Properties

Label 768.2.o.b.95.5
Level 768
Weight 2
Character 768.95
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 95.5
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.988287 - 1.42242i) q^{3} +(-2.70066 + 1.11865i) q^{5} +(-3.28204 - 3.28204i) q^{7} +(-1.04658 + 2.81152i) q^{9} +O(q^{10})\) \(q+(-0.988287 - 1.42242i) q^{3} +(-2.70066 + 1.11865i) q^{5} +(-3.28204 - 3.28204i) q^{7} +(-1.04658 + 2.81152i) q^{9} +(0.276697 - 0.114612i) q^{11} +(0.155281 - 0.374881i) q^{13} +(4.26022 + 2.73593i) q^{15} +1.41723 q^{17} +(2.51972 + 1.04370i) q^{19} +(-1.42485 + 7.91204i) q^{21} +(3.30034 + 3.30034i) q^{23} +(2.50664 - 2.50664i) q^{25} +(5.03350 - 1.28991i) q^{27} +(-0.650676 + 1.57087i) q^{29} +4.16702i q^{31} +(-0.436482 - 0.280311i) q^{33} +(12.5351 + 5.19221i) q^{35} +(2.82757 + 6.82635i) q^{37} +(-0.686701 + 0.149615i) q^{39} +(-3.81949 + 3.81949i) q^{41} +(-2.07136 - 5.00071i) q^{43} +(-0.318658 - 8.76372i) q^{45} -5.44085i q^{47} +14.5435i q^{49} +(-1.40063 - 2.01590i) q^{51} +(-1.85159 - 4.47012i) q^{53} +(-0.619053 + 0.619053i) q^{55} +(-1.00562 - 4.61558i) q^{57} +(-1.37699 - 3.32434i) q^{59} +(10.9629 + 4.54098i) q^{61} +(12.6624 - 5.79262i) q^{63} +1.18613i q^{65} +(-4.19888 + 10.1370i) q^{67} +(1.43280 - 7.95617i) q^{69} +(-3.77857 + 3.77857i) q^{71} +(-3.89137 - 3.89137i) q^{73} +(-6.04279 - 1.08823i) q^{75} +(-1.28429 - 0.531970i) q^{77} +4.81995 q^{79} +(-6.80935 - 5.88497i) q^{81} +(-3.60399 + 8.70081i) q^{83} +(-3.82744 + 1.58538i) q^{85} +(2.87750 - 0.626933i) q^{87} +(3.69926 + 3.69926i) q^{89} +(-1.74001 + 0.720735i) q^{91} +(5.92727 - 4.11821i) q^{93} -7.97242 q^{95} +10.9958 q^{97} +(0.0326483 + 0.897890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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
\(3\) −0.988287 1.42242i −0.570588 0.821237i
\(4\) 0 0
\(5\) −2.70066 + 1.11865i −1.20777 + 0.500275i −0.893502 0.449059i \(-0.851759\pi\)
−0.314269 + 0.949334i \(0.601759\pi\)
\(6\) 0 0
\(7\) −3.28204 3.28204i −1.24049 1.24049i −0.959797 0.280697i \(-0.909435\pi\)
−0.280697 0.959797i \(-0.590565\pi\)
\(8\) 0 0
\(9\) −1.04658 + 2.81152i −0.348860 + 0.937175i
\(10\) 0 0
\(11\) 0.276697 0.114612i 0.0834272 0.0345567i −0.340580 0.940216i \(-0.610623\pi\)
0.424007 + 0.905659i \(0.360623\pi\)
\(12\) 0 0
\(13\) 0.155281 0.374881i 0.0430671 0.103973i −0.900882 0.434064i \(-0.857079\pi\)
0.943949 + 0.330091i \(0.107079\pi\)
\(14\) 0 0
\(15\) 4.26022 + 2.73593i 1.09998 + 0.706415i
\(16\) 0 0
\(17\) 1.41723 0.343728 0.171864 0.985121i \(-0.445021\pi\)
0.171864 + 0.985121i \(0.445021\pi\)
\(18\) 0 0
\(19\) 2.51972 + 1.04370i 0.578062 + 0.239441i 0.652506 0.757784i \(-0.273718\pi\)
−0.0744431 + 0.997225i \(0.523718\pi\)
\(20\) 0 0
\(21\) −1.42485 + 7.91204i −0.310929 + 1.72655i
\(22\) 0 0
\(23\) 3.30034 + 3.30034i 0.688169 + 0.688169i 0.961827 0.273658i \(-0.0882337\pi\)
−0.273658 + 0.961827i \(0.588234\pi\)
\(24\) 0 0
\(25\) 2.50664 2.50664i 0.501328 0.501328i
\(26\) 0 0
\(27\) 5.03350 1.28991i 0.968698 0.248244i
\(28\) 0 0
\(29\) −0.650676 + 1.57087i −0.120827 + 0.291703i −0.972708 0.232033i \(-0.925462\pi\)
0.851880 + 0.523736i \(0.175462\pi\)
\(30\) 0 0
\(31\) 4.16702i 0.748419i 0.927344 + 0.374209i \(0.122086\pi\)
−0.927344 + 0.374209i \(0.877914\pi\)
\(32\) 0 0
\(33\) −0.436482 0.280311i −0.0759817 0.0487959i
\(34\) 0 0
\(35\) 12.5351 + 5.19221i 2.11882 + 0.877644i
\(36\) 0 0
\(37\) 2.82757 + 6.82635i 0.464849 + 1.12225i 0.966383 + 0.257107i \(0.0827693\pi\)
−0.501534 + 0.865138i \(0.667231\pi\)
\(38\) 0 0
\(39\) −0.686701 + 0.149615i −0.109960 + 0.0239575i
\(40\) 0 0
\(41\) −3.81949 + 3.81949i −0.596504 + 0.596504i −0.939380 0.342877i \(-0.888599\pi\)
0.342877 + 0.939380i \(0.388599\pi\)
\(42\) 0 0
\(43\) −2.07136 5.00071i −0.315880 0.762602i −0.999464 0.0327301i \(-0.989580\pi\)
0.683584 0.729872i \(-0.260420\pi\)
\(44\) 0 0
\(45\) −0.318658 8.76372i −0.0475028 1.30642i
\(46\) 0 0
\(47\) 5.44085i 0.793629i −0.917899 0.396815i \(-0.870116\pi\)
0.917899 0.396815i \(-0.129884\pi\)
\(48\) 0 0
\(49\) 14.5435i 2.07765i
\(50\) 0 0
\(51\) −1.40063 2.01590i −0.196127 0.282282i
\(52\) 0 0
\(53\) −1.85159 4.47012i −0.254335 0.614019i 0.744210 0.667946i \(-0.232826\pi\)
−0.998545 + 0.0539269i \(0.982826\pi\)
\(54\) 0 0
\(55\) −0.619053 + 0.619053i −0.0834731 + 0.0834731i
\(56\) 0 0
\(57\) −1.00562 4.61558i −0.133197 0.611348i
\(58\) 0 0
\(59\) −1.37699 3.32434i −0.179268 0.432792i 0.808545 0.588434i \(-0.200255\pi\)
−0.987814 + 0.155642i \(0.950255\pi\)
\(60\) 0 0
\(61\) 10.9629 + 4.54098i 1.40366 + 0.581413i 0.950698 0.310119i \(-0.100369\pi\)
0.452958 + 0.891532i \(0.350369\pi\)
\(62\) 0 0
\(63\) 12.6624 5.79262i 1.59532 0.729801i
\(64\) 0 0
\(65\) 1.18613i 0.147121i
\(66\) 0 0
\(67\) −4.19888 + 10.1370i −0.512974 + 1.23843i 0.429170 + 0.903224i \(0.358806\pi\)
−0.942145 + 0.335206i \(0.891194\pi\)
\(68\) 0 0
\(69\) 1.43280 7.95617i 0.172489 0.957810i
\(70\) 0 0
\(71\) −3.77857 + 3.77857i −0.448434 + 0.448434i −0.894834 0.446400i \(-0.852706\pi\)
0.446400 + 0.894834i \(0.352706\pi\)
\(72\) 0 0
\(73\) −3.89137 3.89137i −0.455450 0.455450i 0.441708 0.897159i \(-0.354373\pi\)
−0.897159 + 0.441708i \(0.854373\pi\)
\(74\) 0 0
\(75\) −6.04279 1.08823i −0.697761 0.125657i
\(76\) 0 0
\(77\) −1.28429 0.531970i −0.146358 0.0606236i
\(78\) 0 0
\(79\) 4.81995 0.542287 0.271143 0.962539i \(-0.412598\pi\)
0.271143 + 0.962539i \(0.412598\pi\)
\(80\) 0 0
\(81\) −6.80935 5.88497i −0.756594 0.653885i
\(82\) 0 0
\(83\) −3.60399 + 8.70081i −0.395590 + 0.955038i 0.593109 + 0.805122i \(0.297900\pi\)
−0.988699 + 0.149916i \(0.952100\pi\)
\(84\) 0 0
\(85\) −3.82744 + 1.58538i −0.415145 + 0.171959i
\(86\) 0 0
\(87\) 2.87750 0.626933i 0.308500 0.0672143i
\(88\) 0 0
\(89\) 3.69926 + 3.69926i 0.392121 + 0.392121i 0.875443 0.483322i \(-0.160570\pi\)
−0.483322 + 0.875443i \(0.660570\pi\)
\(90\) 0 0
\(91\) −1.74001 + 0.720735i −0.182402 + 0.0755536i
\(92\) 0 0
\(93\) 5.92727 4.11821i 0.614629 0.427039i
\(94\) 0 0
\(95\) −7.97242 −0.817953
\(96\) 0 0
\(97\) 10.9958 1.11646 0.558229 0.829687i \(-0.311481\pi\)
0.558229 + 0.829687i \(0.311481\pi\)
\(98\) 0 0
\(99\) 0.0326483 + 0.897890i 0.00328127 + 0.0902413i
\(100\) 0 0
\(101\) −2.51499 + 1.04174i −0.250251 + 0.103657i −0.504283 0.863538i \(-0.668243\pi\)
0.254032 + 0.967196i \(0.418243\pi\)
\(102\) 0 0
\(103\) −0.332885 0.332885i −0.0328001 0.0328001i 0.690517 0.723317i \(-0.257383\pi\)
−0.723317 + 0.690517i \(0.757383\pi\)
\(104\) 0 0
\(105\) −5.00275 22.9616i −0.488219 2.24082i
\(106\) 0 0
\(107\) 0.394269 0.163312i 0.0381154 0.0157879i −0.363544 0.931577i \(-0.618433\pi\)
0.401660 + 0.915789i \(0.368433\pi\)
\(108\) 0 0
\(109\) −1.81782 + 4.38860i −0.174115 + 0.420352i −0.986713 0.162474i \(-0.948053\pi\)
0.812598 + 0.582825i \(0.198053\pi\)
\(110\) 0 0
\(111\) 6.91552 10.7684i 0.656392 1.02209i
\(112\) 0 0
\(113\) 18.5323 1.74337 0.871687 0.490063i \(-0.163026\pi\)
0.871687 + 0.490063i \(0.163026\pi\)
\(114\) 0 0
\(115\) −12.6050 5.22117i −1.17542 0.486876i
\(116\) 0 0
\(117\) 0.891473 + 0.828917i 0.0824167 + 0.0766334i
\(118\) 0 0
\(119\) −4.65139 4.65139i −0.426392 0.426392i
\(120\) 0 0
\(121\) −7.71475 + 7.71475i −0.701341 + 0.701341i
\(122\) 0 0
\(123\) 9.20768 + 1.65818i 0.830229 + 0.149513i
\(124\) 0 0
\(125\) 1.62772 3.92966i 0.145587 0.351479i
\(126\) 0 0
\(127\) 4.80013i 0.425943i 0.977058 + 0.212971i \(0.0683141\pi\)
−0.977058 + 0.212971i \(0.931686\pi\)
\(128\) 0 0
\(129\) −5.06603 + 7.88850i −0.446039 + 0.694543i
\(130\) 0 0
\(131\) −20.2118 8.37202i −1.76592 0.731467i −0.995589 0.0938185i \(-0.970093\pi\)
−0.770328 0.637648i \(1.22009\pi\)
\(132\) 0 0
\(133\) −4.84434 11.6953i −0.420057 1.01411i
\(134\) 0 0
\(135\) −12.1508 + 9.11434i −1.04577 + 0.784437i
\(136\) 0 0
\(137\) −12.7302 + 12.7302i −1.08762 + 1.08762i −0.0918436 + 0.995773i \(0.529276\pi\)
−0.995773 + 0.0918436i \(0.970724\pi\)
\(138\) 0 0
\(139\) −0.193431 0.466984i −0.0164066 0.0396091i 0.915464 0.402400i \(-0.131824\pi\)
−0.931871 + 0.362791i \(0.881824\pi\)
\(140\) 0 0
\(141\) −7.73919 + 5.37712i −0.651758 + 0.452835i
\(142\) 0 0
\(143\) 0.121525i 0.0101624i
\(144\) 0 0
\(145\) 4.97026i 0.412758i
\(146\) 0 0
\(147\) 20.6871 14.3732i 1.70624 1.18548i
\(148\) 0 0
\(149\) 4.31949 + 10.4282i 0.353866 + 0.854308i 0.996136 + 0.0878294i \(0.0279930\pi\)
−0.642269 + 0.766479i \(0.722007\pi\)
\(150\) 0 0
\(151\) −13.7687 + 13.7687i −1.12048 + 1.12048i −0.128814 + 0.991669i \(0.541117\pi\)
−0.991669 + 0.128814i \(0.958883\pi\)
\(152\) 0 0
\(153\) −1.48324 + 3.98457i −0.119913 + 0.322133i
\(154\) 0 0
\(155\) −4.66143 11.2537i −0.374415 0.903918i
\(156\) 0 0
\(157\) −7.94660 3.29159i −0.634208 0.262697i 0.0423321 0.999104i \(-0.486521\pi\)
−0.676540 + 0.736406i \(0.736521\pi\)
\(158\) 0 0
\(159\) −4.52851 + 7.05151i −0.359135 + 0.559221i
\(160\) 0 0
\(161\) 21.6637i 1.70734i
\(162\) 0 0
\(163\) −4.77631 + 11.5310i −0.374110 + 0.903181i 0.618935 + 0.785442i \(0.287565\pi\)
−0.993045 + 0.117739i \(0.962435\pi\)
\(164\) 0 0
\(165\) 1.49236 + 0.268754i 0.116180 + 0.0209225i
\(166\) 0 0
\(167\) 14.7585 14.7585i 1.14205 1.14205i 0.153970 0.988076i \(-0.450794\pi\)
0.988076 0.153970i \(-0.0492059\pi\)
\(168\) 0 0
\(169\) 9.07596 + 9.07596i 0.698151 + 0.698151i
\(170\) 0 0
\(171\) −5.57147 + 5.99193i −0.426061 + 0.458214i
\(172\) 0 0
\(173\) 7.60827 + 3.15145i 0.578446 + 0.239600i 0.652671 0.757641i \(-0.273648\pi\)
−0.0742253 + 0.997241i \(0.523648\pi\)
\(174\) 0 0
\(175\) −16.4538 −1.24379
\(176\) 0 0
\(177\) −3.36776 + 5.24406i −0.253136 + 0.394167i
\(178\) 0 0
\(179\) −1.38731 + 3.34926i −0.103692 + 0.250335i −0.967208 0.253987i \(-0.918258\pi\)
0.863515 + 0.504323i \(0.168258\pi\)
\(180\) 0 0
\(181\) −6.51464 + 2.69845i −0.484229 + 0.200574i −0.611424 0.791303i \(-0.709403\pi\)
0.127194 + 0.991878i \(0.459403\pi\)
\(182\) 0 0
\(183\) −4.37529 20.0817i −0.323431 1.48448i
\(184\) 0 0
\(185\) −15.2726 15.2726i −1.12286 1.12286i
\(186\) 0 0
\(187\) 0.392142 0.162431i 0.0286763 0.0118781i
\(188\) 0 0
\(189\) −20.7537 12.2866i −1.50961 0.893718i
\(190\) 0 0
\(191\) −18.8097 −1.36102 −0.680511 0.732737i \(-0.738242\pi\)
−0.680511 + 0.732737i \(0.738242\pi\)
\(192\) 0 0
\(193\) −11.1498 −0.802582 −0.401291 0.915951i \(-0.631438\pi\)
−0.401291 + 0.915951i \(0.631438\pi\)
\(194\) 0 0
\(195\) 1.68718 1.17224i 0.120821 0.0839455i
\(196\) 0 0
\(197\) 14.7643 6.11558i 1.05191 0.435717i 0.211340 0.977413i \(-0.432217\pi\)
0.840575 + 0.541696i \(0.182217\pi\)
\(198\) 0 0
\(199\) 0.686194 + 0.686194i 0.0486430 + 0.0486430i 0.731010 0.682367i \(-0.239049\pi\)
−0.682367 + 0.731010i \(0.739049\pi\)
\(200\) 0 0
\(201\) 18.5688 4.04566i 1.30974 0.285359i
\(202\) 0 0
\(203\) 7.29119 3.02011i 0.511742 0.211970i
\(204\) 0 0
\(205\) 6.04246 14.5878i 0.422024 1.01886i
\(206\) 0 0
\(207\) −12.7331 + 5.82492i −0.885009 + 0.404860i
\(208\) 0 0
\(209\) 0.816817 0.0565004
\(210\) 0 0
\(211\) −2.25868 0.935575i −0.155494 0.0644076i 0.303579 0.952806i \(-0.401818\pi\)
−0.459073 + 0.888399i \(0.651818\pi\)
\(212\) 0 0
\(213\) 9.10904 + 1.64042i 0.624141 + 0.112400i
\(214\) 0 0
\(215\) 11.1881 + 11.1881i 0.763021 + 0.763021i
\(216\) 0 0
\(217\) 13.6763 13.6763i 0.928409 0.928409i
\(218\) 0 0
\(219\) −1.68939 + 9.38096i −0.114158 + 0.633907i
\(220\) 0 0
\(221\) 0.220068 0.531291i 0.0148034 0.0357385i
\(222\) 0 0
\(223\) 10.3472i 0.692900i −0.938068 0.346450i \(-0.887387\pi\)
0.938068 0.346450i \(-0.112613\pi\)
\(224\) 0 0
\(225\) 4.42409 + 9.67088i 0.294939 + 0.644725i
\(226\) 0 0
\(227\) 10.4804 + 4.34114i 0.695611 + 0.288131i 0.702336 0.711846i \(-0.252141\pi\)
−0.00672494 + 0.999977i \(0.502141\pi\)
\(228\) 0 0
\(229\) 7.39471 + 17.8524i 0.488656 + 1.17972i 0.955396 + 0.295326i \(0.0954284\pi\)
−0.466740 + 0.884395i \(0.654572\pi\)
\(230\) 0 0
\(231\) 0.512559 + 2.35254i 0.0337239 + 0.154786i
\(232\) 0 0
\(233\) 15.9703 15.9703i 1.04625 1.04625i 0.0473714 0.998877i \(-0.484916\pi\)
0.998877 0.0473714i \(-0.0150844\pi\)
\(234\) 0 0
\(235\) 6.08640 + 14.6939i 0.397033 + 0.958522i
\(236\) 0 0
\(237\) −4.76349 6.85601i −0.309422 0.445346i
\(238\) 0 0
\(239\) 22.5155i 1.45641i 0.685361 + 0.728204i \(0.259645\pi\)
−0.685361 + 0.728204i \(0.740355\pi\)
\(240\) 0 0
\(241\) 21.7886i 1.40353i −0.712409 0.701765i \(-0.752396\pi\)
0.712409 0.701765i \(-0.247604\pi\)
\(242\) 0 0
\(243\) −1.64133 + 15.5018i −0.105291 + 0.994441i
\(244\) 0 0
\(245\) −16.2691 39.2771i −1.03939 2.50932i
\(246\) 0 0
\(247\) 0.782526 0.782526i 0.0497909 0.0497909i
\(248\) 0 0
\(249\) 15.9380 3.47249i 1.01003 0.220060i
\(250\) 0 0
\(251\) −5.96821 14.4085i −0.376710 0.909458i −0.992578 0.121609i \(-0.961195\pi\)
0.615868 0.787849i \(1.71119\pi\)
\(252\) 0 0
\(253\) 1.29145 + 0.534937i 0.0811928 + 0.0336312i
\(254\) 0 0
\(255\) 6.03769 + 3.87744i 0.378095 + 0.242815i
\(256\) 0 0
\(257\) 11.8781i 0.740934i −0.928846 0.370467i \(-0.879198\pi\)
0.928846 0.370467i \(-0.120802\pi\)
\(258\) 0 0
\(259\) 13.1242 31.6845i 0.815495 1.96878i
\(260\) 0 0
\(261\) −3.73556 3.47343i −0.231225 0.215000i
\(262\) 0 0
\(263\) 3.29543 3.29543i 0.203205 0.203205i −0.598167 0.801372i \(-0.704104\pi\)
0.801372 + 0.598167i \(0.204104\pi\)
\(264\) 0 0
\(265\) 10.0010 + 10.0010i 0.614357 + 0.614357i
\(266\) 0 0
\(267\) 1.60599 8.91786i 0.0982849 0.545764i
\(268\) 0 0
\(269\) 26.9975 + 11.1827i 1.64607 + 0.681824i 0.996890 0.0788107i \(-0.0251123\pi\)
0.649180 + 0.760635i \(0.275112\pi\)
\(270\) 0 0
\(271\) 3.49827 0.212505 0.106252 0.994339i \(-0.466115\pi\)
0.106252 + 0.994339i \(0.466115\pi\)
\(272\) 0 0
\(273\) 2.74482 + 1.76274i 0.166124 + 0.106686i
\(274\) 0 0
\(275\) 0.406289 0.980869i 0.0245002 0.0591486i
\(276\) 0 0
\(277\) 10.1905 4.22105i 0.612289 0.253619i −0.0549177 0.998491i \(-0.517490\pi\)
0.667207 + 0.744872i \(0.267490\pi\)
\(278\) 0 0
\(279\) −11.7157 4.36112i −0.701399 0.261093i
\(280\) 0 0
\(281\) 14.1081 + 14.1081i 0.841616 + 0.841616i 0.989069 0.147453i \(-0.0471074\pi\)
−0.147453 + 0.989069i \(0.547107\pi\)
\(282\) 0 0
\(283\) −17.2200 + 7.13275i −1.02362 + 0.423998i −0.830406 0.557159i \(-0.811892\pi\)
−0.193215 + 0.981156i \(0.561892\pi\)
\(284\) 0 0
\(285\) 7.87904 + 11.3402i 0.466714 + 0.671733i
\(286\) 0 0
\(287\) 25.0714 1.47992
\(288\) 0 0
\(289\) −14.9915 −0.881851
\(290\) 0 0
\(291\) −10.8670 15.6407i −0.637037 0.916877i
\(292\) 0 0
\(293\) −21.6538 + 8.96928i −1.26503 + 0.523991i −0.911448 0.411414i \(-0.865035\pi\)
−0.353577 + 0.935405i \(0.615035\pi\)
\(294\) 0 0
\(295\) 7.43753 + 7.43753i 0.433030 + 0.433030i
\(296\) 0 0
\(297\) 1.24491 0.933812i 0.0722372 0.0541853i
\(298\) 0 0
\(299\) 1.74971 0.724755i 0.101189 0.0419137i
\(300\) 0 0
\(301\) −9.61423 + 23.2108i −0.554155 + 1.33785i
\(302\) 0 0
\(303\) 3.96733 + 2.54784i 0.227917 + 0.146370i
\(304\) 0 0
\(305\) −34.6868 −1.98616
\(306\) 0 0
\(307\) 19.7154 + 8.16639i 1.12522 + 0.466081i 0.866153 0.499779i \(-0.166585\pi\)
0.259065 + 0.965860i \(0.416585\pi\)
\(308\) 0 0
\(309\) −0.144518 + 0.802489i −0.00822132 + 0.0456520i
\(310\) 0 0
\(311\) 10.5699 + 10.5699i 0.599365 + 0.599365i 0.940144 0.340779i \(-0.110691\pi\)
−0.340779 + 0.940144i \(0.610691\pi\)
\(312\) 0 0
\(313\) −24.0589 + 24.0589i −1.35989 + 1.35989i −0.485846 + 0.874044i \(0.661489\pi\)
−0.874044 + 0.485846i \(0.838511\pi\)
\(314\) 0 0
\(315\) −27.7170 + 29.8087i −1.56168 + 1.67953i
\(316\) 0 0
\(317\) −8.93517 + 21.5714i −0.501849 + 1.21157i 0.446626 + 0.894721i \(0.352625\pi\)
−0.948475 + 0.316851i \(0.897375\pi\)
\(318\) 0 0
\(319\) 0.509230i 0.0285114i
\(320\) 0 0
\(321\) −0.621949 0.399419i −0.0347138 0.0222934i
\(322\) 0 0
\(323\) 3.57101 + 1.47916i 0.198696 + 0.0823027i
\(324\) 0 0
\(325\) −0.550458 1.32892i −0.0305339 0.0737154i
\(326\) 0 0
\(327\) 8.03897 1.75149i 0.444556 0.0968575i
\(328\) 0 0
\(329\) −17.8571 + 17.8571i −0.984492 + 0.984492i
\(330\) 0 0
\(331\) 10.6785 + 25.7802i 0.586943 + 1.41701i 0.886411 + 0.462900i \(0.153191\pi\)
−0.299467 + 0.954107i \(0.596809\pi\)
\(332\) 0 0
\(333\) −22.1517 + 0.805461i −1.21391 + 0.0441390i
\(334\) 0 0
\(335\) 32.0736i 1.75237i
\(336\) 0 0
\(337\) 7.72298i 0.420698i 0.977626 + 0.210349i \(0.0674600\pi\)
−0.977626 + 0.210349i \(0.932540\pi\)
\(338\) 0 0
\(339\) −18.3152 26.3608i −0.994747 1.43172i
\(340\) 0 0
\(341\) 0.477589 + 1.15300i 0.0258629 + 0.0624385i
\(342\) 0 0
\(343\) 24.7581 24.7581i 1.33681 1.33681i
\(344\) 0 0
\(345\) 5.03065 + 23.0897i 0.270841 + 1.24311i
\(346\) 0 0
\(347\) 2.88801 + 6.97227i 0.155037 + 0.374291i 0.982245 0.187604i \(-0.0600723\pi\)
−0.827208 + 0.561896i \(0.810072\pi\)
\(348\) 0 0
\(349\) −3.70439 1.53441i −0.198292 0.0821351i 0.281328 0.959612i \(-0.409225\pi\)
−0.479619 + 0.877477i \(0.659225\pi\)
\(350\) 0 0
\(351\) 0.298041 2.08726i 0.0159083 0.111410i
\(352\) 0 0
\(353\) 33.0427i 1.75869i 0.476189 + 0.879343i \(0.342018\pi\)
−0.476189 + 0.879343i \(0.657982\pi\)
\(354\) 0 0
\(355\) 5.97773 14.4315i 0.317265 0.765945i
\(356\) 0 0
\(357\) −2.01934 + 11.2132i −0.106875 + 0.593463i
\(358\) 0 0
\(359\) 1.02805 1.02805i 0.0542584 0.0542584i −0.679457 0.733715i \(-0.737785\pi\)
0.733715 + 0.679457i \(0.237785\pi\)
\(360\) 0 0
\(361\) −8.17537 8.17537i −0.430283 0.430283i
\(362\) 0 0
\(363\) 18.5980 + 3.34926i 0.976143 + 0.175791i
\(364\) 0 0
\(365\) 14.8623 + 6.15618i 0.777930 + 0.322229i
\(366\) 0 0
\(367\) 11.6801 0.609694 0.304847 0.952401i \(-0.401395\pi\)
0.304847 + 0.952401i \(0.401395\pi\)
\(368\) 0 0
\(369\) −6.74119 14.7360i −0.350932 0.767125i
\(370\) 0 0
\(371\) −8.59414 + 20.7481i −0.446185 + 1.07719i
\(372\) 0 0
\(373\) 11.6155 4.81129i 0.601427 0.249119i −0.0611312 0.998130i \(-0.519471\pi\)
0.662558 + 0.749011i \(0.269471\pi\)
\(374\) 0 0
\(375\) −7.19829 + 1.56832i −0.371718 + 0.0809879i
\(376\) 0 0
\(377\) 0.487851 + 0.487851i 0.0251256 + 0.0251256i
\(378\) 0 0
\(379\) 15.2623 6.32186i 0.783972 0.324732i 0.0454550 0.998966i \(-0.485526\pi\)
0.738517 + 0.674234i \(0.235526\pi\)
\(380\) 0 0
\(381\) 6.82782 4.74390i 0.349800 0.243038i
\(382\) 0 0
\(383\) −28.9536 −1.47946 −0.739729 0.672905i \(-0.765046\pi\)
−0.739729 + 0.672905i \(0.765046\pi\)
\(384\) 0 0
\(385\) 4.06351 0.207096
\(386\) 0 0
\(387\) 16.2275 0.590049i 0.824889 0.0299939i
\(388\) 0 0
\(389\) 6.31149 2.61431i 0.320005 0.132551i −0.216898 0.976194i \(-0.569594\pi\)
0.536903 + 0.843644i \(0.319594\pi\)
\(390\) 0 0
\(391\) 4.67733 + 4.67733i 0.236543 + 0.236543i
\(392\) 0 0
\(393\) 8.06654 + 37.0238i 0.406903 + 1.86760i
\(394\) 0 0
\(395\) −13.0170 + 5.39183i −0.654958 + 0.271293i
\(396\) 0 0
\(397\) 1.66407 4.01741i 0.0835171 0.201628i −0.876604 0.481212i \(-0.840197\pi\)
0.960121 + 0.279584i \(0.0901966\pi\)
\(398\) 0 0
\(399\) −11.8480 + 18.4490i −0.593143 + 0.923604i
\(400\) 0 0
\(401\) 3.93840 0.196674 0.0983371 0.995153i \(-0.468648\pi\)
0.0983371 + 0.995153i \(0.468648\pi\)
\(402\) 0 0
\(403\) 1.56214 + 0.647058i 0.0778155 + 0.0322322i
\(404\) 0 0
\(405\) 24.9729 + 8.27601i 1.24091 + 0.411238i
\(406\) 0 0
\(407\) 1.56476 + 1.56476i 0.0775621 + 0.0775621i
\(408\) 0 0
\(409\) 12.8960 12.8960i 0.637664 0.637664i −0.312314 0.949979i \(-0.601104\pi\)
0.949979 + 0.312314i \(0.101104\pi\)
\(410\) 0 0
\(411\) 30.6889 + 5.52667i 1.51377 + 0.272610i
\(412\) 0 0
\(413\) −6.39128 + 15.4299i −0.314494 + 0.759256i
\(414\) 0 0
\(415\) 27.5295i 1.35137i
\(416\) 0 0
\(417\) −0.473084 + 0.736656i −0.0231670 + 0.0360742i
\(418\) 0 0
\(419\) −5.81232 2.40754i −0.283951 0.117616i 0.236163 0.971714i \(-0.424110\pi\)
−0.520113 + 0.854097i \(0.674110\pi\)
\(420\) 0 0
\(421\) −7.88620 19.0390i −0.384350 0.927903i −0.991113 0.133020i \(-0.957532\pi\)
0.606763 0.794883i \(-0.292468\pi\)
\(422\) 0 0
\(423\) 15.2971 + 5.69428i 0.743770 + 0.276865i
\(424\) 0 0
\(425\) 3.55248 3.55248i 0.172321 0.172321i
\(426\) 0 0
\(427\) −21.0770 50.8843i −1.01999 2.46246i
\(428\) 0 0
\(429\) −0.172860 + 0.120102i −0.00834578 + 0.00579857i
\(430\) 0 0
\(431\) 33.6809i 1.62235i 0.584801 + 0.811177i \(0.301173\pi\)
−0.584801 + 0.811177i \(0.698827\pi\)
\(432\) 0 0
\(433\) 20.3471i 0.977819i −0.872335 0.488909i \(-0.837395\pi\)
0.872335 0.488909i \(-0.162605\pi\)
\(434\) 0 0
\(435\) −7.06982 + 4.91204i −0.338972 + 0.235514i
\(436\) 0 0
\(437\) 4.87135 + 11.7605i 0.233028 + 0.562580i
\(438\) 0 0
\(439\) 12.4753 12.4753i 0.595414 0.595414i −0.343675 0.939089i \(-0.611672\pi\)
0.939089 + 0.343675i \(0.111672\pi\)
\(440\) 0 0
\(441\) −40.8895 15.2209i −1.94712 0.724807i
\(442\) 0 0
\(443\) 10.7190 + 25.8778i 0.509273 + 1.22949i 0.944303 + 0.329077i \(0.106738\pi\)
−0.435030 + 0.900416i \(0.643262\pi\)
\(444\) 0 0
\(445\) −14.1286 5.85227i −0.669761 0.277424i
\(446\) 0 0
\(447\) 10.5644 16.4502i 0.499678 0.778066i
\(448\) 0 0
\(449\) 16.2439i 0.766596i 0.923625 + 0.383298i \(0.125212\pi\)
−0.923625 + 0.383298i \(0.874788\pi\)
\(450\) 0 0
\(451\) −0.619083 + 1.49460i −0.0291515 + 0.0703779i
\(452\) 0 0
\(453\) 33.1924 + 5.97751i 1.55952 + 0.280848i
\(454\) 0 0
\(455\) 3.89292 3.89292i 0.182503 0.182503i
\(456\) 0 0
\(457\) −2.84177 2.84177i −0.132932 0.132932i 0.637510 0.770442i \(-0.279965\pi\)
−0.770442 + 0.637510i \(0.779965\pi\)
\(458\) 0 0
\(459\) 7.13361 1.82810i 0.332968 0.0853284i
\(460\) 0 0
\(461\) −20.8642 8.64224i −0.971743 0.402509i −0.160382 0.987055i \(-0.551273\pi\)
−0.811361 + 0.584546i \(0.801273\pi\)
\(462\) 0 0
\(463\) −22.3599 −1.03915 −0.519576 0.854424i \(-0.673910\pi\)
−0.519576 + 0.854424i \(0.673910\pi\)
\(464\) 0 0
\(465\) −11.4007 + 17.7524i −0.528694 + 0.823248i
\(466\) 0 0
\(467\) 3.58346 8.65124i 0.165823 0.400332i −0.819024 0.573760i \(-0.805484\pi\)
0.984847 + 0.173428i \(0.0554844\pi\)
\(468\) 0 0
\(469\) 47.0508 19.4891i 2.17260 0.899922i
\(470\) 0 0
\(471\) 3.17148 + 14.5565i 0.146134 + 0.670726i
\(472\) 0 0
\(473\) −1.14628 1.14628i −0.0527060 0.0527060i
\(474\) 0 0
\(475\) 8.93220 3.69984i 0.409838 0.169760i
\(476\) 0 0
\(477\) 14.5057 0.527443i 0.664170 0.0241500i
\(478\) 0 0
\(479\) 1.51545 0.0692426 0.0346213 0.999401i \(-0.488977\pi\)
0.0346213 + 0.999401i \(0.488977\pi\)
\(480\) 0 0
\(481\) 2.99813 0.136703
\(482\) 0 0
\(483\) −30.8149 + 21.4099i −1.40213 + 0.974185i
\(484\) 0 0
\(485\) −29.6960 + 12.3005i −1.34843 + 0.558536i
\(486\) 0 0
\(487\) 10.7114 + 10.7114i 0.485378 + 0.485378i 0.906844 0.421466i \(-0.138484\pi\)
−0.421466 + 0.906844i \(0.638484\pi\)
\(488\) 0 0
\(489\) 21.1224 4.60203i 0.955188 0.208111i
\(490\) 0 0
\(491\) 20.2550 8.38989i 0.914095 0.378630i 0.124472 0.992223i \(-0.460276\pi\)
0.789623 + 0.613593i \(0.210276\pi\)
\(492\) 0 0
\(493\) −0.922155 + 2.22628i −0.0415318 + 0.100267i
\(494\) 0 0
\(495\) −1.09260 2.38837i −0.0491085 0.107349i
\(496\) 0 0
\(497\) 24.8028 1.11256
\(498\) 0 0
\(499\) −10.2527 4.24681i −0.458974 0.190113i 0.141203 0.989981i \(-0.454903\pi\)
−0.600177 + 0.799867i \(0.704903\pi\)
\(500\) 0 0
\(501\) −35.5784 6.40720i −1.58953 0.286253i
\(502\) 0 0
\(503\) −14.9291 14.9291i −0.665655 0.665655i 0.291052 0.956707i \(-0.405995\pi\)
−0.956707 + 0.291052i \(0.905995\pi\)
\(504\) 0 0
\(505\) 5.62678 5.62678i 0.250389 0.250389i
\(506\) 0 0
\(507\) 3.94021 21.8795i 0.174991 0.971704i
\(508\) 0 0
\(509\) 0.540947 1.30596i 0.0239770 0.0578857i −0.911438 0.411438i \(-0.865027\pi\)
0.935415 + 0.353553i \(0.115027\pi\)
\(510\) 0 0
\(511\) 25.5432i 1.12997i
\(512\) 0 0
\(513\) 14.0293 + 2.00325i 0.619407 + 0.0884456i
\(514\) 0 0
\(515\) 1.27139 + 0.526627i 0.0560241 + 0.0232059i
\(516\) 0 0
\(517\) −0.623584 1.50547i −0.0274252 0.0662103i
\(518\) 0 0
\(519\) −3.03645 13.9367i −0.133286 0.611754i
\(520\) 0 0
\(521\) 4.02013 4.02013i 0.176125 0.176125i −0.613539 0.789664i \(-0.710255\pi\)
0.789664 + 0.613539i \(0.210255\pi\)
\(522\) 0 0
\(523\) −2.35502 5.68552i −0.102978 0.248610i 0.863990 0.503509i \(-0.167958\pi\)
−0.966968 + 0.254899i \(0.917958\pi\)
\(524\) 0 0
\(525\) 16.2610 + 23.4042i 0.709690 + 1.02144i
\(526\) 0 0
\(527\) 5.90561i 0.257253i
\(528\) 0 0
\(529\) 1.21549i 0.0528475i
\(530\) 0 0
\(531\) 10.7876 0.392248i 0.468141 0.0170221i
\(532\) 0 0
\(533\) 0.838760 + 2.02495i 0.0363307 + 0.0877101i
\(534\) 0 0
\(535\) −0.882097 + 0.882097i −0.0381364 + 0.0381364i
\(536\) 0 0
\(537\) 6.13513 1.33669i 0.264750 0.0576823i
\(538\) 0 0
\(539\) 1.66686 + 4.02415i 0.0717966 + 0.173332i
\(540\) 0 0
\(541\) −27.0891 11.2207i −1.16465 0.482414i −0.285230 0.958459i \(-0.592070\pi\)
−0.879421 + 0.476045i \(0.842070\pi\)
\(542\) 0 0
\(543\) 10.2767 + 6.59973i 0.441014 + 0.283222i
\(544\) 0 0
\(545\) 13.8856i 0.594794i
\(546\) 0 0
\(547\) −2.18960 + 5.28616i −0.0936205 + 0.226020i −0.963752 0.266800i \(-0.914034\pi\)
0.870132 + 0.492820i \(0.164034\pi\)
\(548\) 0 0
\(549\) −24.2406 + 26.0700i −1.03456 + 1.11264i
\(550\) 0 0
\(551\) −3.27904 + 3.27904i −0.139692 + 0.139692i
\(552\) 0 0
\(553\) −15.8193 15.8193i −0.672703 0.672703i
\(554\) 0 0
\(555\) −6.63039 + 36.8178i −0.281445 + 1.56283i
\(556\) 0 0
\(557\) −33.6235 13.9273i −1.42467 0.590119i −0.468644 0.883387i \(-0.655257\pi\)
−0.956030 + 0.293268i \(0.905257\pi\)
\(558\) 0 0
\(559\) −2.19631 −0.0928941
\(560\) 0 0
\(561\) −0.618594 0.397264i −0.0261171 0.0167725i
\(562\) 0 0
\(563\) 10.2970 24.8591i 0.433965 1.04768i −0.544031 0.839065i \(-0.683103\pi\)
0.977997 0.208620i \(-0.0668972\pi\)
\(564\) 0 0
\(565\) −50.0494 + 20.7312i −2.10560 + 0.872166i
\(566\) 0 0
\(567\) 3.03385 + 41.6632i 0.127410 + 1.74969i
\(568\) 0 0
\(569\) −5.01618 5.01618i −0.210289 0.210289i 0.594101 0.804390i \(-0.297508\pi\)
−0.804390 + 0.594101i \(0.797508\pi\)
\(570\) 0 0
\(571\) 8.20928 3.40040i 0.343548 0.142302i −0.204237 0.978921i \(-0.565471\pi\)
0.547785 + 0.836619i \(0.315471\pi\)
\(572\) 0 0
\(573\) 18.5894 + 26.7554i 0.776583 + 1.11772i
\(574\) 0 0
\(575\) 16.5455 0.689997
\(576\) 0 0
\(577\) 36.7704 1.53077 0.765386 0.643571i \(-0.222548\pi\)
0.765386 + 0.643571i \(0.222548\pi\)
\(578\) 0 0
\(579\) 11.0192 + 15.8598i 0.457943 + 0.659109i
\(580\) 0 0
\(581\) 40.3848 16.7279i 1.67544 0.693992i
\(582\) 0 0
\(583\) −1.02466 1.02466i −0.0424369 0.0424369i
\(584\) 0 0
\(585\) −3.33483 1.24138i −0.137878 0.0513246i
\(586\) 0 0
\(587\) 22.3129 9.24233i 0.920954 0.381472i 0.128714 0.991682i \(-0.458915\pi\)
0.792240 + 0.610210i \(0.208915\pi\)
\(588\) 0 0
\(589\) −4.34912 + 10.4997i −0.179202 + 0.432633i
\(590\) 0 0
\(591\) −23.2903 14.9572i −0.958036 0.615256i
\(592\) 0 0
\(593\) 2.15691 0.0885737 0.0442868 0.999019i \(-0.485898\pi\)
0.0442868 + 0.999019i \(0.485898\pi\)
\(594\) 0 0
\(595\) 17.7651 + 7.35854i 0.728297 + 0.301671i
\(596\) 0 0
\(597\) 0.297902 1.65421i 0.0121923 0.0677025i
\(598\) 0 0
\(599\) −4.80949 4.80949i −0.196511 0.196511i 0.601992 0.798502i \(-0.294374\pi\)
−0.798502 + 0.601992i \(0.794374\pi\)
\(600\) 0 0
\(601\) 5.18282 5.18282i 0.211411 0.211411i −0.593455 0.804867i \(-0.702237\pi\)
0.804867 + 0.593455i \(0.202237\pi\)
\(602\) 0 0
\(603\) −24.1059 22.4144i −0.981669 0.912785i
\(604\) 0 0
\(605\) 12.2048 29.4650i 0.496196 1.19792i
\(606\) 0 0
\(607\) 5.19779i 0.210972i −0.994421 0.105486i \(-0.966360\pi\)
0.994421 0.105486i \(-0.0336398\pi\)
\(608\) 0 0
\(609\) −11.5017 7.38643i −0.466071 0.299313i
\(610\) 0 0
\(611\) −2.03967 0.844859i −0.0825162 0.0341793i
\(612\) 0 0
\(613\) −12.1586 29.3536i −0.491083 1.18558i −0.954170 0.299266i \(-0.903258\pi\)
0.463087 0.886313i \(-0.346742\pi\)
\(614\) 0 0
\(615\) −26.7217 + 5.82198i −1.07752 + 0.234765i
\(616\) 0 0
\(617\) 10.7968 10.7968i 0.434663 0.434663i −0.455548 0.890211i \(-0.650557\pi\)
0.890211 + 0.455548i \(0.150557\pi\)
\(618\) 0 0
\(619\) 11.7667 + 28.4074i 0.472944 + 1.14179i 0.962856 + 0.270016i \(0.0870290\pi\)
−0.489912 + 0.871772i \(0.662971\pi\)
\(620\) 0 0
\(621\) 20.8694 + 12.3551i 0.837461 + 0.495794i
\(622\) 0 0
\(623\) 24.2822i 0.972848i
\(624\) 0 0
\(625\) 30.1581i 1.20633i
\(626\) 0 0
\(627\) −0.807250 1.16186i −0.0322384 0.0464002i
\(628\) 0 0
\(629\) 4.00730 + 9.67449i 0.159782 + 0.385747i
\(630\) 0 0
\(631\) −5.17311 + 5.17311i −0.205938 + 0.205938i −0.802539 0.596600i \(-0.796518\pi\)
0.596600 + 0.802539i \(0.296518\pi\)
\(632\) 0 0
\(633\) 0.901437 + 4.13741i 0.0358289 + 0.164447i
\(634\) 0 0
\(635\) −5.36966 12.9635i −0.213088 0.514441i
\(636\) 0 0
\(637\) 5.45209 + 2.25833i 0.216020 + 0.0894782i
\(638\) 0 0
\(639\) −6.66897 14.5781i −0.263820 0.576701i
\(640\) 0 0
\(641\) 35.5298i 1.40334i −0.712500 0.701672i \(-0.752437\pi\)
0.712500 0.701672i \(-0.247563\pi\)
\(642\) 0 0
\(643\) −3.04889 + 7.36067i −0.120237 + 0.290277i −0.972526 0.232793i \(-0.925213\pi\)
0.852290 + 0.523070i \(0.175213\pi\)
\(644\) 0 0
\(645\) 4.85716 26.9712i 0.191251 1.06199i
\(646\) 0 0
\(647\) −9.34579 + 9.34579i −0.367421 + 0.367421i −0.866536 0.499115i \(-0.833659\pi\)
0.499115 + 0.866536i \(0.333659\pi\)
\(648\) 0 0
\(649\) −0.762015 0.762015i −0.0299117 0.0299117i
\(650\) 0 0
\(651\) −32.9696 5.93739i −1.29218 0.232705i
\(652\) 0 0
\(653\) −3.13779 1.29972i −0.122791 0.0508618i 0.320442 0.947268i \(-0.396169\pi\)
−0.443233 + 0.896406i \(0.646169\pi\)
\(654\) 0 0
\(655\) 63.9506 2.49876
\(656\) 0 0
\(657\) 15.0133 6.86805i 0.585725 0.267948i
\(658\) 0 0
\(659\) −12.0747 + 29.1508i −0.470362 + 1.13555i 0.493642 + 0.869665i \(0.335665\pi\)
−0.964004 + 0.265889i \(0.914335\pi\)
\(660\) 0 0
\(661\) −21.5134 + 8.91114i −0.836774 + 0.346603i −0.759581 0.650413i \(-0.774596\pi\)
−0.0771932 + 0.997016i \(0.524596\pi\)
\(662\) 0 0
\(663\) −0.973211 + 0.212038i −0.0377964 + 0.00823487i
\(664\) 0 0
\(665\) 26.1658 + 26.1658i 1.01467 + 1.01467i
\(666\) 0 0
\(667\) −7.33186 + 3.03696i −0.283891 + 0.117591i
\(668\) 0 0
\(669\) −14.7181 + 10.2260i −0.569035 + 0.395360i
\(670\) 0 0
\(671\) 3.55385 0.137195
\(672\) 0 0
\(673\) −27.9251 −1.07643 −0.538216 0.842807i \(-0.680902\pi\)
−0.538216 + 0.842807i \(0.680902\pi\)
\(674\) 0 0
\(675\) 9.38383 15.8505i 0.361184 0.610087i
\(676\) 0 0
\(677\) 6.25960 2.59281i 0.240576 0.0996498i −0.259138 0.965840i \(-0.583438\pi\)
0.499714 + 0.866191i \(0.333438\pi\)
\(678\) 0 0
\(679\) −36.0887 36.0887i −1.38496 1.38496i
\(680\) 0 0
\(681\) −4.18273 19.1979i −0.160283 0.735665i
\(682\) 0 0
\(683\) −26.2767 + 10.8842i −1.00545 + 0.416471i −0.823793 0.566891i \(-0.808146\pi\)
−0.181657 + 0.983362i \(0.558146\pi\)
\(684\) 0 0
\(685\) 20.1393 48.6207i 0.769484 1.85770i
\(686\) 0 0
\(687\) 18.0856 28.1617i 0.690009 1.07444i
\(688\) 0 0
\(689\) −1.96328 −0.0747950
\(690\) 0 0
\(691\) 26.2910 + 10.8901i 1.00016 + 0.414279i 0.821855 0.569697i \(-0.192939\pi\)
0.178303 + 0.983976i \(0.442939\pi\)
\(692\) 0 0
\(693\) 2.83975 3.05406i 0.107873 0.116014i
\(694\) 0 0
\(695\) 1.04478 + 1.04478i 0.0396309 + 0.0396309i
\(696\) 0 0
\(697\) −5.41308 + 5.41308i −0.205035 + 0.205035i
\(698\) 0 0
\(699\) −38.4998 6.93330i −1.45619 0.262241i
\(700\) 0 0
\(701\) 15.7331 37.9830i 0.594230 1.43460i −0.285153 0.958482i \(-0.592044\pi\)
0.879383 0.476116i \(-0.157956\pi\)
\(702\) 0 0
\(703\) 20.1516i 0.760032i
\(704\) 0 0
\(705\) 14.8858 23.1792i 0.560632 0.872979i
\(706\) 0 0
\(707\) 11.6733 + 4.83525i 0.439021 + 0.181848i
\(708\) 0 0
\(709\) −3.26185 7.87481i −0.122501 0.295745i 0.850718 0.525622i \(-0.176167\pi\)
−0.973220 + 0.229877i \(0.926167\pi\)
\(710\) 0 0
\(711\) −5.04446 + 13.5514i −0.189182 + 0.508218i
\(712\) 0 0
\(713\) −13.7526 + 13.7526i −0.515039 + 0.515039i
\(714\) 0 0
\(715\) 0.135944 + 0.328198i 0.00508402 + 0.0122739i
\(716\) 0 0
\(717\) 32.0266 22.2518i 1.19606 0.831008i
\(718\) 0 0
\(719\) 6.72495i 0.250798i −0.992106 0.125399i \(-0.959979\pi\)
0.992106 0.125399i \(-0.0400211\pi\)
\(720\) 0 0
\(721\) 2.18508i 0.0813766i
\(722\) 0 0
\(723\) −30.9927 + 21.5334i −1.15263 + 0.800836i
\(724\) 0 0
\(725\) 2.30660 + 5.56862i 0.0856649 + 0.206813i
\(726\) 0 0
\(727\) −11.8994 + 11.8994i −0.441326 + 0.441326i −0.892457 0.451132i \(-0.851021\pi\)
0.451132 + 0.892457i \(0.351021\pi\)
\(728\) 0 0
\(729\) 23.6722 12.9856i 0.876750 0.480947i
\(730\) 0 0
\(731\) −2.93559 7.08715i −0.108577 0.262128i
\(732\) 0 0
\(733\) 27.8224 + 11.5244i 1.02764 + 0.425664i 0.831861 0.554984i \(-0.187276\pi\)
0.195782 + 0.980647i \(0.437276\pi\)
\(734\) 0 0
\(735\) −39.7901 + 61.9586i −1.46768 + 2.28538i
\(736\) 0 0
\(737\) 3.28611i 0.121045i
\(738\) 0 0
\(739\) 9.46555 22.8519i 0.348196 0.840619i −0.648637 0.761098i \(-0.724661\pi\)
0.996833 0.0795214i \(-0.0253392\pi\)
\(740\) 0 0
\(741\) −1.88644 0.339724i −0.0693002 0.0124801i
\(742\) 0 0
\(743\) −34.0574 + 34.0574i −1.24944 + 1.24944i −0.293479 + 0.955966i \(0.594813\pi\)
−0.955966 + 0.293479i \(0.905187\pi\)
\(744\) 0 0
\(745\) −23.3309 23.3309i −0.854778 0.854778i
\(746\) 0 0
\(747\) −20.6907 19.2388i −0.757033 0.703911i
\(748\) 0 0
\(749\) −1.83000 0.758011i −0.0668667 0.0276971i
\(750\) 0 0
\(751\) −28.4849 −1.03943 −0.519714 0.854341i \(-0.673961\pi\)
−0.519714 + 0.854341i \(0.673961\pi\)
\(752\) 0 0
\(753\) −14.5967 + 22.7291i −0.531935 + 0.828294i
\(754\) 0 0
\(755\) 21.7822 52.5870i 0.792737 1.91384i
\(756\) 0 0
\(757\) −25.6728 + 10.6340i −0.933093 + 0.386500i −0.796851 0.604176i \(-0.793502\pi\)
−0.136242 + 0.990676i \(0.543502\pi\)
\(758\) 0 0
\(759\) −0.515417 2.36566i −0.0187085 0.0858681i
\(760\) 0 0
\(761\) −29.3477 29.3477i −1.06385 1.06385i −0.997817 0.0660371i \(-0.978964\pi\)
−0.0660371 0.997817i \(1.47896\pi\)
\(762\) 0 0
\(763\) 20.3697 8.43740i 0.737432 0.305454i
\(764\) 0 0
\(765\) −0.451611 12.4202i −0.0163280 0.449053i
\(766\) 0 0
\(767\) −1.46005 −0.0527193
\(768\) 0 0
\(769\) −32.2426 −1.16270 −0.581349 0.813654i \(-0.697475\pi\)
−0.581349 + 0.813654i \(0.697475\pi\)
\(770\) 0 0
\(771\) −16.8957 + 11.7389i −0.608482 + 0.422768i
\(772\) 0 0
\(773\) −12.3588 + 5.11920i −0.444517 + 0.184125i −0.593703 0.804684i \(-0.702335\pi\)
0.149186 + 0.988809i \(0.452335\pi\)
\(774\) 0 0
\(775\) 10.4452 + 10.4452i 0.375203 + 0.375203i
\(776\) 0 0
\(777\) −58.0392 + 12.6453i −2.08215 + 0.453647i
\(778\) 0 0
\(779\) −13.6104 + 5.63762i −0.487644 + 0.201989i
\(780\) 0 0
\(781\) −0.612450 + 1.47859i −0.0219152 + 0.0529079i
\(782\) 0 0
\(783\) −1.24889 +