Properties

Label 60.3.f.b.19.4
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 19.4
Root \(-0.656712 + 1.88911i\) of defining polynomial
Character \(\chi\) \(=\) 60.19
Dual form 60.3.f.b.19.3

$q$-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} +(-4.98678 - 8.66787i) 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} +(19.6494 - 3.72827i) 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} +(8.63736 + 15.0132i) 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} +(-5.86091 + 39.5683i) 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} +(49.0804 + 9.54543i) 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} +(-34.0338 + 6.45756i) 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} +(47.6489 + 82.8220i) 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} +(-70.8999 - 37.0569i) 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} +(-14.9603 - 26.0036i) 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 \(-0.739109\pi\)
−0.682504 + 0.730882i \(0.739109\pi\)
\(8\) 6.74766 4.29756i 0.843458 0.537196i
\(9\) 3.00000 0.333333
\(10\) −4.98678 8.66787i −0.498678 0.866787i
\(11\) 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 \(-0.906134\pi\)
0.956835 0.290632i \(-0.0938655\pi\)
\(14\) 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 \(0.168727\pi\)
−0.862770 + 0.505596i \(0.831273\pi\)
\(18\) −1.97014 + 5.66732i −0.109452 + 0.314851i
\(19\) 26.1762i 1.37770i 0.724905 + 0.688849i \(0.241884\pi\)
−0.724905 + 0.688849i \(0.758116\pi\)
\(20\) 19.6494 3.72827i 0.982471 0.186414i
\(21\) 16.5498 0.788087
\(22\) −18.7490 6.51774i −0.852228 0.296261i
\(23\) 1.67451 0.0728047 0.0364023 0.999337i \(-0.488410\pi\)
0.0364023 + 0.999337i \(0.488410\pi\)
\(24\) −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 \(0.501924\pi\)
\(30\) 8.63736 + 15.0132i 0.287912 + 0.500440i
\(31\) 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 \(0.0991051\pi\)
−0.951922 + 0.306342i \(0.900895\pi\)
\(38\) −49.4498 17.1903i −1.30131 0.452375i
\(39\) 13.0881i 0.335593i
\(40\) −5.86091 + 39.5683i −0.146523 + 0.989207i
\(41\) −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 \(-0.338441\pi\)
0.486039 + 0.873937i \(0.338441\pi\)
\(44\) 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 \(-0.547881\pi\)
−0.149857 + 0.988708i \(0.547881\pi\)
\(48\) −6.38658 26.9669i −0.133054 0.561810i
\(49\) 42.2990 0.863245
\(50\) 49.0804 + 9.54543i 0.981608 + 0.190909i
\(51\) 29.7744i 0.583812i
\(52\) −18.7490 + 23.7080i −0.360558 + 0.455923i
\(53\) 22.6693i 0.427723i 0.976864 + 0.213861i \(0.0686041\pi\)
−0.976864 + 0.213861i \(0.931396\pi\)
\(54\) 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 \(0.703117\pi\)
\(60\) −34.0338 + 6.45756i −0.567230 + 0.107626i
\(61\) 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 \(-0.428499\pi\)
0.222744 + 0.974877i \(0.428499\pi\)
\(68\) 42.6525 53.9337i 0.627242 0.793143i
\(69\) −2.90033 −0.0420338
\(70\) 47.6489 + 82.8220i 0.680699 + 1.18317i
\(71\) 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 \(0.0756672\pi\)
−0.971878 + 0.235483i \(0.924333\pi\)
\(74\) −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 \(0.905911\pi\)
\(80\) −70.8999 37.0569i −0.886248 0.463211i
\(81\) 9.00000 0.111111
\(82\) 50.7632 146.026i 0.619063 1.78081i
\(83\) −24.1336 −0.290767 −0.145383 0.989375i \(-0.546442\pi\)
−0.145383 + 0.989375i \(0.546442\pi\)
\(84\) −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 \(0.309679\pi\)
\(90\) −14.9603 26.0036i −0.166226 0.288929i
\(91\) 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 \(0.237888\pi\)
−0.733494 + 0.679696i \(0.762112\pi\)
\(98\) −27.7783 + 79.9074i −0.283452 + 0.815382i
\(99\) 29.7744i 0.300752i
\(100\) −50.2640 + 86.4496i −0.502640 + 0.864496i
\(101\) 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 \(-0.745922\pi\)
−0.697991 + 0.716107i \(0.745922\pi\)
\(104\) −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 \(-0.447552\pi\)
0.164025 + 0.986456i \(0.447552\pi\)
\(108\) 16.3027 + 12.8927i 0.150951 + 0.119377i
\(109\) −151.498 −1.38989 −0.694947 0.719061i \(-0.744572\pi\)
−0.694947 + 0.719061i \(0.744572\pi\)
\(110\) 86.0269 49.4928i 0.782063 0.449935i
\(111\) 39.2644i 0.353733i
\(112\) −35.2323 148.766i −0.314574 1.32827i
\(113\) 32.3031i 0.285868i −0.989732 0.142934i \(-0.954346\pi\)
0.989732 0.142934i \(-0.0456537\pi\)
\(114\) 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
\(120\) 10.1514 68.5343i 0.0845949 0.571119i
\(121\) 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 \(-0.227095\pi\)
0.756116 + 0.654438i \(0.227095\pi\)
\(128\) 91.7908 + 89.2102i 0.717115 + 0.696954i
\(129\) −72.3987 −0.561230
\(130\) −65.4982 + 37.6823i −0.503832 + 0.289864i
\(131\) 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 \(-0.727665\pi\)
0.655791 0.754942i \(-0.272335\pi\)
\(138\) 1.90468 5.47904i 0.0138020 0.0397032i
\(139\) 46.0258i 0.331121i −0.986200 0.165561i \(-0.947057\pi\)
0.986200 0.165561i \(-0.0529433\pi\)
\(140\) −187.751 + 35.6238i −1.34108 + 0.254456i
\(141\) 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 \(0.487553\pi\)
\(150\) −85.0097 16.5332i −0.566732 0.110221i
\(151\) 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 \(0.216163\pi\)
−0.778140 + 0.628090i \(0.783837\pi\)
\(158\) −86.9478 30.2257i −0.550303 0.191302i
\(159\) 39.2644i 0.246946i
\(160\) 116.565 109.602i 0.728532 0.685011i
\(161\) −16.0000 −0.0993789
\(162\) −5.91041 + 17.0020i −0.0364840 + 0.104950i
\(163\) 18.4196 0.113004 0.0565018 0.998402i \(-0.482005\pi\)
0.0565018 + 0.998402i \(0.482005\pi\)
\(164\) 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 \(-0.589711\pi\)
−0.278120 + 0.960546i \(0.589711\pi\)
\(168\) 111.673 71.1240i 0.664718 0.423357i
\(169\) 111.900 0.662132
\(170\) 149.003 85.7241i 0.876488 0.504259i
\(171\) 78.5287i 0.459232i
\(172\) −131.144 103.713i −0.762464 0.602981i
\(173\) 117.501i 0.679198i 0.940570 + 0.339599i \(0.110291\pi\)
−0.940570 + 0.339599i \(0.889709\pi\)
\(174\) −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 \(-0.224399\pi\)
\(180\) 58.9483 11.1848i 0.327490 0.0621379i
\(181\) −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
\(190\) 226.892 130.535i 1.19417 0.687027i
\(191\) 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 \(0.0305825\pi\)
−0.995388 + 0.0959301i \(0.969417\pi\)
\(194\) −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 \(0.164406\pi\)
−0.869554 + 0.493837i \(0.835594\pi\)
\(198\) −56.2471 19.5532i −0.284076 0.0987536i
\(199\) 176.037i 0.884610i −0.896865 0.442305i \(-0.854161\pi\)
0.896865 0.442305i \(-0.145839\pi\)
\(200\) −130.304 151.727i −0.651518 0.758633i
\(201\) −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
\(210\) −82.5304 143.452i −0.393002 0.683104i
\(211\) 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
\(220\) 37.0024 + 195.017i 0.168193 + 0.886439i
\(221\) 129.897 0.587769
\(222\) 74.1746 + 25.7854i 0.334120 + 0.116150i
\(223\) −97.0265 −0.435096 −0.217548 0.976050i \(-0.569806\pi\)
−0.217548 + 0.976050i \(0.569806\pi\)
\(224\) 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 \(-0.854287\pi\)
−0.897040 + 0.441948i \(0.854287\pi\)
\(228\) −112.494 + 142.248i −0.493395 + 0.623895i
\(229\) −7.89702 −0.0344848 −0.0172424 0.999851i \(-0.505489\pi\)
−0.0172424 + 0.999851i \(0.505489\pi\)
\(230\) −8.35040 14.5144i −0.0363061 0.0631061i
\(231\) 164.254i 0.711055i
\(232\) −2.36503 + 1.50628i −0.0101941 + 0.00649260i
\(233\) 28.1483i 0.120808i −0.998174 0.0604042i \(-0.980761\pi\)
0.998174 0.0604042i \(-0.0192390\pi\)
\(234\) 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 \(0.787434\pi\)
\(240\) 122.802 + 64.1844i 0.511676 + 0.267435i
\(241\) 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
\(250\) −196.799 + 154.176i −0.787196 + 0.616703i
\(251\) 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 \(-0.974113\pi\)
0.996695 0.0812352i \(-0.0258865\pi\)
\(258\) 47.5451 136.769i 0.184283 0.530112i
\(259\) 216.606i 0.836318i
\(260\) −28.1724 148.480i −0.108356 0.571075i
\(261\) −1.05149 −0.00402870
\(262\) −80.1505 27.8628i −0.305918 0.106346i
\(263\) 203.283 0.772939 0.386469 0.922302i \(-0.373694\pi\)
0.386469 + 0.922302i \(0.373694\pi\)
\(264\) −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 \(0.649868\pi\)
\(270\) 25.9121 + 45.0396i 0.0959706 + 0.166813i
\(271\) 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 \(-0.649286\pi\)
0.451990 0.892023i \(-0.350714\pi\)
\(278\) 86.9478 + 30.2257i 0.312762 + 0.108726i
\(279\) 138.078i 0.494902i
\(280\) 56.0013 378.077i 0.200005 1.35028i
\(281\) −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 \(-0.314974\pi\)
0.549090 + 0.835763i \(0.314974\pi\)
\(284\) 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
\(290\) 1.74785 + 3.03806i 0.00602707 + 0.0104761i
\(291\) 228.390i 0.784845i
\(292\) 85.3049 107.867i 0.292140 0.369409i
\(293\) 245.207i 0.836886i 0.908243 + 0.418443i \(0.137424\pi\)
−0.908243 + 0.418443i \(0.862576\pi\)
\(294\) 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
\(300\) 87.0599 149.735i 0.290200 0.499117i
\(301\) −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 \(-0.685257\pi\)
−0.549697 + 0.835364i \(0.685257\pi\)
\(308\) −235.297 + 297.531i −0.763952 + 0.966011i
\(309\) 249.045 0.805970
\(310\) −398.946 + 229.521i −1.28692 + 0.740390i
\(311\) 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 \(-0.957223\pi\)
0.990984 0.133984i \(-0.0427770\pi\)
\(314\) −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 \(-0.943368\pi\)
0.984215 0.176978i \(-0.0566323\pi\)
\(318\) 74.1746 + 25.7854i 0.233254 + 0.0810861i
\(319\) 3.47861i 0.0109047i
\(320\) 130.500 + 292.181i 0.407812 + 0.913066i
\(321\) −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
\(330\) −149.003 + 85.7241i −0.451524 + 0.259770i
\(331\) 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 \(-0.990188\pi\)
0.999525 0.0308219i \(-0.00981246\pi\)
\(338\) −73.4863 + 211.392i −0.217415 + 0.625420i
\(339\) 55.9506i 0.165046i
\(340\) 64.0900 + 337.779i 0.188500 + 0.993467i
\(341\) 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 \(-0.504080\pi\)
−0.0128187 + 0.999918i \(0.504080\pi\)
\(348\) −1.90468 1.50628i −0.00547323 0.00432840i
\(349\) 19.4020 0.0555931 0.0277965 0.999614i \(-0.491151\pi\)
0.0277965 + 0.999614i \(0.491151\pi\)
\(350\) −468.966 91.2071i −1.33990 0.260592i
\(351\) 39.2644i 0.111864i
\(352\) 32.3436 315.942i 0.0918853 0.897564i
\(353\) 80.2902i 0.227451i −0.993512 0.113726i \(-0.963722\pi\)
0.993512 0.113726i \(-0.0362784\pi\)
\(354\) 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 \(0.855869\pi\)
\(360\) −17.5827 + 118.705i −0.0488409 + 0.329736i
\(361\) −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 \(-0.274940\pi\)
0.649592 + 0.760283i \(0.274940\pi\)
\(368\) 6.17440 + 26.0709i 0.0167783 + 0.0708450i
\(369\) −231.897 −0.628447
\(370\) 196.495 113.047i 0.531066 0.305532i
\(371\) 216.606i 0.583844i
\(372\) 197.799 250.115i 0.531718 0.672353i
\(373\) 86.1333i 0.230920i 0.993312 + 0.115460i \(0.0368343\pi\)
−0.993312 + 0.115460i \(0.963166\pi\)
\(374\) 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 \(0.681534\pi\)
\(380\) 97.5922 + 514.348i 0.256822 + 1.35355i
\(381\) −332.646 −0.873087
\(382\) −259.201 90.1061i −0.678535 0.235880i
\(383\) −216.742 −0.565907 −0.282953 0.959134i \(-0.591314\pi\)
−0.282953 + 0.959134i \(0.591314\pi\)
\(384\) −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 \(0.290105\pi\)
\(390\) 113.446 65.2676i 0.290888 0.167353i
\(391\) 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 \(-0.982721\pi\)
0.998527 0.0542559i \(-0.0172787\pi\)
\(398\) 332.554 + 115.606i 0.835562 + 0.290467i
\(399\) 433.213i 1.08575i
\(400\) 372.200 146.517i 0.930500 0.366292i
\(401\) −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 \(0.348896\pi\)
\(410\) 385.473 + 670.018i 0.940179 + 1.63419i
\(411\) 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 \(0.966671\pi\)
\(420\) 325.195 61.7023i 0.774273 0.146910i
\(421\) 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
\(430\) −208.444 362.312i −0.484754 0.842586i
\(431\) 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 \(0.262675\pi\)
−0.678397 + 0.734696i \(0.737325\pi\)
\(434\) −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 \(0.659707\pi\)
\(440\) −392.707 58.1683i −0.892517 0.132201i
\(441\) 126.897 0.287748
\(442\) −85.3049 + 245.390i −0.192998 + 0.555180i
\(443\) 612.214 1.38197 0.690986 0.722868i \(-0.257177\pi\)
0.690986 + 0.722868i \(0.257177\pi\)
\(444\) −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 \(0.437245\pi\)
\(450\) 147.241 + 28.6363i 0.327203 + 0.0636362i
\(451\) 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 \(-0.869102\pi\)
0.916631 0.399734i \(-0.130898\pi\)
\(458\) 5.18607 14.9183i 0.0113233 0.0325728i
\(459\) 89.3232i 0.194604i
\(460\) 32.9031 6.24302i 0.0715285 0.0135718i
\(461\) 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 \(-0.468105\pi\)
0.100033 + 0.994984i \(0.468105\pi\)
\(464\) −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 \(-0.724784\pi\)
−0.648932 + 0.760846i \(0.724784\pi\)
\(468\) −56.2471 + 71.1240i −0.120186 + 0.151974i
\(469\) −285.196 −0.608094
\(470\) 70.2467 + 122.101i 0.149461 + 0.259789i
\(471\) 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 \(-0.0463307\pi\)
\(480\) −201.897 + 189.836i −0.420618 + 0.395491i
\(481\) 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 \(-0.433755\pi\)
0.206615 + 0.978422i \(0.433755\pi\)
\(488\) 256.411 163.307i 0.525433 0.334646i
\(489\) −31.9036 −0.0652426
\(490\) −210.936 366.642i −0.430481 0.748250i
\(491\) 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 \(-0.235264\pi\)
\(500\) −162.015 473.024i −0.324029 0.946047i
\(501\) 160.894 0.321145
\(502\) 267.641 + 93.0401i 0.533149 + 0.185339i
\(503\) −436.350 −0.867496 −0.433748 0.901034i \(-0.642809\pi\)
−0.433748 + 0.901034i \(0.642809\pi\)
\(504\) −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 \(0.534320\pi\)
\(510\) −258.081 + 148.478i −0.506041 + 0.291134i
\(511\) 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
\(520\) 298.995 + 44.2875i 0.574991 + 0.0851683i
\(521\) −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 \(-0.386146\pi\)
0.350106 + 0.936710i \(0.386146\pi\)
\(524\) 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
\(530\) 196.495 113.047i 0.370744 0.213296i
\(531\) 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
\(540\) −102.101 + 19.3727i −0.189077 + 0.0358753i
\(541\) 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 \(-0.653581\pi\)
−0.463986 + 0.885843i \(0.653581\pi\)
\(548\) −513.247 + 648.997i −0.936581 + 1.18430i
\(549\) 114.000 0.207650
\(550\) −94.7365 + 487.113i −0.172248 + 0.885660i
\(551\) 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 \(0.250314\pi\)
−0.706410 + 0.707803i \(0.749686\pi\)
\(558\) 260.843 + 90.6772i 0.467461 + 0.162504i
\(559\) 315.854i 0.565035i
\(560\) 677.452 + 354.080i 1.20974 + 0.632286i
\(561\) 295.505 0.526747
\(562\) 28.5026 81.9910i 0.0507164 0.145892i
\(563\) 936.102 1.66270 0.831351 0.555747i \(-0.187568\pi\)
0.831351 + 0.555747i \(0.187568\pi\)
\(564\) −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 \(0.526743\pi\)
\(570\) −392.989 + 226.094i −0.689455 + 0.396656i
\(571\) 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 \(-0.850544\pi\)
0.891781 0.452467i \(-0.149456\pi\)
\(578\) 4.27189 12.2886i 0.00739081 0.0212605i
\(579\) 64.1361i 0.110771i
\(580\) −6.88706 + 1.30675i −0.0118742 + 0.00225301i
\(581\) 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 \(-0.526015\pi\)
−0.0816388 + 0.996662i \(0.526015\pi\)
\(588\) 229.863 + 181.783i 0.390923 + 0.309154i
\(589\) 1204.78 2.04547
\(590\) 821.543 472.648i 1.39245 0.801098i
\(591\) 337.008i 0.570234i
\(592\) −352.946 + 83.5883i −0.596192 + 0.141197i
\(593\) 878.624i 1.48166i −0.671693 0.740829i \(-0.734433\pi\)
0.671693 0.740829i \(-0.265567\pi\)
\(594\) 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 \(-0.299300\pi\)
\(600\) 225.692 + 262.798i 0.376154 + 0.437997i
\(601\) 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 \(-0.711161\pi\)
−0.615786 + 0.787914i \(0.711161\pi\)
\(608\) 85.3049 833.285i 0.140304 1.37053i
\(609\) −5.80066 −0.00952490
\(610\) −189.498 329.379i −0.310652 0.539966i
\(611\) 106.444i 0.174213i
\(612\) 127.957 161.801i 0.209081 0.264381i
\(613\) 457.152i 0.745761i −0.927879 0.372881i \(-0.878370\pi\)
0.927879 0.372881i \(-0.121630\pi\)
\(614\) 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 \(0.212804\pi\)
−0.784725 + 0.619844i \(0.787196\pi\)
\(618\) −163.551 + 470.473i −0.264645 + 0.761283i
\(619\) 365.359i 0.590240i 0.955460 + 0.295120i \(0.0953597\pi\)
−0.955460 + 0.295120i \(0.904640\pi\)
\(620\) −171.597 904.382i −0.276769 1.45868i
\(621\) −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
\(630\) 142.947 + 248.466i 0.226900 + 0.394390i
\(631\) 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
\(640\) −637.662 + 54.6495i −0.996348 + 0.0853899i
\(641\) −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 \(-0.618823\pi\)
−0.364683 + 0.931132i \(0.618823\pi\)
\(644\) 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 \(-0.476175\pi\)
0.0747795 + 0.997200i \(0.476175\pi\)
\(648\) 60.7290 38.6781i 0.0937175 0.0596884i
\(649\) −940.675 −1.44942
\(650\) 72.1294 370.873i 0.110968 0.570573i
\(651\) 761.720i 1.17008i
\(652\) −57.7907 45.7027i −0.0886360 0.0700961i
\(653\) 920.353i 1.40942i 0.709494 + 0.704712i \(0.248924\pi\)
−0.709494 + 0.704712i \(0.751076\pi\)
\(654\) −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 \(0.851986\pi\)
\(660\) −64.0900 337.779i −0.0971060 0.511786i
\(661\) −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
\(670\) −148.844 258.716i −0.222155 0.386143i
\(671\) 377.142i 0.562060i
\(672\) −526.841 53.9337i −0.783990 0.0802585i
\(673\) 556.892i 0.827476i 0.910396 + 0.413738i \(0.135777\pi\)
−0.910396 + 0.413738i \(0.864223\pi\)
\(674\) 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 \(0.0136845\pi\)
−0.999076 + 0.0429779i \(0.986316\pi\)
\(678\) −105.697 36.7435i −0.155895 0.0541939i
\(679\) 1259.94i 1.85558i
\(680\) −680.189 100.750i −1.00028 0.148162i
\(681\) 705.389 1.03581
\(682\) −299.984 + 862.940i −0.439860 + 1.26531i
\(683\) 357.274 0.523096 0.261548 0.965191i \(-0.415767\pi\)
0.261548 + 0.965191i \(0.415767\pi\)
\(684\) 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
\(690\) 14.4633 + 25.1397i 0.0209613 + 0.0364343i
\(691\) 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
\(700\) 480.275 826.030i 0.686108 1.18004i
\(701\) −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 \(0.680288\pi\)
\(710\) 62.3766 35.8864i 0.0878544 0.0505442i
\(711\) 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 \(-0.131154\pi\)
\(720\) −212.700 111.171i −0.295416 0.154404i
\(721\) 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 \(-0.427721\pi\)
0.225125 + 0.974330i \(0.427721\pi\)
\(728\) 310.293 + 487.195i 0.426227 + 0.669224i
\(729\) 27.0000 0.0370370
\(730\) 298.006 171.448i 0.408227 0.234860i
\(731\) 718.542i 0.982958i
\(732\) 206.501 + 163.307i 0.282105 + 0.223098i
\(733\) 947.567i 1.29272i 0.763031 + 0.646362i \(0.223710\pi\)
−0.763031 + 0.646362i \(0.776290\pi\)
\(734\) −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 \(0.960436\pi\)
\(740\) 84.5173 + 445.439i 0.114213 + 0.601944i
\(741\) −342.598 −0.462345
\(742\) 409.193 + 142.248i 0.551473 + 0.191709i
\(743\) 183.712 0.247258 0.123629 0.992329i \(-0.460547\pi\)
0.123629 + 0.992329i \(0.460547\pi\)
\(744\) 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
\(750\) 340.866 267.040i 0.454488 0.356054i
\(751\) 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 \(-0.881808\pi\)
0.931853 0.362837i \(-0.118192\pi\)
\(758\) −1205.32 419.005i −1.59013 0.552778i
\(759\) 28.7852i 0.0379252i
\(760\) −1035.75 153.417i −1.36283 0.201864i
\(761\) 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 \(0.376092\pi\)
\(770\) −821.991 + 472.906i −1.06752 + 0.614164i
\(771\) 72.3216i 0.0938024i
\(772\) 91.8764 116.177i 0.119011 0.150488i
\(773\) 1328.04i 1.71803i −0.511951 0.859015i \(-0.671077\pi\)
0.511951 0.859015i \(-0.328923\pi\)
\(774\) −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 0.482848