Properties

Label 324.5.d.e.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.e.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 \(-0.536122\pi\)
−0.113236 + 0.993568i \(0.536122\pi\)
\(6\) 0 0
\(7\) 52.1456i 1.06420i −0.846683 0.532098i \(-0.821404\pi\)
0.846683 0.532098i \(-0.178596\pi\)
\(8\) −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 \(-0.431924\pi\)
0.212240 + 0.977217i \(0.431924\pi\)
\(18\) 0 0
\(19\) 593.624i 1.64439i 0.569207 + 0.822194i \(0.307250\pi\)
−0.569207 + 0.822194i \(0.692750\pi\)
\(20\) 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 \(-0.644134\pi\)
−0.437495 + 0.899221i \(0.644134\pi\)
\(30\) 0 0
\(31\) 585.927i 0.609705i 0.952400 + 0.304853i \(0.0986072\pi\)
−0.952400 + 0.304853i \(0.901393\pi\)
\(32\) 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 \(-0.174694\pi\)
0.853142 + 0.521678i \(0.174694\pi\)
\(42\) 0 0
\(43\) 2244.52i 1.21391i 0.794736 + 0.606955i \(0.207609\pi\)
−0.794736 + 0.606955i \(0.792391\pi\)
\(44\) 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 \(-0.179028\pi\)
0.845960 + 0.533246i \(0.179028\pi\)
\(54\) 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 \(0.151148\pi\)
−0.889363 + 0.457202i \(0.848852\pi\)
\(68\) −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 \(0.0352911\pi\)
−0.993860 + 0.110643i \(0.964709\pi\)
\(80\) −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 \(-0.564462\pi\)
−0.201133 + 0.979564i \(0.564462\pi\)
\(90\) 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 \(-0.388174\pi\)
0.344130 + 0.938922i \(0.388174\pi\)
\(102\) 0 0
\(103\) 2146.41i 0.202320i −0.994870 0.101160i \(-0.967745\pi\)
0.994870 0.101160i \(-0.0322554\pi\)
\(104\) 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 \(-0.679269\pi\)
−0.533887 + 0.845556i \(0.679269\pi\)
\(114\) 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 \(0.161682\pi\)
−0.873749 + 0.486377i \(0.838318\pi\)
\(128\) −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 \(-0.206244\pi\)
0.797333 + 0.603540i \(0.206244\pi\)
\(138\) 0 0
\(139\) 23846.7i 1.23424i 0.786871 + 0.617118i \(0.211700\pi\)
−0.786871 + 0.617118i \(0.788300\pi\)
\(140\) 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 \(-0.537898\pi\)
−0.118778 + 0.992921i \(0.537898\pi\)
\(150\) 0 0
\(151\) 33424.0i 1.46590i 0.680281 + 0.732951i \(0.261858\pi\)
−0.680281 + 0.732951i \(0.738142\pi\)
\(152\) −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 \(0.197122\pi\)
−0.814298 + 0.580447i \(0.802878\pi\)
\(164\) −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 \(-0.787975\pi\)
−0.786241 + 0.617921i \(0.787975\pi\)
\(174\) 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 \(-0.603632\pi\)
−0.319847 + 0.947469i \(0.603632\pi\)
\(198\) 0 0
\(199\) 12008.5i 0.303237i −0.988439 0.151619i \(-0.951551\pi\)
0.988439 0.151619i \(-0.0484485\pi\)
\(200\) 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 \(0.108438\pi\)
−0.942532 + 0.334117i \(0.891562\pi\)
\(212\) −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 \(0.178699\pi\)
−0.846511 + 0.532371i \(0.821301\pi\)
\(224\) −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 \(-0.390968\pi\)
0.335876 + 0.941906i \(0.390968\pi\)
\(234\) 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 \(-0.310981\pi\)
0.559532 + 0.828809i \(0.310981\pi\)
\(258\) 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 \(-0.414050\pi\)
0.266751 + 0.963765i \(0.414050\pi\)
\(270\) 0 0
\(271\) 12540.3i 0.170753i −0.996349 0.0853767i \(-0.972791\pi\)
0.996349 0.0853767i \(-0.0272094\pi\)
\(272\) 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 \(-0.545091\pi\)
−0.141183 + 0.989983i \(0.545091\pi\)
\(282\) 0 0
\(283\) 24997.7i 0.312123i −0.987747 0.156062i \(-0.950120\pi\)
0.987747 0.156062i \(-0.0498799\pi\)
\(284\) −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 \(-0.456302\pi\)
0.136852 + 0.990592i \(0.456302\pi\)
\(294\) 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 \(-0.945597\pi\)
0.985430 0.170082i \(-0.0544031\pi\)
\(308\) −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 \(-0.266025\pi\)
0.670626 + 0.741795i \(0.266025\pi\)
\(318\) 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 \(-0.752461\pi\)
0.712552 0.701620i \(-0.247539\pi\)
\(332\) 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 \(-0.420494\pi\)
0.247187 + 0.968968i \(0.420494\pi\)
\(354\) 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 \(0.242483\pi\)
−0.723607 + 0.690212i \(0.757517\pi\)
\(368\) 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 \(-0.829042\pi\)
0.859206 0.511630i \(-0.170958\pi\)
\(380\) −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 \(-0.179066\pi\)
0.845897 + 0.533347i \(0.179066\pi\)
\(390\) 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 \(-0.552712\pi\)
−0.164843 + 0.986320i \(0.552712\pi\)
\(402\) 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 \(-0.940078\pi\)
0.982333 0.187140i \(-0.0599220\pi\)
\(440\) 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 \(-0.658754\pi\)
−0.478319 + 0.878186i \(0.658754\pi\)
\(450\) 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 \(-0.596336\pi\)
−0.298050 + 0.954550i \(0.596336\pi\)
\(462\) 0 0
\(463\) 235572.i 1.09891i −0.835524 0.549454i \(-0.814836\pi\)
0.835524 0.549454i \(-0.185164\pi\)
\(464\) −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 \(-0.864993\pi\)
0.911394 0.411536i \(-0.135007\pi\)
\(488\) 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 \(0.00931431\pi\)
−0.999572 + 0.0292576i \(0.990686\pi\)
\(500\) −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 \(-0.628143\pi\)
−0.391787 + 0.920056i \(0.628143\pi\)
\(510\) 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 \(-0.481918\pi\)
0.0567749 + 0.998387i \(0.481918\pi\)
\(522\) 0 0
\(523\) 94412.3i 0.345164i −0.984995 0.172582i \(-0.944789\pi\)
0.984995 0.172582i \(-0.0552109\pi\)
\(524\) −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 \(0.164630\pi\)
−0.869207 + 0.494448i \(0.835370\pi\)
\(548\) −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 \(-0.484296\pi\)
0.0493156 + 0.998783i \(0.484296\pi\)
\(558\) 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 \(-0.651629\pi\)
−0.458545 + 0.888671i \(0.651629\pi\)
\(570\) 0 0
\(571\) 263786.i 0.809058i 0.914525 + 0.404529i \(0.132565\pi\)
−0.914525 + 0.404529i \(0.867435\pi\)
\(572\) −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 \(-0.781792\pi\)
−0.774090 + 0.633076i \(0.781792\pi\)
\(594\) 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 \(0.0175739\pi\)
−0.998476 + 0.0551821i \(0.982426\pi\)
\(608\) 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 \(-0.462260\pi\)
0.118287 + 0.992979i \(0.462260\pi\)
\(618\) 0 0
\(619\) 172488.i 0.450171i 0.974339 + 0.225086i \(0.0722662\pi\)
−0.974339 + 0.225086i \(0.927734\pi\)
\(620\) −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 \(0.0852044\pi\)
−0.964388 + 0.264492i \(0.914796\pi\)
\(632\) −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 \(-0.308769\pi\)
0.565278 + 0.824901i \(0.308769\pi\)
\(642\) 0 0
\(643\) 417977.i 1.01095i 0.862841 + 0.505476i \(0.168683\pi\)
−0.862841 + 0.505476i \(0.831317\pi\)
\(644\) 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 \(-0.625884\pi\)
−0.385247 + 0.922814i \(0.625884\pi\)
\(654\) 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 \(-0.369172\pi\)
0.399533 + 0.916719i \(0.369172\pi\)
\(678\) 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 \(-0.879904\pi\)
0.929666 0.368405i \(-0.120096\pi\)
\(692\) 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 \(-0.282647\pi\)
0.630994 + 0.775788i \(0.282647\pi\)
\(702\) 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 \(0.0944056\pi\)
−0.956340 + 0.292255i \(0.905594\pi\)
\(728\) −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 \(0.118381\pi\)
−0.931637 + 0.363390i \(0.881619\pi\)
\(740\) 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 \(0.199202\pi\)
−0.810488 + 0.585756i \(0.800798\pi\)
\(752\) 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 \(-0.591858\pi\)
−0.284591 + 0.958649i \(0.591858\pi\)
\(762\) 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 \(-0.484397\pi\)
0.0489976 + 0.998799i \(0.484397\pi\)
\(774\) 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
\(787\)