Properties

Label 108.3.k.a.5.6
Level 108
Weight 3
Character 108.5
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.6
Character \(\chi\) \(=\) 108.5
Dual form 108.3.k.a.65.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.99363 - 0.195330i) q^{3} +(-2.50118 - 6.87194i) q^{5} +(-1.62729 - 9.22884i) q^{7} +(8.92369 - 1.16949i) q^{9} +O(q^{10})\) \(q+(2.99363 - 0.195330i) q^{3} +(-2.50118 - 6.87194i) q^{5} +(-1.62729 - 9.22884i) q^{7} +(8.92369 - 1.16949i) q^{9} +(-4.02712 + 11.0644i) q^{11} +(17.4349 + 14.6296i) q^{13} +(-8.82992 - 20.0835i) q^{15} +(-13.5275 - 7.81011i) q^{17} +(9.08487 + 15.7354i) q^{19} +(-6.67419 - 27.3099i) q^{21} +(23.0574 + 4.06564i) q^{23} +(-21.8166 + 18.3063i) q^{25} +(26.4858 - 5.24410i) q^{27} +(-24.8898 - 29.6625i) q^{29} +(-4.47532 + 25.3808i) q^{31} +(-9.89451 + 33.9094i) q^{33} +(-59.3499 + 34.2657i) q^{35} +(1.45889 - 2.52687i) q^{37} +(55.0514 + 40.3903i) q^{39} +(-26.1577 + 31.1736i) q^{41} +(35.7017 + 12.9943i) q^{43} +(-30.3565 - 58.3980i) q^{45} +(-18.5209 + 3.26574i) q^{47} +(-36.4785 + 13.2771i) q^{49} +(-42.0220 - 20.7383i) q^{51} +12.3119i q^{53} +86.1066 q^{55} +(30.2704 + 45.3316i) q^{57} +(4.38973 + 12.0607i) q^{59} +(-15.6708 - 88.8733i) q^{61} +(-25.3145 - 80.4522i) q^{63} +(56.9261 - 156.403i) q^{65} +(-6.68767 - 5.61162i) q^{67} +(69.8195 + 7.66724i) q^{69} +(81.5508 + 47.0834i) q^{71} +(-25.3297 - 43.8724i) q^{73} +(-61.7350 + 59.0637i) q^{75} +(108.665 + 19.1606i) q^{77} +(-78.4939 + 65.8642i) q^{79} +(78.2646 - 20.8724i) q^{81} +(-12.1497 - 14.4795i) q^{83} +(-19.8359 + 112.495i) q^{85} +(-80.3049 - 83.9370i) q^{87} +(-52.8907 + 30.5364i) q^{89} +(106.643 - 184.711i) q^{91} +(-8.43984 + 76.8550i) q^{93} +(85.4102 - 101.788i) q^{95} +(-139.585 - 50.8047i) q^{97} +(-22.9970 + 103.445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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 0
\(3\) 2.99363 0.195330i 0.997878 0.0651100i
\(4\) 0 0
\(5\) −2.50118 6.87194i −0.500236 1.37439i −0.891044 0.453916i \(-0.850027\pi\)
0.390808 0.920472i \(-0.372196\pi\)
\(6\) 0 0
\(7\) −1.62729 9.22884i −0.232470 1.31841i −0.847876 0.530195i \(-0.822119\pi\)
0.615405 0.788211i \(-0.288992\pi\)
\(8\) 0 0
\(9\) 8.92369 1.16949i 0.991521 0.129944i
\(10\) 0 0
\(11\) −4.02712 + 11.0644i −0.366102 + 1.00586i 0.610728 + 0.791840i \(0.290877\pi\)
−0.976830 + 0.214016i \(0.931345\pi\)
\(12\) 0 0
\(13\) 17.4349 + 14.6296i 1.34115 + 1.12536i 0.981329 + 0.192336i \(0.0616063\pi\)
0.359820 + 0.933022i \(0.382838\pi\)
\(14\) 0 0
\(15\) −8.82992 20.0835i −0.588661 1.33890i
\(16\) 0 0
\(17\) −13.5275 7.81011i −0.795736 0.459418i 0.0462422 0.998930i \(-0.485275\pi\)
−0.841978 + 0.539512i \(0.818609\pi\)
\(18\) 0 0
\(19\) 9.08487 + 15.7354i 0.478151 + 0.828182i 0.999686 0.0250481i \(-0.00797389\pi\)
−0.521535 + 0.853230i \(0.674641\pi\)
\(20\) 0 0
\(21\) −6.67419 27.3099i −0.317819 1.30047i
\(22\) 0 0
\(23\) 23.0574 + 4.06564i 1.00250 + 0.176767i 0.650720 0.759318i \(-0.274467\pi\)
0.351775 + 0.936085i \(0.385578\pi\)
\(24\) 0 0
\(25\) −21.8166 + 18.3063i −0.872662 + 0.732251i
\(26\) 0 0
\(27\) 26.4858 5.24410i 0.980957 0.194226i
\(28\) 0 0
\(29\) −24.8898 29.6625i −0.858269 1.02284i −0.999460 0.0328626i \(-0.989538\pi\)
0.141191 0.989982i \(-0.454907\pi\)
\(30\) 0 0
\(31\) −4.47532 + 25.3808i −0.144365 + 0.818735i 0.823510 + 0.567302i \(0.192013\pi\)
−0.967875 + 0.251433i \(0.919098\pi\)
\(32\) 0 0
\(33\) −9.89451 + 33.9094i −0.299834 + 1.02756i
\(34\) 0 0
\(35\) −59.3499 + 34.2657i −1.69571 + 0.979019i
\(36\) 0 0
\(37\) 1.45889 2.52687i 0.0394294 0.0682937i −0.845637 0.533758i \(-0.820779\pi\)
0.885067 + 0.465464i \(0.154113\pi\)
\(38\) 0 0
\(39\) 55.0514 + 40.3903i 1.41158 + 1.03565i
\(40\) 0 0
\(41\) −26.1577 + 31.1736i −0.637993 + 0.760331i −0.984052 0.177882i \(-0.943075\pi\)
0.346058 + 0.938213i \(0.387520\pi\)
\(42\) 0 0
\(43\) 35.7017 + 12.9943i 0.830271 + 0.302194i 0.721970 0.691924i \(-0.243237\pi\)
0.108301 + 0.994118i \(0.465459\pi\)
\(44\) 0 0
\(45\) −30.3565 58.3980i −0.674588 1.29773i
\(46\) 0 0
\(47\) −18.5209 + 3.26574i −0.394063 + 0.0694839i −0.367169 0.930154i \(-0.619673\pi\)
−0.0268941 + 0.999638i \(0.508562\pi\)
\(48\) 0 0
\(49\) −36.4785 + 13.2771i −0.744458 + 0.270961i
\(50\) 0 0
\(51\) −42.0220 20.7383i −0.823960 0.406633i
\(52\) 0 0
\(53\) 12.3119i 0.232300i 0.993232 + 0.116150i \(0.0370554\pi\)
−0.993232 + 0.116150i \(0.962945\pi\)
\(54\) 0 0
\(55\) 86.1066 1.56557
\(56\) 0 0
\(57\) 30.2704 + 45.3316i 0.531059 + 0.795292i
\(58\) 0 0
\(59\) 4.38973 + 12.0607i 0.0744022 + 0.204418i 0.971319 0.237782i \(-0.0764203\pi\)
−0.896916 + 0.442200i \(0.854198\pi\)
\(60\) 0 0
\(61\) −15.6708 88.8733i −0.256898 1.45694i −0.791154 0.611617i \(-0.790520\pi\)
0.534257 0.845322i \(-0.320592\pi\)
\(62\) 0 0
\(63\) −25.3145 80.4522i −0.401818 1.27702i
\(64\) 0 0
\(65\) 56.9261 156.403i 0.875787 2.40620i
\(66\) 0 0
\(67\) −6.68767 5.61162i −0.0998159 0.0837555i 0.591514 0.806295i \(-0.298530\pi\)
−0.691330 + 0.722539i \(0.742975\pi\)
\(68\) 0 0
\(69\) 69.8195 + 7.66724i 1.01188 + 0.111119i
\(70\) 0 0
\(71\) 81.5508 + 47.0834i 1.14860 + 0.663146i 0.948546 0.316638i \(-0.102554\pi\)
0.200057 + 0.979784i \(0.435887\pi\)
\(72\) 0 0
\(73\) −25.3297 43.8724i −0.346983 0.600992i 0.638729 0.769432i \(-0.279460\pi\)
−0.985712 + 0.168440i \(0.946127\pi\)
\(74\) 0 0
\(75\) −61.7350 + 59.0637i −0.823134 + 0.787516i
\(76\) 0 0
\(77\) 108.665 + 19.1606i 1.41123 + 0.248839i
\(78\) 0 0
\(79\) −78.4939 + 65.8642i −0.993593 + 0.833724i −0.986084 0.166248i \(-0.946835\pi\)
−0.00750946 + 0.999972i \(0.502390\pi\)
\(80\) 0 0
\(81\) 78.2646 20.8724i 0.966229 0.257684i
\(82\) 0 0
\(83\) −12.1497 14.4795i −0.146382 0.174451i 0.687871 0.725833i \(-0.258545\pi\)
−0.834253 + 0.551381i \(0.814101\pi\)
\(84\) 0 0
\(85\) −19.8359 + 112.495i −0.233363 + 1.32347i
\(86\) 0 0
\(87\) −80.3049 83.9370i −0.923045 0.964793i
\(88\) 0 0
\(89\) −52.8907 + 30.5364i −0.594277 + 0.343106i −0.766787 0.641902i \(-0.778146\pi\)
0.172510 + 0.985008i \(0.444812\pi\)
\(90\) 0 0
\(91\) 106.643 184.711i 1.17190 2.02979i
\(92\) 0 0
\(93\) −8.43984 + 76.8550i −0.0907510 + 0.826398i
\(94\) 0 0
\(95\) 85.4102 101.788i 0.899055 1.07145i
\(96\) 0 0
\(97\) −139.585 50.8047i −1.43902 0.523760i −0.499516 0.866305i \(-0.666489\pi\)
−0.939501 + 0.342545i \(0.888711\pi\)
\(98\) 0 0
\(99\) −22.9970 + 103.445i −0.232293 + 1.04490i
\(100\) 0 0
\(101\) 3.22458 0.568581i 0.0319266 0.00562952i −0.157662 0.987493i \(-0.550396\pi\)
0.189589 + 0.981864i \(0.439285\pi\)
\(102\) 0 0
\(103\) 18.2867 6.65582i 0.177541 0.0646196i −0.251720 0.967800i \(-0.580996\pi\)
0.429261 + 0.903180i \(0.358774\pi\)
\(104\) 0 0
\(105\) −170.979 + 114.172i −1.62837 + 1.08735i
\(106\) 0 0
\(107\) 24.7281i 0.231103i −0.993301 0.115552i \(-0.963136\pi\)
0.993301 0.115552i \(-0.0368636\pi\)
\(108\) 0 0
\(109\) 1.01801 0.00933957 0.00466979 0.999989i \(-0.498514\pi\)
0.00466979 + 0.999989i \(0.498514\pi\)
\(110\) 0 0
\(111\) 3.87380 7.84947i 0.0348991 0.0707160i
\(112\) 0 0
\(113\) 53.0907 + 145.865i 0.469829 + 1.29084i 0.917888 + 0.396840i \(0.129893\pi\)
−0.448059 + 0.894004i \(0.647884\pi\)
\(114\) 0 0
\(115\) −29.7319 168.618i −0.258538 1.46624i
\(116\) 0 0
\(117\) 172.693 + 110.160i 1.47601 + 0.941542i
\(118\) 0 0
\(119\) −50.0650 + 137.553i −0.420714 + 1.15590i
\(120\) 0 0
\(121\) −13.5123 11.3382i −0.111672 0.0937041i
\(122\) 0 0
\(123\) −72.2175 + 98.4316i −0.587134 + 0.800257i
\(124\) 0 0
\(125\) 22.0364 + 12.7227i 0.176291 + 0.101782i
\(126\) 0 0
\(127\) 35.9061 + 62.1913i 0.282726 + 0.489695i 0.972055 0.234753i \(-0.0754281\pi\)
−0.689330 + 0.724448i \(0.742095\pi\)
\(128\) 0 0
\(129\) 109.416 + 31.9267i 0.848185 + 0.247494i
\(130\) 0 0
\(131\) −17.2894 3.04859i −0.131980 0.0232717i 0.107268 0.994230i \(-0.465790\pi\)
−0.239248 + 0.970958i \(0.576901\pi\)
\(132\) 0 0
\(133\) 130.436 109.449i 0.980723 0.822924i
\(134\) 0 0
\(135\) −102.283 168.893i −0.757652 1.25106i
\(136\) 0 0
\(137\) −13.3559 15.9169i −0.0974881 0.116182i 0.715095 0.699028i \(-0.246384\pi\)
−0.812583 + 0.582846i \(0.801939\pi\)
\(138\) 0 0
\(139\) −1.08034 + 6.12690i −0.00777221 + 0.0440784i −0.988447 0.151565i \(-0.951569\pi\)
0.980675 + 0.195644i \(0.0626797\pi\)
\(140\) 0 0
\(141\) −54.8070 + 13.3941i −0.388702 + 0.0949938i
\(142\) 0 0
\(143\) −232.081 + 133.992i −1.62295 + 0.937008i
\(144\) 0 0
\(145\) −141.585 + 245.233i −0.976449 + 1.69126i
\(146\) 0 0
\(147\) −106.610 + 46.8720i −0.725236 + 0.318857i
\(148\) 0 0
\(149\) 144.811 172.579i 0.971888 1.15825i −0.0154918 0.999880i \(-0.504931\pi\)
0.987380 0.158371i \(-0.0506242\pi\)
\(150\) 0 0
\(151\) −221.794 80.7264i −1.46883 0.534612i −0.521051 0.853526i \(-0.674460\pi\)
−0.947784 + 0.318914i \(0.896682\pi\)
\(152\) 0 0
\(153\) −129.849 53.8747i −0.848687 0.352122i
\(154\) 0 0
\(155\) 185.609 32.7279i 1.19748 0.211148i
\(156\) 0 0
\(157\) −34.1578 + 12.4324i −0.217566 + 0.0791874i −0.448503 0.893781i \(-0.648043\pi\)
0.230938 + 0.972969i \(0.425821\pi\)
\(158\) 0 0
\(159\) 2.40488 + 36.8573i 0.0151251 + 0.231807i
\(160\) 0 0
\(161\) 219.409i 1.36279i
\(162\) 0 0
\(163\) −68.8785 −0.422568 −0.211284 0.977425i \(-0.567764\pi\)
−0.211284 + 0.977425i \(0.567764\pi\)
\(164\) 0 0
\(165\) 257.772 16.8192i 1.56225 0.101935i
\(166\) 0 0
\(167\) 38.6584 + 106.213i 0.231488 + 0.636007i 0.999993 0.00383681i \(-0.00122130\pi\)
−0.768505 + 0.639844i \(0.778999\pi\)
\(168\) 0 0
\(169\) 60.6039 + 343.702i 0.358603 + 2.03374i
\(170\) 0 0
\(171\) 99.4730 + 129.794i 0.581714 + 0.759027i
\(172\) 0 0
\(173\) 46.9901 129.104i 0.271619 0.746267i −0.726625 0.687034i \(-0.758912\pi\)
0.998244 0.0592329i \(-0.0188655\pi\)
\(174\) 0 0
\(175\) 204.448 + 171.552i 1.16827 + 0.980296i
\(176\) 0 0
\(177\) 15.4971 + 35.2478i 0.0875540 + 0.199140i
\(178\) 0 0
\(179\) 166.758 + 96.2777i 0.931608 + 0.537864i 0.887320 0.461155i \(-0.152565\pi\)
0.0442884 + 0.999019i \(0.485898\pi\)
\(180\) 0 0
\(181\) −38.0528 65.9094i −0.210237 0.364140i 0.741552 0.670895i \(-0.234090\pi\)
−0.951788 + 0.306755i \(0.900757\pi\)
\(182\) 0 0
\(183\) −64.2721 262.993i −0.351214 1.43712i
\(184\) 0 0
\(185\) −21.0134 3.70523i −0.113586 0.0200283i
\(186\) 0 0
\(187\) 140.891 118.222i 0.753429 0.632202i
\(188\) 0 0
\(189\) −91.4971 235.900i −0.484112 1.24815i
\(190\) 0 0
\(191\) −132.171 157.515i −0.691992 0.824684i 0.299603 0.954064i \(-0.403146\pi\)
−0.991595 + 0.129380i \(0.958701\pi\)
\(192\) 0 0
\(193\) 50.6060 287.001i 0.262207 1.48705i −0.514665 0.857391i \(-0.672084\pi\)
0.776872 0.629659i \(-0.216805\pi\)
\(194\) 0 0
\(195\) 139.866 479.334i 0.717261 2.45812i
\(196\) 0 0
\(197\) −263.147 + 151.928i −1.33577 + 0.771209i −0.986178 0.165692i \(-0.947014\pi\)
−0.349595 + 0.936901i \(0.613681\pi\)
\(198\) 0 0
\(199\) 133.234 230.767i 0.669515 1.15963i −0.308525 0.951216i \(-0.599835\pi\)
0.978040 0.208418i \(-0.0668314\pi\)
\(200\) 0 0
\(201\) −21.1165 15.4928i −0.105057 0.0770788i
\(202\) 0 0
\(203\) −233.247 + 277.974i −1.14900 + 1.36933i
\(204\) 0 0
\(205\) 279.648 + 101.784i 1.36414 + 0.496505i
\(206\) 0 0
\(207\) 210.512 + 9.31507i 1.01697 + 0.0450004i
\(208\) 0 0
\(209\) −210.689 + 37.1502i −1.00808 + 0.177752i
\(210\) 0 0
\(211\) −83.5395 + 30.4059i −0.395922 + 0.144104i −0.532306 0.846552i \(-0.678674\pi\)
0.136384 + 0.990656i \(0.456452\pi\)
\(212\) 0 0
\(213\) 253.330 + 125.021i 1.18934 + 0.586954i
\(214\) 0 0
\(215\) 277.841i 1.29228i
\(216\) 0 0
\(217\) 241.518 1.11299
\(218\) 0 0
\(219\) −84.3976 126.390i −0.385377 0.577124i
\(220\) 0 0
\(221\) −121.592 334.071i −0.550190 1.51164i
\(222\) 0 0
\(223\) 50.4092 + 285.885i 0.226050 + 1.28199i 0.860667 + 0.509168i \(0.170047\pi\)
−0.634617 + 0.772827i \(0.718842\pi\)
\(224\) 0 0
\(225\) −173.275 + 188.874i −0.770112 + 0.839439i
\(226\) 0 0
\(227\) −63.1774 + 173.578i −0.278315 + 0.764663i 0.719239 + 0.694762i \(0.244490\pi\)
−0.997554 + 0.0699006i \(0.977732\pi\)
\(228\) 0 0
\(229\) −261.099 219.088i −1.14017 0.956715i −0.140724 0.990049i \(-0.544943\pi\)
−0.999444 + 0.0333342i \(0.989387\pi\)
\(230\) 0 0
\(231\) 329.046 + 36.1342i 1.42444 + 0.156425i
\(232\) 0 0
\(233\) 262.837 + 151.749i 1.12806 + 0.651283i 0.943445 0.331528i \(-0.107564\pi\)
0.184611 + 0.982812i \(0.440898\pi\)
\(234\) 0 0
\(235\) 68.7662 + 119.107i 0.292622 + 0.506837i
\(236\) 0 0
\(237\) −222.117 + 212.505i −0.937201 + 0.896648i
\(238\) 0 0
\(239\) −431.057 76.0070i −1.80359 0.318021i −0.832013 0.554756i \(-0.812812\pi\)
−0.971574 + 0.236735i \(0.923923\pi\)
\(240\) 0 0
\(241\) −124.647 + 104.591i −0.517209 + 0.433990i −0.863657 0.504079i \(-0.831832\pi\)
0.346449 + 0.938069i \(0.387387\pi\)
\(242\) 0 0
\(243\) 230.219 77.7717i 0.947401 0.320048i
\(244\) 0 0
\(245\) 182.479 + 217.469i 0.744810 + 0.887630i
\(246\) 0 0
\(247\) −71.8100 + 407.255i −0.290729 + 1.64881i
\(248\) 0 0
\(249\) −39.2001 40.9730i −0.157430 0.164550i
\(250\) 0 0
\(251\) 394.843 227.963i 1.57308 0.908219i 0.577292 0.816538i \(-0.304109\pi\)
0.995788 0.0916811i \(-0.0292240\pi\)
\(252\) 0 0
\(253\) −137.839 + 238.744i −0.544817 + 0.943652i
\(254\) 0 0
\(255\) −37.4077 + 340.643i −0.146697 + 1.33585i
\(256\) 0 0
\(257\) −266.990 + 318.187i −1.03887 + 1.23808i −0.0682006 + 0.997672i \(0.521726\pi\)
−0.970672 + 0.240408i \(0.922719\pi\)
\(258\) 0 0
\(259\) −25.6941 9.35188i −0.0992049 0.0361076i
\(260\) 0 0
\(261\) −256.799 235.591i −0.983904 0.902646i
\(262\) 0 0
\(263\) −420.070 + 74.0696i −1.59722 + 0.281633i −0.900220 0.435435i \(-0.856595\pi\)
−0.697003 + 0.717068i \(0.745483\pi\)
\(264\) 0 0
\(265\) 84.6067 30.7943i 0.319271 0.116205i
\(266\) 0 0
\(267\) −152.371 + 101.746i −0.570676 + 0.381071i
\(268\) 0 0
\(269\) 229.784i 0.854215i −0.904201 0.427108i \(-0.859533\pi\)
0.904201 0.427108i \(-0.140467\pi\)
\(270\) 0 0
\(271\) −247.394 −0.912892 −0.456446 0.889751i \(-0.650878\pi\)
−0.456446 + 0.889751i \(0.650878\pi\)
\(272\) 0 0
\(273\) 283.170 573.788i 1.03725 2.10179i
\(274\) 0 0
\(275\) −114.690 315.109i −0.417056 1.14585i
\(276\) 0 0
\(277\) 25.5477 + 144.888i 0.0922299 + 0.523062i 0.995561 + 0.0941179i \(0.0300031\pi\)
−0.903331 + 0.428944i \(0.858886\pi\)
\(278\) 0 0
\(279\) −10.2537 + 231.724i −0.0367517 + 0.830553i
\(280\) 0 0
\(281\) −15.8083 + 43.4331i −0.0562575 + 0.154566i −0.964638 0.263578i \(-0.915097\pi\)
0.908381 + 0.418145i \(0.137319\pi\)
\(282\) 0 0
\(283\) 94.8323 + 79.5738i 0.335097 + 0.281179i 0.794773 0.606907i \(-0.207590\pi\)
−0.459676 + 0.888087i \(0.652034\pi\)
\(284\) 0 0
\(285\) 235.805 321.399i 0.827385 1.12772i
\(286\) 0 0
\(287\) 330.262 + 190.677i 1.15074 + 0.664379i
\(288\) 0 0
\(289\) −22.5044 38.9787i −0.0778698 0.134874i
\(290\) 0 0
\(291\) −427.789 124.826i −1.47007 0.428954i
\(292\) 0 0
\(293\) 134.669 + 23.7457i 0.459621 + 0.0810435i 0.398664 0.917097i \(-0.369474\pi\)
0.0609563 + 0.998140i \(0.480585\pi\)
\(294\) 0 0
\(295\) 71.9008 60.3319i 0.243731 0.204515i
\(296\) 0 0
\(297\) −48.6387 + 314.169i −0.163767 + 1.05781i
\(298\) 0 0
\(299\) 342.525 + 408.206i 1.14557 + 1.36524i
\(300\) 0 0
\(301\) 61.8256 350.630i 0.205401 1.16489i
\(302\) 0 0
\(303\) 9.54217 2.33198i 0.0314923 0.00769631i
\(304\) 0 0
\(305\) −571.537 + 329.977i −1.87389 + 1.08189i
\(306\) 0 0
\(307\) −148.518 + 257.240i −0.483771 + 0.837915i −0.999826 0.0186398i \(-0.994066\pi\)
0.516056 + 0.856555i \(0.327400\pi\)
\(308\) 0 0
\(309\) 53.4436 23.4970i 0.172957 0.0760422i
\(310\) 0 0
\(311\) 237.230 282.720i 0.762797 0.909067i −0.235224 0.971941i \(-0.575582\pi\)
0.998021 + 0.0628746i \(0.0200268\pi\)
\(312\) 0 0
\(313\) 322.695 + 117.451i 1.03097 + 0.375244i 0.801452 0.598059i \(-0.204061\pi\)
0.229522 + 0.973303i \(0.426284\pi\)
\(314\) 0 0
\(315\) −489.547 + 375.186i −1.55412 + 1.19107i
\(316\) 0 0
\(317\) 537.404 94.7588i 1.69528 0.298924i 0.759239 0.650812i \(-0.225572\pi\)
0.936042 + 0.351889i \(0.114460\pi\)
\(318\) 0 0
\(319\) 428.433 155.937i 1.34305 0.488830i
\(320\) 0 0
\(321\) −4.83013 74.0268i −0.0150471 0.230613i
\(322\) 0 0
\(323\) 283.815i 0.878685i
\(324\) 0 0
\(325\) −648.185 −1.99441
\(326\) 0 0
\(327\) 3.04756 0.198848i 0.00931975 0.000608099i
\(328\) 0 0
\(329\) 60.2780 + 165.612i 0.183216 + 0.503381i
\(330\) 0 0
\(331\) −31.4888 178.582i −0.0951322 0.539522i −0.994707 0.102754i \(-0.967234\pi\)
0.899575 0.436767i \(-0.143877\pi\)
\(332\) 0 0
\(333\) 10.0635 24.2551i 0.0302207 0.0728382i
\(334\) 0 0
\(335\) −21.8356 + 59.9929i −0.0651810 + 0.179083i
\(336\) 0 0
\(337\) −287.391 241.149i −0.852791 0.715577i 0.107611 0.994193i \(-0.465680\pi\)
−0.960403 + 0.278616i \(0.910124\pi\)
\(338\) 0 0
\(339\) 187.426 + 426.298i 0.552879 + 1.25751i
\(340\) 0 0
\(341\) −262.801 151.728i −0.770678 0.444951i
\(342\) 0 0
\(343\) −47.7015 82.6215i −0.139072 0.240879i
\(344\) 0 0
\(345\) −121.943 498.973i −0.353457 1.44630i
\(346\) 0 0
\(347\) 167.538 + 29.5415i 0.482820 + 0.0851341i 0.409760 0.912193i \(-0.365613\pi\)
0.0730598 + 0.997328i \(0.476724\pi\)
\(348\) 0 0
\(349\) 126.546 106.185i 0.362596 0.304254i −0.443229 0.896409i \(-0.646167\pi\)
0.805824 + 0.592155i \(0.201723\pi\)
\(350\) 0 0
\(351\) 538.498 + 296.048i 1.53418 + 0.843442i
\(352\) 0 0
\(353\) −54.0593 64.4254i −0.153143 0.182508i 0.684018 0.729465i \(-0.260231\pi\)
−0.837161 + 0.546956i \(0.815786\pi\)
\(354\) 0 0
\(355\) 119.581 678.177i 0.336847 1.91036i
\(356\) 0 0
\(357\) −123.008 + 421.561i −0.344561 + 1.18084i
\(358\) 0 0
\(359\) 289.723 167.271i 0.807027 0.465937i −0.0388953 0.999243i \(-0.512384\pi\)
0.845922 + 0.533306i \(0.179051\pi\)
\(360\) 0 0
\(361\) 15.4304 26.7263i 0.0427436 0.0740340i
\(362\) 0 0
\(363\) −42.6657 31.3031i −0.117536 0.0862343i
\(364\) 0 0
\(365\) −238.134 + 283.797i −0.652423 + 0.777527i
\(366\) 0 0
\(367\) 149.979 + 54.5880i 0.408663 + 0.148741i 0.538168 0.842838i \(-0.319117\pi\)
−0.129505 + 0.991579i \(0.541339\pi\)
\(368\) 0 0
\(369\) −196.966 + 308.775i −0.533784 + 0.836787i
\(370\) 0 0
\(371\) 113.625 20.0351i 0.306266 0.0540029i
\(372\) 0 0
\(373\) 307.437 111.898i 0.824227 0.299994i 0.104740 0.994500i \(-0.466599\pi\)
0.719487 + 0.694506i \(0.244377\pi\)
\(374\) 0 0
\(375\) 68.4541 + 33.7828i 0.182544 + 0.0900875i
\(376\) 0 0
\(377\) 881.293i 2.33765i
\(378\) 0 0
\(379\) −244.316 −0.644634 −0.322317 0.946632i \(-0.604462\pi\)
−0.322317 + 0.946632i \(0.604462\pi\)
\(380\) 0 0
\(381\) 119.638 + 179.164i 0.314010 + 0.470248i
\(382\) 0 0
\(383\) −132.824 364.931i −0.346799 0.952822i −0.983372 0.181605i \(-0.941871\pi\)
0.636573 0.771217i \(-0.280351\pi\)
\(384\) 0 0
\(385\) −140.121 794.664i −0.363950 2.06406i
\(386\) 0 0
\(387\) 333.787 + 74.2047i 0.862500 + 0.191743i
\(388\) 0 0
\(389\) −183.766 + 504.892i −0.472406 + 1.29792i 0.443408 + 0.896320i \(0.353769\pi\)
−0.915813 + 0.401604i \(0.868453\pi\)
\(390\) 0 0
\(391\) −280.156 235.079i −0.716511 0.601224i
\(392\) 0 0
\(393\) −52.3536 5.74922i −0.133215 0.0146291i
\(394\) 0 0
\(395\) 648.942 + 374.667i 1.64289 + 0.948524i
\(396\) 0 0
\(397\) −8.55286 14.8140i −0.0215437 0.0373148i 0.855053 0.518541i \(-0.173525\pi\)
−0.876596 + 0.481227i \(0.840191\pi\)
\(398\) 0 0
\(399\) 369.100 353.128i 0.925062 0.885033i
\(400\) 0 0
\(401\) 534.855 + 94.3095i 1.33380 + 0.235186i 0.794674 0.607037i \(-0.207642\pi\)
0.539130 + 0.842222i \(0.318753\pi\)
\(402\) 0 0
\(403\) −449.339 + 377.040i −1.11499 + 0.935584i
\(404\) 0 0
\(405\) −339.188 485.624i −0.837501 1.19907i
\(406\) 0 0
\(407\) 22.0832 + 26.3177i 0.0542585 + 0.0646627i
\(408\) 0 0
\(409\) 14.3282 81.2594i 0.0350323 0.198678i −0.962269 0.272102i \(-0.912281\pi\)
0.997301 + 0.0734234i \(0.0233924\pi\)
\(410\) 0 0
\(411\) −43.0916 45.0406i −0.104846 0.109588i
\(412\) 0 0
\(413\) 104.163 60.1384i 0.252210 0.145613i
\(414\) 0 0
\(415\) −69.1134 + 119.708i −0.166538 + 0.288453i
\(416\) 0 0
\(417\) −2.03737 + 18.5527i −0.00488578 + 0.0444909i
\(418\) 0 0
\(419\) 478.636 570.416i 1.14233 1.36137i 0.219755 0.975555i \(-0.429474\pi\)
0.922574 0.385819i \(-0.126081\pi\)
\(420\) 0 0
\(421\) 670.000 + 243.860i 1.59145 + 0.579240i 0.977653 0.210225i \(-0.0674196\pi\)
0.613796 + 0.789465i \(0.289642\pi\)
\(422\) 0 0
\(423\) −161.456 + 50.8026i −0.381693 + 0.120101i
\(424\) 0 0
\(425\) 438.098 77.2484i 1.03082 0.181761i
\(426\) 0 0
\(427\) −794.696 + 289.246i −1.86112 + 0.677391i
\(428\) 0 0
\(429\) −668.593 + 446.456i −1.55849 + 1.04069i
\(430\) 0 0
\(431\) 60.8696i 0.141229i 0.997504 + 0.0706144i \(0.0224960\pi\)
−0.997504 + 0.0706144i \(0.977504\pi\)
\(432\) 0 0
\(433\) 542.738 1.25344 0.626718 0.779246i \(-0.284398\pi\)
0.626718 + 0.779246i \(0.284398\pi\)
\(434\) 0 0
\(435\) −375.953 + 761.792i −0.864259 + 1.75125i
\(436\) 0 0
\(437\) 145.499 + 399.754i 0.332949 + 0.914769i
\(438\) 0 0
\(439\) −6.32635 35.8785i −0.0144108 0.0817278i 0.976754 0.214363i \(-0.0687674\pi\)
−0.991165 + 0.132635i \(0.957656\pi\)
\(440\) 0 0
\(441\) −309.995 + 161.142i −0.702937 + 0.365401i
\(442\) 0 0
\(443\) −102.451 + 281.481i −0.231266 + 0.635398i −0.999991 0.00418102i \(-0.998669\pi\)
0.768725 + 0.639579i \(0.220891\pi\)
\(444\) 0 0
\(445\) 342.134 + 287.084i 0.768840 + 0.645133i
\(446\) 0 0
\(447\) 399.802 544.926i 0.894412 1.21907i
\(448\) 0 0
\(449\) 569.528 + 328.817i 1.26844 + 0.732332i 0.974692 0.223551i \(-0.0717651\pi\)
0.293745 + 0.955884i \(0.405098\pi\)
\(450\) 0 0
\(451\) −239.577 414.960i −0.531213 0.920088i
\(452\) 0 0
\(453\) −679.738 198.342i −1.50053 0.437842i
\(454\) 0 0
\(455\) −1536.06 270.848i −3.37595 0.595271i
\(456\) 0 0
\(457\) −191.262 + 160.488i −0.418517 + 0.351177i −0.827598 0.561321i \(-0.810293\pi\)
0.409082 + 0.912498i \(0.365849\pi\)
\(458\) 0 0
\(459\) −399.244 135.918i −0.869813 0.296117i
\(460\) 0 0
\(461\) −100.503 119.775i −0.218012 0.259816i 0.645943 0.763385i \(-0.276464\pi\)
−0.863955 + 0.503569i \(0.832020\pi\)
\(462\) 0 0
\(463\) −112.206 + 636.349i −0.242345 + 1.37440i 0.584235 + 0.811585i \(0.301395\pi\)
−0.826580 + 0.562820i \(0.809716\pi\)
\(464\) 0 0
\(465\) 549.253 134.230i 1.18119 0.288667i
\(466\) 0 0
\(467\) −142.134 + 82.0612i −0.304356 + 0.175720i −0.644398 0.764690i \(-0.722892\pi\)
0.340042 + 0.940410i \(0.389559\pi\)
\(468\) 0 0
\(469\) −40.9059 + 70.8512i −0.0872195 + 0.151069i
\(470\) 0 0
\(471\) −99.8275 + 43.8902i −0.211948 + 0.0931851i
\(472\) 0 0
\(473\) −287.550 + 342.688i −0.607927 + 0.724500i
\(474\) 0 0
\(475\) −486.258 176.983i −1.02370 0.372597i
\(476\) 0 0
\(477\) 14.3987 + 109.868i 0.0301859 + 0.230331i
\(478\) 0 0
\(479\) −192.731 + 33.9838i −0.402362 + 0.0709473i −0.371167 0.928566i \(-0.621042\pi\)
−0.0311949 + 0.999513i \(0.509931\pi\)
\(480\) 0 0
\(481\) 62.4027 22.7127i 0.129735 0.0472198i
\(482\) 0 0
\(483\) −42.8571 656.830i −0.0887311 1.35990i
\(484\) 0 0
\(485\) 1086.29i 2.23977i
\(486\) 0 0
\(487\) 459.602 0.943741 0.471870 0.881668i \(-0.343579\pi\)
0.471870 + 0.881668i \(0.343579\pi\)
\(488\) 0 0
\(489\) −206.197 + 13.4540i −0.421671 + 0.0275134i
\(490\) 0 0
\(491\) 157.868 + 433.740i 0.321524 + 0.883381i 0.990179 + 0.139807i \(0.0446483\pi\)
−0.668654 + 0.743573i \(0.733129\pi\)
\(492\) 0 0
\(493\) 105.029 + 595.652i 0.213042 + 1.20822i
\(494\) 0 0
\(495\) 768.389 100.701i 1.55230 0.203436i
\(496\) 0 0
\(497\) 301.818 829.238i 0.607279 1.66849i
\(498\) 0 0
\(499\) −55.9965 46.9867i −0.112218 0.0941617i 0.584952 0.811068i \(-0.301113\pi\)
−0.697170 + 0.716906i \(0.745558\pi\)
\(500\) 0 0
\(501\) 136.476 + 310.412i 0.272407 + 0.619585i
\(502\) 0 0
\(503\) −667.951 385.641i −1.32793 0.766683i −0.342954 0.939352i \(-0.611427\pi\)
−0.984980 + 0.172670i \(0.944761\pi\)
\(504\) 0 0
\(505\) −11.9725 20.7370i −0.0237080 0.0410634i
\(506\) 0 0
\(507\) 248.561 + 1017.08i 0.490258 + 2.00607i
\(508\) 0 0
\(509\) −141.711 24.9874i −0.278410 0.0490912i 0.0326996 0.999465i \(-0.489590\pi\)
−0.311110 + 0.950374i \(0.600701\pi\)
\(510\) 0 0
\(511\) −363.672 + 305.157i −0.711687 + 0.597177i
\(512\) 0 0
\(513\) 323.138 + 369.125i 0.629900 + 0.719541i
\(514\) 0 0
\(515\) −91.4768 109.018i −0.177625 0.211685i
\(516\) 0 0
\(517\) 38.4525 218.075i 0.0743762 0.421809i
\(518\) 0 0
\(519\) 115.453 395.669i 0.222453 0.762369i
\(520\) 0 0
\(521\) 19.8121 11.4385i 0.0380271 0.0219550i −0.480866 0.876794i \(-0.659678\pi\)
0.518893 + 0.854839i \(0.326344\pi\)
\(522\) 0 0
\(523\) 504.779 874.303i 0.965160 1.67171i 0.255977 0.966683i \(-0.417603\pi\)
0.709183 0.705024i \(-0.249064\pi\)
\(524\) 0 0
\(525\) 645.550 + 473.629i 1.22962 + 0.902150i
\(526\) 0 0
\(527\) 258.767 308.386i 0.491018 0.585173i
\(528\) 0 0
\(529\) 18.0163 + 6.55741i 0.0340574 + 0.0123959i
\(530\) 0 0
\(531\) 53.2775 + 102.492i 0.100334 + 0.193017i
\(532\) 0 0
\(533\) −912.117 + 160.831i −1.71129 + 0.301746i
\(534\) 0 0
\(535\) −169.930 + 61.8494i −0.317626 + 0.115606i
\(536\) 0 0
\(537\) 518.018 + 255.647i 0.964652 + 0.476066i
\(538\) 0 0
\(539\) 457.081i 0.848017i
\(540\) 0 0
\(541\) −593.097 −1.09630 −0.548149 0.836381i \(-0.684667\pi\)
−0.548149 + 0.836381i \(0.684667\pi\)
\(542\) 0 0
\(543\) −126.790 189.876i −0.233500 0.349679i
\(544\) 0 0
\(545\) −2.54624 6.99573i −0.00467199 0.0128362i
\(546\) 0 0
\(547\) −31.2102 177.002i −0.0570570 0.323586i 0.942898 0.333082i \(-0.108089\pi\)
−0.999955 + 0.00949559i \(0.996977\pi\)
\(548\) 0 0
\(549\) −243.778 774.751i −0.444039 1.41120i
\(550\) 0 0
\(551\) 240.632 661.132i 0.436719 1.19988i
\(552\) 0 0
\(553\) 735.583 + 617.227i 1.33017 + 1.11614i
\(554\) 0 0
\(555\) −63.6302 6.98756i −0.114649 0.0125902i
\(556\) 0 0
\(557\) −312.376 180.351i −0.560819 0.323789i 0.192655 0.981267i \(-0.438290\pi\)
−0.753474 + 0.657477i \(0.771624\pi\)
\(558\) 0 0
\(559\) 432.353 + 748.858i 0.773441 + 1.33964i
\(560\) 0 0
\(561\) 398.685 381.433i 0.710668 0.679916i
\(562\) 0 0
\(563\) 571.890 + 100.840i 1.01579 + 0.179111i 0.656669 0.754179i \(-0.271965\pi\)
0.359122 + 0.933291i \(0.383076\pi\)
\(564\) 0 0
\(565\) 869.589 729.672i 1.53910 1.29145i
\(566\) 0 0
\(567\) −319.987 688.326i −0.564351 1.21398i
\(568\) 0 0
\(569\) −356.121 424.408i −0.625871 0.745884i 0.356197 0.934411i \(-0.384073\pi\)
−0.982068 + 0.188527i \(0.939629\pi\)
\(570\) 0 0
\(571\) −41.9016 + 237.636i −0.0733828 + 0.416175i 0.925881 + 0.377815i \(0.123324\pi\)
−0.999264 + 0.0383598i \(0.987787\pi\)
\(572\) 0 0
\(573\) −426.438 445.725i −0.744219 0.777879i
\(574\) 0 0
\(575\) −577.460 + 333.396i −1.00428 + 0.579820i
\(576\) 0 0
\(577\) 9.74580 16.8802i 0.0168905 0.0292552i −0.857457 0.514556i \(-0.827957\pi\)
0.874347 + 0.485301i \(0.161290\pi\)
\(578\) 0 0
\(579\) 95.4359 869.060i 0.164829 1.50097i
\(580\) 0 0
\(581\) −113.858 + 135.690i −0.195968 + 0.233546i
\(582\) 0 0
\(583\) −136.224 49.5815i −0.233661 0.0850455i
\(584\) 0 0
\(585\) 325.079 1462.27i 0.555690 2.49961i
\(586\) 0 0
\(587\) −489.063 + 86.2350i −0.833156 + 0.146908i −0.573926 0.818907i \(-0.694580\pi\)
−0.259231 + 0.965815i \(0.583469\pi\)
\(588\) 0 0
\(589\) −440.036 + 160.160i −0.747090 + 0.271918i
\(590\) 0 0
\(591\) −758.091 + 506.218i −1.28273 + 0.856545i
\(592\) 0 0
\(593\) 629.836i 1.06212i 0.847335 + 0.531059i \(0.178206\pi\)
−0.847335 + 0.531059i \(0.821794\pi\)
\(594\) 0 0
\(595\) 1070.47 1.79912
\(596\) 0 0
\(597\) 353.777 716.857i 0.592591 1.20077i
\(598\) 0 0
\(599\) 222.199 + 610.488i 0.370951 + 1.01918i 0.974995 + 0.222228i \(0.0713329\pi\)
−0.604044 + 0.796951i \(0.706445\pi\)
\(600\) 0 0
\(601\) 69.7993 + 395.852i 0.116139 + 0.658655i 0.986180 + 0.165677i \(0.0529808\pi\)
−0.870042 + 0.492978i \(0.835908\pi\)
\(602\) 0 0
\(603\) −66.2414 42.2552i −0.109853 0.0700749i
\(604\) 0 0
\(605\) −44.1186 + 121.215i −0.0729233 + 0.200355i
\(606\) 0 0
\(607\) −166.213 139.470i −0.273828 0.229769i 0.495524 0.868594i \(-0.334976\pi\)
−0.769352 + 0.638826i \(0.779421\pi\)
\(608\) 0 0
\(609\) −643.961 + 877.711i −1.05741 + 1.44123i
\(610\) 0 0
\(611\) −370.688 214.017i −0.606691 0.350273i
\(612\) 0 0
\(613\) 469.156 + 812.602i 0.765344 + 1.32562i 0.940064 + 0.340997i \(0.110765\pi\)
−0.174720 + 0.984618i \(0.555902\pi\)
\(614\) 0 0
\(615\) 857.046 + 250.079i 1.39357 + 0.406633i
\(616\) 0 0
\(617\) 474.755 + 83.7120i 0.769456 + 0.135676i 0.544577 0.838711i \(-0.316690\pi\)
0.224879 + 0.974387i \(0.427801\pi\)
\(618\) 0 0
\(619\) 71.9917 60.4082i 0.116303 0.0975900i −0.582781 0.812629i \(-0.698036\pi\)
0.699084 + 0.715039i \(0.253591\pi\)
\(620\) 0 0
\(621\) 632.015 13.2333i 1.01774 0.0213097i
\(622\) 0 0
\(623\) 367.885 + 438.428i 0.590505 + 0.703736i
\(624\) 0 0
\(625\) −91.3226 + 517.916i −0.146116 + 0.828666i
\(626\) 0 0
\(627\) −623.471 + 152.368i −0.994371 + 0.243011i
\(628\) 0 0
\(629\) −39.4702 + 22.7881i −0.0627507 + 0.0362291i
\(630\) 0 0
\(631\) −266.288 + 461.224i −0.422010 + 0.730942i −0.996136 0.0878246i \(-0.972008\pi\)
0.574126 + 0.818767i \(0.305342\pi\)
\(632\) 0 0
\(633\) −244.148 + 107.342i −0.385699 + 0.169576i
\(634\) 0 0
\(635\) 337.567 402.297i 0.531601 0.633538i
\(636\) 0 0
\(637\) −830.238 302.182i −1.30336 0.474383i
\(638\) 0 0
\(639\) 782.798 + 324.785i 1.22504 + 0.508270i
\(640\) 0 0
\(641\) 811.167 143.031i 1.26547 0.223137i 0.499671 0.866215i \(-0.333454\pi\)
0.765800 + 0.643079i \(0.222343\pi\)
\(642\) 0 0
\(643\) 875.130 318.521i 1.36101 0.495367i 0.444644 0.895707i \(-0.353330\pi\)
0.916367 + 0.400340i \(0.131108\pi\)
\(644\) 0 0
\(645\) −54.2706 831.754i −0.0841405 1.28954i
\(646\) 0 0
\(647\) 255.455i 0.394830i −0.980320 0.197415i \(-0.936745\pi\)
0.980320 0.197415i \(-0.0632546\pi\)
\(648\) 0 0
\(649\) −151.122 −0.232854
\(650\) 0 0
\(651\) 723.016 47.1757i 1.11062 0.0724665i
\(652\) 0 0
\(653\) −277.404 762.162i −0.424815 1.16717i −0.948920 0.315516i \(-0.897822\pi\)
0.524105 0.851653i \(-0.324400\pi\)
\(654\) 0 0
\(655\) 22.2942 + 126.437i 0.0340370 + 0.193033i
\(656\) 0 0
\(657\) −277.343 361.881i −0.422136 0.550808i
\(658\) 0 0
\(659\) 118.588 325.819i 0.179952 0.494414i −0.816617 0.577180i \(-0.804153\pi\)
0.996569 + 0.0827659i \(0.0263754\pi\)
\(660\) 0 0
\(661\) −639.014 536.197i −0.966739 0.811190i 0.0152975 0.999883i \(-0.495130\pi\)
−0.982036 + 0.188693i \(0.939575\pi\)
\(662\) 0 0
\(663\) −429.256 976.337i −0.647445 1.47261i
\(664\) 0 0
\(665\) −1078.37 622.598i −1.62161 0.936238i
\(666\) 0 0
\(667\) −453.297 785.133i −0.679605 1.17711i
\(668\) 0 0
\(669\) 206.749 + 845.988i 0.309041 + 1.26456i
\(670\) 0 0
\(671\) 1046.44 + 184.515i 1.55952 + 0.274986i
\(672\) 0 0
\(673\) 118.178 99.1631i 0.175599 0.147345i −0.550752 0.834669i \(-0.685659\pi\)
0.726351 + 0.687324i \(0.241215\pi\)
\(674\) 0 0
\(675\) −481.830 + 599.265i −0.713822 + 0.887800i
\(676\) 0 0
\(677\) −576.975 687.612i −0.852252 1.01567i −0.999646 0.0265971i \(-0.991533\pi\)
0.147394 0.989078i \(-0.452912\pi\)
\(678\) 0 0
\(679\) −241.723 + 1370.88i −0.355998 + 2.01897i
\(680\) 0 0
\(681\) −155.225 + 531.971i −0.227937 + 0.781161i
\(682\) 0 0
\(683\) −666.874 + 385.020i −0.976390 + 0.563719i −0.901178 0.433449i \(-0.857296\pi\)
−0.0752113 + 0.997168i \(0.523963\pi\)
\(684\) 0 0
\(685\) −75.9746 + 131.592i −0.110912 + 0.192105i
\(686\) 0 0
\(687\) −824.428 604.868i −1.20004 0.880448i
\(688\) 0 0
\(689\) −180.119 + 214.657i −0.261421 + 0.311549i
\(690\) 0 0
\(691\) −831.656 302.698i −1.20355 0.438058i −0.339091 0.940754i \(-0.610119\pi\)
−0.864463 + 0.502696i \(0.832342\pi\)
\(692\) 0 0
\(693\) 992.102 + 43.9002i 1.43160 + 0.0633480i
\(694\) 0 0
\(695\) 44.8058 7.90048i 0.0644688 0.0113676i
\(696\) 0 0
\(697\) 597.318 217.406i 0.856984 0.311917i
\(698\) 0 0
\(699\) 816.479 + 402.941i 1.16807 + 0.576454i
\(700\) 0 0
\(701\) 924.832i 1.31930i 0.751571 + 0.659652i \(0.229296\pi\)
−0.751571 + 0.659652i \(0.770704\pi\)
\(702\) 0 0
\(703\) 53.0151 0.0754127
\(704\) 0 0
\(705\) 229.126 + 343.130i 0.325002 + 0.486709i
\(706\) 0 0
\(707\) −10.4947 28.8339i −0.0148440 0.0407835i
\(708\) 0 0
\(709\) −173.003 981.150i −0.244010 1.38385i −0.822780 0.568360i \(-0.807578\pi\)
0.578770 0.815491i \(-0.303533\pi\)
\(710\) 0 0
\(711\) −623.428 + 679.550i −0.876832 + 0.955766i
\(712\) 0 0
\(713\) −206.378 + 567.020i −0.289451 + 0.795259i
\(714\) 0 0
\(715\) 1501.26 + 1259.71i 2.09967 + 1.76183i
\(716\) 0 0
\(717\) −1305.27 143.339i −1.82047 0.199915i
\(718\) 0 0
\(719\) −103.540 59.7791i −0.144006 0.0831420i 0.426266 0.904598i \(-0.359829\pi\)
−0.570272 + 0.821456i \(0.693162\pi\)
\(720\) 0 0
\(721\) −91.1833 157.934i −0.126468 0.219049i
\(722\) 0 0
\(723\) −352.719 + 337.456i −0.487854 + 0.466744i
\(724\) 0 0
\(725\) 1086.02 + 191.495i 1.49796 + 0.264130i
\(726\) 0 0
\(727\) 391.062 328.140i 0.537911 0.451361i −0.332912 0.942958i \(-0.608031\pi\)
0.870823 + 0.491597i \(0.163587\pi\)
\(728\) 0 0
\(729\) 673.999 277.789i 0.924553 0.381054i
\(730\) 0 0
\(731\) −381.467 454.615i −0.521843 0.621908i
\(732\) 0 0
\(733\) −61.0496 + 346.229i −0.0832872 + 0.472345i 0.914426 + 0.404754i \(0.132643\pi\)
−0.997713 + 0.0675919i \(0.978468\pi\)
\(734\) 0 0
\(735\) 588.752 + 615.380i 0.801023 + 0.837252i
\(736\) 0 0
\(737\) 89.0213 51.3965i 0.120789 0.0697374i
\(738\) 0 0
\(739\) 43.2066 74.8360i 0.0584663 0.101267i −0.835311 0.549778i \(-0.814712\pi\)
0.893777 + 0.448511i \(0.148046\pi\)
\(740\) 0 0
\(741\) −135.424 + 1233.20i −0.182758 + 1.66424i
\(742\) 0 0
\(743\) −435.424 + 518.918i −0.586035 + 0.698409i −0.974839 0.222912i \(-0.928444\pi\)
0.388804 + 0.921320i \(0.372888\pi\)
\(744\) 0 0
\(745\) −1548.15 563.482i −2.07806 0.756352i
\(746\) 0 0
\(747\) −125.354 115.001i −0.167810 0.153951i
\(748\) 0 0
\(749\) −228.211 + 40.2398i −0.304688 + 0.0537247i
\(750\) 0 0
\(751\) −378.743 + 137.851i −0.504318 + 0.183557i −0.581635 0.813450i \(-0.697587\pi\)
0.0773173 + 0.997007i \(0.475365\pi\)
\(752\) 0 0
\(753\) 1137.49 759.562i 1.51061 1.00871i
\(754\) 0 0
\(755\) 1726.07i 2.28618i
\(756\) 0 0
\(757\) 463.787 0.612665 0.306332 0.951925i \(-0.400898\pi\)
0.306332 + 0.951925i \(0.400898\pi\)
\(758\) 0 0
\(759\) −366.005 + 741.636i −0.482220 + 0.977122i
\(760\) 0 0
\(761\) −23.5534 64.7125i −0.0309506 0.0850361i 0.923255 0.384188i \(-0.125519\pi\)
−0.954206 + 0.299152i \(0.903296\pi\)
\(762\) 0 0
\(763\) −1.65661 9.39508i −0.00217117 0.0123133i
\(764\) 0 0
\(765\) −45.4473 + 1027.07i −0.0594083 + 1.34257i
\(766\) 0 0
\(767\) −99.9089 + 274.497i −0.130259 + 0.357884i
\(768\) 0 0
\(769\) −587.623 493.074i −0.764139 0.641189i 0.175062 0.984557i \(-0.443988\pi\)
−0.939201 + 0.343369i \(0.888432\pi\)
\(770\) 0 0
\(771\) −737.120 + 1004.69i −0.956057 + 1.30309i
\(772\) 0 0
\(773\) 215.221 + 124.258i 0.278423 + 0.160747i 0.632709 0.774390i \(-0.281943\pi\)
−0.354286 + 0.935137i \(0.615276\pi\)
\(774\) 0 0
\(775\) −366.992 635.648i −0.473538 0.820191i
\(776\) 0 0
\(777\) −78.7454 22.9773i −0.101345 0.0295718i
\(778\) 0 0
\(779\) −728.169 128.396i −0.934749 0.164821i
\(780\) 0 0
\(781\) −849.365 + 712.702i −1.08754 + 0.912551i
\(782\) 0 0
\(783\) −814.780 655.112i −1.04059 0.836669i
\(784\)