Properties

Label 1148.2.k.b.729.9
Level $1148$
Weight $2$
Character 1148.729
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 729.9
Character \(\chi\) \(=\) 1148.729
Dual form 1148.2.k.b.337.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.197445 + 0.197445i) q^{3} +3.12585i q^{5} +(0.707107 - 0.707107i) q^{7} +2.92203i q^{9} +O(q^{10})\) \(q+(-0.197445 + 0.197445i) q^{3} +3.12585i q^{5} +(0.707107 - 0.707107i) q^{7} +2.92203i q^{9} +(-0.0441522 + 0.0441522i) q^{11} +(-3.40539 + 3.40539i) q^{13} +(-0.617183 - 0.617183i) q^{15} +(2.97395 + 2.97395i) q^{17} +(-5.33738 - 5.33738i) q^{19} +0.279229i q^{21} -0.780656 q^{23} -4.77096 q^{25} +(-1.16927 - 1.16927i) q^{27} +(4.24444 - 4.24444i) q^{29} -4.87513 q^{31} -0.0174352i q^{33} +(2.21031 + 2.21031i) q^{35} -1.50079 q^{37} -1.34475i q^{39} +(3.85343 + 5.11381i) q^{41} +2.42062i q^{43} -9.13384 q^{45} +(-4.29984 - 4.29984i) q^{47} -1.00000i q^{49} -1.17438 q^{51} +(-4.07903 + 4.07903i) q^{53} +(-0.138013 - 0.138013i) q^{55} +2.10767 q^{57} -5.85555 q^{59} +8.77946i q^{61} +(2.06619 + 2.06619i) q^{63} +(-10.6447 - 10.6447i) q^{65} +(7.81463 + 7.81463i) q^{67} +(0.154136 - 0.154136i) q^{69} +(6.22855 - 6.22855i) q^{71} -13.3469i q^{73} +(0.942001 - 0.942001i) q^{75} +0.0624407i q^{77} +(-5.78541 + 5.78541i) q^{79} -8.30436 q^{81} -7.21760 q^{83} +(-9.29615 + 9.29615i) q^{85} +1.67608i q^{87} +(-9.01579 + 9.01579i) q^{89} +4.81595i q^{91} +(0.962567 - 0.962567i) q^{93} +(16.6839 - 16.6839i) q^{95} +(11.0205 + 11.0205i) q^{97} +(-0.129014 - 0.129014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −0.197445 + 0.197445i −0.113995 + 0.113995i −0.761803 0.647809i \(-0.775686\pi\)
0.647809 + 0.761803i \(0.275686\pi\)
\(4\) 0 0
\(5\) 3.12585i 1.39792i 0.715159 + 0.698962i \(0.246354\pi\)
−0.715159 + 0.698962i \(0.753646\pi\)
\(6\) 0 0
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0 0
\(9\) 2.92203i 0.974010i
\(10\) 0 0
\(11\) −0.0441522 + 0.0441522i −0.0133124 + 0.0133124i −0.713732 0.700419i \(-0.752996\pi\)
0.700419 + 0.713732i \(0.252996\pi\)
\(12\) 0 0
\(13\) −3.40539 + 3.40539i −0.944485 + 0.944485i −0.998538 0.0540535i \(-0.982786\pi\)
0.0540535 + 0.998538i \(0.482786\pi\)
\(14\) 0 0
\(15\) −0.617183 0.617183i −0.159356 0.159356i
\(16\) 0 0
\(17\) 2.97395 + 2.97395i 0.721290 + 0.721290i 0.968868 0.247578i \(-0.0796347\pi\)
−0.247578 + 0.968868i \(0.579635\pi\)
\(18\) 0 0
\(19\) −5.33738 5.33738i −1.22448 1.22448i −0.966023 0.258455i \(-0.916787\pi\)
−0.258455 0.966023i \(-0.583213\pi\)
\(20\) 0 0
\(21\) 0.279229i 0.0609327i
\(22\) 0 0
\(23\) −0.780656 −0.162778 −0.0813890 0.996682i \(-0.525936\pi\)
−0.0813890 + 0.996682i \(0.525936\pi\)
\(24\) 0 0
\(25\) −4.77096 −0.954193
\(26\) 0 0
\(27\) −1.16927 1.16927i −0.225027 0.225027i
\(28\) 0 0
\(29\) 4.24444 4.24444i 0.788172 0.788172i −0.193022 0.981194i \(-0.561829\pi\)
0.981194 + 0.193022i \(0.0618289\pi\)
\(30\) 0 0
\(31\) −4.87513 −0.875598 −0.437799 0.899073i \(-0.644242\pi\)
−0.437799 + 0.899073i \(0.644242\pi\)
\(32\) 0 0
\(33\) 0.0174352i 0.00303509i
\(34\) 0 0
\(35\) 2.21031 + 2.21031i 0.373611 + 0.373611i
\(36\) 0 0
\(37\) −1.50079 −0.246729 −0.123364 0.992361i \(-0.539368\pi\)
−0.123364 + 0.992361i \(0.539368\pi\)
\(38\) 0 0
\(39\) 1.34475i 0.215332i
\(40\) 0 0
\(41\) 3.85343 + 5.11381i 0.601805 + 0.798643i
\(42\) 0 0
\(43\) 2.42062i 0.369141i 0.982819 + 0.184571i \(0.0590894\pi\)
−0.982819 + 0.184571i \(0.940911\pi\)
\(44\) 0 0
\(45\) −9.13384 −1.36159
\(46\) 0 0
\(47\) −4.29984 4.29984i −0.627196 0.627196i 0.320166 0.947361i \(-0.396261\pi\)
−0.947361 + 0.320166i \(0.896261\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −1.17438 −0.164446
\(52\) 0 0
\(53\) −4.07903 + 4.07903i −0.560298 + 0.560298i −0.929392 0.369094i \(-0.879668\pi\)
0.369094 + 0.929392i \(0.379668\pi\)
\(54\) 0 0
\(55\) −0.138013 0.138013i −0.0186097 0.0186097i
\(56\) 0 0
\(57\) 2.10767 0.279168
\(58\) 0 0
\(59\) −5.85555 −0.762328 −0.381164 0.924507i \(-0.624477\pi\)
−0.381164 + 0.924507i \(0.624477\pi\)
\(60\) 0 0
\(61\) 8.77946i 1.12409i 0.827105 + 0.562047i \(0.189986\pi\)
−0.827105 + 0.562047i \(0.810014\pi\)
\(62\) 0 0
\(63\) 2.06619 + 2.06619i 0.260315 + 0.260315i
\(64\) 0 0
\(65\) −10.6447 10.6447i −1.32032 1.32032i
\(66\) 0 0
\(67\) 7.81463 + 7.81463i 0.954709 + 0.954709i 0.999018 0.0443091i \(-0.0141086\pi\)
−0.0443091 + 0.999018i \(0.514109\pi\)
\(68\) 0 0
\(69\) 0.154136 0.154136i 0.0185558 0.0185558i
\(70\) 0 0
\(71\) 6.22855 6.22855i 0.739193 0.739193i −0.233229 0.972422i \(-0.574929\pi\)
0.972422 + 0.233229i \(0.0749292\pi\)
\(72\) 0 0
\(73\) 13.3469i 1.56213i −0.624447 0.781067i \(-0.714676\pi\)
0.624447 0.781067i \(-0.285324\pi\)
\(74\) 0 0
\(75\) 0.942001 0.942001i 0.108773 0.108773i
\(76\) 0 0
\(77\) 0.0624407i 0.00711578i
\(78\) 0 0
\(79\) −5.78541 + 5.78541i −0.650910 + 0.650910i −0.953212 0.302302i \(-0.902245\pi\)
0.302302 + 0.953212i \(0.402245\pi\)
\(80\) 0 0
\(81\) −8.30436 −0.922707
\(82\) 0 0
\(83\) −7.21760 −0.792234 −0.396117 0.918200i \(-0.629643\pi\)
−0.396117 + 0.918200i \(0.629643\pi\)
\(84\) 0 0
\(85\) −9.29615 + 9.29615i −1.00831 + 1.00831i
\(86\) 0 0
\(87\) 1.67608i 0.179695i
\(88\) 0 0
\(89\) −9.01579 + 9.01579i −0.955672 + 0.955672i −0.999058 0.0433862i \(-0.986185\pi\)
0.0433862 + 0.999058i \(0.486185\pi\)
\(90\) 0 0
\(91\) 4.81595i 0.504848i
\(92\) 0 0
\(93\) 0.962567 0.962567i 0.0998136 0.0998136i
\(94\) 0 0
\(95\) 16.6839 16.6839i 1.71173 1.71173i
\(96\) 0 0
\(97\) 11.0205 + 11.0205i 1.11896 + 1.11896i 0.991895 + 0.127063i \(0.0405552\pi\)
0.127063 + 0.991895i \(0.459445\pi\)
\(98\) 0 0
\(99\) −0.129014 0.129014i −0.0129664 0.0129664i
\(100\) 0 0
\(101\) −10.6473 10.6473i −1.05945 1.05945i −0.998117 0.0613309i \(-0.980466\pi\)
−0.0613309 0.998117i \(-0.519534\pi\)
\(102\) 0 0
\(103\) 19.6105i 1.93228i 0.258026 + 0.966138i \(0.416928\pi\)
−0.258026 + 0.966138i \(0.583072\pi\)
\(104\) 0 0
\(105\) −0.872829 −0.0851794
\(106\) 0 0
\(107\) 1.95499 0.188996 0.0944980 0.995525i \(-0.469875\pi\)
0.0944980 + 0.995525i \(0.469875\pi\)
\(108\) 0 0
\(109\) −4.08789 4.08789i −0.391549 0.391549i 0.483690 0.875239i \(-0.339296\pi\)
−0.875239 + 0.483690i \(0.839296\pi\)
\(110\) 0 0
\(111\) 0.296323 0.296323i 0.0281258 0.0281258i
\(112\) 0 0
\(113\) 6.31266 0.593845 0.296922 0.954902i \(-0.404040\pi\)
0.296922 + 0.954902i \(0.404040\pi\)
\(114\) 0 0
\(115\) 2.44022i 0.227551i
\(116\) 0 0
\(117\) −9.95065 9.95065i −0.919938 0.919938i
\(118\) 0 0
\(119\) 4.20581 0.385546
\(120\) 0 0
\(121\) 10.9961i 0.999646i
\(122\) 0 0
\(123\) −1.77053 0.248855i −0.159644 0.0224385i
\(124\) 0 0
\(125\) 0.715936i 0.0640353i
\(126\) 0 0
\(127\) 10.0950 0.895783 0.447892 0.894088i \(-0.352175\pi\)
0.447892 + 0.894088i \(0.352175\pi\)
\(128\) 0 0
\(129\) −0.477939 0.477939i −0.0420801 0.0420801i
\(130\) 0 0
\(131\) 0.491225i 0.0429185i 0.999770 + 0.0214592i \(0.00683121\pi\)
−0.999770 + 0.0214592i \(0.993169\pi\)
\(132\) 0 0
\(133\) −7.54819 −0.654511
\(134\) 0 0
\(135\) 3.65498 3.65498i 0.314570 0.314570i
\(136\) 0 0
\(137\) 11.8411 + 11.8411i 1.01165 + 1.01165i 0.999931 + 0.0117200i \(0.00373069\pi\)
0.0117200 + 0.999931i \(0.496269\pi\)
\(138\) 0 0
\(139\) 20.0107 1.69729 0.848644 0.528964i \(-0.177420\pi\)
0.848644 + 0.528964i \(0.177420\pi\)
\(140\) 0 0
\(141\) 1.69796 0.142994
\(142\) 0 0
\(143\) 0.300711i 0.0251467i
\(144\) 0 0
\(145\) 13.2675 + 13.2675i 1.10181 + 1.10181i
\(146\) 0 0
\(147\) 0.197445 + 0.197445i 0.0162850 + 0.0162850i
\(148\) 0 0
\(149\) 4.08115 + 4.08115i 0.334341 + 0.334341i 0.854232 0.519891i \(-0.174028\pi\)
−0.519891 + 0.854232i \(0.674028\pi\)
\(150\) 0 0
\(151\) 6.52725 6.52725i 0.531180 0.531180i −0.389743 0.920923i \(-0.627436\pi\)
0.920923 + 0.389743i \(0.127436\pi\)
\(152\) 0 0
\(153\) −8.68999 + 8.68999i −0.702544 + 0.702544i
\(154\) 0 0
\(155\) 15.2389i 1.22402i
\(156\) 0 0
\(157\) 3.69698 3.69698i 0.295051 0.295051i −0.544021 0.839072i \(-0.683099\pi\)
0.839072 + 0.544021i \(0.183099\pi\)
\(158\) 0 0
\(159\) 1.61076i 0.127742i
\(160\) 0 0
\(161\) −0.552007 + 0.552007i −0.0435042 + 0.0435042i
\(162\) 0 0
\(163\) −19.6546 −1.53947 −0.769734 0.638365i \(-0.779611\pi\)
−0.769734 + 0.638365i \(0.779611\pi\)
\(164\) 0 0
\(165\) 0.0545000 0.00424282
\(166\) 0 0
\(167\) −5.13425 + 5.13425i −0.397300 + 0.397300i −0.877280 0.479980i \(-0.840644\pi\)
0.479980 + 0.877280i \(0.340644\pi\)
\(168\) 0 0
\(169\) 10.1933i 0.784102i
\(170\) 0 0
\(171\) 15.5960 15.5960i 1.19265 1.19265i
\(172\) 0 0
\(173\) 3.93744i 0.299358i −0.988735 0.149679i \(-0.952176\pi\)
0.988735 0.149679i \(-0.0478241\pi\)
\(174\) 0 0
\(175\) −3.37358 + 3.37358i −0.255019 + 0.255019i
\(176\) 0 0
\(177\) 1.15615 1.15615i 0.0869013 0.0869013i
\(178\) 0 0
\(179\) 11.7303 + 11.7303i 0.876765 + 0.876765i 0.993198 0.116434i \(-0.0371463\pi\)
−0.116434 + 0.993198i \(0.537146\pi\)
\(180\) 0 0
\(181\) −11.0472 11.0472i −0.821134 0.821134i 0.165136 0.986271i \(-0.447194\pi\)
−0.986271 + 0.165136i \(0.947194\pi\)
\(182\) 0 0
\(183\) −1.73346 1.73346i −0.128141 0.128141i
\(184\) 0 0
\(185\) 4.69126i 0.344908i
\(186\) 0 0
\(187\) −0.262613 −0.0192042
\(188\) 0 0
\(189\) −1.65360 −0.120282
\(190\) 0 0
\(191\) 10.8724 + 10.8724i 0.786697 + 0.786697i 0.980951 0.194254i \(-0.0622286\pi\)
−0.194254 + 0.980951i \(0.562229\pi\)
\(192\) 0 0
\(193\) 14.6058 14.6058i 1.05135 1.05135i 0.0527383 0.998608i \(-0.483205\pi\)
0.998608 0.0527383i \(-0.0167949\pi\)
\(194\) 0 0
\(195\) 4.20350 0.301019
\(196\) 0 0
\(197\) 25.8248i 1.83994i −0.391985 0.919972i \(-0.628211\pi\)
0.391985 0.919972i \(-0.371789\pi\)
\(198\) 0 0
\(199\) 16.4368 + 16.4368i 1.16517 + 1.16517i 0.983327 + 0.181847i \(0.0582076\pi\)
0.181847 + 0.983327i \(0.441792\pi\)
\(200\) 0 0
\(201\) −3.08591 −0.217664
\(202\) 0 0
\(203\) 6.00254i 0.421296i
\(204\) 0 0
\(205\) −15.9850 + 12.0453i −1.11644 + 0.841278i
\(206\) 0 0
\(207\) 2.28110i 0.158547i
\(208\) 0 0
\(209\) 0.471314 0.0326015
\(210\) 0 0
\(211\) −9.17726 9.17726i −0.631788 0.631788i 0.316728 0.948516i \(-0.397416\pi\)
−0.948516 + 0.316728i \(0.897416\pi\)
\(212\) 0 0
\(213\) 2.45959i 0.168528i
\(214\) 0 0
\(215\) −7.56651 −0.516031
\(216\) 0 0
\(217\) −3.44723 + 3.44723i −0.234013 + 0.234013i
\(218\) 0 0
\(219\) 2.63527 + 2.63527i 0.178075 + 0.178075i
\(220\) 0 0
\(221\) −20.2549 −1.36249
\(222\) 0 0
\(223\) −10.6366 −0.712279 −0.356140 0.934433i \(-0.615907\pi\)
−0.356140 + 0.934433i \(0.615907\pi\)
\(224\) 0 0
\(225\) 13.9409i 0.929394i
\(226\) 0 0
\(227\) −0.181481 0.181481i −0.0120453 0.0120453i 0.701058 0.713104i \(-0.252711\pi\)
−0.713104 + 0.701058i \(0.752711\pi\)
\(228\) 0 0
\(229\) 14.8821 + 14.8821i 0.983438 + 0.983438i 0.999865 0.0164271i \(-0.00522915\pi\)
−0.0164271 + 0.999865i \(0.505229\pi\)
\(230\) 0 0
\(231\) −0.0123286 0.0123286i −0.000811161 0.000811161i
\(232\) 0 0
\(233\) 13.8210 13.8210i 0.905441 0.905441i −0.0904593 0.995900i \(-0.528834\pi\)
0.995900 + 0.0904593i \(0.0288335\pi\)
\(234\) 0 0
\(235\) 13.4407 13.4407i 0.876772 0.876772i
\(236\) 0 0
\(237\) 2.28460i 0.148401i
\(238\) 0 0
\(239\) 1.24022 1.24022i 0.0802230 0.0802230i −0.665857 0.746080i \(-0.731934\pi\)
0.746080 + 0.665857i \(0.231934\pi\)
\(240\) 0 0
\(241\) 5.11244i 0.329321i 0.986350 + 0.164661i \(0.0526529\pi\)
−0.986350 + 0.164661i \(0.947347\pi\)
\(242\) 0 0
\(243\) 5.14747 5.14747i 0.330210 0.330210i
\(244\) 0 0
\(245\) 3.12585 0.199703
\(246\) 0 0
\(247\) 36.3517 2.31300
\(248\) 0 0
\(249\) 1.42508 1.42508i 0.0903105 0.0903105i
\(250\) 0 0
\(251\) 6.33802i 0.400052i 0.979791 + 0.200026i \(0.0641027\pi\)
−0.979791 + 0.200026i \(0.935897\pi\)
\(252\) 0 0
\(253\) 0.0344677 0.0344677i 0.00216697 0.00216697i
\(254\) 0 0
\(255\) 3.67095i 0.229884i
\(256\) 0 0
\(257\) 18.1608 18.1608i 1.13284 1.13284i 0.143135 0.989703i \(-0.454282\pi\)
0.989703 0.143135i \(-0.0457182\pi\)
\(258\) 0 0
\(259\) −1.06122 + 1.06122i −0.0659410 + 0.0659410i
\(260\) 0 0
\(261\) 12.4024 + 12.4024i 0.767688 + 0.767688i
\(262\) 0 0
\(263\) −8.59438 8.59438i −0.529952 0.529952i 0.390606 0.920558i \(-0.372266\pi\)
−0.920558 + 0.390606i \(0.872266\pi\)
\(264\) 0 0
\(265\) −12.7504 12.7504i −0.783254 0.783254i
\(266\) 0 0
\(267\) 3.56024i 0.217883i
\(268\) 0 0
\(269\) −2.49990 −0.152422 −0.0762108 0.997092i \(-0.524282\pi\)
−0.0762108 + 0.997092i \(0.524282\pi\)
\(270\) 0 0
\(271\) −20.9761 −1.27420 −0.637102 0.770779i \(-0.719867\pi\)
−0.637102 + 0.770779i \(0.719867\pi\)
\(272\) 0 0
\(273\) −0.950883 0.950883i −0.0575500 0.0575500i
\(274\) 0 0
\(275\) 0.210649 0.210649i 0.0127026 0.0127026i
\(276\) 0 0
\(277\) 1.54775 0.0929953 0.0464977 0.998918i \(-0.485194\pi\)
0.0464977 + 0.998918i \(0.485194\pi\)
\(278\) 0 0
\(279\) 14.2453i 0.852842i
\(280\) 0 0
\(281\) −0.574366 0.574366i −0.0342638 0.0342638i 0.689767 0.724031i \(-0.257713\pi\)
−0.724031 + 0.689767i \(0.757713\pi\)
\(282\) 0 0
\(283\) 21.4316 1.27397 0.636987 0.770875i \(-0.280180\pi\)
0.636987 + 0.770875i \(0.280180\pi\)
\(284\) 0 0
\(285\) 6.58828i 0.390256i
\(286\) 0 0
\(287\) 6.34080 + 0.891222i 0.374285 + 0.0526072i
\(288\) 0 0
\(289\) 0.688802i 0.0405178i
\(290\) 0 0
\(291\) −4.35186 −0.255111
\(292\) 0 0
\(293\) 2.66303 + 2.66303i 0.155576 + 0.155576i 0.780603 0.625027i \(-0.214912\pi\)
−0.625027 + 0.780603i \(0.714912\pi\)
\(294\) 0 0
\(295\) 18.3036i 1.06568i
\(296\) 0 0
\(297\) 0.103252 0.00599129
\(298\) 0 0
\(299\) 2.65844 2.65844i 0.153741 0.153741i
\(300\) 0 0
\(301\) 1.71164 + 1.71164i 0.0986571 + 0.0986571i
\(302\) 0 0
\(303\) 4.20451 0.241543
\(304\) 0 0
\(305\) −27.4433 −1.57140
\(306\) 0 0
\(307\) 14.9715i 0.854466i 0.904141 + 0.427233i \(0.140512\pi\)
−0.904141 + 0.427233i \(0.859488\pi\)
\(308\) 0 0
\(309\) −3.87198 3.87198i −0.220269 0.220269i
\(310\) 0 0
\(311\) 22.4001 + 22.4001i 1.27019 + 1.27019i 0.945987 + 0.324205i \(0.105097\pi\)
0.324205 + 0.945987i \(0.394903\pi\)
\(312\) 0 0
\(313\) 16.5977 + 16.5977i 0.938155 + 0.938155i 0.998196 0.0600412i \(-0.0191232\pi\)
−0.0600412 + 0.998196i \(0.519123\pi\)
\(314\) 0 0
\(315\) −6.45860 + 6.45860i −0.363901 + 0.363901i
\(316\) 0 0
\(317\) 3.17288 3.17288i 0.178207 0.178207i −0.612367 0.790574i \(-0.709783\pi\)
0.790574 + 0.612367i \(0.209783\pi\)
\(318\) 0 0
\(319\) 0.374803i 0.0209849i
\(320\) 0 0
\(321\) −0.386002 + 0.386002i −0.0215445 + 0.0215445i
\(322\) 0 0
\(323\) 31.7462i 1.76641i
\(324\) 0 0
\(325\) 16.2470 16.2470i 0.901220 0.901220i
\(326\) 0 0
\(327\) 1.61427 0.0892691
\(328\) 0 0
\(329\) −6.08089 −0.335250
\(330\) 0 0
\(331\) 0.432919 0.432919i 0.0237954 0.0237954i −0.695109 0.718904i \(-0.744644\pi\)
0.718904 + 0.695109i \(0.244644\pi\)
\(332\) 0 0
\(333\) 4.38536i 0.240316i
\(334\) 0 0
\(335\) −24.4274 + 24.4274i −1.33461 + 1.33461i
\(336\) 0 0
\(337\) 14.6117i 0.795948i 0.917397 + 0.397974i \(0.130287\pi\)
−0.917397 + 0.397974i \(0.869713\pi\)
\(338\) 0 0
\(339\) −1.24640 + 1.24640i −0.0676952 + 0.0676952i
\(340\) 0 0
\(341\) 0.215248 0.215248i 0.0116563 0.0116563i
\(342\) 0 0
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 0 0
\(345\) 0.481807 + 0.481807i 0.0259396 + 0.0259396i
\(346\) 0 0
\(347\) −0.944092 0.944092i −0.0506815 0.0506815i 0.681312 0.731993i \(-0.261410\pi\)
−0.731993 + 0.681312i \(0.761410\pi\)
\(348\) 0 0
\(349\) 8.79145i 0.470596i 0.971923 + 0.235298i \(0.0756066\pi\)
−0.971923 + 0.235298i \(0.924393\pi\)
\(350\) 0 0
\(351\) 7.96366 0.425069
\(352\) 0 0
\(353\) 3.42474 0.182280 0.0911401 0.995838i \(-0.470949\pi\)
0.0911401 + 0.995838i \(0.470949\pi\)
\(354\) 0 0
\(355\) 19.4695 + 19.4695i 1.03334 + 1.03334i
\(356\) 0 0
\(357\) −0.830414 + 0.830414i −0.0439502 + 0.0439502i
\(358\) 0 0
\(359\) −0.293669 −0.0154992 −0.00774962 0.999970i \(-0.502467\pi\)
−0.00774962 + 0.999970i \(0.502467\pi\)
\(360\) 0 0
\(361\) 37.9752i 1.99870i
\(362\) 0 0
\(363\) −2.17112 2.17112i −0.113954 0.113954i
\(364\) 0 0
\(365\) 41.7204 2.18375
\(366\) 0 0
\(367\) 27.2960i 1.42484i −0.701754 0.712419i \(-0.747600\pi\)
0.701754 0.712419i \(-0.252400\pi\)
\(368\) 0 0
\(369\) −14.9427 + 11.2599i −0.777887 + 0.586164i
\(370\) 0 0
\(371\) 5.76862i 0.299492i
\(372\) 0 0
\(373\) −8.02826 −0.415688 −0.207844 0.978162i \(-0.566645\pi\)
−0.207844 + 0.978162i \(0.566645\pi\)
\(374\) 0 0
\(375\) −0.141358 0.141358i −0.00729968 0.00729968i
\(376\) 0 0
\(377\) 28.9079i 1.48883i
\(378\) 0 0
\(379\) 10.1054 0.519080 0.259540 0.965732i \(-0.416429\pi\)
0.259540 + 0.965732i \(0.416429\pi\)
\(380\) 0 0
\(381\) −1.99320 + 1.99320i −0.102115 + 0.102115i
\(382\) 0 0
\(383\) 3.77147 + 3.77147i 0.192713 + 0.192713i 0.796867 0.604154i \(-0.206489\pi\)
−0.604154 + 0.796867i \(0.706489\pi\)
\(384\) 0 0
\(385\) −0.195180 −0.00994732
\(386\) 0 0
\(387\) −7.07313 −0.359547
\(388\) 0 0
\(389\) 3.68798i 0.186988i 0.995620 + 0.0934940i \(0.0298036\pi\)
−0.995620 + 0.0934940i \(0.970196\pi\)
\(390\) 0 0
\(391\) −2.32163 2.32163i −0.117410 0.117410i
\(392\) 0 0
\(393\) −0.0969897 0.0969897i −0.00489248 0.00489248i
\(394\) 0 0
\(395\) −18.0844 18.0844i −0.909923 0.909923i
\(396\) 0 0
\(397\) −25.4075 + 25.4075i −1.27517 + 1.27517i −0.331824 + 0.943341i \(0.607664\pi\)
−0.943341 + 0.331824i \(0.892336\pi\)
\(398\) 0 0
\(399\) 1.49035 1.49035i 0.0746108 0.0746108i
\(400\) 0 0
\(401\) 14.5249i 0.725337i 0.931918 + 0.362669i \(0.118134\pi\)
−0.931918 + 0.362669i \(0.881866\pi\)
\(402\) 0 0
\(403\) 16.6017 16.6017i 0.826989 0.826989i
\(404\) 0 0
\(405\) 25.9582i 1.28987i
\(406\) 0 0
\(407\) 0.0662633 0.0662633i 0.00328455 0.00328455i
\(408\) 0 0
\(409\) −0.302043 −0.0149351 −0.00746754 0.999972i \(-0.502377\pi\)
−0.00746754 + 0.999972i \(0.502377\pi\)
\(410\) 0 0
\(411\) −4.67591 −0.230646
\(412\) 0 0
\(413\) −4.14050 + 4.14050i −0.203741 + 0.203741i
\(414\) 0 0
\(415\) 22.5612i 1.10748i
\(416\) 0 0
\(417\) −3.95101 + 3.95101i −0.193482 + 0.193482i
\(418\) 0 0
\(419\) 33.1732i 1.62062i 0.586002 + 0.810309i \(0.300701\pi\)
−0.586002 + 0.810309i \(0.699299\pi\)
\(420\) 0 0
\(421\) −4.15792 + 4.15792i −0.202645 + 0.202645i −0.801132 0.598488i \(-0.795769\pi\)
0.598488 + 0.801132i \(0.295769\pi\)
\(422\) 0 0
\(423\) 12.5643 12.5643i 0.610895 0.610895i
\(424\) 0 0
\(425\) −14.1886 14.1886i −0.688249 0.688249i
\(426\) 0 0
\(427\) 6.20801 + 6.20801i 0.300427 + 0.300427i
\(428\) 0 0
\(429\) 0.0593738 + 0.0593738i 0.00286659 + 0.00286659i
\(430\) 0 0
\(431\) 13.0184i 0.627074i −0.949576 0.313537i \(-0.898486\pi\)
0.949576 0.313537i \(-0.101514\pi\)
\(432\) 0 0
\(433\) 25.3433 1.21792 0.608961 0.793200i \(-0.291587\pi\)
0.608961 + 0.793200i \(0.291587\pi\)
\(434\) 0 0
\(435\) −5.23919 −0.251200
\(436\) 0 0
\(437\) 4.16665 + 4.16665i 0.199318 + 0.199318i
\(438\) 0 0
\(439\) 7.34677 7.34677i 0.350642 0.350642i −0.509706 0.860348i \(-0.670246\pi\)
0.860348 + 0.509706i \(0.170246\pi\)
\(440\) 0 0
\(441\) 2.92203 0.139144
\(442\) 0 0
\(443\) 14.7528i 0.700929i −0.936576 0.350464i \(-0.886024\pi\)
0.936576 0.350464i \(-0.113976\pi\)
\(444\) 0 0
\(445\) −28.1821 28.1821i −1.33596 1.33596i
\(446\) 0 0
\(447\) −1.61160 −0.0762262
\(448\) 0 0
\(449\) 26.6232i 1.25643i −0.778040 0.628214i \(-0.783786\pi\)
0.778040 0.628214i \(-0.216214\pi\)
\(450\) 0 0
\(451\) −0.395924 0.0556485i −0.0186433 0.00262039i
\(452\) 0 0
\(453\) 2.57754i 0.121103i
\(454\) 0 0
\(455\) −15.0539 −0.705740
\(456\) 0 0
\(457\) 0.826739 + 0.826739i 0.0386732 + 0.0386732i 0.726179 0.687506i \(-0.241294\pi\)
−0.687506 + 0.726179i \(0.741294\pi\)
\(458\) 0 0
\(459\) 6.95473i 0.324619i
\(460\) 0 0
\(461\) −22.4479 −1.04550 −0.522751 0.852485i \(-0.675094\pi\)
−0.522751 + 0.852485i \(0.675094\pi\)
\(462\) 0 0
\(463\) −10.0147 + 10.0147i −0.465421 + 0.465421i −0.900427 0.435006i \(-0.856746\pi\)
0.435006 + 0.900427i \(0.356746\pi\)
\(464\) 0 0
\(465\) 3.00884 + 3.00884i 0.139532 + 0.139532i
\(466\) 0 0
\(467\) −4.21327 −0.194967 −0.0974835 0.995237i \(-0.531079\pi\)
−0.0974835 + 0.995237i \(0.531079\pi\)
\(468\) 0 0
\(469\) 11.0516 0.510313
\(470\) 0 0
\(471\) 1.45990i 0.0672685i
\(472\) 0 0
\(473\) −0.106876 0.106876i −0.00491415 0.00491415i
\(474\) 0 0
\(475\) 25.4644 + 25.4644i 1.16839 + 1.16839i
\(476\) 0 0
\(477\) −11.9190 11.9190i −0.545736 0.545736i
\(478\) 0 0
\(479\) 10.8672 10.8672i 0.496536 0.496536i −0.413822 0.910358i \(-0.635806\pi\)
0.910358 + 0.413822i \(0.135806\pi\)
\(480\) 0 0
\(481\) 5.11078 5.11078i 0.233032 0.233032i
\(482\) 0 0
\(483\) 0.217982i 0.00991851i
\(484\) 0 0
\(485\) −34.4483 + 34.4483i −1.56422 + 1.56422i
\(486\) 0 0
\(487\) 12.9944i 0.588833i −0.955677 0.294416i \(-0.904875\pi\)
0.955677 0.294416i \(-0.0951252\pi\)
\(488\) 0 0
\(489\) 3.88070 3.88070i 0.175491 0.175491i
\(490\) 0 0
\(491\) −38.3827 −1.73219 −0.866094 0.499880i \(-0.833377\pi\)
−0.866094 + 0.499880i \(0.833377\pi\)
\(492\) 0 0
\(493\) 25.2455 1.13700
\(494\) 0 0
\(495\) 0.403280 0.403280i 0.0181261 0.0181261i
\(496\) 0 0
\(497\) 8.80850i 0.395115i
\(498\) 0 0
\(499\) −22.8653 + 22.8653i −1.02359 + 1.02359i −0.0238770 + 0.999715i \(0.507601\pi\)
−0.999715 + 0.0238770i \(0.992399\pi\)
\(500\) 0 0
\(501\) 2.02746i 0.0905802i
\(502\) 0 0
\(503\) −27.1861 + 27.1861i −1.21217 + 1.21217i −0.241853 + 0.970313i \(0.577755\pi\)
−0.970313 + 0.241853i \(0.922245\pi\)
\(504\) 0 0
\(505\) 33.2820 33.2820i 1.48103 1.48103i
\(506\) 0 0
\(507\) 2.01262 + 2.01262i 0.0893835 + 0.0893835i
\(508\) 0 0
\(509\) 2.86448 + 2.86448i 0.126966 + 0.126966i 0.767734 0.640768i \(-0.221384\pi\)
−0.640768 + 0.767734i \(0.721384\pi\)
\(510\) 0 0
\(511\) −9.43767 9.43767i −0.417498 0.417498i
\(512\) 0 0
\(513\) 12.4817i 0.551081i
\(514\) 0 0
\(515\) −61.2994 −2.70118
\(516\) 0 0
\(517\) 0.379695 0.0166990
\(518\) 0 0
\(519\) 0.777427 + 0.777427i 0.0341253 + 0.0341253i
\(520\) 0 0
\(521\) 6.47356 6.47356i 0.283612 0.283612i −0.550936 0.834548i \(-0.685729\pi\)
0.834548 + 0.550936i \(0.185729\pi\)
\(522\) 0 0
\(523\) 5.07244 0.221802 0.110901 0.993831i \(-0.464626\pi\)
0.110901 + 0.993831i \(0.464626\pi\)
\(524\) 0 0
\(525\) 1.33219i 0.0581416i
\(526\) 0 0
\(527\) −14.4984 14.4984i −0.631560 0.631560i
\(528\) 0 0
\(529\) −22.3906 −0.973503
\(530\) 0 0
\(531\) 17.1101i 0.742515i
\(532\) 0 0
\(533\) −30.5369 4.29208i −1.32270 0.185910i
\(534\) 0 0
\(535\) 6.11101i 0.264202i
\(536\) 0 0
\(537\) −4.63217 −0.199893
\(538\) 0 0
\(539\) 0.0441522 + 0.0441522i 0.00190177 + 0.00190177i
\(540\) 0 0
\(541\) 23.3720i 1.00484i 0.864623 + 0.502421i \(0.167557\pi\)
−0.864623 + 0.502421i \(0.832443\pi\)
\(542\) 0 0
\(543\) 4.36243 0.187210
\(544\) 0 0
\(545\) 12.7782 12.7782i 0.547356 0.547356i
\(546\) 0 0
\(547\) 4.86406 + 4.86406i 0.207972 + 0.207972i 0.803405 0.595433i \(-0.203019\pi\)
−0.595433 + 0.803405i \(0.703019\pi\)
\(548\) 0 0
\(549\) −25.6538 −1.09488
\(550\) 0 0
\(551\) −45.3083 −1.93020
\(552\) 0 0
\(553\) 8.18181i 0.347926i
\(554\) 0 0
\(555\) 0.926264 + 0.926264i 0.0393177 + 0.0393177i
\(556\) 0 0
\(557\) −3.76253 3.76253i −0.159424 0.159424i 0.622888 0.782311i \(-0.285959\pi\)
−0.782311 + 0.622888i \(0.785959\pi\)
\(558\) 0 0
\(559\) −8.24315 8.24315i −0.348648 0.348648i
\(560\) 0 0
\(561\) 0.0518516 0.0518516i 0.00218918 0.00218918i
\(562\) 0 0
\(563\) −14.0660 + 14.0660i −0.592809 + 0.592809i −0.938389 0.345580i \(-0.887682\pi\)
0.345580 + 0.938389i \(0.387682\pi\)
\(564\) 0 0
\(565\) 19.7324i 0.830150i
\(566\) 0 0
\(567\) −5.87207 + 5.87207i −0.246604 + 0.246604i
\(568\) 0 0
\(569\) 15.8567i 0.664747i −0.943148 0.332374i \(-0.892151\pi\)
0.943148 0.332374i \(-0.107849\pi\)
\(570\) 0 0
\(571\) −5.86553 + 5.86553i −0.245465 + 0.245465i −0.819106 0.573642i \(-0.805530\pi\)
0.573642 + 0.819106i \(0.305530\pi\)
\(572\) 0 0
\(573\) −4.29338 −0.179359
\(574\) 0 0
\(575\) 3.72448 0.155322
\(576\) 0 0
\(577\) 14.9767 14.9767i 0.623489 0.623489i −0.322933 0.946422i \(-0.604669\pi\)
0.946422 + 0.322933i \(0.104669\pi\)
\(578\) 0 0
\(579\) 5.76766i 0.239696i
\(580\) 0 0
\(581\) −5.10361 + 5.10361i −0.211733 + 0.211733i
\(582\) 0 0
\(583\) 0.360196i 0.0149178i
\(584\) 0 0
\(585\) 31.1043 31.1043i 1.28600 1.28600i
\(586\) 0 0
\(587\) 17.3988 17.3988i 0.718123 0.718123i −0.250097 0.968221i \(-0.580463\pi\)
0.968221 + 0.250097i \(0.0804626\pi\)
\(588\) 0 0
\(589\) 26.0204 + 26.0204i 1.07215 + 1.07215i
\(590\) 0 0
\(591\) 5.09898 + 5.09898i 0.209744 + 0.209744i
\(592\) 0 0
\(593\) 26.0399 + 26.0399i 1.06933 + 1.06933i 0.997410 + 0.0719204i \(0.0229128\pi\)
0.0719204 + 0.997410i \(0.477087\pi\)
\(594\) 0 0
\(595\) 13.1467i 0.538964i
\(596\) 0 0
\(597\) −6.49072 −0.265647
\(598\) 0 0
\(599\) 32.2062 1.31591 0.657956 0.753057i \(-0.271421\pi\)
0.657956 + 0.753057i \(0.271421\pi\)
\(600\) 0 0
\(601\) −5.54445 5.54445i −0.226163 0.226163i 0.584925 0.811088i \(-0.301124\pi\)
−0.811088 + 0.584925i \(0.801124\pi\)
\(602\) 0 0
\(603\) −22.8346 + 22.8346i −0.929896 + 0.929896i
\(604\) 0 0
\(605\) −34.3722 −1.39743
\(606\) 0 0
\(607\) 0.212677i 0.00863230i 0.999991 + 0.00431615i \(0.00137388\pi\)
−0.999991 + 0.00431615i \(0.998626\pi\)
\(608\) 0 0
\(609\) 1.18517 + 1.18517i 0.0480255 + 0.0480255i
\(610\) 0 0
\(611\) 29.2852 1.18475
\(612\) 0 0
\(613\) 40.2498i 1.62568i 0.582490 + 0.812838i \(0.302079\pi\)
−0.582490 + 0.812838i \(0.697921\pi\)
\(614\) 0 0
\(615\) 0.777884 5.53443i 0.0313673 0.223170i
\(616\) 0 0
\(617\) 41.6968i 1.67865i −0.543631 0.839324i \(-0.682951\pi\)
0.543631 0.839324i \(-0.317049\pi\)
\(618\) 0 0
\(619\) −36.7221 −1.47599 −0.737993 0.674809i \(-0.764226\pi\)
−0.737993 + 0.674809i \(0.764226\pi\)
\(620\) 0 0
\(621\) 0.912800 + 0.912800i 0.0366294 + 0.0366294i
\(622\) 0 0
\(623\) 12.7503i 0.510828i
\(624\) 0 0
\(625\) −26.0927 −1.04371
\(626\) 0 0
\(627\) −0.0930585 + 0.0930585i −0.00371640 + 0.00371640i
\(628\) 0 0
\(629\) −4.46329 4.46329i −0.177963 0.177963i
\(630\) 0 0
\(631\) −9.01872 −0.359030 −0.179515 0.983755i \(-0.557453\pi\)
−0.179515 + 0.983755i \(0.557453\pi\)
\(632\) 0 0
\(633\) 3.62400 0.144041
\(634\) 0 0
\(635\) 31.5554i 1.25224i
\(636\) 0 0
\(637\) 3.40539 + 3.40539i 0.134926 + 0.134926i
\(638\) 0 0
\(639\) 18.2000 + 18.2000i 0.719982 + 0.719982i
\(640\) 0 0
\(641\) 27.3192 + 27.3192i 1.07904 + 1.07904i 0.996595 + 0.0824465i \(0.0262734\pi\)
0.0824465 + 0.996595i \(0.473727\pi\)
\(642\) 0 0
\(643\) 27.8634 27.8634i 1.09882 1.09882i 0.104275 0.994548i \(-0.466748\pi\)
0.994548 0.104275i \(-0.0332524\pi\)
\(644\) 0 0
\(645\) 1.49397 1.49397i 0.0588249 0.0588249i
\(646\) 0 0
\(647\) 24.6332i 0.968430i 0.874949 + 0.484215i \(0.160895\pi\)
−0.874949 + 0.484215i \(0.839105\pi\)
\(648\) 0 0
\(649\) 0.258536 0.258536i 0.0101484 0.0101484i
\(650\) 0 0
\(651\) 1.36128i 0.0533526i
\(652\) 0 0
\(653\) 6.70523 6.70523i 0.262396 0.262396i −0.563631 0.826027i \(-0.690596\pi\)
0.826027 + 0.563631i \(0.190596\pi\)
\(654\) 0 0
\(655\) −1.53550 −0.0599968
\(656\) 0 0
\(657\) 39.0000 1.52154
\(658\) 0 0
\(659\) 13.5120 13.5120i 0.526351 0.526351i −0.393131 0.919482i \(-0.628608\pi\)
0.919482 + 0.393131i \(0.128608\pi\)
\(660\) 0 0
\(661\) 46.4896i 1.80823i 0.427285 + 0.904117i \(0.359470\pi\)
−0.427285 + 0.904117i \(0.640530\pi\)
\(662\) 0 0
\(663\) 3.99923 3.99923i 0.155317 0.155317i
\(664\) 0 0
\(665\) 23.5945i 0.914957i
\(666\) 0 0
\(667\) −3.31344 + 3.31344i −0.128297 + 0.128297i
\(668\) 0 0
\(669\) 2.10014 2.10014i 0.0811961 0.0811961i
\(670\) 0 0
\(671\) −0.387633 0.387633i −0.0149644 0.0149644i
\(672\) 0 0
\(673\) 7.17202 + 7.17202i 0.276461 + 0.276461i 0.831695 0.555233i \(-0.187371\pi\)
−0.555233 + 0.831695i \(0.687371\pi\)
\(674\) 0 0
\(675\) 5.57856 + 5.57856i 0.214719 + 0.214719i
\(676\) 0 0
\(677\) 17.3396i 0.666415i −0.942854 0.333208i \(-0.891869\pi\)
0.942854 0.333208i \(-0.108131\pi\)
\(678\) 0 0
\(679\) 15.5853 0.598108
\(680\) 0 0
\(681\) 0.0716649 0.00274621
\(682\) 0 0
\(683\) 9.30935 + 9.30935i 0.356212 + 0.356212i 0.862415 0.506202i \(-0.168951\pi\)
−0.506202 + 0.862415i \(0.668951\pi\)
\(684\) 0 0
\(685\) −37.0135 + 37.0135i −1.41421 + 1.41421i
\(686\) 0 0
\(687\) −5.87679 −0.224213
\(688\) 0 0
\(689\) 27.7813i 1.05838i
\(690\) 0 0
\(691\) −22.1097 22.1097i −0.841094 0.841094i 0.147908 0.989001i \(-0.452746\pi\)
−0.989001 + 0.147908i \(0.952746\pi\)
\(692\) 0 0
\(693\) −0.182454 −0.00693084
\(694\) 0 0
\(695\) 62.5506i 2.37268i
\(696\) 0 0
\(697\) −3.74831 + 26.6682i −0.141977 + 1.01013i
\(698\) 0 0
\(699\) 5.45775i 0.206431i
\(700\) 0 0
\(701\) −7.47646 −0.282382 −0.141191 0.989982i \(-0.545093\pi\)
−0.141191 + 0.989982i \(0.545093\pi\)
\(702\) 0 0
\(703\) 8.01030 + 8.01030i 0.302114 + 0.302114i
\(704\) 0 0
\(705\) 5.30757i 0.199895i
\(706\) 0 0
\(707\) −15.0576 −0.566299
\(708\) 0 0
\(709\) 1.87895 1.87895i 0.0705656 0.0705656i −0.670943 0.741509i \(-0.734111\pi\)
0.741509 + 0.670943i \(0.234111\pi\)
\(710\) 0 0
\(711\) −16.9052 16.9052i −0.633993 0.633993i
\(712\) 0 0
\(713\) 3.80579 0.142528
\(714\) 0 0
\(715\) 0.939978 0.0351532
\(716\) 0 0
\(717\) 0.489748i 0.0182900i
\(718\) 0 0
\(719\) −33.9733 33.9733i −1.26699 1.26699i −0.947636 0.319353i \(-0.896534\pi\)
−0.319353 0.947636i \(-0.603466\pi\)
\(720\) 0 0
\(721\) 13.8667 + 13.8667i 0.516422 + 0.516422i
\(722\) 0 0
\(723\) −1.00942 1.00942i −0.0375409 0.0375409i
\(724\) 0 0
\(725\) −20.2501 + 20.2501i −0.752068 + 0.752068i
\(726\) 0 0
\(727\) −25.5286 + 25.5286i −0.946802 + 0.946802i −0.998655 0.0518532i \(-0.983487\pi\)
0.0518532 + 0.998655i \(0.483487\pi\)
\(728\) 0 0
\(729\) 22.8804i 0.847422i
\(730\) 0 0
\(731\) −7.19881 + 7.19881i −0.266258 + 0.266258i
\(732\) 0 0
\(733\) 25.3586i 0.936639i 0.883559 + 0.468320i \(0.155140\pi\)
−0.883559 + 0.468320i \(0.844860\pi\)
\(734\) 0 0
\(735\) −0.617183 + 0.617183i −0.0227651 + 0.0227651i
\(736\) 0 0
\(737\) −0.690067 −0.0254189
\(738\) 0 0
\(739\) 30.2470 1.11265 0.556327 0.830964i \(-0.312210\pi\)
0.556327 + 0.830964i \(0.312210\pi\)
\(740\) 0 0
\(741\) −7.17744 + 7.17744i −0.263670 + 0.263670i
\(742\) 0 0
\(743\) 40.3795i 1.48138i 0.671848 + 0.740689i \(0.265501\pi\)
−0.671848 + 0.740689i \(0.734499\pi\)
\(744\) 0 0
\(745\) −12.7571 + 12.7571i −0.467383 + 0.467383i
\(746\) 0 0
\(747\) 21.0900i 0.771644i
\(748\) 0 0
\(749\) 1.38239 1.38239i 0.0505113 0.0505113i
\(750\) 0 0
\(751\) −22.1052 + 22.1052i −0.806628 + 0.806628i −0.984122 0.177494i \(-0.943201\pi\)
0.177494 + 0.984122i \(0.443201\pi\)
\(752\) 0 0
\(753\) −1.25141 1.25141i −0.0456039 0.0456039i
\(754\) 0 0
\(755\) 20.4032 + 20.4032i 0.742549 + 0.742549i
\(756\) 0 0
\(757\) −2.38191 2.38191i −0.0865719 0.0865719i 0.662495 0.749067i \(-0.269498\pi\)
−0.749067 + 0.662495i \(0.769498\pi\)
\(758\) 0 0
\(759\) 0.0136109i 0.000494045i
\(760\) 0 0
\(761\) −22.9273 −0.831114 −0.415557 0.909567i \(-0.636413\pi\)
−0.415557 + 0.909567i \(0.636413\pi\)
\(762\) 0 0
\(763\) −5.78115 −0.209292
\(764\) 0 0
\(765\) −27.1636 27.1636i −0.982103 0.982103i
\(766\) 0 0
\(767\) 19.9404 19.9404i 0.720007 0.720007i
\(768\) 0 0
\(769\) −6.07809 −0.219182 −0.109591 0.993977i \(-0.534954\pi\)
−0.109591 + 0.993977i \(0.534954\pi\)
\(770\) 0 0
\(771\) 7.17149i 0.258275i
\(772\) 0 0
\(773\) −32.7106 32.7106i −1.17652 1.17652i −0.980625 0.195894i \(-0.937239\pi\)
−0.195894 0.980625i \(-0.562761\pi\)
\(774\) 0 0
\(775\) 23.2590 0.835489
\(776\) 0 0
\(777\) 0.419065i 0.0150339i
\(778\) 0 0
\(779\) 6.72711 47.8616i 0.241024 1.71482i
\(780\) 0 0
\(781\) 0.550009i 0.0196809i
\(782\) 0 0
\(783\) −9.92582 −0.354720
\(784\) 0 0
\(785\) 11.5562 + 11.5562i 0.412459 + 0.412459i
\(786\) 0 0
\(787\) 23.5774i 0.840442i 0.907422 + 0.420221i \(0.138047\pi\)
−0.907422 + 0.420221i \(0.861953\pi\)
\(788\) 0 0
\(789\) 3.39383 0.120823
\(790\) 0 0
\(791\) 4.46372 4.46372i 0.158712 0.158712i
\(792\) 0 0
\(793\) −29.8975 29.8975i −1.06169 1.06169i
\(794\) 0 0
\(795\) 5.03501 0.178574
\(796\) 0 0
\(797\) 5.77084 0.204414 0.102207 0.994763i \(-0.467410\pi\)
0.102207 + 0.994763i \(0.467410\pi\)
\(798\) 0 0
\(799\) 25.5750i 0.904779i
\(800\) 0 0