Properties

Label 19.7.f.a.3.7
Level $19$
Weight $7$
Character 19.3
Analytic conductor $4.371$
Analytic rank $0$
Dimension $54$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 19.f (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.37102758878\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 3.7
Character \(\chi\) \(=\) 19.3
Dual form 19.7.f.a.13.7

$q$-expansion

\(f(q)\) \(=\) \(q+(4.29634 - 5.12017i) q^{2} +(10.1613 + 27.9178i) q^{3} +(3.35580 + 19.0317i) q^{4} +(-23.2992 + 132.137i) q^{5} +(186.600 + 67.9170i) q^{6} +(-124.815 - 216.186i) q^{7} +(482.323 + 278.470i) q^{8} +(-117.708 + 98.7685i) q^{9} +O(q^{10})\) \(q+(4.29634 - 5.12017i) q^{2} +(10.1613 + 27.9178i) q^{3} +(3.35580 + 19.0317i) q^{4} +(-23.2992 + 132.137i) q^{5} +(186.600 + 67.9170i) q^{6} +(-124.815 - 216.186i) q^{7} +(482.323 + 278.470i) q^{8} +(-117.708 + 98.7685i) q^{9} +(576.461 + 686.999i) q^{10} +(1244.31 - 2155.22i) q^{11} +(-497.225 + 287.073i) q^{12} +(-909.574 + 2499.03i) q^{13} +(-1643.15 - 289.732i) q^{14} +(-3925.72 + 692.210i) q^{15} +(2335.81 - 850.164i) q^{16} +(-1445.53 - 1212.94i) q^{17} +1027.03i q^{18} +(921.105 - 6796.87i) q^{19} -2592.97 q^{20} +(4767.16 - 5681.27i) q^{21} +(-5689.09 - 15630.6i) q^{22} +(971.553 + 5509.95i) q^{23} +(-2873.25 + 16295.0i) q^{24} +(-2234.52 - 813.298i) q^{25} +(8887.65 + 15393.9i) q^{26} +(14803.1 + 8546.59i) q^{27} +(3695.53 - 3100.92i) q^{28} +(-9290.64 - 11072.2i) q^{29} +(-13322.0 + 23074.3i) q^{30} +(4387.12 - 2532.91i) q^{31} +(-6508.58 + 17882.2i) q^{32} +(72812.8 + 12838.9i) q^{33} +(-12420.9 + 2190.14i) q^{34} +(31474.1 - 11455.6i) q^{35} +(-2274.74 - 1908.73i) q^{36} -39054.7i q^{37} +(-30843.8 - 33917.9i) q^{38} -79010.0 q^{39} +(-48033.8 + 57244.4i) q^{40} +(-14855.7 - 40815.8i) q^{41} +(-8607.81 - 48817.3i) q^{42} +(15361.5 - 87119.5i) q^{43} +(45193.1 + 16449.0i) q^{44} +(-10308.4 - 17854.7i) q^{45} +(32386.0 + 18698.1i) q^{46} +(-134106. + 112528. i) q^{47} +(47469.5 + 56571.9i) q^{48} +(27667.0 - 47920.7i) q^{49} +(-13764.5 + 7946.92i) q^{50} +(19174.3 - 52680.9i) q^{51} +(-50613.2 - 8924.48i) q^{52} +(-85945.4 + 15154.5i) q^{53} +(107359. - 39075.6i) q^{54} +(255791. + 214634. i) q^{55} -139028. i q^{56} +(199113. - 43349.5i) q^{57} -96607.1 q^{58} +(-256771. + 306007. i) q^{59} +(-26347.9 - 72390.2i) q^{60} +(5280.20 + 29945.5i) q^{61} +(5879.63 - 33345.1i) q^{62} +(36044.0 + 13118.9i) q^{63} +(143140. + 247925. i) q^{64} +(-309021. - 178413. i) q^{65} +(378565. - 317654. i) q^{66} +(111539. + 132927. i) q^{67} +(18233.4 - 31581.2i) q^{68} +(-143954. + 83111.7i) q^{69} +(76568.5 - 210370. i) q^{70} +(412576. + 72748.3i) q^{71} +(-84277.2 + 14860.3i) q^{72} +(-163746. + 59598.6i) q^{73} +(-199967. - 167792. i) q^{74} -70647.0i q^{75} +(132447. - 5278.77i) q^{76} -621235. q^{77} +(-339453. + 404545. i) q^{78} +(-126908. - 348676. i) q^{79} +(57915.2 + 328453. i) q^{80} +(-107635. + 610429. i) q^{81} +(-272809. - 99294.4i) q^{82} +(-416764. - 721857. i) q^{83} +(124122. + 71661.9i) q^{84} +(193953. - 162746. i) q^{85} +(-380069. - 452948. i) q^{86} +(214706. - 371882. i) q^{87} +(1.20032e6 - 693007. i) q^{88} +(-66885.2 + 183766. i) q^{89} +(-135708. - 23928.9i) q^{90} +(653783. - 115280. i) q^{91} +(-101604. + 36980.7i) q^{92} +(115292. + 96741.5i) q^{93} +1.17010e6i q^{94} +(876654. + 280073. i) q^{95} -565367. q^{96} +(-205729. + 245178. i) q^{97} +(-126496. - 347544. i) q^{98} +(66402.0 + 376584. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9} + O(q^{10}) \) \( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9} - 1689 q^{10} + 1677 q^{11} - 9 q^{12} - 10506 q^{13} + 6105 q^{14} + 24138 q^{15} + 23760 q^{16} - 3438 q^{17} - 30918 q^{19} - 76650 q^{20} - 59055 q^{21} + 20490 q^{22} + 42498 q^{23} + 31848 q^{24} + 7914 q^{25} + 109989 q^{26} + 124821 q^{27} - 109476 q^{28} - 27726 q^{29} - 153516 q^{30} - 30789 q^{31} - 114375 q^{32} + 126039 q^{33} + 359796 q^{34} + 160161 q^{35} + 184995 q^{36} - 245244 q^{38} - 390564 q^{39} - 372678 q^{40} - 24708 q^{41} - 244893 q^{42} - 30726 q^{43} - 301419 q^{44} + 293037 q^{45} + 69246 q^{46} - 71454 q^{47} + 1024041 q^{48} - 350346 q^{49} - 104148 q^{50} - 180672 q^{51} + 921801 q^{52} + 822558 q^{53} + 308469 q^{54} + 623517 q^{55} - 17862 q^{57} - 1150644 q^{58} - 463812 q^{59} - 908130 q^{60} - 583698 q^{61} - 429732 q^{62} - 2576043 q^{63} - 328293 q^{64} - 1056789 q^{65} - 1038756 q^{66} + 1120464 q^{67} + 717270 q^{68} + 3771567 q^{69} + 4845345 q^{70} + 94494 q^{71} + 2351634 q^{72} + 950850 q^{73} + 55149 q^{74} - 218814 q^{76} - 343086 q^{77} + 1833471 q^{78} - 4936494 q^{79} - 9642039 q^{80} - 769551 q^{81} - 8627793 q^{82} - 412131 q^{83} - 3125205 q^{84} - 896910 q^{85} + 8878236 q^{86} + 610737 q^{87} + 13604751 q^{88} + 6653022 q^{89} + 3142734 q^{90} + 3409821 q^{91} - 3043740 q^{92} - 816393 q^{93} + 4839186 q^{95} - 5667138 q^{96} - 853656 q^{97} - 17679315 q^{98} - 13991937 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.29634 5.12017i 0.537042 0.640022i −0.427480 0.904025i \(-0.640598\pi\)
0.964522 + 0.264003i \(0.0850429\pi\)
\(3\) 10.1613 + 27.9178i 0.376343 + 1.03399i 0.972860 + 0.231393i \(0.0743285\pi\)
−0.596517 + 0.802600i \(0.703449\pi\)
\(4\) 3.35580 + 19.0317i 0.0524345 + 0.297371i
\(5\) −23.2992 + 132.137i −0.186394 + 1.05709i 0.737757 + 0.675066i \(0.235885\pi\)
−0.924151 + 0.382027i \(0.875226\pi\)
\(6\) 186.600 + 67.9170i 0.863890 + 0.314430i
\(7\) −124.815 216.186i −0.363891 0.630278i 0.624706 0.780860i \(-0.285219\pi\)
−0.988598 + 0.150581i \(0.951885\pi\)
\(8\) 482.323 + 278.470i 0.942038 + 0.543886i
\(9\) −117.708 + 98.7685i −0.161465 + 0.135485i
\(10\) 576.461 + 686.999i 0.576461 + 0.686999i
\(11\) 1244.31 2155.22i 0.934872 1.61925i 0.160010 0.987115i \(-0.448847\pi\)
0.774862 0.632130i \(-0.217819\pi\)
\(12\) −497.225 + 287.073i −0.287746 + 0.166130i
\(13\) −909.574 + 2499.03i −0.414007 + 1.13748i 0.541034 + 0.841001i \(0.318033\pi\)
−0.955041 + 0.296474i \(0.904189\pi\)
\(14\) −1643.15 289.732i −0.598817 0.105588i
\(15\) −3925.72 + 692.210i −1.16317 + 0.205099i
\(16\) 2335.81 850.164i 0.570265 0.207560i
\(17\) −1445.53 1212.94i −0.294225 0.246884i 0.483711 0.875228i \(-0.339289\pi\)
−0.777936 + 0.628344i \(0.783733\pi\)
\(18\) 1027.03i 0.176102i
\(19\) 921.105 6796.87i 0.134291 0.990942i
\(20\) −2592.97 −0.324122
\(21\) 4767.16 5681.27i 0.514756 0.613462i
\(22\) −5689.09 15630.6i −0.534287 1.46794i
\(23\) 971.553 + 5509.95i 0.0798515 + 0.452860i 0.998349 + 0.0574343i \(0.0182920\pi\)
−0.918498 + 0.395426i \(0.870597\pi\)
\(24\) −2873.25 + 16295.0i −0.207845 + 1.17875i
\(25\) −2234.52 813.298i −0.143009 0.0520510i
\(26\) 8887.65 + 15393.9i 0.505670 + 0.875845i
\(27\) 14803.1 + 8546.59i 0.752077 + 0.434212i
\(28\) 3695.53 3100.92i 0.168346 0.141259i
\(29\) −9290.64 11072.2i −0.380936 0.453982i 0.541174 0.840911i \(-0.317980\pi\)
−0.922109 + 0.386929i \(0.873536\pi\)
\(30\) −13322.0 + 23074.3i −0.493406 + 0.854604i
\(31\) 4387.12 2532.91i 0.147263 0.0850226i −0.424558 0.905401i \(-0.639570\pi\)
0.571821 + 0.820378i \(0.306237\pi\)
\(32\) −6508.58 + 17882.2i −0.198626 + 0.545721i
\(33\) 72812.8 + 12838.9i 2.02612 + 0.357260i
\(34\) −12420.9 + 2190.14i −0.316022 + 0.0557232i
\(35\) 31474.1 11455.6i 0.734090 0.267187i
\(36\) −2274.74 1908.73i −0.0487555 0.0409107i
\(37\) 39054.7i 0.771024i −0.922703 0.385512i \(-0.874025\pi\)
0.922703 0.385512i \(-0.125975\pi\)
\(38\) −30843.8 33917.9i −0.562104 0.618127i
\(39\) −79010.0 −1.33195
\(40\) −48033.8 + 57244.4i −0.750528 + 0.894444i
\(41\) −14855.7 40815.8i −0.215547 0.592211i 0.784047 0.620702i \(-0.213152\pi\)
−0.999594 + 0.0284905i \(0.990930\pi\)
\(42\) −8607.81 48817.3i −0.116184 0.658910i
\(43\) 15361.5 87119.5i 0.193210 1.09575i −0.721736 0.692169i \(-0.756655\pi\)
0.914945 0.403578i \(-0.132233\pi\)
\(44\) 45193.1 + 16449.0i 0.530535 + 0.193099i
\(45\) −10308.4 17854.7i −0.113124 0.195937i
\(46\) 32386.0 + 18698.1i 0.332724 + 0.192098i
\(47\) −134106. + 112528.i −1.29168 + 1.08385i −0.300159 + 0.953889i \(0.597040\pi\)
−0.991520 + 0.129957i \(0.958516\pi\)
\(48\) 47469.5 + 56571.9i 0.429230 + 0.511537i
\(49\) 27667.0 47920.7i 0.235166 0.407320i
\(50\) −13764.5 + 7946.92i −0.110116 + 0.0635753i
\(51\) 19174.3 52680.9i 0.144547 0.397139i
\(52\) −50613.2 8924.48i −0.359960 0.0634706i
\(53\) −85945.4 + 15154.5i −0.577292 + 0.101792i −0.454668 0.890661i \(-0.650242\pi\)
−0.122624 + 0.992453i \(0.539131\pi\)
\(54\) 107359. 39075.6i 0.681802 0.248156i
\(55\) 255791. + 214634.i 1.53744 + 1.29006i
\(56\) 139028.i 0.791662i
\(57\) 199113. 43349.5i 1.07517 0.234078i
\(58\) −96607.1 −0.495137
\(59\) −256771. + 306007.i −1.25023 + 1.48996i −0.446717 + 0.894675i \(0.647407\pi\)
−0.803512 + 0.595289i \(0.797038\pi\)
\(60\) −26347.9 72390.2i −0.121981 0.335140i
\(61\) 5280.20 + 29945.5i 0.0232628 + 0.131930i 0.994227 0.107293i \(-0.0342184\pi\)
−0.970965 + 0.239223i \(0.923107\pi\)
\(62\) 5879.63 33345.1i 0.0246703 0.139912i
\(63\) 36044.0 + 13118.9i 0.144149 + 0.0524659i
\(64\) 143140. + 247925.i 0.546034 + 0.945759i
\(65\) −309021. 178413.i −1.12525 0.649662i
\(66\) 378565. 317654.i 1.31677 1.10490i
\(67\) 111539. + 132927.i 0.370853 + 0.441965i 0.918905 0.394479i \(-0.129075\pi\)
−0.548052 + 0.836444i \(0.684630\pi\)
\(68\) 18233.4 31581.2i 0.0579884 0.100439i
\(69\) −143954. + 83111.7i −0.438203 + 0.252997i
\(70\) 76568.5 210370.i 0.223232 0.613324i
\(71\) 412576. + 72748.3i 1.15273 + 0.203258i 0.717169 0.696900i \(-0.245438\pi\)
0.435564 + 0.900158i \(0.356549\pi\)
\(72\) −84277.2 + 14860.3i −0.225794 + 0.0398136i
\(73\) −163746. + 59598.6i −0.420922 + 0.153203i −0.543793 0.839220i \(-0.683012\pi\)
0.122871 + 0.992423i \(0.460790\pi\)
\(74\) −199967. 167792.i −0.493472 0.414072i
\(75\) 70647.0i 0.167460i
\(76\) 132447. 5278.77i 0.301718 0.0120252i
\(77\) −621235. −1.36077
\(78\) −339453. + 404545.i −0.715314 + 0.852477i
\(79\) −126908. 348676.i −0.257399 0.707198i −0.999326 0.0367168i \(-0.988310\pi\)
0.741927 0.670481i \(-0.233912\pi\)
\(80\) 57915.2 + 328453.i 0.113116 + 0.641511i
\(81\) −107635. + 610429.i −0.202535 + 1.14863i
\(82\) −272809. 99294.4i −0.494786 0.180087i
\(83\) −416764. 721857.i −0.728880 1.26246i −0.957357 0.288908i \(-0.906708\pi\)
0.228477 0.973549i \(-0.426626\pi\)
\(84\) 124122. + 71661.9i 0.209417 + 0.120907i
\(85\) 193953. 162746.i 0.315821 0.265005i
\(86\) −380069. 452948.i −0.597540 0.712120i
\(87\) 214706. 371882.i 0.326052 0.564738i
\(88\) 1.20032e6 693007.i 1.76137 1.01693i
\(89\) −66885.2 + 183766.i −0.0948768 + 0.260672i −0.978048 0.208378i \(-0.933181\pi\)
0.883171 + 0.469050i \(0.155404\pi\)
\(90\) −135708. 23928.9i −0.186156 0.0328243i
\(91\) 653783. 115280.i 0.867580 0.152978i
\(92\) −101604. + 36980.7i −0.130480 + 0.0474910i
\(93\) 115292. + 96741.5i 0.143334 + 0.120272i
\(94\) 1.17010e6i 1.40877i
\(95\) 876654. + 280073.i 1.02249 + 0.326664i
\(96\) −565367. −0.639023
\(97\) −205729. + 245178.i −0.225413 + 0.268637i −0.866883 0.498511i \(-0.833880\pi\)
0.641470 + 0.767148i \(0.278325\pi\)
\(98\) −126496. 347544.i −0.134399 0.369259i
\(99\) 66402.0 + 376584.i 0.0684346 + 0.388112i
\(100\) 7979.85 45256.0i 0.00797985 0.0452560i
\(101\) −181418. 66030.9i −0.176083 0.0640890i 0.252474 0.967604i \(-0.418756\pi\)
−0.428557 + 0.903515i \(0.640978\pi\)
\(102\) −187356. 324511.i −0.176550 0.305794i
\(103\) 1.75686e6 + 1.01433e6i 1.60778 + 0.928252i 0.989866 + 0.142005i \(0.0453551\pi\)
0.617913 + 0.786246i \(0.287978\pi\)
\(104\) −1.13461e6 + 952053.i −1.00867 + 0.846372i
\(105\) 639633. + 762285.i 0.552539 + 0.658490i
\(106\) −291657. + 505164.i −0.244881 + 0.424146i
\(107\) −405119. + 233895.i −0.330698 + 0.190928i −0.656151 0.754630i \(-0.727816\pi\)
0.325453 + 0.945558i \(0.394483\pi\)
\(108\) −112980. + 310410.i −0.0896871 + 0.246413i
\(109\) −2.03923e6 359572.i −1.57466 0.277655i −0.683021 0.730399i \(-0.739334\pi\)
−0.891641 + 0.452744i \(0.850445\pi\)
\(110\) 2.19793e6 387554.i 1.65134 0.291175i
\(111\) 1.09032e6 396845.i 0.797234 0.290169i
\(112\) −475336. 398854.i −0.338335 0.283897i
\(113\) 1.51772e6i 1.05185i −0.850530 0.525927i \(-0.823719\pi\)
0.850530 0.525927i \(-0.176281\pi\)
\(114\) 633501. 1.20574e6i 0.427595 0.813840i
\(115\) −750703. −0.493599
\(116\) 179545. 213973.i 0.115027 0.137083i
\(117\) −139762. 383992.i −0.0872632 0.239754i
\(118\) 463638. + 2.62942e6i 0.282184 + 1.60035i
\(119\) −81797.1 + 463894.i −0.0485397 + 0.275282i
\(120\) −2.08622e6 759323.i −1.20731 0.439423i
\(121\) −2.21086e6 3.82932e6i −1.24797 2.16155i
\(122\) 176012. + 101620.i 0.0969309 + 0.0559631i
\(123\) 988535. 829480.i 0.531223 0.445749i
\(124\) 62927.9 + 74994.6i 0.0330049 + 0.0393337i
\(125\) −888713. + 1.53930e6i −0.455021 + 0.788120i
\(126\) 222028. 128188.i 0.110993 0.0640820i
\(127\) 810471. 2.22675e6i 0.395664 1.08708i −0.568711 0.822537i \(-0.692558\pi\)
0.964375 0.264540i \(-0.0852201\pi\)
\(128\) 684990. + 120782.i 0.326629 + 0.0575935i
\(129\) 2.58828e6 456384.i 1.20571 0.212599i
\(130\) −2.24117e6 + 815718.i −1.02010 + 0.371287i
\(131\) −1.95391e6 1.63952e6i −0.869141 0.729295i 0.0947764 0.995499i \(-0.469786\pi\)
−0.963917 + 0.266203i \(0.914231\pi\)
\(132\) 1.42884e6i 0.621242i
\(133\) −1.58435e6 + 649220.i −0.673437 + 0.275954i
\(134\) 1.15982e6 0.482031
\(135\) −1.47422e6 + 1.75691e6i −0.599185 + 0.714081i
\(136\) −359444. 987564.i −0.142894 0.392598i
\(137\) 554884. + 3.14690e6i 0.215795 + 1.22383i 0.879522 + 0.475857i \(0.157862\pi\)
−0.663728 + 0.747974i \(0.731027\pi\)
\(138\) −192927. + 1.09414e6i −0.0734101 + 0.416330i
\(139\) 1.13236e6 + 412145.i 0.421638 + 0.153464i 0.544121 0.839007i \(-0.316863\pi\)
−0.122483 + 0.992471i \(0.539086\pi\)
\(140\) 323641. + 560563.i 0.117945 + 0.204287i
\(141\) −4.50423e6 2.60052e6i −1.60680 0.927689i
\(142\) 2.14505e6 1.79991e6i 0.749156 0.628616i
\(143\) 4.25416e6 + 5.06991e6i 1.45481 + 1.73377i
\(144\) −190973. + 330775.i −0.0639564 + 0.110776i
\(145\) 1.67950e6 969661.i 0.550905 0.318065i
\(146\) −398352. + 1.09446e6i −0.127999 + 0.351676i
\(147\) 1.61897e6 + 285469.i 0.509669 + 0.0898684i
\(148\) 743277. 131060.i 0.229280 0.0404282i
\(149\) 4.19531e6 1.52697e6i 1.26825 0.461606i 0.381722 0.924277i \(-0.375331\pi\)
0.886530 + 0.462672i \(0.153109\pi\)
\(150\) −361725. 303523.i −0.107178 0.0899328i
\(151\) 3.61162e6i 1.04899i 0.851414 + 0.524495i \(0.175746\pi\)
−0.851414 + 0.524495i \(0.824254\pi\)
\(152\) 2.33699e6 3.02179e6i 0.665467 0.860466i
\(153\) 289950. 0.0809558
\(154\) −2.66904e6 + 3.18083e6i −0.730789 + 0.870921i
\(155\) 232473. + 638714.i 0.0624277 + 0.171519i
\(156\) −265142. 1.50370e6i −0.0698401 0.396083i
\(157\) 1.15049e6 6.52474e6i 0.297292 1.68603i −0.360447 0.932780i \(-0.617376\pi\)
0.657739 0.753246i \(-0.271513\pi\)
\(158\) −2.33052e6 848240.i −0.590856 0.215054i
\(159\) −1.29639e6 2.24542e6i −0.322512 0.558607i
\(160\) −2.21124e6 1.27666e6i −0.539855 0.311685i
\(161\) 1.06991e6 897759.i 0.256371 0.215121i
\(162\) 2.66307e6 + 3.17372e6i 0.626379 + 0.746489i
\(163\) −1.79161e6 + 3.10316e6i −0.413695 + 0.716541i −0.995290 0.0969373i \(-0.969095\pi\)
0.581595 + 0.813478i \(0.302429\pi\)
\(164\) 726942. 419700.i 0.164804 0.0951497i
\(165\) −3.39296e6 + 9.32209e6i −0.755314 + 2.07521i
\(166\) −5.48659e6 967434.i −1.19944 0.211494i
\(167\) 451614. 79631.8i 0.0969657 0.0170977i −0.124955 0.992162i \(-0.539879\pi\)
0.221920 + 0.975065i \(0.428767\pi\)
\(168\) 3.88137e6 1.41270e6i 0.818573 0.297936i
\(169\) −1.72029e6 1.44349e6i −0.356403 0.299058i
\(170\) 1.69229e6i 0.344451i
\(171\) 562895. + 891020.i 0.112574 + 0.178196i
\(172\) 1.70958e6 0.335974
\(173\) 216388. 257881.i 0.0417921 0.0498059i −0.744743 0.667351i \(-0.767428\pi\)
0.786536 + 0.617545i \(0.211873\pi\)
\(174\) −981650. 2.69706e6i −0.186341 0.511968i
\(175\) 103078. + 584582.i 0.0192331 + 0.109076i
\(176\) 1.07419e6 6.09204e6i 0.197035 1.11744i
\(177\) −1.11522e7 4.05906e6i −2.01113 0.731991i
\(178\) 653551. + 1.13198e6i 0.115883 + 0.200715i
\(179\) 2.66677e6 + 1.53966e6i 0.464972 + 0.268452i 0.714133 0.700010i \(-0.246821\pi\)
−0.249160 + 0.968462i \(0.580155\pi\)
\(180\) 305213. 256104.i 0.0523342 0.0439136i
\(181\) 2.97820e6 + 3.54929e6i 0.502249 + 0.598557i 0.956289 0.292425i \(-0.0944621\pi\)
−0.454040 + 0.890981i \(0.650018\pi\)
\(182\) 2.21862e6 3.84276e6i 0.368018 0.637425i
\(183\) −782360. + 451696.i −0.127660 + 0.0737043i
\(184\) −1.06575e6 + 2.92813e6i −0.171081 + 0.470042i
\(185\) 5.16055e6 + 909944.i 0.815044 + 0.143714i
\(186\) 990666. 174681.i 0.153953 0.0271461i
\(187\) −4.41284e6 + 1.60614e6i −0.674828 + 0.245617i
\(188\) −2.59164e6 2.17464e6i −0.390033 0.327276i
\(189\) 4.26696e6i 0.632024i
\(190\) 5.20043e6 3.28533e6i 0.758190 0.478981i
\(191\) −1.15825e7 −1.66228 −0.831139 0.556064i \(-0.812311\pi\)
−0.831139 + 0.556064i \(0.812311\pi\)
\(192\) −5.46705e6 + 6.51538e6i −0.772413 + 0.920526i
\(193\) 1.88150e6 + 5.16938e6i 0.261717 + 0.719062i 0.999052 + 0.0435345i \(0.0138618\pi\)
−0.737335 + 0.675528i \(0.763916\pi\)
\(194\) 371474. + 2.10673e6i 0.0508772 + 0.288539i
\(195\) 1.84087e6 1.04401e7i 0.248268 1.40799i
\(196\) 1.00486e6 + 365739.i 0.133456 + 0.0485739i
\(197\) 2.49358e6 + 4.31901e6i 0.326156 + 0.564919i 0.981746 0.190199i \(-0.0609132\pi\)
−0.655590 + 0.755117i \(0.727580\pi\)
\(198\) 2.21346e6 + 1.27794e6i 0.285152 + 0.164633i
\(199\) 5.01445e6 4.20763e6i 0.636303 0.533922i −0.266577 0.963814i \(-0.585893\pi\)
0.902881 + 0.429892i \(0.141448\pi\)
\(200\) −851281. 1.01452e6i −0.106410 0.126815i
\(201\) −2.57765e6 + 4.46463e6i −0.317421 + 0.549790i
\(202\) −1.11752e6 + 645203.i −0.135582 + 0.0782785i
\(203\) −1.23403e6 + 3.39047e6i −0.147516 + 0.405296i
\(204\) 1.06695e6 + 188133.i 0.125677 + 0.0221602i
\(205\) 5.73939e6 1.01201e6i 0.666199 0.117469i
\(206\) 1.27416e7 4.63756e6i 1.45755 0.530503i
\(207\) −658569. 552605.i −0.0742489 0.0623022i
\(208\) 6.61054e6i 0.734593i
\(209\) −1.35026e7 1.04426e7i −1.47903 1.14385i
\(210\) 6.65111e6 0.718185
\(211\) 1.75472e6 2.09120e6i 0.186793 0.222612i −0.664518 0.747272i \(-0.731363\pi\)
0.851312 + 0.524660i \(0.175808\pi\)
\(212\) −576832. 1.58483e6i −0.0605399 0.166332i
\(213\) 2.16132e6 + 1.22574e7i 0.223656 + 1.26841i
\(214\) −542941. + 3.07917e6i −0.0554002 + 0.314190i
\(215\) 1.11538e7 + 4.05964e6i 1.12229 + 0.408481i
\(216\) 4.75993e6 + 8.24445e6i 0.472324 + 0.818088i
\(217\) −1.09516e6 632288.i −0.107176 0.0618780i
\(218\) −1.06023e7 + 8.89638e6i −1.02336 + 0.858705i
\(219\) −3.32773e6 3.96583e6i −0.316822 0.377574i
\(220\) −3.22647e6 + 5.58842e6i −0.303012 + 0.524833i
\(221\) 4.34599e6 2.50916e6i 0.402635 0.232461i
\(222\) 2.65248e6 7.28762e6i 0.242433 0.666080i
\(223\) 1.47756e7 + 2.60533e6i 1.33238 + 0.234935i 0.794079 0.607815i \(-0.207954\pi\)
0.538305 + 0.842750i \(0.319065\pi\)
\(224\) 4.67823e6 824899.i 0.416234 0.0733934i
\(225\) 343348. 124968.i 0.0301430 0.0109712i
\(226\) −7.77097e6 6.52062e6i −0.673209 0.564890i
\(227\) 5.87131e6i 0.501947i 0.967994 + 0.250973i \(0.0807506\pi\)
−0.967994 + 0.250973i \(0.919249\pi\)
\(228\) 1.49320e6 + 3.64400e6i 0.125984 + 0.307449i
\(229\) −1.00509e7 −0.836950 −0.418475 0.908228i \(-0.637435\pi\)
−0.418475 + 0.908228i \(0.637435\pi\)
\(230\) −3.22527e6 + 3.84373e6i −0.265084 + 0.315914i
\(231\) −6.31253e6 1.73435e7i −0.512115 1.40703i
\(232\) −1.39784e6 7.92752e6i −0.111942 0.634853i
\(233\) −4.21735e6 + 2.39178e7i −0.333405 + 1.89083i 0.109042 + 0.994037i \(0.465222\pi\)
−0.442447 + 0.896795i \(0.645889\pi\)
\(234\) −2.56657e6 934156.i −0.200312 0.0729074i
\(235\) −1.17445e7 2.03421e7i −0.904965 1.56745i
\(236\) −6.68552e6 3.85989e6i −0.508627 0.293656i
\(237\) 8.44474e6 7.08597e6i 0.634368 0.532298i
\(238\) 2.02379e6 + 2.41186e6i 0.150119 + 0.178905i
\(239\) 99152.3 171737.i 0.00726288 0.0125797i −0.862371 0.506277i \(-0.831021\pi\)
0.869634 + 0.493697i \(0.164355\pi\)
\(240\) −8.58122e6 + 4.95437e6i −0.620748 + 0.358389i
\(241\) 4.08271e6 1.12172e7i 0.291674 0.801368i −0.704148 0.710053i \(-0.748671\pi\)
0.995822 0.0913146i \(-0.0291069\pi\)
\(242\) −2.91054e7 5.13206e6i −2.05365 0.362114i
\(243\) −5.86395e6 + 1.03397e6i −0.408669 + 0.0720593i
\(244\) −552195. + 200983.i −0.0380122 + 0.0138353i
\(245\) 5.68746e6 + 4.77235e6i 0.386741 + 0.324514i
\(246\) 8.62520e6i 0.579380i
\(247\) 1.61478e7 + 8.48412e6i 1.07157 + 0.563010i
\(248\) 2.82135e6 0.184970
\(249\) 1.59178e7 1.89701e7i 1.03106 1.22877i
\(250\) 4.06325e6 + 1.11637e7i 0.260048 + 0.714477i
\(251\) −1.81765e6 1.03084e7i −0.114945 0.651884i −0.986778 0.162080i \(-0.948180\pi\)
0.871833 0.489803i \(-0.162931\pi\)
\(252\) −128719. + 730003.i −0.00804344 + 0.0456166i
\(253\) 1.30841e7 + 4.76221e6i 0.807943 + 0.294067i
\(254\) −7.91930e6 1.37166e7i −0.483265 0.837040i
\(255\) 6.51433e6 + 3.76105e6i 0.392870 + 0.226824i
\(256\) −1.04740e7 + 8.78872e6i −0.624299 + 0.523849i
\(257\) −1.17306e6 1.39800e6i −0.0691069 0.0823583i 0.730383 0.683037i \(-0.239341\pi\)
−0.799490 + 0.600679i \(0.794897\pi\)
\(258\) 8.78336e6 1.52132e7i 0.511448 0.885854i
\(259\) −8.44306e6 + 4.87460e6i −0.485960 + 0.280569i
\(260\) 2.35850e6 6.47992e6i 0.134189 0.368680i
\(261\) 2.18716e6 + 385655.i 0.123015 + 0.0216909i
\(262\) −1.67893e7 + 2.96040e6i −0.933530 + 0.164607i
\(263\) −9.11244e6 + 3.31666e6i −0.500919 + 0.182320i −0.580107 0.814540i \(-0.696989\pi\)
0.0791884 + 0.996860i \(0.474767\pi\)
\(264\) 3.15441e7 + 2.64686e7i 1.71438 + 1.43853i
\(265\) 1.17096e7i 0.629224i
\(266\) −3.48279e6 + 1.09014e7i −0.185047 + 0.579213i
\(267\) −5.80998e6 −0.305239
\(268\) −2.15552e6 + 2.56885e6i −0.111982 + 0.133455i
\(269\) −1.47789e6 4.06046e6i −0.0759249 0.208602i 0.895924 0.444208i \(-0.146515\pi\)
−0.971849 + 0.235606i \(0.924293\pi\)
\(270\) 2.66192e6 + 1.50965e7i 0.135240 + 0.766983i
\(271\) −2.82339e6 + 1.60122e7i −0.141861 + 0.804532i 0.827974 + 0.560767i \(0.189494\pi\)
−0.969834 + 0.243765i \(0.921617\pi\)
\(272\) −4.40766e6 1.60426e6i −0.219029 0.0797201i
\(273\) 9.86161e6 + 1.70808e7i 0.484685 + 0.839500i
\(274\) 1.84967e7 + 1.06791e7i 0.899170 + 0.519136i
\(275\) −4.53327e6 + 3.80387e6i −0.217979 + 0.182906i
\(276\) −2.06484e6 2.46078e6i −0.0982107 0.117043i
\(277\) 2.24294e6 3.88488e6i 0.105530 0.182784i −0.808424 0.588600i \(-0.799679\pi\)
0.913955 + 0.405816i \(0.133013\pi\)
\(278\) 6.97525e6 4.02716e6i 0.324657 0.187441i
\(279\) −266227. + 731452.i −0.0122585 + 0.0336801i
\(280\) 1.83707e7 + 3.23926e6i 0.836860 + 0.147561i
\(281\) 1.69374e6 298653.i 0.0763359 0.0134601i −0.135350 0.990798i \(-0.543216\pi\)
0.211686 + 0.977338i \(0.432105\pi\)
\(282\) −3.26668e7 + 1.18897e7i −1.45666 + 0.530182i
\(283\) −1.05317e7 8.83712e6i −0.464663 0.389898i 0.380181 0.924912i \(-0.375862\pi\)
−0.844843 + 0.535014i \(0.820306\pi\)
\(284\) 8.09616e6i 0.353447i
\(285\) 1.08886e6 + 2.73202e7i 0.0470370 + 1.18018i
\(286\) 4.42361e7 1.89095
\(287\) −6.96957e6 + 8.30601e6i −0.294822 + 0.351355i
\(288\) −1.00009e6 2.74771e6i −0.0418658 0.115025i
\(289\) −3.57312e6 2.02642e7i −0.148032 0.839529i
\(290\) 2.25087e6 1.27653e7i 0.0922905 0.523405i
\(291\) −8.93530e6 3.25218e6i −0.362602 0.131976i
\(292\) −1.68376e6 2.91636e6i −0.0676289 0.117137i
\(293\) 6.94124e6 + 4.00753e6i 0.275953 + 0.159321i 0.631590 0.775303i \(-0.282403\pi\)
−0.355637 + 0.934624i \(0.615736\pi\)
\(294\) 8.41731e6 7.06296e6i 0.331231 0.277936i
\(295\) −3.44522e7 4.10585e7i −1.34200 1.59933i
\(296\) 1.08755e7 1.88370e7i 0.419349 0.726334i
\(297\) 3.68395e7 2.12693e7i 1.40619 0.811865i
\(298\) 1.02061e7 2.80411e7i 0.385667 1.05961i
\(299\) −1.46533e7 2.58376e6i −0.548177 0.0966583i
\(300\) 1.34453e6 237078.i 0.0497975 0.00878065i
\(301\) −2.07513e7 + 7.55286e6i −0.760933 + 0.276957i
\(302\) 1.84921e7 + 1.55167e7i 0.671376 + 0.563352i
\(303\) 5.73577e6i 0.206188i
\(304\) −3.62693e6 1.66593e7i −0.129098 0.592973i
\(305\) −4.07992e6 −0.143798
\(306\) 1.24572e6 1.48459e6i 0.0434767 0.0518135i
\(307\) 1.44754e7 + 3.97709e7i 0.500283 + 1.37452i 0.890999 + 0.454006i \(0.150005\pi\)
−0.390715 + 0.920512i \(0.627772\pi\)
\(308\) −2.08474e6 1.18232e7i −0.0713511 0.404652i
\(309\) −1.04658e7 + 5.93546e7i −0.354730 + 2.01177i
\(310\) 4.26911e6 + 1.55383e6i 0.143302 + 0.0521577i
\(311\) 7.15798e6 + 1.23980e7i 0.237963 + 0.412164i 0.960130 0.279555i \(-0.0901870\pi\)
−0.722167 + 0.691719i \(0.756854\pi\)
\(312\) −3.81084e7 2.20019e7i −1.25475 0.724429i
\(313\) −1.00053e7 + 8.39543e6i −0.326285 + 0.273785i −0.791184 0.611578i \(-0.790535\pi\)
0.464899 + 0.885364i \(0.346091\pi\)
\(314\) −2.84649e7 3.39232e7i −0.919435 1.09574i
\(315\) −2.57329e6 + 4.45706e6i −0.0823297 + 0.142599i
\(316\) 6.21003e6 3.58536e6i 0.196803 0.113624i
\(317\) 18082.7 49681.7i 0.000567655 0.00155962i −0.939408 0.342800i \(-0.888625\pi\)
0.939976 + 0.341240i \(0.110847\pi\)
\(318\) −1.70667e7 3.00932e6i −0.530723 0.0935808i
\(319\) −3.54234e7 + 6.24610e6i −1.09123 + 0.192414i
\(320\) −3.60950e7 + 1.31375e7i −1.10153 + 0.400925i
\(321\) −1.06464e7 8.93337e6i −0.321874 0.270085i
\(322\) 9.33519e6i 0.279612i
\(323\) −9.57567e6 + 8.70780e6i −0.284159 + 0.258405i
\(324\) −1.19787e7 −0.352189
\(325\) 4.06491e6 4.84438e6i 0.118414 0.141120i
\(326\) 8.19135e6 + 2.25056e7i 0.236430 + 0.649586i
\(327\) −1.06827e7 6.05846e7i −0.305519 1.73268i
\(328\) 4.20069e6 2.38233e7i 0.119042 0.675119i
\(329\) 4.10654e7 + 1.49466e7i 1.15316 + 0.419714i
\(330\) 3.31534e7 + 5.74234e7i 0.922543 + 1.59789i
\(331\) 2.64732e7 + 1.52843e7i 0.729998 + 0.421465i 0.818421 0.574618i \(-0.194850\pi\)
−0.0884235 + 0.996083i \(0.528183\pi\)
\(332\) 1.23396e7 1.03541e7i 0.337199 0.282944i
\(333\) 3.85737e6 + 4.59703e6i 0.104462 + 0.124493i
\(334\) 1.53256e6 2.65447e6i 0.0411318 0.0712423i
\(335\) −2.01633e7 + 1.16413e7i −0.536323 + 0.309646i
\(336\) 6.30514e6 1.73232e7i 0.166217 0.456679i
\(337\) 5.53638e7 + 9.76214e6i 1.44656 + 0.255068i 0.841131 0.540832i \(-0.181890\pi\)
0.605429 + 0.795899i \(0.293002\pi\)
\(338\) −1.47819e7 + 2.60645e6i −0.382807 + 0.0674992i
\(339\) 4.23713e7 1.54219e7i 1.08761 0.395858i
\(340\) 3.74821e6 + 3.14512e6i 0.0953645 + 0.0800203i
\(341\) 1.26069e7i 0.317941i
\(342\) 6.98056e6 + 945998.i 0.174507 + 0.0236490i
\(343\) −4.31817e7 −1.07008
\(344\) 3.16693e7 3.77421e7i 0.777972 0.927151i
\(345\) −7.62808e6 2.09580e7i −0.185763 0.510378i
\(346\) −390721. 2.21589e6i −0.00943274 0.0534958i
\(347\) 1.58734e6 9.00223e6i 0.0379910 0.215458i −0.959902 0.280335i \(-0.909554\pi\)
0.997893 + 0.0648773i \(0.0206656\pi\)
\(348\) 7.79806e6 + 2.83826e6i 0.185033 + 0.0673464i
\(349\) 4.16941e6 + 7.22163e6i 0.0980840 + 0.169886i 0.910892 0.412646i \(-0.135395\pi\)
−0.812808 + 0.582532i \(0.802062\pi\)
\(350\) 3.43602e6 + 1.98378e6i 0.0801403 + 0.0462690i
\(351\) −3.48228e7 + 2.92198e7i −0.805271 + 0.675702i
\(352\) 3.04412e7 + 3.62785e7i 0.697966 + 0.831804i
\(353\) 704623. 1.22044e6i 0.0160189 0.0277455i −0.857905 0.513809i \(-0.828234\pi\)
0.873924 + 0.486063i \(0.161567\pi\)
\(354\) −6.86966e7 + 3.96620e7i −1.54855 + 0.894056i
\(355\) −1.92254e7 + 5.28214e7i −0.429725 + 1.18066i
\(356\) −3.72183e6 656259.i −0.0824910 0.0145454i
\(357\) −1.37821e7 + 2.43015e6i −0.302908 + 0.0534108i
\(358\) 1.93407e7 7.03944e6i 0.421525 0.153422i
\(359\) 3.07037e7 + 2.57635e7i 0.663602 + 0.556828i 0.911164 0.412044i \(-0.135185\pi\)
−0.247562 + 0.968872i \(0.579629\pi\)
\(360\) 1.14823e7i 0.246106i
\(361\) −4.53490e7 1.25213e7i −0.963932 0.266150i
\(362\) 3.09683e7 0.652818
\(363\) 8.44411e7 1.00633e8i 1.76536 2.10388i
\(364\) 4.38794e6 + 1.20558e7i 0.0909821 + 0.249971i
\(365\) −4.06000e6 2.30254e7i −0.0834925 0.473509i
\(366\) −1.04852e6 + 5.94646e6i −0.0213862 + 0.121287i
\(367\) 5.30849e7 + 1.93213e7i 1.07392 + 0.390876i 0.817642 0.575727i \(-0.195281\pi\)
0.256280 + 0.966603i \(0.417503\pi\)
\(368\) 6.95372e6 + 1.20442e7i 0.139532 + 0.241677i
\(369\) 5.77995e6 + 3.33705e6i 0.115039 + 0.0664177i
\(370\) 2.68305e7 2.25135e7i 0.529693 0.444465i
\(371\) 1.40034e7 + 1.66887e7i 0.274229 + 0.326813i
\(372\) −1.45426e6 + 2.51885e6i −0.0282496 + 0.0489298i
\(373\) −4.64810e7 + 2.68358e7i −0.895673 + 0.517117i −0.875794 0.482685i \(-0.839661\pi\)
−0.0198790 + 0.999802i \(0.506328\pi\)
\(374\) −1.07353e7 + 2.94950e7i −0.205210 + 0.563811i
\(375\) −5.20043e7 9.16975e6i −0.986155 0.173886i
\(376\) −9.60181e7 + 1.69306e7i −1.80630 + 0.318499i
\(377\) 3.61202e7 1.31467e7i 0.674103 0.245353i
\(378\) −2.18476e7 1.83323e7i −0.404509 0.339424i
\(379\) 4.69714e7i 0.862812i 0.902158 + 0.431406i \(0.141982\pi\)
−0.902158 + 0.431406i \(0.858018\pi\)
\(380\) −2.38840e6 + 1.76241e7i −0.0435267 + 0.321186i
\(381\) 7.04015e7 1.27294
\(382\) −4.97625e7 + 5.93046e7i −0.892714 + 1.06389i
\(383\) −1.73125e7 4.75658e7i −0.308152 0.846640i −0.993017 0.117970i \(-0.962361\pi\)
0.684865 0.728670i \(-0.259861\pi\)
\(384\) 3.58838e6 + 2.03507e7i 0.0633731 + 0.359407i
\(385\) 1.44743e7 8.20879e7i 0.253639 1.43846i
\(386\) 3.45517e7 + 1.25758e7i 0.600768 + 0.218662i
\(387\) 6.79649e6 + 1.17719e7i 0.117261 + 0.203101i
\(388\) −5.35654e6 3.09260e6i −0.0917043 0.0529455i
\(389\) −7.52620e7 + 6.31523e7i −1.27858 + 1.07285i −0.285139 + 0.958486i \(0.592040\pi\)
−0.993438 + 0.114368i \(0.963516\pi\)
\(390\) −4.55462e7 5.42798e7i −0.767817 0.915049i
\(391\) 5.27884e6 9.14321e6i 0.0883096 0.152957i
\(392\) 2.66889e7 1.54089e7i 0.443071 0.255807i
\(393\) 2.59178e7 7.12085e7i 0.426992 1.17315i
\(394\) 3.28274e7 + 5.78835e6i 0.536720 + 0.0946382i
\(395\) 4.90297e7 8.64526e6i 0.795551 0.140277i
\(396\) −6.94422e6 + 2.52749e6i −0.111825 + 0.0407009i
\(397\) −7.56270e6 6.34586e6i −0.120866 0.101419i 0.580351 0.814366i \(-0.302915\pi\)
−0.701217 + 0.712947i \(0.747360\pi\)
\(398\) 4.37522e7i 0.693987i
\(399\) −3.42238e7 3.76348e7i −0.538778 0.592476i
\(400\) −5.91083e6 −0.0923568
\(401\) −7.50709e6 + 8.94660e6i −0.116423 + 0.138747i −0.821108 0.570773i \(-0.806644\pi\)
0.704685 + 0.709520i \(0.251088\pi\)
\(402\) 1.17852e7 + 3.23796e7i 0.181409 + 0.498417i
\(403\) 2.33941e6 + 1.32674e7i 0.0357430 + 0.202708i
\(404\) 647877. 3.67429e6i 0.00982536 0.0557224i
\(405\) −7.81522e7 2.84451e7i −1.17646 0.428196i
\(406\) 1.20580e7 + 2.08851e7i 0.180176 + 0.312074i
\(407\) −8.41713e7 4.85963e7i −1.24848 0.720809i
\(408\) 2.39182e7 2.00698e7i 0.352167 0.295503i
\(409\) −4.57586e7 5.45330e7i −0.668810 0.797057i 0.319811 0.947481i \(-0.396380\pi\)
−0.988622 + 0.150424i \(0.951936\pi\)
\(410\) 1.94767e7 3.37346e7i 0.282594 0.489467i
\(411\) −8.22164e7 + 4.74677e7i −1.18422 + 0.683711i
\(412\) −1.34087e7 + 3.68400e7i −0.191732 + 0.526779i
\(413\) 9.82031e7 + 1.73159e7i 1.39404 + 0.245807i
\(414\) −5.65887e6 + 997811.i −0.0797496 + 0.0140620i
\(415\) 1.05094e8 3.82511e7i 1.47039 0.535179i
\(416\) −3.87681e7 3.25303e7i −0.538511 0.451865i
\(417\) 3.58009e7i 0.493726i
\(418\) −1.11480e8 + 2.42705e7i −1.52639 + 0.332315i
\(419\) 1.31690e8 1.79024 0.895120 0.445825i \(-0.147090\pi\)
0.895120 + 0.445825i \(0.147090\pi\)
\(420\) −1.23611e7 + 1.47314e7i −0.166844 + 0.198836i
\(421\) −1.38998e7 3.81895e7i −0.186279 0.511797i 0.811039 0.584992i \(-0.198902\pi\)
−0.997318 + 0.0731956i \(0.976680\pi\)
\(422\) −3.16842e6 1.79690e7i −0.0421604 0.239104i
\(423\) 4.67105e6 2.64909e7i 0.0617154 0.350006i
\(424\) −4.56736e7 1.66238e7i −0.599194 0.218089i
\(425\) 2.24357e6 + 3.88598e6i 0.0292262 + 0.0506213i
\(426\) 7.20460e7 + 4.15958e7i 0.931925 + 0.538047i
\(427\) 5.81474e6 4.87915e6i 0.0746873 0.0626701i
\(428\) −5.81093e6 6.92520e6i −0.0741164 0.0883285i
\(429\) −9.83133e7 + 1.70284e8i −1.24520 + 2.15676i
\(430\) 6.87063e7 3.96676e7i 0.864155 0.498920i
\(431\) −3.50302e7 + 9.62446e7i −0.437533 + 1.20211i 0.503559 + 0.863961i \(0.332023\pi\)
−0.941092 + 0.338150i \(0.890199\pi\)
\(432\) 4.18433e7 + 7.37810e6i 0.519008 + 0.0915152i
\(433\) −2.24977e7 + 3.96696e6i −0.277125 + 0.0488646i −0.310483 0.950579i \(-0.600491\pi\)
0.0333584 + 0.999443i \(0.489380\pi\)
\(434\) −7.94258e6 + 2.89086e6i −0.0971611 + 0.0353638i
\(435\) 4.41367e7 + 3.70351e7i 0.536206 + 0.449930i
\(436\) 4.00167e7i 0.482817i
\(437\) 3.83453e7 1.52828e6i 0.459482 0.0183130i
\(438\) −3.46028e7 −0.411802
\(439\) 8.39969e7 1.00104e8i 0.992818 1.18319i 0.00975007 0.999952i \(-0.496896\pi\)
0.983068 0.183242i \(-0.0586591\pi\)
\(440\) 6.36050e7 + 1.74753e8i 0.746677 + 2.05148i
\(441\) 1.47643e6 + 8.37327e6i 0.0172146 + 0.0976291i
\(442\) 5.82450e6 3.30324e7i 0.0674516 0.382537i
\(443\) 2.09923e7 + 7.64059e6i 0.241463 + 0.0878852i 0.459917 0.887962i \(-0.347879\pi\)
−0.218454 + 0.975847i \(0.570101\pi\)
\(444\) 1.12115e7 + 1.94190e7i 0.128090 + 0.221859i
\(445\) −2.27238e7 1.31196e7i −0.257870 0.148881i
\(446\) 7.68205e7 6.44600e7i 0.865909 0.726584i
\(447\) 8.52593e7 + 1.01608e8i 0.954595 + 1.13764i
\(448\) 3.57319e7 6.18894e7i 0.397394 0.688307i
\(449\) 7.74735e7 4.47293e7i 0.855882 0.494144i −0.00674905 0.999977i \(-0.502148\pi\)
0.862631 + 0.505833i \(0.168815\pi\)
\(450\) 835278. 2.29491e6i 0.00916629 0.0251842i
\(451\) −1.06452e8 1.87704e7i −1.16044 0.204618i
\(452\) 2.88847e7 5.09316e6i 0.312790 0.0551534i
\(453\) −1.00829e8 + 3.66986e7i −1.08465 + 0.394780i
\(454\) 3.00621e7 + 2.52251e7i 0.321257 + 0.269566i
\(455\) 8.90745e7i 0.945626i
\(456\) 1.08109e8 + 3.45385e7i 1.14016 + 0.364258i
\(457\) −7.79912e7 −0.817141 −0.408571 0.912727i \(-0.633973\pi\)
−0.408571 + 0.912727i \(0.633973\pi\)
\(458\) −4.31821e7 + 5.14625e7i −0.449477 + 0.535666i
\(459\) −1.10318e7 3.03096e7i −0.114080 0.313431i
\(460\) −2.51921e6 1.42872e7i −0.0258816 0.146782i
\(461\) −1.12336e7 + 6.37088e7i −0.114661 + 0.650275i 0.872257 + 0.489049i \(0.162656\pi\)
−0.986917 + 0.161226i \(0.948455\pi\)
\(462\) −1.15923e8 4.21924e7i −1.17555 0.427867i
\(463\) −3.35533e7 5.81161e7i −0.338059 0.585536i 0.646008 0.763330i \(-0.276437\pi\)
−0.984068 + 0.177794i \(0.943104\pi\)
\(464\) −3.11143e7 1.79638e7i −0.311463 0.179823i
\(465\) −1.54693e7 + 1.29803e7i −0.153855 + 0.129100i
\(466\) 1.04344e8 + 1.24352e8i 1.03112 + 1.22884i
\(467\) 4.15085e7 7.18949e7i 0.407555 0.705907i −0.587060 0.809544i \(-0.699715\pi\)
0.994615 + 0.103637i \(0.0330480\pi\)
\(468\) 6.83902e6 3.94851e6i 0.0667201 0.0385208i
\(469\) 1.48152e7 4.07043e7i 0.143611 0.394568i
\(470\) −1.54614e8 2.72625e7i −1.48920 0.262587i
\(471\) 1.93847e8 3.41804e7i 1.85522 0.327126i
\(472\) −2.09060e8 + 7.60917e7i −1.98813 + 0.723621i
\(473\) −1.68647e8 1.41511e8i −1.59366 1.33724i
\(474\) 7.36823e7i 0.691875i
\(475\) −7.58610e6 + 1.44386e7i −0.0707844 + 0.134724i
\(476\) −9.10320e6 −0.0844060
\(477\) 8.61965e6 1.02725e7i 0.0794208 0.0946501i
\(478\) −453331. 1.24552e6i −0.00415080 0.0114042i
\(479\) 887465. + 5.03306e6i 0.00807504 + 0.0457958i 0.988579 0.150703i \(-0.0481538\pi\)
−0.980504 + 0.196499i \(0.937043\pi\)
\(480\) 1.31726e7 7.47056e7i 0.119110 0.675507i
\(481\) 9.75989e7 + 3.55231e7i 0.877021 + 0.319209i
\(482\) −3.98931e7 6.90969e7i −0.356252 0.617046i
\(483\) 3.59351e7 + 2.07471e7i 0.318917 + 0.184127i
\(484\) 6.54593e7 5.49268e7i 0.577344 0.484450i
\(485\) −2.76037e7 3.28968e7i −0.241959 0.288355i
\(486\) −1.98994e7 + 3.44667e7i −0.173353 + 0.300256i
\(487\) 3.93343e7 2.27097e7i 0.340553 0.196618i −0.319964 0.947430i \(-0.603671\pi\)
0.660516 + 0.750812i \(0.270337\pi\)
\(488\) −5.79215e6 + 1.59138e7i −0.0498403 + 0.136935i
\(489\) −1.04838e8 1.84858e7i −0.896590 0.158093i
\(490\) 4.88705e7 8.61718e6i 0.415392 0.0732449i
\(491\) 2.81580e7 1.02487e7i 0.237880 0.0865812i −0.220329 0.975426i \(-0.570713\pi\)
0.458209 + 0.888844i \(0.348491\pi\)
\(492\) 1.91038e7 + 1.60300e7i 0.160407 + 0.134597i
\(493\) 2.72741e7i 0.227619i
\(494\) 1.12817e8 4.62288e7i 0.935819 0.383471i
\(495\) −5.13077e7 −0.423026
\(496\) 8.09408e6 9.64615e6i 0.0663319 0.0790513i
\(497\) −3.57684e7 9.82730e7i −0.291361 0.800507i
\(498\) −2.87420e7 1.63004e8i −0.232718 1.31981i
\(499\) −2.31560e7 + 1.31324e8i −0.186364 + 1.05692i 0.737827 + 0.674990i \(0.235852\pi\)
−0.924191 + 0.381931i \(0.875259\pi\)
\(500\) −3.22778e7 1.17482e7i −0.258222 0.0939853i
\(501\) 6.81212e6 + 1.17989e7i 0.0541712 + 0.0938274i
\(502\) −6.05900e7 3.49817e7i −0.478950 0.276522i
\(503\) −8.30635e7 + 6.96985e7i −0.652689 + 0.547671i −0.907885 0.419218i \(-0.862304\pi\)
0.255197 + 0.966889i \(0.417860\pi\)
\(504\) 1.37316e7 + 1.63647e7i 0.107258 + 0.127825i
\(505\) 1.29520e7 2.24335e7i 0.100569 0.174190i
\(506\) 8.05968e7 4.65326e7i 0.622109 0.359175i
\(507\) 2.28189e7 6.26945e7i 0.175094 0.481067i
\(508\) 4.50987e7 + 7.95211e6i 0.344011 + 0.0606585i
\(509\) −1.92061e8 + 3.38655e7i −1.45641 + 0.256805i −0.845111 0.534592i \(-0.820465\pi\)
−0.611303 + 0.791397i \(0.709354\pi\)
\(510\) 4.72450e7 1.71958e7i 0.356160 0.129632i
\(511\) 3.33222e7 + 2.79607e7i 0.249730 + 0.209549i
\(512\) 1.35904e8i 1.01256i
\(513\) 7.17253e7 9.27427e7i 0.531276 0.686954i
\(514\) −1.21979e7 −0.0898244
\(515\) −1.74963e8 + 2.08513e8i −1.28093 + 1.52655i
\(516\) 1.73715e7 + 4.77279e7i 0.126441 + 0.347395i
\(517\) 7.56527e7 + 4.29048e8i 0.547460 + 3.10480i
\(518\) −1.13154e7 + 6.41728e7i −0.0814106 + 0.461702i
\(519\) 9.39825e6 + 3.42068e6i 0.0672272 + 0.0244687i
\(520\) −9.93654e7 1.72106e8i −0.706684 1.22401i
\(521\) 8.12073e7 + 4.68851e7i 0.574225 + 0.331529i 0.758835 0.651283i \(-0.225769\pi\)
−0.184610 + 0.982812i \(0.559102\pi\)
\(522\) 1.13714e7 9.54173e6i 0.0799470 0.0670835i
\(523\) −3.56664e7 4.25056e7i −0.249318 0.297126i 0.626841 0.779147i \(-0.284347\pi\)
−0.876160 + 0.482021i \(0.839903\pi\)
\(524\) 2.46460e7 4.26881e7i 0.171298 0.296697i
\(525\) −1.52729e7 + 8.81779e6i −0.105546 + 0.0609371i
\(526\) −2.21682e7 + 6.09067e7i −0.152326 + 0.418512i
\(527\) −9.41396e6 1.65994e6i −0.0643192 0.0113412i
\(528\) 1.80992e8 3.19137e7i 1.22958 0.216808i
\(529\) 1.09693e8 3.99248e7i 0.740986 0.269697i
\(530\) −5.99553e7 5.03085e7i −0.402717 0.337920i
\(531\) 6.13803e7i 0.409963i
\(532\) −1.76726e7 2.79743e7i −0.117372 0.185791i
\(533\) 1.15512e8 0.762864
\(534\) −2.49616e7 + 2.97481e7i −0.163926 + 0.195360i
\(535\) −2.14672e7 5.89806e7i −0.140189 0.385166i
\(536\) 1.67817e7 + 9.51739e7i 0.108979 + 0.618050i
\(537\) −1.58863e7 + 9.00954e7i −0.102588 + 0.581808i
\(538\) −2.71398e7 9.87807e6i −0.174285 0.0634345i
\(539\) −6.88530e7 1.19257e8i −0.439700 0.761583i
\(540\) −3.83841e7 2.21611e7i −0.243764 0.140737i
\(541\) 1.01839e8 8.54527e7i 0.643162 0.539677i −0.261826 0.965115i \(-0.584325\pi\)
0.904987 + 0.425438i \(0.139880\pi\)
\(542\) 6.98551e7 + 8.32501e7i 0.438733 + 0.522862i
\(543\) −6.88261e7 + 1.19210e8i −0.429886 + 0.744585i
\(544\) 3.10983e7 1.79546e7i 0.193170 0.111527i
\(545\) 9.50251e7 2.61079e8i 0.587015 1.61281i
\(546\) 1.29826e8 + 2.28917e7i 0.797595 + 0.140637i
\(547\) 2.93937e8 5.18290e7i 1.79594 0.316673i 0.826674 0.562681i \(-0.190230\pi\)
0.969268 + 0.246008i \(0.0791190\pi\)
\(548\) −5.80289e7 + 2.11208e7i −0.352616 + 0.128342i
\(549\) −3.57919e6 3.00330e6i −0.0216306 0.0181502i
\(550\) 3.95538e7i 0.237739i
\(551\) −8.38137e7 + 5.29487e7i −0.501026 + 0.316519i
\(552\) −9.25763e7 −0.550405
\(553\) −5.95388e7 + 7.09555e7i −0.352066 + 0.419576i
\(554\) −1.02549e7 2.81750e7i −0.0603115 0.165705i
\(555\) 2.70340e7 + 1.53318e8i 0.158136 + 0.896836i
\(556\) −4.04385e6 + 2.29338e7i −0.0235272 + 0.133430i
\(557\) −2.02884e8 7.38436e7i −1.17404 0.427314i −0.319944 0.947436i \(-0.603664\pi\)
−0.854092 + 0.520122i \(0.825886\pi\)
\(558\) 2.60136e6 + 4.50569e6i 0.0149726 + 0.0259334i
\(559\) 2.03742e8 + 1.17631e8i 1.16639 + 0.673418i
\(560\) 6.37782e7 5.35163e7i 0.363169 0.304735i
\(561\) −8.96799e7 1.06876e8i −0.507933 0.605331i
\(562\) 5.74774e6 9.95538e6i 0.0323808 0.0560853i
\(563\) −2.05409e7 + 1.18593e7i −0.115105 + 0.0664558i −0.556447 0.830883i \(-0.687836\pi\)
0.441342 + 0.897339i \(0.354502\pi\)
\(564\) 3.43770e7 9.44500e7i 0.191615 0.526459i
\(565\) 2.00546e8 + 3.53616e7i 1.11191 + 0.196059i
\(566\) −9.04951e7 + 1.59567e7i −0.499087 + 0.0880025i
\(567\) 1.45400e8 5.29214e7i 0.797658 0.290324i
\(568\) 1.78737e8 + 1.49978e8i 0.975369 + 0.818432i
\(569\) 1.14242e8i 0.620137i −0.950714 0.310068i \(-0.899648\pi\)
0.950714 0.310068i \(-0.100352\pi\)
\(570\) 1.44562e8 + 1.11801e8i 0.780603 + 0.603703i
\(571\) −2.84122e8 −1.52615 −0.763074 0.646311i \(-0.776311\pi\)
−0.763074 + 0.646311i \(0.776311\pi\)
\(572\) −8.22130e7 + 9.79776e7i −0.439291 + 0.523526i
\(573\) −1.17693e8 3.23359e8i −0.625587 1.71879i
\(574\) 1.25846e7 + 7.13708e7i 0.0665432 + 0.377385i
\(575\) 2.31028e6 1.31022e7i 0.0121524 0.0689195i
\(576\) −4.13358e7 1.50450e7i −0.216301 0.0787272i
\(577\) −1.40463e8 2.43289e8i −0.731198 1.26647i −0.956371 0.292154i \(-0.905628\pi\)
0.225173 0.974319i \(-0.427705\pi\)
\(578\) −1.19108e8 6.87668e7i −0.616816 0.356119i
\(579\) −1.25199e8 + 1.05055e8i −0.645010 + 0.541228i
\(580\) 2.40904e7 + 2.87098e7i 0.123470 + 0.147145i
\(581\) −1.04037e8 + 1.80197e8i −0.530467 + 0.918795i
\(582\) −5.50408e7 + 3.17778e7i −0.279200 + 0.161196i
\(583\) −7.42819e7 + 2.04088e8i −0.374867 + 1.02994i
\(584\) −9.55748e7 1.68524e7i −0.479849 0.0846104i
\(585\) 5.39958e7 9.52091e6i 0.269707 0.0475566i
\(586\) 5.03412e7 1.83227e7i 0.250167 0.0910534i
\(587\) 6.83785e7 + 5.73764e7i 0.338069 + 0.283674i 0.795978 0.605325i \(-0.206957\pi\)
−0.457909 + 0.888999i \(0.651401\pi\)
\(588\) 3.17698e7i 0.156273i
\(589\) −1.31748e7 3.21518e7i −0.0644762 0.157347i
\(590\) −3.58245e8 −1.74431
\(591\) −9.52396e7 + 1.13502e8i −0.461376 + 0.549846i
\(592\) −3.32029e7 9.12241e7i −0.160033 0.439688i
\(593\) −2.21638e7 1.25697e8i −0.106287 0.602782i −0.990699 0.136075i \(-0.956551\pi\)
0.884412 0.466707i \(-0.154560\pi\)
\(594\) 4.93724e7 2.80005e8i 0.235573 1.33600i
\(595\) −5.93916e7 2.16168e7i −0.281951 0.102622i
\(596\) 4.31395e7 + 7.47197e7i 0.203768 + 0.352937i
\(597\) 1.68421e8 + 9.72379e7i 0.791540 + 0.456996i
\(598\) −7.61846e7 + 6.39265e7i −0.356257 + 0.298935i
\(599\) −1.57592e7 1.87811e7i −0.0733254 0.0873858i 0.728135 0.685434i \(-0.240388\pi\)
−0.801460 + 0.598048i \(0.795943\pi\)
\(600\) 1.96730e7 3.40747e7i 0.0910789 0.157753i
\(601\) 3.29387e7 1.90172e7i 0.151734 0.0876038i −0.422211 0.906498i \(-0.638746\pi\)
0.573945 + 0.818894i \(0.305412\pi\)
\(602\) −5.04827e7 + 1.38700e8i −0.231394 + 0.635751i
\(603\) −2.62579e7 4.62998e6i −0.119759 0.0211168i
\(604\) −6.87353e7 + 1.21199e7i −0.311939 + 0.0550032i
\(605\) 5.57504e8 2.02915e8i 2.51757 0.916321i
\(606\) −2.93681e7 2.46428e7i −0.131965 0.110732i
\(607\) 1.67780e8i 0.750193i −0.926986 0.375097i \(-0.877610\pi\)
0.926986 0.375097i \(-0.122390\pi\)
\(608\) 1.15548e8 + 6.07093e7i 0.514104 + 0.270113i
\(609\) −1.07194e8 −0.474590
\(610\) −1.75287e7 + 2.08899e7i −0.0772255 + 0.0920338i
\(611\) −1.59233e8 4.37488e8i −0.698085 1.91797i
\(612\) 973014. + 5.51824e6i 0.00424487 + 0.0240739i
\(613\) −2.49898e7 + 1.41724e8i −0.108488 + 0.615265i 0.881282 + 0.472591i \(0.156681\pi\)
−0.989770 + 0.142674i \(0.954430\pi\)
\(614\) 2.65825e8 + 9.67525e7i 1.14839 + 0.417981i
\(615\) 8.65725e7 + 1.49948e8i 0.372181 + 0.644637i
\(616\) −2.99636e8 1.72995e8i −1.28189 0.740102i
\(617\) −1.30257e8 + 1.09298e8i −0.554555 + 0.465327i −0.876480 0.481438i \(-0.840115\pi\)
0.321925 + 0.946765i \(0.395670\pi\)
\(618\) 2.58941e8 + 3.08594e8i 1.09707 + 1.30744i
\(619\) 2.12283e8 3.67685e8i 0.895042 1.55026i 0.0612898 0.998120i \(-0.480479\pi\)
0.833752 0.552139i \(-0.186188\pi\)
\(620\) −1.13757e7 + 6.56776e6i −0.0477313 + 0.0275577i
\(621\) −3.27093e7 + 8.98681e7i −0.136583 + 0.375259i
\(622\) 9.42329e7 + 1.66158e7i 0.391590 + 0.0690479i
\(623\) 4.80757e7 8.47705e6i 0.198821 0.0350575i
\(624\) −1.84552e8 + 6.71714e7i −0.759565 + 0.276459i
\(625\) −2.11153e8 1.77179e8i −0.864884 0.725724i
\(626\) 8.72984e7i 0.355863i
\(627\) 1.54332e8 4.83073e8i 0.626115 1.95979i
\(628\) 1.28038e8 0.516963
\(629\) −4.73710e7 + 5.64545e7i −0.190353 + 0.226854i
\(630\) 1.17652e7 + 3.23247e7i 0.0470521 + 0.129275i
\(631\) −3.43105e7 1.94585e8i −0.136565 0.774499i −0.973757 0.227590i \(-0.926915\pi\)
0.837192 0.546909i \(-0.184196\pi\)
\(632\) 3.58851e7 2.03515e8i 0.142155 0.806203i
\(633\) 7.62119e7 + 2.77389e7i 0.300477 + 0.109365i
\(634\) −176690. 306036.i −0.000693336 0.00120089i
\(635\) 2.75352e8 + 1.58974e8i 1.07539 + 0.620878i
\(636\) 3.83838e7 3.22078e7i 0.149203 0.125196i
\(637\) 9.45903e7 + 1.12728e8i 0.365955 + 0.436129i
\(638\) −1.20210e8 + 2.08209e8i −0.462889 + 0.801748i
\(639\) −5.57486e7 + 3.21865e7i −0.213664 + 0.123359i
\(640\) −3.19195e7 + 8.76981e7i −0.121763 + 0.334542i
\(641\) 1.23143e8 + 2.17134e7i 0.467557 + 0.0824430i 0.402463 0.915436i \(-0.368154\pi\)
0.0650941 + 0.997879i \(0.479265\pi\)
\(642\) −9.14808e7 + 1.61305e7i −0.345720 + 0.0609598i
\(643\) −3.80322e8 + 1.38426e8i −1.43060 + 0.520696i −0.937104 0.349051i \(-0.886504\pi\)
−0.493498 + 0.869747i \(0.664282\pi\)
\(644\) 2.06763e7 + 1.73495e7i 0.0774132 + 0.0649574i
\(645\) 3.52640e8i 1.31417i
\(646\) 3.44516e6 + 8.64408e7i 0.0127794 + 0.320642i
\(647\) −8.19220e6 −0.0302474 −0.0151237 0.999886i \(-0.504814\pi\)
−0.0151237 + 0.999886i \(0.504814\pi\)
\(648\) −2.21901e8 + 2.64451e8i −0.815519 + 0.971898i
\(649\) 3.40009e8 + 9.34166e8i 1.24381 + 3.41735i
\(650\) −7.33981e6 4.16261e7i −0.0267267 0.151574i
\(651\) 6.52396e6 3.69992e7i 0.0236466 0.134106i
\(652\) −6.50707e7 2.36838e7i −0.234770 0.0854493i
\(653\) 1.61470e8 + 2.79675e8i 0.579900 + 1.00442i 0.995490 + 0.0948643i \(0.0302417\pi\)
−0.415590 + 0.909552i \(0.636425\pi\)
\(654\) −3.56100e8 2.05595e8i −1.27303 0.734985i
\(655\) 2.62165e8 2.19983e8i 0.932935 0.782826i
\(656\) −6.94002e7 8.27080e7i −0.245838 0.292979i
\(657\) 1.33877e7 2.31881e7i 0.0472073 0.0817654i
\(658\) 2.52960e8 1.46046e8i 0.887920 0.512641i
\(659\) −1.07480e7 + 2.95299e7i −0.0375553 + 0.103182i −0.957053 0.289913i \(-0.906374\pi\)
0.919498 + 0.393095i \(0.128596\pi\)
\(660\) −1.88802e8 3.32908e7i −0.656710 0.115796i
\(661\) −5.11797e7 + 9.02437e6i −0.177212 + 0.0312473i −0.261550 0.965190i \(-0.584234\pi\)
0.0843378 + 0.996437i \(0.473123\pi\)
\(662\) 1.91996e8 6.98807e7i 0.661786 0.240870i
\(663\) 1.14211e8 + 9.58343e7i 0.391893 + 0.328837i
\(664\) 4.64225e8i 1.58571i
\(665\) −4.88715e7 2.24477e8i −0.166185 0.763321i
\(666\) 4.01102e7 0.135779
\(667\) 5.19807e7 6.19482e7i 0.175172 0.208762i
\(668\) 3.03106e6 + 8.32777e6i 0.0101687 + 0.0279382i
\(669\) 7.74031e7 + 4.38975e8i 0.258512 + 1.46609i
\(670\) −2.70228e7 + 1.53254e8i −0.0898476 + 0.509551i
\(671\) 7.11093e7 + 2.58817e7i 0.235374 + 0.0856692i
\(672\) 7.05661e7 + 1.22224e8i 0.232535 + 0.402763i
\(673\) 2.60414e7 + 1.50350e7i 0.0854318 + 0.0493241i 0.542107 0.840309i \(-0.317627\pi\)
−0.456675 + 0.889633i \(0.650960\pi\)
\(674\) 2.87845e8 2.41531e8i 0.940112 0.788848i
\(675\) −2.61269e7 3.11369e7i −0.0849527 0.101243i
\(676\) 2.16992e7 3.75842e7i 0.0702432 0.121665i
\(677\) −2.07496e7 + 1.19798e7i −0.0668718 + 0.0386085i −0.533063 0.846075i \(-0.678959\pi\)
0.466191 + 0.884684i \(0.345626\pi\)
\(678\) 1.03079e8 2.83206e8i 0.330735 0.908686i
\(679\) 7.86819e7 + 1.38737e7i 0.251342 + 0.0443184i
\(680\) 1.38868e8 2.44862e7i 0.441647 0.0778743i
\(681\) −1.63914e8 + 5.96599e7i −0.519010 + 0.188904i
\(682\) −6.45497e7 5.41636e7i −0.203489 0.170748i
\(683\) 2.42916e7i 0.0762420i 0.999273 + 0.0381210i \(0.0121372\pi\)
−0.999273 + 0.0381210i \(0.987863\pi\)
\(684\) −1.50687e7 + 1.37030e7i −0.0470876 + 0.0428199i
\(685\) −4.28749e8 −1.33393
\(686\) −1.85523e8 + 2.21098e8i −0.574679 + 0.684876i
\(687\) −1.02130e8 2.80600e8i −0.314980 0.865401i
\(688\) −3.81843e7 2.16554e8i −0.117252 0.664968i
\(689\) 4.03021e7 2.28565e8i 0.123217 0.698797i
\(690\) −1.40081e8 5.09854e7i −0.426416 0.155203i
\(691\) −1.44475e8 2.50239e8i −0.437884 0.758438i 0.559642 0.828735i \(-0.310939\pi\)
−0.997526 + 0.0702966i \(0.977605\pi\)
\(692\) 5.63407e6 + 3.25283e6i 0.0170022 + 0.00981620i
\(693\) 7.31242e7 6.13585e7i 0.219716 0.184363i
\(694\) −3.92733e7 4.68040e7i −0.117495 0.140025i
\(695\) −8.08425e7 + 1.40023e8i −0.240816 + 0.417106i
\(696\) 2.07115e8 1.19578e8i 0.614306 0.354670i
\(697\) −2.80328e7 + 7.70194e7i −0.0827880 + 0.227458i
\(698\) 5.48892e7 + 9.67844e6i 0.161406 + 0.0284603i
\(699\) −7.10586e8 + 1.25295e8i −2.08058 + 0.366863i
\(700\) −1.07797e7 + 3.92348e6i −0.0314277 + 0.0114387i
\(701\) −2.30506e8 1.93418e8i −0.669158 0.561490i 0.243658 0.969861i \(-0.421652\pi\)
−0.912816 + 0.408371i \(0.866097\pi\)
\(702\) 3.03837e8i 0.878271i
\(703\) −2.65450e8 3.59734e7i −0.764040 0.103542i
\(704\) 7.12443e8 2.04189
\(705\) 4.48569e8 5.34583e8i 1.28015 1.52563i
\(706\) −3.22158e6 8.85122e6i −0.00915493 0.0251530i
\(707\) 8.36877e6 + 4.74617e7i 0.0236812 + 0.134303i
\(708\) 3.98263e7 2.25866e8i 0.112220 0.636432i
\(709\) −5.80526e8 2.11294e8i −1.62886 0.592856i −0.643817 0.765179i \(-0.722650\pi\)
−0.985040 + 0.172324i \(0.944872\pi\)
\(710\) 1.87856e8 + 3.25376e8i 0.524867 + 0.909097i
\(711\) 4.93762e7 + 2.85074e7i 0.137375 + 0.0793137i
\(712\) −8.34334e7 + 7.00090e7i −0.231153 + 0.193961i
\(713\) 1.82185e7 + 2.17120e7i 0.0502626 + 0.0599006i
\(714\) −4.67697e7 + 8.10074e7i −0.128490 + 0.222551i
\(715\) −7.69039e8 + 4.44005e8i −2.10393 + 1.21470i
\(716\) −2.03532e7 + 5.59201e7i −0.0554491 + 0.152345i
\(717\) 5.80203e6 + 1.02305e6i 0.0157406 + 0.00277550i
\(718\) 2.63827e8 4.65198e7i 0.712764 0.125680i
\(719\) −2.93549e8 + 1.06843e8i −0.789757 + 0.287448i −0.705235 0.708973i \(-0.749159\pi\)
−0.0845222 + 0.996422i \(0.526936\pi\)
\(720\) −3.92579e7 3.29413e7i −0.105179 0.0882558i
\(721\) 5.06411e8i 1.35113i
\(722\) −2.58946e8 + 1.78399e8i −0.688014 + 0.474004i
\(723\) 3.54644e8 0.938379
\(724\) −5.75547e7 + 6.85911e7i −0.151658 + 0.180739i
\(725\) 1.17551e7 + 3.22970e7i 0.0308471 + 0.0847516i
\(726\) −1.52471e8 8.64707e8i −0.398453 2.25974i
\(727\) 8.25054e6 4.67911e7i 0.0214723 0.121776i −0.972188 0.234204i \(-0.924752\pi\)
0.993660 + 0.112428i \(0.0358628\pi\)
\(728\) 3.47437e8 + 1.26457e8i 0.900495 + 0.327754i
\(729\) 1.37483e8 + 2.38127e8i 0.354867 + 0.614647i
\(730\) −1.35337e8 7.81369e7i −0.347895 0.200857i
\(731\) −1.27876e8 + 1.07301e8i −0.327369 + 0.274695i
\(732\) −1.12220e7 1.33739e7i −0.0286113 0.0340976i
\(733\) 9.32374e7 1.61492e8i 0.236744 0.410052i −0.723034 0.690812i \(-0.757253\pi\)
0.959778 + 0.280760i \(0.0905866\pi\)
\(734\) 3.26999e8 1.88793e8i 0.826910 0.477417i
\(735\) −7.54418e7 + 2.07275e8i −0.189998 + 0.522016i
\(736\) −1.04853e8 1.84885e7i −0.262996 0.0463733i
\(737\) 4.25275e8 7.49875e7i 1.06235 0.187321i
\(738\) 4.19189e7 1.52572e7i 0.104290 0.0379583i
\(739\) 2.07345e8 + 1.73983e8i 0.513759 + 0.431095i 0.862450 0.506143i \(-0.168929\pi\)
−0.348691 + 0.937238i \(0.613374\pi\)
\(740\) 1.01268e8i 0.249906i
\(741\) −7.27765e7 + 5.37021e8i −0.178869 + 1.31989i
\(742\) 1.45612e8 0.356440
\(743\) 3.35960e8 4.00382e8i 0.819071 0.976131i −0.180902 0.983501i \(-0.557902\pi\)
0.999973 + 0.00737009i \(0.00234599\pi\)
\(744\) 2.86685e7 + 7.87660e7i 0.0696123 + 0.191258i
\(745\) 1.04021e8 + 5.89931e8i 0.251566 + 1.42670i
\(746\) −6.22940e7 + 3.53287e8i −0.150048 + 0.850964i
\(747\) 1.20353e8 + 4.38049e7i 0.288732 + 0.105090i
\(748\) −4.53762e7 7.85939e7i −0.108424 0.187795i
\(749\) 1.01130e8 + 5.83872e7i 0.240676 + 0.138954i
\(750\) −2.70379e8 + 2.26875e8i −0.640897 + 0.537777i
\(751\) 1.81920e8 + 2.16803e8i 0.429497 + 0.511854i 0.936777 0.349927i \(-0.113794\pi\)
−0.507280 + 0.861781i \(0.669349\pi\)
\(752\) −2.17578e8 + 3.76856e8i −0.511636 + 0.886180i
\(753\) 2.69319e8 1.55491e8i 0.630785 0.364184i
\(754\) 8.78713e7 2.41424e8i 0.204990 0.563206i
\(755\) −4.77227e8 8.41480e7i −1.10888 0.195525i
\(756\) 8.12077e7 1.43191e7i 0.187945 0.0331398i
\(757\) 2.98363e8 1.08595e8i 0.687793 0.250336i 0.0256029 0.999672i \(-0.491849\pi\)
0.662190 + 0.749336i \(0.269627\pi\)
\(758\) 2.40502e8 + 2.01805e8i 0.552218 + 0.463366i
\(759\) 4.13669e8i 0.946078i
\(760\) 3.44839e8 + 3.79207e8i 0.785553 + 0.863846i
\(761\) 6.63279e8 1.50502 0.752510 0.658581i \(-0.228843\pi\)
0.752510 + 0.658581i \(0.228843\pi\)
\(762\) 3.02468e8 3.60468e8i 0.683620 0.814707i
\(763\) 1.76792e8 + 4.85732e8i 0.398006 + 1.09351i
\(764\) −3.88688e7 2.20436e8i −0.0871607 0.494313i