Properties

Label 124.6.f.a.97.4
Level $124$
Weight $6$
Character 124.97
Analytic conductor $19.888$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 124.f (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8875936568\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 97.4
Character \(\chi\) \(=\) 124.97
Dual form 124.6.f.a.101.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.50907 + 13.8775i) q^{3} +78.4326 q^{5} +(-14.7862 + 10.7428i) q^{7} +(24.3383 + 17.6828i) q^{9} +O(q^{10})\) \(q+(-4.50907 + 13.8775i) q^{3} +78.4326 q^{5} +(-14.7862 + 10.7428i) q^{7} +(24.3383 + 17.6828i) q^{9} +(497.817 - 361.685i) q^{11} +(79.1894 - 243.720i) q^{13} +(-353.658 + 1088.45i) q^{15} +(438.635 + 318.687i) q^{17} +(-849.929 - 2615.81i) q^{19} +(-82.4110 - 253.635i) q^{21} +(1680.92 + 1221.26i) q^{23} +3026.67 q^{25} +(-3223.72 + 2342.17i) q^{27} +(2583.40 + 7950.88i) q^{29} +(1027.33 + 5251.07i) q^{31} +(2774.59 + 8539.31i) q^{33} +(-1159.72 + 842.585i) q^{35} +14971.8 q^{37} +(3025.15 + 2197.90i) q^{39} +(1222.38 + 3762.11i) q^{41} +(-6504.72 - 20019.5i) q^{43} +(1908.91 + 1386.91i) q^{45} +(-1530.55 + 4710.55i) q^{47} +(-5090.43 + 15666.7i) q^{49} +(-6400.41 + 4650.17i) q^{51} +(-7988.15 - 5803.73i) q^{53} +(39045.1 - 28367.9i) q^{55} +40133.3 q^{57} +(-1766.19 + 5435.78i) q^{59} -39368.4 q^{61} -549.832 q^{63} +(6211.03 - 19115.6i) q^{65} -21185.3 q^{67} +(-24527.4 + 17820.2i) q^{69} +(62905.7 + 45703.7i) q^{71} +(15247.9 - 11078.3i) q^{73} +(-13647.5 + 42002.6i) q^{75} +(-3475.30 + 10695.9i) q^{77} +(-71525.4 - 51966.3i) q^{79} +(-15708.5 - 48345.6i) q^{81} +(-7914.74 - 24359.1i) q^{83} +(34403.3 + 24995.5i) q^{85} -121987. q^{87} +(-22593.8 + 16415.4i) q^{89} +(1447.32 + 4454.40i) q^{91} +(-77503.9 - 9420.75i) q^{93} +(-66662.2 - 205165. i) q^{95} +(1827.17 - 1327.52i) q^{97} +18511.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 0
\(3\) −4.50907 + 13.8775i −0.289257 + 0.890241i 0.695833 + 0.718203i \(0.255035\pi\)
−0.985090 + 0.172038i \(0.944965\pi\)
\(4\) 0 0
\(5\) 78.4326 1.40305 0.701523 0.712647i \(-0.252504\pi\)
0.701523 + 0.712647i \(0.252504\pi\)
\(6\) 0 0
\(7\) −14.7862 + 10.7428i −0.114054 + 0.0828651i −0.643350 0.765572i \(-0.722456\pi\)
0.529296 + 0.848437i \(0.322456\pi\)
\(8\) 0 0
\(9\) 24.3383 + 17.6828i 0.100157 + 0.0727686i
\(10\) 0 0
\(11\) 497.817 361.685i 1.24048 0.901258i 0.242846 0.970065i \(-0.421919\pi\)
0.997630 + 0.0688067i \(0.0219192\pi\)
\(12\) 0 0
\(13\) 79.1894 243.720i 0.129960 0.399975i −0.864812 0.502095i \(-0.832563\pi\)
0.994772 + 0.102120i \(0.0325627\pi\)
\(14\) 0 0
\(15\) −353.658 + 1088.45i −0.405840 + 1.24905i
\(16\) 0 0
\(17\) 438.635 + 318.687i 0.368113 + 0.267450i 0.756428 0.654077i \(-0.226943\pi\)
−0.388315 + 0.921527i \(0.626943\pi\)
\(18\) 0 0
\(19\) −849.929 2615.81i −0.540131 1.66235i −0.732295 0.680988i \(-0.761551\pi\)
0.192164 0.981363i \(-0.438449\pi\)
\(20\) 0 0
\(21\) −82.4110 253.635i −0.0407790 0.125505i
\(22\) 0 0
\(23\) 1680.92 + 1221.26i 0.662563 + 0.481380i 0.867528 0.497389i \(-0.165708\pi\)
−0.204964 + 0.978769i \(0.565708\pi\)
\(24\) 0 0
\(25\) 3026.67 0.968536
\(26\) 0 0
\(27\) −3223.72 + 2342.17i −0.851037 + 0.618315i
\(28\) 0 0
\(29\) 2583.40 + 7950.88i 0.570422 + 1.75558i 0.651263 + 0.758852i \(0.274240\pi\)
−0.0808405 + 0.996727i \(0.525760\pi\)
\(30\) 0 0
\(31\) 1027.33 + 5251.07i 0.192001 + 0.981395i
\(32\) 0 0
\(33\) 2774.59 + 8539.31i 0.443521 + 1.36502i
\(34\) 0 0
\(35\) −1159.72 + 842.585i −0.160023 + 0.116264i
\(36\) 0 0
\(37\) 14971.8 1.79792 0.898958 0.438034i \(-0.144325\pi\)
0.898958 + 0.438034i \(0.144325\pi\)
\(38\) 0 0
\(39\) 3025.15 + 2197.90i 0.318482 + 0.231391i
\(40\) 0 0
\(41\) 1222.38 + 3762.11i 0.113566 + 0.349520i 0.991645 0.128995i \(-0.0411752\pi\)
−0.878079 + 0.478515i \(0.841175\pi\)
\(42\) 0 0
\(43\) −6504.72 20019.5i −0.536485 1.65113i −0.740418 0.672146i \(-0.765373\pi\)
0.203933 0.978985i \(-0.434627\pi\)
\(44\) 0 0
\(45\) 1908.91 + 1386.91i 0.140525 + 0.102098i
\(46\) 0 0
\(47\) −1530.55 + 4710.55i −0.101066 + 0.311048i −0.988787 0.149333i \(-0.952287\pi\)
0.887721 + 0.460381i \(0.152287\pi\)
\(48\) 0 0
\(49\) −5090.43 + 15666.7i −0.302875 + 0.932154i
\(50\) 0 0
\(51\) −6400.41 + 4650.17i −0.344574 + 0.250348i
\(52\) 0 0
\(53\) −7988.15 5803.73i −0.390622 0.283803i 0.375088 0.926989i \(-0.377612\pi\)
−0.765710 + 0.643186i \(0.777612\pi\)
\(54\) 0 0
\(55\) 39045.1 28367.9i 1.74044 1.26451i
\(56\) 0 0
\(57\) 40133.3 1.63613
\(58\) 0 0
\(59\) −1766.19 + 5435.78i −0.0660553 + 0.203297i −0.978636 0.205598i \(-0.934086\pi\)
0.912581 + 0.408896i \(0.134086\pi\)
\(60\) 0 0
\(61\) −39368.4 −1.35464 −0.677319 0.735689i \(-0.736858\pi\)
−0.677319 + 0.735689i \(0.736858\pi\)
\(62\) 0 0
\(63\) −549.832 −0.0174533
\(64\) 0 0
\(65\) 6211.03 19115.6i 0.182339 0.561183i
\(66\) 0 0
\(67\) −21185.3 −0.576563 −0.288281 0.957546i \(-0.593084\pi\)
−0.288281 + 0.957546i \(0.593084\pi\)
\(68\) 0 0
\(69\) −24527.4 + 17820.2i −0.620196 + 0.450599i
\(70\) 0 0
\(71\) 62905.7 + 45703.7i 1.48096 + 1.07598i 0.977245 + 0.212115i \(0.0680350\pi\)
0.503718 + 0.863868i \(0.331965\pi\)
\(72\) 0 0
\(73\) 15247.9 11078.3i 0.334891 0.243312i −0.407612 0.913155i \(-0.633638\pi\)
0.742503 + 0.669843i \(0.233638\pi\)
\(74\) 0 0
\(75\) −13647.5 + 42002.6i −0.280156 + 0.862230i
\(76\) 0 0
\(77\) −3475.30 + 10695.9i −0.0667984 + 0.205584i
\(78\) 0 0
\(79\) −71525.4 51966.3i −1.28942 0.936815i −0.289622 0.957141i \(-0.593530\pi\)
−0.999793 + 0.0203261i \(0.993530\pi\)
\(80\) 0 0
\(81\) −15708.5 48345.6i −0.266024 0.818738i
\(82\) 0 0
\(83\) −7914.74 24359.1i −0.126108 0.388119i 0.867994 0.496575i \(-0.165409\pi\)
−0.994101 + 0.108456i \(0.965409\pi\)
\(84\) 0 0
\(85\) 34403.3 + 24995.5i 0.516479 + 0.375244i
\(86\) 0 0
\(87\) −121987. −1.72789
\(88\) 0 0
\(89\) −22593.8 + 16415.4i −0.302353 + 0.219672i −0.728608 0.684931i \(-0.759832\pi\)
0.426255 + 0.904603i \(0.359832\pi\)
\(90\) 0 0
\(91\) 1447.32 + 4454.40i 0.0183215 + 0.0563879i
\(92\) 0 0
\(93\) −77503.9 9420.75i −0.929215 0.112948i
\(94\) 0 0
\(95\) −66662.2 205165.i −0.757827 2.33235i
\(96\) 0 0
\(97\) 1827.17 1327.52i 0.0197174 0.0143255i −0.577883 0.816120i \(-0.696121\pi\)
0.597600 + 0.801794i \(0.296121\pi\)
\(98\) 0 0
\(99\) 18511.6 0.189826
\(100\) 0 0
\(101\) 53462.3 + 38842.6i 0.521488 + 0.378883i 0.817164 0.576405i \(-0.195545\pi\)
−0.295676 + 0.955288i \(0.595545\pi\)
\(102\) 0 0
\(103\) −43422.7 133641.i −0.403296 1.24122i −0.922310 0.386452i \(-0.873701\pi\)
0.519013 0.854766i \(-0.326299\pi\)
\(104\) 0 0
\(105\) −6463.71 19893.2i −0.0572148 0.176089i
\(106\) 0 0
\(107\) −8760.94 6365.20i −0.0739761 0.0537468i 0.550183 0.835044i \(-0.314558\pi\)
−0.624159 + 0.781298i \(0.714558\pi\)
\(108\) 0 0
\(109\) 30188.1 92909.3i 0.243371 0.749019i −0.752529 0.658559i \(-0.771166\pi\)
0.995900 0.0904600i \(-0.0288337\pi\)
\(110\) 0 0
\(111\) −67508.8 + 207771.i −0.520060 + 1.60058i
\(112\) 0 0
\(113\) 78718.0 57192.0i 0.579933 0.421346i −0.258767 0.965940i \(-0.583316\pi\)
0.838700 + 0.544594i \(0.183316\pi\)
\(114\) 0 0
\(115\) 131839. + 95786.6i 0.929606 + 0.675399i
\(116\) 0 0
\(117\) 6236.98 4531.43i 0.0421221 0.0306035i
\(118\) 0 0
\(119\) −9909.32 −0.0641470
\(120\) 0 0
\(121\) 67238.2 206938.i 0.417496 1.28492i
\(122\) 0 0
\(123\) −57720.4 −0.344006
\(124\) 0 0
\(125\) −7712.00 −0.0441461
\(126\) 0 0
\(127\) −50590.5 + 155701.i −0.278330 + 0.856610i 0.709990 + 0.704212i \(0.248700\pi\)
−0.988319 + 0.152398i \(0.951300\pi\)
\(128\) 0 0
\(129\) 307150. 1.62509
\(130\) 0 0
\(131\) −87368.2 + 63476.7i −0.444811 + 0.323174i −0.787544 0.616259i \(-0.788647\pi\)
0.342733 + 0.939433i \(0.388647\pi\)
\(132\) 0 0
\(133\) 40668.3 + 29547.3i 0.199355 + 0.144840i
\(134\) 0 0
\(135\) −252845. + 183703.i −1.19404 + 0.867523i
\(136\) 0 0
\(137\) 84741.6 260808.i 0.385740 1.18719i −0.550201 0.835032i \(-0.685449\pi\)
0.935942 0.352155i \(-0.114551\pi\)
\(138\) 0 0
\(139\) 52943.7 162944.i 0.232422 0.715321i −0.765031 0.643993i \(-0.777276\pi\)
0.997453 0.0713276i \(-0.0227236\pi\)
\(140\) 0 0
\(141\) −58469.2 42480.4i −0.247674 0.179945i
\(142\) 0 0
\(143\) −48728.1 149970.i −0.199269 0.613286i
\(144\) 0 0
\(145\) 202623. + 623609.i 0.800328 + 2.46316i
\(146\) 0 0
\(147\) −194462. 141285.i −0.742233 0.539264i
\(148\) 0 0
\(149\) 59850.2 0.220851 0.110426 0.993884i \(-0.464779\pi\)
0.110426 + 0.993884i \(0.464779\pi\)
\(150\) 0 0
\(151\) −150526. + 109363.i −0.537240 + 0.390328i −0.823059 0.567956i \(-0.807734\pi\)
0.285819 + 0.958284i \(0.407734\pi\)
\(152\) 0 0
\(153\) 5040.34 + 15512.6i 0.0174073 + 0.0535741i
\(154\) 0 0
\(155\) 80575.8 + 411855.i 0.269386 + 1.37694i
\(156\) 0 0
\(157\) 31238.2 + 96141.2i 0.101143 + 0.311287i 0.988806 0.149208i \(-0.0476722\pi\)
−0.887663 + 0.460494i \(0.847672\pi\)
\(158\) 0 0
\(159\) 116560. 84686.0i 0.365644 0.265656i
\(160\) 0 0
\(161\) −37974.1 −0.115458
\(162\) 0 0
\(163\) 221386. + 160846.i 0.652651 + 0.474179i 0.864173 0.503194i \(-0.167842\pi\)
−0.211522 + 0.977373i \(0.567842\pi\)
\(164\) 0 0
\(165\) 217618. + 669761.i 0.622280 + 1.91518i
\(166\) 0 0
\(167\) −45055.0 138665.i −0.125012 0.384747i 0.868891 0.495003i \(-0.164833\pi\)
−0.993903 + 0.110256i \(0.964833\pi\)
\(168\) 0 0
\(169\) 247254. + 179640.i 0.665927 + 0.483824i
\(170\) 0 0
\(171\) 25569.0 78693.4i 0.0668689 0.205801i
\(172\) 0 0
\(173\) 48128.4 148124.i 0.122260 0.376279i −0.871132 0.491050i \(-0.836613\pi\)
0.993392 + 0.114771i \(0.0366133\pi\)
\(174\) 0 0
\(175\) −44752.9 + 32514.9i −0.110465 + 0.0802578i
\(176\) 0 0
\(177\) −67471.0 49020.6i −0.161877 0.117610i
\(178\) 0 0
\(179\) −287743. + 209058.i −0.671232 + 0.487679i −0.870437 0.492279i \(-0.836164\pi\)
0.199205 + 0.979958i \(0.436164\pi\)
\(180\) 0 0
\(181\) −145150. −0.329322 −0.164661 0.986350i \(-0.552653\pi\)
−0.164661 + 0.986350i \(0.552653\pi\)
\(182\) 0 0
\(183\) 177515. 546335.i 0.391838 1.20595i
\(184\) 0 0
\(185\) 1.17428e6 2.52256
\(186\) 0 0
\(187\) 333624. 0.697676
\(188\) 0 0
\(189\) 22505.1 69263.6i 0.0458275 0.141043i
\(190\) 0 0
\(191\) −202543. −0.401730 −0.200865 0.979619i \(-0.564375\pi\)
−0.200865 + 0.979619i \(0.564375\pi\)
\(192\) 0 0
\(193\) −573027. + 416328.i −1.10734 + 0.804531i −0.982243 0.187613i \(-0.939925\pi\)
−0.125099 + 0.992144i \(0.539925\pi\)
\(194\) 0 0
\(195\) 237270. + 172387.i 0.446845 + 0.324652i
\(196\) 0 0
\(197\) 787364. 572053.i 1.44547 1.05020i 0.458610 0.888638i \(-0.348348\pi\)
0.986863 0.161560i \(-0.0516525\pi\)
\(198\) 0 0
\(199\) −176323. + 542667.i −0.315629 + 0.971406i 0.659866 + 0.751383i \(0.270613\pi\)
−0.975495 + 0.220022i \(0.929387\pi\)
\(200\) 0 0
\(201\) 95525.7 293998.i 0.166775 0.513280i
\(202\) 0 0
\(203\) −123613. 89810.3i −0.210535 0.152963i
\(204\) 0 0
\(205\) 95874.7 + 295072.i 0.159338 + 0.490392i
\(206\) 0 0
\(207\) 19315.4 + 59446.7i 0.0313312 + 0.0964276i
\(208\) 0 0
\(209\) −1.36921e6 994790.i −2.16823 1.57531i
\(210\) 0 0
\(211\) 36597.7 0.0565910 0.0282955 0.999600i \(-0.490992\pi\)
0.0282955 + 0.999600i \(0.490992\pi\)
\(212\) 0 0
\(213\) −917898. + 666892.i −1.38626 + 1.00718i
\(214\) 0 0
\(215\) −510182. 1.57018e6i −0.752713 2.31661i
\(216\) 0 0
\(217\) −71601.4 66606.9i −0.103222 0.0960219i
\(218\) 0 0
\(219\) 84984.4 + 261555.i 0.119737 + 0.368513i
\(220\) 0 0
\(221\) 112406. 81667.5i 0.154813 0.112478i
\(222\) 0 0
\(223\) 843619. 1.13602 0.568008 0.823023i \(-0.307714\pi\)
0.568008 + 0.823023i \(0.307714\pi\)
\(224\) 0 0
\(225\) 73663.9 + 53520.0i 0.0970060 + 0.0704790i
\(226\) 0 0
\(227\) −441771. 1.35963e6i −0.569027 1.75128i −0.655673 0.755045i \(-0.727615\pi\)
0.0866458 0.996239i \(-0.472385\pi\)
\(228\) 0 0
\(229\) −280853. 864378.i −0.353908 1.08922i −0.956640 0.291274i \(-0.905921\pi\)
0.602731 0.797944i \(-0.294079\pi\)
\(230\) 0 0
\(231\) −132762. 96457.0i −0.163698 0.118933i
\(232\) 0 0
\(233\) −375525. + 1.15575e6i −0.453157 + 1.39467i 0.420128 + 0.907465i \(0.361985\pi\)
−0.873285 + 0.487210i \(0.838015\pi\)
\(234\) 0 0
\(235\) −120045. + 369461.i −0.141799 + 0.436414i
\(236\) 0 0
\(237\) 1.04367e6 758274.i 1.20696 0.876910i
\(238\) 0 0
\(239\) −468685. 340519.i −0.530745 0.385609i 0.289891 0.957060i \(-0.406381\pi\)
−0.820636 + 0.571451i \(0.806381\pi\)
\(240\) 0 0
\(241\) −834546. + 606333.i −0.925567 + 0.672464i −0.944903 0.327349i \(-0.893845\pi\)
0.0193366 + 0.999813i \(0.493845\pi\)
\(242\) 0 0
\(243\) −226546. −0.246116
\(244\) 0 0
\(245\) −399255. + 1.22878e6i −0.424948 + 1.30785i
\(246\) 0 0
\(247\) −704831. −0.735094
\(248\) 0 0
\(249\) 373731. 0.381997
\(250\) 0 0
\(251\) −476020. + 1.46504e6i −0.476915 + 1.46779i 0.366443 + 0.930440i \(0.380575\pi\)
−0.843358 + 0.537352i \(0.819425\pi\)
\(252\) 0 0
\(253\) 1.27850e6 1.25574
\(254\) 0 0
\(255\) −502001. + 364725.i −0.483453 + 0.351249i
\(256\) 0 0
\(257\) 651728. + 473508.i 0.615508 + 0.447193i 0.851350 0.524599i \(-0.175785\pi\)
−0.235842 + 0.971792i \(0.575785\pi\)
\(258\) 0 0
\(259\) −221376. + 160839.i −0.205060 + 0.148985i
\(260\) 0 0
\(261\) −77718.3 + 239192.i −0.0706191 + 0.217343i
\(262\) 0 0
\(263\) 227377. 699796.i 0.202702 0.623852i −0.797098 0.603850i \(-0.793633\pi\)
0.999800 0.0200024i \(-0.00636739\pi\)
\(264\) 0 0
\(265\) −626532. 455202.i −0.548060 0.398189i
\(266\) 0 0
\(267\) −125927. 387563.i −0.108104 0.332709i
\(268\) 0 0
\(269\) −367400. 1.13074e6i −0.309570 0.952759i −0.977932 0.208923i \(-0.933004\pi\)
0.668362 0.743836i \(-0.266996\pi\)
\(270\) 0 0
\(271\) −1.33379e6 969055.i −1.10323 0.801540i −0.121642 0.992574i \(-0.538816\pi\)
−0.981583 + 0.191034i \(0.938816\pi\)
\(272\) 0 0
\(273\) −68342.0 −0.0554985
\(274\) 0 0
\(275\) 1.50673e6 1.09470e6i 1.20144 0.872901i
\(276\) 0 0
\(277\) −506268. 1.55813e6i −0.396444 1.22013i −0.927832 0.372999i \(-0.878329\pi\)
0.531388 0.847128i \(-0.321671\pi\)
\(278\) 0 0
\(279\) −67850.2 + 145968.i −0.0521844 + 0.112266i
\(280\) 0 0
\(281\) 131554. + 404881.i 0.0993889 + 0.305888i 0.988373 0.152051i \(-0.0485879\pi\)
−0.888984 + 0.457939i \(0.848588\pi\)
\(282\) 0 0
\(283\) −764703. + 555589.i −0.567579 + 0.412370i −0.834225 0.551424i \(-0.814085\pi\)
0.266646 + 0.963795i \(0.414085\pi\)
\(284\) 0 0
\(285\) 3.14776e6 2.29556
\(286\) 0 0
\(287\) −58489.9 42495.4i −0.0419156 0.0304535i
\(288\) 0 0
\(289\) −347921. 1.07079e6i −0.245039 0.754153i
\(290\) 0 0
\(291\) 10183.8 + 31342.4i 0.00704979 + 0.0216970i
\(292\) 0 0
\(293\) −2.11679e6 1.53794e6i −1.44049 1.04658i −0.987940 0.154835i \(-0.950515\pi\)
−0.452548 0.891740i \(-0.649485\pi\)
\(294\) 0 0
\(295\) −138527. + 426342.i −0.0926786 + 0.285235i
\(296\) 0 0
\(297\) −757696. + 2.33195e6i −0.498430 + 1.53401i
\(298\) 0 0
\(299\) 430756. 312963.i 0.278647 0.202449i
\(300\) 0 0
\(301\) 311245. + 226133.i 0.198010 + 0.143862i
\(302\) 0 0
\(303\) −780103. + 566778.i −0.488141 + 0.354655i
\(304\) 0 0
\(305\) −3.08777e6 −1.90062
\(306\) 0 0
\(307\) 66234.3 203848.i 0.0401086 0.123441i −0.928997 0.370086i \(-0.879328\pi\)
0.969106 + 0.246645i \(0.0793281\pi\)
\(308\) 0 0
\(309\) 2.05040e6 1.22164
\(310\) 0 0
\(311\) 2.48425e6 1.45644 0.728222 0.685341i \(-0.240347\pi\)
0.728222 + 0.685341i \(0.240347\pi\)
\(312\) 0 0
\(313\) 876008. 2.69607e6i 0.505414 1.55550i −0.294660 0.955602i \(-0.595206\pi\)
0.800074 0.599901i \(-0.204794\pi\)
\(314\) 0 0
\(315\) −43124.8 −0.0244878
\(316\) 0 0
\(317\) −477949. + 347250.i −0.267136 + 0.194086i −0.713287 0.700872i \(-0.752794\pi\)
0.446151 + 0.894958i \(0.352794\pi\)
\(318\) 0 0
\(319\) 4.16178e6 + 3.02371e6i 2.28983 + 1.66366i
\(320\) 0 0
\(321\) 127837. 92878.7i 0.0692457 0.0503099i
\(322\) 0 0
\(323\) 460817. 1.41825e6i 0.245766 0.756390i
\(324\) 0 0
\(325\) 239681. 737661.i 0.125871 0.387390i
\(326\) 0 0
\(327\) 1.15323e6 + 837869.i 0.596411 + 0.433318i
\(328\) 0 0
\(329\) −27973.4 86093.4i −0.0142481 0.0438511i
\(330\) 0 0
\(331\) 641224. + 1.97348e6i 0.321692 + 0.990065i 0.972912 + 0.231176i \(0.0742574\pi\)
−0.651220 + 0.758889i \(0.725743\pi\)
\(332\) 0 0
\(333\) 364387. + 264743.i 0.180075 + 0.130832i
\(334\) 0 0
\(335\) −1.66161e6 −0.808944
\(336\) 0 0
\(337\) −2.66393e6 + 1.93546e6i −1.27775 + 0.928343i −0.999483 0.0321591i \(-0.989762\pi\)
−0.278272 + 0.960502i \(0.589762\pi\)
\(338\) 0 0
\(339\) 438736. + 1.35029e6i 0.207350 + 0.638158i
\(340\) 0 0
\(341\) 2.41066e6 + 2.24251e6i 1.12266 + 1.04435i
\(342\) 0 0
\(343\) −187959. 578479.i −0.0862637 0.265492i
\(344\) 0 0
\(345\) −1.92375e6 + 1.39768e6i −0.870163 + 0.632210i
\(346\) 0 0
\(347\) 976884. 0.435531 0.217766 0.976001i \(-0.430123\pi\)
0.217766 + 0.976001i \(0.430123\pi\)
\(348\) 0 0
\(349\) 377012. + 273915.i 0.165688 + 0.120380i 0.667540 0.744574i \(-0.267348\pi\)
−0.501851 + 0.864954i \(0.667348\pi\)
\(350\) 0 0
\(351\) 315549. + 971161.i 0.136710 + 0.420749i
\(352\) 0 0
\(353\) −711952. 2.19116e6i −0.304098 0.935918i −0.980012 0.198937i \(-0.936251\pi\)
0.675914 0.736980i \(-0.263749\pi\)
\(354\) 0 0
\(355\) 4.93386e6 + 3.58466e6i 2.07786 + 1.50965i
\(356\) 0 0
\(357\) 44681.8 137516.i 0.0185550 0.0571063i
\(358\) 0 0
\(359\) 55449.9 170657.i 0.0227073 0.0698858i −0.939061 0.343751i \(-0.888302\pi\)
0.961768 + 0.273865i \(0.0883023\pi\)
\(360\) 0 0
\(361\) −4.11689e6 + 2.99110e6i −1.66265 + 1.20799i
\(362\) 0 0
\(363\) 2.56859e6 + 1.86619e6i 1.02313 + 0.743344i
\(364\) 0 0
\(365\) 1.19593e6 868896.i 0.469867 0.341378i
\(366\) 0 0
\(367\) −550937. −0.213519 −0.106759 0.994285i \(-0.534047\pi\)
−0.106759 + 0.994285i \(0.534047\pi\)
\(368\) 0 0
\(369\) −36773.8 + 113178.i −0.0140596 + 0.0432710i
\(370\) 0 0
\(371\) 180462. 0.0680694
\(372\) 0 0
\(373\) 520482. 0.193702 0.0968509 0.995299i \(-0.469123\pi\)
0.0968509 + 0.995299i \(0.469123\pi\)
\(374\) 0 0
\(375\) 34773.9 107023.i 0.0127696 0.0393006i
\(376\) 0 0
\(377\) 2.14237e6 0.776320
\(378\) 0 0
\(379\) 306340. 222569.i 0.109548 0.0795915i −0.531662 0.846956i \(-0.678432\pi\)
0.641211 + 0.767365i \(0.278432\pi\)
\(380\) 0 0
\(381\) −1.93263e6 1.40414e6i −0.682081 0.495561i
\(382\) 0 0
\(383\) −1.58738e6 + 1.15330e6i −0.552948 + 0.401740i −0.828871 0.559440i \(-0.811016\pi\)
0.275923 + 0.961180i \(0.411016\pi\)
\(384\) 0 0
\(385\) −272577. + 838906.i −0.0937212 + 0.288444i
\(386\) 0 0
\(387\) 195686. 602261.i 0.0664176 0.204412i
\(388\) 0 0
\(389\) −3.33829e6 2.42541e6i −1.11854 0.812665i −0.134551 0.990907i \(-0.542959\pi\)
−0.983987 + 0.178242i \(0.942959\pi\)
\(390\) 0 0
\(391\) 348111. + 1.07137e6i 0.115153 + 0.354405i
\(392\) 0 0
\(393\) −486948. 1.49867e6i −0.159038 0.489469i
\(394\) 0 0
\(395\) −5.60993e6 4.07585e6i −1.80911 1.31439i
\(396\) 0 0
\(397\) 883247. 0.281259 0.140629 0.990062i \(-0.455087\pi\)
0.140629 + 0.990062i \(0.455087\pi\)
\(398\) 0 0
\(399\) −593418. + 431143.i −0.186607 + 0.135578i
\(400\) 0 0
\(401\) 183320. + 564199.i 0.0569309 + 0.175215i 0.975478 0.220096i \(-0.0706369\pi\)
−0.918547 + 0.395311i \(0.870637\pi\)
\(402\) 0 0
\(403\) 1.36114e6 + 165450.i 0.417486 + 0.0507462i
\(404\) 0 0
\(405\) −1.23205e6 3.79188e6i −0.373244 1.14873i
\(406\) 0 0
\(407\) 7.45322e6 5.41508e6i 2.23027 1.62039i
\(408\) 0 0
\(409\) −5.33469e6 −1.57689 −0.788444 0.615107i \(-0.789113\pi\)
−0.788444 + 0.615107i \(0.789113\pi\)
\(410\) 0 0
\(411\) 3.23725e6 + 2.35200e6i 0.945304 + 0.686804i
\(412\) 0 0
\(413\) −32280.2 99348.2i −0.00931238 0.0286606i
\(414\) 0 0
\(415\) −620774. 1.91054e6i −0.176935 0.544549i
\(416\) 0 0
\(417\) 2.02252e6 + 1.46945e6i 0.569578 + 0.413823i
\(418\) 0 0
\(419\) 1.77728e6 5.46990e6i 0.494562 1.52210i −0.323077 0.946373i \(-0.604717\pi\)
0.817639 0.575731i \(-0.195283\pi\)
\(420\) 0 0
\(421\) −2.14445e6 + 6.59992e6i −0.589671 + 1.81482i −0.0100286 + 0.999950i \(0.503192\pi\)
−0.579642 + 0.814871i \(0.696808\pi\)
\(422\) 0 0
\(423\) −120547. + 87582.2i −0.0327570 + 0.0237993i
\(424\) 0 0
\(425\) 1.32760e6 + 964561.i 0.356530 + 0.259034i
\(426\) 0 0
\(427\) 582108. 422927.i 0.154502 0.112252i
\(428\) 0 0
\(429\) 2.30092e6 0.603613
\(430\) 0 0
\(431\) −660391. + 2.03247e6i −0.171241 + 0.527026i −0.999442 0.0334056i \(-0.989365\pi\)
0.828201 + 0.560432i \(0.189365\pi\)
\(432\) 0 0
\(433\) 2.01357e6 0.516116 0.258058 0.966129i \(-0.416917\pi\)
0.258058 + 0.966129i \(0.416917\pi\)
\(434\) 0 0
\(435\) −9.56776e6 −2.42430
\(436\) 0 0
\(437\) 1.76592e6 5.43496e6i 0.442353 1.36142i
\(438\) 0 0
\(439\) 3.31928e6 0.822020 0.411010 0.911631i \(-0.365176\pi\)
0.411010 + 0.911631i \(0.365176\pi\)
\(440\) 0 0
\(441\) −400923. + 291288.i −0.0981668 + 0.0713223i
\(442\) 0 0
\(443\) −3.17255e6 2.30499e6i −0.768067 0.558034i 0.133307 0.991075i \(-0.457440\pi\)
−0.901374 + 0.433041i \(0.857440\pi\)
\(444\) 0 0
\(445\) −1.77209e6 + 1.28750e6i −0.424215 + 0.308210i
\(446\) 0 0
\(447\) −269869. + 830571.i −0.0638828 + 0.196611i
\(448\) 0 0
\(449\) −184428. + 567612.i −0.0431729 + 0.132873i −0.970320 0.241826i \(-0.922254\pi\)
0.927147 + 0.374698i \(0.122254\pi\)
\(450\) 0 0
\(451\) 1.96922e6 + 1.43072e6i 0.455883 + 0.331218i
\(452\) 0 0
\(453\) −838957. 2.58205e6i −0.192085 0.591178i
\(454\) 0 0
\(455\) 113517. + 349370.i 0.0257059 + 0.0791148i
\(456\) 0 0
\(457\) 4.20718e6 + 3.05670e6i 0.942325 + 0.684639i 0.948979 0.315339i \(-0.102118\pi\)
−0.00665416 + 0.999978i \(0.502118\pi\)
\(458\) 0 0
\(459\) −2.16046e6 −0.478646
\(460\) 0 0
\(461\) 2.26430e6 1.64511e6i 0.496229 0.360532i −0.311346 0.950297i \(-0.600780\pi\)
0.807575 + 0.589765i \(0.200780\pi\)
\(462\) 0 0
\(463\) −12322.6 37925.1i −0.00267147 0.00822194i 0.949712 0.313125i \(-0.101376\pi\)
−0.952383 + 0.304903i \(0.901376\pi\)
\(464\) 0 0
\(465\) −6.07884e6 738894.i −1.30373 0.158471i
\(466\) 0 0
\(467\) 206146. + 634451.i 0.0437403 + 0.134619i 0.970542 0.240933i \(-0.0774533\pi\)
−0.926801 + 0.375552i \(0.877453\pi\)
\(468\) 0 0
\(469\) 313249. 227589.i 0.0657593 0.0477770i
\(470\) 0 0
\(471\) −1.47505e6 −0.306376
\(472\) 0 0
\(473\) −1.04789e7 7.61338e6i −2.15359 1.56468i
\(474\) 0 0
\(475\) −2.57246e6 7.91721e6i −0.523136 1.61005i
\(476\) 0 0
\(477\) −91791.6 282505.i −0.0184717 0.0568500i
\(478\) 0 0
\(479\) 5.52310e6 + 4.01277e6i 1.09988 + 0.799108i 0.981040 0.193806i \(-0.0620832\pi\)
0.118838 + 0.992914i \(0.462083\pi\)
\(480\) 0 0
\(481\) 1.18561e6 3.64892e6i 0.233657 0.719121i
\(482\) 0 0
\(483\) 171228. 526985.i 0.0333969 0.102785i
\(484\) 0 0
\(485\) 143310. 104121.i 0.0276644 0.0200994i
\(486\) 0 0
\(487\) −5.58479e6 4.05758e6i −1.06705 0.775256i −0.0916689 0.995790i \(-0.529220\pi\)
−0.975379 + 0.220534i \(0.929220\pi\)
\(488\) 0 0
\(489\) −3.23039e6 + 2.34701e6i −0.610917 + 0.443858i
\(490\) 0 0
\(491\) −5.55882e6 −1.04059 −0.520294 0.853987i \(-0.674178\pi\)
−0.520294 + 0.853987i \(0.674178\pi\)
\(492\) 0 0
\(493\) −1.40067e6 + 4.31083e6i −0.259549 + 0.798811i
\(494\) 0 0
\(495\) 1.45191e6 0.266335
\(496\) 0 0
\(497\) −1.42112e6 −0.258071
\(498\) 0 0
\(499\) 1.36349e6 4.19639e6i 0.245132 0.754439i −0.750483 0.660890i \(-0.770179\pi\)
0.995615 0.0935488i \(-0.0298211\pi\)
\(500\) 0 0
\(501\) 2.12748e6 0.378678
\(502\) 0 0
\(503\) −7.46780e6 + 5.42567e6i −1.31605 + 0.956166i −0.316078 + 0.948733i \(0.602366\pi\)
−0.999972 + 0.00743317i \(0.997634\pi\)
\(504\) 0 0
\(505\) 4.19319e6 + 3.04653e6i 0.731671 + 0.531590i
\(506\) 0 0
\(507\) −3.60784e6 + 2.62125e6i −0.623344 + 0.452886i
\(508\) 0 0
\(509\) −1.91903e6 + 5.90616e6i −0.328312 + 1.01044i 0.641612 + 0.767030i \(0.278266\pi\)
−0.969923 + 0.243410i \(0.921734\pi\)
\(510\) 0 0
\(511\) −106447. + 327610.i −0.0180335 + 0.0555015i
\(512\) 0 0
\(513\) 8.86662e6 + 6.44198e6i 1.48753 + 1.08075i
\(514\) 0 0
\(515\) −3.40576e6 1.04818e7i −0.565843 1.74148i
\(516\) 0 0
\(517\) 941803. + 2.89857e6i 0.154965 + 0.476933i
\(518\) 0 0
\(519\) 1.83857e6 + 1.33580e6i 0.299614 + 0.217683i
\(520\) 0 0
\(521\) 2.46340e6 0.397595 0.198798 0.980041i \(-0.436296\pi\)
0.198798 + 0.980041i \(0.436296\pi\)
\(522\) 0 0
\(523\) 4.05031e6 2.94272e6i 0.647491 0.470430i −0.214924 0.976631i \(-0.568950\pi\)
0.862416 + 0.506201i \(0.168950\pi\)
\(524\) 0 0
\(525\) −249431. 767670.i −0.0394959 0.121556i
\(526\) 0 0
\(527\) −1.22283e6 + 2.63070e6i −0.191796 + 0.412615i
\(528\) 0 0
\(529\) −654923. 2.01565e6i −0.101754 0.313166i
\(530\) 0 0
\(531\) −139106. + 101066.i −0.0214096 + 0.0155550i
\(532\) 0 0
\(533\) 1.01370e6 0.154558
\(534\) 0 0
\(535\) −687144. 499239.i −0.103792 0.0754092i
\(536\) 0 0
\(537\) −1.60374e6 4.93581e6i −0.239993 0.738623i
\(538\) 0 0
\(539\) 3.13232e6 + 9.64029e6i 0.464402 + 1.42928i
\(540\) 0 0
\(541\) 6.24723e6 + 4.53888e6i 0.917687 + 0.666739i 0.942947 0.332942i \(-0.108041\pi\)
−0.0252603 + 0.999681i \(0.508041\pi\)
\(542\) 0 0
\(543\) 654492. 2.01432e6i 0.0952587 0.293176i
\(544\) 0 0
\(545\) 2.36773e6 7.28712e6i 0.341461 1.05091i
\(546\) 0 0
\(547\) −3.52772e6 + 2.56304e6i −0.504110 + 0.366257i −0.810585 0.585621i \(-0.800851\pi\)
0.306475 + 0.951879i \(0.400851\pi\)
\(548\) 0 0
\(549\) −958158. 696143.i −0.135677 0.0985752i
\(550\) 0 0
\(551\) 1.86023e7 1.35154e7i 2.61029 1.89648i
\(552\) 0 0
\(553\) 1.61585e6 0.224692
\(554\) 0 0
\(555\) −5.29489e6 + 1.62960e7i −0.729667 + 2.24568i
\(556\) 0 0
\(557\) 2.02487e6 0.276541 0.138271 0.990394i \(-0.455846\pi\)
0.138271 + 0.990394i \(0.455846\pi\)
\(558\) 0 0
\(559\) −5.39425e6 −0.730132
\(560\) 0 0
\(561\) −1.50434e6 + 4.62987e6i −0.201808 + 0.621100i
\(562\) 0 0
\(563\) 8.29864e6 1.10341 0.551704 0.834040i \(-0.313978\pi\)
0.551704 + 0.834040i \(0.313978\pi\)
\(564\) 0 0
\(565\) 6.17406e6 4.48572e6i 0.813673 0.591168i
\(566\) 0 0
\(567\) 751635. + 546095.i 0.0981859 + 0.0713363i
\(568\) 0 0
\(569\) −1.42835e6 + 1.03776e6i −0.184950 + 0.134374i −0.676408 0.736528i \(-0.736464\pi\)
0.491458 + 0.870901i \(0.336464\pi\)
\(570\) 0 0
\(571\) 332338. 1.02283e6i 0.0426569 0.131284i −0.927460 0.373922i \(-0.878013\pi\)
0.970117 + 0.242638i \(0.0780127\pi\)
\(572\) 0 0
\(573\) 913280. 2.81079e6i 0.116203 0.357636i
\(574\) 0 0
\(575\) 5.08760e6 + 3.69635e6i 0.641716 + 0.466234i
\(576\) 0 0
\(577\) 3.61832e6 + 1.11360e7i 0.452446 + 1.39249i 0.874107 + 0.485733i \(0.161447\pi\)
−0.421661 + 0.906754i \(0.638553\pi\)
\(578\) 0 0
\(579\) −3.19377e6 9.82943e6i −0.395920 1.21852i
\(580\) 0 0
\(581\) 378713. + 275151.i 0.0465447 + 0.0338167i
\(582\) 0 0
\(583\) −6.07576e6 −0.740337
\(584\) 0 0
\(585\) 489182. 355412.i 0.0590991 0.0429380i
\(586\) 0 0
\(587\) 1.87532e6 + 5.77163e6i 0.224636 + 0.691358i 0.998328 + 0.0577967i \(0.0184075\pi\)
−0.773693 + 0.633561i \(0.781592\pi\)
\(588\) 0 0
\(589\) 1.28627e7 7.15033e6i 1.52772 0.849254i
\(590\) 0 0
\(591\) 4.38838e6 + 1.35061e7i 0.516816 + 1.59060i
\(592\) 0 0
\(593\) −8.72496e6 + 6.33905e6i −1.01889 + 0.740266i −0.966055 0.258337i \(-0.916825\pi\)
−0.0528338 + 0.998603i \(0.516825\pi\)
\(594\) 0 0
\(595\) −777214. −0.0900012
\(596\) 0 0
\(597\) −6.73580e6 4.89384e6i −0.773487 0.561972i
\(598\) 0 0
\(599\) 2.93597e6 + 9.03598e6i 0.334337 + 1.02898i 0.967048 + 0.254595i \(0.0819421\pi\)
−0.632711 + 0.774388i \(0.718058\pi\)
\(600\) 0 0
\(601\) −1.03207e6 3.17639e6i −0.116553 0.358714i 0.875715 0.482829i \(-0.160391\pi\)
−0.992268 + 0.124115i \(0.960391\pi\)
\(602\) 0 0
\(603\) −515612. 374614.i −0.0577470 0.0419557i
\(604\) 0 0
\(605\) 5.27367e6 1.62307e7i 0.585766 1.80280i
\(606\) 0 0
\(607\) 393975. 1.21253e6i 0.0434007 0.133574i −0.927008 0.375041i \(-0.877629\pi\)
0.970409 + 0.241467i \(0.0776286\pi\)
\(608\) 0 0
\(609\) 1.80372e6 1.31048e6i 0.197073 0.143182i
\(610\) 0 0
\(611\) 1.02685e6 + 746051.i 0.111277 + 0.0808473i
\(612\) 0 0
\(613\) −2.45531e6 + 1.78389e6i −0.263910 + 0.191742i −0.711869 0.702312i \(-0.752151\pi\)
0.447959 + 0.894054i \(0.352151\pi\)
\(614\) 0 0
\(615\) −4.52716e6 −0.482656
\(616\) 0 0
\(617\) −5.07840e6 + 1.56297e7i −0.537049 + 1.65287i 0.202131 + 0.979358i \(0.435213\pi\)
−0.739180 + 0.673508i \(0.764787\pi\)
\(618\) 0 0
\(619\) −5.53624e6 −0.580749 −0.290374 0.956913i \(-0.593780\pi\)
−0.290374 + 0.956913i \(0.593780\pi\)
\(620\) 0 0
\(621\) −8.27922e6 −0.861511
\(622\) 0 0
\(623\) 157729. 485441.i 0.0162814 0.0501090i
\(624\) 0 0
\(625\) −1.00632e7 −1.03047
\(626\) 0 0
\(627\) 1.99790e7 1.45156e7i 2.02958 1.47458i
\(628\) 0 0
\(629\) 6.56715e6 + 4.77132e6i 0.661836 + 0.480852i
\(630\) 0 0
\(631\) 2.78018e6 2.01992e6i 0.277971 0.201958i −0.440061 0.897968i \(-0.645043\pi\)
0.718032 + 0.696010i \(0.245043\pi\)
\(632\) 0 0
\(633\) −165021. + 507883.i −0.0163693 + 0.0503796i
\(634\) 0 0
\(635\) −3.96794e6 + 1.22121e7i −0.390509 + 1.20186i
\(636\) 0 0
\(637\) 3.41518e6 + 2.48128e6i 0.333477 + 0.242285i
\(638\) 0 0
\(639\) 722847. + 2.22469e6i 0.0700317 + 0.215535i
\(640\) 0 0
\(641\) −3.57870e6 1.10141e7i −0.344018 1.05878i −0.962108 0.272670i \(-0.912093\pi\)
0.618090 0.786107i \(-0.287907\pi\)
\(642\) 0 0
\(643\) −9.06507e6 6.58616e6i −0.864656 0.628210i 0.0644913 0.997918i \(-0.479458\pi\)
−0.929148 + 0.369709i \(0.879458\pi\)
\(644\) 0 0
\(645\) 2.40906e7 2.28007
\(646\) 0 0
\(647\) −8.18549e6 + 5.94711e6i −0.768748 + 0.558528i −0.901581 0.432610i \(-0.857593\pi\)
0.132833 + 0.991138i \(0.457593\pi\)
\(648\) 0 0
\(649\) 1.08680e6 + 3.34483e6i 0.101283 + 0.311718i
\(650\) 0 0
\(651\) 1.24719e6 693311.i 0.115340 0.0641174i
\(652\) 0 0
\(653\) 190452. + 586151.i 0.0174784 + 0.0537931i 0.959415 0.281997i \(-0.0909968\pi\)
−0.941937 + 0.335790i \(0.890997\pi\)
\(654\) 0 0
\(655\) −6.85252e6 + 4.97864e6i −0.624089 + 0.453427i
\(656\) 0 0
\(657\) 567002. 0.0512473
\(658\) 0 0
\(659\) 2.80255e6 + 2.03617e6i 0.251385 + 0.182642i 0.706340 0.707872i \(-0.250345\pi\)
−0.454955 + 0.890514i \(0.650345\pi\)
\(660\) 0 0
\(661\) 1.50470e6 + 4.63100e6i 0.133951 + 0.412260i 0.995425 0.0955414i \(-0.0304582\pi\)
−0.861474 + 0.507802i \(0.830458\pi\)
\(662\) 0 0
\(663\) 626494. + 1.92815e6i 0.0553520 + 0.170356i
\(664\) 0 0
\(665\) 3.18972e6 + 2.31747e6i 0.279704 + 0.203217i
\(666\) 0 0
\(667\) −5.36761e6 + 1.65198e7i −0.467161 + 1.43777i
\(668\) 0 0
\(669\) −3.80393e6 + 1.17073e7i −0.328600 + 1.01133i
\(670\) 0 0
\(671\) −1.95983e7 + 1.42390e7i −1.68040 + 1.22088i
\(672\) 0 0
\(673\) −7.00359e6 5.08840e6i −0.596050 0.433056i 0.248425 0.968651i \(-0.420087\pi\)
−0.844475 + 0.535595i \(0.820087\pi\)
\(674\) 0 0
\(675\) −9.75716e6 + 7.08899e6i −0.824260 + 0.598860i
\(676\) 0 0
\(677\) 2.50518e6 0.210072 0.105036 0.994468i \(-0.466504\pi\)
0.105036 + 0.994468i \(0.466504\pi\)
\(678\) 0 0
\(679\) −12755.6 + 39257.8i −0.00106176 + 0.00326777i
\(680\) 0 0
\(681\) 2.08602e7 1.72366
\(682\) 0 0
\(683\) 1.12662e7 0.924118 0.462059 0.886849i \(-0.347111\pi\)
0.462059 + 0.886849i \(0.347111\pi\)
\(684\) 0 0
\(685\) 6.64650e6 2.04558e7i 0.541211 1.66568i
\(686\) 0 0
\(687\) 1.32618e7 1.07204
\(688\) 0 0
\(689\) −2.04706e6 + 1.48728e6i −0.164279 + 0.119356i
\(690\) 0 0
\(691\) −3.97349e6 2.88691e6i −0.316575 0.230006i 0.418137 0.908384i \(-0.362683\pi\)
−0.734713 + 0.678378i \(0.762683\pi\)
\(692\) 0 0
\(693\) −273716. + 198866.i −0.0216504 + 0.0157300i
\(694\) 0 0
\(695\) 4.15251e6 1.27801e7i 0.326098 1.00363i
\(696\) 0 0
\(697\) −662755. + 2.03975e6i −0.0516739 + 0.159036i
\(698\) 0 0
\(699\) −1.43456e7 1.04227e7i −1.11052 0.806838i
\(700\) 0 0
\(701\) 154158. + 474449.i 0.0118487 + 0.0364665i 0.956806 0.290727i \(-0.0938971\pi\)
−0.944957 + 0.327193i \(0.893897\pi\)
\(702\) 0 0
\(703\) −1.27250e7 3.91634e7i −0.971110 2.98877i
\(704\) 0 0
\(705\) −4.58589e6 3.33185e6i −0.347497 0.252471i
\(706\) 0 0
\(707\) −1.20778e6 −0.0908740
\(708\) 0 0
\(709\) 1.48695e7 1.08033e7i 1.11091 0.807126i 0.128106 0.991760i \(-0.459110\pi\)
0.982807 + 0.184635i \(0.0591102\pi\)
\(710\) 0 0
\(711\) −821896. 2.52954e6i −0.0609738 0.187658i
\(712\) 0 0
\(713\) −4.68607e6 + 1.00813e7i −0.345211 + 0.742662i
\(714\) 0 0
\(715\) −3.82187e6 1.17625e7i −0.279583 0.860468i
\(716\) 0 0
\(717\) 6.83888e6 4.96874e6i 0.496806 0.360951i
\(718\) 0 0
\(719\) −2.28901e7 −1.65129 −0.825647 0.564187i \(-0.809190\pi\)
−0.825647 + 0.564187i \(0.809190\pi\)
\(720\) 0 0
\(721\) 2.07774e6 + 1.50956e6i 0.148851 + 0.108147i
\(722\) 0 0
\(723\) −4.65135e6 1.43154e7i −0.330928 1.01849i
\(724\) 0 0
\(725\) 7.81911e6 + 2.40647e7i 0.552474 + 1.70034i
\(726\) 0 0
\(727\) −1.17291e7 8.52172e6i −0.823057 0.597986i 0.0945294 0.995522i \(-0.469865\pi\)
−0.917587 + 0.397536i \(0.869865\pi\)
\(728\) 0 0
\(729\) 4.83867e6 1.48919e7i 0.337215 1.03784i
\(730\) 0 0
\(731\) 3.52675e6 1.08542e7i 0.244107 0.751285i
\(732\) 0 0
\(733\) −1.53100e7 + 1.11233e7i −1.05248 + 0.764672i −0.972683 0.232139i \(-0.925428\pi\)
−0.0797983 + 0.996811i \(0.525428\pi\)
\(734\) 0 0
\(735\) −1.52521e7 1.10813e7i −1.04139 0.756612i
\(736\) 0 0
\(737\) −1.05464e7 + 7.66240e6i −0.715212 + 0.519632i
\(738\) 0 0
\(739\) 7.99280e6 0.538379 0.269190 0.963087i \(-0.413244\pi\)
0.269190 + 0.963087i \(0.413244\pi\)
\(740\) 0 0
\(741\) 3.17813e6 9.78128e6i 0.212631 0.654411i
\(742\) 0 0
\(743\) −7.26055e6 −0.482500 −0.241250 0.970463i \(-0.577557\pi\)
−0.241250 + 0.970463i \(0.577557\pi\)
\(744\) 0 0
\(745\) 4.69421e6 0.309864
\(746\) 0 0
\(747\) 238105. 732812.i 0.0156123 0.0480497i
\(748\) 0 0
\(749\) 197921. 0.0128910
\(750\) 0 0
\(751\) 2.29092e7 1.66445e7i 1.48221 1.07689i 0.505376 0.862899i \(-0.331354\pi\)
0.976836 0.213991i \(-0.0686462\pi\)
\(752\) 0 0
\(753\) −1.81846e7 1.32119e7i −1.16874 0.849138i
\(754\) 0 0
\(755\) −1.18061e7 + 8.57765e6i −0.753772 + 0.547647i
\(756\) 0 0
\(757\) 3.13489e6 9.64821e6i 0.198830 0.611937i −0.801080 0.598557i \(-0.795741\pi\)
0.999910 0.0133800i \(-0.00425911\pi\)
\(758\) 0 0
\(759\) −5.76486e6 + 1.77424e7i −0.363232 + 1.11791i
\(760\) 0 0
\(761\) 8.11728e6 + 5.89755e6i 0.508100 + 0.369156i 0.812102 0.583515i \(-0.198323\pi\)
−0.304003 + 0.952671i \(0.598323\pi\)
\(762\) 0 0
\(763\) 551739. + 1.69808e6i 0.0343101 + 0.105596i
\(764\) 0 0
\(765\) 395327. + 1.21669e6i 0.0244232 + 0.0751669i
\(766\) 0 0
\(767\) 1.18494e6 + 860912.i 0.0727293 + 0.0528409i
\(768\) 0 0
\(769\) −2.35703e7 −1.43730 −0.718652 0.695370i \(-0.755241\pi\)
−0.718652 + 0.695370i \(0.755241\pi\)
\(770\) 0 0
\(771\) −9.50979e6 + 6.90927e6i −0.576149 + 0.418597i
\(772\) 0 0
\(773\) −9.32152e6 2.86887e7i −0.561097 1.72688i −0.679273 0.733886i \(-0.737705\pi\)
0.118176 0.992993i \(-0.462295\pi\)
\(774\) 0 0
\(775\) 3.10938e6 + 1.58933e7i 0.185960 + 0.950516i
\(776\) 0 0
\(777\) −1.23384e6 3.79737e6i −0.0733173 0.225647i
\(778\) 0 0
\(779\) 8.80203e6 6.39505e6i 0.519684 0.377572i
\(780\) 0 0
\(781\) 4.78459e7 2.80684
\(782\) 0 0
\(783\) −2.69505e7 1.95807e7i −1.57095 1.14136i
\(784\) 0 0
\(785\) 2.45009e6 + 7.54060e6i 0.141908 + 0.436749i
\(786\) 0 0
\(787\) 8.54975e6 + 2.63134e7i 0.492058 + 1.51440i 0.821492 + 0.570221i \(0.193142\pi\)
−0.329434 + 0.944179i \(0.606858\pi\)
\(788\) 0 0
\(789\) 8.68614e6 + 6.31085e6i 0.496746