Properties

Label 144.6.i.d.49.2
Level $144$
Weight $6$
Character 144.49
Analytic conductor $23.095$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 144.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.0952700531\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{10} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.2
Root \(9.84603i\) of defining polynomial
Character \(\chi\) \(=\) 144.49
Dual form 144.6.i.d.97.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.67637 + 12.9507i) q^{3} +(13.1603 - 22.7942i) q^{5} +(31.6287 + 54.7826i) q^{7} +(-92.4411 - 224.730i) q^{9} +O(q^{10})\) \(q+(-8.67637 + 12.9507i) q^{3} +(13.1603 - 22.7942i) q^{5} +(31.6287 + 54.7826i) q^{7} +(-92.4411 - 224.730i) q^{9} +(49.1194 + 85.0772i) q^{11} +(369.143 - 639.374i) q^{13} +(181.018 + 368.206i) q^{15} +250.060 q^{17} -1102.41 q^{19} +(-983.895 - 65.6998i) q^{21} +(2204.70 - 3818.66i) q^{23} +(1216.12 + 2106.37i) q^{25} +(3712.47 + 752.665i) q^{27} +(3941.06 + 6826.11i) q^{29} +(-2305.65 + 3993.49i) q^{31} +(-1527.99 - 102.032i) q^{33} +1664.97 q^{35} +11896.3 q^{37} +(5077.52 + 10328.1i) q^{39} +(-5040.58 + 8730.55i) q^{41} +(3518.99 + 6095.07i) q^{43} +(-6339.10 - 850.381i) q^{45} +(7459.33 + 12919.9i) q^{47} +(6402.75 - 11089.9i) q^{49} +(-2169.62 + 3238.45i) q^{51} +22451.7 q^{53} +2585.69 q^{55} +(9564.88 - 14276.9i) q^{57} +(5405.25 - 9362.17i) q^{59} +(594.647 + 1029.96i) q^{61} +(9387.50 - 12172.1i) q^{63} +(-9716.02 - 16828.6i) q^{65} +(29590.2 - 51251.8i) q^{67} +(30325.5 + 61684.6i) q^{69} -14326.6 q^{71} -53098.2 q^{73} +(-37830.5 - 2526.14i) q^{75} +(-3107.17 + 5381.77i) q^{77} +(-18695.6 - 32381.6i) q^{79} +(-41958.3 + 41548.6i) q^{81} +(60439.5 + 104684. i) q^{83} +(3290.85 - 5699.93i) q^{85} +(-122597. - 8186.44i) q^{87} +97873.2 q^{89} +46702.1 q^{91} +(-31713.9 - 64508.8i) q^{93} +(-14507.9 + 25128.5i) q^{95} +(-53356.7 - 92416.4i) q^{97} +(14578.8 - 18903.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 12q^{3} - 21q^{5} - 29q^{7} + 12q^{9} + O(q^{10}) \) \( 10q - 12q^{3} - 21q^{5} - 29q^{7} + 12q^{9} - 177q^{11} - 181q^{13} - 117q^{15} + 2280q^{17} + 832q^{19} - 207q^{21} - 399q^{23} - 4778q^{25} + 7128q^{27} - 6033q^{29} - 2759q^{31} + 9603q^{33} - 37146q^{35} - 15172q^{37} - 5529q^{39} - 18435q^{41} - 1469q^{43} - 64089q^{45} + 25155q^{47} - 4056q^{49} - 90612q^{51} + 116844q^{53} - 14778q^{55} + 26934q^{57} + 90537q^{59} + 1403q^{61} + 198255q^{63} - 148407q^{65} - 13907q^{67} + 214425q^{69} - 229368q^{71} + 15200q^{73} - 44640q^{75} - 211983q^{77} - 29993q^{79} - 404172q^{81} + 228951q^{83} - 49662q^{85} - 397323q^{87} + 598332q^{89} - 124930q^{91} + 250041q^{93} + 394764q^{95} + 40541q^{97} + 697239q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −8.67637 + 12.9507i −0.556590 + 0.830788i
\(4\) 0 0
\(5\) 13.1603 22.7942i 0.235418 0.407755i −0.723976 0.689825i \(-0.757688\pi\)
0.959394 + 0.282069i \(0.0910208\pi\)
\(6\) 0 0
\(7\) 31.6287 + 54.7826i 0.243970 + 0.422569i 0.961842 0.273607i \(-0.0882168\pi\)
−0.717871 + 0.696176i \(0.754883\pi\)
\(8\) 0 0
\(9\) −92.4411 224.730i −0.380416 0.924815i
\(10\) 0 0
\(11\) 49.1194 + 85.0772i 0.122397 + 0.211998i 0.920712 0.390242i \(-0.127609\pi\)
−0.798315 + 0.602240i \(0.794275\pi\)
\(12\) 0 0
\(13\) 369.143 639.374i 0.605809 1.04929i −0.386114 0.922451i \(-0.626183\pi\)
0.991923 0.126841i \(-0.0404839\pi\)
\(14\) 0 0
\(15\) 181.018 + 368.206i 0.207727 + 0.422535i
\(16\) 0 0
\(17\) 250.060 0.209856 0.104928 0.994480i \(-0.466539\pi\)
0.104928 + 0.994480i \(0.466539\pi\)
\(18\) 0 0
\(19\) −1102.41 −0.700579 −0.350290 0.936641i \(-0.613917\pi\)
−0.350290 + 0.936641i \(0.613917\pi\)
\(20\) 0 0
\(21\) −983.895 65.6998i −0.486856 0.0325099i
\(22\) 0 0
\(23\) 2204.70 3818.66i 0.869022 1.50519i 0.00602414 0.999982i \(-0.498082\pi\)
0.862998 0.505208i \(-0.168584\pi\)
\(24\) 0 0
\(25\) 1216.12 + 2106.37i 0.389157 + 0.674040i
\(26\) 0 0
\(27\) 3712.47 + 752.665i 0.980061 + 0.198698i
\(28\) 0 0
\(29\) 3941.06 + 6826.11i 0.870197 + 1.50723i 0.861792 + 0.507262i \(0.169342\pi\)
0.00840534 + 0.999965i \(0.497324\pi\)
\(30\) 0 0
\(31\) −2305.65 + 3993.49i −0.430912 + 0.746361i −0.996952 0.0780167i \(-0.975141\pi\)
0.566040 + 0.824377i \(0.308475\pi\)
\(32\) 0 0
\(33\) −1527.99 102.032i −0.244250 0.0163099i
\(34\) 0 0
\(35\) 1664.97 0.229740
\(36\) 0 0
\(37\) 11896.3 1.42859 0.714297 0.699843i \(-0.246747\pi\)
0.714297 + 0.699843i \(0.246747\pi\)
\(38\) 0 0
\(39\) 5077.52 + 10328.1i 0.534552 + 1.08732i
\(40\) 0 0
\(41\) −5040.58 + 8730.55i −0.468297 + 0.811114i −0.999344 0.0362286i \(-0.988466\pi\)
0.531047 + 0.847343i \(0.321799\pi\)
\(42\) 0 0
\(43\) 3518.99 + 6095.07i 0.290233 + 0.502698i 0.973865 0.227129i \(-0.0729338\pi\)
−0.683632 + 0.729827i \(0.739600\pi\)
\(44\) 0 0
\(45\) −6339.10 850.381i −0.466655 0.0626012i
\(46\) 0 0
\(47\) 7459.33 + 12919.9i 0.492555 + 0.853131i 0.999963 0.00857499i \(-0.00272954\pi\)
−0.507408 + 0.861706i \(0.669396\pi\)
\(48\) 0 0
\(49\) 6402.75 11089.9i 0.380957 0.659837i
\(50\) 0 0
\(51\) −2169.62 + 3238.45i −0.116804 + 0.174346i
\(52\) 0 0
\(53\) 22451.7 1.09789 0.548947 0.835857i \(-0.315029\pi\)
0.548947 + 0.835857i \(0.315029\pi\)
\(54\) 0 0
\(55\) 2585.69 0.115258
\(56\) 0 0
\(57\) 9564.88 14276.9i 0.389935 0.582033i
\(58\) 0 0
\(59\) 5405.25 9362.17i 0.202156 0.350144i −0.747067 0.664749i \(-0.768539\pi\)
0.949223 + 0.314605i \(0.101872\pi\)
\(60\) 0 0
\(61\) 594.647 + 1029.96i 0.0204614 + 0.0354401i 0.876075 0.482175i \(-0.160153\pi\)
−0.855613 + 0.517615i \(0.826820\pi\)
\(62\) 0 0
\(63\) 9387.50 12172.1i 0.297988 0.386379i
\(64\) 0 0
\(65\) −9716.02 16828.6i −0.285236 0.494044i
\(66\) 0 0
\(67\) 29590.2 51251.8i 0.805307 1.39483i −0.110776 0.993845i \(-0.535334\pi\)
0.916084 0.400988i \(-0.131333\pi\)
\(68\) 0 0
\(69\) 30325.5 + 61684.6i 0.766805 + 1.55975i
\(70\) 0 0
\(71\) −14326.6 −0.337284 −0.168642 0.985677i \(-0.553938\pi\)
−0.168642 + 0.985677i \(0.553938\pi\)
\(72\) 0 0
\(73\) −53098.2 −1.16620 −0.583099 0.812401i \(-0.698160\pi\)
−0.583099 + 0.812401i \(0.698160\pi\)
\(74\) 0 0
\(75\) −37830.5 2526.14i −0.776585 0.0518566i
\(76\) 0 0
\(77\) −3107.17 + 5381.77i −0.0597225 + 0.103442i
\(78\) 0 0
\(79\) −18695.6 32381.6i −0.337032 0.583756i 0.646841 0.762625i \(-0.276090\pi\)
−0.983873 + 0.178869i \(0.942756\pi\)
\(80\) 0 0
\(81\) −41958.3 + 41548.6i −0.710567 + 0.703629i
\(82\) 0 0
\(83\) 60439.5 + 104684.i 0.962998 + 1.66796i 0.714900 + 0.699226i \(0.246472\pi\)
0.248097 + 0.968735i \(0.420195\pi\)
\(84\) 0 0
\(85\) 3290.85 5699.93i 0.0494039 0.0855701i
\(86\) 0 0
\(87\) −122597. 8186.44i −1.73653 0.115957i
\(88\) 0 0
\(89\) 97873.2 1.30975 0.654875 0.755737i \(-0.272721\pi\)
0.654875 + 0.755737i \(0.272721\pi\)
\(90\) 0 0
\(91\) 46702.1 0.591198
\(92\) 0 0
\(93\) −31713.9 64508.8i −0.380226 0.773413i
\(94\) 0 0
\(95\) −14507.9 + 25128.5i −0.164929 + 0.285665i
\(96\) 0 0
\(97\) −53356.7 92416.4i −0.575784 0.997286i −0.995956 0.0898422i \(-0.971364\pi\)
0.420172 0.907444i \(-0.361970\pi\)
\(98\) 0 0
\(99\) 14578.8 18903.2i 0.149497 0.193842i
\(100\) 0 0
\(101\) −48236.1 83547.3i −0.470510 0.814946i 0.528922 0.848671i \(-0.322597\pi\)
−0.999431 + 0.0337242i \(0.989263\pi\)
\(102\) 0 0
\(103\) 14972.2 25932.6i 0.139057 0.240854i −0.788083 0.615569i \(-0.788926\pi\)
0.927140 + 0.374715i \(0.122260\pi\)
\(104\) 0 0
\(105\) −14445.9 + 21562.5i −0.127871 + 0.190865i
\(106\) 0 0
\(107\) −22758.9 −0.192173 −0.0960865 0.995373i \(-0.530633\pi\)
−0.0960865 + 0.995373i \(0.530633\pi\)
\(108\) 0 0
\(109\) −2671.93 −0.0215407 −0.0107703 0.999942i \(-0.503428\pi\)
−0.0107703 + 0.999942i \(0.503428\pi\)
\(110\) 0 0
\(111\) −103217. + 154066.i −0.795141 + 1.18686i
\(112\) 0 0
\(113\) −65669.6 + 113743.i −0.483803 + 0.837971i −0.999827 0.0186028i \(-0.994078\pi\)
0.516024 + 0.856574i \(0.327412\pi\)
\(114\) 0 0
\(115\) −58028.9 100509.i −0.409166 0.708697i
\(116\) 0 0
\(117\) −177811. 23853.0i −1.20086 0.161094i
\(118\) 0 0
\(119\) 7909.09 + 13698.9i 0.0511987 + 0.0886787i
\(120\) 0 0
\(121\) 75700.1 131116.i 0.470038 0.814130i
\(122\) 0 0
\(123\) −69332.7 141029.i −0.413214 0.840513i
\(124\) 0 0
\(125\) 146269. 0.837293
\(126\) 0 0
\(127\) −236012. −1.29845 −0.649223 0.760598i \(-0.724906\pi\)
−0.649223 + 0.760598i \(0.724906\pi\)
\(128\) 0 0
\(129\) −109467. 7309.72i −0.579176 0.0386746i
\(130\) 0 0
\(131\) 180183. 312086.i 0.917352 1.58890i 0.113930 0.993489i \(-0.463656\pi\)
0.803421 0.595411i \(-0.203011\pi\)
\(132\) 0 0
\(133\) −34867.7 60392.6i −0.170920 0.296043i
\(134\) 0 0
\(135\) 66013.4 74717.5i 0.311744 0.352848i
\(136\) 0 0
\(137\) 118833. + 205825.i 0.540923 + 0.936906i 0.998851 + 0.0479167i \(0.0152582\pi\)
−0.457929 + 0.888989i \(0.651408\pi\)
\(138\) 0 0
\(139\) 81673.4 141462.i 0.358545 0.621018i −0.629173 0.777265i \(-0.716606\pi\)
0.987718 + 0.156247i \(0.0499397\pi\)
\(140\) 0 0
\(141\) −232042. 15494.7i −0.982922 0.0656348i
\(142\) 0 0
\(143\) 72528.2 0.296597
\(144\) 0 0
\(145\) 207461. 0.819440
\(146\) 0 0
\(147\) 88069.1 + 179140.i 0.336148 + 0.683753i
\(148\) 0 0
\(149\) −167803. + 290644.i −0.619205 + 1.07250i 0.370426 + 0.928862i \(0.379212\pi\)
−0.989631 + 0.143633i \(0.954121\pi\)
\(150\) 0 0
\(151\) −67788.5 117413.i −0.241943 0.419058i 0.719325 0.694674i \(-0.244451\pi\)
−0.961268 + 0.275616i \(0.911118\pi\)
\(152\) 0 0
\(153\) −23115.8 56196.1i −0.0798328 0.194078i
\(154\) 0 0
\(155\) 60685.7 + 105111.i 0.202888 + 0.351413i
\(156\) 0 0
\(157\) 212716. 368435.i 0.688733 1.19292i −0.283516 0.958968i \(-0.591501\pi\)
0.972248 0.233952i \(-0.0751659\pi\)
\(158\) 0 0
\(159\) −194800. + 290766.i −0.611076 + 0.912117i
\(160\) 0 0
\(161\) 278928. 0.848062
\(162\) 0 0
\(163\) 158679. 0.467789 0.233895 0.972262i \(-0.424853\pi\)
0.233895 + 0.972262i \(0.424853\pi\)
\(164\) 0 0
\(165\) −22434.4 + 33486.5i −0.0641512 + 0.0957547i
\(166\) 0 0
\(167\) −259223. + 448988.i −0.719254 + 1.24579i 0.242041 + 0.970266i \(0.422183\pi\)
−0.961296 + 0.275519i \(0.911150\pi\)
\(168\) 0 0
\(169\) −86886.2 150491.i −0.234010 0.405317i
\(170\) 0 0
\(171\) 101908. + 247744.i 0.266512 + 0.647907i
\(172\) 0 0
\(173\) 76589.0 + 132656.i 0.194559 + 0.336986i 0.946756 0.321953i \(-0.104339\pi\)
−0.752197 + 0.658938i \(0.771006\pi\)
\(174\) 0 0
\(175\) −76928.4 + 133244.i −0.189885 + 0.328891i
\(176\) 0 0
\(177\) 74348.7 + 151232.i 0.178378 + 0.362835i
\(178\) 0 0
\(179\) 736845. 1.71887 0.859437 0.511242i \(-0.170815\pi\)
0.859437 + 0.511242i \(0.170815\pi\)
\(180\) 0 0
\(181\) 28183.8 0.0639445 0.0319722 0.999489i \(-0.489821\pi\)
0.0319722 + 0.999489i \(0.489821\pi\)
\(182\) 0 0
\(183\) −18498.0 1235.21i −0.0408318 0.00272655i
\(184\) 0 0
\(185\) 156559. 271168.i 0.336316 0.582517i
\(186\) 0 0
\(187\) 12282.8 + 21274.4i 0.0256858 + 0.0444891i
\(188\) 0 0
\(189\) 76187.7 + 227184.i 0.155142 + 0.462619i
\(190\) 0 0
\(191\) 49660.5 + 86014.5i 0.0984981 + 0.170604i 0.911063 0.412267i \(-0.135263\pi\)
−0.812565 + 0.582870i \(0.801929\pi\)
\(192\) 0 0
\(193\) −208636. + 361368.i −0.403177 + 0.698324i −0.994107 0.108399i \(-0.965428\pi\)
0.590930 + 0.806723i \(0.298761\pi\)
\(194\) 0 0
\(195\) 302242. + 20182.3i 0.569205 + 0.0380088i
\(196\) 0 0
\(197\) 254565. 0.467340 0.233670 0.972316i \(-0.424927\pi\)
0.233670 + 0.972316i \(0.424927\pi\)
\(198\) 0 0
\(199\) 599702. 1.07350 0.536751 0.843741i \(-0.319652\pi\)
0.536751 + 0.843741i \(0.319652\pi\)
\(200\) 0 0
\(201\) 407011. + 827894.i 0.710584 + 1.44539i
\(202\) 0 0
\(203\) −249301. + 431803.i −0.424604 + 0.735436i
\(204\) 0 0
\(205\) 132671. + 229792.i 0.220491 + 0.381901i
\(206\) 0 0
\(207\) −1.06197e6 142462.i −1.72261 0.231086i
\(208\) 0 0
\(209\) −54149.4 93789.6i −0.0857488 0.148521i
\(210\) 0 0
\(211\) 378292. 655221.i 0.584953 1.01317i −0.409928 0.912118i \(-0.634446\pi\)
0.994881 0.101051i \(-0.0322206\pi\)
\(212\) 0 0
\(213\) 124303. 185539.i 0.187729 0.280212i
\(214\) 0 0
\(215\) 185243. 0.273304
\(216\) 0 0
\(217\) −291699. −0.420518
\(218\) 0 0
\(219\) 460699. 687658.i 0.649094 0.968863i
\(220\) 0 0
\(221\) 92307.9 159882.i 0.127133 0.220201i
\(222\) 0 0
\(223\) −55602.4 96306.2i −0.0748741 0.129686i 0.826157 0.563439i \(-0.190522\pi\)
−0.901032 + 0.433754i \(0.857189\pi\)
\(224\) 0 0
\(225\) 360947. 468013.i 0.475321 0.616314i
\(226\) 0 0
\(227\) −245380. 425010.i −0.316063 0.547438i 0.663600 0.748088i \(-0.269028\pi\)
−0.979663 + 0.200650i \(0.935695\pi\)
\(228\) 0 0
\(229\) −380511. + 659064.i −0.479488 + 0.830498i −0.999723 0.0235249i \(-0.992511\pi\)
0.520235 + 0.854023i \(0.325844\pi\)
\(230\) 0 0
\(231\) −42738.7 86934.2i −0.0526977 0.107192i
\(232\) 0 0
\(233\) −356267. −0.429918 −0.214959 0.976623i \(-0.568962\pi\)
−0.214959 + 0.976623i \(0.568962\pi\)
\(234\) 0 0
\(235\) 392667. 0.463825
\(236\) 0 0
\(237\) 581574. + 38834.8i 0.672565 + 0.0449107i
\(238\) 0 0
\(239\) −453120. + 784826.i −0.513119 + 0.888748i 0.486765 + 0.873533i \(0.338177\pi\)
−0.999884 + 0.0152152i \(0.995157\pi\)
\(240\) 0 0
\(241\) −261288. 452564.i −0.289785 0.501923i 0.683973 0.729507i \(-0.260251\pi\)
−0.973758 + 0.227584i \(0.926917\pi\)
\(242\) 0 0
\(243\) −174038. 903880.i −0.189073 0.981963i
\(244\) 0 0
\(245\) −168523. 291891.i −0.179368 0.310675i
\(246\) 0 0
\(247\) −406945. + 704849.i −0.424417 + 0.735113i
\(248\) 0 0
\(249\) −1.88013e6 125546.i −1.92172 0.128323i
\(250\) 0 0
\(251\) 625287. 0.626462 0.313231 0.949677i \(-0.398589\pi\)
0.313231 + 0.949677i \(0.398589\pi\)
\(252\) 0 0
\(253\) 433175. 0.425463
\(254\) 0 0
\(255\) 45265.4 + 92073.5i 0.0435929 + 0.0886716i
\(256\) 0 0
\(257\) 651106. 1.12775e6i 0.614921 1.06507i −0.375478 0.926831i \(-0.622521\pi\)
0.990398 0.138243i \(-0.0441454\pi\)
\(258\) 0 0
\(259\) 376266. + 651712.i 0.348534 + 0.603679i
\(260\) 0 0
\(261\) 1.16972e6 1.51669e6i 1.06287 1.37815i
\(262\) 0 0
\(263\) −716761. 1.24147e6i −0.638977 1.10674i −0.985658 0.168757i \(-0.946025\pi\)
0.346681 0.937983i \(-0.387309\pi\)
\(264\) 0 0
\(265\) 295471. 511770.i 0.258464 0.447672i
\(266\) 0 0
\(267\) −849184. + 1.26753e6i −0.728993 + 1.08812i
\(268\) 0 0
\(269\) −1.52329e6 −1.28352 −0.641758 0.766907i \(-0.721795\pi\)
−0.641758 + 0.766907i \(0.721795\pi\)
\(270\) 0 0
\(271\) −1.60134e6 −1.32453 −0.662263 0.749271i \(-0.730404\pi\)
−0.662263 + 0.749271i \(0.730404\pi\)
\(272\) 0 0
\(273\) −405205. + 604824.i −0.329054 + 0.491160i
\(274\) 0 0
\(275\) −119470. + 206927.i −0.0952633 + 0.165001i
\(276\) 0 0
\(277\) 446972. + 774178.i 0.350010 + 0.606235i 0.986251 0.165255i \(-0.0528448\pi\)
−0.636241 + 0.771491i \(0.719511\pi\)
\(278\) 0 0
\(279\) 1.11059e6 + 148985.i 0.854172 + 0.114586i
\(280\) 0 0
\(281\) 14200.0 + 24595.2i 0.0107281 + 0.0185817i 0.871340 0.490680i \(-0.163252\pi\)
−0.860612 + 0.509262i \(0.829918\pi\)
\(282\) 0 0
\(283\) −554783. + 960912.i −0.411772 + 0.713210i −0.995084 0.0990384i \(-0.968423\pi\)
0.583312 + 0.812248i \(0.301757\pi\)
\(284\) 0 0
\(285\) −199555. 405912.i −0.145529 0.296019i
\(286\) 0 0
\(287\) −637709. −0.457002
\(288\) 0 0
\(289\) −1.35733e6 −0.955960
\(290\) 0 0
\(291\) 1.65980e6 + 110834.i 1.14901 + 0.0767253i
\(292\) 0 0
\(293\) −1.22884e6 + 2.12841e6i −0.836230 + 1.44839i 0.0567942 + 0.998386i \(0.481912\pi\)
−0.893025 + 0.450008i \(0.851421\pi\)
\(294\) 0 0
\(295\) −142269. 246417.i −0.0951821 0.164860i
\(296\) 0 0
\(297\) 118319. + 352817.i 0.0778331 + 0.232091i
\(298\) 0 0
\(299\) −1.62770e6 2.81926e6i −1.05292 1.82372i
\(300\) 0 0
\(301\) −222602. + 385559.i −0.141616 + 0.245287i
\(302\) 0 0
\(303\) 1.50051e6 + 100197.i 0.938928 + 0.0626971i
\(304\) 0 0
\(305\) 31302.8 0.0192679
\(306\) 0 0
\(307\) −1.77336e6 −1.07387 −0.536934 0.843624i \(-0.680417\pi\)
−0.536934 + 0.843624i \(0.680417\pi\)
\(308\) 0 0
\(309\) 205941. + 418902.i 0.122701 + 0.249584i
\(310\) 0 0
\(311\) 752855. 1.30398e6i 0.441378 0.764489i −0.556414 0.830905i \(-0.687823\pi\)
0.997792 + 0.0664162i \(0.0211565\pi\)
\(312\) 0 0
\(313\) 406353. + 703823.i 0.234446 + 0.406072i 0.959111 0.283029i \(-0.0913392\pi\)
−0.724666 + 0.689100i \(0.758006\pi\)
\(314\) 0 0
\(315\) −153912. 374169.i −0.0873967 0.212467i
\(316\) 0 0
\(317\) −523798. 907244.i −0.292763 0.507080i 0.681699 0.731632i \(-0.261241\pi\)
−0.974462 + 0.224553i \(0.927908\pi\)
\(318\) 0 0
\(319\) −387164. + 670588.i −0.213019 + 0.368960i
\(320\) 0 0
\(321\) 197465. 294744.i 0.106962 0.159655i
\(322\) 0 0
\(323\) −275668. −0.147021
\(324\) 0 0
\(325\) 1.79568e6 0.943020
\(326\) 0 0
\(327\) 23182.7 34603.4i 0.0119893 0.0178957i
\(328\) 0 0
\(329\) −471858. + 817283.i −0.240338 + 0.416277i
\(330\) 0 0
\(331\) −34002.7 58894.4i −0.0170586 0.0295463i 0.857370 0.514700i \(-0.172097\pi\)
−0.874429 + 0.485154i \(0.838764\pi\)
\(332\) 0 0
\(333\) −1.09971e6 2.67347e6i −0.543460 1.32119i
\(334\) 0 0
\(335\) −778830. 1.34897e6i −0.379167 0.656737i
\(336\) 0 0
\(337\) 208236. 360675.i 0.0998806 0.172998i −0.811755 0.583999i \(-0.801487\pi\)
0.911635 + 0.411001i \(0.134821\pi\)
\(338\) 0 0
\(339\) −903279. 1.83735e6i −0.426897 0.868344i
\(340\) 0 0
\(341\) −453007. −0.210969
\(342\) 0 0
\(343\) 1.87321e6 0.859709
\(344\) 0 0
\(345\) 1.80514e6 + 120539.i 0.816514 + 0.0545229i
\(346\) 0 0
\(347\) −1.40370e6 + 2.43128e6i −0.625822 + 1.08396i 0.362559 + 0.931961i \(0.381903\pi\)
−0.988381 + 0.151995i \(0.951430\pi\)
\(348\) 0 0
\(349\) 240986. + 417401.i 0.105908 + 0.183438i 0.914109 0.405469i \(-0.132892\pi\)
−0.808201 + 0.588907i \(0.799558\pi\)
\(350\) 0 0
\(351\) 1.85166e6 2.09581e6i 0.802222 0.907998i
\(352\) 0 0
\(353\) −2.00019e6 3.46442e6i −0.854346 1.47977i −0.877251 0.480033i \(-0.840625\pi\)
0.0229050 0.999738i \(-0.492708\pi\)
\(354\) 0 0
\(355\) −188541. + 326563.i −0.0794027 + 0.137530i
\(356\) 0 0
\(357\) −246033. 16428.9i −0.102170 0.00682242i
\(358\) 0 0
\(359\) 800858. 0.327959 0.163979 0.986464i \(-0.447567\pi\)
0.163979 + 0.986464i \(0.447567\pi\)
\(360\) 0 0
\(361\) −1.26080e6 −0.509189
\(362\) 0 0
\(363\) 1.04125e6 + 2.11798e6i 0.414751 + 0.843638i
\(364\) 0 0
\(365\) −698785. + 1.21033e6i −0.274544 + 0.475524i
\(366\) 0 0
\(367\) 1.50486e6 + 2.60649e6i 0.583218 + 1.01016i 0.995095 + 0.0989236i \(0.0315399\pi\)
−0.411877 + 0.911239i \(0.635127\pi\)
\(368\) 0 0
\(369\) 2.42797e6 + 325709.i 0.928278 + 0.124527i
\(370\) 0 0
\(371\) 710120. + 1.22996e6i 0.267853 + 0.463936i
\(372\) 0 0
\(373\) −796653. + 1.37984e6i −0.296481 + 0.513520i −0.975328 0.220759i \(-0.929147\pi\)
0.678847 + 0.734280i \(0.262480\pi\)
\(374\) 0 0
\(375\) −1.26909e6 + 1.89429e6i −0.466029 + 0.695613i
\(376\) 0 0
\(377\) 5.81925e6 2.10869
\(378\) 0 0
\(379\) 297930. 0.106541 0.0532703 0.998580i \(-0.483035\pi\)
0.0532703 + 0.998580i \(0.483035\pi\)
\(380\) 0 0
\(381\) 2.04772e6 3.05651e6i 0.722702 1.07873i
\(382\) 0 0
\(383\) −645151. + 1.11743e6i −0.224732 + 0.389247i −0.956239 0.292587i \(-0.905484\pi\)
0.731507 + 0.681834i \(0.238817\pi\)
\(384\) 0 0
\(385\) 81782.2 + 141651.i 0.0281194 + 0.0487043i
\(386\) 0 0
\(387\) 1.04445e6 1.35426e6i 0.354494 0.459647i
\(388\) 0 0
\(389\) −2.49937e6 4.32903e6i −0.837444 1.45050i −0.892025 0.451986i \(-0.850716\pi\)
0.0545807 0.998509i \(-0.482618\pi\)
\(390\) 0 0
\(391\) 551309. 954894.i 0.182370 0.315874i
\(392\) 0 0
\(393\) 2.47840e6 + 5.04127e6i 0.809450 + 1.64649i
\(394\) 0 0
\(395\) −984153. −0.317373
\(396\) 0 0
\(397\) −558980. −0.178000 −0.0890000 0.996032i \(-0.528367\pi\)
−0.0890000 + 0.996032i \(0.528367\pi\)
\(398\) 0 0
\(399\) 1.08465e6 + 72427.8i 0.341081 + 0.0227758i
\(400\) 0 0
\(401\) −47103.6 + 81585.8i −0.0146283 + 0.0253369i −0.873247 0.487278i \(-0.837990\pi\)
0.858619 + 0.512615i \(0.171323\pi\)
\(402\) 0 0
\(403\) 1.70222e6 + 2.94834e6i 0.522101 + 0.904305i
\(404\) 0 0
\(405\) 394887. + 1.50320e6i 0.119629 + 0.455384i
\(406\) 0 0
\(407\) 584340. + 1.01211e6i 0.174856 + 0.302859i
\(408\) 0 0
\(409\) −2.73115e6 + 4.73049e6i −0.807304 + 1.39829i 0.107420 + 0.994214i \(0.465741\pi\)
−0.914724 + 0.404078i \(0.867592\pi\)
\(410\) 0 0
\(411\) −3.69661e6 246842.i −1.07944 0.0720800i
\(412\) 0 0
\(413\) 683845. 0.197280
\(414\) 0 0
\(415\) 3.18159e6 0.906827
\(416\) 0 0
\(417\) 1.12341e6 + 2.28511e6i 0.316372 + 0.643527i
\(418\) 0 0
\(419\) −418486. + 724839.i −0.116452 + 0.201700i −0.918359 0.395748i \(-0.870485\pi\)
0.801907 + 0.597448i \(0.203819\pi\)
\(420\) 0 0
\(421\) 3.21404e6 + 5.56689e6i 0.883785 + 1.53076i 0.847100 + 0.531433i \(0.178346\pi\)
0.0366842 + 0.999327i \(0.488320\pi\)
\(422\) 0 0
\(423\) 2.21395e6 2.87067e6i 0.601613 0.780068i
\(424\) 0 0
\(425\) 304102. + 526720.i 0.0816671 + 0.141452i
\(426\) 0 0
\(427\) −37615.8 + 65152.5i −0.00998392 + 0.0172927i
\(428\) 0 0
\(429\) −629282. + 939291.i −0.165083 + 0.246409i
\(430\) 0 0
\(431\) 5.11509e6 1.32636 0.663178 0.748462i \(-0.269207\pi\)
0.663178 + 0.748462i \(0.269207\pi\)
\(432\) 0 0
\(433\) −1.39089e6 −0.356512 −0.178256 0.983984i \(-0.557045\pi\)
−0.178256 + 0.983984i \(0.557045\pi\)
\(434\) 0 0
\(435\) −1.80001e6 + 2.68677e6i −0.456092 + 0.680780i
\(436\) 0 0
\(437\) −2.43048e6 + 4.20971e6i −0.608819 + 1.05450i
\(438\) 0 0
\(439\) −1.76266e6 3.05301e6i −0.436523 0.756079i 0.560896 0.827886i \(-0.310457\pi\)
−0.997419 + 0.0718069i \(0.977123\pi\)
\(440\) 0 0
\(441\) −3.08411e6 413729.i −0.755150 0.101302i
\(442\) 0 0
\(443\) 1.02216e6 + 1.77043e6i 0.247462 + 0.428617i 0.962821 0.270140i \(-0.0870701\pi\)
−0.715359 + 0.698757i \(0.753737\pi\)
\(444\) 0 0
\(445\) 1.28804e6 2.23094e6i 0.308339 0.534058i
\(446\) 0 0
\(447\) −2.30812e6 4.69490e6i −0.546372 1.11137i
\(448\) 0 0
\(449\) 7.70508e6 1.80369 0.901844 0.432062i \(-0.142214\pi\)
0.901844 + 0.432062i \(0.142214\pi\)
\(450\) 0 0
\(451\) −990361. −0.229273
\(452\) 0 0
\(453\) 2.10874e6 + 140812.i 0.482811 + 0.0322398i
\(454\) 0 0
\(455\) 614611. 1.06454e6i 0.139178 0.241064i
\(456\) 0 0
\(457\) −4.28846e6 7.42783e6i −0.960529 1.66369i −0.721175 0.692753i \(-0.756397\pi\)
−0.239355 0.970932i \(-0.576936\pi\)
\(458\) 0 0
\(459\) 928340. + 188212.i 0.205672 + 0.0416979i
\(460\) 0 0
\(461\) −716317. 1.24070e6i −0.156983 0.271903i 0.776796 0.629752i \(-0.216843\pi\)
−0.933779 + 0.357849i \(0.883510\pi\)
\(462\) 0 0
\(463\) 1.47223e6 2.54998e6i 0.319172 0.552821i −0.661144 0.750259i \(-0.729929\pi\)
0.980315 + 0.197438i \(0.0632621\pi\)
\(464\) 0 0
\(465\) −1.88779e6 126058.i −0.404875 0.0270356i
\(466\) 0 0
\(467\) −4.96160e6 −1.05276 −0.526380 0.850249i \(-0.676451\pi\)
−0.526380 + 0.850249i \(0.676451\pi\)
\(468\) 0 0
\(469\) 3.74361e6 0.785884
\(470\) 0 0
\(471\) 2.92588e6 + 5.95149e6i 0.607722 + 1.23616i
\(472\) 0 0
\(473\) −345701. + 598772.i −0.0710473 + 0.123058i
\(474\) 0 0
\(475\) −1.34065e6 2.32208e6i −0.272635 0.472218i
\(476\) 0 0
\(477\) −2.07546e6 5.04558e6i −0.417657 1.01535i
\(478\) 0 0
\(479\) −120757. 209157.i −0.0240476 0.0416517i 0.853751 0.520681i \(-0.174322\pi\)
−0.877799 + 0.479030i \(0.840989\pi\)
\(480\) 0 0
\(481\) 4.39145e6 7.60621e6i 0.865456 1.49901i
\(482\) 0 0
\(483\) −2.42008e6 + 3.61231e6i −0.472022 + 0.704559i
\(484\) 0 0
\(485\) −2.80875e6 −0.542199
\(486\) 0 0
\(487\) −325055. −0.0621061 −0.0310530 0.999518i \(-0.509886\pi\)
−0.0310530 + 0.999518i \(0.509886\pi\)
\(488\) 0 0
\(489\) −1.37676e6 + 2.05500e6i −0.260367 + 0.388634i
\(490\) 0 0
\(491\) 2.49023e6 4.31321e6i 0.466162 0.807416i −0.533091 0.846058i \(-0.678970\pi\)
0.999253 + 0.0386419i \(0.0123032\pi\)
\(492\) 0 0
\(493\) 985502. + 1.70694e6i 0.182617 + 0.316301i
\(494\) 0 0
\(495\) −239024. 581083.i −0.0438459 0.106592i
\(496\) 0 0
\(497\) −453131. 784846.i −0.0822873 0.142526i
\(498\) 0 0
\(499\) −2.93247e6 + 5.07919e6i −0.527209 + 0.913153i 0.472288 + 0.881444i \(0.343428\pi\)
−0.999497 + 0.0317085i \(0.989905\pi\)
\(500\) 0 0
\(501\) −3.56559e6 7.25270e6i −0.634653 1.29094i
\(502\) 0 0
\(503\) 1.36396e6 0.240370 0.120185 0.992751i \(-0.461651\pi\)
0.120185 + 0.992751i \(0.461651\pi\)
\(504\) 0 0
\(505\) −2.53919e6 −0.443065
\(506\) 0 0
\(507\) 2.70282e6 + 180482.i 0.466980 + 0.0311827i
\(508\) 0 0
\(509\) −1.85023e6 + 3.20470e6i −0.316542 + 0.548268i −0.979764 0.200155i \(-0.935855\pi\)
0.663222 + 0.748423i \(0.269189\pi\)
\(510\) 0 0
\(511\) −1.67943e6 2.90885e6i −0.284517 0.492799i
\(512\) 0 0
\(513\) −4.09264e6 829742.i −0.686610 0.139203i
\(514\) 0 0
\(515\) −394076. 682560.i −0.0654730 0.113403i
\(516\) 0 0
\(517\) −732795. + 1.26924e6i −0.120575 + 0.208841i
\(518\) 0 0
\(519\) −2.38250e6 159092.i −0.388253 0.0259257i
\(520\) 0 0
\(521\) −285260. −0.0460412 −0.0230206 0.999735i \(-0.507328\pi\)
−0.0230206 + 0.999735i \(0.507328\pi\)
\(522\) 0 0
\(523\) −8.28809e6 −1.32495 −0.662476 0.749083i \(-0.730494\pi\)
−0.662476 + 0.749083i \(0.730494\pi\)
\(524\) 0 0
\(525\) −1.05814e6 2.15235e6i −0.167550 0.340812i
\(526\) 0 0
\(527\) −576550. + 998614.i −0.0904296 + 0.156629i
\(528\) 0 0
\(529\) −6.50327e6 1.12640e7i −1.01040 1.75006i
\(530\) 0 0
\(531\) −2.60363e6 349273.i −0.400722 0.0537563i
\(532\) 0 0
\(533\) 3.72139e6 + 6.44564e6i 0.567397 + 0.982761i
\(534\) 0 0
\(535\) −299513. + 518772.i −0.0452409 + 0.0783596i
\(536\) 0 0
\(537\) −6.39315e6 + 9.54266e6i −0.956707 + 1.42802i
\(538\) 0 0
\(539\) 1.25800e6 0.186512
\(540\) 0 0
\(541\) 1.29750e7 1.90596 0.952982 0.303028i \(-0.0979975\pi\)
0.952982 + 0.303028i \(0.0979975\pi\)
\(542\) 0 0
\(543\) −244533. + 365000.i −0.0355908 + 0.0531243i
\(544\) 0 0
\(545\) −35163.3 + 60904.6i −0.00507105 + 0.00878332i
\(546\) 0 0
\(547\) −4.65800e6 8.06790e6i −0.665628 1.15290i −0.979115 0.203309i \(-0.934830\pi\)
0.313487 0.949593i \(-0.398503\pi\)
\(548\) 0 0
\(549\) 176493. 228845.i 0.0249917 0.0324050i
\(550\) 0 0
\(551\) −4.34464e6 7.52514e6i −0.609642 1.05593i
\(552\) 0 0
\(553\) 1.18263e6 2.04838e6i 0.164451 0.284838i
\(554\) 0 0
\(555\) 2.15345e6 + 4.38030e6i 0.296758 + 0.603630i
\(556\) 0 0
\(557\) −4.18234e6 −0.571192 −0.285596 0.958350i \(-0.592191\pi\)
−0.285596 + 0.958350i \(0.592191\pi\)
\(558\) 0 0
\(559\) 5.19604e6 0.703304
\(560\) 0 0
\(561\) −382089. 25514.1i −0.0512575 0.00342273i
\(562\) 0 0
\(563\) −1.65660e6 + 2.86931e6i −0.220265 + 0.381511i −0.954888 0.296965i \(-0.904026\pi\)
0.734623 + 0.678475i \(0.237359\pi\)
\(564\) 0 0
\(565\) 1.72846e6 + 2.99378e6i 0.227792 + 0.394547i
\(566\) 0 0
\(567\) −3.60323e6 984452.i −0.470689 0.128599i
\(568\) 0 0
\(569\) 2.92695e6 + 5.06963e6i 0.378996 + 0.656441i 0.990917 0.134478i \(-0.0429359\pi\)
−0.611920 + 0.790920i \(0.709603\pi\)
\(570\) 0 0
\(571\) 6.75429e6 1.16988e7i 0.866941 1.50159i 0.00183339 0.999998i \(-0.499416\pi\)
0.865107 0.501587i \(-0.167250\pi\)
\(572\) 0 0
\(573\) −1.54482e6 103156.i −0.196558 0.0131252i
\(574\) 0 0
\(575\) 1.07247e7 1.35274
\(576\) 0 0
\(577\) −1.12898e7 −1.41171 −0.705855 0.708356i \(-0.749437\pi\)
−0.705855 + 0.708356i \(0.749437\pi\)
\(578\) 0 0
\(579\) −2.86977e6 5.83735e6i −0.355754 0.723634i
\(580\) 0 0
\(581\) −3.82325e6 + 6.62206e6i −0.469886 + 0.813866i
\(582\) 0 0
\(583\) 1.10282e6 + 1.91013e6i 0.134379 + 0.232751i
\(584\) 0 0
\(585\) −2.88374e6 + 3.73914e6i −0.348391 + 0.451733i
\(586\) 0 0
\(587\) 991398. + 1.71715e6i 0.118755 + 0.205690i 0.919275 0.393617i \(-0.128776\pi\)
−0.800519 + 0.599307i \(0.795443\pi\)
\(588\) 0 0
\(589\) 2.54176e6 4.40245e6i 0.301888 0.522885i
\(590\) 0 0
\(591\) −2.20870e6 + 3.29679e6i −0.260116 + 0.388260i
\(592\) 0 0
\(593\) 1.22629e7 1.43204 0.716021 0.698078i \(-0.245961\pi\)
0.716021 + 0.698078i \(0.245961\pi\)
\(594\) 0 0
\(595\) 416342. 0.0482123
\(596\) 0 0
\(597\) −5.20324e6 + 7.76656e6i −0.597500 + 0.891852i
\(598\) 0 0
\(599\) −7.84977e6 + 1.35962e7i −0.893902 + 1.54828i −0.0587438 + 0.998273i \(0.518710\pi\)
−0.835158 + 0.550010i \(0.814624\pi\)
\(600\) 0 0
\(601\) 2.65972e6 + 4.60677e6i 0.300366 + 0.520248i 0.976219 0.216788i \(-0.0695580\pi\)
−0.675853 + 0.737036i \(0.736225\pi\)
\(602\) 0 0
\(603\) −1.42532e7 1.91204e6i −1.59631 0.214143i
\(604\) 0 0
\(605\) −1.99246e6 3.45105e6i −0.221311 0.383321i
\(606\) 0 0
\(607\) 2.18482e6 3.78422e6i 0.240682 0.416874i −0.720226 0.693739i \(-0.755962\pi\)
0.960909 + 0.276865i \(0.0892954\pi\)
\(608\) 0 0
\(609\) −3.42911e6 6.97511e6i −0.374661 0.762092i
\(610\) 0 0
\(611\) 1.10142e7 1.19358
\(612\) 0 0
\(613\) −7.62875e6 −0.819978 −0.409989 0.912091i \(-0.634467\pi\)
−0.409989 + 0.912091i \(0.634467\pi\)
\(614\) 0 0
\(615\) −4.12707e6 275586.i −0.440002 0.0293812i
\(616\) 0 0
\(617\) 7.16498e6 1.24101e7i 0.757708 1.31239i −0.186309 0.982491i \(-0.559652\pi\)
0.944017 0.329898i \(-0.107014\pi\)
\(618\) 0 0
\(619\) 5.40907e6 + 9.36878e6i 0.567408 + 0.982780i 0.996821 + 0.0796716i \(0.0253871\pi\)
−0.429413 + 0.903108i \(0.641280\pi\)
\(620\) 0 0
\(621\) 1.10591e7 1.25172e7i 1.15077 1.30251i
\(622\) 0 0
\(623\) 3.09560e6 + 5.36174e6i 0.319540 + 0.553460i
\(624\) 0 0
\(625\) −1.87542e6 + 3.24833e6i −0.192043 + 0.332629i
\(626\) 0 0
\(627\) 1.68446e6 + 112480.i 0.171117 + 0.0114264i
\(628\) 0 0
\(629\) 2.97480e6 0.299800
\(630\) 0 0
\(631\) −7.96579e6 −0.796444 −0.398222 0.917289i \(-0.630373\pi\)
−0.398222 + 0.917289i \(0.630373\pi\)
\(632\) 0 0
\(633\) 5.20337e6 + 1.05841e7i 0.516149 + 1.04989i
\(634\) 0 0
\(635\) −3.10597e6 + 5.37970e6i −0.305677 + 0.529448i
\(636\) 0 0
\(637\) −4.72705e6 8.18750e6i −0.461575 0.799471i
\(638\) 0 0
\(639\) 1.32436e6 + 3.21961e6i 0.128308 + 0.311926i
\(640\) 0 0
\(641\) −3.40224e6 5.89285e6i −0.327054 0.566475i 0.654872 0.755740i \(-0.272723\pi\)
−0.981926 + 0.189266i \(0.939389\pi\)
\(642\) 0 0
\(643\) −2.66464e6 + 4.61530e6i −0.254163 + 0.440223i −0.964668 0.263469i \(-0.915133\pi\)
0.710505 + 0.703692i \(0.248467\pi\)
\(644\) 0 0
\(645\) −1.60724e6 + 2.39903e6i −0.152118 + 0.227058i
\(646\) 0 0
\(647\) 5.03021e6 0.472417 0.236208 0.971702i \(-0.424095\pi\)
0.236208 + 0.971702i \(0.424095\pi\)
\(648\) 0 0
\(649\) 1.06201e6 0.0989731
\(650\) 0 0
\(651\) 2.53089e6 3.77770e6i 0.234056 0.349361i
\(652\) 0 0
\(653\) 5.66704e6 9.81560e6i 0.520084 0.900811i −0.479644 0.877463i \(-0.659234\pi\)
0.999727 0.0233481i \(-0.00743260\pi\)
\(654\) 0 0
\(655\) −4.74251e6 8.21427e6i −0.431922 0.748110i
\(656\) 0 0
\(657\) 4.90845e6 + 1.19328e7i 0.443641 + 1.07852i
\(658\) 0 0
\(659\) 1.91003e6 + 3.30828e6i 0.171328 + 0.296748i 0.938884 0.344233i \(-0.111861\pi\)
−0.767557 + 0.640981i \(0.778528\pi\)
\(660\) 0 0
\(661\) −463286. + 802435.i −0.0412426 + 0.0714342i −0.885910 0.463857i \(-0.846465\pi\)
0.844667 + 0.535292i \(0.179798\pi\)
\(662\) 0 0
\(663\) 1.26969e6 + 2.58265e6i 0.112179 + 0.228182i
\(664\) 0 0
\(665\) −1.83547e6 −0.160951
\(666\) 0 0
\(667\) 3.47555e7 3.02488
\(668\) 0 0
\(669\) 1.72966e6 + 115498.i 0.149415 + 0.00997725i
\(670\) 0 0
\(671\) −58417.3 + 101182.i −0.00500882 + 0.00867553i
\(672\) 0 0
\(673\) −2.45146e6 4.24605e6i −0.208635 0.361366i 0.742650 0.669680i \(-0.233569\pi\)
−0.951285 + 0.308314i \(0.900235\pi\)
\(674\) 0 0
\(675\) 2.92939e6 + 8.73517e6i 0.247468 + 0.737924i
\(676\) 0 0
\(677\) 7.37201e6 + 1.27687e7i 0.618179 + 1.07072i 0.989818 + 0.142340i \(0.0454627\pi\)
−0.371639 + 0.928378i \(0.621204\pi\)
\(678\) 0 0
\(679\) 3.37521e6 5.84603e6i 0.280948 0.486616i
\(680\) 0 0
\(681\) 7.63319e6 + 509708.i 0.630722 + 0.0421166i
\(682\) 0 0
\(683\) 6.53893e6 0.536358 0.268179 0.963369i \(-0.413578\pi\)
0.268179 + 0.963369i \(0.413578\pi\)
\(684\) 0 0
\(685\) 6.25548e6 0.509371
\(686\) 0 0
\(687\) −5.23388e6 1.06462e7i −0.423090 0.860600i
\(688\) 0 0
\(689\) 8.28790e6 1.43551e7i 0.665114 1.15201i
\(690\) 0 0
\(691\) −5.45248e6 9.44397e6i −0.434409 0.752419i 0.562838 0.826567i \(-0.309709\pi\)
−0.997247 + 0.0741485i \(0.976376\pi\)
\(692\) 0 0
\(693\) 1.49668e6 + 200777.i 0.118384 + 0.0158811i
\(694\) 0 0
\(695\) −2.14968e6 3.72336e6i −0.168816 0.292397i
\(696\) 0 0
\(697\) −1.26045e6 + 2.18316e6i −0.0982751 + 0.170217i
\(698\) 0 0
\(699\) 3.09111e6 4.61391e6i 0.239288 0.357171i
\(700\) 0 0
\(701\) −1.89162e7 −1.45391 −0.726957 0.686683i \(-0.759066\pi\)
−0.726957 + 0.686683i \(0.759066\pi\)
\(702\) 0 0
\(703\) −1.31146e7 −1.00084
\(704\) 0 0
\(705\) −3.40692e6 + 5.08531e6i −0.258160 + 0.385340i
\(706\) 0 0
\(707\) 3.05129e6 5.28499e6i 0.229581 0.397645i
\(708\) 0 0
\(709\) 9.63661e6 + 1.66911e7i 0.719960 + 1.24701i 0.961015 + 0.276496i \(0.0891733\pi\)
−0.241055 + 0.970512i \(0.577493\pi\)
\(710\) 0 0
\(711\) −5.54889e6 + 7.19485e6i −0.411654 + 0.533762i
\(712\) 0 0
\(713\) 1.01665e7 + 1.76089e7i 0.748943 + 1.29721i
\(714\) 0 0
\(715\) 954489. 1.65322e6i 0.0698242 0.120939i
\(716\) 0 0
\(717\) −6.23261e6 1.26777e7i −0.452764 0.920961i
\(718\) 0 0
\(719\) −1.42859e7 −1.03059 −0.515293 0.857014i \(-0.672317\pi\)
−0.515293 + 0.857014i \(0.672317\pi\)
\(720\) 0 0
\(721\) 1.89421e6 0.135703
\(722\) 0 0
\(723\) 8.12805e6 + 542752.i 0.578283 + 0.0386150i
\(724\) 0 0
\(725\) −9.58556e6 + 1.66027e7i −0.677287 + 1.17310i
\(726\) 0 0
\(727\) 1.41386e7 + 2.44887e7i 0.992132 + 1.71842i 0.604491 + 0.796612i \(0.293377\pi\)
0.387641 + 0.921810i \(0.373290\pi\)
\(728\) 0 0
\(729\) 1.32159e7 + 5.58849e6i 0.921039 + 0.389471i
\(730\) 0 0
\(731\) 879959. + 1.52413e6i 0.0609073 + 0.105494i
\(732\) 0 0
\(733\) −4.93850e6 + 8.55373e6i −0.339496 + 0.588025i −0.984338 0.176291i \(-0.943590\pi\)
0.644842 + 0.764316i \(0.276923\pi\)
\(734\) 0 0
\(735\) 5.24237e6 + 350060.i 0.357939 + 0.0239015i
\(736\) 0 0
\(737\) 5.81381e6 0.394269
\(738\) 0 0
\(739\) −6.31081e6 −0.425083 −0.212542 0.977152i \(-0.568174\pi\)
−0.212542 + 0.977152i \(0.568174\pi\)
\(740\) 0 0
\(741\) −5.59748e6 1.13858e7i −0.374496 0.761757i
\(742\) 0 0
\(743\) −31529.9 + 54611.3i −0.00209532 + 0.00362920i −0.867071 0.498184i \(-0.834000\pi\)
0.864976 + 0.501814i \(0.167334\pi\)
\(744\) 0 0
\(745\) 4.41667e6 + 7.64989e6i 0.291544 + 0.504969i
\(746\) 0 0
\(747\) 1.79386e7 2.32597e7i 1.17622 1.52511i
\(748\) 0 0
\(749\) −719836. 1.24679e6i −0.0468845 0.0812063i
\(750\) 0 0
\(751\) −8.69183e6 + 1.50547e7i −0.562356 + 0.974029i 0.434934 + 0.900462i \(0.356772\pi\)
−0.997290 + 0.0735670i \(0.976562\pi\)
\(752\) 0 0
\(753\) −5.42522e6 + 8.09790e6i −0.348682 + 0.520457i
\(754\) 0 0
\(755\) −3.56845e6 −0.227831
\(756\) 0 0
\(757\) 9.43592e6 0.598473 0.299237 0.954179i \(-0.403268\pi\)
0.299237 + 0.954179i \(0.403268\pi\)
\(758\) 0 0
\(759\) −3.75838e6 + 5.60991e6i −0.236808 + 0.353469i
\(760\) 0 0
\(761\) −8.06409e6 + 1.39674e7i −0.504771 + 0.874288i 0.495214 + 0.868771i \(0.335090\pi\)
−0.999985 + 0.00551731i \(0.998244\pi\)
\(762\) 0 0
\(763\) −84509.8 146375.i −0.00525528 0.00910241i
\(764\) 0 0
\(765\) −1.58516e6 212646.i −0.0979306 0.0131373i
\(766\) 0 0
\(767\) −3.99062e6 6.91196e6i −0.244936 0.424241i
\(768\) 0 0
\(769\) 1.28431e7 2.22450e7i 0.783169 1.35649i −0.146918 0.989149i \(-0.546935\pi\)
0.930087 0.367339i \(-0.119731\pi\)
\(770\) 0 0
\(771\) 8.95590e6 + 1.82171e7i 0.542592 + 1.10368i
\(772\) 0 0
\(773\) −2.01235e7 −1.21131 −0.605654 0.795728i \(-0.707088\pi\)
−0.605654 + 0.795728i \(0.707088\pi\)
\(774\) 0 0
\(775\) −1.12157e7 −0.670769
\(776\) 0 0
\(777\) −1.17047e7 781587.i −0.695520 0.0464435i
\(778\) 0 0
\(779\) 5.55677e6 9.62460e6i 0.328079 0.568250i
\(780\) 0 0
\(781\) −703712. 1.21886e6i −0.0412826 0.0715036i
\(782\) 0 0
\(783\) 9.49327e6 + 2.83080e7i 0.553364 + 1.65008i
\(784\) 0 0
\(785\) −5.59879e6 9.69738e6i −0.324280 0.561669i
\(786\) 0 0
\(787\) 2.87640e6 4.98208e6i 0.165544 0.286730i −0.771304 0.636466i \(-0.780395\pi\)
0.936848 + 0.349736i \(0.113729\pi\)
\(788\) 0 0
\(789\) 2.22968e7 + 1.48887e6i 1.27511 + 0.0851461i
\(790\) 0