Properties

Label 33.6.d.b.32.1
Level $33$
Weight $6$
Character 33.32
Analytic conductor $5.293$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.29266605383\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} - 195 x^{14} - 642 x^{13} + 89670 x^{12} + 53946 x^{11} + 91115757 x^{10} - 2121785838 x^{9} + 37710373995 x^{8} - 835758339660 x^{7} + 12972600642204 x^{6} - 129499271268696 x^{5} + 2168293345395660 x^{4} - 17336133272224368 x^{3} + 169639595563975056 x^{2} - 1075523563426213440 x + 9241272870780234240\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{11}\cdot 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 32.1
Root \(-2.15316 + 11.0840i\) of defining polynomial
Character \(\chi\) \(=\) 33.32
Dual form 33.6.d.b.32.2

$q$-expansion

\(f(q)\) \(=\) \(q-10.1143 q^{2} +(-10.9611 - 11.0840i) q^{3} +70.2982 q^{4} -88.5196i q^{5} +(110.863 + 112.106i) q^{6} -126.220i q^{7} -387.358 q^{8} +(-2.70883 + 242.985i) q^{9} +O(q^{10})\) \(q-10.1143 q^{2} +(-10.9611 - 11.0840i) q^{3} +70.2982 q^{4} -88.5196i q^{5} +(110.863 + 112.106i) q^{6} -126.220i q^{7} -387.358 q^{8} +(-2.70883 + 242.985i) q^{9} +895.310i q^{10} +(-398.959 + 43.3939i) q^{11} +(-770.545 - 779.183i) q^{12} -523.100i q^{13} +1276.62i q^{14} +(-981.149 + 970.272i) q^{15} +1668.30 q^{16} +1039.45 q^{17} +(27.3978 - 2457.61i) q^{18} +842.227i q^{19} -6222.77i q^{20} +(-1399.02 + 1383.51i) q^{21} +(4035.17 - 438.897i) q^{22} +2472.99i q^{23} +(4245.87 + 4293.47i) q^{24} -4710.72 q^{25} +5290.77i q^{26} +(2722.93 - 2633.36i) q^{27} -8873.04i q^{28} -3569.99 q^{29} +(9923.59 - 9813.58i) q^{30} -215.057 q^{31} -4478.13 q^{32} +(4854.00 + 3946.40i) q^{33} -10513.3 q^{34} -11172.9 q^{35} +(-190.426 + 17081.4i) q^{36} -3626.51 q^{37} -8518.50i q^{38} +(-5798.03 + 5733.75i) q^{39} +34288.8i q^{40} +8845.46 q^{41} +(14150.0 - 13993.2i) q^{42} +5262.04i q^{43} +(-28046.1 + 3050.51i) q^{44} +(21508.9 + 239.785i) q^{45} -25012.4i q^{46} -9059.89i q^{47} +(-18286.4 - 18491.4i) q^{48} +875.528 q^{49} +47645.5 q^{50} +(-11393.5 - 11521.2i) q^{51} -36773.0i q^{52} -897.191i q^{53} +(-27540.4 + 26634.4i) q^{54} +(3841.21 + 35315.7i) q^{55} +48892.3i q^{56} +(9335.22 - 9231.73i) q^{57} +36107.8 q^{58} -36226.0i q^{59} +(-68973.0 + 68208.4i) q^{60} -15319.3i q^{61} +2175.14 q^{62} +(30669.5 + 341.908i) q^{63} -8092.58 q^{64} -46304.6 q^{65} +(-49094.6 - 39914.9i) q^{66} -53380.7 q^{67} +73071.6 q^{68} +(27410.5 - 27106.6i) q^{69} +113006. q^{70} +33693.5i q^{71} +(1049.29 - 94122.2i) q^{72} -76140.5i q^{73} +36679.4 q^{74} +(51634.7 + 52213.5i) q^{75} +59207.1i q^{76} +(5477.18 + 50356.5i) q^{77} +(58642.7 - 57992.6i) q^{78} +106783. i q^{79} -147677. i q^{80} +(-59034.3 - 1316.41i) q^{81} -89465.2 q^{82} -20385.5 q^{83} +(-98348.5 + 97258.2i) q^{84} -92011.8i q^{85} -53221.6i q^{86} +(39131.0 + 39569.7i) q^{87} +(154540. - 16809.0i) q^{88} +11850.9i q^{89} +(-217547. - 2425.24i) q^{90} -66025.7 q^{91} +173847. i q^{92} +(2357.26 + 2383.68i) q^{93} +91634.1i q^{94} +74553.6 q^{95} +(49085.2 + 49635.4i) q^{96} -67716.0 q^{97} -8855.32 q^{98} +(-9463.35 - 97058.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 54q^{3} + 316q^{4} - 222q^{9} + O(q^{10}) \) \( 16q - 54q^{3} + 316q^{4} - 222q^{9} - 552q^{12} - 1674q^{15} + 1684q^{16} + 7932q^{22} - 1356q^{25} - 3240q^{27} - 11980q^{31} - 5106q^{33} - 34032q^{34} + 14016q^{36} + 9356q^{37} + 45912q^{42} + 77430q^{45} - 78012q^{48} - 1136q^{49} + 117308q^{55} + 31848q^{58} - 220548q^{60} + 5860q^{64} - 164796q^{66} - 364132q^{67} + 113790q^{69} + 231144q^{70} + 320364q^{75} + 296088q^{78} - 251334q^{81} + 4824q^{82} + 586836q^{88} - 209184q^{91} - 521046q^{93} + 119852q^{97} - 243894q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.1143 −1.78797 −0.893983 0.448102i \(-0.852100\pi\)
−0.893983 + 0.448102i \(0.852100\pi\)
\(3\) −10.9611 11.0840i −0.703155 0.711037i
\(4\) 70.2982 2.19682
\(5\) 88.5196i 1.58349i −0.610854 0.791744i \(-0.709174\pi\)
0.610854 0.791744i \(-0.290826\pi\)
\(6\) 110.863 + 112.106i 1.25722 + 1.27131i
\(7\) 126.220i 0.973605i −0.873512 0.486803i \(-0.838163\pi\)
0.873512 0.486803i \(-0.161837\pi\)
\(8\) −387.358 −2.13987
\(9\) −2.70883 + 242.985i −0.0111475 + 0.999938i
\(10\) 895.310i 2.83122i
\(11\) −398.959 + 43.3939i −0.994137 + 0.108130i
\(12\) −770.545 779.183i −1.54470 1.56202i
\(13\) 523.100i 0.858473i −0.903192 0.429236i \(-0.858783\pi\)
0.903192 0.429236i \(-0.141217\pi\)
\(14\) 1276.62i 1.74077i
\(15\) −981.149 + 970.272i −1.12592 + 1.11344i
\(16\) 1668.30 1.62920
\(17\) 1039.45 0.872332 0.436166 0.899866i \(-0.356336\pi\)
0.436166 + 0.899866i \(0.356336\pi\)
\(18\) 27.3978 2457.61i 0.0199313 1.78785i
\(19\) 842.227i 0.535236i 0.963525 + 0.267618i \(0.0862365\pi\)
−0.963525 + 0.267618i \(0.913764\pi\)
\(20\) 6222.77i 3.47864i
\(21\) −1399.02 + 1383.51i −0.692269 + 0.684595i
\(22\) 4035.17 438.897i 1.77748 0.193333i
\(23\) 2472.99i 0.974770i 0.873187 + 0.487385i \(0.162049\pi\)
−0.873187 + 0.487385i \(0.837951\pi\)
\(24\) 4245.87 + 4293.47i 1.50466 + 1.52153i
\(25\) −4710.72 −1.50743
\(26\) 5290.77i 1.53492i
\(27\) 2722.93 2633.36i 0.718831 0.695185i
\(28\) 8873.04i 2.13883i
\(29\) −3569.99 −0.788265 −0.394133 0.919054i \(-0.628955\pi\)
−0.394133 + 0.919054i \(0.628955\pi\)
\(30\) 9923.59 9813.58i 2.01310 1.99078i
\(31\) −215.057 −0.0401929 −0.0200964 0.999798i \(-0.506397\pi\)
−0.0200964 + 0.999798i \(0.506397\pi\)
\(32\) −4478.13 −0.773074
\(33\) 4854.00 + 3946.40i 0.775916 + 0.630836i
\(34\) −10513.3 −1.55970
\(35\) −11172.9 −1.54169
\(36\) −190.426 + 17081.4i −0.0244889 + 2.19668i
\(37\) −3626.51 −0.435496 −0.217748 0.976005i \(-0.569871\pi\)
−0.217748 + 0.976005i \(0.569871\pi\)
\(38\) 8518.50i 0.956983i
\(39\) −5798.03 + 5733.75i −0.610406 + 0.603639i
\(40\) 34288.8i 3.38846i
\(41\) 8845.46 0.821790 0.410895 0.911683i \(-0.365216\pi\)
0.410895 + 0.911683i \(0.365216\pi\)
\(42\) 14150.0 13993.2i 1.23775 1.22403i
\(43\) 5262.04i 0.433993i 0.976172 + 0.216996i \(0.0696260\pi\)
−0.976172 + 0.216996i \(0.930374\pi\)
\(44\) −28046.1 + 3050.51i −2.18394 + 0.237543i
\(45\) 21508.9 + 239.785i 1.58339 + 0.0176518i
\(46\) 25012.4i 1.74285i
\(47\) 9059.89i 0.598244i −0.954215 0.299122i \(-0.903306\pi\)
0.954215 0.299122i \(-0.0966938\pi\)
\(48\) −18286.4 18491.4i −1.14558 1.15842i
\(49\) 875.528 0.0520931
\(50\) 47645.5 2.69523
\(51\) −11393.5 11521.2i −0.613384 0.620260i
\(52\) 36773.0i 1.88591i
\(53\) 897.191i 0.0438728i −0.999759 0.0219364i \(-0.993017\pi\)
0.999759 0.0219364i \(-0.00698313\pi\)
\(54\) −27540.4 + 26634.4i −1.28525 + 1.24297i
\(55\) 3841.21 + 35315.7i 0.171223 + 1.57420i
\(56\) 48892.3i 2.08339i
\(57\) 9335.22 9231.73i 0.380572 0.376353i
\(58\) 36107.8 1.40939
\(59\) 36226.0i 1.35485i −0.735593 0.677424i \(-0.763096\pi\)
0.735593 0.677424i \(-0.236904\pi\)
\(60\) −68973.0 + 68208.4i −2.47344 + 2.44602i
\(61\) 15319.3i 0.527125i −0.964642 0.263563i \(-0.915102\pi\)
0.964642 0.263563i \(-0.0848976\pi\)
\(62\) 2175.14 0.0718634
\(63\) 30669.5 + 341.908i 0.973545 + 0.0108532i
\(64\) −8092.58 −0.246966
\(65\) −46304.6 −1.35938
\(66\) −49094.6 39914.9i −1.38731 1.12791i
\(67\) −53380.7 −1.45277 −0.726385 0.687288i \(-0.758801\pi\)
−0.726385 + 0.687288i \(0.758801\pi\)
\(68\) 73071.6 1.91636
\(69\) 27410.5 27106.6i 0.693098 0.685414i
\(70\) 113006. 2.75649
\(71\) 33693.5i 0.793233i 0.917984 + 0.396616i \(0.129816\pi\)
−0.917984 + 0.396616i \(0.870184\pi\)
\(72\) 1049.29 94122.2i 0.0238541 2.13974i
\(73\) 76140.5i 1.67228i −0.548518 0.836139i \(-0.684808\pi\)
0.548518 0.836139i \(-0.315192\pi\)
\(74\) 36679.4 0.778652
\(75\) 51634.7 + 52213.5i 1.05996 + 1.07184i
\(76\) 59207.1i 1.17582i
\(77\) 5477.18 + 50356.5i 0.105276 + 0.967897i
\(78\) 58642.7 57992.6i 1.09138 1.07929i
\(79\) 106783.i 1.92502i 0.271251 + 0.962509i \(0.412563\pi\)
−0.271251 + 0.962509i \(0.587437\pi\)
\(80\) 147677.i 2.57981i
\(81\) −59034.3 1316.41i −0.999751 0.0222935i
\(82\) −89465.2 −1.46933
\(83\) −20385.5 −0.324808 −0.162404 0.986724i \(-0.551925\pi\)
−0.162404 + 0.986724i \(0.551925\pi\)
\(84\) −98348.5 + 97258.2i −1.52079 + 1.50393i
\(85\) 92011.8i 1.38133i
\(86\) 53221.6i 0.775964i
\(87\) 39131.0 + 39569.7i 0.554272 + 0.560486i
\(88\) 154540. 16809.0i 2.12732 0.231385i
\(89\) 11850.9i 0.158591i 0.996851 + 0.0792953i \(0.0252670\pi\)
−0.996851 + 0.0792953i \(0.974733\pi\)
\(90\) −217547. 2425.24i −2.83104 0.0315609i
\(91\) −66025.7 −0.835813
\(92\) 173847.i 2.14139i
\(93\) 2357.26 + 2383.68i 0.0282618 + 0.0285786i
\(94\) 91634.1i 1.06964i
\(95\) 74553.6 0.847539
\(96\) 49085.2 + 49635.4i 0.543591 + 0.549685i
\(97\) −67716.0 −0.730738 −0.365369 0.930863i \(-0.619057\pi\)
−0.365369 + 0.930863i \(0.619057\pi\)
\(98\) −8855.32 −0.0931406
\(99\) −9463.35 97058.5i −0.0970414 0.995280i
\(100\) −331155. −3.31155
\(101\) 90346.0 0.881263 0.440631 0.897688i \(-0.354755\pi\)
0.440631 + 0.897688i \(0.354755\pi\)
\(102\) 115237. + 116529.i 1.09671 + 1.10900i
\(103\) −11291.0 −0.104867 −0.0524335 0.998624i \(-0.516698\pi\)
−0.0524335 + 0.998624i \(0.516698\pi\)
\(104\) 202627.i 1.83702i
\(105\) 122468. + 123841.i 1.08405 + 1.09620i
\(106\) 9074.42i 0.0784430i
\(107\) −187842. −1.58611 −0.793054 0.609151i \(-0.791510\pi\)
−0.793054 + 0.609151i \(0.791510\pi\)
\(108\) 191417. 185120.i 1.57914 1.52719i
\(109\) 85380.2i 0.688321i −0.938911 0.344161i \(-0.888164\pi\)
0.938911 0.344161i \(-0.111836\pi\)
\(110\) −38851.0 357192.i −0.306140 2.81462i
\(111\) 39750.5 + 40196.1i 0.306221 + 0.309654i
\(112\) 210572.i 1.58619i
\(113\) 72617.4i 0.534989i −0.963559 0.267494i \(-0.913804\pi\)
0.963559 0.267494i \(-0.0861957\pi\)
\(114\) −94418.8 + 93372.1i −0.680450 + 0.672907i
\(115\) 218908. 1.54354
\(116\) −250964. −1.73168
\(117\) 127105. + 1416.99i 0.858419 + 0.00956978i
\(118\) 366399.i 2.42242i
\(119\) 131199.i 0.849307i
\(120\) 380056. 375843.i 2.40932 2.38261i
\(121\) 157285. 34624.8i 0.976616 0.214992i
\(122\) 154943.i 0.942482i
\(123\) −96955.9 98042.8i −0.577845 0.584323i
\(124\) −15118.1 −0.0882965
\(125\) 140368.i 0.803511i
\(126\) −310200. 3458.15i −1.74066 0.0194052i
\(127\) 151435.i 0.833139i −0.909104 0.416569i \(-0.863232\pi\)
0.909104 0.416569i \(-0.136768\pi\)
\(128\) 225150. 1.21464
\(129\) 58324.3 57677.7i 0.308585 0.305164i
\(130\) 468337. 2.43052
\(131\) −206332. −1.05048 −0.525242 0.850953i \(-0.676025\pi\)
−0.525242 + 0.850953i \(0.676025\pi\)
\(132\) 341228. + 277425.i 1.70455 + 1.38583i
\(133\) 106306. 0.521108
\(134\) 539906. 2.59750
\(135\) −233104. 241033.i −1.10082 1.13826i
\(136\) −402640. −1.86668
\(137\) 275648.i 1.25474i −0.778721 0.627371i \(-0.784131\pi\)
0.778721 0.627371i \(-0.215869\pi\)
\(138\) −277237. + 274164.i −1.23923 + 1.22550i
\(139\) 81387.0i 0.357288i −0.983914 0.178644i \(-0.942829\pi\)
0.983914 0.178644i \(-0.0571710\pi\)
\(140\) −785438. −3.38682
\(141\) −100420. + 99306.4i −0.425374 + 0.420658i
\(142\) 340785.i 1.41827i
\(143\) 22699.4 + 208695.i 0.0928268 + 0.853439i
\(144\) −4519.13 + 405371.i −0.0181614 + 1.62909i
\(145\) 316014.i 1.24821i
\(146\) 770104.i 2.98997i
\(147\) −9596.74 9704.33i −0.0366295 0.0370401i
\(148\) −254937. −0.956706
\(149\) 60929.5 0.224834 0.112417 0.993661i \(-0.464141\pi\)
0.112417 + 0.993661i \(0.464141\pi\)
\(150\) −522246. 528101.i −1.89517 1.91641i
\(151\) 438115.i 1.56367i 0.623483 + 0.781837i \(0.285717\pi\)
−0.623483 + 0.781837i \(0.714283\pi\)
\(152\) 326243.i 1.14534i
\(153\) −2815.70 + 252571.i −0.00972428 + 0.872278i
\(154\) −55397.6 509319.i −0.188230 1.73057i
\(155\) 19036.7i 0.0636449i
\(156\) −407591. + 403072.i −1.34095 + 1.32609i
\(157\) 345267. 1.11791 0.558954 0.829198i \(-0.311203\pi\)
0.558954 + 0.829198i \(0.311203\pi\)
\(158\) 1.08003e6i 3.44186i
\(159\) −9944.43 + 9834.19i −0.0311952 + 0.0308493i
\(160\) 396402.i 1.22415i
\(161\) 312140. 0.949041
\(162\) 597088. + 13314.5i 1.78752 + 0.0398600i
\(163\) 65897.0 0.194266 0.0971330 0.995271i \(-0.469033\pi\)
0.0971330 + 0.995271i \(0.469033\pi\)
\(164\) 621820. 1.80532
\(165\) 349334. 429674.i 0.998920 1.22865i
\(166\) 206185. 0.580746
\(167\) −685804. −1.90287 −0.951434 0.307852i \(-0.900390\pi\)
−0.951434 + 0.307852i \(0.900390\pi\)
\(168\) 541921. 535913.i 1.48137 1.46494i
\(169\) 97659.3 0.263025
\(170\) 930631.i 2.46976i
\(171\) −204648. 2281.45i −0.535203 0.00596652i
\(172\) 369912.i 0.953404i
\(173\) −331628. −0.842434 −0.421217 0.906960i \(-0.638397\pi\)
−0.421217 + 0.906960i \(0.638397\pi\)
\(174\) −395781. 400218.i −0.991019 1.00213i
\(175\) 594587.i 1.46764i
\(176\) −665581. + 72393.9i −1.61964 + 0.176165i
\(177\) −401528. + 397077.i −0.963347 + 0.952668i
\(178\) 119863.i 0.283554i
\(179\) 502450.i 1.17209i −0.810279 0.586044i \(-0.800685\pi\)
0.810279 0.586044i \(-0.199315\pi\)
\(180\) 1.51204e6 + 16856.4i 3.47842 + 0.0387779i
\(181\) −815453. −1.85013 −0.925066 0.379808i \(-0.875990\pi\)
−0.925066 + 0.379808i \(0.875990\pi\)
\(182\) 667801. 1.49440
\(183\) −169799. + 167916.i −0.374806 + 0.370651i
\(184\) 957931.i 2.08588i
\(185\) 321017.i 0.689602i
\(186\) −23841.9 24109.2i −0.0505311 0.0510976i
\(187\) −414698. + 45105.9i −0.867217 + 0.0943255i
\(188\) 636894.i 1.31423i
\(189\) −332382. 343688.i −0.676835 0.699858i
\(190\) −754054. −1.51537
\(191\) 527471.i 1.04620i 0.852271 + 0.523100i \(0.175225\pi\)
−0.852271 + 0.523100i \(0.824775\pi\)
\(192\) 88703.6 + 89697.9i 0.173655 + 0.175602i
\(193\) 572950.i 1.10719i −0.832785 0.553597i \(-0.813255\pi\)
0.832785 0.553597i \(-0.186745\pi\)
\(194\) 684897. 1.30653
\(195\) 507549. + 513239.i 0.955854 + 0.966570i
\(196\) 61548.1 0.114439
\(197\) −284594. −0.522468 −0.261234 0.965276i \(-0.584129\pi\)
−0.261234 + 0.965276i \(0.584129\pi\)
\(198\) 95714.8 + 981674.i 0.173507 + 1.77953i
\(199\) 425383. 0.761461 0.380730 0.924686i \(-0.375673\pi\)
0.380730 + 0.924686i \(0.375673\pi\)
\(200\) 1.82474e6 3.22571
\(201\) 585110. + 591670.i 1.02152 + 1.03297i
\(202\) −913783. −1.57567
\(203\) 450604.i 0.767459i
\(204\) −800944. 809923.i −1.34749 1.36260i
\(205\) 782997.i 1.30129i
\(206\) 114200. 0.187499
\(207\) −600898. 6698.90i −0.974709 0.0108662i
\(208\) 872686.i 1.39862i
\(209\) −36547.5 336014.i −0.0578752 0.532098i
\(210\) −1.23867e6 1.25256e6i −1.93824 1.95997i
\(211\) 120728.i 0.186682i −0.995634 0.0933410i \(-0.970245\pi\)
0.995634 0.0933410i \(-0.0297547\pi\)
\(212\) 63070.9i 0.0963805i
\(213\) 373458. 369318.i 0.564018 0.557765i
\(214\) 1.89988e6 2.83591
\(215\) 465793. 0.687222
\(216\) −1.05475e6 + 1.02005e6i −1.53821 + 1.48761i
\(217\) 27144.5i 0.0391320i
\(218\) 863558.i 1.23069i
\(219\) −843939. + 834583.i −1.18905 + 1.17587i
\(220\) 270030. + 2.48263e6i 0.376146 + 3.45824i
\(221\) 543737.i 0.748873i
\(222\) −402047. 406554.i −0.547512 0.553650i
\(223\) 307332. 0.413853 0.206926 0.978357i \(-0.433654\pi\)
0.206926 + 0.978357i \(0.433654\pi\)
\(224\) 565229.i 0.752669i
\(225\) 12760.6 1.14463e6i 0.0168040 1.50734i
\(226\) 734471.i 0.956542i
\(227\) 458186. 0.590170 0.295085 0.955471i \(-0.404652\pi\)
0.295085 + 0.955471i \(0.404652\pi\)
\(228\) 656249. 648974.i 0.836049 0.826781i
\(229\) 246534. 0.310662 0.155331 0.987862i \(-0.450356\pi\)
0.155331 + 0.987862i \(0.450356\pi\)
\(230\) −2.21409e6 −2.75979
\(231\) 498114. 612672.i 0.614185 0.755436i
\(232\) 1.38287e6 1.68679
\(233\) 599273. 0.723161 0.361580 0.932341i \(-0.382237\pi\)
0.361580 + 0.932341i \(0.382237\pi\)
\(234\) −1.28558e6 14331.8i −1.53482 0.0171104i
\(235\) −801978. −0.947312
\(236\) 2.54663e6i 2.97636i
\(237\) 1.18358e6 1.17046e6i 1.36876 1.35358i
\(238\) 1.32699e6i 1.51853i
\(239\) 357849. 0.405234 0.202617 0.979258i \(-0.435055\pi\)
0.202617 + 0.979258i \(0.435055\pi\)
\(240\) −1.63685e6 + 1.61870e6i −1.83434 + 1.81401i
\(241\) 570630.i 0.632867i 0.948615 + 0.316433i \(0.102485\pi\)
−0.948615 + 0.316433i \(0.897515\pi\)
\(242\) −1.59082e6 + 350204.i −1.74615 + 0.384399i
\(243\) 632490. + 668764.i 0.687128 + 0.726536i
\(244\) 1.07692e6i 1.15800i
\(245\) 77501.4i 0.0824887i
\(246\) 980637. + 991630.i 1.03317 + 1.04475i
\(247\) 440569. 0.459485
\(248\) 83304.0 0.0860076
\(249\) 223448. + 225953.i 0.228390 + 0.230951i
\(250\) 1.41971e6i 1.43665i
\(251\) 823625.i 0.825173i −0.910918 0.412587i \(-0.864625\pi\)
0.910918 0.412587i \(-0.135375\pi\)
\(252\) 2.15601e6 + 24035.6i 2.13870 + 0.0238426i
\(253\) −107313. 986619.i −0.105402 0.969055i
\(254\) 1.53165e6i 1.48962i
\(255\) −1.01986e6 + 1.00855e6i −0.982174 + 0.971286i
\(256\) −2.01827e6 −1.92477
\(257\) 1.66449e6i 1.57198i 0.618238 + 0.785991i \(0.287847\pi\)
−0.618238 + 0.785991i \(0.712153\pi\)
\(258\) −589907. + 583367.i −0.551739 + 0.545623i
\(259\) 457737.i 0.424001i
\(260\) −3.25513e6 −2.98631
\(261\) 9670.51 867454.i 0.00878715 0.788216i
\(262\) 2.08690e6 1.87823
\(263\) −612387. −0.545929 −0.272965 0.962024i \(-0.588004\pi\)
−0.272965 + 0.962024i \(0.588004\pi\)
\(264\) −1.88024e6 1.52867e6i −1.66036 1.34991i
\(265\) −79419.0 −0.0694720
\(266\) −1.07520e6 −0.931723
\(267\) 131355. 129899.i 0.112764 0.111514i
\(268\) −3.75257e6 −3.19147
\(269\) 662606.i 0.558309i −0.960246 0.279155i \(-0.909946\pi\)
0.960246 0.279155i \(-0.0900542\pi\)
\(270\) 2.35767e6 + 2.43787e6i 1.96822 + 2.03517i
\(271\) 1.01210e6i 0.837144i −0.908184 0.418572i \(-0.862531\pi\)
0.908184 0.418572i \(-0.137469\pi\)
\(272\) 1.73411e6 1.42120
\(273\) 723713. + 731826.i 0.587706 + 0.594294i
\(274\) 2.78798e6i 2.24343i
\(275\) 1.87938e6 204417.i 1.49859 0.162999i
\(276\) 1.92691e6 1.90555e6i 1.52261 1.50573i
\(277\) 2.02312e6i 1.58425i 0.610360 + 0.792124i \(0.291025\pi\)
−0.610360 + 0.792124i \(0.708975\pi\)
\(278\) 823169.i 0.638818i
\(279\) 582.553 52255.6i 0.000448048 0.0401904i
\(280\) 4.32793e6 3.29902
\(281\) −818601. −0.618453 −0.309226 0.950988i \(-0.600070\pi\)
−0.309226 + 0.950988i \(0.600070\pi\)
\(282\) 1.01567e6 1.00441e6i 0.760554 0.752122i
\(283\) 1.73555e6i 1.28816i −0.764957 0.644081i \(-0.777240\pi\)
0.764957 0.644081i \(-0.222760\pi\)
\(284\) 2.36860e6i 1.74259i
\(285\) −817189. 826350.i −0.595951 0.602632i
\(286\) −229587. 2.11080e6i −0.165971 1.52592i
\(287\) 1.11647e6i 0.800099i
\(288\) 12130.5 1.08812e6i 0.00861781 0.773026i
\(289\) −339398. −0.239037
\(290\) 3.19625e6i 2.23175i
\(291\) 742241. + 750562.i 0.513822 + 0.519582i
\(292\) 5.35254e6i 3.67369i
\(293\) 2.61963e6 1.78267 0.891336 0.453344i \(-0.149769\pi\)
0.891336 + 0.453344i \(0.149769\pi\)
\(294\) 97063.9 + 98152.1i 0.0654922 + 0.0662264i
\(295\) −3.20671e6 −2.14538
\(296\) 1.40476e6 0.931905
\(297\) −972064. + 1.16876e6i −0.639446 + 0.768836i
\(298\) −616257. −0.401995
\(299\) 1.29362e6 0.836813
\(300\) 3.62983e6 + 3.67052e6i 2.32853 + 2.35464i
\(301\) 664174. 0.422538
\(302\) 4.43121e6i 2.79579i
\(303\) −990291. 1.00139e6i −0.619664 0.626610i
\(304\) 1.40508e6i 0.872004i
\(305\) −1.35606e6 −0.834696
\(306\) 28478.7 2.55457e6i 0.0173867 1.55960i
\(307\) 103438.i 0.0626377i 0.999509 + 0.0313188i \(0.00997072\pi\)
−0.999509 + 0.0313188i \(0.990029\pi\)
\(308\) 385036. + 3.53997e6i 0.231273 + 2.12629i
\(309\) 123762. + 125149.i 0.0737377 + 0.0745643i
\(310\) 192543.i 0.113795i
\(311\) 1.12357e6i 0.658716i −0.944205 0.329358i \(-0.893168\pi\)
0.944205 0.329358i \(-0.106832\pi\)
\(312\) 2.24591e6 2.22101e6i 1.30619 1.29171i
\(313\) −1.99753e6 −1.15248 −0.576239 0.817281i \(-0.695480\pi\)
−0.576239 + 0.817281i \(0.695480\pi\)
\(314\) −3.49212e6 −1.99878
\(315\) 30265.6 2.71486e6i 0.0171859 1.54160i
\(316\) 7.50666e6i 4.22892i
\(317\) 2.55991e6i 1.43079i 0.698720 + 0.715395i \(0.253753\pi\)
−0.698720 + 0.715395i \(0.746247\pi\)
\(318\) 100581. 99465.5i 0.0557759 0.0551575i
\(319\) 1.42428e6 154916.i 0.783643 0.0852353i
\(320\) 716352.i 0.391067i
\(321\) 2.05895e6 + 2.08203e6i 1.11528 + 1.12778i
\(322\) −3.15707e6 −1.69685
\(323\) 875454.i 0.466903i
\(324\) −4.15001e6 92541.3i −2.19627 0.0489748i
\(325\) 2.46418e6i 1.29409i
\(326\) −666499. −0.347341
\(327\) −946352. + 935861.i −0.489422 + 0.483996i
\(328\) −3.42636e6 −1.75852
\(329\) −1.14354e6 −0.582454
\(330\) −3.53325e6 + 4.34584e6i −1.78603 + 2.19679i
\(331\) −537352. −0.269581 −0.134790 0.990874i \(-0.543036\pi\)
−0.134790 + 0.990874i \(0.543036\pi\)
\(332\) −1.43307e6 −0.713545
\(333\) 9823.59 881186.i 0.00485467 0.435469i
\(334\) 6.93640e6 3.40226
\(335\) 4.72524e6i 2.30044i
\(336\) −2.33398e6 + 2.30810e6i −1.12784 + 1.11534i
\(337\) 156793.i 0.0752058i −0.999293 0.0376029i \(-0.988028\pi\)
0.999293 0.0376029i \(-0.0119722\pi\)
\(338\) −987752. −0.470279
\(339\) −804889. + 795966.i −0.380397 + 0.376180i
\(340\) 6.46827e6i 3.03453i
\(341\) 85798.8 9332.16i 0.0399572 0.00434606i
\(342\) 2.06987e6 + 23075.2i 0.956923 + 0.0106679i
\(343\) 2.23189e6i 1.02432i
\(344\) 2.03829e6i 0.928689i
\(345\) −2.39947e6 2.42637e6i −1.08534 1.09751i
\(346\) 3.35417e6 1.50624
\(347\) 1.90705e6 0.850235 0.425117 0.905138i \(-0.360233\pi\)
0.425117 + 0.905138i \(0.360233\pi\)
\(348\) 2.75084e6 + 2.78168e6i 1.21764 + 1.23129i
\(349\) 444271.i 0.195247i 0.995223 + 0.0976236i \(0.0311241\pi\)
−0.995223 + 0.0976236i \(0.968876\pi\)
\(350\) 6.01381e6i 2.62409i
\(351\) −1.37751e6 1.42436e6i −0.596797 0.617097i
\(352\) 1.78659e6 194323.i 0.768542 0.0835927i
\(353\) 3.40494e6i 1.45436i −0.686444 0.727182i \(-0.740829\pi\)
0.686444 0.727182i \(-0.259171\pi\)
\(354\) 4.06116e6 4.01614e6i 1.72243 1.70334i
\(355\) 2.98254e6 1.25607
\(356\) 833099.i 0.348395i
\(357\) −1.45421e6 + 1.43809e6i −0.603889 + 0.597194i
\(358\) 5.08191e6i 2.09565i
\(359\) −585269. −0.239673 −0.119837 0.992794i \(-0.538237\pi\)
−0.119837 + 0.992794i \(0.538237\pi\)
\(360\) −8.33166e6 92882.5i −3.38825 0.0377727i
\(361\) 1.76675e6 0.713523
\(362\) 8.24770e6 3.30797
\(363\) −2.10779e6 1.36382e6i −0.839579 0.543237i
\(364\) −4.64149e6 −1.83613
\(365\) −6.73993e6 −2.64803
\(366\) 1.71739e6 1.69835e6i 0.670140 0.662710i
\(367\) −314950. −0.122061 −0.0610304 0.998136i \(-0.519439\pi\)
−0.0610304 + 0.998136i \(0.519439\pi\)
\(368\) 4.12568e6i 1.58809i
\(369\) −23960.9 + 2.14931e6i −0.00916086 + 0.821739i
\(370\) 3.24685e6i 1.23298i
\(371\) −113243. −0.0427148
\(372\) 165711. + 167569.i 0.0620861 + 0.0627821i
\(373\) 2.27086e6i 0.845121i 0.906335 + 0.422561i \(0.138869\pi\)
−0.906335 + 0.422561i \(0.861131\pi\)
\(374\) 4.19436e6 456212.i 1.55055 0.168651i
\(375\) 1.55583e6 1.53858e6i 0.571326 0.564992i
\(376\) 3.50942e6i 1.28017i
\(377\) 1.86746e6i 0.676704i
\(378\) 3.36180e6 + 3.47615e6i 1.21016 + 1.25132i
\(379\) 3.88525e6 1.38938 0.694691 0.719309i \(-0.255541\pi\)
0.694691 + 0.719309i \(0.255541\pi\)
\(380\) 5.24099e6 1.86189
\(381\) −1.67850e6 + 1.65989e6i −0.592392 + 0.585825i
\(382\) 5.33498e6i 1.87057i
\(383\) 2.31613e6i 0.806801i −0.915023 0.403401i \(-0.867828\pi\)
0.915023 0.403401i \(-0.132172\pi\)
\(384\) −2.46790e6 2.49556e6i −0.854080 0.863655i
\(385\) 4.45754e6 484838.i 1.53265 0.166703i
\(386\) 5.79497e6i 1.97962i
\(387\) −1.27860e6 14254.0i −0.433966 0.00483792i
\(388\) −4.76031e6 −1.60530
\(389\) 3.97451e6i 1.33171i −0.746081 0.665855i \(-0.768067\pi\)
0.746081 0.665855i \(-0.231933\pi\)
\(390\) −5.13348e6 5.19103e6i −1.70903 1.72819i
\(391\) 2.57055e6i 0.850323i
\(392\) −339143. −0.111472
\(393\) 2.26163e6 + 2.28698e6i 0.738652 + 0.746933i
\(394\) 2.87845e6 0.934154
\(395\) 9.45240e6 3.04824
\(396\) −665257. 6.82304e6i −0.213182 2.18645i
\(397\) −2.41352e6 −0.768554 −0.384277 0.923218i \(-0.625549\pi\)
−0.384277 + 0.923218i \(0.625549\pi\)
\(398\) −4.30243e6 −1.36146
\(399\) −1.16523e6 1.17829e6i −0.366420 0.370527i
\(400\) −7.85888e6 −2.45590
\(401\) 2.99915e6i 0.931402i −0.884942 0.465701i \(-0.845802\pi\)
0.884942 0.465701i \(-0.154198\pi\)
\(402\) −5.91796e6 5.98430e6i −1.82645 1.84692i
\(403\) 112496.i 0.0345045i
\(404\) 6.35116e6 1.93598
\(405\) −116528. + 5.22570e6i −0.0353015 + 1.58309i
\(406\) 4.55753e6i 1.37219i
\(407\) 1.44683e6 157368.i 0.432943 0.0470903i
\(408\) 4.41337e6 + 4.46285e6i 1.31256 + 1.32728i
\(409\) 3.05264e6i 0.902335i −0.892439 0.451167i \(-0.851008\pi\)
0.892439 0.451167i \(-0.148992\pi\)
\(410\) 7.91943e6i 2.32667i
\(411\) −3.05528e6 + 3.02141e6i −0.892168 + 0.882277i
\(412\) −793736. −0.230374
\(413\) −4.57245e6 −1.31909
\(414\) 6.07764e6 + 67754.4i 1.74275 + 0.0194284i
\(415\) 1.80452e6i 0.514330i
\(416\) 2.34251e6i 0.663663i
\(417\) −902091. + 892090.i −0.254045 + 0.251228i
\(418\) 369651. + 3.39853e6i 0.103479 + 0.951372i
\(419\) 1.96679e6i 0.547296i −0.961830 0.273648i \(-0.911770\pi\)
0.961830 0.273648i \(-0.0882304\pi\)
\(420\) 8.60926e6 + 8.70577e6i 2.38146 + 2.40815i
\(421\) 3.03122e6 0.833514 0.416757 0.909018i \(-0.363167\pi\)
0.416757 + 0.909018i \(0.363167\pi\)
\(422\) 1.22108e6i 0.333781i
\(423\) 2.20142e6 + 24541.7i 0.598207 + 0.00666890i
\(424\) 347534.i 0.0938821i
\(425\) −4.89657e6 −1.31498
\(426\) −3.77725e6 + 3.73538e6i −1.00844 + 0.997265i
\(427\) −1.93360e6 −0.513212
\(428\) −1.32049e7 −3.48439
\(429\) 2.06436e6 2.53913e6i 0.541555 0.666103i
\(430\) −4.71116e6 −1.22873
\(431\) 1.36368e6 0.353605 0.176802 0.984246i \(-0.443425\pi\)
0.176802 + 0.984246i \(0.443425\pi\)
\(432\) 4.54265e6 4.39322e6i 1.17112 1.13259i
\(433\) −5.36351e6 −1.37477 −0.687384 0.726295i \(-0.741241\pi\)
−0.687384 + 0.726295i \(0.741241\pi\)
\(434\) 274546.i 0.0699666i
\(435\) 3.50269e6 3.46386e6i 0.887522 0.877683i
\(436\) 6.00208e6i 1.51212i
\(437\) −2.08282e6 −0.521732
\(438\) 8.53581e6 8.44119e6i 2.12598 2.10241i
\(439\) 406895.i 0.100768i 0.998730 + 0.0503839i \(0.0160445\pi\)
−0.998730 + 0.0503839i \(0.983956\pi\)
\(440\) −1.48792e6 1.36798e7i −0.366395 3.36859i
\(441\) −2371.66 + 212740.i −0.000580705 + 0.0520898i
\(442\) 5.49950e6i 1.33896i
\(443\) 2.29937e6i 0.556673i −0.960484 0.278337i \(-0.910217\pi\)
0.960484 0.278337i \(-0.0897831\pi\)
\(444\) 2.79439e6 + 2.82571e6i 0.672712 + 0.680253i
\(445\) 1.04904e6 0.251126
\(446\) −3.10844e6 −0.739954
\(447\) −667854. 675341.i −0.158093 0.159865i
\(448\) 1.02145e6i 0.240447i
\(449\) 6.52698e6i 1.52791i 0.645272 + 0.763953i \(0.276744\pi\)
−0.645272 + 0.763953i \(0.723256\pi\)
\(450\) −129064. + 1.15771e7i −0.0300450 + 2.69507i
\(451\) −3.52897e6 + 383839.i −0.816971 + 0.0888603i
\(452\) 5.10488e6i 1.17527i
\(453\) 4.85606e6 4.80222e6i 1.11183 1.09950i
\(454\) −4.63421e6 −1.05520
\(455\) 5.84457e6i 1.32350i
\(456\) −3.61607e6 + 3.57598e6i −0.814376 + 0.805348i
\(457\) 7.61992e6i 1.70671i −0.521330 0.853355i \(-0.674564\pi\)
0.521330 0.853355i \(-0.325436\pi\)
\(458\) −2.49351e6 −0.555453
\(459\) 2.83035e6 2.73725e6i 0.627060 0.606432i
\(460\) 1.53888e7 3.39087
\(461\) 1.84657e6 0.404682 0.202341 0.979315i \(-0.435145\pi\)
0.202341 + 0.979315i \(0.435145\pi\)
\(462\) −5.03806e6 + 6.19672e6i −1.09814 + 1.35069i
\(463\) 8.90164e6 1.92982 0.964912 0.262573i \(-0.0845711\pi\)
0.964912 + 0.262573i \(0.0845711\pi\)
\(464\) −5.95581e6 −1.28424
\(465\) 211003. 208664.i 0.0452539 0.0447522i
\(466\) −6.06120e6 −1.29299
\(467\) 3.83609e6i 0.813947i 0.913440 + 0.406974i \(0.133416\pi\)
−0.913440 + 0.406974i \(0.866584\pi\)
\(468\) 8.93528e6 + 99611.9i 1.88579 + 0.0210231i
\(469\) 6.73770e6i 1.41442i
\(470\) 8.11142e6 1.69376
\(471\) −3.78451e6 3.82693e6i −0.786063 0.794875i
\(472\) 1.40324e7i 2.89920i
\(473\) −228340. 2.09933e6i −0.0469278 0.431448i
\(474\) −1.19710e7 + 1.18383e7i −2.44729 + 2.42016i
\(475\) 3.96750e6i 0.806831i
\(476\) 9.22309e6i 1.86577i
\(477\) 218004. + 2430.34i 0.0438700 + 0.000489070i
\(478\) −3.61938e6 −0.724544
\(479\) −4.28323e6 −0.852968 −0.426484 0.904495i \(-0.640248\pi\)
−0.426484 + 0.904495i \(0.640248\pi\)
\(480\) 4.39371e6 4.34500e6i 0.870418 0.860769i
\(481\) 1.89703e6i 0.373861i
\(482\) 5.77150e6i 1.13154i
\(483\) −3.42140e6 3.45975e6i −0.667323 0.674803i
\(484\) 1.10569e7 2.43406e6i 2.14545 0.472300i
\(485\) 5.99419e6i 1.15711i
\(486\) −6.39716e6 6.76405e6i −1.22856 1.29902i
\(487\) −7.16028e6 −1.36807 −0.684034 0.729450i \(-0.739776\pi\)
−0.684034 + 0.729450i \(0.739776\pi\)
\(488\) 5.93405e6i 1.12798i
\(489\) −722303. 730400.i −0.136599 0.138130i
\(490\) 783869.i 0.147487i
\(491\) 2.57405e6 0.481851 0.240925 0.970544i \(-0.422549\pi\)
0.240925 + 0.970544i \(0.422549\pi\)
\(492\) −6.81583e6 6.89223e6i −1.26942 1.28365i
\(493\) −3.71083e6 −0.687629
\(494\) −4.45603e6 −0.821544
\(495\) −8.59158e6 + 837693.i −1.57601 + 0.153664i
\(496\) −358779. −0.0654821
\(497\) 4.25280e6 0.772296
\(498\) −2.26001e6 2.28534e6i −0.408354 0.412932i
\(499\) 3.30406e6 0.594014 0.297007 0.954875i \(-0.404012\pi\)
0.297007 + 0.954875i \(0.404012\pi\)
\(500\) 9.86759e6i 1.76517i
\(501\) 7.51716e6 + 7.60143e6i 1.33801 + 1.35301i
\(502\) 8.33035e6i 1.47538i
\(503\) 934368. 0.164664 0.0823318 0.996605i \(-0.473763\pi\)
0.0823318 + 0.996605i \(0.473763\pi\)
\(504\) −1.18801e7 132441.i −2.08326 0.0232245i
\(505\) 7.99739e6i 1.39547i
\(506\) 1.08539e6 + 9.97892e6i 0.188455 + 1.73264i
\(507\) −1.07045e6 1.08245e6i −0.184947 0.187020i
\(508\) 1.06456e7i 1.83026i
\(509\) 2.42079e6i 0.414155i −0.978325 0.207077i \(-0.933605\pi\)
0.978325 0.207077i \(-0.0663952\pi\)
\(510\) 1.03151e7 1.02007e7i 1.75609 1.73663i
\(511\) −9.61045e6 −1.62814
\(512\) 1.32085e7 2.22678
\(513\) 2.21788e6 + 2.29332e6i 0.372088 + 0.384744i
\(514\) 1.68350e7i 2.81065i
\(515\) 999474.i 0.166056i
\(516\) 4.10009e6 4.05464e6i 0.677906 0.670390i
\(517\) 393144. + 3.61452e6i 0.0646883 + 0.594737i
\(518\) 4.62967e6i 0.758099i
\(519\) 3.63500e6 + 3.67575e6i 0.592361 + 0.599002i
\(520\) 1.79365e7 2.90890
\(521\) 5.66823e6i 0.914858i −0.889246 0.457429i \(-0.848770\pi\)
0.889246 0.457429i \(-0.151230\pi\)
\(522\) −97810.0 + 8.77366e6i −0.0157111 + 1.40930i
\(523\) 7.10021e6i 1.13506i −0.823354 0.567528i \(-0.807900\pi\)
0.823354 0.567528i \(-0.192100\pi\)
\(524\) −1.45048e7 −2.30772
\(525\) 6.59039e6 6.51733e6i 1.04355 1.03198i
\(526\) 6.19384e6 0.976102
\(527\) −223541. −0.0350615
\(528\) 8.09791e6 + 6.58377e6i 1.26412 + 1.02776i
\(529\) 320681. 0.0498234
\(530\) 803264. 0.124213
\(531\) 8.80238e6 + 98130.2i 1.35476 + 0.0151031i
\(532\) 7.47311e6 1.14478
\(533\) 4.62706e6i 0.705484i
\(534\) −1.32856e6 + 1.31383e6i −0.201618 + 0.199383i
\(535\) 1.66277e7i 2.51158i
\(536\) 2.06774e7 3.10874
\(537\) −5.56914e6 + 5.50740e6i −0.833398 + 0.824159i
\(538\) 6.70177e6i 0.998237i
\(539\) −349299. + 37992.6i −0.0517876 + 0.00563283i
\(540\) −1.63868e7 1.69442e7i −2.41829 2.50055i
\(541\) 4.83518e6i 0.710263i 0.934816 + 0.355132i \(0.115564\pi\)
−0.934816 + 0.355132i \(0.884436\pi\)
\(542\) 1.02366e7i 1.49678i
\(543\) 8.93826e6 + 9.03846e6i 1.30093 + 1.31551i
\(544\) −4.65479e6 −0.674378
\(545\) −7.55783e6 −1.08995
\(546\) −7.31982e6 7.40188e6i −1.05080 1.06258i
\(547\) 5.54075e6i 0.791773i −0.918300 0.395886i \(-0.870437\pi\)
0.918300 0.395886i \(-0.129563\pi\)
\(548\) 1.93776e7i 2.75644i
\(549\) 3.72236e6 + 41497.4i 0.527093 + 0.00587611i
\(550\) −1.90086e7 + 2.06752e6i −2.67943 + 0.291436i
\(551\) 3.00674e6i 0.421908i
\(552\) −1.06177e7 + 1.05000e7i −1.48314 + 1.46670i
\(553\) 1.34782e7 1.87421
\(554\) 2.04624e7i 2.83258i
\(555\) 3.55814e6 3.51870e6i 0.490333 0.484897i
\(556\) 5.72136e6i 0.784896i
\(557\) −7.00403e6 −0.956555 −0.478278 0.878209i \(-0.658739\pi\)
−0.478278 + 0.878209i \(0.658739\pi\)
\(558\) −5892.09 + 528526.i −0.000801094 + 0.0718590i
\(559\) 2.75257e6 0.372571
\(560\) −1.86398e7 −2.51172
\(561\) 5.04550e6 + 4.10209e6i 0.676857 + 0.550298i
\(562\) 8.27954e6 1.10577
\(563\) 7.81431e6 1.03901 0.519505 0.854468i \(-0.326117\pi\)
0.519505 + 0.854468i \(0.326117\pi\)
\(564\) −7.05932e6 + 6.98106e6i −0.934469 + 0.924110i
\(565\) −6.42807e6 −0.847148
\(566\) 1.75538e7i 2.30319i
\(567\) −166157. + 7.45131e6i −0.0217051 + 0.973363i
\(568\) 1.30515e7i 1.69742i
\(569\) −1.22848e7 −1.59069 −0.795347 0.606154i \(-0.792712\pi\)
−0.795347 + 0.606154i \(0.792712\pi\)
\(570\) 8.26526e6 + 8.35792e6i 1.06554 + 1.07748i
\(571\) 1.28754e7i 1.65262i −0.563218 0.826308i \(-0.690437\pi\)
0.563218 0.826308i \(-0.309563\pi\)
\(572\) 1.59572e6 + 1.46709e7i 0.203924 + 1.87485i
\(573\) 5.84647e6 5.78166e6i 0.743887 0.735641i
\(574\) 1.12923e7i 1.43055i
\(575\) 1.16496e7i 1.46940i
\(576\) 21921.4 1.96638e6i 0.00275304 0.246951i
\(577\) −9.45884e6 −1.18276 −0.591382 0.806391i \(-0.701418\pi\)
−0.591382 + 0.806391i \(0.701418\pi\)
\(578\) 3.43276e6 0.427389
\(579\) −6.35056e6 + 6.28016e6i −0.787256 + 0.778528i
\(580\) 2.22153e7i 2.74209i
\(581\) 2.57306e6i 0.316235i
\(582\) −7.50722e6 7.59138e6i −0.918696 0.928994i
\(583\) 38932.6 + 357942.i 0.00474397 + 0.0436155i
\(584\) 2.94936e7i 3.57846i
\(585\) 125431. 1.12513e7i 0.0151536 1.35930i
\(586\) −2.64956e7 −3.18735
\(587\) 1.02802e7i 1.23142i 0.787972 + 0.615711i \(0.211131\pi\)
−0.787972 + 0.615711i \(0.788869\pi\)
\(588\) −674634. 682197.i −0.0804683 0.0813704i
\(589\) 181127.i 0.0215127i
\(590\) 3.24335e7 3.83587
\(591\) 3.11946e6 + 3.15443e6i 0.367376 + 0.371494i
\(592\) −6.05009e6 −0.709508
\(593\) 1.25800e7 1.46907 0.734536 0.678569i \(-0.237400\pi\)
0.734536 + 0.678569i \(0.237400\pi\)
\(594\) 9.83171e6 1.18211e7i 1.14331 1.37465i
\(595\) −1.16137e7 −1.34487
\(596\) 4.28324e6 0.493920
\(597\) −4.66266e6 4.71493e6i −0.535424 0.541427i
\(598\) −1.30840e7 −1.49619
\(599\) 6.21604e6i 0.707858i −0.935272 0.353929i \(-0.884845\pi\)
0.935272 0.353929i \(-0.115155\pi\)
\(600\) −2.00011e7 2.02253e7i −2.26817 2.29360i
\(601\) 1.28321e7i 1.44914i −0.689199 0.724572i \(-0.742038\pi\)
0.689199 0.724572i \(-0.257962\pi\)
\(602\) −6.71763e6 −0.755483
\(603\) 144599. 1.29707e7i 0.0161947 1.45268i
\(604\) 3.07987e7i 3.43511i
\(605\) −3.06497e6 1.39228e7i −0.340438 1.54646i
\(606\) 1.00161e7 + 1.01283e7i 1.10794 + 1.12036i
\(607\) 3.31925e6i 0.365652i 0.983145 + 0.182826i \(0.0585245\pi\)
−0.983145 + 0.182826i \(0.941476\pi\)
\(608\) 3.77160e6i 0.413777i
\(609\) 4.99448e6 4.93912e6i 0.545692 0.539642i
\(610\) 1.37155e7 1.49241
\(611\) −4.73923e6 −0.513576
\(612\) −197939. + 1.77553e7i −0.0213625 + 1.91624i
\(613\) 5.25789e6i 0.565145i 0.959246 + 0.282573i \(0.0911878\pi\)
−0.959246 + 0.282573i \(0.908812\pi\)
\(614\) 1.04620e6i 0.111994i
\(615\) −8.67871e6 + 8.58250e6i −0.925268 + 0.915010i
\(616\) −2.12163e6 1.95060e7i −0.225277 2.07117i
\(617\) 8.52105e6i 0.901115i 0.892748 + 0.450557i \(0.148775\pi\)
−0.892748 + 0.450557i \(0.851225\pi\)
\(618\) −1.25176e6 1.26579e6i −0.131840 0.133318i
\(619\) 1.37799e7 1.44550 0.722751 0.691108i \(-0.242877\pi\)
0.722751 + 0.691108i \(0.242877\pi\)
\(620\) 1.33825e6i 0.139816i
\(621\) 6.51225e6 + 6.73377e6i 0.677645 + 0.700695i
\(622\) 1.13641e7i 1.17776i
\(623\) 1.49582e6 0.154405
\(624\) −9.67283e6 + 9.56559e6i −0.994471 + 0.983446i
\(625\) −2.29572e6 −0.235082
\(626\) 2.02036e7 2.06059
\(627\) −3.32377e6 + 4.08817e6i −0.337646 + 0.415298i
\(628\) 2.42717e7 2.45584
\(629\) −3.76958e6 −0.379897
\(630\) −306114. + 2.74588e7i −0.0307278 + 2.75632i
\(631\) −2.97282e6 −0.297231 −0.148616 0.988895i \(-0.547482\pi\)
−0.148616 + 0.988895i \(0.547482\pi\)
\(632\) 4.13633e7i 4.11929i
\(633\) −1.33815e6 + 1.32331e6i −0.132738 + 0.131266i
\(634\) 2.58916e7i 2.55820i
\(635\) −1.34050e7 −1.31926
\(636\) −699076. + 691326.i −0.0685301 + 0.0677704i
\(637\) 457989.i 0.0447205i
\(638\) −1.44055e7 + 1.56686e6i −1.40113 + 0.152398i
\(639\) −8.18702e6 91270.1i −0.793184 0.00884253i
\(640\) 1.99302e7i 1.92337i
\(641\) 1.03887e7i 0.998658i 0.866413 + 0.499329i \(0.166420\pi\)
−0.866413 + 0.499329i \(0.833580\pi\)
\(642\) −2.08248e7 2.10582e7i −1.99408 2.01644i
\(643\) 2.23793e6 0.213462 0.106731 0.994288i \(-0.465962\pi\)
0.106731 + 0.994288i \(0.465962\pi\)
\(644\) 2.19429e7 2.08487
\(645\) −5.10561e6 5.16284e6i −0.483223 0.488641i
\(646\) 8.85457e6i 0.834807i
\(647\) 9.54481e6i 0.896409i 0.893931 + 0.448205i \(0.147936\pi\)
−0.893931 + 0.448205i \(0.852064\pi\)
\(648\) 2.28674e7 + 509922.i 2.13934 + 0.0477053i
\(649\) 1.57199e6 + 1.44527e7i 0.146500 + 1.34690i
\(650\) 2.49233e7i 2.31378i
\(651\) 300868. 297533.i 0.0278243 0.0275158i
\(652\) 4.63244e6 0.426767
\(653\) 1.60519e7i 1.47314i 0.676360 + 0.736571i \(0.263556\pi\)
−0.676360 + 0.736571i \(0.736444\pi\)
\(654\) 9.57165e6 9.46554e6i 0.875069 0.865368i
\(655\) 1.82645e7i 1.66343i
\(656\) 1.47568e7 1.33886
\(657\) 1.85010e7 + 206252.i 1.67217 + 0.0186416i
\(658\) 1.15661e7 1.04141
\(659\) 1.21513e7 1.08996 0.544979 0.838450i \(-0.316538\pi\)
0.544979 + 0.838450i \(0.316538\pi\)
\(660\) 2.45576e7 3.02053e7i 2.19445 2.69913i
\(661\) 8.00011e6 0.712184 0.356092 0.934451i \(-0.384109\pi\)
0.356092 + 0.934451i \(0.384109\pi\)
\(662\) 5.43492e6 0.482001
\(663\) −6.02677e6 + 5.95995e6i −0.532477 + 0.526574i
\(664\) 7.89651e6 0.695048
\(665\) 9.41015e6i 0.825168i
\(666\) −99358.3 + 8.91255e6i −0.00867998 + 0.778603i
\(667\) 8.82854e6i 0.768377i
\(668\) −4.82108e7 −4.18026
\(669\) −3.36870e6 3.40646e6i −0.291002 0.294265i
\(670\) 4.77923e7i 4.11311i
\(671\) 664764. + 6.11176e6i 0.0569982 + 0.524035i
\(672\) 6.26498e6 6.19552e6i 0.535176 0.529243i
\(673\) 7.19089e6i 0.611991i 0.952033 + 0.305995i \(0.0989892\pi\)
−0.952033 + 0.305995i \(0.901011\pi\)
\(674\) 1.58584e6i 0.134465i
\(675\) −1.28270e7 + 1.24050e7i −1.08359 + 1.04794i
\(676\) 6.86528e6 0.577818
\(677\) −2.50078e6 −0.209703 −0.104851 0.994488i \(-0.533437\pi\)
−0.104851 + 0.994488i \(0.533437\pi\)
\(678\) 8.14086e6 8.05061e6i 0.680136 0.672596i
\(679\) 8.54711e6i 0.711450i
\(680\) 3.56415e7i 2.95586i
\(681\) −5.02222e6 5.07852e6i −0.414981 0.419633i
\(682\) −867791. + 94387.8i −0.0714421 + 0.00777061i
\(683\) 1.69294e6i 0.138864i −0.997587 0.0694319i \(-0.977881\pi\)
0.997587 0.0694319i \(-0.0221187\pi\)
\(684\) −1.43864e7 160382.i −1.17574 0.0131074i
\(685\) −2.44003e7 −1.98687
\(686\) 2.25739e7i 1.83145i
\(687\) −2.70228e6 2.73258e6i −0.218443 0.220892i
\(688\) 8.77864e6i 0.707060i
\(689\) −469320. −0.0376636
\(690\) 2.42689e7 + 2.45409e7i 1.94056 + 1.96231i
\(691\) −8.84676e6 −0.704838 −0.352419 0.935842i \(-0.614641\pi\)
−0.352419 + 0.935842i \(0.614641\pi\)
\(692\) −2.33128e7 −1.85067
\(693\) −1.22507e7 + 1.19446e6i −0.969010 + 0.0944800i
\(694\) −1.92884e7 −1.52019
\(695\) −7.20434e6 −0.565760
\(696\) −1.51577e7 1.53276e7i −1.18607 1.19937i
\(697\) 9.19442e6 0.716874
\(698\) 4.49348e6i 0.349095i
\(699\) −6.56869e6 6.64232e6i −0.508494 0.514194i
\(700\) 4.17984e7i 3.22415i
\(701\) 1.16656e6 0.0896631 0.0448315 0.998995i \(-0.485725\pi\)
0.0448315 + 0.998995i \(0.485725\pi\)
\(702\) 1.39325e7 + 1.44064e7i 1.06705 + 1.10335i
\(703\) 3.05434e6i 0.233093i
\(704\) 3.22861e6 351169.i 0.245518 0.0267045i
\(705\) 8.79056e6 + 8.88911e6i 0.666107 + 0.673574i
\(706\) 3.44385e7i 2.60035i
\(707\) 1.14035e7i 0.858002i
\(708\) −2.82267e7 + 2.79138e7i −2.11630 + 2.09284i
\(709\) 9.21961e6 0.688806 0.344403 0.938822i \(-0.388081\pi\)
0.344403 + 0.938822i \(0.388081\pi\)
\(710\) −3.01662e7 −2.24582
\(711\) −2.59467e7 289257.i −1.92490 0.0214590i
\(712\) 4.59055e6i 0.339363i
\(713\) 531833.i 0.0391788i
\(714\) 1.47083e7 1.45452e7i 1.07973 1.06776i
\(715\) 1.84736e7 2.00934e6i 1.35141 0.146990i
\(716\) 3.53213e7i 2.57486i
\(717\) −3.92242e6 3.96639e6i −0.284942 0.288136i
\(718\) 5.91956e6 0.428527
\(719\) 2.18224e7i 1.57427i −0.616779 0.787136i \(-0.711563\pi\)
0.616779 0.787136i \(-0.288437\pi\)
\(720\) 3.58833e7 + 400032.i 2.57965 + 0.0287583i
\(721\) 1.42515e6i 0.102099i
\(722\) −1.78694e7 −1.27575
\(723\) 6.32485e6 6.25473e6i 0.449992 0.445003i
\(724\) −5.73249e7 −4.06440
\(725\) 1.68172e7 1.18826
\(726\) 2.13188e7 + 1.37940e7i 1.50114 + 0.971289i
\(727\) −741663. −0.0520440 −0.0260220 0.999661i \(-0.508284\pi\)
−0.0260220 + 0.999661i \(0.508284\pi\)
\(728\) 2.55756e7 1.78853
\(729\) 479782. 1.43409e7i 0.0334368 0.999441i
\(730\) 6.81693e7 4.73459
\(731\) 5.46963e6i 0.378586i
\(732\) −1.19365e7 + 1.18042e7i −0.823380 + 0.814252i
\(733\) 6.80074e6i 0.467516i −0.972295 0.233758i \(-0.924898\pi\)
0.972295 0.233758i \(-0.0751023\pi\)
\(734\) 3.18548e6 0.218240
\(735\) −859023. + 849500.i −0.0586525 + 0.0580023i
\(736\) 1.10743e7i 0.753570i
\(737\) 2.12967e7 2.31640e6i 1.44425 0.157088i
\(738\) 242346. 2.17387e7i 0.0163793 1.46924i
\(739\) 9.15287e6i 0.616519i −0.951302 0.308259i \(-0.900254\pi\)
0.951302 0.308259i \(-0.0997465\pi\)
\(740\) 2.25669e7i 1.51493i
\(741\) −4.82912e6 4.88325e6i −0.323089 0.326711i
\(742\) 1.14537e6 0.0763725
\(743\) −1.25723e7 −0.835490 −0.417745 0.908564i \(-0.637180\pi\)
−0.417745 + 0.908564i \(0.637180\pi\)
\(744\) −913103. 923339.i −0.0604766 0.0611546i
\(745\) 5.39346e6i 0.356022i
\(746\) 2.29681e7i 1.51105i
\(747\) 55221.0 4.95338e6i 0.00362078 0.324788i
\(748\) −2.91525e7 + 3.17086e6i −1.90512 + 0.207216i
\(749\) 2.37094e7i 1.54424i
\(750\) −1.57361e7 + 1.55616e7i −1.02151 + 1.01019i
\(751\) 1.79363e7 1.16047 0.580235 0.814449i \(-0.302961\pi\)
0.580235 + 0.814449i \(0.302961\pi\)
\(752\) 1.51146e7i 0.974657i
\(753\) −9.12903e6 + 9.02783e6i −0.586729 + 0.580224i
\(754\) 1.88880e7i 1.20992i
\(755\) 3.87818e7 2.47606
\(756\) −2.33659e7 2.41607e7i −1.48688 1.53746i
\(757\) 1.91439e7 1.21420 0.607099 0.794626i \(-0.292333\pi\)
0.607099 + 0.794626i \(0.292333\pi\)
\(758\) −3.92965e7 −2.48417
\(759\) −9.75940e6 + 1.20039e7i −0.614920 + 0.756340i
\(760\) −2.88789e7 −1.81362
\(761\) 5.64221e6 0.353173 0.176586 0.984285i \(-0.443494\pi\)
0.176586 + 0.984285i \(0.443494\pi\)
\(762\) 1.69768e7 1.67886e7i 1.05918 1.04744i
\(763\) −1.07767e7 −0.670153
\(764\) 3.70803e7i 2.29831i
\(765\) 2.23575e7 + 249245.i 1.38124 + 0.0153983i
\(766\) 2.34260e7i 1.44253i
\(767\) −1.89498e7 −1.16310
\(768\) 2.21224e7 + 2.23704e7i 1.35341 + 1.36858i
\(769\) 5.21462e6i 0.317985i −0.987280 0.158992i \(-0.949175\pi\)
0.987280 0.158992i \(-0.0508246\pi\)
\(770\) −4.50847e7 + 4.90377e6i −2.74033 + 0.298060i
\(771\) 1.84491e7 1.82446e7i 1.11774 1.10535i
\(772\) 4.02774e7i 2.43230i
\(773\) 6.01544e6i 0.362092i −0.983475 0.181046i \(-0.942052\pi\)
0.983475 0.181046i \(-0.0579483\pi\)
\(774\) 1.29320e7 + 144168.i 0.775916 + 0.00865003i
\(775\) 1.01307e6 0.0605880