Properties

Label 804.2.ba.b.41.19
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.19
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.19

$q$-expansion

\(f(q)\) \(=\) \(q+(1.59370 + 0.678318i) q^{3} +(0.306661 - 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(2.07977 + 2.16207i) q^{9} +O(q^{10})\) \(q+(1.59370 + 0.678318i) q^{3} +(0.306661 - 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(2.07977 + 2.16207i) q^{9} +(2.54950 - 1.02066i) q^{11} +(-4.81545 - 5.05030i) q^{13} +(1.93549 - 3.19115i) q^{15} +(-0.521893 + 0.180629i) q^{17} +(-2.78507 - 0.265942i) q^{19} +(1.28813 - 4.06040i) q^{21} +(2.01683 - 0.0960734i) q^{23} +(0.342350 + 0.100523i) q^{25} +(1.84795 + 4.85645i) q^{27} +(2.51027 - 1.44930i) q^{29} +(-0.313059 + 0.328327i) q^{31} +(4.75547 + 0.102736i) q^{33} +(-5.29357 - 0.252164i) q^{35} +(-1.36757 + 2.36869i) q^{37} +(-4.24868 - 11.3151i) q^{39} +(-6.42149 - 1.23764i) q^{41} +(0.627825 + 0.544013i) q^{43} +(5.24922 - 3.77286i) q^{45} +(5.40598 - 10.4861i) q^{47} +(0.934085 - 0.180030i) q^{49} +(-0.954266 - 0.0661411i) q^{51} +(8.67995 + 10.0172i) q^{53} +(-1.39512 - 5.75075i) q^{55} +(-4.25818 - 2.31300i) q^{57} +(3.75489 + 12.7880i) q^{59} +(-2.25071 + 5.62201i) q^{61} +(4.80715 - 5.59731i) q^{63} +(-12.2484 + 8.72202i) q^{65} +(-8.15679 + 0.683270i) q^{67} +(3.27939 + 1.21494i) q^{69} +(8.87305 + 3.07099i) q^{71} +(9.59379 + 3.84077i) q^{73} +(0.477417 + 0.392426i) q^{75} +(-3.09490 - 6.00326i) q^{77} +(4.42862 - 1.07437i) q^{79} +(-0.349130 + 8.99323i) q^{81} +(6.35474 - 8.08070i) q^{83} +(0.225215 + 1.16852i) q^{85} +(4.98371 - 0.606996i) q^{87} +(1.12214 - 1.74608i) q^{89} +(-11.2388 + 12.9702i) q^{91} +(-0.721633 + 0.310901i) q^{93} +(-1.42130 + 5.85866i) q^{95} +(7.31896 + 4.22560i) q^{97} +(7.50911 + 3.38945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

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
\(3\) 1.59370 + 0.678318i 0.920124 + 0.391627i
\(4\) 0 0
\(5\) 0.306661 2.13288i 0.137143 0.953851i −0.798774 0.601631i \(-0.794518\pi\)
0.935917 0.352220i \(-0.114573\pi\)
\(6\) 0 0
\(7\) −0.233782 2.44828i −0.0883614 0.925362i −0.925595 0.378516i \(-0.876434\pi\)
0.837233 0.546846i \(-0.184172\pi\)
\(8\) 0 0
\(9\) 2.07977 + 2.16207i 0.693256 + 0.720691i
\(10\) 0 0
\(11\) 2.54950 1.02066i 0.768702 0.307742i 0.0460363 0.998940i \(-0.485341\pi\)
0.722665 + 0.691198i \(0.242917\pi\)
\(12\) 0 0
\(13\) −4.81545 5.05030i −1.33557 1.40070i −0.850267 0.526352i \(-0.823559\pi\)
−0.485299 0.874348i \(-0.661289\pi\)
\(14\) 0 0
\(15\) 1.93549 3.19115i 0.499743 0.823952i
\(16\) 0 0
\(17\) −0.521893 + 0.180629i −0.126578 + 0.0438090i −0.389622 0.920975i \(-0.627395\pi\)
0.263045 + 0.964784i \(0.415273\pi\)
\(18\) 0 0
\(19\) −2.78507 0.265942i −0.638940 0.0610113i −0.229442 0.973322i \(-0.573690\pi\)
−0.409498 + 0.912311i \(0.634296\pi\)
\(20\) 0 0
\(21\) 1.28813 4.06040i 0.281094 0.886053i
\(22\) 0 0
\(23\) 2.01683 0.0960734i 0.420538 0.0200327i 0.163753 0.986501i \(-0.447640\pi\)
0.256785 + 0.966469i \(0.417337\pi\)
\(24\) 0 0
\(25\) 0.342350 + 0.100523i 0.0684700 + 0.0201046i
\(26\) 0 0
\(27\) 1.84795 + 4.85645i 0.355639 + 0.934623i
\(28\) 0 0
\(29\) 2.51027 1.44930i 0.466145 0.269129i −0.248480 0.968637i \(-0.579931\pi\)
0.714625 + 0.699508i \(0.246598\pi\)
\(30\) 0 0
\(31\) −0.313059 + 0.328327i −0.0562271 + 0.0589693i −0.751247 0.660021i \(-0.770547\pi\)
0.695020 + 0.718991i \(0.255396\pi\)
\(32\) 0 0
\(33\) 4.75547 + 0.102736i 0.827821 + 0.0178841i
\(34\) 0 0
\(35\) −5.29357 0.252164i −0.894776 0.0426234i
\(36\) 0 0
\(37\) −1.36757 + 2.36869i −0.224826 + 0.389411i −0.956267 0.292494i \(-0.905515\pi\)
0.731441 + 0.681905i \(0.238848\pi\)
\(38\) 0 0
\(39\) −4.24868 11.3151i −0.680333 1.81186i
\(40\) 0 0
\(41\) −6.42149 1.23764i −1.00287 0.193287i −0.338720 0.940887i \(-0.609994\pi\)
−0.664149 + 0.747600i \(0.731206\pi\)
\(42\) 0 0
\(43\) 0.627825 + 0.544013i 0.0957424 + 0.0829613i 0.701417 0.712751i \(-0.252551\pi\)
−0.605674 + 0.795713i \(0.707097\pi\)
\(44\) 0 0
\(45\) 5.24922 3.77286i 0.782507 0.562425i
\(46\) 0 0
\(47\) 5.40598 10.4861i 0.788543 1.52956i −0.0586520 0.998278i \(-0.518680\pi\)
0.847195 0.531282i \(-0.178289\pi\)
\(48\) 0 0
\(49\) 0.934085 0.180030i 0.133441 0.0257186i
\(50\) 0 0
\(51\) −0.954266 0.0661411i −0.133624 0.00926161i
\(52\) 0 0
\(53\) 8.67995 + 10.0172i 1.19228 + 1.37597i 0.908929 + 0.416951i \(0.136901\pi\)
0.283353 + 0.959016i \(0.408553\pi\)
\(54\) 0 0
\(55\) −1.39512 5.75075i −0.188118 0.775431i
\(56\) 0 0
\(57\) −4.25818 2.31300i −0.564010 0.306364i
\(58\) 0 0
\(59\) 3.75489 + 12.7880i 0.488845 + 1.66485i 0.721595 + 0.692315i \(0.243409\pi\)
−0.232750 + 0.972536i \(0.574773\pi\)
\(60\) 0 0
\(61\) −2.25071 + 5.62201i −0.288174 + 0.719824i 0.711676 + 0.702508i \(0.247936\pi\)
−0.999850 + 0.0173163i \(0.994488\pi\)
\(62\) 0 0
\(63\) 4.80715 5.59731i 0.605644 0.705194i
\(64\) 0 0
\(65\) −12.2484 + 8.72202i −1.51922 + 1.08183i
\(66\) 0 0
\(67\) −8.15679 + 0.683270i −0.996510 + 0.0834747i
\(68\) 0 0
\(69\) 3.27939 + 1.21494i 0.394793 + 0.146262i
\(70\) 0 0
\(71\) 8.87305 + 3.07099i 1.05304 + 0.364460i 0.798117 0.602502i \(-0.205830\pi\)
0.254920 + 0.966962i \(0.417951\pi\)
\(72\) 0 0
\(73\) 9.59379 + 3.84077i 1.12287 + 0.449528i 0.857431 0.514600i \(-0.172059\pi\)
0.265437 + 0.964128i \(0.414484\pi\)
\(74\) 0 0
\(75\) 0.477417 + 0.392426i 0.0551274 + 0.0453135i
\(76\) 0 0
\(77\) −3.09490 6.00326i −0.352696 0.684135i
\(78\) 0 0
\(79\) 4.42862 1.07437i 0.498259 0.120876i 0.0212489 0.999774i \(-0.493236\pi\)
0.477010 + 0.878898i \(0.341721\pi\)
\(80\) 0 0
\(81\) −0.349130 + 8.99323i −0.0387922 + 0.999247i
\(82\) 0 0
\(83\) 6.35474 8.08070i 0.697523 0.886972i −0.300237 0.953865i \(-0.597066\pi\)
0.997760 + 0.0668921i \(0.0213083\pi\)
\(84\) 0 0
\(85\) 0.225215 + 1.16852i 0.0244280 + 0.126744i
\(86\) 0 0
\(87\) 4.98371 0.606996i 0.534309 0.0650768i
\(88\) 0 0
\(89\) 1.12214 1.74608i 0.118947 0.185084i −0.776675 0.629902i \(-0.783095\pi\)
0.895621 + 0.444817i \(0.146731\pi\)
\(90\) 0 0
\(91\) −11.2388 + 12.9702i −1.17814 + 1.35965i
\(92\) 0 0
\(93\) −0.721633 + 0.310901i −0.0748299 + 0.0322390i
\(94\) 0 0
\(95\) −1.42130 + 5.85866i −0.145822 + 0.601086i
\(96\) 0 0
\(97\) 7.31896 + 4.22560i 0.743128 + 0.429045i 0.823205 0.567744i \(-0.192183\pi\)
−0.0800776 + 0.996789i \(0.525517\pi\)
\(98\) 0 0
\(99\) 7.50911 + 3.38945i 0.754694 + 0.340653i
\(100\) 0 0
\(101\) −0.426724 + 0.599250i −0.0424607 + 0.0596276i −0.835260 0.549854i \(-0.814683\pi\)
0.792800 + 0.609482i \(0.208623\pi\)
\(102\) 0 0
\(103\) −9.36794 8.93231i −0.923050 0.880127i 0.0700322 0.997545i \(-0.477690\pi\)
−0.993083 + 0.117418i \(0.962538\pi\)
\(104\) 0 0
\(105\) −8.26531 3.99260i −0.806612 0.389638i
\(106\) 0 0
\(107\) 4.80701 0.691144i 0.464711 0.0668154i 0.0940174 0.995571i \(-0.470029\pi\)
0.370694 + 0.928755i \(0.379120\pi\)
\(108\) 0 0
\(109\) −2.08024 + 7.08464i −0.199251 + 0.678586i 0.797875 + 0.602823i \(0.205957\pi\)
−0.997126 + 0.0757630i \(0.975861\pi\)
\(110\) 0 0
\(111\) −3.78622 + 2.84734i −0.359372 + 0.270258i
\(112\) 0 0
\(113\) 1.78929 1.40711i 0.168322 0.132370i −0.530445 0.847720i \(-0.677975\pi\)
0.698767 + 0.715350i \(0.253733\pi\)
\(114\) 0 0
\(115\) 0.413571 4.33111i 0.0385657 0.403878i
\(116\) 0 0
\(117\) 0.904101 20.9148i 0.0835842 1.93357i
\(118\) 0 0
\(119\) 0.564239 + 1.23551i 0.0517237 + 0.113259i
\(120\) 0 0
\(121\) −2.50290 + 2.38651i −0.227537 + 0.216956i
\(122\) 0 0
\(123\) −9.39442 6.32825i −0.847067 0.570599i
\(124\) 0 0
\(125\) 4.79509 10.4998i 0.428886 0.939128i
\(126\) 0 0
\(127\) −15.4009 + 1.47061i −1.36661 + 0.130496i −0.752432 0.658670i \(-0.771120\pi\)
−0.614181 + 0.789165i \(0.710513\pi\)
\(128\) 0 0
\(129\) 0.631551 + 1.29286i 0.0556050 + 0.113830i
\(130\) 0 0
\(131\) −3.50834 5.45908i −0.306525 0.476962i 0.653481 0.756943i \(-0.273308\pi\)
−0.960005 + 0.279981i \(0.909672\pi\)
\(132\) 0 0
\(133\) 6.88081i 0.596642i
\(134\) 0 0
\(135\) 10.9249 2.45217i 0.940265 0.211049i
\(136\) 0 0
\(137\) −10.3235 + 6.63453i −0.881999 + 0.566826i −0.901401 0.432985i \(-0.857460\pi\)
0.0194019 + 0.999812i \(0.493824\pi\)
\(138\) 0 0
\(139\) −9.86849 1.41887i −0.837034 0.120347i −0.289549 0.957163i \(-0.593505\pi\)
−0.547485 + 0.836816i \(0.684415\pi\)
\(140\) 0 0
\(141\) 15.7285 13.0448i 1.32458 1.09857i
\(142\) 0 0
\(143\) −17.4316 7.96076i −1.45771 0.665712i
\(144\) 0 0
\(145\) −2.32138 5.79853i −0.192780 0.481542i
\(146\) 0 0
\(147\) 1.61077 + 0.346693i 0.132854 + 0.0285947i
\(148\) 0 0
\(149\) −18.0782 + 8.25602i −1.48102 + 0.676359i −0.981766 0.190096i \(-0.939120\pi\)
−0.499255 + 0.866455i \(0.666393\pi\)
\(150\) 0 0
\(151\) 2.76478 + 7.98830i 0.224994 + 0.650079i 0.999839 + 0.0179272i \(0.00570670\pi\)
−0.774845 + 0.632151i \(0.782172\pi\)
\(152\) 0 0
\(153\) −1.47595 0.752705i −0.119323 0.0608526i
\(154\) 0 0
\(155\) 0.604278 + 0.768401i 0.0485367 + 0.0617195i
\(156\) 0 0
\(157\) 0.0842720 + 1.76909i 0.00672563 + 0.141188i 0.999732 + 0.0231313i \(0.00736357\pi\)
−0.993007 + 0.118057i \(0.962333\pi\)
\(158\) 0 0
\(159\) 7.03839 + 21.8522i 0.558181 + 1.73299i
\(160\) 0 0
\(161\) −0.706714 4.91530i −0.0556968 0.387380i
\(162\) 0 0
\(163\) −3.78670 6.55876i −0.296598 0.513722i 0.678758 0.734362i \(-0.262519\pi\)
−0.975355 + 0.220640i \(0.929185\pi\)
\(164\) 0 0
\(165\) 1.67744 10.1113i 0.130589 0.787165i
\(166\) 0 0
\(167\) −9.87190 7.02975i −0.763910 0.543978i 0.130381 0.991464i \(-0.458380\pi\)
−0.894291 + 0.447486i \(0.852319\pi\)
\(168\) 0 0
\(169\) −1.69839 + 35.6536i −0.130646 + 2.74259i
\(170\) 0 0
\(171\) −5.21732 6.57463i −0.398978 0.502775i
\(172\) 0 0
\(173\) 20.3597 + 4.93922i 1.54792 + 0.375522i 0.916537 0.399949i \(-0.130972\pi\)
0.631384 + 0.775471i \(0.282487\pi\)
\(174\) 0 0
\(175\) 0.166073 0.861669i 0.0125539 0.0651361i
\(176\) 0 0
\(177\) −2.69015 + 22.9272i −0.202204 + 1.72331i
\(178\) 0 0
\(179\) 8.09006 + 5.19917i 0.604679 + 0.388604i 0.806859 0.590745i \(-0.201166\pi\)
−0.202179 + 0.979349i \(0.564802\pi\)
\(180\) 0 0
\(181\) 5.87750 + 3.03006i 0.436871 + 0.225223i 0.662609 0.748965i \(-0.269449\pi\)
−0.225738 + 0.974188i \(0.572479\pi\)
\(182\) 0 0
\(183\) −7.40047 + 7.43310i −0.547059 + 0.549471i
\(184\) 0 0
\(185\) 4.63275 + 3.64323i 0.340606 + 0.267856i
\(186\) 0 0
\(187\) −1.14620 + 0.993190i −0.0838186 + 0.0726292i
\(188\) 0 0
\(189\) 11.4579 5.65966i 0.833441 0.411680i
\(190\) 0 0
\(191\) 3.46682 1.78727i 0.250850 0.129322i −0.328216 0.944603i \(-0.606447\pi\)
0.579067 + 0.815280i \(0.303417\pi\)
\(192\) 0 0
\(193\) 26.3811 7.74620i 1.89896 0.557584i 0.908879 0.417060i \(-0.136939\pi\)
0.990077 0.140524i \(-0.0448787\pi\)
\(194\) 0 0
\(195\) −25.4365 + 5.59200i −1.82155 + 0.400452i
\(196\) 0 0
\(197\) −5.55240 + 16.0426i −0.395592 + 1.14299i 0.554813 + 0.831975i \(0.312790\pi\)
−0.950405 + 0.311014i \(0.899331\pi\)
\(198\) 0 0
\(199\) 7.13663 + 10.0220i 0.505902 + 0.710440i 0.985995 0.166778i \(-0.0533363\pi\)
−0.480092 + 0.877218i \(0.659397\pi\)
\(200\) 0 0
\(201\) −13.4630 4.44397i −0.949604 0.313453i
\(202\) 0 0
\(203\) −4.13515 5.80701i −0.290231 0.407572i
\(204\) 0 0
\(205\) −4.60896 + 13.3167i −0.321903 + 0.930079i
\(206\) 0 0
\(207\) 4.40226 + 4.16073i 0.305978 + 0.289190i
\(208\) 0 0
\(209\) −7.37197 + 2.16461i −0.509930 + 0.149729i
\(210\) 0 0
\(211\) −16.8027 + 8.66237i −1.15674 + 0.596342i −0.926316 0.376748i \(-0.877042\pi\)
−0.230426 + 0.973090i \(0.574012\pi\)
\(212\) 0 0
\(213\) 12.0579 + 10.9130i 0.826192 + 0.747746i
\(214\) 0 0
\(215\) 1.35284 1.17224i 0.0922631 0.0799464i
\(216\) 0 0
\(217\) 0.877024 + 0.689699i 0.0595363 + 0.0468198i
\(218\) 0 0
\(219\) 12.6844 + 12.6287i 0.857130 + 0.853368i
\(220\) 0 0
\(221\) 3.42538 + 1.76591i 0.230416 + 0.118788i
\(222\) 0 0
\(223\) −14.0431 9.02498i −0.940399 0.604358i −0.0218910 0.999760i \(-0.506969\pi\)
−0.918508 + 0.395403i \(0.870605\pi\)
\(224\) 0 0
\(225\) 0.494670 + 0.949251i 0.0329780 + 0.0632834i
\(226\) 0 0
\(227\) −1.17258 + 6.08393i −0.0778270 + 0.403805i 0.922034 + 0.387110i \(0.126527\pi\)
−0.999861 + 0.0166949i \(0.994686\pi\)
\(228\) 0 0
\(229\) −3.04756 0.739331i −0.201389 0.0488563i 0.133796 0.991009i \(-0.457283\pi\)
−0.335184 + 0.942153i \(0.608799\pi\)
\(230\) 0 0
\(231\) −0.860217 11.6667i −0.0565982 0.767615i
\(232\) 0 0
\(233\) 0.317294 6.66082i 0.0207866 0.436365i −0.964354 0.264616i \(-0.914755\pi\)
0.985141 0.171750i \(-0.0549420\pi\)
\(234\) 0 0
\(235\) −20.7078 14.7460i −1.35083 0.961921i
\(236\) 0 0
\(237\) 7.78666 + 1.29179i 0.505798 + 0.0839106i
\(238\) 0 0
\(239\) −12.4911 21.6352i −0.807981 1.39946i −0.914260 0.405127i \(-0.867227\pi\)
0.106279 0.994336i \(-0.466106\pi\)
\(240\) 0 0
\(241\) 0.00925738 + 0.0643865i 0.000596320 + 0.00414750i 0.990117 0.140241i \(-0.0447877\pi\)
−0.989521 + 0.144388i \(0.953879\pi\)
\(242\) 0 0
\(243\) −6.65668 + 14.0957i −0.427026 + 0.904239i
\(244\) 0 0
\(245\) −0.0975342 2.04749i −0.00623123 0.130810i
\(246\) 0 0
\(247\) 12.0683 + 15.3461i 0.767887 + 0.976448i
\(248\) 0 0
\(249\) 15.6088 8.56769i 0.989170 0.542955i
\(250\) 0 0
\(251\) −8.13828 23.5140i −0.513684 1.48419i −0.841923 0.539597i \(-0.818577\pi\)
0.328240 0.944594i \(-0.393545\pi\)
\(252\) 0 0
\(253\) 5.04384 2.30344i 0.317103 0.144816i
\(254\) 0 0
\(255\) −0.433707 + 2.01505i −0.0271598 + 0.126187i
\(256\) 0 0
\(257\) 5.53208 + 13.8185i 0.345082 + 0.861972i 0.994805 + 0.101801i \(0.0324605\pi\)
−0.649723 + 0.760171i \(0.725115\pi\)
\(258\) 0 0
\(259\) 6.11893 + 2.79442i 0.380212 + 0.173637i
\(260\) 0 0
\(261\) 8.35427 + 2.41317i 0.517117 + 0.149371i
\(262\) 0 0
\(263\) −13.2735 1.90845i −0.818482 0.117680i −0.279660 0.960099i \(-0.590222\pi\)
−0.538823 + 0.842419i \(0.681131\pi\)
\(264\) 0 0
\(265\) 24.0272 15.4414i 1.47598 0.948555i
\(266\) 0 0
\(267\) 2.97276 2.02157i 0.181930 0.123718i
\(268\) 0 0
\(269\) 9.15469i 0.558171i 0.960266 + 0.279086i \(0.0900313\pi\)
−0.960266 + 0.279086i \(0.909969\pi\)
\(270\) 0 0
\(271\) −6.35792 9.89311i −0.386216 0.600964i 0.592652 0.805459i \(-0.298081\pi\)
−0.978868 + 0.204495i \(0.934445\pi\)
\(272\) 0 0
\(273\) −26.7092 + 13.0472i −1.61651 + 0.789653i
\(274\) 0 0
\(275\) 0.975420 0.0931413i 0.0588200 0.00561663i
\(276\) 0 0
\(277\) −4.72997 + 10.3572i −0.284196 + 0.622303i −0.996858 0.0792046i \(-0.974762\pi\)
0.712662 + 0.701507i \(0.247489\pi\)
\(278\) 0 0
\(279\) −1.36096 + 0.00598686i −0.0814784 + 0.000358424i
\(280\) 0 0
\(281\) 14.5314 13.8556i 0.866869 0.826558i −0.119204 0.992870i \(-0.538034\pi\)
0.986073 + 0.166312i \(0.0531859\pi\)
\(282\) 0 0
\(283\) 0.292674 + 0.640866i 0.0173976 + 0.0380955i 0.918131 0.396276i \(-0.129698\pi\)
−0.900734 + 0.434372i \(0.856970\pi\)
\(284\) 0 0
\(285\) −6.23916 + 8.37286i −0.369576 + 0.495966i
\(286\) 0 0
\(287\) −1.52886 + 16.0109i −0.0902457 + 0.945096i
\(288\) 0 0
\(289\) −13.1232 + 10.3202i −0.771950 + 0.607069i
\(290\) 0 0
\(291\) 8.79793 + 11.6989i 0.515744 + 0.685804i
\(292\) 0 0
\(293\) −4.70974 + 16.0399i −0.275146 + 0.937061i 0.699748 + 0.714390i \(0.253296\pi\)
−0.974894 + 0.222671i \(0.928522\pi\)
\(294\) 0 0
\(295\) 28.4266 4.08713i 1.65506 0.237962i
\(296\) 0 0
\(297\) 9.66815 + 10.4953i 0.561003 + 0.609002i
\(298\) 0 0
\(299\) −10.1971 9.72295i −0.589716 0.562293i
\(300\) 0 0
\(301\) 1.18512 1.66427i 0.0683093 0.0959270i
\(302\) 0 0
\(303\) −1.08655 + 0.665571i −0.0624209 + 0.0382361i
\(304\) 0 0
\(305\) 11.3008 + 6.52454i 0.647084 + 0.373594i
\(306\) 0 0
\(307\) 2.60375 10.7328i 0.148604 0.612554i −0.847984 0.530021i \(-0.822184\pi\)
0.996588 0.0825328i \(-0.0263009\pi\)
\(308\) 0 0
\(309\) −8.87074 20.5899i −0.504639 1.17132i
\(310\) 0 0
\(311\) −8.51947 + 9.83200i −0.483095 + 0.557521i −0.944007 0.329924i \(-0.892977\pi\)
0.460912 + 0.887446i \(0.347522\pi\)
\(312\) 0 0
\(313\) 7.14245 11.1139i 0.403715 0.628193i −0.578560 0.815640i \(-0.696385\pi\)
0.982275 + 0.187447i \(0.0600213\pi\)
\(314\) 0 0
\(315\) −10.4642 11.9695i −0.589590 0.674406i
\(316\) 0 0
\(317\) 1.34794 + 6.99379i 0.0757080 + 0.392810i 0.999940 + 0.0109782i \(0.00349455\pi\)
−0.924232 + 0.381832i \(0.875293\pi\)
\(318\) 0 0
\(319\) 4.92066 6.25713i 0.275504 0.350332i
\(320\) 0 0
\(321\) 8.12975 + 2.15921i 0.453759 + 0.120515i
\(322\) 0 0
\(323\) 1.50155 0.364271i 0.0835483 0.0202686i
\(324\) 0 0
\(325\) −1.14090 2.21303i −0.0632856 0.122757i
\(326\) 0 0
\(327\) −8.12093 + 9.87974i −0.449088 + 0.546351i
\(328\) 0 0
\(329\) −26.9368 10.7839i −1.48507 0.594534i
\(330\) 0 0
\(331\) 15.5053 + 5.36642i 0.852246 + 0.294965i 0.718052 0.695990i \(-0.245034\pi\)
0.134195 + 0.990955i \(0.457155\pi\)
\(332\) 0 0
\(333\) −7.96551 + 1.96955i −0.436507 + 0.107931i
\(334\) 0 0
\(335\) −1.04404 + 17.6069i −0.0570420 + 0.961970i
\(336\) 0 0
\(337\) −17.8277 + 12.6951i −0.971138 + 0.691544i −0.951302 0.308259i \(-0.900254\pi\)
−0.0198353 + 0.999803i \(0.506314\pi\)
\(338\) 0 0
\(339\) 3.80606 1.02881i 0.206717 0.0558772i
\(340\) 0 0
\(341\) −0.463031 + 1.15660i −0.0250746 + 0.0626332i
\(342\) 0 0
\(343\) −5.50942 18.7634i −0.297481 1.01313i
\(344\) 0 0
\(345\) 3.59698 6.62196i 0.193655 0.356514i
\(346\) 0 0
\(347\) 1.18614 + 4.88934i 0.0636754 + 0.262473i 0.994747 0.102363i \(-0.0326402\pi\)
−0.931072 + 0.364836i \(0.881125\pi\)
\(348\) 0 0
\(349\) −11.0268 12.7256i −0.590252 0.681187i 0.379525 0.925182i \(-0.376088\pi\)
−0.969777 + 0.243995i \(0.921542\pi\)
\(350\) 0 0
\(351\) 15.6278 32.7187i 0.834149 1.74639i
\(352\) 0 0
\(353\) 13.7779 2.65548i 0.733325 0.141337i 0.191100 0.981571i \(-0.438794\pi\)
0.542224 + 0.840234i \(0.317582\pi\)
\(354\) 0 0
\(355\) 9.27106 17.9834i 0.492057 0.954457i
\(356\) 0 0
\(357\) 0.0611585 + 2.35177i 0.00323685 + 0.124469i
\(358\) 0 0
\(359\) 19.3650 + 16.7799i 1.02205 + 0.885609i 0.993483 0.113983i \(-0.0363608\pi\)
0.0285650 + 0.999592i \(0.490906\pi\)
\(360\) 0 0
\(361\) −10.9707 2.11444i −0.577407 0.111286i
\(362\) 0 0
\(363\) −5.60770 + 2.10562i −0.294328 + 0.110517i
\(364\) 0 0
\(365\) 11.1339 19.2845i 0.582777 1.00940i
\(366\) 0 0
\(367\) 16.1306 + 0.768397i 0.842012 + 0.0401100i 0.464155 0.885754i \(-0.346358\pi\)
0.377857 + 0.925864i \(0.376661\pi\)
\(368\) 0 0
\(369\) −10.6793 16.4577i −0.555944 0.856756i
\(370\) 0 0
\(371\) 22.4957 23.5928i 1.16792 1.22488i
\(372\) 0 0
\(373\) 10.0070 5.77757i 0.518145 0.299151i −0.218030 0.975942i \(-0.569963\pi\)
0.736175 + 0.676791i \(0.236630\pi\)
\(374\) 0 0
\(375\) 14.7641 13.4809i 0.762416 0.696151i
\(376\) 0 0
\(377\) −19.4075 5.69855i −0.999536 0.293490i
\(378\) 0 0
\(379\) 33.6176 1.60140i 1.72682 0.0822586i 0.839485 0.543383i \(-0.182857\pi\)
0.887335 + 0.461124i \(0.152554\pi\)
\(380\) 0 0
\(381\) −25.5421 8.10303i −1.30856 0.415131i
\(382\) 0 0
\(383\) 34.1052 + 3.25665i 1.74269 + 0.166407i 0.917312 0.398170i \(-0.130355\pi\)
0.825380 + 0.564577i \(0.190961\pi\)
\(384\) 0 0
\(385\) −13.7533 + 4.76006i −0.700933 + 0.242595i
\(386\) 0 0
\(387\) 0.129533 + 2.48883i 0.00658453 + 0.126514i
\(388\) 0 0
\(389\) −17.0865 17.9198i −0.866318 0.908568i 0.130239 0.991483i \(-0.458426\pi\)
−0.996557 + 0.0829147i \(0.973577\pi\)
\(390\) 0 0
\(391\) −1.03522 + 0.414438i −0.0523531 + 0.0209590i
\(392\) 0 0
\(393\) −1.88825 11.0799i −0.0952494 0.558907i
\(394\) 0 0
\(395\) −0.933415 9.77516i −0.0469652 0.491842i
\(396\) 0 0
\(397\) 1.99460 13.8728i 0.100106 0.696254i −0.876529 0.481350i \(-0.840147\pi\)
0.976635 0.214905i \(-0.0689441\pi\)
\(398\) 0 0
\(399\) −4.66738 + 10.9660i −0.233661 + 0.548984i
\(400\) 0 0
\(401\) 18.0622 0.901983 0.450991 0.892528i \(-0.351070\pi\)
0.450991 + 0.892528i \(0.351070\pi\)
\(402\) 0 0
\(403\) 3.16567 0.157693
\(404\) 0 0
\(405\) 19.0744 + 3.50252i 0.947813 + 0.174042i
\(406\) 0 0
\(407\) −1.06896 + 7.43480i −0.0529865 + 0.368529i
\(408\) 0 0
\(409\) −1.56485 16.3879i −0.0773770 0.810328i −0.947977 0.318338i \(-0.896875\pi\)
0.870600 0.491991i \(-0.163731\pi\)
\(410\) 0 0
\(411\) −20.9530 + 3.57082i −1.03353 + 0.176136i
\(412\) 0 0
\(413\) 30.4307 12.1826i 1.49740 0.599467i
\(414\) 0 0
\(415\) −15.2864 16.0319i −0.750379 0.786975i
\(416\) 0 0
\(417\) −14.7650 8.95524i −0.723044 0.438540i
\(418\) 0 0
\(419\) −25.6749 + 8.88615i −1.25430 + 0.434117i −0.871810 0.489843i \(-0.837054\pi\)
−0.382488 + 0.923960i \(0.624933\pi\)
\(420\) 0 0
\(421\) −27.0960 2.58736i −1.32058 0.126100i −0.589153 0.808021i \(-0.700539\pi\)
−0.731426 + 0.681921i \(0.761145\pi\)
\(422\) 0 0
\(423\) 33.9150 10.1206i 1.64900 0.492081i
\(424\) 0 0
\(425\) −0.196827 + 0.00937605i −0.00954754 + 0.000454805i
\(426\) 0 0
\(427\) 14.2904 + 4.19605i 0.691562 + 0.203061i
\(428\) 0 0
\(429\) −22.3809 24.5113i −1.08056 1.18341i
\(430\) 0 0
\(431\) 29.7965 17.2030i 1.43525 0.828640i 0.437733 0.899105i \(-0.355782\pi\)
0.997514 + 0.0704650i \(0.0224483\pi\)
\(432\) 0 0
\(433\) 12.8252 13.4507i 0.616342 0.646400i −0.339388 0.940646i \(-0.610220\pi\)
0.955730 + 0.294246i \(0.0950685\pi\)
\(434\) 0 0
\(435\) 0.233662 10.8158i 0.0112032 0.518576i
\(436\) 0 0
\(437\) −5.64257 0.268789i −0.269921 0.0128579i
\(438\) 0 0
\(439\) −2.80865 + 4.86473i −0.134050 + 0.232181i −0.925234 0.379397i \(-0.876131\pi\)
0.791184 + 0.611578i \(0.209465\pi\)
\(440\) 0 0
\(441\) 2.33192 + 1.64514i 0.111044 + 0.0783400i
\(442\) 0 0
\(443\) −18.3930 3.54496i −0.873878 0.168426i −0.267457 0.963570i \(-0.586183\pi\)
−0.606421 + 0.795144i \(0.707395\pi\)
\(444\) 0 0
\(445\) −3.38006 2.92884i −0.160230 0.138840i
\(446\) 0 0
\(447\) −34.4114 + 0.894878i −1.62760 + 0.0423263i
\(448\) 0 0
\(449\) 3.99949 7.75792i 0.188747 0.366119i −0.775407 0.631462i \(-0.782455\pi\)
0.964154 + 0.265343i \(0.0854853\pi\)
\(450\) 0 0
\(451\) −17.6348 + 3.39882i −0.830389 + 0.160044i
\(452\) 0 0
\(453\) −1.01238 + 14.6064i −0.0475658 + 0.686267i
\(454\) 0 0
\(455\) 24.2174 + 27.9484i 1.13533 + 1.31024i
\(456\) 0 0
\(457\) 8.20283 + 33.8125i 0.383712 + 1.58168i 0.756645 + 0.653826i \(0.226837\pi\)
−0.372933 + 0.927858i \(0.621648\pi\)
\(458\) 0 0
\(459\) −1.84165 2.20075i −0.0859608 0.102722i
\(460\) 0 0
\(461\) 7.58595 + 25.8354i 0.353313 + 1.20327i 0.924092 + 0.382170i \(0.124823\pi\)
−0.570779 + 0.821104i \(0.693359\pi\)
\(462\) 0 0
\(463\) 11.8761 29.6651i 0.551929 1.37865i −0.345884 0.938277i \(-0.612421\pi\)
0.897814 0.440376i \(-0.145155\pi\)
\(464\) 0 0
\(465\) 0.441817 + 1.63449i 0.0204888 + 0.0757979i
\(466\) 0 0
\(467\) 7.86651 5.60171i 0.364018 0.259216i −0.383382 0.923590i \(-0.625241\pi\)
0.747401 + 0.664373i \(0.231301\pi\)
\(468\) 0 0
\(469\) 3.57975 + 19.8103i 0.165297 + 0.914757i
\(470\) 0 0
\(471\) −1.06570 + 2.87656i −0.0491048 + 0.132545i
\(472\) 0 0
\(473\) 2.15589 + 0.746161i 0.0991280 + 0.0343085i
\(474\) 0 0
\(475\) −0.926737 0.371009i −0.0425216 0.0170231i
\(476\) 0 0
\(477\) −3.60564 + 39.6001i −0.165091 + 1.81316i
\(478\) 0 0
\(479\) 12.3046 + 23.8677i 0.562214 + 1.09054i 0.983038 + 0.183400i \(0.0587105\pi\)
−0.420825 + 0.907142i \(0.638259\pi\)
\(480\) 0 0
\(481\) 18.5480 4.49971i 0.845718 0.205169i
\(482\) 0 0
\(483\) 2.20785 8.31290i 0.100461 0.378250i
\(484\) 0 0
\(485\) 11.2571 14.3146i 0.511160 0.649993i
\(486\) 0 0
\(487\) −6.53877 33.9264i −0.296300 1.53735i −0.759151 0.650915i \(-0.774385\pi\)
0.462851 0.886436i \(-0.346827\pi\)
\(488\) 0 0
\(489\) −1.58594 13.0213i −0.0717189 0.588844i
\(490\) 0 0
\(491\) 4.02285 6.25968i 0.181549 0.282495i −0.738537 0.674213i \(-0.764483\pi\)
0.920085 + 0.391718i \(0.128119\pi\)
\(492\) 0 0
\(493\) −1.04830 + 1.20981i −0.0472133 + 0.0544870i
\(494\) 0 0
\(495\) 9.53203 14.9766i 0.428433 0.673147i
\(496\) 0 0
\(497\) 5.44428 22.4416i 0.244209 1.00665i
\(498\) 0 0
\(499\) −4.30141 2.48342i −0.192557 0.111173i 0.400622 0.916243i \(-0.368794\pi\)
−0.593179 + 0.805070i \(0.702127\pi\)
\(500\) 0 0
\(501\) −10.9644 17.8996i −0.489855 0.799695i
\(502\) 0 0
\(503\) −0.0854197 + 0.119955i −0.00380867 + 0.00534853i −0.816476 0.577380i \(-0.804075\pi\)
0.812667 + 0.582728i \(0.198015\pi\)
\(504\) 0 0
\(505\) 1.14727 + 1.09392i 0.0510527 + 0.0486786i
\(506\) 0 0
\(507\) −26.8912 + 55.6692i −1.19428 + 2.47236i
\(508\) 0 0
\(509\) 6.04361 0.868940i 0.267878 0.0385151i −0.00706679 0.999975i \(-0.502249\pi\)
0.274945 + 0.961460i \(0.411340\pi\)
\(510\) 0 0
\(511\) 7.16043 24.3862i 0.316759 1.07878i
\(512\) 0 0
\(513\) −3.85515 14.0170i −0.170209 0.618866i
\(514\) 0 0
\(515\) −21.9243 + 17.2414i −0.966099 + 0.759749i
\(516\) 0 0
\(517\) 3.07970 32.2520i 0.135445 1.41844i
\(518\) 0 0
\(519\) 29.0970 + 21.6820i 1.27721 + 0.951735i
\(520\) 0 0
\(521\) −10.9594 23.9977i −0.480140 1.05136i −0.982425 0.186658i \(-0.940234\pi\)
0.502285 0.864702i \(-0.332493\pi\)
\(522\) 0 0
\(523\) 15.1168 14.4138i 0.661011 0.630273i −0.283414 0.958998i \(-0.591467\pi\)
0.944426 + 0.328724i \(0.106619\pi\)
\(524\) 0 0
\(525\) 0.849157 1.26059i 0.0370602 0.0550168i
\(526\) 0 0
\(527\) 0.104078 0.227899i 0.00453371 0.00992744i
\(528\) 0 0
\(529\) −18.8375 + 1.79876i −0.819021 + 0.0782070i
\(530\) 0 0
\(531\) −19.8392 + 34.7144i −0.860950 + 1.50647i
\(532\) 0 0
\(533\) 24.6719 + 38.3902i 1.06866 + 1.66287i
\(534\) 0 0
\(535\) 10.4647i 0.452428i
\(536\) 0 0
\(537\) 9.36645 + 13.7736i 0.404192 + 0.594373i
\(538\) 0 0
\(539\) 2.19770 1.41237i 0.0946614 0.0608352i
\(540\) 0 0
\(541\) 32.9306 + 4.73471i 1.41580 + 0.203561i 0.807369 0.590047i \(-0.200891\pi\)
0.608430 + 0.793608i \(0.291800\pi\)
\(542\) 0 0
\(543\) 7.31164 + 8.81584i 0.313772 + 0.378324i
\(544\) 0 0
\(545\) 14.4727 + 6.60948i 0.619944 + 0.283119i
\(546\) 0 0
\(547\) 6.50868 + 16.2579i 0.278291 + 0.695137i 0.999996 + 0.00293625i \(0.000934640\pi\)
−0.721705 + 0.692201i \(0.756641\pi\)
\(548\) 0 0
\(549\) −16.8362 + 6.82626i −0.718550 + 0.291338i
\(550\) 0 0
\(551\) −7.37671 + 3.36883i −0.314258 + 0.143517i
\(552\) 0 0
\(553\) −3.66569 10.5913i −0.155881 0.450389i
\(554\) 0 0
\(555\) 4.91194 + 8.94870i 0.208500 + 0.379851i
\(556\) 0 0
\(557\) −16.6237 21.1388i −0.704369 0.895679i 0.293818 0.955861i \(-0.405074\pi\)
−0.998187 + 0.0601829i \(0.980832\pi\)
\(558\) 0 0
\(559\) −0.275829 5.79037i −0.0116663 0.244907i
\(560\) 0 0
\(561\) −2.50040 + 0.805358i −0.105567 + 0.0340022i
\(562\) 0 0
\(563\) 6.20782 + 43.1764i 0.261629 + 1.81967i 0.520622 + 0.853788i \(0.325700\pi\)
−0.258993 + 0.965879i \(0.583391\pi\)
\(564\) 0 0
\(565\) −2.45249 4.24784i −0.103177 0.178708i
\(566\) 0 0
\(567\) 22.0995 1.24769i 0.928094 0.0523980i
\(568\) 0 0
\(569\) 24.2621 + 17.2770i 1.01712 + 0.724289i 0.961680 0.274173i \(-0.0884040\pi\)
0.0554414 + 0.998462i \(0.482343\pi\)
\(570\) 0 0
\(571\) −0.750998 + 15.7654i −0.0314283 + 0.659761i 0.927109 + 0.374793i \(0.122286\pi\)
−0.958537 + 0.284968i \(0.908017\pi\)
\(572\) 0 0
\(573\) 6.73741 0.496766i 0.281460 0.0207527i
\(574\) 0 0
\(575\) 0.700119 + 0.169847i 0.0291970 + 0.00708312i
\(576\) 0 0
\(577\) 7.92014 41.0936i 0.329720 1.71075i −0.317343 0.948311i \(-0.602791\pi\)
0.647063 0.762437i \(-0.275997\pi\)
\(578\) 0 0
\(579\) 47.2981 + 5.54968i 1.96564 + 0.230637i
\(580\) 0 0
\(581\) −21.2694 13.6690i −0.882405 0.567087i
\(582\) 0 0
\(583\) 32.3537 + 16.6795i 1.33995 + 0.690793i
\(584\) 0 0
\(585\) −44.3314 8.34209i −1.83288 0.344903i
\(586\) 0 0
\(587\) −26.8181 21.0900i −1.10690 0.870477i −0.114489 0.993425i \(-0.536523\pi\)
−0.992413 + 0.122947i \(0.960765\pi\)
\(588\) 0 0
\(589\) 0.959209 0.831159i 0.0395235 0.0342473i
\(590\) 0 0
\(591\) −19.7309 + 21.8008i −0.811620 + 0.896767i
\(592\) 0 0
\(593\) −26.4914 + 13.6573i −1.08787 + 0.560837i −0.906341 0.422548i \(-0.861136\pi\)
−0.181532 + 0.983385i \(0.558105\pi\)
\(594\) 0 0
\(595\) 2.80822 0.824569i 0.115126 0.0338040i
\(596\) 0 0
\(597\) 4.57555 + 20.8130i 0.187265 + 0.851818i
\(598\) 0 0
\(599\) 4.85131 14.0169i 0.198219 0.572717i −0.801460 0.598049i \(-0.795943\pi\)
0.999679 + 0.0253316i \(0.00806417\pi\)
\(600\) 0 0
\(601\) 22.9200 + 32.1867i 0.934927 + 1.31292i 0.949743 + 0.313031i \(0.101344\pi\)
−0.0148163 + 0.999890i \(0.504716\pi\)
\(602\) 0 0
\(603\) −18.4415 16.2145i −0.750996 0.660307i
\(604\) 0 0
\(605\) 4.32259 + 6.07023i 0.175738 + 0.246790i
\(606\) 0 0
\(607\) −4.68718 + 13.5427i −0.190247 + 0.549682i −0.999274 0.0380889i \(-0.987873\pi\)
0.809028 + 0.587771i \(0.199994\pi\)
\(608\) 0 0
\(609\) −2.65120 12.0596i −0.107432 0.488679i
\(610\) 0 0
\(611\) −78.9903 + 23.1937i −3.19561 + 0.938315i
\(612\) 0 0
\(613\) 14.1715 7.30591i 0.572381 0.295083i −0.147633 0.989042i \(-0.547165\pi\)
0.720014 + 0.693959i \(0.244135\pi\)
\(614\) 0 0
\(615\) −16.3783 + 18.0965i −0.660435 + 0.729722i
\(616\) 0 0
\(617\) −10.1060 + 8.75690i −0.406852 + 0.352539i −0.834117 0.551587i \(-0.814022\pi\)
0.427265 + 0.904126i \(0.359477\pi\)
\(618\) 0 0
\(619\) −35.1858 27.6704i −1.41424 1.11217i −0.977102 0.212770i \(-0.931751\pi\)
−0.437133 0.899397i \(-0.644006\pi\)
\(620\) 0 0
\(621\) 4.19358 + 9.61709i 0.168283 + 0.385920i
\(622\) 0 0
\(623\) −4.53723 2.33911i −0.181780 0.0937143i
\(624\) 0 0
\(625\) −19.4234 12.4827i −0.776937 0.499307i
\(626\) 0 0
\(627\) −13.2170 1.55081i −0.527836 0.0619333i
\(628\) 0 0
\(629\) 0.285868 1.48323i 0.0113983 0.0591401i
\(630\) 0 0
\(631\) 32.3998 + 7.86012i 1.28982 + 0.312906i 0.821274 0.570534i \(-0.193264\pi\)
0.468544 + 0.883440i \(0.344779\pi\)
\(632\) 0 0
\(633\) −32.6543 + 2.40768i −1.29789 + 0.0956967i
\(634\) 0 0
\(635\) −1.58624 + 33.2993i −0.0629480 + 1.32144i
\(636\) 0 0
\(637\) −5.40724 3.85048i −0.214243 0.152562i
\(638\) 0 0
\(639\) 11.8142 + 25.5711i 0.467361 + 1.01158i
\(640\) 0 0
\(641\) −5.04283 8.73443i −0.199180 0.344989i 0.749083 0.662476i \(-0.230494\pi\)
−0.948263 + 0.317487i \(0.897161\pi\)
\(642\) 0 0
\(643\) 1.46628 + 10.1982i 0.0578245 + 0.402178i 0.998092 + 0.0617419i \(0.0196656\pi\)
−0.940268 + 0.340436i \(0.889425\pi\)
\(644\) 0 0
\(645\) 2.95118 0.950550i 0.116203 0.0374279i
\(646\) 0 0
\(647\) 2.21980 + 46.5994i 0.0872694 + 1.83201i 0.441969 + 0.897030i \(0.354280\pi\)
−0.354700 + 0.934980i \(0.615417\pi\)
\(648\) 0 0
\(649\) 22.6253 + 28.7704i 0.888120 + 1.12934i
\(650\) 0 0
\(651\) 0.929879 + 1.69408i 0.0364448 + 0.0663961i
\(652\) 0 0
\(653\) −14.8700 42.9640i −0.581907 1.68131i −0.722607 0.691259i \(-0.757056\pi\)
0.140700 0.990052i \(-0.455065\pi\)
\(654\) 0 0
\(655\) −12.7194 + 5.80875i −0.496988 + 0.226967i
\(656\) 0 0
\(657\) 11.6488 + 28.7304i 0.454464 + 1.12088i
\(658\) 0 0
\(659\) −9.29668 23.2220i −0.362147 0.904600i −0.991809 0.127731i \(-0.959231\pi\)
0.629662 0.776870i \(-0.283194\pi\)
\(660\) 0 0
\(661\) −1.56815 0.716148i −0.0609938 0.0278549i 0.384685 0.923048i \(-0.374310\pi\)
−0.445678 + 0.895193i \(0.647037\pi\)
\(662\) 0 0
\(663\) 4.26119 + 5.13782i 0.165491 + 0.199537i
\(664\) 0 0
\(665\) 14.6759 + 2.11008i 0.569107 + 0.0818253i
\(666\) 0 0
\(667\) 4.92354 3.16417i 0.190640 0.122517i
\(668\) 0 0
\(669\) −16.2588 23.9089i −0.628600 0.924370i
\(670\) 0 0
\(671\) 16.6305i 0.642013i
\(672\) 0 0
\(673\) −1.62999 2.53631i −0.0628314 0.0977675i 0.808416 0.588611i \(-0.200325\pi\)
−0.871248 + 0.490844i \(0.836689\pi\)
\(674\) 0 0
\(675\) 0.144463 + 1.84837i 0.00556036 + 0.0711437i
\(676\) 0 0
\(677\) −29.1487 + 2.78336i −1.12028 + 0.106973i −0.638718 0.769441i \(-0.720535\pi\)
−0.481558 + 0.876414i \(0.659929\pi\)
\(678\) 0 0
\(679\) 8.63441 18.9067i 0.331358 0.725574i
\(680\) 0 0
\(681\) −5.99559 + 8.90058i −0.229751 + 0.341071i
\(682\) 0 0
\(683\) 5.63357 5.37160i 0.215563 0.205539i −0.574602 0.818433i \(-0.694843\pi\)
0.790165 + 0.612894i \(0.209995\pi\)
\(684\) 0 0
\(685\) 10.9848 + 24.0534i 0.419708 + 0.919032i
\(686\) 0 0
\(687\) −4.35540 3.24549i −0.166169 0.123823i
\(688\) 0 0
\(689\) 8.79196 92.0736i 0.334947 3.50772i
\(690\) 0 0
\(691\) −11.2652 + 8.85907i −0.428549 + 0.337015i −0.809023 0.587777i \(-0.800003\pi\)
0.380474 + 0.924792i \(0.375761\pi\)
\(692\) 0 0
\(693\) 6.54283 19.1768i 0.248542 0.728466i
\(694\) 0 0
\(695\) −6.05256 + 20.6131i −0.229587 + 0.781901i
\(696\) 0 0
\(697\) 3.57489 0.513991i 0.135408 0.0194688i
\(698\) 0 0
\(699\) 5.02383 10.4001i 0.190019 0.393369i
\(700\) 0 0
\(701\) −18.2157 17.3687i −0.687999 0.656006i 0.263144 0.964757i \(-0.415241\pi\)
−0.951143 + 0.308751i \(0.900089\pi\)
\(702\) 0 0
\(703\) 4.43870 6.23329i 0.167409 0.235093i
\(704\) 0 0
\(705\) −22.9996 37.5472i −0.866215 1.41411i
\(706\) 0 0
\(707\) 1.56689 + 0.904646i 0.0589291 + 0.0340227i
\(708\) 0 0
\(709\) −6.67711 + 27.5234i −0.250764 + 1.03366i 0.697602 + 0.716486i \(0.254250\pi\)
−0.948366 + 0.317178i \(0.897265\pi\)
\(710\) 0 0
\(711\) 11.5334 + 7.34056i 0.432535 + 0.275293i
\(712\) 0 0
\(713\) −0.599844 + 0.692257i −0.0224643 + 0.0259252i
\(714\) 0 0
\(715\) −22.3249 + 34.7382i −0.834904 + 1.29914i
\(716\) 0 0
\(717\) −5.23150 42.9530i −0.195374 1.60411i
\(718\) 0 0
\(719\) 0.513994 + 2.66685i 0.0191687 + 0.0994569i 0.990253 0.139280i \(-0.0444788\pi\)
−0.971084 + 0.238737i \(0.923267\pi\)
\(720\) 0 0
\(721\) −19.6787 + 25.0235i −0.732874 + 0.931925i
\(722\) 0 0
\(723\) −0.0289210 + 0.108892i −0.00107559 + 0.00404975i
\(724\) 0 0
\(725\) 1.00508 0.243829i 0.0373277 0.00905560i
\(726\) 0 0
\(727\) 16.5228 + 32.0498i 0.612798 + 1.18866i 0.967307 + 0.253610i \(0.0816179\pi\)
−0.354508 + 0.935053i \(0.615352\pi\)
\(728\) 0 0
\(729\) −20.1701 + 17.9490i −0.747042 + 0.664777i
\(730\) 0 0
\(731\) −0.425922 0.170513i −0.0157533 0.00630667i
\(732\) 0 0
\(733\) 6.38116 + 2.20854i 0.235694 + 0.0815743i 0.442362 0.896837i \(-0.354141\pi\)
−0.206668 + 0.978411i \(0.566262\pi\)
\(734\) 0 0
\(735\) 1.23341 3.32925i 0.0454951 0.122801i
\(736\) 0 0
\(737\) −20.0983 + 10.0673i −0.740330 + 0.370835i
\(738\) 0 0
\(739\) −9.54596 + 6.79764i −0.351154 + 0.250055i −0.741999 0.670401i \(-0.766122\pi\)
0.390845 + 0.920456i \(0.372183\pi\)
\(740\) 0 0
\(741\) 8.82372 + 32.6432i 0.324147 + 1.19918i
\(742\) 0 0
\(743\) 13.4166 33.5130i 0.492207 1.22947i −0.449573 0.893244i \(-0.648424\pi\)
0.941780 0.336230i \(-0.109152\pi\)
\(744\) 0 0
\(745\) 12.0652 + 41.0902i 0.442034 + 1.50543i
\(746\) 0 0
\(747\) 30.6875 3.06658i 1.12280 0.112200i
\(748\) 0 0
\(749\) −2.81591 11.6073i −0.102891 0.424122i
\(750\) 0 0
\(751\) −24.0876 27.7986i −0.878971 1.01439i −0.999764 0.0217085i \(-0.993089\pi\)
0.120794 0.992678i \(-0.461456\pi\)
\(752\) 0 0
\(753\) 2.98000 42.9947i 0.108597 1.56681i
\(754\) 0 0
\(755\) 17.8859 3.44722i 0.650934 0.125457i
\(756\) 0 0
\(757\) −16.4736 + 31.9542i −0.598742 + 1.16140i 0.373547 + 0.927611i \(0.378142\pi\)
−0.972288 + 0.233785i \(0.924889\pi\)
\(758\) 0 0
\(759\) 9.60084 0.249673i 0.348489 0.00906255i
\(760\) 0 0
\(761\) −0.118608 0.102774i −0.00429952 0.00372556i 0.652708 0.757609i \(-0.273633\pi\)
−0.657008 + 0.753884i \(0.728178\pi\)
\(762\) 0 0
\(763\) 17.8315 + 3.43674i 0.645544 + 0.124418i
\(764\) 0 0
\(765\) −2.05804 + 2.91719i −0.0744087 + 0.105471i
\(766\) 0 0
\(767\) 46.5016 80.5431i 1.67908 2.90824i
\(768\) 0 0
\(769\) −46.3240 2.20669i −1.67049 0.0795751i −0.809148 0.587605i \(-0.800071\pi\)
−0.861340 + 0.508030i \(0.830374\pi\)
\(770\) 0 0
\(771\) −0.556839 + 25.7750i −0.0200541 + 0.928264i
\(772\) 0 0
\(773\) −28.4381 + 29.8250i −1.02285 + 1.07273i −0.0255199 + 0.999674i \(0.508124\pi\)
−0.997328 + 0.0730574i \(0.976724\pi\)