Properties

Label 804.2.y.b.73.4
Level 804
Weight 2
Character 804.73
Analytic conductor 6.420
Analytic rank 0
Dimension 120
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.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 73.4
Character \(\chi\) = 804.73
Dual form 804.2.y.b.793.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415415 + 0.909632i) q^{3} +(1.03511 + 0.303934i) q^{5} +(-4.65735 + 0.897630i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.909632i) q^{3} +(1.03511 + 0.303934i) q^{5} +(-4.65735 + 0.897630i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(3.37592 - 3.21894i) q^{11} +(-0.254078 + 5.33375i) q^{13} +(-0.706467 + 0.815306i) q^{15} +(-1.13889 + 0.895635i) q^{17} +(-5.02744 - 0.968959i) q^{19} +(1.11822 - 4.60936i) q^{21} +(-3.70948 + 0.354212i) q^{23} +(-3.22720 - 2.07400i) q^{25} +(0.959493 - 0.281733i) q^{27} +(-5.06141 + 8.76662i) q^{29} +(-0.338612 - 7.10834i) q^{31} +(1.52564 + 4.40804i) q^{33} +(-5.09367 - 0.486386i) q^{35} +(1.62134 + 2.80824i) q^{37} +(-4.74620 - 2.44684i) q^{39} +(-7.90358 - 3.16412i) q^{41} +(0.383067 + 2.66429i) q^{43} +(-0.448152 - 0.981315i) q^{45} +(-6.39496 - 8.98046i) q^{47} +(14.3866 - 5.75951i) q^{49} +(-0.341585 - 1.40803i) q^{51} +(-0.818964 + 5.69602i) q^{53} +(4.47278 - 2.30588i) q^{55} +(2.96987 - 4.17060i) q^{57} +(2.12121 - 1.36322i) q^{59} +(-0.675562 - 0.644148i) q^{61} +(3.72830 + 2.93197i) q^{63} +(-1.88411 + 5.44377i) q^{65} +(-2.15690 - 7.89606i) q^{67} +(1.21877 - 3.52141i) q^{69} +(7.56521 + 5.94934i) q^{71} +(-1.07574 - 1.02572i) q^{73} +(3.22720 - 2.07400i) q^{75} +(-12.8334 + 18.0220i) q^{77} +(-7.75307 + 3.99699i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(4.07464 + 16.7959i) q^{83} +(-1.45109 + 0.580928i) q^{85} +(-5.87181 - 8.24581i) q^{87} +(-1.53625 - 3.36393i) q^{89} +(-3.60441 - 25.0692i) q^{91} +(6.60664 + 2.64490i) q^{93} +(-4.90943 - 2.53099i) q^{95} +(4.41371 + 7.64477i) q^{97} +(-4.64347 - 0.443397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{20}{33}\right)\) \(1\)

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
\(3\) −0.415415 + 0.909632i −0.239840 + 0.525176i
\(4\) 0 0
\(5\) 1.03511 + 0.303934i 0.462913 + 0.135924i 0.504869 0.863196i \(-0.331541\pi\)
−0.0419559 + 0.999119i \(0.513359\pi\)
\(6\) 0 0
\(7\) −4.65735 + 0.897630i −1.76031 + 0.339272i −0.964058 0.265691i \(-0.914400\pi\)
−0.796253 + 0.604963i \(0.793188\pi\)
\(8\) 0 0
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 0 0
\(11\) 3.37592 3.21894i 1.01788 0.970545i 0.0183078 0.999832i \(-0.494172\pi\)
0.999571 + 0.0292869i \(0.00932364\pi\)
\(12\) 0 0
\(13\) −0.254078 + 5.33375i −0.0704685 + 1.47932i 0.636065 + 0.771636i \(0.280561\pi\)
−0.706533 + 0.707680i \(0.749742\pi\)
\(14\) 0 0
\(15\) −0.706467 + 0.815306i −0.182409 + 0.210511i
\(16\) 0 0
\(17\) −1.13889 + 0.895635i −0.276222 + 0.217223i −0.746654 0.665213i \(-0.768341\pi\)
0.470432 + 0.882436i \(0.344098\pi\)
\(18\) 0 0
\(19\) −5.02744 0.968959i −1.15337 0.222294i −0.423512 0.905890i \(-0.639203\pi\)
−0.729861 + 0.683596i \(0.760415\pi\)
\(20\) 0 0
\(21\) 1.11822 4.60936i 0.244015 1.00585i
\(22\) 0 0
\(23\) −3.70948 + 0.354212i −0.773480 + 0.0738584i −0.474329 0.880348i \(-0.657309\pi\)
−0.299151 + 0.954206i \(0.596703\pi\)
\(24\) 0 0
\(25\) −3.22720 2.07400i −0.645440 0.414799i
\(26\) 0 0
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) 0 0
\(29\) −5.06141 + 8.76662i −0.939880 + 1.62792i −0.174189 + 0.984712i \(0.555730\pi\)
−0.765692 + 0.643208i \(0.777603\pi\)
\(30\) 0 0
\(31\) −0.338612 7.10834i −0.0608165 1.27670i −0.798684 0.601750i \(-0.794470\pi\)
0.737868 0.674945i \(-0.235833\pi\)
\(32\) 0 0
\(33\) 1.52564 + 4.40804i 0.265579 + 0.767341i
\(34\) 0 0
\(35\) −5.09367 0.486386i −0.860987 0.0822143i
\(36\) 0 0
\(37\) 1.62134 + 2.80824i 0.266547 + 0.461672i 0.967968 0.251075i \(-0.0807840\pi\)
−0.701421 + 0.712747i \(0.747451\pi\)
\(38\) 0 0
\(39\) −4.74620 2.44684i −0.760000 0.391807i
\(40\) 0 0
\(41\) −7.90358 3.16412i −1.23433 0.494152i −0.339522 0.940598i \(-0.610265\pi\)
−0.894810 + 0.446446i \(0.852689\pi\)
\(42\) 0 0
\(43\) 0.383067 + 2.66429i 0.0584172 + 0.406301i 0.997959 + 0.0638652i \(0.0203428\pi\)
−0.939541 + 0.342436i \(0.888748\pi\)
\(44\) 0 0
\(45\) −0.448152 0.981315i −0.0668065 0.146286i
\(46\) 0 0
\(47\) −6.39496 8.98046i −0.932800 1.30993i −0.950706 0.310095i \(-0.899639\pi\)
0.0179051 0.999840i \(-0.494300\pi\)
\(48\) 0 0
\(49\) 14.3866 5.75951i 2.05522 0.822788i
\(50\) 0 0
\(51\) −0.341585 1.40803i −0.0478315 0.197164i
\(52\) 0 0
\(53\) −0.818964 + 5.69602i −0.112493 + 0.782408i 0.852987 + 0.521932i \(0.174789\pi\)
−0.965480 + 0.260476i \(0.916121\pi\)
\(54\) 0 0
\(55\) 4.47278 2.30588i 0.603110 0.310925i
\(56\) 0 0
\(57\) 2.96987 4.17060i 0.393369 0.552409i
\(58\) 0 0
\(59\) 2.12121 1.36322i 0.276158 0.177476i −0.395230 0.918582i \(-0.629335\pi\)
0.671387 + 0.741107i \(0.265699\pi\)
\(60\) 0 0
\(61\) −0.675562 0.644148i −0.0864969 0.0824746i 0.645597 0.763678i \(-0.276608\pi\)
−0.732094 + 0.681203i \(0.761457\pi\)
\(62\) 0 0
\(63\) 3.72830 + 2.93197i 0.469721 + 0.369393i
\(64\) 0 0
\(65\) −1.88411 + 5.44377i −0.233695 + 0.675217i
\(66\) 0 0
\(67\) −2.15690 7.89606i −0.263507 0.964658i
\(68\) 0 0
\(69\) 1.21877 3.52141i 0.146723 0.423927i
\(70\) 0 0
\(71\) 7.56521 + 5.94934i 0.897825 + 0.706057i 0.956348 0.292229i \(-0.0943969\pi\)
−0.0585236 + 0.998286i \(0.518639\pi\)
\(72\) 0 0
\(73\) −1.07574 1.02572i −0.125906 0.120051i 0.624510 0.781017i \(-0.285299\pi\)
−0.750417 + 0.660965i \(0.770147\pi\)
\(74\) 0 0
\(75\) 3.22720 2.07400i 0.372645 0.239484i
\(76\) 0 0
\(77\) −12.8334 + 18.0220i −1.46250 + 2.05380i
\(78\) 0 0
\(79\) −7.75307 + 3.99699i −0.872289 + 0.449696i −0.835412 0.549624i \(-0.814771\pi\)
−0.0368766 + 0.999320i \(0.511741\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0 0
\(83\) 4.07464 + 16.7959i 0.447250 + 1.84359i 0.531381 + 0.847133i \(0.321673\pi\)
−0.0841312 + 0.996455i \(0.526811\pi\)
\(84\) 0 0
\(85\) −1.45109 + 0.580928i −0.157393 + 0.0630105i
\(86\) 0 0
\(87\) −5.87181 8.24581i −0.629524 0.884043i
\(88\) 0 0
\(89\) −1.53625 3.36393i −0.162843 0.356576i 0.810567 0.585645i \(-0.199159\pi\)
−0.973410 + 0.229070i \(0.926432\pi\)
\(90\) 0 0
\(91\) −3.60441 25.0692i −0.377844 2.62797i
\(92\) 0 0
\(93\) 6.60664 + 2.64490i 0.685077 + 0.274263i
\(94\) 0 0
\(95\) −4.90943 2.53099i −0.503697 0.259674i
\(96\) 0 0
\(97\) 4.41371 + 7.64477i 0.448144 + 0.776209i 0.998265 0.0588763i \(-0.0187518\pi\)
−0.550121 + 0.835085i \(0.685418\pi\)
\(98\) 0 0
\(99\) −4.64347 0.443397i −0.466686 0.0445631i
\(100\) 0 0
\(101\) 3.41180 + 9.85775i 0.339487 + 0.980883i 0.977514 + 0.210869i \(0.0676294\pi\)
−0.638027 + 0.770014i \(0.720249\pi\)
\(102\) 0 0
\(103\) 0.633034 + 13.2890i 0.0623747 + 1.30941i 0.785574 + 0.618767i \(0.212368\pi\)
−0.723199 + 0.690639i \(0.757329\pi\)
\(104\) 0 0
\(105\) 2.55842 4.43131i 0.249676 0.432452i
\(106\) 0 0
\(107\) −3.78929 + 1.11264i −0.366324 + 0.107563i −0.459714 0.888067i \(-0.652048\pi\)
0.0933895 + 0.995630i \(0.470230\pi\)
\(108\) 0 0
\(109\) −12.4528 8.00295i −1.19277 0.766544i −0.215076 0.976597i \(-0.569000\pi\)
−0.977690 + 0.210053i \(0.932636\pi\)
\(110\) 0 0
\(111\) −3.22800 + 0.308236i −0.306388 + 0.0292565i
\(112\) 0 0
\(113\) 1.81891 7.49766i 0.171109 0.705320i −0.820011 0.572348i \(-0.806033\pi\)
0.991120 0.132972i \(-0.0424522\pi\)
\(114\) 0 0
\(115\) −3.94736 0.760791i −0.368093 0.0709441i
\(116\) 0 0
\(117\) 4.19736 3.30084i 0.388046 0.305163i
\(118\) 0 0
\(119\) 4.50027 5.19359i 0.412539 0.476095i
\(120\) 0 0
\(121\) 0.511905 10.7462i 0.0465368 0.976928i
\(122\) 0 0
\(123\) 6.16145 5.87493i 0.555559 0.529724i
\(124\) 0 0
\(125\) −6.24247 7.20419i −0.558343 0.644363i
\(126\) 0 0
\(127\) 1.27674 0.246072i 0.113292 0.0218353i −0.132290 0.991211i \(-0.542233\pi\)
0.245582 + 0.969376i \(0.421021\pi\)
\(128\) 0 0
\(129\) −2.58266 0.758337i −0.227390 0.0667678i
\(130\) 0 0
\(131\) −5.59843 + 12.2589i −0.489137 + 1.07106i 0.490712 + 0.871322i \(0.336737\pi\)
−0.979849 + 0.199739i \(0.935991\pi\)
\(132\) 0 0
\(133\) 24.2843 2.10571
\(134\) 0 0
\(135\) 1.07880 0.0928487
\(136\) 0 0
\(137\) −1.57903 + 3.45759i −0.134905 + 0.295402i −0.965013 0.262201i \(-0.915552\pi\)
0.830108 + 0.557603i \(0.188279\pi\)
\(138\) 0 0
\(139\) 22.3503 + 6.56264i 1.89573 + 0.556636i 0.991594 + 0.129388i \(0.0413012\pi\)
0.904134 + 0.427248i \(0.140517\pi\)
\(140\) 0 0
\(141\) 10.8255 2.08644i 0.911670 0.175710i
\(142\) 0 0
\(143\) 16.3112 + 18.8242i 1.36401 + 1.57416i
\(144\) 0 0
\(145\) −7.90357 + 7.53604i −0.656356 + 0.625834i
\(146\) 0 0
\(147\) −0.737359 + 15.4791i −0.0608163 + 1.27669i
\(148\) 0 0
\(149\) 9.12813 10.5344i 0.747805 0.863013i −0.246548 0.969130i \(-0.579296\pi\)
0.994354 + 0.106117i \(0.0338419\pi\)
\(150\) 0 0
\(151\) −4.41848 + 3.47473i −0.359571 + 0.282770i −0.781559 0.623832i \(-0.785575\pi\)
0.421988 + 0.906602i \(0.361333\pi\)
\(152\) 0 0
\(153\) 1.42269 + 0.274201i 0.115018 + 0.0221679i
\(154\) 0 0
\(155\) 1.80997 7.46080i 0.145380 0.599266i
\(156\) 0 0
\(157\) 22.5770 2.15584i 1.80184 0.172055i 0.860486 0.509474i \(-0.170160\pi\)
0.941354 + 0.337419i \(0.109554\pi\)
\(158\) 0 0
\(159\) −4.84107 3.11117i −0.383922 0.246732i
\(160\) 0 0
\(161\) 16.9584 4.97943i 1.33651 0.392434i
\(162\) 0 0
\(163\) −1.91746 + 3.32115i −0.150187 + 0.260132i −0.931296 0.364263i \(-0.881321\pi\)
0.781109 + 0.624395i \(0.214654\pi\)
\(164\) 0 0
\(165\) 0.239441 + 5.02648i 0.0186404 + 0.391311i
\(166\) 0 0
\(167\) 3.63748 + 10.5098i 0.281477 + 0.813274i 0.993776 + 0.111398i \(0.0355329\pi\)
−0.712299 + 0.701876i \(0.752346\pi\)
\(168\) 0 0
\(169\) −15.4432 1.47465i −1.18794 0.113434i
\(170\) 0 0
\(171\) 2.55998 + 4.43401i 0.195767 + 0.339078i
\(172\) 0 0
\(173\) 18.7991 + 9.69163i 1.42927 + 0.736841i 0.987102 0.160091i \(-0.0511787\pi\)
0.442169 + 0.896932i \(0.354209\pi\)
\(174\) 0 0
\(175\) 16.8919 + 6.76249i 1.27691 + 0.511196i
\(176\) 0 0
\(177\) 0.358845 + 2.49582i 0.0269724 + 0.187597i
\(178\) 0 0
\(179\) −5.86554 12.8437i −0.438411 0.959986i −0.991887 0.127121i \(-0.959426\pi\)
0.553476 0.832865i \(-0.313301\pi\)
\(180\) 0 0
\(181\) 2.04839 + 2.87656i 0.152255 + 0.213813i 0.883658 0.468133i \(-0.155073\pi\)
−0.731402 + 0.681946i \(0.761134\pi\)
\(182\) 0 0
\(183\) 0.866576 0.346925i 0.0640591 0.0256454i
\(184\) 0 0
\(185\) 0.824736 + 3.39961i 0.0606358 + 0.249944i
\(186\) 0 0
\(187\) −0.961821 + 6.68962i −0.0703354 + 0.489193i
\(188\) 0 0
\(189\) −4.21580 + 2.17340i −0.306654 + 0.158091i
\(190\) 0 0
\(191\) −5.31055 + 7.45763i −0.384258 + 0.539615i −0.960724 0.277506i \(-0.910492\pi\)
0.576466 + 0.817121i \(0.304431\pi\)
\(192\) 0 0
\(193\) 11.8487 7.61469i 0.852887 0.548117i −0.0395869 0.999216i \(-0.512604\pi\)
0.892474 + 0.451099i \(0.148968\pi\)
\(194\) 0 0
\(195\) −4.16914 3.97527i −0.298558 0.284675i
\(196\) 0 0
\(197\) 3.50546 + 2.75673i 0.249754 + 0.196409i 0.735185 0.677866i \(-0.237095\pi\)
−0.485432 + 0.874275i \(0.661338\pi\)
\(198\) 0 0
\(199\) 1.94567 5.62164i 0.137925 0.398508i −0.854793 0.518969i \(-0.826316\pi\)
0.992718 + 0.120461i \(0.0384373\pi\)
\(200\) 0 0
\(201\) 8.07852 + 1.31816i 0.569815 + 0.0929759i
\(202\) 0 0
\(203\) 15.7036 45.3725i 1.10217 3.18452i
\(204\) 0 0
\(205\) −7.21936 5.67737i −0.504222 0.396524i
\(206\) 0 0
\(207\) 2.69689 + 2.57148i 0.187447 + 0.178730i
\(208\) 0 0
\(209\) −20.0912 + 12.9119i −1.38974 + 0.893132i
\(210\) 0 0
\(211\) −0.811481 + 1.13957i −0.0558647 + 0.0784509i −0.841563 0.540159i \(-0.818364\pi\)
0.785699 + 0.618609i \(0.212304\pi\)
\(212\) 0 0
\(213\) −8.55441 + 4.41011i −0.586139 + 0.302176i
\(214\) 0 0
\(215\) −0.413255 + 2.87425i −0.0281838 + 0.196022i
\(216\) 0 0
\(217\) 7.95770 + 32.8021i 0.540204 + 2.22675i
\(218\) 0 0
\(219\) 1.37991 0.552431i 0.0932455 0.0373299i
\(220\) 0 0
\(221\) −4.48772 6.30213i −0.301877 0.423927i
\(222\) 0 0
\(223\) −5.87937 12.8740i −0.393712 0.862109i −0.997869 0.0652438i \(-0.979217\pi\)
0.604157 0.796865i \(-0.293510\pi\)
\(224\) 0 0
\(225\) 0.545945 + 3.79713i 0.0363964 + 0.253142i
\(226\) 0 0
\(227\) −8.04584 3.22107i −0.534021 0.213790i 0.0889480 0.996036i \(-0.471650\pi\)
−0.622969 + 0.782247i \(0.714074\pi\)
\(228\) 0 0
\(229\) 3.38078 + 1.74291i 0.223408 + 0.115175i 0.566298 0.824201i \(-0.308375\pi\)
−0.342889 + 0.939376i \(0.611406\pi\)
\(230\) 0 0
\(231\) −11.0622 19.1603i −0.727840 1.26066i
\(232\) 0 0
\(233\) −18.8655 1.80144i −1.23592 0.118016i −0.543438 0.839449i \(-0.682878\pi\)
−0.692484 + 0.721433i \(0.743484\pi\)
\(234\) 0 0
\(235\) −3.88998 11.2394i −0.253755 0.733176i
\(236\) 0 0
\(237\) −0.415044 8.71285i −0.0269600 0.565961i
\(238\) 0 0
\(239\) 4.20496 7.28320i 0.271996 0.471111i −0.697377 0.716705i \(-0.745650\pi\)
0.969373 + 0.245594i \(0.0789829\pi\)
\(240\) 0 0
\(241\) 13.6429 4.00591i 0.878815 0.258043i 0.188955 0.981986i \(-0.439490\pi\)
0.689860 + 0.723943i \(0.257672\pi\)
\(242\) 0 0
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) 0 0
\(245\) 16.6421 1.58913i 1.06323 0.101526i
\(246\) 0 0
\(247\) 6.44554 26.5689i 0.410120 1.69054i
\(248\) 0 0
\(249\) −16.9707 3.27084i −1.07548 0.207281i
\(250\) 0 0
\(251\) −16.7140 + 13.1440i −1.05498 + 0.829642i −0.985794 0.167962i \(-0.946282\pi\)
−0.0691827 + 0.997604i \(0.522039\pi\)
\(252\) 0 0
\(253\) −11.3827 + 13.1364i −0.715626 + 0.825876i
\(254\) 0 0
\(255\) 0.0743731 1.56128i 0.00465742 0.0977713i
\(256\) 0 0
\(257\) −8.02310 + 7.65001i −0.500467 + 0.477195i −0.897752 0.440501i \(-0.854801\pi\)
0.397285 + 0.917695i \(0.369952\pi\)
\(258\) 0 0
\(259\) −10.0719 11.6236i −0.625838 0.722255i
\(260\) 0 0
\(261\) 9.93989 1.91576i 0.615264 0.118582i
\(262\) 0 0
\(263\) −21.3253 6.26166i −1.31497 0.386111i −0.452296 0.891868i \(-0.649395\pi\)
−0.862676 + 0.505757i \(0.831213\pi\)
\(264\) 0 0
\(265\) −2.57893 + 5.64707i −0.158422 + 0.346897i
\(266\) 0 0
\(267\) 3.69812 0.226321
\(268\) 0 0
\(269\) 25.5099 1.55536 0.777682 0.628658i \(-0.216396\pi\)
0.777682 + 0.628658i \(0.216396\pi\)
\(270\) 0 0
\(271\) −5.69901 + 12.4791i −0.346190 + 0.758050i 0.653809 + 0.756660i \(0.273170\pi\)
−0.999999 + 0.00139065i \(0.999557\pi\)
\(272\) 0 0
\(273\) 24.3011 + 7.13544i 1.47077 + 0.431856i
\(274\) 0 0
\(275\) −17.5708 + 3.38650i −1.05956 + 0.204214i
\(276\) 0 0
\(277\) −11.9592 13.8017i −0.718559 0.829261i 0.272574 0.962135i \(-0.412125\pi\)
−0.991133 + 0.132874i \(0.957580\pi\)
\(278\) 0 0
\(279\) −5.15038 + 4.91088i −0.308345 + 0.294007i
\(280\) 0 0
\(281\) −0.161282 + 3.38572i −0.00962127 + 0.201975i 0.988939 + 0.148326i \(0.0473884\pi\)
−0.998560 + 0.0536495i \(0.982915\pi\)
\(282\) 0 0
\(283\) −3.36175 + 3.87967i −0.199836 + 0.230623i −0.846819 0.531882i \(-0.821485\pi\)
0.646983 + 0.762504i \(0.276030\pi\)
\(284\) 0 0
\(285\) 4.34171 3.41436i 0.257181 0.202249i
\(286\) 0 0
\(287\) 39.6499 + 7.64190i 2.34046 + 0.451087i
\(288\) 0 0
\(289\) −3.51299 + 14.4807i −0.206646 + 0.851808i
\(290\) 0 0
\(291\) −8.78745 + 0.839099i −0.515129 + 0.0491889i
\(292\) 0 0
\(293\) 9.88966 + 6.35570i 0.577760 + 0.371304i 0.796646 0.604447i \(-0.206606\pi\)
−0.218886 + 0.975751i \(0.570242\pi\)
\(294\) 0 0
\(295\) 2.61000 0.766366i 0.151960 0.0446195i
\(296\) 0 0
\(297\) 2.33229 4.03965i 0.135333 0.234404i
\(298\) 0 0
\(299\) −0.946783 19.8754i −0.0547539 1.14943i
\(300\) 0 0
\(301\) −4.17563 12.0647i −0.240679 0.695397i
\(302\) 0 0
\(303\) −10.3842 0.991575i −0.596559 0.0569645i
\(304\) 0 0
\(305\) −0.503500 0.872087i −0.0288303 0.0499356i
\(306\) 0 0
\(307\) −30.9782 15.9704i −1.76802 0.911477i −0.931696 0.363239i \(-0.881671\pi\)
−0.836322 0.548238i \(-0.815299\pi\)
\(308\) 0 0
\(309\) −12.3511 4.94463i −0.702629 0.281290i
\(310\) 0 0
\(311\) 3.20929 + 22.3211i 0.181982 + 1.26571i 0.852068 + 0.523431i \(0.175348\pi\)
−0.670086 + 0.742284i \(0.733743\pi\)
\(312\) 0 0
\(313\) 6.40665 + 14.0286i 0.362125 + 0.792943i 0.999745 + 0.0225919i \(0.00719185\pi\)
−0.637620 + 0.770351i \(0.720081\pi\)
\(314\) 0 0
\(315\) 2.96806 + 4.16805i 0.167231 + 0.234843i
\(316\) 0 0
\(317\) −15.3306 + 6.13744i −0.861052 + 0.344713i −0.759807 0.650148i \(-0.774707\pi\)
−0.101245 + 0.994862i \(0.532282\pi\)
\(318\) 0 0
\(319\) 11.1323 + 45.8878i 0.623287 + 2.56922i
\(320\) 0 0
\(321\) 0.562038 3.90906i 0.0313699 0.218183i
\(322\) 0 0
\(323\) 6.59354 3.39921i 0.366874 0.189137i
\(324\) 0 0
\(325\) 11.8821 16.6861i 0.659102 0.925579i
\(326\) 0 0
\(327\) 12.4528 8.00295i 0.688644 0.442564i
\(328\) 0 0
\(329\) 37.8447 + 36.0848i 2.08644 + 1.98942i
\(330\) 0 0
\(331\) 7.89925 + 6.21204i 0.434182 + 0.341445i 0.811208 0.584758i \(-0.198811\pi\)
−0.377025 + 0.926203i \(0.623053\pi\)
\(332\) 0 0
\(333\) 1.06058 3.06433i 0.0581192 0.167925i
\(334\) 0 0
\(335\) 0.167270 8.82881i 0.00913893 0.482370i
\(336\) 0 0
\(337\) 8.26156 23.8702i 0.450036 1.30029i −0.460792 0.887508i \(-0.652435\pi\)
0.910828 0.412786i \(-0.135444\pi\)
\(338\) 0 0
\(339\) 6.06451 + 4.76918i 0.329379 + 0.259026i
\(340\) 0 0
\(341\) −24.0244 22.9072i −1.30100 1.24050i
\(342\) 0 0
\(343\) −33.9025 + 21.7878i −1.83056 + 1.17643i
\(344\) 0 0
\(345\) 2.33183 3.27460i 0.125542 0.176299i
\(346\) 0 0
\(347\) −10.1450 + 5.23010i −0.544611 + 0.280767i −0.708498 0.705713i \(-0.750627\pi\)
0.163887 + 0.986479i \(0.447597\pi\)
\(348\) 0 0
\(349\) 5.15260 35.8371i 0.275813 1.91832i −0.106553 0.994307i \(-0.533981\pi\)
0.382365 0.924011i \(-0.375110\pi\)
\(350\) 0 0
\(351\) 1.25890 + 5.18928i 0.0671954 + 0.276983i
\(352\) 0 0
\(353\) −8.60028 + 3.44303i −0.457747 + 0.183254i −0.589064 0.808086i \(-0.700504\pi\)
0.131317 + 0.991340i \(0.458079\pi\)
\(354\) 0 0
\(355\) 6.02258 + 8.45753i 0.319645 + 0.448879i
\(356\) 0 0
\(357\) 2.85477 + 6.25108i 0.151091 + 0.330842i
\(358\) 0 0
\(359\) −0.385862 2.68373i −0.0203650 0.141642i 0.977102 0.212771i \(-0.0682489\pi\)
−0.997467 + 0.0711291i \(0.977340\pi\)
\(360\) 0 0
\(361\) 6.69723 + 2.68117i 0.352486 + 0.141114i
\(362\) 0 0
\(363\) 9.56244 + 4.92978i 0.501898 + 0.258746i
\(364\) 0 0
\(365\) −0.801757 1.38868i −0.0419659 0.0726870i
\(366\) 0 0
\(367\) −13.6193 1.30049i −0.710922 0.0678849i −0.266672 0.963787i \(-0.585924\pi\)
−0.444251 + 0.895903i \(0.646530\pi\)
\(368\) 0 0
\(369\) 2.78447 + 8.04518i 0.144953 + 0.418816i
\(370\) 0 0
\(371\) −1.29872 27.2635i −0.0674261 1.41545i
\(372\) 0 0
\(373\) −4.03638 + 6.99122i −0.208996 + 0.361992i −0.951399 0.307962i \(-0.900353\pi\)
0.742402 + 0.669954i \(0.233686\pi\)
\(374\) 0 0
\(375\) 9.14638 2.68562i 0.472317 0.138685i
\(376\) 0 0
\(377\) −45.4730 29.2237i −2.34198 1.50510i
\(378\) 0 0
\(379\) −10.6631 + 1.01820i −0.547728 + 0.0523016i −0.365252 0.930909i \(-0.619017\pi\)
−0.182476 + 0.983210i \(0.558411\pi\)
\(380\) 0 0
\(381\) −0.306543 + 1.26359i −0.0157047 + 0.0647355i
\(382\) 0 0
\(383\) 13.2794 + 2.55940i 0.678547 + 0.130779i 0.516869 0.856064i \(-0.327097\pi\)
0.161678 + 0.986844i \(0.448309\pi\)
\(384\) 0 0
\(385\) −18.7615 + 14.7542i −0.956173 + 0.751943i
\(386\) 0 0
\(387\) 1.76268 2.03424i 0.0896022 0.103406i
\(388\) 0 0
\(389\) 0.886870 18.6177i 0.0449661 0.943954i −0.857843 0.513912i \(-0.828196\pi\)
0.902809 0.430042i \(-0.141501\pi\)
\(390\) 0 0
\(391\) 3.90745 3.72575i 0.197608 0.188419i
\(392\) 0 0
\(393\) −8.82537 10.1850i −0.445181 0.513766i
\(394\) 0 0
\(395\) −9.24007 + 1.78088i −0.464918 + 0.0896057i
\(396\) 0 0
\(397\) 1.56200 + 0.458645i 0.0783945 + 0.0230187i 0.320695 0.947183i \(-0.396084\pi\)
−0.242300 + 0.970201i \(0.577902\pi\)
\(398\) 0 0
\(399\) −10.0881 + 22.0898i −0.505034 + 1.10587i
\(400\) 0 0
\(401\) −22.3658 −1.11689 −0.558447 0.829540i \(-0.688602\pi\)
−0.558447 + 0.829540i \(0.688602\pi\)
\(402\) 0 0
\(403\) 38.0001 1.89292
\(404\) 0 0
\(405\) −0.448152 + 0.981315i −0.0222688 + 0.0487619i
\(406\) 0 0
\(407\) 14.5131 + 4.26142i 0.719386 + 0.211231i
\(408\) 0 0
\(409\) 3.57308 0.688655i 0.176678 0.0340518i −0.100145 0.994973i \(-0.531931\pi\)
0.276823 + 0.960921i \(0.410719\pi\)
\(410\) 0 0
\(411\) −2.48918 2.87267i −0.122782 0.141698i
\(412\) 0 0
\(413\) −8.65554 + 8.25304i −0.425911 + 0.406105i
\(414\) 0 0
\(415\) −0.887167 + 18.6239i −0.0435493 + 0.914213i
\(416\) 0 0
\(417\) −15.2542 + 17.6043i −0.747004 + 0.862088i
\(418\) 0 0
\(419\) −8.37099 + 6.58302i −0.408950 + 0.321602i −0.801353 0.598192i \(-0.795886\pi\)
0.392403 + 0.919793i \(0.371644\pi\)
\(420\) 0 0
\(421\) −38.1980 7.36207i −1.86166 0.358805i −0.870574 0.492038i \(-0.836252\pi\)
−0.991085 + 0.133233i \(0.957464\pi\)
\(422\) 0 0
\(423\) −2.59917 + 10.7139i −0.126376 + 0.520929i
\(424\) 0 0
\(425\) 5.53298 0.528335i 0.268389 0.0256280i
\(426\) 0 0
\(427\) 3.72454 + 2.39361i 0.180243 + 0.115835i
\(428\) 0 0
\(429\) −23.8990 + 7.01738i −1.15386 + 0.338802i
\(430\) 0 0
\(431\) 4.85939 8.41671i 0.234069 0.405419i −0.724933 0.688819i \(-0.758129\pi\)
0.959002 + 0.283401i \(0.0914626\pi\)
\(432\) 0 0
\(433\) 0.206633 + 4.33776i 0.00993014 + 0.208459i 0.998379 + 0.0569075i \(0.0181240\pi\)
−0.988449 + 0.151552i \(0.951573\pi\)
\(434\) 0 0
\(435\) −3.57176 10.3199i −0.171253 0.494802i
\(436\) 0 0
\(437\) 18.9924 + 1.81355i 0.908529 + 0.0867540i
\(438\) 0 0
\(439\) 1.63028 + 2.82374i 0.0778092 + 0.134770i 0.902304 0.431099i \(-0.141874\pi\)
−0.824495 + 0.565869i \(0.808541\pi\)
\(440\) 0 0
\(441\) −13.7739 7.10096i −0.655902 0.338141i
\(442\) 0 0
\(443\) −15.7569 6.30810i −0.748631 0.299707i −0.0342025 0.999415i \(-0.510889\pi\)
−0.714429 + 0.699708i \(0.753313\pi\)
\(444\) 0 0
\(445\) −0.567772 3.94894i −0.0269150 0.187198i
\(446\) 0 0
\(447\) 5.79048 + 12.6794i 0.273881 + 0.599715i
\(448\) 0 0
\(449\) −8.94719 12.5646i −0.422244 0.592959i 0.547583 0.836751i \(-0.315548\pi\)
−0.969827 + 0.243792i \(0.921609\pi\)
\(450\) 0 0
\(451\) −36.8670 + 14.7593i −1.73600 + 0.694989i
\(452\) 0 0
\(453\) −1.32522 5.46265i −0.0622645 0.256658i
\(454\) 0 0
\(455\) 3.88845 27.0448i 0.182293 1.26788i
\(456\) 0 0
\(457\) 31.8010 16.3946i 1.48759 0.766905i 0.492925 0.870072i \(-0.335928\pi\)
0.994664 + 0.103166i \(0.0328974\pi\)
\(458\) 0 0
\(459\) −0.840430 + 1.18022i −0.0392279 + 0.0550879i
\(460\) 0 0
\(461\) −3.30912 + 2.12664i −0.154121 + 0.0990477i −0.615428 0.788193i \(-0.711017\pi\)
0.461307 + 0.887240i \(0.347381\pi\)
\(462\) 0 0
\(463\) −27.0973 25.8372i −1.25932 1.20076i −0.969886 0.243559i \(-0.921685\pi\)
−0.289432 0.957199i \(-0.593466\pi\)
\(464\) 0 0
\(465\) 6.03469 + 4.74574i 0.279852 + 0.220078i
\(466\) 0 0
\(467\) 7.85400 22.6926i 0.363440 1.05009i −0.603999 0.796985i \(-0.706427\pi\)
0.967439 0.253105i \(-0.0814519\pi\)
\(468\) 0 0
\(469\) 17.1332 + 34.8386i 0.791136 + 1.60870i
\(470\) 0 0
\(471\) −7.41780 + 21.4323i −0.341794 + 0.987549i
\(472\) 0 0
\(473\) 9.86939 + 7.76138i 0.453795 + 0.356868i
\(474\) 0 0
\(475\) 14.2149 + 13.5539i 0.652225 + 0.621896i
\(476\) 0 0
\(477\) 4.84107 3.11117i 0.221657 0.142451i
\(478\) 0 0
\(479\) −8.42928 + 11.8373i −0.385144 + 0.540859i −0.960948 0.276729i \(-0.910750\pi\)
0.575804 + 0.817588i \(0.304689\pi\)
\(480\) 0 0
\(481\) −15.3904 + 7.93431i −0.701742 + 0.361773i
\(482\) 0 0
\(483\) −2.51532 + 17.4944i −0.114451 + 0.796023i
\(484\) 0 0
\(485\) 2.24515 + 9.25462i 0.101947 + 0.420231i
\(486\) 0 0
\(487\) −14.7348 + 5.89893i −0.667698 + 0.267306i −0.680649 0.732610i \(-0.738302\pi\)
0.0129504 + 0.999916i \(0.495878\pi\)
\(488\) 0 0
\(489\) −2.22448 3.12384i −0.100594 0.141265i
\(490\) 0 0
\(491\) 3.15340 + 6.90497i 0.142311 + 0.311617i 0.967344 0.253467i \(-0.0815710\pi\)
−0.825033 + 0.565084i \(0.808844\pi\)
\(492\) 0 0
\(493\) −2.08729 14.5174i −0.0940068 0.653831i
\(494\) 0 0
\(495\) −4.67172 1.87027i −0.209978 0.0840625i
\(496\) 0 0
\(497\) −40.5741 20.9174i −1.82000 0.938274i
\(498\) 0 0
\(499\) 4.30138 + 7.45021i 0.192556 + 0.333517i 0.946097 0.323884i \(-0.104989\pi\)
−0.753540 + 0.657402i \(0.771656\pi\)
\(500\) 0 0
\(501\) −11.0711 1.05717i −0.494622 0.0472307i
\(502\) 0 0
\(503\) 10.1743 + 29.3966i 0.453648 + 1.31073i 0.907650 + 0.419728i \(0.137875\pi\)
−0.454002 + 0.891001i \(0.650004\pi\)
\(504\) 0 0
\(505\) 0.535464 + 11.2408i 0.0238278 + 0.500208i
\(506\) 0 0
\(507\) 7.75672 13.4350i 0.344488 0.596671i
\(508\) 0 0
\(509\) 29.8293 8.75868i 1.32216 0.388221i 0.456889 0.889524i \(-0.348964\pi\)
0.865272 + 0.501302i \(0.167146\pi\)
\(510\) 0 0
\(511\) 5.93083 + 3.81151i 0.262364 + 0.168611i
\(512\) 0 0
\(513\) −5.09678 + 0.486683i −0.225028 + 0.0214876i
\(514\) 0 0
\(515\) −3.38374 + 13.9479i −0.149105 + 0.614620i
\(516\) 0 0
\(517\) −50.4964 9.73238i −2.22083 0.428030i
\(518\) 0 0
\(519\) −16.6253 + 13.0742i −0.729768 + 0.573896i
\(520\) 0 0
\(521\) −9.17984 + 10.5941i −0.402176 + 0.464136i −0.920325 0.391155i \(-0.872076\pi\)
0.518149 + 0.855290i \(0.326621\pi\)
\(522\) 0 0
\(523\) 2.06242 43.2955i 0.0901832 1.89318i −0.273820 0.961781i \(-0.588287\pi\)
0.364003 0.931398i \(-0.381410\pi\)
\(524\) 0 0
\(525\) −13.1685 + 12.5561i −0.574721 + 0.547995i
\(526\) 0 0
\(527\) 6.75212 + 7.79236i 0.294127 + 0.339441i
\(528\) 0 0
\(529\) −8.94959 + 1.72489i −0.389113 + 0.0749953i
\(530\) 0 0
\(531\) −2.41935 0.710384i −0.104991 0.0308281i
\(532\) 0 0
\(533\) 18.8847 41.3518i 0.817988 1.79114i
\(534\) 0 0
\(535\) −4.26048 −0.184197
\(536\) 0 0
\(537\) 14.1197 0.609310
\(538\) 0 0
\(539\) 30.0284 65.7531i 1.29342 2.83219i
\(540\) 0 0
\(541\) −21.2048 6.22630i −0.911667 0.267689i −0.207924 0.978145i \(-0.566671\pi\)
−0.703742 + 0.710455i \(0.748489\pi\)
\(542\) 0 0
\(543\) −3.46754 + 0.668314i −0.148806 + 0.0286801i
\(544\) 0 0
\(545\) −10.4576 12.0687i −0.447956 0.516968i
\(546\) 0 0
\(547\) −2.08034 + 1.98360i −0.0889491 + 0.0848128i −0.733249 0.679960i \(-0.761997\pi\)
0.644300 + 0.764773i \(0.277149\pi\)
\(548\) 0 0
\(549\) −0.0444149 + 0.932383i −0.00189558 + 0.0397931i
\(550\) 0 0
\(551\) 33.9404 39.1693i 1.44591 1.66867i
\(552\) 0 0
\(553\) 32.5209 25.5748i 1.38293 1.08755i
\(554\) 0 0
\(555\) −3.43500 0.662042i −0.145808 0.0281021i
\(556\) 0 0
\(557\) −9.48174 + 39.0843i −0.401754 + 1.65605i 0.307836 + 0.951440i \(0.400395\pi\)
−0.709590 + 0.704615i \(0.751120\pi\)
\(558\) 0 0
\(559\) −14.3080 + 1.36625i −0.605164 + 0.0577861i
\(560\) 0 0
\(561\) −5.68553 3.65387i −0.240043 0.154267i
\(562\) 0 0
\(563\) 36.1949 10.6278i 1.52543 0.447907i 0.591783 0.806097i \(-0.298424\pi\)
0.933649 + 0.358190i \(0.116606\pi\)
\(564\) 0 0
\(565\) 4.16156 7.20804i 0.175078 0.303244i
\(566\) 0 0
\(567\) −0.225684 4.73769i −0.00947783 0.198964i
\(568\) 0 0
\(569\) 2.61509 + 7.55581i 0.109630 + 0.316756i 0.986450 0.164064i \(-0.0524603\pi\)
−0.876819 + 0.480820i \(0.840339\pi\)
\(570\) 0 0
\(571\) 6.19650 + 0.591694i 0.259316 + 0.0247616i 0.223904 0.974611i \(-0.428120\pi\)
0.0354115 + 0.999373i \(0.488726\pi\)
\(572\) 0 0
\(573\) −4.57761 7.92866i −0.191233 0.331224i
\(574\) 0 0
\(575\) 12.7059 + 6.55033i 0.529871 + 0.273168i
\(576\) 0 0
\(577\) 3.02361 + 1.21047i 0.125875 + 0.0503926i 0.433745 0.901036i \(-0.357192\pi\)
−0.307870 + 0.951428i \(0.599616\pi\)
\(578\) 0 0
\(579\) 2.00444 + 13.9412i 0.0833018 + 0.579376i
\(580\) 0 0
\(581\) −34.0535 74.5667i −1.41278 3.09355i
\(582\) 0 0
\(583\) 15.5704 + 21.8655i 0.644858 + 0.905577i
\(584\) 0 0
\(585\) 5.34796 2.14100i 0.221111 0.0885194i
\(586\) 0 0
\(587\) 10.1717 + 41.9285i 0.419833 + 1.73058i 0.652291 + 0.757969i \(0.273808\pi\)
−0.232458 + 0.972606i \(0.574677\pi\)
\(588\) 0 0
\(589\) −5.18534 + 36.0648i −0.213658 + 1.48603i
\(590\) 0 0
\(591\) −3.96383 + 2.04350i −0.163050 + 0.0840582i
\(592\) 0 0
\(593\) −4.39706 + 6.17481i −0.180566 + 0.253569i −0.894932 0.446203i \(-0.852776\pi\)
0.714366 + 0.699772i \(0.246715\pi\)
\(594\) 0 0
\(595\) 6.23676 4.00812i 0.255682 0.164317i
\(596\) 0 0
\(597\) 4.30537 + 4.10516i 0.176207 + 0.168013i
\(598\) 0 0
\(599\) 26.6001 + 20.9186i 1.08685 + 0.854709i 0.990067 0.140596i \(-0.0449018\pi\)
0.0967844 + 0.995305i \(0.469144\pi\)
\(600\) 0 0
\(601\) 3.20794 9.26873i 0.130855 0.378079i −0.860473 0.509497i \(-0.829832\pi\)
0.991327 + 0.131417i \(0.0419528\pi\)
\(602\) 0 0
\(603\) −4.55498 + 6.80089i −0.185493 + 0.276954i
\(604\) 0 0
\(605\) 3.79602 10.9679i 0.154330 0.445908i
\(606\) 0 0
\(607\) 10.7321 + 8.43984i 0.435604 + 0.342563i 0.811758 0.583995i \(-0.198511\pi\)
−0.376154 + 0.926557i \(0.622754\pi\)
\(608\) 0 0
\(609\) 34.7487 + 33.1329i 1.40809 + 1.34261i
\(610\) 0 0
\(611\) 49.5243 31.8274i 2.00354 1.28760i
\(612\) 0 0
\(613\) −4.42070 + 6.20801i −0.178551 + 0.250739i −0.894146 0.447776i \(-0.852216\pi\)
0.715595 + 0.698515i \(0.246156\pi\)
\(614\) 0 0
\(615\) 8.16334 4.20850i 0.329178 0.169703i
\(616\) 0 0
\(617\) −0.120395 + 0.837366i −0.00484692 + 0.0337111i −0.992101 0.125439i \(-0.959966\pi\)
0.987254 + 0.159150i \(0.0508753\pi\)
\(618\) 0 0
\(619\) 1.83489 + 7.56353i 0.0737506 + 0.304004i 0.996726 0.0808552i \(-0.0257651\pi\)
−0.922975 + 0.384859i \(0.874250\pi\)
\(620\) 0 0
\(621\) −3.45943 + 1.38495i −0.138822 + 0.0555759i
\(622\) 0 0
\(623\) 10.1744 + 14.2880i 0.407630 + 0.572436i
\(624\) 0 0
\(625\) 3.69602 + 8.09316i 0.147841 + 0.323726i
\(626\) 0 0
\(627\) −3.39884 23.6394i −0.135736 0.944067i
\(628\) 0 0
\(629\) −4.36169 1.74616i −0.173912 0.0696239i
\(630\) 0 0
\(631\) 19.3184 + 9.95931i 0.769052 + 0.396474i 0.797653 0.603117i \(-0.206075\pi\)
−0.0286008 + 0.999591i \(0.509105\pi\)
\(632\) 0 0
\(633\) −0.699484 1.21154i −0.0278020 0.0481545i
\(634\) 0 0
\(635\) 1.39635 + 0.133335i 0.0554125 + 0.00529125i
\(636\) 0 0
\(637\) 27.0645 + 78.1977i 1.07233 + 3.09831i
\(638\) 0 0
\(639\) −0.457942 9.61339i −0.0181159 0.380300i
\(640\) 0 0
\(641\) 11.0182 19.0842i 0.435195 0.753779i −0.562117 0.827058i \(-0.690013\pi\)
0.997312 + 0.0732787i \(0.0233463\pi\)
\(642\) 0 0
\(643\) −33.5286 + 9.84490i −1.32224 + 0.388245i −0.865301 0.501253i \(-0.832873\pi\)
−0.456940 + 0.889498i \(0.651054\pi\)
\(644\) 0 0
\(645\) −2.44284 1.56992i −0.0961867 0.0618154i
\(646\) 0 0
\(647\) −17.9568 + 1.71466i −0.705954 + 0.0674104i −0.441857 0.897086i \(-0.645680\pi\)
−0.264097 + 0.964496i \(0.585074\pi\)
\(648\) 0 0
\(649\) 2.77292 11.4301i 0.108847 0.448672i
\(650\) 0 0
\(651\) −33.1436 6.38790i −1.29900 0.250361i
\(652\) 0 0
\(653\) −21.3419 + 16.7835i −0.835175 + 0.656789i −0.941303 0.337564i \(-0.890397\pi\)
0.106128 + 0.994352i \(0.466155\pi\)
\(654\) 0 0
\(655\) −9.52085 + 10.9876i −0.372010 + 0.429323i
\(656\) 0 0
\(657\) −0.0707248 + 1.48470i −0.00275924 + 0.0579235i
\(658\) 0 0
\(659\) 16.7400 15.9616i 0.652098 0.621774i −0.290034 0.957016i \(-0.593667\pi\)
0.942132 + 0.335242i \(0.108818\pi\)
\(660\) 0 0
\(661\) 13.2498 + 15.2911i 0.515359 + 0.594756i 0.952463 0.304655i \(-0.0985413\pi\)
−0.437104 + 0.899411i \(0.643996\pi\)
\(662\) 0 0
\(663\) 7.59689 1.46418i 0.295039 0.0568640i
\(664\) 0 0
\(665\) 25.1368 + 7.38083i 0.974763 + 0.286216i
\(666\) 0 0
\(667\) 15.6699 34.3124i 0.606743 1.32858i
\(668\) 0 0
\(669\) 14.1530 0.547187
\(670\) 0 0
\(671\) −4.35412 −0.168089
\(672\) 0 0
\(673\) −0.0620713 + 0.135917i −0.00239267 + 0.00523922i −0.910825 0.412794i \(-0.864553\pi\)
0.908432 + 0.418033i \(0.137280\pi\)
\(674\) 0 0
\(675\) −3.68079 1.08078i −0.141674 0.0415991i
\(676\) 0 0
\(677\) −34.1412 + 6.58019i −1.31215 + 0.252897i −0.796885 0.604131i \(-0.793520\pi\)
−0.515270 + 0.857028i \(0.672308\pi\)
\(678\) 0 0
\(679\) −27.4183 31.6425i −1.05222 1.21433i
\(680\) 0 0
\(681\) 6.27235 5.98067i 0.240357 0.229180i
\(682\) 0 0
\(683\) 0.0107125 0.224883i 0.000409902 0.00860491i −0.998653 0.0518839i \(-0.983477\pi\)
0.999063 + 0.0432790i \(0.0137804\pi\)
\(684\) 0 0
\(685\) −2.68534 + 3.09905i −0.102602 + 0.118408i
\(686\) 0 0
\(687\) −2.98983 + 2.35123i −0.114069 + 0.0897051i
\(688\) 0 0
\(689\) −30.1730 5.81538i −1.14950 0.221548i
\(690\) 0 0
\(691\) 4.93416 20.3389i 0.187704 0.773728i −0.797638 0.603137i \(-0.793917\pi\)
0.985342 0.170591i \(-0.0545677\pi\)
\(692\) 0 0
\(693\) 22.0242 2.10306i 0.836632 0.0798887i
\(694\) 0 0
\(695\) 21.1403 + 13.5861i 0.801898 + 0.515348i
\(696\) 0 0
\(697\) 11.8352 3.47513i 0.448291 0.131630i
\(698\) 0 0
\(699\) 9.47568 16.4124i 0.358403 0.620772i
\(700\) 0 0
\(701\) 1.58693 + 33.3139i 0.0599377 + 1.25825i 0.805817 + 0.592165i \(0.201727\pi\)
−0.745879 + 0.666082i \(0.767970\pi\)
\(702\) 0 0
\(703\) −5.43011 15.6893i −0.204800 0.591732i
\(704\) 0 0
\(705\) 11.8397 + 1.13055i 0.445907 + 0.0425790i
\(706\) 0 0
\(707\) −24.7386 42.8484i −0.930389 1.61148i
\(708\) 0 0
\(709\) −19.8239 10.2199i −0.744502 0.383818i 0.0438529 0.999038i \(-0.486037\pi\)
−0.788355 + 0.615220i \(0.789067\pi\)
\(710\) 0 0
\(711\) 8.09791 + 3.24191i 0.303695 + 0.121581i
\(712\) 0 0
\(713\) 3.77394 + 26.2483i 0.141335 + 0.983007i
\(714\) 0 0
\(715\) 11.1625 + 24.4426i 0.417456 + 0.914100i
\(716\) 0 0
\(717\) 4.87823 + 6.85052i 0.182181 + 0.255837i
\(718\) 0 0
\(719\) −10.7709 + 4.31202i −0.401687 + 0.160811i −0.563704 0.825977i \(-0.690624\pi\)
0.162017 + 0.986788i \(0.448200\pi\)
\(720\) 0 0
\(721\) −14.8769 61.3234i −0.554044 2.28380i
\(722\) 0 0
\(723\) −2.02355 + 14.0741i −0.0752567 + 0.523422i
\(724\) 0 0
\(725\) 34.5161 17.7943i 1.28190 0.660863i
\(726\) 0 0
\(727\) −11.9335 + 16.7582i −0.442589 + 0.621529i −0.974261 0.225421i \(-0.927624\pi\)
0.531673 + 0.846950i \(0.321564\pi\)
\(728\) 0 0
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) 0 0
\(731\) −2.82251 2.69125i −0.104394 0.0995396i
\(732\) 0 0
\(733\) −1.70083 1.33755i −0.0628218 0.0494036i 0.586254 0.810127i \(-0.300602\pi\)
−0.649076 + 0.760723i \(0.724844\pi\)
\(734\) 0 0
\(735\) −5.46787 + 15.7984i −0.201685 + 0.582731i
\(736\) 0 0
\(737\) −32.6984 19.7136i −1.20446 0.726159i
\(738\) 0 0
\(739\) −2.85250 + 8.24176i −0.104931 + 0.303178i −0.985229 0.171243i \(-0.945222\pi\)
0.880298 + 0.474422i \(0.157343\pi\)
\(740\) 0 0
\(741\) 21.4903 + 16.9002i 0.789467 + 0.620844i
\(742\) 0 0
\(743\) −19.8002 18.8794i −0.726397 0.692618i 0.233692 0.972311i \(-0.424919\pi\)
−0.960090 + 0.279692i \(0.909768\pi\)
\(744\) 0 0
\(745\) 12.6503 8.12988i 0.463473 0.297856i
\(746\) 0 0
\(747\) 10.0252 14.0784i 0.366802 0.515101i
\(748\) 0 0
\(749\) 16.6493 8.58331i 0.608352 0.313627i
\(750\) 0 0
\(751\) −3.30274 + 22.9711i −0.120519 + 0.838226i 0.836452 + 0.548040i \(0.184626\pi\)
−0.956971 + 0.290185i \(0.906283\pi\)
\(752\) 0 0
\(753\) −5.01298 20.6638i −0.182683 0.753030i
\(754\) 0 0
\(755\) −5.62969 + 2.25379i −0.204885 + 0.0820237i
\(756\) 0 0
\(757\) 1.14728 + 1.61112i 0.0416984 + 0.0585573i 0.834899 0.550403i \(-0.185526\pi\)
−0.793200 + 0.608961i \(0.791587\pi\)
\(758\) 0 0
\(759\) −7.22070 15.8111i −0.262095 0.573908i
\(760\) 0 0
\(761\) 0.580179 + 4.03523i 0.0210315 + 0.146277i 0.997631 0.0687873i \(-0.0219130\pi\)
−0.976600 + 0.215064i \(0.931004\pi\)
\(762\) 0 0
\(763\) 65.1809 + 26.0945i 2.35971 + 0.944684i
\(764\) 0 0
\(765\) 1.38930 + 0.716232i 0.0502301 + 0.0258954i
\(766\) 0 0
\(767\) 6.73211 + 11.6604i 0.243082 + 0.421031i
\(768\) 0 0
\(769\) −22.9732 2.19367i −0.828434 0.0791059i −0.327781 0.944754i \(-0.606301\pi\)
−0.500653 + 0.865648i \(0.666907\pi\)
\(770\) 0 0
\(771\) −3.62578 10.4760i −0.130579 0.377284i
\(772\) 0 0
\(773\) 1.02503 + 21.5181i 0.0368679 + 0.773952i 0.939295 + 0.343110i \(0.111480\pi\)
−0.902427 + 0.430842i \(0.858217\pi\)
\(774\) 0 0
\(775\) −13.6499 + 23.6423i −0.490319 + 0.849257i
\(776\) 0 0
\(777\) 14.7572 4.33311i 0.529412 0.155449i
\(778\) 0