Properties

Label 180.3.f.h.19.4
Level $180$
Weight $3$
Character 180.19
Analytic conductor $4.905$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 180.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.90464475849\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.4
Root \(-0.656712 + 1.88911i\) of defining polynomial
Character \(\chi\) \(=\) 180.19
Dual form 180.3.f.h.19.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.656712 + 1.88911i) q^{2} +(-3.13746 - 2.48120i) q^{4} +(3.27492 + 3.77822i) q^{5} +9.55505 q^{7} +(6.74766 - 4.29756i) q^{8} +O(q^{10})\) \(q+(-0.656712 + 1.88911i) q^{2} +(-3.13746 - 2.48120i) q^{4} +(3.27492 + 3.77822i) q^{5} +9.55505 q^{7} +(6.74766 - 4.29756i) q^{8} +(-9.28814 + 3.70547i) q^{10} -9.92480i q^{11} +7.55643i q^{13} +(-6.27492 + 18.0505i) q^{14} +(3.68729 + 15.5693i) q^{16} +17.1903i q^{17} +26.1762i q^{19} +(-0.900407 - 19.9797i) q^{20} +(18.7490 + 6.51774i) q^{22} +1.67451 q^{23} +(-3.54983 + 24.7467i) q^{25} +(-14.2749 - 4.96240i) q^{26} +(-29.9786 - 23.7080i) q^{28} +0.350497 q^{29} -46.0258i q^{31} +(-31.8336 - 3.25887i) q^{32} +(-32.4743 - 11.2890i) q^{34} +(31.2920 + 36.1010i) q^{35} -22.6693i q^{37} +(-49.4498 - 17.1903i) q^{38} +(38.3352 + 11.4200i) q^{40} +77.2990 q^{41} -41.7994 q^{43} +(-24.6254 + 31.1386i) q^{44} +(-1.09967 + 3.16332i) q^{46} -14.0866 q^{47} +42.2990 q^{49} +(-44.4180 - 22.9575i) q^{50} +(18.7490 - 23.7080i) q^{52} +22.6693i q^{53} +(37.4980 - 32.5029i) q^{55} +(64.4743 - 41.0634i) q^{56} +(-0.230175 + 0.662126i) q^{58} -94.7802i q^{59} +38.0000 q^{61} +(86.9478 + 30.2257i) q^{62} +(27.0619 - 57.9970i) q^{64} +(-28.5498 + 24.7467i) q^{65} -29.8477 q^{67} +(42.6525 - 53.9337i) q^{68} +(-88.7486 + 35.4060i) q^{70} -7.19630i q^{71} -34.3805i q^{73} +(42.8248 + 14.8872i) q^{74} +(64.9485 - 82.1269i) q^{76} -94.8320i q^{77} +46.0258i q^{79} +(-46.7487 + 64.9196i) q^{80} +(-50.7632 + 146.026i) q^{82} -24.1336 q^{83} +(-64.9485 + 56.2967i) q^{85} +(27.4502 - 78.9636i) q^{86} +(-42.6525 - 66.9692i) q^{88} -100.199 q^{89} +72.2021i q^{91} +(-5.25370 - 4.15479i) q^{92} +(9.25083 - 26.6111i) q^{94} +(-98.8995 + 85.7250i) q^{95} -131.861i q^{97} +(-27.7783 + 79.9074i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 10q^{4} - 4q^{5} + O(q^{10}) \) \( 8q - 10q^{4} - 4q^{5} - 42q^{10} - 20q^{14} - 46q^{16} - 52q^{20} + 32q^{25} - 84q^{26} + 184q^{29} + 12q^{34} - 6q^{40} + 256q^{41} - 348q^{44} + 112q^{46} - 24q^{49} - 72q^{50} + 244q^{56} + 304q^{61} - 10q^{64} - 168q^{65} - 104q^{70} + 252q^{74} - 24q^{76} + 308q^{80} + 24q^{85} + 280q^{86} - 560q^{89} + 376q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(91\) \(101\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) 0 0
\(4\) −3.13746 2.48120i −0.784365 0.620300i
\(5\) 3.27492 + 3.77822i 0.654983 + 0.755643i
\(6\) 0 0
\(7\) 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
\(9\) 0 0
\(10\) −9.28814 + 3.70547i −0.928814 + 0.370547i
\(11\) 9.92480i 0.902255i −0.892460 0.451127i \(-0.851022\pi\)
0.892460 0.451127i \(-0.148978\pi\)
\(12\) 0 0
\(13\) 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
\(15\) 0 0
\(16\) 3.68729 + 15.5693i 0.230456 + 0.973083i
\(17\) 17.1903i 1.01119i 0.862770 + 0.505596i \(0.168727\pi\)
−0.862770 + 0.505596i \(0.831273\pi\)
\(18\) 0 0
\(19\) 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
\(21\) 0 0
\(22\) 18.7490 + 6.51774i 0.852228 + 0.296261i
\(23\) 1.67451 0.0728047 0.0364023 0.999337i \(-0.488410\pi\)
0.0364023 + 0.999337i \(0.488410\pi\)
\(24\) 0 0
\(25\) −3.54983 + 24.7467i −0.141993 + 0.989868i
\(26\) −14.2749 4.96240i −0.549035 0.190862i
\(27\) 0 0
\(28\) −29.9786 23.7080i −1.07066 0.846714i
\(29\) 0.350497 0.0120861 0.00604305 0.999982i \(-0.498076\pi\)
0.00604305 + 0.999982i \(0.498076\pi\)
\(30\) 0 0
\(31\) 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
\(33\) 0 0
\(34\) −32.4743 11.2890i −0.955125 0.332031i
\(35\) 31.2920 + 36.1010i 0.894057 + 1.03146i
\(36\) 0 0
\(37\) 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
\(39\) 0 0
\(40\) 38.3352 + 11.4200i 0.958379 + 0.285499i
\(41\) 77.2990 1.88534 0.942671 0.333724i \(-0.108305\pi\)
0.942671 + 0.333724i \(0.108305\pi\)
\(42\) 0 0
\(43\) −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
\(45\) 0 0
\(46\) −1.09967 + 3.16332i −0.0239058 + 0.0687679i
\(47\) −14.0866 −0.299715 −0.149857 0.988708i \(-0.547881\pi\)
−0.149857 + 0.988708i \(0.547881\pi\)
\(48\) 0 0
\(49\) 42.2990 0.863245
\(50\) −44.4180 22.9575i −0.888359 0.459149i
\(51\) 0 0
\(52\) 18.7490 23.7080i 0.360558 0.455923i
\(53\) 22.6693i 0.427723i 0.976864 + 0.213861i \(0.0686041\pi\)
−0.976864 + 0.213861i \(0.931396\pi\)
\(54\) 0 0
\(55\) 37.4980 32.5029i 0.681783 0.590962i
\(56\) 64.4743 41.0634i 1.15133 0.733276i
\(57\) 0 0
\(58\) −0.230175 + 0.662126i −0.00396854 + 0.0114160i
\(59\) 94.7802i 1.60644i −0.595680 0.803222i \(-0.703117\pi\)
0.595680 0.803222i \(-0.296883\pi\)
\(60\) 0 0
\(61\) 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
\(63\) 0 0
\(64\) 27.0619 57.9970i 0.422842 0.906203i
\(65\) −28.5498 + 24.7467i −0.439228 + 0.380718i
\(66\) 0 0
\(67\) −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
\(69\) 0 0
\(70\) −88.7486 + 35.4060i −1.26784 + 0.505800i
\(71\) 7.19630i 0.101356i −0.998715 0.0506782i \(-0.983862\pi\)
0.998715 0.0506782i \(-0.0161383\pi\)
\(72\) 0 0
\(73\) 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
\(75\) 0 0
\(76\) 64.9485 82.1269i 0.854586 1.08062i
\(77\) 94.8320i 1.23158i
\(78\) 0 0
\(79\) 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
\(81\) 0 0
\(82\) −50.7632 + 146.026i −0.619063 + 1.78081i
\(83\) −24.1336 −0.290767 −0.145383 0.989375i \(-0.546442\pi\)
−0.145383 + 0.989375i \(0.546442\pi\)
\(84\) 0 0
\(85\) −64.9485 + 56.2967i −0.764100 + 0.662314i
\(86\) 27.4502 78.9636i 0.319188 0.918181i
\(87\) 0 0
\(88\) −42.6525 66.9692i −0.484687 0.761014i
\(89\) −100.199 −1.12584 −0.562918 0.826513i \(-0.690321\pi\)
−0.562918 + 0.826513i \(0.690321\pi\)
\(90\) 0 0
\(91\) 72.2021i 0.793430i
\(92\) −5.25370 4.15479i −0.0571054 0.0451607i
\(93\) 0 0
\(94\) 9.25083 26.6111i 0.0984131 0.283097i
\(95\) −98.8995 + 85.7250i −1.04105 + 0.902369i
\(96\) 0 0
\(97\) 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
\(99\) 0 0
\(100\) 72.5389 68.8339i 0.725389 0.688339i
\(101\) −29.4502 −0.291586 −0.145793 0.989315i \(-0.546573\pi\)
−0.145793 + 0.989315i \(0.546573\pi\)
\(102\) 0 0
\(103\) 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
\(105\) 0 0
\(106\) −42.8248 14.8872i −0.404007 0.140445i
\(107\) 35.1014 0.328050 0.164025 0.986456i \(-0.447552\pi\)
0.164025 + 0.986456i \(0.447552\pi\)
\(108\) 0 0
\(109\) −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
\(111\) 0 0
\(112\) 35.2323 + 148.766i 0.314574 + 1.32827i
\(113\) 32.3031i 0.285868i −0.989732 0.142934i \(-0.954346\pi\)
0.989732 0.142934i \(-0.0456537\pi\)
\(114\) 0 0
\(115\) 5.48387 + 6.32665i 0.0476858 + 0.0550143i
\(116\) −1.09967 0.869652i −0.00947990 0.00749700i
\(117\) 0 0
\(118\) 179.050 + 62.2433i 1.51737 + 0.527486i
\(119\) 164.254i 1.38028i
\(120\) 0 0
\(121\) 22.4983 0.185937
\(122\) −24.9551 + 71.7861i −0.204550 + 0.588411i
\(123\) 0 0
\(124\) −114.199 + 144.404i −0.920962 + 1.16455i
\(125\) −105.124 + 67.6313i −0.840990 + 0.541051i
\(126\) 0 0
\(127\) −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
\(129\) 0 0
\(130\) −28.0002 70.1852i −0.215386 0.539886i
\(131\) 42.4277i 0.323876i −0.986801 0.161938i \(-0.948226\pi\)
0.986801 0.161938i \(-0.0517744\pi\)
\(132\) 0 0
\(133\) 250.115i 1.88057i
\(134\) 19.6013 56.3855i 0.146279 0.420787i
\(135\) 0 0
\(136\) 73.8762 + 115.994i 0.543208 + 0.852897i
\(137\) 206.854i 1.50988i −0.655791 0.754942i \(-0.727665\pi\)
0.655791 0.754942i \(-0.272335\pi\)
\(138\) 0 0
\(139\) 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
\(141\) 0 0
\(142\) 13.5946 + 4.72590i 0.0957366 + 0.0332810i
\(143\) 74.9961 0.524448
\(144\) 0 0
\(145\) 1.14785 + 1.32425i 0.00791619 + 0.00913277i
\(146\) 64.9485 + 22.5781i 0.444853 + 0.154645i
\(147\) 0 0
\(148\) −56.2471 + 71.1240i −0.380048 + 0.480567i
\(149\) −11.6495 −0.0781846 −0.0390923 0.999236i \(-0.512447\pi\)
−0.0390923 + 0.999236i \(0.512447\pi\)
\(150\) 0 0
\(151\) 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
\(153\) 0 0
\(154\) 179.148 + 62.2773i 1.16330 + 0.404398i
\(155\) 173.896 150.731i 1.12191 0.972457i
\(156\) 0 0
\(157\) 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
\(159\) 0 0
\(160\) −91.9398 130.947i −0.574624 0.818418i
\(161\) 16.0000 0.0993789
\(162\) 0 0
\(163\) −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
\(165\) 0 0
\(166\) 15.8488 45.5910i 0.0954749 0.274645i
\(167\) −92.8920 −0.556240 −0.278120 0.960546i \(-0.589711\pi\)
−0.278120 + 0.960546i \(0.589711\pi\)
\(168\) 0 0
\(169\) 111.900 0.662132
\(170\) −63.6980 159.665i −0.374694 0.939209i
\(171\) 0 0
\(172\) 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 0
\(175\) −33.9189 + 236.456i −0.193822 + 1.35118i
\(176\) 154.522 36.5956i 0.877968 0.207930i
\(177\) 0 0
\(178\) 65.8021 189.287i 0.369675 1.06341i
\(179\) 231.988i 1.29602i 0.761631 + 0.648011i \(0.224399\pi\)
−0.761631 + 0.648011i \(0.775601\pi\)
\(180\) 0 0
\(181\) −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
\(183\) 0 0
\(184\) 11.2990 7.19630i 0.0614076 0.0391103i
\(185\) 85.6495 74.2401i 0.462970 0.401298i
\(186\) 0 0
\(187\) 170.610 0.912352
\(188\) 44.1961 + 34.9516i 0.235085 + 0.185913i
\(189\) 0 0
\(190\) −96.9954 243.129i −0.510502 1.27962i
\(191\) 137.208i 0.718366i −0.933267 0.359183i \(-0.883055\pi\)
0.933267 0.359183i \(-0.116945\pi\)
\(192\) 0 0
\(193\) 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
\(195\) 0 0
\(196\) −132.711 104.952i −0.677099 0.535471i
\(197\) 194.572i 0.987674i 0.869554 + 0.493837i \(0.164406\pi\)
−0.869554 + 0.493837i \(0.835594\pi\)
\(198\) 0 0
\(199\) 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
\(201\) 0 0
\(202\) 19.3403 55.6345i 0.0957440 0.275419i
\(203\) 3.34901 0.0164976
\(204\) 0 0
\(205\) 253.148 + 292.052i 1.23487 + 1.42465i
\(206\) −94.4261 + 271.628i −0.458379 + 1.31858i
\(207\) 0 0
\(208\) −117.649 + 27.8628i −0.565618 + 0.133956i
\(209\) 259.794 1.24303
\(210\) 0 0
\(211\) 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
\(213\) 0 0
\(214\) −23.0515 + 66.3103i −0.107717 + 0.309861i
\(215\) −136.890 157.927i −0.636696 0.734545i
\(216\) 0 0
\(217\) 439.779i 2.02663i
\(218\) 99.4908 286.197i 0.456380 1.31283i
\(219\) 0 0
\(220\) −198.295 + 8.93636i −0.901340 + 0.0406198i
\(221\) −129.897 −0.587769
\(222\) 0 0
\(223\) 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
\(225\) 0 0
\(226\) 61.0241 + 21.2138i 0.270018 + 0.0938666i
\(227\) −407.256 −1.79408 −0.897040 0.441948i \(-0.854287\pi\)
−0.897040 + 0.441948i \(0.854287\pi\)
\(228\) 0 0
\(229\) −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
\(231\) 0 0
\(232\) 2.36503 1.50628i 0.0101941 0.00649260i
\(233\) 28.1483i 0.120808i −0.998174 0.0604042i \(-0.980761\pi\)
0.998174 0.0604042i \(-0.0192390\pi\)
\(234\) 0 0
\(235\) −46.1324 53.2222i −0.196308 0.226477i
\(236\) −235.169 + 297.369i −0.996477 + 1.26004i
\(237\) 0 0
\(238\) −310.293 107.867i −1.30375 0.453225i
\(239\) 296.005i 1.23851i −0.785189 0.619257i \(-0.787434\pi\)
0.785189 0.619257i \(-0.212566\pi\)
\(240\) 0 0
\(241\) 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
\(243\) 0 0
\(244\) −119.223 94.2856i −0.488621 0.386416i
\(245\) 138.526 + 159.815i 0.565411 + 0.652305i
\(246\) 0 0
\(247\) −197.799 −0.800806
\(248\) −197.799 310.567i −0.797577 1.25229i
\(249\) 0 0
\(250\) −58.7268 243.004i −0.234907 0.972018i
\(251\) 141.676i 0.564445i 0.959349 + 0.282223i \(0.0910716\pi\)
−0.959349 + 0.282223i \(0.908928\pi\)
\(252\) 0 0
\(253\) 16.6191i 0.0656883i
\(254\) 126.124 362.810i 0.496550 1.42838i
\(255\) 0 0
\(256\) −228.808 + 114.817i −0.893780 + 0.448505i
\(257\) 41.7549i 0.162470i −0.996695 0.0812352i \(-0.974113\pi\)
0.996695 0.0812352i \(-0.0258865\pi\)
\(258\) 0 0
\(259\) 216.606i 0.836318i
\(260\) 150.975 6.80387i 0.580675 0.0261687i
\(261\) 0 0
\(262\) 80.1505 + 27.8628i 0.305918 + 0.106346i
\(263\) 203.283 0.772939 0.386469 0.922302i \(-0.373694\pi\)
0.386469 + 0.922302i \(0.373694\pi\)
\(264\) 0 0
\(265\) −85.6495 + 74.2401i −0.323206 + 0.280151i
\(266\) −472.495 164.254i −1.77630 0.617495i
\(267\) 0 0
\(268\) 93.6458 + 74.0580i 0.349425 + 0.276336i
\(269\) 244.048 0.907242 0.453621 0.891195i \(-0.350132\pi\)
0.453621 + 0.891195i \(0.350132\pi\)
\(270\) 0 0
\(271\) 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
\(273\) 0 0
\(274\) 390.770 + 135.844i 1.42617 + 0.495780i
\(275\) 245.606 + 35.2314i 0.893113 + 0.128114i
\(276\) 0 0
\(277\) 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
\(279\) 0 0
\(280\) 366.294 + 109.118i 1.30819 + 0.389708i
\(281\) 43.4020 0.154455 0.0772277 0.997013i \(-0.475393\pi\)
0.0772277 + 0.997013i \(0.475393\pi\)
\(282\) 0 0
\(283\) −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
\(285\) 0 0
\(286\) −49.2508 + 141.676i −0.172206 + 0.495370i
\(287\) 738.596 2.57351
\(288\) 0 0
\(289\) −6.50497 −0.0225085
\(290\) −3.25546 + 1.29876i −0.0112257 + 0.00447847i
\(291\) 0 0
\(292\) −85.3049 + 107.867i −0.292140 + 0.369409i
\(293\) 245.207i 0.836886i 0.908243 + 0.418443i \(0.137424\pi\)
−0.908243 + 0.418443i \(0.862576\pi\)
\(294\) 0 0
\(295\) 358.100 310.397i 1.21390 1.05219i
\(296\) −97.4228 152.965i −0.329131 0.516773i
\(297\) 0 0
\(298\) 7.65037 22.0072i 0.0256724 0.0738496i
\(299\) 12.6533i 0.0423187i
\(300\) 0 0
\(301\) −399.395 −1.32689
\(302\) 236.940 + 82.3676i 0.784569 + 0.272740i
\(303\) 0 0
\(304\) −407.547 + 96.5195i −1.34061 + 0.317498i
\(305\) 124.447 + 143.572i 0.408022 + 0.470729i
\(306\) 0 0
\(307\) 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
\(309\) 0 0
\(310\) 170.548 + 427.494i 0.550153 + 1.37901i
\(311\) 427.756i 1.37542i 0.725986 + 0.687710i \(0.241384\pi\)
−0.725986 + 0.687710i \(0.758616\pi\)
\(312\) 0 0
\(313\) 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
\(315\) 0 0
\(316\) 114.199 144.404i 0.361390 0.456975i
\(317\) 112.204i 0.353957i −0.984215 0.176978i \(-0.943368\pi\)
0.984215 0.176978i \(-0.0566323\pi\)
\(318\) 0 0
\(319\) 3.47861i 0.0109047i
\(320\) 307.751 87.6898i 0.961721 0.274031i
\(321\) 0 0
\(322\) −10.5074 + 30.2257i −0.0326317 + 0.0938687i
\(323\) −449.976 −1.39312
\(324\) 0 0
\(325\) −186.997 26.8241i −0.575374 0.0825356i
\(326\) 12.0964 34.7966i 0.0371054 0.106738i
\(327\) 0 0
\(328\) 521.588 332.197i 1.59021 1.01280i
\(329\) −134.598 −0.409113
\(330\) 0 0
\(331\) 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
\(333\) 0 0
\(334\) 61.0033 175.483i 0.182645 0.525398i
\(335\) −97.7487 112.771i −0.291787 0.336630i
\(336\) 0 0
\(337\) 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
\(339\) 0 0
\(340\) 343.457 15.4782i 1.01017 0.0455242i
\(341\) −456.797 −1.33958
\(342\) 0 0
\(343\) −64.0283 −0.186672
\(344\) −282.048 + 179.636i −0.819907 + 0.522196i
\(345\) 0 0
\(346\) −221.973 77.1645i −0.641539 0.223019i
\(347\) −8.89616 −0.0256374 −0.0128187 0.999918i \(-0.504080\pi\)
−0.0128187 + 0.999918i \(0.504080\pi\)
\(348\) 0 0
\(349\) 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
\(351\) 0 0
\(352\) −32.3436 + 315.942i −0.0918853 + 0.897564i
\(353\) 80.2902i 0.227451i −0.993512 0.113726i \(-0.963722\pi\)
0.993512 0.113726i \(-0.0362784\pi\)
\(354\) 0 0
\(355\) 27.1892 23.5673i 0.0765892 0.0663867i
\(356\) 314.371 + 248.615i 0.883065 + 0.698356i
\(357\) 0 0
\(358\) −438.251 152.349i −1.22416 0.425557i
\(359\) 314.115i 0.874972i −0.899225 0.437486i \(-0.855869\pi\)
0.899225 0.437486i \(-0.144131\pi\)
\(360\) 0 0
\(361\) −324.196 −0.898050
\(362\) 143.227 412.008i 0.395653 1.13814i
\(363\) 0 0
\(364\) 179.148 226.531i 0.492164 0.622338i
\(365\) 129.897 112.593i 0.355882 0.308475i
\(366\) 0 0
\(367\) −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
\(369\) 0 0
\(370\) 84.0005 + 210.556i 0.227028 + 0.569069i
\(371\) 216.606i 0.583844i
\(372\) 0 0
\(373\) 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
\(375\) 0 0
\(376\) −95.0515 + 60.5380i −0.252797 + 0.161005i
\(377\) 2.64850i 0.00702521i
\(378\) 0 0
\(379\) 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
\(381\) 0 0
\(382\) 259.201 + 90.1061i 0.678535 + 0.235880i
\(383\) −216.742 −0.565907 −0.282953 0.959134i \(-0.591314\pi\)
−0.282953 + 0.959134i \(0.591314\pi\)
\(384\) 0 0
\(385\) 358.296 310.567i 0.930638 0.806667i
\(386\) 69.9518 + 24.3174i 0.181222 + 0.0629985i
\(387\) 0 0
\(388\) −327.174 + 413.708i −0.843231 + 1.06626i
\(389\) −476.640 −1.22529 −0.612647 0.790356i \(-0.709895\pi\)
−0.612647 + 0.790356i \(0.709895\pi\)
\(390\) 0 0
\(391\) 28.7852i 0.0736195i
\(392\) 285.419 181.783i 0.728111 0.463731i
\(393\) 0 0
\(394\) −367.567 127.778i −0.932912 0.324309i
\(395\) −173.896 + 150.731i −0.440242 + 0.381597i
\(396\) 0 0
\(397\) 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
\(399\) 0 0
\(400\) −398.379 + 35.9798i −0.995946 + 0.0899494i
\(401\) 168.694 0.420684 0.210342 0.977628i \(-0.432542\pi\)
0.210342 + 0.977628i \(0.432542\pi\)
\(402\) 0 0
\(403\) 347.791 0.863005
\(404\) 92.3987 + 73.0718i 0.228710 + 0.180871i
\(405\) 0 0
\(406\) −2.19934 + 6.32665i −0.00541709 + 0.0155829i
\(407\) −224.988 −0.552797
\(408\) 0 0
\(409\) 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
\(411\) 0 0
\(412\) −451.123 356.762i −1.09496 0.865927i
\(413\) 905.630i 2.19281i
\(414\) 0 0
\(415\) −79.0356 91.1820i −0.190447 0.219716i
\(416\) 24.6254 240.549i 0.0591957 0.578242i
\(417\) 0 0
\(418\) −170.610 + 490.779i −0.408158 + 1.17411i
\(419\) 87.5839i 0.209031i −0.994523 0.104515i \(-0.966671\pi\)
0.994523 0.104515i \(-0.0333291\pi\)
\(420\) 0 0
\(421\) 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
\(423\) 0 0
\(424\) 97.4228 + 152.965i 0.229771 + 0.360766i
\(425\) −425.402 61.0226i −1.00095 0.143583i
\(426\) 0 0
\(427\) 363.092 0.850332
\(428\) −110.129 87.0935i −0.257311 0.203490i
\(429\) 0 0
\(430\) 388.238 154.887i 0.902880 0.360201i
\(431\) 247.370i 0.573944i −0.957939 0.286972i \(-0.907351\pi\)
0.957939 0.286972i \(-0.0926487\pi\)
\(432\) 0 0
\(433\) 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
\(435\) 0 0
\(436\) 475.320 + 375.898i 1.09018 + 0.862151i
\(437\) 43.8323i 0.100303i
\(438\) 0 0
\(439\) 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
\(441\) 0 0
\(442\) 85.3049 245.390i 0.192998 0.555180i
\(443\) 612.214 1.38197 0.690986 0.722868i \(-0.257177\pi\)
0.690986 + 0.722868i \(0.257177\pi\)
\(444\) 0 0
\(445\) −328.145 378.575i −0.737403 0.850730i
\(446\) −63.7185 + 183.294i −0.142867 + 0.410972i
\(447\) 0 0
\(448\) 258.578 554.165i 0.577182 1.23697i
\(449\) −175.897 −0.391753 −0.195876 0.980629i \(-0.562755\pi\)
−0.195876 + 0.980629i \(0.562755\pi\)
\(450\) 0 0
\(451\) 767.177i 1.70106i
\(452\) −80.1505 + 101.350i −0.177324 + 0.224225i
\(453\) 0 0
\(454\) 267.450 769.351i 0.589097 1.69461i
\(455\) −272.795 + 236.456i −0.599550 + 0.519683i
\(456\) 0 0
\(457\) 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
\(459\) 0 0
\(460\) −1.50774 33.4562i −0.00327769 0.0727308i
\(461\) −308.350 −0.668873 −0.334437 0.942418i \(-0.608546\pi\)
−0.334437 + 0.942418i \(0.608546\pi\)
\(462\) 0 0
\(463\) −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
\(465\) 0 0
\(466\) 53.1752 + 18.4854i 0.114110 + 0.0396681i
\(467\) −606.103 −1.29786 −0.648932 0.760846i \(-0.724784\pi\)
−0.648932 + 0.760846i \(0.724784\pi\)
\(468\) 0 0
\(469\) −285.196 −0.608094
\(470\) 130.838 52.1974i 0.278379 0.111058i
\(471\) 0 0
\(472\) −407.324 639.545i −0.862975 1.35497i
\(473\) 414.851i 0.877063i
\(474\) 0 0
\(475\) −647.776 92.9214i −1.36374 0.195624i
\(476\) 407.547 515.339i 0.856190 1.08265i
\(477\) 0 0
\(478\) 559.185 + 194.390i 1.16984 + 0.406673i
\(479\) 138.947i 0.290078i 0.989426 + 0.145039i \(0.0463307\pi\)
−0.989426 + 0.145039i \(0.953669\pi\)
\(480\) 0 0
\(481\) 171.299 0.356131
\(482\) −305.893 + 879.935i −0.634632 + 1.82559i
\(483\) 0 0
\(484\) −70.5876 55.8229i −0.145842 0.115337i
\(485\) 498.199 431.834i 1.02722 0.890379i
\(486\) 0 0
\(487\) −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
\(489\) 0 0
\(490\) −392.879 + 156.738i −0.801794 + 0.319873i
\(491\) 347.368i 0.707470i −0.935346 0.353735i \(-0.884911\pi\)
0.935346 0.353735i \(-0.115089\pi\)
\(492\) 0 0
\(493\) 6.02513i 0.0122214i
\(494\) 129.897 373.664i 0.262949 0.756404i
\(495\) 0 0
\(496\) 716.591 169.711i 1.44474 0.342159i
\(497\) 68.7610i 0.138352i
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) −267.641 93.0401i −0.533149 0.185339i
\(503\) −436.350 −0.867496 −0.433748 0.901034i \(-0.642809\pi\)
−0.433748 + 0.901034i \(0.642809\pi\)
\(504\) 0 0
\(505\) −96.4469 111.269i −0.190984 0.220335i
\(506\) 31.3954 + 10.9140i 0.0620462 + 0.0215692i
\(507\) 0 0
\(508\) 602.559 + 476.523i 1.18614 + 0.938037i
\(509\) 109.547 0.215219 0.107610 0.994193i \(-0.465680\pi\)
0.107610 + 0.994193i \(0.465680\pi\)
\(510\) 0 0
\(511\) 328.508i 0.642872i
\(512\) −66.6415 507.644i −0.130159 0.991493i
\(513\) 0 0
\(514\) 78.8796 + 27.4210i 0.153462 + 0.0533482i
\(515\) 470.888 + 543.255i 0.914345 + 1.05486i
\(516\) 0 0
\(517\) 139.807i 0.270419i
\(518\) 409.193 + 142.248i 0.789947 + 0.274610i
\(519\) 0 0
\(520\) −86.2941 + 289.677i −0.165950 + 0.557071i
\(521\) 743.100 1.42629 0.713147 0.701014i \(-0.247269\pi\)
0.713147 + 0.701014i \(0.247269\pi\)
\(522\) 0 0
\(523\) −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
\(525\) 0 0
\(526\) −133.498 + 384.023i −0.253799 + 0.730083i
\(527\) 791.196 1.50132
\(528\) 0 0
\(529\) −526.196 −0.994699
\(530\) −84.0005 210.556i −0.158491 0.397275i
\(531\) 0 0
\(532\) 620.586 784.727i 1.16652 1.47505i
\(533\) 584.105i 1.09588i
\(534\) 0 0
\(535\) 114.954 + 132.621i 0.214867 + 0.247889i
\(536\) −201.402 + 128.272i −0.375750 + 0.239314i
\(537\) 0 0
\(538\) −160.269 + 461.033i −0.297898 + 0.856939i
\(539\) 419.809i 0.778867i
\(540\) 0 0
\(541\) 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
\(543\) 0 0
\(544\) 56.0208 547.228i 0.102979 1.00593i
\(545\) −496.145 572.393i −0.910357 1.05026i
\(546\) 0 0
\(547\) 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
\(549\) 0 0
\(550\) −227.848 + 440.839i −0.414270 + 0.801526i
\(551\) 9.17469i 0.0166510i
\(552\) 0 0
\(553\) 439.779i 0.795261i
\(554\) −933.561 324.534i −1.68513 0.585802i
\(555\) 0 0
\(556\) −114.199 + 144.404i −0.205394 + 0.259720i
\(557\) 788.492i 1.41561i 0.706410 + 0.707803i \(0.250314\pi\)
−0.706410 + 0.707803i \(0.749686\pi\)
\(558\) 0 0
\(559\) 315.854i 0.565035i
\(560\) −446.686 + 620.310i −0.797654 + 1.10770i
\(561\) 0 0
\(562\) −28.5026 + 81.9910i −0.0507164 + 0.145892i
\(563\) 936.102 1.66270 0.831351 0.555747i \(-0.187568\pi\)
0.831351 + 0.555747i \(0.187568\pi\)
\(564\) 0 0
\(565\) 122.048 105.790i 0.216014 0.187239i
\(566\) 204.096 587.107i 0.360594 1.03729i
\(567\) 0 0
\(568\) −30.9266 48.5582i −0.0544482 0.0854898i
\(569\) 95.4983 0.167835 0.0839177 0.996473i \(-0.473257\pi\)
0.0839177 + 0.996473i \(0.473257\pi\)
\(570\) 0 0
\(571\) 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
\(573\) 0 0
\(574\) −485.045 + 1395.29i −0.845026 + 2.43081i
\(575\) −5.94422 + 41.4385i −0.0103378 + 0.0720670i
\(576\) 0 0
\(577\) 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
\(579\) 0 0
\(580\) −0.315590 7.00283i −0.000544120 0.0120738i
\(581\) −230.598 −0.396898
\(582\) 0 0
\(583\) 224.988 0.385915
\(584\) −147.752 231.988i −0.253001 0.397240i
\(585\) 0 0
\(586\) −463.223 161.031i −0.790484 0.274796i
\(587\) −95.8440 −0.163278 −0.0816388 0.996662i \(-0.526015\pi\)
−0.0816388 + 0.996662i \(0.526015\pi\)
\(588\) 0 0
\(589\) 1204.78 2.04547
\(590\) 351.205 + 880.331i 0.595263 + 1.49209i
\(591\) 0 0
\(592\) 352.946 83.5883i 0.596192 0.141197i
\(593\) 878.624i 1.48166i −0.671693 0.740829i \(-0.734433\pi\)
0.671693 0.740829i \(-0.265567\pi\)
\(594\) 0 0
\(595\) −620.586 + 537.918i −1.04300 + 0.904063i
\(596\) 36.5498 + 28.9047i 0.0613252 + 0.0484979i
\(597\) 0 0
\(598\) −23.9034 8.30957i −0.0399723 0.0138956i
\(599\) 967.652i 1.61545i 0.589563 + 0.807723i \(0.299300\pi\)
−0.589563 + 0.807723i \(0.700700\pi\)
\(600\) 0 0
\(601\) 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
\(603\) 0 0
\(604\) −311.203 + 393.513i −0.515236 + 0.651512i
\(605\) 73.6802 + 85.0036i 0.121785 + 0.140502i
\(606\) 0 0
\(607\) 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
\(609\) 0 0
\(610\) −352.949 + 140.808i −0.578605 + 0.230833i
\(611\) 106.444i 0.174213i
\(612\) 0 0
\(613\) 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
\(615\) 0 0
\(616\) −407.547 639.894i −0.661601 1.03879i
\(617\) 764.888i 1.23969i 0.784725 + 0.619844i \(0.212804\pi\)
−0.784725 + 0.619844i \(0.787196\pi\)
\(618\) 0 0
\(619\) 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
\(621\) 0 0
\(622\) −808.077 280.912i −1.29916 0.451627i
\(623\) −957.410 −1.53677
\(624\) 0 0
\(625\) −599.797 175.693i −0.959676 0.281109i
\(626\) −158.447 55.0810i −0.253110 0.0879888i
\(627\) 0 0
\(628\) −489.343 + 618.771i −0.779209 + 0.985304i
\(629\) 389.691 0.619541
\(630\) 0 0
\(631\) 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
\(633\) 0 0
\(634\) 211.966 + 73.6859i 0.334331 + 0.116224i
\(635\) −628.959 725.619i −0.990486 1.14271i
\(636\) 0 0
\(637\) 319.630i 0.501773i
\(638\) 6.57147 + 2.28444i 0.0103001 + 0.00358063i
\(639\) 0 0
\(640\) −36.4480 + 638.961i −0.0569501 + 0.998377i
\(641\) 1111.69 1.73431 0.867154 0.498041i \(-0.165947\pi\)
0.867154 + 0.498041i \(0.165947\pi\)
\(642\) 0 0
\(643\) 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
\(645\) 0 0
\(646\) 295.505 850.054i 0.457438 1.31587i
\(647\) 96.7647 0.149559 0.0747795 0.997200i \(-0.476175\pi\)
0.0747795 + 0.997200i \(0.476175\pi\)
\(648\) 0 0
\(649\) −940.675 −1.44942
\(650\) 173.477 335.641i 0.266887 0.516371i
\(651\) 0 0
\(652\) 57.7907 + 45.7027i 0.0886360 + 0.0700961i
\(653\) 920.353i 1.40942i 0.709494 + 0.704712i \(0.248924\pi\)
−0.709494 + 0.704712i \(0.751076\pi\)
\(654\) 0 0
\(655\) 160.301 138.947i 0.244734 0.212133i
\(656\) 285.024 + 1203.49i 0.434488 + 1.83459i
\(657\) 0 0
\(658\) 88.3921 254.270i 0.134335 0.386429i
\(659\) 591.020i 0.896844i −0.893822 0.448422i \(-0.851986\pi\)
0.893822 0.448422i \(-0.148014\pi\)
\(660\) 0 0
\(661\) −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
\(663\) 0 0
\(664\) −162.846 + 103.716i −0.245249 + 0.156198i
\(665\) −944.990 + 819.107i −1.42104 + 1.23174i
\(666\) 0 0
\(667\) 0.586909 0.000879924
\(668\) 291.445 + 230.484i 0.436295 + 0.345035i
\(669\) 0 0
\(670\) 277.229 110.600i 0.413775 0.165074i
\(671\) 377.142i 0.562060i
\(672\) 0 0
\(673\) 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
\(675\) 0 0
\(676\) −351.083 277.647i −0.519353 0.410721i
\(677\) 58.1920i 0.0859557i 0.999076 + 0.0429779i \(0.0136845\pi\)
−0.999076 + 0.0429779i \(0.986316\pi\)
\(678\) 0 0
\(679\) 1259.94i 1.85558i
\(680\) −196.312 + 658.991i −0.288694 + 0.969105i
\(681\) 0 0
\(682\) 299.984 862.940i 0.439860 1.26531i
\(683\) 357.274 0.523096 0.261548 0.965191i \(-0.415767\pi\)
0.261548 + 0.965191i \(0.415767\pi\)
\(684\) 0 0
\(685\) 781.540 677.430i 1.14093 0.988949i
\(686\) 42.0482 120.956i 0.0612947 0.176321i
\(687\) 0 0
\(688\) −154.127 650.788i −0.224021 0.945913i
\(689\) −171.299 −0.248620
\(690\) 0 0
\(691\) 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
\(693\) 0 0
\(694\) 5.84222 16.8058i 0.00841818 0.0242159i
\(695\) 173.896 150.731i 0.250210 0.216879i
\(696\) 0 0
\(697\) 1328.79i 1.90644i
\(698\) −12.7415 + 36.6524i −0.0182543 + 0.0525107i
\(699\) 0 0
\(700\) 693.113 657.711i 0.990162 0.939587i
\(701\) 886.028 1.26395 0.631975 0.774989i \(-0.282245\pi\)
0.631975 + 0.774989i \(0.282245\pi\)
\(702\) 0 0
\(703\) 593.397 0.844093
\(704\) −575.609 268.584i −0.817626 0.381511i
\(705\) 0 0
\(706\) 151.677 + 52.7276i 0.214840 + 0.0746849i
\(707\) −281.398 −0.398017
\(708\) 0 0
\(709\) −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
\(711\) 0 0
\(712\) −676.111 + 430.613i −0.949594 + 0.604794i
\(713\) 77.0706i 0.108093i
\(714\) 0 0
\(715\) 245.606 + 283.351i 0.343505 + 0.396296i
\(716\) 575.609 727.853i 0.803923 1.01655i
\(717\) 0 0
\(718\) 593.397 + 206.283i 0.826458 + 0.287302i
\(719\) 575.877i 0.800942i 0.916309 + 0.400471i \(0.131154\pi\)
−0.916309 + 0.400471i \(0.868846\pi\)
\(720\) 0 0
\(721\) 1373.88 1.90553
\(722\) 212.903 612.441i 0.294880 0.848257i
\(723\) 0 0
\(724\) 684.268 + 541.141i 0.945122 + 0.747432i
\(725\) −1.24421 + 8.67363i −0.00171615 + 0.0119636i
\(726\) 0 0
\(727\) −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
\(729\) 0 0
\(730\) 127.396 + 319.331i 0.174515 + 0.437440i
\(731\) 718.542i 0.982958i
\(732\) 0 0
\(733\) 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
\(735\) 0 0
\(736\) −53.3056 5.45700i −0.0724261 0.00741440i
\(737\) 296.232i 0.401943i
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) −409.193 142.248i −0.551473 0.191709i
\(743\) 183.712 0.247258 0.123629 0.992329i \(-0.460547\pi\)
0.123629 + 0.992329i \(0.460547\pi\)
\(744\) 0 0
\(745\) −38.1512 44.0143i −0.0512096 0.0590797i
\(746\) 162.715 + 56.5648i 0.218117 + 0.0758241i
\(747\) 0 0
\(748\) −535.281 423.317i −0.715617 0.565932i
\(749\) 335.395 0.447791
\(750\) 0 0
\(751\) 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
\(753\) 0 0
\(754\) −5.00331 1.73930i −0.00663569 0.00230677i
\(755\) 473.880 410.754i 0.627656 0.544045i
\(756\) 0 0
\(757\) 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
\(759\) 0 0
\(760\) −298.932 + 1003.47i −0.393331 + 1.32036i
\(761\) −251.485 −0.330467 −0.165233 0.986255i \(-0.552838\pi\)
−0.165233 + 0.986255i \(0.552838\pi\)
\(762\) 0 0
\(763\) −1447.57 −1.89721
\(764\) −340.440 + 430.484i −0.445602 + 0.563461i
\(765\) 0 0
\(766\) 142.337 409.450i 0.185819 0.534529i
\(767\) 716.200 0.933768
\(768\) 0 0
\(769\) 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
\(771\) 0 0
\(772\) −91.8764 + 116.177i −0.119011 + 0.150488i
\(773\) 1328.04i 1.71803i −0.511951 0.859015i \(-0.671077\pi\)
0.511951 0.859015i \(-0.328923\pi\)
\(774\) 0 0
\(775\) 1138.99 + 163.384i 1.46966 + 0.210818i
\(776\) −566.681 889.753i −0.730259 1.14659i
\(777\) 0 0
\(778\) 313.015 900.424i 0.402333 1.15736i
\(779\) 2023.40i 2.59743i
\(780\) 0 0
\(781\) −71.4219 −0.0914492
\(782\) −54.3784 18.9036i −0.0695376 0.0241734i
\(783\) 0 0
\(784\) 155.969 + 658.567i 0.198940 + 0.840009i
\(785\) 745.141 645.880i 0.949224 0.822778i
\(786\) 0 0
\(787\) −1318.83 −1.67577 −0.837883 0.545850i \(-0.816207\pi\)
−0.837883 + 0.545850i \(0.816207\pi\)
\(788\) 482.772 610.461i 0.612654 0.774697i
\(789\) 0 0