Properties

Label 60.3.f.b.19.5
Level $60$
Weight $3$
Character 60.19
Analytic conductor $1.635$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.63488158616\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.389136420864.4
Defining polynomial: \(x^{8} + 5 x^{6} + 24 x^{4} + 80 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.5
Root \(0.656712 - 1.88911i\) of defining polynomial
Character \(\chi\) \(=\) 60.19
Dual form 60.3.f.b.19.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.656712 - 1.88911i) q^{2} +1.73205 q^{3} +(-3.13746 - 2.48120i) q^{4} +(-3.27492 - 3.77822i) q^{5} +(1.13746 - 3.27203i) q^{6} +9.55505 q^{7} +(-6.74766 + 4.29756i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(0.656712 - 1.88911i) q^{2} +1.73205 q^{3} +(-3.13746 - 2.48120i) q^{4} +(-3.27492 - 3.77822i) q^{5} +(1.13746 - 3.27203i) q^{6} +9.55505 q^{7} +(-6.74766 + 4.29756i) q^{8} +3.00000 q^{9} +(-9.28814 + 3.70547i) q^{10} +9.92480i q^{11} +(-5.43424 - 4.29756i) q^{12} +7.55643i q^{13} +(6.27492 - 18.0505i) q^{14} +(-5.67232 - 6.54406i) q^{15} +(3.68729 + 15.5693i) q^{16} -17.1903i q^{17} +(1.97014 - 5.66732i) q^{18} +26.1762i q^{19} +(0.900407 + 19.9797i) q^{20} +16.5498 q^{21} +(18.7490 + 6.51774i) q^{22} -1.67451 q^{23} +(-11.6873 + 7.44360i) q^{24} +(-3.54983 + 24.7467i) q^{25} +(14.2749 + 4.96240i) q^{26} +5.19615 q^{27} +(-29.9786 - 23.7080i) q^{28} -0.350497 q^{29} +(-16.0875 + 6.41807i) q^{30} -46.0258i q^{31} +(31.8336 + 3.25887i) q^{32} +17.1903i q^{33} +(-32.4743 - 11.2890i) q^{34} +(-31.2920 - 36.1010i) q^{35} +(-9.41238 - 7.44360i) q^{36} -22.6693i q^{37} +(49.4498 + 17.1903i) q^{38} +13.0881i q^{39} +(38.3352 + 11.4200i) q^{40} -77.2990 q^{41} +(10.8685 - 31.2644i) q^{42} -41.7994 q^{43} +(24.6254 - 31.1386i) q^{44} +(-9.82475 - 11.3346i) q^{45} +(-1.09967 + 3.16332i) q^{46} +14.0866 q^{47} +(6.38658 + 26.9669i) q^{48} +42.2990 q^{49} +(44.4180 + 22.9575i) q^{50} -29.7744i q^{51} +(18.7490 - 23.7080i) q^{52} -22.6693i q^{53} +(3.41238 - 9.81609i) q^{54} +(37.4980 - 32.5029i) q^{55} +(-64.4743 + 41.0634i) q^{56} +45.3386i q^{57} +(-0.230175 + 0.662126i) q^{58} +94.7802i q^{59} +(1.55955 + 34.6059i) q^{60} +38.0000 q^{61} +(-86.9478 - 30.2257i) q^{62} +28.6652 q^{63} +(27.0619 - 57.9970i) q^{64} +(28.5498 - 24.7467i) q^{65} +(32.4743 + 11.2890i) q^{66} -29.8477 q^{67} +(-42.6525 + 53.9337i) q^{68} -2.90033 q^{69} +(-88.7486 + 35.4060i) q^{70} +7.19630i q^{71} +(-20.2430 + 12.8927i) q^{72} -34.3805i q^{73} +(-42.8248 - 14.8872i) q^{74} +(-6.14849 + 42.8625i) q^{75} +(64.9485 - 82.1269i) q^{76} +94.8320i q^{77} +(24.7249 + 8.59513i) q^{78} +46.0258i q^{79} +(46.7487 - 64.9196i) q^{80} +9.00000 q^{81} +(-50.7632 + 146.026i) q^{82} +24.1336 q^{83} +(-51.9244 - 41.0634i) q^{84} +(-64.9485 + 56.2967i) q^{85} +(-27.4502 + 78.9636i) q^{86} -0.607078 q^{87} +(-42.6525 - 66.9692i) q^{88} +100.199 q^{89} +(-27.8644 + 11.1164i) q^{90} +72.2021i q^{91} +(5.25370 + 4.15479i) q^{92} -79.7191i q^{93} +(9.25083 - 26.6111i) q^{94} +(98.8995 - 85.7250i) q^{95} +(55.1375 + 5.64452i) q^{96} -131.861i q^{97} +(27.7783 - 79.9074i) q^{98} +29.7744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 10q^{4} + 4q^{5} - 6q^{6} + 24q^{9} + O(q^{10}) \) \( 8q - 10q^{4} + 4q^{5} - 6q^{6} + 24q^{9} - 42q^{10} + 20q^{14} - 46q^{16} + 52q^{20} + 72q^{21} - 18q^{24} + 32q^{25} + 84q^{26} - 184q^{29} - 60q^{30} + 12q^{34} - 30q^{36} - 6q^{40} - 256q^{41} + 348q^{44} + 12q^{45} + 112q^{46} - 24q^{49} + 72q^{50} - 18q^{54} - 244q^{56} + 6q^{60} + 304q^{61} - 10q^{64} + 168q^{65} - 12q^{66} - 144q^{69} - 104q^{70} - 252q^{74} - 24q^{76} - 308q^{80} + 72q^{81} - 204q^{84} + 24q^{85} - 280q^{86} + 560q^{89} - 126q^{90} + 376q^{94} + 426q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.656712 1.88911i 0.328356 0.944554i
\(3\) 1.73205 0.577350
\(4\) −3.13746 2.48120i −0.784365 0.620300i
\(5\) −3.27492 3.77822i −0.654983 0.755643i
\(6\) 1.13746 3.27203i 0.189576 0.545339i
\(7\) 9.55505 1.36501 0.682504 0.730882i \(-0.260891\pi\)
0.682504 + 0.730882i \(0.260891\pi\)
\(8\) −6.74766 + 4.29756i −0.843458 + 0.537196i
\(9\) 3.00000 0.333333
\(10\) −9.28814 + 3.70547i −0.928814 + 0.370547i
\(11\) 9.92480i 0.902255i 0.892460 + 0.451127i \(0.148978\pi\)
−0.892460 + 0.451127i \(0.851022\pi\)
\(12\) −5.43424 4.29756i −0.452853 0.358130i
\(13\) 7.55643i 0.581264i 0.956835 + 0.290632i \(0.0938655\pi\)
−0.956835 + 0.290632i \(0.906134\pi\)
\(14\) 6.27492 18.0505i 0.448208 1.28932i
\(15\) −5.67232 6.54406i −0.378155 0.436271i
\(16\) 3.68729 + 15.5693i 0.230456 + 0.973083i
\(17\) 17.1903i 1.01119i −0.862770 0.505596i \(-0.831273\pi\)
0.862770 0.505596i \(-0.168727\pi\)
\(18\) 1.97014 5.66732i 0.109452 0.314851i
\(19\) 26.1762i 1.37770i 0.724905 + 0.688849i \(0.241884\pi\)
−0.724905 + 0.688849i \(0.758116\pi\)
\(20\) 0.900407 + 19.9797i 0.0450204 + 0.998986i
\(21\) 16.5498 0.788087
\(22\) 18.7490 + 6.51774i 0.852228 + 0.296261i
\(23\) −1.67451 −0.0728047 −0.0364023 0.999337i \(-0.511590\pi\)
−0.0364023 + 0.999337i \(0.511590\pi\)
\(24\) −11.6873 + 7.44360i −0.486971 + 0.310150i
\(25\) −3.54983 + 24.7467i −0.141993 + 0.989868i
\(26\) 14.2749 + 4.96240i 0.549035 + 0.190862i
\(27\) 5.19615 0.192450
\(28\) −29.9786 23.7080i −1.07066 0.846714i
\(29\) −0.350497 −0.0120861 −0.00604305 0.999982i \(-0.501924\pi\)
−0.00604305 + 0.999982i \(0.501924\pi\)
\(30\) −16.0875 + 6.41807i −0.536251 + 0.213936i
\(31\) 46.0258i 1.48470i −0.670010 0.742352i \(-0.733710\pi\)
0.670010 0.742352i \(-0.266290\pi\)
\(32\) 31.8336 + 3.25887i 0.994801 + 0.101840i
\(33\) 17.1903i 0.520917i
\(34\) −32.4743 11.2890i −0.955125 0.332031i
\(35\) −31.2920 36.1010i −0.894057 1.03146i
\(36\) −9.41238 7.44360i −0.261455 0.206767i
\(37\) 22.6693i 0.612684i −0.951922 0.306342i \(-0.900895\pi\)
0.951922 0.306342i \(-0.0991051\pi\)
\(38\) 49.4498 + 17.1903i 1.30131 + 0.452375i
\(39\) 13.0881i 0.335593i
\(40\) 38.3352 + 11.4200i 0.958379 + 0.285499i
\(41\) −77.2990 −1.88534 −0.942671 0.333724i \(-0.891695\pi\)
−0.942671 + 0.333724i \(0.891695\pi\)
\(42\) 10.8685 31.2644i 0.258773 0.744391i
\(43\) −41.7994 −0.972079 −0.486039 0.873937i \(-0.661559\pi\)
−0.486039 + 0.873937i \(0.661559\pi\)
\(44\) 24.6254 31.1386i 0.559668 0.707697i
\(45\) −9.82475 11.3346i −0.218328 0.251881i
\(46\) −1.09967 + 3.16332i −0.0239058 + 0.0687679i
\(47\) 14.0866 0.299715 0.149857 0.988708i \(-0.452119\pi\)
0.149857 + 0.988708i \(0.452119\pi\)
\(48\) 6.38658 + 26.9669i 0.133054 + 0.561810i
\(49\) 42.2990 0.863245
\(50\) 44.4180 + 22.9575i 0.888359 + 0.459149i
\(51\) 29.7744i 0.583812i
\(52\) 18.7490 23.7080i 0.360558 0.455923i
\(53\) 22.6693i 0.427723i −0.976864 0.213861i \(-0.931396\pi\)
0.976864 0.213861i \(-0.0686041\pi\)
\(54\) 3.41238 9.81609i 0.0631921 0.181780i
\(55\) 37.4980 32.5029i 0.681783 0.590962i
\(56\) −64.4743 + 41.0634i −1.15133 + 0.733276i
\(57\) 45.3386i 0.795414i
\(58\) −0.230175 + 0.662126i −0.00396854 + 0.0114160i
\(59\) 94.7802i 1.60644i 0.595680 + 0.803222i \(0.296883\pi\)
−0.595680 + 0.803222i \(0.703117\pi\)
\(60\) 1.55955 + 34.6059i 0.0259925 + 0.576765i
\(61\) 38.0000 0.622951 0.311475 0.950254i \(-0.399177\pi\)
0.311475 + 0.950254i \(0.399177\pi\)
\(62\) −86.9478 30.2257i −1.40238 0.487512i
\(63\) 28.6652 0.455002
\(64\) 27.0619 57.9970i 0.422842 0.906203i
\(65\) 28.5498 24.7467i 0.439228 0.380718i
\(66\) 32.4743 + 11.2890i 0.492034 + 0.171046i
\(67\) −29.8477 −0.445488 −0.222744 0.974877i \(-0.571501\pi\)
−0.222744 + 0.974877i \(0.571501\pi\)
\(68\) −42.6525 + 53.9337i −0.627242 + 0.793143i
\(69\) −2.90033 −0.0420338
\(70\) −88.7486 + 35.4060i −1.26784 + 0.505800i
\(71\) 7.19630i 0.101356i 0.998715 + 0.0506782i \(0.0161383\pi\)
−0.998715 + 0.0506782i \(0.983862\pi\)
\(72\) −20.2430 + 12.8927i −0.281153 + 0.179065i
\(73\) 34.3805i 0.470966i −0.971878 0.235483i \(-0.924333\pi\)
0.971878 0.235483i \(-0.0756672\pi\)
\(74\) −42.8248 14.8872i −0.578713 0.201178i
\(75\) −6.14849 + 42.8625i −0.0819799 + 0.571500i
\(76\) 64.9485 82.1269i 0.854586 1.08062i
\(77\) 94.8320i 1.23158i
\(78\) 24.7249 + 8.59513i 0.316986 + 0.110194i
\(79\) 46.0258i 0.582606i 0.956631 + 0.291303i \(0.0940887\pi\)
−0.956631 + 0.291303i \(0.905911\pi\)
\(80\) 46.7487 64.9196i 0.584359 0.811495i
\(81\) 9.00000 0.111111
\(82\) −50.7632 + 146.026i −0.619063 + 1.78081i
\(83\) 24.1336 0.290767 0.145383 0.989375i \(-0.453558\pi\)
0.145383 + 0.989375i \(0.453558\pi\)
\(84\) −51.9244 41.0634i −0.618148 0.488851i
\(85\) −64.9485 + 56.2967i −0.764100 + 0.662314i
\(86\) −27.4502 + 78.9636i −0.319188 + 0.918181i
\(87\) −0.607078 −0.00697791
\(88\) −42.6525 66.9692i −0.484687 0.761014i
\(89\) 100.199 1.12584 0.562918 0.826513i \(-0.309679\pi\)
0.562918 + 0.826513i \(0.309679\pi\)
\(90\) −27.8644 + 11.1164i −0.309605 + 0.123516i
\(91\) 72.2021i 0.793430i
\(92\) 5.25370 + 4.15479i 0.0571054 + 0.0451607i
\(93\) 79.7191i 0.857195i
\(94\) 9.25083 26.6111i 0.0984131 0.283097i
\(95\) 98.8995 85.7250i 1.04105 0.902369i
\(96\) 55.1375 + 5.64452i 0.574349 + 0.0587971i
\(97\) 131.861i 1.35939i −0.733494 0.679696i \(-0.762112\pi\)
0.733494 0.679696i \(-0.237888\pi\)
\(98\) 27.7783 79.9074i 0.283452 0.815382i
\(99\) 29.7744i 0.300752i
\(100\) 72.5389 68.8339i 0.725389 0.688339i
\(101\) 29.4502 0.291586 0.145793 0.989315i \(-0.453427\pi\)
0.145793 + 0.989315i \(0.453427\pi\)
\(102\) −56.2471 19.5532i −0.551442 0.191698i
\(103\) 143.786 1.39598 0.697991 0.716107i \(-0.254078\pi\)
0.697991 + 0.716107i \(0.254078\pi\)
\(104\) −32.4743 50.9882i −0.312252 0.490272i
\(105\) −54.1993 62.5289i −0.516184 0.595513i
\(106\) −42.8248 14.8872i −0.404007 0.140445i
\(107\) −35.1014 −0.328050 −0.164025 0.986456i \(-0.552448\pi\)
−0.164025 + 0.986456i \(0.552448\pi\)
\(108\) −16.3027 12.8927i −0.150951 0.119377i
\(109\) −151.498 −1.38989 −0.694947 0.719061i \(-0.744572\pi\)
−0.694947 + 0.719061i \(0.744572\pi\)
\(110\) −36.7761 92.1829i −0.334328 0.838026i
\(111\) 39.2644i 0.353733i
\(112\) 35.2323 + 148.766i 0.314574 + 1.32827i
\(113\) 32.3031i 0.285868i 0.989732 + 0.142934i \(0.0456537\pi\)
−0.989732 + 0.142934i \(0.954346\pi\)
\(114\) 85.6495 + 29.7744i 0.751311 + 0.261179i
\(115\) 5.48387 + 6.32665i 0.0476858 + 0.0550143i
\(116\) 1.09967 + 0.869652i 0.00947990 + 0.00749700i
\(117\) 22.6693i 0.193755i
\(118\) 179.050 + 62.2433i 1.51737 + 0.527486i
\(119\) 164.254i 1.38028i
\(120\) 66.3984 + 19.7799i 0.553320 + 0.164833i
\(121\) 22.4983 0.185937
\(122\) 24.9551 71.7861i 0.204550 0.588411i
\(123\) −133.886 −1.08850
\(124\) −114.199 + 144.404i −0.920962 + 1.16455i
\(125\) 105.124 67.6313i 0.840990 0.541051i
\(126\) 18.8248 54.1516i 0.149403 0.429774i
\(127\) −192.053 −1.51223 −0.756116 0.654438i \(-0.772905\pi\)
−0.756116 + 0.654438i \(0.772905\pi\)
\(128\) −91.7908 89.2102i −0.717115 0.696954i
\(129\) −72.3987 −0.561230
\(130\) −28.0002 70.1852i −0.215386 0.539886i
\(131\) 42.4277i 0.323876i 0.986801 + 0.161938i \(0.0517744\pi\)
−0.986801 + 0.161938i \(0.948226\pi\)
\(132\) 42.6525 53.9337i 0.323125 0.408589i
\(133\) 250.115i 1.88057i
\(134\) −19.6013 + 56.3855i −0.146279 + 0.420787i
\(135\) −17.0170 19.6322i −0.126052 0.145424i
\(136\) 73.8762 + 115.994i 0.543208 + 0.852897i
\(137\) 206.854i 1.50988i 0.655791 + 0.754942i \(0.272335\pi\)
−0.655791 + 0.754942i \(0.727665\pi\)
\(138\) −1.90468 + 5.47904i −0.0138020 + 0.0397032i
\(139\) 46.0258i 0.331121i −0.986200 0.165561i \(-0.947057\pi\)
0.986200 0.165561i \(-0.0529433\pi\)
\(140\) 8.60344 + 190.907i 0.0614531 + 1.36362i
\(141\) 24.3987 0.173040
\(142\) 13.5946 + 4.72590i 0.0957366 + 0.0332810i
\(143\) −74.9961 −0.524448
\(144\) 11.0619 + 46.7080i 0.0768186 + 0.324361i
\(145\) 1.14785 + 1.32425i 0.00791619 + 0.00913277i
\(146\) −64.9485 22.5781i −0.444853 0.154645i
\(147\) 73.2640 0.498395
\(148\) −56.2471 + 71.1240i −0.380048 + 0.480567i
\(149\) 11.6495 0.0781846 0.0390923 0.999236i \(-0.487553\pi\)
0.0390923 + 0.999236i \(0.487553\pi\)
\(150\) 76.9342 + 39.7635i 0.512894 + 0.265090i
\(151\) 125.424i 0.830624i −0.909679 0.415312i \(-0.863672\pi\)
0.909679 0.415312i \(-0.136328\pi\)
\(152\) −112.494 176.628i −0.740093 1.16203i
\(153\) 51.5708i 0.337064i
\(154\) 179.148 + 62.2773i 1.16330 + 0.404398i
\(155\) −173.896 + 150.731i −1.12191 + 0.972457i
\(156\) 32.4743 41.0634i 0.208168 0.263227i
\(157\) 197.220i 1.25618i −0.778140 0.628090i \(-0.783837\pi\)
0.778140 0.628090i \(-0.216163\pi\)
\(158\) 86.9478 + 30.2257i 0.550303 + 0.191302i
\(159\) 39.2644i 0.246946i
\(160\) −91.9398 130.947i −0.574624 0.818418i
\(161\) −16.0000 −0.0993789
\(162\) 5.91041 17.0020i 0.0364840 0.104950i
\(163\) −18.4196 −0.113004 −0.0565018 0.998402i \(-0.517995\pi\)
−0.0565018 + 0.998402i \(0.517995\pi\)
\(164\) 242.522 + 191.794i 1.47880 + 1.16948i
\(165\) 64.9485 56.2967i 0.393627 0.341192i
\(166\) 15.8488 45.5910i 0.0954749 0.274645i
\(167\) 92.8920 0.556240 0.278120 0.960546i \(-0.410289\pi\)
0.278120 + 0.960546i \(0.410289\pi\)
\(168\) −111.673 + 71.1240i −0.664718 + 0.423357i
\(169\) 111.900 0.662132
\(170\) 63.6980 + 159.665i 0.374694 + 0.939209i
\(171\) 78.5287i 0.459232i
\(172\) 131.144 + 103.713i 0.762464 + 0.602981i
\(173\) 117.501i 0.679198i −0.940570 0.339599i \(-0.889709\pi\)
0.940570 0.339599i \(-0.110291\pi\)
\(174\) −0.398675 + 1.14684i −0.00229124 + 0.00659101i
\(175\) −33.9189 + 236.456i −0.193822 + 1.35118i
\(176\) −154.522 + 36.5956i −0.877968 + 0.207930i
\(177\) 164.164i 0.927481i
\(178\) 65.8021 189.287i 0.369675 1.06341i
\(179\) 231.988i 1.29602i −0.761631 0.648011i \(-0.775601\pi\)
0.761631 0.648011i \(-0.224399\pi\)
\(180\) 2.70122 + 59.9392i 0.0150068 + 0.332995i
\(181\) −218.096 −1.20495 −0.602476 0.798137i \(-0.705819\pi\)
−0.602476 + 0.798137i \(0.705819\pi\)
\(182\) 136.398 + 47.4160i 0.749437 + 0.260527i
\(183\) 65.8179 0.359661
\(184\) 11.2990 7.19630i 0.0614076 0.0391103i
\(185\) −85.6495 + 74.2401i −0.462970 + 0.401298i
\(186\) −150.598 52.3525i −0.809667 0.281465i
\(187\) 170.610 0.912352
\(188\) −44.1961 34.9516i −0.235085 0.185913i
\(189\) 49.6495 0.262696
\(190\) −96.9954 243.129i −0.510502 1.27962i
\(191\) 137.208i 0.718366i 0.933267 + 0.359183i \(0.116945\pi\)
−0.933267 + 0.359183i \(0.883055\pi\)
\(192\) 46.8725 100.454i 0.244128 0.523197i
\(193\) 37.0290i 0.191860i −0.995388 0.0959301i \(-0.969417\pi\)
0.995388 0.0959301i \(-0.0305825\pi\)
\(194\) −249.100 86.5947i −1.28402 0.446364i
\(195\) 49.4498 42.8625i 0.253589 0.219808i
\(196\) −132.711 104.952i −0.677099 0.535471i
\(197\) 194.572i 0.987674i −0.869554 0.493837i \(-0.835594\pi\)
0.869554 0.493837i \(-0.164406\pi\)
\(198\) 56.2471 + 19.5532i 0.284076 + 0.0987536i
\(199\) 176.037i 0.884610i −0.896865 0.442305i \(-0.854161\pi\)
0.896865 0.442305i \(-0.145839\pi\)
\(200\) −82.3974 182.238i −0.411987 0.911190i
\(201\) −51.6977 −0.257202
\(202\) 19.3403 55.6345i 0.0957440 0.275419i
\(203\) −3.34901 −0.0164976
\(204\) −73.8762 + 93.4159i −0.362138 + 0.457921i
\(205\) 253.148 + 292.052i 1.23487 + 1.42465i
\(206\) 94.4261 271.628i 0.458379 1.31858i
\(207\) −5.02352 −0.0242682
\(208\) −117.649 + 27.8628i −0.565618 + 0.133956i
\(209\) −259.794 −1.24303
\(210\) −153.717 + 61.3250i −0.731986 + 0.292024i
\(211\) 20.7193i 0.0981955i 0.998794 + 0.0490978i \(0.0156346\pi\)
−0.998794 + 0.0490978i \(0.984365\pi\)
\(212\) −56.2471 + 71.1240i −0.265316 + 0.335490i
\(213\) 12.4644i 0.0585181i
\(214\) −23.0515 + 66.3103i −0.107717 + 0.309861i
\(215\) 136.890 + 157.927i 0.636696 + 0.734545i
\(216\) −35.0619 + 22.3308i −0.162324 + 0.103383i
\(217\) 439.779i 2.02663i
\(218\) −99.4908 + 286.197i −0.456380 + 1.31283i
\(219\) 59.5488i 0.271912i
\(220\) −198.295 + 8.93636i −0.901340 + 0.0406198i
\(221\) 129.897 0.587769
\(222\) −74.1746 25.7854i −0.334120 0.116150i
\(223\) 97.0265 0.435096 0.217548 0.976050i \(-0.430194\pi\)
0.217548 + 0.976050i \(0.430194\pi\)
\(224\) 304.172 + 31.1386i 1.35791 + 0.139012i
\(225\) −10.6495 + 74.2401i −0.0473311 + 0.329956i
\(226\) 61.0241 + 21.2138i 0.270018 + 0.0938666i
\(227\) 407.256 1.79408 0.897040 0.441948i \(-0.145713\pi\)
0.897040 + 0.441948i \(0.145713\pi\)
\(228\) 112.494 142.248i 0.493395 0.623895i
\(229\) −7.89702 −0.0344848 −0.0172424 0.999851i \(-0.505489\pi\)
−0.0172424 + 0.999851i \(0.505489\pi\)
\(230\) 15.5530 6.20484i 0.0676220 0.0269776i
\(231\) 164.254i 0.711055i
\(232\) 2.36503 1.50628i 0.0101941 0.00649260i
\(233\) 28.1483i 0.120808i 0.998174 + 0.0604042i \(0.0192390\pi\)
−0.998174 + 0.0604042i \(0.980761\pi\)
\(234\) 42.8248 + 14.8872i 0.183012 + 0.0636205i
\(235\) −46.1324 53.2222i −0.196308 0.226477i
\(236\) 235.169 297.369i 0.996477 1.26004i
\(237\) 79.7191i 0.336368i
\(238\) −310.293 107.867i −1.30375 0.453225i
\(239\) 296.005i 1.23851i 0.785189 + 0.619257i \(0.212566\pi\)
−0.785189 + 0.619257i \(0.787434\pi\)
\(240\) 80.9711 112.444i 0.337380 0.468517i
\(241\) 465.794 1.93276 0.966378 0.257127i \(-0.0827758\pi\)
0.966378 + 0.257127i \(0.0827758\pi\)
\(242\) 14.7749 42.5018i 0.0610534 0.175627i
\(243\) 15.5885 0.0641500
\(244\) −119.223 94.2856i −0.488621 0.386416i
\(245\) −138.526 159.815i −0.565411 0.652305i
\(246\) −87.9244 + 252.925i −0.357416 + 1.02815i
\(247\) −197.799 −0.800806
\(248\) 197.799 + 310.567i 0.797577 + 1.25229i
\(249\) 41.8007 0.167874
\(250\) −58.7268 243.004i −0.234907 0.972018i
\(251\) 141.676i 0.564445i −0.959349 0.282223i \(-0.908928\pi\)
0.959349 0.282223i \(-0.0910716\pi\)
\(252\) −89.9357 71.1240i −0.356888 0.282238i
\(253\) 16.6191i 0.0656883i
\(254\) −126.124 + 362.810i −0.496550 + 1.42838i
\(255\) −112.494 + 97.5087i −0.441153 + 0.382387i
\(256\) −228.808 + 114.817i −0.893780 + 0.448505i
\(257\) 41.7549i 0.162470i 0.996695 + 0.0812352i \(0.0258865\pi\)
−0.996695 + 0.0812352i \(0.974113\pi\)
\(258\) −47.5451 + 136.769i −0.184283 + 0.530112i
\(259\) 216.606i 0.836318i
\(260\) −150.975 + 6.80387i −0.580675 + 0.0261687i
\(261\) −1.05149 −0.00402870
\(262\) 80.1505 + 27.8628i 0.305918 + 0.106346i
\(263\) −203.283 −0.772939 −0.386469 0.922302i \(-0.626306\pi\)
−0.386469 + 0.922302i \(0.626306\pi\)
\(264\) −73.8762 115.994i −0.279834 0.439371i
\(265\) −85.6495 + 74.2401i −0.323206 + 0.280151i
\(266\) 472.495 + 164.254i 1.77630 + 0.617495i
\(267\) 173.550 0.650001
\(268\) 93.6458 + 74.0580i 0.349425 + 0.276336i
\(269\) −244.048 −0.907242 −0.453621 0.891195i \(-0.649868\pi\)
−0.453621 + 0.891195i \(0.649868\pi\)
\(270\) −48.2626 + 19.2542i −0.178750 + 0.0713119i
\(271\) 466.585i 1.72172i 0.508845 + 0.860858i \(0.330073\pi\)
−0.508845 + 0.860858i \(0.669927\pi\)
\(272\) 267.641 63.3855i 0.983973 0.233035i
\(273\) 125.058i 0.458087i
\(274\) 390.770 + 135.844i 1.42617 + 0.495780i
\(275\) −245.606 35.2314i −0.893113 0.128114i
\(276\) 9.09967 + 7.19630i 0.0329698 + 0.0260736i
\(277\) 494.181i 1.78405i 0.451990 + 0.892023i \(0.350714\pi\)
−0.451990 + 0.892023i \(0.649286\pi\)
\(278\) −86.9478 30.2257i −0.312762 0.108726i
\(279\) 138.078i 0.494902i
\(280\) 366.294 + 109.118i 1.30819 + 0.389708i
\(281\) −43.4020 −0.154455 −0.0772277 0.997013i \(-0.524607\pi\)
−0.0772277 + 0.997013i \(0.524607\pi\)
\(282\) 16.0229 46.0917i 0.0568188 0.163446i
\(283\) −310.785 −1.09818 −0.549090 0.835763i \(-0.685026\pi\)
−0.549090 + 0.835763i \(0.685026\pi\)
\(284\) 17.8555 22.5781i 0.0628714 0.0795003i
\(285\) 171.299 148.480i 0.601049 0.520983i
\(286\) −49.2508 + 141.676i −0.172206 + 0.495370i
\(287\) −738.596 −2.57351
\(288\) 95.5009 + 9.77660i 0.331600 + 0.0339465i
\(289\) −6.50497 −0.0225085
\(290\) 3.25546 1.29876i 0.0112257 0.00447847i
\(291\) 228.390i 0.784845i
\(292\) −85.3049 + 107.867i −0.292140 + 0.369409i
\(293\) 245.207i 0.836886i −0.908243 0.418443i \(-0.862576\pi\)
0.908243 0.418443i \(-0.137424\pi\)
\(294\) 48.1134 138.404i 0.163651 0.470761i
\(295\) 358.100 310.397i 1.21390 1.05219i
\(296\) 97.4228 + 152.965i 0.329131 + 0.516773i
\(297\) 51.5708i 0.173639i
\(298\) 7.65037 22.0072i 0.0256724 0.0738496i
\(299\) 12.6533i 0.0423187i
\(300\) 125.641 119.224i 0.418804 0.397413i
\(301\) −399.395 −1.32689
\(302\) −236.940 82.3676i −0.784569 0.272740i
\(303\) 51.0092 0.168347
\(304\) −407.547 + 96.5195i −1.34061 + 0.317498i
\(305\) −124.447 143.572i −0.408022 0.470729i
\(306\) −97.4228 33.8671i −0.318375 0.110677i
\(307\) 337.514 1.09939 0.549697 0.835364i \(-0.314743\pi\)
0.549697 + 0.835364i \(0.314743\pi\)
\(308\) 235.297 297.531i 0.763952 0.966011i
\(309\) 249.045 0.805970
\(310\) 170.548 + 427.494i 0.550153 + 1.37901i
\(311\) 427.756i 1.37542i −0.725986 0.687710i \(-0.758616\pi\)
0.725986 0.687710i \(-0.241384\pi\)
\(312\) −56.2471 88.3142i −0.180279 0.283058i
\(313\) 83.8739i 0.267968i 0.990984 + 0.133984i \(0.0427770\pi\)
−0.990984 + 0.133984i \(0.957223\pi\)
\(314\) −372.571 129.517i −1.18653 0.412475i
\(315\) −93.8760 108.303i −0.298019 0.343820i
\(316\) 114.199 144.404i 0.361390 0.456975i
\(317\) 112.204i 0.353957i 0.984215 + 0.176978i \(0.0566323\pi\)
−0.984215 + 0.176978i \(0.943368\pi\)
\(318\) −74.1746 25.7854i −0.233254 0.0810861i
\(319\) 3.47861i 0.0109047i
\(320\) −307.751 + 87.6898i −0.961721 + 0.274031i
\(321\) −60.7974 −0.189400
\(322\) −10.5074 + 30.2257i −0.0326317 + 0.0938687i
\(323\) 449.976 1.39312
\(324\) −28.2371 22.3308i −0.0871516 0.0689222i
\(325\) −186.997 26.8241i −0.575374 0.0825356i
\(326\) −12.0964 + 34.7966i −0.0371054 + 0.106738i
\(327\) −262.403 −0.802455
\(328\) 521.588 332.197i 1.59021 1.01280i
\(329\) 134.598 0.409113
\(330\) −63.6980 159.665i −0.193024 0.483835i
\(331\) 132.621i 0.400666i −0.979728 0.200333i \(-0.935798\pi\)
0.979728 0.200333i \(-0.0642025\pi\)
\(332\) −75.7182 59.8803i −0.228067 0.180362i
\(333\) 68.0079i 0.204228i
\(334\) 61.0033 175.483i 0.182645 0.525398i
\(335\) 97.7487 + 112.771i 0.291787 + 0.336630i
\(336\) 61.0241 + 257.670i 0.181619 + 0.766874i
\(337\) 20.7739i 0.0616437i 0.999525 + 0.0308219i \(0.00981246\pi\)
−0.999525 + 0.0308219i \(0.990188\pi\)
\(338\) 73.4863 211.392i 0.217415 0.625420i
\(339\) 55.9506i 0.165046i
\(340\) 343.457 15.4782i 1.01017 0.0455242i
\(341\) 456.797 1.33958
\(342\) 148.349 + 51.5708i 0.433770 + 0.150792i
\(343\) −64.0283 −0.186672
\(344\) 282.048 179.636i 0.819907 0.522196i
\(345\) 9.49834 + 10.9581i 0.0275314 + 0.0317625i
\(346\) −221.973 77.1645i −0.641539 0.223019i
\(347\) 8.89616 0.0256374 0.0128187 0.999918i \(-0.495920\pi\)
0.0128187 + 0.999918i \(0.495920\pi\)
\(348\) 1.90468 + 1.50628i 0.00547323 + 0.00432840i
\(349\) 19.4020 0.0555931 0.0277965 0.999614i \(-0.491151\pi\)
0.0277965 + 0.999614i \(0.491151\pi\)
\(350\) 424.416 + 219.360i 1.21262 + 0.626742i
\(351\) 39.2644i 0.111864i
\(352\) −32.3436 + 315.942i −0.0918853 + 0.897564i
\(353\) 80.2902i 0.227451i 0.993512 + 0.113726i \(0.0362784\pi\)
−0.993512 + 0.113726i \(0.963722\pi\)
\(354\) 310.124 + 107.809i 0.876056 + 0.304544i
\(355\) 27.1892 23.5673i 0.0765892 0.0663867i
\(356\) −314.371 248.615i −0.883065 0.698356i
\(357\) 284.496i 0.796907i
\(358\) −438.251 152.349i −1.22416 0.425557i
\(359\) 314.115i 0.874972i 0.899225 + 0.437486i \(0.144131\pi\)
−0.899225 + 0.437486i \(0.855869\pi\)
\(360\) 115.005 + 34.2599i 0.319460 + 0.0951663i
\(361\) −324.196 −0.898050
\(362\) −143.227 + 412.008i −0.395653 + 1.13814i
\(363\) 38.9683 0.107351
\(364\) 179.148 226.531i 0.492164 0.622338i
\(365\) −129.897 + 112.593i −0.355882 + 0.308475i
\(366\) 43.2234 124.337i 0.118097 0.339719i
\(367\) −476.800 −1.29918 −0.649592 0.760283i \(-0.725060\pi\)
−0.649592 + 0.760283i \(0.725060\pi\)
\(368\) −6.17440 26.0709i −0.0167783 0.0708450i
\(369\) −231.897 −0.628447
\(370\) 84.0005 + 210.556i 0.227028 + 0.569069i
\(371\) 216.606i 0.583844i
\(372\) −197.799 + 250.115i −0.531718 + 0.672353i
\(373\) 86.1333i 0.230920i −0.993312 0.115460i \(-0.963166\pi\)
0.993312 0.115460i \(-0.0368343\pi\)
\(374\) 112.042 322.300i 0.299576 0.861766i
\(375\) 182.080 117.141i 0.485546 0.312376i
\(376\) −95.0515 + 60.5380i −0.252797 + 0.161005i
\(377\) 2.64850i 0.00702521i
\(378\) 32.6054 93.7933i 0.0862577 0.248130i
\(379\) 638.035i 1.68347i 0.539891 + 0.841735i \(0.318466\pi\)
−0.539891 + 0.841735i \(0.681534\pi\)
\(380\) −522.994 + 23.5693i −1.37630 + 0.0620244i
\(381\) −332.646 −0.873087
\(382\) 259.201 + 90.1061i 0.678535 + 0.235880i
\(383\) 216.742 0.565907 0.282953 0.959134i \(-0.408686\pi\)
0.282953 + 0.959134i \(0.408686\pi\)
\(384\) −158.986 154.517i −0.414027 0.402387i
\(385\) 358.296 310.567i 0.930638 0.806667i
\(386\) −69.9518 24.3174i −0.181222 0.0629985i
\(387\) −125.398 −0.324026
\(388\) −327.174 + 413.708i −0.843231 + 1.06626i
\(389\) 476.640 1.22529 0.612647 0.790356i \(-0.290105\pi\)
0.612647 + 0.790356i \(0.290105\pi\)
\(390\) −48.4977 121.564i −0.124353 0.311703i
\(391\) 28.7852i 0.0736195i
\(392\) −285.419 + 181.783i −0.728111 + 0.463731i
\(393\) 73.4869i 0.186990i
\(394\) −367.567 127.778i −0.932912 0.324309i
\(395\) 173.896 150.731i 0.440242 0.381597i
\(396\) 73.8762 93.4159i 0.186556 0.235899i
\(397\) 43.0792i 0.108512i 0.998527 + 0.0542559i \(0.0172787\pi\)
−0.998527 + 0.0542559i \(0.982721\pi\)
\(398\) −332.554 115.606i −0.835562 0.290467i
\(399\) 433.213i 1.08575i
\(400\) −398.379 + 35.9798i −0.995946 + 0.0899494i
\(401\) −168.694 −0.420684 −0.210342 0.977628i \(-0.567458\pi\)
−0.210342 + 0.977628i \(0.567458\pi\)
\(402\) −33.9505 + 97.6625i −0.0844540 + 0.242942i
\(403\) 347.791 0.863005
\(404\) −92.3987 73.0718i −0.228710 0.180871i
\(405\) −29.4743 34.0039i −0.0727759 0.0839604i
\(406\) −2.19934 + 6.32665i −0.00541709 + 0.0155829i
\(407\) 224.988 0.552797
\(408\) 127.957 + 200.908i 0.313621 + 0.492421i
\(409\) 373.890 0.914157 0.457079 0.889426i \(-0.348896\pi\)
0.457079 + 0.889426i \(0.348896\pi\)
\(410\) 717.964 286.429i 1.75113 0.698608i
\(411\) 358.282i 0.871732i
\(412\) −451.123 356.762i −1.09496 0.865927i
\(413\) 905.630i 2.19281i
\(414\) −3.29901 + 9.48997i −0.00796862 + 0.0229226i
\(415\) −79.0356 91.1820i −0.190447 0.219716i
\(416\) −24.6254 + 240.549i −0.0591957 + 0.578242i
\(417\) 79.7191i 0.191173i
\(418\) −170.610 + 490.779i −0.408158 + 1.17411i
\(419\) 87.5839i 0.209031i 0.994523 + 0.104515i \(0.0333291\pi\)
−0.994523 + 0.104515i \(0.966671\pi\)
\(420\) 14.9016 + 330.661i 0.0354800 + 0.787288i
\(421\) 70.3023 0.166989 0.0834944 0.996508i \(-0.473392\pi\)
0.0834944 + 0.996508i \(0.473392\pi\)
\(422\) 39.1409 + 13.6066i 0.0927510 + 0.0322431i
\(423\) 42.2597 0.0999048
\(424\) 97.4228 + 152.965i 0.229771 + 0.360766i
\(425\) 425.402 + 61.0226i 1.00095 + 0.143583i
\(426\) 23.5465 + 8.18550i 0.0552735 + 0.0192148i
\(427\) 363.092 0.850332
\(428\) 110.129 + 87.0935i 0.257311 + 0.203490i
\(429\) −129.897 −0.302790
\(430\) 388.238 154.887i 0.902880 0.360201i
\(431\) 247.370i 0.573944i 0.957939 + 0.286972i \(0.0926487\pi\)
−0.957939 + 0.286972i \(0.907351\pi\)
\(432\) 19.1597 + 80.9006i 0.0443512 + 0.187270i
\(433\) 636.247i 1.46939i −0.678397 0.734696i \(-0.737325\pi\)
0.678397 0.734696i \(-0.262675\pi\)
\(434\) −830.791 288.808i −1.91426 0.665457i
\(435\) 1.98813 + 2.29367i 0.00457041 + 0.00527281i
\(436\) 475.320 + 375.898i 1.09018 + 0.862151i
\(437\) 43.8323i 0.100303i
\(438\) −112.494 39.1064i −0.256836 0.0892840i
\(439\) 769.786i 1.75350i 0.480947 + 0.876750i \(0.340293\pi\)
−0.480947 + 0.876750i \(0.659707\pi\)
\(440\) −113.341 + 380.469i −0.257593 + 0.864702i
\(441\) 126.897 0.287748
\(442\) 85.3049 245.390i 0.192998 0.555180i
\(443\) −612.214 −1.38197 −0.690986 0.722868i \(-0.742823\pi\)
−0.690986 + 0.722868i \(0.742823\pi\)
\(444\) −97.4228 + 123.190i −0.219421 + 0.277456i
\(445\) −328.145 378.575i −0.737403 0.850730i
\(446\) 63.7185 183.294i 0.142867 0.410972i
\(447\) 20.1775 0.0451399
\(448\) 258.578 554.165i 0.577182 1.23697i
\(449\) 175.897 0.391753 0.195876 0.980629i \(-0.437245\pi\)
0.195876 + 0.980629i \(0.437245\pi\)
\(450\) 133.254 + 68.8724i 0.296120 + 0.153050i
\(451\) 767.177i 1.70106i
\(452\) 80.1505 101.350i 0.177324 0.224225i
\(453\) 217.241i 0.479561i
\(454\) 267.450 769.351i 0.589097 1.69461i
\(455\) 272.795 236.456i 0.599550 0.519683i
\(456\) −194.846 305.929i −0.427293 0.670898i
\(457\) 365.357i 0.799469i 0.916631 + 0.399734i \(0.130898\pi\)
−0.916631 + 0.399734i \(0.869102\pi\)
\(458\) −5.18607 + 14.9183i −0.0113233 + 0.0325728i
\(459\) 89.3232i 0.194604i
\(460\) −1.50774 33.4562i −0.00327769 0.0727308i
\(461\) 308.350 0.668873 0.334437 0.942418i \(-0.391454\pi\)
0.334437 + 0.942418i \(0.391454\pi\)
\(462\) 310.293 + 107.867i 0.671630 + 0.233479i
\(463\) −92.6302 −0.200065 −0.100033 0.994984i \(-0.531895\pi\)
−0.100033 + 0.994984i \(0.531895\pi\)
\(464\) −1.29238 5.45700i −0.00278531 0.0117608i
\(465\) −301.196 + 261.073i −0.647733 + 0.561448i
\(466\) 53.1752 + 18.4854i 0.114110 + 0.0396681i
\(467\) 606.103 1.29786 0.648932 0.760846i \(-0.275216\pi\)
0.648932 + 0.760846i \(0.275216\pi\)
\(468\) 56.2471 71.1240i 0.120186 0.151974i
\(469\) −285.196 −0.608094
\(470\) −130.838 + 52.1974i −0.278379 + 0.111058i
\(471\) 341.596i 0.725256i
\(472\) −407.324 639.545i −0.862975 1.35497i
\(473\) 414.851i 0.877063i
\(474\) 150.598 + 52.3525i 0.317717 + 0.110448i
\(475\) −647.776 92.9214i −1.36374 0.195624i
\(476\) −407.547 + 515.339i −0.856190 + 1.08265i
\(477\) 68.0079i 0.142574i
\(478\) 559.185 + 194.390i 1.16984 + 0.406673i
\(479\) 138.947i 0.290078i −0.989426 0.145039i \(-0.953669\pi\)
0.989426 0.145039i \(-0.0463307\pi\)
\(480\) −159.244 226.807i −0.331759 0.472514i
\(481\) 171.299 0.356131
\(482\) 305.893 879.935i 0.634632 1.82559i
\(483\) −27.7128 −0.0573764
\(484\) −70.5876 55.8229i −0.145842 0.115337i
\(485\) −498.199 + 431.834i −1.02722 + 0.890379i
\(486\) 10.2371 29.4483i 0.0210640 0.0605932i
\(487\) −201.243 −0.413230 −0.206615 0.978422i \(-0.566245\pi\)
−0.206615 + 0.978422i \(0.566245\pi\)
\(488\) −256.411 + 163.307i −0.525433 + 0.334646i
\(489\) −31.9036 −0.0652426
\(490\) −392.879 + 156.738i −0.801794 + 0.319873i
\(491\) 347.368i 0.707470i 0.935346 + 0.353735i \(0.115089\pi\)
−0.935346 + 0.353735i \(0.884911\pi\)
\(492\) 420.061 + 332.197i 0.853783 + 0.675198i
\(493\) 6.02513i 0.0122214i
\(494\) −129.897 + 373.664i −0.262949 + 0.756404i
\(495\) 112.494 97.5087i 0.227261 0.196987i
\(496\) 716.591 169.711i 1.44474 0.342159i
\(497\) 68.7610i 0.138352i
\(498\) 27.4510 78.9660i 0.0551225 0.158566i
\(499\) 672.277i 1.34725i −0.739074 0.673625i \(-0.764736\pi\)
0.739074 0.673625i \(-0.235264\pi\)
\(500\) −497.628 48.6426i −0.995257 0.0972852i
\(501\) 160.894 0.321145
\(502\) −267.641 93.0401i −0.533149 0.185339i
\(503\) 436.350 0.867496 0.433748 0.901034i \(-0.357191\pi\)
0.433748 + 0.901034i \(0.357191\pi\)
\(504\) −193.423 + 123.190i −0.383775 + 0.244425i
\(505\) −96.4469 111.269i −0.190984 0.220335i
\(506\) −31.3954 10.9140i −0.0620462 0.0215692i
\(507\) 193.817 0.382282
\(508\) 602.559 + 476.523i 1.18614 + 0.938037i
\(509\) −109.547 −0.215219 −0.107610 0.994193i \(-0.534320\pi\)
−0.107610 + 0.994193i \(0.534320\pi\)
\(510\) 110.328 + 276.549i 0.216330 + 0.542252i
\(511\) 328.508i 0.642872i
\(512\) 66.6415 + 507.644i 0.130159 + 0.991493i
\(513\) 136.016i 0.265138i
\(514\) 78.8796 + 27.4210i 0.153462 + 0.0533482i
\(515\) −470.888 543.255i −0.914345 1.05486i
\(516\) 227.148 + 179.636i 0.440209 + 0.348131i
\(517\) 139.807i 0.270419i
\(518\) −409.193 142.248i −0.789947 0.274610i
\(519\) 203.518i 0.392135i
\(520\) −86.2941 + 289.677i −0.165950 + 0.557071i
\(521\) −743.100 −1.42629 −0.713147 0.701014i \(-0.752731\pi\)
−0.713147 + 0.701014i \(0.752731\pi\)
\(522\) −0.690526 + 1.98638i −0.00132285 + 0.00380532i
\(523\) −366.211 −0.700212 −0.350106 0.936710i \(-0.613854\pi\)
−0.350106 + 0.936710i \(0.613854\pi\)
\(524\) 105.272 133.115i 0.200900 0.254037i
\(525\) −58.7492 + 409.554i −0.111903 + 0.780102i
\(526\) −133.498 + 384.023i −0.253799 + 0.730083i
\(527\) −791.196 −1.50132
\(528\) −267.641 + 63.3855i −0.506895 + 0.120048i
\(529\) −526.196 −0.994699
\(530\) 84.0005 + 210.556i 0.158491 + 0.397275i
\(531\) 284.341i 0.535481i
\(532\) 620.586 784.727i 1.16652 1.47505i
\(533\) 584.105i 1.09588i
\(534\) 113.973 327.855i 0.213432 0.613961i
\(535\) 114.954 + 132.621i 0.214867 + 0.247889i
\(536\) 201.402 128.272i 0.375750 0.239314i
\(537\) 401.815i 0.748259i
\(538\) −160.269 + 461.033i −0.297898 + 0.856939i
\(539\) 419.809i 0.778867i
\(540\) 4.67865 + 103.818i 0.00866417 + 0.192255i
\(541\) 170.688 0.315504 0.157752 0.987479i \(-0.449575\pi\)
0.157752 + 0.987479i \(0.449575\pi\)
\(542\) 881.430 + 306.412i 1.62625 + 0.565336i
\(543\) −377.754 −0.695680
\(544\) 56.0208 547.228i 0.102979 1.00593i
\(545\) 496.145 + 572.393i 0.910357 + 1.05026i
\(546\) 236.248 + 82.1269i 0.432688 + 0.150416i
\(547\) 507.600 0.927971 0.463986 0.885843i \(-0.346419\pi\)
0.463986 + 0.885843i \(0.346419\pi\)
\(548\) 513.247 648.997i 0.936581 1.18430i
\(549\) 114.000 0.207650
\(550\) −227.848 + 440.839i −0.414270 + 0.801526i
\(551\) 9.17469i 0.0166510i
\(552\) 19.5705 12.4644i 0.0354537 0.0225804i
\(553\) 439.779i 0.795261i
\(554\) 933.561 + 324.534i 1.68513 + 0.585802i
\(555\) −148.349 + 128.588i −0.267296 + 0.231689i
\(556\) −114.199 + 144.404i −0.205394 + 0.259720i
\(557\) 788.492i 1.41561i −0.706410 0.707803i \(-0.749686\pi\)
0.706410 0.707803i \(-0.250314\pi\)
\(558\) −260.843 90.6772i −0.467461 0.162504i
\(559\) 315.854i 0.565035i
\(560\) 446.686 620.310i 0.797654 1.10770i
\(561\) 295.505 0.526747
\(562\) −28.5026 + 81.9910i −0.0507164 + 0.145892i
\(563\) −936.102 −1.66270 −0.831351 0.555747i \(-0.812432\pi\)
−0.831351 + 0.555747i \(0.812432\pi\)
\(564\) −76.5498 60.5380i −0.135727 0.107337i
\(565\) 122.048 105.790i 0.216014 0.187239i
\(566\) −204.096 + 587.107i −0.360594 + 1.03729i
\(567\) 85.9955 0.151667
\(568\) −30.9266 48.5582i −0.0544482 0.0854898i
\(569\) −95.4983 −0.167835 −0.0839177 0.996473i \(-0.526743\pi\)
−0.0839177 + 0.996473i \(0.526743\pi\)
\(570\) −168.001 421.111i −0.294738 0.738791i
\(571\) 889.123i 1.55713i 0.627562 + 0.778566i \(0.284053\pi\)
−0.627562 + 0.778566i \(0.715947\pi\)
\(572\) 235.297 + 186.080i 0.411359 + 0.325315i
\(573\) 237.651i 0.414749i
\(574\) −485.045 + 1395.29i −0.845026 + 2.43081i
\(575\) 5.94422 41.4385i 0.0103378 0.0720670i
\(576\) 81.1856 173.991i 0.140947 0.302068i
\(577\) 522.147i 0.904934i 0.891781 + 0.452467i \(0.149456\pi\)
−0.891781 + 0.452467i \(0.850544\pi\)
\(578\) −4.27189 + 12.2886i −0.00739081 + 0.0212605i
\(579\) 64.1361i 0.110771i
\(580\) −0.315590 7.00283i −0.000544120 0.0120738i
\(581\) 230.598 0.396898
\(582\) −431.453 149.986i −0.741329 0.257709i
\(583\) 224.988 0.385915
\(584\) 147.752 + 231.988i 0.253001 + 0.397240i
\(585\) 85.6495 74.2401i 0.146409 0.126906i
\(586\) −463.223 161.031i −0.790484 0.274796i
\(587\) 95.8440 0.163278 0.0816388 0.996662i \(-0.473985\pi\)
0.0816388 + 0.996662i \(0.473985\pi\)
\(588\) −229.863 181.783i −0.390923 0.309154i
\(589\) 1204.78 2.04547
\(590\) −351.205 880.331i −0.595263 1.49209i
\(591\) 337.008i 0.570234i
\(592\) 352.946 83.5883i 0.596192 0.141197i
\(593\) 878.624i 1.48166i 0.671693 + 0.740829i \(0.265567\pi\)
−0.671693 + 0.740829i \(0.734433\pi\)
\(594\) 97.4228 + 33.8671i 0.164011 + 0.0570154i
\(595\) −620.586 + 537.918i −1.04300 + 0.904063i
\(596\) −36.5498 28.9047i −0.0613252 0.0484979i
\(597\) 304.906i 0.510730i
\(598\) −23.9034 8.30957i −0.0399723 0.0138956i
\(599\) 967.652i 1.61545i −0.589563 0.807723i \(-0.700700\pi\)
0.589563 0.807723i \(-0.299300\pi\)
\(600\) −142.717 315.645i −0.237861 0.526076i
\(601\) 279.704 0.465398 0.232699 0.972549i \(-0.425244\pi\)
0.232699 + 0.972549i \(0.425244\pi\)
\(602\) −262.288 + 754.501i −0.435694 + 1.25332i
\(603\) −89.5430 −0.148496
\(604\) −311.203 + 393.513i −0.515236 + 0.651512i
\(605\) −73.6802 85.0036i −0.121785 0.140502i
\(606\) 33.4983 96.3619i 0.0552778 0.159013i
\(607\) 747.564 1.23157 0.615786 0.787914i \(-0.288839\pi\)
0.615786 + 0.787914i \(0.288839\pi\)
\(608\) −85.3049 + 833.285i −0.140304 + 1.37053i
\(609\) −5.80066 −0.00952490
\(610\) −352.949 + 140.808i −0.578605 + 0.230833i
\(611\) 106.444i 0.174213i
\(612\) −127.957 + 161.801i −0.209081 + 0.264381i
\(613\) 457.152i 0.745761i 0.927879 + 0.372881i \(0.121630\pi\)
−0.927879 + 0.372881i \(0.878370\pi\)
\(614\) 221.650 637.600i 0.360993 1.03844i
\(615\) 438.465 + 505.850i 0.712951 + 0.822520i
\(616\) −407.547 639.894i −0.661601 1.03879i
\(617\) 764.888i 1.23969i −0.784725 0.619844i \(-0.787196\pi\)
0.784725 0.619844i \(-0.212804\pi\)
\(618\) 163.551 470.473i 0.264645 0.761283i
\(619\) 365.359i 0.590240i 0.955460 + 0.295120i \(0.0953597\pi\)
−0.955460 + 0.295120i \(0.904640\pi\)
\(620\) 919.584 41.4420i 1.48320 0.0668420i
\(621\) −8.70099 −0.0140113
\(622\) −808.077 280.912i −1.29916 0.451627i
\(623\) 957.410 1.53677
\(624\) −203.773 + 48.2598i −0.326560 + 0.0773393i
\(625\) −599.797 175.693i −0.959676 0.281109i
\(626\) 158.447 + 55.0810i 0.253110 + 0.0879888i
\(627\) −449.976 −0.717666
\(628\) −489.343 + 618.771i −0.779209 + 0.985304i
\(629\) −389.691 −0.619541
\(630\) −266.246 + 106.218i −0.422612 + 0.168600i
\(631\) 62.1578i 0.0985067i −0.998786 0.0492534i \(-0.984316\pi\)
0.998786 0.0492534i \(-0.0156842\pi\)
\(632\) −197.799 310.567i −0.312973 0.491403i
\(633\) 35.8868i 0.0566932i
\(634\) 211.966 + 73.6859i 0.334331 + 0.116224i
\(635\) 628.959 + 725.619i 0.990486 + 1.14271i
\(636\) −97.4228 + 123.190i −0.153180 + 0.193696i
\(637\) 319.630i 0.501773i
\(638\) −6.57147 2.28444i −0.0103001 0.00358063i
\(639\) 21.5889i 0.0337855i
\(640\) −36.4480 + 638.961i −0.0569501 + 0.998377i
\(641\) −1111.69 −1.73431 −0.867154 0.498041i \(-0.834053\pi\)
−0.867154 + 0.498041i \(0.834053\pi\)
\(642\) −39.9264 + 114.853i −0.0621906 + 0.178898i
\(643\) 468.983 0.729367 0.364683 0.931132i \(-0.381177\pi\)
0.364683 + 0.931132i \(0.381177\pi\)
\(644\) 50.1993 + 39.6992i 0.0779493 + 0.0616447i
\(645\) 237.100 + 273.538i 0.367596 + 0.424090i
\(646\) 295.505 850.054i 0.457438 1.31587i
\(647\) −96.7647 −0.149559 −0.0747795 0.997200i \(-0.523825\pi\)
−0.0747795 + 0.997200i \(0.523825\pi\)
\(648\) −60.7290 + 38.6781i −0.0937175 + 0.0596884i
\(649\) −940.675 −1.44942
\(650\) −173.477 + 335.641i −0.266887 + 0.516371i
\(651\) 761.720i 1.17008i
\(652\) 57.7907 + 45.7027i 0.0886360 + 0.0700961i
\(653\) 920.353i 1.40942i −0.709494 0.704712i \(-0.751076\pi\)
0.709494 0.704712i \(-0.248924\pi\)
\(654\) −172.323 + 495.707i −0.263491 + 0.757962i
\(655\) 160.301 138.947i 0.244734 0.212133i
\(656\) −285.024 1203.49i −0.434488 1.83459i
\(657\) 103.142i 0.156989i
\(658\) 88.3921 254.270i 0.134335 0.386429i
\(659\) 591.020i 0.896844i 0.893822 + 0.448422i \(0.148014\pi\)
−0.893822 + 0.448422i \(0.851986\pi\)
\(660\) −343.457 + 15.4782i −0.520389 + 0.0234519i
\(661\) −306.193 −0.463226 −0.231613 0.972808i \(-0.574400\pi\)
−0.231613 + 0.972808i \(0.574400\pi\)
\(662\) −250.535 87.0935i −0.378451 0.131561i
\(663\) 224.988 0.339349
\(664\) −162.846 + 103.716i −0.245249 + 0.156198i
\(665\) 944.990 819.107i 1.42104 1.23174i
\(666\) −128.474 44.6616i −0.192904 0.0670595i
\(667\) 0.586909 0.000879924
\(668\) −291.445 230.484i −0.436295 0.345035i
\(669\) 168.055 0.251203
\(670\) 277.229 110.600i 0.413775 0.165074i
\(671\) 377.142i 0.562060i
\(672\) 526.841 + 53.9337i 0.783990 + 0.0802585i
\(673\) 556.892i 0.827476i −0.910396 0.413738i \(-0.864223\pi\)
0.910396 0.413738i \(-0.135777\pi\)
\(674\) 39.2442 + 13.6425i 0.0582258 + 0.0202411i
\(675\) −18.4455 + 128.588i −0.0273266 + 0.190500i
\(676\) −351.083 277.647i −0.519353 0.410721i
\(677\) 58.1920i 0.0859557i −0.999076 0.0429779i \(-0.986316\pi\)
0.999076 0.0429779i \(-0.0136845\pi\)
\(678\) 105.697 + 36.7435i 0.155895 + 0.0541939i
\(679\) 1259.94i 1.85558i
\(680\) 196.312 658.991i 0.288694 0.969105i
\(681\) 705.389 1.03581
\(682\) 299.984 862.940i 0.439860 1.26531i
\(683\) −357.274 −0.523096 −0.261548 0.965191i \(-0.584233\pi\)
−0.261548 + 0.965191i \(0.584233\pi\)
\(684\) 194.846 246.381i 0.284862 0.360206i
\(685\) 781.540 677.430i 1.14093 0.988949i
\(686\) −42.0482 + 120.956i −0.0612947 + 0.176321i
\(687\) −13.6780 −0.0199098
\(688\) −154.127 650.788i −0.224021 0.945913i
\(689\) 171.299 0.248620
\(690\) 26.9387 10.7471i 0.0390416 0.0155755i
\(691\) 614.707i 0.889590i 0.895632 + 0.444795i \(0.146724\pi\)
−0.895632 + 0.444795i \(0.853276\pi\)
\(692\) −291.544 + 368.655i −0.421307 + 0.532739i
\(693\) 284.496i 0.410528i
\(694\) 5.84222 16.8058i 0.00841818 0.0242159i
\(695\) −173.896 + 150.731i −0.250210 + 0.216879i
\(696\) 4.09636 2.60896i 0.00588557 0.00374850i
\(697\) 1328.79i 1.90644i
\(698\) 12.7415 36.6524i 0.0182543 0.0525107i
\(699\) 48.7543i 0.0697487i
\(700\) 693.113 657.711i 0.990162 0.939587i
\(701\) −886.028 −1.26395 −0.631975 0.774989i \(-0.717755\pi\)
−0.631975 + 0.774989i \(0.717755\pi\)
\(702\) 74.1746 + 25.7854i 0.105662 + 0.0367313i
\(703\) 593.397 0.844093
\(704\) 575.609 + 268.584i 0.817626 + 0.381511i
\(705\) −79.9036 92.1835i −0.113338 0.130757i
\(706\) 151.677 + 52.7276i 0.214840 + 0.0746849i
\(707\) 281.398 0.398017
\(708\) 407.324 515.058i 0.575316 0.727483i
\(709\) −760.887 −1.07318 −0.536592 0.843842i \(-0.680288\pi\)
−0.536592 + 0.843842i \(0.680288\pi\)
\(710\) −26.6657 66.8402i −0.0375573 0.0941412i
\(711\) 138.078i 0.194202i
\(712\) −676.111 + 430.613i −0.949594 + 0.604794i
\(713\) 77.0706i 0.108093i
\(714\) −537.444 186.832i −0.752722 0.261669i
\(715\) 245.606 + 283.351i 0.343505 + 0.396296i
\(716\) −575.609 + 727.853i −0.803923 + 1.01655i
\(717\) 512.695i 0.715056i
\(718\) 593.397 + 206.283i 0.826458 + 0.287302i
\(719\) 575.877i 0.800942i −0.916309 0.400471i \(-0.868846\pi\)
0.916309 0.400471i \(-0.131154\pi\)
\(720\) 140.246 194.759i 0.194786 0.270498i
\(721\) 1373.88 1.90553
\(722\) −212.903 + 612.441i −0.294880 + 0.848257i
\(723\) 806.779 1.11588
\(724\) 684.268 + 541.141i 0.945122 + 0.747432i
\(725\) 1.24421 8.67363i 0.00171615 0.0119636i
\(726\) 25.5909 73.6153i 0.0352492 0.101398i
\(727\) −327.332 −0.450250 −0.225125 0.974330i \(-0.572279\pi\)
−0.225125 + 0.974330i \(0.572279\pi\)
\(728\) −310.293 487.195i −0.426227 0.669224i
\(729\) 27.0000 0.0370370
\(730\) 127.396 + 319.331i 0.174515 + 0.437440i
\(731\) 718.542i 0.982958i
\(732\) −206.501 163.307i −0.282105 0.223098i
\(733\) 947.567i 1.29272i −0.763031 0.646362i \(-0.776290\pi\)
0.763031 0.646362i \(-0.223710\pi\)
\(734\) −313.120 + 900.727i −0.426595 + 1.22715i
\(735\) −239.934 276.807i −0.326440 0.376609i
\(736\) −53.3056 5.45700i −0.0724261 0.00741440i
\(737\) 296.232i 0.401943i
\(738\) −152.290 + 438.079i −0.206354 + 0.593602i
\(739\) 183.234i 0.247948i 0.992285 + 0.123974i \(0.0395640\pi\)
−0.992285 + 0.123974i \(0.960436\pi\)
\(740\) 452.926 20.4116i 0.612062 0.0275832i
\(741\) −342.598 −0.462345
\(742\) −409.193 142.248i −0.551473 0.191709i
\(743\) −183.712 −0.247258 −0.123629 0.992329i \(-0.539453\pi\)
−0.123629 + 0.992329i \(0.539453\pi\)
\(744\) 342.598 + 537.918i 0.460481 + 0.723008i
\(745\) −38.1512 44.0143i −0.0512096 0.0590797i
\(746\) −162.715 56.5648i −0.218117 0.0758241i
\(747\) 72.4009 0.0969222
\(748\) −535.281 423.317i −0.715617 0.565932i
\(749\) −335.395 −0.447791
\(750\) −101.718 420.896i −0.135624 0.561195i
\(751\) 345.748i 0.460384i −0.973145 0.230192i \(-0.926065\pi\)
0.973145 0.230192i \(-0.0739354\pi\)
\(752\) 51.9414 + 219.319i 0.0690710 + 0.291647i
\(753\) 245.390i 0.325882i
\(754\) −5.00331 1.73930i −0.00663569 0.00230677i
\(755\) −473.880 + 410.754i −0.627656 + 0.544045i
\(756\) −155.773 123.190i −0.206049 0.162950i
\(757\) 549.335i 0.725674i 0.931853 + 0.362837i \(0.118192\pi\)
−0.931853 + 0.362837i \(0.881808\pi\)
\(758\) 1205.32 + 419.005i 1.59013 + 0.552778i
\(759\) 28.7852i 0.0379252i
\(760\) −298.932 + 1003.47i −0.393331 + 1.32036i
\(761\) 251.485 0.330467 0.165233 0.986255i \(-0.447162\pi\)
0.165233 + 0.986255i \(0.447162\pi\)
\(762\) −218.453 + 628.405i −0.286683 + 0.824678i
\(763\) −1447.57 −1.89721
\(764\) 340.440 430.484i 0.445602 0.563461i
\(765\) −194.846 + 168.890i −0.254700 + 0.220771i
\(766\) 142.337 409.450i 0.185819 0.534529i
\(767\) −716.200 −0.933768
\(768\) −396.307 + 198.869i −0.516024 + 0.258945i
\(769\) 583.691 0.759026 0.379513 0.925186i \(-0.376092\pi\)
0.379513 + 0.925186i \(0.376092\pi\)
\(770\) −351.397 880.812i −0.456360 1.14391i
\(771\) 72.3216i 0.0938024i
\(772\) −91.8764 + 116.177i −0.119011 + 0.150488i
\(773\) 1328.04i 1.71803i 0.511951 + 0.859015i \(0.328923\pi\)
−0.511951 + 0.859015i \(0.671077\pi\)
\(774\) −82.3505 + 236.891i −0.106396 + 0.306060i
\(775\) 1138.99 + 163.384i 1.46966 + 0.210818i
\(776\) 566.681 + 889.753i 0.730259 + 1.14659i
\(777\) 375.173i