Properties

Label 684.3.g.b.343.5
Level $684$
Weight $3$
Character 684.343
Analytic conductor $18.638$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 76)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 343.5
Root \(0.711746 + 1.86907i\) of defining polynomial
Character \(\chi\) \(=\) 684.343
Dual form 684.3.g.b.343.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.711746 - 1.86907i) q^{2} +(-2.98683 + 2.66060i) q^{4} -4.97973 q^{5} -12.2628i q^{7} +(7.09872 + 3.68892i) q^{8} +O(q^{10})\) \(q+(-0.711746 - 1.86907i) q^{2} +(-2.98683 + 2.66060i) q^{4} -4.97973 q^{5} -12.2628i q^{7} +(7.09872 + 3.68892i) q^{8} +(3.54430 + 9.30745i) q^{10} -13.4463i q^{11} +14.1766 q^{13} +(-22.9201 + 8.72803i) q^{14} +(1.84237 - 15.8936i) q^{16} +5.89478 q^{17} -4.35890i q^{19} +(14.8736 - 13.2491i) q^{20} +(-25.1320 + 9.57032i) q^{22} +0.906592i q^{23} -0.202335 q^{25} +(-10.0901 - 26.4969i) q^{26} +(32.6266 + 36.6271i) q^{28} +10.3853 q^{29} -43.2608i q^{31} +(-31.0175 + 7.86868i) q^{32} +(-4.19559 - 11.0178i) q^{34} +61.0656i q^{35} -1.61331 q^{37} +(-8.14708 + 3.10243i) q^{38} +(-35.3497 - 18.3698i) q^{40} -69.3758 q^{41} +32.0147i q^{43} +(35.7752 + 40.1617i) q^{44} +(1.69448 - 0.645264i) q^{46} +38.9732i q^{47} -101.377 q^{49} +(0.144011 + 0.378179i) q^{50} +(-42.3430 + 37.7182i) q^{52} +8.31560 q^{53} +66.9586i q^{55} +(45.2367 - 87.0505i) q^{56} +(-7.39169 - 19.4108i) q^{58} +20.9242i q^{59} -118.329 q^{61} +(-80.8574 + 30.7907i) q^{62} +(36.7837 + 52.3733i) q^{64} -70.5953 q^{65} -57.4499i q^{67} +(-17.6067 + 15.6837i) q^{68} +(114.136 - 43.4632i) q^{70} +11.3393i q^{71} -23.5952 q^{73} +(1.14827 + 3.01539i) q^{74} +(11.5973 + 13.0193i) q^{76} -164.889 q^{77} +0.286369i q^{79} +(-9.17448 + 79.1456i) q^{80} +(49.3780 + 129.668i) q^{82} -24.9311i q^{83} -29.3544 q^{85} +(59.8376 - 22.7863i) q^{86} +(49.6022 - 95.4512i) q^{88} +43.7018 q^{89} -173.845i q^{91} +(-2.41208 - 2.70784i) q^{92} +(72.8436 - 27.7390i) q^{94} +21.7061i q^{95} +115.905 q^{97} +(72.1549 + 189.481i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} + O(q^{10}) \) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.711746 1.86907i −0.355873 0.934534i
\(3\) 0 0
\(4\) −2.98683 + 2.66060i −0.746709 + 0.665151i
\(5\) −4.97973 −0.995945 −0.497973 0.867193i \(-0.665922\pi\)
−0.497973 + 0.867193i \(0.665922\pi\)
\(6\) 0 0
\(7\) 12.2628i 1.75183i −0.482461 0.875917i \(-0.660257\pi\)
0.482461 0.875917i \(-0.339743\pi\)
\(8\) 7.09872 + 3.68892i 0.887340 + 0.461116i
\(9\) 0 0
\(10\) 3.54430 + 9.30745i 0.354430 + 0.930745i
\(11\) 13.4463i 1.22239i −0.791481 0.611193i \(-0.790690\pi\)
0.791481 0.611193i \(-0.209310\pi\)
\(12\) 0 0
\(13\) 14.1766 1.09050 0.545252 0.838272i \(-0.316434\pi\)
0.545252 + 0.838272i \(0.316434\pi\)
\(14\) −22.9201 + 8.72803i −1.63715 + 0.623431i
\(15\) 0 0
\(16\) 1.84237 15.8936i 0.115148 0.993348i
\(17\) 5.89478 0.346752 0.173376 0.984856i \(-0.444532\pi\)
0.173376 + 0.984856i \(0.444532\pi\)
\(18\) 0 0
\(19\) 4.35890i 0.229416i
\(20\) 14.8736 13.2491i 0.743681 0.662454i
\(21\) 0 0
\(22\) −25.1320 + 9.57032i −1.14236 + 0.435014i
\(23\) 0.906592i 0.0394171i 0.999806 + 0.0197085i \(0.00627383\pi\)
−0.999806 + 0.0197085i \(0.993726\pi\)
\(24\) 0 0
\(25\) −0.202335 −0.00809341
\(26\) −10.0901 26.4969i −0.388081 1.01911i
\(27\) 0 0
\(28\) 32.6266 + 36.6271i 1.16524 + 1.30811i
\(29\) 10.3853 0.358114 0.179057 0.983839i \(-0.442695\pi\)
0.179057 + 0.983839i \(0.442695\pi\)
\(30\) 0 0
\(31\) 43.2608i 1.39551i −0.716337 0.697755i \(-0.754183\pi\)
0.716337 0.697755i \(-0.245817\pi\)
\(32\) −31.0175 + 7.86868i −0.969296 + 0.245896i
\(33\) 0 0
\(34\) −4.19559 11.0178i −0.123400 0.324052i
\(35\) 61.0656i 1.74473i
\(36\) 0 0
\(37\) −1.61331 −0.0436030 −0.0218015 0.999762i \(-0.506940\pi\)
−0.0218015 + 0.999762i \(0.506940\pi\)
\(38\) −8.14708 + 3.10243i −0.214397 + 0.0816429i
\(39\) 0 0
\(40\) −35.3497 18.3698i −0.883742 0.459246i
\(41\) −69.3758 −1.69209 −0.846047 0.533109i \(-0.821024\pi\)
−0.846047 + 0.533109i \(0.821024\pi\)
\(42\) 0 0
\(43\) 32.0147i 0.744527i 0.928127 + 0.372264i \(0.121418\pi\)
−0.928127 + 0.372264i \(0.878582\pi\)
\(44\) 35.7752 + 40.1617i 0.813072 + 0.912767i
\(45\) 0 0
\(46\) 1.69448 0.645264i 0.0368366 0.0140275i
\(47\) 38.9732i 0.829217i 0.910000 + 0.414609i \(0.136082\pi\)
−0.910000 + 0.414609i \(0.863918\pi\)
\(48\) 0 0
\(49\) −101.377 −2.06893
\(50\) 0.144011 + 0.378179i 0.00288023 + 0.00756357i
\(51\) 0 0
\(52\) −42.3430 + 37.7182i −0.814289 + 0.725350i
\(53\) 8.31560 0.156898 0.0784491 0.996918i \(-0.475003\pi\)
0.0784491 + 0.996918i \(0.475003\pi\)
\(54\) 0 0
\(55\) 66.9586i 1.21743i
\(56\) 45.2367 87.0505i 0.807798 1.55447i
\(57\) 0 0
\(58\) −7.39169 19.4108i −0.127443 0.334669i
\(59\) 20.9242i 0.354648i 0.984153 + 0.177324i \(0.0567440\pi\)
−0.984153 + 0.177324i \(0.943256\pi\)
\(60\) 0 0
\(61\) −118.329 −1.93983 −0.969913 0.243453i \(-0.921720\pi\)
−0.969913 + 0.243453i \(0.921720\pi\)
\(62\) −80.8574 + 30.7907i −1.30415 + 0.496624i
\(63\) 0 0
\(64\) 36.7837 + 52.3733i 0.574745 + 0.818333i
\(65\) −70.5953 −1.08608
\(66\) 0 0
\(67\) 57.4499i 0.857462i −0.903432 0.428731i \(-0.858961\pi\)
0.903432 0.428731i \(-0.141039\pi\)
\(68\) −17.6067 + 15.6837i −0.258923 + 0.230642i
\(69\) 0 0
\(70\) 114.136 43.4632i 1.63051 0.620903i
\(71\) 11.3393i 0.159709i 0.996807 + 0.0798545i \(0.0254456\pi\)
−0.996807 + 0.0798545i \(0.974554\pi\)
\(72\) 0 0
\(73\) −23.5952 −0.323222 −0.161611 0.986855i \(-0.551669\pi\)
−0.161611 + 0.986855i \(0.551669\pi\)
\(74\) 1.14827 + 3.01539i 0.0155171 + 0.0407485i
\(75\) 0 0
\(76\) 11.5973 + 13.0193i 0.152596 + 0.171307i
\(77\) −164.889 −2.14142
\(78\) 0 0
\(79\) 0.286369i 0.00362492i 0.999998 + 0.00181246i \(0.000576925\pi\)
−0.999998 + 0.00181246i \(0.999423\pi\)
\(80\) −9.17448 + 79.1456i −0.114681 + 0.989320i
\(81\) 0 0
\(82\) 49.3780 + 129.668i 0.602170 + 1.58132i
\(83\) 24.9311i 0.300375i −0.988658 0.150188i \(-0.952012\pi\)
0.988658 0.150188i \(-0.0479878\pi\)
\(84\) 0 0
\(85\) −29.3544 −0.345346
\(86\) 59.8376 22.7863i 0.695786 0.264957i
\(87\) 0 0
\(88\) 49.6022 95.4512i 0.563662 1.08467i
\(89\) 43.7018 0.491031 0.245515 0.969393i \(-0.421043\pi\)
0.245515 + 0.969393i \(0.421043\pi\)
\(90\) 0 0
\(91\) 173.845i 1.91038i
\(92\) −2.41208 2.70784i −0.0262183 0.0294331i
\(93\) 0 0
\(94\) 72.8436 27.7390i 0.774932 0.295096i
\(95\) 21.7061i 0.228485i
\(96\) 0 0
\(97\) 115.905 1.19490 0.597448 0.801908i \(-0.296182\pi\)
0.597448 + 0.801908i \(0.296182\pi\)
\(98\) 72.1549 + 189.481i 0.736275 + 1.93348i
\(99\) 0 0
\(100\) 0.604342 0.538334i 0.00604342 0.00538334i
\(101\) 10.3010 0.101990 0.0509950 0.998699i \(-0.483761\pi\)
0.0509950 + 0.998699i \(0.483761\pi\)
\(102\) 0 0
\(103\) 110.807i 1.07579i 0.843011 + 0.537897i \(0.180781\pi\)
−0.843011 + 0.537897i \(0.819219\pi\)
\(104\) 100.635 + 52.2962i 0.967648 + 0.502848i
\(105\) 0 0
\(106\) −5.91860 15.5424i −0.0558358 0.146627i
\(107\) 29.6484i 0.277088i −0.990356 0.138544i \(-0.955758\pi\)
0.990356 0.138544i \(-0.0442422\pi\)
\(108\) 0 0
\(109\) −1.00851 −0.00925235 −0.00462617 0.999989i \(-0.501473\pi\)
−0.00462617 + 0.999989i \(0.501473\pi\)
\(110\) 125.150 47.6576i 1.13773 0.433251i
\(111\) 0 0
\(112\) −194.900 22.5927i −1.74018 0.201720i
\(113\) 59.0375 0.522456 0.261228 0.965277i \(-0.415873\pi\)
0.261228 + 0.965277i \(0.415873\pi\)
\(114\) 0 0
\(115\) 4.51458i 0.0392572i
\(116\) −31.0192 + 27.6312i −0.267407 + 0.238200i
\(117\) 0 0
\(118\) 39.1088 14.8927i 0.331431 0.126210i
\(119\) 72.2868i 0.607452i
\(120\) 0 0
\(121\) −59.8017 −0.494229
\(122\) 84.2205 + 221.166i 0.690332 + 1.81283i
\(123\) 0 0
\(124\) 115.100 + 129.213i 0.928225 + 1.04204i
\(125\) 125.501 1.00401
\(126\) 0 0
\(127\) 209.454i 1.64925i 0.565681 + 0.824624i \(0.308613\pi\)
−0.565681 + 0.824624i \(0.691387\pi\)
\(128\) 71.7086 106.028i 0.560224 0.828341i
\(129\) 0 0
\(130\) 50.2460 + 131.948i 0.386507 + 1.01498i
\(131\) 46.0795i 0.351752i −0.984412 0.175876i \(-0.943724\pi\)
0.984412 0.175876i \(-0.0562758\pi\)
\(132\) 0 0
\(133\) −53.4525 −0.401899
\(134\) −107.378 + 40.8898i −0.801327 + 0.305147i
\(135\) 0 0
\(136\) 41.8454 + 21.7454i 0.307687 + 0.159893i
\(137\) −206.272 −1.50564 −0.752819 0.658228i \(-0.771306\pi\)
−0.752819 + 0.658228i \(0.771306\pi\)
\(138\) 0 0
\(139\) 125.355i 0.901835i 0.892566 + 0.450918i \(0.148903\pi\)
−0.892566 + 0.450918i \(0.851097\pi\)
\(140\) −162.471 182.393i −1.16051 1.30281i
\(141\) 0 0
\(142\) 21.1940 8.07073i 0.149253 0.0568361i
\(143\) 190.621i 1.33302i
\(144\) 0 0
\(145\) −51.7159 −0.356661
\(146\) 16.7938 + 44.1011i 0.115026 + 0.302062i
\(147\) 0 0
\(148\) 4.81869 4.29238i 0.0325587 0.0290026i
\(149\) 170.871 1.14679 0.573394 0.819280i \(-0.305626\pi\)
0.573394 + 0.819280i \(0.305626\pi\)
\(150\) 0 0
\(151\) 131.745i 0.872482i −0.899830 0.436241i \(-0.856310\pi\)
0.899830 0.436241i \(-0.143690\pi\)
\(152\) 16.0796 30.9426i 0.105787 0.203570i
\(153\) 0 0
\(154\) 117.359 + 308.189i 0.762074 + 2.00123i
\(155\) 215.427i 1.38985i
\(156\) 0 0
\(157\) −3.40126 −0.0216641 −0.0108320 0.999941i \(-0.503448\pi\)
−0.0108320 + 0.999941i \(0.503448\pi\)
\(158\) 0.535243 0.203822i 0.00338761 0.00129001i
\(159\) 0 0
\(160\) 154.459 39.1839i 0.965366 0.244899i
\(161\) 11.1174 0.0690522
\(162\) 0 0
\(163\) 170.519i 1.04613i −0.852293 0.523064i \(-0.824789\pi\)
0.852293 0.523064i \(-0.175211\pi\)
\(164\) 207.214 184.582i 1.26350 1.12550i
\(165\) 0 0
\(166\) −46.5980 + 17.7446i −0.280711 + 0.106895i
\(167\) 245.186i 1.46818i −0.679053 0.734089i \(-0.737610\pi\)
0.679053 0.734089i \(-0.262390\pi\)
\(168\) 0 0
\(169\) 31.9746 0.189199
\(170\) 20.8929 + 54.8654i 0.122899 + 0.322738i
\(171\) 0 0
\(172\) −85.1784 95.6225i −0.495223 0.555945i
\(173\) −62.3081 −0.360162 −0.180081 0.983652i \(-0.557636\pi\)
−0.180081 + 0.983652i \(0.557636\pi\)
\(174\) 0 0
\(175\) 2.48121i 0.0141783i
\(176\) −213.709 24.7729i −1.21426 0.140755i
\(177\) 0 0
\(178\) −31.1046 81.6816i −0.174745 0.458885i
\(179\) 129.080i 0.721115i −0.932737 0.360557i \(-0.882586\pi\)
0.932737 0.360557i \(-0.117414\pi\)
\(180\) 0 0
\(181\) −198.677 −1.09766 −0.548831 0.835933i \(-0.684927\pi\)
−0.548831 + 0.835933i \(0.684927\pi\)
\(182\) −324.928 + 123.733i −1.78532 + 0.679854i
\(183\) 0 0
\(184\) −3.34435 + 6.43565i −0.0181758 + 0.0349763i
\(185\) 8.03384 0.0434261
\(186\) 0 0
\(187\) 79.2628i 0.423865i
\(188\) −103.692 116.407i −0.551555 0.619184i
\(189\) 0 0
\(190\) 40.5702 15.4492i 0.213528 0.0813118i
\(191\) 380.217i 1.99067i 0.0965041 + 0.995333i \(0.469234\pi\)
−0.0965041 + 0.995333i \(0.530766\pi\)
\(192\) 0 0
\(193\) −264.689 −1.37145 −0.685724 0.727862i \(-0.740514\pi\)
−0.685724 + 0.727862i \(0.740514\pi\)
\(194\) −82.4948 216.634i −0.425231 1.11667i
\(195\) 0 0
\(196\) 302.797 269.725i 1.54488 1.37615i
\(197\) −125.565 −0.637386 −0.318693 0.947858i \(-0.603244\pi\)
−0.318693 + 0.947858i \(0.603244\pi\)
\(198\) 0 0
\(199\) 14.4081i 0.0724026i −0.999345 0.0362013i \(-0.988474\pi\)
0.999345 0.0362013i \(-0.0115258\pi\)
\(200\) −1.43632 0.746400i −0.00718161 0.00373200i
\(201\) 0 0
\(202\) −7.33168 19.2532i −0.0362955 0.0953131i
\(203\) 127.353i 0.627356i
\(204\) 0 0
\(205\) 345.473 1.68523
\(206\) 207.105 78.8663i 1.00537 0.382846i
\(207\) 0 0
\(208\) 26.1184 225.316i 0.125569 1.08325i
\(209\) −58.6109 −0.280435
\(210\) 0 0
\(211\) 81.1242i 0.384475i −0.981348 0.192237i \(-0.938426\pi\)
0.981348 0.192237i \(-0.0615744\pi\)
\(212\) −24.8373 + 22.1245i −0.117157 + 0.104361i
\(213\) 0 0
\(214\) −55.4148 + 21.1021i −0.258948 + 0.0986080i
\(215\) 159.424i 0.741508i
\(216\) 0 0
\(217\) −530.500 −2.44470
\(218\) 0.717800 + 1.88497i 0.00329266 + 0.00864664i
\(219\) 0 0
\(220\) −178.150 199.994i −0.809775 0.909066i
\(221\) 83.5677 0.378134
\(222\) 0 0
\(223\) 181.944i 0.815892i 0.913006 + 0.407946i \(0.133755\pi\)
−0.913006 + 0.407946i \(0.866245\pi\)
\(224\) 96.4924 + 380.363i 0.430770 + 1.69805i
\(225\) 0 0
\(226\) −42.0197 110.345i −0.185928 0.488253i
\(227\) 423.077i 1.86377i −0.362748 0.931887i \(-0.618162\pi\)
0.362748 0.931887i \(-0.381838\pi\)
\(228\) 0 0
\(229\) 360.509 1.57427 0.787137 0.616778i \(-0.211562\pi\)
0.787137 + 0.616778i \(0.211562\pi\)
\(230\) −8.43806 + 3.21324i −0.0366872 + 0.0139706i
\(231\) 0 0
\(232\) 73.7223 + 38.3106i 0.317769 + 0.165132i
\(233\) −2.13039 −0.00914329 −0.00457164 0.999990i \(-0.501455\pi\)
−0.00457164 + 0.999990i \(0.501455\pi\)
\(234\) 0 0
\(235\) 194.076i 0.825855i
\(236\) −55.6711 62.4972i −0.235894 0.264819i
\(237\) 0 0
\(238\) −135.109 + 51.4499i −0.567685 + 0.216176i
\(239\) 228.926i 0.957847i 0.877857 + 0.478924i \(0.158973\pi\)
−0.877857 + 0.478924i \(0.841027\pi\)
\(240\) 0 0
\(241\) 245.133 1.01715 0.508575 0.861017i \(-0.330172\pi\)
0.508575 + 0.861017i \(0.330172\pi\)
\(242\) 42.5636 + 111.774i 0.175883 + 0.461874i
\(243\) 0 0
\(244\) 353.430 314.828i 1.44848 1.29028i
\(245\) 504.831 2.06054
\(246\) 0 0
\(247\) 61.7942i 0.250179i
\(248\) 159.586 307.096i 0.643491 1.23829i
\(249\) 0 0
\(250\) −89.3246 234.569i −0.357299 0.938278i
\(251\) 178.193i 0.709934i −0.934879 0.354967i \(-0.884492\pi\)
0.934879 0.354967i \(-0.115508\pi\)
\(252\) 0 0
\(253\) 12.1903 0.0481829
\(254\) 391.485 149.078i 1.54128 0.586923i
\(255\) 0 0
\(256\) −249.211 58.5636i −0.973482 0.228764i
\(257\) 239.267 0.930998 0.465499 0.885048i \(-0.345875\pi\)
0.465499 + 0.885048i \(0.345875\pi\)
\(258\) 0 0
\(259\) 19.7838i 0.0763852i
\(260\) 210.857 187.826i 0.810987 0.722409i
\(261\) 0 0
\(262\) −86.1257 + 32.7969i −0.328724 + 0.125179i
\(263\) 39.7564i 0.151165i −0.997140 0.0755825i \(-0.975918\pi\)
0.997140 0.0755825i \(-0.0240816\pi\)
\(264\) 0 0
\(265\) −41.4094 −0.156262
\(266\) 38.0446 + 99.9064i 0.143025 + 0.375588i
\(267\) 0 0
\(268\) 152.852 + 171.593i 0.570342 + 0.640274i
\(269\) 25.6332 0.0952905 0.0476453 0.998864i \(-0.484828\pi\)
0.0476453 + 0.998864i \(0.484828\pi\)
\(270\) 0 0
\(271\) 53.7535i 0.198353i −0.995070 0.0991763i \(-0.968379\pi\)
0.995070 0.0991763i \(-0.0316208\pi\)
\(272\) 10.8604 93.6892i 0.0399278 0.344446i
\(273\) 0 0
\(274\) 146.813 + 385.537i 0.535816 + 1.40707i
\(275\) 2.72065i 0.00989328i
\(276\) 0 0
\(277\) 353.449 1.27599 0.637995 0.770040i \(-0.279764\pi\)
0.637995 + 0.770040i \(0.279764\pi\)
\(278\) 234.297 89.2210i 0.842796 0.320939i
\(279\) 0 0
\(280\) −225.266 + 433.488i −0.804523 + 1.54817i
\(281\) −221.272 −0.787445 −0.393722 0.919229i \(-0.628813\pi\)
−0.393722 + 0.919229i \(0.628813\pi\)
\(282\) 0 0
\(283\) 81.0003i 0.286220i 0.989707 + 0.143110i \(0.0457103\pi\)
−0.989707 + 0.143110i \(0.954290\pi\)
\(284\) −30.1695 33.8687i −0.106231 0.119256i
\(285\) 0 0
\(286\) −356.285 + 135.674i −1.24575 + 0.474385i
\(287\) 850.745i 2.96427i
\(288\) 0 0
\(289\) −254.252 −0.879763
\(290\) 36.8086 + 96.6606i 0.126926 + 0.333312i
\(291\) 0 0
\(292\) 70.4750 62.7776i 0.241353 0.214992i
\(293\) −517.659 −1.76675 −0.883377 0.468664i \(-0.844736\pi\)
−0.883377 + 0.468664i \(0.844736\pi\)
\(294\) 0 0
\(295\) 104.197i 0.353210i
\(296\) −11.4524 5.95138i −0.0386906 0.0201060i
\(297\) 0 0
\(298\) −121.617 319.371i −0.408111 1.07171i
\(299\) 12.8524i 0.0429845i
\(300\) 0 0
\(301\) 392.591 1.30429
\(302\) −246.240 + 93.7688i −0.815364 + 0.310493i
\(303\) 0 0
\(304\) −69.2785 8.03069i −0.227890 0.0264167i
\(305\) 589.248 1.93196
\(306\) 0 0
\(307\) 249.101i 0.811405i −0.914005 0.405703i \(-0.867027\pi\)
0.914005 0.405703i \(-0.132973\pi\)
\(308\) 492.497 438.705i 1.59902 1.42437i
\(309\) 0 0
\(310\) 402.648 153.329i 1.29886 0.494610i
\(311\) 252.481i 0.811835i −0.913910 0.405917i \(-0.866952\pi\)
0.913910 0.405917i \(-0.133048\pi\)
\(312\) 0 0
\(313\) −595.875 −1.90376 −0.951878 0.306478i \(-0.900849\pi\)
−0.951878 + 0.306478i \(0.900849\pi\)
\(314\) 2.42083 + 6.35719i 0.00770966 + 0.0202458i
\(315\) 0 0
\(316\) −0.761914 0.855337i −0.00241112 0.00270676i
\(317\) −491.836 −1.55153 −0.775766 0.631020i \(-0.782636\pi\)
−0.775766 + 0.631020i \(0.782636\pi\)
\(318\) 0 0
\(319\) 139.643i 0.437753i
\(320\) −183.173 260.805i −0.572414 0.815014i
\(321\) 0 0
\(322\) −7.91277 20.7792i −0.0245738 0.0645316i
\(323\) 25.6948i 0.0795504i
\(324\) 0 0
\(325\) −2.86842 −0.00882590
\(326\) −318.711 + 121.366i −0.977643 + 0.372289i
\(327\) 0 0
\(328\) −492.480 255.922i −1.50146 0.780251i
\(329\) 477.923 1.45265
\(330\) 0 0
\(331\) 413.971i 1.25067i −0.780358 0.625333i \(-0.784963\pi\)
0.780358 0.625333i \(-0.215037\pi\)
\(332\) 66.3319 + 74.4652i 0.199795 + 0.224293i
\(333\) 0 0
\(334\) −458.269 + 174.510i −1.37206 + 0.522485i
\(335\) 286.085i 0.853985i
\(336\) 0 0
\(337\) 393.328 1.16715 0.583573 0.812061i \(-0.301654\pi\)
0.583573 + 0.812061i \(0.301654\pi\)
\(338\) −22.7578 59.7627i −0.0673307 0.176813i
\(339\) 0 0
\(340\) 87.6768 78.1005i 0.257873 0.229707i
\(341\) −581.696 −1.70585
\(342\) 0 0
\(343\) 642.295i 1.87258i
\(344\) −118.100 + 227.263i −0.343313 + 0.660649i
\(345\) 0 0
\(346\) 44.3475 + 116.458i 0.128172 + 0.336584i
\(347\) 476.716i 1.37382i −0.726742 0.686911i \(-0.758966\pi\)
0.726742 0.686911i \(-0.241034\pi\)
\(348\) 0 0
\(349\) −118.794 −0.340383 −0.170191 0.985411i \(-0.554439\pi\)
−0.170191 + 0.985411i \(0.554439\pi\)
\(350\) 4.63754 1.76599i 0.0132501 0.00504568i
\(351\) 0 0
\(352\) 105.804 + 417.069i 0.300580 + 1.18485i
\(353\) −297.291 −0.842185 −0.421092 0.907018i \(-0.638353\pi\)
−0.421092 + 0.907018i \(0.638353\pi\)
\(354\) 0 0
\(355\) 56.4668i 0.159061i
\(356\) −130.530 + 116.273i −0.366657 + 0.326610i
\(357\) 0 0
\(358\) −241.259 + 91.8719i −0.673907 + 0.256625i
\(359\) 212.978i 0.593252i 0.954994 + 0.296626i \(0.0958615\pi\)
−0.954994 + 0.296626i \(0.904139\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) 141.407 + 371.341i 0.390628 + 1.02580i
\(363\) 0 0
\(364\) 462.532 + 519.246i 1.27069 + 1.42650i
\(365\) 117.498 0.321912
\(366\) 0 0
\(367\) 326.797i 0.890456i −0.895417 0.445228i \(-0.853123\pi\)
0.895417 0.445228i \(-0.146877\pi\)
\(368\) 14.4090 + 1.67028i 0.0391549 + 0.00453879i
\(369\) 0 0
\(370\) −5.71805 15.0158i −0.0154542 0.0405832i
\(371\) 101.973i 0.274860i
\(372\) 0 0
\(373\) 235.813 0.632205 0.316103 0.948725i \(-0.397626\pi\)
0.316103 + 0.948725i \(0.397626\pi\)
\(374\) −148.148 + 56.4150i −0.396116 + 0.150842i
\(375\) 0 0
\(376\) −143.769 + 276.660i −0.382365 + 0.735798i
\(377\) 147.228 0.390524
\(378\) 0 0
\(379\) 471.811i 1.24489i 0.782666 + 0.622443i \(0.213860\pi\)
−0.782666 + 0.622443i \(0.786140\pi\)
\(380\) −57.7514 64.8326i −0.151977 0.170612i
\(381\) 0 0
\(382\) 710.652 270.618i 1.86034 0.708424i
\(383\) 131.099i 0.342294i −0.985246 0.171147i \(-0.945253\pi\)
0.985246 0.171147i \(-0.0547473\pi\)
\(384\) 0 0
\(385\) 821.104 2.13274
\(386\) 188.392 + 494.722i 0.488061 + 1.28166i
\(387\) 0 0
\(388\) −346.189 + 308.377i −0.892239 + 0.794786i
\(389\) −20.4959 −0.0526887 −0.0263444 0.999653i \(-0.508387\pi\)
−0.0263444 + 0.999653i \(0.508387\pi\)
\(390\) 0 0
\(391\) 5.34417i 0.0136679i
\(392\) −719.650 373.973i −1.83584 0.954014i
\(393\) 0 0
\(394\) 89.3704 + 234.690i 0.226828 + 0.595659i
\(395\) 1.42604i 0.00361022i
\(396\) 0 0
\(397\) 9.07740 0.0228650 0.0114325 0.999935i \(-0.496361\pi\)
0.0114325 + 0.999935i \(0.496361\pi\)
\(398\) −26.9298 + 10.2549i −0.0676628 + 0.0257661i
\(399\) 0 0
\(400\) −0.372776 + 3.21583i −0.000931939 + 0.00803958i
\(401\) 336.682 0.839606 0.419803 0.907615i \(-0.362099\pi\)
0.419803 + 0.907615i \(0.362099\pi\)
\(402\) 0 0
\(403\) 613.289i 1.52181i
\(404\) −30.7673 + 27.4068i −0.0761568 + 0.0678387i
\(405\) 0 0
\(406\) −238.032 + 90.6432i −0.586286 + 0.223259i
\(407\) 21.6930i 0.0532997i
\(408\) 0 0
\(409\) 75.6667 0.185004 0.0925020 0.995712i \(-0.470514\pi\)
0.0925020 + 0.995712i \(0.470514\pi\)
\(410\) −245.889 645.712i −0.599729 1.57491i
\(411\) 0 0
\(412\) −294.813 330.961i −0.715565 0.803304i
\(413\) 256.591 0.621285
\(414\) 0 0
\(415\) 124.150i 0.299157i
\(416\) −439.721 + 111.551i −1.05702 + 0.268151i
\(417\) 0 0
\(418\) 41.7160 + 109.548i 0.0997992 + 0.262076i
\(419\) 619.532i 1.47860i 0.673378 + 0.739298i \(0.264843\pi\)
−0.673378 + 0.739298i \(0.735157\pi\)
\(420\) 0 0
\(421\) −18.4384 −0.0437967 −0.0218983 0.999760i \(-0.506971\pi\)
−0.0218983 + 0.999760i \(0.506971\pi\)
\(422\) −151.627 + 57.7398i −0.359305 + 0.136824i
\(423\) 0 0
\(424\) 59.0301 + 30.6756i 0.139222 + 0.0723482i
\(425\) −1.19272 −0.00280641
\(426\) 0 0
\(427\) 1451.05i 3.39825i
\(428\) 78.8826 + 88.5548i 0.184305 + 0.206904i
\(429\) 0 0
\(430\) −297.975 + 113.470i −0.692965 + 0.263883i
\(431\) 496.147i 1.15115i 0.817748 + 0.575577i \(0.195222\pi\)
−0.817748 + 0.575577i \(0.804778\pi\)
\(432\) 0 0
\(433\) 623.687 1.44039 0.720193 0.693774i \(-0.244053\pi\)
0.720193 + 0.693774i \(0.244053\pi\)
\(434\) 377.582 + 991.542i 0.870004 + 2.28466i
\(435\) 0 0
\(436\) 3.01224 2.68324i 0.00690881 0.00615421i
\(437\) 3.95174 0.00904289
\(438\) 0 0
\(439\) 105.337i 0.239947i −0.992777 0.119974i \(-0.961719\pi\)
0.992777 0.119974i \(-0.0382810\pi\)
\(440\) −247.005 + 475.321i −0.561376 + 1.08027i
\(441\) 0 0
\(442\) −59.4790 156.194i −0.134568 0.353380i
\(443\) 113.329i 0.255821i 0.991786 + 0.127911i \(0.0408271\pi\)
−0.991786 + 0.127911i \(0.959173\pi\)
\(444\) 0 0
\(445\) −217.623 −0.489040
\(446\) 340.066 129.498i 0.762479 0.290354i
\(447\) 0 0
\(448\) 642.246 451.072i 1.43358 1.00686i
\(449\) −413.979 −0.922003 −0.461001 0.887399i \(-0.652510\pi\)
−0.461001 + 0.887399i \(0.652510\pi\)
\(450\) 0 0
\(451\) 932.845i 2.06839i
\(452\) −176.335 + 157.076i −0.390122 + 0.347512i
\(453\) 0 0
\(454\) −790.760 + 301.123i −1.74176 + 0.663267i
\(455\) 865.700i 1.90264i
\(456\) 0 0
\(457\) 320.223 0.700707 0.350353 0.936618i \(-0.386061\pi\)
0.350353 + 0.936618i \(0.386061\pi\)
\(458\) −256.591 673.816i −0.560242 1.47121i
\(459\) 0 0
\(460\) 12.0115 + 13.4843i 0.0261120 + 0.0293137i
\(461\) 460.179 0.998218 0.499109 0.866539i \(-0.333661\pi\)
0.499109 + 0.866539i \(0.333661\pi\)
\(462\) 0 0
\(463\) 323.224i 0.698108i 0.937103 + 0.349054i \(0.113497\pi\)
−0.937103 + 0.349054i \(0.886503\pi\)
\(464\) 19.1335 165.059i 0.0412360 0.355732i
\(465\) 0 0
\(466\) 1.51629 + 3.98184i 0.00325385 + 0.00854472i
\(467\) 523.352i 1.12067i −0.828267 0.560334i \(-0.810673\pi\)
0.828267 0.560334i \(-0.189327\pi\)
\(468\) 0 0
\(469\) −704.500 −1.50213
\(470\) −362.741 + 138.133i −0.771790 + 0.293900i
\(471\) 0 0
\(472\) −77.1879 + 148.535i −0.163534 + 0.314693i
\(473\) 430.477 0.910100
\(474\) 0 0
\(475\) 0.881959i 0.00185676i
\(476\) 192.327 + 215.909i 0.404048 + 0.453590i
\(477\) 0 0
\(478\) 427.878 162.937i 0.895141 0.340872i
\(479\) 458.055i 0.956274i −0.878285 0.478137i \(-0.841312\pi\)
0.878285 0.478137i \(-0.158688\pi\)
\(480\) 0 0
\(481\) −22.8712 −0.0475492
\(482\) −174.473 458.171i −0.361977 0.950562i
\(483\) 0 0
\(484\) 178.618 159.109i 0.369045 0.328737i
\(485\) −577.174 −1.19005
\(486\) 0 0
\(487\) 49.8747i 0.102412i 0.998688 + 0.0512060i \(0.0163065\pi\)
−0.998688 + 0.0512060i \(0.983693\pi\)
\(488\) −839.987 436.508i −1.72128 0.894484i
\(489\) 0 0
\(490\) −359.312 943.565i −0.733289 1.92564i
\(491\) 381.364i 0.776709i −0.921510 0.388354i \(-0.873044\pi\)
0.921510 0.388354i \(-0.126956\pi\)
\(492\) 0 0
\(493\) 61.2191 0.124177
\(494\) −115.498 + 43.9817i −0.233801 + 0.0890319i
\(495\) 0 0
\(496\) −687.569 79.7022i −1.38623 0.160690i
\(497\) 139.053 0.279784
\(498\) 0 0
\(499\) 191.567i 0.383903i −0.981404 0.191951i \(-0.938518\pi\)
0.981404 0.191951i \(-0.0614816\pi\)
\(500\) −374.850 + 333.908i −0.749700 + 0.667816i
\(501\) 0 0
\(502\) −333.056 + 126.829i −0.663458 + 0.252646i
\(503\) 393.811i 0.782925i 0.920194 + 0.391463i \(0.128031\pi\)
−0.920194 + 0.391463i \(0.871969\pi\)
\(504\) 0 0
\(505\) −51.2961 −0.101576
\(506\) −8.67638 22.7845i −0.0171470 0.0450286i
\(507\) 0 0
\(508\) −557.276 625.606i −1.09700 1.23151i
\(509\) 711.118 1.39709 0.698544 0.715567i \(-0.253832\pi\)
0.698544 + 0.715567i \(0.253832\pi\)
\(510\) 0 0
\(511\) 289.345i 0.566232i
\(512\) 67.9159 + 507.476i 0.132648 + 0.991163i
\(513\) 0 0
\(514\) −170.297 447.206i −0.331317 0.870050i
\(515\) 551.787i 1.07143i
\(516\) 0 0
\(517\) 524.044 1.01362
\(518\) 36.9772 14.0810i 0.0713846 0.0271834i
\(519\) 0 0
\(520\) −501.137 260.421i −0.963724 0.500809i
\(521\) −401.456 −0.770549 −0.385274 0.922802i \(-0.625893\pi\)
−0.385274 + 0.922802i \(0.625893\pi\)
\(522\) 0 0
\(523\) 83.5113i 0.159677i −0.996808 0.0798387i \(-0.974559\pi\)
0.996808 0.0798387i \(-0.0254405\pi\)
\(524\) 122.599 + 137.632i 0.233968 + 0.262656i
\(525\) 0 0
\(526\) −74.3074 + 28.2965i −0.141269 + 0.0537956i
\(527\) 255.013i 0.483896i
\(528\) 0 0
\(529\) 528.178 0.998446
\(530\) 29.4730 + 77.3970i 0.0556094 + 0.146032i
\(531\) 0 0
\(532\) 159.654 142.216i 0.300101 0.267323i
\(533\) −983.510 −1.84523
\(534\) 0 0
\(535\) 147.641i 0.275964i
\(536\) 211.928 407.821i 0.395389 0.760860i
\(537\) 0 0
\(538\) −18.2443 47.9101i −0.0339113 0.0890523i
\(539\) 1363.15i 2.52903i
\(540\) 0 0
\(541\) 315.779 0.583694 0.291847 0.956465i \(-0.405730\pi\)
0.291847 + 0.956465i \(0.405730\pi\)
\(542\) −100.469 + 38.2589i −0.185367 + 0.0705883i
\(543\) 0 0
\(544\) −182.841 + 46.3842i −0.336105 + 0.0852650i
\(545\) 5.02208 0.00921483
\(546\) 0 0
\(547\) 115.726i 0.211564i 0.994389 + 0.105782i \(0.0337346\pi\)
−0.994389 + 0.105782i \(0.966265\pi\)
\(548\) 616.101 548.809i 1.12427 1.00148i
\(549\) 0 0
\(550\) 5.08508 1.93641i 0.00924561 0.00352075i
\(551\) 45.2684i 0.0821569i
\(552\) 0 0
\(553\) 3.51170 0.00635027
\(554\) −251.566 660.621i −0.454091 1.19246i
\(555\) 0 0
\(556\) −333.520 374.415i −0.599857 0.673408i
\(557\) 597.571 1.07284 0.536419 0.843952i \(-0.319777\pi\)
0.536419 + 0.843952i \(0.319777\pi\)
\(558\) 0 0
\(559\) 453.857i 0.811910i
\(560\) 970.551 + 112.505i 1.73313 + 0.200902i
\(561\) 0 0
\(562\) 157.490 + 413.573i 0.280230 + 0.735894i
\(563\) 622.336i 1.10539i 0.833383 + 0.552696i \(0.186401\pi\)
−0.833383 + 0.552696i \(0.813599\pi\)
\(564\) 0 0
\(565\) −293.991 −0.520337
\(566\) 151.395 57.6516i 0.267482 0.101858i
\(567\) 0 0
\(568\) −41.8300 + 80.4948i −0.0736443 + 0.141716i
\(569\) −497.207 −0.873826 −0.436913 0.899504i \(-0.643928\pi\)
−0.436913 + 0.899504i \(0.643928\pi\)
\(570\) 0 0
\(571\) 623.096i 1.09124i −0.838034 0.545619i \(-0.816295\pi\)
0.838034 0.545619i \(-0.183705\pi\)
\(572\) 507.168 + 569.355i 0.886658 + 0.995376i
\(573\) 0 0
\(574\) 1590.10 605.514i 2.77021 1.05490i
\(575\) 0.183436i 0.000319019i
\(576\) 0 0
\(577\) −934.139 −1.61896 −0.809479 0.587148i \(-0.800251\pi\)
−0.809479 + 0.587148i \(0.800251\pi\)
\(578\) 180.963 + 475.214i 0.313084 + 0.822169i
\(579\) 0 0
\(580\) 154.467 137.596i 0.266322 0.237234i
\(581\) −305.727 −0.526208
\(582\) 0 0
\(583\) 111.814i 0.191790i
\(584\) −167.496 87.0410i −0.286808 0.149043i
\(585\) 0 0
\(586\) 368.442 + 967.540i 0.628740 + 1.65109i
\(587\) 778.304i 1.32590i −0.748663 0.662951i \(-0.769304\pi\)
0.748663 0.662951i \(-0.230696\pi\)
\(588\) 0 0
\(589\) −188.569 −0.320152
\(590\) −194.751 + 74.1617i −0.330087 + 0.125698i
\(591\) 0 0
\(592\) −2.97231 + 25.6412i −0.00502079 + 0.0433129i
\(593\) 1012.64 1.70766 0.853832 0.520549i \(-0.174273\pi\)
0.853832 + 0.520549i \(0.174273\pi\)
\(594\) 0 0
\(595\) 359.969i 0.604989i
\(596\) −510.365 + 454.621i −0.856317 + 0.762788i
\(597\) 0 0
\(598\) 24.0219 9.14761i 0.0401705 0.0152970i
\(599\) 37.3119i 0.0622903i −0.999515 0.0311452i \(-0.990085\pi\)
0.999515 0.0311452i \(-0.00991541\pi\)
\(600\) 0 0
\(601\) −181.988 −0.302808 −0.151404 0.988472i \(-0.548379\pi\)
−0.151404 + 0.988472i \(0.548379\pi\)
\(602\) −279.425 733.779i −0.464161 1.21890i
\(603\) 0 0
\(604\) 350.521 + 393.500i 0.580332 + 0.651490i
\(605\) 297.796 0.492225
\(606\) 0 0
\(607\) 218.379i 0.359767i −0.983688 0.179884i \(-0.942428\pi\)
0.983688 0.179884i \(-0.0575721\pi\)
\(608\) 34.2988 + 135.202i 0.0564125 + 0.222372i
\(609\) 0 0
\(610\) −419.395 1101.34i −0.687532 1.80548i
\(611\) 552.506i 0.904265i
\(612\) 0 0
\(613\) 641.406 1.04634 0.523170 0.852229i \(-0.324749\pi\)
0.523170 + 0.852229i \(0.324749\pi\)
\(614\) −465.588 + 177.297i −0.758286 + 0.288757i
\(615\) 0 0
\(616\) −1170.50 608.264i −1.90017 0.987442i
\(617\) 223.015 0.361450 0.180725 0.983534i \(-0.442156\pi\)
0.180725 + 0.983534i \(0.442156\pi\)
\(618\) 0 0
\(619\) 126.536i 0.204420i −0.994763 0.102210i \(-0.967409\pi\)
0.994763 0.102210i \(-0.0325914\pi\)
\(620\) −573.166 643.445i −0.924461 1.03781i
\(621\) 0 0
\(622\) −471.903 + 179.702i −0.758687 + 0.288910i
\(623\) 535.908i 0.860205i
\(624\) 0 0
\(625\) −619.901 −0.991841
\(626\) 424.112 + 1113.73i 0.677495 + 1.77912i
\(627\) 0 0
\(628\) 10.1590 9.04941i 0.0161768 0.0144099i
\(629\) −9.51011 −0.0151194
\(630\) 0 0
\(631\) 250.558i 0.397081i −0.980093 0.198541i \(-0.936380\pi\)
0.980093 0.198541i \(-0.0636202\pi\)
\(632\) −1.05639 + 2.03285i −0.00167151 + 0.00321654i
\(633\) 0 0
\(634\) 350.062 + 919.275i 0.552149 + 1.44996i
\(635\) 1043.03i 1.64256i
\(636\) 0 0
\(637\) −1437.18 −2.25617
\(638\) −261.003 + 99.3906i −0.409095 + 0.155785i
\(639\) 0 0
\(640\) −357.089 + 527.989i −0.557952 + 0.824982i
\(641\) 744.927 1.16213 0.581067 0.813856i \(-0.302636\pi\)
0.581067 + 0.813856i \(0.302636\pi\)
\(642\) 0 0
\(643\) 1161.89i 1.80699i −0.428604 0.903493i \(-0.640994\pi\)
0.428604 0.903493i \(-0.359006\pi\)
\(644\) −33.2058 + 29.5790i −0.0515619 + 0.0459301i
\(645\) 0 0
\(646\) −48.0253 + 18.2882i −0.0743425 + 0.0283098i
\(647\) 550.347i 0.850614i −0.905049 0.425307i \(-0.860166\pi\)
0.905049 0.425307i \(-0.139834\pi\)
\(648\) 0 0
\(649\) 281.352 0.433517
\(650\) 2.04158 + 5.36127i 0.00314090 + 0.00824810i
\(651\) 0 0
\(652\) 453.683 + 509.312i 0.695833 + 0.781153i
\(653\) 170.874 0.261675 0.130838 0.991404i \(-0.458233\pi\)
0.130838 + 0.991404i \(0.458233\pi\)
\(654\) 0 0
\(655\) 229.463i 0.350326i
\(656\) −127.816 + 1102.63i −0.194841 + 1.68084i
\(657\) 0 0
\(658\) −340.160 893.270i −0.516960 1.35755i
\(659\) 933.406i 1.41640i −0.706013 0.708199i \(-0.749508\pi\)
0.706013 0.708199i \(-0.250492\pi\)
\(660\) 0 0
\(661\) −498.493 −0.754150 −0.377075 0.926183i \(-0.623070\pi\)
−0.377075 + 0.926183i \(0.623070\pi\)
\(662\) −773.740 + 294.642i −1.16879 + 0.445079i
\(663\) 0 0
\(664\) 91.9691 176.979i 0.138508 0.266535i
\(665\) 266.179 0.400269
\(666\) 0 0
\(667\) 9.41523i 0.0141158i
\(668\) 652.342 + 732.329i 0.976560 + 1.09630i
\(669\) 0 0
\(670\) 534.712 203.620i 0.798078 0.303910i
\(671\) 1591.09i 2.37122i
\(672\) 0 0
\(673\) 779.779 1.15866 0.579331 0.815093i \(-0.303314\pi\)
0.579331 + 0.815093i \(0.303314\pi\)
\(674\) −279.950 735.157i −0.415356 1.09074i
\(675\) 0 0
\(676\) −95.5028 + 85.0718i −0.141276 + 0.125846i
\(677\) −910.302 −1.34461 −0.672306 0.740273i \(-0.734696\pi\)
−0.672306 + 0.740273i \(0.734696\pi\)
\(678\) 0 0
\(679\) 1421.32i 2.09326i
\(680\) −208.379 108.286i −0.306439 0.159244i
\(681\) 0 0
\(682\) 414.020 + 1087.23i 0.607067 + 1.59418i
\(683\) 93.5131i 0.136915i −0.997654 0.0684576i \(-0.978192\pi\)
0.997654 0.0684576i \(-0.0218078\pi\)
\(684\) 0 0
\(685\) 1027.18 1.49953
\(686\) 1200.49 457.151i 1.74999 0.666401i
\(687\) 0 0
\(688\) 508.827 + 58.9827i 0.739575 + 0.0857307i
\(689\) 117.887 0.171098
\(690\) 0 0
\(691\) 663.683i 0.960468i −0.877140 0.480234i \(-0.840552\pi\)
0.877140 0.480234i \(-0.159448\pi\)
\(692\) 186.104 165.777i 0.268936 0.239562i
\(693\) 0 0
\(694\) −891.015 + 339.301i −1.28388 + 0.488906i
\(695\) 624.234i 0.898179i
\(696\) 0 0
\(697\) −408.956 −0.586737
\(698\) 84.5509 + 222.033i 0.121133 + 0.318099i
\(699\) 0 0
\(700\) −6.60151 7.41095i −0.00943073 0.0105871i
\(701\) −959.216 −1.36835 −0.684177 0.729316i \(-0.739838\pi\)
−0.684177 + 0.729316i \(0.739838\pi\)
\(702\) 0 0
\(703\) 7.03225i 0.0100032i
\(704\) 704.225 494.603i 1.00032 0.702560i
\(705\) 0 0
\(706\) 211.596 + 555.658i 0.299711 + 0.787051i
\(707\) 126.319i 0.178670i
\(708\) 0 0
\(709\) 825.957 1.16496 0.582480 0.812845i \(-0.302082\pi\)
0.582480 + 0.812845i \(0.302082\pi\)
\(710\) −105.540 + 40.1900i −0.148648 + 0.0566056i
\(711\) 0 0
\(712\) 310.227 + 161.212i 0.435711 + 0.226422i
\(713\) 39.2199 0.0550069
\(714\) 0 0
\(715\) 949.243i 1.32761i
\(716\) 343.430 + 385.539i 0.479650 + 0.538463i
\(717\) 0 0
\(718\) 398.070 151.586i 0.554414 0.211122i
\(719\) 1019.44i 1.41786i −0.705281 0.708928i \(-0.749179\pi\)
0.705281 0.708928i \(-0.250821\pi\)
\(720\) 0 0
\(721\) 1358.81 1.88461
\(722\) 13.5232 + 35.5123i 0.0187302 + 0.0491860i
\(723\) 0 0
\(724\) 593.415 528.601i 0.819634 0.730111i
\(725\) −2.10131 −0.00289836
\(726\) 0 0
\(727\) 227.791i 0.313330i −0.987652 0.156665i \(-0.949926\pi\)
0.987652 0.156665i \(-0.0500742\pi\)
\(728\) 641.301 1234.08i 0.880907 1.69516i
\(729\) 0 0
\(730\) −83.6286 219.611i −0.114560 0.300837i
\(731\) 188.720i 0.258166i
\(732\) 0 0
\(733\) −998.335 −1.36198 −0.680992 0.732291i \(-0.738451\pi\)
−0.680992 + 0.732291i \(0.738451\pi\)
\(734\) −610.807 + 232.597i −0.832162 + 0.316889i
\(735\) 0 0
\(736\) −7.13369 28.1202i −0.00969251 0.0382068i
\(737\) −772.486 −1.04815
\(738\) 0 0
\(739\) 614.741i 0.831856i −0.909398 0.415928i \(-0.863457\pi\)
0.909398 0.415928i \(-0.136543\pi\)
\(740\) −23.9957 + 21.3749i −0.0324267 + 0.0288850i
\(741\) 0 0
\(742\) −190.594 + 72.5788i −0.256866 + 0.0978151i
\(743\) 156.926i 0.211206i −0.994408 0.105603i \(-0.966323\pi\)
0.994408 0.105603i \(-0.0336772\pi\)
\(744\) 0 0
\(745\) −850.893 −1.14214
\(746\) −167.839 440.750i −0.224985 0.590817i
\(747\) 0 0
\(748\) 210.887 + 236.745i 0.281934 + 0.316504i
\(749\) −363.573 −0.485412
\(750\) 0 0
\(751\) 766.925i 1.02120i 0.859817 + 0.510602i \(0.170578\pi\)
−0.859817 + 0.510602i \(0.829422\pi\)
\(752\) 619.424 + 71.8030i 0.823702 + 0.0954827i
\(753\) 0 0
\(754\) −104.789 275.179i −0.138977 0.364958i
\(755\) 656.053i 0.868944i
\(756\) 0 0
\(757\) 163.896 0.216507 0.108253 0.994123i \(-0.465474\pi\)
0.108253 + 0.994123i \(0.465474\pi\)
\(758\) 881.848 335.810i 1.16339 0.443021i
\(759\) 0 0
\(760\) −80.0722 + 154.086i −0.105358 + 0.202744i
\(761\) 512.227 0.673098 0.336549 0.941666i \(-0.390740\pi\)
0.336549 + 0.941666i \(0.390740\pi\)
\(762\) 0 0
\(763\) 12.3672i 0.0162086i
\(764\) −1011.61 1135.65i −1.32409 1.48645i
\(765\) 0 0
\(766\) −245.032 + 93.3089i −0.319886 + 0.121813i
\(767\) 296.633i 0.386745i
\(768\) 0 0
\(769\) 1124.70 1.46255 0.731275 0.682083i \(-0.238926\pi\)
0.731275 + 0.682083i \(0.238926\pi\)
\(770\) −584.417 1534.70i −0.758983 1.99312i
\(771\) 0 0
\(772\) 790.583 704.234i 1.02407 0.912220i
\(773\) −669.217 −0.865740 −0.432870 0.901456i \(-0.642499\pi\)
−0.432870 + 0.901456i \(0.642499\pi\)
\(774\) 0 0
\(775\) 8.75319i 0.0112944i
\(776\) 822.776 + 427.564i 1.06028 + 0.550985i
\(777\) 0 0
\(778\) 14.5879 + 38.3083i 0.0187505 + 0.0492394i
\(779\) 302.402i 0.388193i
\(780\) 0 0
\(781\) 152.472 0.195226
\(782\) 9.98861 3.80369i 0.0127732 0.00486405i
\(783\) 0 0
\(784\) −186.774 + 1611.25i −0.238232 + 2.05516i
\(785\) 16.9373 0.0215762
\(786\) 0 0
\(787\) 1456.58i 1.85080i −0.378995 0.925399i \(-0.623730\pi\)
0.378995 0.925399i \(-0.376270\pi\)
\(788\) 375.042 334.079i 0.475942 0.423958i
\(789\) 0 0
\(790\) −2.66536 + 1.01498i −0.00337388 + 0.00128478i