Properties

Label 403.2.c.b.311.4
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.4
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.29

$q$-expansion

\(f(q)\) \(=\) \(q-2.44691i q^{2} +2.35527 q^{3} -3.98738 q^{4} -2.67528i q^{5} -5.76313i q^{6} +0.955539i q^{7} +4.86294i q^{8} +2.54728 q^{9} +O(q^{10})\) \(q-2.44691i q^{2} +2.35527 q^{3} -3.98738 q^{4} -2.67528i q^{5} -5.76313i q^{6} +0.955539i q^{7} +4.86294i q^{8} +2.54728 q^{9} -6.54617 q^{10} +0.164829i q^{11} -9.39134 q^{12} +(-0.630924 - 3.54992i) q^{13} +2.33812 q^{14} -6.30099i q^{15} +3.92444 q^{16} +0.846913 q^{17} -6.23297i q^{18} +4.61345i q^{19} +10.6674i q^{20} +2.25055i q^{21} +0.403323 q^{22} +3.55282 q^{23} +11.4535i q^{24} -2.15711 q^{25} +(-8.68634 + 1.54381i) q^{26} -1.06627 q^{27} -3.81010i q^{28} +5.07494 q^{29} -15.4180 q^{30} +1.00000i q^{31} +0.123131i q^{32} +0.388217i q^{33} -2.07232i q^{34} +2.55633 q^{35} -10.1570 q^{36} -7.21115i q^{37} +11.2887 q^{38} +(-1.48599 - 8.36101i) q^{39} +13.0097 q^{40} -0.599311i q^{41} +5.50690 q^{42} -4.14544 q^{43} -0.657238i q^{44} -6.81468i q^{45} -8.69344i q^{46} +11.9496i q^{47} +9.24310 q^{48} +6.08695 q^{49} +5.27827i q^{50} +1.99471 q^{51} +(2.51573 + 14.1549i) q^{52} +9.33924 q^{53} +2.60908i q^{54} +0.440965 q^{55} -4.64673 q^{56} +10.8659i q^{57} -12.4179i q^{58} +7.75933i q^{59} +25.1245i q^{60} -6.21514 q^{61} +2.44691 q^{62} +2.43403i q^{63} +8.15017 q^{64} +(-9.49702 + 1.68790i) q^{65} +0.949934 q^{66} +0.784589i q^{67} -3.37696 q^{68} +8.36783 q^{69} -6.25512i q^{70} -2.65426i q^{71} +12.3873i q^{72} +0.941589i q^{73} -17.6451 q^{74} -5.08058 q^{75} -18.3956i q^{76} -0.157501 q^{77} +(-20.4587 + 3.63610i) q^{78} +10.0747 q^{79} -10.4990i q^{80} -10.1532 q^{81} -1.46646 q^{82} +7.61624i q^{83} -8.97379i q^{84} -2.26573i q^{85} +10.1435i q^{86} +11.9528 q^{87} -0.801556 q^{88} -17.3013i q^{89} -16.6749 q^{90} +(3.39209 - 0.602872i) q^{91} -14.1664 q^{92} +2.35527i q^{93} +29.2396 q^{94} +12.3423 q^{95} +0.290007i q^{96} -6.09051i q^{97} -14.8942i q^{98} +0.419867i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.44691i 1.73023i −0.501575 0.865114i \(-0.667246\pi\)
0.501575 0.865114i \(-0.332754\pi\)
\(3\) 2.35527 1.35981 0.679907 0.733298i \(-0.262020\pi\)
0.679907 + 0.733298i \(0.262020\pi\)
\(4\) −3.98738 −1.99369
\(5\) 2.67528i 1.19642i −0.801339 0.598210i \(-0.795879\pi\)
0.801339 0.598210i \(-0.204121\pi\)
\(6\) 5.76313i 2.35279i
\(7\) 0.955539i 0.361160i 0.983560 + 0.180580i \(0.0577974\pi\)
−0.983560 + 0.180580i \(0.942203\pi\)
\(8\) 4.86294i 1.71931i
\(9\) 2.54728 0.849094
\(10\) −6.54617 −2.07008
\(11\) 0.164829i 0.0496979i 0.999691 + 0.0248490i \(0.00791049\pi\)
−0.999691 + 0.0248490i \(0.992090\pi\)
\(12\) −9.39134 −2.71105
\(13\) −0.630924 3.54992i −0.174987 0.984571i
\(14\) 2.33812 0.624889
\(15\) 6.30099i 1.62691i
\(16\) 3.92444 0.981110
\(17\) 0.846913 0.205407 0.102703 0.994712i \(-0.467251\pi\)
0.102703 + 0.994712i \(0.467251\pi\)
\(18\) 6.23297i 1.46913i
\(19\) 4.61345i 1.05840i 0.848498 + 0.529199i \(0.177507\pi\)
−0.848498 + 0.529199i \(0.822493\pi\)
\(20\) 10.6674i 2.38529i
\(21\) 2.25055i 0.491110i
\(22\) 0.403323 0.0859888
\(23\) 3.55282 0.740814 0.370407 0.928870i \(-0.379218\pi\)
0.370407 + 0.928870i \(0.379218\pi\)
\(24\) 11.4535i 2.33794i
\(25\) −2.15711 −0.431423
\(26\) −8.68634 + 1.54381i −1.70353 + 0.302767i
\(27\) −1.06627 −0.205205
\(28\) 3.81010i 0.720041i
\(29\) 5.07494 0.942393 0.471197 0.882028i \(-0.343822\pi\)
0.471197 + 0.882028i \(0.343822\pi\)
\(30\) −15.4180 −2.81492
\(31\) 1.00000i 0.179605i
\(32\) 0.123131i 0.0217667i
\(33\) 0.388217i 0.0675799i
\(34\) 2.07232i 0.355400i
\(35\) 2.55633 0.432099
\(36\) −10.1570 −1.69283
\(37\) 7.21115i 1.18551i −0.805384 0.592753i \(-0.798041\pi\)
0.805384 0.592753i \(-0.201959\pi\)
\(38\) 11.2887 1.83127
\(39\) −1.48599 8.36101i −0.237949 1.33883i
\(40\) 13.0097 2.05702
\(41\) 0.599311i 0.0935967i −0.998904 0.0467984i \(-0.985098\pi\)
0.998904 0.0467984i \(-0.0149018\pi\)
\(42\) 5.50690 0.849733
\(43\) −4.14544 −0.632173 −0.316087 0.948730i \(-0.602369\pi\)
−0.316087 + 0.948730i \(0.602369\pi\)
\(44\) 0.657238i 0.0990823i
\(45\) 6.81468i 1.01587i
\(46\) 8.69344i 1.28178i
\(47\) 11.9496i 1.74303i 0.490373 + 0.871513i \(0.336861\pi\)
−0.490373 + 0.871513i \(0.663139\pi\)
\(48\) 9.24310 1.33413
\(49\) 6.08695 0.869564
\(50\) 5.27827i 0.746460i
\(51\) 1.99471 0.279315
\(52\) 2.51573 + 14.1549i 0.348869 + 1.96293i
\(53\) 9.33924 1.28284 0.641421 0.767189i \(-0.278345\pi\)
0.641421 + 0.767189i \(0.278345\pi\)
\(54\) 2.60908i 0.355051i
\(55\) 0.440965 0.0594596
\(56\) −4.64673 −0.620946
\(57\) 10.8659i 1.43922i
\(58\) 12.4179i 1.63056i
\(59\) 7.75933i 1.01018i 0.863067 + 0.505089i \(0.168541\pi\)
−0.863067 + 0.505089i \(0.831459\pi\)
\(60\) 25.1245i 3.24355i
\(61\) −6.21514 −0.795768 −0.397884 0.917436i \(-0.630255\pi\)
−0.397884 + 0.917436i \(0.630255\pi\)
\(62\) 2.44691 0.310758
\(63\) 2.43403i 0.306658i
\(64\) 8.15017 1.01877
\(65\) −9.49702 + 1.68790i −1.17796 + 0.209358i
\(66\) 0.949934 0.116929
\(67\) 0.784589i 0.0958528i 0.998851 + 0.0479264i \(0.0152613\pi\)
−0.998851 + 0.0479264i \(0.984739\pi\)
\(68\) −3.37696 −0.409517
\(69\) 8.36783 1.00737
\(70\) 6.25512i 0.747630i
\(71\) 2.65426i 0.315002i −0.987519 0.157501i \(-0.949656\pi\)
0.987519 0.157501i \(-0.0503438\pi\)
\(72\) 12.3873i 1.45986i
\(73\) 0.941589i 0.110205i 0.998481 + 0.0551023i \(0.0175485\pi\)
−0.998481 + 0.0551023i \(0.982451\pi\)
\(74\) −17.6451 −2.05120
\(75\) −5.08058 −0.586654
\(76\) 18.3956i 2.11012i
\(77\) −0.157501 −0.0179489
\(78\) −20.4587 + 3.63610i −2.31649 + 0.411707i
\(79\) 10.0747 1.13349 0.566746 0.823893i \(-0.308202\pi\)
0.566746 + 0.823893i \(0.308202\pi\)
\(80\) 10.4990i 1.17382i
\(81\) −10.1532 −1.12813
\(82\) −1.46646 −0.161944
\(83\) 7.61624i 0.835991i 0.908449 + 0.417995i \(0.137267\pi\)
−0.908449 + 0.417995i \(0.862733\pi\)
\(84\) 8.97379i 0.979121i
\(85\) 2.26573i 0.245753i
\(86\) 10.1435i 1.09380i
\(87\) 11.9528 1.28148
\(88\) −0.801556 −0.0854462
\(89\) 17.3013i 1.83394i −0.398958 0.916969i \(-0.630628\pi\)
0.398958 0.916969i \(-0.369372\pi\)
\(90\) −16.6749 −1.75769
\(91\) 3.39209 0.602872i 0.355587 0.0631982i
\(92\) −14.1664 −1.47695
\(93\) 2.35527i 0.244230i
\(94\) 29.2396 3.01583
\(95\) 12.3423 1.26629
\(96\) 0.290007i 0.0295987i
\(97\) 6.09051i 0.618398i −0.950997 0.309199i \(-0.899939\pi\)
0.950997 0.309199i \(-0.100061\pi\)
\(98\) 14.8942i 1.50454i
\(99\) 0.419867i 0.0421982i
\(100\) 8.60123 0.860123
\(101\) 19.4595 1.93629 0.968144 0.250394i \(-0.0805601\pi\)
0.968144 + 0.250394i \(0.0805601\pi\)
\(102\) 4.88087i 0.483278i
\(103\) −14.9051 −1.46864 −0.734322 0.678802i \(-0.762500\pi\)
−0.734322 + 0.678802i \(0.762500\pi\)
\(104\) 17.2631 3.06815i 1.69278 0.300857i
\(105\) 6.02084 0.587574
\(106\) 22.8523i 2.21961i
\(107\) −14.5314 −1.40480 −0.702400 0.711783i \(-0.747888\pi\)
−0.702400 + 0.711783i \(0.747888\pi\)
\(108\) 4.25164 0.409114
\(109\) 0.473449i 0.0453482i −0.999743 0.0226741i \(-0.992782\pi\)
0.999743 0.0226741i \(-0.00721801\pi\)
\(110\) 1.07900i 0.102879i
\(111\) 16.9842i 1.61207i
\(112\) 3.74995i 0.354337i
\(113\) −6.36649 −0.598909 −0.299455 0.954111i \(-0.596805\pi\)
−0.299455 + 0.954111i \(0.596805\pi\)
\(114\) 26.5879 2.49019
\(115\) 9.50478i 0.886325i
\(116\) −20.2357 −1.87884
\(117\) −1.60714 9.04264i −0.148580 0.835993i
\(118\) 18.9864 1.74784
\(119\) 0.809258i 0.0741846i
\(120\) 30.6414 2.79716
\(121\) 10.9728 0.997530
\(122\) 15.2079i 1.37686i
\(123\) 1.41154i 0.127274i
\(124\) 3.98738i 0.358077i
\(125\) 7.60551i 0.680258i
\(126\) 5.95585 0.530589
\(127\) −21.1327 −1.87522 −0.937611 0.347687i \(-0.886967\pi\)
−0.937611 + 0.347687i \(0.886967\pi\)
\(128\) 19.6965i 1.74094i
\(129\) −9.76361 −0.859638
\(130\) 4.13013 + 23.2384i 0.362237 + 2.03814i
\(131\) −12.9701 −1.13320 −0.566601 0.823992i \(-0.691742\pi\)
−0.566601 + 0.823992i \(0.691742\pi\)
\(132\) 1.54797i 0.134733i
\(133\) −4.40833 −0.382251
\(134\) 1.91982 0.165847
\(135\) 2.85258i 0.245511i
\(136\) 4.11849i 0.353158i
\(137\) 19.3568i 1.65376i 0.562379 + 0.826880i \(0.309886\pi\)
−0.562379 + 0.826880i \(0.690114\pi\)
\(138\) 20.4754i 1.74298i
\(139\) −0.820777 −0.0696174 −0.0348087 0.999394i \(-0.511082\pi\)
−0.0348087 + 0.999394i \(0.511082\pi\)
\(140\) −10.1931 −0.861472
\(141\) 28.1445i 2.37019i
\(142\) −6.49473 −0.545026
\(143\) 0.585131 0.103995i 0.0489311 0.00869648i
\(144\) 9.99665 0.833054
\(145\) 13.5769i 1.12750i
\(146\) 2.30399 0.190679
\(147\) 14.3364 1.18244
\(148\) 28.7536i 2.36353i
\(149\) 10.4194i 0.853589i 0.904349 + 0.426795i \(0.140357\pi\)
−0.904349 + 0.426795i \(0.859643\pi\)
\(150\) 12.4317i 1.01505i
\(151\) 1.28956i 0.104943i 0.998622 + 0.0524713i \(0.0167098\pi\)
−0.998622 + 0.0524713i \(0.983290\pi\)
\(152\) −22.4349 −1.81971
\(153\) 2.15732 0.174409
\(154\) 0.385391i 0.0310557i
\(155\) 2.67528 0.214884
\(156\) 5.92522 + 33.3385i 0.474397 + 2.66922i
\(157\) 3.21524 0.256604 0.128302 0.991735i \(-0.459047\pi\)
0.128302 + 0.991735i \(0.459047\pi\)
\(158\) 24.6519i 1.96120i
\(159\) 21.9964 1.74443
\(160\) 0.329410 0.0260422
\(161\) 3.39486i 0.267552i
\(162\) 24.8440i 1.95193i
\(163\) 3.97579i 0.311408i −0.987804 0.155704i \(-0.950235\pi\)
0.987804 0.155704i \(-0.0497646\pi\)
\(164\) 2.38968i 0.186603i
\(165\) 1.03859 0.0808541
\(166\) 18.6363 1.44646
\(167\) 14.6209i 1.13140i 0.824612 + 0.565699i \(0.191394\pi\)
−0.824612 + 0.565699i \(0.808606\pi\)
\(168\) −10.9443 −0.844371
\(169\) −12.2039 + 4.47946i −0.938759 + 0.344574i
\(170\) −5.54404 −0.425208
\(171\) 11.7517i 0.898679i
\(172\) 16.5294 1.26036
\(173\) 2.37223 0.180357 0.0901787 0.995926i \(-0.471256\pi\)
0.0901787 + 0.995926i \(0.471256\pi\)
\(174\) 29.2476i 2.21725i
\(175\) 2.06121i 0.155812i
\(176\) 0.646863i 0.0487591i
\(177\) 18.2753i 1.37366i
\(178\) −42.3349 −3.17313
\(179\) 7.91369 0.591497 0.295749 0.955266i \(-0.404431\pi\)
0.295749 + 0.955266i \(0.404431\pi\)
\(180\) 27.1727i 2.02534i
\(181\) −13.0489 −0.969919 −0.484960 0.874537i \(-0.661166\pi\)
−0.484960 + 0.874537i \(0.661166\pi\)
\(182\) −1.47518 8.30014i −0.109347 0.615247i
\(183\) −14.6383 −1.08210
\(184\) 17.2772i 1.27369i
\(185\) −19.2918 −1.41836
\(186\) 5.76313 0.422573
\(187\) 0.139596i 0.0102083i
\(188\) 47.6475i 3.47505i
\(189\) 1.01887i 0.0741117i
\(190\) 30.2004i 2.19097i
\(191\) −9.81737 −0.710360 −0.355180 0.934798i \(-0.615580\pi\)
−0.355180 + 0.934798i \(0.615580\pi\)
\(192\) 19.1958 1.38534
\(193\) 19.9690i 1.43740i 0.695321 + 0.718699i \(0.255262\pi\)
−0.695321 + 0.718699i \(0.744738\pi\)
\(194\) −14.9030 −1.06997
\(195\) −22.3680 + 3.97545i −1.60181 + 0.284688i
\(196\) −24.2710 −1.73364
\(197\) 16.5253i 1.17738i −0.808359 0.588689i \(-0.799644\pi\)
0.808359 0.588689i \(-0.200356\pi\)
\(198\) 1.02738 0.0730125
\(199\) 20.6068 1.46078 0.730388 0.683032i \(-0.239339\pi\)
0.730388 + 0.683032i \(0.239339\pi\)
\(200\) 10.4899i 0.741749i
\(201\) 1.84792i 0.130342i
\(202\) 47.6156i 3.35022i
\(203\) 4.84930i 0.340354i
\(204\) −7.95365 −0.556867
\(205\) −1.60332 −0.111981
\(206\) 36.4715i 2.54109i
\(207\) 9.05003 0.629020
\(208\) −2.47602 13.9314i −0.171681 0.965972i
\(209\) −0.760432 −0.0526002
\(210\) 14.7325i 1.01664i
\(211\) −20.3309 −1.39964 −0.699819 0.714320i \(-0.746736\pi\)
−0.699819 + 0.714320i \(0.746736\pi\)
\(212\) −37.2391 −2.55759
\(213\) 6.25148i 0.428344i
\(214\) 35.5570i 2.43062i
\(215\) 11.0902i 0.756345i
\(216\) 5.18523i 0.352810i
\(217\) −0.955539 −0.0648662
\(218\) −1.15849 −0.0784627
\(219\) 2.21769i 0.149858i
\(220\) −1.75829 −0.118544
\(221\) −0.534337 3.00647i −0.0359434 0.202237i
\(222\) −41.5588 −2.78924
\(223\) 3.70952i 0.248408i 0.992257 + 0.124204i \(0.0396377\pi\)
−0.992257 + 0.124204i \(0.960362\pi\)
\(224\) −0.117657 −0.00786127
\(225\) −5.49477 −0.366318
\(226\) 15.5782i 1.03625i
\(227\) 13.1733i 0.874340i −0.899379 0.437170i \(-0.855981\pi\)
0.899379 0.437170i \(-0.144019\pi\)
\(228\) 43.3265i 2.86937i
\(229\) 19.1936i 1.26835i 0.773191 + 0.634173i \(0.218659\pi\)
−0.773191 + 0.634173i \(0.781341\pi\)
\(230\) −23.2574 −1.53354
\(231\) −0.370957 −0.0244072
\(232\) 24.6792i 1.62027i
\(233\) −1.99780 −0.130880 −0.0654401 0.997856i \(-0.520845\pi\)
−0.0654401 + 0.997856i \(0.520845\pi\)
\(234\) −22.1266 + 3.93253i −1.44646 + 0.257078i
\(235\) 31.9685 2.08539
\(236\) 30.9394i 2.01398i
\(237\) 23.7286 1.54134
\(238\) 1.98018 0.128356
\(239\) 12.1146i 0.783631i 0.920044 + 0.391816i \(0.128153\pi\)
−0.920044 + 0.391816i \(0.871847\pi\)
\(240\) 24.7279i 1.59618i
\(241\) 16.0688i 1.03509i 0.855657 + 0.517543i \(0.173153\pi\)
−0.855657 + 0.517543i \(0.826847\pi\)
\(242\) 26.8496i 1.72595i
\(243\) −20.7147 −1.32885
\(244\) 24.7821 1.58651
\(245\) 16.2843i 1.04036i
\(246\) −3.45391 −0.220213
\(247\) 16.3774 2.91073i 1.04207 0.185206i
\(248\) −4.86294 −0.308797
\(249\) 17.9383i 1.13679i
\(250\) −18.6100 −1.17700
\(251\) 18.8448 1.18947 0.594737 0.803921i \(-0.297256\pi\)
0.594737 + 0.803921i \(0.297256\pi\)
\(252\) 9.70539i 0.611382i
\(253\) 0.585609i 0.0368169i
\(254\) 51.7098i 3.24456i
\(255\) 5.33639i 0.334178i
\(256\) −31.8952 −1.99345
\(257\) −28.0808 −1.75163 −0.875816 0.482645i \(-0.839676\pi\)
−0.875816 + 0.482645i \(0.839676\pi\)
\(258\) 23.8907i 1.48737i
\(259\) 6.89054 0.428157
\(260\) 37.8682 6.73028i 2.34849 0.417394i
\(261\) 12.9273 0.800180
\(262\) 31.7367i 1.96070i
\(263\) 21.4892 1.32508 0.662540 0.749026i \(-0.269478\pi\)
0.662540 + 0.749026i \(0.269478\pi\)
\(264\) −1.88788 −0.116191
\(265\) 24.9851i 1.53482i
\(266\) 10.7868i 0.661381i
\(267\) 40.7493i 2.49381i
\(268\) 3.12845i 0.191101i
\(269\) −22.7854 −1.38925 −0.694626 0.719371i \(-0.744430\pi\)
−0.694626 + 0.719371i \(0.744430\pi\)
\(270\) 6.98002 0.424790
\(271\) 22.7290i 1.38069i 0.723480 + 0.690345i \(0.242541\pi\)
−0.723480 + 0.690345i \(0.757459\pi\)
\(272\) 3.32366 0.201526
\(273\) 7.98927 1.41992i 0.483533 0.0859377i
\(274\) 47.3643 2.86138
\(275\) 0.355556i 0.0214408i
\(276\) −33.3657 −2.00838
\(277\) −1.05029 −0.0631057 −0.0315529 0.999502i \(-0.510045\pi\)
−0.0315529 + 0.999502i \(0.510045\pi\)
\(278\) 2.00837i 0.120454i
\(279\) 2.54728i 0.152502i
\(280\) 12.4313i 0.742912i
\(281\) 5.80404i 0.346240i 0.984901 + 0.173120i \(0.0553849\pi\)
−0.984901 + 0.173120i \(0.944615\pi\)
\(282\) 68.8670 4.10097
\(283\) −16.0917 −0.956551 −0.478275 0.878210i \(-0.658738\pi\)
−0.478275 + 0.878210i \(0.658738\pi\)
\(284\) 10.5835i 0.628017i
\(285\) 29.0693 1.72192
\(286\) −0.254466 1.43177i −0.0150469 0.0846620i
\(287\) 0.572665 0.0338034
\(288\) 0.313650i 0.0184820i
\(289\) −16.2827 −0.957808
\(290\) −33.2214 −1.95083
\(291\) 14.3448i 0.840906i
\(292\) 3.75447i 0.219714i
\(293\) 19.3398i 1.12984i 0.825145 + 0.564922i \(0.191094\pi\)
−0.825145 + 0.564922i \(0.808906\pi\)
\(294\) 35.0799i 2.04590i
\(295\) 20.7584 1.20860
\(296\) 35.0674 2.03825
\(297\) 0.175753i 0.0101982i
\(298\) 25.4953 1.47690
\(299\) −2.24156 12.6122i −0.129633 0.729384i
\(300\) 20.2582 1.16961
\(301\) 3.96113i 0.228316i
\(302\) 3.15543 0.181575
\(303\) 45.8322 2.63299
\(304\) 18.1052i 1.03840i
\(305\) 16.6272i 0.952073i
\(306\) 5.27878i 0.301768i
\(307\) 15.2126i 0.868227i −0.900858 0.434113i \(-0.857062\pi\)
0.900858 0.434113i \(-0.142938\pi\)
\(308\) 0.628016 0.0357845
\(309\) −35.1055 −1.99708
\(310\) 6.54617i 0.371798i
\(311\) −2.16175 −0.122582 −0.0612908 0.998120i \(-0.519522\pi\)
−0.0612908 + 0.998120i \(0.519522\pi\)
\(312\) 40.6591 7.22630i 2.30187 0.409109i
\(313\) 13.3466 0.754396 0.377198 0.926133i \(-0.376888\pi\)
0.377198 + 0.926133i \(0.376888\pi\)
\(314\) 7.86740i 0.443983i
\(315\) 6.51170 0.366893
\(316\) −40.1716 −2.25983
\(317\) 30.2692i 1.70009i −0.526714 0.850043i \(-0.676576\pi\)
0.526714 0.850043i \(-0.323424\pi\)
\(318\) 53.8232i 3.01826i
\(319\) 0.836500i 0.0468350i
\(320\) 21.8040i 1.21888i
\(321\) −34.2252 −1.91027
\(322\) 8.30692 0.462926
\(323\) 3.90719i 0.217402i
\(324\) 40.4847 2.24915
\(325\) 1.36097 + 7.65758i 0.0754932 + 0.424766i
\(326\) −9.72842 −0.538807
\(327\) 1.11510i 0.0616651i
\(328\) 2.91442 0.160922
\(329\) −11.4183 −0.629511
\(330\) 2.54134i 0.139896i
\(331\) 7.60712i 0.418125i −0.977902 0.209063i \(-0.932959\pi\)
0.977902 0.209063i \(-0.0670412\pi\)
\(332\) 30.3688i 1.66671i
\(333\) 18.3688i 1.00661i
\(334\) 35.7760 1.95758
\(335\) 2.09899 0.114680
\(336\) 8.83214i 0.481833i
\(337\) −13.7524 −0.749139 −0.374569 0.927199i \(-0.622209\pi\)
−0.374569 + 0.927199i \(0.622209\pi\)
\(338\) 10.9608 + 29.8618i 0.596191 + 1.62427i
\(339\) −14.9948 −0.814405
\(340\) 9.03432i 0.489955i
\(341\) −0.164829 −0.00892601
\(342\) 28.7555 1.55492
\(343\) 12.5051i 0.675211i
\(344\) 20.1590i 1.08690i
\(345\) 22.3863i 1.20524i
\(346\) 5.80464i 0.312060i
\(347\) −14.5798 −0.782687 −0.391344 0.920245i \(-0.627990\pi\)
−0.391344 + 0.920245i \(0.627990\pi\)
\(348\) −47.6605 −2.55487
\(349\) 13.7796i 0.737606i −0.929508 0.368803i \(-0.879768\pi\)
0.929508 0.368803i \(-0.120232\pi\)
\(350\) −5.04359 −0.269591
\(351\) 0.672738 + 3.78519i 0.0359081 + 0.202038i
\(352\) −0.0202957 −0.00108176
\(353\) 13.5153i 0.719348i 0.933078 + 0.359674i \(0.117112\pi\)
−0.933078 + 0.359674i \(0.882888\pi\)
\(354\) 44.7180 2.37674
\(355\) −7.10087 −0.376875
\(356\) 68.9870i 3.65630i
\(357\) 1.90602i 0.100877i
\(358\) 19.3641i 1.02343i
\(359\) 15.0739i 0.795569i −0.917479 0.397784i \(-0.869779\pi\)
0.917479 0.397784i \(-0.130221\pi\)
\(360\) 33.1394 1.74660
\(361\) −2.28390 −0.120205
\(362\) 31.9296i 1.67818i
\(363\) 25.8439 1.35646
\(364\) −13.5255 + 2.40388i −0.708931 + 0.125998i
\(365\) 2.51901 0.131851
\(366\) 35.8187i 1.87227i
\(367\) −18.5321 −0.967367 −0.483684 0.875243i \(-0.660701\pi\)
−0.483684 + 0.875243i \(0.660701\pi\)
\(368\) 13.9428 0.726820
\(369\) 1.52661i 0.0794724i
\(370\) 47.2054i 2.45409i
\(371\) 8.92400i 0.463311i
\(372\) 9.39134i 0.486918i
\(373\) 13.1741 0.682129 0.341065 0.940040i \(-0.389212\pi\)
0.341065 + 0.940040i \(0.389212\pi\)
\(374\) 0.341580 0.0176627
\(375\) 17.9130i 0.925024i
\(376\) −58.1102 −2.99680
\(377\) −3.20190 18.0156i −0.164906 0.927853i
\(378\) −2.49308 −0.128230
\(379\) 0.643695i 0.0330644i −0.999863 0.0165322i \(-0.994737\pi\)
0.999863 0.0165322i \(-0.00526260\pi\)
\(380\) −49.2133 −2.52459
\(381\) −49.7731 −2.54995
\(382\) 24.0222i 1.22909i
\(383\) 0.638046i 0.0326027i −0.999867 0.0163013i \(-0.994811\pi\)
0.999867 0.0163013i \(-0.00518910\pi\)
\(384\) 46.3905i 2.36735i
\(385\) 0.421359i 0.0214744i
\(386\) 48.8623 2.48703
\(387\) −10.5596 −0.536774
\(388\) 24.2852i 1.23289i
\(389\) 3.50021 0.177468 0.0887339 0.996055i \(-0.471718\pi\)
0.0887339 + 0.996055i \(0.471718\pi\)
\(390\) 9.72757 + 54.7326i 0.492574 + 2.77149i
\(391\) 3.00893 0.152168
\(392\) 29.6005i 1.49505i
\(393\) −30.5480 −1.54094
\(394\) −40.4359 −2.03713
\(395\) 26.9526i 1.35613i
\(396\) 1.67417i 0.0841301i
\(397\) 36.5004i 1.83190i −0.401287 0.915952i \(-0.631437\pi\)
0.401287 0.915952i \(-0.368563\pi\)
\(398\) 50.4230i 2.52748i
\(399\) −10.3828 −0.519790
\(400\) −8.46546 −0.423273
\(401\) 5.71571i 0.285429i −0.989764 0.142715i \(-0.954417\pi\)
0.989764 0.142715i \(-0.0455831\pi\)
\(402\) 4.52169 0.225521
\(403\) 3.54992 0.630924i 0.176834 0.0314285i
\(404\) −77.5922 −3.86036
\(405\) 27.1626i 1.34972i
\(406\) 11.8658 0.588891
\(407\) 1.18861 0.0589172
\(408\) 9.70014i 0.480229i
\(409\) 32.8297i 1.62333i −0.584126 0.811663i \(-0.698562\pi\)
0.584126 0.811663i \(-0.301438\pi\)
\(410\) 3.92320i 0.193753i
\(411\) 45.5903i 2.24881i
\(412\) 59.4323 2.92802
\(413\) −7.41434 −0.364836
\(414\) 22.1446i 1.08835i
\(415\) 20.3756 1.00020
\(416\) 0.437106 0.0776864i 0.0214309 0.00380889i
\(417\) −1.93315 −0.0946667
\(418\) 1.86071i 0.0910103i
\(419\) 33.3911 1.63126 0.815630 0.578573i \(-0.196390\pi\)
0.815630 + 0.578573i \(0.196390\pi\)
\(420\) −24.0074 −1.17144
\(421\) 31.5645i 1.53836i −0.639033 0.769179i \(-0.720665\pi\)
0.639033 0.769179i \(-0.279335\pi\)
\(422\) 49.7480i 2.42169i
\(423\) 30.4389i 1.47999i
\(424\) 45.4162i 2.20561i
\(425\) −1.82689 −0.0886170
\(426\) −15.2968 −0.741134
\(427\) 5.93881i 0.287399i
\(428\) 57.9420 2.80073
\(429\) 1.37814 0.244935i 0.0665372 0.0118256i
\(430\) 27.1368 1.30865
\(431\) 13.7218i 0.660954i −0.943814 0.330477i \(-0.892790\pi\)
0.943814 0.330477i \(-0.107210\pi\)
\(432\) −4.18453 −0.201328
\(433\) 4.35155 0.209122 0.104561 0.994518i \(-0.466656\pi\)
0.104561 + 0.994518i \(0.466656\pi\)
\(434\) 2.33812i 0.112233i
\(435\) 31.9772i 1.53319i
\(436\) 1.88782i 0.0904103i
\(437\) 16.3907i 0.784075i
\(438\) 5.42650 0.259288
\(439\) 1.65440 0.0789601 0.0394800 0.999220i \(-0.487430\pi\)
0.0394800 + 0.999220i \(0.487430\pi\)
\(440\) 2.14439i 0.102230i
\(441\) 15.5052 0.738341
\(442\) −7.35658 + 1.30748i −0.349917 + 0.0621903i
\(443\) −10.9699 −0.521194 −0.260597 0.965448i \(-0.583919\pi\)
−0.260597 + 0.965448i \(0.583919\pi\)
\(444\) 67.7224i 3.21396i
\(445\) −46.2859 −2.19416
\(446\) 9.07687 0.429802
\(447\) 24.5404i 1.16072i
\(448\) 7.78780i 0.367939i
\(449\) 2.08348i 0.0983254i 0.998791 + 0.0491627i \(0.0156553\pi\)
−0.998791 + 0.0491627i \(0.984345\pi\)
\(450\) 13.4452i 0.633814i
\(451\) 0.0987842 0.00465156
\(452\) 25.3856 1.19404
\(453\) 3.03725i 0.142702i
\(454\) −32.2338 −1.51281
\(455\) −1.61285 9.07478i −0.0756116 0.425432i
\(456\) −52.8403 −2.47447
\(457\) 5.71250i 0.267220i −0.991034 0.133610i \(-0.957343\pi\)
0.991034 0.133610i \(-0.0426569\pi\)
\(458\) 46.9650 2.19453
\(459\) −0.903042 −0.0421504
\(460\) 37.8992i 1.76706i
\(461\) 11.8887i 0.553713i 0.960911 + 0.276856i \(0.0892926\pi\)
−0.960911 + 0.276856i \(0.910707\pi\)
\(462\) 0.907699i 0.0422300i
\(463\) 0.451563i 0.0209859i 0.999945 + 0.0104930i \(0.00334007\pi\)
−0.999945 + 0.0104930i \(0.996660\pi\)
\(464\) 19.9163 0.924591
\(465\) 6.30099 0.292202
\(466\) 4.88844i 0.226453i
\(467\) 26.5720 1.22960 0.614802 0.788682i \(-0.289236\pi\)
0.614802 + 0.788682i \(0.289236\pi\)
\(468\) 6.40828 + 36.0565i 0.296223 + 1.66671i
\(469\) −0.749705 −0.0346182
\(470\) 78.2240i 3.60820i
\(471\) 7.57274 0.348934
\(472\) −37.7332 −1.73681
\(473\) 0.683290i 0.0314177i
\(474\) 58.0618i 2.66687i
\(475\) 9.95173i 0.456617i
\(476\) 3.22682i 0.147901i
\(477\) 23.7897 1.08925
\(478\) 29.6435 1.35586
\(479\) 11.7579i 0.537233i −0.963247 0.268617i \(-0.913433\pi\)
0.963247 0.268617i \(-0.0865665\pi\)
\(480\) 0.775849 0.0354125
\(481\) −25.5990 + 4.54969i −1.16721 + 0.207448i
\(482\) 39.3191 1.79093
\(483\) 7.99579i 0.363821i
\(484\) −43.7528 −1.98877
\(485\) −16.2938 −0.739864
\(486\) 50.6870i 2.29921i
\(487\) 21.1168i 0.956894i −0.878116 0.478447i \(-0.841200\pi\)
0.878116 0.478447i \(-0.158800\pi\)
\(488\) 30.2239i 1.36817i
\(489\) 9.36405i 0.423457i
\(490\) −39.8462 −1.80007
\(491\) 24.8938 1.12344 0.561722 0.827326i \(-0.310139\pi\)
0.561722 + 0.827326i \(0.310139\pi\)
\(492\) 5.62834i 0.253745i
\(493\) 4.29803 0.193574
\(494\) −7.12231 40.0740i −0.320448 1.80301i
\(495\) 1.12326 0.0504868
\(496\) 3.92444i 0.176213i
\(497\) 2.53625 0.113766
\(498\) 43.8934 1.96691
\(499\) 18.5383i 0.829890i −0.909847 0.414945i \(-0.863801\pi\)
0.909847 0.414945i \(-0.136199\pi\)
\(500\) 30.3261i 1.35622i
\(501\) 34.4361i 1.53849i
\(502\) 46.1116i 2.05806i
\(503\) 36.0174 1.60593 0.802967 0.596023i \(-0.203253\pi\)
0.802967 + 0.596023i \(0.203253\pi\)
\(504\) −11.8365 −0.527241
\(505\) 52.0595i 2.31662i
\(506\) 1.43293 0.0637017
\(507\) −28.7434 + 10.5503i −1.27654 + 0.468556i
\(508\) 84.2640 3.73861
\(509\) 20.9608i 0.929072i 0.885554 + 0.464536i \(0.153779\pi\)
−0.885554 + 0.464536i \(0.846221\pi\)
\(510\) −13.0577 −0.578204
\(511\) −0.899725 −0.0398015
\(512\) 38.6519i 1.70819i
\(513\) 4.91920i 0.217188i
\(514\) 68.7113i 3.03072i
\(515\) 39.8753i 1.75712i
\(516\) 38.9312 1.71385
\(517\) −1.96964 −0.0866248
\(518\) 16.8605i 0.740809i
\(519\) 5.58724 0.245253
\(520\) −8.20815 46.1835i −0.359951 2.02528i
\(521\) 25.4300 1.11411 0.557054 0.830476i \(-0.311931\pi\)
0.557054 + 0.830476i \(0.311931\pi\)
\(522\) 31.6320i 1.38449i
\(523\) −3.07473 −0.134449 −0.0672244 0.997738i \(-0.521414\pi\)
−0.0672244 + 0.997738i \(0.521414\pi\)
\(524\) 51.7167 2.25926
\(525\) 4.85469i 0.211876i
\(526\) 52.5822i 2.29269i
\(527\) 0.846913i 0.0368921i
\(528\) 1.52353i 0.0663033i
\(529\) −10.3775 −0.451195
\(530\) −61.1362 −2.65559
\(531\) 19.7652i 0.857736i
\(532\) 17.5777 0.762089
\(533\) −2.12751 + 0.378120i −0.0921526 + 0.0163782i
\(534\) −99.7099 −4.31487
\(535\) 38.8754i 1.68073i
\(536\) −3.81541 −0.164801
\(537\) 18.6389 0.804326
\(538\) 55.7539i 2.40372i
\(539\) 1.00331i 0.0432155i
\(540\) 11.3743i 0.489473i
\(541\) 9.16670i 0.394107i 0.980393 + 0.197054i \(0.0631373\pi\)
−0.980393 + 0.197054i \(0.936863\pi\)
\(542\) 55.6159 2.38891
\(543\) −30.7337 −1.31891
\(544\) 0.104281i 0.00447103i
\(545\) −1.26661 −0.0542555
\(546\) −3.47443 19.5490i −0.148692 0.836622i
\(547\) −24.3063 −1.03926 −0.519630 0.854391i \(-0.673930\pi\)
−0.519630 + 0.854391i \(0.673930\pi\)
\(548\) 77.1828i 3.29708i
\(549\) −15.8317 −0.675681
\(550\) −0.870014 −0.0370975
\(551\) 23.4130i 0.997426i
\(552\) 40.6923i 1.73198i
\(553\) 9.62677i 0.409372i
\(554\) 2.56997i 0.109187i
\(555\) −45.4374 −1.92871
\(556\) 3.27275 0.138796
\(557\) 9.13477i 0.387052i 0.981095 + 0.193526i \(0.0619925\pi\)
−0.981095 + 0.193526i \(0.938008\pi\)
\(558\) 6.23297 0.263863
\(559\) 2.61546 + 14.7160i 0.110622 + 0.622420i
\(560\) 10.0322 0.423937
\(561\) 0.328786i 0.0138814i
\(562\) 14.2020 0.599074
\(563\) 30.1418 1.27032 0.635162 0.772379i \(-0.280933\pi\)
0.635162 + 0.772379i \(0.280933\pi\)
\(564\) 112.223i 4.72542i
\(565\) 17.0321i 0.716547i
\(566\) 39.3749i 1.65505i
\(567\) 9.70178i 0.407437i
\(568\) 12.9075 0.541587
\(569\) 29.0683 1.21861 0.609303 0.792937i \(-0.291449\pi\)
0.609303 + 0.792937i \(0.291449\pi\)
\(570\) 71.1300i 2.97931i
\(571\) −20.7284 −0.867454 −0.433727 0.901044i \(-0.642802\pi\)
−0.433727 + 0.901044i \(0.642802\pi\)
\(572\) −2.33314 + 0.414667i −0.0975535 + 0.0173381i
\(573\) −23.1225 −0.965957
\(574\) 1.40126i 0.0584876i
\(575\) −7.66383 −0.319604
\(576\) 20.7608 0.865032
\(577\) 14.0634i 0.585469i 0.956194 + 0.292734i \(0.0945652\pi\)
−0.956194 + 0.292734i \(0.905435\pi\)
\(578\) 39.8424i 1.65723i
\(579\) 47.0323i 1.95459i
\(580\) 54.1362i 2.24788i
\(581\) −7.27761 −0.301926
\(582\) −35.1004 −1.45496
\(583\) 1.53938i 0.0637546i
\(584\) −4.57890 −0.189476
\(585\) −24.1916 + 4.29955i −1.00020 + 0.177764i
\(586\) 47.3228 1.95489
\(587\) 38.4922i 1.58874i −0.607431 0.794372i \(-0.707800\pi\)
0.607431 0.794372i \(-0.292200\pi\)
\(588\) −57.1646 −2.35743
\(589\) −4.61345 −0.190094
\(590\) 50.7939i 2.09115i
\(591\) 38.9215i 1.60102i
\(592\) 28.2997i 1.16311i
\(593\) 18.7114i 0.768387i 0.923253 + 0.384193i \(0.125520\pi\)
−0.923253 + 0.384193i \(0.874480\pi\)
\(594\) −0.430053 −0.0176453
\(595\) 2.16499 0.0887560
\(596\) 41.5460i 1.70179i
\(597\) 48.5345 1.98638
\(598\) −30.8610 + 5.48489i −1.26200 + 0.224294i
\(599\) 37.0994 1.51584 0.757919 0.652348i \(-0.226216\pi\)
0.757919 + 0.652348i \(0.226216\pi\)
\(600\) 24.7066i 1.00864i
\(601\) −11.2787 −0.460069 −0.230035 0.973182i \(-0.573884\pi\)
−0.230035 + 0.973182i \(0.573884\pi\)
\(602\) −9.69253 −0.395038
\(603\) 1.99857i 0.0813880i
\(604\) 5.14195i 0.209223i
\(605\) 29.3554i 1.19347i
\(606\) 112.147i 4.55568i
\(607\) −6.57246 −0.266768 −0.133384 0.991064i \(-0.542584\pi\)
−0.133384 + 0.991064i \(0.542584\pi\)
\(608\) −0.568060 −0.0230379
\(609\) 11.4214i 0.462819i
\(610\) 40.6854 1.64730
\(611\) 42.4201 7.53927i 1.71613 0.305006i
\(612\) −8.60207 −0.347718
\(613\) 37.0931i 1.49817i −0.662471 0.749087i \(-0.730492\pi\)
0.662471 0.749087i \(-0.269508\pi\)
\(614\) −37.2238 −1.50223
\(615\) −3.77626 −0.152273
\(616\) 0.765918i 0.0308597i
\(617\) 13.0949i 0.527182i −0.964635 0.263591i \(-0.915093\pi\)
0.964635 0.263591i \(-0.0849069\pi\)
\(618\) 85.9001i 3.45541i
\(619\) 20.6820i 0.831281i −0.909529 0.415640i \(-0.863557\pi\)
0.909529 0.415640i \(-0.136443\pi\)
\(620\) −10.6674 −0.428411
\(621\) −3.78828 −0.152018
\(622\) 5.28962i 0.212094i
\(623\) 16.5321 0.662345
\(624\) −5.83169 32.8123i −0.233454 1.31354i
\(625\) −31.1324 −1.24530
\(626\) 32.6580i 1.30528i
\(627\) −1.79102 −0.0715264
\(628\) −12.8204 −0.511589
\(629\) 6.10722i 0.243511i
\(630\) 15.9336i 0.634808i
\(631\) 46.6562i 1.85736i −0.370888 0.928678i \(-0.620947\pi\)
0.370888 0.928678i \(-0.379053\pi\)
\(632\) 48.9927i 1.94882i
\(633\) −47.8848 −1.90325
\(634\) −74.0660 −2.94154
\(635\) 56.5358i 2.24355i
\(636\) −87.7080 −3.47785
\(637\) −3.84040 21.6082i −0.152162 0.856147i
\(638\) 2.04684 0.0810352
\(639\) 6.76114i 0.267466i
\(640\) −52.6936 −2.08290
\(641\) −46.4680 −1.83537 −0.917687 0.397304i \(-0.869946\pi\)
−0.917687 + 0.397304i \(0.869946\pi\)
\(642\) 83.7461i 3.30520i
\(643\) 18.1376i 0.715278i −0.933860 0.357639i \(-0.883582\pi\)
0.933860 0.357639i \(-0.116418\pi\)
\(644\) 13.5366i 0.533416i
\(645\) 26.1204i 1.02849i
\(646\) 9.56055 0.376155
\(647\) −27.8566 −1.09516 −0.547578 0.836755i \(-0.684450\pi\)
−0.547578 + 0.836755i \(0.684450\pi\)
\(648\) 49.3745i 1.93961i
\(649\) −1.27897 −0.0502038
\(650\) 18.7374 3.33018i 0.734942 0.130621i
\(651\) −2.25055 −0.0882060
\(652\) 15.8530i 0.620851i
\(653\) −7.49659 −0.293364 −0.146682 0.989184i \(-0.546859\pi\)
−0.146682 + 0.989184i \(0.546859\pi\)
\(654\) −2.72855 −0.106695
\(655\) 34.6986i 1.35579i
\(656\) 2.35196i 0.0918286i
\(657\) 2.39849i 0.0935741i
\(658\) 27.9396i 1.08920i
\(659\) −18.8622 −0.734768 −0.367384 0.930069i \(-0.619747\pi\)
−0.367384 + 0.930069i \(0.619747\pi\)
\(660\) −4.14125 −0.161198
\(661\) 0.0711000i 0.00276547i 0.999999 + 0.00138274i \(0.000440139\pi\)
−0.999999 + 0.00138274i \(0.999560\pi\)
\(662\) −18.6140 −0.723452
\(663\) −1.25851 7.08105i −0.0488764 0.275005i
\(664\) −37.0374 −1.43733
\(665\) 11.7935i 0.457333i
\(666\) −44.9469 −1.74166
\(667\) 18.0303 0.698138
\(668\) 58.2990i 2.25566i
\(669\) 8.73690i 0.337788i
\(670\) 5.13605i 0.198423i
\(671\) 1.02444i 0.0395480i
\(672\) −0.277113 −0.0106899
\(673\) 13.3225 0.513545 0.256773 0.966472i \(-0.417341\pi\)
0.256773 + 0.966472i \(0.417341\pi\)
\(674\) 33.6508i 1.29618i
\(675\) 2.30007 0.0885299
\(676\) 48.6615 17.8613i 1.87159 0.686973i
\(677\) −28.6510 −1.10115 −0.550574 0.834786i \(-0.685591\pi\)
−0.550574 + 0.834786i \(0.685591\pi\)
\(678\) 36.6909i 1.40911i
\(679\) 5.81972 0.223340
\(680\) 11.0181 0.422525
\(681\) 31.0265i 1.18894i
\(682\) 0.403323i 0.0154440i
\(683\) 18.5015i 0.707939i −0.935257 0.353970i \(-0.884832\pi\)
0.935257 0.353970i \(-0.115168\pi\)
\(684\) 46.8587i 1.79169i
\(685\) 51.7847 1.97859
\(686\) 30.5989 1.16827
\(687\) 45.2060i 1.72472i
\(688\) −16.2685 −0.620232
\(689\) −5.89234 33.1535i −0.224480 1.26305i
\(690\) −54.7773 −2.08534
\(691\) 3.41864i 0.130051i 0.997884 + 0.0650255i \(0.0207129\pi\)
−0.997884 + 0.0650255i \(0.979287\pi\)
\(692\) −9.45899 −0.359577
\(693\) −0.401199 −0.0152403
\(694\) 35.6756i 1.35423i
\(695\) 2.19581i 0.0832917i
\(696\) 58.1260i 2.20326i
\(697\) 0.507565i 0.0192254i
\(698\) −33.7175 −1.27623
\(699\) −4.70535 −0.177973
\(700\) 8.21881i 0.310642i
\(701\) 18.7003 0.706301 0.353151 0.935566i \(-0.385110\pi\)
0.353151 + 0.935566i \(0.385110\pi\)
\(702\) 9.26203 1.64613i 0.349573 0.0621292i
\(703\) 33.2683 1.25474
\(704\) 1.34339i 0.0506308i
\(705\) 75.2942 2.83574
\(706\) 33.0708 1.24464
\(707\) 18.5943i 0.699309i
\(708\) 72.8705i 2.73864i
\(709\) 2.87246i 0.107878i 0.998544 + 0.0539388i \(0.0171776\pi\)
−0.998544 + 0.0539388i \(0.982822\pi\)
\(710\) 17.3752i 0.652080i
\(711\) 25.6631 0.962441
\(712\) 84.1355 3.15311
\(713\) 3.55282i 0.133054i
\(714\) 4.66386 0.174541
\(715\) −0.278215 1.56539i −0.0104046 0.0585422i
\(716\) −31.5549 −1.17926
\(717\) 28.5332i 1.06559i
\(718\) −36.8844 −1.37652
\(719\) 27.9855 1.04368 0.521842 0.853042i \(-0.325245\pi\)
0.521842 + 0.853042i \(0.325245\pi\)
\(720\) 26.7438i 0.996683i
\(721\) 14.2424i 0.530415i
\(722\) 5.58850i 0.207982i
\(723\) 37.8464i 1.40752i
\(724\) 52.0310 1.93372
\(725\) −10.9472 −0.406570
\(726\) 63.2379i 2.34698i
\(727\) −52.3092 −1.94004 −0.970021 0.243020i \(-0.921862\pi\)
−0.970021 + 0.243020i \(0.921862\pi\)
\(728\) 2.93173 + 16.4955i 0.108657 + 0.611365i
\(729\) −18.3290 −0.678851
\(730\) 6.16380i 0.228133i
\(731\) −3.51083 −0.129853
\(732\) 58.3686 2.15736
\(733\) 31.3469i 1.15782i −0.815390 0.578912i \(-0.803478\pi\)
0.815390 0.578912i \(-0.196522\pi\)
\(734\) 45.3464i 1.67377i
\(735\) 38.3538i 1.41470i
\(736\) 0.437463i 0.0161251i
\(737\) −0.129323 −0.00476368
\(738\) −3.73549 −0.137505
\(739\) 34.1803i 1.25734i 0.777671 + 0.628671i \(0.216401\pi\)
−0.777671 + 0.628671i \(0.783599\pi\)
\(740\) 76.9239 2.82778
\(741\) 38.5731 6.85555i 1.41702 0.251845i
\(742\) 21.8363 0.801634
\(743\) 0.574231i 0.0210665i −0.999945 0.0105332i \(-0.996647\pi\)
0.999945 0.0105332i \(-0.00335290\pi\)
\(744\) −11.4535 −0.419907
\(745\) 27.8747 1.02125
\(746\) 32.2359i 1.18024i
\(747\) 19.4007i 0.709835i
\(748\) 0.556623i 0.0203521i
\(749\) 13.8853i 0.507357i
\(750\) −43.8316 −1.60050
\(751\) 39.2613 1.43266 0.716332 0.697760i \(-0.245820\pi\)
0.716332 + 0.697760i \(0.245820\pi\)
\(752\) 46.8954i 1.71010i
\(753\) 44.3845 1.61746
\(754\) −44.0827 + 7.83477i −1.60540 + 0.285326i
\(755\) 3.44992 0.125556
\(756\) 4.06261i 0.147756i
\(757\) 41.5394 1.50978 0.754888 0.655854i \(-0.227691\pi\)
0.754888 + 0.655854i \(0.227691\pi\)
\(758\) −1.57507 −0.0572090
\(759\) 1.37927i 0.0500642i
\(760\) 60.0197i 2.17714i
\(761\) 50.6181i 1.83490i 0.397847 + 0.917452i \(0.369757\pi\)
−0.397847 + 0.917452i \(0.630243\pi\)
\(762\) 121.790i 4.41200i
\(763\) 0.452399 0.0163779
\(764\) 39.1456 1.41624
\(765\) 5.77144i 0.208667i
\(766\) −1.56124 −0.0564100
\(767\) 27.5450 4.89555i 0.994593 0.176768i
\(768\) −75.1218 −2.71072
\(769\) 30.6558i 1.10548i 0.833355 + 0.552739i \(0.186417\pi\)
−0.833355 + 0.552739i \(0.813583\pi\)
\(770\) 1.03103 0.0371557
\(771\) −66.1378 −2.38189
\(772\) 79.6239i 2.86573i
\(773\) 24.6737i 0.887450i 0.896163 + 0.443725i \(0.146343\pi\)
−0.896163 + 0.443725i \(0.853657\pi\)
\(774\) 25.8384i 0.928742i
\(775\) 2.15711i 0.0774858i
\(776\) 29.6178 1.06322
\(777\) 16.2290 0.582214
\(778\) 8.56472i 0.307060i
\(779\) 2.76489 0.0990625
\(780\) 89.1898 15.8516i 3.19351 0.567579i
\(781\) 0.437500 0.0156550
\(782\) 7.36258i 0.263285i
\(783\) −5.41128 −0.193383