Properties

Label 33.6.d.b.32.13
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 32.13
Root \(-6.11708 + 10.4175i\) of defining polynomial
Character \(\chi\) \(=\) 33.32
Dual form 33.6.d.b.32.14

$q$-expansion

\(f(q)\) \(=\) \(q+8.47928 q^{2} +(11.5964 - 10.4175i) q^{3} +39.8981 q^{4} +35.7023i q^{5} +(98.3287 - 88.3330i) q^{6} +11.5666i q^{7} +66.9703 q^{8} +(25.9508 - 241.610i) q^{9} +O(q^{10})\) \(q+8.47928 q^{2} +(11.5964 - 10.4175i) q^{3} +39.8981 q^{4} +35.7023i q^{5} +(98.3287 - 88.3330i) q^{6} +11.5666i q^{7} +66.9703 q^{8} +(25.9508 - 241.610i) q^{9} +302.729i q^{10} +(-202.832 - 346.281i) q^{11} +(462.673 - 415.639i) q^{12} +933.326i q^{13} +98.0760i q^{14} +(371.929 + 414.016i) q^{15} -708.880 q^{16} -25.0813 q^{17} +(220.044 - 2048.68i) q^{18} +743.695i q^{19} +1424.45i q^{20} +(120.495 + 134.130i) q^{21} +(-1719.86 - 2936.21i) q^{22} -594.979i q^{23} +(776.611 - 697.664i) q^{24} +1850.35 q^{25} +7913.93i q^{26} +(-2216.04 - 3072.14i) q^{27} +461.484i q^{28} -3975.05 q^{29} +(3153.69 + 3510.56i) q^{30} -3071.33 q^{31} -8153.84 q^{32} +(-5959.49 - 1902.59i) q^{33} -212.671 q^{34} -412.952 q^{35} +(1035.39 - 9639.80i) q^{36} +10317.8 q^{37} +6306.00i q^{38} +(9722.94 + 10823.2i) q^{39} +2390.99i q^{40} +17759.6 q^{41} +(1021.71 + 1137.32i) q^{42} -22910.3i q^{43} +(-8092.60 - 13815.9i) q^{44} +(8626.04 + 926.502i) q^{45} -5044.99i q^{46} -3402.05i q^{47} +(-8220.42 + 7384.77i) q^{48} +16673.2 q^{49} +15689.6 q^{50} +(-290.852 + 261.285i) q^{51} +37238.0i q^{52} +12325.8i q^{53} +(-18790.5 - 26049.5i) q^{54} +(12363.0 - 7241.55i) q^{55} +774.615i q^{56} +(7747.46 + 8624.15i) q^{57} -33705.5 q^{58} -30346.5i q^{59} +(14839.3 + 16518.5i) q^{60} +36444.5i q^{61} -26042.7 q^{62} +(2794.60 + 300.161i) q^{63} -46454.5 q^{64} -33321.9 q^{65} +(-50532.2 - 16132.6i) q^{66} -28572.0 q^{67} -1000.70 q^{68} +(-6198.20 - 6899.59i) q^{69} -3501.54 q^{70} +59302.3i q^{71} +(1737.93 - 16180.7i) q^{72} -72406.9i q^{73} +87487.9 q^{74} +(21457.3 - 19276.0i) q^{75} +29672.0i q^{76} +(4005.27 - 2346.06i) q^{77} +(82443.5 + 91772.7i) q^{78} +26947.6i q^{79} -25308.6i q^{80} +(-57702.1 - 12540.0i) q^{81} +150589. q^{82} +32457.1 q^{83} +(4807.51 + 5351.53i) q^{84} -895.460i q^{85} -194263. i q^{86} +(-46096.0 + 41410.1i) q^{87} +(-13583.7 - 23190.5i) q^{88} +10808.1i q^{89} +(73142.6 + 7856.07i) q^{90} -10795.4 q^{91} -23738.5i q^{92} +(-35616.3 + 31995.7i) q^{93} -28846.9i q^{94} -26551.6 q^{95} +(-94554.8 + 84942.7i) q^{96} -105449. q^{97} +141377. q^{98} +(-88928.6 + 40019.9i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.47928 1.49894 0.749469 0.662039i \(-0.230309\pi\)
0.749469 + 0.662039i \(0.230309\pi\)
\(3\) 11.5964 10.4175i 0.743906 0.668284i
\(4\) 39.8981 1.24682
\(5\) 35.7023i 0.638662i 0.947643 + 0.319331i \(0.103458\pi\)
−0.947643 + 0.319331i \(0.896542\pi\)
\(6\) 98.3287 88.3330i 1.11507 1.00172i
\(7\) 11.5666i 0.0892193i 0.999004 + 0.0446096i \(0.0142044\pi\)
−0.999004 + 0.0446096i \(0.985796\pi\)
\(8\) 66.9703 0.369962
\(9\) 25.9508 241.610i 0.106793 0.994281i
\(10\) 302.729i 0.957315i
\(11\) −202.832 346.281i −0.505422 0.862873i
\(12\) 462.673 415.639i 0.927514 0.833227i
\(13\) 933.326i 1.53170i 0.643017 + 0.765852i \(0.277683\pi\)
−0.643017 + 0.765852i \(0.722317\pi\)
\(14\) 98.0760i 0.133734i
\(15\) 371.929 + 414.016i 0.426807 + 0.475105i
\(16\) −708.880 −0.692266
\(17\) −25.0813 −0.0210488 −0.0105244 0.999945i \(-0.503350\pi\)
−0.0105244 + 0.999945i \(0.503350\pi\)
\(18\) 220.044 2048.68i 0.160077 1.49037i
\(19\) 743.695i 0.472619i 0.971678 + 0.236309i \(0.0759379\pi\)
−0.971678 + 0.236309i \(0.924062\pi\)
\(20\) 1424.45i 0.796294i
\(21\) 120.495 + 134.130i 0.0596238 + 0.0663708i
\(22\) −1719.86 2936.21i −0.757596 1.29339i
\(23\) 594.979i 0.234521i −0.993101 0.117261i \(-0.962589\pi\)
0.993101 0.117261i \(-0.0374113\pi\)
\(24\) 776.611 697.664i 0.275217 0.247240i
\(25\) 1850.35 0.592111
\(26\) 7913.93i 2.29593i
\(27\) −2216.04 3072.14i −0.585018 0.811020i
\(28\) 461.484i 0.111240i
\(29\) −3975.05 −0.877702 −0.438851 0.898560i \(-0.644614\pi\)
−0.438851 + 0.898560i \(0.644614\pi\)
\(30\) 3153.69 + 3510.56i 0.639758 + 0.712152i
\(31\) −3071.33 −0.574014 −0.287007 0.957928i \(-0.592660\pi\)
−0.287007 + 0.957928i \(0.592660\pi\)
\(32\) −8153.84 −1.40763
\(33\) −5959.49 1902.59i −0.952630 0.304131i
\(34\) −212.671 −0.0315509
\(35\) −412.952 −0.0569810
\(36\) 1035.39 9639.80i 0.133152 1.23969i
\(37\) 10317.8 1.23904 0.619519 0.784982i \(-0.287328\pi\)
0.619519 + 0.784982i \(0.287328\pi\)
\(38\) 6306.00i 0.708426i
\(39\) 9722.94 + 10823.2i 1.02361 + 1.13944i
\(40\) 2390.99i 0.236281i
\(41\) 17759.6 1.64996 0.824982 0.565160i \(-0.191185\pi\)
0.824982 + 0.565160i \(0.191185\pi\)
\(42\) 1021.71 + 1137.32i 0.0893724 + 0.0994857i
\(43\) 22910.3i 1.88956i −0.327711 0.944778i \(-0.606277\pi\)
0.327711 0.944778i \(-0.393723\pi\)
\(44\) −8092.60 13815.9i −0.630168 1.07584i
\(45\) 8626.04 + 926.502i 0.635009 + 0.0682048i
\(46\) 5044.99i 0.351533i
\(47\) 3402.05i 0.224644i −0.993672 0.112322i \(-0.964171\pi\)
0.993672 0.112322i \(-0.0358289\pi\)
\(48\) −8220.42 + 7384.77i −0.514981 + 0.462630i
\(49\) 16673.2 0.992040
\(50\) 15689.6 0.887538
\(51\) −290.852 + 261.285i −0.0156584 + 0.0140666i
\(52\) 37238.0i 1.90975i
\(53\) 12325.8i 0.602734i 0.953508 + 0.301367i \(0.0974430\pi\)
−0.953508 + 0.301367i \(0.902557\pi\)
\(54\) −18790.5 26049.5i −0.876906 1.21567i
\(55\) 12363.0 7241.55i 0.551084 0.322794i
\(56\) 774.615i 0.0330078i
\(57\) 7747.46 + 8624.15i 0.315844 + 0.351584i
\(58\) −33705.5 −1.31562
\(59\) 30346.5i 1.13496i −0.823389 0.567478i \(-0.807919\pi\)
0.823389 0.567478i \(-0.192081\pi\)
\(60\) 14839.3 + 16518.5i 0.532150 + 0.592368i
\(61\) 36444.5i 1.25403i 0.779008 + 0.627014i \(0.215723\pi\)
−0.779008 + 0.627014i \(0.784277\pi\)
\(62\) −26042.7 −0.860412
\(63\) 2794.60 + 300.161i 0.0887091 + 0.00952803i
\(64\) −46454.5 −1.41768
\(65\) −33321.9 −0.978241
\(66\) −50532.2 16132.6i −1.42793 0.455874i
\(67\) −28572.0 −0.777595 −0.388798 0.921323i \(-0.627109\pi\)
−0.388798 + 0.921323i \(0.627109\pi\)
\(68\) −1000.70 −0.0262440
\(69\) −6198.20 6899.59i −0.156727 0.174462i
\(70\) −3501.54 −0.0854109
\(71\) 59302.3i 1.39613i 0.716035 + 0.698065i \(0.245955\pi\)
−0.716035 + 0.698065i \(0.754045\pi\)
\(72\) 1737.93 16180.7i 0.0395095 0.367846i
\(73\) 72406.9i 1.59028i −0.606428 0.795139i \(-0.707398\pi\)
0.606428 0.795139i \(-0.292602\pi\)
\(74\) 87487.9 1.85724
\(75\) 21457.3 19276.0i 0.440475 0.395698i
\(76\) 29672.0i 0.589269i
\(77\) 4005.27 2346.06i 0.0769849 0.0450934i
\(78\) 82443.5 + 91772.7i 1.53433 + 1.70796i
\(79\) 26947.6i 0.485794i 0.970052 + 0.242897i \(0.0780978\pi\)
−0.970052 + 0.242897i \(0.921902\pi\)
\(80\) 25308.6i 0.442124i
\(81\) −57702.1 12540.0i −0.977190 0.212365i
\(82\) 150589. 2.47319
\(83\) 32457.1 0.517148 0.258574 0.965991i \(-0.416747\pi\)
0.258574 + 0.965991i \(0.416747\pi\)
\(84\) 4807.51 + 5351.53i 0.0743399 + 0.0827522i
\(85\) 895.460i 0.0134431i
\(86\) 194263.i 2.83233i
\(87\) −46096.0 + 41410.1i −0.652928 + 0.586554i
\(88\) −13583.7 23190.5i −0.186987 0.319230i
\(89\) 10808.1i 0.144635i 0.997382 + 0.0723176i \(0.0230395\pi\)
−0.997382 + 0.0723176i \(0.976960\pi\)
\(90\) 73142.6 + 7856.07i 0.951840 + 0.102235i
\(91\) −10795.4 −0.136658
\(92\) 23738.5i 0.292405i
\(93\) −35616.3 + 31995.7i −0.427013 + 0.383605i
\(94\) 28846.9i 0.336728i
\(95\) −26551.6 −0.301844
\(96\) −94554.8 + 84942.7i −1.04714 + 0.940694i
\(97\) −105449. −1.13792 −0.568962 0.822364i \(-0.692655\pi\)
−0.568962 + 0.822364i \(0.692655\pi\)
\(98\) 141377. 1.48701
\(99\) −88928.6 + 40019.9i −0.911914 + 0.410382i
\(100\) 73825.4 0.738254
\(101\) −158525. −1.54630 −0.773150 0.634223i \(-0.781320\pi\)
−0.773150 + 0.634223i \(0.781320\pi\)
\(102\) −2466.21 + 2215.51i −0.0234709 + 0.0210849i
\(103\) 116352. 1.08064 0.540321 0.841459i \(-0.318303\pi\)
0.540321 + 0.841459i \(0.318303\pi\)
\(104\) 62505.1i 0.566673i
\(105\) −4788.74 + 4301.94i −0.0423885 + 0.0380795i
\(106\) 104514.i 0.903462i
\(107\) −46004.0 −0.388451 −0.194225 0.980957i \(-0.562219\pi\)
−0.194225 + 0.980957i \(0.562219\pi\)
\(108\) −88416.0 122573.i −0.729410 1.01119i
\(109\) 121732.i 0.981385i −0.871333 0.490693i \(-0.836744\pi\)
0.871333 0.490693i \(-0.163256\pi\)
\(110\) 104829. 61403.1i 0.826041 0.483848i
\(111\) 119649. 107486.i 0.921728 0.828029i
\(112\) 8199.30i 0.0617635i
\(113\) 191518.i 1.41096i 0.708731 + 0.705479i \(0.249268\pi\)
−0.708731 + 0.705479i \(0.750732\pi\)
\(114\) 65692.8 + 73126.6i 0.473430 + 0.527003i
\(115\) 21242.1 0.149780
\(116\) −158597. −1.09433
\(117\) 225501. + 24220.5i 1.52295 + 0.163576i
\(118\) 257316.i 1.70123i
\(119\) 290.104i 0.00187796i
\(120\) 24908.2 + 27726.8i 0.157903 + 0.175771i
\(121\) −78769.7 + 140473.i −0.489098 + 0.872229i
\(122\) 309023.i 1.87971i
\(123\) 205947. 185011.i 1.22742 1.10264i
\(124\) −122540. −0.715690
\(125\) 177631.i 1.01682i
\(126\) 23696.2 + 2545.15i 0.132969 + 0.0142819i
\(127\) 74201.3i 0.408227i −0.978947 0.204114i \(-0.934569\pi\)
0.978947 0.204114i \(-0.0654312\pi\)
\(128\) −132978. −0.717387
\(129\) −238668. 265676.i −1.26276 1.40565i
\(130\) −282545. −1.46632
\(131\) 88605.0 0.451107 0.225554 0.974231i \(-0.427581\pi\)
0.225554 + 0.974231i \(0.427581\pi\)
\(132\) −237772. 75909.9i −1.18775 0.379196i
\(133\) −8601.99 −0.0421667
\(134\) −242270. −1.16557
\(135\) 109682. 79117.9i 0.517968 0.373629i
\(136\) −1679.70 −0.00778727
\(137\) 176386.i 0.802904i 0.915880 + 0.401452i \(0.131494\pi\)
−0.915880 + 0.401452i \(0.868506\pi\)
\(138\) −52556.3 58503.5i −0.234924 0.261507i
\(139\) 385558.i 1.69259i 0.532712 + 0.846297i \(0.321173\pi\)
−0.532712 + 0.846297i \(0.678827\pi\)
\(140\) −16476.0 −0.0710448
\(141\) −35440.9 39451.3i −0.150126 0.167114i
\(142\) 502841.i 2.09271i
\(143\) 323193. 189308.i 1.32167 0.774157i
\(144\) −18396.0 + 171273.i −0.0739294 + 0.688307i
\(145\) 141918.i 0.560555i
\(146\) 613958.i 2.38373i
\(147\) 193348. 173693.i 0.737985 0.662964i
\(148\) 411663. 1.54485
\(149\) −228625. −0.843642 −0.421821 0.906679i \(-0.638609\pi\)
−0.421821 + 0.906679i \(0.638609\pi\)
\(150\) 181942. 163447.i 0.660245 0.593127i
\(151\) 152707.i 0.545026i 0.962152 + 0.272513i \(0.0878548\pi\)
−0.962152 + 0.272513i \(0.912145\pi\)
\(152\) 49805.5i 0.174851i
\(153\) −650.879 + 6059.90i −0.00224787 + 0.0209284i
\(154\) 33961.8 19892.9i 0.115396 0.0675922i
\(155\) 109654.i 0.366601i
\(156\) 387927. + 431824.i 1.27626 + 1.42068i
\(157\) −206031. −0.667089 −0.333545 0.942734i \(-0.608245\pi\)
−0.333545 + 0.942734i \(0.608245\pi\)
\(158\) 228496.i 0.728176i
\(159\) 128404. + 142935.i 0.402798 + 0.448378i
\(160\) 291111.i 0.898997i
\(161\) 6881.85 0.0209238
\(162\) −489272. 106330.i −1.46475 0.318322i
\(163\) 363134. 1.07053 0.535264 0.844685i \(-0.320212\pi\)
0.535264 + 0.844685i \(0.320212\pi\)
\(164\) 708576. 2.05720
\(165\) 67926.9 212767.i 0.194237 0.608409i
\(166\) 275213. 0.775173
\(167\) −514079. −1.42639 −0.713196 0.700965i \(-0.752753\pi\)
−0.713196 + 0.700965i \(0.752753\pi\)
\(168\) 8069.57 + 8982.71i 0.0220586 + 0.0245547i
\(169\) −499804. −1.34612
\(170\) 7592.85i 0.0201503i
\(171\) 179684. + 19299.5i 0.469916 + 0.0504725i
\(172\) 914078.i 2.35593i
\(173\) 437300. 1.11087 0.555436 0.831559i \(-0.312551\pi\)
0.555436 + 0.831559i \(0.312551\pi\)
\(174\) −390861. + 351128.i −0.978699 + 0.879209i
\(175\) 21402.1i 0.0528277i
\(176\) 143783. + 245472.i 0.349886 + 0.597337i
\(177\) −316135. 351909.i −0.758472 0.844301i
\(178\) 91644.8i 0.216799i
\(179\) 205264.i 0.478828i −0.970918 0.239414i \(-0.923045\pi\)
0.970918 0.239414i \(-0.0769553\pi\)
\(180\) 344163. + 36965.7i 0.791740 + 0.0850389i
\(181\) 274310. 0.622366 0.311183 0.950350i \(-0.399275\pi\)
0.311183 + 0.950350i \(0.399275\pi\)
\(182\) −91536.9 −0.204841
\(183\) 379661. + 422623.i 0.838046 + 0.932879i
\(184\) 39845.9i 0.0867640i
\(185\) 368371.i 0.791326i
\(186\) −302000. + 271300.i −0.640066 + 0.575000i
\(187\) 5087.28 + 8685.17i 0.0106385 + 0.0181625i
\(188\) 135735.i 0.280090i
\(189\) 35534.1 25632.0i 0.0723587 0.0521949i
\(190\) −225138. −0.452445
\(191\) 631297.i 1.25213i −0.779770 0.626066i \(-0.784664\pi\)
0.779770 0.626066i \(-0.215336\pi\)
\(192\) −538703. + 483940.i −1.05462 + 0.947412i
\(193\) 5646.93i 0.0109124i 0.999985 + 0.00545619i \(0.00173677\pi\)
−0.999985 + 0.00545619i \(0.998263\pi\)
\(194\) −894131. −1.70568
\(195\) −386412. + 347131.i −0.727720 + 0.653743i
\(196\) 665230. 1.23689
\(197\) −739771. −1.35810 −0.679050 0.734092i \(-0.737608\pi\)
−0.679050 + 0.734092i \(0.737608\pi\)
\(198\) −754051. + 339340.i −1.36690 + 0.615138i
\(199\) 215092. 0.385027 0.192513 0.981294i \(-0.438336\pi\)
0.192513 + 0.981294i \(0.438336\pi\)
\(200\) 123918. 0.219059
\(201\) −331331. + 297649.i −0.578458 + 0.519654i
\(202\) −1.34418e6 −2.31781
\(203\) 45977.6i 0.0783080i
\(204\) −11604.4 + 10424.8i −0.0195231 + 0.0175384i
\(205\) 634059.i 1.05377i
\(206\) 986584. 1.61982
\(207\) −143753. 15440.2i −0.233180 0.0250453i
\(208\) 661616.i 1.06035i
\(209\) 257527. 150845.i 0.407810 0.238872i
\(210\) −40605.0 + 36477.3i −0.0635377 + 0.0570788i
\(211\) 197876.i 0.305975i −0.988228 0.152988i \(-0.951111\pi\)
0.988228 0.152988i \(-0.0488895\pi\)
\(212\) 491777.i 0.751499i
\(213\) 617783. + 687690.i 0.933011 + 1.03859i
\(214\) −390081. −0.582264
\(215\) 817950. 1.20679
\(216\) −148409. 205742.i −0.216434 0.300047i
\(217\) 35524.7i 0.0512132i
\(218\) 1.03220e6i 1.47104i
\(219\) −754300. 839656.i −1.06276 1.18302i
\(220\) 493261. 288924.i 0.687100 0.402464i
\(221\) 23409.0i 0.0322406i
\(222\) 1.01454e6 911406.i 1.38161 1.24116i
\(223\) 122438. 0.164875 0.0824374 0.996596i \(-0.473730\pi\)
0.0824374 + 0.996596i \(0.473730\pi\)
\(224\) 94311.8i 0.125587i
\(225\) 48017.9 447063.i 0.0632335 0.588725i
\(226\) 1.62394e6i 2.11494i
\(227\) 385235. 0.496205 0.248102 0.968734i \(-0.420193\pi\)
0.248102 + 0.968734i \(0.420193\pi\)
\(228\) 309109. + 344087.i 0.393799 + 0.438361i
\(229\) 651870. 0.821434 0.410717 0.911763i \(-0.365278\pi\)
0.410717 + 0.911763i \(0.365278\pi\)
\(230\) 180118. 0.224511
\(231\) 22006.4 68930.8i 0.0271344 0.0849930i
\(232\) −266210. −0.324717
\(233\) −830485. −1.00217 −0.501085 0.865398i \(-0.667066\pi\)
−0.501085 + 0.865398i \(0.667066\pi\)
\(234\) 1.91209e6 + 205373.i 2.28280 + 0.245190i
\(235\) 121461. 0.143472
\(236\) 1.21077e6i 1.41508i
\(237\) 280727. + 312494.i 0.324648 + 0.361385i
\(238\) 2459.87i 0.00281495i
\(239\) 1.00232e6 1.13504 0.567518 0.823361i \(-0.307904\pi\)
0.567518 + 0.823361i \(0.307904\pi\)
\(240\) −263653. 293488.i −0.295464 0.328899i
\(241\) 1.51157e6i 1.67643i −0.545341 0.838214i \(-0.683600\pi\)
0.545341 0.838214i \(-0.316400\pi\)
\(242\) −667910. + 1.19111e6i −0.733128 + 1.30742i
\(243\) −799769. + 455695.i −0.868858 + 0.495061i
\(244\) 1.45407e6i 1.56354i
\(245\) 595272.i 0.633578i
\(246\) 1.74628e6 1.56876e6i 1.83982 1.65279i
\(247\) −694110. −0.723912
\(248\) −205688. −0.212364
\(249\) 376384. 338122.i 0.384710 0.345602i
\(250\) 1.50618e6i 1.52415i
\(251\) 605116.i 0.606254i 0.952950 + 0.303127i \(0.0980306\pi\)
−0.952950 + 0.303127i \(0.901969\pi\)
\(252\) 111499. + 11975.9i 0.110604 + 0.0118797i
\(253\) −206030. + 120681.i −0.202362 + 0.118532i
\(254\) 629173.i 0.611908i
\(255\) −9328.47 10384.1i −0.00898379 0.0100004i
\(256\) 358990. 0.342360
\(257\) 825395.i 0.779523i 0.920916 + 0.389762i \(0.127443\pi\)
−0.920916 + 0.389762i \(0.872557\pi\)
\(258\) −2.02374e6 2.25274e6i −1.89280 2.10699i
\(259\) 119342.i 0.110546i
\(260\) −1.32948e6 −1.21969
\(261\) −103156. + 960412.i −0.0937328 + 0.872683i
\(262\) 751306. 0.676182
\(263\) −1.11413e6 −0.993218 −0.496609 0.867974i \(-0.665422\pi\)
−0.496609 + 0.867974i \(0.665422\pi\)
\(264\) −399109. 127417.i −0.352437 0.112517i
\(265\) −440060. −0.384944
\(266\) −72938.6 −0.0632053
\(267\) 112593. + 125334.i 0.0966574 + 0.107595i
\(268\) −1.13997e6 −0.969518
\(269\) 895983.i 0.754952i −0.926019 0.377476i \(-0.876792\pi\)
0.926019 0.377476i \(-0.123208\pi\)
\(270\) 930028. 670862.i 0.776402 0.560046i
\(271\) 983707.i 0.813659i −0.913504 0.406830i \(-0.866634\pi\)
0.913504 0.406830i \(-0.133366\pi\)
\(272\) 17779.6 0.0145714
\(273\) −125187. + 112461.i −0.101660 + 0.0913261i
\(274\) 1.49563e6i 1.20350i
\(275\) −375309. 640740.i −0.299266 0.510916i
\(276\) −247297. 275280.i −0.195409 0.217522i
\(277\) 1.30268e6i 1.02009i −0.860149 0.510043i \(-0.829629\pi\)
0.860149 0.510043i \(-0.170371\pi\)
\(278\) 3.26925e6i 2.53709i
\(279\) −79703.5 + 742066.i −0.0613009 + 0.570732i
\(280\) −27655.5 −0.0210808
\(281\) 1.05493e6 0.796997 0.398499 0.917169i \(-0.369531\pi\)
0.398499 + 0.917169i \(0.369531\pi\)
\(282\) −300513. 334519.i −0.225030 0.250494i
\(283\) 964342.i 0.715756i −0.933768 0.357878i \(-0.883500\pi\)
0.933768 0.357878i \(-0.116500\pi\)
\(284\) 2.36605e6i 1.74072i
\(285\) −307902. + 276602.i −0.224543 + 0.201717i
\(286\) 2.74044e6 1.60519e6i 1.98110 1.16041i
\(287\) 205418.i 0.147209i
\(288\) −211598. + 1.97005e6i −0.150325 + 1.39958i
\(289\) −1.41923e6 −0.999557
\(290\) 1.20336e6i 0.840237i
\(291\) −1.22282e6 + 1.09852e6i −0.846509 + 0.760456i
\(292\) 2.88890e6i 1.98278i
\(293\) −113600. −0.0773056 −0.0386528 0.999253i \(-0.512307\pi\)
−0.0386528 + 0.999253i \(0.512307\pi\)
\(294\) 1.63946e6 1.47279e6i 1.10619 0.993743i
\(295\) 1.08344e6 0.724853
\(296\) 690989. 0.458397
\(297\) −614340. + 1.39050e6i −0.404126 + 0.914703i
\(298\) −1.93857e6 −1.26457
\(299\) 555309. 0.359217
\(300\) 856105. 769077.i 0.549192 0.493363i
\(301\) 264993. 0.168585
\(302\) 1.29485e6i 0.816960i
\(303\) −1.83831e6 + 1.65144e6i −1.15030 + 1.03337i
\(304\) 527191.i 0.327178i
\(305\) −1.30115e6 −0.800900
\(306\) −5518.99 + 51383.6i −0.00336942 + 0.0313705i
\(307\) 873188.i 0.528764i 0.964418 + 0.264382i \(0.0851679\pi\)
−0.964418 + 0.264382i \(0.914832\pi\)
\(308\) 159803. 93603.4i 0.0959860 0.0562231i
\(309\) 1.34926e6 1.21210e6i 0.803897 0.722176i
\(310\) 929783.i 0.549512i
\(311\) 2.69881e6i 1.58223i −0.611665 0.791117i \(-0.709500\pi\)
0.611665 0.791117i \(-0.290500\pi\)
\(312\) 651148. + 724831.i 0.378698 + 0.421551i
\(313\) 1.55310e6 0.896060 0.448030 0.894018i \(-0.352126\pi\)
0.448030 + 0.894018i \(0.352126\pi\)
\(314\) −1.74700e6 −0.999925
\(315\) −10716.4 + 99773.5i −0.00608519 + 0.0566551i
\(316\) 1.07516e6i 0.605696i
\(317\) 710129.i 0.396907i 0.980110 + 0.198454i \(0.0635920\pi\)
−0.980110 + 0.198454i \(0.936408\pi\)
\(318\) 1.08878e6 + 1.21198e6i 0.603769 + 0.672091i
\(319\) 806265. + 1.37648e6i 0.443610 + 0.757345i
\(320\) 1.65853e6i 0.905417i
\(321\) −533479. + 479247.i −0.288971 + 0.259596i
\(322\) 58353.1 0.0313635
\(323\) 18652.8i 0.00994807i
\(324\) −2.30221e6 500321.i −1.21838 0.264780i
\(325\) 1.72698e6i 0.906939i
\(326\) 3.07911e6 1.60465
\(327\) −1.26815e6 1.41165e6i −0.655844 0.730059i
\(328\) 1.18937e6 0.610424
\(329\) 39349.9 0.0200426
\(330\) 575971. 1.80411e6i 0.291149 0.911967i
\(331\) −1.75491e6 −0.880408 −0.440204 0.897898i \(-0.645094\pi\)
−0.440204 + 0.897898i \(0.645094\pi\)
\(332\) 1.29498e6 0.644788
\(333\) 267756. 2.49290e6i 0.132321 1.23195i
\(334\) −4.35902e6 −2.13807
\(335\) 1.02009e6i 0.496620i
\(336\) −85416.3 95081.9i −0.0412755 0.0459462i
\(337\) 2.45919e6i 1.17955i 0.807566 + 0.589777i \(0.200785\pi\)
−0.807566 + 0.589777i \(0.799215\pi\)
\(338\) −4.23798e6 −2.01775
\(339\) 1.99514e6 + 2.22091e6i 0.942920 + 1.04962i
\(340\) 35727.2i 0.0167610i
\(341\) 622964. + 1.06354e6i 0.290119 + 0.495301i
\(342\) 1.52359e6 + 163646.i 0.704375 + 0.0756552i
\(343\) 387251.i 0.177728i
\(344\) 1.53431e6i 0.699064i
\(345\) 246331. 221290.i 0.111422 0.100095i
\(346\) 3.70799e6 1.66513
\(347\) −267251. −0.119150 −0.0595752 0.998224i \(-0.518975\pi\)
−0.0595752 + 0.998224i \(0.518975\pi\)
\(348\) −1.83915e6 + 1.65219e6i −0.814082 + 0.731325i
\(349\) 1.61566e6i 0.710044i −0.934858 0.355022i \(-0.884473\pi\)
0.934858 0.355022i \(-0.115527\pi\)
\(350\) 181475.i 0.0791855i
\(351\) 2.86731e6 2.06829e6i 1.24224 0.896075i
\(352\) 1.65386e6 + 2.82352e6i 0.711445 + 1.21460i
\(353\) 2.34705e6i 1.00250i −0.865302 0.501252i \(-0.832873\pi\)
0.865302 0.501252i \(-0.167127\pi\)
\(354\) −2.68060e6 2.98393e6i −1.13690 1.26555i
\(355\) −2.11723e6 −0.891655
\(356\) 431223.i 0.180334i
\(357\) −3022.16 3364.15i −0.00125501 0.00139703i
\(358\) 1.74049e6i 0.717734i
\(359\) 2.46802e6 1.01068 0.505338 0.862922i \(-0.331368\pi\)
0.505338 + 0.862922i \(0.331368\pi\)
\(360\) 577689. + 62048.1i 0.234929 + 0.0252332i
\(361\) 1.92302e6 0.776631
\(362\) 2.32595e6 0.932888
\(363\) 549942. + 2.44956e6i 0.219053 + 0.975713i
\(364\) −430715. −0.170387
\(365\) 2.58509e6 1.01565
\(366\) 3.21925e6 + 3.58354e6i 1.25618 + 1.39833i
\(367\) 775093. 0.300392 0.150196 0.988656i \(-0.452009\pi\)
0.150196 + 0.988656i \(0.452009\pi\)
\(368\) 421769.i 0.162351i
\(369\) 460876. 4.29091e6i 0.176205 1.64053i
\(370\) 3.12352e6i 1.18615i
\(371\) −142567. −0.0537755
\(372\) −1.42102e6 + 1.27657e6i −0.532407 + 0.478284i
\(373\) 1.09178e6i 0.406315i 0.979146 + 0.203158i \(0.0651204\pi\)
−0.979146 + 0.203158i \(0.934880\pi\)
\(374\) 43136.5 + 73644.0i 0.0159465 + 0.0272244i
\(375\) 1.85048e6 + 2.05987e6i 0.679525 + 0.756419i
\(376\) 227836.i 0.0831099i
\(377\) 3.71001e6i 1.34438i
\(378\) 301303. 217341.i 0.108461 0.0782369i
\(379\) 171895. 0.0614701 0.0307351 0.999528i \(-0.490215\pi\)
0.0307351 + 0.999528i \(0.490215\pi\)
\(380\) −1.05936e6 −0.376343
\(381\) −772993. 860464.i −0.272812 0.303683i
\(382\) 5.35294e6i 1.87687i
\(383\) 364164.i 0.126853i 0.997987 + 0.0634263i \(0.0202028\pi\)
−0.997987 + 0.0634263i \(0.979797\pi\)
\(384\) −1.54205e6 + 1.38530e6i −0.533669 + 0.479418i
\(385\) 83759.8 + 142997.i 0.0287994 + 0.0491673i
\(386\) 47881.9i 0.0163570i
\(387\) −5.53537e6 594540.i −1.87875 0.201792i
\(388\) −4.20722e6 −1.41878
\(389\) 1.57588e6i 0.528020i 0.964520 + 0.264010i \(0.0850451\pi\)
−0.964520 + 0.264010i \(0.914955\pi\)
\(390\) −3.27650e6 + 2.94342e6i −1.09081 + 0.979920i
\(391\) 14922.8i 0.00493639i
\(392\) 1.11661e6 0.367017
\(393\) 1.02749e6 923044.i 0.335582 0.301468i
\(394\) −6.27272e6 −2.03571
\(395\) −962091. −0.310258
\(396\) −3.54809e6 + 1.59672e6i −1.13699 + 0.511671i
\(397\) −2.37799e6 −0.757241 −0.378620 0.925552i \(-0.623601\pi\)
−0.378620 + 0.925552i \(0.623601\pi\)
\(398\) 1.82382e6 0.577132
\(399\) −99751.7 + 89611.3i −0.0313681 + 0.0281793i
\(400\) −1.31167e6 −0.409898
\(401\) 794365.i 0.246694i 0.992364 + 0.123347i \(0.0393629\pi\)
−0.992364 + 0.123347i \(0.960637\pi\)
\(402\) −2.80945e6 + 2.52385e6i −0.867073 + 0.778930i
\(403\) 2.86656e6i 0.879221i
\(404\) −6.32484e6 −1.92795
\(405\) 447705. 2.06010e6i 0.135630 0.624094i
\(406\) 389857.i 0.117379i
\(407\) −2.09278e6 3.57287e6i −0.626237 1.06913i
\(408\) −19478.4 + 17498.3i −0.00579300 + 0.00520411i
\(409\) 2.20976e6i 0.653185i 0.945165 + 0.326593i \(0.105901\pi\)
−0.945165 + 0.326593i \(0.894099\pi\)
\(410\) 5.37636e6i 1.57953i
\(411\) 1.83751e6 + 2.04544e6i 0.536567 + 0.597285i
\(412\) 4.64224e6 1.34736
\(413\) 351005. 0.101260
\(414\) −1.21892e6 130921.i −0.349522 0.0375414i
\(415\) 1.15879e6i 0.330283i
\(416\) 7.61019e6i 2.15607i
\(417\) 4.01656e6 + 4.47107e6i 1.13113 + 1.25913i
\(418\) 2.18365e6 1.27906e6i 0.611282 0.358054i
\(419\) 7.13523e6i 1.98551i 0.120136 + 0.992757i \(0.461667\pi\)
−0.120136 + 0.992757i \(0.538333\pi\)
\(420\) −191062. + 171639.i −0.0528507 + 0.0474781i
\(421\) 608256. 0.167256 0.0836279 0.996497i \(-0.473349\pi\)
0.0836279 + 0.996497i \(0.473349\pi\)
\(422\) 1.67784e6i 0.458638i
\(423\) −821969. 88285.7i −0.223360 0.0239905i
\(424\) 825464.i 0.222989i
\(425\) −46409.1 −0.0124632
\(426\) 5.23835e6 + 5.83112e6i 1.39853 + 1.55678i
\(427\) −421537. −0.111883
\(428\) −1.83547e6 −0.484327
\(429\) 1.77574e6 5.56215e6i 0.465839 1.45915i
\(430\) 6.93563e6 1.80890
\(431\) 3.42629e6 0.888445 0.444222 0.895917i \(-0.353480\pi\)
0.444222 + 0.895917i \(0.353480\pi\)
\(432\) 1.57091e6 + 2.17778e6i 0.404988 + 0.561442i
\(433\) 6.94631e6 1.78047 0.890234 0.455503i \(-0.150541\pi\)
0.890234 + 0.455503i \(0.150541\pi\)
\(434\) 301224.i 0.0767654i
\(435\) −1.47844e6 1.64573e6i −0.374610 0.417000i
\(436\) 4.85689e6i 1.22361i
\(437\) 442483. 0.110839
\(438\) −6.39592e6 7.11968e6i −1.59301 1.77327i
\(439\) 2.33491e6i 0.578240i 0.957293 + 0.289120i \(0.0933627\pi\)
−0.957293 + 0.289120i \(0.906637\pi\)
\(440\) 827955. 484969.i 0.203880 0.119421i
\(441\) 432683. 4.02842e6i 0.105943 0.986367i
\(442\) 198492.i 0.0483266i
\(443\) 101850.i 0.0246576i 0.999924 + 0.0123288i \(0.00392448\pi\)
−0.999924 + 0.0123288i \(0.996076\pi\)
\(444\) 4.77378e6 4.28850e6i 1.14923 1.03240i
\(445\) −385874. −0.0923730
\(446\) 1.03819e6 0.247137
\(447\) −2.65122e6 + 2.38170e6i −0.627590 + 0.563792i
\(448\) 537318.i 0.126484i
\(449\) 3.38226e6i 0.791756i 0.918303 + 0.395878i \(0.129560\pi\)
−0.918303 + 0.395878i \(0.870440\pi\)
\(450\) 407157. 3.79077e6i 0.0947831 0.882462i
\(451\) −3.60221e6 6.14982e6i −0.833927 1.42371i
\(452\) 7.64121e6i 1.75920i
\(453\) 1.59083e6 + 1.77085e6i 0.364232 + 0.405448i
\(454\) 3.26651e6 0.743781
\(455\) 385419.i 0.0872780i
\(456\) 518849. + 577562.i 0.116850 + 0.130073i
\(457\) 409738.i 0.0917731i −0.998947 0.0458865i \(-0.985389\pi\)
0.998947 0.0458865i \(-0.0146113\pi\)
\(458\) 5.52739e6 1.23128
\(459\) 55581.3 + 77053.3i 0.0123139 + 0.0170710i
\(460\) 847520. 0.186748
\(461\) −4.36832e6 −0.957331 −0.478666 0.877997i \(-0.658879\pi\)
−0.478666 + 0.877997i \(0.658879\pi\)
\(462\) 186599. 584483.i 0.0406727 0.127399i
\(463\) −597751. −0.129589 −0.0647945 0.997899i \(-0.520639\pi\)
−0.0647945 + 0.997899i \(0.520639\pi\)
\(464\) 2.81783e6 0.607603
\(465\) −1.14232e6 1.27158e6i −0.244994 0.272717i
\(466\) −7.04191e6 −1.50219
\(467\) 1.49460e6i 0.317126i −0.987349 0.158563i \(-0.949314\pi\)
0.987349 0.158563i \(-0.0506860\pi\)
\(468\) 8.99707e6 + 966354.i 1.89883 + 0.203949i
\(469\) 330479.i 0.0693765i
\(470\) 1.02990e6 0.215055
\(471\) −2.38921e6 + 2.14633e6i −0.496252 + 0.445805i
\(472\) 2.03232e6i 0.419891i
\(473\) −7.93340e6 + 4.64693e6i −1.63045 + 0.955023i
\(474\) 2.38036e6 + 2.64972e6i 0.486628 + 0.541695i
\(475\) 1.37609e6i 0.279843i
\(476\) 11574.6i 0.00234147i
\(477\) 2.97804e6 + 319865.i 0.599288 + 0.0643680i
\(478\) 8.49891e6 1.70135
\(479\) 1.50621e6 0.299948 0.149974 0.988690i \(-0.452081\pi\)
0.149974 + 0.988690i \(0.452081\pi\)
\(480\) −3.03265e6 3.37582e6i −0.600785 0.668769i
\(481\) 9.62991e6i 1.89784i
\(482\) 1.28170e7i 2.51286i
\(483\) 79804.4 71691.8i 0.0155654 0.0139830i
\(484\) −3.14276e6 + 5.60462e6i −0.609815 + 1.08751i
\(485\) 3.76477e6i 0.726749i
\(486\) −6.78146e6 + 3.86396e6i −1.30237 + 0.742066i
\(487\) −7.28245e6 −1.39141 −0.695705 0.718328i \(-0.744908\pi\)
−0.695705 + 0.718328i \(0.744908\pi\)
\(488\) 2.44070e6i 0.463943i
\(489\) 4.21103e6 3.78295e6i 0.796372 0.715416i
\(490\) 5.04747e6i 0.949694i
\(491\) −8.22691e6 −1.54004 −0.770022 0.638017i \(-0.779755\pi\)
−0.770022 + 0.638017i \(0.779755\pi\)
\(492\) 8.21689e6 7.38160e6i 1.53036 1.37479i
\(493\) 99699.4 0.0184746
\(494\) −5.88555e6 −1.08510
\(495\) −1.42880e6 3.17496e6i −0.262095 0.582404i
\(496\) 2.17721e6 0.397371
\(497\) −685923. −0.124562
\(498\) 3.19146e6 2.86703e6i 0.576656 0.518035i
\(499\) −8.77367e6 −1.57736 −0.788678 0.614806i \(-0.789234\pi\)
−0.788678 + 0.614806i \(0.789234\pi\)
\(500\) 7.08715e6i 1.26779i
\(501\) −5.96144e6 + 5.35543e6i −1.06110 + 0.953234i
\(502\) 5.13095e6i 0.908737i
\(503\) 4.73850e6 0.835066 0.417533 0.908662i \(-0.362895\pi\)
0.417533 + 0.908662i \(0.362895\pi\)
\(504\) 187155. + 20101.9i 0.0328190 + 0.00352501i
\(505\) 5.65970e6i 0.987563i
\(506\) −1.74698e6 + 1.02328e6i −0.303328 + 0.177672i
\(507\) −5.79591e6 + 5.20672e6i −1.00139 + 0.899589i
\(508\) 2.96049e6i 0.508985i
\(509\) 1.42203e6i 0.243285i −0.992574 0.121642i \(-0.961184\pi\)
0.992574 0.121642i \(-0.0388161\pi\)
\(510\) −79098.6 88049.4i −0.0134662 0.0149900i
\(511\) 837498. 0.141883
\(512\) 7.29926e6 1.23056
\(513\) 2.28474e6 1.64806e6i 0.383303 0.276490i
\(514\) 6.99875e6i 1.16846i
\(515\) 4.15405e6i 0.690165i
\(516\) −9.52242e6 1.06000e7i −1.57443 1.75259i
\(517\) −1.17806e6 + 690042.i −0.193839 + 0.113540i
\(518\) 1.01193e6i 0.165702i
\(519\) 5.07108e6 4.55558e6i 0.826385 0.742378i
\(520\) −2.23158e6 −0.361912
\(521\) 5.82338e6i 0.939898i 0.882694 + 0.469949i \(0.155728\pi\)
−0.882694 + 0.469949i \(0.844272\pi\)
\(522\) −874684. + 8.14360e6i −0.140500 + 1.30810i
\(523\) 7.18394e6i 1.14844i −0.818701 0.574220i \(-0.805305\pi\)
0.818701 0.574220i \(-0.194695\pi\)
\(524\) 3.53517e6 0.562448
\(525\) 222957. + 248187.i 0.0353039 + 0.0392989i
\(526\) −9.44698e6 −1.48877
\(527\) 77033.1 0.0120823
\(528\) 4.22456e6 + 1.34871e6i 0.659473 + 0.210540i
\(529\) 6.08234e6 0.945000
\(530\) −3.73139e6 −0.577007
\(531\) −7.33203e6 787516.i −1.12846 0.121206i
\(532\) −343203. −0.0525741
\(533\) 1.65755e7i 2.52726i
\(534\) 954711. + 1.06275e6i 0.144883 + 0.161278i
\(535\) 1.64245e6i 0.248089i
\(536\) −1.91348e6 −0.287681
\(537\) −2.13834e6 2.38031e6i −0.319993 0.356203i
\(538\) 7.59729e6i 1.13163i
\(539\) −3.38185e6 5.77361e6i −0.501398 0.856004i
\(540\) 4.37612e6 3.15665e6i 0.645811 0.465846i
\(541\) 6.78324e6i 0.996424i −0.867055 0.498212i \(-0.833990\pi\)
0.867055 0.498212i \(-0.166010\pi\)
\(542\) 8.34112e6i 1.21962i
\(543\) 3.18100e6 2.85763e6i 0.462982 0.415917i
\(544\) 204509. 0.0296289
\(545\) 4.34612e6 0.626773
\(546\) −1.06149e6 + 953587.i −0.152383 + 0.136892i
\(547\) 1.36297e6i 0.194768i 0.995247 + 0.0973842i \(0.0310476\pi\)
−0.995247 + 0.0973842i \(0.968952\pi\)
\(548\) 7.03748e6i 1.00107i
\(549\) 8.80536e6 + 945762.i 1.24686 + 0.133922i
\(550\) −3.18235e6 5.43301e6i −0.448581 0.765832i
\(551\) 2.95622e6i 0.414819i
\(552\) −415095. 462067.i −0.0579830 0.0645443i
\(553\) −311691. −0.0433422
\(554\) 1.10458e7i 1.52905i
\(555\) 3.83751e6 + 4.27176e6i 0.528831 + 0.588673i
\(556\) 1.53830e7i 2.11035i
\(557\) −7.72310e6 −1.05476 −0.527380 0.849629i \(-0.676826\pi\)
−0.527380 + 0.849629i \(0.676826\pi\)
\(558\) −675828. + 6.29218e6i −0.0918863 + 0.855492i
\(559\) 2.13828e7 2.89424
\(560\) 292734. 0.0394460
\(561\) 149472. + 47719.5i 0.0200517 + 0.00640160i
\(562\) 8.94502e6 1.19465
\(563\) 7.28192e6 0.968222 0.484111 0.875007i \(-0.339143\pi\)
0.484111 + 0.875007i \(0.339143\pi\)
\(564\) −1.41402e6 1.57403e6i −0.187180 0.208361i
\(565\) −6.83764e6 −0.901125
\(566\) 8.17692e6i 1.07287i
\(567\) 145044. 667414.i 0.0189471 0.0871842i
\(568\) 3.97149e6i 0.516515i
\(569\) 8.25749e6 1.06922 0.534610 0.845099i \(-0.320458\pi\)
0.534610 + 0.845099i \(0.320458\pi\)
\(570\) −2.61079e6 + 2.34538e6i −0.336577 + 0.302362i
\(571\) 2.50822e6i 0.321940i 0.986959 + 0.160970i \(0.0514623\pi\)
−0.986959 + 0.160970i \(0.948538\pi\)
\(572\) 1.28948e7 7.55303e6i 1.64787 0.965231i
\(573\) −6.57654e6 7.32074e6i −0.836780 0.931469i
\(574\) 1.74179e6i 0.220657i
\(575\) 1.10092e6i 0.138863i
\(576\) −1.20553e6 + 1.12239e7i −0.151399 + 1.40957i
\(577\) 1.64671e6 0.205910 0.102955 0.994686i \(-0.467170\pi\)
0.102955 + 0.994686i \(0.467170\pi\)
\(578\) −1.20340e7 −1.49827
\(579\) 58827.0 + 65483.8i 0.00729257 + 0.00811779i
\(580\) 5.66227e6i 0.698909i
\(581\) 375417.i 0.0461396i
\(582\) −1.03687e7 + 9.31463e6i −1.26886 + 1.13988i
\(583\) 4.26819e6 2.50006e6i 0.520083 0.304635i
\(584\) 4.84911e6i 0.588342i
\(585\) −864728. + 8.05091e6i −0.104470 + 0.972647i
\(586\) −963249. −0.115876
\(587\) 2.51572e6i 0.301348i 0.988584 + 0.150674i \(0.0481443\pi\)
−0.988584 + 0.150674i \(0.951856\pi\)
\(588\) 7.71424e6 6.93004e6i 0.920131 0.826595i
\(589\) 2.28414e6i 0.271290i
\(590\) 9.18679e6 1.08651
\(591\) −8.57865e6 + 7.70658e6i −1.01030 + 0.907597i
\(592\) −7.31412e6 −0.857744
\(593\) 1.66834e6 0.194827 0.0974133 0.995244i \(-0.468943\pi\)
0.0974133 + 0.995244i \(0.468943\pi\)
\(594\) −5.20915e6 + 1.17904e7i −0.605761 + 1.37108i
\(595\) 10357.4 0.00119938
\(596\) −9.12171e6 −1.05187
\(597\) 2.49428e6 2.24072e6i 0.286424 0.257307i
\(598\) 4.70862e6 0.538444
\(599\) 1.36017e7i 1.54891i −0.632628 0.774456i \(-0.718024\pi\)
0.632628 0.774456i \(-0.281976\pi\)
\(600\) 1.43700e6 1.29092e6i 0.162959 0.146393i
\(601\) 1.08809e7i 1.22880i −0.788996 0.614399i \(-0.789399\pi\)
0.788996 0.614399i \(-0.210601\pi\)
\(602\) 2.24695e6 0.252698
\(603\) −741465. + 6.90329e6i −0.0830420 + 0.773148i
\(604\) 6.09273e6i 0.679547i
\(605\) −5.01522e6 2.81226e6i −0.557059 0.312368i
\(606\) −1.55875e7 + 1.40030e7i −1.72423 + 1.54895i
\(607\) 1.54469e7i 1.70164i 0.525453 + 0.850822i \(0.323896\pi\)
−0.525453 + 0.850822i \(0.676104\pi\)
\(608\) 6.06397e6i 0.665270i
\(609\) −478972. 533172.i −0.0523320 0.0582538i
\(610\) −1.10328e7 −1.20050
\(611\) 3.17522e6 0.344089
\(612\) −25968.9 + 241779.i −0.00280269 + 0.0260939i
\(613\) 1.71306e7i 1.84128i −0.390409 0.920641i \(-0.627666\pi\)
0.390409 0.920641i \(-0.372334\pi\)
\(614\) 7.40400e6i 0.792584i
\(615\) 6.60532e6 + 7.35277e6i 0.704216 + 0.783905i
\(616\) 268234. 157116.i 0.0284815 0.0166828i
\(617\) 1.25814e7i 1.33050i −0.746620 0.665251i \(-0.768325\pi\)
0.746620 0.665251i \(-0.231675\pi\)
\(618\) 1.14408e7 1.02778e7i 1.20499 1.08250i
\(619\) 8.53512e6 0.895330 0.447665 0.894201i \(-0.352256\pi\)
0.447665 + 0.894201i \(0.352256\pi\)
\(620\) 4.37497e6i 0.457084i
\(621\) −1.82786e6 + 1.31850e6i −0.190201 + 0.137199i
\(622\) 2.28839e7i 2.37167i
\(623\) −125012. −0.0129043
\(624\) −6.89240e6 7.67233e6i −0.708612 0.788798i
\(625\) −559506. −0.0572934
\(626\) 1.31691e7 1.34314
\(627\) 1.41495e6 4.43205e6i 0.143738 0.450231i
\(628\) −8.22026e6 −0.831737
\(629\) −258785. −0.0260803
\(630\) −90867.6 + 846007.i −0.00912132 + 0.0849225i
\(631\) 1.89108e7 1.89076 0.945382 0.325964i \(-0.105689\pi\)
0.945382 + 0.325964i \(0.105689\pi\)
\(632\) 1.80469e6i 0.179725i
\(633\) −2.06137e6 2.29464e6i −0.204478 0.227617i
\(634\) 6.02138e6i 0.594940i
\(635\) 2.64916e6 0.260719
\(636\) 5.12309e6 + 5.70282e6i 0.502215 + 0.559045i
\(637\) 1.55615e7i 1.51951i
\(638\) 6.83654e6 + 1.16716e7i 0.664944 + 1.13521i
\(639\) 1.43281e7 + 1.53894e6i 1.38815 + 0.149097i
\(640\) 4.74760e6i 0.458168i
\(641\) 1.39715e7i 1.34307i 0.740975 + 0.671533i \(0.234364\pi\)
−0.740975 + 0.671533i \(0.765636\pi\)
\(642\) −4.52351e6 + 4.06367e6i −0.433150 + 0.389118i
\(643\) −8.35019e6 −0.796469 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(644\) 274573. 0.0260881
\(645\) 9.48524e6 8.52101e6i 0.897737 0.806477i
\(646\) 158163.i 0.0149115i
\(647\) 5.28911e6i 0.496732i −0.968666 0.248366i \(-0.920106\pi\)
0.968666 0.248366i \(-0.0798935\pi\)
\(648\) −3.86433e6 839804.i −0.361523 0.0785671i
\(649\) −1.05084e7 + 6.15523e6i −0.979322 + 0.573631i
\(650\) 1.46435e7i 1.35945i
\(651\) −370080. 411957.i −0.0342249 0.0380978i
\(652\) 1.44884e7 1.33475
\(653\) 1.31576e7i 1.20752i 0.797167 + 0.603759i \(0.206331\pi\)
−0.797167 + 0.603759i \(0.793669\pi\)
\(654\) −1.07530e7 1.19698e7i −0.983070 1.09431i
\(655\) 3.16340e6i 0.288105i
\(656\) −1.25894e7 −1.14221
\(657\) −1.74943e7 1.87902e6i −1.58118 0.169831i
\(658\) 333659. 0.0300426
\(659\) 5.31432e6 0.476688 0.238344 0.971181i \(-0.423395\pi\)
0.238344 + 0.971181i \(0.423395\pi\)
\(660\) 2.71016e6 8.48902e6i 0.242178 0.758574i
\(661\) −1.46817e7 −1.30699 −0.653496 0.756930i \(-0.726698\pi\)
−0.653496 + 0.756930i \(0.726698\pi\)
\(662\) −1.48803e7 −1.31968
\(663\) −243864. 271459.i −0.0215459 0.0239840i
\(664\) 2.17366e6 0.191325
\(665\) 307111.i 0.0269303i
\(666\) 2.27038e6 2.11380e7i 0.198341 1.84662i
\(667\) 2.36507e6i 0.205840i
\(668\) −2.05108e7 −1.77845
\(669\) 1.41984e6 1.27550e6i 0.122651 0.110183i
\(670\) 8.64959e6i 0.744403i
\(671\) 1.26200e7 7.39209e6i 1.08207 0.633813i
\(672\) −982495. 1.09367e6i −0.0839280 0.0934252i
\(673\) 9.05171e6i 0.770359i 0.922842 + 0.385179i \(0.125860\pi\)
−0.922842 + 0.385179i \(0.874140\pi\)
\(674\) 2.08522e7i 1.76808i
\(675\) −4.10045e6 5.68453e6i −0.346396 0.480214i
\(676\) −1.99413e7 −1.67836
\(677\) −1.80121e7 −1.51040 −0.755199 0.655495i \(-0.772460\pi\)
−0.755199 + 0.655495i \(0.772460\pi\)
\(678\) 1.69174e7 + 1.88317e7i 1.41338 + 1.57332i
\(679\) 1.21968e6i 0.101525i
\(680\) 59969.2i 0.00497343i
\(681\) 4.46732e6 4.01319e6i 0.369130 0.331606i
\(682\) 5.28228e6 + 9.01808e6i 0.434871 + 0.742426i
\(683\) 4.17593e6i 0.342532i −0.985225 0.171266i \(-0.945214\pi\)
0.985225 0.171266i \(-0.0547857\pi\)
\(684\) 7.16907e6 + 770013.i 0.585899 + 0.0629300i
\(685\) −6.29739e6 −0.512784
\(686\) 3.28360e6i 0.266404i
\(687\) 7.55932e6 6.79087e6i 0.611070 0.548951i
\(688\) 1.62407e7i 1.30807i
\(689\) −1.15040e7 −0.923211
\(690\) 2.08871e6 1.87638e6i 0.167015 0.150037i
\(691\) −1.40556e7 −1.11983 −0.559917 0.828549i \(-0.689167\pi\)
−0.559917 + 0.828549i \(0.689167\pi\)
\(692\) 1.74474e7 1.38505
\(693\) −462893. 1.02860e6i −0.0366140 0.0813603i
\(694\) −2.26609e6 −0.178599
\(695\) −1.37653e7 −1.08099
\(696\) −3.08707e6 + 2.77325e6i −0.241559 + 0.217003i
\(697\) −445435. −0.0347298
\(698\) 1.36996e7i 1.06431i
\(699\) −9.63059e6 + 8.65159e6i −0.745521 + 0.669735i
\(700\) 853905.i 0.0658665i
\(701\) 1.12544e7 0.865021 0.432510 0.901629i \(-0.357628\pi\)
0.432510 + 0.901629i \(0.357628\pi\)
\(702\) 2.43127e7 1.75376e7i 1.86205 1.34316i
\(703\) 7.67333e6i 0.585593i
\(704\) 9.42244e6 + 1.60863e7i 0.716525 + 1.22328i
\(705\) 1.40850e6 1.26532e6i 0.106730 0.0958799i
\(706\) 1.99013e7i 1.50269i
\(707\) 1.83359e6i 0.137960i
\(708\) −1.26132e7 1.40405e7i −0.945676 1.05269i
\(709\) −1.03584e7 −0.773886 −0.386943 0.922104i \(-0.626469\pi\)
−0.386943 + 0.922104i \(0.626469\pi\)
\(710\) −1.79526e7 −1.33654
\(711\) 6.51082e6 + 699311.i 0.483016 + 0.0518796i
\(712\) 723821.i 0.0535096i
\(713\) 1.82738e6i 0.134619i
\(714\) −25625.8 28525.6i −0.00188118 0.00209406i
\(715\) 6.75873e6 + 1.15387e7i 0.494424 + 0.844097i
\(716\) 8.18964e6i 0.597011i
\(717\) 1.16232e7 1.04416e7i 0.844360 0.758526i
\(718\) 2.09270e7 1.51494
\(719\) 2.24287e7i 1.61802i −0.587798 0.809008i \(-0.700005\pi\)
0.587798 0.809008i \(-0.299995\pi\)
\(720\) −6.11483e6 656779.i −0.439595 0.0472159i
\(721\) 1.34580e6i 0.0964142i
\(722\) 1.63058e7 1.16412
\(723\) −1.57468e7 1.75287e7i −1.12033 1.24711i
\(724\) 1.09445e7 0.775976
\(725\) −7.35522e6 −0.519697
\(726\) 4.66311e6 + 2.07705e7i 0.328348 + 1.46253i
\(727\) −997757. −0.0700146 −0.0350073 0.999387i \(-0.511145\pi\)
−0.0350073 + 0.999387i \(0.511145\pi\)
\(728\) −722969. −0.0505581
\(729\) −4.52720e6 + 1.36160e7i −0.315508 + 0.948923i
\(730\) 2.19197e7 1.52240
\(731\) 574620.i 0.0397729i
\(732\) 1.51478e7 + 1.68619e7i 1.04489 + 1.16313i
\(733\) 7.84829e6i 0.539529i 0.962926 + 0.269765i \(0.0869459\pi\)
−0.962926 + 0.269765i \(0.913054\pi\)
\(734\) 6.57223e6 0.450270
\(735\) 6.20125e6 + 6.90298e6i 0.423410 + 0.471323i
\(736\) 4.85136e6i 0.330118i
\(737\) 5.79530e6 + 9.89393e6i 0.393013 + 0.670965i
\(738\) 3.90790e6 3.63838e7i 0.264120 2.45905i
\(739\) 1.45015e7i 0.976793i −0.872622 0.488396i \(-0.837582\pi\)
0.872622 0.488396i \(-0.162418\pi\)
\(740\) 1.46973e7i 0.986639i
\(741\) −8.04915e6 + 7.23090e6i −0.538523 + 0.483779i
\(742\) −1.20887e6 −0.0806062
\(743\) 1.82193e7 1.21076 0.605382 0.795935i \(-0.293021\pi\)
0.605382 + 0.795935i \(0.293021\pi\)
\(744\) −2.38523e6 + 2.14276e6i −0.157979 + 0.141919i
\(745\) 8.16243e6i 0.538802i
\(746\) 9.25750e6i 0.609041i
\(747\) 842287. 7.84197e6i 0.0552279 0.514190i
\(748\) 202973. + 346522.i 0.0132643 + 0.0226452i
\(749\) 532108.i 0.0346573i
\(750\) 1.56907e7 + 1.74662e7i 1.01857 + 1.13383i
\(751\) 7.12675e6 0.461097 0.230548 0.973061i \(-0.425948\pi\)
0.230548 + 0.973061i \(0.425948\pi\)
\(752\) 2.41164e6i 0.155514i
\(753\) 6.30381e6 + 7.01714e6i 0.405150 + 0.450996i
\(754\) 3.14582e7i 2.01514i
\(755\) −5.45200e6 −0.348087
\(756\) 1.41774e6 1.02267e6i 0.0902180 0.0650774i
\(757\) 1.78957e7 1.13503 0.567516 0.823362i \(-0.307904\pi\)
0.567516 + 0.823362i \(0.307904\pi\)
\(758\) 1.45754e6 0.0921399
\(759\) −1.13200e6 + 3.54577e6i −0.0713252 + 0.223412i
\(760\) −1.77817e6 −0.111671
\(761\) −1.04149e7 −0.651916 −0.325958 0.945384i \(-0.605687\pi\)
−0.325958 + 0.945384i \(0.605687\pi\)
\(762\) −6.55442e6 7.29612e6i −0.408928 0.455202i
\(763\) 1.40802e6 0.0875585
\(764\) 2.51876e7i 1.56118i
\(765\) −216352. 23237.9i −0.0133662 0.00143563i
\(766\) 3.08784e6i 0.190144i
\(767\) 2.83232e7 1.73842
\(768\) 4.16298e6 3.73979e6i 0.254684 0.228794i
\(769\) 1.29678e7i 0.790772i −0.918515 0.395386i \(-0.870611\pi\)
0.918515 0.395386i \(-0.129389\pi\)
\(770\) 710222. + 1.21251e6i 0.0431685 + 0.0736988i
\(771\) 8.59856e6 + 9.57157e6i 0.520943 + 0.579892i
\(772\) 225302.i 0.0136057i
\(773\) 9.88927e6i 0.595272i −0.954679 0.297636i \(-0.903802\pi\)
0.954679 0.297636i \(-0.0961982\pi\)
\(774\) −4.69359e7 5.04127e6i −2.81613 0.302474i
\(775\) −5.68303e6 −0.339880