Properties

Label 804.2.o.c.365.1
Level 804
Weight 2
Character 804.365
Analytic conductor 6.420
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 365.1
Root \(1.22474 - 0.707107i\)
Character \(\chi\) = 804.365
Dual form 804.2.o.c.641.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.41421i) q^{3} -2.00000 q^{5} +(-0.949490 - 0.548188i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.41421i) q^{3} -2.00000 q^{5} +(-0.949490 - 0.548188i) q^{7} +(-1.00000 - 2.82843i) q^{9} +(0.724745 - 1.25529i) q^{11} +(4.50000 - 2.59808i) q^{13} +(-2.00000 + 2.82843i) q^{15} +(-5.17423 + 2.98735i) q^{17} +(-1.50000 - 2.59808i) q^{19} +(-1.72474 + 0.794593i) q^{21} +(-0.825765 + 0.476756i) q^{23} -1.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +(-4.62372 - 2.66951i) q^{29} +(-1.50000 - 0.866025i) q^{31} +(-1.05051 - 2.28024i) q^{33} +(1.89898 + 1.09638i) q^{35} +(-4.94949 - 8.57277i) q^{37} +(0.825765 - 8.96204i) q^{39} +(-1.72474 + 2.98735i) q^{41} +1.27135i q^{43} +(2.00000 + 5.65685i) q^{45} +(-0.275255 - 0.158919i) q^{47} +(-2.89898 - 5.02118i) q^{49} +(-0.949490 + 10.3048i) q^{51} +6.00000 q^{53} +(-1.44949 + 2.51059i) q^{55} +(-5.17423 - 0.476756i) q^{57} -0.635674i q^{59} +(9.39898 - 5.42650i) q^{61} +(-0.601021 + 3.23375i) q^{63} +(-9.00000 + 5.19615i) q^{65} +(8.00000 + 1.73205i) q^{67} +(-0.151531 + 1.64456i) q^{69} +(11.1742 + 6.45145i) q^{71} +(2.94949 + 5.10867i) q^{73} +(-1.00000 + 1.41421i) q^{75} +(-1.37628 + 0.794593i) q^{77} +(0.398979 + 0.230351i) q^{79} +(-7.00000 + 5.65685i) q^{81} +(-10.0732 + 5.81577i) q^{83} +(10.3485 - 5.97469i) q^{85} +(-8.39898 + 3.86943i) q^{87} -4.73545i q^{89} -5.69694 q^{91} +(-2.72474 + 1.25529i) q^{93} +(3.00000 + 5.19615i) q^{95} +(11.8485 - 6.84072i) q^{97} +(-4.27526 - 0.794593i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} - 8q^{5} + 6q^{7} - 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} - 8q^{5} + 6q^{7} - 4q^{9} - 2q^{11} + 18q^{13} - 8q^{15} - 6q^{17} - 6q^{19} - 2q^{21} - 18q^{23} - 4q^{25} - 20q^{27} + 6q^{29} - 6q^{31} - 14q^{33} - 12q^{35} - 10q^{37} + 18q^{39} - 2q^{41} + 8q^{45} - 6q^{47} + 8q^{49} + 6q^{51} + 24q^{53} + 4q^{55} - 6q^{57} + 18q^{61} - 22q^{63} - 36q^{65} + 32q^{67} - 30q^{69} + 30q^{71} + 2q^{73} - 4q^{75} - 30q^{77} - 18q^{79} - 28q^{81} - 6q^{83} + 12q^{85} - 14q^{87} + 36q^{91} - 6q^{93} + 12q^{95} + 18q^{97} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) 0 0
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) −0.949490 0.548188i −0.358873 0.207196i 0.309713 0.950830i \(-0.399767\pi\)
−0.668586 + 0.743634i \(0.733100\pi\)
\(8\) 0 0
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 0 0
\(11\) 0.724745 1.25529i 0.218519 0.378486i −0.735837 0.677159i \(-0.763211\pi\)
0.954355 + 0.298674i \(0.0965442\pi\)
\(12\) 0 0
\(13\) 4.50000 2.59808i 1.24808 0.720577i 0.277350 0.960769i \(-0.410544\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 0 0
\(15\) −2.00000 + 2.82843i −0.516398 + 0.730297i
\(16\) 0 0
\(17\) −5.17423 + 2.98735i −1.25494 + 0.724538i −0.972086 0.234626i \(-0.924613\pi\)
−0.282851 + 0.959164i \(0.591280\pi\)
\(18\) 0 0
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) 0 0
\(21\) −1.72474 + 0.794593i −0.376370 + 0.173394i
\(22\) 0 0
\(23\) −0.825765 + 0.476756i −0.172184 + 0.0994105i −0.583615 0.812030i \(-0.698362\pi\)
0.411431 + 0.911441i \(0.365029\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 0 0
\(29\) −4.62372 2.66951i −0.858604 0.495715i 0.00494052 0.999988i \(-0.498427\pi\)
−0.863545 + 0.504273i \(0.831761\pi\)
\(30\) 0 0
\(31\) −1.50000 0.866025i −0.269408 0.155543i 0.359211 0.933257i \(-0.383046\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) −1.05051 2.28024i −0.182870 0.396939i
\(34\) 0 0
\(35\) 1.89898 + 1.09638i 0.320986 + 0.185321i
\(36\) 0 0
\(37\) −4.94949 8.57277i −0.813691 1.40935i −0.910264 0.414028i \(-0.864121\pi\)
0.0965729 0.995326i \(-0.469212\pi\)
\(38\) 0 0
\(39\) 0.825765 8.96204i 0.132228 1.43507i
\(40\) 0 0
\(41\) −1.72474 + 2.98735i −0.269360 + 0.466545i −0.968697 0.248247i \(-0.920145\pi\)
0.699337 + 0.714792i \(0.253479\pi\)
\(42\) 0 0
\(43\) 1.27135i 0.193879i 0.995290 + 0.0969395i \(0.0309053\pi\)
−0.995290 + 0.0969395i \(0.969095\pi\)
\(44\) 0 0
\(45\) 2.00000 + 5.65685i 0.298142 + 0.843274i
\(46\) 0 0
\(47\) −0.275255 0.158919i −0.0401501 0.0231807i 0.479791 0.877383i \(-0.340713\pi\)
−0.519941 + 0.854202i \(0.674046\pi\)
\(48\) 0 0
\(49\) −2.89898 5.02118i −0.414140 0.717311i
\(50\) 0 0
\(51\) −0.949490 + 10.3048i −0.132955 + 1.44296i
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −1.44949 + 2.51059i −0.195449 + 0.338528i
\(56\) 0 0
\(57\) −5.17423 0.476756i −0.685344 0.0631479i
\(58\) 0 0
\(59\) 0.635674i 0.0827578i −0.999144 0.0413789i \(-0.986825\pi\)
0.999144 0.0413789i \(-0.0131751\pi\)
\(60\) 0 0
\(61\) 9.39898 5.42650i 1.20342 0.694793i 0.242103 0.970251i \(-0.422163\pi\)
0.961313 + 0.275458i \(0.0888295\pi\)
\(62\) 0 0
\(63\) −0.601021 + 3.23375i −0.0757215 + 0.407414i
\(64\) 0 0
\(65\) −9.00000 + 5.19615i −1.11631 + 0.644503i
\(66\) 0 0
\(67\) 8.00000 + 1.73205i 0.977356 + 0.211604i
\(68\) 0 0
\(69\) −0.151531 + 1.64456i −0.0182422 + 0.197982i
\(70\) 0 0
\(71\) 11.1742 + 6.45145i 1.32614 + 0.765646i 0.984700 0.174258i \(-0.0557528\pi\)
0.341438 + 0.939904i \(0.389086\pi\)
\(72\) 0 0
\(73\) 2.94949 + 5.10867i 0.345212 + 0.597924i 0.985392 0.170300i \(-0.0544738\pi\)
−0.640181 + 0.768224i \(0.721140\pi\)
\(74\) 0 0
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 0 0
\(77\) −1.37628 + 0.794593i −0.156841 + 0.0905523i
\(78\) 0 0
\(79\) 0.398979 + 0.230351i 0.0448887 + 0.0259165i 0.522276 0.852776i \(-0.325083\pi\)
−0.477388 + 0.878693i \(0.658416\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 0 0
\(83\) −10.0732 + 5.81577i −1.10568 + 0.638364i −0.937707 0.347428i \(-0.887055\pi\)
−0.167972 + 0.985792i \(0.553722\pi\)
\(84\) 0 0
\(85\) 10.3485 5.97469i 1.12245 0.648046i
\(86\) 0 0
\(87\) −8.39898 + 3.86943i −0.900465 + 0.414846i
\(88\) 0 0
\(89\) 4.73545i 0.501957i −0.967993 0.250978i \(-0.919248\pi\)
0.967993 0.250978i \(-0.0807523\pi\)
\(90\) 0 0
\(91\) −5.69694 −0.597201
\(92\) 0 0
\(93\) −2.72474 + 1.25529i −0.282543 + 0.130168i
\(94\) 0 0
\(95\) 3.00000 + 5.19615i 0.307794 + 0.533114i
\(96\) 0 0
\(97\) 11.8485 6.84072i 1.20303 0.694570i 0.241802 0.970326i \(-0.422262\pi\)
0.961228 + 0.275756i \(0.0889282\pi\)
\(98\) 0 0
\(99\) −4.27526 0.794593i −0.429679 0.0798596i
\(100\) 0 0
\(101\) 6.72474 11.6476i 0.669137 1.15898i −0.309009 0.951059i \(-0.599997\pi\)
0.978146 0.207920i \(-0.0666695\pi\)
\(102\) 0 0
\(103\) 1.94949 3.37662i 0.192089 0.332708i −0.753853 0.657043i \(-0.771807\pi\)
0.945942 + 0.324335i \(0.105140\pi\)
\(104\) 0 0
\(105\) 3.44949 1.58919i 0.336636 0.155089i
\(106\) 0 0
\(107\) 9.12096i 0.881756i −0.897567 0.440878i \(-0.854667\pi\)
0.897567 0.440878i \(-0.145333\pi\)
\(108\) 0 0
\(109\) 5.02118i 0.480942i 0.970656 + 0.240471i \(0.0773019\pi\)
−0.970656 + 0.240471i \(0.922698\pi\)
\(110\) 0 0
\(111\) −17.0732 1.57313i −1.62052 0.149315i
\(112\) 0 0
\(113\) 3.27526 5.67291i 0.308110 0.533662i −0.669839 0.742507i \(-0.733637\pi\)
0.977949 + 0.208844i \(0.0669702\pi\)
\(114\) 0 0
\(115\) 1.65153 0.953512i 0.154006 0.0889154i
\(116\) 0 0
\(117\) −11.8485 10.1298i −1.09539 0.936505i
\(118\) 0 0
\(119\) 6.55051 0.600484
\(120\) 0 0
\(121\) 4.44949 + 7.70674i 0.404499 + 0.700613i
\(122\) 0 0
\(123\) 2.50000 + 5.42650i 0.225417 + 0.489291i
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 4.39898 7.61926i 0.390346 0.676100i −0.602149 0.798384i \(-0.705689\pi\)
0.992495 + 0.122284i \(0.0390219\pi\)
\(128\) 0 0
\(129\) 1.79796 + 1.27135i 0.158301 + 0.111936i
\(130\) 0 0
\(131\) 6.29253i 0.549781i 0.961476 + 0.274890i \(0.0886416\pi\)
−0.961476 + 0.274890i \(0.911358\pi\)
\(132\) 0 0
\(133\) 3.28913i 0.285204i
\(134\) 0 0
\(135\) 10.0000 + 2.82843i 0.860663 + 0.243432i
\(136\) 0 0
\(137\) 9.10102 0.777553 0.388776 0.921332i \(-0.372898\pi\)
0.388776 + 0.921332i \(0.372898\pi\)
\(138\) 0 0
\(139\) 7.21393i 0.611878i 0.952051 + 0.305939i \(0.0989703\pi\)
−0.952051 + 0.305939i \(0.901030\pi\)
\(140\) 0 0
\(141\) −0.500000 + 0.230351i −0.0421076 + 0.0193990i
\(142\) 0 0
\(143\) 7.53177i 0.629838i
\(144\) 0 0
\(145\) 9.24745 + 5.33902i 0.767959 + 0.443381i
\(146\) 0 0
\(147\) −10.0000 0.921404i −0.824786 0.0759961i
\(148\) 0 0
\(149\) 14.7778i 1.21065i −0.795980 0.605323i \(-0.793044\pi\)
0.795980 0.605323i \(-0.206956\pi\)
\(150\) 0 0
\(151\) −4.39898 7.61926i −0.357984 0.620046i 0.629640 0.776887i \(-0.283202\pi\)
−0.987624 + 0.156841i \(0.949869\pi\)
\(152\) 0 0
\(153\) 13.6237 + 11.6476i 1.10141 + 0.941653i
\(154\) 0 0
\(155\) 3.00000 + 1.73205i 0.240966 + 0.139122i
\(156\) 0 0
\(157\) 6.94949 + 12.0369i 0.554630 + 0.960647i 0.997932 + 0.0642747i \(0.0204734\pi\)
−0.443303 + 0.896372i \(0.646193\pi\)
\(158\) 0 0
\(159\) 6.00000 8.48528i 0.475831 0.672927i
\(160\) 0 0
\(161\) 1.04541 0.0823897
\(162\) 0 0
\(163\) −11.2980 + 19.5686i −0.884924 + 1.53273i −0.0391242 + 0.999234i \(0.512457\pi\)
−0.845800 + 0.533500i \(0.820877\pi\)
\(164\) 0 0
\(165\) 2.10102 + 4.56048i 0.163564 + 0.355033i
\(166\) 0 0
\(167\) −22.0732 12.7440i −1.70808 0.986158i −0.936941 0.349487i \(-0.886356\pi\)
−0.771136 0.636671i \(-0.780311\pi\)
\(168\) 0 0
\(169\) 7.00000 12.1244i 0.538462 0.932643i
\(170\) 0 0
\(171\) −5.84847 + 6.84072i −0.447244 + 0.523123i
\(172\) 0 0
\(173\) 10.6237 6.13361i 0.807707 0.466330i −0.0384521 0.999260i \(-0.512243\pi\)
0.846159 + 0.532931i \(0.178909\pi\)
\(174\) 0 0
\(175\) 0.949490 + 0.548188i 0.0717747 + 0.0414391i
\(176\) 0 0
\(177\) −0.898979 0.635674i −0.0675714 0.0477802i
\(178\) 0 0
\(179\) −13.5959 −1.01621 −0.508103 0.861296i \(-0.669653\pi\)
−0.508103 + 0.861296i \(0.669653\pi\)
\(180\) 0 0
\(181\) 1.05051 1.81954i 0.0780838 0.135245i −0.824339 0.566096i \(-0.808453\pi\)
0.902423 + 0.430851i \(0.141786\pi\)
\(182\) 0 0
\(183\) 1.72474 18.7187i 0.127497 1.38372i
\(184\) 0 0
\(185\) 9.89898 + 17.1455i 0.727787 + 1.26056i
\(186\) 0 0
\(187\) 8.66025i 0.633300i
\(188\) 0 0
\(189\) 3.97219 + 4.08372i 0.288935 + 0.297047i
\(190\) 0 0
\(191\) −8.72474 15.1117i −0.631300 1.09344i −0.987286 0.158953i \(-0.949188\pi\)
0.355986 0.934491i \(-0.384145\pi\)
\(192\) 0 0
\(193\) −12.8990 −0.928489 −0.464244 0.885707i \(-0.653674\pi\)
−0.464244 + 0.885707i \(0.653674\pi\)
\(194\) 0 0
\(195\) −1.65153 + 17.9241i −0.118269 + 1.28357i
\(196\) 0 0
\(197\) 1.62372 2.81237i 0.115686 0.200373i −0.802368 0.596830i \(-0.796427\pi\)
0.918054 + 0.396456i \(0.129760\pi\)
\(198\) 0 0
\(199\) 5.50000 + 9.52628i 0.389885 + 0.675300i 0.992434 0.122782i \(-0.0391815\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) 0 0
\(201\) 10.4495 9.58166i 0.737050 0.675838i
\(202\) 0 0
\(203\) 2.92679 + 5.06934i 0.205420 + 0.355798i
\(204\) 0 0
\(205\) 3.44949 5.97469i 0.240923 0.417291i
\(206\) 0 0
\(207\) 2.17423 + 1.85886i 0.151120 + 0.129200i
\(208\) 0 0
\(209\) −4.34847 −0.300790
\(210\) 0 0
\(211\) 2.94949 + 5.10867i 0.203051 + 0.351695i 0.949510 0.313737i \(-0.101581\pi\)
−0.746459 + 0.665432i \(0.768248\pi\)
\(212\) 0 0
\(213\) 20.2980 9.35131i 1.39079 0.640741i
\(214\) 0 0
\(215\) 2.54270i 0.173411i
\(216\) 0 0
\(217\) 0.949490 + 1.64456i 0.0644556 + 0.111640i
\(218\) 0 0
\(219\) 10.1742 + 0.937458i 0.687511 + 0.0633475i
\(220\) 0 0
\(221\) −15.5227 + 26.8861i −1.04417 + 1.80856i
\(222\) 0 0
\(223\) 20.6969 1.38597 0.692985 0.720952i \(-0.256295\pi\)
0.692985 + 0.720952i \(0.256295\pi\)
\(224\) 0 0
\(225\) 1.00000 + 2.82843i 0.0666667 + 0.188562i
\(226\) 0 0
\(227\) 23.4217 + 13.5225i 1.55455 + 0.897521i 0.997762 + 0.0668675i \(0.0213005\pi\)
0.556790 + 0.830653i \(0.312033\pi\)
\(228\) 0 0
\(229\) −8.84847 + 5.10867i −0.584723 + 0.337590i −0.763008 0.646389i \(-0.776278\pi\)
0.178285 + 0.983979i \(0.442945\pi\)
\(230\) 0 0
\(231\) −0.252551 + 2.74094i −0.0166167 + 0.180341i
\(232\) 0 0
\(233\) 9.27526 16.0652i 0.607642 1.05247i −0.383986 0.923339i \(-0.625449\pi\)
0.991628 0.129128i \(-0.0412178\pi\)
\(234\) 0 0
\(235\) 0.550510 + 0.317837i 0.0359113 + 0.0207334i
\(236\) 0 0
\(237\) 0.724745 0.333891i 0.0470772 0.0216886i
\(238\) 0 0
\(239\) −5.62372 + 9.74058i −0.363768 + 0.630066i −0.988578 0.150712i \(-0.951843\pi\)
0.624809 + 0.780777i \(0.285177\pi\)
\(240\) 0 0
\(241\) 4.00000 0.257663 0.128831 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) 0 0
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 0 0
\(245\) 5.79796 + 10.0424i 0.370418 + 0.641583i
\(246\) 0 0
\(247\) −13.5000 7.79423i −0.858984 0.495935i
\(248\) 0 0
\(249\) −1.84847 + 20.0614i −0.117142 + 1.27134i
\(250\) 0 0
\(251\) 10.0732 + 17.4473i 0.635816 + 1.10126i 0.986342 + 0.164712i \(0.0526695\pi\)
−0.350526 + 0.936553i \(0.613997\pi\)
\(252\) 0 0
\(253\) 1.38211i 0.0868922i
\(254\) 0 0
\(255\) 1.89898 20.6096i 0.118919 1.29063i
\(256\) 0 0
\(257\) −13.0732 7.54782i −0.815485 0.470820i 0.0333722 0.999443i \(-0.489375\pi\)
−0.848857 + 0.528623i \(0.822709\pi\)
\(258\) 0 0
\(259\) 10.8530i 0.674373i
\(260\) 0 0
\(261\) −2.92679 + 15.7474i −0.181163 + 0.974738i
\(262\) 0 0
\(263\) 7.84961i 0.484027i 0.970273 + 0.242014i \(0.0778079\pi\)
−0.970273 + 0.242014i \(0.922192\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) −6.69694 4.73545i −0.409846 0.289805i
\(268\) 0 0
\(269\) 6.00680i 0.366241i 0.983090 + 0.183121i \(0.0586199\pi\)
−0.983090 + 0.183121i \(0.941380\pi\)
\(270\) 0 0
\(271\) 9.75663i 0.592673i −0.955084 0.296337i \(-0.904235\pi\)
0.955084 0.296337i \(-0.0957650\pi\)
\(272\) 0 0
\(273\) −5.69694 + 8.05669i −0.344794 + 0.487613i
\(274\) 0 0
\(275\) −0.724745 + 1.25529i −0.0437038 + 0.0756971i
\(276\) 0 0
\(277\) 25.7980 1.55005 0.775025 0.631931i \(-0.217737\pi\)
0.775025 + 0.631931i \(0.217737\pi\)
\(278\) 0 0
\(279\) −0.949490 + 5.10867i −0.0568445 + 0.305848i
\(280\) 0 0
\(281\) 3.72474 + 6.45145i 0.222200 + 0.384861i 0.955476 0.295070i \(-0.0953430\pi\)
−0.733276 + 0.679931i \(0.762010\pi\)
\(282\) 0 0
\(283\) −7.79796 −0.463541 −0.231770 0.972771i \(-0.574452\pi\)
−0.231770 + 0.972771i \(0.574452\pi\)
\(284\) 0 0
\(285\) 10.3485 + 0.953512i 0.612990 + 0.0564812i
\(286\) 0 0
\(287\) 3.27526 1.89097i 0.193332 0.111620i
\(288\) 0 0
\(289\) 9.34847 16.1920i 0.549910 0.952472i
\(290\) 0 0
\(291\) 2.17423 23.5970i 0.127456 1.38328i
\(292\) 0 0
\(293\) 29.2699i 1.70997i −0.518657 0.854983i \(-0.673568\pi\)
0.518657 0.854983i \(-0.326432\pi\)
\(294\) 0 0
\(295\) 1.27135i 0.0740208i
\(296\) 0 0
\(297\) −5.39898 + 5.25153i −0.313281 + 0.304725i
\(298\) 0 0
\(299\) −2.47730 + 4.29080i −0.143266 + 0.248144i
\(300\) 0 0
\(301\) 0.696938 1.20713i 0.0401709 0.0695780i
\(302\) 0 0
\(303\) −9.74745 21.1578i −0.559976 1.21549i
\(304\) 0 0
\(305\) −18.7980 + 10.8530i −1.07637 + 0.621441i
\(306\) 0 0
\(307\) −4.29796 7.44428i −0.245297 0.424868i 0.716918 0.697158i \(-0.245552\pi\)
−0.962215 + 0.272290i \(0.912219\pi\)
\(308\) 0 0
\(309\) −2.82577 6.13361i −0.160752 0.348929i
\(310\) 0 0
\(311\) −14.2020 −0.805324 −0.402662 0.915349i \(-0.631915\pi\)
−0.402662 + 0.915349i \(0.631915\pi\)
\(312\) 0 0
\(313\) 11.6637i 0.659269i −0.944109 0.329634i \(-0.893075\pi\)
0.944109 0.329634i \(-0.106925\pi\)
\(314\) 0 0
\(315\) 1.20204 6.46750i 0.0677273 0.364402i
\(316\) 0 0
\(317\) 16.3207 9.42274i 0.916660 0.529234i 0.0340918 0.999419i \(-0.489146\pi\)
0.882568 + 0.470185i \(0.155813\pi\)
\(318\) 0 0
\(319\) −6.70204 + 3.86943i −0.375242 + 0.216646i
\(320\) 0 0
\(321\) −12.8990 9.12096i −0.719951 0.509082i
\(322\) 0 0
\(323\) 15.5227 + 8.96204i 0.863706 + 0.498661i
\(324\) 0 0
\(325\) −4.50000 + 2.59808i −0.249615 + 0.144115i
\(326\) 0 0
\(327\) 7.10102 + 5.02118i 0.392687 + 0.277672i
\(328\) 0 0
\(329\) 0.174235 + 0.301783i 0.00960587 + 0.0166378i
\(330\) 0 0
\(331\) −12.0959 6.98358i −0.664852 0.383852i 0.129271 0.991609i \(-0.458736\pi\)
−0.794123 + 0.607757i \(0.792070\pi\)
\(332\) 0 0
\(333\) −19.2980 + 22.5720i −1.05752 + 1.23694i
\(334\) 0 0
\(335\) −16.0000 3.46410i −0.874173 0.189264i
\(336\) 0 0
\(337\) −15.9495 + 9.20844i −0.868824 + 0.501616i −0.866957 0.498382i \(-0.833928\pi\)
−0.00186678 + 0.999998i \(0.500594\pi\)
\(338\) 0 0
\(339\) −4.74745 10.3048i −0.257846 0.559681i
\(340\) 0 0
\(341\) −2.17423 + 1.25529i −0.117741 + 0.0679780i
\(342\) 0 0
\(343\) 14.0314i 0.757623i
\(344\) 0 0
\(345\) 0.303062 3.28913i 0.0163163 0.177081i
\(346\) 0 0
\(347\) 6.07321 10.5191i 0.326027 0.564696i −0.655693 0.755028i \(-0.727623\pi\)
0.981720 + 0.190332i \(0.0609566\pi\)
\(348\) 0 0
\(349\) 2.20204 0.117873 0.0589363 0.998262i \(-0.481229\pi\)
0.0589363 + 0.998262i \(0.481229\pi\)
\(350\) 0 0
\(351\) −26.1742 + 6.62642i −1.39708 + 0.353692i
\(352\) 0 0
\(353\) −3.17423 5.49794i −0.168947 0.292626i 0.769103 0.639125i \(-0.220703\pi\)
−0.938050 + 0.346500i \(0.887370\pi\)
\(354\) 0 0
\(355\) −22.3485 12.9029i −1.18613 0.684815i
\(356\) 0 0
\(357\) 6.55051 9.26382i 0.346690 0.490293i
\(358\) 0 0
\(359\) 13.5065i 0.712844i −0.934325 0.356422i \(-0.883997\pi\)
0.934325 0.356422i \(-0.116003\pi\)
\(360\) 0 0
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) 0 0
\(363\) 15.3485 + 1.41421i 0.805586 + 0.0742270i
\(364\) 0 0
\(365\) −5.89898 10.2173i −0.308767 0.534800i
\(366\) 0 0
\(367\) 13.5000 + 7.79423i 0.704694 + 0.406855i 0.809093 0.587680i \(-0.199959\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) 0 0
\(369\) 10.1742 + 1.89097i 0.529649 + 0.0984399i
\(370\) 0 0
\(371\) −5.69694 3.28913i −0.295770 0.170763i
\(372\) 0 0
\(373\) 0.398979 + 0.230351i 0.0206584 + 0.0119271i 0.510294 0.860000i \(-0.329537\pi\)
−0.489635 + 0.871927i \(0.662870\pi\)
\(374\) 0 0
\(375\) 12.0000 16.9706i 0.619677 0.876356i
\(376\) 0 0
\(377\) −27.7423 −1.42880
\(378\) 0 0
\(379\) −20.6010 + 11.8940i −1.05820 + 0.610954i −0.924935 0.380126i \(-0.875881\pi\)
−0.133269 + 0.991080i \(0.542547\pi\)
\(380\) 0 0
\(381\) −6.37628 13.8404i −0.326666 0.709063i
\(382\) 0 0
\(383\) 12.0732 + 20.9114i 0.616912 + 1.06852i 0.990046 + 0.140746i \(0.0449501\pi\)
−0.373133 + 0.927778i \(0.621717\pi\)
\(384\) 0 0
\(385\) 2.75255 1.58919i 0.140283 0.0809924i
\(386\) 0 0
\(387\) 3.59592 1.27135i 0.182791 0.0646263i
\(388\) 0 0
\(389\) 8.97219 5.18010i 0.454908 0.262641i −0.254993 0.966943i \(-0.582073\pi\)
0.709901 + 0.704302i \(0.248740\pi\)
\(390\) 0 0
\(391\) 2.84847 4.93369i 0.144053 0.249508i
\(392\) 0 0
\(393\) 8.89898 + 6.29253i 0.448894 + 0.317416i
\(394\) 0 0
\(395\) −0.797959 0.460702i −0.0401497 0.0231804i
\(396\) 0 0
\(397\) −26.6969 −1.33988 −0.669940 0.742415i \(-0.733680\pi\)
−0.669940 + 0.742415i \(0.733680\pi\)
\(398\) 0 0
\(399\) 4.65153 + 3.28913i 0.232868 + 0.164662i
\(400\) 0 0
\(401\) −5.10102 −0.254733 −0.127366 0.991856i \(-0.540652\pi\)
−0.127366 + 0.991856i \(0.540652\pi\)
\(402\) 0 0
\(403\) −9.00000 −0.448322
\(404\) 0 0
\(405\) 14.0000 11.3137i 0.695666 0.562183i
\(406\) 0 0
\(407\) −14.3485 −0.711227
\(408\) 0 0
\(409\) −16.5000 9.52628i −0.815872 0.471044i 0.0331186 0.999451i \(-0.489456\pi\)
−0.848991 + 0.528407i \(0.822789\pi\)
\(410\) 0 0
\(411\) 9.10102 12.8708i 0.448920 0.634869i
\(412\) 0 0
\(413\) −0.348469 + 0.603566i −0.0171470 + 0.0296996i
\(414\) 0 0
\(415\) 20.1464 11.6315i 0.988949 0.570970i
\(416\) 0 0
\(417\) 10.2020 + 7.21393i 0.499596 + 0.353268i
\(418\) 0 0
\(419\) −22.3207 + 12.8868i −1.09044 + 0.629563i −0.933692 0.358076i \(-0.883433\pi\)
−0.156743 + 0.987639i \(0.550100\pi\)
\(420\) 0 0
\(421\) −6.50000 11.2583i −0.316791 0.548697i 0.663026 0.748596i \(-0.269272\pi\)
−0.979817 + 0.199899i \(0.935939\pi\)
\(422\) 0 0
\(423\) −0.174235 + 0.937458i −0.00847158 + 0.0455808i
\(424\) 0 0
\(425\) 5.17423 2.98735i 0.250987 0.144908i
\(426\) 0 0
\(427\) −11.8990 −0.575832
\(428\) 0 0
\(429\) −10.6515 7.53177i −0.514261 0.363637i
\(430\) 0 0
\(431\) −27.7702 16.0331i −1.33764 0.772287i −0.351184 0.936306i \(-0.614221\pi\)
−0.986457 + 0.164019i \(0.947554\pi\)
\(432\) 0 0
\(433\) −13.5000 7.79423i −0.648769 0.374567i 0.139216 0.990262i \(-0.455542\pi\)
−0.787984 + 0.615695i \(0.788875\pi\)
\(434\) 0 0
\(435\) 16.7980 7.73885i 0.805400 0.371049i
\(436\) 0 0
\(437\) 2.47730 + 1.43027i 0.118505 + 0.0684190i
\(438\) 0 0
\(439\) −4.60102 7.96920i −0.219595 0.380349i 0.735089 0.677970i \(-0.237140\pi\)
−0.954684 + 0.297621i \(0.903807\pi\)
\(440\) 0 0
\(441\) −11.3031 + 13.2207i −0.538241 + 0.629559i
\(442\) 0 0
\(443\) 16.6237 28.7931i 0.789817 1.36800i −0.136262 0.990673i \(-0.543509\pi\)
0.926079 0.377330i \(-0.123158\pi\)
\(444\) 0 0
\(445\) 9.47090i 0.448964i
\(446\) 0 0
\(447\) −20.8990 14.7778i −0.988488 0.698966i
\(448\) 0 0
\(449\) −14.1742 8.18350i −0.668923 0.386203i 0.126745 0.991935i \(-0.459547\pi\)
−0.795669 + 0.605732i \(0.792880\pi\)
\(450\) 0 0
\(451\) 2.50000 + 4.33013i 0.117720 + 0.203898i
\(452\) 0 0
\(453\) −15.1742 1.39816i −0.712948 0.0656913i
\(454\) 0 0
\(455\) 11.3939 0.534153
\(456\) 0 0
\(457\) 18.1969 31.5180i 0.851217 1.47435i −0.0288939 0.999582i \(-0.509198\pi\)
0.880111 0.474768i \(-0.157468\pi\)
\(458\) 0 0
\(459\) 30.0959 7.61926i 1.40476 0.355636i
\(460\) 0 0
\(461\) 42.1407i 1.96269i 0.192263 + 0.981344i \(0.438417\pi\)
−0.192263 + 0.981344i \(0.561583\pi\)
\(462\) 0 0
\(463\) −7.19694 + 4.15515i −0.334470 + 0.193106i −0.657824 0.753172i \(-0.728523\pi\)
0.323354 + 0.946278i \(0.395190\pi\)
\(464\) 0 0
\(465\) 5.44949 2.51059i 0.252714 0.116426i
\(466\) 0 0
\(467\) 35.1742 20.3079i 1.62767 0.939735i 0.642883 0.765964i \(-0.277738\pi\)
0.984786 0.173771i \(-0.0555954\pi\)
\(468\) 0 0
\(469\) −6.64643 6.03007i −0.306904 0.278443i
\(470\) 0 0
\(471\) 23.9722 + 2.20881i 1.10458 + 0.101776i
\(472\) 0 0
\(473\) 1.59592 + 0.921404i 0.0733804 + 0.0423662i
\(474\) 0 0
\(475\) 1.50000 + 2.59808i 0.0688247 + 0.119208i
\(476\) 0 0
\(477\) −6.00000 16.9706i −0.274721 0.777029i
\(478\) 0 0
\(479\) 17.7247 10.2334i 0.809864 0.467575i −0.0370445 0.999314i \(-0.511794\pi\)
0.846909 + 0.531738i \(0.178461\pi\)
\(480\) 0 0
\(481\) −44.5454 25.7183i −2.03110 1.17265i
\(482\) 0 0
\(483\) 1.04541 1.47843i 0.0475677 0.0672709i
\(484\) 0 0
\(485\) −23.6969 + 13.6814i −1.07602 + 0.621242i
\(486\) 0 0
\(487\) −8.60102 + 4.96580i −0.389749 + 0.225022i −0.682052 0.731304i \(-0.738912\pi\)
0.292302 + 0.956326i \(0.405579\pi\)
\(488\) 0 0
\(489\) 16.3763 + 35.5464i 0.740561 + 1.60746i
\(490\) 0 0
\(491\) 11.6637i 0.526373i 0.964745 + 0.263187i \(0.0847735\pi\)
−0.964745 + 0.263187i \(0.915226\pi\)
\(492\) 0 0
\(493\) 31.8990 1.43666
\(494\) 0 0
\(495\) 8.55051 + 1.58919i 0.384317 + 0.0714286i
\(496\) 0 0
\(497\) −7.07321 12.2512i −0.317277 0.549540i
\(498\) 0 0
\(499\) −3.39898 + 1.96240i −0.152159 + 0.0878492i −0.574147 0.818753i \(-0.694666\pi\)
0.421987 + 0.906602i \(0.361333\pi\)
\(500\) 0 0
\(501\) −40.0959 + 18.4723i −1.79135 + 0.825280i
\(502\) 0 0
\(503\) −22.1742 + 38.4069i −0.988700 + 1.71248i −0.364528 + 0.931193i \(0.618770\pi\)
−0.624173 + 0.781287i \(0.714564\pi\)
\(504\) 0 0
\(505\) −13.4495 + 23.2952i −0.598494 + 1.03662i
\(506\) 0 0
\(507\) −10.1464 22.0239i −0.450619 0.978114i
\(508\) 0 0
\(509\) 2.82843i 0.125368i −0.998033 0.0626839i \(-0.980034\pi\)
0.998033 0.0626839i \(-0.0199660\pi\)
\(510\) 0 0
\(511\) 6.46750i 0.286105i
\(512\) 0 0
\(513\) 3.82577 + 15.1117i 0.168912 + 0.667198i
\(514\) 0 0
\(515\) −3.89898 + 6.75323i −0.171810 + 0.297583i
\(516\) 0 0
\(517\) −0.398979 + 0.230351i −0.0175471 + 0.0101308i
\(518\) 0 0
\(519\) 1.94949 21.1578i 0.0855731 0.928725i
\(520\) 0 0
\(521\) 40.2929 1.76526 0.882631 0.470066i \(-0.155770\pi\)
0.882631 + 0.470066i \(0.155770\pi\)
\(522\) 0 0
\(523\) 22.6464 + 39.2248i 0.990259 + 1.71518i 0.615712 + 0.787971i \(0.288869\pi\)
0.374547 + 0.927208i \(0.377798\pi\)
\(524\) 0 0
\(525\) 1.72474 0.794593i 0.0752740 0.0346789i
\(526\) 0 0
\(527\) 10.3485 0.450786
\(528\) 0 0
\(529\) −11.0454 + 19.1312i −0.480235 + 0.831792i
\(530\) 0 0
\(531\) −1.79796 + 0.635674i −0.0780248 + 0.0275859i
\(532\) 0 0
\(533\) 17.9241i 0.776378i
\(534\) 0 0
\(535\) 18.2419i 0.788667i
\(536\) 0 0
\(537\) −13.5959 + 19.2275i −0.586707 + 0.829729i
\(538\) 0 0
\(539\) −8.40408 −0.361989
\(540\) 0 0
\(541\) 38.6766i 1.66284i −0.555648 0.831418i \(-0.687530\pi\)
0.555648 0.831418i \(-0.312470\pi\)
\(542\) 0 0
\(543\) −1.52270 3.30518i −0.0653455 0.141839i
\(544\) 0 0
\(545\) 10.0424i 0.430167i
\(546\) 0 0
\(547\) 17.8485 + 10.3048i 0.763145 + 0.440602i 0.830424 0.557132i \(-0.188098\pi\)
−0.0672785 + 0.997734i \(0.521432\pi\)
\(548\) 0 0
\(549\) −24.7474 21.1578i −1.05620 0.902994i
\(550\) 0 0
\(551\) 16.0171i 0.682349i
\(552\) 0 0
\(553\) −0.252551 0.437432i −0.0107396 0.0186015i
\(554\) 0 0
\(555\) 34.1464 + 3.14626i 1.44944 + 0.133551i
\(556\) 0 0
\(557\) 7.07321 + 4.08372i 0.299702 + 0.173033i 0.642309 0.766446i \(-0.277977\pi\)
−0.342607 + 0.939479i \(0.611310\pi\)
\(558\) 0 0
\(559\) 3.30306 + 5.72107i 0.139705 + 0.241975i
\(560\) 0 0
\(561\) 12.2474 + 8.66025i 0.517088 + 0.365636i
\(562\) 0 0
\(563\) 42.2929 1.78243 0.891216 0.453580i \(-0.149853\pi\)
0.891216 + 0.453580i \(0.149853\pi\)
\(564\) 0 0
\(565\) −6.55051 + 11.3458i −0.275582 + 0.477322i
\(566\) 0 0
\(567\) 9.74745 1.53381i 0.409354 0.0644139i
\(568\) 0 0
\(569\) −23.4217 13.5225i −0.981888 0.566893i −0.0790484 0.996871i \(-0.525188\pi\)
−0.902840 + 0.429977i \(0.858522\pi\)
\(570\) 0 0
\(571\) −18.8485 + 32.6465i −0.788784 + 1.36621i 0.137928 + 0.990442i \(0.455956\pi\)
−0.926712 + 0.375772i \(0.877378\pi\)
\(572\) 0 0
\(573\) −30.0959 2.77305i −1.25728 0.115846i
\(574\) 0 0
\(575\) 0.825765 0.476756i 0.0344368 0.0198821i
\(576\) 0 0
\(577\) −26.8485 15.5010i −1.11772 0.645314i −0.176899 0.984229i \(-0.556607\pi\)
−0.940817 + 0.338915i \(0.889940\pi\)
\(578\) 0 0
\(579\) −12.8990 + 18.2419i −0.536063 + 0.758108i
\(580\) 0 0
\(581\) 12.7526 0.529065
\(582\) 0 0
\(583\) 4.34847 7.53177i 0.180095 0.311934i
\(584\) 0 0
\(585\) 23.6969 + 20.2597i 0.979748 + 0.837635i
\(586\) 0 0
\(587\) −8.27526 14.3332i −0.341556 0.591593i 0.643166 0.765727i \(-0.277621\pi\)
−0.984722 + 0.174134i \(0.944287\pi\)
\(588\) 0 0
\(589\) 5.19615i 0.214104i
\(590\) 0 0
\(591\) −2.35357 5.10867i −0.0968130 0.210142i
\(592\) 0 0
\(593\) −11.9722 20.7364i −0.491639 0.851544i 0.508315 0.861171i \(-0.330269\pi\)
−0.999954 + 0.00962762i \(0.996935\pi\)
\(594\) 0 0
\(595\) −13.1010 −0.537089
\(596\) 0 0
\(597\) 18.9722 + 1.74810i 0.776480 + 0.0715452i
\(598\) 0 0
\(599\) 8.17423 14.1582i 0.333990 0.578488i −0.649300 0.760532i \(-0.724938\pi\)
0.983290 + 0.182044i \(0.0582714\pi\)
\(600\) 0 0
\(601\) −1.39898 2.42310i −0.0570656 0.0988405i 0.836081 0.548605i \(-0.184841\pi\)
−0.893147 + 0.449765i \(0.851508\pi\)
\(602\) 0 0
\(603\) −3.10102 24.3595i −0.126283 0.991994i
\(604\) 0 0
\(605\) −8.89898 15.4135i −0.361795 0.626647i
\(606\) 0 0
\(607\) −9.84847 + 17.0580i −0.399737 + 0.692365i −0.993693 0.112133i \(-0.964232\pi\)
0.593956 + 0.804497i \(0.297565\pi\)
\(608\) 0 0
\(609\) 10.0959 + 0.930242i 0.409107 + 0.0376953i
\(610\) 0 0
\(611\) −1.65153 −0.0668138
\(612\) 0 0
\(613\) 13.1969 + 22.8578i 0.533019 + 0.923217i 0.999256 + 0.0385567i \(0.0122760\pi\)
−0.466237 + 0.884660i \(0.654391\pi\)
\(614\) 0 0
\(615\) −5.00000 10.8530i −0.201619 0.437635i
\(616\) 0 0
\(617\) 26.7272i 1.07600i 0.842946 + 0.537998i \(0.180819\pi\)
−0.842946 + 0.537998i \(0.819181\pi\)
\(618\) 0 0
\(619\) −2.94949 5.10867i −0.118550 0.205335i 0.800643 0.599141i \(-0.204491\pi\)
−0.919193 + 0.393807i \(0.871158\pi\)
\(620\) 0 0
\(621\) 4.80306 1.21597i 0.192740 0.0487952i
\(622\) 0 0
\(623\) −2.59592 + 4.49626i −0.104003 + 0.180139i
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) −4.34847 + 6.14966i −0.173661 + 0.245594i
\(628\) 0 0
\(629\) 51.2196 + 29.5717i 2.04226 + 1.17910i
\(630\) 0 0
\(631\) 23.5454 13.5939i 0.937328 0.541167i 0.0482062 0.998837i \(-0.484650\pi\)
0.889122 + 0.457671i \(0.151316\pi\)
\(632\) 0 0
\(633\) 10.1742 + 0.937458i 0.404390 + 0.0372606i
\(634\) 0 0
\(635\) −8.79796 + 15.2385i −0.349136 + 0.604722i
\(636\) 0 0
\(637\) −26.0908 15.0635i −1.03376 0.596839i
\(638\) 0 0
\(639\) 7.07321 38.0570i 0.279812 1.50551i
\(640\) 0 0
\(641\) −21.5227 + 37.2784i −0.850096 + 1.47241i 0.0310256 + 0.999519i \(0.490123\pi\)
−0.881121 + 0.472890i \(0.843211\pi\)
\(642\) 0 0
\(643\) 29.1918 1.15121 0.575607 0.817727i \(-0.304766\pi\)
0.575607 + 0.817727i \(0.304766\pi\)
\(644\) 0 0
\(645\) −3.59592 2.54270i −0.141589 0.100119i
\(646\) 0 0
\(647\) −0.174235 0.301783i −0.00684987 0.0118643i 0.862580 0.505920i \(-0.168847\pi\)
−0.869430 + 0.494056i \(0.835514\pi\)
\(648\) 0 0
\(649\) −0.797959 0.460702i −0.0313226 0.0180841i
\(650\) 0 0
\(651\) 3.27526 + 0.301783i 0.128367 + 0.0118278i
\(652\) 0 0
\(653\) −9.62372 16.6688i −0.376605 0.652300i 0.613960 0.789337i \(-0.289575\pi\)
−0.990566 + 0.137037i \(0.956242\pi\)
\(654\) 0 0
\(655\) 12.5851i 0.491739i
\(656\) 0 0
\(657\) 11.5000 13.4511i 0.448658 0.524777i
\(658\) 0 0
\(659\) −5.72474 3.30518i −0.223004 0.128752i 0.384336 0.923193i \(-0.374430\pi\)
−0.607341 + 0.794442i \(0.707764\pi\)
\(660\) 0 0
\(661\) 37.1195i 1.44378i 0.692007 + 0.721891i \(0.256727\pi\)
−0.692007 + 0.721891i \(0.743273\pi\)
\(662\) 0 0
\(663\) 22.5000 + 48.8385i 0.873828 + 1.89673i
\(664\) 0 0
\(665\) 6.57826i 0.255094i
\(666\) 0 0
\(667\) 5.09082 0.197117
\(668\) 0 0
\(669\) 20.6969 29.2699i 0.800190 1.13164i
\(670\) 0 0
\(671\) 15.7313i 0.607301i
\(672\) 0 0
\(673\) 4.38551i 0.169049i 0.996421 + 0.0845244i \(0.0269371\pi\)
−0.996421 + 0.0845244i \(0.973063\pi\)
\(674\) 0 0
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) 0 0
\(677\) −17.2753 + 29.9216i −0.663942 + 1.14998i 0.315629 + 0.948883i \(0.397784\pi\)
−0.979571 + 0.201099i \(0.935549\pi\)
\(678\) 0 0
\(679\) −15.0000 −0.575647
\(680\) 0 0
\(681\) 42.5454 19.6007i 1.63034 0.751102i
\(682\) 0 0
\(683\) −16.1742 28.0146i −0.618890 1.07195i −0.989689 0.143235i \(-0.954249\pi\)
0.370799 0.928713i \(-0.379084\pi\)
\(684\) 0 0
\(685\) −18.2020 −0.695464
\(686\) 0 0
\(687\) −1.62372 + 17.6223i −0.0619489 + 0.672332i
\(688\) 0 0
\(689\) 27.0000 15.5885i 1.02862 0.593873i
\(690\) 0 0
\(691\) −13.6464 + 23.6363i −0.519135 + 0.899167i 0.480618 + 0.876930i \(0.340412\pi\)
−0.999753 + 0.0222375i \(0.992921\pi\)
\(692\) 0 0
\(693\) 3.62372 + 3.09810i 0.137654 + 0.117687i
\(694\) 0 0
\(695\) 14.4279i 0.547280i
\(696\) 0 0
\(697\) 20.6096i 0.780646i
\(698\) 0 0
\(699\) −13.4444 29.1824i −0.508513 1.10378i
\(700\) 0 0
\(701\) 6.82577 11.8226i 0.257806 0.446532i −0.707848 0.706365i \(-0.750334\pi\)
0.965654 + 0.259832i \(0.0836673\pi\)
\(702\) 0 0
\(703\) −14.8485 + 25.7183i −0.560021 + 0.969984i
\(704\) 0 0
\(705\) 1.00000 0.460702i 0.0376622 0.0173510i
\(706\) 0 0
\(707\) −12.7702 + 7.37285i −0.480271 + 0.277285i
\(708\) 0 0
\(709\) 12.7474 + 22.0792i 0.478740 + 0.829203i 0.999703 0.0243768i \(-0.00776015\pi\)
−0.520962 + 0.853580i \(0.674427\pi\)
\(710\) 0 0
\(711\) 0.252551 1.35884i 0.00947141 0.0509603i
\(712\) 0 0
\(713\) 1.65153 0.0618503
\(714\) 0 0
\(715\) 15.0635i 0.563344i
\(716\) 0 0
\(717\) 8.15153 + 17.6937i 0.304424 + 0.660784i
\(718\) 0 0
\(719\) 14.6691 8.46923i 0.547066 0.315849i −0.200872 0.979618i \(-0.564377\pi\)
0.747938 + 0.663769i \(0.231044\pi\)
\(720\) 0 0
\(721\) −3.70204 + 2.13737i −0.137871 + 0.0796000i
\(722\) 0 0
\(723\) 4.00000 5.65685i 0.148762 0.210381i
\(724\) 0 0
\(725\) 4.62372 + 2.66951i 0.171721 + 0.0991431i
\(726\) 0 0
\(727\) 45.8939 26.4968i 1.70211 0.982713i 0.758488 0.651687i \(-0.225938\pi\)
0.943621 0.331027i \(-0.107395\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 0 0
\(731\) −3.79796 6.57826i −0.140473 0.243306i
\(732\) 0 0
\(733\) 14.0505 + 8.11207i 0.518967 + 0.299626i 0.736512 0.676424i \(-0.236471\pi\)
−0.217545 + 0.976050i \(0.569805\pi\)
\(734\) 0 0
\(735\) 20.0000 + 1.84281i 0.737711 + 0.0679730i
\(736\) 0 0
\(737\) 7.97219 8.78706i 0.293660 0.323676i
\(738\) 0 0
\(739\) −36.6464 + 21.1578i −1.34806 + 0.778303i −0.987975 0.154616i \(-0.950586\pi\)
−0.360086 + 0.932919i \(0.617253\pi\)
\(740\) 0 0
\(741\) −24.5227 + 11.2977i −0.900864 + 0.415030i
\(742\) 0 0
\(743\) 6.27526 3.62302i 0.230217 0.132916i −0.380455 0.924799i \(-0.624233\pi\)
0.610672 + 0.791884i \(0.290899\pi\)
\(744\) 0 0
\(745\) 29.5556i 1.08283i
\(746\) 0 0
\(747\) 26.5227 + 22.6756i 0.970415 + 0.829656i
\(748\) 0 0
\(749\) −5.00000 + 8.66025i −0.182696 + 0.316439i
\(750\) 0 0
\(751\) 15.3939 0.561731 0.280865 0.959747i \(-0.409379\pi\)
0.280865 + 0.959747i \(0.409379\pi\)
\(752\) 0 0
\(753\) 34.7474 + 3.20164i 1.26627 + 0.116674i
\(754\) 0 0
\(755\) 8.79796 + 15.2385i 0.320191 + 0.554586i
\(756\) 0 0
\(757\) −17.0505 9.84412i −0.619711 0.357791i 0.157045 0.987591i \(-0.449803\pi\)
−0.776757 + 0.629801i \(0.783136\pi\)
\(758\) 0 0
\(759\) 1.95459 + 1.38211i 0.0709472 + 0.0501673i
\(760\) 0 0
\(761\) 17.9562i 0.650911i −0.945557 0.325456i \(-0.894482\pi\)
0.945557 0.325456i \(-0.105518\pi\)
\(762\) 0 0
\(763\) 2.75255 4.76756i 0.0996490 0.172597i
\(764\) 0 0
\(765\) −27.2474 23.2952i −0.985134 0.842240i
\(766\) 0 0
\(767\) −1.65153 2.86054i −0.0596333 0.103288i
\(768\) 0 0
\(769\) −10.7474 6.20504i −0.387563 0.223760i 0.293541 0.955947i \(-0.405166\pi\)
−0.681104 + 0.732187i \(0.738500\pi\)
\(770\) 0 0
\(771\) −23.7474 + 10.9405i −0.855243 + 0.394012i
\(772\) 0 0
\(773\) −2.97219 1.71600i −0.106902 0.0617201i 0.445596 0.895234i \(-0.352992\pi\)
−0.552498 + 0.833514i \(0.686325\pi\)
\(774\) 0 0
\(775\) 1.50000 + 0.866025i 0.0538816 + 0.0311086i
\(776\) 0 0
\(777\) 15.3485 + 10.8530i 0.550623 + 0.389349i
\(778\) 0 0
\(779\) 10.3485 0.370772
\(780\) 0 0
\(781\) 16.1969 9.35131i 0.579572 0.334616i
\(782\) 0 0
\(783\) 19.3434 + 19.8865i 0.691276 + 0.710685i
\(784\) 0 0
\(785\) −13.8990 24.0737i −0.496076 0.859229i
\(786\) 0 0
\(787\) 18.6464 10.7655i 0.664673 0.383749i −0.129382 0.991595i \(-0.541299\pi\)
0.794055 + 0.607845i \(0.207966\pi\)
\(788\) 0 0
\(789\) 11.1010 + 7.84961i 0.395207 + 0.279453i
\(790\) 0 0
\(791\) −6.21964 + 3.59091i −0.221145 + 0.127678i
\(792\) 0 0
\(793\) 28.1969 48.8385i 1.00130 1.73431i
\(794\) 0 0
\(795\) −12.0000 + 16.9706i −0.425596 + 0.601884i
\(796\) 0 0
\(797\) −11.1742 6.45145i −0.395812 0.228522i 0.288864 0.957370i \(-0.406723\pi\)
−0.684675 + 0.728848i \(0.740056\pi\)
\(798\) 0 0
\(799\) 1.89898 0.0671811
\(800\) 0 0
\(801\)