Properties

Label 13.7.f.a.6.3
Level 13
Weight 7
Character 13.6
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 6.3
Character \(\chi\) = 13.6
Dual form 13.7.f.a.11.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.397723 - 1.48432i) q^{2} +(-0.503519 + 0.872121i) q^{3} +(53.3806 - 30.8193i) q^{4} +(84.5480 - 84.5480i) q^{5} +(1.49477 + 0.400522i) q^{6} +(41.0022 - 153.022i) q^{7} +(-136.519 - 136.519i) q^{8} +(363.993 + 630.454i) q^{9} +O(q^{10})\) \(q+(-0.397723 - 1.48432i) q^{2} +(-0.503519 + 0.872121i) q^{3} +(53.3806 - 30.8193i) q^{4} +(84.5480 - 84.5480i) q^{5} +(1.49477 + 0.400522i) q^{6} +(41.0022 - 153.022i) q^{7} +(-136.519 - 136.519i) q^{8} +(363.993 + 630.454i) q^{9} +(-159.123 - 91.8697i) q^{10} +(-1010.62 + 270.795i) q^{11} +62.0725i q^{12} +(-1383.55 + 1706.63i) q^{13} -243.442 q^{14} +(31.1645 + 116.308i) q^{15} +(1824.09 - 3159.42i) q^{16} +(-1495.03 + 863.153i) q^{17} +(791.028 - 791.028i) q^{18} +(6576.65 + 1762.21i) q^{19} +(1907.51 - 7118.93i) q^{20} +(112.809 + 112.809i) q^{21} +(803.894 + 1392.38i) q^{22} +(-3373.09 - 1947.46i) q^{23} +(187.801 - 50.3210i) q^{24} +1328.27i q^{25} +(3083.46 + 1374.87i) q^{26} -1467.24 q^{27} +(-2527.32 - 9432.09i) q^{28} +(-17563.9 + 30421.6i) q^{29} +(160.243 - 92.5164i) q^{30} +(-12140.0 + 12140.0i) q^{31} +(-17350.3 - 4649.00i) q^{32} +(272.701 - 1017.73i) q^{33} +(1875.80 + 1875.80i) q^{34} +(-9471.08 - 16404.4i) q^{35} +(38860.3 + 22436.0i) q^{36} +(55534.6 - 14880.5i) q^{37} -10462.7i q^{38} +(-791.747 - 2065.95i) q^{39} -23084.8 q^{40} +(-19534.1 - 72902.3i) q^{41} +(122.578 - 212.311i) q^{42} +(56257.3 - 32480.2i) q^{43} +(-45601.9 + 45601.9i) q^{44} +(84078.5 + 22528.8i) q^{45} +(-1549.09 + 5781.30i) q^{46} +(-64283.9 - 64283.9i) q^{47} +(1836.93 + 3181.66i) q^{48} +(80152.3 + 46276.0i) q^{49} +(1971.58 - 528.282i) q^{50} -1738.46i q^{51} +(-21257.5 + 133741. i) q^{52} -272670. q^{53} +(583.555 + 2177.86i) q^{54} +(-62550.8 + 108341. i) q^{55} +(-26488.0 + 15292.9i) q^{56} +(-4848.33 + 4848.33i) q^{57} +(52141.0 + 13971.2i) q^{58} +(74113.8 - 276596. i) q^{59} +(5248.10 + 5248.10i) q^{60} +(98976.0 + 171431. i) q^{61} +(22848.1 + 13191.3i) q^{62} +(111398. - 29849.1i) q^{63} -205882. i q^{64} +(27316.1 + 261269. i) q^{65} -1619.10 q^{66} +(-149296. - 557182. i) q^{67} +(-53203.6 + 92151.3i) q^{68} +(3396.84 - 1961.16i) q^{69} +(-20582.5 + 20582.5i) q^{70} +(366966. + 98328.2i) q^{71} +(36376.9 - 135761. i) q^{72} +(188403. + 188403. i) q^{73} +(-44174.7 - 76512.9i) q^{74} +(-1158.41 - 668.809i) q^{75} +(405376. - 108620. i) q^{76} +165751. i q^{77} +(-2751.63 + 1996.88i) q^{78} -716299. q^{79} +(-112899. - 421347. i) q^{80} +(-264612. + 458322. i) q^{81} +(-100441. + 57989.8i) q^{82} +(-406773. + 406773. i) q^{83} +(9498.48 + 2545.11i) q^{84} +(-53423.5 + 199379. i) q^{85} +(-70585.8 - 70585.8i) q^{86} +(-17687.6 - 30635.8i) q^{87} +(174937. + 101000. i) q^{88} +(270869. - 72579.1i) q^{89} -133760. i q^{90} +(204425. + 281690. i) q^{91} -240077. q^{92} +(-4474.84 - 16700.3i) q^{93} +(-69850.7 + 120985. i) q^{94} +(705034. - 407052. i) q^{95} +(12790.7 - 12790.7i) q^{96} +(-254823. - 68279.7i) q^{97} +(36810.0 - 137377. i) q^{98} +(-538583. - 538583. 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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.397723 1.48432i −0.0497153 0.185540i 0.936603 0.350393i \(-0.113952\pi\)
−0.986318 + 0.164853i \(0.947285\pi\)
\(3\) −0.503519 + 0.872121i −0.0186489 + 0.0323008i −0.875199 0.483763i \(-0.839270\pi\)
0.856550 + 0.516063i \(0.172603\pi\)
\(4\) 53.3806 30.8193i 0.834072 0.481552i
\(5\) 84.5480 84.5480i 0.676384 0.676384i −0.282796 0.959180i \(-0.591262\pi\)
0.959180 + 0.282796i \(0.0912619\pi\)
\(6\) 1.49477 + 0.400522i 0.00692023 + 0.00185427i
\(7\) 41.0022 153.022i 0.119540 0.446130i −0.880046 0.474888i \(-0.842489\pi\)
0.999586 + 0.0287583i \(0.00915530\pi\)
\(8\) −136.519 136.519i −0.266638 0.266638i
\(9\) 363.993 + 630.454i 0.499304 + 0.864821i
\(10\) −159.123 91.8697i −0.159123 0.0918697i
\(11\) −1010.62 + 270.795i −0.759295 + 0.203452i −0.617637 0.786463i \(-0.711910\pi\)
−0.141658 + 0.989916i \(0.545243\pi\)
\(12\) 62.0725i 0.0359216i
\(13\) −1383.55 + 1706.63i −0.629745 + 0.776802i
\(14\) −243.442 −0.0887179
\(15\) 31.1645 + 116.308i 0.00923394 + 0.0344615i
\(16\) 1824.09 3159.42i 0.445336 0.771344i
\(17\) −1495.03 + 863.153i −0.304300 + 0.175688i −0.644373 0.764711i \(-0.722882\pi\)
0.340073 + 0.940399i \(0.389548\pi\)
\(18\) 791.028 791.028i 0.135636 0.135636i
\(19\) 6576.65 + 1762.21i 0.958835 + 0.256919i 0.704107 0.710094i \(-0.251347\pi\)
0.254728 + 0.967013i \(0.418014\pi\)
\(20\) 1907.51 7118.93i 0.238439 0.889867i
\(21\) 112.809 + 112.809i 0.0121810 + 0.0121810i
\(22\) 803.894 + 1392.38i 0.0754972 + 0.130765i
\(23\) −3373.09 1947.46i −0.277233 0.160061i 0.354937 0.934890i \(-0.384502\pi\)
−0.632170 + 0.774830i \(0.717836\pi\)
\(24\) 187.801 50.3210i 0.0135851 0.00364012i
\(25\) 1328.27i 0.0850092i
\(26\) 3083.46 + 1374.87i 0.175436 + 0.0782240i
\(27\) −1467.24 −0.0745436
\(28\) −2527.32 9432.09i −0.115129 0.429669i
\(29\) −17563.9 + 30421.6i −0.720158 + 1.24735i 0.240778 + 0.970580i \(0.422598\pi\)
−0.960936 + 0.276770i \(0.910736\pi\)
\(30\) 160.243 92.5164i 0.00593493 0.00342653i
\(31\) −12140.0 + 12140.0i −0.407507 + 0.407507i −0.880868 0.473361i \(-0.843041\pi\)
0.473361 + 0.880868i \(0.343041\pi\)
\(32\) −17350.3 4649.00i −0.529490 0.141876i
\(33\) 272.701 1017.73i 0.00758831 0.0283200i
\(34\) 1875.80 + 1875.80i 0.0477255 + 0.0477255i
\(35\) −9471.08 16404.4i −0.220900 0.382610i
\(36\) 38860.3 + 22436.0i 0.832912 + 0.480882i
\(37\) 55534.6 14880.5i 1.09637 0.293773i 0.335087 0.942187i \(-0.391234\pi\)
0.761287 + 0.648415i \(0.224568\pi\)
\(38\) 10462.7i 0.190675i
\(39\) −791.747 2065.95i −0.0133473 0.0348277i
\(40\) −23084.8 −0.360699
\(41\) −19534.1 72902.3i −0.283428 1.05777i −0.949981 0.312309i \(-0.898898\pi\)
0.666553 0.745458i \(-0.267769\pi\)
\(42\) 122.578 212.311i 0.00165449 0.00286566i
\(43\) 56257.3 32480.2i 0.707577 0.408520i −0.102586 0.994724i \(-0.532712\pi\)
0.810163 + 0.586204i \(0.199378\pi\)
\(44\) −45601.9 + 45601.9i −0.535334 + 0.535334i
\(45\) 84078.5 + 22528.8i 0.922672 + 0.247229i
\(46\) −1549.09 + 5781.30i −0.0159149 + 0.0593953i
\(47\) −64283.9 64283.9i −0.619168 0.619168i 0.326150 0.945318i \(-0.394248\pi\)
−0.945318 + 0.326150i \(0.894248\pi\)
\(48\) 1836.93 + 3181.66i 0.0166100 + 0.0287694i
\(49\) 80152.3 + 46276.0i 0.681284 + 0.393339i
\(50\) 1971.58 528.282i 0.0157726 0.00422626i
\(51\) 1738.46i 0.0131055i
\(52\) −21257.5 + 133741.i −0.151183 + 0.951163i
\(53\) −272670. −1.83151 −0.915756 0.401735i \(-0.868407\pi\)
−0.915756 + 0.401735i \(0.868407\pi\)
\(54\) 583.555 + 2177.86i 0.00370596 + 0.0138308i
\(55\) −62550.8 + 108341.i −0.375963 + 0.651187i
\(56\) −26488.0 + 15292.9i −0.150829 + 0.0870812i
\(57\) −4848.33 + 4848.33i −0.0261799 + 0.0261799i
\(58\) 52141.0 + 13971.2i 0.267236 + 0.0716058i
\(59\) 74113.8 276596.i 0.360863 1.34676i −0.512080 0.858938i \(-0.671125\pi\)
0.872943 0.487822i \(-0.162209\pi\)
\(60\) 5248.10 + 5248.10i 0.0242968 + 0.0242968i
\(61\) 98976.0 + 171431.i 0.436054 + 0.755268i 0.997381 0.0723264i \(-0.0230423\pi\)
−0.561327 + 0.827594i \(0.689709\pi\)
\(62\) 22848.1 + 13191.3i 0.0958682 + 0.0553496i
\(63\) 111398. 29849.1i 0.445509 0.119374i
\(64\) 205882.i 0.785376i
\(65\) 27316.1 + 261269.i 0.0994668 + 0.951366i
\(66\) −1619.10 −0.00563175
\(67\) −149296. 557182.i −0.496392 1.85256i −0.522087 0.852892i \(-0.674846\pi\)
0.0256948 0.999670i \(-0.491820\pi\)
\(68\) −53203.6 + 92151.3i −0.169205 + 0.293072i
\(69\) 3396.84 1961.16i 0.0103402 0.00596990i
\(70\) −20582.5 + 20582.5i −0.0600074 + 0.0600074i
\(71\) 366966. + 98328.2i 1.02530 + 0.274728i 0.732009 0.681295i \(-0.238583\pi\)
0.293290 + 0.956023i \(0.405250\pi\)
\(72\) 36376.9 135761.i 0.0974605 0.363728i
\(73\) 188403. + 188403.i 0.484306 + 0.484306i 0.906504 0.422197i \(-0.138741\pi\)
−0.422197 + 0.906504i \(0.638741\pi\)
\(74\) −44174.7 76512.9i −0.109013 0.188816i
\(75\) −1158.41 668.809i −0.00274586 0.00158532i
\(76\) 405376. 108620.i 0.923457 0.247440i
\(77\) 165751.i 0.363065i
\(78\) −2751.63 + 1996.88i −0.00579838 + 0.00420793i
\(79\) −716299. −1.45282 −0.726412 0.687260i \(-0.758813\pi\)
−0.726412 + 0.687260i \(0.758813\pi\)
\(80\) −112899. 421347.i −0.220507 0.822943i
\(81\) −264612. + 458322.i −0.497914 + 0.862413i
\(82\) −100441. + 57989.8i −0.182167 + 0.105174i
\(83\) −406773. + 406773.i −0.711406 + 0.711406i −0.966829 0.255423i \(-0.917785\pi\)
0.255423 + 0.966829i \(0.417785\pi\)
\(84\) 9498.48 + 2545.11i 0.0160257 + 0.00429407i
\(85\) −53423.5 + 199379.i −0.0869913 + 0.324656i
\(86\) −70585.8 70585.8i −0.110974 0.110974i
\(87\) −17687.6 30635.8i −0.0268603 0.0465234i
\(88\) 174937. + 101000.i 0.256705 + 0.148209i
\(89\) 270869. 72579.1i 0.384228 0.102954i −0.0615341 0.998105i \(-0.519599\pi\)
0.445762 + 0.895151i \(0.352933\pi\)
\(90\) 133760.i 0.183484i
\(91\) 204425. + 281690.i 0.271274 + 0.373807i
\(92\) −240077. −0.308310
\(93\) −4474.84 16700.3i −0.00556325 0.0207623i
\(94\) −69850.7 + 120985.i −0.0840983 + 0.145663i
\(95\) 705034. 407052.i 0.822317 0.474765i
\(96\) 12790.7 12790.7i 0.0144571 0.0144571i
\(97\) −254823. 68279.7i −0.279206 0.0748129i 0.116499 0.993191i \(-0.462833\pi\)
−0.395704 + 0.918378i \(0.629500\pi\)
\(98\) 36810.0 137377.i 0.0391100 0.145960i
\(99\) −538583. 538583.i −0.555069 0.555069i
\(100\) 40936.3 + 70903.8i 0.0409363 + 0.0709038i
\(101\) 1.06736e6 + 616242.i 1.03597 + 0.598118i 0.918690 0.394980i \(-0.129249\pi\)
0.117282 + 0.993099i \(0.462582\pi\)
\(102\) −2580.43 + 691.424i −0.00243160 + 0.000651544i
\(103\) 1.27482e6i 1.16664i −0.812243 0.583319i \(-0.801754\pi\)
0.812243 0.583319i \(-0.198246\pi\)
\(104\) 421868. 44106.9i 0.375039 0.0392109i
\(105\) 19075.5 0.0164781
\(106\) 108447. + 404730.i 0.0910542 + 0.339819i
\(107\) 312612. 541461.i 0.255185 0.441993i −0.709761 0.704443i \(-0.751197\pi\)
0.964946 + 0.262450i \(0.0845303\pi\)
\(108\) −78322.2 + 45219.4i −0.0621747 + 0.0358966i
\(109\) 205640. 205640.i 0.158792 0.158792i −0.623239 0.782031i \(-0.714184\pi\)
0.782031 + 0.623239i \(0.214184\pi\)
\(110\) 185691. + 49755.7i 0.139512 + 0.0373822i
\(111\) −14985.2 + 55925.5i −0.0109570 + 0.0408923i
\(112\) −408671. 408671.i −0.290884 0.290884i
\(113\) 40925.7 + 70885.4i 0.0283636 + 0.0491271i 0.879859 0.475235i \(-0.157637\pi\)
−0.851495 + 0.524362i \(0.824304\pi\)
\(114\) 9124.77 + 5268.19i 0.00615896 + 0.00355588i
\(115\) −449842. + 120535.i −0.295778 + 0.0792536i
\(116\) 2.16523e6i 1.38717i
\(117\) −1.57956e6 251062.i −0.986229 0.156756i
\(118\) −440034. −0.267818
\(119\) 70782.5 + 264164.i 0.0420034 + 0.156759i
\(120\) 11623.6 20132.7i 0.00672664 0.0116509i
\(121\) −586191. + 338438.i −0.330890 + 0.191039i
\(122\) 215094. 215094.i 0.118454 0.118454i
\(123\) 73415.5 + 19671.6i 0.0394523 + 0.0105712i
\(124\) −273895. + 1.02219e6i −0.143654 + 0.536126i
\(125\) 1.43337e6 + 1.43337e6i 0.733883 + 0.733883i
\(126\) −88611.1 153479.i −0.0442972 0.0767251i
\(127\) −2.65501e6 1.53287e6i −1.29615 0.748332i −0.316412 0.948622i \(-0.602478\pi\)
−0.979737 + 0.200290i \(0.935812\pi\)
\(128\) −1.41601e6 + 379420.i −0.675208 + 0.180922i
\(129\) 65417.6i 0.0304737i
\(130\) 376943. 144458.i 0.171572 0.0657525i
\(131\) 3.63996e6 1.61913 0.809567 0.587028i \(-0.199702\pi\)
0.809567 + 0.587028i \(0.199702\pi\)
\(132\) −16808.9 62731.8i −0.00730833 0.0272751i
\(133\) 539315. 934121.i 0.229238 0.397053i
\(134\) −767658. + 443208.i −0.319046 + 0.184201i
\(135\) −124052. + 124052.i −0.0504201 + 0.0504201i
\(136\) 321936. + 86262.4i 0.127983 + 0.0342929i
\(137\) 640244. 2.38942e6i 0.248991 0.929247i −0.722344 0.691534i \(-0.756935\pi\)
0.971335 0.237714i \(-0.0763980\pi\)
\(138\) −4262.00 4262.00i −0.00162172 0.00162172i
\(139\) −22648.9 39229.0i −0.00843339 0.0146071i 0.861778 0.507286i \(-0.169351\pi\)
−0.870211 + 0.492679i \(0.836018\pi\)
\(140\) −1.01114e6 583784.i −0.368493 0.212749i
\(141\) 88431.5 23695.1i 0.0315464 0.00845283i
\(142\) 583802.i 0.203892i
\(143\) 936097. 2.09942e6i 0.320120 0.717945i
\(144\) 2.65583e6 0.889432
\(145\) 1.08709e6 + 4.05709e6i 0.356585 + 1.33079i
\(146\) 204719. 354583.i 0.0657808 0.113936i
\(147\) −80716.5 + 46601.7i −0.0254103 + 0.0146707i
\(148\) 2.50587e6 2.50587e6i 0.772988 0.772988i
\(149\) −4.59923e6 1.23236e6i −1.39036 0.372545i −0.515485 0.856899i \(-0.672388\pi\)
−0.874872 + 0.484354i \(0.839055\pi\)
\(150\) −532.001 + 1985.45i −0.000157630 + 0.000588283i
\(151\) 1.85287e6 + 1.85287e6i 0.538163 + 0.538163i 0.922989 0.384826i \(-0.125739\pi\)
−0.384826 + 0.922989i \(0.625739\pi\)
\(152\) −657261. 1.13841e6i −0.187158 0.324166i
\(153\) −1.08836e6 628364.i −0.303877 0.175443i
\(154\) 246028. 65922.9i 0.0673630 0.0180499i
\(155\) 2.05283e6i 0.551263i
\(156\) −105935. 85880.4i −0.0279039 0.0226214i
\(157\) 1.39574e6 0.360665 0.180333 0.983606i \(-0.442283\pi\)
0.180333 + 0.983606i \(0.442283\pi\)
\(158\) 284888. + 1.06322e6i 0.0722276 + 0.269557i
\(159\) 137295. 237801.i 0.0341556 0.0591593i
\(160\) −1.86000e6 + 1.07387e6i −0.454101 + 0.262175i
\(161\) −436309. + 436309.i −0.104548 + 0.104548i
\(162\) 785538. + 210484.i 0.184766 + 0.0495079i
\(163\) −1.72601e6 + 6.44157e6i −0.398548 + 1.48740i 0.417103 + 0.908859i \(0.363045\pi\)
−0.815651 + 0.578544i \(0.803621\pi\)
\(164\) −3.28954e6 3.28954e6i −0.745768 0.745768i
\(165\) −62991.1 109104.i −0.0140226 0.0242878i
\(166\) 765564. + 441998.i 0.167362 + 0.0966266i
\(167\) −8.35095e6 + 2.23763e6i −1.79302 + 0.480440i −0.992854 0.119333i \(-0.961924\pi\)
−0.800171 + 0.599773i \(0.795258\pi\)
\(168\) 30801.0i 0.00649586i
\(169\) −998387. 4.72243e6i −0.206842 0.978374i
\(170\) 317191. 0.0645615
\(171\) 1.28286e6 + 4.78771e6i 0.256562 + 0.957501i
\(172\) 2.00203e6 3.46762e6i 0.393447 0.681470i
\(173\) 2.56885e6 1.48313e6i 0.496135 0.286444i −0.230981 0.972958i \(-0.574193\pi\)
0.727116 + 0.686514i \(0.240860\pi\)
\(174\) −38438.6 + 38438.6i −0.00729658 + 0.00729658i
\(175\) 203255. + 54462.0i 0.0379251 + 0.0101620i
\(176\) −987912. + 3.68694e6i −0.181209 + 0.676282i
\(177\) 203908. + 203908.i 0.0367717 + 0.0367717i
\(178\) −215461. 373190.i −0.0382041 0.0661714i
\(179\) 2.29060e6 + 1.32248e6i 0.399384 + 0.230584i 0.686218 0.727396i \(-0.259270\pi\)
−0.286834 + 0.957980i \(0.592603\pi\)
\(180\) 5.18248e6 1.38864e6i 0.888629 0.238107i
\(181\) 1.21255e6i 0.204486i −0.994759 0.102243i \(-0.967398\pi\)
0.994759 0.102243i \(-0.0326019\pi\)
\(182\) 336814. 415466.i 0.0558697 0.0689162i
\(183\) −199345. −0.0325277
\(184\) 194626. + 726355.i 0.0312426 + 0.116599i
\(185\) 3.43723e6 5.95346e6i 0.542867 0.940273i
\(186\) −23008.9 + 13284.2i −0.00357567 + 0.00206441i
\(187\) 1.27717e6 1.27717e6i 0.195309 0.195309i
\(188\) −5.41269e6 1.45033e6i −0.814592 0.218269i
\(189\) −60160.2 + 224521.i −0.00891094 + 0.0332561i
\(190\) −884603. 884603.i −0.128970 0.128970i
\(191\) 503963. + 872890.i 0.0723267 + 0.125274i 0.899921 0.436054i \(-0.143624\pi\)
−0.827594 + 0.561327i \(0.810291\pi\)
\(192\) 179554. + 103665.i 0.0253683 + 0.0146464i
\(193\) 199106. 53350.3i 0.0276957 0.00742104i −0.244945 0.969537i \(-0.578770\pi\)
0.272640 + 0.962116i \(0.412103\pi\)
\(194\) 405396.i 0.0555232i
\(195\) −241612. 107731.i −0.0325848 0.0145290i
\(196\) 5.70477e6 0.757653
\(197\) −361964. 1.35087e6i −0.0473442 0.176691i 0.938205 0.346080i \(-0.112487\pi\)
−0.985549 + 0.169389i \(0.945821\pi\)
\(198\) −585223. + 1.01364e6i −0.0753921 + 0.130583i
\(199\) 7.29852e6 4.21380e6i 0.926138 0.534706i 0.0405496 0.999178i \(-0.487089\pi\)
0.885588 + 0.464472i \(0.153756\pi\)
\(200\) 181333. 181333.i 0.0226667 0.0226667i
\(201\) 561104. + 150347.i 0.0690964 + 0.0185143i
\(202\) 490187. 1.82940e6i 0.0594713 0.221950i
\(203\) 3.93503e6 + 3.93503e6i 0.470392 + 0.470392i
\(204\) −53578.1 92799.9i −0.00631098 0.0109309i
\(205\) −7.81532e6 4.51218e6i −0.907162 0.523750i
\(206\) −1.89224e6 + 507023.i −0.216458 + 0.0579998i
\(207\) 2.83544e6i 0.319676i
\(208\) 2.86825e6 + 7.48428e6i 0.318733 + 0.831688i
\(209\) −7.12370e6 −0.780309
\(210\) −7586.76 28314.2i −0.000819216 0.00305735i
\(211\) −6.18071e6 + 1.07053e7i −0.657947 + 1.13960i 0.323200 + 0.946331i \(0.395241\pi\)
−0.981146 + 0.193266i \(0.938092\pi\)
\(212\) −1.45553e7 + 8.40350e6i −1.52761 + 0.881967i
\(213\) −270529. + 270529.i −0.0279946 + 0.0279946i
\(214\) −928034. 248666.i −0.0946940 0.0253732i
\(215\) 2.01031e6 7.50258e6i 0.202277 0.754910i
\(216\) 200306. + 200306.i 0.0198762 + 0.0198762i
\(217\) 1.35993e6 + 2.35547e6i 0.133088 + 0.230514i
\(218\) −387023. 223448.i −0.0373566 0.0215678i
\(219\) −259175. + 69445.8i −0.0246752 + 0.00661171i
\(220\) 7.71109e6i 0.724182i
\(221\) 595356. 3.74568e6i 0.0551569 0.347019i
\(222\) 88971.4 0.00813189
\(223\) −1.45822e6 5.44215e6i −0.131495 0.490745i 0.868493 0.495702i \(-0.165089\pi\)
−0.999988 + 0.00495630i \(0.998422\pi\)
\(224\) −1.42280e6 + 2.46437e6i −0.126590 + 0.219261i
\(225\) −837412. + 483480.i −0.0735177 + 0.0424455i
\(226\) 88939.6 88939.6i 0.00770495 0.00770495i
\(227\) 1.73975e7 + 4.66164e6i 1.48733 + 0.398530i 0.908836 0.417153i \(-0.136972\pi\)
0.578499 + 0.815683i \(0.303639\pi\)
\(228\) −109385. + 408229.i −0.00922894 + 0.0344429i
\(229\) 2.46115e6 + 2.46115e6i 0.204942 + 0.204942i 0.802114 0.597171i \(-0.203709\pi\)
−0.597171 + 0.802114i \(0.703709\pi\)
\(230\) 357825. + 619770.i 0.0294094 + 0.0509386i
\(231\) −144555. 83458.8i −0.0117273 0.00677074i
\(232\) 6.55093e6 1.75532e6i 0.524613 0.140570i
\(233\) 7.92328e6i 0.626379i −0.949691 0.313189i \(-0.898603\pi\)
0.949691 0.313189i \(-0.101397\pi\)
\(234\) 255568. + 2.44442e6i 0.0199462 + 0.190778i
\(235\) −1.08701e7 −0.837590
\(236\) −4.56827e6 1.70490e7i −0.347549 1.29707i
\(237\) 360670. 624699.i 0.0270935 0.0469273i
\(238\) 363952. 210128.i 0.0269969 0.0155866i
\(239\) −4.71743e6 + 4.71743e6i −0.345551 + 0.345551i −0.858449 0.512898i \(-0.828572\pi\)
0.512898 + 0.858449i \(0.328572\pi\)
\(240\) 424312. + 113694.i 0.0306939 + 0.00822440i
\(241\) 3.92690e6 1.46554e7i 0.280542 1.04700i −0.671493 0.741010i \(-0.734347\pi\)
0.952036 0.305987i \(-0.0989865\pi\)
\(242\) 735492. + 735492.i 0.0518957 + 0.0518957i
\(243\) −801284. 1.38786e6i −0.0558429 0.0967227i
\(244\) 1.05668e7 + 6.10074e6i 0.727401 + 0.419965i
\(245\) 1.06893e7 2.86418e6i 0.726858 0.194761i
\(246\) 116796.i 0.00784553i
\(247\) −1.21066e7 + 8.78583e6i −0.803397 + 0.583031i
\(248\) 3.31469e6 0.217314
\(249\) −149937. 559573.i −0.00971206 0.0362459i
\(250\) 1.55749e6 2.69766e6i 0.0996795 0.172650i
\(251\) 1.46092e7 8.43462e6i 0.923857 0.533389i 0.0389938 0.999239i \(-0.487585\pi\)
0.884864 + 0.465850i \(0.154251\pi\)
\(252\) 5.02657e6 5.02657e6i 0.314102 0.314102i
\(253\) 3.93628e6 + 1.05472e6i 0.243066 + 0.0651294i
\(254\) −1.21931e6 + 4.55054e6i −0.0744071 + 0.277691i
\(255\) −146983. 146983.i −0.00886435 0.00886435i
\(256\) −5.46185e6 9.46020e6i −0.325552 0.563872i
\(257\) 1.40648e7 + 8.12030e6i 0.828578 + 0.478380i 0.853365 0.521313i \(-0.174558\pi\)
−0.0247877 + 0.999693i \(0.507891\pi\)
\(258\) 97100.7 26018.0i 0.00565410 0.00151501i
\(259\) 9.10818e6i 0.524242i
\(260\) 9.51027e6 + 1.31048e7i 0.541094 + 0.745609i
\(261\) −2.55726e7 −1.43831
\(262\) −1.44769e6 5.40287e6i −0.0804957 0.300414i
\(263\) −8.94641e6 + 1.54956e7i −0.491792 + 0.851809i −0.999955 0.00945184i \(-0.996991\pi\)
0.508163 + 0.861261i \(0.330325\pi\)
\(264\) −176169. + 101711.i −0.00957452 + 0.00552785i
\(265\) −2.30537e7 + 2.30537e7i −1.23881 + 1.23881i
\(266\) −1.60103e6 428995.i −0.0850658 0.0227933i
\(267\) −73090.0 + 272776.i −0.00383994 + 0.0143308i
\(268\) −2.51415e7 2.51415e7i −1.30613 1.30613i
\(269\) 1.39538e7 + 2.41688e7i 0.716864 + 1.24165i 0.962236 + 0.272216i \(0.0877566\pi\)
−0.245372 + 0.969429i \(0.578910\pi\)
\(270\) 233472. + 134795.i 0.0118616 + 0.00684830i
\(271\) −4.43066e6 + 1.18719e6i −0.222618 + 0.0596503i −0.368404 0.929666i \(-0.620096\pi\)
0.145786 + 0.989316i \(0.453429\pi\)
\(272\) 6.29789e6i 0.312960i
\(273\) −348600. + 36446.6i −0.0171332 + 0.00179130i
\(274\) −3.80131e6 −0.184791
\(275\) −359689. 1.34238e6i −0.0172953 0.0645470i
\(276\) 120883. 209376.i 0.00574963 0.00995864i
\(277\) 1.19929e7 6.92409e6i 0.564266 0.325779i −0.190590 0.981670i \(-0.561040\pi\)
0.754856 + 0.655891i \(0.227707\pi\)
\(278\) −49220.5 + 49220.5i −0.00229093 + 0.00229093i
\(279\) −1.20726e7 3.23485e6i −0.555891 0.148950i
\(280\) −946527. + 3.53249e6i −0.0431180 + 0.160919i
\(281\) −2.60746e6 2.60746e6i −0.117517 0.117517i 0.645903 0.763419i \(-0.276481\pi\)
−0.763419 + 0.645903i \(0.776481\pi\)
\(282\) −70342.4 121837.i −0.00313668 0.00543288i
\(283\) 2.12903e7 + 1.22920e7i 0.939339 + 0.542328i 0.889753 0.456442i \(-0.150877\pi\)
0.0495859 + 0.998770i \(0.484210\pi\)
\(284\) 2.26193e7 6.06081e6i 0.987469 0.264591i
\(285\) 819833.i 0.0354153i
\(286\) −3.48852e6 554482.i −0.149122 0.0237022i
\(287\) −1.19566e7 −0.505782
\(288\) −3.38441e6 1.26308e7i −0.141679 0.528753i
\(289\) −1.05787e7 + 1.83229e7i −0.438268 + 0.759102i
\(290\) 5.58965e6 3.22719e6i 0.229188 0.132321i
\(291\) 187857. 187857.i 0.00762338 0.00762338i
\(292\) 1.58636e7 + 4.25063e6i 0.637165 + 0.170728i
\(293\) 2.10986e6 7.87411e6i 0.0838786 0.313039i −0.911221 0.411918i \(-0.864859\pi\)
0.995099 + 0.0988789i \(0.0315256\pi\)
\(294\) 101275. + 101275.i 0.00398528 + 0.00398528i
\(295\) −1.71195e7 2.96518e7i −0.666845 1.15501i
\(296\) −9.61298e6 5.55005e6i −0.370666 0.214004i
\(297\) 1.48283e6 397322.i 0.0566006 0.0151661i
\(298\) 7.31687e6i 0.276488i
\(299\) 7.99044e6 3.06223e6i 0.298921 0.114558i
\(300\) −82448.9 −0.00305366
\(301\) −2.66352e6 9.94039e6i −0.0976689 0.364505i
\(302\) 2.01332e6 3.48718e6i 0.0730958 0.126606i
\(303\) −1.07488e6 + 620580.i −0.0386394 + 0.0223085i
\(304\) 1.75640e7 1.75640e7i 0.625176 0.625176i
\(305\) 2.28624e7 + 6.12596e6i 0.805791 + 0.215911i
\(306\) −499829. + 1.86539e6i −0.0174444 + 0.0651035i
\(307\) 3.47630e7 + 3.47630e7i 1.20144 + 1.20144i 0.973729 + 0.227712i \(0.0731244\pi\)
0.227712 + 0.973729i \(0.426876\pi\)
\(308\) 5.10833e6 + 8.84789e6i 0.174834 + 0.302822i
\(309\) 1.11179e6 + 641895.i 0.0376833 + 0.0217565i
\(310\) 3.04706e6 816458.i 0.102281 0.0274062i
\(311\) 4.30507e7i 1.43119i −0.698513 0.715597i \(-0.746155\pi\)
0.698513 0.715597i \(-0.253845\pi\)
\(312\) −173952. + 390129.i −0.00572751 + 0.0128453i
\(313\) 1.32699e7 0.432748 0.216374 0.976311i \(-0.430577\pi\)
0.216374 + 0.976311i \(0.430577\pi\)
\(314\) −555116. 2.07172e6i −0.0179306 0.0669179i
\(315\) 6.89482e6 1.19422e7i 0.220593 0.382078i
\(316\) −3.82365e7 + 2.20758e7i −1.21176 + 0.699610i
\(317\) −2.15384e7 + 2.15384e7i −0.676139 + 0.676139i −0.959124 0.282985i \(-0.908675\pi\)
0.282985 + 0.959124i \(0.408675\pi\)
\(318\) −407578. 109210.i −0.0126745 0.00339611i
\(319\) 9.51246e6 3.55010e7i 0.293036 1.09362i
\(320\) −1.74069e7 1.74069e7i −0.531216 0.531216i
\(321\) 314813. + 545272.i 0.00951782 + 0.0164853i
\(322\) 821152. + 474093.i 0.0245955 + 0.0142002i
\(323\) −1.13533e7 + 3.04211e6i −0.336911 + 0.0902751i
\(324\) 3.26206e7i 0.959086i
\(325\) −2.26687e6 1.83773e6i −0.0660353 0.0535341i
\(326\) 1.02478e7 0.295787
\(327\) 75799.2 + 282887.i 0.00216781 + 0.00809038i
\(328\) −7.28576e6 + 1.26193e7i −0.206468 + 0.357613i
\(329\) −1.24727e7 + 7.20109e6i −0.350244 + 0.202214i
\(330\) −136892. + 136892.i −0.00380922 + 0.00380922i
\(331\) −2.58957e7 6.93873e6i −0.714075 0.191336i −0.116548 0.993185i \(-0.537183\pi\)
−0.597526 + 0.801849i \(0.703850\pi\)
\(332\) −9.17732e6 + 3.42502e7i −0.250785 + 0.935942i
\(333\) 2.95957e7 + 2.95957e7i 0.801485 + 0.801485i
\(334\) 6.64272e6 + 1.15055e7i 0.178282 + 0.308793i
\(335\) −5.97314e7 3.44859e7i −1.58880 0.917291i
\(336\) 562184. 150637.i 0.0148204 0.00397112i
\(337\) 1.33912e7i 0.349888i 0.984578 + 0.174944i \(0.0559745\pi\)
−0.984578 + 0.174944i \(0.944025\pi\)
\(338\) −6.61251e6 + 3.36014e6i −0.171244 + 0.0870177i
\(339\) −82427.6 −0.00211579
\(340\) 3.29295e6 + 1.22895e7i 0.0837816 + 0.312677i
\(341\) 8.98152e6 1.55565e7i 0.226510 0.392326i
\(342\) 6.59627e6 3.80836e6i 0.164900 0.0952050i
\(343\) 2.35468e7 2.35468e7i 0.583510 0.583510i
\(344\) −1.21143e7 3.24602e6i −0.297594 0.0797400i
\(345\) 121383. 453008.i 0.00295598 0.0110319i
\(346\) −3.22312e6 3.22312e6i −0.0778123 0.0778123i
\(347\) 1.22247e7 + 2.11738e7i 0.292583 + 0.506769i 0.974420 0.224736i \(-0.0721519\pi\)
−0.681837 + 0.731504i \(0.738819\pi\)
\(348\) −1.88835e6 1.09024e6i −0.0448068 0.0258692i
\(349\) −4.40479e7 + 1.18026e7i −1.03621 + 0.277653i −0.736543 0.676390i \(-0.763543\pi\)
−0.299670 + 0.954043i \(0.596877\pi\)
\(350\) 323356.i 0.00754183i
\(351\) 2.03000e6 2.50404e6i 0.0469435 0.0579056i
\(352\) 1.87935e7 0.430904
\(353\) 1.25723e7 + 4.69204e7i 0.285818 + 1.06669i 0.948239 + 0.317556i \(0.102862\pi\)
−0.662421 + 0.749131i \(0.730471\pi\)
\(354\) 221566. 383763.i 0.00499451 0.00865075i
\(355\) 3.93397e7 2.27128e7i 0.879318 0.507674i
\(356\) 1.22223e7 1.22223e7i 0.270897 0.270897i
\(357\) −266023. 71280.7i −0.00584675 0.00156663i
\(358\) 1.05196e6 3.92597e6i 0.0229271 0.0855653i
\(359\) −3.07062e7 3.07062e7i −0.663656 0.663656i 0.292584 0.956240i \(-0.405485\pi\)
−0.956240 + 0.292584i \(0.905485\pi\)
\(360\) −8.40269e6 1.45539e7i −0.180099 0.311940i
\(361\) −595963. 344079.i −0.0126677 0.00731370i
\(362\) −1.79981e6 + 482258.i −0.0379403 + 0.0101661i
\(363\) 681640.i 0.0142507i
\(364\) 1.95938e7 + 8.73656e6i 0.406270 + 0.181149i
\(365\) 3.18583e7 0.655154
\(366\) 79284.1 + 295892.i 0.00161712 + 0.00603518i
\(367\) 3.17736e7 5.50335e7i 0.642788 1.11334i −0.342019 0.939693i \(-0.611111\pi\)
0.984808 0.173649i \(-0.0555559\pi\)
\(368\) −1.23057e7 + 7.10469e6i −0.246923 + 0.142561i
\(369\) 3.88513e7 3.88513e7i 0.773262 0.773262i
\(370\) −1.02039e7 2.73413e6i −0.201447 0.0539776i
\(371\) −1.11801e7 + 4.17246e7i −0.218939 + 0.817091i
\(372\) −753562. 753562.i −0.0146383 0.0146383i
\(373\) −5.95820e6 1.03199e7i −0.114812 0.198861i 0.802892 0.596124i \(-0.203293\pi\)
−0.917705 + 0.397263i \(0.869960\pi\)
\(374\) −2.40368e6 1.38777e6i −0.0459476 0.0265278i
\(375\) −1.97180e6 + 528341.i −0.0373911 + 0.0100189i
\(376\) 1.75519e7i 0.330187i
\(377\) −2.76180e7 7.20651e7i −0.515428 1.34493i
\(378\) 357188. 0.00661335
\(379\) 1.93903e7 + 7.23656e7i 0.356178 + 1.32927i 0.878996 + 0.476830i \(0.158214\pi\)
−0.522818 + 0.852445i \(0.675119\pi\)
\(380\) 2.50901e7 4.34573e7i 0.457248 0.791976i
\(381\) 2.67370e6 1.54366e6i 0.0483434 0.0279111i
\(382\) 1.09521e6 1.09521e6i 0.0196475 0.0196475i
\(383\) −1.14935e7 3.07968e6i −0.204577 0.0548163i 0.155075 0.987903i \(-0.450438\pi\)
−0.359652 + 0.933086i \(0.617105\pi\)
\(384\) 382091. 1.42598e6i 0.00674796 0.0251837i
\(385\) 1.40139e7 + 1.40139e7i 0.245571 + 0.245571i
\(386\) −158378. 274319.i −0.00275380 0.00476973i
\(387\) 4.09545e7 + 2.36451e7i 0.706592 + 0.407951i
\(388\) −1.57070e7 + 4.20867e6i −0.268904 + 0.0720525i
\(389\) 3.78373e7i 0.642794i −0.946945 0.321397i \(-0.895848\pi\)
0.946945 0.321397i \(-0.104152\pi\)
\(390\) −63812.7 + 401477.i −0.00107576 + 0.00676810i
\(391\) 6.72382e6 0.112483
\(392\) −4.62476e6 1.72598e7i −0.0767769 0.286535i
\(393\) −1.83279e6 + 3.17449e6i −0.0301950 + 0.0522993i
\(394\) −1.86116e6 + 1.07454e6i −0.0304295 + 0.0175685i
\(395\) −6.05616e7 + 6.05616e7i −0.982667 + 0.982667i
\(396\) −4.53486e7 1.21511e7i −0.730262 0.195673i
\(397\) −2.79128e7 + 1.04172e8i −0.446100 + 1.66487i 0.266915 + 0.963720i \(0.413996\pi\)
−0.713015 + 0.701149i \(0.752671\pi\)
\(398\) −9.15742e6 9.15742e6i −0.145253 0.145253i
\(399\) 543111. + 940696.i 0.00855007 + 0.0148092i
\(400\) 4.19656e6 + 2.42289e6i 0.0655713 + 0.0378576i
\(401\) −4.23629e7 + 1.13511e7i −0.656981 + 0.176038i −0.571883 0.820335i \(-0.693787\pi\)
−0.0850980 + 0.996373i \(0.527120\pi\)
\(402\) 892655.i 0.0137406i
\(403\) −3.92225e6 3.75150e7i −0.0599266 0.573178i
\(404\) 7.59686e7 1.15210
\(405\) 1.63778e7 + 6.11226e7i 0.246541 + 0.920104i
\(406\) 4.27580e6 7.40590e6i 0.0638909 0.110662i
\(407\) −5.20949e7 + 3.00770e7i −0.772702 + 0.446120i
\(408\) −237332. + 237332.i −0.00349443 + 0.00349443i
\(409\) −3.15517e7 8.45425e6i −0.461161 0.123568i 0.0207560 0.999785i \(-0.493393\pi\)
−0.481917 + 0.876217i \(0.660059\pi\)
\(410\) −3.58919e6 + 1.33950e7i −0.0520768 + 0.194353i
\(411\) 1.76149e6 + 1.76149e6i 0.0253720 + 0.0253720i
\(412\) −3.92890e7 6.80505e7i −0.561796 0.973060i
\(413\) −3.92866e7 2.26821e7i −0.557692 0.321984i
\(414\) −4.20871e6 + 1.12772e6i −0.0593127 + 0.0158928i
\(415\) 6.87836e7i 0.962367i
\(416\) 3.19392e7 2.31785e7i 0.443653 0.321963i
\(417\) 45616.6 0.000629093
\(418\) 2.83326e6 + 1.05739e7i 0.0387933 + 0.144779i
\(419\) −3.53659e7 + 6.12555e7i −0.480775 + 0.832727i −0.999757 0.0220584i \(-0.992978\pi\)
0.518981 + 0.854785i \(0.326311\pi\)
\(420\) 1.01826e6 587894.i 0.0137439 0.00793507i
\(421\) 6.36893e7 6.36893e7i 0.853533 0.853533i −0.137033 0.990566i \(-0.543757\pi\)
0.990566 + 0.137033i \(0.0437567\pi\)
\(422\) 1.83483e7 + 4.91641e6i 0.244151 + 0.0654201i
\(423\) 1.71292e7 6.39269e7i 0.226316 0.844622i
\(424\) 3.72245e7 + 3.72245e7i 0.488351 + 0.488351i
\(425\) −1.14650e6 1.98580e6i −0.0149351 0.0258683i
\(426\) 509146. + 293956.i 0.00658588 + 0.00380236i
\(427\) 3.02911e7 8.11647e6i 0.389073 0.104252i
\(428\) 3.85380e7i 0.491539i
\(429\) 1.35960e6 + 1.87349e6i 0.0172203 + 0.0237290i
\(430\) −1.19358e7 −0.150122
\(431\) 255099. + 952044.i 0.00318623 + 0.0118912i 0.967501 0.252869i \(-0.0813740\pi\)
−0.964314 + 0.264760i \(0.914707\pi\)
\(432\) −2.67639e6 + 4.63564e6i −0.0331969 + 0.0574987i
\(433\) 4.92899e7 2.84576e7i 0.607148 0.350537i −0.164700 0.986344i \(-0.552666\pi\)
0.771848 + 0.635807i \(0.219332\pi\)
\(434\) 2.95539e6 2.95539e6i 0.0361532 0.0361532i
\(435\) −4.08564e6 1.09474e6i −0.0496355 0.0132998i
\(436\) 4.63950e6 1.73149e7i 0.0559773 0.208910i
\(437\) −1.87518e7 1.87518e7i −0.224698 0.224698i
\(438\) 206160. + 357079.i 0.00245348 + 0.00424954i
\(439\) −8.79431e7 5.07740e7i −1.03946 0.600133i −0.119781 0.992800i \(-0.538219\pi\)
−0.919681 + 0.392667i \(0.871552\pi\)
\(440\) 2.33300e7 6.25124e6i 0.273877 0.0733852i
\(441\) 6.73765e7i 0.785584i
\(442\) −5.79657e6 + 606041.i −0.0671281 + 0.00701835i
\(443\) 1.09735e8 1.26222 0.631109 0.775694i \(-0.282600\pi\)
0.631109 + 0.775694i \(0.282600\pi\)
\(444\) 923667. + 3.44717e6i 0.0105528 + 0.0393835i
\(445\) 1.67650e7 2.90379e7i 0.190250 0.329522i
\(446\) −7.49793e6 + 4.32893e6i −0.0845156 + 0.0487951i
\(447\) 3.39057e6 3.39057e6i 0.0379621 0.0379621i
\(448\) −3.15045e7 8.44161e6i −0.350380 0.0938839i
\(449\) 1.78438e7 6.65939e7i 0.197128 0.735691i −0.794578 0.607162i \(-0.792308\pi\)
0.991706 0.128529i \(-0.0410254\pi\)
\(450\) 1.05070e6 + 1.05070e6i 0.0115303 + 0.0115303i
\(451\) 3.94832e7 + 6.83869e7i 0.430410 + 0.745493i
\(452\) 4.36928e6 + 2.52260e6i 0.0473145 + 0.0273170i
\(453\) −2.54888e6 + 682971.i −0.0274192 + 0.00734695i
\(454\) 2.76775e7i 0.295773i
\(455\) 4.11000e7 + 6.53264e6i 0.436323 + 0.0693513i
\(456\) 1.32378e6 0.0139611
\(457\) −2.91466e7 1.08776e8i −0.305379 1.13969i −0.932619 0.360863i \(-0.882482\pi\)
0.627240 0.778826i \(-0.284184\pi\)
\(458\) 2.67428e6 4.63199e6i 0.0278363 0.0482138i
\(459\) 2.19356e6 1.26645e6i 0.0226836 0.0130964i
\(460\) −2.02980e7 + 2.02980e7i −0.208536 + 0.208536i
\(461\) 9.98675e7 + 2.67594e7i 1.01934 + 0.273133i 0.729529 0.683950i \(-0.239739\pi\)
0.289816 + 0.957082i \(0.406406\pi\)
\(462\) −66386.9 + 247759.i −0.000673219 + 0.00251249i
\(463\) 6.63536e6 + 6.63536e6i 0.0668531 + 0.0668531i 0.739743 0.672890i \(-0.234947\pi\)
−0.672890 + 0.739743i \(0.734947\pi\)
\(464\) 6.40766e7 + 1.10984e8i 0.641424 + 1.11098i
\(465\) −1.79032e6 1.03364e6i −0.0178062 0.0102804i
\(466\) −1.17607e7 + 3.15127e6i −0.116218 + 0.0311406i
\(467\) 5.57195e6i 0.0547087i −0.999626 0.0273544i \(-0.991292\pi\)
0.999626 0.0273544i \(-0.00870825\pi\)
\(468\) −9.20553e7 + 3.52790e7i −0.898072 + 0.344174i
\(469\) −9.13828e7 −0.885821
\(470\) 4.32330e6 + 1.61348e7i 0.0416411 + 0.155407i
\(471\) −702781. + 1.21725e6i −0.00672600 + 0.0116498i
\(472\) −4.78785e7 + 2.76427e7i −0.455317 + 0.262878i
\(473\) −4.80594e7 + 4.80594e7i −0.454145 + 0.454145i
\(474\) −1.07070e6 286893.i −0.0100539 0.00269393i
\(475\) −2.34069e6 + 8.73556e6i −0.0218405 + 0.0815098i
\(476\) 1.19198e7 + 1.19198e7i 0.110521 + 0.110521i
\(477\) −9.92499e7 1.71906e8i −0.914482 1.58393i
\(478\) 8.87841e6 + 5.12595e6i 0.0812927 + 0.0469344i
\(479\) −8.77395e7 + 2.35097e7i −0.798341 + 0.213915i −0.634856 0.772631i \(-0.718940\pi\)
−0.163486 + 0.986546i \(0.552274\pi\)
\(480\) 2.16286e6i 0.0195571i
\(481\) −5.14394e7 + 1.15365e8i −0.462233 + 1.03667i
\(482\) −2.33151e7 −0.208207
\(483\) −160824. 600204.i −0.00142728 0.00532669i
\(484\) −2.08608e7 + 3.61320e7i −0.183991 + 0.318681i
\(485\) −2.73177e7 + 1.57719e7i −0.239452 + 0.138248i
\(486\) −1.74135e6 + 1.74135e6i −0.0151697 + 0.0151697i
\(487\) 1.06893e7 + 2.86420e6i 0.0925474 + 0.0247980i 0.304796 0.952418i \(-0.401412\pi\)
−0.212248 + 0.977216i \(0.568079\pi\)
\(488\) 9.89152e6 3.69157e7i 0.0851145 0.317652i
\(489\) −4.74875e6 4.74875e6i −0.0406118 0.0406118i
\(490\) −8.50272e6 1.47271e7i −0.0722719 0.125179i
\(491\) 1.53346e8 + 8.85343e7i 1.29547 + 0.747940i 0.979618 0.200868i \(-0.0643762\pi\)
0.315852 + 0.948808i \(0.397710\pi\)
\(492\) 4.52523e6 1.21253e6i 0.0379966 0.0101812i
\(493\) 6.06415e7i 0.506092i
\(494\) 1.78560e7 + 1.44757e7i 0.148117 + 0.120077i
\(495\) −9.10722e7 −0.750880
\(496\) 1.62110e7 + 6.05001e7i 0.132851 + 0.495805i
\(497\) 3.00928e7 5.21223e7i 0.245129 0.424575i
\(498\) −770952. + 445110.i −0.00624223 + 0.00360395i
\(499\) 5.94289e7 5.94289e7i 0.478295 0.478295i −0.426291 0.904586i \(-0.640180\pi\)
0.904586 + 0.426291i \(0.140180\pi\)
\(500\) 1.20689e8 + 3.23386e7i 0.965514 + 0.258709i
\(501\) 2.25338e6 8.40973e6i 0.0179193 0.0668758i
\(502\) −1.83301e7 1.83301e7i −0.144895 0.144895i
\(503\) 9.88201e7 + 1.71161e8i 0.776500 + 1.34494i 0.933948 + 0.357410i \(0.116340\pi\)
−0.157447 + 0.987527i \(0.550326\pi\)
\(504\) −1.92829e7 1.11330e7i −0.150619 0.0869600i
\(505\) 1.42345e8 3.81413e7i 1.10527 0.296157i
\(506\) 6.26219e6i 0.0483365i
\(507\) 4.62124e6 + 1.50712e6i 0.0354596 + 0.0115644i
\(508\) −1.88968e8 −1.44144
\(509\) −6.19958e7 2.31372e8i −0.470121 1.75451i −0.639329 0.768933i \(-0.720788\pi\)
0.169208 0.985580i \(-0.445879\pi\)
\(510\) −159712. + 276629.i −0.00120400 + 0.00208539i
\(511\) 3.65549e7 2.11050e7i 0.273957 0.158169i
\(512\) −7.82117e7 + 7.82117e7i −0.582723 + 0.582723i
\(513\) −9.64953e6 2.58559e6i −0.0714750 0.0191517i
\(514\) 6.45925e6 2.41063e7i 0.0475656 0.177517i
\(515\) −1.07783e8 1.07783e8i −0.789095 0.789095i
\(516\) 2.01612e6 + 3.49203e6i 0.0146747 + 0.0254173i
\(517\) 8.23744e7 + 4.75589e7i 0.596102 + 0.344160i
\(518\) −1.35195e7 + 3.62253e6i −0.0972680 + 0.0260629i
\(519\) 2.98713e6i 0.0213674i
\(520\) 3.19389e7 3.93972e7i 0.227149 0.280192i
\(521\) 3.39064e7 0.239756 0.119878 0.992789i \(-0.461750\pi\)
0.119878 + 0.992789i \(0.461750\pi\)
\(522\) 1.01708e7 + 3.79579e7i 0.0715062 + 0.266865i
\(523\) −7.00345e7 + 1.21303e8i −0.489561 + 0.847945i −0.999928 0.0120119i \(-0.996176\pi\)
0.510367 + 0.859957i \(0.329510\pi\)
\(524\) 1.94303e8 1.12181e8i 1.35047 0.779697i
\(525\) −149840. + 149840.i −0.00103550 + 0.00103550i
\(526\) 2.65587e7 + 7.11638e6i 0.182494 + 0.0488992i
\(527\) 7.67096e6 2.86284e7i 0.0524104 0.195598i
\(528\) −2.71802e6 2.71802e6i −0.0184651 0.0184651i
\(529\) −6.64328e7 1.15065e8i −0.448761 0.777277i
\(530\) 4.33881e7 + 2.50501e7i 0.291436 + 0.168260i
\(531\) 2.01358e8 5.39538e7i 1.34489 0.360361i
\(532\) 6.64852e7i 0.441561i
\(533\) 1.51444e8 + 6.75264e7i 1.00016 + 0.445956i
\(534\) 433956. 0.00284985
\(535\) −1.93487e7 7.22102e7i −0.126354 0.471560i
\(536\) −5.56840e7 + 9.64475e7i −0.361606 + 0.626321i
\(537\) −2.30672e6 + 1.33179e6i −0.0148961 + 0.00860027i
\(538\) 3.03244e7 3.03244e7i 0.194736 0.194736i
\(539\) −9.35350e7 2.50626e7i −0.597321 0.160052i
\(540\) −2.79878e6 + 1.04452e7i −0.0177741 + 0.0663339i
\(541\) 3.54479e7 + 3.54479e7i 0.223872 + 0.223872i 0.810127 0.586255i \(-0.199398\pi\)
−0.586255 + 0.810127i \(0.699398\pi\)
\(542\) 3.52435e6 + 6.10435e6i 0.0221351 + 0.0383390i
\(543\) 1.05749e6 + 610542.i 0.00660506 + 0.00381343i
\(544\) 2.99520e7 8.02561e6i 0.186050 0.0498518i
\(545\) 3.47729e7i 0.214808i
\(546\) 192744. + 502938.i 0.00118414 + 0.00308984i
\(547\) −1.61004e8 −0.983725 −0.491862 0.870673i \(-0.663684\pi\)
−0.491862 + 0.870673i \(0.663684\pi\)
\(548\) −3.94637e7 1.47281e8i −0.239804 0.894961i
\(549\) −7.20531e7 + 1.24800e8i −0.435447 + 0.754217i
\(550\) −1.84946e6 + 1.06779e6i −0.0111162 + 0.00641795i
\(551\) −1.69121e8 + 1.69121e8i −1.01098 + 1.01098i
\(552\) −731467. 195996.i −0.00434888 0.00116528i
\(553\) −2.93699e7 + 1.09610e8i −0.173671 + 0.648148i
\(554\) −1.50474e7 1.50474e7i −0.0884977 0.0884977i
\(555\) 3.46142e6 + 5.99536e6i 0.0202477 + 0.0350700i
\(556\) −2.41802e6 1.39605e6i −0.0140681 0.00812223i
\(557\) −1.05515e6 + 282727.i −0.00610589 + 0.00163607i −0.261871 0.965103i \(-0.584339\pi\)
0.255765 + 0.966739i \(0.417673\pi\)
\(558\) 1.92062e7i 0.110545i
\(559\) −2.24030e7 + 1.40949e8i −0.128254 + 0.806910i
\(560\) −6.91046e7 −0.393498
\(561\) 470766. + 1.75692e6i 0.00266635 + 0.00995094i
\(562\) −2.83326e6 + 4.90735e6i −0.0159617 + 0.0276464i
\(563\) −1.70250e8 + 9.82938e7i −0.954029 + 0.550809i −0.894330 0.447408i \(-0.852347\pi\)
−0.0596987 + 0.998216i \(0.519014\pi\)
\(564\) 3.99026e6 3.99026e6i 0.0222415 0.0222415i
\(565\) 9.45341e6 + 2.53303e6i 0.0524135 + 0.0140442i
\(566\) 9.77758e6 3.64904e7i 0.0539240 0.201247i
\(567\) 5.92838e7 + 5.92838e7i 0.325227 + 0.325227i
\(568\) −3.66741e7 6.35213e7i −0.200131 0.346637i
\(569\) 2.79573e6 + 1.61412e6i 0.0151760 + 0.00876189i 0.507569 0.861611i \(-0.330544\pi\)
−0.492393 + 0.870373i \(0.663878\pi\)
\(570\) 1.21690e6 326066.i 0.00657096 0.00176068i
\(571\) 5.73160e7i 0.307870i 0.988081 + 0.153935i \(0.0491946\pi\)
−0.988081 + 0.153935i \(0.950805\pi\)
\(572\) −1.47332e7 1.40918e8i −0.0787244 0.752972i
\(573\) −1.01502e6 −0.00539525
\(574\) 4.75542e6 + 1.77475e7i 0.0251451 + 0.0938428i
\(575\) 2.58674e6 4.48037e6i 0.0136066 0.0235673i
\(576\) 1.29799e8 7.49395e7i 0.679210 0.392142i
\(577\) −7.62964e7 + 7.62964e7i −0.397170 + 0.397170i −0.877234 0.480064i \(-0.840614\pi\)
0.480064 + 0.877234i \(0.340614\pi\)
\(578\) 3.14044e7 + 8.41479e6i 0.162632 + 0.0435772i
\(579\) −53725.8 + 200508.i −0.000276788 + 0.00103299i
\(580\) 1.83066e8 + 1.83066e8i 0.938262 + 0.938262i
\(581\) 4.55668e7 + 7.89239e7i 0.232338 + 0.402421i
\(582\) −353554. 204125.i −0.00179344 0.00103544i
\(583\) 2.75566e8 7.38377e7i 1.39066 0.372625i
\(584\) 5.14412e7i 0.258269i
\(585\) −1.54775e8 + 1.12322e8i −0.773097 + 0.561042i
\(586\) −1.25268e7 −0.0622514
\(587\) −6.86741e7 2.56295e8i −0.339530 1.26714i −0.898873 0.438208i \(-0.855613\pi\)
0.559343 0.828936i \(-0.311053\pi\)
\(588\) −2.87246e6 + 4.97525e6i −0.0141294 + 0.0244728i
\(589\) −1.01234e8 + 5.84475e7i −0.495428 + 0.286036i
\(590\) −3.72040e7 + 3.72040e7i −0.181148 + 0.181148i
\(591\) 1.36038e6 + 364512.i 0.00659018 + 0.00176583i
\(592\) 5.42867e7 2.02601e8i 0.261655 0.976509i
\(593\) −9.62915e7 9.62915e7i −0.461768 0.461768i 0.437467 0.899235i \(-0.355876\pi\)
−0.899235 + 0.437467i \(0.855876\pi\)
\(594\) −1.17951e6 2.04296e6i −0.00562783 0.00974769i
\(595\) 2.83190e7 + 1.63500e7i 0.134440 + 0.0776188i
\(596\) −2.83490e8 + 7.59610e7i −1.33906 + 0.358799i
\(597\) 8.48692e6i 0.0398866i
\(598\) −7.72331e6 1.06425e7i −0.0361160 0.0497666i
\(599\) 8.14581e7 0.379013 0.189506 0.981879i \(-0.439311\pi\)
0.189506 + 0.981879i \(0.439311\pi\)
\(600\) 66839.8 + 249450.i 0.000309444 + 0.00115486i
\(601\) 8.68715e7 1.50466e8i 0.400178 0.693129i −0.593569 0.804783i \(-0.702281\pi\)
0.993747 + 0.111654i \(0.0356148\pi\)
\(602\) −1.36954e7 + 7.90703e6i −0.0627747 + 0.0362430i
\(603\) 2.96935e8 2.96935e8i 1.35428 1.35428i
\(604\) 1.56011e8 + 4.18031e7i 0.708020 + 0.189713i
\(605\) −2.09471e7 + 7.81756e7i −0.0945926 + 0.353024i
\(606\) 1.34864e6 + 1.34864e6i 0.00606008 + 0.00606008i
\(607\) 2.02330e7 + 3.50446e7i 0.0904678 + 0.156695i 0.907708 0.419602i \(-0.137830\pi\)
−0.817240 + 0.576297i \(0.804497\pi\)
\(608\) −1.05914e8 6.11497e7i −0.471243 0.272072i
\(609\) −5.41319e6 + 1.45046e6i −0.0239663 + 0.00642176i
\(610\) 3.63716e7i 0.160241i
\(611\) 1.98649e8 2.07691e7i 0.870889 0.0910528i
\(612\) −7.74629e7 −0.337940
\(613\) 5.62710e7 + 2.10006e8i 0.244289 + 0.911698i 0.973740 + 0.227665i \(0.0731090\pi\)
−0.729451 + 0.684033i \(0.760224\pi\)
\(614\) 3.77734e7 6.54255e7i 0.163185 0.282645i
\(615\) 7.87033e6 4.54394e6i 0.0338351 0.0195347i
\(616\) 2.26281e7 2.26281e7i 0.0968068 0.0968068i
\(617\) 2.53229e8 + 6.78525e7i 1.07810 + 0.288875i 0.753816 0.657086i \(-0.228211\pi\)
0.324281 + 0.945961i \(0.394878\pi\)
\(618\) 510592. 1.90556e6i 0.00216326 0.00807339i
\(619\) −2.25903e8 2.25903e8i −0.952466 0.952466i 0.0464548 0.998920i \(-0.485208\pi\)
−0.998920 + 0.0464548i \(0.985208\pi\)
\(620\) 6.32669e7 + 1.09581e8i 0.265461 + 0.459793i
\(621\) 4.94914e6 + 2.85739e6i 0.0206659 + 0.0119315i
\(622\) −6.39010e7 + 1.71222e7i −0.265544 + 0.0711523i
\(623\) 4.44250e7i 0.183723i
\(624\) −7.97142e6 1.26702e6i −0.0328082 0.00521469i
\(625\) 2.21622e8 0.907764
\(626\) −5.27774e6 1.96968e7i −0.0215142 0.0802921i
\(627\) 3.58692e6 6.21273e6i 0.0145519 0.0252046i
\(628\) 7.45053e7 4.30156e7i 0.300821 0.173679i
\(629\) −7.01816e7 + 7.01816e7i −0.282014 + 0.282014i
\(630\) −2.04682e7 5.48445e6i −0.0818576 0.0219337i
\(631\) 6.35382e7 2.37128e8i 0.252899 0.943832i −0.716348 0.697743i \(-0.754188\pi\)
0.969247 0.246089i \(-0.0791455\pi\)
\(632\) 9.77882e7 + 9.77882e7i 0.387378 + 0.387378i
\(633\) −6.22421e6 1.07806e7i −0.0245399 0.0425044i
\(634\) 4.05362e7 + 2.34036e7i 0.159065 + 0.0918364i
\(635\) −3.54077e8 + 9.48746e7i −1.38285 + 0.370535i
\(636\) 1.69253e7i 0.0657908i
\(637\) −1.89871e8 + 7.27655e7i −0.734582 + 0.281519i
\(638\) −5.64782e7 −0.217480
\(639\) 7.15815e7 + 2.67146e8i 0.274346 + 1.02387i
\(640\) −8.76420e7 + 1.51800e8i −0.334328 + 0.579073i
\(641\) −1.69848e8 + 9.80620e7i −0.644892 + 0.372329i −0.786497 0.617595i \(-0.788107\pi\)
0.141604 + 0.989923i \(0.454774\pi\)
\(642\) 684150. 684150.i 0.00258551 0.00258551i
\(643\) −3.56549e8 9.55371e7i −1.34118 0.359368i −0.484307 0.874898i \(-0.660928\pi\)
−0.856871 + 0.515531i \(0.827595\pi\)
\(644\) −9.84370e6 + 3.67372e7i −0.0368554 + 0.137546i
\(645\) 5.53093e6 + 5.53093e6i 0.0206119 + 0.0206119i
\(646\) 9.03094e6 + 1.56421e7i 0.0334993 + 0.0580225i
\(647\) −2.14030e8 1.23571e8i −0.790247 0.456249i 0.0498027 0.998759i \(-0.484141\pi\)
−0.840049 + 0.542510i \(0.817474\pi\)
\(648\) 9.86939e7 2.64450e7i 0.362715 0.0971892i
\(649\) 2.99604e8i 1.09601i
\(650\) −1.82619e6 + 4.09566e6i −0.00664976 + 0.0149137i
\(651\) −2.73900e6 −0.00992773
\(652\) 1.06389e8 + 3.97049e8i 0.383843 + 1.43252i
\(653\) 1.72426e8 2.98651e8i 0.619246 1.07257i −0.370378 0.928881i \(-0.620772\pi\)
0.989624 0.143684i \(-0.0458950\pi\)
\(654\) 389747. 225021.i 0.00139332 0.000804432i
\(655\) 3.07751e8 3.07751e8i 1.09516 1.09516i
\(656\) −2.65961e8 7.12642e7i −0.942122 0.252441i
\(657\) −5.02022e7 + 1.87357e8i −0.177022 + 0.660655i
\(658\) 1.56494e7 + 1.56494e7i 0.0549313 + 0.0549313i
\(659\) −2.05050e7 3.55158e7i −0.0716480 0.124098i 0.827976 0.560764i \(-0.189492\pi\)
−0.899624 + 0.436666i \(0.856159\pi\)
\(660\) −6.72501e6 3.88268e6i −0.0233917 0.0135052i
\(661\) −6.81872e7 + 1.82707e7i −0.236101 + 0.0632631i −0.374929 0.927053i \(-0.622333\pi\)
0.138828 + 0.990316i \(0.455666\pi\)
\(662\) 4.11972e7i 0.142002i
\(663\) 2.96691e6 + 2.40524e6i 0.0101804 + 0.00825313i
\(664\) 1.11064e8 0.379376
\(665\) −3.33801e7 1.24576e8i −0.113507 0.423613i
\(666\) 3.21586e7 5.57003e7i 0.108862 0.188554i
\(667\) 1.18490e8 6.84100e7i 0.399303 0.230538i
\(668\) −3.76816e8 + 3.76816e8i −1.26416 + 1.26416i
\(669\) 5.48046e6 + 1.46848e6i 0.0183037 + 0.00490446i
\(670\) −2.74317e7 + 1.02376e8i −0.0912069 + 0.340389i
\(671\) −1.46450e8 1.46450e8i −0.484755 0.484755i
\(672\) −1.43282e6 2.48171e6i −0.00472154 0.00817794i
\(673\) 6.56515e7 + 3.79039e7i 0.215377 + 0.124348i 0.603808 0.797130i \(-0.293649\pi\)
−0.388431 + 0.921478i \(0.626983\pi\)
\(674\) 1.98768e7 5.32598e6i 0.0649183 0.0173948i
\(675\) 1.94889e6i 0.00633689i
\(676\) −1.98836e8 2.21316e8i −0.643659 0.716429i
\(677\) 5.03333e8 1.62214 0.811072 0.584947i \(-0.198885\pi\)
0.811072 + 0.584947i \(0.198885\pi\)
\(678\) 32783.3 + 122349.i 0.000105187 + 0.000392565i
\(679\) −2.08967e7 + 3.61941e7i −0.0667525 + 0.115619i
\(680\) 3.45123e7 1.99257e7i 0.109761 0.0633704i
\(681\) −1.28255e7 + 1.28255e7i −0.0406099 + 0.0406099i
\(682\) −2.66629e7 7.14431e6i −0.0840532 0.0225220i
\(683\) −7.04794e7 + 2.63033e8i −0.221208 + 0.825559i 0.762681 + 0.646775i \(0.223883\pi\)
−0.983888 + 0.178783i \(0.942784\pi\)
\(684\) 2.16034e8 + 2.16034e8i 0.675077 + 0.675077i
\(685\) −1.47890e8 2.56152e8i −0.460115 0.796942i
\(686\) −4.43160e7 2.55859e7i −0.137274 0.0792552i
\(687\) −3.38566e6 + 907185.i −0.0104417 + 0.00279786i
\(688\) 2.36988e8i 0.727713i
\(689\) 3.77253e8 4.65348e8i 1.15339 1.42272i
\(690\) −720686. −0.00219381
\(691\) 1.21826e6 + 4.54662e6i 0.00369238 + 0.0137802i 0.967747 0.251922i \(-0.0810628\pi\)
−0.964055 + 0.265703i \(0.914396\pi\)
\(692\) 9.14178e7 1.58340e8i 0.275875 0.477829i
\(693\) −1.04498e8 + 6.03322e7i −0.313986 + 0.181280i
\(694\) 2.65666e7 2.65666e7i 0.0794800 0.0794800i
\(695\) −5.23165e6 1.40182e6i −0.0155842 0.00417577i
\(696\) −1.76767e6 + 6.59704e6i −0.00524293 + 0.0195669i
\(697\) 9.21299e7 + 9.21299e7i 0.272084 + 0.272084i
\(698\) 3.50377e7 + 6.06871e7i 0.103031 + 0.178456i
\(699\) 6.91006e6 + 3.98952e6i 0.0202325 + 0.0116813i
\(700\) 1.25283e7 3.35696e6i 0.0365258 0.00978706i
\(701\) 1.17358e8i 0.340689i 0.985385 + 0.170344i \(0.0544880\pi\)
−0.985385 + 0.170344i \(0.945512\pi\)
\(702\) −4.52418e6 2.01726e6i −0.0130776 0.00583110i
\(703\) 3.91454e8 1.12672
\(704\) 5.57518e7 + 2.08068e8i 0.159787 + 0.596332i
\(705\) 5.47333e6 9.48008e6i 0.0156201 0.0270548i
\(706\) 6.46446e7 3.73226e7i 0.183704 0.106061i
\(707\) 1.38063e8 1.38063e8i 0.390678 0.390678i
\(708\) 1.71690e7 + 4.60042e6i 0.0483777 + 0.0129628i
\(709\) −8.01441e7 + 2.99102e8i −0.224871 + 0.839229i 0.757585 + 0.652736i \(0.226379\pi\)
−0.982456 + 0.186493i \(0.940288\pi\)
\(710\) −4.93593e7 4.93593e7i −0.137909 0.137909i
\(711\) −2.60728e8 4.51594e8i −0.725401 1.25643i
\(712\) −4.68871e7 2.70703e7i −0.129901 0.0749985i
\(713\) 6.45917e7 1.73073e7i 0.178200 0.0477486i
\(714\) 423214.i 0.00116269i
\(715\) −9.83566e7 2.56647e8i −0.269082 0.702130i
\(716\) 1.63032e8 0.444153
\(717\) −1.73885e6 6.48949e6i −0.00471743 0.0176057i
\(718\) −3.33653e7 + 5.77904e7i −0.0901409 + 0.156129i
\(719\) 7.91977e7 4.57248e7i 0.213072 0.123017i −0.389666 0.920956i \(-0.627410\pi\)
0.602738 + 0.797939i \(0.294076\pi\)
\(720\) 2.24545e8 2.24545e8i 0.601598 0.601598i
\(721\) −1.95075e8 5.22703e7i −0.520471 0.139460i
\(722\) −273696. + 1.02145e6i −0.000727205 + 0.00271397i
\(723\) 1.08040e7 + 1.08040e7i 0.0285871 + 0.0285871i
\(724\) −3.73699e7 6.47266e7i −0.0984706 0.170556i
\(725\) −4.04081e7 2.33296e7i −0.106036 0.0612201i
\(726\) −1.01177e6 + 271104.i −0.00264407 + 0.000708476i
\(727\) 6.46738e8i 1.68316i 0.540134 + 0.841579i \(0.318374\pi\)
−0.540134 + 0.841579i \(0.681626\pi\)
\(728\) 1.05482e7 6.63637e7i 0.0273390 0.172003i
\(729\) −3.84191e8 −0.991663
\(730\) −1.26708e7 4.72879e7i −0.0325712 0.121557i
\(731\) −5.60707e7 + 9.71174e7i −0.143544 + 0.248625i
\(732\) −1.06412e7 + 6.14368e6i −0.0271304 + 0.0156637i
\(733\) −2.74415e7 + 2.74415e7i −0.0696781 + 0.0696781i −0.741087 0.671409i \(-0.765689\pi\)
0.671409 + 0.741087i \(0.265689\pi\)
\(734\) −9.43244e7 2.52741e7i −0.238526 0.0639129i
\(735\) −2.88434e6 + 1.07645e7i −0.00726414 + 0.0271102i
\(736\) 4.94705e7 + 4.94705e7i 0.124083 + 0.124083i
\(737\) 3.01764e8 + 5.22671e8i 0.753816 + 1.30565i
\(738\) −7.31198e7 4.22158e7i −0.181914 0.105028i
\(739\) −1.43432e8 + 3.84325e7i −0.355396 + 0.0952281i −0.432100 0.901826i \(-0.642227\pi\)
0.0767035 + 0.997054i \(0.475561\pi\)
\(740\) 4.23732e8i 1.04567i
\(741\) −1.56642e6 1.49822e7i −0.00384993 0.0368232i
\(742\) 6.63793e7 0.162488
\(743\) 1.72605e8 + 6.44171e8i 0.420811 + 1.57049i 0.772904 + 0.634523i \(0.218803\pi\)
−0.352093 + 0.935965i \(0.614530\pi\)
\(744\) −1.66901e6 + 2.89081e6i −0.00405266 + 0.00701941i
\(745\) −4.93049e8 + 2.84662e8i −1.19240 + 0.688432i
\(746\) −1.29483e7 + 1.29483e7i −0.0311887 + 0.0311887i
\(747\) −4.04514e8 1.08389e8i −0.970447 0.260030i
\(748\) 2.88145e7 1.07537e8i 0.0688505 0.256953i
\(749\) −7.00378e7 7.00378e7i −0.166681 0.166681i
\(750\) 1.56845e6 + 2.71664e6i 0.00371782 + 0.00643945i
\(751\) −2.62130e8 1.51341e8i −0.618866 0.357302i 0.157561 0.987509i \(-0.449637\pi\)
−0.776427 + 0.630207i \(0.782970\pi\)
\(752\) −3.20360e8 + 8.58402e7i −0.753329 + 0.201854i
\(753\) 1.69880e7i 0.0397884i
\(754\) −9.59834e7 + 6.96559e7i −0.223914 + 0.162496i
\(755\) 3.13313e8 0.728009
\(756\) 3.70819e6 + 1.38392e7i 0.00858216 + 0.0320291i
\(757\) 1.13017e8 1.95751e8i 0.260529 0.451250i −0.705854 0.708358i \(-0.749436\pi\)
0.966383 + 0.257108i \(0.0827697\pi\)
\(758\) 9.97018e7 5.75629e7i 0.228926 0.132171i
\(759\) −2.90184e6 + 2.90184e6i −0.00663664 + 0.00663664i
\(760\) −1.51820e8 4.06802e7i −0.345851 0.0926706i
\(761\) −2.47488e7 + 9.23639e7i −0.0561566 + 0.209579i −0.988303 0.152502i \(-0.951267\pi\)
0.932147 + 0.362081i \(0.117934\pi\)
\(762\) −3.35468e6 3.35468e6i −0.00758203 0.00758203i
\(763\) −2.30358e7 3.98992e7i −0.0518597