Properties

Label 76.3.b.b.39.10
Level $76$
Weight $3$
Character 76.39
Analytic conductor $2.071$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07085000914\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.10
Root \(0.711746 - 1.86907i\) of defining polynomial
Character \(\chi\) \(=\) 76.39
Dual form 76.3.b.b.39.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.711746 + 1.86907i) q^{2} +4.44946i q^{3} +(-2.98683 + 2.66060i) q^{4} +4.97973 q^{5} +(-8.31634 + 3.16688i) q^{6} -12.2628i q^{7} +(-7.09872 - 3.68892i) q^{8} -10.7977 q^{9} +O(q^{10})\) \(q+(0.711746 + 1.86907i) q^{2} +4.44946i q^{3} +(-2.98683 + 2.66060i) q^{4} +4.97973 q^{5} +(-8.31634 + 3.16688i) q^{6} -12.2628i q^{7} +(-7.09872 - 3.68892i) q^{8} -10.7977 q^{9} +(3.54430 + 9.30745i) q^{10} +13.4463i q^{11} +(-11.8382 - 13.2898i) q^{12} +14.1766 q^{13} +(22.9201 - 8.72803i) q^{14} +22.1571i q^{15} +(1.84237 - 15.8936i) q^{16} -5.89478 q^{17} +(-7.68520 - 20.1816i) q^{18} -4.35890i q^{19} +(-14.8736 + 13.2491i) q^{20} +54.5630 q^{21} +(-25.1320 + 9.57032i) q^{22} -0.906592i q^{23} +(16.4137 - 31.5855i) q^{24} -0.202335 q^{25} +(10.0901 + 26.4969i) q^{26} -7.99863i q^{27} +(32.6266 + 36.6271i) q^{28} -10.3853 q^{29} +(-41.4131 + 15.7702i) q^{30} -43.2608i q^{31} +(31.0175 - 7.86868i) q^{32} -59.8285 q^{33} +(-4.19559 - 11.0178i) q^{34} -61.0656i q^{35} +(32.2508 - 28.7283i) q^{36} -1.61331 q^{37} +(8.14708 - 3.10243i) q^{38} +63.0779i q^{39} +(-35.3497 - 18.3698i) q^{40} +69.3758 q^{41} +(38.8350 + 101.982i) q^{42} +32.0147i q^{43} +(-35.7752 - 40.1617i) q^{44} -53.7694 q^{45} +(1.69448 - 0.645264i) q^{46} -38.9732i q^{47} +(70.7178 + 8.19753i) q^{48} -101.377 q^{49} +(-0.144011 - 0.378179i) q^{50} -26.2286i q^{51} +(-42.3430 + 37.7182i) q^{52} -8.31560 q^{53} +(14.9500 - 5.69299i) q^{54} +66.9586i q^{55} +(-45.2367 + 87.0505i) q^{56} +19.3947 q^{57} +(-7.39169 - 19.4108i) q^{58} -20.9242i q^{59} +(-58.9512 - 66.1795i) q^{60} -118.329 q^{61} +(80.8574 - 30.7907i) q^{62} +132.410i q^{63} +(36.7837 + 52.3733i) q^{64} +70.5953 q^{65} +(-42.5827 - 111.824i) q^{66} -57.4499i q^{67} +(17.6067 - 15.6837i) q^{68} +4.03384 q^{69} +(114.136 - 43.4632i) q^{70} -11.3393i q^{71} +(76.6496 + 39.8318i) q^{72} -23.5952 q^{73} +(-1.14827 - 3.01539i) q^{74} -0.900282i q^{75} +(11.5973 + 13.0193i) q^{76} +164.889 q^{77} +(-117.897 + 44.8955i) q^{78} +0.286369i q^{79} +(9.17448 - 79.1456i) q^{80} -61.5894 q^{81} +(49.3780 + 129.668i) q^{82} +24.9311i q^{83} +(-162.971 + 145.171i) q^{84} -29.3544 q^{85} +(-59.8376 + 22.7863i) q^{86} -46.2089i q^{87} +(49.6022 - 95.4512i) q^{88} -43.7018 q^{89} +(-38.2702 - 100.499i) q^{90} -173.845i q^{91} +(2.41208 + 2.70784i) q^{92} +192.487 q^{93} +(72.8436 - 27.7390i) q^{94} -21.7061i q^{95} +(35.0113 + 138.011i) q^{96} +115.905 q^{97} +(-72.1549 - 189.481i) q^{98} -145.188i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} + O(q^{10}) \) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} - 12q^{10} + 4q^{12} + 54q^{13} + 30q^{14} + 58q^{16} + 34q^{17} + 36q^{18} + 32q^{20} - 38q^{21} + 36q^{22} - 98q^{24} - 86q^{25} - 16q^{26} + 18q^{28} + 54q^{29} - 204q^{30} + 72q^{32} + 20q^{33} - 82q^{34} + 96q^{36} + 100q^{37} - 148q^{40} + 224q^{41} + 224q^{42} - 96q^{44} - 168q^{45} + 46q^{46} + 296q^{48} - 220q^{49} - 58q^{50} - 288q^{52} + 14q^{53} - 128q^{54} + 12q^{56} + 38q^{57} - 72q^{58} + 188q^{60} + 28q^{61} + 396q^{62} - 118q^{64} - 472q^{65} - 32q^{66} + 30q^{68} + 122q^{69} + 156q^{70} + 80q^{72} + 70q^{73} - 224q^{74} + 228q^{77} + 274q^{78} - 348q^{80} + 334q^{81} - 400q^{82} - 216q^{84} + 48q^{85} - 124q^{86} + 472q^{88} + 416q^{90} + 126q^{92} - 176q^{93} - 88q^{94} - 106q^{96} + 308q^{97} + 68q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.711746 + 1.86907i 0.355873 + 0.934534i
\(3\) 4.44946i 1.48315i 0.670869 + 0.741576i \(0.265921\pi\)
−0.670869 + 0.741576i \(0.734079\pi\)
\(4\) −2.98683 + 2.66060i −0.746709 + 0.665151i
\(5\) 4.97973 0.995945 0.497973 0.867193i \(-0.334078\pi\)
0.497973 + 0.867193i \(0.334078\pi\)
\(6\) −8.31634 + 3.16688i −1.38606 + 0.527814i
\(7\) 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
\(9\) −10.7977 −1.19974
\(10\) 3.54430 + 9.30745i 0.354430 + 0.930745i
\(11\) 13.4463i 1.22239i 0.791481 + 0.611193i \(0.209310\pi\)
−0.791481 + 0.611193i \(0.790690\pi\)
\(12\) −11.8382 13.2898i −0.986520 1.10748i
\(13\) 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
\(15\) 22.1571i 1.47714i
\(16\) 1.84237 15.8936i 0.115148 0.993348i
\(17\) −5.89478 −0.346752 −0.173376 0.984856i \(-0.555468\pi\)
−0.173376 + 0.984856i \(0.555468\pi\)
\(18\) −7.68520 20.1816i −0.426955 1.12120i
\(19\) 4.35890i 0.229416i
\(20\) −14.8736 + 13.2491i −0.743681 + 0.662454i
\(21\) 54.5630 2.59824
\(22\) −25.1320 + 9.57032i −1.14236 + 0.435014i
\(23\) 0.906592i 0.0394171i −0.999806 0.0197085i \(-0.993726\pi\)
0.999806 0.0197085i \(-0.00627383\pi\)
\(24\) 16.4137 31.5855i 0.683905 1.31606i
\(25\) −0.202335 −0.00809341
\(26\) 10.0901 + 26.4969i 0.388081 + 1.01911i
\(27\) 7.99863i 0.296246i
\(28\) 32.6266 + 36.6271i 1.16524 + 1.30811i
\(29\) −10.3853 −0.358114 −0.179057 0.983839i \(-0.557305\pi\)
−0.179057 + 0.983839i \(0.557305\pi\)
\(30\) −41.4131 + 15.7702i −1.38044 + 0.525674i
\(31\) 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
\(33\) −59.8285 −1.81299
\(34\) −4.19559 11.0178i −0.123400 0.324052i
\(35\) 61.0656i 1.74473i
\(36\) 32.2508 28.7283i 0.895857 0.798009i
\(37\) −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
\(39\) 63.0779i 1.61738i
\(40\) −35.3497 18.3698i −0.883742 0.459246i
\(41\) 69.3758 1.69209 0.846047 0.533109i \(-0.178976\pi\)
0.846047 + 0.533109i \(0.178976\pi\)
\(42\) 38.8350 + 101.982i 0.924643 + 2.42814i
\(43\) 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
\(45\) −53.7694 −1.19488
\(46\) 1.69448 0.645264i 0.0368366 0.0140275i
\(47\) 38.9732i 0.829217i −0.910000 0.414609i \(-0.863918\pi\)
0.910000 0.414609i \(-0.136082\pi\)
\(48\) 70.7178 + 8.19753i 1.47329 + 0.170782i
\(49\) −101.377 −2.06893
\(50\) −0.144011 0.378179i −0.00288023 0.00756357i
\(51\) 26.2286i 0.514286i
\(52\) −42.3430 + 37.7182i −0.814289 + 0.725350i
\(53\) −8.31560 −0.156898 −0.0784491 0.996918i \(-0.524997\pi\)
−0.0784491 + 0.996918i \(0.524997\pi\)
\(54\) 14.9500 5.69299i 0.276852 0.105426i
\(55\) 66.9586i 1.21743i
\(56\) −45.2367 + 87.0505i −0.807798 + 1.55447i
\(57\) 19.3947 0.340258
\(58\) −7.39169 19.4108i −0.127443 0.334669i
\(59\) 20.9242i 0.354648i −0.984153 0.177324i \(-0.943256\pi\)
0.984153 0.177324i \(-0.0567440\pi\)
\(60\) −58.9512 66.1795i −0.982520 1.10299i
\(61\) −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
\(63\) 132.410i 2.10175i
\(64\) 36.7837 + 52.3733i 0.574745 + 0.818333i
\(65\) 70.5953 1.08608
\(66\) −42.5827 111.824i −0.645193 1.69430i
\(67\) 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
\(69\) 4.03384 0.0584615
\(70\) 114.136 43.4632i 1.63051 0.620903i
\(71\) 11.3393i 0.159709i −0.996807 0.0798545i \(-0.974554\pi\)
0.996807 0.0798545i \(-0.0254456\pi\)
\(72\) 76.6496 + 39.8318i 1.06458 + 0.553219i
\(73\) −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
\(75\) 0.900282i 0.0120038i
\(76\) 11.5973 + 13.0193i 0.152596 + 0.171307i
\(77\) 164.889 2.14142
\(78\) −117.897 + 44.8955i −1.51150 + 0.575583i
\(79\) 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
\(81\) −61.5894 −0.760363
\(82\) 49.3780 + 129.668i 0.602170 + 1.58132i
\(83\) 24.9311i 0.300375i 0.988658 + 0.150188i \(0.0479878\pi\)
−0.988658 + 0.150188i \(0.952012\pi\)
\(84\) −162.971 + 145.171i −1.94013 + 1.72822i
\(85\) −29.3544 −0.345346
\(86\) −59.8376 + 22.7863i −0.695786 + 0.264957i
\(87\) 46.2089i 0.531137i
\(88\) 49.6022 95.4512i 0.563662 1.08467i
\(89\) −43.7018 −0.491031 −0.245515 0.969393i \(-0.578957\pi\)
−0.245515 + 0.969393i \(0.578957\pi\)
\(90\) −38.2702 100.499i −0.425224 1.11665i
\(91\) 173.845i 1.91038i
\(92\) 2.41208 + 2.70784i 0.0262183 + 0.0294331i
\(93\) 192.487 2.06975
\(94\) 72.8436 27.7390i 0.774932 0.295096i
\(95\) 21.7061i 0.228485i
\(96\) 35.0113 + 138.011i 0.364702 + 1.43761i
\(97\) 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
\(99\) 145.188i 1.46655i
\(100\) 0.604342 0.538334i 0.00604342 0.00538334i
\(101\) −10.3010 −0.101990 −0.0509950 0.998699i \(-0.516239\pi\)
−0.0509950 + 0.998699i \(0.516239\pi\)
\(102\) 49.0230 18.6681i 0.480618 0.183021i
\(103\) 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
\(105\) 271.709 2.58770
\(106\) −5.91860 15.5424i −0.0558358 0.146627i
\(107\) 29.6484i 0.277088i 0.990356 + 0.138544i \(0.0442422\pi\)
−0.990356 + 0.138544i \(0.955758\pi\)
\(108\) 21.2812 + 23.8906i 0.197048 + 0.221209i
\(109\) −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
\(111\) 7.17835i 0.0646698i
\(112\) −194.900 22.5927i −1.74018 0.201720i
\(113\) −59.0375 −0.522456 −0.261228 0.965277i \(-0.584127\pi\)
−0.261228 + 0.965277i \(0.584127\pi\)
\(114\) 13.8041 + 36.2501i 0.121089 + 0.317983i
\(115\) 4.51458i 0.0392572i
\(116\) 31.0192 27.6312i 0.267407 0.238200i
\(117\) −153.074 −1.30832
\(118\) 39.1088 14.8927i 0.331431 0.126210i
\(119\) 72.2868i 0.607452i
\(120\) 81.7358 157.287i 0.681131 1.31072i
\(121\) −59.8017 −0.494229
\(122\) −84.2205 221.166i −0.690332 1.81283i
\(123\) 308.685i 2.50963i
\(124\) 115.100 + 129.213i 0.928225 + 1.04204i
\(125\) −125.501 −1.00401
\(126\) −247.484 + 94.2424i −1.96416 + 0.747955i
\(127\) 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
\(129\) −142.448 −1.10425
\(130\) 50.2460 + 131.948i 0.386507 + 1.01498i
\(131\) 46.0795i 0.351752i 0.984412 + 0.175876i \(0.0562758\pi\)
−0.984412 + 0.175876i \(0.943724\pi\)
\(132\) 178.698 159.180i 1.35377 1.20591i
\(133\) −53.4525 −0.401899
\(134\) 107.378 40.8898i 0.801327 0.305147i
\(135\) 39.8310i 0.295044i
\(136\) 41.8454 + 21.7454i 0.307687 + 0.159893i
\(137\) 206.272 1.50564 0.752819 0.658228i \(-0.228694\pi\)
0.752819 + 0.658228i \(0.228694\pi\)
\(138\) 2.87107 + 7.53953i 0.0208049 + 0.0546343i
\(139\) 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
\(141\) 173.410 1.22986
\(142\) 21.1940 8.07073i 0.149253 0.0568361i
\(143\) 190.621i 1.33302i
\(144\) −19.8933 + 171.613i −0.138148 + 1.19176i
\(145\) −51.7159 −0.356661
\(146\) −16.7938 44.1011i −0.115026 0.302062i
\(147\) 451.074i 3.06853i
\(148\) 4.81869 4.29238i 0.0325587 0.0290026i
\(149\) −170.871 −1.14679 −0.573394 0.819280i \(-0.694374\pi\)
−0.573394 + 0.819280i \(0.694374\pi\)
\(150\) 1.68269 0.640772i 0.0112179 0.00427182i
\(151\) 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
\(153\) 63.6499 0.416012
\(154\) 117.359 + 308.189i 0.762074 + 2.00123i
\(155\) 215.427i 1.38985i
\(156\) −167.825 188.403i −1.07580 1.20771i
\(157\) −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
\(159\) 36.9999i 0.232704i
\(160\) 154.459 39.1839i 0.965366 0.244899i
\(161\) −11.1174 −0.0690522
\(162\) −43.8360 115.115i −0.270593 0.710585i
\(163\) 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
\(165\) −297.930 −1.80563
\(166\) −46.5980 + 17.7446i −0.280711 + 0.106895i
\(167\) 245.186i 1.46818i 0.679053 + 0.734089i \(0.262390\pi\)
−0.679053 + 0.734089i \(0.737610\pi\)
\(168\) −387.327 201.279i −2.30552 1.19809i
\(169\) 31.9746 0.189199
\(170\) −20.8929 54.8654i −0.122899 0.322738i
\(171\) 47.0659i 0.275239i
\(172\) −85.1784 95.6225i −0.495223 0.555945i
\(173\) 62.3081 0.360162 0.180081 0.983652i \(-0.442364\pi\)
0.180081 + 0.983652i \(0.442364\pi\)
\(174\) 86.3676 32.8890i 0.496366 0.189017i
\(175\) 2.48121i 0.0141783i
\(176\) 213.709 + 24.7729i 1.21426 + 0.140755i
\(177\) 93.1014 0.525997
\(178\) −31.1046 81.6816i −0.174745 0.458885i
\(179\) 129.080i 0.721115i 0.932737 + 0.360557i \(0.117414\pi\)
−0.932737 + 0.360557i \(0.882586\pi\)
\(180\) 160.600 143.059i 0.892224 0.794773i
\(181\) −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
\(183\) 526.501i 2.87706i
\(184\) −3.34435 + 6.43565i −0.0181758 + 0.0349763i
\(185\) −8.03384 −0.0434261
\(186\) 137.002 + 359.771i 0.736569 + 1.93426i
\(187\) 79.2628i 0.423865i
\(188\) 103.692 + 116.407i 0.551555 + 0.619184i
\(189\) −98.0860 −0.518973
\(190\) 40.5702 15.4492i 0.213528 0.0813118i
\(191\) 380.217i 1.99067i −0.0965041 0.995333i \(-0.530766\pi\)
0.0965041 0.995333i \(-0.469234\pi\)
\(192\) −233.033 + 163.667i −1.21371 + 0.852434i
\(193\) −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
\(195\) 314.111i 1.61082i
\(196\) 302.797 269.725i 1.54488 1.37615i
\(197\) 125.565 0.637386 0.318693 0.947858i \(-0.396756\pi\)
0.318693 + 0.947858i \(0.396756\pi\)
\(198\) 271.367 103.337i 1.37054 0.521904i
\(199\) 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
\(201\) 255.621 1.27175
\(202\) −7.33168 19.2532i −0.0362955 0.0953131i
\(203\) 127.353i 0.627356i
\(204\) 69.7839 + 78.3405i 0.342078 + 0.384022i
\(205\) 345.473 1.68523
\(206\) −207.105 + 78.8663i −1.00537 + 0.382846i
\(207\) 9.78908i 0.0472902i
\(208\) 26.1184 225.316i 0.125569 1.08325i
\(209\) 58.6109 0.280435
\(210\) 193.388 + 507.842i 0.920893 + 2.41830i
\(211\) 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
\(213\) 50.4539 0.236873
\(214\) −55.4148 + 21.1021i −0.258948 + 0.0986080i
\(215\) 159.424i 0.741508i
\(216\) −29.5063 + 56.7800i −0.136603 + 0.262871i
\(217\) −530.500 −2.44470
\(218\) −0.717800 1.88497i −0.00329266 0.00864664i
\(219\) 104.986i 0.479388i
\(220\) −178.150 199.994i −0.809775 0.909066i
\(221\) −83.5677 −0.378134
\(222\) 13.4168 5.10916i 0.0604362 0.0230142i
\(223\) 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
\(225\) 2.18475 0.00970999
\(226\) −42.0197 110.345i −0.185928 0.488253i
\(227\) 423.077i 1.86377i 0.362748 + 0.931887i \(0.381838\pi\)
−0.362748 + 0.931887i \(0.618162\pi\)
\(228\) −57.9289 + 51.6017i −0.254074 + 0.226323i
\(229\) 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
\(231\) 733.668i 3.17605i
\(232\) 73.7223 + 38.3106i 0.317769 + 0.165132i
\(233\) 2.13039 0.00914329 0.00457164 0.999990i \(-0.498545\pi\)
0.00457164 + 0.999990i \(0.498545\pi\)
\(234\) −108.950 286.105i −0.465596 1.22267i
\(235\) 194.076i 0.825855i
\(236\) 55.6711 + 62.4972i 0.235894 + 0.264819i
\(237\) −1.27419 −0.00537631
\(238\) −135.109 + 51.4499i −0.567685 + 0.216176i
\(239\) 228.926i 0.957847i −0.877857 0.478924i \(-0.841027\pi\)
0.877857 0.478924i \(-0.158973\pi\)
\(240\) 352.155 + 40.8214i 1.46731 + 0.170089i
\(241\) 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
\(243\) 346.027i 1.42398i
\(244\) 353.430 314.828i 1.44848 1.29028i
\(245\) −504.831 −2.06054
\(246\) −576.953 + 219.705i −2.34534 + 0.893110i
\(247\) 61.7942i 0.250179i
\(248\) −159.586 + 307.096i −0.643491 + 1.23829i
\(249\) −110.930 −0.445502
\(250\) −89.3246 234.569i −0.357299 0.938278i
\(251\) 178.193i 0.709934i 0.934879 + 0.354967i \(0.115508\pi\)
−0.934879 + 0.354967i \(0.884492\pi\)
\(252\) −352.291 395.487i −1.39798 1.56939i
\(253\) 12.1903 0.0481829
\(254\) −391.485 + 149.078i −1.54128 + 0.586923i
\(255\) 130.611i 0.512201i
\(256\) −249.211 58.5636i −0.973482 0.228764i
\(257\) −239.267 −0.930998 −0.465499 0.885048i \(-0.654125\pi\)
−0.465499 + 0.885048i \(0.654125\pi\)
\(258\) −101.387 266.245i −0.392972 1.03196i
\(259\) 19.7838i 0.0763852i
\(260\) −210.857 + 187.826i −0.810987 + 0.722409i
\(261\) 112.137 0.429643
\(262\) −86.1257 + 32.7969i −0.328724 + 0.125179i
\(263\) 39.7564i 0.151165i 0.997140 + 0.0755825i \(0.0240816\pi\)
−0.997140 + 0.0755825i \(0.975918\pi\)
\(264\) 424.706 + 220.703i 1.60873 + 0.835996i
\(265\) −41.4094 −0.156262
\(266\) −38.0446 99.9064i −0.143025 0.375588i
\(267\) 194.449i 0.728274i
\(268\) 152.852 + 171.593i 0.570342 + 0.640274i
\(269\) −25.6332 −0.0952905 −0.0476453 0.998864i \(-0.515172\pi\)
−0.0476453 + 0.998864i \(0.515172\pi\)
\(270\) 74.4468 28.3495i 0.275729 0.104998i
\(271\) 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
\(273\) 773.515 2.83339
\(274\) 146.813 + 385.537i 0.535816 + 1.40707i
\(275\) 2.72065i 0.00989328i
\(276\) −12.0484 + 10.7325i −0.0436537 + 0.0388857i
\(277\) 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
\(279\) 467.116i 1.67425i
\(280\) −225.266 + 433.488i −0.804523 + 1.54817i
\(281\) 221.272 0.787445 0.393722 0.919229i \(-0.371187\pi\)
0.393722 + 0.919229i \(0.371187\pi\)
\(282\) 123.424 + 324.115i 0.437673 + 1.14934i
\(283\) 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
\(285\) 96.5804 0.338879
\(286\) −356.285 + 135.674i −1.24575 + 0.474385i
\(287\) 850.745i 2.96427i
\(288\) −334.916 + 84.9634i −1.16290 + 0.295012i
\(289\) −254.252 −0.879763
\(290\) −36.8086 96.6606i −0.126926 0.333312i
\(291\) 515.714i 1.77221i
\(292\) 70.4750 62.7776i 0.241353 0.214992i
\(293\) 517.659 1.76675 0.883377 0.468664i \(-0.155264\pi\)
0.883377 + 0.468664i \(0.155264\pi\)
\(294\) 843.089 321.050i 2.86765 1.09201i
\(295\) 104.197i 0.353210i
\(296\) 11.4524 + 5.95138i 0.0386906 + 0.0201060i
\(297\) 107.552 0.362127
\(298\) −121.617 319.371i −0.408111 1.07171i
\(299\) 12.8524i 0.0429845i
\(300\) 2.39529 + 2.68899i 0.00798432 + 0.00896331i
\(301\) 392.591 1.30429
\(302\) 246.240 93.7688i 0.815364 0.310493i
\(303\) 45.8338i 0.151267i
\(304\) −69.2785 8.03069i −0.227890 0.0264167i
\(305\) −589.248 −1.93196
\(306\) 45.3026 + 118.966i 0.148048 + 0.388778i
\(307\) 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
\(309\) −493.030 −1.59557
\(310\) 402.648 153.329i 1.29886 0.494610i
\(311\) 252.481i 0.811835i 0.913910 + 0.405917i \(0.133048\pi\)
−0.913910 + 0.405917i \(0.866952\pi\)
\(312\) 232.690 447.773i 0.745801 1.43517i
\(313\) −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
\(315\) 659.366i 2.09322i
\(316\) −0.761914 0.855337i −0.00241112 0.00270676i
\(317\) 491.836 1.55153 0.775766 0.631020i \(-0.217364\pi\)
0.775766 + 0.631020i \(0.217364\pi\)
\(318\) 69.1554 26.3345i 0.217470 0.0828130i
\(319\) 139.643i 0.437753i
\(320\) 183.173 + 260.805i 0.572414 + 0.815014i
\(321\) −131.919 −0.410963
\(322\) −7.91277 20.7792i −0.0245738 0.0645316i
\(323\) 25.6948i 0.0795504i
\(324\) 183.957 163.865i 0.567770 0.505756i
\(325\) −2.86842 −0.00882590
\(326\) 318.711 121.366i 0.977643 0.372289i
\(327\) 4.48730i 0.0137226i
\(328\) −492.480 255.922i −1.50146 0.780251i
\(329\) −477.923 −1.45265
\(330\) −212.050 556.851i −0.642576 1.68743i
\(331\) 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
\(333\) 17.4200 0.0523122
\(334\) −458.269 + 174.510i −1.37206 + 0.522485i
\(335\) 286.085i 0.853985i
\(336\) 100.525 867.201i 0.299182 2.58096i
\(337\) 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
\(339\) 262.685i 0.774882i
\(340\) 87.6768 78.1005i 0.257873 0.229707i
\(341\) 581.696 1.70585
\(342\) −87.9695 + 33.4990i −0.257221 + 0.0979503i
\(343\) 642.295i 1.87258i
\(344\) 118.100 227.263i 0.343313 0.660649i
\(345\) 20.0874 0.0582244
\(346\) 44.3475 + 116.458i 0.128172 + 0.336584i
\(347\) 476.716i 1.37382i 0.726742 + 0.686911i \(0.241034\pi\)
−0.726742 + 0.686911i \(0.758966\pi\)
\(348\) 122.944 + 138.018i 0.353286 + 0.396605i
\(349\) −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
\(351\) 113.393i 0.323057i
\(352\) 105.804 + 417.069i 0.300580 + 1.18485i
\(353\) 297.291 0.842185 0.421092 0.907018i \(-0.361647\pi\)
0.421092 + 0.907018i \(0.361647\pi\)
\(354\) 66.2646 + 174.013i 0.187188 + 0.491562i
\(355\) 56.4668i 0.159061i
\(356\) 130.530 116.273i 0.366657 0.326610i
\(357\) −321.637 −0.900944
\(358\) −241.259 + 91.8719i −0.673907 + 0.256625i
\(359\) 212.978i 0.593252i −0.954994 0.296626i \(-0.904139\pi\)
0.954994 0.296626i \(-0.0958615\pi\)
\(360\) 381.694 + 198.351i 1.06026 + 0.550976i
\(361\) −19.0000 −0.0526316
\(362\) −141.407 371.341i −0.390628 1.02580i
\(363\) 266.085i 0.733017i
\(364\) 462.532 + 519.246i 1.27069 + 1.42650i
\(365\) −117.498 −0.321912
\(366\) 984.067 374.735i 2.68871 1.02387i
\(367\) 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
\(369\) −749.097 −2.03007
\(370\) −5.71805 15.0158i −0.0154542 0.0405832i
\(371\) 101.973i 0.274860i
\(372\) −574.927 + 512.132i −1.54550 + 1.37670i
\(373\) 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
\(375\) 558.410i 1.48909i
\(376\) −143.769 + 276.660i −0.382365 + 0.735798i
\(377\) −147.228 −0.390524
\(378\) −69.8123 183.329i −0.184689 0.484998i
\(379\) 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
\(381\) −931.959 −2.44609
\(382\) 710.652 270.618i 1.86034 0.708424i
\(383\) 131.099i 0.342294i 0.985246 + 0.171147i \(0.0547473\pi\)
−0.985246 + 0.171147i \(0.945253\pi\)
\(384\) −471.766 319.064i −1.22856 0.830897i
\(385\) 821.104 2.13274
\(386\) −188.392 494.722i −0.488061 1.28166i
\(387\) 345.684i 0.893239i
\(388\) −346.189 + 308.377i −0.892239 + 0.794786i
\(389\) 20.4959 0.0526887 0.0263444 0.999653i \(-0.491613\pi\)
0.0263444 + 0.999653i \(0.491613\pi\)
\(390\) −587.095 + 223.567i −1.50537 + 0.573249i
\(391\) 5.34417i 0.0136679i
\(392\) 719.650 + 373.973i 1.83584 + 0.954014i
\(393\) −205.029 −0.521702
\(394\) 89.3704 + 234.690i 0.226828 + 0.595659i
\(395\) 1.42604i 0.00361022i
\(396\) 386.288 + 433.653i 0.975475 + 1.09508i
\(397\) 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
\(399\) 237.835i 0.596077i
\(400\) −0.372776 + 3.21583i −0.000931939 + 0.00803958i
\(401\) −336.682 −0.839606 −0.419803 0.907615i \(-0.637901\pi\)
−0.419803 + 0.907615i \(0.637901\pi\)
\(402\) 181.937 + 477.773i 0.452580 + 1.18849i
\(403\) 613.289i 1.52181i
\(404\) 30.7673 27.4068i 0.0761568 0.0678387i
\(405\) −306.698 −0.757280
\(406\) −238.032 + 90.6432i −0.586286 + 0.223259i
\(407\) 21.6930i 0.0532997i
\(408\) −96.7553 + 186.189i −0.237145 + 0.456347i
\(409\) 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
\(411\) 917.800i 2.23309i
\(412\) −294.813 330.961i −0.715565 0.803304i
\(413\) −256.591 −0.621285
\(414\) −18.2965 + 6.96734i −0.0441944 + 0.0168293i
\(415\) 124.150i 0.299157i
\(416\) 439.721 111.551i 1.05702 0.268151i
\(417\) −557.762 −1.33756
\(418\) 41.7160 + 109.548i 0.0997992 + 0.262076i
\(419\) 619.532i 1.47860i −0.673378 0.739298i \(-0.735157\pi\)
0.673378 0.739298i \(-0.264843\pi\)
\(420\) −811.549 + 722.910i −1.93226 + 1.72121i
\(421\) −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
\(423\) 420.820i 0.994846i
\(424\) 59.0301 + 30.6756i 0.139222 + 0.0723482i
\(425\) 1.19272 0.00280641
\(426\) 35.9104 + 94.3018i 0.0842966 + 0.221366i
\(427\) 1451.05i 3.39825i
\(428\) −78.8826 88.5548i −0.184305 0.206904i
\(429\) −848.162 −1.97707
\(430\) −297.975 + 113.470i −0.692965 + 0.263883i
\(431\) 496.147i 1.15115i −0.817748 0.575577i \(-0.804778\pi\)
0.817748 0.575577i \(-0.195222\pi\)
\(432\) −127.127 14.7364i −0.294275 0.0341121i
\(433\) 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
\(435\) 230.108i 0.528983i
\(436\) 3.01224 2.68324i 0.00690881 0.00615421i
\(437\) −3.95174 −0.00904289
\(438\) 196.226 74.7233i 0.448004 0.170601i
\(439\) 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
\(441\) 1094.64 2.48217
\(442\) −59.4790 156.194i −0.134568 0.353380i
\(443\) 113.329i 0.255821i −0.991786 0.127911i \(-0.959173\pi\)
0.991786 0.127911i \(-0.0408271\pi\)
\(444\) 19.0987 + 21.4405i 0.0430152 + 0.0482895i
\(445\) −217.623 −0.489040
\(446\) −340.066 + 129.498i −0.762479 + 0.290354i
\(447\) 760.285i 1.70086i
\(448\) 642.246 451.072i 1.43358 1.00686i
\(449\) 413.979 0.922003 0.461001 0.887399i \(-0.347490\pi\)
0.461001 + 0.887399i \(0.347490\pi\)
\(450\) 1.55499 + 4.08345i 0.00345553 + 0.00907432i
\(451\) 932.845i 2.06839i
\(452\) 176.335 157.076i 0.390122 0.347512i
\(453\) 586.192 1.29402
\(454\) −790.760 + 301.123i −1.74176 + 0.663267i
\(455\) 865.700i 1.90264i
\(456\) −137.678 71.5457i −0.301925 0.156898i
\(457\) 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
\(459\) 47.1502i 0.102724i
\(460\) 12.0115 + 13.4843i 0.0261120 + 0.0293137i
\(461\) −460.179 −0.998218 −0.499109 0.866539i \(-0.666339\pi\)
−0.499109 + 0.866539i \(0.666339\pi\)
\(462\) −1371.28 + 522.185i −2.96813 + 1.13027i
\(463\) 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
\(465\) 958.533 2.06136
\(466\) 1.51629 + 3.98184i 0.00325385 + 0.00854472i
\(467\) 523.352i 1.12067i 0.828267 + 0.560334i \(0.189327\pi\)
−0.828267 + 0.560334i \(0.810673\pi\)
\(468\) 457.206 407.268i 0.976935 0.870232i
\(469\) −704.500 −1.50213
\(470\) 362.741 138.133i 0.771790 0.293900i
\(471\) 15.1338i 0.0321311i
\(472\) −77.1879 + 148.535i −0.163534 + 0.314693i
\(473\) −430.477 −0.910100
\(474\) −0.906897 2.38154i −0.00191328 0.00502435i
\(475\) 0.881959i 0.00185676i
\(476\) −192.327 215.909i −0.404048 0.453590i
\(477\) 89.7891 0.188237
\(478\) 427.878 162.937i 0.895141 0.340872i
\(479\) 458.055i 0.956274i 0.878285 + 0.478137i \(0.158688\pi\)
−0.878285 + 0.478137i \(0.841312\pi\)
\(480\) 174.347 + 687.256i 0.363223 + 1.43178i
\(481\) −22.8712 −0.0475492
\(482\) 174.473 + 458.171i 0.361977 + 0.950562i
\(483\) 49.4664i 0.102415i
\(484\) 178.618 159.109i 0.369045 0.328737i
\(485\) 577.174 1.19005
\(486\) 646.748 246.283i 1.33076 0.506756i
\(487\) 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
\(489\) 758.716 1.55157
\(490\) −359.312 943.565i −0.733289 1.92564i
\(491\) 381.364i 0.776709i 0.921510 + 0.388354i \(0.126956\pi\)
−0.921510 + 0.388354i \(0.873044\pi\)
\(492\) −821.288 921.990i −1.66928 1.87396i
\(493\) 61.2191 0.124177
\(494\) 115.498 43.9817i 0.233801 0.0890319i
\(495\) 722.997i 1.46060i
\(496\) −687.569 79.7022i −1.38623 0.160690i
\(497\) −139.053 −0.279784
\(498\) −78.9540 207.336i −0.158542 0.416337i
\(499\) 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
\(501\) −1090.94 −2.17753
\(502\) −333.056 + 126.829i −0.663458 + 0.252646i
\(503\) 393.811i 0.782925i −0.920194 0.391463i \(-0.871969\pi\)
0.920194 0.391463i \(-0.128031\pi\)
\(504\) 488.451 939.942i 0.969148 1.86496i
\(505\) −51.2961 −0.101576
\(506\) 8.67638 + 22.7845i 0.0171470 + 0.0450286i
\(507\) 142.270i 0.280611i
\(508\) −557.276 625.606i −1.09700 1.23151i
\(509\) −711.118 −1.39709 −0.698544 0.715567i \(-0.746168\pi\)
−0.698544 + 0.715567i \(0.746168\pi\)
\(510\) 244.121 92.9620i 0.478669 0.182278i
\(511\) 289.345i 0.566232i
\(512\) −67.9159 507.476i −0.132648 0.991163i
\(513\) −34.8652 −0.0679634
\(514\) −170.297 447.206i −0.331317 0.870050i
\(515\) 551.787i 1.07143i
\(516\) 425.468 378.997i 0.824551 0.734491i
\(517\) 524.044 1.01362
\(518\) −36.9772 + 14.0810i −0.0713846 + 0.0271834i
\(519\) 277.237i 0.534176i
\(520\) −501.137 260.421i −0.963724 0.500809i
\(521\) 401.456 0.770549 0.385274 0.922802i \(-0.374107\pi\)
0.385274 + 0.922802i \(0.374107\pi\)
\(522\) 79.8130 + 209.592i 0.152898 + 0.401516i
\(523\) 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
\(525\) −11.0400 −0.0210286
\(526\) −74.3074 + 28.2965i −0.141269 + 0.0537956i
\(527\) 255.013i 0.483896i
\(528\) −110.226 + 950.889i −0.208761 + 1.80093i
\(529\) 528.178 0.998446
\(530\) −29.4730 77.3970i −0.0556094 0.146032i
\(531\) 225.933i 0.425486i
\(532\) 159.654 142.216i 0.300101 0.267323i
\(533\) 983.510 1.84523
\(534\) 363.439 138.398i 0.680597 0.259173i
\(535\) 147.641i 0.275964i
\(536\) −211.928 + 407.821i −0.395389 + 0.760860i
\(537\) −574.334 −1.06952
\(538\) −18.2443 47.9101i −0.0339113 0.0890523i
\(539\) 1363.15i 2.52903i
\(540\) 105.975 + 118.969i 0.196249 + 0.220312i
\(541\) 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
\(543\) 884.004i 1.62800i
\(544\) −182.841 + 46.3842i −0.336105 + 0.0852650i
\(545\) −5.02208 −0.00921483
\(546\) 550.546 + 1445.75i 1.00833 + 2.64790i
\(547\) 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
\(549\) 1277.68 2.32729
\(550\) 5.08508 1.93641i 0.00924561 0.00352075i
\(551\) 45.2684i 0.0821569i
\(552\) −28.6351 14.8805i −0.0518752 0.0269575i
\(553\) 3.51170 0.00635027
\(554\) 251.566 + 660.621i 0.454091 + 1.19246i
\(555\) 35.7462i 0.0644076i
\(556\) −333.520 374.415i −0.599857 0.673408i
\(557\) −597.571 −1.07284 −0.536419 0.843952i \(-0.680223\pi\)
−0.536419 + 0.843952i \(0.680223\pi\)
\(558\) −873.071 + 332.468i −1.56464 + 0.595820i
\(559\) 453.857i 0.811910i
\(560\) −970.551 112.505i −1.73313 0.200902i
\(561\) 352.676 0.628656
\(562\) 157.490 + 413.573i 0.280230 + 0.735894i
\(563\) 622.336i 1.10539i −0.833383 0.552696i \(-0.813599\pi\)
0.833383 0.552696i \(-0.186401\pi\)
\(564\) −517.946 + 461.375i −0.918344 + 0.818040i
\(565\) −293.991 −0.520337
\(566\) −151.395 + 57.6516i −0.267482 + 0.101858i
\(567\) 755.261i 1.33203i
\(568\) −41.8300 + 80.4948i −0.0736443 + 0.141716i
\(569\) 497.207 0.873826 0.436913 0.899504i \(-0.356072\pi\)
0.436913 + 0.899504i \(0.356072\pi\)
\(570\) 68.7408 + 180.515i 0.120598 + 0.316694i
\(571\) 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
\(573\) 1691.76 2.95246
\(574\) 1590.10 605.514i 2.77021 1.05490i
\(575\) 0.183436i 0.000319019i
\(576\) −397.178 565.509i −0.689545 0.981787i
\(577\) −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
\(579\) 1177.72i 2.03406i
\(580\) 154.467 137.596i 0.266322 0.237234i
\(581\) 305.727 0.526208
\(582\) −963.904 + 367.057i −1.65619 + 0.630682i
\(583\) 111.814i 0.191790i
\(584\) 167.496 + 87.0410i 0.286808 + 0.149043i
\(585\) −762.265 −1.30302
\(586\) 368.442 + 967.540i 0.628740 + 1.65109i
\(587\) 778.304i 1.32590i 0.748663 + 0.662951i \(0.230696\pi\)
−0.748663 + 0.662951i \(0.769304\pi\)
\(588\) 1200.13 + 1347.28i 2.04104 + 2.29130i
\(589\) −188.569 −0.320152
\(590\) 194.751 74.1617i 0.330087 0.125698i
\(591\) 558.696i 0.945340i
\(592\) −2.97231 + 25.6412i −0.00502079 + 0.0433129i
\(593\) −1012.64 −1.70766 −0.853832 0.520549i \(-0.825727\pi\)
−0.853832 + 0.520549i \(0.825727\pi\)
\(594\) 76.5494 + 201.021i 0.128871 + 0.338420i
\(595\) 359.969i 0.604989i
\(596\) 510.365 454.621i 0.856317 0.762788i
\(597\) 64.1083 0.107384
\(598\) 24.0219 9.14761i 0.0401705 0.0152970i
\(599\) 37.3119i 0.0622903i 0.999515 + 0.0311452i \(0.00991541\pi\)
−0.999515 + 0.0311452i \(0.990085\pi\)
\(600\) −3.32107 + 6.39085i −0.00553512 + 0.0106514i
\(601\) −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
\(603\) 620.325i 1.02873i
\(604\) 350.521 + 393.500i 0.580332 + 0.651490i
\(605\) −297.796 −0.492225
\(606\) 85.6665 32.6220i 0.141364 0.0538317i
\(607\) 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
\(609\) −566.653 −0.930464
\(610\) −419.395 1101.34i −0.687532 1.80548i
\(611\) 552.506i 0.904265i
\(612\) −190.112 + 169.347i −0.310640 + 0.276711i
\(613\) 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
\(615\) 1537.17i 2.49946i
\(616\) −1170.50 608.264i −1.90017 0.987442i
\(617\) −223.015 −0.361450 −0.180725 0.983534i \(-0.557844\pi\)
−0.180725 + 0.983534i \(0.557844\pi\)
\(618\) −350.912 921.506i −0.567819 1.49111i
\(619\) 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
\(621\) −7.25150 −0.0116771
\(622\) −471.903 + 179.702i −0.758687 + 0.288910i
\(623\) 535.908i 0.860205i
\(624\) 1002.53 + 116.213i 1.60663 + 0.186238i
\(625\) −619.901 −0.991841
\(626\) −424.112 1113.73i −0.677495 1.77912i
\(627\) 260.786i 0.415927i
\(628\) 10.1590 9.04941i 0.0161768 0.0144099i
\(629\) 9.51011 0.0151194
\(630\) −1232.40 + 469.301i −1.95619 + 0.744922i
\(631\) 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
\(633\) 360.959 0.570235
\(634\) 350.062 + 919.275i 0.552149 + 1.44996i
\(635\) 1043.03i 1.64256i
\(636\) 98.4421 + 110.513i 0.154783 + 0.173762i
\(637\) −1437.18 −2.25617
\(638\) 261.003 99.3906i 0.409095 0.155785i
\(639\) 122.438i 0.191609i
\(640\) −357.089 + 527.989i −0.557952 + 0.824982i
\(641\) −744.927 −1.16213 −0.581067 0.813856i \(-0.697364\pi\)
−0.581067 + 0.813856i \(0.697364\pi\)
\(642\) −93.8929 246.566i −0.146251 0.384059i
\(643\) 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
\(645\) −709.351 −1.09977
\(646\) −48.0253 + 18.2882i −0.0743425 + 0.0283098i
\(647\) 550.347i 0.850614i 0.905049 + 0.425307i \(0.139834\pi\)
−0.905049 + 0.425307i \(0.860166\pi\)
\(648\) 437.206 + 227.199i 0.674701 + 0.350615i
\(649\) 281.352 0.433517
\(650\) −2.04158 5.36127i −0.00314090 0.00824810i
\(651\) 2360.44i 3.62587i
\(652\) 453.683 + 509.312i 0.695833 + 0.781153i
\(653\) −170.874 −0.261675 −0.130838 0.991404i \(-0.541767\pi\)
−0.130838 + 0.991404i \(0.541767\pi\)
\(654\) 8.38708 3.19382i 0.0128243 0.00488352i
\(655\) 229.463i 0.350326i
\(656\) 127.816 1102.63i 0.194841 1.68084i
\(657\) 254.773 0.387783
\(658\) −340.160 893.270i −0.516960 1.35755i
\(659\) 933.406i 1.41640i 0.706013 + 0.708199i \(0.250492\pi\)
−0.706013 + 0.708199i \(0.749508\pi\)
\(660\) 889.867 792.673i 1.34828 1.20102i
\(661\) −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
\(663\) 371.831i 0.560831i
\(664\) 91.9691 176.979i 0.138508 0.266535i
\(665\) −266.179 −0.400269
\(666\) 12.3986 + 32.5591i 0.0186165 + 0.0488876i
\(667\) 9.41523i 0.0141158i
\(668\) −652.342 732.329i −0.976560 1.09630i
\(669\) −809.551 −1.21009
\(670\) 534.712 203.620i 0.798078 0.303910i
\(671\) 1591.09i 2.37122i
\(672\) 1692.41 429.339i 2.51846 0.638897i
\(673\) 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
\(675\) 1.61841i 0.00239764i
\(676\) −95.5028 + 85.0718i −0.141276 + 0.125846i
\(677\) 910.302 1.34461 0.672306 0.740273i \(-0.265304\pi\)
0.672306 + 0.740273i \(0.265304\pi\)
\(678\) 490.976 186.965i 0.724154 0.275760i
\(679\) 1421.32i 2.09326i
\(680\) 208.379 + 108.286i 0.306439 + 0.159244i
\(681\) −1882.46 −2.76426
\(682\) 414.020 + 1087.23i 0.607067 + 1.59418i
\(683\) 93.5131i 0.136915i 0.997654 + 0.0684576i \(0.0218078\pi\)
−0.997654 + 0.0684576i \(0.978192\pi\)
\(684\) −125.224 140.578i −0.183076 0.205524i
\(685\) 1027.18 1.49953
\(686\) −1200.49 + 457.151i −1.74999 + 0.666401i
\(687\) 1604.07i 2.33489i
\(688\) 508.827 + 58.9827i 0.739575 + 0.0857307i
\(689\) −117.887 −0.171098
\(690\) 14.2972 + 37.5448i 0.0207205 + 0.0544127i
\(691\) 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
\(693\) −1780.42 −2.56915
\(694\) −891.015 + 339.301i −1.28388 + 0.488906i
\(695\) 624.234i 0.898179i
\(696\) −170.461 + 328.024i −0.244916 + 0.471299i
\(697\) −408.956 −0.586737
\(698\) −84.5509 222.033i −0.121133 0.318099i
\(699\) 9.47906i 0.0135609i
\(700\) −6.60151 7.41095i −0.00943073 0.0105871i
\(701\) 959.216 1.36835 0.684177 0.729316i \(-0.260162\pi\)
0.684177 + 0.729316i \(0.260162\pi\)
\(702\) 211.939 80.7070i 0.301908 0.114967i
\(703\) 7.03225i 0.0100032i
\(704\) −704.225 + 494.603i −1.00032 + 0.702560i
\(705\) 863.532 1.22487
\(706\) 211.596 + 555.658i 0.299711 + 0.787051i
\(707\) 126.319i 0.178670i
\(708\) −278.079 + 247.706i −0.392766 + 0.349867i
\(709\) 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
\(711\) 3.09212i 0.00434897i
\(712\) 310.227 + 161.212i 0.435711 + 0.226422i
\(713\) −39.2199 −0.0550069
\(714\) −228.924 601.162i −0.320622 0.841963i
\(715\) 949.243i 1.32761i
\(716\) −343.430 385.539i −0.479650 0.538463i
\(717\) 1018.59 1.42063
\(718\) 398.070 151.586i 0.554414 0.211122i
\(719\) 1019.44i 1.41786i 0.705281 + 0.708928i \(0.250821\pi\)
−0.705281 + 0.708928i \(0.749179\pi\)
\(720\) −99.0630 + 854.588i −0.137587 + 1.18693i
\(721\) 1358.81 1.88461
\(722\) −13.5232 35.5123i −0.0187302 0.0491860i
\(723\) 1090.71i 1.50859i
\(724\) 593.415 528.601i 0.819634 0.730111i
\(725\) 2.10131 0.00289836
\(726\) 497.331 189.385i 0.685030 0.260861i
\(727\) 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
\(729\) 985.328 1.35162
\(730\) −83.6286 219.611i −0.114560 0.300837i
\(731\) 188.720i 0.258166i
\(732\) 1400.81 + 1572.57i 1.91368 + 2.14832i
\(733\) −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
\(735\) 2246.23i 3.05609i
\(736\) −7.13369 28.1202i −0.00969251 0.0382068i
\(737\) 772.486 1.04815
\(738\) −533.167 1400.11i −0.722448 1.89717i
\(739\) 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
\(741\) 274.950 0.371053
\(742\) −190.594 + 72.5788i −0.256866 + 0.0978151i
\(743\) 156.926i 0.211206i 0.994408 + 0.105603i \(0.0336772\pi\)
−0.994408 + 0.105603i \(0.966323\pi\)
\(744\) −1366.41 710.070i −1.83657 0.954395i
\(745\) −850.893 −1.14214
\(746\) 167.839 + 440.750i 0.224985 + 0.590817i
\(747\) 269.198i 0.360372i
\(748\) 210.887 + 236.745i 0.281934 + 0.316504i
\(749\) 363.573 0.485412
\(750\) 1043.71 397.446i 1.39161 0.529928i
\(751\) 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
\(753\) −792.864 −1.05294
\(754\) −104.789 275.179i −0.138977 0.364958i
\(755\) 656.053i 0.868944i
\(756\) 292.967 260.968i 0.387522 0.345196i
\(757\) 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
\(759\) 54.2401i 0.0714626i
\(760\) −80.0722 + 154.086i −0.105358 + 0.202744i
\(761\) −512.227 −0.673098 −0.336549 0.941666i \(-0.609260\pi\)
−0.336549 + 0.941666i \(0.609260\pi\)
\(762\) −663.318 1741.89i −0.870496 2.28595i
\(763\) 12.3672i 0.0162086i
\(764\) 1011.61 + 1135.65i 1.32409 + 1.48645i
\(765\) 316.959 0.414326
\(766\) −245.032 + 93.3089i −0.319886 + 0.121813i
\(767\) 296.633i 0.386745i
\(768\) 260.576 1108.86i 0.339292 1.44382i
\(769\) 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
\(771\) 1064.61i 1.38081i
\(772\) 790.583 704.234i 1.02407 0.912220i
\(773\) 669.217 0.865740 0.432870 0.901456i \(-0.357501\pi\)
0.432870 + 0.901456i \(0.357501\pi\)
\(774\) 646.106 246.039i 0.834763 0.317880i
\(775\) 8.75319i 0.0112944i
\(776\) −822.776 427.564i −1.06028 0.550985i
\(777\) −88.0270 −0.113291
\(778\) 14.5879 + 38.3083i 0.0187505 + 0.0492394i
\(779\) 302.402i 0.388193i