Properties

Label 690.3.c.a.91.9
Level $690$
Weight $3$
Character 690.91
Analytic conductor $18.801$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.9
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.16

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} -7.36146i q^{7} -2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} -7.36146i q^{7} -2.82843 q^{8} +3.00000 q^{9} +3.16228i q^{10} -16.6371i q^{11} +3.46410 q^{12} +9.09640 q^{13} +10.4107i q^{14} -3.87298i q^{15} +4.00000 q^{16} +4.72753i q^{17} -4.24264 q^{18} +11.5103i q^{19} -4.47214i q^{20} -12.7504i q^{21} +23.5285i q^{22} +(-18.8188 - 13.2232i) q^{23} -4.89898 q^{24} -5.00000 q^{25} -12.8643 q^{26} +5.19615 q^{27} -14.7229i q^{28} -8.88295 q^{29} +5.47723i q^{30} -45.3476 q^{31} -5.65685 q^{32} -28.8164i q^{33} -6.68573i q^{34} -16.4607 q^{35} +6.00000 q^{36} -9.59572i q^{37} -16.2780i q^{38} +15.7554 q^{39} +6.32456i q^{40} +20.7143 q^{41} +18.0318i q^{42} +21.4012i q^{43} -33.2743i q^{44} -6.70820i q^{45} +(26.6138 + 18.7005i) q^{46} -31.0064 q^{47} +6.92820 q^{48} -5.19104 q^{49} +7.07107 q^{50} +8.18832i q^{51} +18.1928 q^{52} -70.7020i q^{53} -7.34847 q^{54} -37.2018 q^{55} +20.8213i q^{56} +19.9364i q^{57} +12.5624 q^{58} -47.6249 q^{59} -7.74597i q^{60} +16.1273i q^{61} +64.1312 q^{62} -22.0844i q^{63} +8.00000 q^{64} -20.3402i q^{65} +40.7525i q^{66} -11.8203i q^{67} +9.45505i q^{68} +(-32.5951 - 22.9033i) q^{69} +23.2790 q^{70} -2.91130 q^{71} -8.48528 q^{72} +136.473 q^{73} +13.5704i q^{74} -8.66025 q^{75} +23.0206i q^{76} -122.474 q^{77} -22.2815 q^{78} +37.4347i q^{79} -8.94427i q^{80} +9.00000 q^{81} -29.2945 q^{82} -108.327i q^{83} -25.5008i q^{84} +10.5711 q^{85} -30.2659i q^{86} -15.3857 q^{87} +47.0570i q^{88} -10.9382i q^{89} +9.48683i q^{90} -66.9628i q^{91} +(-37.6375 - 26.4465i) q^{92} -78.5444 q^{93} +43.8497 q^{94} +25.7378 q^{95} -9.79796 q^{96} -70.0663i q^{97} +7.34124 q^{98} -49.9114i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) 1.73205 0.577350
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) −2.44949 −0.408248
\(7\) 7.36146i 1.05164i −0.850597 0.525818i \(-0.823759\pi\)
0.850597 0.525818i \(-0.176241\pi\)
\(8\) −2.82843 −0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 16.6371i 1.51247i −0.654301 0.756234i \(-0.727037\pi\)
0.654301 0.756234i \(-0.272963\pi\)
\(12\) 3.46410 0.288675
\(13\) 9.09640 0.699723 0.349862 0.936801i \(-0.386229\pi\)
0.349862 + 0.936801i \(0.386229\pi\)
\(14\) 10.4107i 0.743619i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 4.72753i 0.278090i 0.990286 + 0.139045i \(0.0444032\pi\)
−0.990286 + 0.139045i \(0.955597\pi\)
\(18\) −4.24264 −0.235702
\(19\) 11.5103i 0.605806i 0.953021 + 0.302903i \(0.0979558\pi\)
−0.953021 + 0.302903i \(0.902044\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 12.7504i 0.607163i
\(22\) 23.5285i 1.06948i
\(23\) −18.8188 13.2232i −0.818207 0.574924i
\(24\) −4.89898 −0.204124
\(25\) −5.00000 −0.200000
\(26\) −12.8643 −0.494779
\(27\) 5.19615 0.192450
\(28\) 14.7229i 0.525818i
\(29\) −8.88295 −0.306308 −0.153154 0.988202i \(-0.548943\pi\)
−0.153154 + 0.988202i \(0.548943\pi\)
\(30\) 5.47723i 0.182574i
\(31\) −45.3476 −1.46283 −0.731413 0.681934i \(-0.761139\pi\)
−0.731413 + 0.681934i \(0.761139\pi\)
\(32\) −5.65685 −0.176777
\(33\) 28.8164i 0.873224i
\(34\) 6.68573i 0.196639i
\(35\) −16.4607 −0.470306
\(36\) 6.00000 0.166667
\(37\) 9.59572i 0.259344i −0.991557 0.129672i \(-0.958608\pi\)
0.991557 0.129672i \(-0.0413924\pi\)
\(38\) 16.2780i 0.428369i
\(39\) 15.7554 0.403985
\(40\) 6.32456i 0.158114i
\(41\) 20.7143 0.505228 0.252614 0.967567i \(-0.418710\pi\)
0.252614 + 0.967567i \(0.418710\pi\)
\(42\) 18.0318i 0.429329i
\(43\) 21.4012i 0.497702i 0.968542 + 0.248851i \(0.0800530\pi\)
−0.968542 + 0.248851i \(0.919947\pi\)
\(44\) 33.2743i 0.756234i
\(45\) 6.70820i 0.149071i
\(46\) 26.6138 + 18.7005i 0.578560 + 0.406532i
\(47\) −31.0064 −0.659712 −0.329856 0.944031i \(-0.607000\pi\)
−0.329856 + 0.944031i \(0.607000\pi\)
\(48\) 6.92820 0.144338
\(49\) −5.19104 −0.105940
\(50\) 7.07107 0.141421
\(51\) 8.18832i 0.160555i
\(52\) 18.1928 0.349862
\(53\) 70.7020i 1.33400i −0.745058 0.667000i \(-0.767578\pi\)
0.745058 0.667000i \(-0.232422\pi\)
\(54\) −7.34847 −0.136083
\(55\) −37.2018 −0.676396
\(56\) 20.8213i 0.371810i
\(57\) 19.9364i 0.349762i
\(58\) 12.5624 0.216593
\(59\) −47.6249 −0.807201 −0.403600 0.914935i \(-0.632241\pi\)
−0.403600 + 0.914935i \(0.632241\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 16.1273i 0.264382i 0.991224 + 0.132191i \(0.0422012\pi\)
−0.991224 + 0.132191i \(0.957799\pi\)
\(62\) 64.1312 1.03437
\(63\) 22.0844i 0.350546i
\(64\) 8.00000 0.125000
\(65\) 20.3402i 0.312926i
\(66\) 40.7525i 0.617462i
\(67\) 11.8203i 0.176423i −0.996102 0.0882116i \(-0.971885\pi\)
0.996102 0.0882116i \(-0.0281152\pi\)
\(68\) 9.45505i 0.139045i
\(69\) −32.5951 22.9033i −0.472392 0.331932i
\(70\) 23.2790 0.332557
\(71\) −2.91130 −0.0410042 −0.0205021 0.999790i \(-0.506526\pi\)
−0.0205021 + 0.999790i \(0.506526\pi\)
\(72\) −8.48528 −0.117851
\(73\) 136.473 1.86949 0.934745 0.355319i \(-0.115628\pi\)
0.934745 + 0.355319i \(0.115628\pi\)
\(74\) 13.5704i 0.183384i
\(75\) −8.66025 −0.115470
\(76\) 23.0206i 0.302903i
\(77\) −122.474 −1.59057
\(78\) −22.2815 −0.285661
\(79\) 37.4347i 0.473856i 0.971527 + 0.236928i \(0.0761406\pi\)
−0.971527 + 0.236928i \(0.923859\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) −29.2945 −0.357250
\(83\) 108.327i 1.30514i −0.757729 0.652569i \(-0.773691\pi\)
0.757729 0.652569i \(-0.226309\pi\)
\(84\) 25.5008i 0.303581i
\(85\) 10.5711 0.124366
\(86\) 30.2659i 0.351929i
\(87\) −15.3857 −0.176847
\(88\) 47.0570i 0.534738i
\(89\) 10.9382i 0.122901i −0.998110 0.0614503i \(-0.980427\pi\)
0.998110 0.0614503i \(-0.0195726\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 66.9628i 0.735855i
\(92\) −37.6375 26.4465i −0.409104 0.287462i
\(93\) −78.5444 −0.844563
\(94\) 43.8497 0.466487
\(95\) 25.7378 0.270924
\(96\) −9.79796 −0.102062
\(97\) 70.0663i 0.722333i −0.932501 0.361167i \(-0.882379\pi\)
0.932501 0.361167i \(-0.117621\pi\)
\(98\) 7.34124 0.0749106
\(99\) 49.9114i 0.504156i
\(100\) −10.0000 −0.100000
\(101\) −34.4854 −0.341439 −0.170720 0.985320i \(-0.554609\pi\)
−0.170720 + 0.985320i \(0.554609\pi\)
\(102\) 11.5800i 0.113530i
\(103\) 71.8118i 0.697202i 0.937271 + 0.348601i \(0.113343\pi\)
−0.937271 + 0.348601i \(0.886657\pi\)
\(104\) −25.7285 −0.247390
\(105\) −28.5108 −0.271531
\(106\) 99.9877i 0.943280i
\(107\) 120.386i 1.12510i −0.826763 0.562550i \(-0.809820\pi\)
0.826763 0.562550i \(-0.190180\pi\)
\(108\) 10.3923 0.0962250
\(109\) 115.918i 1.06347i −0.846912 0.531734i \(-0.821541\pi\)
0.846912 0.531734i \(-0.178459\pi\)
\(110\) 52.6113 0.478284
\(111\) 16.6203i 0.149732i
\(112\) 29.4458i 0.262909i
\(113\) 104.989i 0.929108i −0.885545 0.464554i \(-0.846215\pi\)
0.885545 0.464554i \(-0.153785\pi\)
\(114\) 28.1944i 0.247319i
\(115\) −29.5681 + 42.0800i −0.257114 + 0.365913i
\(116\) −17.7659 −0.153154
\(117\) 27.2892 0.233241
\(118\) 67.3517 0.570777
\(119\) 34.8015 0.292449
\(120\) 10.9545i 0.0912871i
\(121\) −155.795 −1.28756
\(122\) 22.8074i 0.186946i
\(123\) 35.8783 0.291693
\(124\) −90.6952 −0.731413
\(125\) 11.1803i 0.0894427i
\(126\) 31.2320i 0.247873i
\(127\) 26.1241 0.205701 0.102851 0.994697i \(-0.467204\pi\)
0.102851 + 0.994697i \(0.467204\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 37.0679i 0.287348i
\(130\) 28.7653i 0.221272i
\(131\) −251.807 −1.92219 −0.961096 0.276216i \(-0.910920\pi\)
−0.961096 + 0.276216i \(0.910920\pi\)
\(132\) 57.6328i 0.436612i
\(133\) 84.7326 0.637087
\(134\) 16.7165i 0.124750i
\(135\) 11.6190i 0.0860663i
\(136\) 13.3715i 0.0983196i
\(137\) 51.7087i 0.377436i 0.982031 + 0.188718i \(0.0604332\pi\)
−0.982031 + 0.188718i \(0.939567\pi\)
\(138\) 46.0964 + 32.3902i 0.334032 + 0.234712i
\(139\) 38.3182 0.275670 0.137835 0.990455i \(-0.455986\pi\)
0.137835 + 0.990455i \(0.455986\pi\)
\(140\) −32.9214 −0.235153
\(141\) −53.7047 −0.380885
\(142\) 4.11719 0.0289943
\(143\) 151.338i 1.05831i
\(144\) 12.0000 0.0833333
\(145\) 19.8629i 0.136985i
\(146\) −193.002 −1.32193
\(147\) −8.99115 −0.0611643
\(148\) 19.1914i 0.129672i
\(149\) 46.9760i 0.315275i −0.987497 0.157638i \(-0.949612\pi\)
0.987497 0.157638i \(-0.0503878\pi\)
\(150\) 12.2474 0.0816497
\(151\) −25.8294 −0.171055 −0.0855277 0.996336i \(-0.527258\pi\)
−0.0855277 + 0.996336i \(0.527258\pi\)
\(152\) 32.5561i 0.214185i
\(153\) 14.1826i 0.0926966i
\(154\) 173.204 1.12470
\(155\) 101.400i 0.654196i
\(156\) 31.5109 0.201993
\(157\) 130.106i 0.828701i 0.910117 + 0.414351i \(0.135991\pi\)
−0.910117 + 0.414351i \(0.864009\pi\)
\(158\) 52.9406i 0.335067i
\(159\) 122.459i 0.770185i
\(160\) 12.6491i 0.0790569i
\(161\) −97.3423 + 138.534i −0.604611 + 0.860457i
\(162\) −12.7279 −0.0785674
\(163\) 235.517 1.44489 0.722445 0.691428i \(-0.243018\pi\)
0.722445 + 0.691428i \(0.243018\pi\)
\(164\) 41.4287 0.252614
\(165\) −64.4354 −0.390517
\(166\) 153.197i 0.922872i
\(167\) −9.15117 −0.0547974 −0.0273987 0.999625i \(-0.508722\pi\)
−0.0273987 + 0.999625i \(0.508722\pi\)
\(168\) 36.0636i 0.214664i
\(169\) −86.2555 −0.510387
\(170\) −14.9497 −0.0879397
\(171\) 34.5309i 0.201935i
\(172\) 42.8024i 0.248851i
\(173\) 27.8008 0.160698 0.0803490 0.996767i \(-0.474397\pi\)
0.0803490 + 0.996767i \(0.474397\pi\)
\(174\) 21.7587 0.125050
\(175\) 36.8073i 0.210327i
\(176\) 66.5486i 0.378117i
\(177\) −82.4887 −0.466038
\(178\) 15.4689i 0.0869038i
\(179\) 243.048 1.35781 0.678906 0.734225i \(-0.262454\pi\)
0.678906 + 0.734225i \(0.262454\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 2.69386i 0.0148832i 0.999972 + 0.00744160i \(0.00236876\pi\)
−0.999972 + 0.00744160i \(0.997631\pi\)
\(182\) 94.6997i 0.520328i
\(183\) 27.9333i 0.152641i
\(184\) 53.2275 + 37.4010i 0.289280 + 0.203266i
\(185\) −21.4567 −0.115982
\(186\) 111.079 0.597196
\(187\) 78.6525 0.420602
\(188\) −62.0129 −0.329856
\(189\) 38.2513i 0.202388i
\(190\) −36.3988 −0.191573
\(191\) 72.7322i 0.380797i 0.981707 + 0.190398i \(0.0609780\pi\)
−0.981707 + 0.190398i \(0.939022\pi\)
\(192\) 13.8564 0.0721688
\(193\) −34.1113 −0.176743 −0.0883714 0.996088i \(-0.528166\pi\)
−0.0883714 + 0.996088i \(0.528166\pi\)
\(194\) 99.0888i 0.510767i
\(195\) 35.2302i 0.180668i
\(196\) −10.3821 −0.0529698
\(197\) 352.408 1.78887 0.894436 0.447196i \(-0.147577\pi\)
0.894436 + 0.447196i \(0.147577\pi\)
\(198\) 70.5854i 0.356492i
\(199\) 3.97739i 0.0199869i −0.999950 0.00999345i \(-0.996819\pi\)
0.999950 0.00999345i \(-0.00318107\pi\)
\(200\) 14.1421 0.0707107
\(201\) 20.4734i 0.101858i
\(202\) 48.7697 0.241434
\(203\) 65.3914i 0.322125i
\(204\) 16.3766i 0.0802776i
\(205\) 46.3187i 0.225945i
\(206\) 101.557i 0.492996i
\(207\) −56.4563 39.6697i −0.272736 0.191641i
\(208\) 36.3856 0.174931
\(209\) 191.499 0.916261
\(210\) 40.3204 0.192002
\(211\) 9.97835 0.0472907 0.0236454 0.999720i \(-0.492473\pi\)
0.0236454 + 0.999720i \(0.492473\pi\)
\(212\) 141.404i 0.667000i
\(213\) −5.04251 −0.0236738
\(214\) 170.251i 0.795566i
\(215\) 47.8545 0.222579
\(216\) −14.6969 −0.0680414
\(217\) 333.825i 1.53836i
\(218\) 163.933i 0.751985i
\(219\) 236.378 1.07935
\(220\) −74.4036 −0.338198
\(221\) 43.0035i 0.194586i
\(222\) 23.5046i 0.105877i
\(223\) 239.893 1.07575 0.537877 0.843023i \(-0.319226\pi\)
0.537877 + 0.843023i \(0.319226\pi\)
\(224\) 41.6427i 0.185905i
\(225\) −15.0000 −0.0666667
\(226\) 148.477i 0.656978i
\(227\) 64.1819i 0.282740i −0.989957 0.141370i \(-0.954849\pi\)
0.989957 0.141370i \(-0.0451506\pi\)
\(228\) 39.8729i 0.174881i
\(229\) 193.637i 0.845577i 0.906228 + 0.422789i \(0.138949\pi\)
−0.906228 + 0.422789i \(0.861051\pi\)
\(230\) 41.8156 59.5102i 0.181807 0.258740i
\(231\) −212.131 −0.918314
\(232\) 25.1248 0.108296
\(233\) 313.193 1.34418 0.672088 0.740472i \(-0.265398\pi\)
0.672088 + 0.740472i \(0.265398\pi\)
\(234\) −38.5928 −0.164926
\(235\) 69.3325i 0.295032i
\(236\) −95.2497 −0.403600
\(237\) 64.8387i 0.273581i
\(238\) −49.2167 −0.206793
\(239\) 211.636 0.885508 0.442754 0.896643i \(-0.354001\pi\)
0.442754 + 0.896643i \(0.354001\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 305.383i 1.26715i 0.773682 + 0.633574i \(0.218413\pi\)
−0.773682 + 0.633574i \(0.781587\pi\)
\(242\) 220.327 0.910441
\(243\) 15.5885 0.0641500
\(244\) 32.2546i 0.132191i
\(245\) 11.6075i 0.0473776i
\(246\) −50.7395 −0.206258
\(247\) 104.702i 0.423896i
\(248\) 128.262 0.517187
\(249\) 187.627i 0.753522i
\(250\) 15.8114i 0.0632456i
\(251\) 319.715i 1.27376i 0.770962 + 0.636882i \(0.219776\pi\)
−0.770962 + 0.636882i \(0.780224\pi\)
\(252\) 44.1687i 0.175273i
\(253\) −219.997 + 313.091i −0.869553 + 1.23751i
\(254\) −36.9450 −0.145453
\(255\) 18.3096 0.0718025
\(256\) 16.0000 0.0625000
\(257\) 47.3441 0.184218 0.0921091 0.995749i \(-0.470639\pi\)
0.0921091 + 0.995749i \(0.470639\pi\)
\(258\) 52.4220i 0.203186i
\(259\) −70.6385 −0.272735
\(260\) 40.6803i 0.156463i
\(261\) −26.6488 −0.102103
\(262\) 356.109 1.35919
\(263\) 183.744i 0.698648i 0.937002 + 0.349324i \(0.113589\pi\)
−0.937002 + 0.349324i \(0.886411\pi\)
\(264\) 81.5050i 0.308731i
\(265\) −158.094 −0.596583
\(266\) −119.830 −0.450489
\(267\) 18.9454i 0.0709567i
\(268\) 23.6407i 0.0882116i
\(269\) −364.416 −1.35471 −0.677354 0.735657i \(-0.736873\pi\)
−0.677354 + 0.735657i \(0.736873\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) −345.337 −1.27431 −0.637153 0.770738i \(-0.719888\pi\)
−0.637153 + 0.770738i \(0.719888\pi\)
\(272\) 18.9101i 0.0695224i
\(273\) 115.983i 0.424846i
\(274\) 73.1271i 0.266887i
\(275\) 83.1857i 0.302494i
\(276\) −65.1901 45.8067i −0.236196 0.165966i
\(277\) 209.498 0.756310 0.378155 0.925742i \(-0.376559\pi\)
0.378155 + 0.925742i \(0.376559\pi\)
\(278\) −54.1901 −0.194928
\(279\) −136.043 −0.487609
\(280\) 46.5579 0.166278
\(281\) 244.704i 0.870834i 0.900229 + 0.435417i \(0.143399\pi\)
−0.900229 + 0.435417i \(0.856601\pi\)
\(282\) 75.9500 0.269326
\(283\) 292.192i 1.03248i −0.856444 0.516240i \(-0.827331\pi\)
0.856444 0.516240i \(-0.172669\pi\)
\(284\) −5.82259 −0.0205021
\(285\) 44.5792 0.156418
\(286\) 214.024i 0.748337i
\(287\) 152.488i 0.531316i
\(288\) −16.9706 −0.0589256
\(289\) 266.650 0.922666
\(290\) 28.0903i 0.0968632i
\(291\) 121.358i 0.417039i
\(292\) 272.946 0.934745
\(293\) 180.937i 0.617533i 0.951138 + 0.308766i \(0.0999162\pi\)
−0.951138 + 0.308766i \(0.900084\pi\)
\(294\) 12.7154 0.0432497
\(295\) 106.492i 0.360991i
\(296\) 27.1408i 0.0916919i
\(297\) 86.4491i 0.291075i
\(298\) 66.4341i 0.222933i
\(299\) −171.183 120.284i −0.572519 0.402287i
\(300\) −17.3205 −0.0577350
\(301\) 157.544 0.523402
\(302\) 36.5283 0.120954
\(303\) −59.7304 −0.197130
\(304\) 46.0412i 0.151451i
\(305\) 36.0617 0.118235
\(306\) 20.0572i 0.0655464i
\(307\) 60.1754 0.196011 0.0980056 0.995186i \(-0.468754\pi\)
0.0980056 + 0.995186i \(0.468754\pi\)
\(308\) −244.947 −0.795283
\(309\) 124.382i 0.402530i
\(310\) 143.402i 0.462586i
\(311\) −275.681 −0.886434 −0.443217 0.896414i \(-0.646163\pi\)
−0.443217 + 0.896414i \(0.646163\pi\)
\(312\) −44.5631 −0.142830
\(313\) 110.944i 0.354455i −0.984170 0.177227i \(-0.943287\pi\)
0.984170 0.177227i \(-0.0567128\pi\)
\(314\) 183.998i 0.585980i
\(315\) −49.3822 −0.156769
\(316\) 74.8693i 0.236928i
\(317\) 515.941 1.62757 0.813787 0.581163i \(-0.197402\pi\)
0.813787 + 0.581163i \(0.197402\pi\)
\(318\) 173.184i 0.544603i
\(319\) 147.787i 0.463282i
\(320\) 17.8885i 0.0559017i
\(321\) 208.514i 0.649577i
\(322\) 137.663 195.916i 0.427524 0.608435i
\(323\) −54.4153 −0.168468
\(324\) 18.0000 0.0555556
\(325\) −45.4820 −0.139945
\(326\) −333.071 −1.02169
\(327\) 200.776i 0.613993i
\(328\) −58.5890 −0.178625
\(329\) 228.253i 0.693777i
\(330\) 91.1254 0.276138
\(331\) 559.830 1.69133 0.845664 0.533715i \(-0.179205\pi\)
0.845664 + 0.533715i \(0.179205\pi\)
\(332\) 216.653i 0.652569i
\(333\) 28.7872i 0.0864479i
\(334\) 12.9417 0.0387476
\(335\) −26.4311 −0.0788988
\(336\) 51.0017i 0.151791i
\(337\) 510.476i 1.51477i −0.652970 0.757383i \(-0.726477\pi\)
0.652970 0.757383i \(-0.273523\pi\)
\(338\) 121.984 0.360898
\(339\) 181.847i 0.536421i
\(340\) 21.1421 0.0621828
\(341\) 754.455i 2.21248i
\(342\) 48.8341i 0.142790i
\(343\) 322.498i 0.940227i
\(344\) 60.5317i 0.175964i
\(345\) −51.2134 + 72.8848i −0.148445 + 0.211260i
\(346\) −39.3162 −0.113631
\(347\) −423.608 −1.22077 −0.610386 0.792104i \(-0.708986\pi\)
−0.610386 + 0.792104i \(0.708986\pi\)
\(348\) −30.7714 −0.0884236
\(349\) 206.336 0.591220 0.295610 0.955309i \(-0.404477\pi\)
0.295610 + 0.955309i \(0.404477\pi\)
\(350\) 52.0534i 0.148724i
\(351\) 47.2663 0.134662
\(352\) 94.1139i 0.267369i
\(353\) 458.010 1.29748 0.648739 0.761011i \(-0.275297\pi\)
0.648739 + 0.761011i \(0.275297\pi\)
\(354\) 116.657 0.329538
\(355\) 6.50986i 0.0183376i
\(356\) 21.8763i 0.0614503i
\(357\) 60.2779 0.168846
\(358\) −343.722 −0.960118
\(359\) 396.012i 1.10310i 0.834142 + 0.551549i \(0.185963\pi\)
−0.834142 + 0.551549i \(0.814037\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 228.513 0.633000
\(362\) 3.80969i 0.0105240i
\(363\) −269.844 −0.743372
\(364\) 133.926i 0.367927i
\(365\) 305.162i 0.836061i
\(366\) 39.5036i 0.107933i
\(367\) 209.492i 0.570824i −0.958405 0.285412i \(-0.907870\pi\)
0.958405 0.285412i \(-0.0921304\pi\)
\(368\) −75.2751 52.8930i −0.204552 0.143731i
\(369\) 62.1430 0.168409
\(370\) 30.3443 0.0820117
\(371\) −520.470 −1.40288
\(372\) −157.089 −0.422282
\(373\) 680.917i 1.82552i −0.408501 0.912758i \(-0.633948\pi\)
0.408501 0.912758i \(-0.366052\pi\)
\(374\) −111.231 −0.297410
\(375\) 19.3649i 0.0516398i
\(376\) 87.6995 0.233243
\(377\) −80.8028 −0.214331
\(378\) 54.0954i 0.143110i
\(379\) 354.412i 0.935123i −0.883960 0.467562i \(-0.845133\pi\)
0.883960 0.467562i \(-0.154867\pi\)
\(380\) 51.4757 0.135462
\(381\) 45.2482 0.118762
\(382\) 102.859i 0.269264i
\(383\) 211.762i 0.552904i −0.961028 0.276452i \(-0.910841\pi\)
0.961028 0.276452i \(-0.0891586\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 273.859i 0.711323i
\(386\) 48.2407 0.124976
\(387\) 64.2036i 0.165901i
\(388\) 140.133i 0.361167i
\(389\) 741.982i 1.90741i −0.300745 0.953705i \(-0.597235\pi\)
0.300745 0.953705i \(-0.402765\pi\)
\(390\) 49.8230i 0.127751i
\(391\) 62.5132 88.9662i 0.159880 0.227535i
\(392\) 14.6825 0.0374553
\(393\) −436.143 −1.10978
\(394\) −498.380 −1.26492
\(395\) 83.7064 0.211915
\(396\) 99.8229i 0.252078i
\(397\) −308.016 −0.775859 −0.387930 0.921689i \(-0.626810\pi\)
−0.387930 + 0.921689i \(0.626810\pi\)
\(398\) 5.62489i 0.0141329i
\(399\) 146.761 0.367823
\(400\) −20.0000 −0.0500000
\(401\) 764.284i 1.90595i 0.303055 + 0.952973i \(0.401993\pi\)
−0.303055 + 0.952973i \(0.598007\pi\)
\(402\) 28.9538i 0.0720244i
\(403\) −412.500 −1.02357
\(404\) −68.9707 −0.170720
\(405\) 20.1246i 0.0496904i
\(406\) 92.4774i 0.227777i
\(407\) −159.645 −0.392249
\(408\) 23.1601i 0.0567648i
\(409\) −187.717 −0.458965 −0.229483 0.973313i \(-0.573703\pi\)
−0.229483 + 0.973313i \(0.573703\pi\)
\(410\) 65.5045i 0.159767i
\(411\) 89.5621i 0.217913i
\(412\) 143.624i 0.348601i
\(413\) 350.588i 0.848882i
\(414\) 79.8413 + 56.1015i 0.192853 + 0.135511i
\(415\) −242.225 −0.583676
\(416\) −51.4570 −0.123695
\(417\) 66.3690 0.159158
\(418\) −270.820 −0.647895
\(419\) 271.010i 0.646801i 0.946262 + 0.323401i \(0.104826\pi\)
−0.946262 + 0.323401i \(0.895174\pi\)
\(420\) −57.0216 −0.135766
\(421\) 436.703i 1.03730i 0.854987 + 0.518650i \(0.173565\pi\)
−0.854987 + 0.518650i \(0.826435\pi\)
\(422\) −14.1115 −0.0334396
\(423\) −93.0193 −0.219904
\(424\) 199.975i 0.471640i
\(425\) 23.6376i 0.0556180i
\(426\) 7.13119 0.0167399
\(427\) 118.720 0.278034
\(428\) 240.771i 0.562550i
\(429\) 262.125i 0.611015i
\(430\) −67.6765 −0.157387
\(431\) 785.010i 1.82137i −0.413103 0.910684i \(-0.635555\pi\)
0.413103 0.910684i \(-0.364445\pi\)
\(432\) 20.7846 0.0481125
\(433\) 483.665i 1.11701i 0.829502 + 0.558504i \(0.188625\pi\)
−0.829502 + 0.558504i \(0.811375\pi\)
\(434\) 472.099i 1.08779i
\(435\) 34.4035i 0.0790885i
\(436\) 231.836i 0.531734i
\(437\) 152.204 216.610i 0.348292 0.495674i
\(438\) −334.289 −0.763216
\(439\) −727.424 −1.65700 −0.828501 0.559987i \(-0.810806\pi\)
−0.828501 + 0.559987i \(0.810806\pi\)
\(440\) 105.223 0.239142
\(441\) −15.5731 −0.0353132
\(442\) 60.8161i 0.137593i
\(443\) −92.6907 −0.209234 −0.104617 0.994513i \(-0.533362\pi\)
−0.104617 + 0.994513i \(0.533362\pi\)
\(444\) 33.2406i 0.0748661i
\(445\) −24.4585 −0.0549628
\(446\) −339.260 −0.760673
\(447\) 81.3648i 0.182024i
\(448\) 58.8917i 0.131455i
\(449\) 571.226 1.27222 0.636109 0.771599i \(-0.280543\pi\)
0.636109 + 0.771599i \(0.280543\pi\)
\(450\) 21.2132 0.0471405
\(451\) 344.627i 0.764140i
\(452\) 209.978i 0.464554i
\(453\) −44.7378 −0.0987589
\(454\) 90.7669i 0.199927i
\(455\) −149.733 −0.329084
\(456\) 56.3888i 0.123660i
\(457\) 702.228i 1.53660i −0.640088 0.768302i \(-0.721102\pi\)
0.640088 0.768302i \(-0.278898\pi\)
\(458\) 273.844i 0.597913i
\(459\) 24.5649i 0.0535184i
\(460\) −59.1361 + 84.1601i −0.128557 + 0.182957i
\(461\) −105.378 −0.228585 −0.114292 0.993447i \(-0.536460\pi\)
−0.114292 + 0.993447i \(0.536460\pi\)
\(462\) 299.998 0.649346
\(463\) 279.994 0.604739 0.302370 0.953191i \(-0.402222\pi\)
0.302370 + 0.953191i \(0.402222\pi\)
\(464\) −35.5318 −0.0765771
\(465\) 175.631i 0.377700i
\(466\) −442.922 −0.950475
\(467\) 580.243i 1.24249i 0.783616 + 0.621246i \(0.213373\pi\)
−0.783616 + 0.621246i \(0.786627\pi\)
\(468\) 54.5784 0.116621
\(469\) −87.0150 −0.185533
\(470\) 98.0510i 0.208619i
\(471\) 225.350i 0.478451i
\(472\) 134.703 0.285389
\(473\) 356.055 0.752758
\(474\) 91.6958i 0.193451i
\(475\) 57.5515i 0.121161i
\(476\) 69.6030 0.146225
\(477\) 212.106i 0.444667i
\(478\) −299.299 −0.626149
\(479\) 475.037i 0.991727i −0.868400 0.495864i \(-0.834852\pi\)
0.868400 0.495864i \(-0.165148\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 87.2865i 0.181469i
\(482\) 431.876i 0.896008i
\(483\) −168.602 + 239.947i −0.349072 + 0.496785i
\(484\) −311.589 −0.643779
\(485\) −156.673 −0.323037
\(486\) −22.0454 −0.0453609
\(487\) −68.8375 −0.141350 −0.0706751 0.997499i \(-0.522515\pi\)
−0.0706751 + 0.997499i \(0.522515\pi\)
\(488\) 45.6149i 0.0934731i
\(489\) 407.928 0.834208
\(490\) 16.4155i 0.0335011i
\(491\) 473.549 0.964459 0.482230 0.876045i \(-0.339827\pi\)
0.482230 + 0.876045i \(0.339827\pi\)
\(492\) 71.7566 0.145847
\(493\) 41.9944i 0.0851812i
\(494\) 148.072i 0.299740i
\(495\) −111.605 −0.225465
\(496\) −181.390 −0.365707
\(497\) 21.4314i 0.0431215i
\(498\) 265.345i 0.532821i
\(499\) 730.312 1.46355 0.731776 0.681545i \(-0.238692\pi\)
0.731776 + 0.681545i \(0.238692\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −15.8503 −0.0316373
\(502\) 452.145i 0.900687i
\(503\) 506.085i 1.00613i −0.864247 0.503067i \(-0.832205\pi\)
0.864247 0.503067i \(-0.167795\pi\)
\(504\) 62.4640i 0.123937i
\(505\) 77.1116i 0.152696i
\(506\) 311.123 442.777i 0.614867 0.875053i
\(507\) −149.399 −0.294672
\(508\) 52.2481 0.102851
\(509\) 594.057 1.16711 0.583553 0.812075i \(-0.301662\pi\)
0.583553 + 0.812075i \(0.301662\pi\)
\(510\) −25.8937 −0.0507720
\(511\) 1004.64i 1.96602i
\(512\) −22.6274 −0.0441942
\(513\) 59.8093i 0.116587i
\(514\) −66.9546 −0.130262
\(515\) 160.576 0.311798
\(516\) 74.1359i 0.143674i
\(517\) 515.859i 0.997792i
\(518\) 99.8979 0.192853
\(519\) 48.1523 0.0927791
\(520\) 57.5307i 0.110636i
\(521\) 151.644i 0.291063i −0.989354 0.145531i \(-0.953511\pi\)
0.989354 0.145531i \(-0.0464892\pi\)
\(522\) 37.6871 0.0721976
\(523\) 460.148i 0.879824i 0.898041 + 0.439912i \(0.144990\pi\)
−0.898041 + 0.439912i \(0.855010\pi\)
\(524\) −503.614 −0.961096
\(525\) 63.7521i 0.121433i
\(526\) 259.854i 0.494019i
\(527\) 214.382i 0.406797i
\(528\) 115.266i 0.218306i
\(529\) 179.292 + 497.690i 0.338926 + 0.940813i
\(530\) 223.579 0.421848
\(531\) −142.875 −0.269067
\(532\) 169.465 0.318544
\(533\) 188.426 0.353520
\(534\) 26.7929i 0.0501740i
\(535\) −269.191 −0.503160
\(536\) 33.4330i 0.0623750i
\(537\) 420.972 0.783933
\(538\) 515.363 0.957923
\(539\) 86.3641i 0.160230i
\(540\) 23.2379i 0.0430331i
\(541\) −746.487 −1.37983 −0.689914 0.723891i \(-0.742352\pi\)
−0.689914 + 0.723891i \(0.742352\pi\)
\(542\) 488.380 0.901070
\(543\) 4.66590i 0.00859282i
\(544\) 26.7429i 0.0491598i
\(545\) −259.200 −0.475597
\(546\) 164.025i 0.300411i
\(547\) −452.047 −0.826412 −0.413206 0.910638i \(-0.635591\pi\)
−0.413206 + 0.910638i \(0.635591\pi\)
\(548\) 103.417i 0.188718i
\(549\) 48.3819i 0.0881273i
\(550\) 117.642i 0.213895i
\(551\) 102.245i 0.185563i
\(552\) 92.1927 + 64.7804i 0.167016 + 0.117356i
\(553\) 275.574 0.498325
\(554\) −296.275 −0.534792
\(555\) −37.1641 −0.0669623
\(556\) 76.6363 0.137835
\(557\) 992.369i 1.78163i 0.454365 + 0.890816i \(0.349866\pi\)
−0.454365 + 0.890816i \(0.650134\pi\)
\(558\) 192.394 0.344792
\(559\) 194.674i 0.348254i
\(560\) −65.8429 −0.117577
\(561\) 136.230 0.242835
\(562\) 346.064i 0.615772i
\(563\) 761.693i 1.35292i 0.736481 + 0.676459i \(0.236486\pi\)
−0.736481 + 0.676459i \(0.763514\pi\)
\(564\) −107.409 −0.190442
\(565\) −234.763 −0.415510
\(566\) 413.222i 0.730074i
\(567\) 66.2531i 0.116849i
\(568\) 8.23439 0.0144972
\(569\) 444.757i 0.781647i 0.920466 + 0.390823i \(0.127810\pi\)
−0.920466 + 0.390823i \(0.872190\pi\)
\(570\) −63.0445 −0.110604
\(571\) 1028.85i 1.80184i −0.433982 0.900922i \(-0.642892\pi\)
0.433982 0.900922i \(-0.357108\pi\)
\(572\) 302.676i 0.529154i
\(573\) 125.976i 0.219853i
\(574\) 215.650i 0.375697i
\(575\) 94.0938 + 66.1162i 0.163641 + 0.114985i
\(576\) 24.0000 0.0416667
\(577\) −642.647 −1.11377 −0.556886 0.830589i \(-0.688004\pi\)
−0.556886 + 0.830589i \(0.688004\pi\)
\(578\) −377.101 −0.652423
\(579\) −59.0826 −0.102042
\(580\) 39.7257i 0.0684927i
\(581\) −797.441 −1.37253
\(582\) 171.627i 0.294891i
\(583\) −1176.28 −2.01763
\(584\) −386.003 −0.660965
\(585\) 61.0205i 0.104309i
\(586\) 255.884i 0.436662i
\(587\) 461.581 0.786338 0.393169 0.919466i \(-0.371379\pi\)
0.393169 + 0.919466i \(0.371379\pi\)
\(588\) −17.9823 −0.0305821
\(589\) 521.965i 0.886188i
\(590\) 150.603i 0.255259i
\(591\) 610.388 1.03281
\(592\) 38.3829i 0.0648359i
\(593\) 611.226 1.03073 0.515367 0.856969i \(-0.327655\pi\)
0.515367 + 0.856969i \(0.327655\pi\)
\(594\) 122.258i 0.205821i
\(595\) 77.8185i 0.130787i
\(596\) 93.9520i 0.157638i
\(597\) 6.88905i 0.0115394i
\(598\) 242.089 + 170.107i 0.404832 + 0.284460i
\(599\) 341.070 0.569400 0.284700 0.958617i \(-0.408106\pi\)
0.284700 + 0.958617i \(0.408106\pi\)
\(600\) 24.4949 0.0408248
\(601\) 103.870 0.172828 0.0864142 0.996259i \(-0.472459\pi\)
0.0864142 + 0.996259i \(0.472459\pi\)
\(602\) −222.801 −0.370101
\(603\) 35.4610i 0.0588077i
\(604\) −51.6588 −0.0855277
\(605\) 348.367i 0.575814i
\(606\) 84.4716 0.139392
\(607\) −209.656 −0.345398 −0.172699 0.984975i \(-0.555249\pi\)
−0.172699 + 0.984975i \(0.555249\pi\)
\(608\) 65.1121i 0.107092i
\(609\) 113.261i 0.185979i
\(610\) −50.9990 −0.0836049
\(611\) −282.047 −0.461616
\(612\) 28.3652i 0.0463483i
\(613\) 790.819i 1.29008i 0.764149 + 0.645040i \(0.223159\pi\)
−0.764149 + 0.645040i \(0.776841\pi\)
\(614\) −85.1009 −0.138601
\(615\) 80.2263i 0.130449i
\(616\) 346.408 0.562350
\(617\) 446.127i 0.723059i 0.932361 + 0.361529i \(0.117745\pi\)
−0.932361 + 0.361529i \(0.882255\pi\)
\(618\) 175.902i 0.284632i
\(619\) 931.416i 1.50471i −0.658758 0.752355i \(-0.728918\pi\)
0.658758 0.752355i \(-0.271082\pi\)
\(620\) 202.801i 0.327098i
\(621\) −97.7852 68.7100i −0.157464 0.110644i
\(622\) 389.872 0.626803
\(623\) −80.5207 −0.129247
\(624\) 63.0217 0.100996
\(625\) 25.0000 0.0400000
\(626\) 156.899i 0.250637i
\(627\) 331.685 0.529004
\(628\) 260.212i 0.414351i
\(629\) 45.3640 0.0721209
\(630\) 69.8369 0.110852
\(631\) 578.467i 0.916747i 0.888760 + 0.458373i \(0.151568\pi\)
−0.888760 + 0.458373i \(0.848432\pi\)
\(632\) 105.881i 0.167534i
\(633\) 17.2830 0.0273033
\(634\) −729.651 −1.15087
\(635\) 58.4152i 0.0919925i
\(636\) 244.919i 0.385092i
\(637\) −47.2198 −0.0741284
\(638\) 209.002i 0.327590i
\(639\) −8.73389 −0.0136681
\(640\) 25.2982i 0.0395285i
\(641\) 198.212i 0.309223i 0.987975 + 0.154611i \(0.0494125\pi\)
−0.987975 + 0.154611i \(0.950587\pi\)
\(642\) 294.884i 0.459320i
\(643\) 91.4978i 0.142298i 0.997466 + 0.0711491i \(0.0226666\pi\)
−0.997466 + 0.0711491i \(0.977333\pi\)
\(644\) −194.685 + 277.067i −0.302305 + 0.430228i
\(645\) 82.8864 0.128506
\(646\) 76.9548 0.119125
\(647\) −178.939 −0.276568 −0.138284 0.990393i \(-0.544159\pi\)
−0.138284 + 0.990393i \(0.544159\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 792.342i 1.22087i
\(650\) 64.3213 0.0989558
\(651\) 578.201i 0.888174i
\(652\) 471.034 0.722445
\(653\) 298.195 0.456654 0.228327 0.973585i \(-0.426674\pi\)
0.228327 + 0.973585i \(0.426674\pi\)
\(654\) 283.940i 0.434159i
\(655\) 563.058i 0.859630i
\(656\) 82.8573 0.126307
\(657\) 409.418 0.623163
\(658\) 322.798i 0.490574i
\(659\) 686.401i 1.04158i −0.853685 0.520790i \(-0.825638\pi\)
0.853685 0.520790i \(-0.174362\pi\)
\(660\) −128.871 −0.195259
\(661\) 1101.62i 1.66660i −0.552823 0.833299i \(-0.686449\pi\)
0.552823 0.833299i \(-0.313551\pi\)
\(662\) −791.719 −1.19595
\(663\) 74.4842i 0.112344i
\(664\) 306.394i 0.461436i
\(665\) 189.468i 0.284914i
\(666\) 40.7112i 0.0611279i
\(667\) 167.166 + 117.461i 0.250624 + 0.176104i
\(668\) −18.3023 −0.0273987
\(669\) 415.507 0.621087
\(670\) 37.3792 0.0557899
\(671\) 268.312 0.399869
\(672\) 72.1272i 0.107332i
\(673\) 963.161 1.43114 0.715572 0.698539i \(-0.246166\pi\)
0.715572 + 0.698539i \(0.246166\pi\)
\(674\) 721.923i 1.07110i
\(675\) −25.9808 −0.0384900
\(676\) −172.511 −0.255194
\(677\) 1066.82i 1.57581i 0.615799 + 0.787903i \(0.288833\pi\)
−0.615799 + 0.787903i \(0.711167\pi\)
\(678\) 257.170i 0.379307i
\(679\) −515.790 −0.759632
\(680\) −29.8995 −0.0439699
\(681\) 111.166i 0.163240i
\(682\) 1066.96i 1.56446i
\(683\) −280.062 −0.410047 −0.205024 0.978757i \(-0.565727\pi\)
−0.205024 + 0.978757i \(0.565727\pi\)
\(684\) 69.0618i 0.100968i
\(685\) 115.624 0.168794
\(686\) 456.081i 0.664841i
\(687\) 335.389i 0.488194i
\(688\) 85.6048i 0.124426i
\(689\) 643.134i 0.933430i
\(690\) 72.4267 103.075i 0.104966 0.149383i
\(691\) 1165.91 1.68727 0.843637 0.536914i \(-0.180410\pi\)
0.843637 + 0.536914i \(0.180410\pi\)
\(692\) 55.6015 0.0803490
\(693\) −367.421 −0.530189
\(694\) 599.072 0.863217
\(695\) 85.6820i 0.123284i
\(696\) 43.5174 0.0625250
\(697\) 97.9275i 0.140499i
\(698\) −291.803 −0.418055
\(699\) 542.466 0.776060
\(700\) 73.6146i 0.105164i
\(701\) 508.137i 0.724875i 0.932008 + 0.362437i \(0.118055\pi\)
−0.932008 + 0.362437i \(0.881945\pi\)
\(702\) −66.8446 −0.0952203
\(703\) 110.450 0.157112
\(704\) 133.097i 0.189058i
\(705\) 120.087i 0.170337i
\(706\) −647.724 −0.917456
\(707\) 253.863i 0.359070i
\(708\) −164.977 −0.233019
\(709\) 51.5395i 0.0726932i −0.999339 0.0363466i \(-0.988428\pi\)
0.999339 0.0363466i \(-0.0115720\pi\)
\(710\) 9.20633i 0.0129667i
\(711\) 112.304i 0.157952i
\(712\) 30.9378i 0.0434519i
\(713\) 853.386 + 599.643i 1.19690 + 0.841013i
\(714\) −85.2459 −0.119392
\(715\) −338.402 −0.473290
\(716\) 486.097 0.678906
\(717\) 366.565 0.511248
\(718\) 560.046i 0.780008i
\(719\) 849.242 1.18114 0.590571 0.806985i \(-0.298902\pi\)
0.590571 + 0.806985i \(0.298902\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 528.640 0.733203
\(722\) −323.166 −0.447598
\(723\) 528.938i 0.731588i
\(724\) 5.38772i 0.00744160i
\(725\) 44.4147 0.0612617
\(726\) 381.617 0.525644
\(727\) 467.357i 0.642858i −0.946934 0.321429i \(-0.895837\pi\)
0.946934 0.321429i \(-0.104163\pi\)
\(728\) 189.399i 0.260164i
\(729\) 27.0000 0.0370370
\(730\) 431.565i 0.591185i
\(731\) −101.175 −0.138406
\(732\) 55.8666i 0.0763205i
\(733\) 1031.67i 1.40746i −0.710469 0.703729i \(-0.751517\pi\)
0.710469 0.703729i \(-0.248483\pi\)
\(734\) 296.267i 0.403634i
\(735\) 20.1048i 0.0273535i
\(736\) 106.455 + 74.8020i 0.144640 + 0.101633i
\(737\) −196.657 −0.266834
\(738\) −87.8835 −0.119083
\(739\) −561.453 −0.759747 −0.379873 0.925039i \(-0.624032\pi\)
−0.379873 + 0.925039i \(0.624032\pi\)
\(740\) −42.9134 −0.0579910
\(741\) 181.350i 0.244737i
\(742\) 736.055 0.991988
\(743\) 878.524i 1.18240i −0.806524 0.591201i \(-0.798654\pi\)
0.806524 0.591201i \(-0.201346\pi\)
\(744\) 222.157 0.298598
\(745\) −105.042 −0.140995
\(746\) 962.963i 1.29083i
\(747\) 324.980i 0.435046i
\(748\) 157.305 0.210301
\(749\) −886.214 −1.18320
\(750\) 27.3861i 0.0365148i
\(751\) 59.7825i 0.0796038i −0.999208 0.0398019i \(-0.987327\pi\)
0.999208 0.0398019i \(-0.0126727\pi\)
\(752\) −124.026 −0.164928
\(753\) 553.762i 0.735408i
\(754\) 114.272 0.151555
\(755\) 57.7562i 0.0764983i
\(756\) 76.5025i 0.101194i
\(757\) 666.974i 0.881076i −0.897734 0.440538i \(-0.854788\pi\)
0.897734 0.440538i \(-0.145212\pi\)
\(758\) 501.214i 0.661232i
\(759\) −381.046 + 542.289i −0.502037 + 0.714478i
\(760\) −72.7976 −0.0957863
\(761\) 520.271 0.683668 0.341834 0.939760i \(-0.388952\pi\)
0.341834 + 0.939760i \(0.388952\pi\)
\(762\) −63.9907 −0.0839772
\(763\) −853.325 −1.11838
\(764\) 145.464i 0.190398i
\(765\) 31.7132 0.0414552
\(766\) 299.477i 0.390962i
\(767\) −433.215 −0.564817
\(768\) 27.7128 0.0360844
\(769\) 417.949i 0.543497i −0.962368 0.271749i \(-0.912398\pi\)
0.962368 0.271749i \(-0.0876019\pi\)
\(770\) 387.296i 0.502981i
\(771\) 82.0023 0.106358
\(772\) −68.2227 −0.0883714
\(773\) 308.047i 0.398509i −0.979948 0.199254i \(-0.936148\pi\)
0.979948 0.199254i \(-0.0638520\pi\)
\(774\) 90.7976i 0.117310i
\(775\) 226.738 0.292565
\(776\) 198.178i 0.255383i
\(777\) −122.349 −0.157464
\(778\) 1049.32i 1.34874i
\(779\) 238.428i 0.306070i
\(780\) 70.4604i 0.0903339i
\(781\) 48.4356i 0.0620175i
\(782\) −88.4070 + 125.817i −0.113052 + 0.160892i
\(783\) −46.1571 −0.0589491
\(784\) −20.7642 −0.0264849
\(785\) 290.926 0.370607
\(786\) 616.799 0.784731
\(787\) 444.989i 0.565424i 0.959205 + 0.282712i \(0.0912341\pi\)
−0.959205 + 0.282712i \(0.908766\pi\)
\(788\) 704.815 0.894436
\(789\) 318.255i 0.403365i
\(790\) −118.379 −0.149847
\(791\) −772.873 −0.977084
\(792\) 141.171i