Properties

Label 13.7.f.a.7.2
Level 13
Weight 7
Character 13.7
Analytic conductor 2.991
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 13.f (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.99070308706\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 7.2
Character \(\chi\) = 13.7
Dual form 13.7.f.a.2.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.37184 + 2.51118i) q^{2} +(10.4091 - 18.0291i) q^{3} +(26.0998 - 15.0687i) q^{4} +(160.035 + 160.035i) q^{5} +(-52.2782 + 195.105i) q^{6} +(162.036 + 43.4174i) q^{7} +(232.320 - 232.320i) q^{8} +(147.801 + 255.999i) q^{9} +O(q^{10})\) \(q+(-9.37184 + 2.51118i) q^{2} +(10.4091 - 18.0291i) q^{3} +(26.0998 - 15.0687i) q^{4} +(160.035 + 160.035i) q^{5} +(-52.2782 + 195.105i) q^{6} +(162.036 + 43.4174i) q^{7} +(232.320 - 232.320i) q^{8} +(147.801 + 255.999i) q^{9} +(-1901.70 - 1097.95i) q^{10} +(-264.307 - 986.407i) q^{11} -627.408i q^{12} +(189.333 + 2188.83i) q^{13} -1627.60 q^{14} +(4551.12 - 1219.47i) q^{15} +(-2558.27 + 4431.05i) q^{16} +(1836.32 - 1060.20i) q^{17} +(-2028.03 - 2028.03i) q^{18} +(334.793 - 1249.46i) q^{19} +(6588.42 + 1765.36i) q^{20} +(2469.42 - 2469.42i) q^{21} +(4954.09 + 8580.73i) q^{22} +(-11932.9 - 6889.45i) q^{23} +(-1770.27 - 6606.75i) q^{24} +35597.7i q^{25} +(-7270.93 - 20037.9i) q^{26} +21330.4 q^{27} +(4883.35 - 1308.49i) q^{28} +(12087.9 - 20936.9i) q^{29} +(-39590.1 + 22857.3i) q^{30} +(-26370.1 - 26370.1i) q^{31} +(7406.29 - 27640.6i) q^{32} +(-20535.2 - 5502.40i) q^{33} +(-14547.4 + 14547.4i) q^{34} +(18983.1 + 32879.8i) q^{35} +(7715.15 + 4454.34i) q^{36} +(-7417.14 - 27681.1i) q^{37} +12550.5i q^{38} +(41433.4 + 19370.2i) q^{39} +74358.7 q^{40} +(83471.8 - 22366.2i) q^{41} +(-16941.9 + 29344.2i) q^{42} +(-102720. + 59305.2i) q^{43} +(-21762.3 - 21762.3i) q^{44} +(-17315.5 + 64622.2i) q^{45} +(129134. + 34601.3i) q^{46} +(2437.23 - 2437.23i) q^{47} +(53258.5 + 92246.5i) q^{48} +(-77516.5 - 44754.2i) q^{49} +(-89392.1 - 333616. i) q^{50} -44143.0i q^{51} +(37924.4 + 54274.9i) q^{52} -262002. q^{53} +(-199905. + 53564.4i) q^{54} +(115562. - 200159. i) q^{55} +(47730.8 - 27557.4i) q^{56} +(-19041.8 - 19041.8i) q^{57} +(-60709.8 + 226572. i) q^{58} +(148193. + 39708.1i) q^{59} +(100408. - 100408. i) q^{60} +(14741.0 + 25532.2i) q^{61} +(313357. + 180917. i) q^{62} +(12834.3 + 47898.1i) q^{63} -49815.7i q^{64} +(-319990. + 380590. i) q^{65} +206271. q^{66} +(86045.8 - 23055.9i) q^{67} +(31951.7 - 55342.1i) q^{68} +(-248421. + 143426. i) q^{69} +(-260474. - 260474. i) q^{70} +(172572. - 644048. i) q^{71} +(93810.6 + 25136.5i) q^{72} +(46511.6 - 46511.6i) q^{73} +(139025. + 240798. i) q^{74} +(641794. + 370540. i) q^{75} +(-10089.8 - 37655.7i) q^{76} -171309. i q^{77} +(-436949. - 77488.2i) q^{78} +169972. q^{79} +(-1.11854e6 + 299711. i) q^{80} +(114283. - 197945. i) q^{81} +(-726119. + 419225. i) q^{82} +(378696. + 378696. i) q^{83} +(27240.4 - 101663. i) q^{84} +(463546. + 124207. i) q^{85} +(813746. - 813746. i) q^{86} +(-251649. - 435869. i) q^{87} +(-290565. - 167758. i) q^{88} +(37362.9 + 139440. i) q^{89} -649112. i q^{90} +(-64354.3 + 362889. i) q^{91} -415261. q^{92} +(-749920. + 200940. i) q^{93} +(-16721.0 + 28961.6i) q^{94} +(253537. - 146380. i) q^{95} +(-421243. - 421243. i) q^{96} +(-54694.5 + 204123. i) q^{97} +(838858. + 224771. i) q^{98} +(213454. - 213454. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + O(q^{10}) \) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + 4674q^{10} + 228q^{11} - 1552q^{13} - 14616q^{14} + 7486q^{15} - 2138q^{16} + 20898q^{17} - 5630q^{18} - 14036q^{19} - 14634q^{20} - 314q^{21} + 37852q^{22} + 29634q^{23} + 47154q^{24} + 510q^{26} - 107060q^{27} - 40572q^{28} + 1026q^{29} - 247734q^{30} - 118116q^{31} + 180876q^{32} + 306046q^{33} + 101898q^{34} + 104862q^{35} + 105066q^{36} - 31470q^{37} + 28510q^{39} - 275328q^{40} - 357216q^{41} - 25636q^{42} - 480486q^{43} - 797712q^{44} + 464248q^{45} + 1012050q^{46} + 140028q^{47} + 676102q^{48} + 854562q^{49} + 756714q^{50} - 771704q^{52} - 1397076q^{53} - 1271048q^{54} - 205490q^{55} - 1461108q^{56} - 1483394q^{57} + 1133806q^{58} + 1568052q^{59} + 886808q^{60} + 768676q^{61} + 3741966q^{62} + 1336264q^{63} - 946968q^{65} - 5076928q^{66} - 1489892q^{67} - 569052q^{68} - 1475766q^{69} - 2626556q^{70} + 2136948q^{71} + 4787052q^{72} + 326326q^{73} + 2159718q^{74} + 3466008q^{75} + 1522158q^{76} - 1573544q^{78} - 1734344q^{79} - 5214300q^{80} - 773072q^{81} - 3540426q^{82} - 3642132q^{83} + 2952364q^{84} + 3509916q^{85} - 132324q^{86} + 531698q^{87} + 4478052q^{88} + 632754q^{89} - 2946788q^{91} - 1656060q^{92} - 295514q^{93} + 1552210q^{94} - 2753718q^{95} - 3979208q^{96} + 2258214q^{97} + 4984308q^{98} + 4336480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.37184 + 2.51118i −1.17148 + 0.313897i −0.791542 0.611115i \(-0.790721\pi\)
−0.379938 + 0.925012i \(0.624055\pi\)
\(3\) 10.4091 18.0291i 0.385523 0.667745i −0.606319 0.795222i \(-0.707355\pi\)
0.991842 + 0.127477i \(0.0406879\pi\)
\(4\) 26.0998 15.0687i 0.407809 0.235449i
\(5\) 160.035 + 160.035i 1.28028 + 1.28028i 0.940506 + 0.339777i \(0.110352\pi\)
0.339777 + 0.940506i \(0.389648\pi\)
\(6\) −52.2782 + 195.105i −0.242029 + 0.903264i
\(7\) 162.036 + 43.4174i 0.472408 + 0.126581i 0.487165 0.873310i \(-0.338031\pi\)
−0.0147576 + 0.999891i \(0.504698\pi\)
\(8\) 232.320 232.320i 0.453749 0.453749i
\(9\) 147.801 + 255.999i 0.202745 + 0.351164i
\(10\) −1901.70 1097.95i −1.90170 1.09795i
\(11\) −264.307 986.407i −0.198578 0.741102i −0.991312 0.131534i \(-0.958010\pi\)
0.792734 0.609568i \(-0.208657\pi\)
\(12\) 627.408i 0.363083i
\(13\) 189.333 + 2188.83i 0.0861780 + 0.996280i
\(14\) −1627.60 −0.593150
\(15\) 4551.12 1219.47i 1.34848 0.361324i
\(16\) −2558.27 + 4431.05i −0.624577 + 1.08180i
\(17\) 1836.32 1060.20i 0.373768 0.215795i −0.301335 0.953518i \(-0.597432\pi\)
0.675103 + 0.737723i \(0.264099\pi\)
\(18\) −2028.03 2028.03i −0.347741 0.347741i
\(19\) 334.793 1249.46i 0.0488108 0.182164i −0.937217 0.348748i \(-0.886607\pi\)
0.986027 + 0.166584i \(0.0532736\pi\)
\(20\) 6588.42 + 1765.36i 0.823553 + 0.220670i
\(21\) 2469.42 2469.42i 0.266648 0.266648i
\(22\) 4954.09 + 8580.73i 0.465260 + 0.805854i
\(23\) −11932.9 6889.45i −0.980758 0.566241i −0.0782591 0.996933i \(-0.524936\pi\)
−0.902499 + 0.430692i \(0.858269\pi\)
\(24\) −1770.27 6606.75i −0.128058 0.477919i
\(25\) 35597.7i 2.27825i
\(26\) −7270.93 20037.9i −0.413685 1.14007i
\(27\) 21330.4 1.08370
\(28\) 4883.35 1308.49i 0.222456 0.0596068i
\(29\) 12087.9 20936.9i 0.495630 0.858456i −0.504357 0.863495i \(-0.668271\pi\)
0.999987 + 0.00503870i \(0.00160387\pi\)
\(30\) −39590.1 + 22857.3i −1.46630 + 0.846568i
\(31\) −26370.1 26370.1i −0.885171 0.885171i 0.108883 0.994055i \(-0.465273\pi\)
−0.994055 + 0.108883i \(0.965273\pi\)
\(32\) 7406.29 27640.6i 0.226022 0.843525i
\(33\) −20535.2 5502.40i −0.571423 0.153112i
\(34\) −14547.4 + 14547.4i −0.370124 + 0.370124i
\(35\) 18983.1 + 32879.8i 0.442756 + 0.766875i
\(36\) 7715.15 + 4454.34i 0.165362 + 0.0954720i
\(37\) −7417.14 27681.1i −0.146430 0.546486i −0.999688 0.0249953i \(-0.992043\pi\)
0.853257 0.521490i \(-0.174624\pi\)
\(38\) 12550.5i 0.228723i
\(39\) 41433.4 + 19370.2i 0.698484 + 0.326543i
\(40\) 74358.7 1.16186
\(41\) 83471.8 22366.2i 1.21112 0.324519i 0.403920 0.914794i \(-0.367647\pi\)
0.807202 + 0.590275i \(0.200981\pi\)
\(42\) −16941.9 + 29344.2i −0.228673 + 0.396072i
\(43\) −102720. + 59305.2i −1.29196 + 0.745912i −0.979001 0.203856i \(-0.934653\pi\)
−0.312956 + 0.949768i \(0.601319\pi\)
\(44\) −21762.3 21762.3i −0.255474 0.255474i
\(45\) −17315.5 + 64622.2i −0.190019 + 0.709160i
\(46\) 129134. + 34601.3i 1.32668 + 0.355483i
\(47\) 2437.23 2437.23i 0.0234748 0.0234748i −0.695272 0.718747i \(-0.744716\pi\)
0.718747 + 0.695272i \(0.244716\pi\)
\(48\) 53258.5 + 92246.5i 0.481577 + 0.834115i
\(49\) −77516.5 44754.2i −0.658879 0.380404i
\(50\) −89392.1 333616.i −0.715137 2.66893i
\(51\) 44143.0i 0.332775i
\(52\) 37924.4 + 54274.9i 0.269717 + 0.386002i
\(53\) −262002. −1.75986 −0.879928 0.475108i \(-0.842409\pi\)
−0.879928 + 0.475108i \(0.842409\pi\)
\(54\) −199905. + 53564.4i −1.26953 + 0.340169i
\(55\) 115562. 200159.i 0.694585 1.20306i
\(56\) 47730.8 27557.4i 0.271791 0.156918i
\(57\) −19041.8 19041.8i −0.102822 0.102822i
\(58\) −60709.8 + 226572.i −0.311154 + 1.16124i
\(59\) 148193. + 39708.1i 0.721557 + 0.193341i 0.600866 0.799350i \(-0.294822\pi\)
0.120691 + 0.992690i \(0.461489\pi\)
\(60\) 100408. 100408.i 0.464850 0.464850i
\(61\) 14741.0 + 25532.2i 0.0649439 + 0.112486i 0.896669 0.442701i \(-0.145980\pi\)
−0.831725 + 0.555188i \(0.812646\pi\)
\(62\) 313357. + 180917.i 1.31481 + 0.759108i
\(63\) 12834.3 + 47898.1i 0.0513274 + 0.191556i
\(64\) 49815.7i 0.190032i
\(65\) −319990. + 380590.i −1.16519 + 1.38585i
\(66\) 206271. 0.717473
\(67\) 86045.8 23055.9i 0.286092 0.0766580i −0.112919 0.993604i \(-0.536020\pi\)
0.399011 + 0.916946i \(0.369354\pi\)
\(68\) 31951.7 55342.1i 0.101617 0.176006i
\(69\) −248421. + 143426.i −0.756209 + 0.436597i
\(70\) −260474. 260474.i −0.759400 0.759400i
\(71\) 172572. 644048.i 0.482165 1.79946i −0.110337 0.993894i \(-0.535193\pi\)
0.592501 0.805569i \(-0.298140\pi\)
\(72\) 93810.6 + 25136.5i 0.251336 + 0.0673452i
\(73\) 46511.6 46511.6i 0.119562 0.119562i −0.644794 0.764356i \(-0.723057\pi\)
0.764356 + 0.644794i \(0.223057\pi\)
\(74\) 139025. + 240798.i 0.343081 + 0.594233i
\(75\) 641794. + 370540.i 1.52129 + 0.878317i
\(76\) −10089.8 37655.7i −0.0229849 0.0857807i
\(77\) 171309.i 0.375239i
\(78\) −436949. 77488.2i −0.920761 0.163287i
\(79\) 169972. 0.344743 0.172371 0.985032i \(-0.444857\pi\)
0.172371 + 0.985032i \(0.444857\pi\)
\(80\) −1.11854e6 + 299711.i −2.18464 + 0.585373i
\(81\) 114283. 197945.i 0.215044 0.372468i
\(82\) −726119. + 419225.i −1.31694 + 0.760336i
\(83\) 378696. + 378696.i 0.662302 + 0.662302i 0.955922 0.293620i \(-0.0948601\pi\)
−0.293620 + 0.955922i \(0.594860\pi\)
\(84\) 27240.4 101663.i 0.0459595 0.171523i
\(85\) 463546. + 124207.i 0.754807 + 0.202250i
\(86\) 813746. 813746.i 1.27936 1.27936i
\(87\) −251649. 435869.i −0.382153 0.661909i
\(88\) −290565. 167758.i −0.426379 0.246170i
\(89\) 37362.9 + 139440.i 0.0529993 + 0.197796i 0.987349 0.158561i \(-0.0506854\pi\)
−0.934350 + 0.356357i \(0.884019\pi\)
\(90\) 649112.i 0.890414i
\(91\) −64354.3 + 362889.i −0.0853991 + 0.481559i
\(92\) −415261. −0.533283
\(93\) −749920. + 200940.i −0.932322 + 0.249815i
\(94\) −16721.0 + 28961.6i −0.0201316 + 0.0348690i
\(95\) 253537. 146380.i 0.295713 0.170730i
\(96\) −421243. 421243.i −0.476123 0.476123i
\(97\) −54694.5 + 204123.i −0.0599278 + 0.223654i −0.989395 0.145252i \(-0.953601\pi\)
0.929467 + 0.368905i \(0.120267\pi\)
\(98\) 838858. + 224771.i 0.891272 + 0.238816i
\(99\) 213454. 213454.i 0.219988 0.219988i
\(100\) 536412. + 929092.i 0.536412 + 0.929092i
\(101\) −523979. 302519.i −0.508569 0.293622i 0.223677 0.974663i \(-0.428194\pi\)
−0.732245 + 0.681041i \(0.761527\pi\)
\(102\) 110851. + 413701.i 0.104457 + 0.389840i
\(103\) 603662.i 0.552436i 0.961095 + 0.276218i \(0.0890812\pi\)
−0.961095 + 0.276218i \(0.910919\pi\)
\(104\) 552493. + 464521.i 0.491164 + 0.412958i
\(105\) 790391. 0.682769
\(106\) 2.45544e6 657933.i 2.06164 0.552414i
\(107\) −548498. + 950027.i −0.447738 + 0.775505i −0.998238 0.0593298i \(-0.981104\pi\)
0.550500 + 0.834835i \(0.314437\pi\)
\(108\) 556719. 321422.i 0.441941 0.255155i
\(109\) −639560. 639560.i −0.493857 0.493857i 0.415662 0.909519i \(-0.363550\pi\)
−0.909519 + 0.415662i \(0.863550\pi\)
\(110\) −580391. + 2.16605e6i −0.436057 + 1.62739i
\(111\) −576272. 154412.i −0.421365 0.112904i
\(112\) −606915. + 606915.i −0.431990 + 0.431990i
\(113\) −226130. 391669.i −0.156720 0.271447i 0.776964 0.629545i \(-0.216759\pi\)
−0.933684 + 0.358098i \(0.883425\pi\)
\(114\) 226274. + 130640.i 0.152729 + 0.0881780i
\(115\) −807127. 3.01224e6i −0.530699 1.98060i
\(116\) 728598.i 0.466782i
\(117\) −532353. + 371980.i −0.332386 + 0.232253i
\(118\) −1.48855e6 −0.905979
\(119\) 343581. 92062.2i 0.203886 0.0546312i
\(120\) 774008. 1.34062e6i 0.447921 0.775822i
\(121\) 631076. 364352.i 0.356226 0.205667i
\(122\) −202267. 202267.i −0.111390 0.111390i
\(123\) 465624. 1.73773e6i 0.250219 0.933830i
\(124\) −1.08562e6 290891.i −0.569394 0.152569i
\(125\) −3.19633e6 + 3.19633e6i −1.63652 + 1.63652i
\(126\) −240561. 416664.i −0.120258 0.208293i
\(127\) −1.83707e6 1.06063e6i −0.896840 0.517791i −0.0206664 0.999786i \(-0.506579\pi\)
−0.876174 + 0.481996i \(0.839912\pi\)
\(128\) 599099. + 2.23587e6i 0.285672 + 1.06614i
\(129\) 2.46926e6i 1.15026i
\(130\) 2.04317e6 4.37038e6i 0.929980 1.98925i
\(131\) 1.82952e6 0.813811 0.406906 0.913470i \(-0.366608\pi\)
0.406906 + 0.913470i \(0.366608\pi\)
\(132\) −618880. + 165828.i −0.269082 + 0.0721003i
\(133\) 108497. 187922.i 0.0461171 0.0798772i
\(134\) −748510. + 432152.i −0.311088 + 0.179607i
\(135\) 3.41362e6 + 3.41362e6i 1.38744 + 1.38744i
\(136\) 180308. 672919.i 0.0716801 0.267514i
\(137\) −1.12688e6 301946.i −0.438244 0.117427i 0.0329497 0.999457i \(-0.489510\pi\)
−0.471193 + 0.882030i \(0.656177\pi\)
\(138\) 1.96800e6 1.96800e6i 0.748837 0.748837i
\(139\) 273227. + 473243.i 0.101737 + 0.176214i 0.912400 0.409299i \(-0.134227\pi\)
−0.810663 + 0.585513i \(0.800893\pi\)
\(140\) 990913. + 572104.i 0.361120 + 0.208493i
\(141\) −18571.7 69310.4i −0.00662511 0.0247253i
\(142\) 6.46927e6i 2.25939i
\(143\) 2.10903e6 765282.i 0.721232 0.261706i
\(144\) −1.51246e6 −0.506518
\(145\) 5.28514e6 1.41615e6i 1.73361 0.464521i
\(146\) −319100. + 552698.i −0.102534 + 0.177594i
\(147\) −1.61376e6 + 931702.i −0.508026 + 0.293309i
\(148\) −610705. 610705.i −0.188385 0.188385i
\(149\) 668891. 2.49633e6i 0.202207 0.754647i −0.788076 0.615578i \(-0.788922\pi\)
0.990283 0.139069i \(-0.0444109\pi\)
\(150\) −6.94528e6 1.86098e6i −2.05786 0.551403i
\(151\) −3.30562e6 + 3.30562e6i −0.960113 + 0.960113i −0.999234 0.0391212i \(-0.987544\pi\)
0.0391212 + 0.999234i \(0.487544\pi\)
\(152\) −212496. 368054.i −0.0605090 0.104805i
\(153\) 542820. + 313397.i 0.151559 + 0.0875026i
\(154\) 430187. + 1.60548e6i 0.117786 + 0.439585i
\(155\) 8.44031e6i 2.26654i
\(156\) 1.37329e6 118789.i 0.361733 0.0312898i
\(157\) 3.52959e6 0.912064 0.456032 0.889963i \(-0.349270\pi\)
0.456032 + 0.889963i \(0.349270\pi\)
\(158\) −1.59295e6 + 426829.i −0.403859 + 0.108214i
\(159\) −2.72721e6 + 4.72366e6i −0.678464 + 1.17513i
\(160\) 5.60875e6 3.23821e6i 1.36932 0.790579i
\(161\) −1.63443e6 1.63443e6i −0.391642 0.391642i
\(162\) −573972. + 2.14209e6i −0.135004 + 0.503841i
\(163\) 326202. + 87405.5i 0.0753223 + 0.0201825i 0.296283 0.955100i \(-0.404253\pi\)
−0.220961 + 0.975283i \(0.570919\pi\)
\(164\) 1.84157e6 1.84157e6i 0.417500 0.417500i
\(165\) −2.40579e6 4.16694e6i −0.535556 0.927611i
\(166\) −4.50005e6 2.59810e6i −0.983768 0.567979i
\(167\) 1.80514e6 + 6.73689e6i 0.387581 + 1.44647i 0.834058 + 0.551677i \(0.186012\pi\)
−0.446477 + 0.894795i \(0.647322\pi\)
\(168\) 1.14739e6i 0.241982i
\(169\) −4.75511e6 + 828835.i −0.985147 + 0.171715i
\(170\) −4.65619e6 −0.947728
\(171\) 369344. 98965.4i 0.0738657 0.0197922i
\(172\) −1.78731e6 + 3.09571e6i −0.351248 + 0.608380i
\(173\) 5.61268e6 3.24048e6i 1.08401 0.625851i 0.152032 0.988376i \(-0.451418\pi\)
0.931974 + 0.362524i \(0.118085\pi\)
\(174\) 3.45296e6 + 3.45296e6i 0.655456 + 0.655456i
\(175\) −1.54556e6 + 5.76810e6i −0.288384 + 1.07626i
\(176\) 5.04698e6 + 1.35234e6i 0.925750 + 0.248054i
\(177\) 2.25845e6 2.25845e6i 0.407278 0.407278i
\(178\) −700318. 1.21299e6i −0.124175 0.215078i
\(179\) −4.32238e6 2.49553e6i −0.753640 0.435114i 0.0733676 0.997305i \(-0.476625\pi\)
−0.827008 + 0.562191i \(0.809959\pi\)
\(180\) 521844. + 1.94755e6i 0.0894795 + 0.333942i
\(181\) 833309.i 0.140530i 0.997528 + 0.0702652i \(0.0223846\pi\)
−0.997528 + 0.0702652i \(0.977615\pi\)
\(182\) −308159. 3.56254e6i −0.0511165 0.590943i
\(183\) 613764. 0.100149
\(184\) −4.37280e6 + 1.17169e6i −0.701950 + 0.188087i
\(185\) 3.24296e6 5.61697e6i 0.512184 0.887129i
\(186\) 6.52353e6 3.76636e6i 1.01378 0.585306i
\(187\) −1.53114e6 1.53114e6i −0.234148 0.234148i
\(188\) 26885.2 100337.i 0.00404613 0.0151004i
\(189\) 3.45629e6 + 926109.i 0.511946 + 0.137176i
\(190\) −2.00853e6 + 2.00853e6i −0.292831 + 0.292831i
\(191\) −2.97799e6 5.15804e6i −0.427389 0.740260i 0.569251 0.822164i \(-0.307233\pi\)
−0.996640 + 0.0819036i \(0.973900\pi\)
\(192\) −898133. 518537.i −0.126893 0.0732616i
\(193\) 2.45986e6 + 9.18032e6i 0.342167 + 1.27699i 0.895887 + 0.444282i \(0.146541\pi\)
−0.553720 + 0.832703i \(0.686792\pi\)
\(194\) 2.05035e6i 0.280817i
\(195\) 3.53088e6 + 9.73073e6i 0.476189 + 1.31233i
\(196\) −2.69755e6 −0.358263
\(197\) −1.92518e6 + 515850.i −0.251810 + 0.0674722i −0.382516 0.923949i \(-0.624942\pi\)
0.130706 + 0.991421i \(0.458276\pi\)
\(198\) −1.46444e6 + 2.53648e6i −0.188658 + 0.326765i
\(199\) −2.21118e6 + 1.27662e6i −0.280585 + 0.161996i −0.633688 0.773589i \(-0.718460\pi\)
0.353103 + 0.935584i \(0.385126\pi\)
\(200\) 8.27004e6 + 8.27004e6i 1.03375 + 1.03375i
\(201\) 479983. 1.79132e6i 0.0591068 0.220590i
\(202\) 5.67033e6 + 1.51936e6i 0.687945 + 0.184334i
\(203\) 2.86770e6 2.86770e6i 0.342804 0.342804i
\(204\) −665178. 1.15212e6i −0.0783516 0.135709i
\(205\) 1.69378e7 + 9.77906e6i 1.96606 + 1.13510i
\(206\) −1.51590e6 5.65742e6i −0.173408 0.647168i
\(207\) 4.07307e6i 0.459209i
\(208\) −1.01832e7 4.76066e6i −1.13160 0.529026i
\(209\) −1.32097e6 −0.144695
\(210\) −7.40742e6 + 1.98481e6i −0.799851 + 0.214319i
\(211\) −1.57657e6 + 2.73070e6i −0.167829 + 0.290688i −0.937656 0.347564i \(-0.887009\pi\)
0.769827 + 0.638252i \(0.220342\pi\)
\(212\) −6.83820e6 + 3.94804e6i −0.717685 + 0.414356i
\(213\) −9.81528e6 9.81528e6i −1.01570 1.01570i
\(214\) 2.75475e6 1.02809e7i 0.281087 1.04903i
\(215\) −2.59297e7 6.94785e6i −2.60905 0.699093i
\(216\) 4.95547e6 4.95547e6i 0.491726 0.491726i
\(217\) −3.12798e6 5.41783e6i −0.306116 0.530208i
\(218\) 7.59990e6 + 4.38780e6i 0.733565 + 0.423524i
\(219\) −354418. 1.32271e6i −0.0337430 0.125930i
\(220\) 6.96547e6i 0.654157i
\(221\) 2.66827e6 + 3.81866e6i 0.247203 + 0.353781i
\(222\) 5.78849e6 0.529061
\(223\) −1.35490e6 + 363044.i −0.122178 + 0.0327374i −0.319390 0.947623i \(-0.603478\pi\)
0.197212 + 0.980361i \(0.436811\pi\)
\(224\) 2.40017e6 4.15721e6i 0.213549 0.369878i
\(225\) −9.11296e6 + 5.26137e6i −0.800040 + 0.461903i
\(226\) 3.10281e6 + 3.10281e6i 0.268800 + 0.268800i
\(227\) 3.83117e6 1.42981e7i 0.327532 1.22237i −0.584210 0.811602i \(-0.698596\pi\)
0.911742 0.410763i \(-0.134738\pi\)
\(228\) −783924. 210052.i −0.0661408 0.0177224i
\(229\) −5.86941e6 + 5.86941e6i −0.488752 + 0.488752i −0.907912 0.419161i \(-0.862324\pi\)
0.419161 + 0.907912i \(0.362324\pi\)
\(230\) 1.51285e7 + 2.62034e7i 1.24341 + 2.15365i
\(231\) −3.08854e6 1.78317e6i −0.250564 0.144663i
\(232\) −2.05579e6 7.67231e6i −0.164632 0.614416i
\(233\) 5.82716e6i 0.460669i 0.973112 + 0.230334i \(0.0739820\pi\)
−0.973112 + 0.230334i \(0.926018\pi\)
\(234\) 4.05502e6 4.82297e6i 0.316480 0.376415i
\(235\) 780085. 0.0601088
\(236\) 4.46615e6 1.19670e6i 0.339779 0.0910436i
\(237\) 1.76925e6 3.06443e6i 0.132906 0.230200i
\(238\) −2.98880e6 + 1.72559e6i −0.221700 + 0.127999i
\(239\) 5.26700e6 + 5.26700e6i 0.385806 + 0.385806i 0.873189 0.487382i \(-0.162048\pi\)
−0.487382 + 0.873189i \(0.662048\pi\)
\(240\) −6.23945e6 + 2.32860e7i −0.451349 + 1.68446i
\(241\) 2.42770e7 + 6.50501e6i 1.73438 + 0.464726i 0.981185 0.193071i \(-0.0618449\pi\)
0.753195 + 0.657797i \(0.228512\pi\)
\(242\) −4.99939e6 + 4.99939e6i −0.352753 + 0.352753i
\(243\) 5.39575e6 + 9.34571e6i 0.376039 + 0.651319i
\(244\) 769476. + 444257.i 0.0529695 + 0.0305819i
\(245\) −5.24313e6 1.95676e7i −0.356527 1.33058i
\(246\) 1.74550e7i 1.17251i
\(247\) 2.79825e6 + 496239.i 0.185693 + 0.0329306i
\(248\) −1.22526e7 −0.803291
\(249\) 1.07694e7 2.88566e6i 0.697581 0.186916i
\(250\) 2.19290e7 3.79821e7i 1.40345 2.43085i
\(251\) −1.43021e7 + 8.25732e6i −0.904437 + 0.522177i −0.878637 0.477490i \(-0.841547\pi\)
−0.0258001 + 0.999667i \(0.508213\pi\)
\(252\) 1.05673e6 + 1.05673e6i 0.0660335 + 0.0660335i
\(253\) −3.64186e6 + 1.35916e7i −0.224886 + 0.839285i
\(254\) 1.98802e7 + 5.32688e6i 1.21316 + 0.325066i
\(255\) 7.06444e6 7.06444e6i 0.426047 0.426047i
\(256\) −9.63521e6 1.66887e7i −0.574303 0.994723i
\(257\) −136082. 78566.9i −0.00801680 0.00462850i 0.495986 0.868330i \(-0.334807\pi\)
−0.504003 + 0.863702i \(0.668140\pi\)
\(258\) −6.20075e6 2.31415e7i −0.361064 1.34751i
\(259\) 4.80737e6i 0.276699i
\(260\) −2.61667e6 + 1.47552e7i −0.148877 + 0.839506i
\(261\) 7.14642e6 0.401946
\(262\) −1.71460e7 + 4.59426e6i −0.953364 + 0.255453i
\(263\) −1.65537e7 + 2.86719e7i −0.909974 + 1.57612i −0.0958757 + 0.995393i \(0.530565\pi\)
−0.814098 + 0.580727i \(0.802768\pi\)
\(264\) −6.04905e6 + 3.49242e6i −0.328758 + 0.189808i
\(265\) −4.19296e7 4.19296e7i −2.25311 2.25311i
\(266\) −544910. + 2.03363e6i −0.0289521 + 0.108051i
\(267\) 2.90290e6 + 777829.i 0.152510 + 0.0408649i
\(268\) 1.89835e6 1.89835e6i 0.0986218 0.0986218i
\(269\) 9.93564e6 + 1.72090e7i 0.510433 + 0.884096i 0.999927 + 0.0120895i \(0.00384830\pi\)
−0.489494 + 0.872007i \(0.662818\pi\)
\(270\) −4.05641e7 2.34197e7i −2.06087 1.18984i
\(271\) −192013. 716602.i −0.00964767 0.0360056i 0.960934 0.276777i \(-0.0892663\pi\)
−0.970582 + 0.240771i \(0.922600\pi\)
\(272\) 1.08491e7i 0.539122i
\(273\) 5.87269e6 + 4.93760e6i 0.288635 + 0.242677i
\(274\) 1.13192e7 0.550254
\(275\) 3.51138e7 9.40871e6i 1.68842 0.452410i
\(276\) −4.32250e6 + 7.48679e6i −0.205593 + 0.356097i
\(277\) 2.30529e7 1.33096e7i 1.08464 0.626219i 0.152498 0.988304i \(-0.451268\pi\)
0.932145 + 0.362085i \(0.117935\pi\)
\(278\) −3.74904e6 3.74904e6i −0.174496 0.174496i
\(279\) 2.85319e6 1.06483e7i 0.131377 0.490304i
\(280\) 1.20488e7 + 3.22846e6i 0.548869 + 0.147069i
\(281\) −1.31657e7 + 1.31657e7i −0.593371 + 0.593371i −0.938540 0.345169i \(-0.887821\pi\)
0.345169 + 0.938540i \(0.387821\pi\)
\(282\) 348101. + 602929.i 0.0155224 + 0.0268856i
\(283\) 1.85879e7 + 1.07318e7i 0.820110 + 0.473491i 0.850454 0.526049i \(-0.176327\pi\)
−0.0303444 + 0.999540i \(0.509660\pi\)
\(284\) −5.20088e6 1.94100e7i −0.227050 0.847363i
\(285\) 6.09473e6i 0.263281i
\(286\) −1.78438e7 + 1.24683e7i −0.762761 + 0.532976i
\(287\) 1.44965e7 0.613222
\(288\) 8.17062e6 2.18931e6i 0.342041 0.0916495i
\(289\) −9.82073e6 + 1.70100e7i −0.406865 + 0.704711i
\(290\) −4.59753e7 + 2.65438e7i −1.88508 + 1.08835i
\(291\) 3.11083e6 + 3.11083e6i 0.126240 + 0.126240i
\(292\) 513072. 1.91481e6i 0.0206077 0.0769091i
\(293\) 2.02819e6 + 543451.i 0.0806316 + 0.0216052i 0.298909 0.954282i \(-0.403377\pi\)
−0.218278 + 0.975887i \(0.570044\pi\)
\(294\) 1.27842e7 1.27842e7i 0.503073 0.503073i
\(295\) 1.73614e7 + 3.00708e7i 0.676266 + 1.17133i
\(296\) −8.15402e6 4.70772e6i −0.314410 0.181525i
\(297\) −5.63777e6 2.10404e7i −0.215198 0.803129i
\(298\) 2.50750e7i 0.947527i
\(299\) 1.28205e7 2.74234e7i 0.479615 1.02591i
\(300\) 2.23343e7 0.827195
\(301\) −1.92191e7 + 5.14975e6i −0.704749 + 0.188837i
\(302\) 2.26788e7 3.92808e7i 0.823377 1.42613i
\(303\) −1.09083e7 + 6.29791e6i −0.392129 + 0.226396i
\(304\) 4.67994e6 + 4.67994e6i 0.166579 + 0.166579i
\(305\) −1.72697e6 + 6.44515e6i −0.0608675 + 0.227161i
\(306\) −5.87422e6 1.57399e6i −0.205015 0.0549336i
\(307\) 2.33578e7 2.33578e7i 0.807267 0.807267i −0.176953 0.984219i \(-0.556624\pi\)
0.984219 + 0.176953i \(0.0566240\pi\)
\(308\) −2.58141e6 4.47113e6i −0.0883495 0.153026i
\(309\) 1.08835e7 + 6.28358e6i 0.368886 + 0.212977i
\(310\) 2.11951e7 + 7.91013e7i 0.711461 + 2.65521i
\(311\) 1.99611e7i 0.663596i −0.943350 0.331798i \(-0.892345\pi\)
0.943350 0.331798i \(-0.107655\pi\)
\(312\) 1.41259e7 5.12570e6i 0.465105 0.168768i
\(313\) −3.23854e7 −1.05613 −0.528063 0.849205i \(-0.677081\pi\)
−0.528063 + 0.849205i \(0.677081\pi\)
\(314\) −3.30788e7 + 8.86343e6i −1.06847 + 0.286294i
\(315\) −5.61145e6 + 9.71932e6i −0.179533 + 0.310960i
\(316\) 4.43622e6 2.56125e6i 0.140589 0.0811693i
\(317\) 1.49729e7 + 1.49729e7i 0.470031 + 0.470031i 0.901925 0.431893i \(-0.142154\pi\)
−0.431893 + 0.901925i \(0.642154\pi\)
\(318\) 1.36970e7 5.11179e7i 0.425936 1.58961i
\(319\) −2.38472e7 6.38984e6i −0.734625 0.196842i
\(320\) 7.97228e6 7.97228e6i 0.243295 0.243295i
\(321\) 1.14188e7 + 1.97779e7i 0.345226 + 0.597949i
\(322\) 1.94220e7 + 1.12133e7i 0.581736 + 0.335866i
\(323\) −709895. 2.64937e6i −0.0210662 0.0786202i
\(324\) 6.88842e6i 0.202528i
\(325\) −7.79171e7 + 6.73982e6i −2.26978 + 0.196335i
\(326\) −3.27660e6 −0.0945738
\(327\) −1.81879e7 + 4.87344e6i −0.520164 + 0.139377i
\(328\) 1.41960e7 2.45882e7i 0.402296 0.696796i
\(329\) 500736. 289100.i 0.0140612 0.00811821i
\(330\) 3.30106e7 + 3.30106e7i 0.918568 + 0.918568i
\(331\) 4.20969e6 1.57108e7i 0.116082 0.433225i −0.883283 0.468840i \(-0.844672\pi\)
0.999366 + 0.0356146i \(0.0113389\pi\)
\(332\) 1.55903e7 + 4.17742e6i 0.426031 + 0.114155i
\(333\) 5.99008e6 5.99008e6i 0.162218 0.162218i
\(334\) −3.38351e7 5.86040e7i −0.908087 1.57285i
\(335\) 1.74601e7 + 1.00806e7i 0.464422 + 0.268134i
\(336\) 4.62469e6 + 1.72596e7i 0.121917 + 0.455001i
\(337\) 1.54316e7i 0.403201i 0.979468 + 0.201600i \(0.0646142\pi\)
−0.979468 + 0.201600i \(0.935386\pi\)
\(338\) 4.24828e7 1.97086e7i 1.10018 0.510395i
\(339\) −9.41527e6 −0.241676
\(340\) 1.39701e7 3.74328e6i 0.355437 0.0952391i
\(341\) −1.90419e7 + 3.29815e7i −0.480227 + 0.831778i
\(342\) −3.21291e6 + 1.85498e6i −0.0803195 + 0.0463725i
\(343\) −2.45727e7 2.45727e7i −0.608934 0.608934i
\(344\) −1.00860e7 + 3.76416e7i −0.247768 + 0.924682i
\(345\) −6.27095e7 1.68030e7i −1.52713 0.409193i
\(346\) −4.44637e7 + 4.44637e7i −1.07344 + 1.07344i
\(347\) −3.75387e7 6.50189e7i −0.898443 1.55615i −0.829485 0.558530i \(-0.811366\pi\)
−0.0689584 0.997620i \(-0.521968\pi\)
\(348\) −1.31360e7 7.58406e6i −0.311691 0.179955i
\(349\) −5.00643e6 1.86843e7i −0.117775 0.439541i 0.881705 0.471801i \(-0.156396\pi\)
−0.999479 + 0.0322604i \(0.989729\pi\)
\(350\) 5.79389e7i 1.35134i
\(351\) 4.03855e6 + 4.66885e7i 0.0933908 + 1.07966i
\(352\) −2.92225e7 −0.670022
\(353\) 5.05743e6 1.35513e6i 0.114976 0.0308076i −0.200872 0.979617i \(-0.564378\pi\)
0.315848 + 0.948810i \(0.397711\pi\)
\(354\) −1.54945e7 + 2.68373e7i −0.349275 + 0.604962i
\(355\) 1.30688e8 7.54528e7i 2.92113 1.68652i
\(356\) 3.07635e6 + 3.07635e6i 0.0681845 + 0.0681845i
\(357\) 1.91657e6 7.15274e6i 0.0421231 0.157206i
\(358\) 4.67754e7 + 1.25334e7i 1.01946 + 0.273162i
\(359\) −1.77805e7 + 1.77805e7i −0.384292 + 0.384292i −0.872646 0.488354i \(-0.837597\pi\)
0.488354 + 0.872646i \(0.337597\pi\)
\(360\) 1.09903e7 + 1.90357e7i 0.235560 + 0.408002i
\(361\) 3.92939e7 + 2.26863e7i 0.835224 + 0.482217i
\(362\) −2.09259e6 7.80965e6i −0.0441121 0.164629i
\(363\) 1.51703e7i 0.317157i
\(364\) 3.78863e6 + 1.04411e7i 0.0785558 + 0.216491i
\(365\) 1.48870e7 0.306146
\(366\) −5.75210e6 + 1.54127e6i −0.117323 + 0.0314366i
\(367\) −2.04112e6 + 3.53532e6i −0.0412924 + 0.0715206i −0.885933 0.463813i \(-0.846481\pi\)
0.844641 + 0.535334i \(0.179814\pi\)
\(368\) 6.10550e7 3.52501e7i 1.22512 0.707322i
\(369\) 1.80629e7 + 1.80629e7i 0.359508 + 0.359508i
\(370\) −1.62873e7 + 6.07850e7i −0.321546 + 1.20003i
\(371\) −4.24537e7 1.13754e7i −0.831369 0.222765i
\(372\) −1.65448e7 + 1.65448e7i −0.321391 + 0.321391i
\(373\) 9.66679e6 + 1.67434e7i 0.186275 + 0.322639i 0.944006 0.329930i \(-0.107025\pi\)
−0.757730 + 0.652568i \(0.773692\pi\)
\(374\) 1.81946e7 + 1.05047e7i 0.347798 + 0.200802i
\(375\) 2.43561e7 + 9.08980e7i 0.461863 + 1.72370i
\(376\) 1.13243e6i 0.0213034i
\(377\) 4.81159e7 + 2.24943e7i 0.897975 + 0.419806i
\(378\) −3.47174e7 −0.642794
\(379\) 8.33021e6 2.23207e6i 0.153016 0.0410006i −0.181498 0.983391i \(-0.558094\pi\)
0.334514 + 0.942391i \(0.391428\pi\)
\(380\) 4.41151e6 7.64097e6i 0.0803965 0.139251i
\(381\) −3.82446e7 + 2.20805e7i −0.691504 + 0.399240i
\(382\) 4.08621e7 + 4.08621e7i 0.733044 + 0.733044i
\(383\) −1.77683e7 + 6.63122e7i −0.316264 + 1.18031i 0.606543 + 0.795051i \(0.292556\pi\)
−0.922807 + 0.385262i \(0.874111\pi\)
\(384\) 4.65467e7 + 1.24722e7i 0.822045 + 0.220266i
\(385\) 2.74155e7 2.74155e7i 0.480412 0.480412i
\(386\) −4.61068e7 7.98594e7i −0.801684 1.38856i
\(387\) −3.03641e7 1.75307e7i −0.523875 0.302459i
\(388\) 1.64835e6 + 6.15173e6i 0.0282199 + 0.105318i
\(389\) 7.51491e7i 1.27666i −0.769763 0.638329i \(-0.779626\pi\)
0.769763 0.638329i \(-0.220374\pi\)
\(390\) −5.75265e7 8.23282e7i −0.969782 1.38789i
\(391\) −2.92168e7 −0.488768
\(392\) −2.84059e7 + 7.61133e6i −0.471574 + 0.126358i
\(393\) 1.90437e7 3.29846e7i 0.313743 0.543418i
\(394\) 1.67471e7 9.66893e6i 0.273811 0.158085i
\(395\) 2.72015e7 + 2.72015e7i 0.441368 + 0.441368i
\(396\) 2.35463e6 8.78759e6i 0.0379173 0.141509i
\(397\) −3.65718e6 979937.i −0.0584486 0.0156613i 0.229476 0.973314i \(-0.426299\pi\)
−0.287925 + 0.957653i \(0.592965\pi\)
\(398\) 1.75170e7 1.75170e7i 0.277850 0.277850i
\(399\) −2.25871e6 3.91220e6i −0.0355584 0.0615889i
\(400\) −1.57735e8 9.10683e7i −2.46461 1.42294i
\(401\) 3.98812e6 + 1.48839e7i 0.0618494 + 0.230825i 0.989931 0.141552i \(-0.0452094\pi\)
−0.928081 + 0.372377i \(0.878543\pi\)
\(402\) 1.79933e7i 0.276970i
\(403\) 5.27269e7 6.27124e7i 0.805596 0.958160i
\(404\) −1.82343e7 −0.276532
\(405\) 4.99675e7 1.33888e7i 0.752182 0.201547i
\(406\) −1.96743e7 + 3.40769e7i −0.293983 + 0.509193i
\(407\) −2.53445e7 + 1.46326e7i −0.375924 + 0.217040i
\(408\) −1.02553e7 1.02553e7i −0.150997 0.150997i
\(409\) 1.57037e7 5.86069e7i 0.229526 0.856601i −0.751015 0.660285i \(-0.770435\pi\)
0.980541 0.196316i \(-0.0628979\pi\)
\(410\) −1.83296e8 4.91139e7i −2.65950 0.712612i
\(411\) −1.71736e7 + 1.71736e7i −0.247364 + 0.247364i
\(412\) 9.09641e6 + 1.57555e7i 0.130070 + 0.225289i
\(413\) 2.22885e7 + 1.28683e7i 0.316396 + 0.182671i
\(414\) 1.02282e7 + 3.81722e7i 0.144145 + 0.537955i
\(415\) 1.21209e8i 1.69587i
\(416\) 6.19028e7 + 1.09778e7i 0.859865 + 0.152488i
\(417\) 1.13762e7 0.156888
\(418\) 1.23799e7 3.31719e6i 0.169507 0.0454194i
\(419\) −5.54749e6 + 9.60854e6i −0.0754144 + 0.130622i −0.901266 0.433265i \(-0.857361\pi\)
0.825852 + 0.563887i \(0.190695\pi\)
\(420\) 2.06290e7 1.19102e7i 0.278440 0.160757i
\(421\) −5.69651e7 5.69651e7i −0.763419 0.763419i 0.213520 0.976939i \(-0.431507\pi\)
−0.976939 + 0.213520i \(0.931507\pi\)
\(422\) 7.91810e6 2.95508e7i 0.105362 0.393216i
\(423\) 984151. + 263703.i 0.0130029 + 0.00348412i
\(424\) −6.08682e7 + 6.08682e7i −0.798533 + 0.798533i
\(425\) 3.77407e7 + 6.53688e7i 0.491635 + 0.851537i
\(426\) 1.16635e8 + 6.73394e7i 1.50869 + 0.871044i
\(427\) 1.28003e6 + 4.77715e6i 0.0164414 + 0.0613600i
\(428\) 3.30607e7i 0.421678i
\(429\) 8.15580e6 4.59899e7i 0.103299 0.582492i
\(430\) 2.60457e8 3.27589
\(431\) 9.39536e7 2.51748e7i 1.17350 0.314437i 0.381152 0.924512i \(-0.375527\pi\)
0.792344 + 0.610075i \(0.208861\pi\)
\(432\) −5.45688e7 + 9.45159e7i −0.676851 + 1.17234i
\(433\) −1.06785e8 + 6.16526e7i −1.31537 + 0.759430i −0.982980 0.183712i \(-0.941189\pi\)
−0.332391 + 0.943142i \(0.607855\pi\)
\(434\) 4.29201e7 + 4.29201e7i 0.525039 + 0.525039i
\(435\) 2.94817e7 1.10027e8i 0.358166 1.33669i
\(436\) −2.63297e7 7.05503e6i −0.317678 0.0851215i
\(437\) −1.26032e7 + 1.26032e7i −0.151020 + 0.151020i
\(438\) 6.64310e6 + 1.15062e7i 0.0790585 + 0.136933i
\(439\) −4.36371e7 2.51939e7i −0.515777 0.297784i 0.219428 0.975629i \(-0.429581\pi\)
−0.735205 + 0.677845i \(0.762914\pi\)
\(440\) −1.96535e7 7.33480e7i −0.230719 0.861054i
\(441\) 2.64588e7i 0.308500i
\(442\) −3.45960e7 2.90874e7i −0.400644 0.336851i
\(443\) −6.24926e7 −0.718815 −0.359408 0.933181i \(-0.617021\pi\)
−0.359408 + 0.933181i \(0.617021\pi\)
\(444\) −1.73674e7 + 4.65357e6i −0.198420 + 0.0531664i
\(445\) −1.63360e7 + 2.82947e7i −0.185381 + 0.321089i
\(446\) 1.17862e7 6.80478e6i 0.132853 0.0767025i
\(447\) −3.80441e7 3.80441e7i −0.425956 0.425956i
\(448\) 2.16287e6 8.07193e6i 0.0240545 0.0897725i
\(449\) 9.55183e7 + 2.55940e7i 1.05523 + 0.282748i 0.744412 0.667721i \(-0.232730\pi\)
0.310819 + 0.950469i \(0.399397\pi\)
\(450\) 7.21930e7 7.21930e7i 0.792241 0.792241i
\(451\) −4.41244e7 7.64256e7i −0.481004 0.833124i
\(452\) −1.18039e7 6.81500e6i −0.127824 0.0737990i
\(453\) 2.51888e7 + 9.40060e7i 0.270965 + 1.01126i
\(454\) 1.43620e8i 1.53479i
\(455\) −6.83740e7 + 4.77761e7i −0.725867 + 0.507196i
\(456\) −8.84758e6 −0.0933104
\(457\) 5.43112e7 1.45526e7i 0.569037 0.152473i 0.0371820 0.999309i \(-0.488162\pi\)
0.531855 + 0.846836i \(0.321495\pi\)
\(458\) 4.02681e7 6.97463e7i 0.419145 0.725981i
\(459\) 3.91694e7 2.26145e7i 0.405051 0.233856i
\(460\) −6.64565e7 6.64565e7i −0.682753 0.682753i
\(461\) 8.73835e6 3.26120e7i 0.0891921 0.332870i −0.906883 0.421383i \(-0.861545\pi\)
0.996075 + 0.0885132i \(0.0282116\pi\)
\(462\) 3.34232e7 + 8.95572e6i 0.338940 + 0.0908186i
\(463\) −6.00127e7 + 6.00127e7i −0.604645 + 0.604645i −0.941542 0.336897i \(-0.890623\pi\)
0.336897 + 0.941542i \(0.390623\pi\)
\(464\) 6.18482e7 + 1.07124e8i 0.619118 + 1.07234i
\(465\) −1.52171e8 8.78561e7i −1.51347 0.873802i
\(466\) −1.46330e7 5.46112e7i −0.144603 0.539665i
\(467\) 1.59772e8i 1.56873i 0.620298 + 0.784367i \(0.287012\pi\)
−0.620298 + 0.784367i \(0.712988\pi\)
\(468\) −8.28905e6 + 1.77305e7i −0.0808663 + 0.172975i
\(469\) 1.49435e7 0.144855
\(470\) −7.31084e6 + 1.95893e6i −0.0704163 + 0.0188680i
\(471\) 3.67399e7 6.36354e7i 0.351621 0.609026i
\(472\) 4.36530e7 2.52031e7i 0.415134 0.239678i
\(473\) 8.56486e7 + 8.56486e7i 0.809351 + 0.809351i
\(474\) −8.88581e6 + 3.31623e7i −0.0834377 + 0.311394i
\(475\) 4.44780e7 + 1.19178e7i 0.415016 + 0.111203i
\(476\) 7.58013e6 7.58013e6i 0.0702839 0.0702839i
\(477\) −3.87241e7 6.70722e7i −0.356801 0.617998i
\(478\) −6.25878e7 3.61351e7i −0.573068 0.330861i
\(479\) −3.96180e7 1.47856e8i −0.360484 1.34534i −0.873441 0.486929i \(-0.838117\pi\)
0.512958 0.858414i \(-0.328550\pi\)
\(480\) 1.34828e8i 1.21914i
\(481\) 5.91849e7 2.14758e7i 0.531834 0.192981i
\(482\) −2.43856e8 −2.17767
\(483\) −4.64803e7 + 1.24544e7i −0.412504 + 0.110530i
\(484\) 1.09806e7 1.90190e7i 0.0968482 0.167746i
\(485\) −4.14199e7 + 2.39138e7i −0.363064 + 0.209615i
\(486\) −7.40368e7 7.40368e7i −0.644969 0.644969i
\(487\) −5.82216e7 + 2.17286e8i −0.504077 + 1.88124i −0.0323927 + 0.999475i \(0.510313\pi\)
−0.471685 + 0.881767i \(0.656354\pi\)
\(488\) 9.35626e6 + 2.50700e6i 0.0805087 + 0.0215723i
\(489\) 4.97131e6 4.97131e6i 0.0425152 0.0425152i
\(490\) 9.82756e7 + 1.70218e8i 0.835329 + 1.44683i
\(491\) 6.73158e7 + 3.88648e7i 0.568686 + 0.328331i 0.756624 0.653850i \(-0.226847\pi\)
−0.187939 + 0.982181i \(0.560181\pi\)
\(492\) −1.40327e7 5.23709e7i −0.117828 0.439739i
\(493\) 5.12625e7i 0.427818i
\(494\) −2.74709e7 + 2.37623e6i −0.227872 + 0.0197109i
\(495\) 6.83204e7 0.563294
\(496\) 1.84309e8 4.93855e7i 1.51043 0.404720i
\(497\) 5.59257e7 9.68662e7i 0.455557 0.789047i
\(498\) −9.36830e7 + 5.40879e7i −0.758530 + 0.437937i
\(499\) −4.04648e7 4.04648e7i −0.325668 0.325668i 0.525268 0.850937i \(-0.323965\pi\)
−0.850937 + 0.525268i \(0.823965\pi\)
\(500\) −3.52590e7 + 1.31588e8i −0.282072 + 1.05271i
\(501\) 1.40250e8 + 3.75799e7i 1.11530 + 0.298842i
\(502\) 1.13301e8 1.13301e8i 0.895621 0.895621i
\(503\) −3.93752e7 6.81999e7i −0.309399 0.535895i 0.668832 0.743414i \(-0.266795\pi\)
−0.978231 + 0.207518i \(0.933461\pi\)
\(504\) 1.41093e7 + 8.14601e6i 0.110208 + 0.0636288i
\(505\) −3.54414e7 1.32269e8i −0.275192 1.02703i
\(506\) 1.36524e8i 1.05380i
\(507\) −3.45534e7 + 9.43579e7i −0.265135 + 0.724026i
\(508\) −6.39296e7 −0.487653
\(509\) −1.98778e8 + 5.32625e7i −1.50736 + 0.403895i −0.915556 0.402190i \(-0.868249\pi\)
−0.591800 + 0.806085i \(0.701583\pi\)
\(510\) −4.84668e7 + 8.39469e7i −0.365370 + 0.632840i
\(511\) 9.55595e6 5.51713e6i 0.0716162 0.0413476i
\(512\) 2.74548e7 + 2.74548e7i 0.204554 + 0.204554i
\(513\) 7.14126e6 2.66516e7i 0.0528960 0.197411i
\(514\) 1.47263e6 + 394591.i 0.0108444 + 0.00290575i
\(515\) −9.66073e7 + 9.66073e7i −0.707275 + 0.707275i
\(516\) 3.72086e7 + 6.44471e7i 0.270828 + 0.469088i
\(517\) −3.04827e6 1.75992e6i −0.0220588 0.0127357i
\(518\) 1.20722e7 + 4.50539e7i 0.0868551 + 0.324148i
\(519\) 1.34922e8i 0.965119i
\(520\) 1.40786e7 + 1.62758e8i 0.100126 + 1.15753i
\(521\) 1.40196e8 0.991343 0.495671 0.868510i \(-0.334922\pi\)
0.495671 + 0.868510i \(0.334922\pi\)
\(522\) −6.69752e7 + 1.79459e7i −0.470871 + 0.126170i
\(523\) −2.49046e7 + 4.31361e7i −0.174091 + 0.301534i −0.939846 0.341598i \(-0.889032\pi\)
0.765756 + 0.643132i \(0.222365\pi\)
\(524\) 4.77502e7 2.75686e7i 0.331880 0.191611i
\(525\) 8.79057e7 + 8.79057e7i 0.607490 + 0.607490i
\(526\) 8.31388e7 3.10278e8i 0.571276 2.13203i
\(527\) −7.63817e7 2.04664e7i −0.521864 0.139833i
\(528\) 7.69160e7 7.69160e7i 0.522534 0.522534i
\(529\) 2.09112e7 + 3.62192e7i 0.141258 + 0.244665i
\(530\) 4.98250e8 + 2.87665e8i 3.34672 + 1.93223i
\(531\) 1.17378e7 + 4.38060e7i 0.0783976 + 0.292584i
\(532\) 6.53964e6i 0.0434329i
\(533\) 6.47597e7 + 1.78471e8i 0.427684 + 1.17865i
\(534\) −2.91587e7 −0.191490
\(535\) −2.39817e8 + 6.42588e7i −1.56610 + 0.419635i
\(536\) 1.46338e7 2.53465e7i 0.0950303 0.164597i
\(537\) −8.99843e7 + 5.19524e7i −0.581090 + 0.335493i
\(538\) −1.36330e8 1.36330e8i −0.875478 0.875478i
\(539\) −2.36577e7 + 8.82917e7i −0.151080 + 0.563837i
\(540\) 1.40534e8 + 3.76559e7i 0.892481 + 0.239139i
\(541\) 1.89076e8 1.89076e8i 1.19411 1.19411i 0.218212 0.975901i \(-0.429977\pi\)
0.975901 0.218212i \(-0.0700226\pi\)
\(542\) 3.59903e6 + 6.23370e6i 0.0226041 + 0.0391515i
\(543\) 1.50238e7 + 8.67401e6i 0.0938385 + 0.0541777i
\(544\) −1.57043e7 5.86092e7i −0.0975488 0.364057i
\(545\) 2.04704e8i 1.26455i
\(546\) −6.74371e7 3.15270e7i −0.414306 0.193689i
\(547\) 1.90723e8 1.16531 0.582654 0.812721i \(-0.302014\pi\)
0.582654 + 0.812721i \(0.302014\pi\)
\(548\) −3.39613e7 + 9.09989e6i −0.206368 + 0.0552961i
\(549\) −4.35748e6 + 7.54737e6i −0.0263341 + 0.0456119i
\(550\) −3.05454e8 + 1.76354e8i −1.83594 + 1.05998i
\(551\) −2.21129e7 2.21129e7i −0.132188 0.132188i
\(552\) −2.43924e7 + 9.10338e7i −0.145023 + 0.541235i
\(553\) 2.75415e7 + 7.37972e6i 0.162859 + 0.0436379i
\(554\) −1.82626e8 + 1.82626e8i −1.07407 + 1.07407i
\(555\) −6.75126e7 1.16935e8i −0.394917 0.684016i
\(556\) 1.42623e7 + 8.23437e6i 0.0829787 + 0.0479077i
\(557\) −2.22742e7 8.31285e7i −0.128895 0.481044i 0.871053 0.491189i \(-0.163437\pi\)
−0.999949 + 0.0101449i \(0.996771\pi\)
\(558\) 1.06959e8i 0.615621i
\(559\) −1.49257e8 2.13607e8i −0.854475 1.22287i
\(560\) −1.94256e8 −1.10614
\(561\) −4.35429e7 + 1.16673e7i −0.246621 + 0.0660818i
\(562\) 9.03258e7 1.56449e8i 0.508865 0.881380i
\(563\) −1.30569e7 + 7.53841e6i −0.0731670 + 0.0422430i −0.536137 0.844131i \(-0.680117\pi\)
0.462970 + 0.886374i \(0.346784\pi\)
\(564\) −1.52914e6 1.52914e6i −0.00852332 0.00852332i
\(565\) 2.64921e7 9.88699e7i 0.146883 0.548174i
\(566\) −2.01153e8 5.38987e7i −1.10937 0.297255i
\(567\) 2.71122e7 2.71122e7i 0.148736 0.148736i
\(568\) −1.09533e8 1.89717e8i −0.597723 1.03529i
\(569\) 2.84280e7 + 1.64129e7i 0.154316 + 0.0890941i 0.575169 0.818034i \(-0.304936\pi\)
−0.420854 + 0.907128i \(0.638269\pi\)
\(570\) 1.53050e7 + 5.71189e7i 0.0826433 + 0.308429i
\(571\) 1.33271e8i 0.715857i 0.933749 + 0.357929i \(0.116517\pi\)
−0.933749 + 0.357929i \(0.883483\pi\)
\(572\) 4.35135e7 5.17541e7i 0.232507 0.276539i
\(573\) −1.23993e8 −0.659073
\(574\) −1.35859e8 + 3.64033e7i −0.718377 + 0.192489i
\(575\) 2.45248e8 4.24783e8i 1.29004 2.23441i
\(576\) 1.27528e7 7.36281e6i 0.0667324 0.0385280i
\(577\) 2.45904e8 + 2.45904e8i 1.28008 + 1.28008i 0.940619 + 0.339464i \(0.110246\pi\)
0.339464 + 0.940619i \(0.389754\pi\)
\(578\) 4.93232e7 1.84077e8i 0.255428 0.953269i
\(579\) 1.91118e8 + 5.12099e7i 0.984613 + 0.263826i
\(580\) 1.16602e8 1.16602e8i 0.597613 0.597613i
\(581\) 4.49203e7 + 7.78042e7i 0.229041 + 0.396711i
\(582\) −3.69660e7 2.13423e7i −0.187514 0.108261i
\(583\) 6.92490e7 + 2.58441e8i 0.349468 + 1.30423i
\(584\) 2.16111e7i 0.108502i
\(585\) −1.44725e8 2.56654e7i −0.722898 0.128198i
\(586\) −2.03726e7 −0.101240
\(587\) −2.48817e8 + 6.66704e7i −1.23017 + 0.329624i −0.814647 0.579958i \(-0.803069\pi\)
−0.415526 + 0.909581i \(0.636402\pi\)
\(588\) −2.80791e7 + 4.86345e7i −0.138118 + 0.239228i
\(589\) −4.17771e7 + 2.41200e7i −0.204452 + 0.118041i
\(590\) −2.38221e8 2.38221e8i −1.15991 1.15991i
\(591\) −1.07391e7 + 4.00788e7i −0.0520241 + 0.194157i
\(592\) 1.41631e8 + 3.79500e7i 0.682644 + 0.182914i
\(593\) −1.13225e8 + 1.13225e8i −0.542972 + 0.542972i −0.924399 0.381427i \(-0.875433\pi\)
0.381427 + 0.924399i \(0.375433\pi\)
\(594\) 1.05673e8 + 1.83030e8i 0.504200 + 0.873300i
\(595\) 6.97183e7 + 4.02519e7i 0.330976 + 0.191089i
\(596\) −2.01587e7 7.52332e7i −0.0952189 0.355362i
\(597\) 5.31540e7i 0.249812i
\(598\) −5.12869e7 + 2.89203e8i −0.239830 + 1.35238i
\(599\) 3.63641e8 1.69197 0.845985 0.533206i \(-0.179013\pi\)
0.845985 + 0.533206i \(0.179013\pi\)
\(600\) 2.35185e8 6.30176e7i 1.08882 0.291748i
\(601\) −1.54068e8 + 2.66854e8i −0.709724 + 1.22928i 0.255236 + 0.966879i \(0.417847\pi\)
−0.964960 + 0.262398i \(0.915487\pi\)
\(602\) 1.67187e8 9.65253e7i 0.766324 0.442437i
\(603\) 1.86199e7 + 1.86199e7i 0.0849231 + 0.0849231i
\(604\) −3.64646e7 + 1.36088e8i −0.165486 + 0.617601i
\(605\) 1.59304e8 + 4.26853e7i 0.719382 + 0.192758i
\(606\) 8.64157e7 8.64157e7i 0.388307 0.388307i
\(607\) 1.45142e8 + 2.51393e8i 0.648972 + 1.12405i 0.983369 + 0.181620i \(0.0581340\pi\)
−0.334397 + 0.942432i \(0.608533\pi\)
\(608\) −3.20564e7 1.85078e7i −0.142628 0.0823462i
\(609\) −2.18519e7 8.15523e7i −0.0967468 0.361064i
\(610\) 6.47396e7i 0.285220i
\(611\) 5.79611e6 + 4.87322e6i 0.0254105 + 0.0213645i
\(612\) 1.88900e7 0.0824095
\(613\) 2.25841e8 6.05138e7i 0.980439 0.262708i 0.267209 0.963638i \(-0.413898\pi\)
0.713229 + 0.700931i \(0.247232\pi\)
\(614\) −1.60250e8 + 2.77561e8i −0.692298 + 1.19910i
\(615\) 3.52615e8 2.03583e8i 1.51592 0.875216i
\(616\) −3.97984e7 3.97984e7i −0.170264 0.170264i
\(617\) −3.95522e7 + 1.47611e8i −0.168390 + 0.628439i 0.829194 + 0.558961i \(0.188800\pi\)
−0.997583 + 0.0694778i \(0.977867\pi\)
\(618\) −1.17777e8 3.15584e7i −0.498996 0.133705i
\(619\) 1.68000e8 1.68000e8i 0.708334 0.708334i −0.257851 0.966185i \(-0.583014\pi\)
0.966185 + 0.257851i \(0.0830144\pi\)
\(620\) −1.27185e8 2.20290e8i −0.533654 0.924316i
\(621\) −2.54533e8 1.46955e8i −1.06284 0.613633i
\(622\) 5.01259e7 + 1.87072e8i 0.208301 + 0.777390i
\(623\) 2.42165e7i 0.100149i
\(624\) −1.91828e8 + 1.34039e8i −0.789511 + 0.551667i
\(625\) −4.66840e8 −1.91218
\(626\) 3.03510e8 8.13254e7i 1.23723 0.331515i
\(627\) −1.37501e7 + 2.38159e7i −0.0557832 + 0.0966193i
\(628\) 9.21216e7 5.31864e7i 0.371948 0.214744i
\(629\) −4.29678e7 4.29678e7i −0.172660 0.172660i
\(630\) 2.81827e7 1.05179e8i 0.112710 0.420638i
\(631\) −2.31363e8 6.19936e7i −0.920887 0.246751i −0.232922 0.972495i \(-0.574829\pi\)
−0.687964 + 0.725744i \(0.741495\pi\)
\(632\) 3.94877e7 3.94877e7i 0.156427 0.156427i
\(633\) 3.28214e7 + 5.68483e7i 0.129403 + 0.224133i
\(634\) −1.77923e8 1.02724e8i −0.698174 0.403091i
\(635\) −1.24258e8 4.63736e8i −0.485290 1.81113i
\(636\) 1.64382e8i 0.638974i
\(637\) 8.32827e7 1.78144e8i 0.322208 0.689211i
\(638\) 2.39538e8 0.922387
\(639\) 1.90382e8 5.10126e7i 0.729664 0.195513i
\(640\) −2.61941e8 + 4.53695e8i −0.999225 + 1.73071i
\(641\) −2.43991e8 + 1.40868e8i −0.926402 + 0.534858i −0.885672 0.464312i \(-0.846302\pi\)
−0.0407302 + 0.999170i \(0.512968\pi\)
\(642\) −1.56681e8 1.56681e8i −0.592120 0.592120i
\(643\) 6.66712e7 2.48820e8i 0.250787 0.935950i −0.719599 0.694390i \(-0.755674\pi\)
0.970386 0.241560i \(-0.0776591\pi\)
\(644\) −6.72872e7 1.80295e7i −0.251927 0.0675036i
\(645\) −3.95169e8 + 3.95169e8i −1.47266 + 1.47266i
\(646\) 1.33061e7 + 2.30468e7i 0.0493573 + 0.0854894i
\(647\) −3.80998e8 2.19969e8i −1.40673 0.812175i −0.411657 0.911339i \(-0.635050\pi\)
−0.995071 + 0.0991641i \(0.968383\pi\)
\(648\) −1.94361e7 7.25367e7i −0.0714307 0.266583i
\(649\) 1.56673e8i 0.573141i
\(650\) 7.13302e8 2.58828e8i 2.59737 0.942479i
\(651\) −1.30238e8 −0.472058
\(652\) 9.83089e6 2.63418e6i 0.0354691 0.00950392i
\(653\) 2.25913e8 3.91293e8i 0.811339 1.40528i −0.100588 0.994928i \(-0.532072\pi\)
0.911927 0.410352i \(-0.134594\pi\)
\(654\) 1.58216e8 9.13463e7i 0.565611 0.326556i
\(655\) 2.92788e8 + 2.92788e8i 1.04191 + 1.04191i
\(656\) −1.14437e8 + 4.27086e8i −0.405374 + 1.51288i
\(657\) 1.87814e7 + 5.03245e6i 0.0662263 + 0.0177453i
\(658\) −3.96684e6 + 3.96684e6i −0.0139241 + 0.0139241i
\(659\) −6.68129e7 1.15723e8i −0.233456 0.404357i 0.725367 0.688362i \(-0.241670\pi\)
−0.958823 + 0.284005i \(0.908337\pi\)
\(660\) −1.25581e8 7.25043e7i −0.436810 0.252192i
\(661\) 1.13777e8 + 4.24621e8i 0.393958 + 1.47027i 0.823548 + 0.567247i \(0.191991\pi\)
−0.429590 + 0.903024i \(0.641342\pi\)
\(662\) 1.57810e8i 0.543952i
\(663\) 9.66213e7 8.35773e6i 0.331537 0.0286779i
\(664\) 1.75957e8 0.601038
\(665\) 4.74375e7 1.27108e7i 0.161308 0.0432225i
\(666\) −4.10959e7 + 7.11802e7i −0.139116 + 0.240955i
\(667\) −2.88487e8 + 1.66558e8i −0.972186 + 0.561292i
\(668\) 1.48630e8 + 1.48630e8i 0.498629 + 0.498629i
\(669\) −7.55793e6 + 2.82066e7i −0.0252420 + 0.0942046i
\(670\) −1.88948e8 5.06284e7i −0.628228 0.168333i
\(671\) 2.12890e7 2.12890e7i 0.0704673 0.0704673i
\(672\) −4.99672e7 8.65457e7i −0.164656 0.285192i
\(673\) −2.61519e8 1.50988e8i −0.857944 0.495334i 0.00537952 0.999986i \(-0.498288\pi\)
−0.863323 + 0.504652i \(0.831621\pi\)
\(674\) −3.87515e7 1.44623e8i −0.126564 0.472342i
\(675\) 7.59312e8i 2.46893i
\(676\) −1.11618e8 + 9.32860e7i −0.361322 + 0.301979i
\(677\) −3.45180e8 −1.11245 −0.556224 0.831032i \(-0.687750\pi\)
−0.556224 + 0.831032i \(0.687750\pi\)
\(678\) 8.82384e7 2.36434e7i 0.283119 0.0758614i
\(679\) −1.77249e7 + 3.07005e7i −0.0566207 + 0.0980699i
\(680\) 1.36547e8 7.88352e7i 0.434264 0.250722i
\(681\) −2.17903e8 2.17903e8i −0.689957 0.689957i
\(682\) 9.56351e7 3.56915e8i 0.301484 1.12515i
\(683\) 7.53340e7 + 2.01857e7i 0.236444 + 0.0633551i 0.375095 0.926986i \(-0.377610\pi\)
−0.138651 + 0.990341i \(0.544277\pi\)
\(684\) 8.14852e6 8.14852e6i 0.0254631 0.0254631i
\(685\) −1.32018e8 2.28663e8i −0.410736 0.711416i
\(686\) 2.91998e8 + 1.68585e8i 0.904497 + 0.522211i
\(687\) 4.47249e7 + 1.66916e8i 0.137936 + 0.514786i
\(688\) 6.06874e8i 1.86352i
\(689\) −4.96057e7 5.73477e8i −0.151661 1.75331i
\(690\) 6.29899e8 1.91745
\(691\) −2.78996e6 + 747567.i −0.00845597 + 0.00226577i −0.263045 0.964784i \(-0.584727\pi\)
0.254589 + 0.967049i \(0.418060\pi\)
\(692\) 9.76599e7 1.69152e8i 0.294712 0.510456i
\(693\) 4.38548e7 2.53196e7i 0.131770 0.0760776i
\(694\) 5.15081e8 + 5.15081e8i 1.54098 + 1.54098i
\(695\) −3.20096e7 + 1.19462e8i −0.0953513 + 0.355856i
\(696\) −1.59724e8 4.27979e7i −0.473742 0.126939i
\(697\) 1.29568e8 1.29568e8i 0.382649 0.382649i
\(698\) 9.38390e7 + 1.62534e8i 0.275941 + 0.477945i
\(699\) 1.05058e8 + 6.06555e7i 0.307609 + 0.177598i
\(700\) 4.65791e7 + 1.73836e8i 0.135799 + 0.506810i
\(701\) 2.34962e8i 0.682093i 0.940046 + 0.341047i \(0.110781\pi\)
−0.940046 + 0.341047i \(0.889219\pi\)
\(702\) −1.55092e8 4.27416e8i −0.448309 1.23549i
\(703\) −3.70698e7 −0.106698
\(704\) −4.91386e7 + 1.31667e7i −0.140833 + 0.0377361i
\(705\) 8.11999e6 1.40642e7i 0.0231733 0.0401374i
\(706\) −4.39944e7 + 2.54002e7i −0.125021 + 0.0721810i
\(707\) −7.17687e7 7.17687e7i −0.203085 0.203085i
\(708\) 2.49132e7 9.29772e7i 0.0701987 0.261985i
\(709\) −2.40296e8 6.43870e7i −0.674228 0.180659i −0.0945696 0.995518i \(-0.530147\pi\)
−0.579659 + 0.814859i \(0.696814\pi\)
\(710\) −1.03531e9 + 1.03531e9i −2.89265 + 2.89265i
\(711\) 2.51220e7 + 4.35125e7i 0.0698948 + 0.121061i
\(712\) 4.10748e7 + 2.37146e7i 0.113798 + 0.0657015i
\(713\) 1.32996e8 + 4.96348e8i 0.366919 + 1.36936i
\(714\) 7.18472e7i 0.197386i
\(715\) 4.59992e8 + 2.15048e8i 1.25844 + 0.588324i
\(716\) −1.50418e8 −0.409789
\(717\) 1.49784e8 4.01345e7i 0.406357 0.108883i
\(718\) 1.21986e8 2.11286e8i 0.329562 0.570818i
\(719\) 2.69345e8 1.55506e8i 0.724640 0.418371i −0.0918179 0.995776i \(-0.529268\pi\)
0.816458 + 0.577405i \(0.195934\pi\)
\(720\) −2.42047e8 2.42047e8i −0.648487 0.648487i
\(721\) −2.62094e7 + 9.78148e7i −0.0699280 + 0.260975i
\(722\) −4.25225e8 1.13939e8i −1.12982 0.302733i
\(723\) 3.69982e8 3.69982e8i 0.978961 0.978961i
\(724\) 1.25569e7 + 2.17492e7i 0.0330877 + 0.0573097i
\(725\) 7.45305e8 + 4.30302e8i 1.95578 + 1.12917i
\(726\) 3.80953e7 + 1.42174e8i 0.0995548 + 0.371543i
\(727\) 2.02898e8i 0.528049i −0.964516 0.264025i \(-0.914950\pi\)
0.964516 0.264025i \(-0.0850500\pi\)
\(728\) 6.93554e7 + 9.92569e7i 0.179757 + 0.257257i
\(729\) 3.91285e8 1.00997
\(730\) −1.39519e8 + 3.73839e7i −0.358644 + 0.0960983i
\(731\) −1.25751e8 + 2.17807e8i −0.321928 + 0.557596i
\(732\) 1.60191e7 9.24864e6i 0.0408418 0.0235801i
\(733\) −1.28400e8 1.28400e8i −0.326026 0.326026i 0.525047 0.851073i \(-0.324048\pi\)
−0.851073 + 0.525047i \(0.824048\pi\)
\(734\) 1.02512e7 3.82581e7i 0.0259232 0.0967466i
\(735\) −4.07363e8 1.09153e8i −1.02594 0.274898i
\(736\) −2.78807e8 + 2.78807e8i −0.699311 + 0.699311i
\(737\) −4.54850e7 7.87823e7i −0.113623 0.196801i
\(738\) −2.14642e8 1.23924e8i −0.534006 0.308308i
\(739\) −1.53035e8 5.71133e8i −0.379190 1.41516i −0.847125 0.531393i \(-0.821669\pi\)
0.467936 0.883763i \(-0.344998\pi\)
\(740\) 1.95469e8i 0.482373i
\(741\) 3.80740e7 4.52845e7i 0.0935780 0.111300i
\(742\) 4.26435e8 1.04386
\(743\) 2.63549e8 7.06178e7i 0.642533 0.172166i 0.0771826 0.997017i \(-0.475408\pi\)
0.565351 + 0.824851i \(0.308741\pi\)
\(744\) −1.27539e8 + 2.20903e8i −0.309687 + 0.536394i
\(745\) 5.06548e8 2.92456e8i 1.22504 0.707280i
\(746\) −1.32641e8 1.32641e8i −0.319493 0.319493i
\(747\) −4.09740e7 + 1.52917e8i −0.0982985 + 0.366855i
\(748\) −6.30349e7 1.68901e7i −0.150618 0.0403579i
\(749\) −1.30124e8 + 1.30124e8i −0.309679 + 0.309679i
\(750\) −4.56522e8 7.90720e8i −1.08213 1.87430i
\(751\) 1.40650e7 + 8.12046e6i 0.0332064 + 0.0191717i 0.516511 0.856280i \(-0.327230\pi\)
−0.483305 + 0.875452i \(0.660564\pi\)
\(752\) 4.56439e6 + 1.70345e7i 0.0107332 + 0.0400568i
\(753\) 3.43805e8i 0.805244i
\(754\) −5.07422e8 8.99857e7i −1.18374 0.209923i
\(755\) −1.05803e9 −2.45843
\(756\) 1.04164e8 2.79106e7i 0.241074 0.0645956i
\(757\) −1.16055e7 + 2.01012e7i −0.0267531 + 0.0463378i −0.879092 0.476652i \(-0.841850\pi\)
0.852339 + 0.522990i \(0.175183\pi\)
\(758\) −7.24643e7 + 4.18373e7i −0.166386 + 0.0960629i
\(759\) 2.07136e8 + 2.07136e8i 0.473729 + 0.473729i
\(760\) 2.48948e7 9.29086e7i 0.0567110 0.211648i
\(761\) 3.36905e7 + 9.02735e6i 0.0764458 + 0.0204836i 0.296839 0.954927i \(-0.404067\pi\)
−0.220393 + 0.975411i \(0.570734\pi\)
\(762\) 3.02974e8 3.02974e8i 0.684763 0.684763i
\(763\) −7.58636e7 1.31400e8i −0.170789 0.295815i