.1i −0.279239 0.161219i
\(76\) 137051.i 0.312206i
\(77\) 145172. 44416.2i 0.317988 0.0972902i
\(78\) −39156.7 −0.0825130
\(79\) −16591.8 + 28737.9i −0.0336521 + 0.0582872i −0.882361 0.470573i \(-0.844047\pi\)
0.848709 + 0.528860i \(0.177380\pi\)
\(80\) −127164. + 73418.4i −0.248368 + 0.143395i
\(81\) −29524.5 51137.9i −0.0555556 0.0962250i
\(82\) −119203. 68821.8i −0.216195 0.124820i
\(83\) 984986.i 1.72264i 0.508059 + 0.861322i \(0.330363\pi\)
−0.508059 + 0.861322i \(0.669637\pi\)
\(84\) 185907. 199444.i 0.313660 0.336498i
\(85\) −522434. −0.850697
\(86\) −272646. + 472237.i −0.428651 + 0.742446i
\(87\) −314206. + 181407.i −0.477152 + 0.275484i
\(88\) 91779.9 + 158967.i 0.134679 + 0.233271i
\(89\) −227430. 131307.i −0.322609 0.186259i 0.329946 0.944000i \(-0.392970\pi\)
−0.652555 + 0.757741i \(0.726303\pi\)
\(90\) 72791.1i 0.0998507i
\(91\) −232786. 53692.3i −0.308910 0.0712505i
\(92\) −804193. −1.03275
\(93\) 370593. 641886.i 0.460732 0.798012i
\(94\) −157038. + 90666.0i −0.189070 + 0.109159i
\(95\) −111616. 193325.i −0.130184 0.225484i
\(96\) 444394. + 256571.i 0.502290 + 0.289997i
\(97\) 575147.i 0.630179i −0.949062 0.315089i \(-0.897966\pi\)
0.949062 0.315089i \(-0.102034\pi\)
\(98\) −351664. + 237411.i −0.373637 + 0.252245i
\(99\) 107554. 0.110846
\(100\) 222489. 385362.i 0.222489 0.385362i
\(101\) 634688. 366437.i 0.616022 0.355661i −0.159297 0.987231i \(-0.550923\pi\)
0.775319 + 0.631570i \(0.217589\pi\)
\(102\) 176809. + 306242.i 0.166611 + 0.288579i
\(103\) 908207. + 524353.i 0.831138 + 0.479858i 0.854242 0.519875i \(-0.174022\pi\)
−0.0231042 + 0.999733i \(0.507355\pi\)
\(104\) 288852.i 0.256788i
\(105\) 99812.3 432741.i 0.0862216 0.373818i
\(106\) 719700. 0.604274
\(107\) −587412. + 1.01743e6i −0.479503 + 0.830524i −0.999724 0.0235083i \(-0.992516\pi\)
0.520221 + 0.854032i \(0.325850\pi\)
\(108\) 167283. 96580.9i 0.132795 0.0766690i
\(109\) −367045. 635741.i −0.283426 0.490908i 0.688800 0.724951i \(-0.258138\pi\)
−0.972226 + 0.234043i \(0.924804\pi\)
\(110\) 114821. + 66292.1i 0.0862669 + 0.0498062i
\(111\) 158375.i 0.115803i
\(112\) 443561. + 413457.i 0.315718 + 0.294291i
\(113\) 2.04925e6 1.42023 0.710116 0.704085i \(-0.248643\pi\)
0.710116 + 0.704085i \(0.248643\pi\)
\(114\) −75549.2 + 130855.i −0.0509935 + 0.0883234i
\(115\) −1.13440e6 + 654945.i −0.745885 + 0.430637i
\(116\) −593421. 1.02783e6i −0.380180 0.658490i
\(117\) −146573. 84624.0i −0.0915159 0.0528367i
\(118\) 1.39653e6i 0.849969i
\(119\) 631201. + 2.06304e6i 0.374564 + 1.22424i
\(120\) 536967. 0.310745
\(121\) 787829. 1.36456e6i 0.444709 0.770259i
\(122\) −36798.9 + 21245.8i −0.0202654 + 0.0117002i
\(123\) −297470. 515233.i −0.159856 0.276878i
\(124\) 2.09975e6 + 1.21229e6i 1.10129 + 0.635830i
\(125\) 2.02259e6i 1.03556i
\(126\) −287445. + 87945.6i −0.143696 + 0.0439645i
\(127\) −1.64688e6 −0.803991 −0.401995 0.915642i \(-0.631683\pi\)
−0.401995 + 0.915642i \(0.631683\pi\)
\(128\) −1.04332e6 + 1.80709e6i −0.497495 + 0.861687i
\(129\) −2.04116e6 + 1.17846e6i −0.950841 + 0.548968i
\(130\) −104318. 180684.i −0.0474821 0.0822413i
\(131\) −1.78472e6 1.03041e6i −0.793882 0.458348i 0.0474457 0.998874i \(-0.484892\pi\)
−0.841327 + 0.540526i \(0.818225\pi\)
\(132\) 351831.i 0.152972i
\(133\) −628568. + 674335.i −0.267176 + 0.286629i
\(134\) 1.38589e6 0.575989
\(135\) 157313. 272475.i 0.0639388 0.110745i
\(136\) −2.25909e6 + 1.30429e6i −0.898085 + 0.518510i
\(137\) −1.61460e6 2.79657e6i −0.627919 1.08759i −0.987969 0.154654i \(-0.950574\pi\)
0.360050 0.932933i \(-0.382760\pi\)
\(138\) 767836. + 443310.i 0.292167 + 0.168683i
\(139\) 4.06719e6i 1.51443i 0.653163 + 0.757217i \(0.273442\pi\)
−0.653163 + 0.757217i \(0.726558\pi\)
\(140\) 1.41559e6 + 326507.i 0.515885 + 0.118990i
\(141\) −783776. −0.279598
\(142\) 281533. 487630.i 0.0983252 0.170304i
\(143\) 266973. 154137.i 0.0912976 0.0527107i
\(144\) 214795. + 372037.i 0.0719346 + 0.124594i
\(145\) −1.67416e6 966578.i −0.549153 0.317054i
\(146\) 1.35438e6i 0.435194i
\(147\) −1.82945e6 + 128684.i −0.575927 + 0.0405111i
\(148\) 518080. 0.159813
\(149\) 1.39737e6 2.42031e6i 0.422427 0.731666i −0.573749 0.819031i \(-0.694511\pi\)
0.996176 + 0.0873655i \(0.0278448\pi\)
\(150\) −424860. + 245293.i −0.125884 + 0.0726794i
\(151\) −301549. 522299.i −0.0875846 0.151701i 0.818905 0.573929i \(-0.194581\pi\)
−0.906490 + 0.422228i \(0.861248\pi\)
\(152\) −965293. 557312.i −0.274871 0.158697i
\(153\) 1.52845e6i 0.426754i
\(154\) 123055. 533512.i 0.0336929 0.146077i
\(155\) 3.94921e6 1.06051
\(156\) 276823. 479472.i 0.0729170 0.126296i
\(157\) −1.23763e6 + 714546.i −0.319810 + 0.184642i −0.651308 0.758814i \(-0.725779\pi\)
0.331498 + 0.943456i \(0.392446\pi\)
\(158\) 59838.4 + 103643.i 0.0151708 + 0.0262766i
\(159\) 2.69401e6 + 1.55539e6i 0.670206 + 0.386943i
\(160\) 2.73414e6i 0.667514i
\(161\) 3.95689e6 + 3.68833e6i 0.948148 + 0.883797i
\(162\) −212960. −0.0500903
\(163\) 2.78644e6 4.82625e6i 0.643408 1.11442i −0.341259 0.939969i \(-0.610853\pi\)
0.984667 0.174446i \(-0.0558135\pi\)
\(164\) 1.68544e6 973087.i 0.382103 0.220607i
\(165\) 286536. + 496295.i 0.0637862 + 0.110481i
\(166\) 3.07643e6 + 1.77618e6i 0.672546 + 0.388295i
\(167\) 2.24388e6i 0.481781i −0.970552 0.240890i \(-0.922561\pi\)
0.970552 0.240890i \(-0.0774394\pi\)
\(168\) −648758. 2.12043e6i −0.136822 0.447194i
\(169\) 4.34171e6 0.899498
\(170\) −942080. + 1.63173e6i −0.191752 + 0.332125i
\(171\) −565597. + 326548.i −0.113115 + 0.0653068i
\(172\) −3.85501e6 6.67707e6i −0.757600 1.31220i
\(173\) −5.95864e6 3.44022e6i −1.15082 0.664428i −0.201736 0.979440i \(-0.564658\pi\)
−0.949088 + 0.315012i \(0.897992\pi\)
\(174\) 1.30849e6i 0.248383i
\(175\) −2.86213e6 + 875685.i −0.534041 + 0.163393i
\(176\) −782471. −0.143526
\(177\) 3.01812e6 5.22754e6i 0.544273 0.942708i
\(178\) −820225. + 473557.i −0.145436 + 0.0839677i
\(179\) 3.94643e6 + 6.83543e6i 0.688091 + 1.19181i 0.972455 + 0.233092i \(0.0748843\pi\)
−0.284364 + 0.958716i \(0.591782\pi\)
\(180\) 891323. + 514606.i 0.152833 + 0.0882383i
\(181\) 2.63639e6i 0.444604i −0.974978 0.222302i \(-0.928643\pi\)
0.974978 0.222302i \(-0.0713571\pi\)
\(182\) −587469. + 630243.i −0.0974475 + 0.104543i
\(183\) −183663. −0.0299687
\(184\) −3.27022e6 + 5.66418e6i −0.524956 + 0.909251i
\(185\) 730805. 421931.i 0.115421 0.0666386i
\(186\) −1.33654e6 2.31496e6i −0.207704 0.359754i
\(187\) −2.41099e6 1.39199e6i −0.368698 0.212868i
\(188\) 2.56390e6i 0.385858i
\(189\) −1.26604e6 292014.i −0.187527 0.0432532i
\(190\) −805087. −0.117377
\(191\) −6.17120e6 + 1.06888e7i −0.885665 + 1.53402i −0.0407156 + 0.999171i \(0.512964\pi\)
−0.844949 + 0.534846i \(0.820370\pi\)
\(192\) 75272.3 43458.5i 0.0106349 0.00614004i
\(193\) 6.69614e6 + 1.15981e7i 0.931435 + 1.61329i 0.780871 + 0.624692i \(0.214776\pi\)
0.150564 + 0.988600i \(0.451891\pi\)
\(194\) −1.79637e6 1.03713e6i −0.246031 0.142046i
\(195\) 901793.i 0.121619i
\(196\) −420954. 5.98451e6i −0.0559071 0.794804i
\(197\) −9.42468e6 −1.23273 −0.616365 0.787460i \(-0.711396\pi\)
−0.616365 + 0.787460i \(0.711396\pi\)
\(198\) 193946. 335925.i 0.0249854 0.0432760i
\(199\) 4.91639e6 2.83848e6i 0.623860 0.360186i −0.154510 0.987991i \(-0.549380\pi\)
0.778370 + 0.627805i \(0.216047\pi\)
\(200\) −1.80948e6 3.13411e6i −0.226185 0.391764i
\(201\) 5.18772e6 + 2.99513e6i 0.638834 + 0.368831i
\(202\) 2.64311e6i 0.320672i
\(203\) −1.79422e6 + 7.77892e6i −0.214480 + 0.929890i
\(204\) −4.99989e6 −0.588939
\(205\) 1.58499e6 2.74528e6i 0.183977 0.318658i
\(206\) 3.27545e6 1.89108e6i 0.374687 0.216326i
\(207\) 1.91613e6 + 3.31883e6i 0.216030 + 0.374175i
\(208\) 1.06634e6 + 615653.i 0.118497 + 0.0684142i
\(209\) 1.18957e6i 0.130302i
\(210\) −1.17160e6 1.09209e6i −0.126509 0.117923i
\(211\) 1.05196e6 0.111983 0.0559914 0.998431i \(-0.482168\pi\)
0.0559914 + 0.998431i \(0.482168\pi\)
\(212\) −5.08801e6 + 8.81269e6i −0.533999 + 0.924913i
\(213\) 2.10770e6 1.21688e6i 0.218107 0.125924i
\(214\) 2.11850e6 + 3.66935e6i 0.216166 + 0.374410i
\(215\) −1.08758e7 6.27913e6i −1.09432 0.631807i
\(216\) 1.57097e6i 0.155886i
\(217\) −4.77141e6 1.55951e7i −0.466946 1.52619i
\(218\) −2.64750e6 −0.255544
\(219\) 2.92704e6 5.06978e6i 0.278674 0.482677i
\(220\) −1.62348e6 + 937319.i −0.152469 + 0.0880277i
\(221\) 2.19045e6 + 3.79397e6i 0.202935 + 0.351493i
\(222\) −494657. 285591.i −0.0452111 0.0261027i
\(223\) 9.96615e6i 0.898696i 0.893357 + 0.449348i \(0.148344\pi\)
−0.893357 + 0.449348i \(0.851656\pi\)
\(224\) 1.07969e7 3.30336e6i 0.960624 0.293908i
\(225\) −2.12047e6 −0.186159
\(226\) 3.69531e6 6.40046e6i 0.320129 0.554480i
\(227\) 1.59963e7 9.23545e6i 1.36754 0.789552i 0.376930 0.926242i \(-0.376980\pi\)
0.990614 + 0.136690i \(0.0436464\pi\)
\(228\) −1.06821e6 1.85019e6i −0.0901262 0.156103i
\(229\) 1.17915e7 + 6.80784e6i 0.981892 + 0.566896i 0.902841 0.429975i \(-0.141478\pi\)
0.0790512 + 0.996871i \(0.474811\pi\)
\(230\) 4.72412e6i 0.388273i
\(231\) 1.61363e6 1.73112e6i 0.130909 0.140440i
\(232\) −9.65248e6 −0.772992
\(233\) −5103.02 + 8838.68i −0.000403422 + 0.000698747i −0.866227 0.499651i \(-0.833462\pi\)
0.865824 + 0.500349i \(0.166795\pi\)
\(234\) −528616. + 305196.i −0.0412565 + 0.0238195i
\(235\) −2.08807e6 3.61664e6i −0.160895 0.278678i
\(236\) 1.71004e7 + 9.87291e6i 1.30098 + 0.751120i
\(237\) 517281.i 0.0388581i
\(238\) 7.58176e6 + 1.74874e6i 0.562392 + 0.129717i
\(239\) 2.49567e6 0.182807 0.0914037 0.995814i \(-0.470865\pi\)
0.0914037 + 0.995814i \(0.470865\pi\)
\(240\) −1.14448e6 + 1.98230e6i −0.0827894 + 0.143395i
\(241\) −4.73752e6 + 2.73521e6i −0.338454 + 0.195407i −0.659588 0.751627i \(-0.729269\pi\)
0.321134 + 0.947034i \(0.395936\pi\)
\(242\) −2.84131e6 4.92129e6i −0.200480 0.347242i
\(243\) −797162. 460241.i −0.0555556 0.0320750i
\(244\) 600800.i 0.0413581i
\(245\) −5.46766e6 8.09894e6i −0.371795 0.550719i
\(246\) −2.14565e6 −0.144130
\(247\) −935961. + 1.62113e6i −0.0621108 + 0.107579i
\(248\) 1.70771e7 9.85944e6i 1.11959 0.646394i
\(249\) 7.67720e6 + 1.32973e7i 0.497285 + 0.861322i
\(250\) −6.31718e6 3.64723e6i −0.404300 0.233423i
\(251\) 2.18424e6i 0.138127i −0.997612 0.0690637i \(-0.977999\pi\)
0.997612 0.0690637i \(-0.0220012\pi\)
\(252\) 955241. 4.14149e6i 0.0596913 0.258795i
\(253\) −6.98020e6 −0.431029
\(254\) −2.96974e6 + 5.14374e6i −0.181225 + 0.313890i
\(255\) −7.05286e6 + 4.07197e6i −0.425349 + 0.245575i
\(256\) 3.94117e6 + 6.82631e6i 0.234912 + 0.406880i
\(257\) −2.72638e7 1.57408e7i −1.60615 0.927313i −0.990220 0.139514i \(-0.955446\pi\)
−0.615933 0.787799i \(-0.711221\pi\)
\(258\) 8.50027e6i 0.494964i
\(259\) −2.54912e6 2.37611e6i −0.146720 0.136762i
\(260\) 2.94996e6 0.167840
\(261\) −2.82785e6 + 4.89799e6i −0.159051 + 0.275484i
\(262\) −6.43659e6 + 3.71616e6i −0.357892 + 0.206629i
\(263\) −3.28881e6 5.69639e6i −0.180789 0.313136i 0.761360 0.648329i \(-0.224532\pi\)
−0.942149 + 0.335193i \(0.891198\pi\)
\(264\) 2.47806e6 + 1.43071e6i 0.134679 + 0.0777569i
\(265\) 1.65749e7i 0.890665i
\(266\) 972699. + 3.17921e6i 0.0516813 + 0.168918i
\(267\) −4.09373e6 −0.215073
\(268\) −9.79771e6 + 1.69701e7i −0.509003 + 0.881619i
\(269\) 190420. 109939.i 0.00978263 0.00564801i −0.495101 0.868836i \(-0.664869\pi\)
0.504883 + 0.863188i \(0.331536\pi\)
\(270\) −567351. 982680.i −0.0288244 0.0499253i
\(271\) −2.41082e7 1.39189e7i −1.21132 0.699354i −0.248270 0.968691i \(-0.579862\pi\)
−0.963046 + 0.269337i \(0.913196\pi\)
\(272\) 1.11197e7i 0.552570i
\(273\) −3.56109e6 + 1.08954e6i −0.175023 + 0.0535494i
\(274\) −1.16461e7 −0.566147
\(275\) 1.93115e6 3.34485e6i 0.0928576 0.160834i
\(276\) −1.08566e7 + 6.26807e6i −0.516377 + 0.298130i
\(277\) 2.87725e6 + 4.98354e6i 0.135375 + 0.234476i 0.925741 0.378159i \(-0.123443\pi\)
−0.790366 + 0.612635i \(0.790109\pi\)
\(278\) 1.27032e7 + 7.33417e6i 0.591258 + 0.341363i
\(279\) 1.15540e7i 0.532008i
\(280\) 8.05612e6 8.64270e6i 0.366988 0.393709i
\(281\) 1.75833e7 0.792467 0.396233 0.918150i \(-0.370317\pi\)
0.396233 + 0.918150i \(0.370317\pi\)
\(282\) −1.41334e6 + 2.44798e6i −0.0630232 + 0.109159i
\(283\) 1.27466e7 7.35922e6i 0.562385 0.324693i −0.191717 0.981450i \(-0.561406\pi\)
0.754102 + 0.656757i \(0.228072\pi\)
\(284\) 3.98067e6 + 6.89472e6i 0.173780 + 0.300997i
\(285\) −3.01363e6 1.73992e6i −0.130184 0.0751615i
\(286\) 1.11179e6i 0.0475253i
\(287\) −1.27558e7 2.94215e6i −0.539589 0.124457i
\(288\) 7.99909e6 0.334860
\(289\) 7.71280e6 1.33590e7i 0.319535 0.553451i
\(290\) −6.03787e6 + 3.48597e6i −0.247565 + 0.142932i
\(291\) −4.48283e6 7.76448e6i −0.181917 0.315089i
\(292\) 1.65843e7 + 9.57497e6i 0.666115 + 0.384582i
\(293\) 3.49743e6i 0.139042i 0.997580 + 0.0695210i \(0.0221471\pi\)
−0.997580 + 0.0695210i \(0.977853\pi\)
\(294\) −2.89703e6 + 5.94600e6i −0.114001 + 0.233982i
\(295\) 3.21625e7 1.25280
\(296\) 2.10675e6 3.64900e6i 0.0812339 0.140701i
\(297\) 1.45198e6 838299.i 0.0554230 0.0319985i
\(298\) −5.03961e6 8.72886e6i −0.190436 0.329844i
\(299\) 9.51254e6 + 5.49207e6i 0.355863 + 0.205458i
\(300\) 6.93651e6i 0.256908i
\(301\) −1.16557e7 + 5.05338e7i −0.427404 + 1.85303i
\(302\) −2.17508e6 −0.0789685
\(303\) 5.71219e6 9.89381e6i 0.205341 0.355661i
\(304\) 4.11481e6 2.37569e6i 0.146463 0.0845607i
\(305\) −489299. 847490.i −0.0172455 0.0298700i
\(306\) 4.77385e6 + 2.75618e6i 0.166611 + 0.0961930i
\(307\) 3.99694e7i 1.38138i −0.723152 0.690689i \(-0.757308\pi\)
0.723152 0.690689i \(-0.242692\pi\)
\(308\) 5.66287e6 + 5.27853e6i 0.193814 + 0.180659i
\(309\) 1.63477e7 0.554092
\(310\) 7.12142e6 1.23347e7i 0.239046 0.414040i
\(311\) −2.88815e7 + 1.66747e7i −0.960148 + 0.554342i −0.896219 0.443613i \(-0.853697\pi\)
−0.0639296 + 0.997954i \(0.520363\pi\)
\(312\) −2.25138e6 3.89950e6i −0.0741284 0.128394i
\(313\) 1.62725e7 + 9.39495e6i 0.530667 + 0.306381i 0.741288 0.671187i \(-0.234215\pi\)
−0.210621 + 0.977568i \(0.567549\pi\)
\(314\) 5.15402e6i 0.166478i
\(315\) −2.02542e6 6.61996e6i −0.0648012 0.211799i
\(316\) −1.69214e6 −0.0536259
\(317\) 1.01986e7 1.76645e7i 0.320156 0.554527i −0.660364 0.750946i \(-0.729598\pi\)
0.980520 + 0.196419i \(0.0629312\pi\)
\(318\) 9.71596e6 5.60951e6i 0.302137 0.174439i
\(319\) −5.15075e6 8.92136e6i −0.158671 0.274827i
\(320\) 401068. + 231557.i 0.0122396 + 0.00706656i
\(321\) 1.83137e7i 0.553682i
\(322\) 1.86551e7 5.70764e6i 0.558766 0.170958i
\(323\) 1.69050e7 0.501659
\(324\) 1.50555e6 2.60768e6i 0.0442649 0.0766690i
\(325\) −5.26349e6 + 3.03888e6i −0.153329 + 0.0885244i
\(326\) −1.00493e7 1.74059e7i −0.290056 0.502393i
\(327\) −9.91021e6 5.72167e6i −0.283426 0.163636i
\(328\) 1.58281e7i 0.448545i
\(329\) −1.17590e7 + 1.26152e7i −0.330204 + 0.354247i
\(330\) 2.06678e6 0.0575113
\(331\) 1.06774e7 1.84939e7i 0.294431 0.509969i −0.680422 0.732821i \(-0.738203\pi\)
0.974852 + 0.222852i \(0.0715366\pi\)
\(332\) −4.34983e7 + 2.51138e7i −1.18866 + 0.686274i
\(333\) −1.23441e6 2.13807e6i −0.0334294 0.0579014i
\(334\) −7.00834e6 4.04627e6i −0.188094 0.108596i
\(335\) 3.19175e7i 0.848974i
\(336\) 9.21066e6 + 2.12445e6i 0.242813 + 0.0560052i
\(337\) −1.98824e7 −0.519493 −0.259746 0.965677i \(-0.583639\pi\)
−0.259746 + 0.965677i \(0.583639\pi\)
\(338\) 7.82918e6 1.35605e7i 0.202753 0.351178i
\(339\) 2.76649e7 1.59723e7i 0.710116 0.409986i
\(340\) −1.33203e7 2.30714e7i −0.338904 0.586999i
\(341\) 1.82253e7 + 1.05224e7i 0.459633 + 0.265369i
\(342\) 2.35539e6i 0.0588823i
\(343\) −2.53760e7 + 3.13763e7i −0.628840 + 0.777535i
\(344\) −6.27049e7 −1.54037
\(345\) −1.02096e7 + 1.76835e7i −0.248628 + 0.430637i
\(346\) −2.14898e7 + 1.24072e7i −0.518806 + 0.299533i
\(347\) 1.66198e7 + 2.87863e7i 0.397774 + 0.688965i 0.993451 0.114259i \(-0.0364495\pi\)
−0.595677 + 0.803224i \(0.703116\pi\)
\(348\) −1.60224e7 9.25051e6i −0.380180 0.219497i
\(349\) 2.57850e7i 0.606584i 0.952898 + 0.303292i \(0.0980858\pi\)
−0.952898 + 0.303292i \(0.901914\pi\)
\(350\) −2.42609e6 + 1.05184e7i −0.0565851 + 0.245328i
\(351\) −2.63832e6 −0.0610106
\(352\) −7.28490e6 + 1.26178e7i −0.167030 + 0.289305i
\(353\) −4.82036e7 + 2.78303e7i −1.09586 + 0.632695i −0.935130 0.354304i \(-0.884718\pi\)
−0.160729 + 0.986999i \(0.551385\pi\)
\(354\) −1.08848e7 1.88531e7i −0.245365 0.424985i
\(355\) 1.12303e7 + 6.48381e6i 0.251019 + 0.144926i
\(356\) 1.33915e7i 0.296810i
\(357\) 2.46010e7 + 2.29314e7i 0.540691 + 0.503994i
\(358\) 2.84656e7 0.620400
\(359\) 8.08714e6 1.40073e7i 0.174788 0.302742i −0.765300 0.643674i \(-0.777409\pi\)
0.940088 + 0.340932i \(0.110743\pi\)
\(360\) 7.24905e6 4.18524e6i 0.155372 0.0897043i
\(361\) −1.99112e7 3.44873e7i −0.423230 0.733056i
\(362\) −8.23428e6 4.75406e6i −0.173580 0.100217i
\(363\) 2.45621e7i 0.513506i
\(364\) −3.56411e6 1.16491e7i −0.0739004 0.241539i
\(365\) 3.11919e7 0.641451
\(366\) −331190. + 573637.i −0.00675513 + 0.0117002i
\(367\) 9.72318e6 5.61368e6i 0.196703 0.113566i −0.398414 0.917206i \(-0.630439\pi\)
0.595117 + 0.803639i \(0.297106\pi\)
\(368\) −1.39401e7 2.41450e7i −0.279720 0.484490i
\(369\) −8.03169e6 4.63710e6i −0.159856 0.0922926i
\(370\) 3.04339e6i 0.0600830i
\(371\) 6.54529e7 2.00257e7i 1.28176 0.392162i
\(372\) 3.77954e7 0.734194
\(373\) −1.99988e7 + 3.46389e7i −0.385369 + 0.667479i −0.991820 0.127642i \(-0.959259\pi\)
0.606451 + 0.795121i \(0.292593\pi\)
\(374\) −8.69524e6 + 5.02020e6i −0.166214 + 0.0959635i
\(375\) −1.57645e7 2.73049e7i −0.298942 0.517782i
\(376\) −1.80583e7 1.04260e7i −0.339714 0.196134i
\(377\) 1.62106e7i 0.302534i
\(378\) −3.19504e6 + 3.42768e6i −0.0591564 + 0.0634636i
\(379\) 2.92098e7 0.536551 0.268276 0.963342i \(-0.413546\pi\)
0.268276 + 0.963342i \(0.413546\pi\)
\(380\) 5.69166e6 9.85824e6i 0.103726 0.179659i
\(381\) −2.22329e7 + 1.28362e7i −0.401995 + 0.232092i
\(382\) 2.22564e7 + 3.85493e7i 0.399269 + 0.691554i
\(383\) 3.97181e7 + 2.29312e7i 0.706955 + 0.408161i 0.809933 0.586523i \(-0.199504\pi\)
−0.102978 + 0.994684i \(0.532837\pi\)
\(384\) 3.25276e7i 0.574458i
\(385\) 1.22870e7 + 2.83400e6i 0.215309 + 0.0496613i
\(386\) 4.82993e7 0.839805
\(387\) −1.83704e7 + 3.18185e7i −0.316947 + 0.548968i
\(388\) 2.53993e7 1.46643e7i 0.434837 0.251053i
\(389\) −7.72431e6 1.33789e7i −0.131223 0.227285i 0.792925 0.609319i \(-0.208557\pi\)
−0.924148 + 0.382034i \(0.875224\pi\)
\(390\) −2.81659e6 1.62616e6i −0.0474821 0.0274138i
\(391\) 9.91960e7i 1.65945i
\(392\) −4.38625e7 2.13708e7i −0.728174 0.354783i
\(393\) −3.21249e7 −0.529254
\(394\) −1.69951e7 + 2.94363e7i −0.277865 + 0.481277i
\(395\) −2.38693e6 + 1.37810e6i −0.0387302 + 0.0223609i
\(396\) 2.74225e6 + 4.74972e6i 0.0441593 + 0.0764861i
\(397\) 2.54737e7 + 1.47073e7i 0.407118 + 0.235050i 0.689551 0.724237i \(-0.257808\pi\)
−0.282433 + 0.959287i \(0.591141\pi\)
\(398\) 2.04740e7i 0.324753i
\(399\) −3.22975e6 + 1.40027e7i −0.0508452 + 0.220442i
\(400\) 1.54268e7 0.241043
\(401\) 5.70055e7 9.87364e7i 0.884064 1.53124i 0.0372810 0.999305i \(-0.488130\pi\)
0.846783 0.531939i \(-0.178536\pi\)
\(402\) 1.87095e7 1.08019e7i 0.287995 0.166274i
\(403\) −1.65581e7 2.86796e7i −0.252986 0.438185i
\(404\) 3.23648e7 + 1.86858e7i 0.490827 + 0.283379i
\(405\) 4.90455e6i 0.0738302i
\(406\) 2.10607e7 + 1.96313e7i 0.314698 + 0.293339i
\(407\) 4.49681e6 0.0666992
\(408\) −2.03318e7 + 3.52158e7i −0.299362 + 0.518510i
\(409\) 2.99288e7 1.72794e7i 0.437442 0.252557i −0.265070 0.964229i \(-0.585395\pi\)
0.702512 + 0.711672i \(0.252062\pi\)
\(410\) −5.71626e6 9.90086e6i −0.0829393 0.143655i
\(411\) −4.35942e7 2.51691e7i −0.627919 0.362529i
\(412\) 5.34769e7i 0.764671i
\(413\) −3.88584e7 1.27007e8i −0.551614 1.80292i
\(414\) 1.38210e7 0.194778
\(415\) −4.09059e7 + 7.08511e7i −0.572324 + 0.991294i
\(416\) 1.98556e7 1.14636e7i 0.275805 0.159236i
\(417\) 3.17006e7 + 5.49071e7i 0.437180 + 0.757217i
\(418\) −3.71541e6 2.14509e6i −0.0508719 0.0293709i
\(419\) 3.73902e7i 0.508294i 0.967166 + 0.254147i \(0.0817948\pi\)
−0.967166 + 0.254147i \(0.918205\pi\)
\(420\) 2.16553e7 6.62557e6i 0.292292 0.0894284i
\(421\) −5.93910e7 −0.795929 −0.397965 0.917401i \(-0.630283\pi\)
−0.397965 + 0.917401i \(0.630283\pi\)
\(422\) 1.89694e6 3.28560e6i 0.0252416 0.0437198i
\(423\) −1.05810e7 + 6.10893e6i −0.139799 + 0.0807131i
\(424\) 4.13803e7 + 7.16728e7i 0.542870 + 0.940279i
\(425\) 4.75338e7 + 2.74436e7i 0.619206 + 0.357499i
\(426\) 8.77734e6i 0.113536i
\(427\) −2.75549e6 + 2.95612e6i −0.0353929 + 0.0379699i
\(428\) −5.99080e7 −0.764105
\(429\) 2.40276e6 4.16170e6i 0.0304325 0.0527107i
\(430\) −3.92235e7 + 2.26457e7i −0.493334 + 0.284826i
\(431\) 2.97697e7 + 5.15627e7i 0.371829 + 0.644026i 0.989847 0.142137i \(-0.0453975\pi\)
−0.618018 + 0.786164i \(0.712064\pi\)
\(432\) 5.79948e6 + 3.34833e6i 0.0719346 + 0.0415314i
\(433\) 6.40730e7i 0.789244i 0.918843 + 0.394622i \(0.129124\pi\)
−0.918843 + 0.394622i \(0.870876\pi\)
\(434\) −5.73125e7 1.32192e7i −0.701100 0.161710i
\(435\) −3.01349e7 −0.366102
\(436\) 1.87168e7 3.24184e7i 0.225825 0.391140i
\(437\) 3.67071e7 2.11928e7i 0.439851 0.253948i
\(438\) −1.05564e7 1.82842e7i −0.125630 0.217597i
\(439\) −1.31778e8 7.60819e7i −1.55757 0.899265i −0.997488 0.0708286i \(-0.977436\pi\)
−0.560084 0.828436i \(-0.689231\pi\)
\(440\) 1.52463e7i 0.178980i
\(441\) −2.36945e7 + 1.59964e7i −0.276269 + 0.186511i
\(442\) 1.57997e7 0.182971
\(443\) −1.72920e7 + 2.99506e7i −0.198899 + 0.344504i −0.948172 0.317758i \(-0.897070\pi\)
0.749273 + 0.662262i \(0.230403\pi\)
\(444\) 6.99408e6 4.03803e6i 0.0799064 0.0461340i
\(445\) −1.09062e7 1.88901e7i −0.123763 0.214365i
\(446\) 3.11275e7 + 1.79715e7i 0.350864 + 0.202572i
\(447\) 4.35656e7i 0.487777i
\(448\) 429829. 1.86355e6i 0.00478037 0.0207255i
\(449\) −1.33795e8 −1.47809 −0.739047 0.673654i \(-0.764724\pi\)
−0.739047 + 0.673654i \(0.764724\pi\)
\(450\) −3.82374e6 + 6.62291e6i −0.0419615 + 0.0726794i
\(451\) 1.46292e7 8.44616e6i 0.159474 0.0920724i
\(452\) 5.22488e7 + 9.04976e7i 0.565798 + 0.979990i
\(453\) −8.14183e6 4.70069e6i −0.0875846 0.0505670i
\(454\) 6.66153e7i 0.711880i
\(455\) −1.45147e7 1.35296e7i −0.154090 0.143632i
\(456\) −1.73753e7 −0.183247
\(457\) −7.62638e6 + 1.32093e7i −0.0799043 + 0.138398i −0.903208 0.429202i \(-0.858795\pi\)
0.823304 + 0.567600i \(0.192128\pi\)
\(458\) 4.25262e7 2.45525e7i 0.442649 0.255564i
\(459\) 1.19131e7 + 2.06341e7i 0.123193 + 0.213377i
\(460\) −5.78465e7 3.33977e7i −0.594298 0.343118i
\(461\) 3.05013e7i 0.311326i 0.987810 + 0.155663i \(0.0497514\pi\)
−0.987810 + 0.155663i \(0.950249\pi\)
\(462\) −2.49707e6 8.16153e6i −0.0253224 0.0827648i
\(463\) −1.61661e8 −1.62878 −0.814388 0.580320i \(-0.802927\pi\)
−0.814388 + 0.580320i \(0.802927\pi\)
\(464\) 2.05731e7 3.56336e7i 0.205942 0.356703i
\(465\) 5.33144e7 3.07811e7i 0.530256 0.306143i
\(466\) 18404.0 + 31876.7i 0.000181868 + 0.000315004i
\(467\) 5.70833e7 + 3.29570e7i 0.560478 + 0.323592i 0.753337 0.657635i \(-0.228443\pi\)
−0.192860 + 0.981226i \(0.561776\pi\)
\(468\) 8.63049e6i 0.0841972i
\(469\) 1.26039e8 3.85624e7i 1.22176 0.373806i
\(470\) −1.50612e7 −0.145067
\(471\) −1.11387e7 + 1.92927e7i −0.106603 + 0.184642i
\(472\) 1.39076e8 8.02955e7i 1.32259 0.763599i
\(473\) −3.34605e7 5.79553e7i −0.316191 0.547659i
\(474\) 1.61564e6 + 932788.i 0.0151708 + 0.00875886i
\(475\) 2.34529e7i 0.218834i
\(476\) −7.50134e7 + 8.04753e7i −0.695534 + 0.746176i
\(477\) 4.84922e7 0.446804
\(478\) 4.50032e6 7.79479e6i 0.0412060 0.0713708i
\(479\) −7.96535e7 + 4.59880e7i −0.724767 + 0.418444i −0.816505 0.577339i \(-0.804091\pi\)
0.0917379 + 0.995783i \(0.470758\pi\)
\(480\) 2.13105e7 + 3.69109e7i 0.192695 + 0.333757i
\(481\) −6.12820e6 3.53812e6i −0.0550678 0.0317934i
\(482\) 1.97291e7i 0.176183i
\(483\) 8.21657e7 + 1.89516e7i 0.729204 + 0.168192i
\(484\) 8.03478e7 0.708660
\(485\) 2.38855e7 4.13710e7i 0.209368 0.362636i
\(486\) −2.87496e6 + 1.65986e6i −0.0250451 + 0.0144598i
\(487\) 9.53763e7 + 1.65197e8i 0.825759 + 1.43026i 0.901338 + 0.433117i \(0.142586\pi\)
−0.0755785 + 0.997140i \(0.524080\pi\)
\(488\) −4.23162e6 2.44313e6i −0.0364122 0.0210226i
\(489\) 8.68725e7i 0.742944i
\(490\) −3.51551e7 + 2.47284e6i −0.298814 + 0.0210188i
\(491\) 8.85504e7 0.748077 0.374038 0.927413i \(-0.377973\pi\)
0.374038 + 0.927413i \(0.377973\pi\)
\(492\) 1.51689e7 2.62734e7i 0.127368 0.220607i
\(493\) 1.26782e8 7.31975e7i 1.05807 0.610880i
\(494\) 3.37554e6 + 5.84661e6i 0.0280003 + 0.0484980i
\(495\) 7.73647e6 + 4.46665e6i 0.0637862 + 0.0368270i
\(496\) 8.40569e7i 0.688856i
\(497\) 1.20356e7 5.21810e7i 0.0980391 0.425053i
\(498\) 5.53757e7 0.448364
\(499\) 2.61754e7 4.53371e7i 0.210665 0.364882i −0.741258 0.671220i \(-0.765770\pi\)
0.951923 + 0.306338i \(0.0991038\pi\)
\(500\) 8.93202e7 5.15690e7i 0.714561 0.412552i
\(501\) −1.74893e7 3.02923e7i −0.139078 0.240890i
\(502\) −6.82210e6 3.93874e6i −0.0539271 0.0311348i
\(503\) 1.34114e8i 1.05383i 0.849919 + 0.526914i \(0.176651\pi\)
−0.849919 + 0.526914i \(0.823349\pi\)
\(504\) −2.52854e7 2.35693e7i −0.197505 0.184100i
\(505\) 6.08718e7 0.472653
\(506\) −1.25871e7 + 2.18014e7i −0.0971566 + 0.168280i
\(507\) 5.86130e7 3.38402e7i 0.449749 0.259663i
\(508\) −4.19898e7 7.27285e7i −0.320297 0.554771i
\(509\) −1.62222e8 9.36588e7i −1.23014 0.710224i −0.263084 0.964773i \(-0.584740\pi\)
−0.967060 + 0.254549i \(0.918073\pi\)
\(510\) 2.93711e7i 0.221417i
\(511\) −3.76858e7 1.23174e8i −0.282432 0.923115i
\(512\) −1.05118e8 −0.783188
\(513\) −5.09038e6 + 8.81679e6i −0.0377049 + 0.0653068i
\(514\) −9.83269e7 + 5.67690e7i −0.724074 + 0.418044i
\(515\) 4.35522e7 + 7.54347e7i 0.318852 + 0.552267i
\(516\) −1.04085e8 6.00936e7i −0.757600 0.437401i
\(517\) 2.22540e7i 0.161041i
\(518\) −1.20180e7 + 3.67699e6i −0.0864658 + 0.0264547i
\(519\) −1.07255e8 −0.767216
\(520\) 1.19959e7 2.07774e7i 0.0853142 0.147769i
\(521\) −3.89027e7 + 2.24605e7i −0.275085 + 0.158820i −0.631196 0.775623i \(-0.717436\pi\)
0.356111 + 0.934444i \(0.384102\pi\)
\(522\) 1.01987e7 + 1.76646e7i 0.0717021 + 0.124192i
\(523\) 1.43752e8 + 8.29951e7i 1.00487 + 0.580160i 0.909684 0.415300i \(-0.136324\pi\)
0.0951815 + 0.995460i \(0.469657\pi\)
\(524\) 1.05087e8i 0.730394i
\(525\) −3.18134e7 + 3.41298e7i −0.219853 + 0.235861i
\(526\) −2.37222e7 −0.163004
\(527\) −1.49534e8 + 2.59000e8i −1.02166 + 1.76957i
\(528\) −1.05634e7 + 6.09876e6i −0.0717629 + 0.0414324i
\(529\) −5.03382e7 8.71883e7i −0.340041 0.588967i
\(530\) 5.17689e7 + 2.98888e7i 0.347729 + 0.200761i
\(531\) 9.40956e7i 0.628472i
\(532\) −4.58059e7 1.05652e7i −0.304219 0.0701685i
\(533\) −2.65820e7 −0.175552
\(534\) −7.38202e6 + 1.27860e7i −0.0484788 + 0.0839677i
\(535\) −8.45064e7 + 4.87898e7i −0.551859 + 0.318616i
\(536\) 7.96839e7 + 1.38017e8i 0.517459 + 0.896266i
\(537\) 1.06554e8 + 6.15188e7i 0.688091 + 0.397269i
\(538\) 792991.i 0.00509238i
\(539\) −3.65378e6 5.19441e7i −0.0233333 0.331718i
\(540\) 1.60438e7 0.101889
\(541\) −6.31514e7 + 1.09381e8i −0.398833 + 0.690799i −0.993582 0.113112i \(-0.963918\pi\)
0.594749 + 0.803911i \(0.297251\pi\)
\(542\) −8.69464e7 + 5.01985e7i −0.546077 + 0.315278i
\(543\) −2.05486e7 3.55912e7i −0.128346 0.222302i
\(544\) −1.79312e8 1.03526e8i −1.11382 0.643062i
\(545\) 6.09727e7i 0.376657i
\(546\) −3.01857e6 + 1.30871e7i −0.0185448 + 0.0804021i
\(547\) 2.31931e8 1.41709 0.708545 0.705666i \(-0.249352\pi\)
0.708545 + 0.705666i \(0.249352\pi\)
\(548\) 8.23336e7 1.42606e8i 0.500306 0.866555i
\(549\) −2.47945e6 + 1.43151e6i −0.0149843 + 0.00865121i
\(550\) −6.96468e6 1.20632e7i −0.0418614 0.0725060i
\(551\) 5.41729e7 + 3.12767e7i 0.323838 + 0.186968i
\(552\) 1.01955e8i 0.606167i
\(553\) 8.32585e6 + 7.76078e6i 0.0492327 + 0.0458912i
\(554\) 2.07536e7 0.122057
\(555\) 6.57725e6 1.13921e7i 0.0384738 0.0666386i
\(556\) −1.79613e8 + 1.03700e8i −1.04499 + 0.603326i
\(557\) −1.20538e8 2.08779e8i −0.697525 1.20815i −0.969322 0.245794i \(-0.920951\pi\)
0.271797 0.962355i \(-0.412382\pi\)
\(558\) −3.60867e7 2.08347e7i −0.207704 0.119918i
\(559\) 1.05308e8i 0.602872i
\(560\) 1.47352e7 + 4.81613e7i 0.0839060 + 0.274242i
\(561\) −4.33978e7 −0.245799
\(562\) 3.17071e7 5.49182e7i 0.178627 0.309391i
\(563\) −1.01477e8 + 5.85878e7i −0.568647 + 0.328308i −0.756609 0.653868i \(-0.773145\pi\)
0.187962 + 0.982176i \(0.439812\pi\)
\(564\) −1.99836e7 3.46126e7i −0.111387 0.192929i
\(565\) 1.47405e8 + 8.51042e7i 0.817271 + 0.471852i
\(566\) 5.30821e7i 0.292751i
\(567\) −1.93676e7 + 5.92563e6i −0.106249 + 0.0325076i
\(568\) 6.47488e7 0.353335
\(569\) 6.04302e7 1.04668e8i 0.328033 0.568170i −0.654088 0.756418i \(-0.726948\pi\)
0.982121 + 0.188248i \(0.0602809\pi\)
\(570\) −1.08687e7 + 6.27503e6i −0.0586884 + 0.0338837i
\(571\) −5.39062e7 9.33683e7i −0.289555 0.501523i 0.684149 0.729342i \(-0.260174\pi\)
−0.973703 + 0.227819i \(0.926841\pi\)
\(572\) 1.36138e7 + 7.85993e6i 0.0727430 + 0.0419982i
\(573\) 1.92399e8i 1.02268i
\(574\) −3.21912e7 + 3.45351e7i −0.170217 + 0.182610i
\(575\) 1.37618e8 0.723887
\(576\) 677451. 1.17338e6i 0.00354495 0.00614004i
\(577\) −6.79444e7 + 3.92277e7i −0.353693 + 0.204205i −0.666310 0.745674i \(-0.732127\pi\)
0.312618 + 0.949879i \(0.398794\pi\)
\(578\) −2.78162e7 4.81791e7i −0.144050 0.249503i
\(579\) 1.80796e8 + 1.04382e8i 0.931435 + 0.537764i
\(580\) 9.85778e7i 0.505237i
\(581\) 3.29207e8 + 7.59319e7i 1.67857 + 0.387165i
\(582\) −3.23346e7 −0.164021
\(583\) −4.41627e7 + 7.64920e7i −0.222869 + 0.386020i
\(584\) 1.34879e8 7.78724e7i 0.677182 0.390971i
\(585\) −7.02878e6 1.21742e7i −0.0351085 0.0608097i
\(586\) 1.09236e7 + 6.30674e6i 0.0542841 + 0.0313410i
\(587\) 1.98030e8i 0.979075i −0.871982 0.489538i \(-0.837166\pi\)
0.871982 0.489538i \(-0.162834\pi\)
\(588\) −5.23275e7 7.75098e7i −0.257394 0.381263i
\(589\) −1.27789e8 −0.625387
\(590\) 5.79970e7 1.00454e8i 0.282390 0.489114i
\(591\) −1.27233e8 + 7.34581e7i −0.616365 + 0.355859i
\(592\) 8.98056e6 + 1.55548e7i 0.0432851 + 0.0749720i
\(593\) −3.26564e6 1.88542e6i −0.0156605 0.00904157i 0.492149 0.870511i \(-0.336211\pi\)
−0.507810 + 0.861469i \(0.669545\pi\)
\(594\) 6.04665e6i 0.0288506i
\(595\) −4.02742e7 + 1.74611e8i −0.191195 + 0.828933i
\(596\) 1.42512e8 0.673153
\(597\) 4.42475e7 7.66389e7i 0.207953 0.360186i
\(598\) 3.43070e7 1.98071e7i 0.160428 0.0926229i
\(599\) −1.33653e8 2.31493e8i −0.621867 1.07710i −0.989138 0.146991i \(-0.953041\pi\)
0.367271 0.930114i \(-0.380292\pi\)
\(600\) −4.88560e7 2.82070e7i −0.226185 0.130588i
\(601\) 9.26866e7i 0.426966i −0.976947 0.213483i \(-0.931519\pi\)
0.976947 0.213483i \(-0.0684809\pi\)
\(602\) 1.36815e8 + 1.27530e8i 0.627112 + 0.584550i
\(603\) 9.33790e7 0.425890
\(604\) 1.53770e7 2.66337e7i 0.0697846 0.120870i
\(605\) 1.13339e8 6.54363e7i 0.511815 0.295497i
\(606\) −2.06010e7 3.56820e7i −0.0925702 0.160336i
\(607\) 1.38921e8 + 8.02061e7i 0.621158 + 0.358625i 0.777320 0.629106i \(-0.216579\pi\)
−0.156162 + 0.987731i \(0.549912\pi\)
\(608\) 8.84718e7i 0.393635i
\(609\) 3.64088e7 + 1.19000e8i 0.161196 + 0.526860i
\(610\) −3.52931e6 −0.0155489
\(611\) −1.75096e7 + 3.03275e7i −0.0767631 + 0.132958i
\(612\) −6.74985e7 + 3.89703e7i −0.294469 + 0.170012i
\(613\) −3.60980e7 6.25236e7i −0.156712 0.271433i 0.776969 0.629539i \(-0.216756\pi\)
−0.933681 + 0.358106i \(0.883423\pi\)
\(614\) −1.24837e8 7.20748e7i −0.539311 0.311371i
\(615\) 4.94151e7i 0.212439i
\(616\) 6.02061e7 1.84204e7i 0.257572 0.0788056i
\(617\) 3.16720e6 0.0134841 0.00674203 0.999977i \(-0.497854\pi\)
0.00674203 + 0.999977i \(0.497854\pi\)
\(618\) 2.94790e7 5.10592e7i 0.124896 0.216326i
\(619\) 1.20117e8 6.93494e7i 0.506444 0.292396i −0.224927 0.974376i \(-0.572214\pi\)
0.731371 + 0.681980i \(0.238881\pi\)
\(620\) 1.00691e8 + 1.74403e8i 0.422491 + 0.731776i
\(621\) 5.17355e7 + 2.98695e7i 0.216030 + 0.124725i
\(622\) 1.20275e8i 0.499809i
\(623\) −6.14183e7 + 6.58903e7i −0.254000 + 0.272494i
\(624\) 1.91942e7 0.0789979
\(625\) 1.58233e7 2.74068e7i 0.0648124 0.112258i
\(626\) 5.86869e7 3.38829e7i 0.239231 0.138120i
\(627\) −9.27178e6 1.60592e7i −0.0376150 0.0651510i
\(628\) −6.31107e7 3.64370e7i −0.254814 0.147117i
\(629\) 6.39043e7i 0.256790i
\(630\) −2.43286e7 5.61142e6i −0.0972961 0.0224415i
\(631\) −1.98716e8 −0.790944 −0.395472 0.918478i \(-0.629419\pi\)
−0.395472 + 0.918478i \(0.629419\pi\)
\(632\) −6.88100e6 + 1.19182e7i −0.0272584 + 0.0472129i
\(633\) 1.42014e7 8.19920e6i 0.0559914 0.0323266i
\(634\) −3.67812e7 6.37069e7i −0.144331 0.249988i
\(635\) −1.18462e8 6.83941e7i −0.462656 0.267114i
\(636\) 1.58628e8i 0.616608i
\(637\) −3.58906e7 + 7.36636e7i −0.138855 + 0.284993i
\(638\) −3.71523e7 −0.143062
\(639\) 1.89693e7 3.28557e7i 0.0727022 0.125924i
\(640\) −1.50095e8 + 8.66573e7i −0.572567 + 0.330571i
\(641\) −7.21736e7 1.25008e8i −0.274034 0.474641i 0.695857 0.718180i \(-0.255025\pi\)
−0.969891 + 0.243540i \(0.921691\pi\)
\(642\) 5.71995e7 + 3.30242e7i 0.216166 + 0.124803i
\(643\) 2.68271e8i 1.00911i −0.863378 0.504557i \(-0.831656\pi\)
0.863378 0.504557i \(-0.168344\pi\)
\(644\) −6.19948e7 + 2.68781e8i −0.232112 + 1.00633i
\(645\) −1.95764e8 −0.729548
\(646\) 3.04840e7 5.27999e7i 0.113077 0.195855i
\(647\) −3.38971e8 + 1.95705e8i −1.25155 + 0.722585i −0.971418 0.237375i \(-0.923713\pi\)
−0.280136 + 0.959960i \(0.590380\pi\)
\(648\) −1.22445e7 2.12081e7i −0.0450003 0.0779428i
\(649\) 1.48427e8 + 8.56944e7i 0.542974 + 0.313486i
\(650\) 2.19194e7i 0.0798158i
\(651\) −1.85966e8 1.73344e8i −0.674046 0.628299i
\(652\) 2.84179e8 1.02529
\(653\) −2.30591e8 + 3.99396e8i −0.828139 + 1.43438i 0.0713566 + 0.997451i \(0.477267\pi\)
−0.899496 + 0.436929i \(0.856066\pi\)
\(654\) −3.57412e7 + 2.06352e7i −0.127772 + 0.0737692i
\(655\) −8.55845e7 1.48237e8i −0.304559 0.527512i
\(656\) 5.84318e7 + 3.37356e7i 0.206984 + 0.119503i
\(657\) 9.12561e7i 0.321785i
\(658\) 1.81969e7 + 5.94754e7i 0.0638732 + 0.208766i
\(659\) 2.90612e8 1.01545 0.507724 0.861520i \(-0.330487\pi\)
0.507724 + 0.861520i \(0.330487\pi\)
\(660\) −1.46114e7 + 2.53076e7i −0.0508228 + 0.0880277i
\(661\) −2.43164e8 + 1.40391e8i −0.841965 + 0.486109i −0.857932 0.513764i \(-0.828251\pi\)
0.0159666 + 0.999873i \(0.494917\pi\)
\(662\) −3.85082e7 6.66981e7i −0.132733 0.229900i
\(663\) 5.91421e7 + 3.41457e7i 0.202935 + 0.117164i
\(664\) 4.08496e8i 1.39535i
\(665\) −7.32183e7 + 2.24016e7i −0.248975 + 0.0761752i
\(666\) −8.90383e6 −0.0301408
\(667\) 1.83527e8 3.17878e8i 0.618475 1.07123i
\(668\) 9.90926e7 5.72111e7i 0.332439 0.191934i
\(669\) 7.76784e7 + 1.34543e8i 0.259431 + 0.449348i
\(670\) 9.96886e7 + 5.75553e7i 0.331452 + 0.191364i
\(671\) 5.21480e6i 0.0172611i
\(672\) 1.20010e8 1.28749e8i 0.395468 0.424262i
\(673\) −2.35293e8 −0.771904 −0.385952 0.922519i \(-0.626127\pi\)
−0.385952 + 0.922519i \(0.626127\pi\)
\(674\) −3.58530e7 + 6.20992e7i −0.117097 + 0.202818i
\(675\) −2.86264e7 + 1.65274e7i −0.0930796 + 0.0537396i
\(676\) 1.10699e8 + 1.91736e8i 0.358346 + 0.620673i
\(677\) −5.35332e8 3.09074e8i −1.72527 0.996085i −0.906835 0.421486i \(-0.861509\pi\)
−0.818435 0.574599i \(-0.805158\pi\)
\(678\) 1.15208e8i 0.369653i
\(679\) −1.92228e8 4.43377e7i −0.614056 0.141633i
\(680\) −2.16665e8 −0.689069
\(681\) 1.43966e8 2.49357e8i 0.455848 0.789552i
\(682\) 6.57295e7 3.79490e7i 0.207208 0.119632i
\(683\) −6.53722e6 1.13228e7i −0.0205178 0.0355379i 0.855584 0.517664i \(-0.173198\pi\)
−0.876102 + 0.482126i \(0.839865\pi\)
\(684\) −2.88416e7 1.66517e7i −0.0901262 0.0520344i
\(685\) 2.68214e8i 0.834468i
\(686\) 5.22391e7 + 1.35837e8i 0.161817 + 0.420770i
\(687\) 2.12248e8 0.654595
\(688\) 1.33648e8 2.31485e8i 0.410390 0.710817i
\(689\) 1.20369e8 6.94949e7i 0.368007 0.212469i
\(690\) 3.68209e7 + 6.37756e7i 0.112085 + 0.194137i
\(691\) 2.37346e8 + 1.37032e8i 0.719362 + 0.415324i 0.814518 0.580138i \(-0.197002\pi\)
−0.0951555 + 0.995462i \(0.530335\pi\)
\(692\) 3.50855e8i 1.05879i
\(693\) 8.29126e6 3.59471e7i 0.0249127 0.108010i
\(694\) 1.19878e8 0.358643
\(695\) −1.68908e8 + 2.92558e8i −0.503149 + 0.871480i
\(696\) −1.30308e8 + 7.52336e7i −0.386496 + 0.223143i
\(697\) 1.20029e8 + 2.07896e8i 0.354476 + 0.613971i
\(698\) 8.05349e7 + 4.64968e7i 0.236820 + 0.136728i
\(699\) 159096.i 0.000465831i
\(700\) −1.11646e8 1.04069e8i −0.325498 0.303407i
\(701\) 4.35624e8 1.26461 0.632307 0.774718i \(-0.282108\pi\)
0.632307 + 0.774718i \(0.282108\pi\)
\(702\) −4.75754e6 + 8.24031e6i −0.0137522 + 0.0238195i
\(703\) −2.36475e7 + 1.36529e7i −0.0680644 + 0.0392970i
\(704\) 1.23393e6 + 2.13723e6i 0.00353649 + 0.00612539i
\(705\) −5.63779e7 3.25498e7i −0.160895 0.0928925i
\(706\) 2.00740e8i 0.570454i
\(707\) −7.35448e7 2.40377e8i −0.208110 0.680197i
\(708\) 3.07807e8 0.867318
\(709\) 1.80906e8 3.13339e8i 0.507592 0.879176i −0.492369 0.870387i \(-0.663869\pi\)
0.999961 0.00878924i \(-0.00279774\pi\)
\(710\) 4.05020e7 2.33839e7i 0.113162 0.0653343i
\(711\) 4.03181e6 + 6.98330e6i 0.0112174 + 0.0194291i
\(712\) −9.43202e7 5.44558e7i −0.261315 0.150870i
\(713\) 7.49848e8i 2.06873i
\(714\) 1.15984e8 3.54860e7i 0.318642 0.0974904i
\(715\) 2.56049e7 0.0700495
\(716\) −2.01241e8 + 3.48560e8i −0.548249 + 0.949595i
\(717\) 3.36916e7 1.94518e7i 0.0914037 0.0527720i
\(718\) −2.91663e7 5.05174e7i −0.0787966 0.136480i
\(719\) −2.12503e8 1.22689e8i −0.571713 0.330079i 0.186120 0.982527i \(-0.440409\pi\)
−0.757833 + 0.652448i \(0.773742\pi\)
\(720\) 3.56814e7i 0.0955969i
\(721\) 2.45265e8 2.63123e8i 0.654380 0.702026i
\(722\) −1.43620e8 −0.381595
\(723\) −4.26377e7 + 7.38506e7i −0.112818 + 0.195407i
\(724\) 1.16426e8 6.72188e7i 0.306786 0.177123i
\(725\) 1.01549e8 + 1.75888e8i 0.266479 + 0.461555i
\(726\) −7.67153e7 4.42916e7i −0.200480 0.115747i
\(727\) 2.59949e8i 0.676526i −0.941052 0.338263i \(-0.890161\pi\)
0.941052 0.338263i \(-0.109839\pi\)
\(728\) −9.65415e7 2.22674e7i −0.250219 0.0577133i
\(729\) −1.43489e7 −0.0370370
\(730\) 5.62468e7 9.74223e7i 0.144587 0.250432i
\(731\) 8.23606e8 4.75509e8i 2.10847 1.21733i
\(732\) −4.68277e6 8.11080e6i −0.0119390 0.0206790i
\(733\) −1.08280e8 6.25152e7i −0.274938 0.158735i 0.356192 0.934413i \(-0.384075\pi\)
−0.631129 + 0.775678i \(0.717408\pi\)
\(734\) 4.04915e7i 0.102394i
\(735\) −1.36938e8 6.67195e7i −0.344876 0.168031i
\(736\) −5.19138e8 −1.30212
\(737\) −8.50418e7 + 1.47297e8i −0.212437 + 0.367951i
\(738\) −2.89663e7 + 1.67237e7i −0.0720649 + 0.0416067i
\(739\) 2.82361e8 + 4.89063e8i 0.699634 + 1.21180i 0.968593 + 0.248650i \(0.0799869\pi\)
−0.268960 + 0.963151i \(0.586680\pi\)
\(740\) 3.72661e7 + 2.15156e7i 0.0919641 + 0.0530955i
\(741\) 2.91804e7i 0.0717194i
\(742\) 5.54813e7 2.40542e8i 0.135811 0.588815i
\(743\) 2.68677e8 0.655035 0.327518 0.944845i \(-0.393788\pi\)
0.327518 + 0.944845i \(0.393788\pi\)
\(744\) 1.53694e8 2.66205e8i 0.373196 0.646394i
\(745\) 2.01029e8 1.16064e8i 0.486171 0.280691i
\(746\) 7.21256e7 + 1.24925e8i 0.173729 + 0.300908i
\(747\) 2.07284e8 + 1.19676e8i 0.497285 + 0.287107i
\(748\) 1.41964e8i 0.339213i
\(749\) 2.94766e8 + 2.74760e8i 0.701507 + 0.653896i
\(750\) −1.13709e8 −0.269533
\(751\) −1.95480e8 + 3.38581e8i −0.461512 + 0.799362i −0.999037 0.0438862i \(-0.986026\pi\)
0.537525 + 0.843248i \(0.319359\pi\)
\(752\) 7.69783e7 4.44434e7i 0.181015 0.104509i
\(753\) −1.70245e7 2.94873e7i −0.0398740 0.0690637i
\(754\) 5.06308e7 + 2.92317e7i 0.118114 + 0.0681930i
\(755\) 5.00927e7i 0.116395i
\(756\) −1.93840e7 6.33555e7i −0.0448619 0.146629i
\(757\) −5.67872e8 −1.30907 −0.654535 0.756031i \(-0.727136\pi\)
−0.654535 + 0.756031i \(0.727136\pi\)
\(758\) 5.26726e7 9.12317e7i 0.120942 0.209478i
\(759\) −9.42327e7 + 5.44053e7i −0.215515 + 0.124427i
\(760\) −4.62897e7 8.01762e7i −0.105449 0.182644i
\(761\) −1.66316e8 9.60225e7i −0.377381 0.217881i 0.299297 0.954160i \(-0.403248\pi\)
−0.676678 + 0.736279i \(0.736581\pi\)
\(762\) 9.25873e7i 0.209260i
\(763\) −2.40776e8 + 7.36667e7i −0.542049 + 0.165843i
\(764\) −6.29378e8 −1.41134
\(765\) −6.34758e7 + 1.09943e8i −0.141783 + 0.245575i
\(766\) 1.43243e8 8.27015e7i