Properties

Label 105.3.h.a.76.12
Level 105
Weight 3
Character 105.76
Analytic conductor 2.861
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.12
Root \(1.31896 + 2.28450i\) of \(x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} - 5472 x^{3} + 4950 x^{2} - 1638 x + 441\)
Character \(\chi\) \(=\) 105.76
Dual form 105.3.h.a.76.11

$q$-expansion

\(f(q)\) \(=\) \(q+3.50369 q^{2} +1.73205i q^{3} +8.27584 q^{4} -2.23607i q^{5} +6.06857i q^{6} +(-6.69736 + 2.03600i) q^{7} +14.9812 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+3.50369 q^{2} +1.73205i q^{3} +8.27584 q^{4} -2.23607i q^{5} +6.06857i q^{6} +(-6.69736 + 2.03600i) q^{7} +14.9812 q^{8} -3.00000 q^{9} -7.83449i q^{10} -2.03112 q^{11} +14.3342i q^{12} -18.0174i q^{13} +(-23.4655 + 7.13352i) q^{14} +3.87298 q^{15} +19.3861 q^{16} +1.07289i q^{17} -10.5111 q^{18} +28.7852i q^{19} -18.5053i q^{20} +(-3.52646 - 11.6002i) q^{21} -7.11640 q^{22} +24.8710 q^{23} +25.9482i q^{24} -5.00000 q^{25} -63.1275i q^{26} -5.19615i q^{27} +(-55.4263 + 16.8496i) q^{28} -38.4300 q^{29} +13.5697 q^{30} -44.0899i q^{31} +7.99812 q^{32} -3.51800i q^{33} +3.75906i q^{34} +(4.55264 + 14.9758i) q^{35} -24.8275 q^{36} +37.2832 q^{37} +100.855i q^{38} +31.2071 q^{39} -33.4990i q^{40} +49.9206i q^{41} +(-12.3556 - 40.6434i) q^{42} -9.58871 q^{43} -16.8092 q^{44} +6.70820i q^{45} +87.1402 q^{46} +55.6978i q^{47} +33.5777i q^{48} +(40.7094 - 27.2717i) q^{49} -17.5184 q^{50} -1.85829 q^{51} -149.109i q^{52} +57.4656 q^{53} -18.2057i q^{54} +4.54171i q^{55} +(-100.335 + 30.5018i) q^{56} -49.8575 q^{57} -134.647 q^{58} +101.697i q^{59} +32.0522 q^{60} -31.9530i q^{61} -154.477i q^{62} +(20.0921 - 6.10801i) q^{63} -49.5215 q^{64} -40.2882 q^{65} -12.3260i q^{66} +95.7318 q^{67} +8.87902i q^{68} +43.0778i q^{69} +(15.9510 + 52.4704i) q^{70} -25.8039 q^{71} -44.9436 q^{72} -95.6803i q^{73} +130.629 q^{74} -8.66025i q^{75} +238.222i q^{76} +(13.6031 - 4.13536i) q^{77} +109.340 q^{78} +28.1212 q^{79} -43.3487i q^{80} +9.00000 q^{81} +174.906i q^{82} -103.374i q^{83} +(-29.1844 - 96.0012i) q^{84} +2.39905 q^{85} -33.5959 q^{86} -66.5628i q^{87} -30.4286 q^{88} +29.3629i q^{89} +23.5035i q^{90} +(36.6835 + 120.669i) q^{91} +205.828 q^{92} +76.3659 q^{93} +195.148i q^{94} +64.3658 q^{95} +13.8531i q^{96} -67.6473i q^{97} +(142.633 - 95.5515i) q^{98} +6.09335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10}) \) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} - 16q^{11} - 40q^{14} + 92q^{16} + 12q^{18} + 36q^{21} - 88q^{22} - 64q^{23} - 60q^{25} + 88q^{28} + 104q^{29} - 228q^{32} + 60q^{35} - 132q^{36} + 32q^{37} - 24q^{39} - 60q^{42} + 152q^{43} + 192q^{44} + 200q^{46} + 60q^{49} + 20q^{50} + 24q^{51} + 176q^{53} - 368q^{56} - 240q^{57} - 400q^{58} + 24q^{63} - 20q^{64} - 240q^{65} + 168q^{67} - 60q^{70} + 32q^{71} - 12q^{72} + 184q^{74} + 8q^{77} + 456q^{78} + 120q^{79} + 108q^{81} + 108q^{84} + 120q^{85} + 400q^{86} - 536q^{88} + 24q^{91} + 192q^{92} + 48q^{93} + 884q^{98} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.50369 1.75184 0.875922 0.482452i \(-0.160254\pi\)
0.875922 + 0.482452i \(0.160254\pi\)
\(3\) 1.73205i 0.577350i
\(4\) 8.27584 2.06896
\(5\) 2.23607i 0.447214i
\(6\) 6.06857i 1.01143i
\(7\) −6.69736 + 2.03600i −0.956766 + 0.290857i
\(8\) 14.9812 1.87265
\(9\) −3.00000 −0.333333
\(10\) 7.83449i 0.783449i
\(11\) −2.03112 −0.184647 −0.0923235 0.995729i \(-0.529429\pi\)
−0.0923235 + 0.995729i \(0.529429\pi\)
\(12\) 14.3342i 1.19451i
\(13\) 18.0174i 1.38596i −0.720958 0.692978i \(-0.756298\pi\)
0.720958 0.692978i \(-0.243702\pi\)
\(14\) −23.4655 + 7.13352i −1.67611 + 0.509537i
\(15\) 3.87298 0.258199
\(16\) 19.3861 1.21163
\(17\) 1.07289i 0.0631109i 0.999502 + 0.0315555i \(0.0100461\pi\)
−0.999502 + 0.0315555i \(0.989954\pi\)
\(18\) −10.5111 −0.583948
\(19\) 28.7852i 1.51501i 0.652828 + 0.757506i \(0.273583\pi\)
−0.652828 + 0.757506i \(0.726417\pi\)
\(20\) 18.5053i 0.925267i
\(21\) −3.52646 11.6002i −0.167927 0.552389i
\(22\) −7.11640 −0.323473
\(23\) 24.8710 1.08135 0.540674 0.841232i \(-0.318169\pi\)
0.540674 + 0.841232i \(0.318169\pi\)
\(24\) 25.9482i 1.08117i
\(25\) −5.00000 −0.200000
\(26\) 63.1275i 2.42798i
\(27\) 5.19615i 0.192450i
\(28\) −55.4263 + 16.8496i −1.97951 + 0.601772i
\(29\) −38.4300 −1.32517 −0.662587 0.748985i \(-0.730542\pi\)
−0.662587 + 0.748985i \(0.730542\pi\)
\(30\) 13.5697 0.452324
\(31\) 44.0899i 1.42225i −0.703064 0.711127i \(-0.748185\pi\)
0.703064 0.711127i \(-0.251815\pi\)
\(32\) 7.99812 0.249941
\(33\) 3.51800i 0.106606i
\(34\) 3.75906i 0.110561i
\(35\) 4.55264 + 14.9758i 0.130075 + 0.427879i
\(36\) −24.8275 −0.689653
\(37\) 37.2832 1.00765 0.503827 0.863804i \(-0.331925\pi\)
0.503827 + 0.863804i \(0.331925\pi\)
\(38\) 100.855i 2.65407i
\(39\) 31.2071 0.800182
\(40\) 33.4990i 0.837474i
\(41\) 49.9206i 1.21758i 0.793333 + 0.608788i \(0.208344\pi\)
−0.793333 + 0.608788i \(0.791656\pi\)
\(42\) −12.3556 40.6434i −0.294181 0.967700i
\(43\) −9.58871 −0.222993 −0.111497 0.993765i \(-0.535564\pi\)
−0.111497 + 0.993765i \(0.535564\pi\)
\(44\) −16.8092 −0.382027
\(45\) 6.70820i 0.149071i
\(46\) 87.1402 1.89435
\(47\) 55.6978i 1.18506i 0.805549 + 0.592529i \(0.201871\pi\)
−0.805549 + 0.592529i \(0.798129\pi\)
\(48\) 33.5777i 0.699536i
\(49\) 40.7094 27.2717i 0.830804 0.556565i
\(50\) −17.5184 −0.350369
\(51\) −1.85829 −0.0364371
\(52\) 149.109i 2.86749i
\(53\) 57.4656 1.08426 0.542128 0.840296i \(-0.317619\pi\)
0.542128 + 0.840296i \(0.317619\pi\)
\(54\) 18.2057i 0.337143i
\(55\) 4.54171i 0.0825766i
\(56\) −100.335 + 30.5018i −1.79169 + 0.544674i
\(57\) −49.8575 −0.874693
\(58\) −134.647 −2.32150
\(59\) 101.697i 1.72368i 0.507178 + 0.861841i \(0.330689\pi\)
−0.507178 + 0.861841i \(0.669311\pi\)
\(60\) 32.0522 0.534203
\(61\) 31.9530i 0.523819i −0.965092 0.261910i \(-0.915648\pi\)
0.965092 0.261910i \(-0.0843523\pi\)
\(62\) 154.477i 2.49157i
\(63\) 20.0921 6.10801i 0.318922 0.0969525i
\(64\) −49.5215 −0.773774
\(65\) −40.2882 −0.619819
\(66\) 12.3260i 0.186757i
\(67\) 95.7318 1.42883 0.714416 0.699721i \(-0.246692\pi\)
0.714416 + 0.699721i \(0.246692\pi\)
\(68\) 8.87902i 0.130574i
\(69\) 43.0778i 0.624316i
\(70\) 15.9510 + 52.4704i 0.227872 + 0.749577i
\(71\) −25.8039 −0.363435 −0.181718 0.983351i \(-0.558166\pi\)
−0.181718 + 0.983351i \(0.558166\pi\)
\(72\) −44.9436 −0.624217
\(73\) 95.6803i 1.31069i −0.755330 0.655345i \(-0.772523\pi\)
0.755330 0.655345i \(-0.227477\pi\)
\(74\) 130.629 1.76525
\(75\) 8.66025i 0.115470i
\(76\) 238.222i 3.13450i
\(77\) 13.6031 4.13536i 0.176664 0.0537059i
\(78\) 109.340 1.40180
\(79\) 28.1212 0.355965 0.177982 0.984034i \(-0.443043\pi\)
0.177982 + 0.984034i \(0.443043\pi\)
\(80\) 43.3487i 0.541858i
\(81\) 9.00000 0.111111
\(82\) 174.906i 2.13301i
\(83\) 103.374i 1.24547i −0.782435 0.622733i \(-0.786022\pi\)
0.782435 0.622733i \(-0.213978\pi\)
\(84\) −29.1844 96.0012i −0.347433 1.14287i
\(85\) 2.39905 0.0282241
\(86\) −33.5959 −0.390650
\(87\) 66.5628i 0.765090i
\(88\) −30.4286 −0.345779
\(89\) 29.3629i 0.329920i 0.986300 + 0.164960i \(0.0527496\pi\)
−0.986300 + 0.164960i \(0.947250\pi\)
\(90\) 23.5035i 0.261150i
\(91\) 36.6835 + 120.669i 0.403116 + 1.32604i
\(92\) 205.828 2.23726
\(93\) 76.3659 0.821138
\(94\) 195.148i 2.07604i
\(95\) 64.3658 0.677534
\(96\) 13.8531i 0.144304i
\(97\) 67.6473i 0.697395i −0.937235 0.348697i \(-0.886624\pi\)
0.937235 0.348697i \(-0.113376\pi\)
\(98\) 142.633 95.5515i 1.45544 0.975016i
\(99\) 6.09335 0.0615490
\(100\) −41.3792 −0.413792
\(101\) 73.3301i 0.726040i 0.931781 + 0.363020i \(0.118254\pi\)
−0.931781 + 0.363020i \(0.881746\pi\)
\(102\) −6.51088 −0.0638321
\(103\) 57.3431i 0.556729i −0.960476 0.278365i \(-0.910208\pi\)
0.960476 0.278365i \(-0.0897923\pi\)
\(104\) 269.923i 2.59541i
\(105\) −25.9388 + 7.88540i −0.247036 + 0.0750991i
\(106\) 201.342 1.89945
\(107\) −39.8399 −0.372336 −0.186168 0.982518i \(-0.559607\pi\)
−0.186168 + 0.982518i \(0.559607\pi\)
\(108\) 43.0025i 0.398171i
\(109\) −185.052 −1.69773 −0.848863 0.528613i \(-0.822712\pi\)
−0.848863 + 0.528613i \(0.822712\pi\)
\(110\) 15.9128i 0.144661i
\(111\) 64.5764i 0.581770i
\(112\) −129.836 + 39.4702i −1.15925 + 0.352412i
\(113\) −120.716 −1.06829 −0.534143 0.845394i \(-0.679366\pi\)
−0.534143 + 0.845394i \(0.679366\pi\)
\(114\) −174.685 −1.53233
\(115\) 55.6132i 0.483593i
\(116\) −318.041 −2.74173
\(117\) 54.0523i 0.461986i
\(118\) 356.316i 3.01962i
\(119\) −2.18440 7.18551i −0.0183563 0.0603824i
\(120\) 58.0219 0.483516
\(121\) −116.875 −0.965906
\(122\) 111.953i 0.917650i
\(123\) −86.4651 −0.702968
\(124\) 364.880i 2.94258i
\(125\) 11.1803i 0.0894427i
\(126\) 70.3964 21.4006i 0.558702 0.169846i
\(127\) −83.5096 −0.657556 −0.328778 0.944407i \(-0.606637\pi\)
−0.328778 + 0.944407i \(0.606637\pi\)
\(128\) −205.501 −1.60547
\(129\) 16.6081i 0.128745i
\(130\) −141.157 −1.08583
\(131\) 198.248i 1.51334i −0.653796 0.756671i \(-0.726825\pi\)
0.653796 0.756671i \(-0.273175\pi\)
\(132\) 29.1144i 0.220563i
\(133\) −58.6068 192.785i −0.440653 1.44951i
\(134\) 335.414 2.50309
\(135\) −11.6190 −0.0860663
\(136\) 16.0731i 0.118185i
\(137\) −24.1635 −0.176376 −0.0881880 0.996104i \(-0.528108\pi\)
−0.0881880 + 0.996104i \(0.528108\pi\)
\(138\) 150.931i 1.09371i
\(139\) 61.6370i 0.443432i 0.975111 + 0.221716i \(0.0711658\pi\)
−0.975111 + 0.221716i \(0.928834\pi\)
\(140\) 37.6769 + 123.937i 0.269121 + 0.885264i
\(141\) −96.4714 −0.684194
\(142\) −90.4088 −0.636682
\(143\) 36.5955i 0.255913i
\(144\) −58.1583 −0.403877
\(145\) 85.9322i 0.592636i
\(146\) 335.234i 2.29612i
\(147\) 47.2360 + 70.5107i 0.321333 + 0.479665i
\(148\) 308.550 2.08480
\(149\) −28.8271 −0.193470 −0.0967351 0.995310i \(-0.530840\pi\)
−0.0967351 + 0.995310i \(0.530840\pi\)
\(150\) 30.3428i 0.202286i
\(151\) 248.311 1.64445 0.822223 0.569166i \(-0.192734\pi\)
0.822223 + 0.569166i \(0.192734\pi\)
\(152\) 431.237i 2.83709i
\(153\) 3.21866i 0.0210370i
\(154\) 47.6611 14.4890i 0.309488 0.0940844i
\(155\) −98.5879 −0.636051
\(156\) 258.265 1.65554
\(157\) 41.3848i 0.263597i 0.991277 + 0.131799i \(0.0420752\pi\)
−0.991277 + 0.131799i \(0.957925\pi\)
\(158\) 98.5280 0.623595
\(159\) 99.5334i 0.625996i
\(160\) 17.8843i 0.111777i
\(161\) −166.570 + 50.6374i −1.03460 + 0.314518i
\(162\) 31.5332 0.194649
\(163\) −51.8103 −0.317855 −0.158927 0.987290i \(-0.550804\pi\)
−0.158927 + 0.987290i \(0.550804\pi\)
\(164\) 413.135i 2.51912i
\(165\) −7.86648 −0.0476756
\(166\) 362.189i 2.18186i
\(167\) 41.9711i 0.251324i 0.992073 + 0.125662i \(0.0401055\pi\)
−0.992073 + 0.125662i \(0.959895\pi\)
\(168\) −52.8306 173.785i −0.314468 1.03443i
\(169\) −155.628 −0.920876
\(170\) 8.40551 0.0494442
\(171\) 86.3557i 0.505004i
\(172\) −79.3546 −0.461364
\(173\) 98.0199i 0.566589i −0.959033 0.283295i \(-0.908573\pi\)
0.959033 0.283295i \(-0.0914274\pi\)
\(174\) 233.215i 1.34032i
\(175\) 33.4868 10.1800i 0.191353 0.0581715i
\(176\) −39.3754 −0.223724
\(177\) −176.145 −0.995168
\(178\) 102.879i 0.577969i
\(179\) 68.5830 0.383145 0.191573 0.981478i \(-0.438641\pi\)
0.191573 + 0.981478i \(0.438641\pi\)
\(180\) 55.5160i 0.308422i
\(181\) 105.124i 0.580798i −0.956906 0.290399i \(-0.906212\pi\)
0.956906 0.290399i \(-0.0937880\pi\)
\(182\) 128.528 + 422.788i 0.706196 + 2.32301i
\(183\) 55.3442 0.302427
\(184\) 372.597 2.02499
\(185\) 83.3678i 0.450637i
\(186\) 267.562 1.43851
\(187\) 2.17916i 0.0116532i
\(188\) 460.946i 2.45184i
\(189\) 10.5794 + 34.8005i 0.0559755 + 0.184130i
\(190\) 225.518 1.18693
\(191\) 229.803 1.20316 0.601579 0.798813i \(-0.294539\pi\)
0.601579 + 0.798813i \(0.294539\pi\)
\(192\) 85.7738i 0.446739i
\(193\) 111.530 0.577877 0.288939 0.957348i \(-0.406698\pi\)
0.288939 + 0.957348i \(0.406698\pi\)
\(194\) 237.015i 1.22173i
\(195\) 69.7812i 0.357852i
\(196\) 336.904 225.696i 1.71890 1.15151i
\(197\) −172.865 −0.877486 −0.438743 0.898613i \(-0.644576\pi\)
−0.438743 + 0.898613i \(0.644576\pi\)
\(198\) 21.3492 0.107824
\(199\) 117.944i 0.592685i 0.955082 + 0.296343i \(0.0957670\pi\)
−0.955082 + 0.296343i \(0.904233\pi\)
\(200\) −74.9060 −0.374530
\(201\) 165.812i 0.824937i
\(202\) 256.926i 1.27191i
\(203\) 257.380 78.2437i 1.26788 0.385437i
\(204\) −15.3789 −0.0753869
\(205\) 111.626 0.544517
\(206\) 200.912i 0.975303i
\(207\) −74.6130 −0.360449
\(208\) 349.288i 1.67927i
\(209\) 58.4662i 0.279742i
\(210\) −90.8814 + 27.6280i −0.432769 + 0.131562i
\(211\) −391.940 −1.85754 −0.928769 0.370660i \(-0.879131\pi\)
−0.928769 + 0.370660i \(0.879131\pi\)
\(212\) 475.576 2.24328
\(213\) 44.6936i 0.209829i
\(214\) −139.587 −0.652274
\(215\) 21.4410i 0.0997256i
\(216\) 77.8446i 0.360392i
\(217\) 89.7670 + 295.286i 0.413673 + 1.36076i
\(218\) −648.365 −2.97415
\(219\) 165.723 0.756727
\(220\) 37.5865i 0.170848i
\(221\) 19.3306 0.0874690
\(222\) 226.256i 1.01917i
\(223\) 96.2512i 0.431620i −0.976435 0.215810i \(-0.930761\pi\)
0.976435 0.215810i \(-0.0692391\pi\)
\(224\) −53.5663 + 16.2842i −0.239135 + 0.0726972i
\(225\) 15.0000 0.0666667
\(226\) −422.952 −1.87147
\(227\) 91.6962i 0.403948i −0.979391 0.201974i \(-0.935264\pi\)
0.979391 0.201974i \(-0.0647357\pi\)
\(228\) −412.612 −1.80970
\(229\) 323.972i 1.41472i −0.706852 0.707361i \(-0.749885\pi\)
0.706852 0.707361i \(-0.250115\pi\)
\(230\) 194.852i 0.847180i
\(231\) 7.16265 + 23.5613i 0.0310071 + 0.101997i
\(232\) −575.728 −2.48159
\(233\) 182.918 0.785055 0.392528 0.919740i \(-0.371601\pi\)
0.392528 + 0.919740i \(0.371601\pi\)
\(234\) 189.382i 0.809327i
\(235\) 124.544 0.529974
\(236\) 841.630i 3.56623i
\(237\) 48.7074i 0.205516i
\(238\) −7.65345 25.1758i −0.0321573 0.105781i
\(239\) −42.9240 −0.179598 −0.0897992 0.995960i \(-0.528623\pi\)
−0.0897992 + 0.995960i \(0.528623\pi\)
\(240\) 75.0821 0.312842
\(241\) 99.8942i 0.414499i 0.978288 + 0.207249i \(0.0664511\pi\)
−0.978288 + 0.207249i \(0.933549\pi\)
\(242\) −409.492 −1.69212
\(243\) 15.5885i 0.0641500i
\(244\) 264.438i 1.08376i
\(245\) −60.9814 91.0290i −0.248904 0.371547i
\(246\) −302.947 −1.23149
\(247\) 518.636 2.09974
\(248\) 660.519i 2.66338i
\(249\) 179.048 0.719070
\(250\) 39.1724i 0.156690i
\(251\) 404.945i 1.61333i 0.591011 + 0.806663i \(0.298729\pi\)
−0.591011 + 0.806663i \(0.701271\pi\)
\(252\) 166.279 50.5489i 0.659837 0.200591i
\(253\) −50.5159 −0.199668
\(254\) −292.592 −1.15194
\(255\) 4.15527i 0.0162952i
\(256\) −521.924 −2.03876
\(257\) 102.697i 0.399600i −0.979837 0.199800i \(-0.935971\pi\)
0.979837 0.199800i \(-0.0640292\pi\)
\(258\) 58.1897i 0.225542i
\(259\) −249.699 + 75.9087i −0.964090 + 0.293084i
\(260\) −333.419 −1.28238
\(261\) 115.290 0.441725
\(262\) 694.598i 2.65114i
\(263\) 281.479 1.07026 0.535132 0.844769i \(-0.320262\pi\)
0.535132 + 0.844769i \(0.320262\pi\)
\(264\) 52.7038i 0.199636i
\(265\) 128.497i 0.484894i
\(266\) −205.340 675.460i −0.771955 2.53932i
\(267\) −50.8581 −0.190480
\(268\) 792.260 2.95620
\(269\) 176.412i 0.655808i 0.944711 + 0.327904i \(0.106342\pi\)
−0.944711 + 0.327904i \(0.893658\pi\)
\(270\) −40.7092 −0.150775
\(271\) 306.041i 1.12930i 0.825330 + 0.564651i \(0.190989\pi\)
−0.825330 + 0.564651i \(0.809011\pi\)
\(272\) 20.7991i 0.0764672i
\(273\) −209.005 + 63.5378i −0.765588 + 0.232739i
\(274\) −84.6614 −0.308983
\(275\) 10.1556 0.0369294
\(276\) 356.505i 1.29169i
\(277\) 43.7993 0.158120 0.0790601 0.996870i \(-0.474808\pi\)
0.0790601 + 0.996870i \(0.474808\pi\)
\(278\) 215.957i 0.776824i
\(279\) 132.270i 0.474084i
\(280\) 68.2040 + 224.355i 0.243586 + 0.801267i
\(281\) 499.502 1.77759 0.888794 0.458307i \(-0.151544\pi\)
0.888794 + 0.458307i \(0.151544\pi\)
\(282\) −338.006 −1.19860
\(283\) 122.672i 0.433470i 0.976231 + 0.216735i \(0.0695407\pi\)
−0.976231 + 0.216735i \(0.930459\pi\)
\(284\) −213.549 −0.751932
\(285\) 111.485i 0.391175i
\(286\) 128.219i 0.448319i
\(287\) −101.639 334.337i −0.354141 1.16494i
\(288\) −23.9944 −0.0833137
\(289\) 287.849 0.996017
\(290\) 301.080i 1.03821i
\(291\) 117.169 0.402641
\(292\) 791.835i 2.71176i
\(293\) 123.871i 0.422769i −0.977403 0.211385i \(-0.932203\pi\)
0.977403 0.211385i \(-0.0677972\pi\)
\(294\) 165.500 + 247.048i 0.562926 + 0.840298i
\(295\) 227.402 0.770854
\(296\) 558.547 1.88698
\(297\) 10.5540i 0.0355353i
\(298\) −101.001 −0.338930
\(299\) 448.112i 1.49870i
\(300\) 71.6708i 0.238903i
\(301\) 64.2191 19.5226i 0.213352 0.0648593i
\(302\) 870.006 2.88081
\(303\) −127.011 −0.419180
\(304\) 558.034i 1.83564i
\(305\) −71.4490 −0.234259
\(306\) 11.2772i 0.0368535i
\(307\) 225.577i 0.734778i 0.930067 + 0.367389i \(0.119748\pi\)
−0.930067 + 0.367389i \(0.880252\pi\)
\(308\) 112.577 34.2235i 0.365511 0.111115i
\(309\) 99.3211 0.321428
\(310\) −345.421 −1.11426
\(311\) 52.9648i 0.170305i 0.996368 + 0.0851525i \(0.0271377\pi\)
−0.996368 + 0.0851525i \(0.972862\pi\)
\(312\) 467.520 1.49846
\(313\) 374.563i 1.19669i 0.801240 + 0.598343i \(0.204174\pi\)
−0.801240 + 0.598343i \(0.795826\pi\)
\(314\) 144.999i 0.461782i
\(315\) −13.6579 44.9273i −0.0433585 0.142626i
\(316\) 232.727 0.736477
\(317\) 12.0550 0.0380283 0.0190142 0.999819i \(-0.493947\pi\)
0.0190142 + 0.999819i \(0.493947\pi\)
\(318\) 348.734i 1.09665i
\(319\) 78.0559 0.244689
\(320\) 110.734i 0.346042i
\(321\) 69.0048i 0.214968i
\(322\) −583.610 + 177.418i −1.81245 + 0.550987i
\(323\) −30.8833 −0.0956138
\(324\) 74.4825 0.229884
\(325\) 90.0872i 0.277191i
\(326\) −181.527 −0.556832
\(327\) 320.520i 0.980183i
\(328\) 747.871i 2.28009i
\(329\) −113.401 373.028i −0.344683 1.13382i
\(330\) −27.5617 −0.0835203
\(331\) −376.184 −1.13651 −0.568254 0.822853i \(-0.692381\pi\)
−0.568254 + 0.822853i \(0.692381\pi\)
\(332\) 855.503i 2.57682i
\(333\) −111.850 −0.335885
\(334\) 147.054i 0.440281i
\(335\) 214.063i 0.638993i
\(336\) −68.3643 224.882i −0.203465 0.669293i
\(337\) −108.973 −0.323363 −0.161682 0.986843i \(-0.551692\pi\)
−0.161682 + 0.986843i \(0.551692\pi\)
\(338\) −545.272 −1.61323
\(339\) 209.087i 0.616775i
\(340\) 19.8541 0.0583944
\(341\) 89.5516i 0.262615i
\(342\) 302.564i 0.884689i
\(343\) −217.120 + 265.533i −0.633004 + 0.774148i
\(344\) −143.650 −0.417588
\(345\) 96.3250 0.279203
\(346\) 343.431i 0.992576i
\(347\) −206.351 −0.594671 −0.297335 0.954773i \(-0.596098\pi\)
−0.297335 + 0.954773i \(0.596098\pi\)
\(348\) 550.863i 1.58294i
\(349\) 373.475i 1.07013i −0.844811 0.535064i \(-0.820287\pi\)
0.844811 0.535064i \(-0.179713\pi\)
\(350\) 117.327 35.6676i 0.335221 0.101907i
\(351\) −93.6213 −0.266727
\(352\) −16.2451 −0.0461509
\(353\) 646.142i 1.83043i 0.402964 + 0.915216i \(0.367980\pi\)
−0.402964 + 0.915216i \(0.632020\pi\)
\(354\) −617.157 −1.74338
\(355\) 57.6992i 0.162533i
\(356\) 243.003i 0.682592i
\(357\) 12.4457 3.78349i 0.0348618 0.0105980i
\(358\) 240.294 0.671211
\(359\) 175.261 0.488192 0.244096 0.969751i \(-0.421509\pi\)
0.244096 + 0.969751i \(0.421509\pi\)
\(360\) 100.497i 0.279158i
\(361\) −467.590 −1.29526
\(362\) 368.323i 1.01747i
\(363\) 202.433i 0.557666i
\(364\) 303.587 + 998.640i 0.834030 + 2.74352i
\(365\) −213.948 −0.586158
\(366\) 193.909 0.529805
\(367\) 106.477i 0.290127i −0.989422 0.145063i \(-0.953661\pi\)
0.989422 0.145063i \(-0.0463386\pi\)
\(368\) 482.152 1.31020
\(369\) 149.762i 0.405859i
\(370\) 292.095i 0.789446i
\(371\) −384.868 + 117.000i −1.03738 + 0.315364i
\(372\) 631.991 1.69890
\(373\) 223.324 0.598723 0.299362 0.954140i \(-0.403226\pi\)
0.299362 + 0.954140i \(0.403226\pi\)
\(374\) 7.63508i 0.0204147i
\(375\) −19.3649 −0.0516398
\(376\) 834.419i 2.21920i
\(377\) 692.411i 1.83663i
\(378\) 37.0668 + 121.930i 0.0980604 + 0.322567i
\(379\) 119.075 0.314183 0.157092 0.987584i \(-0.449788\pi\)
0.157092 + 0.987584i \(0.449788\pi\)
\(380\) 532.680 1.40179
\(381\) 144.643i 0.379640i
\(382\) 805.159 2.10775
\(383\) 494.637i 1.29148i 0.763557 + 0.645740i \(0.223451\pi\)
−0.763557 + 0.645740i \(0.776549\pi\)
\(384\) 355.937i 0.926920i
\(385\) −9.24694 30.4175i −0.0240180 0.0790065i
\(386\) 390.767 1.01235
\(387\) 28.7661 0.0743311
\(388\) 559.838i 1.44288i
\(389\) −270.578 −0.695574 −0.347787 0.937574i \(-0.613067\pi\)
−0.347787 + 0.937574i \(0.613067\pi\)
\(390\) 244.492i 0.626902i
\(391\) 26.6837i 0.0682448i
\(392\) 609.875 408.563i 1.55580 1.04225i
\(393\) 343.375 0.873728
\(394\) −605.664 −1.53722
\(395\) 62.8810i 0.159192i
\(396\) 50.4276 0.127342
\(397\) 37.1881i 0.0936727i −0.998903 0.0468364i \(-0.985086\pi\)
0.998903 0.0468364i \(-0.0149139\pi\)
\(398\) 413.240i 1.03829i
\(399\) 333.914 101.510i 0.836877 0.254411i
\(400\) −96.9306 −0.242326
\(401\) −36.7102 −0.0915467 −0.0457733 0.998952i \(-0.514575\pi\)
−0.0457733 + 0.998952i \(0.514575\pi\)
\(402\) 580.955i 1.44516i
\(403\) −794.386 −1.97118
\(404\) 606.868i 1.50215i
\(405\) 20.1246i 0.0496904i
\(406\) 901.780 274.141i 2.22113 0.675225i
\(407\) −75.7266 −0.186060
\(408\) −27.8394 −0.0682339
\(409\) 495.325i 1.21106i −0.795821 0.605532i \(-0.792960\pi\)
0.795821 0.605532i \(-0.207040\pi\)
\(410\) 391.103 0.953909
\(411\) 41.8524i 0.101831i
\(412\) 474.562i 1.15185i
\(413\) −207.056 681.104i −0.501346 1.64916i
\(414\) −261.421 −0.631451
\(415\) −231.151 −0.556989
\(416\) 144.106i 0.346408i
\(417\) −106.758 −0.256016
\(418\) 204.847i 0.490065i
\(419\) 269.297i 0.642713i 0.946958 + 0.321357i \(0.104139\pi\)
−0.946958 + 0.321357i \(0.895861\pi\)
\(420\) −214.665 + 65.2583i −0.511107 + 0.155377i
\(421\) 756.722 1.79744 0.898719 0.438524i \(-0.144499\pi\)
0.898719 + 0.438524i \(0.144499\pi\)
\(422\) −1373.24 −3.25412
\(423\) 167.093i 0.395020i
\(424\) 860.904 2.03043
\(425\) 5.36443i 0.0126222i
\(426\) 156.593i 0.367588i
\(427\) 65.0563 + 214.001i 0.152357 + 0.501173i
\(428\) −329.709 −0.770347
\(429\) −63.3853 −0.147751
\(430\) 75.1226i 0.174704i
\(431\) 185.182 0.429657 0.214828 0.976652i \(-0.431081\pi\)
0.214828 + 0.976652i \(0.431081\pi\)
\(432\) 100.733i 0.233179i
\(433\) 642.846i 1.48463i −0.670049 0.742317i \(-0.733727\pi\)
0.670049 0.742317i \(-0.266273\pi\)
\(434\) 314.516 + 1034.59i 0.724691 + 2.38385i
\(435\) −148.839 −0.342158
\(436\) −1531.46 −3.51253
\(437\) 715.918i 1.63826i
\(438\) 580.643 1.32567
\(439\) 464.239i 1.05749i 0.848780 + 0.528745i \(0.177337\pi\)
−0.848780 + 0.528745i \(0.822663\pi\)
\(440\) 68.0403i 0.154637i
\(441\) −122.128 + 81.8151i −0.276935 + 0.185522i
\(442\) 67.7286 0.153232
\(443\) −115.228 −0.260109 −0.130054 0.991507i \(-0.541515\pi\)
−0.130054 + 0.991507i \(0.541515\pi\)
\(444\) 534.424i 1.20366i
\(445\) 65.6575 0.147545
\(446\) 337.234i 0.756130i
\(447\) 49.9299i 0.111700i
\(448\) 331.664 100.826i 0.740321 0.225058i
\(449\) 333.955 0.743774 0.371887 0.928278i \(-0.378711\pi\)
0.371887 + 0.928278i \(0.378711\pi\)
\(450\) 52.5553 0.116790
\(451\) 101.395i 0.224822i
\(452\) −999.028 −2.21024
\(453\) 430.088i 0.949421i
\(454\) 321.275i 0.707654i
\(455\) 269.825 82.0269i 0.593022 0.180279i
\(456\) −746.925 −1.63799
\(457\) 354.152 0.774949 0.387474 0.921880i \(-0.373348\pi\)
0.387474 + 0.921880i \(0.373348\pi\)
\(458\) 1135.10i 2.47837i
\(459\) 5.57488 0.0121457
\(460\) 460.246i 1.00053i
\(461\) 128.906i 0.279623i 0.990178 + 0.139811i \(0.0446497\pi\)
−0.990178 + 0.139811i \(0.955350\pi\)
\(462\) 25.0957 + 82.5515i 0.0543197 + 0.178683i
\(463\) −302.175 −0.652645 −0.326322 0.945259i \(-0.605810\pi\)
−0.326322 + 0.945259i \(0.605810\pi\)
\(464\) −745.009 −1.60562
\(465\) 170.759i 0.367224i
\(466\) 640.887 1.37530
\(467\) 808.227i 1.73068i −0.501186 0.865339i \(-0.667103\pi\)
0.501186 0.865339i \(-0.332897\pi\)
\(468\) 447.328i 0.955829i
\(469\) −641.151 + 194.910i −1.36706 + 0.415587i
\(470\) 436.363 0.928433
\(471\) −71.6805 −0.152188
\(472\) 1523.55i 3.22785i
\(473\) 19.4758 0.0411750
\(474\) 170.656i 0.360033i
\(475\) 143.926i 0.303003i
\(476\) −18.0777 59.4661i −0.0379784 0.124929i
\(477\) −172.397 −0.361419
\(478\) −150.392 −0.314628
\(479\) 48.8836i 0.102053i 0.998697 + 0.0510267i \(0.0162494\pi\)
−0.998697 + 0.0510267i \(0.983751\pi\)
\(480\) 30.9766 0.0645345
\(481\) 671.748i 1.39657i
\(482\) 349.998i 0.726137i
\(483\) −87.7066 288.508i −0.181587 0.597325i
\(484\) −967.235 −1.99842
\(485\) −151.264 −0.311884
\(486\) 54.6171i 0.112381i
\(487\) 334.433 0.686720 0.343360 0.939204i \(-0.388435\pi\)
0.343360 + 0.939204i \(0.388435\pi\)
\(488\) 478.694i 0.980930i
\(489\) 89.7381i 0.183514i
\(490\) −213.660 318.937i −0.436040 0.650892i
\(491\) −549.151 −1.11843 −0.559217 0.829021i \(-0.688898\pi\)
−0.559217 + 0.829021i \(0.688898\pi\)
\(492\) −715.571 −1.45441
\(493\) 41.2310i 0.0836329i
\(494\) 1817.14 3.67842
\(495\) 13.6251i 0.0275255i
\(496\) 854.731i 1.72325i
\(497\) 172.818 52.5368i 0.347722 0.105708i
\(498\) 627.330 1.25970
\(499\) −462.450 −0.926754 −0.463377 0.886161i \(-0.653362\pi\)
−0.463377 + 0.886161i \(0.653362\pi\)
\(500\) 92.5267i 0.185053i
\(501\) −72.6961 −0.145102
\(502\) 1418.80i 2.82630i
\(503\) 676.817i 1.34556i 0.739842 + 0.672781i \(0.234900\pi\)
−0.739842 + 0.672781i \(0.765100\pi\)
\(504\) 301.004 91.5053i 0.597229 0.181558i
\(505\) 163.971 0.324695
\(506\) −176.992 −0.349786
\(507\) 269.556i 0.531668i
\(508\) −691.112 −1.36046
\(509\) 31.5959i 0.0620744i 0.999518 + 0.0310372i \(0.00988104\pi\)
−0.999518 + 0.0310372i \(0.990119\pi\)
\(510\) 14.5588i 0.0285466i
\(511\) 194.805 + 640.806i 0.381224 + 1.25402i
\(512\) −1006.66 −1.96613
\(513\) 149.572 0.291564
\(514\) 359.819i 0.700036i
\(515\) −128.223 −0.248977
\(516\) 137.446i 0.266369i
\(517\) 113.129i 0.218817i
\(518\) −874.869 + 265.961i −1.68894 + 0.513437i
\(519\) 169.775 0.327120
\(520\) −603.566 −1.16070
\(521\) 793.420i 1.52288i −0.648236 0.761440i \(-0.724493\pi\)
0.648236 0.761440i \(-0.275507\pi\)
\(522\) 403.941 0.773833
\(523\) 593.508i 1.13481i 0.823438 + 0.567407i \(0.192053\pi\)
−0.823438 + 0.567407i \(0.807947\pi\)
\(524\) 1640.67i 3.13104i
\(525\) 17.6323 + 58.0009i 0.0335853 + 0.110478i
\(526\) 986.216 1.87494
\(527\) 47.3034 0.0897597
\(528\) 68.2003i 0.129167i
\(529\) 89.5666 0.169313
\(530\) 450.214i 0.849460i
\(531\) 305.092i 0.574561i
\(532\) −485.020 1595.46i −0.911692 2.99898i
\(533\) 899.442 1.68751
\(534\) −178.191 −0.333691
\(535\) 89.0848i 0.166514i
\(536\) 1434.18 2.67570
\(537\) 118.789i 0.221209i
\(538\) 618.094i 1.14887i
\(539\) −82.6855 + 55.3920i −0.153405 + 0.102768i
\(540\) −96.1565 −0.178068
\(541\) 217.690 0.402385 0.201192 0.979552i \(-0.435518\pi\)
0.201192 + 0.979552i \(0.435518\pi\)
\(542\) 1072.27i 1.97836i
\(543\) 182.081 0.335324
\(544\) 8.58106i 0.0157740i
\(545\) 413.789i 0.759246i
\(546\) −732.290 + 222.617i −1.34119 + 0.407723i
\(547\) −137.891 −0.252085 −0.126043 0.992025i \(-0.540228\pi\)
−0.126043 + 0.992025i \(0.540228\pi\)
\(548\) −199.973 −0.364915
\(549\) 95.8589i 0.174606i
\(550\) 35.5820 0.0646945
\(551\) 1106.22i 2.00766i
\(552\) 645.358i 1.16913i
\(553\) −188.338 + 57.2549i −0.340575 + 0.103535i
\(554\) 153.459 0.277002
\(555\) 144.397 0.260175
\(556\) 510.098i 0.917442i
\(557\) −316.337 −0.567930 −0.283965 0.958835i \(-0.591650\pi\)
−0.283965 + 0.958835i \(0.591650\pi\)
\(558\) 463.431i 0.830522i
\(559\) 172.764i 0.309059i
\(560\) 88.2580 + 290.322i 0.157604 + 0.518432i
\(561\) 3.77441 0.00672800
\(562\) 1750.10 3.11406
\(563\) 151.482i 0.269063i −0.990909 0.134531i \(-0.957047\pi\)
0.990909 0.134531i \(-0.0429529\pi\)
\(564\) −798.381 −1.41557
\(565\) 269.930i 0.477752i
\(566\) 429.804i 0.759371i
\(567\) −60.2763 + 18.3240i −0.106307 + 0.0323175i
\(568\) −386.573 −0.680586
\(569\) −213.993 −0.376086 −0.188043 0.982161i \(-0.560214\pi\)
−0.188043 + 0.982161i \(0.560214\pi\)
\(570\) 390.608i 0.685277i
\(571\) −204.492 −0.358129 −0.179065 0.983837i \(-0.557307\pi\)
−0.179065 + 0.983837i \(0.557307\pi\)
\(572\) 302.858i 0.529473i
\(573\) 398.031i 0.694643i
\(574\) −356.110 1171.41i −0.620400 2.04079i
\(575\) −124.355 −0.216270
\(576\) 148.565 0.257925
\(577\) 957.823i 1.66001i 0.557759 + 0.830003i \(0.311661\pi\)
−0.557759 + 0.830003i \(0.688339\pi\)
\(578\) 1008.53 1.74487
\(579\) 193.176i 0.333638i
\(580\) 711.161i 1.22614i
\(581\) 210.469 + 692.331i 0.362253 + 1.19162i
\(582\) 410.522 0.705364
\(583\) −116.719 −0.200205
\(584\) 1433.41i 2.45446i
\(585\) 120.865 0.206606
\(586\) 434.007i 0.740626i
\(587\) 981.279i 1.67168i −0.548969 0.835842i \(-0.684980\pi\)
0.548969 0.835842i \(-0.315020\pi\)
\(588\) 390.917 + 583.535i 0.664825 + 0.992407i
\(589\) 1269.14 2.15473
\(590\) 796.746 1.35042
\(591\) 299.410i 0.506617i
\(592\) 722.777 1.22091
\(593\) 708.384i 1.19458i 0.802026 + 0.597288i \(0.203755\pi\)
−0.802026 + 0.597288i \(0.796245\pi\)
\(594\) 36.9779i 0.0622523i
\(595\) −16.0673 + 4.88446i −0.0270038 + 0.00820918i
\(596\) −238.568 −0.400282
\(597\) −204.286 −0.342187
\(598\) 1570.04i 2.62549i
\(599\) −928.994 −1.55091 −0.775454 0.631404i \(-0.782479\pi\)
−0.775454 + 0.631404i \(0.782479\pi\)
\(600\) 129.741i 0.216235i
\(601\) 466.882i 0.776842i 0.921482 + 0.388421i \(0.126979\pi\)
−0.921482 + 0.388421i \(0.873021\pi\)
\(602\) 225.004 68.4012i 0.373760 0.113623i
\(603\) −287.195 −0.476277
\(604\) 2054.98 3.40229
\(605\) 261.339i 0.431966i
\(606\) −445.009 −0.734338
\(607\) 988.757i 1.62892i −0.580216 0.814462i \(-0.697032\pi\)
0.580216 0.814462i \(-0.302968\pi\)
\(608\) 230.228i 0.378664i
\(609\) 135.522 + 445.795i 0.222532 + 0.732012i
\(610\) −250.335 −0.410386
\(611\) 1003.53 1.64244
\(612\) 26.6371i 0.0435246i
\(613\) 469.962 0.766660 0.383330 0.923612i \(-0.374777\pi\)
0.383330 + 0.923612i \(0.374777\pi\)
\(614\) 790.351i 1.28722i
\(615\) 193.342i 0.314377i
\(616\) 203.791 61.9526i 0.330830 0.100572i
\(617\) 1081.72 1.75320 0.876598 0.481223i \(-0.159807\pi\)
0.876598 + 0.481223i \(0.159807\pi\)
\(618\) 347.990 0.563091
\(619\) 553.956i 0.894921i 0.894304 + 0.447461i \(0.147672\pi\)
−0.894304 + 0.447461i \(0.852328\pi\)
\(620\) −815.897 −1.31596
\(621\) 129.234i 0.208105i
\(622\) 185.572i 0.298348i
\(623\) −59.7829 196.654i −0.0959598 0.315657i
\(624\) 604.985 0.969527
\(625\) 25.0000 0.0400000
\(626\) 1312.35i 2.09641i
\(627\) 101.266 0.161509
\(628\) 342.494i 0.545372i
\(629\) 40.0006i 0.0635940i
\(630\) −47.8531 157.411i −0.0759573 0.249859i
\(631\) −77.8822 −0.123427 −0.0617133 0.998094i \(-0.519656\pi\)
−0.0617133 + 0.998094i \(0.519656\pi\)
\(632\) 421.290 0.666597
\(633\) 678.861i 1.07245i
\(634\) 42.2369 0.0666197
\(635\) 186.733i 0.294068i
\(636\) 823.722i 1.29516i
\(637\) −491.366 733.479i −0.771375 1.15146i
\(638\) 273.484 0.428658
\(639\) 77.4117 0.121145
\(640\) 459.513i 0.717989i
\(641\) −360.619 −0.562589 −0.281294 0.959622i \(-0.590764\pi\)
−0.281294 + 0.959622i \(0.590764\pi\)
\(642\) 241.771i 0.376591i
\(643\) 793.158i 1.23353i −0.787148 0.616764i \(-0.788443\pi\)
0.787148 0.616764i \(-0.211557\pi\)
\(644\) −1378.51 + 419.067i −2.14054 + 0.650725i
\(645\) −37.1369 −0.0575766
\(646\) −108.205 −0.167501
\(647\) 405.244i 0.626344i 0.949696 + 0.313172i \(0.101392\pi\)
−0.949696 + 0.313172i \(0.898608\pi\)
\(648\) 134.831 0.208072
\(649\) 206.559i 0.318273i
\(650\) 315.637i 0.485596i
\(651\) −511.450 + 155.481i −0.785638 + 0.238834i
\(652\) −428.774 −0.657629
\(653\) 493.508 0.755755 0.377877 0.925856i \(-0.376654\pi\)
0.377877 + 0.925856i \(0.376654\pi\)
\(654\) 1123.00i 1.71713i
\(655\) −443.295 −0.676787
\(656\) 967.767i 1.47526i
\(657\) 287.041i 0.436896i
\(658\) −397.321 1306.97i −0.603831 1.98628i
\(659\) −1120.88 −1.70088 −0.850441 0.526070i \(-0.823665\pi\)
−0.850441 + 0.526070i \(0.823665\pi\)
\(660\) −65.1017 −0.0986389
\(661\) 1134.48i 1.71631i −0.513393 0.858154i \(-0.671612\pi\)
0.513393 0.858154i \(-0.328388\pi\)
\(662\) −1318.03 −1.99098
\(663\) 33.4817i 0.0505002i
\(664\) 1548.66i 2.33232i
\(665\) −431.081 + 131.049i −0.648242 + 0.197066i
\(666\) −391.887 −0.588418
\(667\) −955.794 −1.43297
\(668\) 347.346i 0.519979i
\(669\) 166.712 0.249196
\(670\) 750.009i 1.11942i
\(671\) 64.9002i 0.0967216i
\(672\) −28.2050 92.7796i −0.0419718 0.138065i
\(673\) −763.267 −1.13413 −0.567063 0.823674i \(-0.691920\pi\)
−0.567063 + 0.823674i \(0.691920\pi\)
\(674\) −381.809 −0.566482
\(675\) 25.9808i 0.0384900i
\(676\) −1287.95 −1.90525
\(677\) 456.611i 0.674463i 0.941422 + 0.337232i \(0.109491\pi\)
−0.941422 + 0.337232i \(0.890509\pi\)
\(678\) 732.575i 1.08049i
\(679\) 137.730 + 453.058i 0.202842 + 0.667244i
\(680\) 35.9406 0.0528538
\(681\) 158.822 0.233219
\(682\) 313.761i 0.460060i
\(683\) −219.276 −0.321049 −0.160524 0.987032i \(-0.551319\pi\)
−0.160524 + 0.987032i \(0.551319\pi\)
\(684\) 714.666i 1.04483i
\(685\) 54.0313i 0.0788777i
\(686\) −760.722 + 930.345i −1.10892 + 1.35619i
\(687\) 561.135 0.816791
\(688\) −185.888 −0.270186
\(689\) 1035.38i 1.50273i
\(690\) 337.493 0.489120
\(691\) 396.801i 0.574242i −0.957894 0.287121i \(-0.907302\pi\)
0.957894 0.287121i \(-0.0926982\pi\)
\(692\) 811.197i 1.17225i
\(693\) −40.8094 + 12.4061i −0.0588880 + 0.0179020i
\(694\) −722.989 −1.04177
\(695\) 137.825 0.198309
\(696\) 997.190i 1.43274i
\(697\) −53.5591 −0.0768424
\(698\) 1308.54i 1.87470i
\(699\) 316.823i 0.453252i
\(700\) 277.131 84.2481i 0.395902 0.120354i
\(701\) −493.156 −0.703503 −0.351752 0.936093i \(-0.614414\pi\)
−0.351752 + 0.936093i \(0.614414\pi\)
\(702\) −328.020 −0.467265
\(703\) 1073.21i 1.52661i
\(704\) 100.584 0.142875
\(705\) 215.717i 0.305981i
\(706\) 2263.88i 3.20663i
\(707\) −149.300 491.118i −0.211174 0.694651i
\(708\) −1457.75 −2.05896
\(709\) 859.326 1.21202 0.606012 0.795455i \(-0.292768\pi\)
0.606012 + 0.795455i \(0.292768\pi\)
\(710\) 202.160i 0.284733i
\(711\) −84.3637 −0.118655
\(712\) 439.892i 0.617825i
\(713\) 1096.56i 1.53795i
\(714\) 43.6057 13.2562i 0.0610724 0.0185661i
\(715\) 81.8300 0.114448
\(716\) 567.582 0.792712
\(717\) 74.3466i 0.103691i
\(718\) 614.060 0.855237
\(719\) 385.539i 0.536216i 0.963389 + 0.268108i \(0.0863983\pi\)
−0.963389 + 0.268108i \(0.913602\pi\)
\(720\) 130.046i 0.180619i
\(721\) 116.751 + 384.048i 0.161929 + 0.532660i
\(722\) −1638.29 −2.26910
\(723\) −173.022 −0.239311
\(724\) 869.992i 1.20165i
\(725\) 192.150 0.265035
\(726\) 709.261i 0.976944i
\(727\) 114.722i 0.157802i 0.996882 + 0.0789012i \(0.0251412\pi\)
−0.996882 + 0.0789012i \(0.974859\pi\)
\(728\) 549.563 + 1807.77i 0.754895 + 2.48320i
\(729\) −27.0000 −0.0370370
\(730\) −749.606 −1.02686
\(731\) 10.2876i 0.0140733i
\(732\) 458.019 0.625710
\(733\) 140.433i 0.191586i 0.995401 + 0.0957932i \(0.0305388\pi\)
−0.995401 + 0.0957932i \(0.969461\pi\)
\(734\) 373.061i 0.508257i
\(735\) 157.667 105.623i 0.214513 0.143705i
\(736\) 198.921 0.270273
\(737\) −194.442 −0.263830
\(738\) 524.719i 0.711002i
\(739\) −50.8609 −0.0688239 −0.0344120 0.999408i \(-0.510956\pi\)
−0.0344120 + 0.999408i \(0.510956\pi\)
\(740\) 689.939i 0.932349i
\(741\) 898.304i 1.21229i
\(742\) −1348.46 + 409.932i −1.81733 + 0.552469i
\(743\) 930.694 1.25262 0.626309 0.779575i \(-0.284565\pi\)
0.626309 + 0.779575i \(0.284565\pi\)
\(744\) 1144.05 1.53770
\(745\) 64.4593i 0.0865225i
\(746\) 782.457 1.04887
\(747\) 310.121i 0.415155i
\(748\) 18.0343i 0.0241101i
\(749\) 266.822 81.1142i 0.356238 0.108297i
\(750\) −67.8486 −0.0904649
\(751\) −446.702 −0.594809 −0.297404 0.954752i \(-0.596121\pi\)
−0.297404 + 0.954752i \(0.596121\pi\)
\(752\) 1079.76i 1.43586i
\(753\) −701.385 −0.931455
\(754\) 2425.99i 3.21750i
\(755\) 555.241i 0.735419i
\(756\) 87.5532 + 288.003i 0.115811 + 0.380957i
\(757\) 27.2042 0.0359369 0.0179684 0.999839i \(-0.494280\pi\)
0.0179684 + 0.999839i \(0.494280\pi\)
\(758\) 417.203 0.550400
\(759\) 87.4961i 0.115278i
\(760\) 964.276 1.26878
\(761\) 333.536i 0.438287i −0.975693 0.219143i \(-0.929674\pi\)
0.975693 0.219143i \(-0.0703262\pi\)
\(762\) 506.784i 0.665070i
\(763\) 1239.36 376.767i 1.62433 0.493796i
\(764\) 1901.81 2.48928
\(765\) −7.19714 −0.00940802
\(766\) 1733.05i 2.26247i
\(767\) 1832.32 2.38895
\(768\) 903.998i 1.17708i
\(769\) 56.3903i 0.0733294i 0.999328 + 0.0366647i \(0.0116734\pi\)
−0.999328 + 0.0366647i \(0.988327\pi\)
\(770\) −32.3984 106.574i −0.0420758 0.138407i
\(771\) 177.877 0.230709
\(772\) 923.006 1.19560
\(773\) 296.398i 0.383438i 0.981450 + 0.191719i \(0.0614063\pi\)
−0.981450 + 0.191719i \(0.938594\pi\)
\(774\) 100.788 0.130217
\(775\) 220.449i 0.284451i
\(776\) 1013.44i 1.30598i
\(777\) −131.478 432.492i −0.169212 0.556618i
\(778\) −948.022 −1.21854
\(779\) −1436.98 −1.84464
\(780\) 577.498i 0.740382i
\(781\) 52.4107 0.0671072
\(782\) 93.4915i 0.119554i
\(783\) 199.688i 0.255030i
\(784\) 789.197 528.692i 1.00663 0.674352i
\(785\) 92.5392 0.117884
\(786\) 1203.08 1.53064
\(787\)