Properties

Label 690.3.f.a.229.1
Level $690$
Weight $3$
Character 690.229
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.1
Character \(\chi\) \(=\) 690.229
Dual form 690.3.f.a.229.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(-1.71908 + 4.69518i) q^{5} +2.44949 q^{6} -12.9397 q^{7} +2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(-1.71908 + 4.69518i) q^{5} +2.44949 q^{6} -12.9397 q^{7} +2.82843i q^{8} -3.00000 q^{9} +(6.63999 + 2.43115i) q^{10} +18.3935i q^{11} -3.46410i q^{12} -7.60366i q^{13} +18.2995i q^{14} +(-8.13230 - 2.97754i) q^{15} +4.00000 q^{16} +19.9407 q^{17} +4.24264i q^{18} -24.3487i q^{19} +(3.43816 - 9.39037i) q^{20} -22.4122i q^{21} +26.0123 q^{22} +(-22.9301 - 1.79238i) q^{23} -4.89898 q^{24} +(-19.0895 - 16.1428i) q^{25} -10.7532 q^{26} -5.19615i q^{27} +25.8794 q^{28} +32.2461 q^{29} +(-4.21087 + 11.5008i) q^{30} +3.18657 q^{31} -5.65685i q^{32} -31.8584 q^{33} -28.2004i q^{34} +(22.2444 - 60.7542i) q^{35} +6.00000 q^{36} +11.0170 q^{37} -34.4342 q^{38} +13.1699 q^{39} +(-13.2800 - 4.86230i) q^{40} -60.4391 q^{41} -31.6956 q^{42} -50.3599 q^{43} -36.7869i q^{44} +(5.15724 - 14.0856i) q^{45} +(-2.53481 + 32.4280i) q^{46} -79.4647i q^{47} +6.92820i q^{48} +118.435 q^{49} +(-22.8294 + 26.9967i) q^{50} +34.5383i q^{51} +15.2073i q^{52} +92.1165 q^{53} -7.34847 q^{54} +(-86.3608 - 31.6199i) q^{55} -36.5989i q^{56} +42.1731 q^{57} -45.6028i q^{58} +5.16200 q^{59} +(16.2646 + 5.95507i) q^{60} +10.5265i q^{61} -4.50650i q^{62} +38.8190 q^{63} -8.00000 q^{64} +(35.7006 + 13.0713i) q^{65} +45.0546i q^{66} +72.2321 q^{67} -39.8814 q^{68} +(3.10449 - 39.7160i) q^{69} +(-85.9194 - 31.4583i) q^{70} -8.94916 q^{71} -8.48528i q^{72} -70.6321i q^{73} -15.5805i q^{74} +(27.9602 - 33.0640i) q^{75} +48.6973i q^{76} -238.006i q^{77} -18.6251i q^{78} +1.35260i q^{79} +(-6.87633 + 18.7807i) q^{80} +9.00000 q^{81} +85.4739i q^{82} -135.372 q^{83} +44.8244i q^{84} +(-34.2797 + 93.6253i) q^{85} +71.2197i q^{86} +55.8518i q^{87} -52.0246 q^{88} +41.9425i q^{89} +(-19.9200 - 7.29345i) q^{90} +98.3889i q^{91} +(45.8601 + 3.58476i) q^{92} +5.51931i q^{93} -112.380 q^{94} +(114.321 + 41.8573i) q^{95} +9.79796 q^{96} -165.650 q^{97} -167.493i q^{98} -55.1804i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 96q^{4} - 144q^{9} + O(q^{10}) \) \( 48q - 96q^{4} - 144q^{9} + 192q^{16} + 96q^{25} + 64q^{26} - 152q^{29} - 8q^{31} + 56q^{35} + 288q^{36} - 48q^{39} + 40q^{41} - 160q^{46} + 424q^{49} + 96q^{50} + 32q^{55} + 360q^{59} - 384q^{64} + 192q^{69} - 496q^{70} - 152q^{71} + 144q^{75} + 432q^{81} - 136q^{85} + 256q^{94} + 496q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 1.73205i 0.577350i
\(4\) −2.00000 −0.500000
\(5\) −1.71908 + 4.69518i −0.343816 + 0.939037i
\(6\) 2.44949 0.408248
\(7\) −12.9397 −1.84853 −0.924263 0.381757i \(-0.875319\pi\)
−0.924263 + 0.381757i \(0.875319\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −3.00000 −0.333333
\(10\) 6.63999 + 2.43115i 0.663999 + 0.243115i
\(11\) 18.3935i 1.67213i 0.548627 + 0.836067i \(0.315151\pi\)
−0.548627 + 0.836067i \(0.684849\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 7.60366i 0.584897i −0.956281 0.292448i \(-0.905530\pi\)
0.956281 0.292448i \(-0.0944699\pi\)
\(14\) 18.2995i 1.30710i
\(15\) −8.13230 2.97754i −0.542153 0.198502i
\(16\) 4.00000 0.250000
\(17\) 19.9407 1.17298 0.586491 0.809956i \(-0.300509\pi\)
0.586491 + 0.809956i \(0.300509\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 24.3487i 1.28151i −0.767746 0.640754i \(-0.778622\pi\)
0.767746 0.640754i \(-0.221378\pi\)
\(20\) 3.43816 9.39037i 0.171908 0.469518i
\(21\) 22.4122i 1.06725i
\(22\) 26.0123 1.18238
\(23\) −22.9301 1.79238i −0.996959 0.0779296i
\(24\) −4.89898 −0.204124
\(25\) −19.0895 16.1428i −0.763581 0.645712i
\(26\) −10.7532 −0.413584
\(27\) 5.19615i 0.192450i
\(28\) 25.8794 0.924263
\(29\) 32.2461 1.11193 0.555967 0.831205i \(-0.312348\pi\)
0.555967 + 0.831205i \(0.312348\pi\)
\(30\) −4.21087 + 11.5008i −0.140362 + 0.383360i
\(31\) 3.18657 0.102793 0.0513963 0.998678i \(-0.483633\pi\)
0.0513963 + 0.998678i \(0.483633\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −31.8584 −0.965407
\(34\) 28.2004i 0.829424i
\(35\) 22.2444 60.7542i 0.635553 1.73583i
\(36\) 6.00000 0.166667
\(37\) 11.0170 0.297758 0.148879 0.988855i \(-0.452433\pi\)
0.148879 + 0.988855i \(0.452433\pi\)
\(38\) −34.4342 −0.906163
\(39\) 13.1699 0.337690
\(40\) −13.2800 4.86230i −0.332000 0.121557i
\(41\) −60.4391 −1.47413 −0.737063 0.675824i \(-0.763788\pi\)
−0.737063 + 0.675824i \(0.763788\pi\)
\(42\) −31.6956 −0.754657
\(43\) −50.3599 −1.17116 −0.585581 0.810614i \(-0.699133\pi\)
−0.585581 + 0.810614i \(0.699133\pi\)
\(44\) 36.7869i 0.836067i
\(45\) 5.15724 14.0856i 0.114605 0.313012i
\(46\) −2.53481 + 32.4280i −0.0551045 + 0.704956i
\(47\) 79.4647i 1.69074i −0.534182 0.845369i \(-0.679380\pi\)
0.534182 0.845369i \(-0.320620\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 118.435 2.41705
\(50\) −22.8294 + 26.9967i −0.456588 + 0.539933i
\(51\) 34.5383i 0.677222i
\(52\) 15.2073i 0.292448i
\(53\) 92.1165 1.73805 0.869024 0.494770i \(-0.164748\pi\)
0.869024 + 0.494770i \(0.164748\pi\)
\(54\) −7.34847 −0.136083
\(55\) −86.3608 31.6199i −1.57020 0.574907i
\(56\) 36.5989i 0.653552i
\(57\) 42.1731 0.739879
\(58\) 45.6028i 0.786256i
\(59\) 5.16200 0.0874916 0.0437458 0.999043i \(-0.486071\pi\)
0.0437458 + 0.999043i \(0.486071\pi\)
\(60\) 16.2646 + 5.95507i 0.271077 + 0.0992512i
\(61\) 10.5265i 0.172565i 0.996271 + 0.0862827i \(0.0274988\pi\)
−0.996271 + 0.0862827i \(0.972501\pi\)
\(62\) 4.50650i 0.0726854i
\(63\) 38.8190 0.616175
\(64\) −8.00000 −0.125000
\(65\) 35.7006 + 13.0713i 0.549240 + 0.201097i
\(66\) 45.0546i 0.682646i
\(67\) 72.2321 1.07809 0.539046 0.842276i \(-0.318785\pi\)
0.539046 + 0.842276i \(0.318785\pi\)
\(68\) −39.8814 −0.586491
\(69\) 3.10449 39.7160i 0.0449927 0.575594i
\(70\) −85.9194 31.4583i −1.22742 0.449404i
\(71\) −8.94916 −0.126045 −0.0630223 0.998012i \(-0.520074\pi\)
−0.0630223 + 0.998012i \(0.520074\pi\)
\(72\) 8.48528i 0.117851i
\(73\) 70.6321i 0.967564i −0.875189 0.483782i \(-0.839263\pi\)
0.875189 0.483782i \(-0.160737\pi\)
\(74\) 15.5805i 0.210547i
\(75\) 27.9602 33.0640i 0.372802 0.440854i
\(76\) 48.6973i 0.640754i
\(77\) 238.006i 3.09098i
\(78\) 18.6251i 0.238783i
\(79\) 1.35260i 0.0171215i 0.999963 + 0.00856076i \(0.00272501\pi\)
−0.999963 + 0.00856076i \(0.997275\pi\)
\(80\) −6.87633 + 18.7807i −0.0859541 + 0.234759i
\(81\) 9.00000 0.111111
\(82\) 85.4739i 1.04236i
\(83\) −135.372 −1.63099 −0.815494 0.578765i \(-0.803535\pi\)
−0.815494 + 0.578765i \(0.803535\pi\)
\(84\) 44.8244i 0.533623i
\(85\) −34.2797 + 93.6253i −0.403291 + 1.10147i
\(86\) 71.2197i 0.828136i
\(87\) 55.8518i 0.641975i
\(88\) −52.0246 −0.591189
\(89\) 41.9425i 0.471263i 0.971842 + 0.235632i \(0.0757159\pi\)
−0.971842 + 0.235632i \(0.924284\pi\)
\(90\) −19.9200 7.29345i −0.221333 0.0810383i
\(91\) 98.3889i 1.08120i
\(92\) 45.8601 + 3.58476i 0.498479 + 0.0389648i
\(93\) 5.51931i 0.0593474i
\(94\) −112.380 −1.19553
\(95\) 114.321 + 41.8573i 1.20338 + 0.440604i
\(96\) 9.79796 0.102062
\(97\) −165.650 −1.70773 −0.853867 0.520491i \(-0.825749\pi\)
−0.853867 + 0.520491i \(0.825749\pi\)
\(98\) 167.493i 1.70911i
\(99\) 55.1804i 0.557378i
\(100\) 38.1790 + 32.2856i 0.381790 + 0.322856i
\(101\) 20.2266 0.200264 0.100132 0.994974i \(-0.468074\pi\)
0.100132 + 0.994974i \(0.468074\pi\)
\(102\) 48.8445 0.478868
\(103\) −10.1077 −0.0981328 −0.0490664 0.998796i \(-0.515625\pi\)
−0.0490664 + 0.998796i \(0.515625\pi\)
\(104\) 21.5064 0.206792
\(105\) 105.229 + 38.5284i 1.00218 + 0.366937i
\(106\) 130.272i 1.22899i
\(107\) 59.9270 0.560065 0.280033 0.959990i \(-0.409655\pi\)
0.280033 + 0.959990i \(0.409655\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 44.0489i 0.404118i −0.979373 0.202059i \(-0.935237\pi\)
0.979373 0.202059i \(-0.0647633\pi\)
\(110\) −44.7173 + 122.133i −0.406521 + 1.11030i
\(111\) 19.0821i 0.171911i
\(112\) −51.7587 −0.462131
\(113\) −162.943 −1.44197 −0.720987 0.692948i \(-0.756311\pi\)
−0.720987 + 0.692948i \(0.756311\pi\)
\(114\) 59.6418i 0.523174i
\(115\) 47.8342 104.580i 0.415949 0.909388i
\(116\) −64.4921 −0.555967
\(117\) 22.8110i 0.194966i
\(118\) 7.30017i 0.0618659i
\(119\) −258.026 −2.16829
\(120\) 8.42175 23.0016i 0.0701812 0.191680i
\(121\) −217.320 −1.79603
\(122\) 14.8867 0.122022
\(123\) 104.684i 0.851087i
\(124\) −6.37315 −0.0513963
\(125\) 108.610 61.8780i 0.868879 0.495024i
\(126\) 54.8984i 0.435702i
\(127\) 78.3423i 0.616869i 0.951246 + 0.308434i \(0.0998050\pi\)
−0.951246 + 0.308434i \(0.900195\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 87.2260i 0.676170i
\(130\) 18.4856 50.4882i 0.142197 0.388371i
\(131\) 243.523 1.85896 0.929479 0.368876i \(-0.120257\pi\)
0.929479 + 0.368876i \(0.120257\pi\)
\(132\) 63.7169 0.482704
\(133\) 315.064i 2.36890i
\(134\) 102.152i 0.762326i
\(135\) 24.3969 + 8.93261i 0.180718 + 0.0661675i
\(136\) 56.4008i 0.414712i
\(137\) −68.6757 −0.501282 −0.250641 0.968080i \(-0.580641\pi\)
−0.250641 + 0.968080i \(0.580641\pi\)
\(138\) −56.1669 4.39042i −0.407007 0.0318146i
\(139\) −136.802 −0.984184 −0.492092 0.870543i \(-0.663768\pi\)
−0.492092 + 0.870543i \(0.663768\pi\)
\(140\) −44.4887 + 121.508i −0.317777 + 0.867917i
\(141\) 137.637 0.976148
\(142\) 12.6560i 0.0891270i
\(143\) 139.858 0.978026
\(144\) −12.0000 −0.0833333
\(145\) −55.4336 + 151.401i −0.382301 + 1.04415i
\(146\) −99.8889 −0.684171
\(147\) 205.136i 1.39548i
\(148\) −22.0341 −0.148879
\(149\) 147.155i 0.987620i −0.869570 0.493810i \(-0.835604\pi\)
0.869570 0.493810i \(-0.164396\pi\)
\(150\) −46.7596 39.5417i −0.311731 0.263611i
\(151\) −4.21892 −0.0279398 −0.0139699 0.999902i \(-0.504447\pi\)
−0.0139699 + 0.999902i \(0.504447\pi\)
\(152\) 68.8684 0.453082
\(153\) −59.8221 −0.390994
\(154\) −336.591 −2.18565
\(155\) −5.47798 + 14.9616i −0.0353418 + 0.0965261i
\(156\) −26.3398 −0.168845
\(157\) 127.989 0.815216 0.407608 0.913157i \(-0.366363\pi\)
0.407608 + 0.913157i \(0.366363\pi\)
\(158\) 1.91287 0.0121067
\(159\) 159.550i 1.00346i
\(160\) 26.5600 + 9.72459i 0.166000 + 0.0607787i
\(161\) 296.707 + 23.1928i 1.84290 + 0.144055i
\(162\) 12.7279i 0.0785674i
\(163\) 53.8931i 0.330633i 0.986241 + 0.165316i \(0.0528645\pi\)
−0.986241 + 0.165316i \(0.947136\pi\)
\(164\) 120.878 0.737063
\(165\) 54.7672 149.581i 0.331923 0.906553i
\(166\) 191.445i 1.15328i
\(167\) 189.614i 1.13541i −0.823232 0.567705i \(-0.807831\pi\)
0.823232 0.567705i \(-0.192169\pi\)
\(168\) 63.3912 0.377329
\(169\) 111.184 0.657896
\(170\) 132.406 + 48.4788i 0.778860 + 0.285169i
\(171\) 73.0460i 0.427169i
\(172\) 100.720 0.585581
\(173\) 73.4027i 0.424293i 0.977238 + 0.212147i \(0.0680454\pi\)
−0.977238 + 0.212147i \(0.931955\pi\)
\(174\) 78.9864 0.453945
\(175\) 247.012 + 208.883i 1.41150 + 1.19362i
\(176\) 73.5739i 0.418034i
\(177\) 8.94085i 0.0505133i
\(178\) 59.3156 0.333234
\(179\) −279.042 −1.55889 −0.779447 0.626468i \(-0.784500\pi\)
−0.779447 + 0.626468i \(0.784500\pi\)
\(180\) −10.3145 + 28.1711i −0.0573027 + 0.156506i
\(181\) 151.434i 0.836654i −0.908296 0.418327i \(-0.862617\pi\)
0.908296 0.418327i \(-0.137383\pi\)
\(182\) 139.143 0.764521
\(183\) −18.2324 −0.0996307
\(184\) 5.06962 64.8560i 0.0275523 0.352478i
\(185\) −18.9392 + 51.7271i −0.102374 + 0.279606i
\(186\) 7.80548 0.0419649
\(187\) 366.779i 1.96138i
\(188\) 158.929i 0.845369i
\(189\) 67.2365i 0.355749i
\(190\) 59.1952 161.675i 0.311554 0.850921i
\(191\) 296.805i 1.55395i −0.629530 0.776976i \(-0.716752\pi\)
0.629530 0.776976i \(-0.283248\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 26.9147i 0.139455i −0.997566 0.0697273i \(-0.977787\pi\)
0.997566 0.0697273i \(-0.0222129\pi\)
\(194\) 234.265i 1.20755i
\(195\) −22.6402 + 61.8352i −0.116103 + 0.317104i
\(196\) −236.870 −1.20852
\(197\) 61.5882i 0.312630i −0.987707 0.156315i \(-0.950038\pi\)
0.987707 0.156315i \(-0.0499615\pi\)
\(198\) −78.0369 −0.394126
\(199\) 35.3336i 0.177556i −0.996051 0.0887780i \(-0.971704\pi\)
0.996051 0.0887780i \(-0.0282962\pi\)
\(200\) 45.6588 53.9933i 0.228294 0.269967i
\(201\) 125.110i 0.622437i
\(202\) 28.6048i 0.141608i
\(203\) −417.254 −2.05544
\(204\) 69.0766i 0.338611i
\(205\) 103.900 283.773i 0.506828 1.38426i
\(206\) 14.2944i 0.0693904i
\(207\) 68.7902 + 5.37714i 0.332320 + 0.0259765i
\(208\) 30.4146i 0.146224i
\(209\) 447.856 2.14285
\(210\) 54.4873 148.817i 0.259464 0.708651i
\(211\) −142.017 −0.673064 −0.336532 0.941672i \(-0.609254\pi\)
−0.336532 + 0.941672i \(0.609254\pi\)
\(212\) −184.233 −0.869024
\(213\) 15.5004i 0.0727719i
\(214\) 84.7496i 0.396026i
\(215\) 86.5728 236.449i 0.402664 1.09976i
\(216\) 14.6969 0.0680414
\(217\) −41.2332 −0.190015
\(218\) −62.2945 −0.285755
\(219\) 122.338 0.558623
\(220\) 172.722 + 63.2398i 0.785098 + 0.287453i
\(221\) 151.622i 0.686074i
\(222\) 26.9861 0.121559
\(223\) 122.920i 0.551211i 0.961271 + 0.275605i \(0.0888783\pi\)
−0.961271 + 0.275605i \(0.911122\pi\)
\(224\) 73.1979i 0.326776i
\(225\) 57.2685 + 48.4284i 0.254527 + 0.215237i
\(226\) 230.436i 1.01963i
\(227\) −284.494 −1.25328 −0.626639 0.779310i \(-0.715570\pi\)
−0.626639 + 0.779310i \(0.715570\pi\)
\(228\) −84.3462 −0.369940
\(229\) 427.020i 1.86472i −0.361536 0.932358i \(-0.617747\pi\)
0.361536 0.932358i \(-0.382253\pi\)
\(230\) −147.898 67.6478i −0.643034 0.294121i
\(231\) 412.238 1.78458
\(232\) 91.2056i 0.393128i
\(233\) 377.271i 1.61919i 0.586988 + 0.809595i \(0.300313\pi\)
−0.586988 + 0.809595i \(0.699687\pi\)
\(234\) 32.2596 0.137861
\(235\) 373.101 + 136.606i 1.58767 + 0.581304i
\(236\) −10.3240 −0.0437458
\(237\) −2.34277 −0.00988511
\(238\) 364.904i 1.53321i
\(239\) 112.849 0.472171 0.236086 0.971732i \(-0.424135\pi\)
0.236086 + 0.971732i \(0.424135\pi\)
\(240\) −32.5292 11.9101i −0.135538 0.0496256i
\(241\) 149.271i 0.619380i 0.950838 + 0.309690i \(0.100225\pi\)
−0.950838 + 0.309690i \(0.899775\pi\)
\(242\) 307.337i 1.26999i
\(243\) 15.5885i 0.0641500i
\(244\) 21.0530i 0.0862827i
\(245\) −203.600 + 556.075i −0.831020 + 2.26970i
\(246\) −148.045 −0.601809
\(247\) −185.139 −0.749550
\(248\) 9.01299i 0.0363427i
\(249\) 234.471i 0.941652i
\(250\) −87.5087 153.598i −0.350035 0.614390i
\(251\) 357.872i 1.42579i −0.701273 0.712893i \(-0.747385\pi\)
0.701273 0.712893i \(-0.252615\pi\)
\(252\) −77.6381 −0.308088
\(253\) 32.9681 421.763i 0.130309 1.66705i
\(254\) 110.793 0.436192
\(255\) −162.164 59.3742i −0.635936 0.232840i
\(256\) 16.0000 0.0625000
\(257\) 58.9536i 0.229391i 0.993401 + 0.114696i \(0.0365893\pi\)
−0.993401 + 0.114696i \(0.963411\pi\)
\(258\) −123.356 −0.478125
\(259\) −142.557 −0.550413
\(260\) −71.4011 26.1426i −0.274620 0.100549i
\(261\) −96.7382 −0.370644
\(262\) 344.394i 1.31448i
\(263\) 121.126 0.460557 0.230278 0.973125i \(-0.426036\pi\)
0.230278 + 0.973125i \(0.426036\pi\)
\(264\) 90.1093i 0.341323i
\(265\) −158.356 + 432.504i −0.597569 + 1.63209i
\(266\) 445.568 1.67507
\(267\) −72.6465 −0.272084
\(268\) −144.464 −0.539046
\(269\) 313.321 1.16476 0.582381 0.812916i \(-0.302121\pi\)
0.582381 + 0.812916i \(0.302121\pi\)
\(270\) 12.6326 34.5024i 0.0467875 0.127787i
\(271\) −17.1800 −0.0633948 −0.0316974 0.999498i \(-0.510091\pi\)
−0.0316974 + 0.999498i \(0.510091\pi\)
\(272\) 79.7628 0.293246
\(273\) −170.415 −0.624229
\(274\) 97.1221i 0.354460i
\(275\) 296.922 351.123i 1.07972 1.27681i
\(276\) −6.20899 + 79.4320i −0.0224963 + 0.287797i
\(277\) 268.440i 0.969098i −0.874764 0.484549i \(-0.838984\pi\)
0.874764 0.484549i \(-0.161016\pi\)
\(278\) 193.467i 0.695923i
\(279\) −9.55972 −0.0342642
\(280\) 171.839 + 62.9166i 0.613710 + 0.224702i
\(281\) 386.651i 1.37598i 0.725719 + 0.687991i \(0.241507\pi\)
−0.725719 + 0.687991i \(0.758493\pi\)
\(282\) 194.648i 0.690241i
\(283\) 54.5729 0.192837 0.0964185 0.995341i \(-0.469261\pi\)
0.0964185 + 0.995341i \(0.469261\pi\)
\(284\) 17.8983 0.0630223
\(285\) −72.4990 + 198.011i −0.254383 + 0.694774i
\(286\) 197.789i 0.691569i
\(287\) 782.063 2.72496
\(288\) 16.9706i 0.0589256i
\(289\) 108.632 0.375888
\(290\) 214.114 + 78.3950i 0.738323 + 0.270327i
\(291\) 286.915i 0.985961i
\(292\) 141.264i 0.483782i
\(293\) 87.8588 0.299859 0.149930 0.988697i \(-0.452095\pi\)
0.149930 + 0.988697i \(0.452095\pi\)
\(294\) 290.106 0.986755
\(295\) −8.87390 + 24.2366i −0.0300810 + 0.0821578i
\(296\) 31.1609i 0.105273i
\(297\) 95.5753 0.321802
\(298\) −208.109 −0.698353
\(299\) −13.6286 + 174.352i −0.0455808 + 0.583118i
\(300\) −55.9203 + 66.1280i −0.186401 + 0.220427i
\(301\) 651.641 2.16492
\(302\) 5.96645i 0.0197565i
\(303\) 35.0336i 0.115622i
\(304\) 97.3946i 0.320377i
\(305\) −49.4238 18.0959i −0.162045 0.0593308i
\(306\) 84.6012i 0.276475i
\(307\) 436.714i 1.42252i 0.702928 + 0.711261i \(0.251876\pi\)
−0.702928 + 0.711261i \(0.748124\pi\)
\(308\) 476.011i 1.54549i
\(309\) 17.5070i 0.0566570i
\(310\) 21.1588 + 7.74703i 0.0682543 + 0.0249904i
\(311\) −95.4124 −0.306792 −0.153396 0.988165i \(-0.549021\pi\)
−0.153396 + 0.988165i \(0.549021\pi\)
\(312\) 37.2502i 0.119392i
\(313\) −277.575 −0.886820 −0.443410 0.896319i \(-0.646231\pi\)
−0.443410 + 0.896319i \(0.646231\pi\)
\(314\) 181.004i 0.576445i
\(315\) −66.7331 + 182.263i −0.211851 + 0.578611i
\(316\) 2.70520i 0.00856076i
\(317\) 43.9312i 0.138584i 0.997596 + 0.0692921i \(0.0220741\pi\)
−0.997596 + 0.0692921i \(0.977926\pi\)
\(318\) 225.638 0.709555
\(319\) 593.117i 1.85930i
\(320\) 13.7527 37.5615i 0.0429770 0.117380i
\(321\) 103.797i 0.323354i
\(322\) 32.7996 419.608i 0.101862 1.30313i
\(323\) 485.529i 1.50319i
\(324\) −18.0000 −0.0555556
\(325\) −122.744 + 145.150i −0.377675 + 0.446616i
\(326\) 76.2164 0.233793
\(327\) 76.2949 0.233318
\(328\) 170.948i 0.521182i
\(329\) 1028.25i 3.12537i
\(330\) −211.540 77.4526i −0.641030 0.234705i
\(331\) −449.865 −1.35911 −0.679554 0.733626i \(-0.737827\pi\)
−0.679554 + 0.733626i \(0.737827\pi\)
\(332\) 270.744 0.815494
\(333\) −33.0511 −0.0992527
\(334\) −268.154 −0.802857
\(335\) −124.173 + 339.143i −0.370666 + 1.01237i
\(336\) 89.6487i 0.266812i
\(337\) −199.863 −0.593066 −0.296533 0.955023i \(-0.595830\pi\)
−0.296533 + 0.955023i \(0.595830\pi\)
\(338\) 157.239i 0.465203i
\(339\) 282.226i 0.832525i
\(340\) 68.5594 187.251i 0.201645 0.550737i
\(341\) 58.6122i 0.171883i
\(342\) 103.303 0.302054
\(343\) −898.470 −2.61945
\(344\) 142.439i 0.414068i
\(345\) 181.137 + 82.8513i 0.525035 + 0.240149i
\(346\) 103.807 0.300021
\(347\) 290.365i 0.836786i 0.908266 + 0.418393i \(0.137406\pi\)
−0.908266 + 0.418393i \(0.862594\pi\)
\(348\) 111.704i 0.320987i
\(349\) −126.648 −0.362888 −0.181444 0.983401i \(-0.558077\pi\)
−0.181444 + 0.983401i \(0.558077\pi\)
\(350\) 295.405 349.328i 0.844014 0.998080i
\(351\) −39.5098 −0.112563
\(352\) 104.049 0.295594
\(353\) 497.700i 1.40992i −0.709249 0.704958i \(-0.750966\pi\)
0.709249 0.704958i \(-0.249034\pi\)
\(354\) 12.6443 0.0357183
\(355\) 15.3843 42.0180i 0.0433362 0.118360i
\(356\) 83.8849i 0.235632i
\(357\) 446.915i 1.25186i
\(358\) 394.625i 1.10231i
\(359\) 329.021i 0.916494i −0.888825 0.458247i \(-0.848477\pi\)
0.888825 0.458247i \(-0.151523\pi\)
\(360\) 39.8400 + 14.5869i 0.110667 + 0.0405191i
\(361\) −231.857 −0.642264
\(362\) −214.161 −0.591604
\(363\) 376.409i 1.03694i
\(364\) 196.778i 0.540598i
\(365\) 331.631 + 121.422i 0.908578 + 0.332664i
\(366\) 25.7845i 0.0704496i
\(367\) −172.395 −0.469742 −0.234871 0.972027i \(-0.575467\pi\)
−0.234871 + 0.972027i \(0.575467\pi\)
\(368\) −91.7202 7.16952i −0.249240 0.0194824i
\(369\) 181.317 0.491375
\(370\) 73.1531 + 26.7841i 0.197711 + 0.0723894i
\(371\) −1191.96 −3.21282
\(372\) 11.0386i 0.0296737i
\(373\) −175.718 −0.471095 −0.235548 0.971863i \(-0.575688\pi\)
−0.235548 + 0.971863i \(0.575688\pi\)
\(374\) 518.704 1.38691
\(375\) 107.176 + 188.118i 0.285802 + 0.501648i
\(376\) 224.760 0.597766
\(377\) 245.188i 0.650366i
\(378\) 95.0868 0.251552
\(379\) 423.074i 1.11629i −0.829744 0.558145i \(-0.811513\pi\)
0.829744 0.558145i \(-0.188487\pi\)
\(380\) −228.643 83.7147i −0.601692 0.220302i
\(381\) −135.693 −0.356149
\(382\) −419.746 −1.09881
\(383\) −401.734 −1.04891 −0.524457 0.851437i \(-0.675732\pi\)
−0.524457 + 0.851437i \(0.675732\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 1117.48 + 409.151i 2.90255 + 1.06273i
\(386\) −38.0632 −0.0986092
\(387\) 151.080 0.390387
\(388\) 331.300 0.853867
\(389\) 346.765i 0.891427i 0.895176 + 0.445714i \(0.147050\pi\)
−0.895176 + 0.445714i \(0.852950\pi\)
\(390\) 87.4482 + 32.0180i 0.224226 + 0.0820975i
\(391\) −457.241 35.7413i −1.16942 0.0914100i
\(392\) 334.985i 0.854555i
\(393\) 421.795i 1.07327i
\(394\) −87.0988 −0.221063
\(395\) −6.35071 2.32523i −0.0160777 0.00588666i
\(396\) 110.361i 0.278689i
\(397\) 98.9151i 0.249157i −0.992210 0.124578i \(-0.960242\pi\)
0.992210 0.124578i \(-0.0397578\pi\)
\(398\) −49.9693 −0.125551
\(399\) −545.707 −1.36769
\(400\) −76.3581 64.5712i −0.190895 0.161428i
\(401\) 625.874i 1.56078i −0.625291 0.780392i \(-0.715020\pi\)
0.625291 0.780392i \(-0.284980\pi\)
\(402\) 176.932 0.440129
\(403\) 24.2296i 0.0601231i
\(404\) −40.4533 −0.100132
\(405\) −15.4717 + 42.2567i −0.0382018 + 0.104337i
\(406\) 590.086i 1.45341i
\(407\) 202.642i 0.497891i
\(408\) −97.6891 −0.239434
\(409\) 410.570 1.00384 0.501920 0.864914i \(-0.332627\pi\)
0.501920 + 0.864914i \(0.332627\pi\)
\(410\) −401.316 146.937i −0.978818 0.358382i
\(411\) 118.950i 0.289415i
\(412\) 20.2154 0.0490664
\(413\) −66.7946 −0.161730
\(414\) 7.60443 97.2840i 0.0183682 0.234985i
\(415\) 232.716 635.597i 0.560761 1.53156i
\(416\) −43.0128 −0.103396
\(417\) 236.947i 0.568219i
\(418\) 633.365i 1.51523i
\(419\) 36.3204i 0.0866834i −0.999060 0.0433417i \(-0.986200\pi\)
0.999060 0.0433417i \(-0.0138004\pi\)
\(420\) −210.459 77.0567i −0.501092 0.183468i
\(421\) 545.508i 1.29574i −0.761750 0.647871i \(-0.775659\pi\)
0.761750 0.647871i \(-0.224341\pi\)
\(422\) 200.842i 0.475928i
\(423\) 238.394i 0.563580i
\(424\) 260.545i 0.614493i
\(425\) −380.658 321.899i −0.895667 0.757409i
\(426\) −21.9209 −0.0514575
\(427\) 136.209i 0.318992i
\(428\) −119.854 −0.280033
\(429\) 242.241i 0.564663i
\(430\) −334.390 122.432i −0.777650 0.284727i
\(431\) 156.738i 0.363662i −0.983330 0.181831i \(-0.941798\pi\)
0.983330 0.181831i \(-0.0582024\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) 10.8320 0.0250162 0.0125081 0.999922i \(-0.496018\pi\)
0.0125081 + 0.999922i \(0.496018\pi\)
\(434\) 58.3126i 0.134361i
\(435\) −262.235 96.0138i −0.602838 0.220721i
\(436\) 88.0978i 0.202059i
\(437\) −43.6421 + 558.316i −0.0998674 + 1.27761i
\(438\) 173.013i 0.395006i
\(439\) 10.1988 0.0232319 0.0116159 0.999933i \(-0.496302\pi\)
0.0116159 + 0.999933i \(0.496302\pi\)
\(440\) 89.4345 244.265i 0.203260 0.555148i
\(441\) −355.306 −0.805682
\(442\) −214.426 −0.485127
\(443\) 23.7800i 0.0536794i −0.999640 0.0268397i \(-0.991456\pi\)
0.999640 0.0268397i \(-0.00854437\pi\)
\(444\) 38.1642i 0.0859553i
\(445\) −196.928 72.1025i −0.442534 0.162028i
\(446\) 173.835 0.389765
\(447\) 254.881 0.570203
\(448\) 103.517 0.231066
\(449\) −417.771 −0.930448 −0.465224 0.885193i \(-0.654026\pi\)
−0.465224 + 0.885193i \(0.654026\pi\)
\(450\) 68.4881 80.9900i 0.152196 0.179978i
\(451\) 1111.69i 2.46494i
\(452\) 325.886 0.720987
\(453\) 7.30738i 0.0161311i
\(454\) 402.335i 0.886201i
\(455\) −461.954 169.138i −1.01528 0.371733i
\(456\) 119.284i 0.261587i
\(457\) −197.215 −0.431543 −0.215772 0.976444i \(-0.569227\pi\)
−0.215772 + 0.976444i \(0.569227\pi\)
\(458\) −603.898 −1.31855
\(459\) 103.615i 0.225741i
\(460\) −95.6684 + 209.159i −0.207975 + 0.454694i
\(461\) −791.818 −1.71761 −0.858805 0.512303i \(-0.828792\pi\)
−0.858805 + 0.512303i \(0.828792\pi\)
\(462\) 582.992i 1.26189i
\(463\) 225.166i 0.486320i −0.969986 0.243160i \(-0.921816\pi\)
0.969986 0.243160i \(-0.0781840\pi\)
\(464\) 128.984 0.277983
\(465\) −25.9142 9.48814i −0.0557294 0.0204046i
\(466\) 533.542 1.14494
\(467\) 4.35994 0.00933607 0.00466803 0.999989i \(-0.498514\pi\)
0.00466803 + 0.999989i \(0.498514\pi\)
\(468\) 45.6219i 0.0974828i
\(469\) −934.661 −1.99288
\(470\) 193.191 527.645i 0.411044 1.12265i
\(471\) 221.683i 0.470665i
\(472\) 14.6003i 0.0309329i
\(473\) 926.294i 1.95834i
\(474\) 3.31318i 0.00698983i
\(475\) −393.056 + 464.804i −0.827486 + 0.978535i
\(476\) 516.053 1.08414
\(477\) −276.350 −0.579349
\(478\) 159.593i 0.333876i
\(479\) 262.797i 0.548637i 0.961639 + 0.274318i \(0.0884522\pi\)
−0.961639 + 0.274318i \(0.911548\pi\)
\(480\) −16.8435 + 46.0032i −0.0350906 + 0.0958401i
\(481\) 83.7698i 0.174158i
\(482\) 211.100 0.437968
\(483\) −40.1712 + 513.912i −0.0831701 + 1.06400i
\(484\) 434.640 0.898016
\(485\) 284.766 777.758i 0.587147 1.60363i
\(486\) 22.0454 0.0453609
\(487\) 320.366i 0.657835i 0.944359 + 0.328917i \(0.106684\pi\)
−0.944359 + 0.328917i \(0.893316\pi\)
\(488\) −29.7734 −0.0610111
\(489\) −93.3456 −0.190891
\(490\) 786.409 + 287.934i 1.60492 + 0.587620i
\(491\) 179.242 0.365055 0.182528 0.983201i \(-0.441572\pi\)
0.182528 + 0.983201i \(0.441572\pi\)
\(492\) 209.367i 0.425543i
\(493\) 643.009 1.30428
\(494\) 261.826i 0.530012i
\(495\) 259.082 + 94.8597i 0.523399 + 0.191636i
\(496\) 12.7463 0.0256982
\(497\) 115.799 0.232997
\(498\) −331.593 −0.665848
\(499\) −14.9582 −0.0299763 −0.0149882 0.999888i \(-0.504771\pi\)
−0.0149882 + 0.999888i \(0.504771\pi\)
\(500\) −217.220 + 123.756i −0.434440 + 0.247512i
\(501\) 328.420 0.655530
\(502\) −506.108 −1.00818
\(503\) −694.560 −1.38084 −0.690418 0.723411i \(-0.742573\pi\)
−0.690418 + 0.723411i \(0.742573\pi\)
\(504\) 109.797i 0.217851i
\(505\) −34.7713 + 94.9678i −0.0688540 + 0.188055i
\(506\) −596.463 46.6239i −1.17878 0.0921422i
\(507\) 192.577i 0.379836i
\(508\) 156.685i 0.308434i
\(509\) −401.121 −0.788057 −0.394028 0.919098i \(-0.628919\pi\)
−0.394028 + 0.919098i \(0.628919\pi\)
\(510\) −83.9678 + 229.334i −0.164643 + 0.449675i
\(511\) 913.957i 1.78857i
\(512\) 22.6274i 0.0441942i
\(513\) −126.519 −0.246626
\(514\) 83.3730 0.162204
\(515\) 17.3759 47.4574i 0.0337397 0.0921503i
\(516\) 174.452i 0.338085i
\(517\) 1461.63 2.82714
\(518\) 201.606i 0.389201i
\(519\) −127.137 −0.244966
\(520\) −36.9712 + 100.976i −0.0710985 + 0.194186i
\(521\) 832.880i 1.59862i −0.600920 0.799309i \(-0.705199\pi\)
0.600920 0.799309i \(-0.294801\pi\)
\(522\) 136.808i 0.262085i
\(523\) −303.690 −0.580670 −0.290335 0.956925i \(-0.593767\pi\)
−0.290335 + 0.956925i \(0.593767\pi\)
\(524\) −487.047 −0.929479
\(525\) −361.796 + 427.838i −0.689134 + 0.814929i
\(526\) 171.299i 0.325663i
\(527\) 63.5425 0.120574
\(528\) −127.434 −0.241352
\(529\) 522.575 + 82.1988i 0.987854 + 0.155385i
\(530\) 611.653 + 223.949i 1.15406 + 0.422545i
\(531\) −15.4860 −0.0291639
\(532\) 630.128i 1.18445i
\(533\) 459.558i 0.862211i
\(534\) 102.738i 0.192393i
\(535\) −103.019 + 281.368i −0.192560 + 0.525922i
\(536\) 204.303i 0.381163i
\(537\) 483.315i 0.900028i
\(538\) 443.103i 0.823612i
\(539\) 2178.44i 4.04162i
\(540\) −48.7938 17.8652i −0.0903589 0.0330837i
\(541\) 802.731 1.48379 0.741896 0.670515i \(-0.233927\pi\)
0.741896 + 0.670515i \(0.233927\pi\)
\(542\) 24.2962i 0.0448269i
\(543\) 262.292 0.483043
\(544\) 112.802i 0.207356i
\(545\) 206.818 + 75.7236i 0.379482 + 0.138942i
\(546\) 241.003i 0.441397i
\(547\) 555.494i 1.01553i −0.861496 0.507764i \(-0.830472\pi\)
0.861496 0.507764i \(-0.169528\pi\)
\(548\) 137.351 0.250641
\(549\) 31.5795i 0.0575218i
\(550\) −496.562 419.912i −0.902840 0.763476i
\(551\) 785.148i 1.42495i
\(552\) 112.334 + 8.78084i 0.203503 + 0.0159073i
\(553\) 17.5022i 0.0316496i
\(554\) −379.632 −0.685256
\(555\) −89.5939 32.8037i −0.161430 0.0591057i
\(556\) 273.603 0.492092
\(557\) −697.030 −1.25140 −0.625700 0.780064i \(-0.715187\pi\)
−0.625700 + 0.780064i \(0.715187\pi\)
\(558\) 13.5195i 0.0242285i
\(559\) 382.920i 0.685008i
\(560\) 88.9774 243.017i 0.158888 0.433958i
\(561\) −635.280 −1.13241
\(562\) 546.807 0.972966
\(563\) 24.7377 0.0439390 0.0219695 0.999759i \(-0.493006\pi\)
0.0219695 + 0.999759i \(0.493006\pi\)
\(564\) −275.274 −0.488074
\(565\) 280.113 765.048i 0.495775 1.35407i
\(566\) 77.1777i 0.136356i
\(567\) −116.457 −0.205392
\(568\) 25.3121i 0.0445635i
\(569\) 475.965i 0.836495i −0.908333 0.418247i \(-0.862645\pi\)
0.908333 0.418247i \(-0.137355\pi\)
\(570\) 280.029 + 102.529i 0.491279 + 0.179876i
\(571\) 558.821i 0.978671i 0.872096 + 0.489336i \(0.162761\pi\)
−0.872096 + 0.489336i \(0.837239\pi\)
\(572\) −279.715 −0.489013
\(573\) 514.081 0.897175
\(574\) 1106.00i 1.92684i
\(575\) 408.790 + 404.371i 0.710938 + 0.703254i
\(576\) 24.0000 0.0416667
\(577\) 1114.51i 1.93156i −0.259365 0.965779i \(-0.583513\pi\)
0.259365 0.965779i \(-0.416487\pi\)
\(578\) 153.628i 0.265793i
\(579\) 46.6177 0.0805141
\(580\) 110.867 302.802i 0.191150 0.522073i
\(581\) 1751.67 3.01492
\(582\) −405.758 −0.697179
\(583\) 1694.34i 2.90625i
\(584\) 199.778 0.342085
\(585\) −107.102 39.2139i −0.183080 0.0670323i
\(586\) 124.251i 0.212032i
\(587\) 396.273i 0.675082i −0.941311 0.337541i \(-0.890405\pi\)
0.941311 0.337541i \(-0.109595\pi\)
\(588\) 410.272i 0.697741i
\(589\) 77.5888i 0.131730i
\(590\) 34.2757 + 12.5496i 0.0580943 + 0.0212705i
\(591\) 106.674 0.180497
\(592\) 44.0682 0.0744395
\(593\) 888.386i 1.49812i 0.662501 + 0.749061i \(0.269495\pi\)
−0.662501 + 0.749061i \(0.730505\pi\)
\(594\) 135.164i 0.227549i
\(595\) 443.568 1211.48i 0.745493 2.03610i
\(596\) 294.311i 0.493810i
\(597\) 61.1997 0.102512
\(598\) 246.571 + 19.2738i 0.412327 + 0.0322305i
\(599\) −902.768 −1.50713 −0.753563 0.657376i \(-0.771666\pi\)
−0.753563 + 0.657376i \(0.771666\pi\)
\(600\) 93.5192 + 79.0833i 0.155865 + 0.131806i
\(601\) 685.970 1.14138 0.570691 0.821165i \(-0.306675\pi\)
0.570691 + 0.821165i \(0.306675\pi\)
\(602\) 921.560i 1.53083i
\(603\) −216.696 −0.359364
\(604\) 8.43783 0.0139699
\(605\) 373.591 1020.36i 0.617505 1.68654i
\(606\) 49.5450 0.0817574
\(607\) 790.719i 1.30267i 0.758791 + 0.651334i \(0.225790\pi\)
−0.758791 + 0.651334i \(0.774210\pi\)
\(608\) −137.737 −0.226541
\(609\) 722.705i 1.18671i
\(610\) −25.5915 + 69.8959i −0.0419532 + 0.114583i
\(611\) −604.222 −0.988907
\(612\) 119.644 0.195497
\(613\) −563.868 −0.919850 −0.459925 0.887958i \(-0.652124\pi\)
−0.459925 + 0.887958i \(0.652124\pi\)
\(614\) 617.607 1.00587
\(615\) 491.509 + 179.960i 0.799202 + 0.292618i
\(616\) 673.182 1.09283
\(617\) 803.130 1.30167 0.650835 0.759219i \(-0.274419\pi\)
0.650835 + 0.759219i \(0.274419\pi\)
\(618\) −24.7587 −0.0400625
\(619\) 242.335i 0.391494i −0.980654 0.195747i \(-0.937287\pi\)
0.980654 0.195747i \(-0.0627131\pi\)
\(620\) 10.9560 29.9231i 0.0176709 0.0482631i
\(621\) −9.31348 + 119.148i −0.0149976 + 0.191865i
\(622\) 134.934i 0.216935i
\(623\) 542.722i 0.871142i
\(624\) 52.6797 0.0844226
\(625\) 103.819 + 616.317i 0.166111 + 0.986107i
\(626\) 392.550i 0.627076i
\(627\) 775.710i 1.23718i
\(628\) −255.978 −0.407608
\(629\) 219.688 0.349265
\(630\) 257.758 + 94.3748i 0.409140 + 0.149801i
\(631\) 713.068i 1.13006i −0.825070 0.565031i \(-0.808864\pi\)
0.825070 0.565031i \(-0.191136\pi\)
\(632\) −3.82573 −0.00605337
\(633\) 245.980i 0.388594i
\(634\) 62.1281 0.0979939
\(635\) −367.832 134.677i −0.579263 0.212090i
\(636\) 319.101i 0.501731i
\(637\) 900.541i 1.41372i
\(638\) 838.794 1.31472
\(639\) 26.8475 0.0420149
\(640\) −53.1199 19.4492i −0.0829999 0.0303894i
\(641\) 320.213i 0.499553i −0.968304 0.249776i \(-0.919643\pi\)
0.968304 0.249776i \(-0.0803571\pi\)
\(642\) 146.791 0.228646
\(643\) 441.300 0.686315 0.343157 0.939278i \(-0.388504\pi\)
0.343157 + 0.939278i \(0.388504\pi\)
\(644\) −593.415 46.3857i −0.921452 0.0720274i
\(645\) 409.542 + 149.949i 0.634949 + 0.232478i
\(646\) −686.642 −1.06291
\(647\) 935.951i 1.44660i −0.690533 0.723301i \(-0.742624\pi\)
0.690533 0.723301i \(-0.257376\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 94.9472i 0.146298i
\(650\) 205.273 + 173.587i 0.315805 + 0.267057i
\(651\) 71.4181i 0.109705i
\(652\) 107.786i 0.165316i
\(653\) 779.044i 1.19302i −0.802604 0.596512i \(-0.796553\pi\)
0.802604 0.596512i \(-0.203447\pi\)
\(654\) 107.897i 0.164981i
\(655\) −418.637 + 1143.39i −0.639140 + 1.74563i
\(656\) −241.757 −0.368531
\(657\) 211.896i 0.322521i
\(658\) 1454.16 2.20997
\(659\) 990.231i 1.50263i 0.659946 + 0.751313i \(0.270579\pi\)
−0.659946 + 0.751313i \(0.729421\pi\)
\(660\) −109.534 + 299.162i −0.165961 + 0.453276i
\(661\) 82.8711i 0.125372i −0.998033 0.0626862i \(-0.980033\pi\)
0.998033 0.0626862i \(-0.0199667\pi\)
\(662\) 636.205i 0.961034i
\(663\) 262.617 0.396105
\(664\) 382.890i 0.576642i
\(665\) −1479.28 541.620i −2.22449 0.814467i
\(666\) 46.7414i 0.0701822i
\(667\) −739.404 57.7972i −1.10855 0.0866525i
\(668\) 379.227i 0.567705i
\(669\) −212.904 −0.318242
\(670\) 479.621 + 175.607i 0.715852 + 0.262100i
\(671\) −193.619 −0.288553
\(672\) −126.782 −0.188664
\(673\) 461.012i 0.685010i 0.939516 + 0.342505i \(0.111275\pi\)
−0.939516 + 0.342505i \(0.888725\pi\)
\(674\) 282.649i 0.419361i
\(675\) −83.8805 + 99.1920i −0.124267 + 0.146951i
\(676\) −222.369 −0.328948
\(677\) 1137.48 1.68017 0.840085 0.542454i \(-0.182505\pi\)
0.840085 + 0.542454i \(0.182505\pi\)
\(678\) −399.128 −0.588684
\(679\) 2143.46 3.15679
\(680\) −264.812 96.9576i −0.389430 0.142585i
\(681\) 492.758i 0.723580i
\(682\) 82.8901 0.121540
\(683\) 27.4834i 0.0402393i −0.999798 0.0201196i \(-0.993595\pi\)
0.999798 0.0201196i \(-0.00640471\pi\)
\(684\) 146.092i 0.213585i
\(685\) 118.059 322.445i 0.172349 0.470723i
\(686\) 1270.63i 1.85223i
\(687\) 739.621 1.07659
\(688\) −201.440 −0.292790
\(689\) 700.422i 1.01658i
\(690\) 117.169 256.167i 0.169811 0.371256i
\(691\) 202.309 0.292777 0.146388 0.989227i \(-0.453235\pi\)
0.146388 + 0.989227i \(0.453235\pi\)
\(692\) 146.805i 0.212147i
\(693\) 714.017i 1.03033i
\(694\) 410.638 0.591697
\(695\) 235.173 642.309i 0.338378 0.924185i
\(696\) −157.973 −0.226972
\(697\) −1205.20 −1.72912
\(698\) 179.107i 0.256600i
\(699\) −653.453 −0.934840
\(700\) −494.024 417.766i −0.705749 0.596808i
\(701\) 720.064i 1.02719i 0.858031 + 0.513597i \(0.171687\pi\)
−0.858031 + 0.513597i \(0.828313\pi\)
\(702\) 55.8752i 0.0795944i
\(703\) 268.250i 0.381579i
\(704\) 147.148i 0.209017i
\(705\) −236.609 + 646.231i −0.335616 + 0.916639i
\(706\) −703.855 −0.996961
\(707\) −261.726 −0.370193
\(708\) 17.8817i 0.0252566i
\(709\) 1116.63i 1.57493i 0.616357 + 0.787467i \(0.288608\pi\)
−0.616357 + 0.787467i \(0.711392\pi\)
\(710\) −59.4224 21.7567i −0.0836935 0.0306433i
\(711\) 4.05780i 0.00570717i
\(712\) −118.631 −0.166617
\(713\) −73.0683 5.71155i −0.102480 0.00801059i
\(714\) −632.033 −0.885200
\(715\) −240.427 + 656.658i −0.336261 + 0.918402i
\(716\) 558.084 0.779447
\(717\) 195.460i 0.272608i
\(718\) −465.307 −0.648059
\(719\) −276.958 −0.385199 −0.192600 0.981277i \(-0.561692\pi\)
−0.192600 + 0.981277i \(0.561692\pi\)
\(720\) 20.6290 56.3422i 0.0286514 0.0782531i
\(721\) 130.790 0.181401
\(722\) 327.896i 0.454149i
\(723\) −258.544 −0.357599
\(724\) 302.869i 0.418327i
\(725\) −615.562 520.542i −0.849051 0.717989i
\(726\) −532.323 −0.733227
\(727\) −1175.60 −1.61706 −0.808530 0.588455i \(-0.799736\pi\)
−0.808530 + 0.588455i \(0.799736\pi\)
\(728\) −278.286 −0.382261
\(729\) −27.0000 −0.0370370
\(730\) 171.717 468.997i 0.235229 0.642462i
\(731\) −1004.21 −1.37375
\(732\) 36.4648 0.0498154
\(733\) −620.255 −0.846187 −0.423093 0.906086i \(-0.639056\pi\)
−0.423093 + 0.906086i \(0.639056\pi\)
\(734\) 243.804i 0.332158i
\(735\) −963.151 352.645i −1.31041 0.479790i
\(736\) −10.1392 + 129.712i −0.0137761 + 0.176239i
\(737\) 1328.60i 1.80271i
\(738\) 256.422i 0.347455i
\(739\) −147.282 −0.199298 −0.0996492 0.995023i \(-0.531772\pi\)
−0.0996492 + 0.995023i \(0.531772\pi\)
\(740\) 37.8784 103.454i 0.0511870 0.139803i
\(741\) 320.670i 0.432753i
\(742\) 1685.68i 2.27181i
\(743\) 722.303 0.972143 0.486072 0.873919i \(-0.338429\pi\)
0.486072 + 0.873919i \(0.338429\pi\)
\(744\) −15.6110 −0.0209825
\(745\) 690.922 + 252.972i 0.927412 + 0.339560i
\(746\) 248.503i 0.333114i
\(747\) 406.116 0.543663
\(748\) 733.558i 0.980692i
\(749\) −775.436 −1.03529
\(750\) 266.039 151.570i 0.354719 0.202093i
\(751\) 1411.00i 1.87883i 0.342781 + 0.939415i \(0.388631\pi\)
−0.342781 + 0.939415i \(0.611369\pi\)
\(752\) 317.859i 0.422685i
\(753\) 619.853 0.823178
\(754\) −346.748 −0.459878
\(755\) 7.25266 19.8086i 0.00960618 0.0262365i
\(756\) 134.473i 0.177874i
\(757\) −407.669 −0.538532 −0.269266 0.963066i \(-0.586781\pi\)
−0.269266 + 0.963066i \(0.586781\pi\)
\(758\) −598.317 −0.789336
\(759\) 730.516 + 57.1024i 0.962471 + 0.0752338i
\(760\) −118.390 + 323.350i −0.155777 + 0.425460i
\(761\) 696.139 0.914769 0.457385 0.889269i \(-0.348786\pi\)
0.457385 + 0.889269i \(0.348786\pi\)
\(762\) 191.899i 0.251836i
\(763\) 569.978i 0.747023i
\(764\) 593.610i 0.776976i
\(765\) 102.839 280.876i 0.134430 0.367158i
\(766\) 568.138i 0.741694i
\(767\) 39.2501i 0.0511735i
\(768\) 27.7128i 0.0360844i
\(769\) 320.918i 0.417319i −0.977988 0.208659i \(-0.933090\pi\)
0.977988 0.208659i \(-0.0669100\pi\)
\(770\) 578.627 1580.36i 0.751464 2.05241i
\(771\) −102.111 −0.132439
\(772\) 53.8294i 0.0697273i
\(773\) −582.738 −0.753865 −0.376933 0.926241i \(-0.623021\pi\)
−0.376933 + 0.926241i \(0.623021\pi\)
\(774\) 213.659i 0.276045i
\(775\) −60.8301 51.4403i −0.0784905 0.0663745i
\(776\) 468.529i 0.603775i
\(777\) 246.916i 0.317781i
\(778\) 490.400 0.630334
\(779\) 1471.61i 1.88910i
\(780\) 45.2803 123.670i 0.0580517 0.158552i
\(781\) 164.606i 0.210763i
\(782\) −50.5459 + 646.637i −0.0646367 + 0.826902i
\(783\) 167.555i 0.213992i
\(784\) 473.741 0.604261
\(785\) −220.023 + 600.932i −0.280285 + 0.765518i
\(786\) 596.508 0.758916
\(787\) −463.279 −0.588665 −0.294333 0.955703i \(-0.595097\pi\)
−0.294333 + 0.955703i \(0.595097\pi\)