Properties

Label 128.3.h.a.47.5
Level $128$
Weight $3$
Character 128.47
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 47.5
Character \(\chi\) \(=\) 128.47
Dual form 128.3.h.a.79.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.10785 - 2.67458i) q^{3} +(2.95565 + 7.13556i) q^{5} +(4.18452 + 4.18452i) q^{7} +(0.437918 + 0.437918i) q^{9} +O(q^{10})\) \(q+(1.10785 - 2.67458i) q^{3} +(2.95565 + 7.13556i) q^{5} +(4.18452 + 4.18452i) q^{7} +(0.437918 + 0.437918i) q^{9} +(-1.42655 - 3.44399i) q^{11} +(8.39996 - 20.2793i) q^{13} +22.3590 q^{15} +1.73115i q^{17} +(-14.2459 - 5.90085i) q^{19} +(15.8276 - 6.55601i) q^{21} +(-15.1565 + 15.1565i) q^{23} +(-24.5027 + 24.5027i) q^{25} +(25.7276 - 10.6567i) q^{27} +(-6.74107 - 2.79224i) q^{29} +31.1695i q^{31} -10.7916 q^{33} +(-17.4909 + 42.2268i) q^{35} +(5.30038 + 12.7962i) q^{37} +(-44.9327 - 44.9327i) q^{39} +(-18.5776 - 18.5776i) q^{41} +(-31.0691 - 75.0074i) q^{43} +(-1.83046 + 4.41911i) q^{45} +16.2824 q^{47} -13.9797i q^{49} +(4.63009 + 1.91784i) q^{51} +(-29.0670 + 12.0399i) q^{53} +(20.3584 - 20.3584i) q^{55} +(-31.5646 + 31.5646i) q^{57} +(-34.1002 + 14.1248i) q^{59} +(-68.7647 - 28.4833i) q^{61} +3.66495i q^{63} +169.531 q^{65} +(-10.5147 + 25.3846i) q^{67} +(23.7462 + 57.3284i) q^{69} +(32.2012 + 32.2012i) q^{71} +(-28.5494 - 28.5494i) q^{73} +(38.3891 + 92.6796i) q^{75} +(8.44203 - 20.3809i) q^{77} -22.4049 q^{79} -75.0427i q^{81} +(123.286 + 51.0669i) q^{83} +(-12.3527 + 5.11665i) q^{85} +(-14.9361 + 14.9361i) q^{87} +(61.0281 - 61.0281i) q^{89} +(120.009 - 49.7093i) q^{91} +(83.3652 + 34.5310i) q^{93} -119.093i q^{95} -69.9064 q^{97} +(0.883474 - 2.13290i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.10785 2.67458i 0.369282 0.891526i −0.624586 0.780956i \(-0.714732\pi\)
0.993868 0.110570i \(-0.0352677\pi\)
\(4\) 0 0
\(5\) 2.95565 + 7.13556i 0.591129 + 1.42711i 0.882413 + 0.470475i \(0.155917\pi\)
−0.291284 + 0.956637i \(0.594083\pi\)
\(6\) 0 0
\(7\) 4.18452 + 4.18452i 0.597788 + 0.597788i 0.939723 0.341935i \(-0.111082\pi\)
−0.341935 + 0.939723i \(0.611082\pi\)
\(8\) 0 0
\(9\) 0.437918 + 0.437918i 0.0486575 + 0.0486575i
\(10\) 0 0
\(11\) −1.42655 3.44399i −0.129686 0.313090i 0.845677 0.533695i \(-0.179197\pi\)
−0.975363 + 0.220605i \(0.929197\pi\)
\(12\) 0 0
\(13\) 8.39996 20.2793i 0.646151 1.55995i −0.172096 0.985080i \(-0.555054\pi\)
0.818247 0.574866i \(-0.194946\pi\)
\(14\) 0 0
\(15\) 22.3590 1.49060
\(16\) 0 0
\(17\) 1.73115i 0.101832i 0.998703 + 0.0509161i \(0.0162141\pi\)
−0.998703 + 0.0509161i \(0.983786\pi\)
\(18\) 0 0
\(19\) −14.2459 5.90085i −0.749785 0.310571i −0.0251314 0.999684i \(-0.508000\pi\)
−0.724654 + 0.689113i \(0.758000\pi\)
\(20\) 0 0
\(21\) 15.8276 6.55601i 0.753696 0.312191i
\(22\) 0 0
\(23\) −15.1565 + 15.1565i −0.658979 + 0.658979i −0.955139 0.296159i \(-0.904294\pi\)
0.296159 + 0.955139i \(0.404294\pi\)
\(24\) 0 0
\(25\) −24.5027 + 24.5027i −0.980107 + 0.980107i
\(26\) 0 0
\(27\) 25.7276 10.6567i 0.952874 0.394693i
\(28\) 0 0
\(29\) −6.74107 2.79224i −0.232451 0.0962842i 0.263418 0.964682i \(-0.415150\pi\)
−0.495869 + 0.868398i \(0.665150\pi\)
\(30\) 0 0
\(31\) 31.1695i 1.00547i 0.864442 + 0.502733i \(0.167672\pi\)
−0.864442 + 0.502733i \(0.832328\pi\)
\(32\) 0 0
\(33\) −10.7916 −0.327019
\(34\) 0 0
\(35\) −17.4909 + 42.2268i −0.499740 + 1.20648i
\(36\) 0 0
\(37\) 5.30038 + 12.7962i 0.143253 + 0.345844i 0.979179 0.202998i \(-0.0650686\pi\)
−0.835926 + 0.548843i \(0.815069\pi\)
\(38\) 0 0
\(39\) −44.9327 44.9327i −1.15212 1.15212i
\(40\) 0 0
\(41\) −18.5776 18.5776i −0.453111 0.453111i 0.443275 0.896386i \(-0.353817\pi\)
−0.896386 + 0.443275i \(0.853817\pi\)
\(42\) 0 0
\(43\) −31.0691 75.0074i −0.722537 1.74436i −0.665993 0.745958i \(-0.731992\pi\)
−0.0565443 0.998400i \(-0.518008\pi\)
\(44\) 0 0
\(45\) −1.83046 + 4.41911i −0.0406768 + 0.0982026i
\(46\) 0 0
\(47\) 16.2824 0.346435 0.173217 0.984884i \(-0.444584\pi\)
0.173217 + 0.984884i \(0.444584\pi\)
\(48\) 0 0
\(49\) 13.9797i 0.285299i
\(50\) 0 0
\(51\) 4.63009 + 1.91784i 0.0907860 + 0.0376048i
\(52\) 0 0
\(53\) −29.0670 + 12.0399i −0.548434 + 0.227169i −0.639655 0.768662i \(-0.720923\pi\)
0.0912216 + 0.995831i \(0.470923\pi\)
\(54\) 0 0
\(55\) 20.3584 20.3584i 0.370153 0.370153i
\(56\) 0 0
\(57\) −31.5646 + 31.5646i −0.553765 + 0.553765i
\(58\) 0 0
\(59\) −34.1002 + 14.1248i −0.577969 + 0.239403i −0.652465 0.757819i \(-0.726265\pi\)
0.0744962 + 0.997221i \(0.476265\pi\)
\(60\) 0 0
\(61\) −68.7647 28.4833i −1.12729 0.466939i −0.260432 0.965492i \(-0.583865\pi\)
−0.866859 + 0.498553i \(0.833865\pi\)
\(62\) 0 0
\(63\) 3.66495i 0.0581737i
\(64\) 0 0
\(65\) 169.531 2.60818
\(66\) 0 0
\(67\) −10.5147 + 25.3846i −0.156935 + 0.378875i −0.982717 0.185115i \(-0.940734\pi\)
0.825782 + 0.563990i \(0.190734\pi\)
\(68\) 0 0
\(69\) 23.7462 + 57.3284i 0.344148 + 0.830847i
\(70\) 0 0
\(71\) 32.2012 + 32.2012i 0.453538 + 0.453538i 0.896527 0.442989i \(-0.146082\pi\)
−0.442989 + 0.896527i \(0.646082\pi\)
\(72\) 0 0
\(73\) −28.5494 28.5494i −0.391088 0.391088i 0.483987 0.875075i \(-0.339188\pi\)
−0.875075 + 0.483987i \(0.839188\pi\)
\(74\) 0 0
\(75\) 38.3891 + 92.6796i 0.511855 + 1.23573i
\(76\) 0 0
\(77\) 8.44203 20.3809i 0.109637 0.264686i
\(78\) 0 0
\(79\) −22.4049 −0.283606 −0.141803 0.989895i \(-0.545290\pi\)
−0.141803 + 0.989895i \(0.545290\pi\)
\(80\) 0 0
\(81\) 75.0427i 0.926453i
\(82\) 0 0
\(83\) 123.286 + 51.0669i 1.48538 + 0.615264i 0.970306 0.241882i \(-0.0777648\pi\)
0.515073 + 0.857146i \(0.327765\pi\)
\(84\) 0 0
\(85\) −12.3527 + 5.11665i −0.145326 + 0.0601959i
\(86\) 0 0
\(87\) −14.9361 + 14.9361i −0.171680 + 0.171680i
\(88\) 0 0
\(89\) 61.0281 61.0281i 0.685709 0.685709i −0.275572 0.961280i \(-0.588867\pi\)
0.961280 + 0.275572i \(0.0888672\pi\)
\(90\) 0 0
\(91\) 120.009 49.7093i 1.31878 0.546256i
\(92\) 0 0
\(93\) 83.3652 + 34.5310i 0.896400 + 0.371301i
\(94\) 0 0
\(95\) 119.093i 1.25362i
\(96\) 0 0
\(97\) −69.9064 −0.720684 −0.360342 0.932820i \(-0.617340\pi\)
−0.360342 + 0.932820i \(0.617340\pi\)
\(98\) 0 0
\(99\) 0.883474 2.13290i 0.00892398 0.0215444i
\(100\) 0 0
\(101\) −10.4825 25.3069i −0.103787 0.250564i 0.863452 0.504431i \(-0.168298\pi\)
−0.967239 + 0.253867i \(0.918298\pi\)
\(102\) 0 0
\(103\) −116.721 116.721i −1.13322 1.13322i −0.989639 0.143579i \(-0.954139\pi\)
−0.143579 0.989639i \(-0.545861\pi\)
\(104\) 0 0
\(105\) 93.5616 + 93.5616i 0.891063 + 0.891063i
\(106\) 0 0
\(107\) 21.6236 + 52.2039i 0.202090 + 0.487887i 0.992137 0.125159i \(-0.0399440\pi\)
−0.790047 + 0.613046i \(0.789944\pi\)
\(108\) 0 0
\(109\) −28.8284 + 69.5980i −0.264481 + 0.638514i −0.999206 0.0398518i \(-0.987311\pi\)
0.734725 + 0.678366i \(0.237311\pi\)
\(110\) 0 0
\(111\) 40.0965 0.361230
\(112\) 0 0
\(113\) 130.141i 1.15169i 0.817559 + 0.575845i \(0.195327\pi\)
−0.817559 + 0.575845i \(0.804673\pi\)
\(114\) 0 0
\(115\) −152.948 63.3530i −1.32998 0.550895i
\(116\) 0 0
\(117\) 12.5592 5.20217i 0.107343 0.0444630i
\(118\) 0 0
\(119\) −7.24401 + 7.24401i −0.0608740 + 0.0608740i
\(120\) 0 0
\(121\) 75.7339 75.7339i 0.625900 0.625900i
\(122\) 0 0
\(123\) −70.2682 + 29.1060i −0.571286 + 0.236635i
\(124\) 0 0
\(125\) −68.8726 28.5280i −0.550981 0.228224i
\(126\) 0 0
\(127\) 56.3580i 0.443764i 0.975074 + 0.221882i \(0.0712200\pi\)
−0.975074 + 0.221882i \(0.928780\pi\)
\(128\) 0 0
\(129\) −235.033 −1.82196
\(130\) 0 0
\(131\) 39.2631 94.7895i 0.299718 0.723584i −0.700235 0.713912i \(-0.746921\pi\)
0.999953 0.00967128i \(-0.00307851\pi\)
\(132\) 0 0
\(133\) −34.9201 84.3045i −0.262557 0.633868i
\(134\) 0 0
\(135\) 152.083 + 152.083i 1.12654 + 1.12654i
\(136\) 0 0
\(137\) 62.6423 + 62.6423i 0.457243 + 0.457243i 0.897750 0.440506i \(-0.145201\pi\)
−0.440506 + 0.897750i \(0.645201\pi\)
\(138\) 0 0
\(139\) −11.6343 28.0877i −0.0837000 0.202070i 0.876488 0.481423i \(-0.159880\pi\)
−0.960188 + 0.279353i \(0.909880\pi\)
\(140\) 0 0
\(141\) 18.0384 43.5487i 0.127932 0.308856i
\(142\) 0 0
\(143\) −81.8247 −0.572201
\(144\) 0 0
\(145\) 56.3542i 0.388649i
\(146\) 0 0
\(147\) −37.3897 15.4873i −0.254352 0.105356i
\(148\) 0 0
\(149\) −52.6977 + 21.8281i −0.353676 + 0.146497i −0.552446 0.833549i \(-0.686305\pi\)
0.198770 + 0.980046i \(0.436305\pi\)
\(150\) 0 0
\(151\) 48.5998 48.5998i 0.321853 0.321853i −0.527625 0.849478i \(-0.676917\pi\)
0.849478 + 0.527625i \(0.176917\pi\)
\(152\) 0 0
\(153\) −0.758099 + 0.758099i −0.00495490 + 0.00495490i
\(154\) 0 0
\(155\) −222.412 + 92.1259i −1.43491 + 0.594361i
\(156\) 0 0
\(157\) 121.622 + 50.3774i 0.774661 + 0.320875i 0.734759 0.678328i \(-0.237295\pi\)
0.0399023 + 0.999204i \(0.487295\pi\)
\(158\) 0 0
\(159\) 91.0803i 0.572832i
\(160\) 0 0
\(161\) −126.845 −0.787860
\(162\) 0 0
\(163\) 13.0161 31.4236i 0.0798533 0.192783i −0.878911 0.476986i \(-0.841729\pi\)
0.958764 + 0.284203i \(0.0917291\pi\)
\(164\) 0 0
\(165\) −31.8962 77.0043i −0.193310 0.466692i
\(166\) 0 0
\(167\) 138.734 + 138.734i 0.830744 + 0.830744i 0.987619 0.156875i \(-0.0501419\pi\)
−0.156875 + 0.987619i \(0.550142\pi\)
\(168\) 0 0
\(169\) −221.190 221.190i −1.30881 1.30881i
\(170\) 0 0
\(171\) −3.65445 8.82263i −0.0213711 0.0515943i
\(172\) 0 0
\(173\) −69.7574 + 168.409i −0.403222 + 0.973464i 0.583656 + 0.812001i \(0.301621\pi\)
−0.986879 + 0.161464i \(0.948379\pi\)
\(174\) 0 0
\(175\) −205.064 −1.17179
\(176\) 0 0
\(177\) 106.852i 0.603682i
\(178\) 0 0
\(179\) −45.0027 18.6407i −0.251411 0.104138i 0.253419 0.967357i \(-0.418445\pi\)
−0.504830 + 0.863219i \(0.668445\pi\)
\(180\) 0 0
\(181\) 118.928 49.2615i 0.657060 0.272163i −0.0291408 0.999575i \(-0.509277\pi\)
0.686201 + 0.727412i \(0.259277\pi\)
\(182\) 0 0
\(183\) −152.362 + 152.362i −0.832577 + 0.832577i
\(184\) 0 0
\(185\) −75.6423 + 75.6423i −0.408877 + 0.408877i
\(186\) 0 0
\(187\) 5.96206 2.46956i 0.0318827 0.0132062i
\(188\) 0 0
\(189\) 152.251 + 63.0643i 0.805559 + 0.333674i
\(190\) 0 0
\(191\) 179.282i 0.938649i −0.883026 0.469325i \(-0.844497\pi\)
0.883026 0.469325i \(-0.155503\pi\)
\(192\) 0 0
\(193\) 179.924 0.932249 0.466125 0.884719i \(-0.345650\pi\)
0.466125 + 0.884719i \(0.345650\pi\)
\(194\) 0 0
\(195\) 187.815 453.425i 0.963153 2.32526i
\(196\) 0 0
\(197\) −93.2938 225.231i −0.473573 1.14331i −0.962573 0.271022i \(-0.912638\pi\)
0.489000 0.872284i \(-0.337362\pi\)
\(198\) 0 0
\(199\) 131.782 + 131.782i 0.662220 + 0.662220i 0.955903 0.293683i \(-0.0948810\pi\)
−0.293683 + 0.955903i \(0.594881\pi\)
\(200\) 0 0
\(201\) 56.2446 + 56.2446i 0.279824 + 0.279824i
\(202\) 0 0
\(203\) −16.5239 39.8923i −0.0813987 0.196514i
\(204\) 0 0
\(205\) 77.6526 187.470i 0.378793 0.914487i
\(206\) 0 0
\(207\) −13.2746 −0.0641286
\(208\) 0 0
\(209\) 57.4807i 0.275027i
\(210\) 0 0
\(211\) 182.694 + 75.6743i 0.865848 + 0.358646i 0.770992 0.636845i \(-0.219761\pi\)
0.0948559 + 0.995491i \(0.469761\pi\)
\(212\) 0 0
\(213\) 121.799 50.4506i 0.571824 0.236857i
\(214\) 0 0
\(215\) 443.391 443.391i 2.06228 2.06228i
\(216\) 0 0
\(217\) −130.429 + 130.429i −0.601056 + 0.601056i
\(218\) 0 0
\(219\) −107.986 + 44.7293i −0.493087 + 0.204243i
\(220\) 0 0
\(221\) 35.1064 + 14.5416i 0.158853 + 0.0657989i
\(222\) 0 0
\(223\) 175.414i 0.786612i 0.919408 + 0.393306i \(0.128669\pi\)
−0.919408 + 0.393306i \(0.871331\pi\)
\(224\) 0 0
\(225\) −21.4603 −0.0953792
\(226\) 0 0
\(227\) −157.825 + 381.024i −0.695265 + 1.67852i 0.0386277 + 0.999254i \(0.487701\pi\)
−0.733893 + 0.679265i \(0.762299\pi\)
\(228\) 0 0
\(229\) 57.0597 + 137.754i 0.249169 + 0.601547i 0.998134 0.0610623i \(-0.0194488\pi\)
−0.748965 + 0.662610i \(0.769449\pi\)
\(230\) 0 0
\(231\) −45.1577 45.1577i −0.195488 0.195488i
\(232\) 0 0
\(233\) 275.512 + 275.512i 1.18246 + 1.18246i 0.979106 + 0.203349i \(0.0651826\pi\)
0.203349 + 0.979106i \(0.434817\pi\)
\(234\) 0 0
\(235\) 48.1251 + 116.184i 0.204788 + 0.494401i
\(236\) 0 0
\(237\) −24.8212 + 59.9236i −0.104731 + 0.252842i
\(238\) 0 0
\(239\) 63.0374 0.263755 0.131877 0.991266i \(-0.457899\pi\)
0.131877 + 0.991266i \(0.457899\pi\)
\(240\) 0 0
\(241\) 194.368i 0.806507i 0.915088 + 0.403253i \(0.132121\pi\)
−0.915088 + 0.403253i \(0.867879\pi\)
\(242\) 0 0
\(243\) 30.8408 + 12.7747i 0.126917 + 0.0525708i
\(244\) 0 0
\(245\) 99.7526 41.3189i 0.407154 0.168649i
\(246\) 0 0
\(247\) −239.330 + 239.330i −0.968949 + 0.968949i
\(248\) 0 0
\(249\) 273.165 273.165i 1.09705 1.09705i
\(250\) 0 0
\(251\) 317.091 131.343i 1.26331 0.523281i 0.352387 0.935854i \(-0.385370\pi\)
0.910924 + 0.412574i \(0.135370\pi\)
\(252\) 0 0
\(253\) 73.8205 + 30.5774i 0.291781 + 0.120859i
\(254\) 0 0
\(255\) 38.7067i 0.151791i
\(256\) 0 0
\(257\) −180.756 −0.703330 −0.351665 0.936126i \(-0.614384\pi\)
−0.351665 + 0.936126i \(0.614384\pi\)
\(258\) 0 0
\(259\) −31.3666 + 75.7256i −0.121106 + 0.292377i
\(260\) 0 0
\(261\) −1.72926 4.17480i −0.00662552 0.0159954i
\(262\) 0 0
\(263\) −266.626 266.626i −1.01379 1.01379i −0.999904 0.0138830i \(-0.995581\pi\)
−0.0138830 0.999904i \(-0.504419\pi\)
\(264\) 0 0
\(265\) −171.823 171.823i −0.648390 0.648390i
\(266\) 0 0
\(267\) −95.6146 230.834i −0.358107 0.864547i
\(268\) 0 0
\(269\) −156.911 + 378.816i −0.583311 + 1.40824i 0.306483 + 0.951876i \(0.400848\pi\)
−0.889794 + 0.456362i \(0.849152\pi\)
\(270\) 0 0
\(271\) 323.931 1.19532 0.597659 0.801750i \(-0.296098\pi\)
0.597659 + 0.801750i \(0.296098\pi\)
\(272\) 0 0
\(273\) 376.043i 1.37745i
\(274\) 0 0
\(275\) 119.341 + 49.4328i 0.433969 + 0.179756i
\(276\) 0 0
\(277\) −289.883 + 120.073i −1.04651 + 0.433478i −0.838644 0.544680i \(-0.816651\pi\)
−0.207864 + 0.978158i \(0.566651\pi\)
\(278\) 0 0
\(279\) −13.6497 + 13.6497i −0.0489235 + 0.0489235i
\(280\) 0 0
\(281\) 297.826 297.826i 1.05988 1.05988i 0.0617901 0.998089i \(-0.480319\pi\)
0.998089 0.0617901i \(-0.0196809\pi\)
\(282\) 0 0
\(283\) 132.389 54.8372i 0.467804 0.193771i −0.136314 0.990666i \(-0.543526\pi\)
0.604118 + 0.796895i \(0.293526\pi\)
\(284\) 0 0
\(285\) −318.525 131.937i −1.11763 0.462938i
\(286\) 0 0
\(287\) 155.476i 0.541729i
\(288\) 0 0
\(289\) 286.003 0.989630
\(290\) 0 0
\(291\) −77.4455 + 186.970i −0.266136 + 0.642509i
\(292\) 0 0
\(293\) 18.1180 + 43.7407i 0.0618361 + 0.149286i 0.951777 0.306790i \(-0.0992548\pi\)
−0.889941 + 0.456075i \(0.849255\pi\)
\(294\) 0 0
\(295\) −201.576 201.576i −0.683309 0.683309i
\(296\) 0 0
\(297\) −73.4033 73.4033i −0.247149 0.247149i
\(298\) 0 0
\(299\) 180.050 + 434.678i 0.602172 + 1.45377i
\(300\) 0 0
\(301\) 183.861 443.879i 0.610833 1.47468i
\(302\) 0 0
\(303\) −79.2984 −0.261711
\(304\) 0 0
\(305\) 574.861i 1.88479i
\(306\) 0 0
\(307\) −532.332 220.499i −1.73398 0.718239i −0.999202 0.0399320i \(-0.987286\pi\)
−0.734779 0.678307i \(-0.762714\pi\)
\(308\) 0 0
\(309\) −441.490 + 182.871i −1.42877 + 0.591816i
\(310\) 0 0
\(311\) −383.582 + 383.582i −1.23338 + 1.23338i −0.270725 + 0.962657i \(0.587263\pi\)
−0.962657 + 0.270725i \(0.912737\pi\)
\(312\) 0 0
\(313\) −362.165 + 362.165i −1.15708 + 1.15708i −0.171974 + 0.985101i \(0.555015\pi\)
−0.985101 + 0.171974i \(0.944985\pi\)
\(314\) 0 0
\(315\) −26.1514 + 10.8323i −0.0830204 + 0.0343882i
\(316\) 0 0
\(317\) −487.277 201.837i −1.53715 0.636709i −0.556215 0.831038i \(-0.687747\pi\)
−0.980936 + 0.194329i \(0.937747\pi\)
\(318\) 0 0
\(319\) 27.1995i 0.0852648i
\(320\) 0 0
\(321\) 163.579 0.509592
\(322\) 0 0
\(323\) 10.2152 24.6618i 0.0316261 0.0763523i
\(324\) 0 0
\(325\) 291.076 + 702.719i 0.895618 + 2.16221i
\(326\) 0 0
\(327\) 154.208 + 154.208i 0.471584 + 0.471584i
\(328\) 0 0
\(329\) 68.1341 + 68.1341i 0.207095 + 0.207095i
\(330\) 0 0
\(331\) −20.5475 49.6062i −0.0620772 0.149868i 0.889797 0.456356i \(-0.150846\pi\)
−0.951874 + 0.306489i \(0.900846\pi\)
\(332\) 0 0
\(333\) −3.28257 + 7.92483i −0.00985757 + 0.0237983i
\(334\) 0 0
\(335\) −212.211 −0.633466
\(336\) 0 0
\(337\) 627.680i 1.86255i 0.364315 + 0.931276i \(0.381303\pi\)
−0.364315 + 0.931276i \(0.618697\pi\)
\(338\) 0 0
\(339\) 348.072 + 144.176i 1.02676 + 0.425299i
\(340\) 0 0
\(341\) 107.347 44.4648i 0.314802 0.130395i
\(342\) 0 0
\(343\) 263.539 263.539i 0.768336 0.768336i
\(344\) 0 0
\(345\) −338.885 + 338.885i −0.982275 + 0.982275i
\(346\) 0 0
\(347\) −320.625 + 132.807i −0.923992 + 0.382730i −0.793396 0.608706i \(-0.791689\pi\)
−0.130596 + 0.991436i \(0.541689\pi\)
\(348\) 0 0
\(349\) 14.5498 + 6.02674i 0.0416901 + 0.0172686i 0.403431 0.915010i \(-0.367818\pi\)
−0.361741 + 0.932279i \(0.617818\pi\)
\(350\) 0 0
\(351\) 611.254i 1.74146i
\(352\) 0 0
\(353\) 283.828 0.804045 0.402023 0.915630i \(-0.368307\pi\)
0.402023 + 0.915630i \(0.368307\pi\)
\(354\) 0 0
\(355\) −134.598 + 324.949i −0.379150 + 0.915349i
\(356\) 0 0
\(357\) 11.3494 + 27.3999i 0.0317911 + 0.0767505i
\(358\) 0 0
\(359\) −388.417 388.417i −1.08194 1.08194i −0.996329 0.0856121i \(-0.972715\pi\)
−0.0856121 0.996329i \(-0.527285\pi\)
\(360\) 0 0
\(361\) −87.1393 87.1393i −0.241383 0.241383i
\(362\) 0 0
\(363\) −118.655 286.458i −0.326872 0.789140i
\(364\) 0 0
\(365\) 119.334 288.098i 0.326943 0.789309i
\(366\) 0 0
\(367\) 529.617 1.44310 0.721548 0.692364i \(-0.243431\pi\)
0.721548 + 0.692364i \(0.243431\pi\)
\(368\) 0 0
\(369\) 16.2709i 0.0440945i
\(370\) 0 0
\(371\) −172.013 71.2499i −0.463646 0.192048i
\(372\) 0 0
\(373\) −36.8515 + 15.2644i −0.0987975 + 0.0409233i −0.431535 0.902096i \(-0.642028\pi\)
0.332737 + 0.943020i \(0.392028\pi\)
\(374\) 0 0
\(375\) −152.601 + 152.601i −0.406935 + 0.406935i
\(376\) 0 0
\(377\) −113.249 + 113.249i −0.300396 + 0.300396i
\(378\) 0 0
\(379\) 463.955 192.176i 1.22415 0.507061i 0.325426 0.945567i \(-0.394492\pi\)
0.898728 + 0.438506i \(0.144492\pi\)
\(380\) 0 0
\(381\) 150.734 + 62.4361i 0.395627 + 0.163874i
\(382\) 0 0
\(383\) 304.650i 0.795432i 0.917509 + 0.397716i \(0.130197\pi\)
−0.917509 + 0.397716i \(0.869803\pi\)
\(384\) 0 0
\(385\) 170.380 0.442547
\(386\) 0 0
\(387\) 19.2414 46.4528i 0.0497193 0.120033i
\(388\) 0 0
\(389\) −72.6039 175.281i −0.186642 0.450594i 0.802667 0.596428i \(-0.203414\pi\)
−0.989309 + 0.145833i \(0.953414\pi\)
\(390\) 0 0
\(391\) −26.2382 26.2382i −0.0671053 0.0671053i
\(392\) 0 0
\(393\) −210.024 210.024i −0.534413 0.534413i
\(394\) 0 0
\(395\) −66.2209 159.871i −0.167648 0.404737i
\(396\) 0 0
\(397\) 79.4405 191.786i 0.200102 0.483089i −0.791694 0.610917i \(-0.790801\pi\)
0.991796 + 0.127829i \(0.0408007\pi\)
\(398\) 0 0
\(399\) −264.165 −0.662068
\(400\) 0 0
\(401\) 58.9969i 0.147124i −0.997291 0.0735622i \(-0.976563\pi\)
0.997291 0.0735622i \(-0.0234368\pi\)
\(402\) 0 0
\(403\) 632.095 + 261.822i 1.56847 + 0.649683i
\(404\) 0 0
\(405\) 535.471 221.800i 1.32215 0.547653i
\(406\) 0 0
\(407\) 36.5089 36.5089i 0.0897025 0.0897025i
\(408\) 0 0
\(409\) 110.309 110.309i 0.269704 0.269704i −0.559277 0.828981i \(-0.688921\pi\)
0.828981 + 0.559277i \(0.188921\pi\)
\(410\) 0 0
\(411\) 236.940 98.1437i 0.576496 0.238792i
\(412\) 0 0
\(413\) −201.798 83.5875i −0.488615 0.202391i
\(414\) 0 0
\(415\) 1030.65i 2.48350i
\(416\) 0 0
\(417\) −88.0117 −0.211059
\(418\) 0 0
\(419\) −4.61960 + 11.1527i −0.0110253 + 0.0266174i −0.929296 0.369335i \(-0.879585\pi\)
0.918271 + 0.395952i \(0.129585\pi\)
\(420\) 0 0
\(421\) 32.5432 + 78.5662i 0.0772998 + 0.186618i 0.957805 0.287418i \(-0.0927967\pi\)
−0.880506 + 0.474036i \(0.842797\pi\)
\(422\) 0 0
\(423\) 7.13037 + 7.13037i 0.0168567 + 0.0168567i
\(424\) 0 0
\(425\) −42.4177 42.4177i −0.0998064 0.0998064i
\(426\) 0 0
\(427\) −168.558 406.936i −0.394750 0.953012i
\(428\) 0 0
\(429\) −90.6492 + 218.847i −0.211304 + 0.510132i
\(430\) 0 0
\(431\) 201.982 0.468636 0.234318 0.972160i \(-0.424714\pi\)
0.234318 + 0.972160i \(0.424714\pi\)
\(432\) 0 0
\(433\) 643.404i 1.48592i −0.669334 0.742961i \(-0.733421\pi\)
0.669334 0.742961i \(-0.266579\pi\)
\(434\) 0 0
\(435\) −150.724 62.4318i −0.346491 0.143521i
\(436\) 0 0
\(437\) 305.355 126.482i 0.698753 0.289433i
\(438\) 0 0
\(439\) 218.953 218.953i 0.498753 0.498753i −0.412296 0.911050i \(-0.635273\pi\)
0.911050 + 0.412296i \(0.135273\pi\)
\(440\) 0 0
\(441\) 6.12194 6.12194i 0.0138819 0.0138819i
\(442\) 0 0
\(443\) −275.767 + 114.227i −0.622499 + 0.257848i −0.671562 0.740948i \(-0.734376\pi\)
0.0490630 + 0.998796i \(0.484376\pi\)
\(444\) 0 0
\(445\) 615.847 + 255.092i 1.38392 + 0.573240i
\(446\) 0 0
\(447\) 165.126i 0.369410i
\(448\) 0 0
\(449\) −264.162 −0.588334 −0.294167 0.955754i \(-0.595042\pi\)
−0.294167 + 0.955754i \(0.595042\pi\)
\(450\) 0 0
\(451\) −37.4792 + 90.4828i −0.0831024 + 0.200627i
\(452\) 0 0
\(453\) −76.1428 183.825i −0.168086 0.405795i
\(454\) 0 0
\(455\) 709.407 + 709.407i 1.55914 + 1.55914i
\(456\) 0 0
\(457\) 324.484 + 324.484i 0.710030 + 0.710030i 0.966541 0.256511i \(-0.0825731\pi\)
−0.256511 + 0.966541i \(0.582573\pi\)
\(458\) 0 0
\(459\) 18.4483 + 44.5382i 0.0401925 + 0.0970332i
\(460\) 0 0
\(461\) −46.5472 + 112.375i −0.100970 + 0.243763i −0.966290 0.257457i \(-0.917115\pi\)
0.865320 + 0.501220i \(0.167115\pi\)
\(462\) 0 0
\(463\) 602.217 1.30069 0.650343 0.759641i \(-0.274625\pi\)
0.650343 + 0.759641i \(0.274625\pi\)
\(464\) 0 0
\(465\) 696.918i 1.49875i
\(466\) 0 0
\(467\) −327.171 135.519i −0.700580 0.290190i 0.00382006 0.999993i \(-0.498784\pi\)
−0.704400 + 0.709803i \(0.748784\pi\)
\(468\) 0 0
\(469\) −150.221 + 62.2237i −0.320301 + 0.132673i
\(470\) 0 0
\(471\) 269.477 269.477i 0.572137 0.572137i
\(472\) 0 0
\(473\) −214.003 + 214.003i −0.452439 + 0.452439i
\(474\) 0 0
\(475\) 493.650 204.477i 1.03926 0.430477i
\(476\) 0 0
\(477\) −18.0014 7.45644i −0.0377389 0.0156320i
\(478\) 0 0
\(479\) 151.023i 0.315289i −0.987496 0.157644i \(-0.949610\pi\)
0.987496 0.157644i \(-0.0503900\pi\)
\(480\) 0 0
\(481\) 304.022 0.632062
\(482\) 0 0
\(483\) −140.525 + 339.258i −0.290943 + 0.702398i
\(484\) 0 0
\(485\) −206.618 498.821i −0.426017 1.02850i
\(486\) 0 0
\(487\) −382.894 382.894i −0.786231 0.786231i 0.194643 0.980874i \(-0.437645\pi\)
−0.980874 + 0.194643i \(0.937645\pi\)
\(488\) 0 0
\(489\) −69.6251 69.6251i −0.142383 0.142383i
\(490\) 0 0
\(491\) −205.776 496.786i −0.419095 1.01178i −0.982610 0.185679i \(-0.940552\pi\)
0.563516 0.826105i \(-0.309448\pi\)
\(492\) 0 0
\(493\) 4.83378 11.6698i 0.00980483 0.0236709i
\(494\) 0 0
\(495\) 17.8306 0.0360215
\(496\) 0 0
\(497\) 269.493i 0.542239i
\(498\) 0 0
\(499\) −604.867 250.544i −1.21216 0.502093i −0.317250 0.948342i \(-0.602760\pi\)
−0.894909 + 0.446249i \(0.852760\pi\)
\(500\) 0 0
\(501\) 524.752 217.359i 1.04741 0.433851i
\(502\) 0 0
\(503\) −324.203 + 324.203i −0.644539 + 0.644539i −0.951668 0.307129i \(-0.900632\pi\)
0.307129 + 0.951668i \(0.400632\pi\)
\(504\) 0 0
\(505\) 149.597 149.597i 0.296231 0.296231i
\(506\) 0 0
\(507\) −836.633 + 346.545i −1.65016 + 0.683521i
\(508\) 0 0
\(509\) 734.614 + 304.287i 1.44325 + 0.597813i 0.960584 0.277991i \(-0.0896686\pi\)
0.482666 + 0.875805i \(0.339669\pi\)
\(510\) 0 0
\(511\) 238.931i 0.467575i
\(512\) 0 0
\(513\) −429.397 −0.837031
\(514\) 0 0
\(515\) 487.886 1177.86i 0.947351 2.28711i
\(516\) 0 0
\(517\) −23.2277 56.0766i −0.0449278 0.108465i
\(518\) 0 0
\(519\) 373.143 + 373.143i 0.718966 + 0.718966i
\(520\) 0 0
\(521\) −16.7805 16.7805i −0.0322082 0.0322082i 0.690819 0.723027i \(-0.257250\pi\)
−0.723027 + 0.690819i \(0.757250\pi\)
\(522\) 0 0
\(523\) 250.400 + 604.519i 0.478776 + 1.15587i 0.960183 + 0.279371i \(0.0901259\pi\)
−0.481407 + 0.876497i \(0.659874\pi\)
\(524\) 0 0
\(525\) −227.179 + 548.459i −0.432722 + 1.04468i
\(526\) 0 0
\(527\) −53.9589 −0.102389
\(528\) 0 0
\(529\) 69.5595i 0.131492i
\(530\) 0 0
\(531\) −21.1185 8.74759i −0.0397713 0.0164738i
\(532\) 0 0
\(533\) −532.791 + 220.689i −0.999607 + 0.414051i
\(534\) 0 0
\(535\) −308.593 + 308.593i −0.576809 + 0.576809i
\(536\) 0 0
\(537\) −99.7121 + 99.7121i −0.185684 + 0.185684i
\(538\) 0 0
\(539\) −48.1458 + 19.9427i −0.0893244 + 0.0369994i
\(540\) 0 0
\(541\) −870.996 360.778i −1.60997 0.666873i −0.617192 0.786812i \(-0.711730\pi\)
−0.992781 + 0.119939i \(0.961730\pi\)
\(542\) 0 0
\(543\) 372.656i 0.686291i
\(544\) 0 0
\(545\) −581.827 −1.06757
\(546\) 0 0
\(547\) −36.1835 + 87.3546i −0.0661489 + 0.159698i −0.953497 0.301403i \(-0.902545\pi\)
0.887348 + 0.461100i \(0.152545\pi\)
\(548\) 0 0
\(549\) −17.6400 42.5866i −0.0321311 0.0775713i
\(550\) 0 0
\(551\) 79.5561 + 79.5561i 0.144385 + 0.144385i
\(552\) 0 0
\(553\) −93.7536 93.7536i −0.169536 0.169536i
\(554\) 0 0
\(555\) 118.511 + 286.111i 0.213534 + 0.515516i
\(556\) 0 0
\(557\) 288.342 696.118i 0.517669 1.24976i −0.421663 0.906753i \(-0.638553\pi\)
0.939332 0.343010i \(-0.111447\pi\)
\(558\) 0 0
\(559\) −1782.08 −3.18797
\(560\) 0 0
\(561\) 18.6819i 0.0333010i
\(562\) 0 0
\(563\) 609.320 + 252.389i 1.08227 + 0.448293i 0.851306 0.524669i \(-0.175811\pi\)
0.230968 + 0.972961i \(0.425811\pi\)
\(564\) 0 0
\(565\) −928.629 + 384.651i −1.64359 + 0.680797i
\(566\) 0 0
\(567\) 314.017 314.017i 0.553822 0.553822i
\(568\) 0 0
\(569\) 256.311 256.311i 0.450459 0.450459i −0.445047 0.895507i \(-0.646813\pi\)
0.895507 + 0.445047i \(0.146813\pi\)
\(570\) 0 0
\(571\) −346.136 + 143.374i −0.606193 + 0.251094i −0.664600 0.747199i \(-0.731398\pi\)
0.0584066 + 0.998293i \(0.481398\pi\)
\(572\) 0 0
\(573\) −479.504 198.617i −0.836830 0.346626i
\(574\) 0 0
\(575\) 742.751i 1.29174i
\(576\) 0 0
\(577\) −354.659 −0.614661 −0.307330 0.951603i \(-0.599436\pi\)
−0.307330 + 0.951603i \(0.599436\pi\)
\(578\) 0 0
\(579\) 199.328 481.221i 0.344263 0.831124i
\(580\) 0 0
\(581\) 302.204 + 729.584i 0.520144 + 1.25574i
\(582\) 0 0
\(583\) 82.9309 + 82.9309i 0.142249 + 0.142249i
\(584\) 0 0
\(585\) 74.2408 + 74.2408i 0.126907 + 0.126907i
\(586\) 0 0
\(587\) 230.018 + 555.312i 0.391853 + 0.946018i 0.989536 + 0.144285i \(0.0460882\pi\)
−0.597683 + 0.801733i \(0.703912\pi\)
\(588\) 0 0
\(589\) 183.926 444.038i 0.312269 0.753884i
\(590\) 0 0
\(591\) −705.754 −1.19417
\(592\) 0 0
\(593\) 458.661i 0.773460i −0.922193 0.386730i \(-0.873605\pi\)
0.922193 0.386730i \(-0.126395\pi\)
\(594\) 0 0
\(595\) −73.1008 30.2793i −0.122858 0.0508896i
\(596\) 0 0
\(597\) 498.454 206.467i 0.834932 0.345840i
\(598\) 0 0
\(599\) −265.583 + 265.583i −0.443377 + 0.443377i −0.893145 0.449768i \(-0.851507\pi\)
0.449768 + 0.893145i \(0.351507\pi\)
\(600\) 0 0
\(601\) 466.600 466.600i 0.776373 0.776373i −0.202839 0.979212i \(-0.565017\pi\)
0.979212 + 0.202839i \(0.0650168\pi\)
\(602\) 0 0
\(603\) −15.7209 + 6.51182i −0.0260712 + 0.0107990i
\(604\) 0 0
\(605\) 764.246 + 316.561i 1.26322 + 0.523241i
\(606\) 0 0
\(607\) 90.4302i 0.148979i −0.997222 0.0744894i \(-0.976267\pi\)
0.997222 0.0744894i \(-0.0237327\pi\)
\(608\) 0 0
\(609\) −125.001 −0.205256
\(610\) 0 0
\(611\) 136.772 330.197i 0.223849 0.540420i
\(612\) 0 0
\(613\) 63.5389 + 153.397i 0.103652 + 0.250239i 0.967194 0.254038i \(-0.0817589\pi\)
−0.863542 + 0.504277i \(0.831759\pi\)
\(614\) 0 0
\(615\) −415.376 415.376i −0.675408 0.675408i
\(616\) 0 0
\(617\) 181.842 + 181.842i 0.294720 + 0.294720i 0.838942 0.544221i \(-0.183175\pi\)
−0.544221 + 0.838942i \(0.683175\pi\)
\(618\) 0 0
\(619\) 388.636 + 938.250i 0.627844 + 1.51575i 0.842296 + 0.539016i \(0.181204\pi\)
−0.214451 + 0.976735i \(0.568796\pi\)
\(620\) 0 0
\(621\) −228.422 + 551.460i −0.367829 + 0.888019i
\(622\) 0 0
\(623\) 510.746 0.819817
\(624\) 0 0
\(625\) 290.538i 0.464860i
\(626\) 0 0
\(627\) 153.737 + 63.6798i 0.245194 + 0.101563i
\(628\) 0 0
\(629\) −22.1522 + 9.17573i −0.0352181 + 0.0145878i
\(630\) 0 0
\(631\) 241.593 241.593i 0.382873 0.382873i −0.489263 0.872136i \(-0.662734\pi\)
0.872136 + 0.489263i \(0.162734\pi\)
\(632\) 0 0
\(633\) 404.793 404.793i 0.639484 0.639484i
\(634\) 0 0
\(635\) −402.146 + 166.574i −0.633301 + 0.262322i
\(636\) 0 0
\(637\) −283.498 117.429i −0.445051 0.184346i
\(638\) 0 0
\(639\) 28.2029i 0.0441361i
\(640\) 0 0
\(641\) −385.038 −0.600684 −0.300342 0.953832i \(-0.597101\pi\)
−0.300342 + 0.953832i \(0.597101\pi\)
\(642\) 0 0
\(643\) −144.485 + 348.818i −0.224705 + 0.542486i −0.995518 0.0945760i \(-0.969850\pi\)
0.770813 + 0.637062i \(0.219850\pi\)
\(644\) 0 0
\(645\) −694.674 1677.09i −1.07701 2.60014i
\(646\) 0 0
\(647\) 580.537 + 580.537i 0.897276 + 0.897276i 0.995194 0.0979186i \(-0.0312185\pi\)
−0.0979186 + 0.995194i \(0.531218\pi\)
\(648\) 0 0
\(649\) 97.2911 + 97.2911i 0.149909 + 0.149909i
\(650\) 0 0
\(651\) 204.347 + 493.338i 0.313898 + 0.757816i
\(652\) 0 0
\(653\) −467.055 + 1127.57i −0.715246 + 1.72676i −0.0287882 + 0.999586i \(0.509165\pi\)
−0.686457 + 0.727170i \(0.740835\pi\)
\(654\) 0 0
\(655\) 792.423 1.20981
\(656\) 0 0
\(657\) 25.0046i 0.0380587i
\(658\) 0 0
\(659\) 287.435 + 119.060i 0.436169 + 0.180667i 0.589953 0.807437i \(-0.299146\pi\)
−0.153784 + 0.988104i \(0.549146\pi\)
\(660\) 0 0
\(661\) −478.625 + 198.253i −0.724093 + 0.299929i −0.714122 0.700021i \(-0.753174\pi\)
−0.00997082 + 0.999950i \(0.503174\pi\)
\(662\) 0 0
\(663\) 77.7851 77.7851i 0.117323 0.117323i
\(664\) 0 0
\(665\) 498.348 498.348i 0.749396 0.749396i
\(666\) 0 0
\(667\) 144.492 59.8505i 0.216629 0.0897309i
\(668\) 0 0
\(669\) 469.160 + 194.332i 0.701285 + 0.290482i
\(670\) 0 0
\(671\) 277.458i 0.413499i
\(672\) 0 0
\(673\) 831.026 1.23481 0.617405 0.786646i \(-0.288184\pi\)
0.617405 + 0.786646i \(0.288184\pi\)
\(674\) 0 0
\(675\) −369.277 + 891.513i −0.547077 + 1.32076i
\(676\) 0 0
\(677\) −16.6301 40.1487i −0.0245644 0.0593038i 0.911121 0.412138i \(-0.135218\pi\)
−0.935686 + 0.352834i \(0.885218\pi\)
\(678\) 0 0
\(679\) −292.524 292.524i −0.430816 0.430816i
\(680\) 0 0
\(681\) 844.232 + 844.232i 1.23969 + 1.23969i
\(682\) 0 0
\(683\) −411.955 994.547i −0.603155 1.45614i −0.870317 0.492493i \(-0.836086\pi\)
0.267162 0.963652i \(-0.413914\pi\)
\(684\) 0 0
\(685\) −261.839 + 632.136i −0.382247 + 0.922827i
\(686\) 0 0
\(687\) 431.648 0.628309
\(688\) 0 0
\(689\) 690.593i 1.00231i
\(690\) 0 0
\(691\) −657.136 272.195i −0.950993 0.393914i −0.147389 0.989079i \(-0.547087\pi\)
−0.803604 + 0.595164i \(0.797087\pi\)
\(692\) 0 0
\(693\) 12.6220 5.22822i 0.0182136 0.00754433i
\(694\) 0 0
\(695\) 166.034 166.034i 0.238898 0.238898i
\(696\) 0 0
\(697\) 32.1605 32.1605i 0.0461413 0.0461413i
\(698\) 0 0
\(699\) 1042.10 431.653i 1.49085 0.617530i
\(700\) 0 0
\(701\) 57.0623 + 23.6360i 0.0814012 + 0.0337175i 0.423013 0.906124i \(-0.360973\pi\)
−0.341611 + 0.939841i \(0.610973\pi\)
\(702\) 0 0
\(703\) 213.571i 0.303799i
\(704\) 0 0
\(705\) 364.059 0.516396
\(706\) 0 0
\(707\) 62.0332 149.761i 0.0877414 0.211827i
\(708\) 0 0
\(709\) −167.767 405.025i −0.236625 0.571262i 0.760305 0.649566i \(-0.225049\pi\)
−0.996930 + 0.0783041i \(0.975049\pi\)
\(710\) 0 0
\(711\) −9.81149 9.81149i −0.0137996 0.0137996i
\(712\) 0 0
\(713\) −472.421 472.421i −0.662582 0.662582i
\(714\) 0 0
\(715\) −241.845 583.865i −0.338245 0.816595i
\(716\) 0 0
\(717\) 69.8358 168.598i 0.0973999 0.235144i
\(718\) 0 0
\(719\) −1154.30 −1.60542 −0.802712 0.596367i \(-0.796610\pi\)
−0.802712 + 0.596367i \(0.796610\pi\)
\(720\) 0 0
\(721\) 976.846i 1.35485i
\(722\) 0 0
\(723\) 519.853 + 215.330i 0.719022 + 0.297829i
\(724\) 0 0
\(725\) 233.592 96.7569i 0.322195 0.133458i
\(726\) 0 0
\(727\) 644.722 644.722i 0.886825 0.886825i −0.107392 0.994217i \(-0.534250\pi\)
0.994217 + 0.107392i \(0.0342500\pi\)
\(728\) 0 0
\(729\) 545.902 545.902i 0.748837 0.748837i
\(730\) 0 0
\(731\) 129.849 53.7851i 0.177632 0.0735775i
\(732\) 0 0
\(733\) 508.297 + 210.544i 0.693448 + 0.287235i 0.701436 0.712733i \(-0.252543\pi\)
−0.00798801 + 0.999968i \(0.502543\pi\)
\(734\) 0 0
\(735\) 312.571i 0.425267i
\(736\) 0 0
\(737\) 102.424 0.138974
\(738\) 0 0
\(739\) 479.243 1157.00i 0.648503 1.56562i −0.166421 0.986055i \(-0.553221\pi\)
0.814923 0.579569i \(-0.196779\pi\)
\(740\) 0 0
\(741\) 374.967 + 905.249i 0.506028 + 1.22166i
\(742\) 0 0
\(743\) 106.350 + 106.350i 0.143136 + 0.143136i 0.775044 0.631908i \(-0.217728\pi\)
−0.631908 + 0.775044i \(0.717728\pi\)
\(744\) 0 0
\(745\) −311.511 311.511i −0.418136 0.418136i
\(746\) 0 0
\(747\) 31.6262 + 76.3524i 0.0423376 + 0.102212i
\(748\) 0 0
\(749\) −127.964 + 308.932i −0.170846 + 0.412460i
\(750\) 0 0
\(751\) 186.540 0.248389 0.124195 0.992258i \(-0.460365\pi\)
0.124195 + 0.992258i \(0.460365\pi\)
\(752\) 0 0
\(753\) 993.594i 1.31951i
\(754\) 0 0
\(755\) 490.430 + 203.143i 0.649577 + 0.269064i
\(756\) 0 0
\(757\) 1190.57 493.151i 1.57275 0.651454i 0.585506 0.810668i \(-0.300896\pi\)
0.987244 + 0.159214i \(0.0508959\pi\)
\(758\) 0 0
\(759\) 163.564 163.564i 0.215499 0.215499i
\(760\) 0 0
\(761\) −1042.65 + 1042.65i −1.37010 + 1.37010i −0.509823 + 0.860279i \(0.670289\pi\)
−0.860279 + 0.509823i \(0.829711\pi\)
\(762\) 0 0
\(763\) −411.867 + 170.601i −0.539800 + 0.223592i
\(764\) 0 0
\(765\) −7.65014 3.16879i −0.0100002 0.00414221i
\(766\) 0 0
\(767\) 810.175i 1.05629i
\(768\) 0 0
\(769\) 362.542 0.471446 0.235723 0.971820i \(-0.424254\pi\)
0.235723 + 0.971820i \(0.424254\pi\)
\(770\) 0 0
\(771\) −200.250 + 483.445i −0.259727 + 0.627037i
\(772\) 0 0
\(773\) 259.669 + 626.896i 0.335924 + 0.810991i 0.998098 + 0.0616419i \(0.0196337\pi\)
−0.662175 + 0.749350i \(0.730366\pi\)
\(774\) 0 0
\(775\) −763.736 763.736i −0.985465 0.985465i
\(776\) 0 0
\(777\) 167.785 + 167.785i 0.215939 + 0.215939i
\(778\) 0 0
\(779\) 155.031 + 374.278i 0.199013 + 0.480459i
\(780\) 0 0
\(781\) 64.9641 156.837i 0.0831807 0.200816i
\(782\) 0 0
\(783\) −203.188 −0.259499
\(784\) 0 0
\(785\) 1016.74i 1.29521i
\(786\) 0 0
\(787\) 148.037 + 61.3188i 0.188103 + 0.0779147i 0.474747 0.880122i \(-0.342540\pi\)
−0.286644 + 0.958037i \(0.592540\pi\)
\(788\) 0 0
\(789\) −1008.49 + 417.731i −1.27819 + 0.529444i
\(790\) 0 0
\(791\) −544.577 + 544.577i −0.688466 + 0.688466i
\(792\) 0 0
\(793\) −1155.24 + 1155.24i −1.45680 + 1.45680i
\(794\) 0 0
\(795\) −649.909 + 269.201i −0.817495 + 0.338618i
\(796\) 0 0
\(797\) −173.793 71.9875i −0.218059 0.0903231i 0.270980 0.962585i \(-0.412652\pi\)
−0.4