Properties

Label 76.6.e.a.49.2
Level $76$
Weight $6$
Character 76.49
Analytic conductor $12.189$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} - 863969476320 x^{9} + 79755165392064 x^{8} - 375077568148992 x^{7} + 12736924096193536 x^{6} - 57314532742553600 x^{5} + 977121800205220864 x^{4} - 4977732006498379776 x^{3} + 53672321824823513088 x^{2} - 185653809995679793152 x + 804303742853852430336\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{3}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.2
Root \(11.1685 + 19.3444i\) of defining polynomial
Character \(\chi\) \(=\) 76.49
Dual form 76.6.e.a.45.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-11.6685 + 20.2105i) q^{3} +(-25.2470 + 43.7291i) q^{5} -187.942 q^{7} +(-150.808 - 261.208i) q^{9} +O(q^{10})\) \(q+(-11.6685 + 20.2105i) q^{3} +(-25.2470 + 43.7291i) q^{5} -187.942 q^{7} +(-150.808 - 261.208i) q^{9} +411.164 q^{11} +(286.794 + 496.742i) q^{13} +(-589.191 - 1020.51i) q^{15} +(559.243 - 968.637i) q^{17} +(-1048.98 - 1172.92i) q^{19} +(2193.01 - 3798.40i) q^{21} +(-72.0483 - 124.791i) q^{23} +(287.675 + 498.268i) q^{25} +1367.94 q^{27} +(-2616.14 - 4531.29i) q^{29} -6724.09 q^{31} +(-4797.68 + 8309.82i) q^{33} +(4744.99 - 8218.56i) q^{35} +12337.9 q^{37} -13385.8 q^{39} +(-5964.03 + 10330.0i) q^{41} +(-2611.95 + 4524.03i) q^{43} +15229.9 q^{45} +(-10457.1 - 18112.3i) q^{47} +18515.4 q^{49} +(13051.1 + 22605.1i) q^{51} +(4550.48 + 7881.66i) q^{53} +(-10380.7 + 17979.9i) q^{55} +(35945.2 - 7514.28i) q^{57} +(-12030.3 + 20837.0i) q^{59} +(-21555.9 - 37335.8i) q^{61} +(28343.3 + 49092.0i) q^{63} -28962.8 q^{65} +(-8051.46 - 13945.5i) q^{67} +3362.78 q^{69} +(-39902.4 + 69113.1i) q^{71} +(-17210.0 + 29808.6i) q^{73} -13427.0 q^{75} -77275.3 q^{77} +(16379.2 - 28369.7i) q^{79} +(20684.6 - 35826.8i) q^{81} +49610.5 q^{83} +(28238.4 + 48910.4i) q^{85} +122106. q^{87} +(-39238.1 - 67962.3i) q^{89} +(-53900.8 - 93359.0i) q^{91} +(78460.1 - 135897. i) q^{93} +(77774.3 - 16258.6i) q^{95} +(62657.4 - 108526. i) q^{97} +(-62007.0 - 107399. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −11.6685 + 20.2105i −0.748535 + 1.29650i 0.199989 + 0.979798i \(0.435909\pi\)
−0.948525 + 0.316703i \(0.897424\pi\)
\(4\) 0 0
\(5\) −25.2470 + 43.7291i −0.451633 + 0.782251i −0.998488 0.0549767i \(-0.982492\pi\)
0.546855 + 0.837227i \(0.315825\pi\)
\(6\) 0 0
\(7\) −187.942 −1.44971 −0.724853 0.688904i \(-0.758092\pi\)
−0.724853 + 0.688904i \(0.758092\pi\)
\(8\) 0 0
\(9\) −150.808 261.208i −0.620610 1.07493i
\(10\) 0 0
\(11\) 411.164 1.02455 0.512276 0.858821i \(-0.328803\pi\)
0.512276 + 0.858821i \(0.328803\pi\)
\(12\) 0 0
\(13\) 286.794 + 496.742i 0.470665 + 0.815216i 0.999437 0.0335480i \(-0.0106807\pi\)
−0.528772 + 0.848764i \(0.677347\pi\)
\(14\) 0 0
\(15\) −589.191 1020.51i −0.676126 1.17108i
\(16\) 0 0
\(17\) 559.243 968.637i 0.469330 0.812903i −0.530056 0.847963i \(-0.677829\pi\)
0.999385 + 0.0350601i \(0.0111623\pi\)
\(18\) 0 0
\(19\) −1048.98 1172.92i −0.666630 0.745388i
\(20\) 0 0
\(21\) 2193.01 3798.40i 1.08516 1.87955i
\(22\) 0 0
\(23\) −72.0483 124.791i −0.0283991 0.0491886i 0.851477 0.524393i \(-0.175708\pi\)
−0.879876 + 0.475204i \(0.842374\pi\)
\(24\) 0 0
\(25\) 287.675 + 498.268i 0.0920560 + 0.159446i
\(26\) 0 0
\(27\) 1367.94 0.361125
\(28\) 0 0
\(29\) −2616.14 4531.29i −0.577652 1.00052i −0.995748 0.0921194i \(-0.970636\pi\)
0.418096 0.908403i \(-0.362697\pi\)
\(30\) 0 0
\(31\) −6724.09 −1.25669 −0.628347 0.777934i \(-0.716268\pi\)
−0.628347 + 0.777934i \(0.716268\pi\)
\(32\) 0 0
\(33\) −4797.68 + 8309.82i −0.766913 + 1.32833i
\(34\) 0 0
\(35\) 4744.99 8218.56i 0.654734 1.13403i
\(36\) 0 0
\(37\) 12337.9 1.48162 0.740811 0.671713i \(-0.234441\pi\)
0.740811 + 0.671713i \(0.234441\pi\)
\(38\) 0 0
\(39\) −13385.8 −1.40924
\(40\) 0 0
\(41\) −5964.03 + 10330.0i −0.554090 + 0.959712i 0.443884 + 0.896084i \(0.353600\pi\)
−0.997974 + 0.0636278i \(0.979733\pi\)
\(42\) 0 0
\(43\) −2611.95 + 4524.03i −0.215424 + 0.373125i −0.953404 0.301698i \(-0.902447\pi\)
0.737980 + 0.674823i \(0.235780\pi\)
\(44\) 0 0
\(45\) 15229.9 1.12115
\(46\) 0 0
\(47\) −10457.1 18112.3i −0.690507 1.19599i −0.971672 0.236333i \(-0.924054\pi\)
0.281165 0.959659i \(-0.409279\pi\)
\(48\) 0 0
\(49\) 18515.4 1.10165
\(50\) 0 0
\(51\) 13051.1 + 22605.1i 0.702620 + 1.21697i
\(52\) 0 0
\(53\) 4550.48 + 7881.66i 0.222519 + 0.385414i 0.955572 0.294757i \(-0.0952387\pi\)
−0.733053 + 0.680171i \(0.761905\pi\)
\(54\) 0 0
\(55\) −10380.7 + 17979.9i −0.462721 + 0.801456i
\(56\) 0 0
\(57\) 35945.2 7514.28i 1.46539 0.306338i
\(58\) 0 0
\(59\) −12030.3 + 20837.0i −0.449930 + 0.779301i −0.998381 0.0568813i \(-0.981884\pi\)
0.548451 + 0.836183i \(0.315218\pi\)
\(60\) 0 0
\(61\) −21555.9 37335.8i −0.741721 1.28470i −0.951711 0.306995i \(-0.900676\pi\)
0.209990 0.977704i \(-0.432657\pi\)
\(62\) 0 0
\(63\) 28343.3 + 49092.0i 0.899703 + 1.55833i
\(64\) 0 0
\(65\) −28962.8 −0.850271
\(66\) 0 0
\(67\) −8051.46 13945.5i −0.219123 0.379532i 0.735417 0.677615i \(-0.236986\pi\)
−0.954540 + 0.298083i \(0.903653\pi\)
\(68\) 0 0
\(69\) 3362.78 0.0850308
\(70\) 0 0
\(71\) −39902.4 + 69113.1i −0.939407 + 1.62710i −0.172826 + 0.984952i \(0.555290\pi\)
−0.766581 + 0.642148i \(0.778044\pi\)
\(72\) 0 0
\(73\) −17210.0 + 29808.6i −0.377985 + 0.654688i −0.990769 0.135562i \(-0.956716\pi\)
0.612784 + 0.790250i \(0.290049\pi\)
\(74\) 0 0
\(75\) −13427.0 −0.275629
\(76\) 0 0
\(77\) −77275.3 −1.48530
\(78\) 0 0
\(79\) 16379.2 28369.7i 0.295274 0.511430i −0.679774 0.733421i \(-0.737922\pi\)
0.975049 + 0.221991i \(0.0712556\pi\)
\(80\) 0 0
\(81\) 20684.6 35826.8i 0.350296 0.606730i
\(82\) 0 0
\(83\) 49610.5 0.790457 0.395229 0.918583i \(-0.370665\pi\)
0.395229 + 0.918583i \(0.370665\pi\)
\(84\) 0 0
\(85\) 28238.4 + 48910.4i 0.423929 + 0.734267i
\(86\) 0 0
\(87\) 122106. 1.72957
\(88\) 0 0
\(89\) −39238.1 67962.3i −0.525089 0.909480i −0.999573 0.0292164i \(-0.990699\pi\)
0.474484 0.880264i \(-0.342635\pi\)
\(90\) 0 0
\(91\) −53900.8 93359.0i −0.682326 1.18182i
\(92\) 0 0
\(93\) 78460.1 135897.i 0.940679 1.62930i
\(94\) 0 0
\(95\) 77774.3 16258.6i 0.884153 0.184830i
\(96\) 0 0
\(97\) 62657.4 108526.i 0.676149 1.17113i −0.299982 0.953945i \(-0.596981\pi\)
0.976131 0.217180i \(-0.0696860\pi\)
\(98\) 0 0
\(99\) −62007.0 107399.i −0.635847 1.10132i
\(100\) 0 0
\(101\) −64376.2 111503.i −0.627945 1.08763i −0.987963 0.154688i \(-0.950563\pi\)
0.360018 0.932945i \(-0.382770\pi\)
\(102\) 0 0
\(103\) −185375. −1.72170 −0.860851 0.508857i \(-0.830068\pi\)
−0.860851 + 0.508857i \(0.830068\pi\)
\(104\) 0 0
\(105\) 110734. + 191797.i 0.980184 + 1.69773i
\(106\) 0 0
\(107\) −51720.8 −0.436723 −0.218361 0.975868i \(-0.570071\pi\)
−0.218361 + 0.975868i \(0.570071\pi\)
\(108\) 0 0
\(109\) −10666.1 + 18474.1i −0.0859879 + 0.148935i −0.905812 0.423680i \(-0.860738\pi\)
0.819824 + 0.572616i \(0.194071\pi\)
\(110\) 0 0
\(111\) −143965. + 249355.i −1.10905 + 1.92093i
\(112\) 0 0
\(113\) 181009. 1.33353 0.666767 0.745266i \(-0.267678\pi\)
0.666767 + 0.745266i \(0.267678\pi\)
\(114\) 0 0
\(115\) 7276.02 0.0513038
\(116\) 0 0
\(117\) 86501.9 149826.i 0.584199 1.01186i
\(118\) 0 0
\(119\) −105105. + 182048.i −0.680390 + 1.17847i
\(120\) 0 0
\(121\) 8005.17 0.0497058
\(122\) 0 0
\(123\) −139183. 241072.i −0.829512 1.43676i
\(124\) 0 0
\(125\) −186846. −1.06957
\(126\) 0 0
\(127\) 909.283 + 1574.92i 0.00500253 + 0.00866464i 0.868516 0.495661i \(-0.165074\pi\)
−0.863513 + 0.504326i \(0.831741\pi\)
\(128\) 0 0
\(129\) −60955.1 105577.i −0.322504 0.558594i
\(130\) 0 0
\(131\) −39930.7 + 69162.1i −0.203296 + 0.352119i −0.949589 0.313499i \(-0.898499\pi\)
0.746292 + 0.665618i \(0.231832\pi\)
\(132\) 0 0
\(133\) 197149. + 220441.i 0.966418 + 1.08059i
\(134\) 0 0
\(135\) −34536.4 + 59818.8i −0.163096 + 0.282490i
\(136\) 0 0
\(137\) 99388.3 + 172146.i 0.452412 + 0.783600i 0.998535 0.0541044i \(-0.0172304\pi\)
−0.546123 + 0.837705i \(0.683897\pi\)
\(138\) 0 0
\(139\) −188358. 326246.i −0.826890 1.43222i −0.900466 0.434926i \(-0.856775\pi\)
0.0735761 0.997290i \(-0.476559\pi\)
\(140\) 0 0
\(141\) 488077. 2.06748
\(142\) 0 0
\(143\) 117920. + 204243.i 0.482221 + 0.835231i
\(144\) 0 0
\(145\) 264199. 1.04355
\(146\) 0 0
\(147\) −216047. + 374204.i −0.824622 + 1.42829i
\(148\) 0 0
\(149\) −115828. + 200620.i −0.427413 + 0.740300i −0.996642 0.0818781i \(-0.973908\pi\)
0.569230 + 0.822179i \(0.307242\pi\)
\(150\) 0 0
\(151\) 465504. 1.66143 0.830714 0.556700i \(-0.187933\pi\)
0.830714 + 0.556700i \(0.187933\pi\)
\(152\) 0 0
\(153\) −337354. −1.16508
\(154\) 0 0
\(155\) 169763. 294039.i 0.567564 0.983049i
\(156\) 0 0
\(157\) −256177. + 443712.i −0.829451 + 1.43665i 0.0690177 + 0.997615i \(0.478013\pi\)
−0.898469 + 0.439037i \(0.855320\pi\)
\(158\) 0 0
\(159\) −212389. −0.666254
\(160\) 0 0
\(161\) 13540.9 + 23453.6i 0.0411703 + 0.0713090i
\(162\) 0 0
\(163\) 551349. 1.62539 0.812694 0.582690i \(-0.198000\pi\)
0.812694 + 0.582690i \(0.198000\pi\)
\(164\) 0 0
\(165\) −242254. 419597.i −0.692726 1.19984i
\(166\) 0 0
\(167\) 24265.6 + 42029.2i 0.0673286 + 0.116617i 0.897725 0.440557i \(-0.145219\pi\)
−0.830396 + 0.557174i \(0.811886\pi\)
\(168\) 0 0
\(169\) 21144.6 36623.6i 0.0569487 0.0986380i
\(170\) 0 0
\(171\) −148179. + 450888.i −0.387522 + 1.17918i
\(172\) 0 0
\(173\) −84590.8 + 146516.i −0.214886 + 0.372193i −0.953237 0.302223i \(-0.902271\pi\)
0.738351 + 0.674416i \(0.235605\pi\)
\(174\) 0 0
\(175\) −54066.3 93645.7i −0.133454 0.231149i
\(176\) 0 0
\(177\) −280750. 486274.i −0.673577 1.16667i
\(178\) 0 0
\(179\) −560804. −1.30821 −0.654106 0.756403i \(-0.726955\pi\)
−0.654106 + 0.756403i \(0.726955\pi\)
\(180\) 0 0
\(181\) 186731. + 323428.i 0.423663 + 0.733806i 0.996295 0.0860068i \(-0.0274107\pi\)
−0.572631 + 0.819813i \(0.694077\pi\)
\(182\) 0 0
\(183\) 1.00610e6 2.22082
\(184\) 0 0
\(185\) −311496. + 539526.i −0.669149 + 1.15900i
\(186\) 0 0
\(187\) 229941. 398269.i 0.480852 0.832861i
\(188\) 0 0
\(189\) −257094. −0.523525
\(190\) 0 0
\(191\) −603335. −1.19667 −0.598336 0.801245i \(-0.704171\pi\)
−0.598336 + 0.801245i \(0.704171\pi\)
\(192\) 0 0
\(193\) 52.8895 91.6073i 0.000102206 0.000177026i −0.865974 0.500089i \(-0.833301\pi\)
0.866077 + 0.499911i \(0.166634\pi\)
\(194\) 0 0
\(195\) 337953. 585352.i 0.636458 1.10238i
\(196\) 0 0
\(197\) −704077. −1.29257 −0.646285 0.763096i \(-0.723678\pi\)
−0.646285 + 0.763096i \(0.723678\pi\)
\(198\) 0 0
\(199\) 81423.6 + 141030.i 0.145753 + 0.252452i 0.929654 0.368435i \(-0.120106\pi\)
−0.783901 + 0.620886i \(0.786773\pi\)
\(200\) 0 0
\(201\) 375794. 0.656085
\(202\) 0 0
\(203\) 491684. + 851622.i 0.837425 + 1.45046i
\(204\) 0 0
\(205\) −301148. 521604.i −0.500490 0.866875i
\(206\) 0 0
\(207\) −21731.0 + 37639.1i −0.0352495 + 0.0610539i
\(208\) 0 0
\(209\) −431305. 482261.i −0.682997 0.763689i
\(210\) 0 0
\(211\) 349140. 604728.i 0.539875 0.935091i −0.459035 0.888418i \(-0.651805\pi\)
0.998910 0.0466728i \(-0.0148618\pi\)
\(212\) 0 0
\(213\) −931204. 1.61289e6i −1.40636 2.43588i
\(214\) 0 0
\(215\) −131888. 228436.i −0.194585 0.337030i
\(216\) 0 0
\(217\) 1.26374e6 1.82184
\(218\) 0 0
\(219\) −401630. 695644.i −0.565870 0.980115i
\(220\) 0 0
\(221\) 641550. 0.883588
\(222\) 0 0
\(223\) −93703.3 + 162299.i −0.126181 + 0.218551i −0.922194 0.386728i \(-0.873605\pi\)
0.796013 + 0.605279i \(0.206939\pi\)
\(224\) 0 0
\(225\) 86767.6 150286.i 0.114262 0.197907i
\(226\) 0 0
\(227\) 606601. 0.781338 0.390669 0.920531i \(-0.372244\pi\)
0.390669 + 0.920531i \(0.372244\pi\)
\(228\) 0 0
\(229\) −215431. −0.271469 −0.135734 0.990745i \(-0.543339\pi\)
−0.135734 + 0.990745i \(0.543339\pi\)
\(230\) 0 0
\(231\) 901687. 1.56177e6i 1.11180 1.92569i
\(232\) 0 0
\(233\) −511411. + 885789.i −0.617135 + 1.06891i 0.372871 + 0.927883i \(0.378373\pi\)
−0.990006 + 0.141026i \(0.954960\pi\)
\(234\) 0 0
\(235\) 1.05605e6 1.24742
\(236\) 0 0
\(237\) 382242. + 662063.i 0.442047 + 0.765647i
\(238\) 0 0
\(239\) −1.31113e6 −1.48474 −0.742371 0.669989i \(-0.766299\pi\)
−0.742371 + 0.669989i \(0.766299\pi\)
\(240\) 0 0
\(241\) 4784.45 + 8286.91i 0.00530627 + 0.00919073i 0.868666 0.495398i \(-0.164978\pi\)
−0.863360 + 0.504588i \(0.831644\pi\)
\(242\) 0 0
\(243\) 648922. + 1.12397e6i 0.704980 + 1.22106i
\(244\) 0 0
\(245\) −467458. + 809662.i −0.497540 + 0.861764i
\(246\) 0 0
\(247\) 281794. 857460.i 0.293893 0.894276i
\(248\) 0 0
\(249\) −578881. + 1.00265e6i −0.591685 + 1.02483i
\(250\) 0 0
\(251\) −228222. 395293.i −0.228651 0.396036i 0.728757 0.684772i \(-0.240098\pi\)
−0.957409 + 0.288736i \(0.906765\pi\)
\(252\) 0 0
\(253\) −29623.7 51309.7i −0.0290963 0.0503963i
\(254\) 0 0
\(255\) −1.31800e6 −1.26930
\(256\) 0 0
\(257\) 259837. + 450050.i 0.245396 + 0.425038i 0.962243 0.272192i \(-0.0877487\pi\)
−0.716847 + 0.697231i \(0.754415\pi\)
\(258\) 0 0
\(259\) −2.31882e6 −2.14792
\(260\) 0 0
\(261\) −789072. + 1.36671e6i −0.716993 + 1.24187i
\(262\) 0 0
\(263\) −159146. + 275650.i −0.141876 + 0.245736i −0.928203 0.372074i \(-0.878647\pi\)
0.786327 + 0.617810i \(0.211980\pi\)
\(264\) 0 0
\(265\) −459544. −0.401987
\(266\) 0 0
\(267\) 1.83140e6 1.57219
\(268\) 0 0
\(269\) −71668.3 + 124133.i −0.0603874 + 0.104594i −0.894639 0.446790i \(-0.852567\pi\)
0.834251 + 0.551385i \(0.185900\pi\)
\(270\) 0 0
\(271\) 304619. 527616.i 0.251961 0.436410i −0.712104 0.702074i \(-0.752258\pi\)
0.964066 + 0.265664i \(0.0855911\pi\)
\(272\) 0 0
\(273\) 2.51577e6 2.04298
\(274\) 0 0
\(275\) 118282. + 204870.i 0.0943161 + 0.163360i
\(276\) 0 0
\(277\) −1.94146e6 −1.52030 −0.760151 0.649746i \(-0.774875\pi\)
−0.760151 + 0.649746i \(0.774875\pi\)
\(278\) 0 0
\(279\) 1.01405e6 + 1.75638e6i 0.779917 + 1.35086i
\(280\) 0 0
\(281\) −286688. 496557.i −0.216592 0.375149i 0.737172 0.675706i \(-0.236161\pi\)
−0.953764 + 0.300557i \(0.902828\pi\)
\(282\) 0 0
\(283\) −1.04413e6 + 1.80849e6i −0.774977 + 1.34230i 0.159831 + 0.987144i \(0.448905\pi\)
−0.934808 + 0.355155i \(0.884428\pi\)
\(284\) 0 0
\(285\) −578917. + 1.76157e6i −0.422187 + 1.28466i
\(286\) 0 0
\(287\) 1.12090e6 1.94145e6i 0.803268 1.39130i
\(288\) 0 0
\(289\) 84423.8 + 146226.i 0.0594593 + 0.102987i
\(290\) 0 0
\(291\) 1.46224e6 + 2.53267e6i 1.01224 + 1.75326i
\(292\) 0 0
\(293\) −598199. −0.407077 −0.203538 0.979067i \(-0.565244\pi\)
−0.203538 + 0.979067i \(0.565244\pi\)
\(294\) 0 0
\(295\) −607456. 1.05215e6i −0.406406 0.703916i
\(296\) 0 0
\(297\) 562448. 0.369991
\(298\) 0 0
\(299\) 41326.0 71578.8i 0.0267329 0.0463027i
\(300\) 0 0
\(301\) 490896. 850257.i 0.312301 0.540921i
\(302\) 0 0
\(303\) 3.00470e6 1.88016
\(304\) 0 0
\(305\) 2.17689e6 1.33994
\(306\) 0 0
\(307\) 71331.2 123549.i 0.0431950 0.0748159i −0.843620 0.536941i \(-0.819580\pi\)
0.886815 + 0.462125i \(0.152913\pi\)
\(308\) 0 0
\(309\) 2.16305e6 3.74651e6i 1.28876 2.23219i
\(310\) 0 0
\(311\) −3.33734e6 −1.95659 −0.978294 0.207219i \(-0.933559\pi\)
−0.978294 + 0.207219i \(0.933559\pi\)
\(312\) 0 0
\(313\) 1.12350e6 + 1.94596e6i 0.648205 + 1.12272i 0.983551 + 0.180628i \(0.0578131\pi\)
−0.335347 + 0.942095i \(0.608854\pi\)
\(314\) 0 0
\(315\) −2.86234e6 −1.62534
\(316\) 0 0
\(317\) −29587.8 51247.6i −0.0165373 0.0286434i 0.857638 0.514253i \(-0.171931\pi\)
−0.874176 + 0.485610i \(0.838598\pi\)
\(318\) 0 0
\(319\) −1.07566e6 1.86310e6i −0.591834 1.02509i
\(320\) 0 0
\(321\) 603505. 1.04530e6i 0.326902 0.566212i
\(322\) 0 0
\(323\) −1.72277e6 + 360141.i −0.918798 + 0.192073i
\(324\) 0 0
\(325\) −165007. + 285801.i −0.0866551 + 0.150091i
\(326\) 0 0
\(327\) −248914. 431132.i −0.128730 0.222967i
\(328\) 0 0
\(329\) 1.96534e6 + 3.40407e6i 1.00103 + 1.73384i
\(330\) 0 0
\(331\) 2.35196e6 1.17994 0.589970 0.807425i \(-0.299140\pi\)
0.589970 + 0.807425i \(0.299140\pi\)
\(332\) 0 0
\(333\) −1.86066e6 3.22276e6i −0.919510 1.59264i
\(334\) 0 0
\(335\) 813102. 0.395852
\(336\) 0 0
\(337\) −82853.0 + 143506.i −0.0397405 + 0.0688326i −0.885212 0.465189i \(-0.845986\pi\)
0.845471 + 0.534021i \(0.179320\pi\)
\(338\) 0 0
\(339\) −2.11211e6 + 3.65827e6i −0.998197 + 1.72893i
\(340\) 0 0
\(341\) −2.76471e6 −1.28755
\(342\) 0 0
\(343\) −321077. −0.147358
\(344\) 0 0
\(345\) −84900.3 + 147052.i −0.0384027 + 0.0665154i
\(346\) 0 0
\(347\) 407820. 706365.i 0.181821 0.314924i −0.760679 0.649128i \(-0.775134\pi\)
0.942501 + 0.334204i \(0.108467\pi\)
\(348\) 0 0
\(349\) 1.07255e6 0.471359 0.235680 0.971831i \(-0.424268\pi\)
0.235680 + 0.971831i \(0.424268\pi\)
\(350\) 0 0
\(351\) 392317. + 679513.i 0.169969 + 0.294395i
\(352\) 0 0
\(353\) −3.70760e6 −1.58364 −0.791819 0.610756i \(-0.790866\pi\)
−0.791819 + 0.610756i \(0.790866\pi\)
\(354\) 0 0
\(355\) −2.01484e6 3.48980e6i −0.848533 1.46970i
\(356\) 0 0
\(357\) −2.45285e6 4.24846e6i −1.01859 1.76425i
\(358\) 0 0
\(359\) −440125. + 762318.i −0.180235 + 0.312176i −0.941961 0.335724i \(-0.891019\pi\)
0.761725 + 0.647900i \(0.224353\pi\)
\(360\) 0 0
\(361\) −275361. + 2.46074e6i −0.111208 + 0.993797i
\(362\) 0 0
\(363\) −93408.4 + 161788.i −0.0372066 + 0.0644437i
\(364\) 0 0
\(365\) −869003. 1.50516e6i −0.341420 0.591357i
\(366\) 0 0
\(367\) 1.32405e6 + 2.29332e6i 0.513143 + 0.888789i 0.999884 + 0.0152431i \(0.00485222\pi\)
−0.486741 + 0.873546i \(0.661814\pi\)
\(368\) 0 0
\(369\) 3.59770e6 1.37550
\(370\) 0 0
\(371\) −855228. 1.48130e6i −0.322587 0.558737i
\(372\) 0 0
\(373\) 1.42105e6 0.528856 0.264428 0.964405i \(-0.414817\pi\)
0.264428 + 0.964405i \(0.414817\pi\)
\(374\) 0 0
\(375\) 2.18021e6 3.77624e6i 0.800609 1.38670i
\(376\) 0 0
\(377\) 1.50059e6 2.59909e6i 0.543761 0.941822i
\(378\) 0 0
\(379\) 4.14092e6 1.48081 0.740405 0.672161i \(-0.234634\pi\)
0.740405 + 0.672161i \(0.234634\pi\)
\(380\) 0 0
\(381\) −42439.9 −0.0149783
\(382\) 0 0
\(383\) 932604. 1.61532e6i 0.324863 0.562679i −0.656622 0.754220i \(-0.728015\pi\)
0.981485 + 0.191541i \(0.0613485\pi\)
\(384\) 0 0
\(385\) 1.95097e6 3.37918e6i 0.670809 1.16188i
\(386\) 0 0
\(387\) 1.57561e6 0.534777
\(388\) 0 0
\(389\) −225886. 391246.i −0.0756859 0.131092i 0.825698 0.564112i \(-0.190781\pi\)
−0.901384 + 0.433020i \(0.857448\pi\)
\(390\) 0 0
\(391\) −161170. −0.0533141
\(392\) 0 0
\(393\) −931865. 1.61404e6i −0.304349 0.527147i
\(394\) 0 0
\(395\) 827054. + 1.43250e6i 0.266711 + 0.461957i
\(396\) 0 0
\(397\) 387696. 671509.i 0.123457 0.213833i −0.797672 0.603092i \(-0.793935\pi\)
0.921129 + 0.389258i \(0.127269\pi\)
\(398\) 0 0
\(399\) −6.75564e6 + 1.41225e6i −2.12439 + 0.444099i
\(400\) 0 0
\(401\) −3.11762e6 + 5.39987e6i −0.968193 + 1.67696i −0.267412 + 0.963582i \(0.586168\pi\)
−0.700781 + 0.713376i \(0.747165\pi\)
\(402\) 0 0
\(403\) −1.92843e6 3.34014e6i −0.591482 1.02448i
\(404\) 0 0
\(405\) 1.04445e6 + 1.80904e6i 0.316410 + 0.548038i
\(406\) 0 0
\(407\) 5.07291e6 1.51800
\(408\) 0 0
\(409\) −2.43708e6 4.22114e6i −0.720379 1.24773i −0.960848 0.277077i \(-0.910634\pi\)
0.240468 0.970657i \(-0.422699\pi\)
\(410\) 0 0
\(411\) −4.63886e6 −1.35459
\(412\) 0 0
\(413\) 2.26100e6 3.91616e6i 0.652266 1.12976i
\(414\) 0 0
\(415\) −1.25252e6 + 2.16942e6i −0.356996 + 0.618336i
\(416\) 0 0
\(417\) 8.79144e6 2.47583
\(418\) 0 0
\(419\) 3.11548e6 0.866943 0.433471 0.901167i \(-0.357289\pi\)
0.433471 + 0.901167i \(0.357289\pi\)
\(420\) 0 0
\(421\) −2.17883e6 + 3.77384e6i −0.599125 + 1.03771i 0.393826 + 0.919185i \(0.371151\pi\)
−0.992951 + 0.118529i \(0.962182\pi\)
\(422\) 0 0
\(423\) −3.15405e6 + 5.46297e6i −0.857071 + 1.48449i
\(424\) 0 0
\(425\) 643520. 0.172818
\(426\) 0 0
\(427\) 4.05126e6 + 7.01699e6i 1.07528 + 1.86244i
\(428\) 0 0
\(429\) −5.50378e6 −1.44384
\(430\) 0 0
\(431\) 3.39109e6 + 5.87353e6i 0.879317 + 1.52302i 0.852091 + 0.523393i \(0.175334\pi\)
0.0272262 + 0.999629i \(0.491333\pi\)
\(432\) 0 0
\(433\) −16420.8 28441.7i −0.00420896 0.00729014i 0.863913 0.503641i \(-0.168006\pi\)
−0.868122 + 0.496351i \(0.834673\pi\)
\(434\) 0 0
\(435\) −3.08281e6 + 5.33958e6i −0.781131 + 1.35296i
\(436\) 0 0
\(437\) −70792.0 + 215411.i −0.0177329 + 0.0539589i
\(438\) 0 0
\(439\) −2.63969e6 + 4.57208e6i −0.653720 + 1.13228i 0.328493 + 0.944506i \(0.393459\pi\)
−0.982213 + 0.187770i \(0.939874\pi\)
\(440\) 0 0
\(441\) −2.79227e6 4.83636e6i −0.683694 1.18419i
\(442\) 0 0
\(443\) −3.86131e6 6.68798e6i −0.934813 1.61914i −0.774967 0.632002i \(-0.782233\pi\)
−0.159846 0.987142i \(-0.551100\pi\)
\(444\) 0 0
\(445\) 3.96258e6 0.948589
\(446\) 0 0
\(447\) −2.70308e6 4.68187e6i −0.639867 1.10828i
\(448\) 0 0
\(449\) 6.68110e6 1.56398 0.781992 0.623288i \(-0.214204\pi\)
0.781992 + 0.623288i \(0.214204\pi\)
\(450\) 0 0
\(451\) −2.45220e6 + 4.24733e6i −0.567694 + 0.983275i
\(452\) 0 0
\(453\) −5.43174e6 + 9.40806e6i −1.24364 + 2.15404i
\(454\) 0 0
\(455\) 5.44334e6 1.23264
\(456\) 0 0
\(457\) −1.15454e6 −0.258593 −0.129297 0.991606i \(-0.541272\pi\)
−0.129297 + 0.991606i \(0.541272\pi\)
\(458\) 0 0
\(459\) 765010. 1.32504e6i 0.169487 0.293559i
\(460\) 0 0
\(461\) 3.99643e6 6.92202e6i 0.875830 1.51698i 0.0199544 0.999801i \(-0.493648\pi\)
0.855876 0.517181i \(-0.173019\pi\)
\(462\) 0 0
\(463\) −4.73362e6 −1.02622 −0.513111 0.858322i \(-0.671507\pi\)
−0.513111 + 0.858322i \(0.671507\pi\)
\(464\) 0 0
\(465\) 3.96177e6 + 6.86199e6i 0.849683 + 1.47169i
\(466\) 0 0
\(467\) −3.37127e6 −0.715322 −0.357661 0.933851i \(-0.616426\pi\)
−0.357661 + 0.933851i \(0.616426\pi\)
\(468\) 0 0
\(469\) 1.51321e6 + 2.62096e6i 0.317664 + 0.550210i
\(470\) 0 0
\(471\) −5.97841e6 1.03549e7i −1.24175 2.15077i
\(472\) 0 0
\(473\) −1.07394e6 + 1.86012e6i −0.220713 + 0.382285i
\(474\) 0 0
\(475\) 282659. 860093.i 0.0574816 0.174909i
\(476\) 0 0
\(477\) 1.37250e6 2.37724e6i 0.276195 0.478384i
\(478\) 0 0
\(479\) 3.45446e6 + 5.98330e6i 0.687925 + 1.19152i 0.972508 + 0.232870i \(0.0748117\pi\)
−0.284583 + 0.958652i \(0.591855\pi\)
\(480\) 0 0
\(481\) 3.53844e6 + 6.12876e6i 0.697348 + 1.20784i
\(482\) 0 0
\(483\) −632010. −0.123270
\(484\) 0 0
\(485\) 3.16382e6 + 5.47990e6i 0.610742 + 1.05784i
\(486\) 0 0
\(487\) −3.84736e6 −0.735089 −0.367545 0.930006i \(-0.619801\pi\)
−0.367545 + 0.930006i \(0.619801\pi\)
\(488\) 0 0
\(489\) −6.43342e6 + 1.11430e7i −1.21666 + 2.10732i
\(490\) 0 0
\(491\) 4.95587e6 8.58382e6i 0.927719 1.60686i 0.140590 0.990068i \(-0.455100\pi\)
0.787129 0.616788i \(-0.211567\pi\)
\(492\) 0 0
\(493\) −5.85223e6 −1.08444
\(494\) 0 0
\(495\) 6.26197e6 1.14868
\(496\) 0 0
\(497\) 7.49937e6 1.29893e7i 1.36186 2.35882i
\(498\) 0 0
\(499\) −3.50894e6 + 6.07766e6i −0.630847 + 1.09266i 0.356532 + 0.934283i \(0.383959\pi\)
−0.987379 + 0.158376i \(0.949374\pi\)
\(500\) 0 0
\(501\) −1.13257e6 −0.201591
\(502\) 0 0
\(503\) 1.11612e6 + 1.93318e6i 0.196694 + 0.340684i 0.947455 0.319890i \(-0.103646\pi\)
−0.750760 + 0.660575i \(0.770313\pi\)
\(504\) 0 0
\(505\) 6.50123e6 1.13440
\(506\) 0 0
\(507\) 493453. + 854686.i 0.0852562 + 0.147668i
\(508\) 0 0
\(509\) 787950. + 1.36477e6i 0.134804 + 0.233488i 0.925523 0.378692i \(-0.123626\pi\)
−0.790718 + 0.612180i \(0.790293\pi\)
\(510\) 0 0
\(511\) 3.23449e6 5.60231e6i 0.547966 0.949106i
\(512\) 0 0
\(513\) −1.43495e6 1.60448e6i −0.240737 0.269178i
\(514\) 0 0
\(515\) 4.68017e6 8.10629e6i 0.777577 1.34680i
\(516\) 0 0
\(517\) −4.29960e6 7.44713e6i −0.707460 1.22536i
\(518\) 0 0
\(519\) −1.97410e6 3.41924e6i −0.321700 0.557200i
\(520\) 0 0
\(521\) −4.35615e6 −0.703086 −0.351543 0.936172i \(-0.614343\pi\)
−0.351543 + 0.936172i \(0.614343\pi\)
\(522\) 0 0
\(523\) −2.64694e6 4.58464e6i −0.423146 0.732911i 0.573099 0.819486i \(-0.305741\pi\)
−0.996245 + 0.0865752i \(0.972408\pi\)
\(524\) 0 0
\(525\) 2.52350e6 0.399580
\(526\) 0 0
\(527\) −3.76040e6 + 6.51320e6i −0.589803 + 1.02157i
\(528\) 0 0
\(529\) 3.20779e6 5.55605e6i 0.498387 0.863232i
\(530\) 0 0
\(531\) 7.25705e6 1.11692
\(532\) 0 0
\(533\) −6.84180e6 −1.04316
\(534\) 0 0
\(535\) 1.30580e6 2.26171e6i 0.197238 0.341627i
\(536\) 0 0
\(537\) 6.54374e6 1.13341e7i 0.979243 1.69610i
\(538\) 0 0
\(539\) 7.61286e6 1.12869
\(540\) 0 0
\(541\) −5.45983e6 9.45670e6i −0.802021 1.38914i −0.918284 0.395923i \(-0.870425\pi\)
0.116263 0.993218i \(-0.462909\pi\)
\(542\) 0 0
\(543\) −8.71551e6 −1.26851
\(544\) 0 0
\(545\) −538572. 932835.i −0.0776699 0.134528i
\(546\) 0 0
\(547\) −1.49890e6 2.59617e6i −0.214192 0.370992i 0.738830 0.673892i \(-0.235379\pi\)
−0.953022 + 0.302900i \(0.902045\pi\)
\(548\) 0 0
\(549\) −6.50161e6 + 1.12611e7i −0.920640 + 1.59460i
\(550\) 0 0
\(551\) −2.57053e6 + 7.82176e6i −0.360697 + 1.09755i
\(552\) 0 0
\(553\) −3.07835e6 + 5.33186e6i −0.428061 + 0.741423i
\(554\) 0 0
\(555\) −7.26938e6 1.25909e7i −1.00176 1.73510i
\(556\) 0 0
\(557\) 197093. + 341375.i 0.0269174 + 0.0466223i 0.879170 0.476508i \(-0.158098\pi\)
−0.852253 + 0.523130i \(0.824764\pi\)
\(558\) 0 0
\(559\) −2.99637e6 −0.405569
\(560\) 0 0
\(561\) 5.36613e6 + 9.29441e6i 0.719870 + 1.24685i
\(562\) 0 0
\(563\) 1.10461e7 1.46872 0.734361 0.678760i \(-0.237482\pi\)
0.734361 + 0.678760i \(0.237482\pi\)
\(564\) 0 0
\(565\) −4.56994e6 + 7.91537e6i −0.602267 + 1.04316i
\(566\) 0 0
\(567\) −3.88752e6 + 6.73338e6i −0.507826 + 0.879580i
\(568\) 0 0
\(569\) −7.21256e6 −0.933918 −0.466959 0.884279i \(-0.654651\pi\)
−0.466959 + 0.884279i \(0.654651\pi\)
\(570\) 0 0
\(571\) 3.09113e6 0.396760 0.198380 0.980125i \(-0.436432\pi\)
0.198380 + 0.980125i \(0.436432\pi\)
\(572\) 0 0
\(573\) 7.04003e6 1.21937e7i 0.895752 1.55149i
\(574\) 0 0
\(575\) 41453.0 71798.6i 0.00522861 0.00905621i
\(576\) 0 0
\(577\) −2.16381e6 −0.270570 −0.135285 0.990807i \(-0.543195\pi\)
−0.135285 + 0.990807i \(0.543195\pi\)
\(578\) 0 0
\(579\) 1234.28 + 2137.84i 0.000153009 + 0.000265020i
\(580\) 0 0
\(581\) −9.32392e6 −1.14593
\(582\) 0 0
\(583\) 1.87099e6 + 3.24066e6i 0.227982 + 0.394877i
\(584\) 0 0
\(585\) 4.36783e6 + 7.56531e6i 0.527687 + 0.913981i
\(586\) 0 0
\(587\) −632835. + 1.09610e6i −0.0758045 + 0.131297i −0.901436 0.432913i \(-0.857486\pi\)
0.825631 + 0.564210i \(0.190819\pi\)
\(588\) 0 0
\(589\) 7.05347e6 + 7.88679e6i 0.837750 + 0.936725i
\(590\) 0 0
\(591\) 8.21553e6 1.42297e7i 0.967535 1.67582i
\(592\) 0 0
\(593\) −8.38325e6 1.45202e7i −0.978984 1.69565i −0.666106 0.745857i \(-0.732040\pi\)
−0.312878 0.949793i \(-0.601293\pi\)
\(594\) 0 0
\(595\) −5.30720e6 9.19234e6i −0.614573 1.06447i
\(596\) 0 0
\(597\) −3.80037e6 −0.436405
\(598\) 0 0
\(599\) 2.31238e6 + 4.00516e6i 0.263325 + 0.456092i 0.967123 0.254308i \(-0.0818475\pi\)
−0.703798 + 0.710400i \(0.748514\pi\)
\(600\) 0 0
\(601\) −568699. −0.0642238 −0.0321119 0.999484i \(-0.510223\pi\)
−0.0321119 + 0.999484i \(0.510223\pi\)
\(602\) 0 0
\(603\) −2.42846e6 + 4.20621e6i −0.271980 + 0.471083i
\(604\) 0 0
\(605\) −202107. + 350059.i −0.0224488 + 0.0388824i
\(606\) 0 0
\(607\) 9.98344e6 1.09979 0.549893 0.835235i \(-0.314668\pi\)
0.549893 + 0.835235i \(0.314668\pi\)
\(608\) 0 0
\(609\) −2.29489e7 −2.50737
\(610\) 0 0
\(611\) 5.99809e6 1.03890e7i 0.649995 1.12582i
\(612\) 0 0
\(613\) −2.93664e6 + 5.08641e6i −0.315645 + 0.546714i −0.979574 0.201082i \(-0.935554\pi\)
0.663929 + 0.747796i \(0.268888\pi\)
\(614\) 0 0
\(615\) 1.40558e7 1.49854
\(616\) 0 0
\(617\) −4.31577e6 7.47513e6i −0.456400 0.790508i 0.542368 0.840141i \(-0.317528\pi\)
−0.998767 + 0.0496336i \(0.984195\pi\)
\(618\) 0 0
\(619\) −6.29725e6 −0.660578 −0.330289 0.943880i \(-0.607146\pi\)
−0.330289 + 0.943880i \(0.607146\pi\)
\(620\) 0 0
\(621\) −98557.6 170707.i −0.0102556 0.0177632i
\(622\) 0 0
\(623\) 7.37450e6 + 1.27730e7i 0.761224 + 1.31848i
\(624\) 0 0
\(625\) 3.81831e6 6.61351e6i 0.390995 0.677224i
\(626\) 0 0
\(627\) 1.47794e7 3.08961e6i 1.50137 0.313859i
\(628\) 0 0
\(629\) 6.89989e6 1.19510e7i 0.695369 1.20441i
\(630\) 0 0
\(631\) 2.14448e6 + 3.71434e6i 0.214411 + 0.371371i 0.953090 0.302686i \(-0.0978833\pi\)
−0.738679 + 0.674057i \(0.764550\pi\)
\(632\) 0 0
\(633\) 8.14788e6 + 1.41125e7i 0.808231 + 1.39990i
\(634\) 0 0
\(635\) −91826.8 −0.00903723
\(636\) 0 0
\(637\) 5.31010e6 + 9.19737e6i 0.518507 + 0.898080i
\(638\) 0 0
\(639\) 2.40705e7 2.33202
\(640\) 0 0
\(641\) −5.61057e6 + 9.71779e6i −0.539339 + 0.934163i 0.459600 + 0.888126i \(0.347993\pi\)
−0.998940 + 0.0460372i \(0.985341\pi\)
\(642\) 0 0
\(643\) −2.20567e6 + 3.82032e6i −0.210384 + 0.364395i −0.951835 0.306612i \(-0.900805\pi\)
0.741451 + 0.671007i \(0.234138\pi\)
\(644\) 0 0
\(645\) 6.15574e6 0.582614
\(646\) 0 0
\(647\) 7.20279e6 0.676457 0.338229 0.941064i \(-0.390172\pi\)
0.338229 + 0.941064i \(0.390172\pi\)
\(648\) 0 0
\(649\) −4.94641e6 + 8.56744e6i −0.460976 + 0.798434i
\(650\) 0 0
\(651\) −1.47460e7 + 2.55408e7i −1.36371 + 2.36201i
\(652\) 0 0
\(653\) −4.23537e6 −0.388695 −0.194347 0.980933i \(-0.562259\pi\)
−0.194347 + 0.980933i \(0.562259\pi\)
\(654\) 0 0
\(655\) −2.01627e6 3.49227e6i −0.183630 0.318057i
\(656\) 0 0
\(657\) 1.03817e7 0.938325
\(658\) 0 0
\(659\) −3.24491e6 5.62036e6i −0.291065 0.504139i 0.682997 0.730421i \(-0.260676\pi\)
−0.974062 + 0.226282i \(0.927343\pi\)
\(660\) 0 0
\(661\) −5.60734e6 9.71219e6i −0.499175 0.864597i 0.500824 0.865549i \(-0.333030\pi\)
−1.00000 0.000952002i \(0.999697\pi\)
\(662\) 0 0
\(663\) −7.48594e6 + 1.29660e7i −0.661397 + 1.14557i
\(664\) 0 0
\(665\) −1.46171e7 + 3.05568e6i −1.28176 + 0.267950i
\(666\) 0 0
\(667\) −376977. + 652943.i −0.0328095 + 0.0568278i
\(668\) 0 0
\(669\) −2.18676e6 3.78757e6i −0.188901 0.327187i
\(670\) 0 0
\(671\) −8.86300e6 1.53512e7i −0.759932 1.31624i
\(672\) 0 0
\(673\) 301881. 0.0256920 0.0128460 0.999917i \(-0.495911\pi\)
0.0128460 + 0.999917i \(0.495911\pi\)
\(674\) 0 0
\(675\) 393522. + 681600.i 0.0332437 + 0.0575798i
\(676\) 0 0
\(677\) −470872. −0.0394849 −0.0197424 0.999805i \(-0.506285\pi\)
−0.0197424 + 0.999805i \(0.506285\pi\)
\(678\) 0 0
\(679\) −1.17760e7 + 2.03966e7i −0.980218 + 1.69779i
\(680\) 0 0
\(681\) −7.07813e6 + 1.22597e7i −0.584859 + 1.01301i
\(682\) 0 0
\(683\) −1.01992e7 −0.836589 −0.418295 0.908311i \(-0.637372\pi\)
−0.418295 + 0.908311i \(0.637372\pi\)
\(684\) 0 0
\(685\) −1.00370e7 −0.817296
\(686\) 0 0
\(687\) 2.51376e6 4.35396e6i 0.203204 0.351960i
\(688\) 0 0
\(689\) −2.61010e6 + 4.52083e6i −0.209464 + 0.362802i
\(690\) 0 0
\(691\) 4.81669e6 0.383754 0.191877 0.981419i \(-0.438542\pi\)
0.191877 + 0.981419i \(0.438542\pi\)
\(692\) 0 0
\(693\) 1.16538e7 + 2.01849e7i 0.921792 + 1.59659i
\(694\) 0 0
\(695\) 1.90220e7 1.49380
\(696\) 0 0
\(697\) 6.67068e6 + 1.15540e7i 0.520102 + 0.900843i
\(698\) 0 0
\(699\) −1.19348e7 2.06717e7i −0.923895 1.60023i
\(700\) 0 0
\(701\) 2.09052e6 3.62088e6i 0.160679 0.278304i −0.774434 0.632655i \(-0.781965\pi\)
0.935112 + 0.354351i \(0.115298\pi\)
\(702\) 0 0
\(703\) −1.29423e7 1.44713e7i −0.987694 1.10438i
\(704\) 0 0
\(705\) −1.23225e7 + 2.13432e7i −0.933739 + 1.61728i
\(706\) 0 0
\(707\) 1.20990e7 + 2.09561e7i 0.910336 + 1.57675i
\(708\) 0 0
\(709\) −4.41436e6 7.64589e6i −0.329801 0.571232i 0.652671 0.757641i \(-0.273648\pi\)
−0.982472 + 0.186409i \(0.940315\pi\)
\(710\) 0 0
\(711\) −9.88050e6 −0.733001
\(712\) 0 0
\(713\) 484459. + 839107.i 0.0356889 + 0.0618150i
\(714\) 0 0
\(715\) −1.19085e7 −0.871146
\(716\) 0 0
\(717\) 1.52989e7 2.64985e7i 1.11138 1.92497i
\(718\) 0 0
\(719\) −2.62278e6 + 4.54279e6i −0.189208 + 0.327718i −0.944986 0.327109i \(-0.893925\pi\)
0.755778 + 0.654828i \(0.227259\pi\)
\(720\) 0 0
\(721\) 3.48398e7 2.49596
\(722\) 0 0
\(723\) −223310. −0.0158877
\(724\) 0 0
\(725\) 1.50520e6 2.60708e6i 0.106353 0.184208i
\(726\) 0 0
\(727\) 9.18888e6 1.59156e7i 0.644802 1.11683i −0.339545 0.940590i \(-0.610273\pi\)
0.984347 0.176241i \(-0.0563937\pi\)
\(728\) 0 0
\(729\) −2.02351e7 −1.41022
\(730\) 0 0
\(731\) 2.92142e6 + 5.06006e6i 0.202209 + 0.350237i
\(732\) 0 0
\(733\) 2.42837e7 1.66938 0.834689 0.550721i \(-0.185647\pi\)
0.834689 + 0.550721i \(0.185647\pi\)
\(734\) 0 0
\(735\) −1.09091e7 1.88951e7i −0.744852 1.29012i
\(736\) 0 0
\(737\) −3.31048e6 5.73391e6i −0.224503 0.388850i
\(738\) 0 0
\(739\) −1.29261e6 + 2.23886e6i −0.0870674 + 0.150805i −0.906270 0.422699i \(-0.861083\pi\)
0.819203 + 0.573504i \(0.194416\pi\)
\(740\) 0 0
\(741\) 1.40415e7 + 1.57005e7i 0.939441 + 1.05043i
\(742\) 0 0
\(743\) 9.08526e6 1.57361e7i 0.603761 1.04575i −0.388485 0.921455i \(-0.627001\pi\)
0.992246 0.124290i \(-0.0396653\pi\)
\(744\) 0 0
\(745\) −5.84862e6 1.01301e7i −0.386067 0.668688i
\(746\) 0 0
\(747\) −7.48168e6 1.29586e7i −0.490566 0.849685i
\(748\) 0 0
\(749\) 9.72054e6 0.633120
\(750\) 0 0
\(751\) −7.21562e6 1.24978e7i −0.466846 0.808601i 0.532437 0.846470i \(-0.321276\pi\)
−0.999283 + 0.0378689i \(0.987943\pi\)
\(752\) 0 0
\(753\) 1.06521e7 0.684615
\(754\) 0 0
\(755\) −1.17526e7 + 2.03561e7i −0.750355 + 1.29965i
\(756\) 0 0
\(757\) −1.51265e6 + 2.61999e6i −0.0959399 + 0.166173i −0.910001 0.414607i \(-0.863919\pi\)
0.814061 + 0.580780i \(0.197252\pi\)
\(758\) 0 0
\(759\) 1.38266e6 0.0871184
\(760\) 0 0
\(761\) 1.91756e7 1.20029 0.600147 0.799890i \(-0.295109\pi\)
0.600147 + 0.799890i \(0.295109\pi\)
\(762\) 0 0
\(763\) 2.00460e6 3.47208e6i 0.124657 0.215913i
\(764\) 0 0
\(765\) 8.51718e6 1.47522e7i 0.526190 0.911387i
\(766\) 0 0
\(767\) −1.38008e7 −0.847065
\(768\) 0 0
\(769\) −1.08868e7 1.88565e7i −0.663872 1.14986i −0.979590 0.201007i \(-0.935579\pi\)
0.315718 0.948853i \(-0.397755\pi\)
\(770\) 0 0
\(771\) −1.21276e7 −0.734750
\(772\) 0 0
\(773\) 1.04601e6 + 1.81174e6i 0.0629631 + 0.109055i 0.895789 0.444480i \(-0.146612\pi\)
−0.832826 + 0.553536i \(0.813278\pi\)
\(774\) 0 0
\(775\) −1.93435e6 3.35040e6i −0.115686 0.200374i
\(776\) 0 0
\(777\) 2.70572e7 4.68644e7i 1.60779 2.78478i
\(778\) 0 0
\(779\) 1.83724e7 3.84072e6i 1.08473 0.226761i
\(780\) 0 0
\(781\) −1.64065e7 + 2.84168e7i −0.962471 + 1.66705i
\(782\) 0 0
\(783\) −3.57872e6 6.19852e6i −0.208604 0.361313i
\(784\) 0 0
\(785\) −1.29354e7 2.24048e7i −0.749215 1.29768i
\(786\) 0 0
\(787\) 3.41901e7 1.96772 0.983860 0.178942i \(-0.0572673\pi\)
0.983860 + 0.178942i \(0.0572673\pi\)
\(788\) 0 0
\(789\) −3.71400e6