Properties

Label 128.3.h.a.79.5
Level $128$
Weight $3$
Character 128.79
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 79.5
Character \(\chi\) \(=\) 128.79
Dual form 128.3.h.a.47.5

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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 0.993868 + 0.110570i \(0.0352677\pi\)
−0.624586 + 0.780956i \(0.714732\pi\)
\(4\) 0 0
\(5\) 2.95565 7.13556i 0.591129 1.42711i −0.291284 0.956637i \(-0.594083\pi\)
0.882413 0.470475i \(-0.155917\pi\)
\(6\) 0 0
\(7\) 4.18452 4.18452i 0.597788 0.597788i −0.341935 0.939723i \(-0.611082\pi\)
0.939723 + 0.341935i \(0.111082\pi\)
\(8\) 0 0
\(9\) 0.437918 0.437918i 0.0486575 0.0486575i
\(10\) 0 0
\(11\) −1.42655 + 3.44399i −0.129686 + 0.313090i −0.975363 0.220605i \(-0.929197\pi\)
0.845677 + 0.533695i \(0.179197\pi\)
\(12\) 0 0
\(13\) 8.39996 + 20.2793i 0.646151 + 1.55995i 0.818247 + 0.574866i \(0.194946\pi\)
−0.172096 + 0.985080i \(0.555054\pi\)
\(14\) 0 0
\(15\) 22.3590 1.49060
\(16\) 0 0
\(17\) 1.73115i 0.101832i −0.998703 0.0509161i \(-0.983786\pi\)
0.998703 0.0509161i \(-0.0162141\pi\)
\(18\) 0 0
\(19\) −14.2459 + 5.90085i −0.749785 + 0.310571i −0.724654 0.689113i \(-0.758000\pi\)
−0.0251314 + 0.999684i \(0.508000\pi\)
\(20\) 0 0
\(21\) 15.8276 + 6.55601i 0.753696 + 0.312191i
\(22\) 0 0
\(23\) −15.1565 15.1565i −0.658979 0.658979i 0.296159 0.955139i \(-0.404294\pi\)
−0.955139 + 0.296159i \(0.904294\pi\)
\(24\) 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 −0.495869 0.868398i \(-0.665150\pi\)
0.263418 + 0.964682i \(0.415150\pi\)
\(30\) 0 0
\(31\) 31.1695i 1.00547i −0.864442 0.502733i \(-0.832328\pi\)
0.864442 0.502733i \(-0.167672\pi\)
\(32\) 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 −0.835926 0.548843i \(-0.815069\pi\)
0.979179 + 0.202998i \(0.0650686\pi\)
\(38\) 0 0
\(39\) −44.9327 + 44.9327i −1.15212 + 1.15212i
\(40\) 0 0
\(41\) −18.5776 + 18.5776i −0.453111 + 0.453111i −0.896386 0.443275i \(-0.853817\pi\)
0.443275 + 0.896386i \(0.353817\pi\)
\(42\) 0 0
\(43\) −31.0691 + 75.0074i −0.722537 + 1.74436i −0.0565443 + 0.998400i \(0.518008\pi\)
−0.665993 + 0.745958i \(0.731992\pi\)
\(44\) 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 0.0912216 0.995831i \(-0.470923\pi\)
−0.639655 + 0.768662i \(0.720923\pi\)
\(54\) 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 0.0744962 0.997221i \(-0.476265\pi\)
−0.652465 + 0.757819i \(0.726265\pi\)
\(60\) 0 0
\(61\) −68.7647 + 28.4833i −1.12729 + 0.466939i −0.866859 0.498553i \(-0.833865\pi\)
−0.260432 + 0.965492i \(0.583865\pi\)
\(62\) 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 0.825782 0.563990i \(-0.190734\pi\)
−0.982717 + 0.185115i \(0.940734\pi\)
\(68\) 0 0
\(69\) 23.7462 57.3284i 0.344148 0.830847i
\(70\) 0 0
\(71\) 32.2012 32.2012i 0.453538 0.453538i −0.442989 0.896527i \(-0.646082\pi\)
0.896527 + 0.442989i \(0.146082\pi\)
\(72\) 0 0
\(73\) −28.5494 + 28.5494i −0.391088 + 0.391088i −0.875075 0.483987i \(-0.839188\pi\)
0.483987 + 0.875075i \(0.339188\pi\)
\(74\) 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 0.515073 0.857146i \(-0.327765\pi\)
0.970306 + 0.241882i \(0.0777648\pi\)
\(84\) 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 0.961280 0.275572i \(-0.0888672\pi\)
−0.275572 + 0.961280i \(0.588867\pi\)
\(90\) 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 −0.967239 0.253867i \(-0.918298\pi\)
0.863452 + 0.504431i \(0.168298\pi\)
\(102\) 0 0
\(103\) −116.721 + 116.721i −1.13322 + 1.13322i −0.143579 + 0.989639i \(0.545861\pi\)
−0.989639 + 0.143579i \(0.954139\pi\)
\(104\) 0 0
\(105\) 93.5616 93.5616i 0.891063 0.891063i
\(106\) 0 0
\(107\) 21.6236 52.2039i 0.202090 0.487887i −0.790047 0.613046i \(-0.789944\pi\)
0.992137 + 0.125159i \(0.0399440\pi\)
\(108\) 0 0
\(109\) −28.8284 69.5980i −0.264481 0.638514i 0.734725 0.678366i \(-0.237311\pi\)
−0.999206 + 0.0398518i \(0.987311\pi\)
\(110\) 0 0
\(111\) 40.0965 0.361230
\(112\) 0 0
\(113\) 130.141i 1.15169i −0.817559 0.575845i \(-0.804673\pi\)
0.817559 0.575845i \(-0.195327\pi\)
\(114\) 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 \(-0.928780\pi\)
0.975074 0.221882i \(-0.0712200\pi\)
\(128\) 0 0
\(129\) −235.033 −1.82196
\(130\) 0 0
\(131\) 39.2631 + 94.7895i 0.299718 + 0.723584i 0.999953 + 0.00967128i \(0.00307851\pi\)
−0.700235 + 0.713912i \(0.746921\pi\)
\(132\) 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 −0.440506 0.897750i \(-0.645201\pi\)
0.897750 + 0.440506i \(0.145201\pi\)
\(138\) 0 0
\(139\) −11.6343 + 28.0877i −0.0837000 + 0.202070i −0.960188 0.279353i \(-0.909880\pi\)
0.876488 + 0.481423i \(0.159880\pi\)
\(140\) 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 0.198770 0.980046i \(-0.436305\pi\)
−0.552446 + 0.833549i \(0.686305\pi\)
\(150\) 0 0
\(151\) 48.5998 + 48.5998i 0.321853 + 0.321853i 0.849478 0.527625i \(-0.176917\pi\)
−0.527625 + 0.849478i \(0.676917\pi\)
\(152\) 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 0.0399023 0.999204i \(-0.487295\pi\)
0.734759 + 0.678328i \(0.237295\pi\)
\(158\) 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 0.958764 0.284203i \(-0.0917291\pi\)
−0.878911 + 0.476986i \(0.841729\pi\)
\(164\) 0 0
\(165\) −31.8962 + 77.0043i −0.193310 + 0.466692i
\(166\) 0 0
\(167\) 138.734 138.734i 0.830744 0.830744i −0.156875 0.987619i \(-0.550142\pi\)
0.987619 + 0.156875i \(0.0501419\pi\)
\(168\) 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 −0.986879 0.161464i \(-0.948379\pi\)
0.583656 0.812001i \(-0.301621\pi\)
\(174\) 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 −0.504830 0.863219i \(-0.668445\pi\)
0.253419 + 0.967357i \(0.418445\pi\)
\(180\) 0 0
\(181\) 118.928 + 49.2615i 0.657060 + 0.272163i 0.686201 0.727412i \(-0.259277\pi\)
−0.0291408 + 0.999575i \(0.509277\pi\)
\(182\) 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 \(0.155503\pi\)
−0.883026 + 0.469325i \(0.844497\pi\)
\(192\) 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 0.489000 + 0.872284i \(0.337362\pi\)
−0.962573 + 0.271022i \(0.912638\pi\)
\(198\) 0 0
\(199\) 131.782 131.782i 0.662220 0.662220i −0.293683 0.955903i \(-0.594881\pi\)
0.955903 + 0.293683i \(0.0948810\pi\)
\(200\) 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 0.0948559 0.995491i \(-0.469761\pi\)
0.770992 + 0.636845i \(0.219761\pi\)
\(212\) 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 \(-0.871331\pi\)
0.919408 0.393306i \(-0.128669\pi\)
\(224\) 0 0
\(225\) −21.4603 −0.0953792
\(226\) 0 0
\(227\) −157.825 381.024i −0.695265 1.67852i −0.733893 0.679265i \(-0.762299\pi\)
0.0386277 0.999254i \(-0.487701\pi\)
\(228\) 0 0
\(229\) 57.0597 137.754i 0.249169 0.601547i −0.748965 0.662610i \(-0.769449\pi\)
0.998134 + 0.0610623i \(0.0194488\pi\)
\(230\) 0 0
\(231\) −45.1577 + 45.1577i −0.195488 + 0.195488i
\(232\) 0 0
\(233\) 275.512 275.512i 1.18246 1.18246i 0.203349 0.979106i \(-0.434817\pi\)
0.979106 0.203349i \(-0.0651826\pi\)
\(234\) 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 \(-0.867879\pi\)
0.915088 0.403253i \(-0.132121\pi\)
\(242\) 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 0.910924 0.412574i \(-0.135370\pi\)
0.352387 + 0.935854i \(0.385370\pi\)
\(252\) 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 −0.0138830 + 0.999904i \(0.504419\pi\)
−0.999904 + 0.0138830i \(0.995581\pi\)
\(264\) 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 −0.889794 0.456362i \(-0.849152\pi\)
0.306483 0.951876i \(-0.400848\pi\)
\(270\) 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 −0.207864 0.978158i \(-0.566651\pi\)
−0.838644 + 0.544680i \(0.816651\pi\)
\(278\) 0 0
\(279\) −13.6497 13.6497i −0.0489235 0.0489235i
\(280\) 0 0
\(281\) 297.826 + 297.826i 1.05988 + 1.05988i 0.998089 + 0.0617901i \(0.0196809\pi\)
0.0617901 + 0.998089i \(0.480319\pi\)
\(282\) 0 0
\(283\) 132.389 + 54.8372i 0.467804 + 0.193771i 0.604118 0.796895i \(-0.293526\pi\)
−0.136314 + 0.990666i \(0.543526\pi\)
\(284\) 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 −0.889941 0.456075i \(-0.849255\pi\)
0.951777 + 0.306790i \(0.0992548\pi\)
\(294\) 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 −0.734779 + 0.678307i \(0.762714\pi\)
−0.999202 + 0.0399320i \(0.987286\pi\)
\(308\) 0 0
\(309\) −441.490 182.871i −1.42877 0.591816i
\(310\) 0 0
\(311\) −383.582 383.582i −1.23338 1.23338i −0.962657 0.270725i \(-0.912737\pi\)
−0.270725 0.962657i \(-0.587263\pi\)
\(312\) 0 0
\(313\) −362.165 362.165i −1.15708 1.15708i −0.985101 0.171974i \(-0.944985\pi\)
−0.171974 0.985101i \(-0.555015\pi\)
\(314\) 0 0
\(315\) −26.1514 10.8323i −0.0830204 0.0343882i
\(316\) 0 0
\(317\) −487.277 + 201.837i −1.53715 + 0.636709i −0.980936 0.194329i \(-0.937747\pi\)
−0.556215 + 0.831038i \(0.687747\pi\)
\(318\) 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 −0.951874 0.306489i \(-0.900846\pi\)
0.889797 + 0.456356i \(0.150846\pi\)
\(332\) 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 \(-0.618697\pi\)
0.364315 0.931276i \(-0.381303\pi\)
\(338\) 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 −0.130596 0.991436i \(-0.541689\pi\)
−0.793396 + 0.608706i \(0.791689\pi\)
\(348\) 0 0
\(349\) 14.5498 6.02674i 0.0416901 0.0172686i −0.361741 0.932279i \(-0.617818\pi\)
0.403431 + 0.915010i \(0.367818\pi\)
\(350\) 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 −0.0856121 + 0.996329i \(0.527285\pi\)
−0.996329 + 0.0856121i \(0.972715\pi\)
\(360\) 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 0.332737 0.943020i \(-0.392028\pi\)
−0.431535 + 0.902096i \(0.642028\pi\)
\(374\) 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 0.898728 0.438506i \(-0.144492\pi\)
0.325426 + 0.945567i \(0.394492\pi\)
\(380\) 0 0
\(381\) 150.734 62.4361i 0.395627 0.163874i
\(382\) 0 0
\(383\) 304.650i 0.795432i −0.917509 0.397716i \(-0.869803\pi\)
0.917509 0.397716i \(-0.130197\pi\)
\(384\) 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 −0.989309 0.145833i \(-0.953414\pi\)
0.802667 + 0.596428i \(0.203414\pi\)
\(390\) 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 0.991796 0.127829i \(-0.0408007\pi\)
−0.791694 + 0.610917i \(0.790801\pi\)
\(398\) 0 0
\(399\) −264.165 −0.662068
\(400\) 0 0
\(401\) 58.9969i 0.147124i 0.997291 + 0.0735622i \(0.0234368\pi\)
−0.997291 + 0.0735622i \(0.976563\pi\)
\(402\) 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 0.828981 0.559277i \(-0.188921\pi\)
−0.559277 + 0.828981i \(0.688921\pi\)
\(410\) 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 0.918271 0.395952i \(-0.129585\pi\)
−0.929296 + 0.369335i \(0.879585\pi\)
\(420\) 0 0
\(421\) 32.5432 78.5662i 0.0772998 0.186618i −0.880506 0.474036i \(-0.842797\pi\)
0.957805 + 0.287418i \(0.0927967\pi\)
\(422\) 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 \(0.266579\pi\)
−0.669334 + 0.742961i \(0.733421\pi\)
\(434\) 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 0.911050 0.412296i \(-0.135273\pi\)
−0.412296 + 0.911050i \(0.635273\pi\)
\(440\) 0 0
\(441\) 6.12194 + 6.12194i 0.0138819 + 0.0138819i
\(442\) 0 0
\(443\) −275.767 114.227i −0.622499 0.257848i 0.0490630 0.998796i \(-0.484376\pi\)
−0.671562 + 0.740948i \(0.734376\pi\)
\(444\) 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 −0.256511 0.966541i \(-0.582573\pi\)
0.966541 + 0.256511i \(0.0825731\pi\)
\(458\) 0 0
\(459\) 18.4483 44.5382i 0.0401925 0.0970332i
\(460\) 0 0
\(461\) −46.5472 112.375i −0.100970 0.243763i 0.865320 0.501220i \(-0.167115\pi\)
−0.966290 + 0.257457i \(0.917115\pi\)
\(462\) 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 −0.704400 0.709803i \(-0.748784\pi\)
0.00382006 + 0.999993i \(0.498784\pi\)
\(468\) 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 \(0.0503900\pi\)
−0.987496 + 0.157644i \(0.949610\pi\)
\(480\) 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 −0.980874 0.194643i \(-0.937645\pi\)
0.194643 + 0.980874i \(0.437645\pi\)
\(488\) 0 0
\(489\) −69.6251 + 69.6251i −0.142383 + 0.142383i
\(490\) 0 0
\(491\) −205.776 + 496.786i −0.419095 + 1.01178i 0.563516 + 0.826105i \(0.309448\pi\)
−0.982610 + 0.185679i \(0.940552\pi\)
\(492\) 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 −0.894909 0.446249i \(-0.852760\pi\)
−0.317250 + 0.948342i \(0.602760\pi\)
\(500\) 0 0
\(501\) 524.752 + 217.359i 1.04741 + 0.433851i
\(502\) 0 0
\(503\) −324.203 324.203i −0.644539 0.644539i 0.307129 0.951668i \(-0.400632\pi\)
−0.951668 + 0.307129i \(0.900632\pi\)
\(504\) 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 0.482666 0.875805i \(-0.339669\pi\)
0.960584 + 0.277991i \(0.0896686\pi\)
\(510\) 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 −0.723027 0.690819i \(-0.757250\pi\)
0.690819 + 0.723027i \(0.257250\pi\)
\(522\) 0 0
\(523\) 250.400 604.519i 0.478776 1.15587i −0.481407 0.876497i \(-0.659874\pi\)
0.960183 0.279371i \(-0.0901259\pi\)
\(524\) 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 −0.992781 0.119939i \(-0.961730\pi\)
−0.617192 + 0.786812i \(0.711730\pi\)
\(542\) 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 0.887348 0.461100i \(-0.152545\pi\)
−0.953497 + 0.301403i \(0.902545\pi\)
\(548\) 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 0.939332 + 0.343010i \(0.111447\pi\)
−0.421663 + 0.906753i \(0.638553\pi\)
\(558\) 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 0.230968 0.972961i \(-0.425811\pi\)
0.851306 + 0.524669i \(0.175811\pi\)
\(564\) 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 0.895507 0.445047i \(-0.146813\pi\)
−0.445047 + 0.895507i \(0.646813\pi\)
\(570\) 0 0
\(571\) −346.136 143.374i −0.606193 0.251094i 0.0584066 0.998293i \(-0.481398\pi\)
−0.664600 + 0.747199i \(0.731398\pi\)
\(572\) 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 −0.597683 0.801733i \(-0.703912\pi\)
0.989536 0.144285i \(-0.0460882\pi\)
\(588\) 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 \(0.126395\pi\)
−0.922193 + 0.386730i \(0.873605\pi\)
\(594\) 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 0.449768 0.893145i \(-0.351507\pi\)
−0.893145 + 0.449768i \(0.851507\pi\)
\(600\) 0 0
\(601\) 466.600 + 466.600i 0.776373 + 0.776373i 0.979212 0.202839i \(-0.0650168\pi\)
−0.202839 + 0.979212i \(0.565017\pi\)
\(602\) 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 \(0.0237327\pi\)
−0.997222 + 0.0744894i \(0.976267\pi\)
\(608\) 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 −0.863542 0.504277i \(-0.831759\pi\)
0.967194 + 0.254038i \(0.0817589\pi\)
\(614\) 0 0
\(615\) −415.376 + 415.376i −0.675408 + 0.675408i
\(616\) 0 0
\(617\) 181.842 181.842i 0.294720 0.294720i −0.544221 0.838942i \(-0.683175\pi\)
0.838942 + 0.544221i \(0.183175\pi\)
\(618\) 0 0
\(619\) 388.636 938.250i 0.627844 1.51575i −0.214451 0.976735i \(-0.568796\pi\)
0.842296 0.539016i \(-0.181204\pi\)
\(620\) 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 0.872136 0.489263i \(-0.162734\pi\)
−0.489263 + 0.872136i \(0.662734\pi\)
\(632\) 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 0.770813 0.637062i \(-0.219850\pi\)
−0.995518 + 0.0945760i \(0.969850\pi\)
\(644\) 0 0
\(645\) −694.674 + 1677.09i −1.07701 + 2.60014i
\(646\) 0 0
\(647\) 580.537 580.537i 0.897276 0.897276i −0.0979186 0.995194i \(-0.531218\pi\)
0.995194 + 0.0979186i \(0.0312185\pi\)
\(648\) 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 −0.686457 0.727170i \(-0.740835\pi\)
−0.0287882 0.999586i \(-0.509165\pi\)
\(654\) 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 −0.153784 0.988104i \(-0.549146\pi\)
0.589953 + 0.807437i \(0.299146\pi\)
\(660\) 0 0
\(661\) −478.625 198.253i −0.724093 0.299929i −0.00997082 0.999950i \(-0.503174\pi\)
−0.714122 + 0.700021i \(0.753174\pi\)
\(662\) 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 −0.935686 0.352834i \(-0.885218\pi\)
0.911121 + 0.412138i \(0.135218\pi\)
\(678\) 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 0.267162 + 0.963652i \(0.413914\pi\)
−0.870317 + 0.492493i \(0.836086\pi\)
\(684\) 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 −0.803604 0.595164i \(-0.797087\pi\)
−0.147389 + 0.989079i \(0.547087\pi\)
\(692\) 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 −0.341611 0.939841i \(-0.610973\pi\)
0.423013 + 0.906124i \(0.360973\pi\)
\(702\) 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 −0.996930 0.0783041i \(-0.975049\pi\)
0.760305 + 0.649566i \(0.225049\pi\)
\(710\) 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 0.994217 0.107392i \(-0.0342500\pi\)
−0.107392 + 0.994217i \(0.534250\pi\)
\(728\) 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 −0.00798801 0.999968i \(-0.502543\pi\)
0.701436 + 0.712733i \(0.252543\pi\)
\(734\) 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 0.814923 + 0.579569i \(0.196779\pi\)
−0.166421 + 0.986055i \(0.553221\pi\)
\(740\) 0 0
\(741\) 374.967 905.249i 0.506028 1.22166i
\(742\) 0 0
\(743\) 106.350 106.350i 0.143136 0.143136i −0.631908 0.775044i \(-0.717728\pi\)
0.775044 + 0.631908i \(0.217728\pi\)
\(744\) 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 0.987244 0.159214i \(-0.0508959\pi\)
0.585506 + 0.810668i \(0.300896\pi\)
\(758\) 0 0
\(759\) 163.564 + 163.564i 0.215499 + 0.215499i
\(760\) 0 0
\(761\) −1042.65 1042.65i −1.37010 1.37010i −0.860279 0.509823i \(-0.829711\pi\)
−0.509823 0.860279i \(-0.670289\pi\)
\(762\) 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 −0.662175 0.749350i \(-0.730366\pi\)
0.998098 0.0616419i \(-0.0196337\pi\)
\(774\) 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 −0.286644 0.958037i \(-0.592540\pi\)
0.474747 + 0.880122i \(0.342540\pi\)
\(788\) 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 −0.489039 0.872262i \(-0.662652\pi\)