Properties

Label 784.2.bp.c.495.10
Level $784$
Weight $2$
Character 784.495
Analytic conductor $6.260$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.bp (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(10\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 495.10
Character \(\chi\) \(=\) 784.495
Dual form 784.2.bp.c.255.10

$q$-expansion

\(f(q)\) \(=\) \(q+(2.52689 + 1.72281i) q^{3} +(-0.607633 - 0.0455358i) q^{5} +(-2.56115 + 0.663712i) q^{7} +(2.32110 + 5.91407i) q^{9} +O(q^{10})\) \(q+(2.52689 + 1.72281i) q^{3} +(-0.607633 - 0.0455358i) q^{5} +(-2.56115 + 0.663712i) q^{7} +(2.32110 + 5.91407i) q^{9} +(5.84067 + 2.29229i) q^{11} +(-1.03918 + 0.828717i) q^{13} +(-1.45698 - 1.16190i) q^{15} +(-1.89256 - 2.03969i) q^{17} +(-2.73256 + 4.73293i) q^{19} +(-7.61520 - 2.73524i) q^{21} +(4.76777 - 5.13843i) q^{23} +(-4.57701 - 0.689873i) q^{25} +(-2.28201 + 9.99815i) q^{27} +(1.81141 + 7.93629i) q^{29} +(-2.65442 - 4.59759i) q^{31} +(10.8096 + 15.8547i) q^{33} +(1.58646 - 0.286669i) q^{35} +(6.69524 + 2.06521i) q^{37} +(-4.05361 + 0.303776i) q^{39} +(1.41792 + 2.94434i) q^{41} +(1.22494 - 2.54362i) q^{43} +(-1.14108 - 3.69928i) q^{45} +(0.120128 - 0.0181063i) q^{47} +(6.11897 - 3.39973i) q^{49} +(-1.26829 - 8.41459i) q^{51} +(-5.13106 + 1.58272i) q^{53} +(-3.44460 - 1.65883i) q^{55} +(-15.0588 + 7.25194i) q^{57} +(-0.675569 - 9.01484i) q^{59} +(-0.474172 + 1.53723i) q^{61} +(-9.86993 - 13.6063i) q^{63} +(0.669176 - 0.456236i) q^{65} +(8.76814 - 5.06229i) q^{67} +(20.9002 - 4.77032i) q^{69} +(-5.66850 - 1.29380i) q^{71} +(0.427054 - 2.83332i) q^{73} +(-10.3771 - 9.62854i) q^{75} +(-16.4802 - 1.99439i) q^{77} +(8.97875 + 5.18389i) q^{79} +(-9.01949 + 8.36887i) q^{81} +(8.22316 - 10.3115i) q^{83} +(1.05710 + 1.32556i) q^{85} +(-9.09546 + 23.1749i) q^{87} +(-8.82948 + 3.46532i) q^{89} +(2.11146 - 2.81218i) q^{91} +(1.21332 - 16.1907i) q^{93} +(1.87591 - 2.75146i) q^{95} -15.8417i q^{97} +39.8628i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 6 q^{5} + 12 q^{9} + O(q^{10}) \) \( 120 q + 6 q^{5} + 12 q^{9} - 32 q^{17} - 14 q^{21} - 8 q^{25} - 28 q^{29} + 42 q^{33} + 28 q^{37} + 56 q^{41} + 186 q^{45} + 84 q^{49} + 128 q^{53} - 70 q^{57} + 8 q^{61} + 4 q^{65} - 56 q^{69} + 60 q^{73} + 84 q^{77} + 34 q^{81} + 12 q^{85} + 22 q^{89} - 112 q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{29}{42}\right)\)

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
\(3\) 2.52689 + 1.72281i 1.45890 + 0.994663i 0.994009 + 0.109296i \(0.0348596\pi\)
0.464893 + 0.885367i \(0.346093\pi\)
\(4\) 0 0
\(5\) −0.607633 0.0455358i −0.271742 0.0203642i −0.0618378 0.998086i \(-0.519696\pi\)
−0.209904 + 0.977722i \(0.567315\pi\)
\(6\) 0 0
\(7\) −2.56115 + 0.663712i −0.968024 + 0.250859i
\(8\) 0 0
\(9\) 2.32110 + 5.91407i 0.773701 + 1.97136i
\(10\) 0 0
\(11\) 5.84067 + 2.29229i 1.76103 + 0.691152i 0.999051 + 0.0435474i \(0.0138659\pi\)
0.761976 + 0.647605i \(0.224229\pi\)
\(12\) 0 0
\(13\) −1.03918 + 0.828717i −0.288216 + 0.229845i −0.756915 0.653513i \(-0.773294\pi\)
0.468699 + 0.883358i \(0.344723\pi\)
\(14\) 0 0
\(15\) −1.45698 1.16190i −0.376189 0.300001i
\(16\) 0 0
\(17\) −1.89256 2.03969i −0.459012 0.494698i 0.460554 0.887631i \(-0.347651\pi\)
−0.919567 + 0.392934i \(0.871460\pi\)
\(18\) 0 0
\(19\) −2.73256 + 4.73293i −0.626892 + 1.08581i 0.361279 + 0.932458i \(0.382340\pi\)
−0.988172 + 0.153352i \(0.950993\pi\)
\(20\) 0 0
\(21\) −7.61520 2.73524i −1.66177 0.596878i
\(22\) 0 0
\(23\) 4.76777 5.13843i 0.994148 1.07144i −0.00329681 0.999995i \(-0.501049\pi\)
0.997445 0.0714421i \(-0.0227601\pi\)
\(24\) 0 0
\(25\) −4.57701 0.689873i −0.915402 0.137975i
\(26\) 0 0
\(27\) −2.28201 + 9.99815i −0.439173 + 1.92414i
\(28\) 0 0
\(29\) 1.81141 + 7.93629i 0.336370 + 1.47373i 0.806552 + 0.591163i \(0.201331\pi\)
−0.470182 + 0.882569i \(0.655812\pi\)
\(30\) 0 0
\(31\) −2.65442 4.59759i −0.476748 0.825751i 0.522897 0.852396i \(-0.324851\pi\)
−0.999645 + 0.0266446i \(0.991518\pi\)
\(32\) 0 0
\(33\) 10.8096 + 15.8547i 1.88170 + 2.75995i
\(34\) 0 0
\(35\) 1.58646 0.286669i 0.268161 0.0484560i
\(36\) 0 0
\(37\) 6.69524 + 2.06521i 1.10069 + 0.339518i 0.791307 0.611419i \(-0.209401\pi\)
0.309384 + 0.950937i \(0.399877\pi\)
\(38\) 0 0
\(39\) −4.05361 + 0.303776i −0.649097 + 0.0486431i
\(40\) 0 0
\(41\) 1.41792 + 2.94434i 0.221442 + 0.459828i 0.981861 0.189605i \(-0.0607206\pi\)
−0.760419 + 0.649433i \(0.775006\pi\)
\(42\) 0 0
\(43\) 1.22494 2.54362i 0.186802 0.387898i −0.786445 0.617660i \(-0.788081\pi\)
0.973247 + 0.229762i \(0.0737949\pi\)
\(44\) 0 0
\(45\) −1.14108 3.69928i −0.170102 0.551456i
\(46\) 0 0
\(47\) 0.120128 0.0181063i 0.0175224 0.00264108i −0.140275 0.990113i \(-0.544799\pi\)
0.157798 + 0.987471i \(0.449561\pi\)
\(48\) 0 0
\(49\) 6.11897 3.39973i 0.874139 0.485676i
\(50\) 0 0
\(51\) −1.26829 8.41459i −0.177597 1.17828i
\(52\) 0 0
\(53\) −5.13106 + 1.58272i −0.704806 + 0.217404i −0.626382 0.779516i \(-0.715465\pi\)
−0.0784237 + 0.996920i \(0.524989\pi\)
\(54\) 0 0
\(55\) −3.44460 1.65883i −0.464470 0.223677i
\(56\) 0 0
\(57\) −15.0588 + 7.25194i −1.99459 + 0.960543i
\(58\) 0 0
\(59\) −0.675569 9.01484i −0.0879515 1.17363i −0.850240 0.526395i \(-0.823543\pi\)
0.762289 0.647237i \(-0.224076\pi\)
\(60\) 0 0
\(61\) −0.474172 + 1.53723i −0.0607115 + 0.196822i −0.980848 0.194777i \(-0.937602\pi\)
0.920136 + 0.391599i \(0.128078\pi\)
\(62\) 0 0
\(63\) −9.86993 13.6063i −1.24349 1.71423i
\(64\) 0 0
\(65\) 0.669176 0.456236i 0.0830010 0.0565891i
\(66\) 0 0
\(67\) 8.76814 5.06229i 1.07120 0.618457i 0.142690 0.989767i \(-0.454425\pi\)
0.928509 + 0.371311i \(0.121092\pi\)
\(68\) 0 0
\(69\) 20.9002 4.77032i 2.51608 0.574279i
\(70\) 0 0
\(71\) −5.66850 1.29380i −0.672727 0.153546i −0.127506 0.991838i \(-0.540697\pi\)
−0.545221 + 0.838292i \(0.683554\pi\)
\(72\) 0 0
\(73\) 0.427054 2.83332i 0.0499829 0.331615i −0.949839 0.312739i \(-0.898753\pi\)
0.999822 0.0188753i \(-0.00600854\pi\)
\(74\) 0 0
\(75\) −10.3771 9.62854i −1.19824 1.11181i
\(76\) 0 0
\(77\) −16.4802 1.99439i −1.87810 0.227281i
\(78\) 0 0
\(79\) 8.97875 + 5.18389i 1.01019 + 0.583233i 0.911247 0.411860i \(-0.135121\pi\)
0.0989419 + 0.995093i \(0.468454\pi\)
\(80\) 0 0
\(81\) −9.01949 + 8.36887i −1.00217 + 0.929874i
\(82\) 0 0
\(83\) 8.22316 10.3115i 0.902609 1.13184i −0.0881376 0.996108i \(-0.528092\pi\)
0.990746 0.135727i \(-0.0433370\pi\)
\(84\) 0 0
\(85\) 1.05710 + 1.32556i 0.114659 + 0.143778i
\(86\) 0 0
\(87\) −9.09546 + 23.1749i −0.975136 + 2.48461i
\(88\) 0 0
\(89\) −8.82948 + 3.46532i −0.935923 + 0.367323i −0.783782 0.621036i \(-0.786712\pi\)
−0.152141 + 0.988359i \(0.548617\pi\)
\(90\) 0 0
\(91\) 2.11146 2.81218i 0.221341 0.294797i
\(92\) 0 0
\(93\) 1.21332 16.1907i 0.125816 1.67889i
\(94\) 0 0
\(95\) 1.87591 2.75146i 0.192465 0.282294i
\(96\) 0 0
\(97\) 15.8417i 1.60848i −0.594307 0.804239i \(-0.702573\pi\)
0.594307 0.804239i \(-0.297427\pi\)
\(98\) 0 0
\(99\) 39.8628i 4.00636i
\(100\) 0 0
\(101\) 9.06548 13.2966i 0.902049 1.32306i −0.0439975 0.999032i \(-0.514009\pi\)
0.946046 0.324031i \(-0.105038\pi\)
\(102\) 0 0
\(103\) 0.527915 7.04454i 0.0520171 0.694119i −0.908852 0.417118i \(-0.863040\pi\)
0.960869 0.277002i \(-0.0893407\pi\)
\(104\) 0 0
\(105\) 4.50270 + 2.00879i 0.439418 + 0.196037i
\(106\) 0 0
\(107\) −5.67577 + 2.22758i −0.548698 + 0.215348i −0.623463 0.781853i \(-0.714275\pi\)
0.0747648 + 0.997201i \(0.476179\pi\)
\(108\) 0 0
\(109\) −3.74772 + 9.54904i −0.358967 + 0.914633i 0.631311 + 0.775530i \(0.282517\pi\)
−0.990278 + 0.139103i \(0.955578\pi\)
\(110\) 0 0
\(111\) 13.3602 + 16.7532i 1.26809 + 1.59014i
\(112\) 0 0
\(113\) −2.32036 + 2.90965i −0.218282 + 0.273716i −0.878901 0.477005i \(-0.841722\pi\)
0.660619 + 0.750721i \(0.270294\pi\)
\(114\) 0 0
\(115\) −3.13104 + 2.90518i −0.291971 + 0.270909i
\(116\) 0 0
\(117\) −7.31313 4.22224i −0.676099 0.390346i
\(118\) 0 0
\(119\) 6.20089 + 3.96784i 0.568434 + 0.363731i
\(120\) 0 0
\(121\) 20.7952 + 19.2951i 1.89047 + 1.75410i
\(122\) 0 0
\(123\) −1.48960 + 9.88283i −0.134312 + 0.891105i
\(124\) 0 0
\(125\) 5.72003 + 1.30556i 0.511615 + 0.116773i
\(126\) 0 0
\(127\) 11.8208 2.69803i 1.04893 0.239411i 0.336885 0.941546i \(-0.390627\pi\)
0.712045 + 0.702134i \(0.247769\pi\)
\(128\) 0 0
\(129\) 7.47745 4.31711i 0.658353 0.380100i
\(130\) 0 0
\(131\) 0.568703 0.387735i 0.0496878 0.0338765i −0.538221 0.842803i \(-0.680904\pi\)
0.587909 + 0.808927i \(0.299951\pi\)
\(132\) 0 0
\(133\) 3.85719 13.9354i 0.334461 1.20835i
\(134\) 0 0
\(135\) 1.84190 5.97130i 0.158526 0.513927i
\(136\) 0 0
\(137\) −0.714708 9.53712i −0.0610616 0.814811i −0.940716 0.339197i \(-0.889845\pi\)
0.879654 0.475614i \(-0.157774\pi\)
\(138\) 0 0
\(139\) 11.6115 5.59179i 0.984872 0.474289i 0.129094 0.991632i \(-0.458793\pi\)
0.855778 + 0.517343i \(0.173079\pi\)
\(140\) 0 0
\(141\) 0.334744 + 0.161204i 0.0281905 + 0.0135758i
\(142\) 0 0
\(143\) −7.96916 + 2.45816i −0.666414 + 0.205562i
\(144\) 0 0
\(145\) −0.739286 4.90484i −0.0613943 0.407325i
\(146\) 0 0
\(147\) 21.3191 + 1.95106i 1.75837 + 0.160920i
\(148\) 0 0
\(149\) −12.1030 + 1.82424i −0.991517 + 0.149447i −0.624716 0.780852i \(-0.714785\pi\)
−0.366801 + 0.930299i \(0.619547\pi\)
\(150\) 0 0
\(151\) −5.19312 16.8357i −0.422610 1.37007i −0.877524 0.479533i \(-0.840806\pi\)
0.454913 0.890536i \(-0.349670\pi\)
\(152\) 0 0
\(153\) 7.67006 15.9270i 0.620088 1.28763i
\(154\) 0 0
\(155\) 1.40356 + 2.91452i 0.112737 + 0.234100i
\(156\) 0 0
\(157\) 0.802185 0.0601155i 0.0640214 0.00479774i −0.0426809 0.999089i \(-0.513590\pi\)
0.106702 + 0.994291i \(0.465971\pi\)
\(158\) 0 0
\(159\) −15.6924 4.84045i −1.24449 0.383873i
\(160\) 0 0
\(161\) −8.80053 + 16.3247i −0.693579 + 1.28657i
\(162\) 0 0
\(163\) 1.74712 + 2.56256i 0.136845 + 0.200715i 0.888544 0.458792i \(-0.151718\pi\)
−0.751699 + 0.659507i \(0.770765\pi\)
\(164\) 0 0
\(165\) −5.84629 10.1261i −0.455133 0.788314i
\(166\) 0 0
\(167\) 3.44560 + 15.0961i 0.266628 + 1.16818i 0.913908 + 0.405922i \(0.133050\pi\)
−0.647279 + 0.762253i \(0.724093\pi\)
\(168\) 0 0
\(169\) −2.49965 + 10.9517i −0.192281 + 0.842438i
\(170\) 0 0
\(171\) −34.3335 5.17494i −2.62555 0.395737i
\(172\) 0 0
\(173\) 2.90407 3.12985i 0.220793 0.237958i −0.612936 0.790133i \(-0.710011\pi\)
0.833728 + 0.552175i \(0.186202\pi\)
\(174\) 0 0
\(175\) 12.1803 1.27095i 0.920743 0.0960745i
\(176\) 0 0
\(177\) 13.8237 23.9434i 1.03906 1.79970i
\(178\) 0 0
\(179\) 1.21331 + 1.30763i 0.0906868 + 0.0977372i 0.776765 0.629791i \(-0.216859\pi\)
−0.686078 + 0.727528i \(0.740669\pi\)
\(180\) 0 0
\(181\) −15.9292 12.7031i −1.18401 0.944215i −0.184752 0.982785i \(-0.559148\pi\)
−0.999256 + 0.0385704i \(0.987720\pi\)
\(182\) 0 0
\(183\) −3.84653 + 3.06751i −0.284344 + 0.226757i
\(184\) 0 0
\(185\) −3.97421 1.55976i −0.292190 0.114676i
\(186\) 0 0
\(187\) −6.37822 16.2514i −0.466422 1.18842i
\(188\) 0 0
\(189\) −0.791313 27.1214i −0.0575595 1.97279i
\(190\) 0 0
\(191\) 9.94239 + 0.745079i 0.719406 + 0.0539121i 0.429402 0.903113i \(-0.358724\pi\)
0.290004 + 0.957025i \(0.406343\pi\)
\(192\) 0 0
\(193\) −8.73424 5.95491i −0.628705 0.428644i 0.206604 0.978425i \(-0.433759\pi\)
−0.835309 + 0.549781i \(0.814711\pi\)
\(194\) 0 0
\(195\) 2.47694 0.177377
\(196\) 0 0
\(197\) −8.34180 −0.594328 −0.297164 0.954826i \(-0.596041\pi\)
−0.297164 + 0.954826i \(0.596041\pi\)
\(198\) 0 0
\(199\) 4.25104 + 2.89831i 0.301348 + 0.205456i 0.704548 0.709656i \(-0.251150\pi\)
−0.403200 + 0.915112i \(0.632102\pi\)
\(200\) 0 0
\(201\) 30.8775 + 2.31395i 2.17793 + 0.163213i
\(202\) 0 0
\(203\) −9.90669 19.1238i −0.695314 1.34223i
\(204\) 0 0
\(205\) −0.727502 1.85364i −0.0508109 0.129464i
\(206\) 0 0
\(207\) 41.4555 + 16.2701i 2.88136 + 1.13085i
\(208\) 0 0
\(209\) −26.8092 + 21.3797i −1.85443 + 1.47886i
\(210\) 0 0
\(211\) −4.01958 3.20551i −0.276719 0.220676i 0.475289 0.879830i \(-0.342343\pi\)
−0.752008 + 0.659153i \(0.770915\pi\)
\(212\) 0 0
\(213\) −12.0947 13.0350i −0.828717 0.893144i
\(214\) 0 0
\(215\) −0.860141 + 1.48981i −0.0586611 + 0.101604i
\(216\) 0 0
\(217\) 9.84983 + 10.0133i 0.668650 + 0.679750i
\(218\) 0 0
\(219\) 5.96037 6.42376i 0.402765 0.434077i
\(220\) 0 0
\(221\) 3.65703 + 0.551208i 0.245998 + 0.0370783i
\(222\) 0 0
\(223\) −3.82015 + 16.7372i −0.255816 + 1.12080i 0.669860 + 0.742487i \(0.266354\pi\)
−0.925676 + 0.378317i \(0.876503\pi\)
\(224\) 0 0
\(225\) −6.54375 28.6700i −0.436250 1.91134i
\(226\) 0 0
\(227\) 5.23237 + 9.06272i 0.347284 + 0.601514i 0.985766 0.168123i \(-0.0537705\pi\)
−0.638482 + 0.769637i \(0.720437\pi\)
\(228\) 0 0
\(229\) −4.80204 7.04330i −0.317328 0.465435i 0.634124 0.773231i \(-0.281361\pi\)
−0.951452 + 0.307797i \(0.900408\pi\)
\(230\) 0 0
\(231\) −38.2079 33.4319i −2.51389 2.19966i
\(232\) 0 0
\(233\) −6.46866 1.99532i −0.423776 0.130718i 0.0755296 0.997144i \(-0.475935\pi\)
−0.499305 + 0.866426i \(0.666411\pi\)
\(234\) 0 0
\(235\) −0.0738181 + 0.00553190i −0.00481536 + 0.000360862i
\(236\) 0 0
\(237\) 13.7575 + 28.5678i 0.893647 + 1.85568i
\(238\) 0 0
\(239\) −6.36736 + 13.2219i −0.411870 + 0.855257i 0.587084 + 0.809526i \(0.300276\pi\)
−0.998954 + 0.0457307i \(0.985438\pi\)
\(240\) 0 0
\(241\) 3.71383 + 12.0399i 0.239229 + 0.775561i 0.992968 + 0.118387i \(0.0377723\pi\)
−0.753739 + 0.657174i \(0.771751\pi\)
\(242\) 0 0
\(243\) −6.78704 + 1.02298i −0.435389 + 0.0656243i
\(244\) 0 0
\(245\) −3.87290 + 1.78716i −0.247431 + 0.114177i
\(246\) 0 0
\(247\) −1.08264 7.18288i −0.0688870 0.457036i
\(248\) 0 0
\(249\) 38.5438 11.8892i 2.44261 0.753446i
\(250\) 0 0
\(251\) −22.8830 11.0199i −1.44437 0.695570i −0.462758 0.886484i \(-0.653140\pi\)
−0.981607 + 0.190915i \(0.938855\pi\)
\(252\) 0 0
\(253\) 39.6257 19.0827i 2.49125 1.19972i
\(254\) 0 0
\(255\) 0.387493 + 5.17074i 0.0242658 + 0.323804i
\(256\) 0 0
\(257\) −4.69048 + 15.2062i −0.292584 + 0.948535i 0.683280 + 0.730156i \(0.260553\pi\)
−0.975864 + 0.218378i \(0.929923\pi\)
\(258\) 0 0
\(259\) −18.5182 0.845598i −1.15067 0.0525429i
\(260\) 0 0
\(261\) −42.7314 + 29.1337i −2.64500 + 1.80333i
\(262\) 0 0
\(263\) 3.06421 1.76912i 0.188947 0.109089i −0.402543 0.915401i \(-0.631873\pi\)
0.591490 + 0.806313i \(0.298540\pi\)
\(264\) 0 0
\(265\) 3.18988 0.728068i 0.195952 0.0447249i
\(266\) 0 0
\(267\) −28.2812 6.45501i −1.73078 0.395040i
\(268\) 0 0
\(269\) 1.24235 8.24243i 0.0757472 0.502550i −0.918498 0.395425i \(-0.870597\pi\)
0.994246 0.107125i \(-0.0341645\pi\)
\(270\) 0 0
\(271\) 1.72109 + 1.59694i 0.104549 + 0.0970072i 0.730716 0.682682i \(-0.239187\pi\)
−0.626167 + 0.779689i \(0.715377\pi\)
\(272\) 0 0
\(273\) 10.1803 3.46844i 0.616139 0.209920i
\(274\) 0 0
\(275\) −25.1514 14.5212i −1.51669 0.875659i
\(276\) 0 0
\(277\) 12.6463 11.7341i 0.759845 0.705033i −0.201771 0.979433i \(-0.564670\pi\)
0.961616 + 0.274400i \(0.0884792\pi\)
\(278\) 0 0
\(279\) 21.0293 26.3699i 1.25899 1.57872i
\(280\) 0 0
\(281\) 1.08750 + 1.36368i 0.0648747 + 0.0813503i 0.813210 0.581970i \(-0.197718\pi\)
−0.748335 + 0.663321i \(0.769147\pi\)
\(282\) 0 0
\(283\) 0.0232741 0.0593014i 0.00138350 0.00352510i −0.930180 0.367103i \(-0.880350\pi\)
0.931564 + 0.363578i \(0.118445\pi\)
\(284\) 0 0
\(285\) 9.48046 3.72081i 0.561574 0.220402i
\(286\) 0 0
\(287\) −5.58569 6.59980i −0.329713 0.389574i
\(288\) 0 0
\(289\) 0.691843 9.23201i 0.0406967 0.543059i
\(290\) 0 0
\(291\) 27.2921 40.0302i 1.59989 2.34661i
\(292\) 0 0
\(293\) 2.65962i 0.155377i 0.996978 + 0.0776883i \(0.0247539\pi\)
−0.996978 + 0.0776883i \(0.975246\pi\)
\(294\) 0 0
\(295\) 5.50848i 0.320716i
\(296\) 0 0
\(297\) −36.2472 + 53.1648i −2.10327 + 3.08494i
\(298\) 0 0
\(299\) −0.696255 + 9.29087i −0.0402654 + 0.537305i
\(300\) 0 0
\(301\) −1.44903 + 7.32759i −0.0835207 + 0.422355i
\(302\) 0 0
\(303\) 45.8150 17.9811i 2.63200 1.03298i
\(304\) 0 0
\(305\) 0.358122 0.912480i 0.0205060 0.0522484i
\(306\) 0 0
\(307\) 14.5505 + 18.2458i 0.830443 + 1.04134i 0.998455 + 0.0555575i \(0.0176936\pi\)
−0.168013 + 0.985785i \(0.553735\pi\)
\(308\) 0 0
\(309\) 13.4704 16.8913i 0.766302 0.960913i
\(310\) 0 0
\(311\) 11.4105 10.5874i 0.647028 0.600354i −0.286838 0.957979i \(-0.592604\pi\)
0.933865 + 0.357625i \(0.116414\pi\)
\(312\) 0 0
\(313\) −22.7466 13.1327i −1.28571 0.742307i −0.307827 0.951442i \(-0.599602\pi\)
−0.977887 + 0.209136i \(0.932935\pi\)
\(314\) 0 0
\(315\) 5.37773 + 8.71707i 0.303001 + 0.491151i
\(316\) 0 0
\(317\) 10.8582 + 10.0749i 0.609857 + 0.565865i 0.923463 0.383689i \(-0.125346\pi\)
−0.313605 + 0.949553i \(0.601537\pi\)
\(318\) 0 0
\(319\) −7.61248 + 50.5055i −0.426217 + 2.82777i
\(320\) 0 0
\(321\) −18.1798 4.14941i −1.01470 0.231598i
\(322\) 0 0
\(323\) 14.8252 3.38376i 0.824899 0.188278i
\(324\) 0 0
\(325\) 5.32804 3.07614i 0.295546 0.170634i
\(326\) 0 0
\(327\) −25.9213 + 17.6728i −1.43345 + 0.977309i
\(328\) 0 0
\(329\) −0.295648 + 0.126103i −0.0162996 + 0.00695230i
\(330\) 0 0
\(331\) 7.99942 25.9335i 0.439688 1.42543i −0.416673 0.909056i \(-0.636804\pi\)
0.856361 0.516377i \(-0.172720\pi\)
\(332\) 0 0
\(333\) 3.32655 + 44.3897i 0.182294 + 2.43254i
\(334\) 0 0
\(335\) −5.55833 + 2.67675i −0.303684 + 0.146246i
\(336\) 0 0
\(337\) 8.94647 + 4.30839i 0.487345 + 0.234693i 0.661386 0.750045i \(-0.269968\pi\)
−0.174041 + 0.984738i \(0.555683\pi\)
\(338\) 0 0
\(339\) −10.8761 + 3.35482i −0.590707 + 0.182209i
\(340\) 0 0
\(341\) −4.96456 32.9377i −0.268846 1.78368i
\(342\) 0 0
\(343\) −13.4152 + 12.7684i −0.724351 + 0.689431i
\(344\) 0 0
\(345\) −12.9169 + 1.94690i −0.695420 + 0.104818i
\(346\) 0 0
\(347\) 1.46062 + 4.73522i 0.0784103 + 0.254200i 0.986287 0.165036i \(-0.0527741\pi\)
−0.907877 + 0.419236i \(0.862298\pi\)
\(348\) 0 0
\(349\) −14.1471 + 29.3769i −0.757279 + 1.57251i 0.0613041 + 0.998119i \(0.480474\pi\)
−0.818583 + 0.574388i \(0.805240\pi\)
\(350\) 0 0
\(351\) −5.91422 12.2810i −0.315678 0.655511i
\(352\) 0 0
\(353\) −22.7410 + 1.70420i −1.21038 + 0.0907055i −0.664585 0.747213i \(-0.731392\pi\)
−0.545796 + 0.837918i \(0.683773\pi\)
\(354\) 0 0
\(355\) 3.38546 + 1.04427i 0.179681 + 0.0554243i
\(356\) 0 0
\(357\) 8.83315 + 20.7092i 0.467500 + 1.09605i
\(358\) 0 0
\(359\) −9.26707 13.5923i −0.489097 0.717374i 0.499773 0.866157i \(-0.333417\pi\)
−0.988870 + 0.148783i \(0.952465\pi\)
\(360\) 0 0
\(361\) −5.43377 9.41157i −0.285988 0.495346i
\(362\) 0 0
\(363\) 19.3055 + 84.5829i 1.01328 + 4.43945i
\(364\) 0 0
\(365\) −0.388510 + 1.70217i −0.0203355 + 0.0890957i
\(366\) 0 0
\(367\) 5.02290 + 0.757080i 0.262193 + 0.0395193i 0.278823 0.960342i \(-0.410056\pi\)
−0.0166301 + 0.999862i \(0.505294\pi\)
\(368\) 0 0
\(369\) −14.1219 + 15.2198i −0.735157 + 0.792311i
\(370\) 0 0
\(371\) 12.0909 7.45914i 0.627731 0.387259i
\(372\) 0 0
\(373\) −2.03849 + 3.53076i −0.105549 + 0.182816i −0.913962 0.405799i \(-0.866993\pi\)
0.808413 + 0.588615i \(0.200327\pi\)
\(374\) 0 0
\(375\) 12.2047 + 13.1535i 0.630247 + 0.679244i
\(376\) 0 0
\(377\) −8.45931 6.74608i −0.435677 0.347441i
\(378\) 0 0
\(379\) −22.1361 + 17.6530i −1.13706 + 0.906771i −0.996524 0.0833047i \(-0.973453\pi\)
−0.140531 + 0.990076i \(0.544881\pi\)
\(380\) 0 0
\(381\) 34.5182 + 13.5474i 1.76842 + 0.694054i
\(382\) 0 0
\(383\) 6.40912 + 16.3302i 0.327491 + 0.834433i 0.995885 + 0.0906260i \(0.0288868\pi\)
−0.668394 + 0.743807i \(0.733018\pi\)
\(384\) 0 0
\(385\) 9.92313 + 1.96230i 0.505730 + 0.100008i
\(386\) 0 0
\(387\) 17.8863 + 1.34040i 0.909214 + 0.0681362i
\(388\) 0 0
\(389\) −5.44430 3.71186i −0.276037 0.188199i 0.417387 0.908729i \(-0.362946\pi\)
−0.693423 + 0.720530i \(0.743898\pi\)
\(390\) 0 0
\(391\) −19.5041 −0.986363
\(392\) 0 0
\(393\) 2.10504 0.106185
\(394\) 0 0
\(395\) −5.21974 3.55876i −0.262634 0.179061i
\(396\) 0 0
\(397\) −19.3892 1.45302i −0.973117 0.0729250i −0.421327 0.906909i \(-0.638436\pi\)
−0.551789 + 0.833984i \(0.686055\pi\)
\(398\) 0 0
\(399\) 33.7547 28.5680i 1.68985 1.43019i
\(400\) 0 0
\(401\) −6.98388 17.7946i −0.348758 0.888622i −0.992373 0.123272i \(-0.960661\pi\)
0.643615 0.765350i \(-0.277434\pi\)
\(402\) 0 0
\(403\) 6.56851 + 2.57795i 0.327201 + 0.128417i
\(404\) 0 0
\(405\) 5.86163 4.67449i 0.291267 0.232277i
\(406\) 0 0
\(407\) 34.3706 + 27.4097i 1.70369 + 1.35865i
\(408\) 0 0
\(409\) 23.0745 + 24.8684i 1.14096 + 1.22966i 0.969663 + 0.244445i \(0.0786059\pi\)
0.171299 + 0.985219i \(0.445204\pi\)
\(410\) 0 0
\(411\) 14.6246 25.3306i 0.721379 1.24947i
\(412\) 0 0
\(413\) 7.71348 + 22.6400i 0.379556 + 1.11404i
\(414\) 0 0
\(415\) −5.46621 + 5.89117i −0.268326 + 0.289186i
\(416\) 0 0
\(417\) 38.9745 + 5.87446i 1.90859 + 0.287674i
\(418\) 0 0
\(419\) 1.42669 6.25073i 0.0696983 0.305368i −0.928049 0.372459i \(-0.878515\pi\)
0.997747 + 0.0670910i \(0.0213718\pi\)
\(420\) 0 0
\(421\) 5.61140 + 24.5852i 0.273483 + 1.19821i 0.905870 + 0.423555i \(0.139218\pi\)
−0.632388 + 0.774652i \(0.717925\pi\)
\(422\) 0 0
\(423\) 0.385911 + 0.668418i 0.0187636 + 0.0324996i
\(424\) 0 0
\(425\) 7.25512 + 10.6413i 0.351925 + 0.516179i
\(426\) 0 0
\(427\) 0.194150 4.25179i 0.00939556 0.205758i
\(428\) 0 0
\(429\) −24.3721 7.51781i −1.17670 0.362963i
\(430\) 0 0
\(431\) −19.7399 + 1.47930i −0.950839 + 0.0712556i −0.541110 0.840952i \(-0.681996\pi\)
−0.409729 + 0.912207i \(0.634377\pi\)
\(432\) 0 0
\(433\) 1.13296 + 2.35262i 0.0544467 + 0.113060i 0.926417 0.376499i \(-0.122872\pi\)
−0.871970 + 0.489559i \(0.837158\pi\)
\(434\) 0 0
\(435\) 6.58199 13.6677i 0.315582 0.655314i
\(436\) 0 0
\(437\) 11.2916 + 36.6066i 0.540152 + 1.75113i
\(438\) 0 0
\(439\) −25.4158 + 3.83081i −1.21303 + 0.182835i −0.724228 0.689560i \(-0.757804\pi\)
−0.488801 + 0.872395i \(0.662566\pi\)
\(440\) 0 0
\(441\) 34.3090 + 28.2969i 1.63376 + 1.34747i
\(442\) 0 0
\(443\) 5.49472 + 36.4551i 0.261062 + 1.73203i 0.607817 + 0.794077i \(0.292046\pi\)
−0.346755 + 0.937956i \(0.612716\pi\)
\(444\) 0 0
\(445\) 5.52289 1.70358i 0.261810 0.0807577i
\(446\) 0 0
\(447\) −33.7258 16.2415i −1.59518 0.768197i
\(448\) 0 0
\(449\) −23.9520 + 11.5347i −1.13037 + 0.544356i −0.903080 0.429472i \(-0.858700\pi\)
−0.227286 + 0.973828i \(0.572985\pi\)
\(450\) 0 0
\(451\) 1.53231 + 20.4472i 0.0721534 + 0.962821i
\(452\) 0 0
\(453\) 15.8822 51.4887i 0.746210 2.41915i
\(454\) 0 0
\(455\) −1.41105 + 1.61263i −0.0661510 + 0.0756012i
\(456\) 0 0
\(457\) 27.5712 18.7977i 1.28972 0.879319i 0.292684 0.956209i \(-0.405451\pi\)
0.997040 + 0.0768901i \(0.0244991\pi\)
\(458\) 0 0
\(459\) 24.7120 14.2675i 1.15346 0.665948i
\(460\) 0 0
\(461\) −37.3408 + 8.52280i −1.73914 + 0.396947i −0.970186 0.242362i \(-0.922078\pi\)
−0.768950 + 0.639308i \(0.779221\pi\)
\(462\) 0 0
\(463\) −18.2163 4.15776i −0.846585 0.193228i −0.222840 0.974855i \(-0.571533\pi\)
−0.623745 + 0.781628i \(0.714390\pi\)
\(464\) 0 0
\(465\) −1.47451 + 9.78274i −0.0683788 + 0.453664i
\(466\) 0 0
\(467\) 3.88925 + 3.60869i 0.179973 + 0.166990i 0.765015 0.644013i \(-0.222732\pi\)
−0.585042 + 0.811003i \(0.698922\pi\)
\(468\) 0 0
\(469\) −19.0966 + 18.7848i −0.881799 + 0.867401i
\(470\) 0 0
\(471\) 2.13060 + 1.23010i 0.0981730 + 0.0566802i
\(472\) 0 0
\(473\) 12.9852 12.0485i 0.597060 0.553990i
\(474\) 0 0
\(475\) 15.7721 19.7776i 0.723673 0.907457i
\(476\) 0 0
\(477\) −21.2701 26.6718i −0.973889 1.22122i
\(478\) 0 0
\(479\) 1.96234 4.99996i 0.0896616 0.228454i −0.879008 0.476807i \(-0.841794\pi\)
0.968670 + 0.248353i \(0.0798893\pi\)
\(480\) 0 0
\(481\) −8.66902 + 3.40234i −0.395273 + 0.155133i
\(482\) 0 0
\(483\) −50.3623 + 26.0892i −2.29156 + 1.18710i
\(484\) 0 0
\(485\) −0.721363 + 9.62592i −0.0327554 + 0.437091i
\(486\) 0 0
\(487\) 4.08858 5.99685i 0.185271 0.271743i −0.722355 0.691523i \(-0.756940\pi\)
0.907626 + 0.419779i \(0.137893\pi\)
\(488\) 0 0
\(489\) 9.48527i 0.428939i
\(490\) 0 0
\(491\) 17.4661i 0.788235i 0.919060 + 0.394118i \(0.128950\pi\)
−0.919060 + 0.394118i \(0.871050\pi\)
\(492\) 0 0
\(493\) 12.7594 18.7146i 0.574654 0.842863i
\(494\) 0 0
\(495\) 1.81518 24.2220i 0.0815865 1.08870i
\(496\) 0 0
\(497\) 15.3766 0.448639i 0.689734 0.0201242i
\(498\) 0 0
\(499\) −13.6176 + 5.34453i −0.609610 + 0.239254i −0.650005 0.759930i \(-0.725233\pi\)
0.0403958 + 0.999184i \(0.487138\pi\)
\(500\) 0 0
\(501\) −17.3011 + 44.0824i −0.772955 + 1.96946i
\(502\) 0 0
\(503\) −8.82683 11.0685i −0.393569 0.493520i 0.545085 0.838381i \(-0.316497\pi\)
−0.938654 + 0.344861i \(0.887926\pi\)
\(504\) 0 0
\(505\) −6.11396 + 7.66666i −0.272068 + 0.341162i
\(506\) 0 0
\(507\) −25.1840 + 23.3673i −1.11846 + 1.03778i
\(508\) 0 0
\(509\) −22.0982 12.7584i −0.979487 0.565507i −0.0773715 0.997002i \(-0.524653\pi\)
−0.902115 + 0.431495i \(0.857986\pi\)
\(510\) 0 0
\(511\) 0.786756 + 7.53999i 0.0348041 + 0.333549i
\(512\) 0 0
\(513\) −41.0848 38.1212i −1.81394 1.68309i
\(514\) 0 0
\(515\) −0.641558 + 4.25646i −0.0282704 + 0.187562i
\(516\) 0 0
\(517\) 0.743131 + 0.169615i 0.0326829 + 0.00745965i
\(518\) 0 0
\(519\) 12.7304 2.90563i 0.558803 0.127543i
\(520\) 0 0
\(521\) 8.44592 4.87625i 0.370022 0.213632i −0.303446 0.952849i \(-0.598137\pi\)
0.673468 + 0.739216i \(0.264804\pi\)
\(522\) 0 0
\(523\) 33.3622 22.7460i 1.45883 0.994611i 0.464807 0.885412i \(-0.346124\pi\)
0.994020 0.109199i \(-0.0348285\pi\)
\(524\) 0 0
\(525\) 32.9679 + 17.7727i 1.43884 + 0.775665i
\(526\) 0 0
\(527\) −4.35402 + 14.1154i −0.189664 + 0.614876i
\(528\) 0 0
\(529\) −1.95307 26.0620i −0.0849163 1.13313i
\(530\) 0 0
\(531\) 51.7463 24.9197i 2.24560 1.08142i
\(532\) 0 0
\(533\) −3.91349 1.88464i −0.169512 0.0816328i
\(534\) 0 0
\(535\) 3.55022 1.09510i 0.153490 0.0473453i
\(536\) 0 0
\(537\) 0.813097 + 5.39455i 0.0350877 + 0.232792i
\(538\) 0 0
\(539\) 43.5321 5.83021i 1.87506 0.251125i
\(540\) 0 0
\(541\) −17.8606 + 2.69206i −0.767889 + 0.115741i −0.521293 0.853378i \(-0.674550\pi\)
−0.246596 + 0.969118i \(0.579312\pi\)
\(542\) 0 0
\(543\) −18.3664 59.5423i −0.788177 2.55521i
\(544\) 0 0
\(545\) 2.71207 5.63166i 0.116172 0.241234i
\(546\) 0 0
\(547\) −2.70505 5.61708i −0.115659 0.240169i 0.835101 0.550097i \(-0.185409\pi\)
−0.950760 + 0.309928i \(0.899695\pi\)
\(548\) 0 0
\(549\) −10.1919 + 0.763776i −0.434979 + 0.0325972i
\(550\) 0 0
\(551\) −42.5117 13.1131i −1.81106 0.558638i
\(552\) 0 0
\(553\) −26.4365 7.31740i −1.12420 0.311168i
\(554\) 0 0
\(555\) −7.35524 10.7882i −0.312212 0.457932i
\(556\) 0 0
\(557\) −1.43462 2.48483i −0.0607866 0.105286i 0.834031 0.551718i \(-0.186028\pi\)
−0.894817 + 0.446433i \(0.852694\pi\)
\(558\) 0 0
\(559\) 0.835006 + 3.65840i 0.0353170 + 0.154734i
\(560\) 0 0
\(561\) 11.8810 52.0541i 0.501617 2.19773i
\(562\) 0 0
\(563\) −18.7424 2.82497i −0.789899 0.119058i −0.258312 0.966062i \(-0.583166\pi\)
−0.531587 + 0.847004i \(0.678404\pi\)
\(564\) 0 0
\(565\) 1.54242 1.66234i 0.0648903 0.0699351i
\(566\) 0 0
\(567\) 17.5458 27.4203i 0.736852 1.15154i
\(568\) 0 0
\(569\) −16.4374 + 28.4704i −0.689092 + 1.19354i 0.283040 + 0.959108i \(0.408657\pi\)
−0.972132 + 0.234435i \(0.924676\pi\)
\(570\) 0 0
\(571\) −26.4504 28.5068i −1.10692 1.19297i −0.979568 0.201112i \(-0.935544\pi\)
−0.127347 0.991858i \(-0.540646\pi\)
\(572\) 0 0
\(573\) 23.8397 + 19.0116i 0.995919 + 0.794219i
\(574\) 0 0
\(575\) −25.3670 + 20.2295i −1.05788 + 0.843628i
\(576\) 0 0
\(577\) −18.7313 7.35150i −0.779795 0.306047i −0.0581477 0.998308i \(-0.518519\pi\)
−0.721647 + 0.692261i \(0.756615\pi\)
\(578\) 0 0
\(579\) −11.8113 30.0948i −0.490863 1.25070i
\(580\) 0 0
\(581\) −14.2169 + 31.8671i −0.589815 + 1.32207i
\(582\) 0 0
\(583\) −33.5969 2.51774i −1.39144 0.104274i
\(584\) 0 0
\(585\) 4.25144 + 2.89858i 0.175775 + 0.119842i
\(586\) 0 0
\(587\) −6.40317 −0.264287 −0.132144 0.991231i \(-0.542186\pi\)
−0.132144 + 0.991231i \(0.542186\pi\)
\(588\) 0 0
\(589\) 29.0134 1.19548
\(590\) 0 0
\(591\) −21.0788 14.3713i −0.867067 0.591156i
\(592\) 0 0
\(593\) −26.8607 2.01293i −1.10304 0.0826612i −0.489258 0.872139i \(-0.662732\pi\)
−0.613779 + 0.789478i \(0.710351\pi\)
\(594\) 0 0
\(595\) −3.58719 2.69335i −0.147060 0.110417i
\(596\) 0 0
\(597\) 5.74870 + 14.6474i 0.235279 + 0.599480i
\(598\) 0 0
\(599\) 43.5263 + 17.0828i 1.77844 + 0.697984i 0.997285 + 0.0736413i \(0.0234620\pi\)
0.781150 + 0.624343i \(0.214633\pi\)
\(600\) 0 0
\(601\) 15.9633 12.7303i 0.651155 0.519279i −0.241280 0.970456i \(-0.577567\pi\)
0.892434 + 0.451177i \(0.148996\pi\)
\(602\) 0 0
\(603\) 50.2905 + 40.1053i 2.04799 + 1.63321i
\(604\) 0 0
\(605\) −11.7573 12.6713i −0.478000 0.515162i
\(606\) 0 0
\(607\) −7.44788 + 12.9001i −0.302300 + 0.523599i −0.976657 0.214807i \(-0.931088\pi\)
0.674356 + 0.738406i \(0.264421\pi\)
\(608\) 0 0
\(609\) 7.91342 65.3911i 0.320668 2.64978i
\(610\) 0 0
\(611\) −0.109829 + 0.118368i −0.00444321 + 0.00478864i
\(612\) 0 0
\(613\) 42.0781 + 6.34226i 1.69952 + 0.256161i 0.925976 0.377581i \(-0.123244\pi\)
0.773544 + 0.633743i \(0.218482\pi\)
\(614\) 0 0
\(615\) 1.35515 5.93731i 0.0546450 0.239415i
\(616\) 0 0
\(617\) 3.09852 + 13.5755i 0.124742 + 0.546530i 0.998219 + 0.0596637i \(0.0190028\pi\)
−0.873477 + 0.486866i \(0.838140\pi\)
\(618\) 0 0
\(619\) −11.6473 20.1738i −0.468146 0.810853i 0.531191 0.847252i \(-0.321745\pi\)
−0.999337 + 0.0363992i \(0.988411\pi\)
\(620\) 0 0
\(621\) 40.4947 + 59.3948i 1.62500 + 2.38343i
\(622\) 0 0
\(623\) 20.3137 14.7354i 0.813849 0.590362i
\(624\) 0 0
\(625\) 18.6991 + 5.76791i 0.747964 + 0.230716i
\(626\) 0 0
\(627\) −104.577 + 7.83697i −4.17641 + 0.312978i
\(628\) 0 0
\(629\) −8.45873 17.5647i −0.337272 0.700352i
\(630\) 0 0
\(631\) 17.8283 37.0208i 0.709733 1.47378i −0.163535 0.986538i \(-0.552290\pi\)
0.873269 0.487239i \(-0.161996\pi\)
\(632\) 0 0
\(633\) −4.63457 15.0249i −0.184208 0.597187i
\(634\) 0 0
\(635\) −7.30559 + 1.10114i −0.289914 + 0.0436975i
\(636\) 0 0
\(637\) −3.54129 + 8.60382i −0.140311 + 0.340896i
\(638\) 0 0
\(639\) −5.50555 36.5270i −0.217796 1.44498i
\(640\) 0 0
\(641\) −13.1898 + 4.06852i −0.520967 + 0.160697i −0.544076 0.839036i \(-0.683120\pi\)
0.0231091 + 0.999733i \(0.492643\pi\)
\(642\) 0 0
\(643\) 14.8339 + 7.14362i 0.584991 + 0.281717i 0.702878 0.711310i \(-0.251898\pi\)
−0.117887 + 0.993027i \(0.537612\pi\)
\(644\) 0 0
\(645\) −4.74013 + 2.28273i −0.186643 + 0.0898823i
\(646\) 0 0
\(647\) −0.276330 3.68737i −0.0108637 0.144966i 0.989134 0.147015i \(-0.0469666\pi\)
−0.999998 + 0.00204962i \(0.999348\pi\)
\(648\) 0 0
\(649\) 16.7189 54.2013i 0.656273 2.12759i
\(650\) 0 0
\(651\) 7.63843 + 42.2720i 0.299374 + 1.65677i
\(652\) 0 0
\(653\) 36.3023 24.7505i 1.42062 0.968561i 0.422556 0.906337i \(-0.361133\pi\)
0.998062 0.0622243i \(-0.0198194\pi\)
\(654\) 0 0
\(655\) −0.363218 + 0.209704i −0.0141921 + 0.00819382i
\(656\) 0 0
\(657\) 17.7477 4.05079i 0.692403 0.158036i
\(658\) 0 0
\(659\) −1.48701 0.339401i −0.0579258 0.0132212i 0.193460 0.981108i \(-0.438029\pi\)
−0.251386 + 0.967887i \(0.580886\pi\)
\(660\) 0 0
\(661\) 3.38988 22.4904i 0.131851 0.874775i −0.820911 0.571056i \(-0.806534\pi\)
0.952762 0.303718i \(-0.0982281\pi\)
\(662\) 0 0
\(663\) 8.29129 + 7.69320i 0.322007 + 0.298779i
\(664\) 0 0
\(665\) −2.97832 + 8.29196i −0.115494 + 0.321549i
\(666\) 0 0
\(667\) 49.4164 + 28.5306i 1.91341 + 1.10471i
\(668\) 0 0
\(669\) −38.4880 + 35.7117i −1.48803 + 1.38069i
\(670\) 0 0
\(671\) −6.29326 + 7.89150i −0.242949 + 0.304648i
\(672\) 0 0
\(673\) −8.72482 10.9406i −0.336317 0.421728i 0.584701 0.811249i \(-0.301212\pi\)
−0.921018 + 0.389521i \(0.872641\pi\)
\(674\) 0 0
\(675\) 17.3422 44.1873i 0.667503 1.70077i
\(676\) 0 0
\(677\) 14.1872 5.56808i 0.545260 0.213999i −0.0766911 0.997055i \(-0.524436\pi\)
0.621951 + 0.783056i \(0.286340\pi\)
\(678\) 0 0
\(679\) 10.5143 + 40.5729i 0.403502 + 1.55704i
\(680\) 0 0
\(681\) −2.39169 + 31.9149i −0.0916498 + 1.22298i
\(682\) 0 0
\(683\) 8.93609 13.1068i 0.341930 0.501519i −0.616303 0.787509i \(-0.711370\pi\)
0.958232 + 0.285990i \(0.0923226\pi\)
\(684\) 0 0
\(685\) 5.82762i 0.222662i
\(686\) 0 0
\(687\) 26.0707i 0.994658i
\(688\) 0 0
\(689\) 4.02046 5.89693i 0.153167 0.224655i
\(690\) 0 0
\(691\) −1.23813 + 16.5217i −0.0471007 + 0.628515i 0.922842 + 0.385180i \(0.125861\pi\)
−0.969942 + 0.243335i \(0.921758\pi\)
\(692\) 0 0
\(693\) −26.4574 102.095i −1.00503 3.87825i
\(694\) 0 0
\(695\) −7.31014 + 2.86902i −0.277290 + 0.108828i
\(696\) 0 0
\(697\) 3.32205 8.46444i 0.125832 0.320614i
\(698\) 0 0
\(699\) −12.9081 16.1862i −0.488228 0.612218i
\(700\) 0 0
\(701\) 15.6510 19.6257i 0.591128 0.741252i −0.392838 0.919608i \(-0.628507\pi\)
0.983966 + 0.178356i \(0.0570780\pi\)
\(702\) 0 0
\(703\) −28.0696 + 26.0448i −1.05867 + 0.982299i
\(704\) 0 0
\(705\) −0.196061 0.113196i −0.00738408 0.00426320i
\(706\) 0 0
\(707\) −14.3929 + 40.0715i −0.541302 + 1.50704i
\(708\) 0 0
\(709\) −16.2783 15.1041i −0.611345 0.567245i 0.312546 0.949903i \(-0.398818\pi\)
−0.923890 + 0.382658i \(0.875009\pi\)
\(710\) 0 0
\(711\) −9.81727 + 65.1333i −0.368176 + 2.44269i
\(712\) 0 0
\(713\) −36.2800 8.28068i −1.35870 0.310114i
\(714\) 0 0
\(715\) 4.95426 1.13078i 0.185279 0.0422887i
\(716\) 0 0
\(717\) −38.8685 + 22.4407i −1.45157 + 0.838064i
\(718\) 0 0
\(719\) −24.1147 + 16.4411i −0.899327 + 0.613151i −0.922253 0.386586i \(-0.873654\pi\)
0.0229263 + 0.999737i \(0.492702\pi\)
\(720\) 0 0
\(721\) 3.32347 + 18.3925i 0.123773 + 0.684973i
\(722\) 0 0
\(723\) −11.3580 + 36.8219i −0.422410 + 1.36942i
\(724\) 0 0
\(725\) −2.81579 37.5741i −0.104576 1.39547i
\(726\) 0 0
\(727\) 41.7019 20.0826i 1.54664 0.744822i 0.550688 0.834711i \(-0.314366\pi\)
0.995952 + 0.0898890i \(0.0286512\pi\)
\(728\) 0 0
\(729\) 14.3441 + 6.90776i 0.531263 + 0.255843i
\(730\) 0 0
\(731\) −7.50646 + 2.31544i −0.277636 + 0.0856395i
\(732\) 0 0
\(733\) 5.70029 + 37.8190i 0.210545 + 1.39688i 0.805252 + 0.592933i \(0.202030\pi\)
−0.594707 + 0.803943i \(0.702732\pi\)
\(734\) 0 0
\(735\) −12.8653 2.15631i −0.474545 0.0795366i
\(736\) 0 0
\(737\) 62.8160 9.46799i 2.31386 0.348758i
\(738\) 0 0
\(739\) 2.50652 + 8.12593i 0.0922038 + 0.298917i 0.989914 0.141669i \(-0.0452468\pi\)
−0.897710 + 0.440586i \(0.854771\pi\)
\(740\) 0 0
\(741\) 9.63898 20.0156i 0.354097 0.735290i
\(742\) 0 0
\(743\) −14.0659 29.2081i −0.516026 1.07154i −0.982372 0.186937i \(-0.940144\pi\)
0.466346 0.884603i \(-0.345570\pi\)
\(744\) 0 0
\(745\) 7.43726 0.557346i 0.272480 0.0204196i
\(746\) 0 0
\(747\) 80.0698 + 24.6983i 2.92960 + 0.903662i
\(748\) 0 0
\(749\) 13.0580 9.47224i 0.477130 0.346108i
\(750\) 0 0
\(751\) 25.9137 + 38.0084i 0.945604 + 1.38695i 0.921985 + 0.387226i \(0.126567\pi\)
0.0236197 + 0.999721i \(0.492481\pi\)
\(752\) 0 0
\(753\) −38.8379 67.2691i −1.41533 2.45142i
\(754\) 0 0
\(755\) 2.38889 + 10.4664i 0.0869405 + 0.380911i
\(756\) 0 0
\(757\) −7.25933 + 31.8052i −0.263845 + 1.15598i 0.653197 + 0.757188i \(0.273428\pi\)
−0.917042 + 0.398792i \(0.869430\pi\)
\(758\) 0 0
\(759\) 133.006 + 20.0474i 4.82781 + 0.727675i
\(760\) 0 0
\(761\) −31.5193 + 33.9697i −1.14257 + 1.23140i −0.173444 + 0.984844i \(0.555489\pi\)
−0.969129 + 0.246556i \(0.920701\pi\)
\(762\) 0 0
\(763\) 3.26067 26.9439i 0.118044 0.975436i
\(764\) 0 0
\(765\) −5.38584 + 9.32854i −0.194725 + 0.337274i
\(766\) 0 0
\(767\) 8.17278 + 8.80817i 0.295102 + 0.318044i
\(768\) 0 0
\(769\) 26.6859 + 21.2813i 0.962318 + 0.767423i 0.972591 0.232524i \(-0.0746986\pi\)
−0.0102728 + 0.999947i \(0.503270\pi\)
\(770\) 0 0
\(771\) −38.0496 + 30.3436i −1.37032 + 1.09280i
\(772\) 0 0
\(773\) 25.0838 + 9.84467i 0.902202 + 0.354088i 0.770678 0.637225i \(-0.219918\pi\)
0.131524 + 0.991313i \(0.458013\pi\)
\(774\) 0 0
\(775\) 8.97754 + 22.8744i 0.322483 + 0.821673i
\(776\) 0 0
\(777\) −45.3368 34.0400i −1.62645 1.22118i
\(778\) 0 0
\(779\) −17.8099 1.33467i −0.638106 0.0478194i
\(780\) 0 0
\(781\) −30.1421 20.5505i −1.07857 0.735355i
\(782\) 0 0
\(783\) −83.4819 −2.98340
\(784\) 0 0
\(785\) −0.490172 −0.0174950
\(786\) 0 0
\(787\) −2.32684 1.58642i −0.0829431 0.0565496i 0.521138 0.853472i \(-0.325508\pi\)
−0.604082 + 0.796923i \(0.706460\pi\)
\(788\) 0 0
\(789\) 10.7908 + 0.808656i 0.384162 + 0.0287889i
\(790\) 0 0
\(791\) 4.01164 8.99209i 0.142637 0.319722i
\(792\) 0 0
\(793\) −0.781178 1.99041i −0.0277404 0.0706815i
\(794\) 0 0
\(795\) 9.31479 + 3.65579i 0.330362 + 0.129657i
\(796\) 0