Properties

Label 324.5.d.f.163.11
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.11
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.f.163.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.328300 - 3.98650i) q^{2} +(-15.7844 + 2.61754i) q^{4} +5.66182 q^{5} +52.1456i q^{7} +(15.6169 + 62.0654i) q^{8} +O(q^{10})\) \(q+(-0.328300 - 3.98650i) q^{2} +(-15.7844 + 2.61754i) q^{4} +5.66182 q^{5} +52.1456i q^{7} +(15.6169 + 62.0654i) q^{8} +(-1.85878 - 22.5709i) q^{10} +106.664i q^{11} -122.137 q^{13} +(207.879 - 17.1194i) q^{14} +(242.297 - 82.6328i) q^{16} -122.675 q^{17} -593.624i q^{19} +(-89.3686 + 14.8200i) q^{20} +(425.216 - 35.0178i) q^{22} -546.922i q^{23} -592.944 q^{25} +(40.0976 + 486.900i) q^{26} +(-136.493 - 823.090i) q^{28} +735.866 q^{29} -585.927i q^{31} +(-408.962 - 938.790i) q^{32} +(40.2742 + 489.044i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-2366.49 + 194.887i) q^{38} +(88.4199 + 351.403i) q^{40} -2868.26 q^{41} -2244.52i q^{43} +(-279.197 - 1683.63i) q^{44} +(-2180.31 + 179.555i) q^{46} -1054.85i q^{47} -318.168 q^{49} +(194.664 + 2363.77i) q^{50} +(1927.87 - 319.699i) q^{52} -4752.60 q^{53} +603.911i q^{55} +(-3236.44 + 814.352i) q^{56} +(-241.585 - 2933.53i) q^{58} +2152.65i q^{59} -66.3319 q^{61} +(-2335.80 + 192.360i) q^{62} +(-3608.23 + 1938.53i) q^{64} -691.518 q^{65} -4104.76i q^{67} +(1936.36 - 321.107i) q^{68} +(1176.97 - 96.9271i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(-751.574 - 9126.26i) q^{74} +(1553.84 + 9370.03i) q^{76} -5562.06 q^{77} -1381.05i q^{79} +(1371.84 - 467.852i) q^{80} +(941.652 + 11434.4i) q^{82} +3008.36i q^{83} -694.563 q^{85} +(-8947.79 + 736.876i) q^{86} +(-6620.13 + 1665.76i) q^{88} +3186.35 q^{89} -6368.92i q^{91} +(1431.59 + 8632.86i) q^{92} +(-4205.18 + 346.309i) q^{94} -3360.99i q^{95} -4814.06 q^{97} +(104.455 + 1268.38i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + O(q^{10}) \) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + 14q^{10} + 2q^{13} - 252q^{14} + q^{16} - 28q^{17} + 140q^{20} + 33q^{22} + 1752q^{25} + 548q^{26} - 258q^{28} - 526q^{29} + 121q^{32} - 385q^{34} - 4q^{37} - 1395q^{38} + 2276q^{40} + 2762q^{41} + 3357q^{44} + 1788q^{46} - 3428q^{49} - 6375q^{50} - 1438q^{52} - 5044q^{53} + 7506q^{56} + 4064q^{58} + 2q^{61} - 9162q^{62} + 4513q^{64} + 2014q^{65} + 11405q^{68} - 3666q^{70} - 1708q^{73} - 14620q^{74} - 1581q^{76} + 3942q^{77} + 22760q^{80} - 4243q^{82} + 1252q^{85} - 22113q^{86} - 1995q^{88} + 6524q^{89} + 30294q^{92} - 7524q^{94} - 5638q^{97} - 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.328300 3.98650i −0.0820750 0.996626i
\(3\) 0 0
\(4\) −15.7844 + 2.61754i −0.986527 + 0.163596i
\(5\) 5.66182 0.226473 0.113236 0.993568i \(-0.463878\pi\)
0.113236 + 0.993568i \(0.463878\pi\)
\(6\) 0 0
\(7\) 52.1456i 1.06420i 0.846683 + 0.532098i \(0.178596\pi\)
−0.846683 + 0.532098i \(0.821404\pi\)
\(8\) 15.6169 + 62.0654i 0.244014 + 0.969772i
\(9\) 0 0
\(10\) −1.85878 22.5709i −0.0185878 0.225709i
\(11\) 106.664i 0.881519i 0.897625 + 0.440760i \(0.145291\pi\)
−0.897625 + 0.440760i \(0.854709\pi\)
\(12\) 0 0
\(13\) −122.137 −0.722705 −0.361352 0.932429i \(-0.617685\pi\)
−0.361352 + 0.932429i \(0.617685\pi\)
\(14\) 207.879 17.1194i 1.06061 0.0873440i
\(15\) 0 0
\(16\) 242.297 82.6328i 0.946473 0.322784i
\(17\) −122.675 −0.424481 −0.212240 0.977217i \(-0.568076\pi\)
−0.212240 + 0.977217i \(0.568076\pi\)
\(18\) 0 0
\(19\) 593.624i 1.64439i −0.569207 0.822194i \(-0.692750\pi\)
0.569207 0.822194i \(-0.307250\pi\)
\(20\) −89.3686 + 14.8200i −0.223422 + 0.0370501i
\(21\) 0 0
\(22\) 425.216 35.0178i 0.878545 0.0723507i
\(23\) 546.922i 1.03388i −0.856022 0.516940i \(-0.827071\pi\)
0.856022 0.516940i \(-0.172929\pi\)
\(24\) 0 0
\(25\) −592.944 −0.948710
\(26\) 40.0976 + 486.900i 0.0593160 + 0.720266i
\(27\) 0 0
\(28\) −136.493 823.090i −0.174099 1.04986i
\(29\) 735.866 0.874989 0.437495 0.899221i \(-0.355866\pi\)
0.437495 + 0.899221i \(0.355866\pi\)
\(30\) 0 0
\(31\) 585.927i 0.609705i −0.952400 0.304853i \(-0.901393\pi\)
0.952400 0.304853i \(-0.0986072\pi\)
\(32\) −408.962 938.790i −0.399377 0.916787i
\(33\) 0 0
\(34\) 40.2742 + 489.044i 0.0348393 + 0.423049i
\(35\) 295.239i 0.241012i
\(36\) 0 0
\(37\) 2289.29 1.67223 0.836117 0.548551i \(-0.184820\pi\)
0.836117 + 0.548551i \(0.184820\pi\)
\(38\) −2366.49 + 194.887i −1.63884 + 0.134963i
\(39\) 0 0
\(40\) 88.4199 + 351.403i 0.0552624 + 0.219627i
\(41\) −2868.26 −1.70628 −0.853142 0.521678i \(-0.825306\pi\)
−0.853142 + 0.521678i \(0.825306\pi\)
\(42\) 0 0
\(43\) 2244.52i 1.21391i −0.794736 0.606955i \(-0.792391\pi\)
0.794736 0.606955i \(-0.207609\pi\)
\(44\) −279.197 1683.63i −0.144213 0.869643i
\(45\) 0 0
\(46\) −2180.31 + 179.555i −1.03039 + 0.0848557i
\(47\) 1054.85i 0.477526i −0.971078 0.238763i \(-0.923258\pi\)
0.971078 0.238763i \(-0.0767419\pi\)
\(48\) 0 0
\(49\) −318.168 −0.132515
\(50\) 194.664 + 2363.77i 0.0778654 + 0.945509i
\(51\) 0 0
\(52\) 1927.87 319.699i 0.712968 0.118232i
\(53\) −4752.60 −1.69192 −0.845960 0.533246i \(-0.820972\pi\)
−0.845960 + 0.533246i \(0.820972\pi\)
\(54\) 0 0
\(55\) 603.911i 0.199640i
\(56\) −3236.44 + 814.352i −1.03203 + 0.259678i
\(57\) 0 0
\(58\) −241.585 2933.53i −0.0718148 0.872037i
\(59\) 2152.65i 0.618399i 0.950997 + 0.309200i \(0.100061\pi\)
−0.950997 + 0.309200i \(0.899939\pi\)
\(60\) 0 0
\(61\) −66.3319 −0.0178264 −0.00891319 0.999960i \(-0.502837\pi\)
−0.00891319 + 0.999960i \(0.502837\pi\)
\(62\) −2335.80 + 192.360i −0.607648 + 0.0500416i
\(63\) 0 0
\(64\) −3608.23 + 1938.53i −0.880915 + 0.473275i
\(65\) −691.518 −0.163673
\(66\) 0 0
\(67\) 4104.76i 0.914404i −0.889363 0.457202i \(-0.848852\pi\)
0.889363 0.457202i \(-0.151148\pi\)
\(68\) 1936.36 321.107i 0.418762 0.0694435i
\(69\) 0 0
\(70\) 1176.97 96.9271i 0.240198 0.0197810i
\(71\) 5031.65i 0.998145i −0.866560 0.499072i \(-0.833674\pi\)
0.866560 0.499072i \(-0.166326\pi\)
\(72\) 0 0
\(73\) 2705.16 0.507631 0.253815 0.967253i \(-0.418314\pi\)
0.253815 + 0.967253i \(0.418314\pi\)
\(74\) −751.574 9126.26i −0.137249 1.66659i
\(75\) 0 0
\(76\) 1553.84 + 9370.03i 0.269016 + 1.62223i
\(77\) −5562.06 −0.938110
\(78\) 0 0
\(79\) 1381.05i 0.221286i −0.993860 0.110643i \(-0.964709\pi\)
0.993860 0.110643i \(-0.0352911\pi\)
\(80\) 1371.84 467.852i 0.214350 0.0731019i
\(81\) 0 0
\(82\) 941.652 + 11434.4i 0.140043 + 1.70053i
\(83\) 3008.36i 0.436690i 0.975872 + 0.218345i \(0.0700658\pi\)
−0.975872 + 0.218345i \(0.929934\pi\)
\(84\) 0 0
\(85\) −694.563 −0.0961333
\(86\) −8947.79 + 736.876i −1.20981 + 0.0996317i
\(87\) 0 0
\(88\) −6620.13 + 1665.76i −0.854873 + 0.215103i
\(89\) 3186.35 0.402267 0.201133 0.979564i \(-0.435538\pi\)
0.201133 + 0.979564i \(0.435538\pi\)
\(90\) 0 0
\(91\) 6368.92i 0.769100i
\(92\) 1431.59 + 8632.86i 0.169139 + 1.01995i
\(93\) 0 0
\(94\) −4205.18 + 346.309i −0.475915 + 0.0391930i
\(95\) 3360.99i 0.372409i
\(96\) 0 0
\(97\) −4814.06 −0.511644 −0.255822 0.966724i \(-0.582346\pi\)
−0.255822 + 0.966724i \(0.582346\pi\)
\(98\) 104.455 + 1268.38i 0.0108762 + 0.132068i
\(99\) 0 0
\(100\) 9359.28 1552.05i 0.935928 0.155205i
\(101\) −7020.93 −0.688259 −0.344130 0.938922i \(-0.611826\pi\)
−0.344130 + 0.938922i \(0.611826\pi\)
\(102\) 0 0
\(103\) 2146.41i 0.202320i 0.994870 + 0.101160i \(0.0322554\pi\)
−0.994870 + 0.101160i \(0.967745\pi\)
\(104\) −1907.40 7580.49i −0.176350 0.700859i
\(105\) 0 0
\(106\) 1560.28 + 18946.3i 0.138864 + 1.68621i
\(107\) 13846.7i 1.20943i 0.796443 + 0.604713i \(0.206712\pi\)
−0.796443 + 0.604713i \(0.793288\pi\)
\(108\) 0 0
\(109\) −19384.9 −1.63159 −0.815793 0.578344i \(-0.803699\pi\)
−0.815793 + 0.578344i \(0.803699\pi\)
\(110\) 2407.50 198.264i 0.198967 0.0163855i
\(111\) 0 0
\(112\) 4308.94 + 12634.7i 0.343506 + 1.00723i
\(113\) 13634.4 1.06777 0.533887 0.845556i \(-0.320731\pi\)
0.533887 + 0.845556i \(0.320731\pi\)
\(114\) 0 0
\(115\) 3096.57i 0.234145i
\(116\) −11615.2 + 1926.16i −0.863201 + 0.143145i
\(117\) 0 0
\(118\) 8581.54 706.715i 0.616313 0.0507551i
\(119\) 6396.96i 0.451731i
\(120\) 0 0
\(121\) 3263.82 0.222923
\(122\) 21.7768 + 264.433i 0.00146310 + 0.0177662i
\(123\) 0 0
\(124\) 1533.69 + 9248.52i 0.0997455 + 0.601491i
\(125\) −6895.78 −0.441330
\(126\) 0 0
\(127\) 15689.6i 0.972754i −0.873749 0.486377i \(-0.838318\pi\)
0.873749 0.486377i \(-0.161682\pi\)
\(128\) 8912.56 + 13747.8i 0.543979 + 0.839099i
\(129\) 0 0
\(130\) 227.025 + 2756.74i 0.0134335 + 0.163121i
\(131\) 8371.86i 0.487842i −0.969795 0.243921i \(-0.921566\pi\)
0.969795 0.243921i \(-0.0784338\pi\)
\(132\) 0 0
\(133\) 30954.9 1.74995
\(134\) −16363.6 + 1347.59i −0.911319 + 0.0750497i
\(135\) 0 0
\(136\) −1915.80 7613.87i −0.103579 0.411650i
\(137\) −29930.3 −1.59467 −0.797333 0.603540i \(-0.793756\pi\)
−0.797333 + 0.603540i \(0.793756\pi\)
\(138\) 0 0
\(139\) 23846.7i 1.23424i −0.786871 0.617118i \(-0.788300\pi\)
0.786871 0.617118i \(-0.211700\pi\)
\(140\) −772.800 4660.18i −0.0394286 0.237764i
\(141\) 0 0
\(142\) −20058.7 + 1651.89i −0.994777 + 0.0819228i
\(143\) 13027.6i 0.637078i
\(144\) 0 0
\(145\) 4166.34 0.198161
\(146\) −888.106 10784.2i −0.0416638 0.505918i
\(147\) 0 0
\(148\) −36135.1 + 5992.30i −1.64970 + 0.273571i
\(149\) 5273.96 0.237555 0.118778 0.992921i \(-0.462102\pi\)
0.118778 + 0.992921i \(0.462102\pi\)
\(150\) 0 0
\(151\) 33424.0i 1.46590i −0.680281 0.732951i \(-0.738142\pi\)
0.680281 0.732951i \(-0.261858\pi\)
\(152\) 36843.5 9270.55i 1.59468 0.401253i
\(153\) 0 0
\(154\) 1826.02 + 22173.2i 0.0769954 + 0.934945i
\(155\) 3317.41i 0.138082i
\(156\) 0 0
\(157\) 17001.5 0.689742 0.344871 0.938650i \(-0.387923\pi\)
0.344871 + 0.938650i \(0.387923\pi\)
\(158\) −5505.55 + 453.398i −0.220540 + 0.0181621i
\(159\) 0 0
\(160\) −2315.47 5315.26i −0.0904480 0.207627i
\(161\) 28519.6 1.10025
\(162\) 0 0
\(163\) 30843.8i 1.16089i −0.814298 0.580447i \(-0.802878\pi\)
0.814298 0.580447i \(-0.197122\pi\)
\(164\) 45273.9 7507.80i 1.68330 0.279142i
\(165\) 0 0
\(166\) 11992.8 987.644i 0.435216 0.0358413i
\(167\) 15798.7i 0.566485i 0.959048 + 0.283243i \(0.0914102\pi\)
−0.959048 + 0.283243i \(0.908590\pi\)
\(168\) 0 0
\(169\) −13643.5 −0.477698
\(170\) 228.025 + 2768.88i 0.00789015 + 0.0958090i
\(171\) 0 0
\(172\) 5875.12 + 35428.5i 0.198591 + 1.19756i
\(173\) 47062.8 1.57248 0.786241 0.617921i \(-0.212025\pi\)
0.786241 + 0.617921i \(0.212025\pi\)
\(174\) 0 0
\(175\) 30919.4i 1.00961i
\(176\) 8813.93 + 25844.3i 0.284541 + 0.834334i
\(177\) 0 0
\(178\) −1046.08 12702.4i −0.0330161 0.400909i
\(179\) 2545.69i 0.0794511i −0.999211 0.0397256i \(-0.987352\pi\)
0.999211 0.0397256i \(-0.0126484\pi\)
\(180\) 0 0
\(181\) 5676.58 0.173272 0.0866362 0.996240i \(-0.472388\pi\)
0.0866362 + 0.996240i \(0.472388\pi\)
\(182\) −25389.7 + 2090.92i −0.766505 + 0.0631239i
\(183\) 0 0
\(184\) 33944.9 8541.21i 1.00263 0.252281i
\(185\) 12961.5 0.378715
\(186\) 0 0
\(187\) 13085.0i 0.374188i
\(188\) 2761.12 + 16650.3i 0.0781214 + 0.471092i
\(189\) 0 0
\(190\) −13398.6 + 1103.41i −0.371153 + 0.0305655i
\(191\) 32478.5i 0.890284i 0.895460 + 0.445142i \(0.146847\pi\)
−0.895460 + 0.445142i \(0.853153\pi\)
\(192\) 0 0
\(193\) 787.434 0.0211397 0.0105699 0.999944i \(-0.496635\pi\)
0.0105699 + 0.999944i \(0.496635\pi\)
\(194\) 1580.46 + 19191.3i 0.0419932 + 0.509918i
\(195\) 0 0
\(196\) 5022.11 832.818i 0.130730 0.0216789i
\(197\) 24825.9 0.639694 0.319847 0.947469i \(-0.396368\pi\)
0.319847 + 0.947469i \(0.396368\pi\)
\(198\) 0 0
\(199\) 12008.5i 0.303237i 0.988439 + 0.151619i \(0.0484485\pi\)
−0.988439 + 0.151619i \(0.951551\pi\)
\(200\) −9259.93 36801.3i −0.231498 0.920032i
\(201\) 0 0
\(202\) 2304.97 + 27989.0i 0.0564889 + 0.685937i
\(203\) 38372.2i 0.931161i
\(204\) 0 0
\(205\) −16239.6 −0.386427
\(206\) 8556.69 704.668i 0.201638 0.0166054i
\(207\) 0 0
\(208\) −29593.5 + 10092.5i −0.684020 + 0.233278i
\(209\) 63318.3 1.44956
\(210\) 0 0
\(211\) 29750.5i 0.668235i −0.942532 0.334117i \(-0.891562\pi\)
0.942532 0.334117i \(-0.108438\pi\)
\(212\) 75017.2 12440.1i 1.66913 0.276792i
\(213\) 0 0
\(214\) 55200.0 4545.88i 1.20535 0.0992637i
\(215\) 12708.1i 0.274917i
\(216\) 0 0
\(217\) 30553.5 0.648846
\(218\) 6364.06 + 77277.9i 0.133912 + 1.62608i
\(219\) 0 0
\(220\) −1580.76 9532.40i −0.0326604 0.196950i
\(221\) 14983.2 0.306774
\(222\) 0 0
\(223\) 52948.5i 1.06474i −0.846511 0.532371i \(-0.821301\pi\)
0.846511 0.532371i \(-0.178699\pi\)
\(224\) 48953.8 21325.6i 0.975642 0.425016i
\(225\) 0 0
\(226\) −4476.18 54353.6i −0.0876376 1.06417i
\(227\) 37635.8i 0.730380i −0.930933 0.365190i \(-0.881004\pi\)
0.930933 0.365190i \(-0.118996\pi\)
\(228\) 0 0
\(229\) −57238.4 −1.09148 −0.545741 0.837954i \(-0.683752\pi\)
−0.545741 + 0.837954i \(0.683752\pi\)
\(230\) −12344.5 + 1016.61i −0.233356 + 0.0192175i
\(231\) 0 0
\(232\) 11491.9 + 45671.8i 0.213509 + 0.848540i
\(233\) −36468.7 −0.671751 −0.335876 0.941906i \(-0.609032\pi\)
−0.335876 + 0.941906i \(0.609032\pi\)
\(234\) 0 0
\(235\) 5972.39i 0.108147i
\(236\) −5634.64 33978.3i −0.101168 0.610068i
\(237\) 0 0
\(238\) −25501.5 + 2100.12i −0.450207 + 0.0370759i
\(239\) 52357.1i 0.916600i −0.888798 0.458300i \(-0.848459\pi\)
0.888798 0.458300i \(-0.151541\pi\)
\(240\) 0 0
\(241\) −13511.1 −0.232625 −0.116313 0.993213i \(-0.537107\pi\)
−0.116313 + 0.993213i \(0.537107\pi\)
\(242\) −1071.51 13011.2i −0.0182964 0.222171i
\(243\) 0 0
\(244\) 1047.01 173.627i 0.0175862 0.00291633i
\(245\) −1801.41 −0.0300110
\(246\) 0 0
\(247\) 72503.6i 1.18841i
\(248\) 36365.8 9150.34i 0.591275 0.148776i
\(249\) 0 0
\(250\) 2263.88 + 27490.0i 0.0362221 + 0.439841i
\(251\) 111309.i 1.76678i 0.468635 + 0.883392i \(0.344746\pi\)
−0.468635 + 0.883392i \(0.655254\pi\)
\(252\) 0 0
\(253\) 58336.8 0.911385
\(254\) −62546.5 + 5150.88i −0.969472 + 0.0798388i
\(255\) 0 0
\(256\) 51879.6 40043.4i 0.791620 0.611013i
\(257\) −73913.1 −1.11906 −0.559532 0.828809i \(-0.689019\pi\)
−0.559532 + 0.828809i \(0.689019\pi\)
\(258\) 0 0
\(259\) 119376.i 1.77959i
\(260\) 10915.2 1810.08i 0.161468 0.0267763i
\(261\) 0 0
\(262\) −33374.5 + 2748.48i −0.486197 + 0.0400397i
\(263\) 7367.96i 0.106521i 0.998581 + 0.0532606i \(0.0169614\pi\)
−0.998581 + 0.0532606i \(0.983039\pi\)
\(264\) 0 0
\(265\) −26908.4 −0.383174
\(266\) −10162.5 123402.i −0.143627 1.74405i
\(267\) 0 0
\(268\) 10744.4 + 64791.3i 0.149593 + 0.902084i
\(269\) −38604.8 −0.533502 −0.266751 0.963765i \(-0.585950\pi\)
−0.266751 + 0.963765i \(0.585950\pi\)
\(270\) 0 0
\(271\) 12540.3i 0.170753i 0.996349 + 0.0853767i \(0.0272094\pi\)
−0.996349 + 0.0853767i \(0.972791\pi\)
\(272\) −29723.8 + 10137.0i −0.401759 + 0.137016i
\(273\) 0 0
\(274\) 9826.12 + 119317.i 0.130882 + 1.58929i
\(275\) 63245.7i 0.836306i
\(276\) 0 0
\(277\) −92104.7 −1.20039 −0.600195 0.799854i \(-0.704910\pi\)
−0.600195 + 0.799854i \(0.704910\pi\)
\(278\) −95064.9 + 7828.87i −1.23007 + 0.101300i
\(279\) 0 0
\(280\) −18324.1 + 4610.71i −0.233726 + 0.0588101i
\(281\) 22295.9 0.282366 0.141183 0.989983i \(-0.454909\pi\)
0.141183 + 0.989983i \(0.454909\pi\)
\(282\) 0 0
\(283\) 24997.7i 0.312123i 0.987747 + 0.156062i \(0.0498799\pi\)
−0.987747 + 0.156062i \(0.950120\pi\)
\(284\) 13170.5 + 79421.7i 0.163293 + 0.984697i
\(285\) 0 0
\(286\) −51934.6 + 4276.97i −0.634929 + 0.0522882i
\(287\) 149568.i 1.81582i
\(288\) 0 0
\(289\) −68471.9 −0.819816
\(290\) −1367.81 16609.1i −0.0162641 0.197493i
\(291\) 0 0
\(292\) −42699.5 + 7080.88i −0.500792 + 0.0830465i
\(293\) −23497.1 −0.273703 −0.136852 0.990592i \(-0.543698\pi\)
−0.136852 + 0.990592i \(0.543698\pi\)
\(294\) 0 0
\(295\) 12187.9i 0.140051i
\(296\) 35751.5 + 142086.i 0.408048 + 1.62169i
\(297\) 0 0
\(298\) −1731.44 21024.7i −0.0194974 0.236754i
\(299\) 66799.5i 0.747190i
\(300\) 0 0
\(301\) 117042. 1.29184
\(302\) −133245. + 10973.1i −1.46096 + 0.120314i
\(303\) 0 0
\(304\) −49052.8 143833.i −0.530783 1.55637i
\(305\) −375.559 −0.00403719
\(306\) 0 0
\(307\) 32060.0i 0.340163i 0.985430 + 0.170082i \(0.0544031\pi\)
−0.985430 + 0.170082i \(0.945597\pi\)
\(308\) 87793.9 14558.9i 0.925471 0.153471i
\(309\) 0 0
\(310\) −13224.9 + 1089.11i −0.137616 + 0.0113331i
\(311\) 70946.4i 0.733516i 0.930316 + 0.366758i \(0.119532\pi\)
−0.930316 + 0.366758i \(0.880468\pi\)
\(312\) 0 0
\(313\) 118519. 1.20976 0.604882 0.796315i \(-0.293220\pi\)
0.604882 + 0.796315i \(0.293220\pi\)
\(314\) −5581.58 67776.4i −0.0566106 0.687415i
\(315\) 0 0
\(316\) 3614.95 + 21799.1i 0.0362016 + 0.218305i
\(317\) −134781. −1.34125 −0.670626 0.741795i \(-0.733975\pi\)
−0.670626 + 0.741795i \(0.733975\pi\)
\(318\) 0 0
\(319\) 78490.3i 0.771320i
\(320\) −20429.1 + 10975.6i −0.199503 + 0.107184i
\(321\) 0 0
\(322\) −9362.99 113694.i −0.0903032 1.09654i
\(323\) 72822.8i 0.698011i
\(324\) 0 0
\(325\) 72420.4 0.685637
\(326\) −122959. + 10126.0i −1.15698 + 0.0952804i
\(327\) 0 0
\(328\) −44793.3 178020.i −0.416357 1.65471i
\(329\) 55006.1 0.508181
\(330\) 0 0
\(331\) 153740.i 1.40324i 0.712552 + 0.701620i \(0.247539\pi\)
−0.712552 + 0.701620i \(0.752461\pi\)
\(332\) −7874.49 47485.2i −0.0714408 0.430806i
\(333\) 0 0
\(334\) 62981.6 5186.72i 0.564574 0.0464943i
\(335\) 23240.4i 0.207087i
\(336\) 0 0
\(337\) −22943.7 −0.202024 −0.101012 0.994885i \(-0.532208\pi\)
−0.101012 + 0.994885i \(0.532208\pi\)
\(338\) 4479.17 + 54390.0i 0.0392071 + 0.476086i
\(339\) 0 0
\(340\) 10963.3 1818.05i 0.0948382 0.0157271i
\(341\) 62497.2 0.537467
\(342\) 0 0
\(343\) 108611.i 0.923175i
\(344\) 139307. 35052.4i 1.17722 0.296211i
\(345\) 0 0
\(346\) −15450.7 187616.i −0.129061 1.56718i
\(347\) 7229.43i 0.0600406i −0.999549 0.0300203i \(-0.990443\pi\)
0.999549 0.0300203i \(-0.00955720\pi\)
\(348\) 0 0
\(349\) 110565. 0.907753 0.453877 0.891065i \(-0.350041\pi\)
0.453877 + 0.891065i \(0.350041\pi\)
\(350\) −123260. + 10150.9i −1.00621 + 0.0828641i
\(351\) 0 0
\(352\) 100135. 43621.5i 0.808165 0.352059i
\(353\) −61603.4 −0.494374 −0.247187 0.968968i \(-0.579506\pi\)
−0.247187 + 0.968968i \(0.579506\pi\)
\(354\) 0 0
\(355\) 28488.3i 0.226053i
\(356\) −50294.8 + 8340.41i −0.396847 + 0.0658093i
\(357\) 0 0
\(358\) −10148.4 + 835.752i −0.0791831 + 0.00652095i
\(359\) 84462.7i 0.655354i −0.944790 0.327677i \(-0.893734\pi\)
0.944790 0.327677i \(-0.106266\pi\)
\(360\) 0 0
\(361\) −222069. −1.70401
\(362\) −1863.62 22629.7i −0.0142213 0.172688i
\(363\) 0 0
\(364\) 16670.9 + 100530.i 0.125822 + 0.758738i
\(365\) 15316.1 0.114965
\(366\) 0 0
\(367\) 185928.i 1.38042i −0.723607 0.690212i \(-0.757517\pi\)
0.723607 0.690212i \(-0.242483\pi\)
\(368\) −45193.7 132518.i −0.333720 0.978538i
\(369\) 0 0
\(370\) −4255.27 51671.2i −0.0310831 0.377438i
\(371\) 247828.i 1.80054i
\(372\) 0 0
\(373\) −85091.3 −0.611600 −0.305800 0.952096i \(-0.598924\pi\)
−0.305800 + 0.952096i \(0.598924\pi\)
\(374\) −52163.3 + 4295.80i −0.372926 + 0.0307115i
\(375\) 0 0
\(376\) 65470.0 16473.5i 0.463091 0.116523i
\(377\) −89876.5 −0.632359
\(378\) 0 0
\(379\) 146982.i 1.02326i 0.859206 + 0.511630i \(0.170958\pi\)
−0.859206 + 0.511630i \(0.829042\pi\)
\(380\) 8797.53 + 53051.4i 0.0609247 + 0.367392i
\(381\) 0 0
\(382\) 129475. 10662.7i 0.887280 0.0730701i
\(383\) 186199.i 1.26935i 0.772780 + 0.634674i \(0.218866\pi\)
−0.772780 + 0.634674i \(0.781134\pi\)
\(384\) 0 0
\(385\) −31491.3 −0.212456
\(386\) −258.515 3139.11i −0.00173504 0.0210684i
\(387\) 0 0
\(388\) 75987.2 12601.0i 0.504751 0.0837030i
\(389\) −256004. −1.69179 −0.845897 0.533347i \(-0.820934\pi\)
−0.845897 + 0.533347i \(0.820934\pi\)
\(390\) 0 0
\(391\) 67093.7i 0.438862i
\(392\) −4968.79 19747.2i −0.0323354 0.128509i
\(393\) 0 0
\(394\) −8150.35 98968.5i −0.0525029 0.637536i
\(395\) 7819.24i 0.0501153i
\(396\) 0 0
\(397\) −260735. −1.65432 −0.827159 0.561968i \(-0.810044\pi\)
−0.827159 + 0.561968i \(0.810044\pi\)
\(398\) 47871.9 3942.39i 0.302214 0.0248882i
\(399\) 0 0
\(400\) −143668. + 48996.6i −0.897928 + 0.306229i
\(401\) 53014.0 0.329687 0.164843 0.986320i \(-0.447288\pi\)
0.164843 + 0.986320i \(0.447288\pi\)
\(402\) 0 0
\(403\) 71563.4i 0.440637i
\(404\) 110821. 18377.6i 0.678986 0.112597i
\(405\) 0 0
\(406\) 152971. 12597.6i 0.928019 0.0764251i
\(407\) 244184.i 1.47411i
\(408\) 0 0
\(409\) 147396. 0.881126 0.440563 0.897722i \(-0.354779\pi\)
0.440563 + 0.897722i \(0.354779\pi\)
\(410\) 5331.46 + 64739.2i 0.0317160 + 0.385123i
\(411\) 0 0
\(412\) −5618.33 33879.9i −0.0330988 0.199594i
\(413\) −112251. −0.658099
\(414\) 0 0
\(415\) 17032.8i 0.0988983i
\(416\) 49949.5 + 114661.i 0.288632 + 0.662566i
\(417\) 0 0
\(418\) −20787.4 252419.i −0.118973 1.44467i
\(419\) 232592.i 1.32485i −0.749127 0.662426i \(-0.769527\pi\)
0.749127 0.662426i \(-0.230473\pi\)
\(420\) 0 0
\(421\) −69801.5 −0.393823 −0.196911 0.980421i \(-0.563091\pi\)
−0.196911 + 0.980421i \(0.563091\pi\)
\(422\) −118600. + 9767.08i −0.665980 + 0.0548454i
\(423\) 0 0
\(424\) −74220.8 294972.i −0.412852 1.64078i
\(425\) 72739.4 0.402709
\(426\) 0 0
\(427\) 3458.92i 0.0189708i
\(428\) −36244.4 218563.i −0.197858 1.19313i
\(429\) 0 0
\(430\) −50660.7 + 4172.06i −0.273990 + 0.0225639i
\(431\) 147873.i 0.796037i 0.917377 + 0.398019i \(0.130302\pi\)
−0.917377 + 0.398019i \(0.869698\pi\)
\(432\) 0 0
\(433\) 294850. 1.57262 0.786312 0.617830i \(-0.211988\pi\)
0.786312 + 0.617830i \(0.211988\pi\)
\(434\) −10030.7 121802.i −0.0532541 0.646657i
\(435\) 0 0
\(436\) 305979. 50740.7i 1.60960 0.266921i
\(437\) −324666. −1.70010
\(438\) 0 0
\(439\) 72131.8i 0.374281i 0.982333 + 0.187140i \(0.0599220\pi\)
−0.982333 + 0.187140i \(0.940078\pi\)
\(440\) −37482.0 + 9431.20i −0.193605 + 0.0487149i
\(441\) 0 0
\(442\) −4918.98 59730.5i −0.0251785 0.305739i
\(443\) 190907.i 0.972781i −0.873741 0.486391i \(-0.838313\pi\)
0.873741 0.486391i \(-0.161687\pi\)
\(444\) 0 0
\(445\) 18040.6 0.0911024
\(446\) −211080. + 17383.0i −1.06115 + 0.0873887i
\(447\) 0 0
\(448\) −101086. 188153.i −0.503658 0.937467i
\(449\) 192859. 0.956639 0.478319 0.878186i \(-0.341246\pi\)
0.478319 + 0.878186i \(0.341246\pi\)
\(450\) 0 0
\(451\) 305940.i 1.50412i
\(452\) −215211. + 35688.6i −1.05339 + 0.174684i
\(453\) 0 0
\(454\) −150035. + 12355.8i −0.727916 + 0.0599460i
\(455\) 36059.7i 0.174180i
\(456\) 0 0
\(457\) −5925.33 −0.0283713 −0.0141857 0.999899i \(-0.504516\pi\)
−0.0141857 + 0.999899i \(0.504516\pi\)
\(458\) 18791.4 + 228181.i 0.0895834 + 1.08780i
\(459\) 0 0
\(460\) 8105.41 + 48877.7i 0.0383053 + 0.230991i
\(461\) 126684. 0.596100 0.298050 0.954550i \(-0.403664\pi\)
0.298050 + 0.954550i \(0.403664\pi\)
\(462\) 0 0
\(463\) 235572.i 1.09891i 0.835524 + 0.549454i \(0.185164\pi\)
−0.835524 + 0.549454i \(0.814836\pi\)
\(464\) 178298. 60806.7i 0.828153 0.282433i
\(465\) 0 0
\(466\) 11972.7 + 145383.i 0.0551340 + 0.669485i
\(467\) 97776.2i 0.448332i 0.974551 + 0.224166i \(0.0719658\pi\)
−0.974551 + 0.224166i \(0.928034\pi\)
\(468\) 0 0
\(469\) 214045. 0.973105
\(470\) −23809.0 + 1960.74i −0.107782 + 0.00887613i
\(471\) 0 0
\(472\) −133605. + 33617.6i −0.599706 + 0.150898i
\(473\) 239409. 1.07009
\(474\) 0 0
\(475\) 351986.i 1.56005i
\(476\) 16744.3 + 100972.i 0.0739015 + 0.445645i
\(477\) 0 0
\(478\) −208722. + 17188.8i −0.913508 + 0.0752300i
\(479\) 403178.i 1.75722i 0.477543 + 0.878608i \(0.341527\pi\)
−0.477543 + 0.878608i \(0.658473\pi\)
\(480\) 0 0
\(481\) −279607. −1.20853
\(482\) 4435.70 + 53862.1i 0.0190927 + 0.231841i
\(483\) 0 0
\(484\) −51517.6 + 8543.18i −0.219920 + 0.0364694i
\(485\) −27256.3 −0.115873
\(486\) 0 0
\(487\) 195207.i 0.823071i 0.911394 + 0.411536i \(0.135007\pi\)
−0.911394 + 0.411536i \(0.864993\pi\)
\(488\) −1035.90 4116.92i −0.00434988 0.0172875i
\(489\) 0 0
\(490\) 591.403 + 7181.33i 0.00246315 + 0.0299097i
\(491\) 76137.6i 0.315818i −0.987454 0.157909i \(-0.949525\pi\)
0.987454 0.157909i \(-0.0504752\pi\)
\(492\) 0 0
\(493\) −90272.3 −0.371416
\(494\) 289036. 23802.9i 1.18440 0.0975386i
\(495\) 0 0
\(496\) −48416.8 141968.i −0.196803 0.577069i
\(497\) 262379. 1.06222
\(498\) 0 0
\(499\) 14570.3i 0.0585152i −0.999572 0.0292576i \(-0.990686\pi\)
0.999572 0.0292576i \(-0.00931431\pi\)
\(500\) 108846. 18050.0i 0.435384 0.0721999i
\(501\) 0 0
\(502\) 443735. 36542.8i 1.76082 0.145009i
\(503\) 280154.i 1.10729i −0.832753 0.553645i \(-0.813236\pi\)
0.832753 0.553645i \(-0.186764\pi\)
\(504\) 0 0
\(505\) −39751.2 −0.155872
\(506\) −19152.0 232560.i −0.0748019 0.908310i
\(507\) 0 0
\(508\) 41068.0 + 247651.i 0.159139 + 0.959649i
\(509\) 203009. 0.783573 0.391787 0.920056i \(-0.371857\pi\)
0.391787 + 0.920056i \(0.371857\pi\)
\(510\) 0 0
\(511\) 141063.i 0.540219i
\(512\) −176665. 193672.i −0.673924 0.738801i
\(513\) 0 0
\(514\) 24265.7 + 294655.i 0.0918472 + 1.11529i
\(515\) 12152.6i 0.0458200i
\(516\) 0 0
\(517\) 112515. 0.420948
\(518\) 475895. 39191.3i 1.77358 0.146060i
\(519\) 0 0
\(520\) −10799.3 42919.3i −0.0399384 0.158725i
\(521\) −30822.1 −0.113550 −0.0567749 0.998387i \(-0.518082\pi\)
−0.0567749 + 0.998387i \(0.518082\pi\)
\(522\) 0 0
\(523\) 94412.3i 0.345164i 0.984995 + 0.172582i \(0.0552109\pi\)
−0.984995 + 0.172582i \(0.944789\pi\)
\(524\) 21913.7 + 132145.i 0.0798092 + 0.481270i
\(525\) 0 0
\(526\) 29372.4 2418.90i 0.106162 0.00874273i
\(527\) 71878.5i 0.258808i
\(528\) 0 0
\(529\) −19282.9 −0.0689066
\(530\) 8834.03 + 107270.i 0.0314490 + 0.381881i
\(531\) 0 0
\(532\) −488606. + 81025.8i −1.72638 + 0.286286i
\(533\) 350322. 1.23314
\(534\) 0 0
\(535\) 78397.6i 0.273902i
\(536\) 254763. 64103.5i 0.886763 0.223127i
\(537\) 0 0
\(538\) 12673.9 + 153898.i 0.0437872 + 0.531702i
\(539\) 33937.0i 0.116814i
\(540\) 0 0
\(541\) 166561. 0.569087 0.284544 0.958663i \(-0.408158\pi\)
0.284544 + 0.958663i \(0.408158\pi\)
\(542\) 49992.0 4116.98i 0.170177 0.0140146i
\(543\) 0 0
\(544\) 50169.4 + 115166.i 0.169528 + 0.389158i
\(545\) −109754. −0.369510
\(546\) 0 0
\(547\) 295887.i 0.988897i −0.869207 0.494448i \(-0.835370\pi\)
0.869207 0.494448i \(-0.164630\pi\)
\(548\) 472433. 78343.7i 1.57318 0.260881i
\(549\) 0 0
\(550\) −252129. + 20763.6i −0.833485 + 0.0686399i
\(551\) 436828.i 1.43882i
\(552\) 0 0
\(553\) 72015.6 0.235492
\(554\) 30238.0 + 367176.i 0.0985220 + 1.19634i
\(555\) 0 0
\(556\) 62419.6 + 376406.i 0.201916 + 1.21761i
\(557\) −30600.2 −0.0986312 −0.0493156 0.998783i \(-0.515704\pi\)
−0.0493156 + 0.998783i \(0.515704\pi\)
\(558\) 0 0
\(559\) 274139.i 0.877298i
\(560\) 24396.4 + 71535.5i 0.0777948 + 0.228111i
\(561\) 0 0
\(562\) −7319.76 88882.9i −0.0231752 0.281414i
\(563\) 242796.i 0.765992i 0.923750 + 0.382996i \(0.125108\pi\)
−0.923750 + 0.382996i \(0.874892\pi\)
\(564\) 0 0
\(565\) 77195.5 0.241822
\(566\) 99653.3 8206.73i 0.311070 0.0256175i
\(567\) 0 0
\(568\) 312291. 78578.6i 0.967973 0.243561i
\(569\) 296918. 0.917090 0.458545 0.888671i \(-0.348371\pi\)
0.458545 + 0.888671i \(0.348371\pi\)
\(570\) 0 0
\(571\) 263786.i 0.809058i −0.914525 0.404529i \(-0.867435\pi\)
0.914525 0.404529i \(-0.132565\pi\)
\(572\) 34100.3 + 205634.i 0.104224 + 0.628495i
\(573\) 0 0
\(574\) −596252. + 49103.0i −1.80970 + 0.149034i
\(575\) 324294.i 0.980852i
\(576\) 0 0
\(577\) 350367. 1.05238 0.526188 0.850368i \(-0.323621\pi\)
0.526188 + 0.850368i \(0.323621\pi\)
\(578\) 22479.3 + 272963.i 0.0672864 + 0.817050i
\(579\) 0 0
\(580\) −65763.3 + 10905.6i −0.195491 + 0.0324184i
\(581\) −156873. −0.464724
\(582\) 0 0
\(583\) 506931.i 1.49146i
\(584\) 42246.2 + 167897.i 0.123869 + 0.492286i
\(585\) 0 0
\(586\) 7714.12 + 93671.5i 0.0224642 + 0.272780i
\(587\) 6888.66i 0.0199921i −0.999950 0.00999606i \(-0.996818\pi\)
0.999950 0.00999606i \(-0.00318190\pi\)
\(588\) 0 0
\(589\) −347820. −1.00259
\(590\) 48587.1 4001.29i 0.139578 0.0114947i
\(591\) 0 0
\(592\) 554688. 189170.i 1.58272 0.539771i
\(593\) 544416. 1.54818 0.774090 0.633076i \(-0.218208\pi\)
0.774090 + 0.633076i \(0.218208\pi\)
\(594\) 0 0
\(595\) 36218.4i 0.102305i
\(596\) −83246.5 + 13804.8i −0.234355 + 0.0388631i
\(597\) 0 0
\(598\) 266296. 21930.3i 0.744669 0.0613256i
\(599\) 141764.i 0.395104i 0.980292 + 0.197552i \(0.0632992\pi\)
−0.980292 + 0.197552i \(0.936701\pi\)
\(600\) 0 0
\(601\) −530760. −1.46943 −0.734715 0.678376i \(-0.762684\pi\)
−0.734715 + 0.678376i \(0.762684\pi\)
\(602\) −38424.9 466588.i −0.106028 1.28748i
\(603\) 0 0
\(604\) 87488.8 + 527580.i 0.239816 + 1.44615i
\(605\) 18479.2 0.0504861
\(606\) 0 0
\(607\) 40663.6i 0.110364i −0.998476 0.0551821i \(-0.982426\pi\)
0.998476 0.0551821i \(-0.0175739\pi\)
\(608\) −557288. + 242770.i −1.50755 + 0.656731i
\(609\) 0 0
\(610\) 123.296 + 1497.17i 0.000331352 + 0.00402357i
\(611\) 128837.i 0.345110i
\(612\) 0 0
\(613\) −498556. −1.32676 −0.663382 0.748281i \(-0.730879\pi\)
−0.663382 + 0.748281i \(0.730879\pi\)
\(614\) 127807. 10525.3i 0.339015 0.0279189i
\(615\) 0 0
\(616\) −86861.9 345211.i −0.228912 0.909753i
\(617\) −90060.9 −0.236573 −0.118287 0.992979i \(-0.537740\pi\)
−0.118287 + 0.992979i \(0.537740\pi\)
\(618\) 0 0
\(619\) 172488.i 0.450171i −0.974339 0.225086i \(-0.927734\pi\)
0.974339 0.225086i \(-0.0722662\pi\)
\(620\) 8683.45 + 52363.5i 0.0225896 + 0.136221i
\(621\) 0 0
\(622\) 282828. 23291.7i 0.731042 0.0602034i
\(623\) 166154.i 0.428091i
\(624\) 0 0
\(625\) 331547. 0.848761
\(626\) −38909.9 472478.i −0.0992914 1.20568i
\(627\) 0 0
\(628\) −268358. + 44502.0i −0.680449 + 0.112839i
\(629\) −280838. −0.709831
\(630\) 0 0
\(631\) 210621.i 0.528985i −0.964388 0.264492i \(-0.914796\pi\)
0.964388 0.264492i \(-0.0852044\pi\)
\(632\) 85715.2 21567.6i 0.214597 0.0539968i
\(633\) 0 0
\(634\) 44248.7 + 537306.i 0.110083 + 1.33673i
\(635\) 88831.4i 0.220302i
\(636\) 0 0
\(637\) 38860.1 0.0957691
\(638\) 312902. 25768.4i 0.768718 0.0633061i
\(639\) 0 0
\(640\) 50461.3 + 77837.5i 0.123196 + 0.190033i
\(641\) −464524. −1.13056 −0.565278 0.824901i \(-0.691231\pi\)
−0.565278 + 0.824901i \(0.691231\pi\)
\(642\) 0 0
\(643\) 417977.i 1.01095i −0.862841 0.505476i \(-0.831317\pi\)
0.862841 0.505476i \(-0.168683\pi\)
\(644\) −450166. + 74651.2i −1.08543 + 0.179997i
\(645\) 0 0
\(646\) 290309. 23907.7i 0.695656 0.0572893i
\(647\) 825841.i 1.97282i −0.164299 0.986411i \(-0.552536\pi\)
0.164299 0.986411i \(-0.447464\pi\)
\(648\) 0 0
\(649\) −229610. −0.545131
\(650\) −23775.6 288704.i −0.0562737 0.683324i
\(651\) 0 0
\(652\) 80734.8 + 486852.i 0.189918 + 1.14525i
\(653\) 328545. 0.770493 0.385247 0.922814i \(-0.374116\pi\)
0.385247 + 0.922814i \(0.374116\pi\)
\(654\) 0 0
\(655\) 47400.0i 0.110483i
\(656\) −694972. + 237013.i −1.61495 + 0.550762i
\(657\) 0 0
\(658\) −18058.5 219282.i −0.0417090 0.506467i
\(659\) 167361.i 0.385374i 0.981260 + 0.192687i \(0.0617202\pi\)
−0.981260 + 0.192687i \(0.938280\pi\)
\(660\) 0 0
\(661\) −305233. −0.698599 −0.349300 0.937011i \(-0.613580\pi\)
−0.349300 + 0.937011i \(0.613580\pi\)
\(662\) 612886. 50473.0i 1.39851 0.115171i
\(663\) 0 0
\(664\) −186715. + 46981.1i −0.423489 + 0.106558i
\(665\) 175261. 0.396317
\(666\) 0 0
\(667\) 402461.i 0.904633i
\(668\) −41353.7 249374.i −0.0926749 0.558853i
\(669\) 0 0
\(670\) −92647.9 + 7629.82i −0.206389 + 0.0169967i
\(671\) 7075.22i 0.0157143i
\(672\) 0 0
\(673\) 806065. 1.77967 0.889836 0.456281i \(-0.150819\pi\)
0.889836 + 0.456281i \(0.150819\pi\)
\(674\) 7532.41 + 91465.0i 0.0165811 + 0.201342i
\(675\) 0 0
\(676\) 215355. 35712.5i 0.471262 0.0781496i
\(677\) −366235. −0.799065 −0.399533 0.916719i \(-0.630828\pi\)
−0.399533 + 0.916719i \(0.630828\pi\)
\(678\) 0 0
\(679\) 251032.i 0.544490i
\(680\) −10846.9 43108.3i −0.0234578 0.0932274i
\(681\) 0 0
\(682\) −20517.8 249145.i −0.0441126 0.535654i
\(683\) 398332.i 0.853894i 0.904277 + 0.426947i \(0.140411\pi\)
−0.904277 + 0.426947i \(0.859589\pi\)
\(684\) 0 0
\(685\) −169460. −0.361148
\(686\) 432977. 35656.9i 0.920060 0.0757696i
\(687\) 0 0
\(688\) −185471. 543840.i −0.391831 1.14893i
\(689\) 580469. 1.22276
\(690\) 0 0
\(691\) 351812.i 0.736809i 0.929666 + 0.368405i \(0.120096\pi\)
−0.929666 + 0.368405i \(0.879904\pi\)
\(692\) −742860. + 123189.i −1.55130 + 0.257252i
\(693\) 0 0
\(694\) −28820.2 + 2373.42i −0.0598381 + 0.00492784i
\(695\) 135016.i 0.279521i
\(696\) 0 0
\(697\) 351864. 0.724285
\(698\) −36298.6 440769.i −0.0745039 0.904691i
\(699\) 0 0
\(700\) 80932.9 + 488046.i 0.165169 + 0.996012i
\(701\) −620142. −1.26199 −0.630994 0.775788i \(-0.717353\pi\)
−0.630994 + 0.775788i \(0.717353\pi\)
\(702\) 0 0
\(703\) 1.35898e6i 2.74980i
\(704\) −206772. 384867.i −0.417201 0.776543i
\(705\) 0 0
\(706\) 20224.4 + 245582.i 0.0405758 + 0.492706i
\(707\) 366111.i 0.732443i
\(708\) 0 0
\(709\) 314897. 0.626434 0.313217 0.949682i \(-0.398593\pi\)
0.313217 + 0.949682i \(0.398593\pi\)
\(710\) −113569. + 9352.70i −0.225290 + 0.0185533i
\(711\) 0 0
\(712\) 49760.9 + 197762.i 0.0981585 + 0.390107i
\(713\) −320456. −0.630362
\(714\) 0 0
\(715\) 73760.0i 0.144281i
\(716\) 6663.45 + 40182.3i 0.0129979 + 0.0783807i
\(717\) 0 0
\(718\) −336711. + 27729.1i −0.653143 + 0.0537882i
\(719\) 361941.i 0.700132i 0.936725 + 0.350066i \(0.113841\pi\)
−0.936725 + 0.350066i \(0.886159\pi\)
\(720\) 0 0
\(721\) −111926. −0.215308
\(722\) 72905.2 + 885278.i 0.139857 + 1.69826i
\(723\) 0 0
\(724\) −89601.6 + 14858.7i −0.170938 + 0.0283467i
\(725\) −436327. −0.830111
\(726\) 0 0
\(727\) 308930.i 0.584510i −0.956340 0.292255i \(-0.905594\pi\)
0.956340 0.292255i \(-0.0944056\pi\)
\(728\) 395289. 99462.6i 0.745852 0.187671i
\(729\) 0 0
\(730\) −5028.29 61057.9i −0.00943572 0.114577i
\(731\) 275346.i 0.515281i
\(732\) 0 0
\(733\) 882544. 1.64259 0.821293 0.570506i \(-0.193253\pi\)
0.821293 + 0.570506i \(0.193253\pi\)
\(734\) −741202. + 61040.2i −1.37577 + 0.113298i
\(735\) 0 0
\(736\) −513445. + 223670.i −0.947847 + 0.412908i
\(737\) 437829. 0.806065
\(738\) 0 0
\(739\) 396910.i 0.726781i −0.931637 0.363390i \(-0.881619\pi\)
0.931637 0.363390i \(-0.118381\pi\)
\(740\) −204590. + 33927.3i −0.373613 + 0.0619564i
\(741\) 0 0
\(742\) −987966. + 81361.8i −1.79446 + 0.147779i
\(743\) 959979.i 1.73894i −0.493988 0.869469i \(-0.664461\pi\)
0.493988 0.869469i \(-0.335539\pi\)
\(744\) 0 0
\(745\) 29860.2 0.0537998
\(746\) 27935.5 + 339217.i 0.0501971 + 0.609536i
\(747\) 0 0
\(748\) 34250.5 + 206539.i 0.0612158 + 0.369147i
\(749\) −722046. −1.28707
\(750\) 0 0
\(751\) 660734.i 1.17151i −0.810488 0.585756i \(-0.800798\pi\)
0.810488 0.585756i \(-0.199202\pi\)
\(752\) −87165.6 255588.i −0.154138 0.451965i
\(753\) 0 0
\(754\) 29506.5 + 358293.i 0.0519009 + 0.630225i
\(755\) 189241.i 0.331987i
\(756\) 0 0
\(757\) 326842. 0.570356 0.285178 0.958475i \(-0.407947\pi\)
0.285178 + 0.958475i \(0.407947\pi\)
\(758\) 585945. 48254.2i 1.01981 0.0839841i
\(759\) 0 0
\(760\) 208601. 52488.2i 0.361152 0.0908729i
\(761\) 329626. 0.569183 0.284591 0.958649i \(-0.408142\pi\)
0.284591 + 0.958649i \(0.408142\pi\)
\(762\) 0 0
\(763\) 1.01084e6i 1.73633i
\(764\) −85013.7 512654.i −0.145647 0.878290i
\(765\) 0 0
\(766\) 742285. 61129.3i 1.26507 0.104182i
\(767\) 262918.i 0.446920i
\(768\) 0 0
\(769\) −599476. −1.01372 −0.506862 0.862027i \(-0.669194\pi\)
−0.506862 + 0.862027i \(0.669194\pi\)
\(770\) 10338.6 + 125540.i 0.0174374 + 0.211740i
\(771\) 0 0
\(772\) −12429.2 + 2061.14i −0.0208549 + 0.00345838i
\(773\) −58555.0 −0.0979952 −0.0489976 0.998799i \(-0.515603\pi\)
−0.0489976 + 0.998799i \(0.515603\pi\)
\(774\) 0 0
\(775\) 347422.i 0.578433i
\(776\) −75180.5 298786.i −0.124848 0.496178i
\(777\) 0 0
\(778\) 84046.1 + 1.02056e6i 0.138854 + 1.68609i
\(779\) 1.70267e6i 2.80580i
\(780\) 0 0
\(781\) 536695. 0.879884
\(782\) 267469. 22026.9i 0.437381 0.0360196i
\(783\) 0 0
\(784\) −77091.2 + 26291.1i −0.125422 + 0.0427737i
\(785\) 96259.1 0.156208
\(786\) 0 0
\(787\) 638842.i 1.03144i 0.856757 + 0.515720i \(0.172476\pi\)
−0.856757 + 0.515720i