Properties

Label 33.6.d.b.32.8
Level $33$
Weight $6$
Character 33.32
Analytic conductor $5.293$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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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 32.8
Root \(-6.72395 - 15.5879i\) of defining polynomial
Character \(\chi\) \(=\) 33.32
Dual form 33.6.d.b.32.7

$q$-expansion

\(f(q)\) \(=\) \(q-3.58998 q^{2} +(0.133977 + 15.5879i) q^{3} -19.1121 q^{4} +11.8803i q^{5} +(-0.480974 - 55.9601i) q^{6} -150.804i q^{7} +183.491 q^{8} +(-242.964 + 4.17684i) q^{9} +O(q^{10})\) \(q-3.58998 q^{2} +(0.133977 + 15.5879i) q^{3} -19.1121 q^{4} +11.8803i q^{5} +(-0.480974 - 55.9601i) q^{6} -150.804i q^{7} +183.491 q^{8} +(-242.964 + 4.17684i) q^{9} -42.6500i q^{10} +(-352.626 - 191.588i) q^{11} +(-2.56058 - 297.917i) q^{12} -778.957i q^{13} +541.384i q^{14} +(-185.188 + 1.59169i) q^{15} -47.1432 q^{16} -1255.02 q^{17} +(872.236 - 14.9947i) q^{18} +1214.37i q^{19} -227.057i q^{20} +(2350.72 - 20.2043i) q^{21} +(1265.92 + 687.798i) q^{22} +880.210i q^{23} +(24.5836 + 2860.24i) q^{24} +2983.86 q^{25} +2796.44i q^{26} +(-97.6596 - 3786.74i) q^{27} +2882.18i q^{28} -3201.27 q^{29} +(664.823 - 5.71411i) q^{30} -6446.10 q^{31} -5702.47 q^{32} +(2939.21 - 5522.36i) q^{33} +4505.50 q^{34} +1791.60 q^{35} +(4643.54 - 79.8279i) q^{36} -9311.53 q^{37} -4359.58i q^{38} +(12142.3 - 104.362i) q^{39} +2179.93i q^{40} -5398.38 q^{41} +(-8439.03 + 72.5330i) q^{42} -20867.6i q^{43} +(6739.40 + 3661.65i) q^{44} +(-49.6220 - 2886.48i) q^{45} -3159.93i q^{46} +11289.4i q^{47} +(-6.31611 - 734.863i) q^{48} -5934.91 q^{49} -10712.0 q^{50} +(-168.144 - 19563.1i) q^{51} +14887.5i q^{52} +23978.4i q^{53} +(350.596 + 13594.3i) q^{54} +(2276.12 - 4189.29i) q^{55} -27671.2i q^{56} +(-18929.5 + 162.698i) q^{57} +11492.5 q^{58} -22954.8i q^{59} +(3539.33 - 30.4204i) q^{60} +27244.5i q^{61} +23141.4 q^{62} +(629.884 + 36640.0i) q^{63} +21980.3 q^{64} +9254.23 q^{65} +(-10551.7 + 19825.1i) q^{66} +20257.5 q^{67} +23986.0 q^{68} +(-13720.6 + 117.928i) q^{69} -6431.79 q^{70} -56465.7i q^{71} +(-44581.8 + 766.412i) q^{72} +12025.4i q^{73} +33428.2 q^{74} +(399.768 + 46512.0i) q^{75} -23209.2i q^{76} +(-28892.3 + 53177.5i) q^{77} +(-43590.5 + 374.658i) q^{78} +11065.5i q^{79} -560.075i q^{80} +(59014.1 - 2029.64i) q^{81} +19380.1 q^{82} +51574.3 q^{83} +(-44927.1 + 386.146i) q^{84} -14910.0i q^{85} +74914.4i q^{86} +(-428.897 - 49901.1i) q^{87} +(-64703.7 - 35154.8i) q^{88} -84147.7i q^{89} +(178.142 + 10362.4i) q^{90} -117470. q^{91} -16822.6i q^{92} +(-863.629 - 100481. i) q^{93} -40528.8i q^{94} -14427.1 q^{95} +(-764.000 - 88889.5i) q^{96} +99342.9 q^{97} +21306.2 q^{98} +(86475.6 + 45076.2i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.58998 −0.634624 −0.317312 0.948321i \(-0.602780\pi\)
−0.317312 + 0.948321i \(0.602780\pi\)
\(3\) 0.133977 + 15.5879i 0.00859463 + 0.999963i
\(4\) −19.1121 −0.597252
\(5\) 11.8803i 0.212521i 0.994338 + 0.106261i \(0.0338877\pi\)
−0.994338 + 0.106261i \(0.966112\pi\)
\(6\) −0.480974 55.9601i −0.00545436 0.634601i
\(7\) 150.804i 1.16324i −0.813461 0.581619i \(-0.802420\pi\)
0.813461 0.581619i \(-0.197580\pi\)
\(8\) 183.491 1.01365
\(9\) −242.964 + 4.17684i −0.999852 + 0.0171886i
\(10\) 42.6500i 0.134871i
\(11\) −352.626 191.588i −0.878683 0.477405i
\(12\) −2.56058 297.917i −0.00513316 0.597230i
\(13\) 778.957i 1.27837i −0.769055 0.639183i \(-0.779273\pi\)
0.769055 0.639183i \(-0.220727\pi\)
\(14\) 541.384i 0.738219i
\(15\) −185.188 + 1.59169i −0.212513 + 0.00182654i
\(16\) −47.1432 −0.0460383
\(17\) −1255.02 −1.05324 −0.526622 0.850100i \(-0.676542\pi\)
−0.526622 + 0.850100i \(0.676542\pi\)
\(18\) 872.236 14.9947i 0.634531 0.0109083i
\(19\) 1214.37i 0.771736i 0.922554 + 0.385868i \(0.126098\pi\)
−0.922554 + 0.385868i \(0.873902\pi\)
\(20\) 227.057i 0.126929i
\(21\) 2350.72 20.2043i 1.16319 0.00999759i
\(22\) 1265.92 + 687.798i 0.557634 + 0.302973i
\(23\) 880.210i 0.346950i 0.984838 + 0.173475i \(0.0554996\pi\)
−0.984838 + 0.173475i \(0.944500\pi\)
\(24\) 24.5836 + 2860.24i 0.00871199 + 1.01362i
\(25\) 2983.86 0.954835
\(26\) 2796.44i 0.811282i
\(27\) −97.6596 3786.74i −0.0257813 0.999668i
\(28\) 2882.18i 0.694746i
\(29\) −3201.27 −0.706851 −0.353425 0.935463i \(-0.614983\pi\)
−0.353425 + 0.935463i \(0.614983\pi\)
\(30\) 664.823 5.71411i 0.134866 0.00115917i
\(31\) −6446.10 −1.20474 −0.602369 0.798218i \(-0.705777\pi\)
−0.602369 + 0.798218i \(0.705777\pi\)
\(32\) −5702.47 −0.984438
\(33\) 2939.21 5522.36i 0.469836 0.882754i
\(34\) 4505.50 0.668414
\(35\) 1791.60 0.247212
\(36\) 4643.54 79.8279i 0.597164 0.0102659i
\(37\) −9311.53 −1.11819 −0.559096 0.829103i \(-0.688852\pi\)
−0.559096 + 0.829103i \(0.688852\pi\)
\(38\) 4359.58i 0.489762i
\(39\) 12142.3 104.362i 1.27832 0.0109871i
\(40\) 2179.93i 0.215423i
\(41\) −5398.38 −0.501538 −0.250769 0.968047i \(-0.580683\pi\)
−0.250769 + 0.968047i \(0.580683\pi\)
\(42\) −8439.03 + 72.5330i −0.738192 + 0.00634472i
\(43\) 20867.6i 1.72108i −0.509379 0.860542i \(-0.670125\pi\)
0.509379 0.860542i \(-0.329875\pi\)
\(44\) 6739.40 + 3661.65i 0.524795 + 0.285131i
\(45\) −49.6220 2886.48i −0.00365294 0.212490i
\(46\) 3159.93i 0.220183i
\(47\) 11289.4i 0.745465i 0.927939 + 0.372732i \(0.121579\pi\)
−0.927939 + 0.372732i \(0.878421\pi\)
\(48\) −6.31611 734.863i −0.000395682 0.0460366i
\(49\) −5934.91 −0.353122
\(50\) −10712.0 −0.605961
\(51\) −168.144 19563.1i −0.00905223 1.05320i
\(52\) 14887.5i 0.763506i
\(53\) 23978.4i 1.17255i 0.810113 + 0.586274i \(0.199406\pi\)
−0.810113 + 0.586274i \(0.800594\pi\)
\(54\) 350.596 + 13594.3i 0.0163615 + 0.634413i
\(55\) 2276.12 4189.29i 0.101459 0.186739i
\(56\) 27671.2i 1.17912i
\(57\) −18929.5 + 162.698i −0.771707 + 0.00663278i
\(58\) 11492.5 0.448585
\(59\) 22954.8i 0.858507i −0.903184 0.429254i \(-0.858777\pi\)
0.903184 0.429254i \(-0.141223\pi\)
\(60\) 3539.33 30.4204i 0.126924 0.00109090i
\(61\) 27244.5i 0.937462i 0.883341 + 0.468731i \(0.155289\pi\)
−0.883341 + 0.468731i \(0.844711\pi\)
\(62\) 23141.4 0.764557
\(63\) 629.884 + 36640.0i 0.0199945 + 1.16307i
\(64\) 21980.3 0.670787
\(65\) 9254.23 0.271680
\(66\) −10551.7 + 19825.1i −0.298169 + 0.560217i
\(67\) 20257.5 0.551312 0.275656 0.961256i \(-0.411105\pi\)
0.275656 + 0.961256i \(0.411105\pi\)
\(68\) 23986.0 0.629051
\(69\) −13720.6 + 117.928i −0.346937 + 0.00298191i
\(70\) −6431.79 −0.156887
\(71\) 56465.7i 1.32935i −0.747133 0.664674i \(-0.768570\pi\)
0.747133 0.664674i \(-0.231430\pi\)
\(72\) −44581.8 + 766.412i −1.01351 + 0.0174233i
\(73\) 12025.4i 0.264116i 0.991242 + 0.132058i \(0.0421585\pi\)
−0.991242 + 0.132058i \(0.957842\pi\)
\(74\) 33428.2 0.709632
\(75\) 399.768 + 46512.0i 0.00820645 + 0.954800i
\(76\) 23209.2i 0.460921i
\(77\) −28892.3 + 53177.5i −0.555336 + 1.02212i
\(78\) −43590.5 + 374.658i −0.811252 + 0.00697267i
\(79\) 11065.5i 0.199481i 0.995013 + 0.0997407i \(0.0318013\pi\)
−0.995013 + 0.0997407i \(0.968199\pi\)
\(80\) 560.075i 0.00978411i
\(81\) 59014.1 2029.64i 0.999409 0.0343722i
\(82\) 19380.1 0.318288
\(83\) 51574.3 0.821747 0.410873 0.911692i \(-0.365224\pi\)
0.410873 + 0.911692i \(0.365224\pi\)
\(84\) −44927.1 + 386.146i −0.694720 + 0.00597108i
\(85\) 14910.0i 0.223836i
\(86\) 74914.4i 1.09224i
\(87\) −428.897 49901.1i −0.00607512 0.706825i
\(88\) −64703.7 35154.8i −0.890682 0.483924i
\(89\) 84147.7i 1.12608i −0.826431 0.563038i \(-0.809633\pi\)
0.826431 0.563038i \(-0.190367\pi\)
\(90\) 178.142 + 10362.4i 0.00231825 + 0.134851i
\(91\) −117470. −1.48704
\(92\) 16822.6i 0.207216i
\(93\) −863.629 100481.i −0.0103543 1.20469i
\(94\) 40528.8i 0.473090i
\(95\) −14427.1 −0.164010
\(96\) −764.000 88889.5i −0.00846088 0.984402i
\(97\) 99342.9 1.07203 0.536016 0.844208i \(-0.319929\pi\)
0.536016 + 0.844208i \(0.319929\pi\)
\(98\) 21306.2 0.224100
\(99\) 86475.6 + 45076.2i 0.886759 + 0.462231i
\(100\) −57027.7 −0.570277
\(101\) 8413.56 0.0820685 0.0410343 0.999158i \(-0.486935\pi\)
0.0410343 + 0.999158i \(0.486935\pi\)
\(102\) 603.633 + 70231.1i 0.00574477 + 0.668389i
\(103\) 11603.9 0.107773 0.0538864 0.998547i \(-0.482839\pi\)
0.0538864 + 0.998547i \(0.482839\pi\)
\(104\) 142932.i 1.29582i
\(105\) 240.033 + 27927.2i 0.00212470 + 0.247203i
\(106\) 86082.0i 0.744128i
\(107\) −181478. −1.53238 −0.766188 0.642616i \(-0.777849\pi\)
−0.766188 + 0.642616i \(0.777849\pi\)
\(108\) 1866.48 + 72372.3i 0.0153980 + 0.597053i
\(109\) 153350.i 1.23628i 0.786067 + 0.618141i \(0.212114\pi\)
−0.786067 + 0.618141i \(0.787886\pi\)
\(110\) −8171.23 + 15039.5i −0.0643881 + 0.118509i
\(111\) −1247.53 145147.i −0.00961045 1.11815i
\(112\) 7109.40i 0.0535535i
\(113\) 209395.i 1.54266i 0.636435 + 0.771330i \(0.280408\pi\)
−0.636435 + 0.771330i \(0.719592\pi\)
\(114\) 67956.6 584.083i 0.489744 0.00420933i
\(115\) −10457.1 −0.0737341
\(116\) 61182.9 0.422168
\(117\) 3253.57 + 189259.i 0.0219733 + 1.27818i
\(118\) 82407.3i 0.544830i
\(119\) 189262.i 1.22517i
\(120\) −33980.5 + 292.060i −0.215415 + 0.00185148i
\(121\) 87638.8 + 135118.i 0.544168 + 0.838976i
\(122\) 97807.0i 0.594936i
\(123\) −723.259 84149.3i −0.00431053 0.501519i
\(124\) 123198. 0.719532
\(125\) 72575.0i 0.415443i
\(126\) −2261.27 131537.i −0.0126890 0.738110i
\(127\) 117065.i 0.644046i −0.946732 0.322023i \(-0.895637\pi\)
0.946732 0.322023i \(-0.104363\pi\)
\(128\) 103570. 0.558740
\(129\) 325282. 2795.78i 1.72102 0.0147921i
\(130\) −33222.5 −0.172414
\(131\) −176896. −0.900614 −0.450307 0.892874i \(-0.648686\pi\)
−0.450307 + 0.892874i \(0.648686\pi\)
\(132\) −56174.4 + 105544.i −0.280610 + 0.527226i
\(133\) 183133. 0.897712
\(134\) −72723.8 −0.349876
\(135\) 44987.5 1160.22i 0.212450 0.00547908i
\(136\) −230285. −1.06763
\(137\) 347712.i 1.58277i −0.611318 0.791385i \(-0.709360\pi\)
0.611318 0.791385i \(-0.290640\pi\)
\(138\) 49256.7 423.359i 0.220175 0.00189239i
\(139\) 8720.60i 0.0382833i −0.999817 0.0191417i \(-0.993907\pi\)
0.999817 0.0191417i \(-0.00609335\pi\)
\(140\) −34241.1 −0.147648
\(141\) −175978. + 1512.52i −0.745437 + 0.00640699i
\(142\) 202711.i 0.843637i
\(143\) −149239. + 274680.i −0.610299 + 1.12328i
\(144\) 11454.1 196.909i 0.0460315 0.000791335i
\(145\) 38032.0i 0.150221i
\(146\) 43171.1i 0.167614i
\(147\) −795.142 92512.7i −0.00303495 0.353109i
\(148\) 177962. 0.667843
\(149\) −354108. −1.30668 −0.653342 0.757063i \(-0.726634\pi\)
−0.653342 + 0.757063i \(0.726634\pi\)
\(150\) −1435.16 166977.i −0.00520801 0.605939i
\(151\) 493279.i 1.76056i −0.474457 0.880278i \(-0.657356\pi\)
0.474457 0.880278i \(-0.342644\pi\)
\(152\) 222827.i 0.782274i
\(153\) 304925. 5242.02i 1.05309 0.0181038i
\(154\) 103723. 190906.i 0.352430 0.648661i
\(155\) 76581.5i 0.256032i
\(156\) −232064. + 1994.58i −0.763478 + 0.00656205i
\(157\) −94457.3 −0.305834 −0.152917 0.988239i \(-0.548867\pi\)
−0.152917 + 0.988239i \(0.548867\pi\)
\(158\) 39724.8i 0.126596i
\(159\) −373773. + 3212.56i −1.17251 + 0.0100776i
\(160\) 67747.0i 0.209214i
\(161\) 132739. 0.403585
\(162\) −211859. + 7286.37i −0.634249 + 0.0218134i
\(163\) −296304. −0.873510 −0.436755 0.899580i \(-0.643872\pi\)
−0.436755 + 0.899580i \(0.643872\pi\)
\(164\) 103174. 0.299544
\(165\) 65607.2 + 34918.7i 0.187604 + 0.0998500i
\(166\) −185151. −0.521501
\(167\) 571023. 1.58439 0.792196 0.610267i \(-0.208938\pi\)
0.792196 + 0.610267i \(0.208938\pi\)
\(168\) 431336. 3707.31i 1.17908 0.0101341i
\(169\) −235481. −0.634219
\(170\) 53526.6i 0.142052i
\(171\) −5072.24 295049.i −0.0132651 0.771622i
\(172\) 398824.i 1.02792i
\(173\) 12657.7 0.0321545 0.0160772 0.999871i \(-0.494882\pi\)
0.0160772 + 0.999871i \(0.494882\pi\)
\(174\) 1539.73 + 179144.i 0.00385542 + 0.448568i
\(175\) 449979.i 1.11070i
\(176\) 16623.9 + 9032.09i 0.0404531 + 0.0219789i
\(177\) 357817. 3075.42i 0.858476 0.00737855i
\(178\) 302089.i 0.714635i
\(179\) 46770.9i 0.109105i −0.998511 0.0545523i \(-0.982627\pi\)
0.998511 0.0545523i \(-0.0173732\pi\)
\(180\) 948.379 + 55166.6i 0.00218173 + 0.126910i
\(181\) 118107. 0.267965 0.133983 0.990984i \(-0.457223\pi\)
0.133983 + 0.990984i \(0.457223\pi\)
\(182\) 421715. 0.943714
\(183\) −424683. + 3650.13i −0.937427 + 0.00805714i
\(184\) 161511.i 0.351688i
\(185\) 110624.i 0.237639i
\(186\) 3100.41 + 360725.i 0.00657108 + 0.764528i
\(187\) 442553. + 240447.i 0.925467 + 0.502824i
\(188\) 215764.i 0.445230i
\(189\) −571056. + 14727.5i −1.16285 + 0.0299898i
\(190\) 51793.0 0.104085
\(191\) 540991.i 1.07302i −0.843895 0.536509i \(-0.819743\pi\)
0.843895 0.536509i \(-0.180257\pi\)
\(192\) 2944.86 + 342627.i 0.00576516 + 0.670762i
\(193\) 610969.i 1.18066i 0.807161 + 0.590331i \(0.201003\pi\)
−0.807161 + 0.590331i \(0.798997\pi\)
\(194\) −356639. −0.680337
\(195\) 1239.85 + 144254.i 0.00233498 + 0.271670i
\(196\) 113428. 0.210903
\(197\) −365903. −0.671739 −0.335869 0.941909i \(-0.609030\pi\)
−0.335869 + 0.941909i \(0.609030\pi\)
\(198\) −310446. 161823.i −0.562759 0.293343i
\(199\) −218381. −0.390915 −0.195457 0.980712i \(-0.562619\pi\)
−0.195457 + 0.980712i \(0.562619\pi\)
\(200\) 547512. 0.967873
\(201\) 2714.03 + 315771.i 0.00473833 + 0.551292i
\(202\) −30204.5 −0.0520827
\(203\) 482765.i 0.822235i
\(204\) 3213.58 + 373891.i 0.00540646 + 0.629028i
\(205\) 64134.3i 0.106587i
\(206\) −41657.6 −0.0683953
\(207\) −3676.49 213859.i −0.00596359 0.346899i
\(208\) 36722.5i 0.0588538i
\(209\) 232660. 428220.i 0.368431 0.678111i
\(210\) −861.713 100258.i −0.00134839 0.156881i
\(211\) 697135.i 1.07798i −0.842312 0.538990i \(-0.818806\pi\)
0.842312 0.538990i \(-0.181194\pi\)
\(212\) 458277.i 0.700307i
\(213\) 880181. 7565.11i 1.32930 0.0114253i
\(214\) 651503. 0.972483
\(215\) 247914. 0.365767
\(216\) −17919.7 694833.i −0.0261334 1.01332i
\(217\) 972099.i 1.40140i
\(218\) 550523.i 0.784575i
\(219\) −187451. + 1611.13i −0.264106 + 0.00226998i
\(220\) −43501.4 + 80066.1i −0.0605964 + 0.111530i
\(221\) 977607.i 1.34643i
\(222\) 4478.61 + 521075.i 0.00609903 + 0.709606i
\(223\) −1.13148e6 −1.52365 −0.761826 0.647781i \(-0.775697\pi\)
−0.761826 + 0.647781i \(0.775697\pi\)
\(224\) 859957.i 1.14514i
\(225\) −724971. + 12463.1i −0.954694 + 0.0164123i
\(226\) 751724.i 0.979010i
\(227\) 1.33675e6 1.72181 0.860904 0.508767i \(-0.169899\pi\)
0.860904 + 0.508767i \(0.169899\pi\)
\(228\) 361782. 3109.50i 0.460904 0.00396144i
\(229\) 936509. 1.18011 0.590056 0.807362i \(-0.299106\pi\)
0.590056 + 0.807362i \(0.299106\pi\)
\(230\) 37540.9 0.0467935
\(231\) −832795. 443246.i −1.02685 0.546531i
\(232\) −587405. −0.716503
\(233\) −675682. −0.815366 −0.407683 0.913124i \(-0.633663\pi\)
−0.407683 + 0.913124i \(0.633663\pi\)
\(234\) −11680.3 679434.i −0.0139448 0.811162i
\(235\) −134122. −0.158427
\(236\) 438714.i 0.512745i
\(237\) −172487. + 1482.52i −0.199474 + 0.00171447i
\(238\) 679448.i 0.777524i
\(239\) −596353. −0.675319 −0.337659 0.941268i \(-0.609635\pi\)
−0.337659 + 0.941268i \(0.609635\pi\)
\(240\) 8730.38 75.0372i 0.00978374 8.40908e-5i
\(241\) 1.24321e6i 1.37880i −0.724381 0.689400i \(-0.757874\pi\)
0.724381 0.689400i \(-0.242126\pi\)
\(242\) −314621. 485070.i −0.345342 0.532435i
\(243\) 39544.4 + 919633.i 0.0429604 + 0.999077i
\(244\) 520698.i 0.559901i
\(245\) 70508.5i 0.0750458i
\(246\) 2596.48 + 302094.i 0.00273557 + 0.318276i
\(247\) 945945. 0.986560
\(248\) −1.18280e6 −1.22119
\(249\) 6909.77 + 803934.i 0.00706261 + 0.821716i
\(250\) 260543.i 0.263651i
\(251\) 1.76567e6i 1.76899i −0.466551 0.884494i \(-0.654504\pi\)
0.466551 0.884494i \(-0.345496\pi\)
\(252\) −12038.4 700266.i −0.0119417 0.694643i
\(253\) 168638. 310385.i 0.165636 0.304859i
\(254\) 420260.i 0.408727i
\(255\) 232415. 1997.60i 0.223828 0.00192379i
\(256\) −1.07519e6 −1.02538
\(257\) 347788.i 0.328459i 0.986422 + 0.164230i \(0.0525138\pi\)
−0.986422 + 0.164230i \(0.947486\pi\)
\(258\) −1.16776e6 + 10036.8i −1.09220 + 0.00938742i
\(259\) 1.40422e6i 1.30072i
\(260\) −176867. −0.162261
\(261\) 777794. 13371.2i 0.706746 0.0121498i
\(262\) 635051. 0.571552
\(263\) 985521. 0.878570 0.439285 0.898348i \(-0.355232\pi\)
0.439285 + 0.898348i \(0.355232\pi\)
\(264\) 539319. 1.01330e6i 0.476251 0.894808i
\(265\) −284871. −0.249191
\(266\) −657443. −0.569710
\(267\) 1.31169e6 11273.9i 1.12603 0.00967820i
\(268\) −387162. −0.329272
\(269\) 1.36787e6i 1.15257i 0.817250 + 0.576283i \(0.195497\pi\)
−0.817250 + 0.576283i \(0.804503\pi\)
\(270\) −161504. + 4165.18i −0.134826 + 0.00347716i
\(271\) 346976.i 0.286996i 0.989651 + 0.143498i \(0.0458351\pi\)
−0.989651 + 0.143498i \(0.954165\pi\)
\(272\) 59165.7 0.0484895
\(273\) −15738.3 1.83111e6i −0.0127806 1.48699i
\(274\) 1.24828e6i 1.00446i
\(275\) −1.05219e6 571672.i −0.838997 0.455843i
\(276\) 262229. 2253.85i 0.207209 0.00178095i
\(277\) 1.92307e6i 1.50590i 0.658079 + 0.752949i \(0.271369\pi\)
−0.658079 + 0.752949i \(0.728631\pi\)
\(278\) 31306.8i 0.0242955i
\(279\) 1.56617e6 26924.3i 1.20456 0.0207078i
\(280\) 328742. 0.250588
\(281\) 1.51815e6 1.14696 0.573482 0.819218i \(-0.305592\pi\)
0.573482 + 0.819218i \(0.305592\pi\)
\(282\) 631758. 5429.93i 0.473073 0.00406603i
\(283\) 195988.i 0.145466i 0.997351 + 0.0727332i \(0.0231721\pi\)
−0.997351 + 0.0727332i \(0.976828\pi\)
\(284\) 1.07918e6i 0.793956i
\(285\) −1932.90 224888.i −0.00140961 0.164004i
\(286\) 535765. 986096.i 0.387310 0.712860i
\(287\) 814098.i 0.583408i
\(288\) 1.38550e6 23818.3i 0.984293 0.0169211i
\(289\) 155220. 0.109321
\(290\) 136534.i 0.0953337i
\(291\) 13309.7 + 1.54855e6i 0.00921371 + 1.07199i
\(292\) 229831.i 0.157744i
\(293\) −2.75485e6 −1.87469 −0.937345 0.348403i \(-0.886724\pi\)
−0.937345 + 0.348403i \(0.886724\pi\)
\(294\) 2854.54 + 332119.i 0.00192605 + 0.224091i
\(295\) 272710. 0.182451
\(296\) −1.70858e6 −1.13346
\(297\) −691057. + 1.35401e6i −0.454593 + 0.890699i
\(298\) 1.27124e6 0.829254
\(299\) 685646. 0.443529
\(300\) −7640.40 888941.i −0.00490132 0.570256i
\(301\) −3.14693e6 −2.00203
\(302\) 1.77086e6i 1.11729i
\(303\) 1127.22 + 131150.i 0.000705348 + 0.0820655i
\(304\) 57249.5i 0.0355294i
\(305\) −323672. −0.199230
\(306\) −1.09467e6 + 18818.7i −0.668315 + 0.0114891i
\(307\) 684538.i 0.414526i 0.978285 + 0.207263i \(0.0664556\pi\)
−0.978285 + 0.207263i \(0.933544\pi\)
\(308\) 552192. 1.01633e6i 0.331675 0.610461i
\(309\) 1554.65 + 180880.i 0.000926268 + 0.107769i
\(310\) 274926.i 0.162484i
\(311\) 414984.i 0.243294i 0.992573 + 0.121647i \(0.0388175\pi\)
−0.992573 + 0.121647i \(0.961182\pi\)
\(312\) 2.22800e6 19149.6i 1.29577 0.0111371i
\(313\) 1.28268e6 0.740043 0.370022 0.929023i \(-0.379350\pi\)
0.370022 + 0.929023i \(0.379350\pi\)
\(314\) 339099. 0.194090
\(315\) −435294. + 7483.21i −0.247176 + 0.00424924i
\(316\) 211484.i 0.119141i
\(317\) 2.70836e6i 1.51376i −0.653553 0.756881i \(-0.726722\pi\)
0.653553 0.756881i \(-0.273278\pi\)
\(318\) 1.34184e6 11533.0i 0.744101 0.00639550i
\(319\) 1.12885e6 + 613326.i 0.621098 + 0.337454i
\(320\) 261133.i 0.142556i
\(321\) −24313.9 2.82886e6i −0.0131702 1.53232i
\(322\) −476532. −0.256125
\(323\) 1.52407e6i 0.812825i
\(324\) −1.12788e6 + 38790.6i −0.596899 + 0.0205288i
\(325\) 2.32430e6i 1.22063i
\(326\) 1.06372e6 0.554351
\(327\) −2.39040e6 + 20545.4i −1.23624 + 0.0106254i
\(328\) −990555. −0.508386
\(329\) 1.70249e6 0.867153
\(330\) −235528. 125357.i −0.119058 0.0633672i
\(331\) −1.10525e6 −0.554486 −0.277243 0.960800i \(-0.589421\pi\)
−0.277243 + 0.960800i \(0.589421\pi\)
\(332\) −985691. −0.490790
\(333\) 2.26237e6 38892.7i 1.11803 0.0192202i
\(334\) −2.04996e6 −1.00549
\(335\) 240664.i 0.117165i
\(336\) −110820. + 952.496i −0.0535515 + 0.000460272i
\(337\) 1.20295e6i 0.576996i −0.957480 0.288498i \(-0.906844\pi\)
0.957480 0.288498i \(-0.0931559\pi\)
\(338\) 845371. 0.402491
\(339\) −3.26403e6 + 28054.1i −1.54260 + 0.0132586i
\(340\) 284961.i 0.133687i
\(341\) 2.27306e6 + 1.23500e6i 1.05858 + 0.575149i
\(342\) 18209.2 + 1.05922e6i 0.00841834 + 0.489690i
\(343\) 1.63956e6i 0.752473i
\(344\) 3.82903e6i 1.74459i
\(345\) −1401.02 163005.i −0.000633718 0.0737314i
\(346\) −45441.0 −0.0204060
\(347\) −1.61441e6 −0.719765 −0.359882 0.932998i \(-0.617183\pi\)
−0.359882 + 0.932998i \(0.617183\pi\)
\(348\) 8197.10 + 953712.i 0.00362838 + 0.422152i
\(349\) 3.17188e6i 1.39397i −0.717085 0.696986i \(-0.754524\pi\)
0.717085 0.696986i \(-0.245476\pi\)
\(350\) 1.61541e6i 0.704877i
\(351\) −2.94970e6 + 76072.6i −1.27794 + 0.0329580i
\(352\) 2.01084e6 + 1.09253e6i 0.865009 + 0.469976i
\(353\) 675430.i 0.288499i 0.989541 + 0.144249i \(0.0460767\pi\)
−0.989541 + 0.144249i \(0.953923\pi\)
\(354\) −1.28456e6 + 11040.7i −0.544810 + 0.00468261i
\(355\) 670829. 0.282515
\(356\) 1.60824e6i 0.672551i
\(357\) −2.95020e6 + 25356.8i −1.22513 + 0.0105299i
\(358\) 167906.i 0.0692404i
\(359\) 2.48053e6 1.01580 0.507900 0.861416i \(-0.330422\pi\)
0.507900 + 0.861416i \(0.330422\pi\)
\(360\) −9105.20 529644.i −0.00370282 0.215391i
\(361\) 1.00139e6 0.404424
\(362\) −424001. −0.170057
\(363\) −2.09446e6 + 1.38421e6i −0.834268 + 0.551359i
\(364\) 2.24509e6 0.888139
\(365\) −142866. −0.0561301
\(366\) 1.52460e6 13103.9i 0.594914 0.00511326i
\(367\) −2.46844e6 −0.956659 −0.478329 0.878181i \(-0.658757\pi\)
−0.478329 + 0.878181i \(0.658757\pi\)
\(368\) 41495.9i 0.0159730i
\(369\) 1.31161e6 22548.1i 0.501464 0.00862075i
\(370\) 397136.i 0.150812i
\(371\) 3.61605e6 1.36395
\(372\) 16505.7 + 1.92040e6i 0.00618411 + 0.719506i
\(373\) 2.16792e6i 0.806809i 0.915022 + 0.403405i \(0.132173\pi\)
−0.915022 + 0.403405i \(0.867827\pi\)
\(374\) −1.58875e6 863201.i −0.587324 0.319104i
\(375\) −1.13129e6 + 9723.38i −0.415428 + 0.00357058i
\(376\) 2.07151e6i 0.755644i
\(377\) 2.49365e6i 0.903614i
\(378\) 2.05008e6 52871.3i 0.737974 0.0190323i
\(379\) 3.73283e6 1.33487 0.667437 0.744666i \(-0.267391\pi\)
0.667437 + 0.744666i \(0.267391\pi\)
\(380\) 275732. 0.0979553
\(381\) 1.82479e6 15684.0i 0.644022 0.00553534i
\(382\) 1.94215e6i 0.680963i
\(383\) 2.18000e6i 0.759382i −0.925113 0.379691i \(-0.876030\pi\)
0.925113 0.379691i \(-0.123970\pi\)
\(384\) 13876.0 + 1.61444e6i 0.00480217 + 0.558720i
\(385\) −631763. 343249.i −0.217221 0.118021i
\(386\) 2.19336e6i 0.749277i
\(387\) 87160.7 + 5.07009e6i 0.0295831 + 1.72083i
\(388\) −1.89865e6 −0.640273
\(389\) 2.48481e6i 0.832567i −0.909235 0.416284i \(-0.863332\pi\)
0.909235 0.416284i \(-0.136668\pi\)
\(390\) −4451.05 517868.i −0.00148184 0.172408i
\(391\) 1.10468e6i 0.365423i
\(392\) −1.08900e6 −0.357943
\(393\) −23699.9 2.75743e6i −0.00774045 0.900581i
\(394\) 1.31358e6 0.426302
\(395\) −131461. −0.0423940
\(396\) −1.65273e6 861499.i −0.529619 0.276069i
\(397\) −54162.3 −0.0172473 −0.00862364 0.999963i \(-0.502745\pi\)
−0.00862364 + 0.999963i \(0.502745\pi\)
\(398\) 783983. 0.248084
\(399\) 24535.6 + 2.85465e6i 0.00771550 + 0.897679i
\(400\) −140669. −0.0439590
\(401\) 3.15932e6i 0.981144i −0.871401 0.490572i \(-0.836788\pi\)
0.871401 0.490572i \(-0.163212\pi\)
\(402\) −9743.32 1.13361e6i −0.00300706 0.349863i
\(403\) 5.02123e6i 1.54010i
\(404\) −160801. −0.0490156
\(405\) 24112.7 + 701105.i 0.00730481 + 0.212395i
\(406\) 1.73312e6i 0.521811i
\(407\) 3.28348e6 + 1.78398e6i 0.982537 + 0.533831i
\(408\) −30852.9 3.58966e6i −0.00917584 1.06759i
\(409\) 3.24246e6i 0.958444i −0.877694 0.479222i \(-0.840919\pi\)
0.877694 0.479222i \(-0.159081\pi\)
\(410\) 230241.i 0.0676429i
\(411\) 5.42009e6 46585.4i 1.58271 0.0136033i
\(412\) −221774. −0.0643675
\(413\) −3.46168e6 −0.998648
\(414\) 13198.5 + 767751.i 0.00378464 + 0.220150i
\(415\) 612717.i 0.174638i
\(416\) 4.44198e6i 1.25847i
\(417\) 135936. 1168.36i 0.0382819 0.000329031i
\(418\) −835244. + 1.53730e6i −0.233815 + 0.430346i
\(419\) 540226.i 0.150328i −0.997171 0.0751642i \(-0.976052\pi\)
0.997171 0.0751642i \(-0.0239481\pi\)
\(420\) −4587.52 533746.i −0.00126898 0.147643i
\(421\) −3.05118e6 −0.839003 −0.419501 0.907755i \(-0.637795\pi\)
−0.419501 + 0.907755i \(0.637795\pi\)
\(422\) 2.50270e6i 0.684112i
\(423\) −47154.1 2.74293e6i −0.0128135 0.745355i
\(424\) 4.39983e6i 1.18856i
\(425\) −3.74480e6 −1.00567
\(426\) −3.15983e6 + 27158.6i −0.843606 + 0.00725075i
\(427\) 4.10858e6 1.09049
\(428\) 3.46843e6 0.915215
\(429\) −4.30168e6 2.28952e6i −1.12848 0.600622i
\(430\) −890004. −0.232124
\(431\) −2.10023e6 −0.544596 −0.272298 0.962213i \(-0.587784\pi\)
−0.272298 + 0.962213i \(0.587784\pi\)
\(432\) 4603.99 + 178519.i 0.00118693 + 0.0460230i
\(433\) −3.92143e6 −1.00514 −0.502568 0.864538i \(-0.667611\pi\)
−0.502568 + 0.864538i \(0.667611\pi\)
\(434\) 3.48981e6i 0.889361i
\(435\) 592839. 5095.42i 0.150215 0.00129109i
\(436\) 2.93084e6i 0.738372i
\(437\) −1.06890e6 −0.267754
\(438\) 672946. 5783.93i 0.167608 0.00144058i
\(439\) 1.31281e6i 0.325118i −0.986699 0.162559i \(-0.948025\pi\)
0.986699 0.162559i \(-0.0519748\pi\)
\(440\) 417649. 768699.i 0.102844 0.189289i
\(441\) 1.44197e6 24789.2i 0.353069 0.00606967i
\(442\) 3.50959e6i 0.854477i
\(443\) 6.39479e6i 1.54816i 0.633086 + 0.774082i \(0.281788\pi\)
−0.633086 + 0.774082i \(0.718212\pi\)
\(444\) 23842.9 + 2.77406e6i 0.00573986 + 0.667818i
\(445\) 999699. 0.239315
\(446\) 4.06200e6 0.966947
\(447\) −47442.4 5.51980e6i −0.0112305 1.30664i
\(448\) 3.31473e6i 0.780284i
\(449\) 4.54884e6i 1.06484i 0.846480 + 0.532420i \(0.178717\pi\)
−0.846480 + 0.532420i \(0.821283\pi\)
\(450\) 2.60263e6 44742.2i 0.605872 0.0104156i
\(451\) 1.90361e6 + 1.03427e6i 0.440693 + 0.239437i
\(452\) 4.00197e6i 0.921357i
\(453\) 7.68917e6 66088.0i 1.76049 0.0151313i
\(454\) −4.79889e6 −1.09270
\(455\) 1.39558e6i 0.316028i
\(456\) −3.47340e6 + 29853.7i −0.782245 + 0.00672335i
\(457\) 2.25014e6i 0.503987i −0.967729 0.251993i \(-0.918914\pi\)
0.967729 0.251993i \(-0.0810861\pi\)
\(458\) −3.36205e6 −0.748928
\(459\) 122565. + 4.75243e6i 0.0271540 + 1.05289i
\(460\) 199858. 0.0440379
\(461\) −3.13541e6 −0.687136 −0.343568 0.939128i \(-0.611636\pi\)
−0.343568 + 0.939128i \(0.611636\pi\)
\(462\) 2.98971e6 + 1.59124e6i 0.651666 + 0.346842i
\(463\) −5.47459e6 −1.18686 −0.593429 0.804886i \(-0.702226\pi\)
−0.593429 + 0.804886i \(0.702226\pi\)
\(464\) 150918. 0.0325422
\(465\) 1.19374e6 10260.2i 0.256023 0.00220050i
\(466\) 2.42568e6 0.517451
\(467\) 8.52104e6i 1.80801i −0.427524 0.904004i \(-0.640614\pi\)
0.427524 0.904004i \(-0.359386\pi\)
\(468\) −62182.5 3.61712e6i −0.0131236 0.763393i
\(469\) 3.05491e6i 0.641307i
\(470\) 481494. 0.100542
\(471\) −12655.1 1.47239e6i −0.00262853 0.305823i
\(472\) 4.21201e6i 0.870230i
\(473\) −3.99800e6 + 7.35847e6i −0.821655 + 1.51229i
\(474\) 619226. 5322.21i 0.126591 0.00108804i
\(475\) 3.62352e6i 0.736880i
\(476\) 3.61720e6i 0.731736i
\(477\) −100154. 5.82590e6i −0.0201545 1.17238i
\(478\) 2.14089e6 0.428574
\(479\) −8568.59 −0.00170636 −0.000853180 1.00000i \(-0.500272\pi\)
−0.000853180 1.00000i \(0.500272\pi\)
\(480\) 1.05603e6 9076.54i 0.209206 0.00179811i
\(481\) 7.25328e6i 1.42946i
\(482\) 4.46309e6i 0.875020i
\(483\) 17784.0 + 2.06913e6i 0.00346866 + 0.403570i
\(484\) −1.67496e6 2.58238e6i −0.325006 0.501080i
\(485\) 1.18022e6i 0.227829i
\(486\) −141963. 3.30146e6i −0.0272637 0.634038i
\(487\) 440964. 0.0842520 0.0421260 0.999112i \(-0.486587\pi\)
0.0421260 + 0.999112i \(0.486587\pi\)
\(488\) 4.99912e6i 0.950263i
\(489\) −39697.9 4.61875e6i −0.00750750 0.873478i
\(490\) 253124.i 0.0476259i
\(491\) 179754. 0.0336493 0.0168246 0.999858i \(-0.494644\pi\)
0.0168246 + 0.999858i \(0.494644\pi\)
\(492\) 13823.0 + 1.60827e6i 0.00257447 + 0.299533i
\(493\) 4.01766e6 0.744486
\(494\) −3.39592e6 −0.626095
\(495\) −535518. + 1.02736e6i −0.0982339 + 0.188455i
\(496\) 303890. 0.0554641
\(497\) −8.51527e6 −1.54635
\(498\) −24805.9 2.88610e6i −0.00448210 0.521481i
\(499\) 4.77108e6 0.857759 0.428879 0.903362i \(-0.358908\pi\)
0.428879 + 0.903362i \(0.358908\pi\)
\(500\) 1.38706e6i 0.248124i
\(501\) 76504.0 + 8.90105e6i 0.0136173 + 1.58433i
\(502\) 6.33871e6i 1.12264i
\(503\) −270590. −0.0476860 −0.0238430 0.999716i \(-0.507590\pi\)
−0.0238430 + 0.999716i \(0.507590\pi\)
\(504\) 115578. + 6.72312e6i 0.0202675 + 1.17895i
\(505\) 99955.6i 0.0174413i
\(506\) −605407. + 1.11427e6i −0.105116 + 0.193471i
\(507\) −31549.0 3.67065e6i −0.00545087 0.634195i
\(508\) 2.23735e6i 0.384658i
\(509\) 3.74567e6i 0.640819i 0.947279 + 0.320410i \(0.103821\pi\)
−0.947279 + 0.320410i \(0.896179\pi\)
\(510\) −834366. + 7171.33i −0.142047 + 0.00122088i
\(511\) 1.81349e6 0.307229
\(512\) 545645. 0.0919888
\(513\) 4.59852e6 118595.i 0.771479 0.0198964i
\(514\) 1.24855e6i 0.208448i
\(515\) 137857.i 0.0229040i
\(516\) −6.21682e6 + 53433.2i −1.02788 + 0.00883460i
\(517\) 2.16292e6 3.98094e6i 0.355889 0.655027i
\(518\) 5.04111e6i 0.825471i
\(519\) 1695.85 + 197307.i 0.000276356 + 0.0321533i
\(520\) 1.69807e6 0.275389
\(521\) 6.27808e6i 1.01329i −0.862156 0.506644i \(-0.830886\pi\)
0.862156 0.506644i \(-0.169114\pi\)
\(522\) −2.79226e6 + 48002.3i −0.448518 + 0.00771055i
\(523\) 5.76389e6i 0.921428i 0.887549 + 0.460714i \(0.152407\pi\)
−0.887549 + 0.460714i \(0.847593\pi\)
\(524\) 3.38084e6 0.537894
\(525\) 7.01421e6 60286.8i 1.11066 0.00954605i
\(526\) −3.53800e6 −0.557562
\(527\) 8.08999e6 1.26888
\(528\) −138564. + 260342.i −0.0216304 + 0.0406405i
\(529\) 5.66157e6 0.879626
\(530\) 1.02268e6 0.158143
\(531\) 95878.5 + 5.57720e6i 0.0147566 + 0.858380i
\(532\) −3.50005e6 −0.536160
\(533\) 4.20510e6i 0.641149i
\(534\) −4.70892e6 + 40472.9i −0.714609 + 0.00614202i
\(535\) 2.15601e6i 0.325662i
\(536\) 3.71706e6 0.558841
\(537\) 729059. 6266.22i 0.109101 0.000937713i
\(538\) 4.91064e6i 0.731446i
\(539\) 2.09280e6 + 1.13706e6i 0.310282 + 0.168582i
\(540\) −859804. + 22174.3i −0.126886 + 0.00327239i
\(541\) 7.90557e6i 1.16129i 0.814157 + 0.580644i \(0.197199\pi\)
−0.814157 + 0.580644i \(0.802801\pi\)
\(542\) 1.24564e6i 0.182135i
\(543\) 15823.6 + 1.84104e6i 0.00230306 + 0.267955i
\(544\) 7.15672e6 1.03685
\(545\) −1.82184e6 −0.262736
\(546\) 56500.1 + 6.57364e6i 0.00811087 + 0.943679i
\(547\) 721261.i 0.103068i −0.998671 0.0515341i \(-0.983589\pi\)
0.998671 0.0515341i \(-0.0164111\pi\)
\(548\) 6.64549e6i 0.945312i
\(549\) −113796. 6.61943e6i −0.0161137 0.937323i
\(550\) 3.77732e6 + 2.05229e6i 0.532448 + 0.289289i
\(551\) 3.88754e6i 0.545502i
\(552\) −2.51761e6 + 21638.7i −0.351675 + 0.00302262i
\(553\) 1.66872e6 0.232044
\(554\) 6.90377e6i 0.955679i
\(555\) 1.72439e6 14821.0i 0.237631 0.00204242i
\(556\) 166669.i 0.0228648i
\(557\) 8.49710e6 1.16047 0.580233 0.814450i \(-0.302961\pi\)
0.580233 + 0.814450i \(0.302961\pi\)
\(558\) −5.62252e6 + 96657.6i −0.764444 + 0.0131417i
\(559\) −1.62550e7 −2.20018
\(560\) −84461.7 −0.0113812
\(561\) −3.68877e6 + 6.93067e6i −0.494851 + 0.929754i
\(562\) −5.45013e6 −0.727891
\(563\) 1.78249e6 0.237005 0.118502 0.992954i \(-0.462191\pi\)
0.118502 + 0.992954i \(0.462191\pi\)
\(564\) 3.36331e6 28907.4i 0.445214 0.00382659i
\(565\) −2.48767e6 −0.327848
\(566\) 703591.i 0.0923165i
\(567\) −306079. 8.89958e6i −0.0399830 1.16255i
\(568\) 1.03610e7i 1.34750i
\(569\) −1.16476e7 −1.50819 −0.754094 0.656767i \(-0.771924\pi\)
−0.754094 + 0.656767i \(0.771924\pi\)
\(570\) 6939.07 + 807344.i 0.000894570 + 0.104081i
\(571\) 7.50760e6i 0.963632i 0.876272 + 0.481816i \(0.160023\pi\)
−0.876272 + 0.481816i \(0.839977\pi\)
\(572\) 2.85227e6 5.24971e6i 0.364502 0.670880i
\(573\) 8.43291e6 72480.4i 1.07298 0.00922219i
\(574\) 2.92260e6i 0.370245i
\(575\) 2.62642e6i 0.331280i
\(576\) −5.34043e6 + 91808.2i −0.670688 + 0.0115299i
\(577\) −1.53192e7 −1.91557 −0.957784 0.287488i \(-0.907180\pi\)
−0.957784 + 0.287488i \(0.907180\pi\)
\(578\) −557237. −0.0693778
\(579\) −9.52371e6 + 81855.7i −1.18062 + 0.0101474i
\(580\) 726871.i 0.0897196i
\(581\) 7.77762e6i 0.955887i
\(582\) −47781.4 5.55924e6i −0.00584725 0.680312i
\(583\) 4.59399e6 8.45541e6i 0.559781 1.03030i
\(584\) 2.20656e6i 0.267722i
\(585\) −2.24845e6 + 38653.4i −0.271639 + 0.00466980i
\(586\) 9.88986e6 1.18972
\(587\) 2.66999e6i 0.319826i 0.987131 + 0.159913i \(0.0511214\pi\)
−0.987131 + 0.159913i \(0.948879\pi\)
\(588\) 15196.8 + 1.76811e6i 0.00181263 + 0.210895i
\(589\) 7.82798e6i 0.929740i
\(590\) −979022. −0.115788
\(591\) −49022.6 5.70365e6i −0.00577334 0.671714i
\(592\) 438975. 0.0514797
\(593\) 814291. 0.0950918 0.0475459 0.998869i \(-0.484860\pi\)
0.0475459 + 0.998869i \(0.484860\pi\)
\(594\) 2.48088e6 4.86087e6i 0.288496 0.565259i
\(595\) −2.24849e6 −0.260375
\(596\) 6.76774e6 0.780419
\(597\) −29258.0 3.40410e6i −0.00335977 0.390900i
\(598\) −2.46145e6 −0.281474
\(599\) 1.21744e6i 0.138637i 0.997595 + 0.0693187i \(0.0220825\pi\)
−0.997595 + 0.0693187i \(0.977917\pi\)
\(600\) 73354.0 + 8.53455e6i 0.00831851 + 0.967837i
\(601\) 3.13293e6i 0.353806i −0.984228 0.176903i \(-0.943392\pi\)
0.984228 0.176903i \(-0.0566078\pi\)
\(602\) 1.12974e7 1.27054
\(603\) −4.92183e6 + 84612.0i −0.551231 + 0.00947630i
\(604\) 9.42757e6i 1.05150i
\(605\) −1.60524e6 + 1.04117e6i −0.178300 + 0.115647i
\(606\) −4046.71 470824.i −0.000447631 0.0520808i
\(607\) 1.32997e7i 1.46511i −0.680707 0.732556i \(-0.738327\pi\)
0.680707 0.732556i \(-0.261673\pi\)
\(608\) 6.92494e6i 0.759726i
\(609\) −7.52529e6 + 64679.5i −0.822205 + 0.00706681i
\(610\) 1.16198e6 0.126436
\(611\) 8.79398e6 0.952977
\(612\) −5.82775e6 + 100186.i −0.628959 + 0.0108125i
\(613\) 2.10731e6i 0.226504i 0.993566 + 0.113252i \(0.0361268\pi\)
−0.993566 + 0.113252i \(0.963873\pi\)
\(614\) 2.45748e6i 0.263068i
\(615\) 999718. 8592.52i 0.106583 0.000916079i
\(616\) −5.30149e6 + 9.75759e6i −0.562919 + 1.03607i
\(617\) 4.13947e6i 0.437756i 0.975752 + 0.218878i \(0.0702397\pi\)
−0.975752 + 0.218878i \(0.929760\pi\)
\(618\) −5581.16 649354.i −0.000587832 0.0683928i
\(619\) −5.30546e6 −0.556540 −0.278270 0.960503i \(-0.589761\pi\)
−0.278270 + 0.960503i \(0.589761\pi\)
\(620\) 1.46363e6i 0.152916i
\(621\) 3.33312e6 85961.0i 0.346835 0.00894484i
\(622\) 1.48978e6i 0.154400i
\(623\) −1.26898e7 −1.30989
\(624\) −572426. + 4919.97i −0.0588516 + 0.000505826i
\(625\) 8.46235e6 0.866544
\(626\) −4.60479e6 −0.469649
\(627\) 6.70621e6 + 3.56930e6i 0.681253 + 0.362589i
\(628\) 1.80527e6 0.182660
\(629\) 1.16862e7 1.17773
\(630\) 1.56270e6 26864.5i 0.156864 0.00269667i
\(631\) 8.10190e6 0.810053 0.405027 0.914305i \(-0.367262\pi\)
0.405027 + 0.914305i \(0.367262\pi\)
\(632\) 2.03042e6i 0.202205i
\(633\) 1.08669e7 93400.0i 1.07794 0.00926483i
\(634\) 9.72293e6i 0.960670i
\(635\) 1.39076e6 0.136873
\(636\) 7.14357e6 61398.6i 0.700281 0.00601888i
\(637\) 4.62304e6i 0.451418i
\(638\) −4.05255e6 2.20183e6i −0.394164 0.214157i
\(639\) 235848. + 1.37191e7i 0.0228497 + 1.32915i
\(640\) 1.23044e6i 0.118744i
\(641\) 1.82583e6i 0.175515i −0.996142 0.0877576i \(-0.972030\pi\)
0.996142 0.0877576i \(-0.0279701\pi\)
\(642\) 87286.5 + 1.01556e7i 0.00835813 + 0.972447i
\(643\) −3.69890e6 −0.352813 −0.176407 0.984317i \(-0.556447\pi\)
−0.176407 + 0.984317i \(0.556447\pi\)
\(644\) −2.53692e6 −0.241042
\(645\) 33214.7 + 3.86445e6i 0.00314363 + 0.365753i
\(646\) 5.47136e6i 0.515839i
\(647\) 1.07732e7i 1.01178i −0.862599 0.505888i \(-0.831165\pi\)
0.862599 0.505888i \(-0.168835\pi\)
\(648\) 1.08286e7 372421.i 1.01306 0.0348415i
\(649\) −4.39788e6 + 8.09446e6i −0.409856 + 0.754356i
\(650\) 8.34418e6i 0.774640i
\(651\) −1.51530e7 + 130239.i −1.40135 + 0.0120445i
\(652\) 5.66297e6 0.521706
\(653\) 1.06326e7i 0.975791i 0.872902 + 0.487896i \(0.162235\pi\)
−0.872902 + 0.487896i \(0.837765\pi\)
\(654\) 8.58149e6 73757.4i 0.784546 0.00674313i
\(655\) 2.10157e6i 0.191400i
\(656\) 254497. 0.0230899
\(657\) −50228.3 2.92175e6i −0.00453978 0.264077i
\(658\) −6.11191e6 −0.550316
\(659\) −6.09424e6 −0.546645 −0.273323 0.961922i \(-0.588123\pi\)
−0.273323 + 0.961922i \(0.588123\pi\)
\(660\) −1.25389e6 667368.i −0.112047 0.0596356i
\(661\) 1.01212e7 0.901004 0.450502 0.892775i \(-0.351245\pi\)
0.450502 + 0.892775i \(0.351245\pi\)
\(662\) 3.96782e6 0.351890
\(663\) −1.52388e7 + 130977.i −1.34638 + 0.0115721i
\(664\) 9.46342e6 0.832968
\(665\) 2.17567e6i 0.190783i
\(666\) −8.12185e6 + 139624.i −0.709528 + 0.0121976i
\(667\) 2.81779e6i 0.245242i
\(668\) −1.09134e7 −0.946281
\(669\) −151593. 1.76374e7i −0.0130952 1.52360i
\(670\) 863980.i 0.0743561i
\(671\) 5.21972e6 9.60710e6i 0.447549 0.823732i
\(672\) −1.34049e7 + 115214.i −1.14509 + 0.00984201i
\(673\) 1.28100e7i 1.09022i 0.838366 + 0.545108i \(0.183511\pi\)
−0.838366 + 0.545108i \(0.816489\pi\)
\(674\) 4.31857e6i 0.366176i
\(675\) −291403. 1.12991e7i −0.0246169 0.954517i
\(676\) 4.50053e6 0.378788
\(677\) −1.11938e7 −0.938656 −0.469328 0.883024i \(-0.655504\pi\)
−0.469328 + 0.883024i \(0.655504\pi\)
\(678\) 1.17178e7 100714.i 0.978974 0.00841423i
\(679\) 1.49813e7i 1.24703i
\(680\) 2.73585e6i 0.226893i
\(681\) 179093. + 2.08371e7i 0.0147983 + 1.72174i
\(682\) −8.16024e6 4.43361e6i −0.671803 0.365003i
\(683\) 577600.i 0.0473779i −0.999719 0.0236889i \(-0.992459\pi\)
0.999719 0.0236889i \(-0.00754113\pi\)
\(684\) 96941.0 + 5.63900e6i 0.00792259 + 0.460853i
\(685\) 4.13091e6 0.336372
\(686\) 5.88597e6i 0.477538i
\(687\) 125471. + 1.45982e7i 0.0101426 + 1.18007i
\(688\) 983768.i 0.0792358i
\(689\) 1.86782e7 1.49895
\(690\) 5029.62 + 585184.i 0.000402173 + 0.0467918i
\(691\) 7.05063e6 0.561737 0.280868 0.959746i \(-0.409378\pi\)
0.280868 + 0.959746i \(0.409378\pi\)
\(692\) −241916. −0.0192043
\(693\) 6.79768e6 1.30409e7i 0.537685 1.03151i
\(694\) 5.79570e6 0.456780
\(695\) 103603. 0.00813601
\(696\) −78698.8 9.15640e6i −0.00615808 0.716476i
\(697\) 6.77508e6 0.528241
\(698\) 1.13870e7i 0.884648i
\(699\) −90525.8 1.05324e7i −0.00700777 0.815336i
\(700\) 8.60002e6i 0.663367i
\(701\) −5.52192e6 −0.424419 −0.212209 0.977224i \(-0.568066\pi\)
−0.212209 + 0.977224i \(0.568066\pi\)
\(702\) 1.05894e7 273099.i 0.811012 0.0209159i
\(703\) 1.13077e7i 0.862949i
\(704\) −7.75083e6 4.21118e6i −0.589409 0.320237i
\(705\) −17969.2 2.09067e6i −0.00136162 0.158421i
\(706\) 2.42478e6i 0.183088i
\(707\) 1.26880e6i 0.0954652i
\(708\) −6.83862e6 + 58777.6i −0.512726 + 0.00440685i
\(709\) −9.02213e6 −0.674052 −0.337026 0.941495i \(-0.609421\pi\)
−0.337026 + 0.941495i \(0.609421\pi\)
\(710\) −2.40826e6 −0.179291
\(711\) −46218.7 2.68851e6i −0.00342881 0.199452i
\(712\) 1.54404e7i 1.14145i
\(713\) 5.67392e6i 0.417984i
\(714\) 1.05912e7 91030.4i 0.777495 0.00668253i
\(715\) −3.26328e6 1.77300e6i −0.238720 0.129701i
\(716\) 893888.i 0.0651629i
\(717\) −79897.6 9.29588e6i −0.00580411 0.675294i
\(718\) −8.90505e6 −0.644652
\(719\) 1.01462e7i 0.731949i −0.930625 0.365974i \(-0.880736\pi\)
0.930625 0.365974i \(-0.119264\pi\)
\(720\) 2339.34 + 136078.i 0.000168175 + 0.00978266i
\(721\) 1.74991e6i 0.125365i
\(722\) −3.59498e6 −0.256657
\(723\) 1.93790e7 166561.i 1.37875 0.0118503i
\(724\) −2.25726e6 −0.160043
\(725\) −9.55215e6 −0.674926
\(726\) 7.51907e6 4.96927e6i 0.529447 0.349906i
\(727\) −1.92374e7 −1.34993 −0.674965 0.737850i \(-0.735841\pi\)
−0.674965 + 0.737850i \(0.735841\pi\)
\(728\) −2.15547e7 −1.50735
\(729\) −1.43298e7 + 739622.i −0.998671 + 0.0515456i
\(730\) 512885. 0.0356215
\(731\) 2.61893e7i 1.81272i
\(732\) 8.11658e6 69761.5i 0.559880 0.00481214i
\(733\) 1.22590e7i 0.842743i 0.906888 + 0.421371i \(0.138451\pi\)
−0.906888 + 0.421371i \(0.861549\pi\)
\(734\) 8.86164e6 0.607119
\(735\) 1.09908e6 9446.52i 0.0750430 0.000644990i
\(736\) 5.01938e6i 0.341551i
\(737\) −7.14330e6 3.88109e6i −0.484429 0.263200i
\(738\) −4.70866e6 + 80947.3i −0.318241 + 0.00547094i
\(739\) 1.89627e6i 0.127729i −0.997959 0.0638645i \(-0.979657\pi\)
0.997959 0.0638645i \(-0.0203425\pi\)
\(740\) 2.11425e6i 0.141931i
\(741\) 126735. + 1.47453e7i 0.00847912 + 0.986524i
\(742\) −1.29815e7 −0.865598
\(743\) −6.60277e6 −0.438787 −0.219394 0.975636i \(-0.570408\pi\)
−0.219394 + 0.975636i \(0.570408\pi\)
\(744\) −158468. 1.84374e7i −0.0104957 1.22114i
\(745\) 4.20691e6i 0.277698i
\(746\) 7.78278e6i 0.512021i
\(747\) −1.25307e7 + 215417.i −0.821625 + 0.0141247i
\(748\) −8.45809e6 4.59544e6i −0.552737 0.300313i
\(749\) 2.73677e7i 1.78252i
\(750\) 4.06131e6 34906.7i 0.263641 0.00226598i
\(751\) 3.98388e6 0.257754 0.128877 0.991661i \(-0.458863\pi\)
0.128877 + 0.991661i \(0.458863\pi\)
\(752\) 532220.i 0.0343199i
\(753\) 2.75230e7 236559.i 1.76892 0.0152038i
\(754\) 8.95216e6i 0.573455i
\(755\) 5.86029e6 0.374155
\(756\) 1.09141e7 281473.i 0.694515 0.0179115i
\(757\) 1.21560e7 0.770994 0.385497 0.922709i \(-0.374030\pi\)
0.385497 + 0.922709i \(0.374030\pi\)
\(758\) −1.34008e7 −0.847143
\(759\) 4.86083e6 + 2.58712e6i 0.306271 + 0.163009i
\(760\) −2.64725e6 −0.166250
\(761\) 1.46323e7 0.915904 0.457952 0.888977i \(-0.348583\pi\)
0.457952 + 0.888977i \(0.348583\pi\)
\(762\) −6.55096e6 + 56305.2i −0.408712 + 0.00351286i
\(763\) 2.31258e7 1.43809
\(764\) 1.03395e7i 0.640862i
\(765\) 62276.6 + 3.62260e6i 0.00384744 + 0.223803i
\(766\) 7.82616e6i 0.481922i
\(767\) −1.78808e7 −1.09749
\(768\) −144050. 1.67599e7i −0.00881273 1.02534i
\(769\) 6.23273e6i 0.380069i −0.981777 0.190034i \(-0.939140\pi\)
0.981777 0.190034i \(-0.0608600\pi\)
\(770\) 2.26802e6 + 1.23226e6i 0.137854 + 0.0748987i
\(771\) −5.42128e6 + 46595.6i −0.328447 + 0.00282299i
\(772\) 1.16769e7i 0.705153i
\(773\) 2.38906e7i 1.43806i −0.694978 0.719031i \(-0.744586\pi\)
0.694978 0.719031i \(-0.255414\pi\)
\(774\) −312905. 1.82015e7i −0.0187741 1.09208i
\(775\) −1.92343e7 −1.15033 <