Properties

Label 804.2.ba.b.41.12
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 41.12
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0450273 + 1.73147i) q^{3} +(-0.306661 + 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(-2.99595 - 0.155926i) q^{9} +O(q^{10})\) \(q+(-0.0450273 + 1.73147i) q^{3} +(-0.306661 + 2.13288i) q^{5} +(-0.233782 - 2.44828i) q^{7} +(-2.99595 - 0.155926i) q^{9} +(-2.54950 + 1.02066i) q^{11} +(-4.81545 - 5.05030i) q^{13} +(-3.67919 - 0.627011i) q^{15} +(0.521893 - 0.180629i) q^{17} +(-2.78507 - 0.265942i) q^{19} +(4.24964 - 0.294547i) q^{21} +(-2.01683 + 0.0960734i) q^{23} +(0.342350 + 0.100523i) q^{25} +(0.404880 - 5.18035i) q^{27} +(-2.51027 + 1.44930i) q^{29} +(-0.313059 + 0.328327i) q^{31} +(-1.65245 - 4.46032i) q^{33} +(5.29357 + 0.252164i) q^{35} +(-1.36757 + 2.36869i) q^{37} +(8.96124 - 8.11038i) q^{39} +(6.42149 + 1.23764i) q^{41} +(0.627825 + 0.544013i) q^{43} +(1.25131 - 6.34216i) q^{45} +(-5.40598 + 10.4861i) q^{47} +(0.934085 - 0.180030i) q^{49} +(0.289253 + 0.911773i) q^{51} +(-8.67995 - 10.0172i) q^{53} +(-1.39512 - 5.75075i) q^{55} +(0.585874 - 4.81028i) q^{57} +(-3.75489 - 12.7880i) q^{59} +(-2.25071 + 5.62201i) q^{61} +(0.318648 + 7.37136i) q^{63} +(12.2484 - 8.72202i) q^{65} +(-8.15679 + 0.683270i) q^{67} +(-0.0755355 - 3.49640i) q^{69} +(-8.87305 - 3.07099i) q^{71} +(9.59379 + 3.84077i) q^{73} +(-0.189467 + 0.588241i) q^{75} +(3.09490 + 6.00326i) q^{77} +(4.42862 - 1.07437i) q^{79} +(8.95137 + 0.934293i) q^{81} +(-6.35474 + 8.08070i) q^{83} +(0.225215 + 1.16852i) q^{85} +(-2.39639 - 4.41170i) q^{87} +(-1.12214 + 1.74608i) q^{89} +(-11.2388 + 12.9702i) q^{91} +(-0.554391 - 0.556835i) q^{93} +(1.42130 - 5.85866i) q^{95} +(7.31896 + 4.22560i) q^{97} +(7.79730 - 2.66032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) −0.0450273 + 1.73147i −0.0259965 + 0.999662i
\(4\) 0 0
\(5\) −0.306661 + 2.13288i −0.137143 + 0.953851i 0.798774 + 0.601631i \(0.205482\pi\)
−0.935917 + 0.352220i \(0.885427\pi\)
\(6\) 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
\(9\) −2.99595 0.155926i −0.998648 0.0519754i
\(10\) 0 0
\(11\) −2.54950 + 1.02066i −0.768702 + 0.307742i −0.722665 0.691198i \(-0.757083\pi\)
−0.0460363 + 0.998940i \(0.514659\pi\)
\(12\) 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
\(15\) −3.67919 0.627011i −0.949963 0.161893i
\(16\) 0 0
\(17\) 0.521893 0.180629i 0.126578 0.0438090i −0.263045 0.964784i \(-0.584727\pi\)
0.389622 + 0.920975i \(0.372605\pi\)
\(18\) 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
\(21\) 4.24964 0.294547i 0.927347 0.0642754i
\(22\) 0 0
\(23\) −2.01683 + 0.0960734i −0.420538 + 0.0200327i −0.256785 0.966469i \(-0.582663\pi\)
−0.163753 + 0.986501i \(0.552360\pi\)
\(24\) 0 0
\(25\) 0.342350 + 0.100523i 0.0684700 + 0.0201046i
\(26\) 0 0
\(27\) 0.404880 5.18035i 0.0779192 0.996960i
\(28\) 0 0
\(29\) −2.51027 + 1.44930i −0.466145 + 0.269129i −0.714625 0.699508i \(-0.753402\pi\)
0.248480 + 0.968637i \(0.420069\pi\)
\(30\) 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
\(33\) −1.65245 4.46032i −0.287654 0.776442i
\(34\) 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
\(39\) 8.96124 8.11038i 1.43495 1.29870i
\(40\) 0 0
\(41\) 6.42149 + 1.23764i 1.00287 + 0.193287i 0.664149 0.747600i \(-0.268794\pi\)
0.338720 + 0.940887i \(0.390006\pi\)
\(42\) 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
\(45\) 1.25131 6.34216i 0.186534 0.945433i
\(46\) 0 0
\(47\) −5.40598 + 10.4861i −0.788543 + 1.52956i 0.0586520 + 0.998278i \(0.481320\pi\)
−0.847195 + 0.531282i \(0.821711\pi\)
\(48\) 0 0
\(49\) 0.934085 0.180030i 0.133441 0.0257186i
\(50\) 0 0
\(51\) 0.289253 + 0.911773i 0.0405036 + 0.127674i
\(52\) 0 0
\(53\) −8.67995 10.0172i −1.19228 1.37597i −0.908929 0.416951i \(-0.863099\pi\)
−0.283353 0.959016i \(-0.591447\pi\)
\(54\) 0 0
\(55\) −1.39512 5.75075i −0.188118 0.775431i
\(56\) 0 0
\(57\) 0.585874 4.81028i 0.0776009 0.637138i
\(58\) 0 0
\(59\) −3.75489 12.7880i −0.488845 1.66485i −0.721595 0.692315i \(-0.756591\pi\)
0.232750 0.972536i \(-0.425227\pi\)
\(60\) 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
\(63\) 0.318648 + 7.37136i 0.0401459 + 0.928704i
\(64\) 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
\(69\) −0.0755355 3.49640i −0.00909341 0.420917i
\(70\) 0 0
\(71\) −8.87305 3.07099i −1.05304 0.364460i −0.254920 0.966962i \(-0.582049\pi\)
−0.798117 + 0.602502i \(0.794170\pi\)
\(72\) 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
\(75\) −0.189467 + 0.588241i −0.0218778 + 0.0679242i
\(76\) 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
\(81\) 8.95137 + 0.934293i 0.994597 + 0.103810i
\(82\) 0 0
\(83\) −6.35474 + 8.08070i −0.697523 + 0.886972i −0.997760 0.0668921i \(-0.978692\pi\)
0.300237 + 0.953865i \(0.402934\pi\)
\(84\) 0 0
\(85\) 0.225215 + 1.16852i 0.0244280 + 0.126744i
\(86\) 0 0
\(87\) −2.39639 4.41170i −0.256920 0.472984i
\(88\) 0 0
\(89\) −1.12214 + 1.74608i −0.118947 + 0.185084i −0.895621 0.444817i \(-0.853269\pi\)
0.776675 + 0.629902i \(0.216905\pi\)
\(90\) 0 0
\(91\) −11.2388 + 12.9702i −1.17814 + 1.35965i
\(92\) 0 0
\(93\) −0.554391 0.556835i −0.0574876 0.0577411i
\(94\) 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
\(99\) 7.79730 2.66032i 0.783658 0.267372i
\(100\) 0 0
\(101\) 0.426724 0.599250i 0.0424607 0.0596276i −0.792800 0.609482i \(-0.791377\pi\)
0.835260 + 0.549854i \(0.185317\pi\)
\(102\) 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
\(105\) −0.674967 + 9.15427i −0.0658701 + 0.893365i
\(106\) 0 0
\(107\) −4.80701 + 0.691144i −0.464711 + 0.0668154i −0.370694 0.928755i \(-0.620880\pi\)
−0.0940174 + 0.995571i \(0.529971\pi\)
\(108\) 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
\(111\) −4.03973 2.47455i −0.383434 0.234874i
\(112\) 0 0
\(113\) −1.78929 + 1.40711i −0.168322 + 0.132370i −0.698767 0.715350i \(-0.746267\pi\)
0.530445 + 0.847720i \(0.322025\pi\)
\(114\) 0 0
\(115\) 0.413571 4.33111i 0.0385657 0.403878i
\(116\) 0 0
\(117\) 13.6393 + 15.8813i 1.26096 + 1.46822i
\(118\) 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
\(123\) −2.43207 + 11.0629i −0.219293 + 0.997505i
\(124\) 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
\(129\) −0.970210 + 1.06256i −0.0854222 + 0.0935534i
\(130\) 0 0
\(131\) 3.50834 + 5.45908i 0.306525 + 0.476962i 0.960005 0.279981i \(-0.0903283\pi\)
−0.653481 + 0.756943i \(0.726692\pi\)
\(132\) 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 −0.0194019 0.999812i \(-0.506176\pi\)
0.901401 + 0.432985i \(0.142540\pi\)
\(138\) 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
\(141\) −17.9130 9.83243i −1.50854 0.828040i
\(142\) 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
\(147\) 0.269657 + 1.62544i 0.0222409 + 0.134064i
\(148\) 0 0
\(149\) 18.0782 8.25602i 1.48102 0.676359i 0.499255 0.866455i \(-0.333607\pi\)
0.981766 + 0.190096i \(0.0608799\pi\)
\(150\) 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
\(153\) −1.59173 + 0.459778i −0.128684 + 0.0371708i
\(154\) 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
\(159\) 17.7353 14.5780i 1.40650 1.15611i
\(160\) 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
\(165\) 10.0200 2.15666i 0.780060 0.167896i
\(166\) 0 0
\(167\) 9.87190 + 7.02975i 0.763910 + 0.543978i 0.894291 0.447486i \(-0.147681\pi\)
−0.130381 + 0.991464i \(0.541620\pi\)
\(168\) 0 0
\(169\) −1.69839 + 35.6536i −0.130646 + 2.74259i
\(170\) 0 0
\(171\) 8.30246 + 1.23101i 0.634905 + 0.0941380i
\(172\) 0 0
\(173\) −20.3597 4.93922i −1.54792 0.375522i −0.631384 0.775471i \(-0.717513\pi\)
−0.916537 + 0.399949i \(0.869028\pi\)
\(174\) 0 0
\(175\) 0.166073 0.861669i 0.0125539 0.0651361i
\(176\) 0 0
\(177\) 22.3110 5.92565i 1.67700 0.445399i
\(178\) 0 0
\(179\) −8.09006 5.19917i −0.604679 0.388604i 0.202179 0.979349i \(-0.435198\pi\)
−0.806859 + 0.590745i \(0.798834\pi\)
\(180\) 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
\(183\) −9.63297 4.15017i −0.712089 0.306790i
\(184\) 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
\(189\) −12.7776 + 0.219815i −0.929434 + 0.0159892i
\(190\) 0 0
\(191\) −3.46682 + 1.78727i −0.250850 + 0.129322i −0.579067 0.815280i \(-0.696583\pi\)
0.328216 + 0.944603i \(0.393553\pi\)
\(192\) 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
\(195\) 14.5504 + 21.6003i 1.04197 + 1.54683i
\(196\) 0 0
\(197\) 5.55240 16.0426i 0.395592 1.14299i −0.554813 0.831975i \(-0.687210\pi\)
0.950405 0.311014i \(-0.100669\pi\)
\(198\) 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
\(201\) −0.815780 14.1540i −0.0575407 0.998343i
\(202\) 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
\(207\) 6.05729 + 0.0266461i 0.421011 + 0.00185203i
\(208\) 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
\(213\) 5.71685 15.2251i 0.391712 1.04321i
\(214\) 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
\(219\) −7.08215 + 16.4384i −0.478567 + 1.11080i
\(220\) 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
\(225\) −1.00999 0.354543i −0.0673325 0.0236362i
\(226\) 0 0
\(227\) 1.17258 6.08393i 0.0778270 0.403805i −0.922034 0.387110i \(-0.873473\pi\)
0.999861 0.0166949i \(-0.00531440\pi\)
\(228\) 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
\(231\) −10.5338 + 5.08840i −0.693073 + 0.334792i
\(232\) 0 0
\(233\) −0.317294 + 6.66082i −0.0207866 + 0.436365i 0.964354 + 0.264616i \(0.0852450\pi\)
−0.985141 + 0.171750i \(0.945058\pi\)
\(234\) 0 0
\(235\) −20.7078 14.7460i −1.35083 0.961921i
\(236\) 0 0
\(237\) 1.66083 + 7.71638i 0.107882 + 0.501233i
\(238\) 0 0
\(239\) 12.4911 + 21.6352i 0.807981 + 1.39946i 0.914260 + 0.405127i \(0.132773\pi\)
−0.106279 + 0.994336i \(0.533894\pi\)
\(240\) 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
\(243\) −2.02075 + 15.4569i −0.129631 + 0.991562i
\(244\) 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
\(249\) −13.7053 11.3669i −0.868539 0.720345i
\(250\) 0 0
\(251\) 8.13828 + 23.5140i 0.513684 + 1.48419i 0.841923 + 0.539597i \(0.181423\pi\)
−0.328240 + 0.944594i \(0.606455\pi\)
\(252\) 0 0
\(253\) 5.04384 2.30344i 0.317103 0.144816i
\(254\) 0 0
\(255\) −2.03340 + 0.337336i −0.127336 + 0.0211248i
\(256\) 0 0
\(257\) −5.53208 13.8185i −0.345082 0.861972i −0.994805 0.101801i \(-0.967539\pi\)
0.649723 0.760171i \(-0.274885\pi\)
\(258\) 0 0
\(259\) 6.11893 + 2.79442i 0.380212 + 0.173637i
\(260\) 0 0
\(261\) 7.74661 3.95062i 0.479503 0.244537i
\(262\) 0 0
\(263\) 13.2735 + 1.90845i 0.818482 + 0.117680i 0.538823 0.842419i \(-0.318869\pi\)
0.279660 + 0.960099i \(0.409778\pi\)
\(264\) 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 \(-0.909969\pi\)
0.960266 0.279086i \(-0.0900313\pi\)
\(270\) 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
\(273\) −21.9515 20.0436i −1.32856 1.21309i
\(274\) 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
\(279\) 0.989103 0.934836i 0.0592161 0.0559671i
\(280\) 0 0
\(281\) −14.5314 + 13.8556i −0.866869 + 0.826558i −0.986073 0.166312i \(-0.946814\pi\)
0.119204 + 0.992870i \(0.461966\pi\)
\(282\) 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
\(285\) 10.0801 + 2.72472i 0.597092 + 0.161399i
\(286\) 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
\(291\) −7.64604 + 12.4823i −0.448219 + 0.731723i
\(292\) 0 0
\(293\) 4.70974 16.0399i 0.275146 0.937061i −0.699748 0.714390i \(-0.746704\pi\)
0.974894 0.222671i \(-0.0714775\pi\)
\(294\) 0 0
\(295\) 28.4266 4.08713i 1.65506 0.237962i
\(296\) 0 0
\(297\) 4.25516 + 13.6205i 0.246909 + 0.790344i
\(298\) 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
\(303\) 1.01837 + 0.765841i 0.0585037 + 0.0439964i
\(304\) 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
\(309\) 15.8878 15.8181i 0.903825 0.899858i
\(310\) 0 0
\(311\) 8.51947 9.83200i 0.483095 0.557521i −0.460912 0.887446i \(-0.652478\pi\)
0.944007 + 0.329924i \(0.107023\pi\)
\(312\) 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
\(315\) −15.8199 1.58087i −0.891351 0.0890722i
\(316\) 0 0
\(317\) −1.34794 6.99379i −0.0757080 0.392810i −0.999940 0.0109782i \(-0.996505\pi\)
0.924232 0.381832i \(-0.124707\pi\)
\(318\) 0 0
\(319\) 4.92066 6.25713i 0.275504 0.350332i
\(320\) 0 0
\(321\) −0.980245 8.35429i −0.0547119 0.466291i
\(322\) 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
\(327\) −12.1731 3.92086i −0.673177 0.216824i
\(328\) 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
\(333\) 4.46649 6.88323i 0.244762 0.377199i
\(334\) 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
\(339\) −2.35580 3.16145i −0.127949 0.171706i
\(340\) 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
\(345\) 7.48054 + 0.911101i 0.402739 + 0.0490520i
\(346\) 0 0
\(347\) −1.18614 4.88934i −0.0636754 0.262473i 0.931072 0.364836i \(-0.118875\pi\)
−0.994747 + 0.102363i \(0.967360\pi\)
\(348\) 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
\(351\) −28.1120 + 22.9010i −1.50051 + 1.22236i
\(352\) 0 0
\(353\) −13.7779 + 2.65548i −0.733325 + 0.141337i −0.542224 0.840234i \(-0.682418\pi\)
−0.191100 + 0.981571i \(0.561206\pi\)
\(354\) 0 0
\(355\) 9.27106 17.9834i 0.492057 0.954457i
\(356\) 0 0
\(357\) 2.16465 0.921329i 0.114566 0.0487619i
\(358\) 0 0
\(359\) −19.3650 16.7799i −1.02205 0.885609i −0.0285650 0.999592i \(-0.509094\pi\)
−0.993483 + 0.113983i \(0.963639\pi\)
\(360\) 0 0
\(361\) −10.9707 2.11444i −0.577407 0.111286i
\(362\) 0 0
\(363\) −4.01947 4.44115i −0.210967 0.233100i
\(364\) 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
\(369\) −19.0455 4.70918i −0.991467 0.245150i
\(370\) 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
\(375\) −17.9641 8.77530i −0.927661 0.453155i
\(376\) 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
\(381\) −1.85285 26.7324i −0.0949245 1.36954i
\(382\) 0 0
\(383\) −34.1052 3.25665i −1.74269 0.166407i −0.825380 0.564577i \(-0.809039\pi\)
−0.917312 + 0.398170i \(0.869645\pi\)
\(384\) 0 0
\(385\) −13.7533 + 4.76006i −0.700933 + 0.242595i
\(386\) 0 0
\(387\) −1.79610 1.72773i −0.0913011 0.0878254i
\(388\) 0 0
\(389\) 17.0865 + 17.9198i 0.866318 + 0.908568i 0.996557 0.0829147i \(-0.0264229\pi\)
−0.130239 + 0.991483i \(0.541574\pi\)
\(390\) 0 0
\(391\) −1.03522 + 0.414438i −0.0523531 + 0.0209590i
\(392\) 0 0
\(393\) −9.61017 + 5.82875i −0.484769 + 0.294022i
\(394\) 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
\(399\) −11.9139 0.309824i −0.596440 0.0155106i
\(400\) 0 0
\(401\) −18.0622 −0.901983 −0.450991 0.892528i \(-0.648930\pi\)
−0.450991 + 0.892528i \(0.648930\pi\)
\(402\) 0 0
\(403\) 3.16567 0.157693
\(404\) 0 0
\(405\) −4.73777 + 18.8057i −0.235422 + 0.934460i
\(406\) 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
\(411\) 11.0226 + 18.1736i 0.543706 + 0.896436i
\(412\) 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
\(417\) 2.90108 17.0231i 0.142067 0.833623i
\(418\) 0 0
\(419\) 25.6749 8.88615i 1.25430 0.434117i 0.382488 0.923960i \(-0.375067\pi\)
0.871810 + 0.489843i \(0.162946\pi\)
\(420\) 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
\(423\) 17.8311 30.5730i 0.866977 1.48651i
\(424\) 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
\(429\) −14.5687 + 29.8238i −0.703382 + 1.43991i
\(430\) 0 0
\(431\) −29.7965 + 17.2030i −1.43525 + 0.828640i −0.997514 0.0704650i \(-0.977552\pi\)
−0.437733 + 0.899105i \(0.644218\pi\)
\(432\) 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
\(435\) 10.1445 3.75830i 0.486391 0.180197i
\(436\) 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
\(441\) −2.82654 + 0.393712i −0.134597 + 0.0187482i
\(442\) 0 0
\(443\) 18.3930 + 3.54496i 0.873878 + 0.168426i 0.606421 0.795144i \(-0.292605\pi\)
0.267457 + 0.963570i \(0.413817\pi\)
\(444\) 0 0
\(445\) −3.38006 2.92884i −0.160230 0.138840i
\(446\) 0 0
\(447\) 13.4810 + 31.6734i 0.637629 + 1.49810i
\(448\) 0 0
\(449\) −3.99949 + 7.75792i −0.188747 + 0.366119i −0.964154 0.265343i \(-0.914515\pi\)
0.775407 + 0.631462i \(0.217545\pi\)
\(450\) 0 0
\(451\) −17.6348 + 3.39882i −0.830389 + 0.160044i
\(452\) 0 0
\(453\) −13.9560 + 4.42742i −0.655708 + 0.208019i
\(454\) 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
\(459\) −0.724418 2.77672i −0.0338129 0.129606i
\(460\) 0 0
\(461\) −7.58595 25.8354i −0.353313 1.20327i −0.924092 0.382170i \(-0.875177\pi\)
0.570779 0.821104i \(-0.306641\pi\)
\(462\) 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
\(465\) 1.35767 1.01169i 0.0629604 0.0469158i
\(466\) 0 0
\(467\) −7.86651 + 5.60171i −0.364018 + 0.259216i −0.747401 0.664373i \(-0.768699\pi\)
0.383382 + 0.923590i \(0.374759\pi\)
\(468\) 0 0
\(469\) 3.57975 + 19.8103i 0.165297 + 0.914757i
\(470\) 0 0
\(471\) −3.06691 + 0.0662569i −0.141316 + 0.00305296i
\(472\) 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
\(477\) 24.4427 + 31.3644i 1.11915 + 1.43608i
\(478\) 0 0
\(479\) −12.3046 23.8677i −0.562214 1.09054i −0.983038 0.183400i \(-0.941289\pi\)
0.420825 0.907142i \(-0.361741\pi\)
\(480\) 0 0
\(481\) 18.5480 4.49971i 0.845718 0.205169i
\(482\) 0 0
\(483\) −8.54250 + 1.00233i −0.388697 + 0.0456075i
\(484\) 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
\(489\) 11.5268 6.26122i 0.521259 0.283142i
\(490\) 0 0
\(491\) −4.02285 + 6.25968i −0.181549 + 0.282495i −0.920085 0.391718i \(-0.871881\pi\)
0.738537 + 0.674213i \(0.235517\pi\)
\(492\) 0 0
\(493\) −1.04830 + 1.20981i −0.0472133 + 0.0544870i
\(494\) 0 0
\(495\) 3.28300 + 17.4465i 0.147560 + 0.784161i
\(496\) 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
\(501\) −12.6163 + 16.7763i −0.563653 + 0.749511i
\(502\) 0 0
\(503\) 0.0854197 0.119955i 0.00380867 0.00534853i −0.812667 0.582728i \(-0.801985\pi\)
0.816476 + 0.577380i \(0.195925\pi\)
\(504\) 0 0
\(505\) 1.14727 + 1.09392i 0.0510527 + 0.0486786i
\(506\) 0 0
\(507\) −61.6566 4.54609i −2.73826 0.201899i
\(508\) 0 0
\(509\) −6.04361 + 0.868940i −0.267878 + 0.0385151i −0.274945 0.961460i \(-0.588660\pi\)
0.00706679 + 0.999975i \(0.497751\pi\)
\(510\) 0 0
\(511\) 7.16043 24.3862i 0.316759 1.07878i
\(512\) 0 0
\(513\) −2.50530 + 14.3200i −0.110612 + 0.632243i
\(514\) 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
\(519\) 9.46882 35.0298i 0.415635 1.53764i
\(520\) 0 0
\(521\) 10.9594 + 23.9977i 0.480140 + 1.05136i 0.982425 + 0.186658i \(0.0597656\pi\)
−0.502285 + 0.864702i \(0.667507\pi\)
\(522\) 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
\(525\) 1.48447 + 0.326348i 0.0647877 + 0.0142430i
\(526\) 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
\(531\) 9.25545 + 38.8975i 0.401652 + 1.68801i
\(532\) 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
\(543\) −5.51110 + 10.0403i −0.236504 + 0.430869i
\(544\) 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
\(549\) 7.61963 16.4923i 0.325198 0.703873i
\(550\) 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
\(555\) 6.51673 7.85740i 0.276620 0.333528i
\(556\) 0 0
\(557\) 16.6237 + 21.1388i 0.704369 + 0.895679i 0.998187 0.0601829i \(-0.0191684\pi\)
−0.293818 + 0.955861i \(0.594926\pi\)
\(558\) 0 0
\(559\) −0.275829 5.79037i −0.0116663 0.244907i
\(560\) 0 0
\(561\) −1.66806 2.02933i −0.0704257 0.0856784i
\(562\) 0 0
\(563\) −6.20782 43.1764i −0.261629 1.81967i −0.520622 0.853788i \(-0.674300\pi\)
0.258993 0.965879i \(-0.416609\pi\)
\(564\) 0 0
\(565\) −2.45249 4.24784i −0.103177 0.178708i
\(566\) 0 0
\(567\) 0.194738 22.1339i 0.00817822 0.929536i
\(568\) 0 0
\(569\) −24.2621 17.2770i −1.01712 0.724289i −0.0554414 0.998462i \(-0.517657\pi\)
−0.961680 + 0.274173i \(0.911596\pi\)
\(570\) 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
\(573\) −2.93849 6.08316i −0.122757 0.254127i
\(574\) 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
\(579\) 12.2244 + 46.0268i 0.508029 + 1.91281i
\(580\) 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
\(585\) −38.0554 + 24.2209i −1.57340 + 1.00141i
\(586\) 0 0
\(587\) 26.8181 + 21.0900i 1.10690 + 0.870477i 0.992413 0.122947i \(-0.0392346\pi\)
0.114489 + 0.993425i \(0.463477\pi\)
\(588\) 0 0
\(589\) 0.959209 0.831159i 0.0395235 0.0342473i
\(590\) 0 0
\(591\) 27.5272 + 10.3361i 1.13232 + 0.425172i
\(592\) 0 0
\(593\) 26.4914 13.6573i 1.08787 0.560837i 0.181532 0.983385i \(-0.441895\pi\)
0.906341 + 0.422548i \(0.138864\pi\)
\(594\) 0 0
\(595\) 2.80822 0.824569i 0.115126 0.0338040i
\(596\) 0 0
\(597\) −17.6741 + 11.9056i −0.723352 + 0.487262i
\(598\) 0 0
\(599\) −4.85131 + 14.0169i −0.198219 + 0.572717i −0.999679 0.0253316i \(-0.991936\pi\)
0.801460 + 0.598049i \(0.204057\pi\)
\(600\) 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
\(603\) 24.5438 0.775182i 0.999502 0.0315678i
\(604\) 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
\(609\) −10.2408 + 6.89840i −0.414980 + 0.279537i
\(610\) 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
\(615\) −22.8499 8.57986i −0.921396 0.345973i
\(616\) 0 0
\(617\) 10.1060 8.75690i 0.406852 0.352539i −0.427265 0.904126i \(-0.640523\pi\)
0.834117 + 0.551587i \(0.185978\pi\)
\(618\) 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
\(621\) −0.318880 + 10.4868i −0.0127962 + 0.420820i
\(622\) 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
\(627\) 3.41600 + 12.8618i 0.136422 + 0.513650i
\(628\) 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
\(633\) −14.2420 29.4833i −0.566069 1.17185i
\(634\) 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
\(639\) 26.1043 + 10.5841i 1.03267 + 0.418699i
\(640\) 0 0
\(641\) 5.04283 + 8.73443i 0.199180 + 0.344989i 0.948263 0.317487i \(-0.102839\pi\)
−0.749083 + 0.662476i \(0.769506\pi\)
\(642\) 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
\(645\) −1.96879 2.39518i −0.0775209 0.0943102i
\(646\) 0 0
\(647\) −2.21980 46.5994i −0.0872694 1.83201i −0.441969 0.897030i \(-0.645720\pi\)
0.354700 0.934980i \(-0.384583\pi\)
\(648\) 0 0
\(649\) 22.6253 + 28.7704i 0.888120 + 1.12934i
\(650\) 0 0
\(651\) −1.23368 + 1.48748i −0.0483517 + 0.0582990i
\(652\) 0 0
\(653\) 14.8700 + 42.9640i 0.581907 + 1.68131i 0.722607 + 0.691259i \(0.242944\pi\)
−0.140700 + 0.990052i \(0.544935\pi\)
\(654\) 0 0
\(655\) −12.7194 + 5.80875i −0.496988 + 0.226967i
\(656\) 0 0
\(657\) −28.1436 13.0027i −1.09799 0.507282i
\(658\) 0 0
\(659\) 9.29668 + 23.2220i 0.362147 + 0.904600i 0.991809 + 0.127731i \(0.0407693\pi\)
−0.629662 + 0.776870i \(0.716806\pi\)
\(660\) 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
\(663\) 3.21184 5.85141i 0.124738 0.227250i
\(664\) 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
\(675\) 0.659356 1.73279i 0.0253786 0.0666953i
\(676\) 0 0
\(677\) 29.1487 2.78336i 1.12028 0.106973i 0.481558 0.876414i \(-0.340071\pi\)
0.638718 + 0.769441i \(0.279465\pi\)
\(678\) 0 0
\(679\) 8.63441 18.9067i 0.331358 0.725574i
\(680\) 0 0
\(681\) 10.4813 + 2.30423i 0.401645 + 0.0882982i
\(682\) 0 0
\(683\) −5.63357 + 5.37160i −0.215563 + 0.205539i −0.790165 0.612894i \(-0.790005\pi\)
0.574602 + 0.818433i \(0.305157\pi\)
\(684\) 0 0
\(685\) 10.9848 + 24.0534i 0.419708 + 0.919032i
\(686\) 0 0
\(687\) 1.41735 5.24346i 0.0540752 0.200050i
\(688\) 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
\(693\) −8.33607 18.4680i −0.316661 0.701542i
\(694\) 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
\(699\) −11.5187 0.849303i −0.435677 0.0321236i
\(700\) 0 0
\(701\) 18.2157 + 17.3687i 0.687999 + 0.656006i 0.951143 0.308751i \(-0.0999109\pi\)
−0.263144 + 0.964757i \(0.584759\pi\)
\(702\) 0 0
\(703\) 4.43870 6.23329i 0.167409 0.235093i
\(704\) 0 0
\(705\) 26.4646 35.1909i 0.996713 1.32537i
\(706\) 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
\(711\) −13.4354 + 2.52822i −0.503868 + 0.0948157i
\(712\) 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
\(717\) −38.0230 + 20.6537i −1.42000 + 0.771327i
\(718\) 0 0
\(719\) −0.513994 2.66685i −0.0191687 0.0994569i 0.971084 0.238737i \(-0.0767333\pi\)
−0.990253 + 0.139280i \(0.955521\pi\)
\(720\) 0 0
\(721\) −19.6787 + 25.0235i −0.732874 + 0.931925i
\(722\) 0 0
\(723\) −0.111900 + 0.0131297i −0.00416160 + 0.000488298i
\(724\) 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
\(729\) −26.6721 4.19485i −0.987857 0.155365i
\(730\) 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
\(735\) −3.54956 + 0.0766840i −0.130927 + 0.00282853i
\(736\) 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
\(741\) −27.1146 + 20.2048i −0.996080 + 0.742243i
\(742\) 0 0
\(743\) −13.4166 + 33.5130i −0.492207 + 1.22947i 0.449573 + 0.893244i \(0.351576\pi\)
−0.941780 + 0.336230i \(0.890848\pi\)
\(744\) 0 0
\(745\) 12.0652 + 41.0902i 0.442034 + 1.50543i
\(746\) 0 0
\(747\) 20.2984 23.2185i 0.742681 0.849519i
\(748\) 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
\(753\) −41.0801 + 13.0324i −1.49704 + 0.474926i
\(754\) 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
\(759\) 3.76122 + 8.83695i 0.136524 + 0.320761i
\(760\) 0 0
\(761\) 0.118608 + 0.102774i 0.00429952 + 0.00372556i 0.657008 0.753884i \(-0.271822\pi\)
−0.652708 + 0.757609i \(0.726367\pi\)
\(762\) 0 0
\(763\) 17.8315 + 3.43674i 0.645544 + 0.124418i
\(764\) 0 0
\(765\) −0.492527 3.53595i −0.0178074 0.127843i
\(766\) 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
\(771\) 24.1753 8.95639i 0.870652 0.322557i
\(772\) 0 0
\(773\) 28.4381 29.8250i 1.02285 1.07273i 0.0255199 0.999674i \(-0.491876\pi\)
0.997328 0.0730574i