Properties

Label 1170.2.bs.h.361.1
Level $1170$
Weight $2$
Character 1170.361
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
Defining polynomial: \(x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(-1.35234 + 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 1170.361
Dual form 1170.2.bs.h.901.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-2.34233 - 1.35234i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-2.34233 - 1.35234i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(2.59808 - 1.50000i) q^{11} +(-3.34233 + 1.35234i) q^{13} +2.70469 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.34233 - 3.08440i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(3.95042 + 6.84233i) q^{23} -1.00000 q^{25} +(2.21837 - 2.84233i) q^{26} +(-2.34233 + 1.35234i) q^{28} +(-1.24573 - 2.15767i) q^{29} -0.972638i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.35234 + 2.34233i) q^{35} +(-1.50000 + 0.866025i) q^{37} +6.16879 q^{38} +1.00000 q^{40} +(-5.19615 + 3.00000i) q^{41} +(-4.84233 + 8.38716i) q^{43} -3.00000i q^{44} +(-6.84233 - 3.95042i) q^{46} +3.00000i q^{47} +(0.157671 + 0.273094i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-0.500000 + 3.57071i) q^{52} -2.70469 q^{53} +(-1.50000 - 2.59808i) q^{55} +(1.35234 - 2.34233i) q^{56} +(2.15767 + 1.24573i) q^{58} +(-6.65511 - 3.84233i) q^{59} +(-6.68466 + 11.5782i) q^{61} +(0.486319 + 0.842329i) q^{62} -1.00000 q^{64} +(1.35234 + 3.34233i) q^{65} +(-1.68466 + 0.972638i) q^{67} -2.70469i q^{70} +(5.19615 + 3.00000i) q^{71} -6.92820i q^{73} +(0.866025 - 1.50000i) q^{74} +(-5.34233 + 3.08440i) q^{76} -8.11407 q^{77} +5.68466 q^{79} +(-0.866025 + 0.500000i) q^{80} +(3.00000 - 5.19615i) q^{82} +15.3693i q^{83} -9.68466i q^{86} +(1.50000 + 2.59808i) q^{88} +(4.05703 - 2.34233i) q^{89} +(9.65767 + 1.35234i) q^{91} +7.90084 q^{92} +(-1.50000 - 2.59808i) q^{94} +(-3.08440 + 5.34233i) q^{95} +(-7.68466 - 4.43674i) q^{97} +(-0.273094 - 0.157671i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 6 q^{7} + O(q^{10}) \) \( 8 q + 4 q^{4} + 6 q^{7} + 4 q^{10} - 2 q^{13} - 4 q^{16} - 18 q^{19} - 12 q^{22} - 8 q^{25} + 6 q^{28} - 12 q^{37} + 8 q^{40} - 14 q^{43} - 30 q^{46} + 26 q^{49} - 4 q^{52} - 12 q^{55} + 42 q^{58} - 4 q^{61} - 8 q^{64} + 36 q^{67} - 18 q^{76} - 4 q^{79} + 24 q^{82} + 12 q^{88} + 102 q^{91} - 12 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −2.34233 1.35234i −0.885317 0.511138i −0.0129093 0.999917i \(-0.504109\pi\)
−0.872408 + 0.488779i \(0.837443\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 2.59808 1.50000i 0.783349 0.452267i −0.0542666 0.998526i \(-0.517282\pi\)
0.837616 + 0.546259i \(0.183949\pi\)
\(12\) 0 0
\(13\) −3.34233 + 1.35234i −0.926995 + 0.375073i
\(14\) 2.70469 0.722858
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) −5.34233 3.08440i −1.22561 0.707609i −0.259505 0.965742i \(-0.583559\pi\)
−0.966109 + 0.258133i \(0.916893\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 0 0
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) 3.95042 + 6.84233i 0.823720 + 1.42672i 0.902894 + 0.429863i \(0.141438\pi\)
−0.0791743 + 0.996861i \(0.525228\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 2.21837 2.84233i 0.435058 0.557427i
\(27\) 0 0
\(28\) −2.34233 + 1.35234i −0.442659 + 0.255569i
\(29\) −1.24573 2.15767i −0.231327 0.400669i 0.726872 0.686773i \(-0.240973\pi\)
−0.958199 + 0.286103i \(0.907640\pi\)
\(30\) 0 0
\(31\) 0.972638i 0.174691i −0.996178 0.0873455i \(-0.972162\pi\)
0.996178 0.0873455i \(-0.0278384\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.35234 + 2.34233i −0.228588 + 0.395926i
\(36\) 0 0
\(37\) −1.50000 + 0.866025i −0.246598 + 0.142374i −0.618206 0.786016i \(-0.712140\pi\)
0.371607 + 0.928390i \(0.378807\pi\)
\(38\) 6.16879 1.00071
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −5.19615 + 3.00000i −0.811503 + 0.468521i −0.847477 0.530831i \(-0.821880\pi\)
0.0359748 + 0.999353i \(0.488546\pi\)
\(42\) 0 0
\(43\) −4.84233 + 8.38716i −0.738448 + 1.27903i 0.214746 + 0.976670i \(0.431108\pi\)
−0.953194 + 0.302360i \(0.902226\pi\)
\(44\) 3.00000i 0.452267i
\(45\) 0 0
\(46\) −6.84233 3.95042i −1.00885 0.582458i
\(47\) 3.00000i 0.437595i 0.975770 + 0.218797i \(0.0702134\pi\)
−0.975770 + 0.218797i \(0.929787\pi\)
\(48\) 0 0
\(49\) 0.157671 + 0.273094i 0.0225244 + 0.0390134i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) 0 0
\(52\) −0.500000 + 3.57071i −0.0693375 + 0.495169i
\(53\) −2.70469 −0.371518 −0.185759 0.982595i \(-0.559474\pi\)
−0.185759 + 0.982595i \(0.559474\pi\)
\(54\) 0 0
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) 1.35234 2.34233i 0.180715 0.313007i
\(57\) 0 0
\(58\) 2.15767 + 1.24573i 0.283316 + 0.163573i
\(59\) −6.65511 3.84233i −0.866421 0.500229i −0.000264050 1.00000i \(-0.500084\pi\)
−0.866157 + 0.499771i \(0.833417\pi\)
\(60\) 0 0
\(61\) −6.68466 + 11.5782i −0.855883 + 1.48243i 0.0199408 + 0.999801i \(0.493652\pi\)
−0.875824 + 0.482631i \(0.839681\pi\)
\(62\) 0.486319 + 0.842329i 0.0617626 + 0.106976i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.35234 + 3.34233i 0.167738 + 0.414565i
\(66\) 0 0
\(67\) −1.68466 + 0.972638i −0.205814 + 0.118827i −0.599364 0.800476i \(-0.704580\pi\)
0.393551 + 0.919303i \(0.371247\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 2.70469i 0.323272i
\(71\) 5.19615 + 3.00000i 0.616670 + 0.356034i 0.775571 0.631260i \(-0.217462\pi\)
−0.158901 + 0.987294i \(0.550795\pi\)
\(72\) 0 0
\(73\) 6.92820i 0.810885i −0.914121 0.405442i \(-0.867117\pi\)
0.914121 0.405442i \(-0.132883\pi\)
\(74\) 0.866025 1.50000i 0.100673 0.174371i
\(75\) 0 0
\(76\) −5.34233 + 3.08440i −0.612807 + 0.353804i
\(77\) −8.11407 −0.924684
\(78\) 0 0
\(79\) 5.68466 0.639574 0.319787 0.947489i \(-0.396389\pi\)
0.319787 + 0.947489i \(0.396389\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 15.3693i 1.68700i 0.537128 + 0.843501i \(0.319509\pi\)
−0.537128 + 0.843501i \(0.680491\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 9.68466i 1.04432i
\(87\) 0 0
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 4.05703 2.34233i 0.430045 0.248286i −0.269321 0.963050i \(-0.586799\pi\)
0.699366 + 0.714764i \(0.253466\pi\)
\(90\) 0 0
\(91\) 9.65767 + 1.35234i 1.01240 + 0.141764i
\(92\) 7.90084 0.823720
\(93\) 0 0
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) −3.08440 + 5.34233i −0.316452 + 0.548111i
\(96\) 0 0
\(97\) −7.68466 4.43674i −0.780259 0.450483i 0.0562632 0.998416i \(-0.482081\pi\)
−0.836522 + 0.547933i \(0.815415\pi\)
\(98\) −0.273094 0.157671i −0.0275866 0.0159272i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −5.40938 9.36932i −0.538253 0.932282i −0.998998 0.0447493i \(-0.985751\pi\)
0.460745 0.887533i \(-0.347582\pi\)
\(102\) 0 0
\(103\) −14.6847 −1.44692 −0.723461 0.690365i \(-0.757450\pi\)
−0.723461 + 0.690365i \(0.757450\pi\)
\(104\) −1.35234 3.34233i −0.132608 0.327742i
\(105\) 0 0
\(106\) 2.34233 1.35234i 0.227507 0.131351i
\(107\) −2.70469 4.68466i −0.261472 0.452883i 0.705161 0.709047i \(-0.250875\pi\)
−0.966633 + 0.256164i \(0.917541\pi\)
\(108\) 0 0
\(109\) 12.3376i 1.18173i −0.806772 0.590863i \(-0.798787\pi\)
0.806772 0.590863i \(-0.201213\pi\)
\(110\) 2.59808 + 1.50000i 0.247717 + 0.143019i
\(111\) 0 0
\(112\) 2.70469i 0.255569i
\(113\) 1.24573 2.15767i 0.117189 0.202977i −0.801464 0.598043i \(-0.795945\pi\)
0.918653 + 0.395067i \(0.129278\pi\)
\(114\) 0 0
\(115\) 6.84233 3.95042i 0.638050 0.368379i
\(116\) −2.49146 −0.231327
\(117\) 0 0
\(118\) 7.68466 0.707430
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) 13.3693i 1.21040i
\(123\) 0 0
\(124\) −0.842329 0.486319i −0.0756434 0.0436727i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −1.34233 2.32498i −0.119112 0.206309i 0.800304 0.599595i \(-0.204672\pi\)
−0.919416 + 0.393286i \(0.871338\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −2.84233 2.21837i −0.249289 0.194564i
\(131\) −20.9978 −1.83459 −0.917295 0.398209i \(-0.869632\pi\)
−0.917295 + 0.398209i \(0.869632\pi\)
\(132\) 0 0
\(133\) 8.34233 + 14.4493i 0.723372 + 1.25292i
\(134\) 0.972638 1.68466i 0.0840231 0.145532i
\(135\) 0 0
\(136\) 0 0
\(137\) −17.0474 9.84233i −1.45646 0.840887i −0.457624 0.889146i \(-0.651299\pi\)
−0.998835 + 0.0482589i \(0.984633\pi\)
\(138\) 0 0
\(139\) −4.65767 + 8.06732i −0.395058 + 0.684261i −0.993109 0.117197i \(-0.962609\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(140\) 1.35234 + 2.34233i 0.114294 + 0.197963i
\(141\) 0 0
\(142\) −6.00000 −0.503509
\(143\) −6.65511 + 8.52699i −0.556528 + 0.713063i
\(144\) 0 0
\(145\) −2.15767 + 1.24573i −0.179185 + 0.103452i
\(146\) 3.46410 + 6.00000i 0.286691 + 0.496564i
\(147\) 0 0
\(148\) 1.73205i 0.142374i
\(149\) 8.93335 + 5.15767i 0.731848 + 0.422533i 0.819098 0.573654i \(-0.194474\pi\)
−0.0872496 + 0.996186i \(0.527808\pi\)
\(150\) 0 0
\(151\) 14.2829i 1.16232i 0.813788 + 0.581161i \(0.197401\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 3.08440 5.34233i 0.250177 0.433320i
\(153\) 0 0
\(154\) 7.02699 4.05703i 0.566251 0.326925i
\(155\) −0.972638 −0.0781242
\(156\) 0 0
\(157\) 8.36932 0.667944 0.333972 0.942583i \(-0.391611\pi\)
0.333972 + 0.942583i \(0.391611\pi\)
\(158\) −4.92306 + 2.84233i −0.391658 + 0.226124i
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 21.3693i 1.68414i
\(162\) 0 0
\(163\) −15.8423 9.14657i −1.24087 0.716415i −0.271596 0.962411i \(-0.587552\pi\)
−0.969271 + 0.245996i \(0.920885\pi\)
\(164\) 6.00000i 0.468521i
\(165\) 0 0
\(166\) −7.68466 13.3102i −0.596445 1.03307i
\(167\) −5.51599 + 3.18466i −0.426840 + 0.246436i −0.698000 0.716098i \(-0.745926\pi\)
0.271159 + 0.962534i \(0.412593\pi\)
\(168\) 0 0
\(169\) 9.34233 9.03996i 0.718641 0.695382i
\(170\) 0 0
\(171\) 0 0
\(172\) 4.84233 + 8.38716i 0.369224 + 0.639515i
\(173\) −4.05703 + 7.02699i −0.308451 + 0.534252i −0.978024 0.208494i \(-0.933144\pi\)
0.669573 + 0.742746i \(0.266477\pi\)
\(174\) 0 0
\(175\) 2.34233 + 1.35234i 0.177063 + 0.102228i
\(176\) −2.59808 1.50000i −0.195837 0.113067i
\(177\) 0 0
\(178\) −2.34233 + 4.05703i −0.175565 + 0.304087i
\(179\) 6.44188 + 11.1577i 0.481489 + 0.833963i 0.999774 0.0212443i \(-0.00676279\pi\)
−0.518285 + 0.855208i \(0.673429\pi\)
\(180\) 0 0
\(181\) 5.36932 0.399098 0.199549 0.979888i \(-0.436052\pi\)
0.199549 + 0.979888i \(0.436052\pi\)
\(182\) −9.03996 + 3.65767i −0.670086 + 0.271125i
\(183\) 0 0
\(184\) −6.84233 + 3.95042i −0.504423 + 0.291229i
\(185\) 0.866025 + 1.50000i 0.0636715 + 0.110282i
\(186\) 0 0
\(187\) 0 0
\(188\) 2.59808 + 1.50000i 0.189484 + 0.109399i
\(189\) 0 0
\(190\) 6.16879i 0.447531i
\(191\) 10.6055 18.3693i 0.767389 1.32916i −0.171585 0.985169i \(-0.554889\pi\)
0.938974 0.343988i \(-0.111778\pi\)
\(192\) 0 0
\(193\) 13.6847 7.90084i 0.985043 0.568715i 0.0812543 0.996693i \(-0.474107\pi\)
0.903789 + 0.427978i \(0.140774\pi\)
\(194\) 8.87348 0.637079
\(195\) 0 0
\(196\) 0.315342 0.0225244
\(197\) 17.3673 10.0270i 1.23737 0.714393i 0.268811 0.963193i \(-0.413369\pi\)
0.968555 + 0.248800i \(0.0800361\pi\)
\(198\) 0 0
\(199\) 8.68466 15.0423i 0.615639 1.06632i −0.374633 0.927173i \(-0.622231\pi\)
0.990272 0.139145i \(-0.0444354\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 9.36932 + 5.40938i 0.659223 + 0.380602i
\(203\) 6.73863i 0.472959i
\(204\) 0 0
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) 12.7173 7.34233i 0.886055 0.511564i
\(207\) 0 0
\(208\) 2.84233 + 2.21837i 0.197080 + 0.153816i
\(209\) −18.5064 −1.28011
\(210\) 0 0
\(211\) 3.34233 + 5.78908i 0.230095 + 0.398537i 0.957836 0.287316i \(-0.0927628\pi\)
−0.727741 + 0.685853i \(0.759429\pi\)
\(212\) −1.35234 + 2.34233i −0.0928794 + 0.160872i
\(213\) 0 0
\(214\) 4.68466 + 2.70469i 0.320237 + 0.184889i
\(215\) 8.38716 + 4.84233i 0.572000 + 0.330244i
\(216\) 0 0
\(217\) −1.31534 + 2.27824i −0.0892912 + 0.154657i
\(218\) 6.16879 + 10.6847i 0.417803 + 0.723656i
\(219\) 0 0
\(220\) −3.00000 −0.202260
\(221\) 0 0
\(222\) 0 0
\(223\) 6.65767 3.84381i 0.445831 0.257400i −0.260237 0.965545i \(-0.583801\pi\)
0.706068 + 0.708144i \(0.250467\pi\)
\(224\) −1.35234 2.34233i −0.0903573 0.156503i
\(225\) 0 0
\(226\) 2.49146i 0.165730i
\(227\) 2.91791 + 1.68466i 0.193669 + 0.111815i 0.593699 0.804687i \(-0.297667\pi\)
−0.400030 + 0.916502i \(0.631000\pi\)
\(228\) 0 0
\(229\) 26.1940i 1.73095i −0.500954 0.865474i \(-0.667018\pi\)
0.500954 0.865474i \(-0.332982\pi\)
\(230\) −3.95042 + 6.84233i −0.260483 + 0.451170i
\(231\) 0 0
\(232\) 2.15767 1.24573i 0.141658 0.0817863i
\(233\) −12.8838 −0.844044 −0.422022 0.906586i \(-0.638679\pi\)
−0.422022 + 0.906586i \(0.638679\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) −6.65511 + 3.84233i −0.433211 + 0.250114i
\(237\) 0 0
\(238\) 0 0
\(239\) 24.7386i 1.60021i 0.599861 + 0.800105i \(0.295223\pi\)
−0.599861 + 0.800105i \(0.704777\pi\)
\(240\) 0 0
\(241\) −5.81534 3.35749i −0.374599 0.216275i 0.300867 0.953666i \(-0.402724\pi\)
−0.675466 + 0.737391i \(0.736057\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) 6.68466 + 11.5782i 0.427941 + 0.741216i
\(245\) 0.273094 0.157671i 0.0174473 0.0100732i
\(246\) 0 0
\(247\) 22.0270 + 3.08440i 1.40154 + 0.196255i
\(248\) 0.972638 0.0617626
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 2.59808 4.50000i 0.163989 0.284037i −0.772307 0.635250i \(-0.780897\pi\)
0.936296 + 0.351212i \(0.114230\pi\)
\(252\) 0 0
\(253\) 20.5270 + 11.8513i 1.29052 + 0.745082i
\(254\) 2.32498 + 1.34233i 0.145882 + 0.0842252i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 11.6380 + 20.1577i 0.725961 + 1.25740i 0.958577 + 0.284832i \(0.0919380\pi\)
−0.232617 + 0.972569i \(0.574729\pi\)
\(258\) 0 0
\(259\) 4.68466 0.291091
\(260\) 3.57071 + 0.500000i 0.221446 + 0.0310087i
\(261\) 0 0
\(262\) 18.1847 10.4989i 1.12345 0.648625i
\(263\) 15.9083 + 27.5540i 0.980947 + 1.69905i 0.658719 + 0.752389i \(0.271099\pi\)
0.322228 + 0.946662i \(0.395568\pi\)
\(264\) 0 0
\(265\) 2.70469i 0.166148i
\(266\) −14.4493 8.34233i −0.885946 0.511501i
\(267\) 0 0
\(268\) 1.94528i 0.118827i
\(269\) 5.40938 9.36932i 0.329816 0.571257i −0.652659 0.757651i \(-0.726347\pi\)
0.982475 + 0.186394i \(0.0596801\pi\)
\(270\) 0 0
\(271\) 11.5270 6.65511i 0.700215 0.404269i −0.107213 0.994236i \(-0.534193\pi\)
0.807427 + 0.589967i \(0.200859\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 19.6847 1.18919
\(275\) −2.59808 + 1.50000i −0.156670 + 0.0904534i
\(276\) 0 0
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) 9.31534i 0.558697i
\(279\) 0 0
\(280\) −2.34233 1.35234i −0.139981 0.0808180i
\(281\) 24.7386i 1.47578i −0.674919 0.737892i \(-0.735822\pi\)
0.674919 0.737892i \(-0.264178\pi\)
\(282\) 0 0
\(283\) 6.52699 + 11.3051i 0.387989 + 0.672017i 0.992179 0.124824i \(-0.0398365\pi\)
−0.604190 + 0.796840i \(0.706503\pi\)
\(284\) 5.19615 3.00000i 0.308335 0.178017i
\(285\) 0 0
\(286\) 1.50000 10.7121i 0.0886969 0.633422i
\(287\) 16.2281 0.957916
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 1.24573 2.15767i 0.0731519 0.126703i
\(291\) 0 0
\(292\) −6.00000 3.46410i −0.351123 0.202721i
\(293\) 19.6455 + 11.3423i 1.14770 + 0.662626i 0.948326 0.317297i \(-0.102775\pi\)
0.199376 + 0.979923i \(0.436109\pi\)
\(294\) 0 0
\(295\) −3.84233 + 6.65511i −0.223709 + 0.387475i
\(296\) −0.866025 1.50000i −0.0503367 0.0871857i
\(297\) 0 0
\(298\) −10.3153 −0.597552
\(299\) −22.4568 17.5270i −1.29871 1.01361i
\(300\) 0 0
\(301\) 22.6847 13.0970i 1.30752 0.754898i
\(302\) −7.14143 12.3693i −0.410943 0.711774i
\(303\) 0 0
\(304\) 6.16879i 0.353804i
\(305\) 11.5782 + 6.68466i 0.662964 + 0.382762i
\(306\) 0 0
\(307\) 14.2829i 0.815166i −0.913168 0.407583i \(-0.866372\pi\)
0.913168 0.407583i \(-0.133628\pi\)
\(308\) −4.05703 + 7.02699i −0.231171 + 0.400400i
\(309\) 0 0
\(310\) 0.842329 0.486319i 0.0478411 0.0276211i
\(311\) −4.98293 −0.282556 −0.141278 0.989970i \(-0.545121\pi\)
−0.141278 + 0.989970i \(0.545121\pi\)
\(312\) 0 0
\(313\) −5.36932 −0.303492 −0.151746 0.988420i \(-0.548490\pi\)
−0.151746 + 0.988420i \(0.548490\pi\)
\(314\) −7.24804 + 4.18466i −0.409031 + 0.236154i
\(315\) 0 0
\(316\) 2.84233 4.92306i 0.159894 0.276944i
\(317\) 29.4233i 1.65258i −0.563247 0.826288i \(-0.690448\pi\)
0.563247 0.826288i \(-0.309552\pi\)
\(318\) 0 0
\(319\) −6.47301 3.73720i −0.362419 0.209243i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) 10.6847 + 18.5064i 0.595433 + 1.03132i
\(323\) 0 0
\(324\) 0 0
\(325\) 3.34233 1.35234i 0.185399 0.0750146i
\(326\) 18.2931 1.01316
\(327\) 0 0
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) 4.05703 7.02699i 0.223671 0.387410i
\(330\) 0 0
\(331\) 8.05398 + 4.64996i 0.442687 + 0.255585i 0.704737 0.709469i \(-0.251065\pi\)
−0.262050 + 0.965054i \(0.584399\pi\)
\(332\) 13.3102 + 7.68466i 0.730493 + 0.421750i
\(333\) 0 0
\(334\) 3.18466 5.51599i 0.174257 0.301822i
\(335\) 0.972638 + 1.68466i 0.0531409 + 0.0920427i
\(336\) 0 0
\(337\) −29.3693 −1.59985 −0.799924 0.600101i \(-0.795127\pi\)
−0.799924 + 0.600101i \(0.795127\pi\)
\(338\) −3.57071 + 12.5000i −0.194221 + 0.679910i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.45896 2.52699i −0.0790070 0.136844i
\(342\) 0 0
\(343\) 18.0799i 0.976224i
\(344\) −8.38716 4.84233i −0.452205 0.261081i
\(345\) 0 0
\(346\) 8.11407i 0.436215i
\(347\) 2.49146 4.31534i 0.133749 0.231660i −0.791370 0.611337i \(-0.790632\pi\)
0.925119 + 0.379678i \(0.123965\pi\)
\(348\) 0 0
\(349\) −29.0540 + 16.7743i −1.55522 + 0.897909i −0.557521 + 0.830163i \(0.688247\pi\)
−0.997703 + 0.0677460i \(0.978419\pi\)
\(350\) −2.70469 −0.144572
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) −13.3102 + 7.68466i −0.708431 + 0.409013i −0.810480 0.585766i \(-0.800794\pi\)
0.102049 + 0.994779i \(0.467460\pi\)
\(354\) 0 0
\(355\) 3.00000 5.19615i 0.159223 0.275783i
\(356\) 4.68466i 0.248286i
\(357\) 0 0
\(358\) −11.1577 6.44188i −0.589701 0.340464i
\(359\) 2.63068i 0.138842i −0.997587 0.0694211i \(-0.977885\pi\)
0.997587 0.0694211i \(-0.0221152\pi\)
\(360\) 0 0
\(361\) 9.52699 + 16.5012i 0.501420 + 0.868486i
\(362\) −4.64996 + 2.68466i −0.244397 + 0.141103i
\(363\) 0 0
\(364\) 6.00000 7.68762i 0.314485 0.402941i
\(365\) −6.92820 −0.362639
\(366\) 0 0
\(367\) −11.6847 20.2384i −0.609934 1.05644i −0.991251 0.131992i \(-0.957863\pi\)
0.381317 0.924445i \(-0.375471\pi\)
\(368\) 3.95042 6.84233i 0.205930 0.356681i
\(369\) 0 0
\(370\) −1.50000 0.866025i −0.0779813 0.0450225i
\(371\) 6.33527 + 3.65767i 0.328911 + 0.189897i
\(372\) 0 0
\(373\) 0.526988 0.912769i 0.0272864 0.0472614i −0.852060 0.523445i \(-0.824647\pi\)
0.879346 + 0.476183i \(0.157980\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) 7.08156 + 5.52699i 0.364719 + 0.284654i
\(378\) 0 0
\(379\) −0.288354 + 0.166481i −0.0148117 + 0.00855157i −0.507388 0.861718i \(-0.669389\pi\)
0.492576 + 0.870270i \(0.336055\pi\)
\(380\) 3.08440 + 5.34233i 0.158226 + 0.274056i
\(381\) 0 0
\(382\) 21.2111i 1.08525i
\(383\) 6.65511 + 3.84233i 0.340060 + 0.196334i 0.660299 0.751003i \(-0.270430\pi\)
−0.320238 + 0.947337i \(0.603763\pi\)
\(384\) 0 0
\(385\) 8.11407i 0.413531i
\(386\) −7.90084 + 13.6847i −0.402142 + 0.696531i
\(387\) 0 0
\(388\) −7.68466 + 4.43674i −0.390129 + 0.225241i
\(389\) 24.1290 1.22339 0.611694 0.791095i \(-0.290488\pi\)
0.611694 + 0.791095i \(0.290488\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.273094 + 0.157671i −0.0137933 + 0.00796358i
\(393\) 0 0
\(394\) −10.0270 + 17.3673i −0.505152 + 0.874950i
\(395\) 5.68466i 0.286026i
\(396\) 0 0
\(397\) −30.1847 17.4271i −1.51492 0.874642i −0.999847 0.0174986i \(-0.994430\pi\)
−0.515078 0.857143i \(-0.672237\pi\)
\(398\) 17.3693i 0.870645i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 1.77879 1.02699i 0.0888288 0.0512853i −0.454928 0.890528i \(-0.650335\pi\)
0.543756 + 0.839243i \(0.317002\pi\)
\(402\) 0 0
\(403\) 1.31534 + 3.25088i 0.0655218 + 0.161938i
\(404\) −10.8188 −0.538253
\(405\) 0 0
\(406\) −3.36932 5.83583i −0.167216 0.289627i
\(407\) −2.59808 + 4.50000i −0.128782 + 0.223057i
\(408\) 0 0
\(409\) −11.7116 6.76172i −0.579104 0.334346i 0.181673 0.983359i \(-0.441849\pi\)
−0.760777 + 0.649013i \(0.775182\pi\)
\(410\) −5.19615 3.00000i −0.256620 0.148159i
\(411\) 0 0
\(412\) −7.34233 + 12.7173i −0.361731 + 0.626536i
\(413\) 10.3923 + 18.0000i 0.511372 + 0.885722i
\(414\) 0 0
\(415\) 15.3693 0.754450
\(416\) −3.57071 0.500000i −0.175069 0.0245145i
\(417\) 0 0
\(418\) 16.0270 9.25319i 0.783906 0.452588i
\(419\) 0.213225 + 0.369317i 0.0104167 + 0.0180423i 0.871187 0.490952i \(-0.163351\pi\)
−0.860770 + 0.508994i \(0.830018\pi\)
\(420\) 0 0
\(421\) 26.6204i 1.29740i 0.761044 + 0.648700i \(0.224687\pi\)
−0.761044 + 0.648700i \(0.775313\pi\)
\(422\) −5.78908 3.34233i −0.281808 0.162702i
\(423\) 0 0
\(424\) 2.70469i 0.131351i
\(425\) 0 0
\(426\) 0 0
\(427\) 31.3153 18.0799i 1.51546 0.874949i
\(428\) −5.40938 −0.261472
\(429\) 0 0
\(430\) −9.68466 −0.467036
\(431\) 2.91791 1.68466i 0.140551 0.0811471i −0.428076 0.903743i \(-0.640808\pi\)
0.568627 + 0.822596i \(0.307475\pi\)
\(432\) 0 0
\(433\) 17.6847 30.6307i 0.849870 1.47202i −0.0314530 0.999505i \(-0.510013\pi\)
0.881323 0.472514i \(-0.156653\pi\)
\(434\) 2.63068i 0.126277i
\(435\) 0 0
\(436\) −10.6847 6.16879i −0.511702 0.295431i
\(437\) 48.7386i 2.33149i
\(438\) 0 0
\(439\) 3.31534 + 5.74234i 0.158233 + 0.274067i 0.934231 0.356667i \(-0.116087\pi\)
−0.775999 + 0.630734i \(0.782754\pi\)
\(440\) 2.59808 1.50000i 0.123858 0.0715097i
\(441\) 0 0
\(442\) 0 0
\(443\) 10.3923 0.493753 0.246877 0.969047i \(-0.420596\pi\)
0.246877 + 0.969047i \(0.420596\pi\)
\(444\) 0 0
\(445\) −2.34233 4.05703i −0.111037 0.192322i
\(446\) −3.84381 + 6.65767i −0.182010 + 0.315250i
\(447\) 0 0
\(448\) 2.34233 + 1.35234i 0.110665 + 0.0638923i
\(449\) −24.8416 14.3423i −1.17235 0.676856i −0.218117 0.975923i \(-0.569992\pi\)
−0.954232 + 0.299066i \(0.903325\pi\)
\(450\) 0 0
\(451\) −9.00000 + 15.5885i −0.423793 + 0.734032i
\(452\) −1.24573 2.15767i −0.0585943 0.101488i
\(453\) 0 0
\(454\) −3.36932 −0.158130
\(455\) 1.35234 9.65767i 0.0633989 0.452759i
\(456\) 0 0
\(457\) −3.00000 + 1.73205i −0.140334 + 0.0810219i −0.568523 0.822667i \(-0.692485\pi\)
0.428189 + 0.903689i \(0.359152\pi\)
\(458\) 13.0970 + 22.6847i 0.611982 + 1.05998i
\(459\) 0 0
\(460\) 7.90084i 0.368379i
\(461\) 3.73720 + 2.15767i 0.174059 + 0.100493i 0.584498 0.811395i \(-0.301291\pi\)
−0.410440 + 0.911888i \(0.634625\pi\)
\(462\) 0 0
\(463\) 30.0845i 1.39815i −0.715050 0.699074i \(-0.753596\pi\)
0.715050 0.699074i \(-0.246404\pi\)
\(464\) −1.24573 + 2.15767i −0.0578316 + 0.100167i
\(465\) 0 0
\(466\) 11.1577 6.44188i 0.516869 0.298415i
\(467\) −21.6375 −1.00126 −0.500632 0.865660i \(-0.666899\pi\)
−0.500632 + 0.865660i \(0.666899\pi\)
\(468\) 0 0
\(469\) 5.26137 0.242947
\(470\) −2.59808 + 1.50000i −0.119840 + 0.0691898i
\(471\) 0 0
\(472\) 3.84233 6.65511i 0.176858 0.306326i
\(473\) 29.0540i 1.33590i
\(474\) 0 0
\(475\) 5.34233 + 3.08440i 0.245123 + 0.141522i
\(476\) 0 0
\(477\) 0 0
\(478\) −12.3693 21.4243i −0.565759 0.979924i
\(479\) 23.7025 13.6847i 1.08300 0.625268i 0.151293 0.988489i \(-0.451656\pi\)
0.931703 + 0.363221i \(0.118323\pi\)
\(480\) 0 0
\(481\) 3.84233 4.92306i 0.175195 0.224472i
\(482\) 6.71498 0.305859
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) −4.43674 + 7.68466i −0.201462 + 0.348942i
\(486\) 0 0
\(487\) −17.3423 10.0126i −0.785856 0.453714i 0.0526457 0.998613i \(-0.483235\pi\)
−0.838502 + 0.544899i \(0.816568\pi\)
\(488\) −11.5782 6.68466i −0.524119 0.302600i
\(489\) 0 0
\(490\) −0.157671 + 0.273094i −0.00712284 + 0.0123371i
\(491\) 6.54850 + 11.3423i 0.295530 + 0.511872i 0.975108 0.221731i \(-0.0711706\pi\)
−0.679578 + 0.733603i \(0.737837\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −20.6181 + 8.34233i −0.927653 + 0.375339i
\(495\) 0 0
\(496\) −0.842329 + 0.486319i −0.0378217 + 0.0218364i
\(497\) −8.11407 14.0540i −0.363966 0.630407i
\(498\) 0 0
\(499\) 32.0298i 1.43385i 0.697150 + 0.716926i \(0.254451\pi\)
−0.697150 + 0.716926i \(0.745549\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 0 0
\(502\) 5.19615i 0.231916i
\(503\) 14.2361 24.6577i 0.634757 1.09943i −0.351810 0.936072i \(-0.614434\pi\)
0.986567 0.163360i \(-0.0522331\pi\)
\(504\) 0 0
\(505\) −9.36932 + 5.40938i −0.416929 + 0.240714i
\(506\) −23.7025 −1.05371
\(507\) 0 0
\(508\) −2.68466 −0.119112
\(509\) 8.93335 5.15767i 0.395964 0.228610i −0.288777 0.957396i \(-0.593249\pi\)
0.684741 + 0.728787i \(0.259915\pi\)
\(510\) 0 0
\(511\) −9.36932 + 16.2281i −0.414474 + 0.717890i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −20.1577 11.6380i −0.889117 0.513332i
\(515\) 14.6847i 0.647083i
\(516\) 0 0
\(517\) 4.50000 + 7.79423i 0.197910 + 0.342790i
\(518\) −4.05703 + 2.34233i −0.178256 + 0.102916i
\(519\) 0 0
\(520\) −3.34233 + 1.35234i −0.146571 + 0.0593042i
\(521\) −13.0970 −0.573790 −0.286895 0.957962i \(-0.592623\pi\)
−0.286895 + 0.957962i \(0.592623\pi\)
\(522\) 0 0
\(523\) −0.526988 0.912769i −0.0230436 0.0399126i 0.854274 0.519824i \(-0.174002\pi\)
−0.877317 + 0.479911i \(0.840669\pi\)
\(524\) −10.4989 + 18.1847i −0.458647 + 0.794400i
\(525\) 0 0
\(526\) −27.5540 15.9083i −1.20141 0.693635i
\(527\) 0 0
\(528\) 0 0
\(529\) −19.7116 + 34.1416i −0.857028 + 1.48442i
\(530\) −1.35234 2.34233i −0.0587421 0.101744i
\(531\) 0 0
\(532\) 16.6847 0.723372
\(533\) 13.3102 17.0540i 0.576530 0.738690i
\(534\) 0 0
\(535\) −4.68466 + 2.70469i −0.202535 + 0.116934i
\(536\) −0.972638 1.68466i −0.0420116 0.0727662i
\(537\) 0 0
\(538\) 10.8188i 0.466430i
\(539\) 0.819281 + 0.473012i 0.0352889 + 0.0203741i
\(540\) 0 0
\(541\) 40.0504i 1.72190i −0.508689 0.860950i \(-0.669870\pi\)
0.508689 0.860950i \(-0.330130\pi\)
\(542\) −6.65511 + 11.5270i −0.285861 + 0.495127i
\(543\) 0 0
\(544\) 0 0
\(545\) −12.3376 −0.528484
\(546\) 0 0
\(547\) −32.1080 −1.37284 −0.686418 0.727207i \(-0.740818\pi\)
−0.686418 + 0.727207i \(0.740818\pi\)
\(548\) −17.0474 + 9.84233i −0.728229 + 0.420443i
\(549\) 0 0
\(550\) 1.50000 2.59808i 0.0639602 0.110782i
\(551\) 15.3693i 0.654755i
\(552\) 0 0
\(553\) −13.3153 7.68762i −0.566226 0.326911i
\(554\) 1.00000i 0.0424859i
\(555\) 0 0
\(556\) 4.65767 + 8.06732i 0.197529 + 0.342131i
\(557\) −1.13912 + 0.657671i −0.0482660 + 0.0278664i −0.523939 0.851756i \(-0.675538\pi\)
0.475673 + 0.879622i \(0.342205\pi\)
\(558\) 0 0
\(559\) 4.84233 34.5811i 0.204809 1.46263i
\(560\) 2.70469 0.114294
\(561\) 0 0
\(562\) 12.3693 + 21.4243i 0.521768 + 0.903729i
\(563\) −12.8838 + 22.3153i −0.542986 + 0.940480i 0.455745 + 0.890111i \(0.349373\pi\)
−0.998731 + 0.0503689i \(0.983960\pi\)
\(564\) 0 0
\(565\) −2.15767 1.24573i −0.0907739 0.0524083i
\(566\) −11.3051 6.52699i −0.475188 0.274350i
\(567\) 0 0
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) −14.6626 25.3963i −0.614687 1.06467i −0.990439 0.137949i \(-0.955949\pi\)
0.375753 0.926720i \(-0.377384\pi\)
\(570\) 0 0
\(571\) −40.0540 −1.67621 −0.838103 0.545511i \(-0.816335\pi\)
−0.838103 + 0.545511i \(0.816335\pi\)
\(572\) 4.05703 + 10.0270i 0.169633 + 0.419249i
\(573\) 0 0
\(574\) −14.0540 + 8.11407i −0.586602 + 0.338675i
\(575\) −3.95042 6.84233i −0.164744 0.285345i
\(576\) 0 0
\(577\) 29.2316i 1.21693i 0.793581 + 0.608465i \(0.208214\pi\)
−0.793581 + 0.608465i \(0.791786\pi\)
\(578\) −14.7224 8.50000i −0.612372 0.353553i
\(579\) 0 0
\(580\) 2.49146i 0.103452i
\(581\) 20.7846 36.0000i 0.862291 1.49353i
\(582\) 0 0
\(583\) −7.02699 + 4.05703i −0.291028 + 0.168025i
\(584\) 6.92820 0.286691
\(585\) 0 0
\(586\) −22.6847 −0.937095
\(587\) 8.11407 4.68466i 0.334903 0.193357i −0.323113 0.946361i \(-0.604729\pi\)
0.658016 + 0.753004i \(0.271396\pi\)
\(588\) 0 0
\(589\) −3.00000 + 5.19615i −0.123613 + 0.214104i
\(590\) 7.68466i 0.316372i
\(591\) 0 0
\(592\) 1.50000 + 0.866025i 0.0616496 + 0.0355934i
\(593\) 38.4233i 1.57786i −0.614486 0.788928i \(-0.710637\pi\)
0.614486 0.788928i \(-0.289363\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.93335 5.15767i 0.365924 0.211266i
\(597\) 0 0
\(598\) 28.2116 + 3.95042i 1.15366 + 0.161545i
\(599\) 0.426450 0.0174243 0.00871215 0.999962i \(-0.497227\pi\)
0.00871215 + 0.999962i \(0.497227\pi\)
\(600\) 0 0
\(601\) 17.5000 + 30.3109i 0.713840 + 1.23641i 0.963405 + 0.268049i \(0.0863789\pi\)
−0.249565 + 0.968358i \(0.580288\pi\)
\(602\) −13.0970 + 22.6847i −0.533794 + 0.924558i
\(603\) 0 0
\(604\) 12.3693 + 7.14143i 0.503300 + 0.290581i
\(605\) 1.73205 + 1.00000i 0.0704179 + 0.0406558i
\(606\) 0 0
\(607\) −2.97301 + 5.14941i −0.120671 + 0.209008i −0.920032 0.391842i \(-0.871838\pi\)
0.799362 + 0.600850i \(0.205171\pi\)
\(608\) −3.08440 5.34233i −0.125089 0.216660i
\(609\) 0 0
\(610\) −13.3693 −0.541308
\(611\) −4.05703 10.0270i −0.164130 0.405649i
\(612\) 0 0
\(613\) −10.5000 + 6.06218i −0.424091 + 0.244849i −0.696826 0.717240i \(-0.745405\pi\)
0.272735 + 0.962089i \(0.412072\pi\)
\(614\) 7.14143 + 12.3693i 0.288205 + 0.499185i
\(615\) 0 0
\(616\) 8.11407i 0.326925i
\(617\) 11.8513 + 6.84233i 0.477114 + 0.275462i 0.719213 0.694790i \(-0.244503\pi\)
−0.242099 + 0.970252i \(0.577836\pi\)
\(618\) 0 0
\(619\) 3.13114i 0.125851i 0.998018 + 0.0629256i \(0.0200431\pi\)
−0.998018 + 0.0629256i \(0.979957\pi\)
\(620\) −0.486319 + 0.842329i −0.0195310 + 0.0338288i
\(621\) 0 0
\(622\) 4.31534 2.49146i 0.173029 0.0998986i
\(623\) −12.6705 −0.507635
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 4.64996 2.68466i 0.185850 0.107301i
\(627\) 0 0
\(628\) 4.18466 7.24804i 0.166986 0.289228i
\(629\) 0 0
\(630\) 0 0
\(631\) −19.6847 11.3649i −0.783634 0.452431i 0.0540827 0.998536i \(-0.482777\pi\)
−0.837717 + 0.546105i \(0.816110\pi\)
\(632\) 5.68466i 0.226124i
\(633\) 0 0
\(634\) 14.7116 + 25.4813i 0.584274 + 1.01199i
\(635\) −2.32498 + 1.34233i −0.0922641 + 0.0532687i
\(636\) 0 0
\(637\) −0.896305 0.699544i −0.0355129 0.0277170i
\(638\) 7.47439 0.295914
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 19.8587 34.3963i 0.784372 1.35857i −0.145001 0.989431i \(-0.546319\pi\)
0.929373 0.369141i \(-0.120348\pi\)
\(642\) 0 0
\(643\) −29.0540 16.7743i −1.14578 0.661515i −0.197922 0.980218i \(-0.563419\pi\)
−0.947855 + 0.318703i \(0.896753\pi\)
\(644\) −18.5064 10.6847i −0.729253 0.421035i
\(645\) 0 0
\(646\) 0 0
\(647\) 17.3673 + 30.0810i 0.682777 + 1.18260i 0.974130 + 0.225989i \(0.0725613\pi\)
−0.291353 + 0.956616i \(0.594105\pi\)
\(648\) 0 0
\(649\) −23.0540 −0.904948
\(650\) −2.21837 + 2.84233i −0.0870116 + 0.111485i
\(651\) 0 0
\(652\) −15.8423 + 9.14657i −0.620433 + 0.358207i
\(653\) −11.5314 19.9730i −0.451259 0.781604i 0.547205 0.836999i \(-0.315692\pi\)
−0.998465 + 0.0553942i \(0.982358\pi\)
\(654\) 0 0
\(655\) 20.9978i 0.820453i
\(656\) 5.19615 + 3.00000i 0.202876 + 0.117130i
\(657\) 0 0
\(658\) 8.11407i 0.316319i
\(659\) −16.8342 + 29.1577i −0.655767 + 1.13582i 0.325934 + 0.945393i \(0.394321\pi\)
−0.981701 + 0.190429i \(0.939012\pi\)
\(660\) 0 0
\(661\) 9.00000 5.19615i 0.350059 0.202107i −0.314652 0.949207i \(-0.601888\pi\)
0.664711 + 0.747100i \(0.268554\pi\)
\(662\) −9.29993 −0.361452
\(663\) 0 0
\(664\) −15.3693 −0.596445
\(665\) 14.4493 8.34233i 0.560321 0.323502i
\(666\) 0 0
\(667\) 9.84233 17.0474i 0.381097 0.660079i
\(668\) 6.36932i 0.246436i
\(669\) 0 0
\(670\) −1.68466 0.972638i −0.0650840 0.0375763i
\(671\) 40.1080i 1.54835i
\(672\) 0 0
\(673\) −16.0000 27.7128i −0.616755 1.06825i −0.990074 0.140548i \(-0.955114\pi\)
0.373319 0.927703i \(-0.378220\pi\)
\(674\) 25.4346 14.6847i 0.979703 0.565632i
\(675\) 0 0
\(676\) −3.15767 12.6107i −0.121449 0.485026i
\(677\) −36.5863 −1.40613 −0.703063 0.711128i \(-0.748185\pi\)
−0.703063 + 0.711128i \(0.748185\pi\)
\(678\) 0 0
\(679\) 12.0000 + 20.7846i 0.460518 + 0.797640i
\(680\) 0 0
\(681\) 0 0
\(682\) 2.52699 + 1.45896i 0.0967634 + 0.0558664i
\(683\) 2.27824 + 1.31534i 0.0871744 + 0.0503301i 0.542954 0.839763i \(-0.317306\pi\)
−0.455779 + 0.890093i \(0.650639\pi\)
\(684\) 0 0
\(685\) −9.84233 + 17.0474i −0.376056 + 0.651348i
\(686\) −9.03996 15.6577i −0.345147 0.597813i
\(687\) 0 0
\(688\) 9.68466 0.369224
\(689\) 9.03996 3.65767i 0.344395 0.139346i
\(690\) 0 0
\(691\) −4.02699 + 2.32498i −0.153194 + 0.0884465i −0.574637 0.818408i \(-0.694857\pi\)
0.421444 + 0.906855i \(0.361524\pi\)
\(692\) 4.05703 + 7.02699i 0.154225 + 0.267126i
\(693\) 0 0
\(694\) 4.98293i 0.189149i
\(695\) 8.06732 + 4.65767i 0.306011 + 0.176676i
\(696\) 0 0
\(697\) 0 0
\(698\) 16.7743 29.0540i 0.634917 1.09971i
\(699\) 0 0
\(700\) 2.34233 1.35234i 0.0885317 0.0511138i
\(701\) −23.2761 −0.879125 −0.439563 0.898212i \(-0.644867\pi\)
−0.439563 + 0.898212i \(0.644867\pi\)
\(702\) 0 0
\(703\) 10.6847 0.402980
\(704\) −2.59808 + 1.50000i −0.0979187 + 0.0565334i
\(705\) 0 0
\(706\) 7.68466 13.3102i 0.289216 0.500937i
\(707\) 29.2614i 1.10049i
\(708\) 0 0
\(709\) −27.3693 15.8017i −1.02788 0.593445i −0.111501 0.993764i \(-0.535566\pi\)
−0.916376 + 0.400320i \(0.868899\pi\)
\(710\) 6.00000i 0.225176i
\(711\) 0 0
\(712\) 2.34233 + 4.05703i 0.0877825 + 0.152044i
\(713\) 6.65511 3.84233i 0.249236 0.143896i
\(714\) 0 0
\(715\) 8.52699 + 6.65511i 0.318891 + 0.248887i
\(716\) 12.8838 0.481489
\(717\) 0 0
\(718\) 1.31534 + 2.27824i 0.0490881 + 0.0850231i
\(719\) −4.98293 + 8.63068i −0.185832 + 0.321870i −0.943857 0.330356i \(-0.892831\pi\)
0.758025 + 0.652226i \(0.226165\pi\)
\(720\) 0 0
\(721\) 34.3963 + 19.8587i 1.28099 + 0.739577i
\(722\) −16.5012 9.52699i −0.614112 0.354558i
\(723\) 0 0
\(724\) 2.68466 4.64996i 0.0997745 0.172815i
\(725\) 1.24573 + 2.15767i 0.0462653 + 0.0801339i
\(726\) 0 0
\(727\) −36.6847 −1.36056 −0.680279 0.732953i \(-0.738142\pi\)
−0.680279 + 0.732953i \(0.738142\pi\)
\(728\) −1.35234 + 9.65767i −0.0501212 + 0.357937i
\(729\) 0 0
\(730\) 6.00000 3.46410i 0.222070 0.128212i
\(731\) 0 0
\(732\) 0 0
\(733\) 26.5269i 0.979795i 0.871780 + 0.489898i \(0.162966\pi\)
−0.871780 + 0.489898i \(0.837034\pi\)
\(734\) 20.2384 + 11.6847i 0.747014 + 0.431289i
\(735\) 0 0
\(736\) 7.90084i 0.291229i
\(737\) −2.91791 + 5.05398i −0.107483 + 0.186166i
\(738\) 0 0
\(739\) 1.97301 1.13912i 0.0725784 0.0419032i −0.463272 0.886216i \(-0.653325\pi\)
0.535850 + 0.844313i \(0.319991\pi\)
\(740\) 1.73205 0.0636715
\(741\) 0 0
\(742\) −7.31534 −0.268555
\(743\) 17.0474 9.84233i 0.625409 0.361080i −0.153563 0.988139i \(-0.549075\pi\)
0.778972 + 0.627059i \(0.215741\pi\)
\(744\) 0 0
\(745\) 5.15767 8.93335i 0.188962 0.327293i
\(746\) 1.05398i 0.0385888i
\(747\) 0 0
\(748\) 0 0
\(749\) 14.6307i 0.534594i
\(750\) 0 0
\(751\) 17.8423 + 30.9038i 0.651076 + 1.12770i 0.982862 + 0.184342i \(0.0590154\pi\)
−0.331786 + 0.943355i \(0.607651\pi\)
\(752\) 2.59808 1.50000i 0.0947421 0.0546994i
\(753\) 0 0
\(754\) −8.89630 1.24573i −0.323984 0.0453669i
\(755\) 14.2829 0.519806
\(756\) 0 0
\(757\) −18.0270 31.2237i −0.655202 1.13484i −0.981843 0.189695i \(-0.939250\pi\)
0.326641 0.945148i \(-0.394083\pi\)
\(758\) 0.166481 0.288354i 0.00604687 0.0104735i
\(759\) 0 0
\(760\) −5.34233 3.08440i −0.193787 0.111883i
\(761\) 12.1711 + 7.02699i 0.441202 + 0.254728i 0.704107 0.710094i \(-0.251347\pi\)
−0.262905 + 0.964822i \(0.584681\pi\)
\(762\) 0 0
\(763\) −16.6847 + 28.8987i −0.604025 + 1.04620i
\(764\) −10.6055 18.3693i −0.383695 0.664579i
\(765\) 0 0
\(766\) −7.68466 −0.277658
\(767\) 27.4397 + 3.84233i 0.990791 + 0.138738i
\(768\) 0 0
\(769\) −19.2116 + 11.0918i −0.692790 + 0.399982i −0.804656 0.593741i \(-0.797650\pi\)
0.111867 + 0.993723i \(0.464317\pi\)
\(770\) −4.05703 7.02699i −0.146205 0.253235i
\(771\) 0 0
\(772\) 15.8017i 0.568715i
\(773\) −35.2339 20.3423i −1.26728 0.731663i −0.292805 0.956172i \(-0.594589\pi\)
−0.974472 + 0.224509i \(0.927922\pi\)
\(774\) 0 0
\(775\) 0.972638i 0.0349382i
\(776\) 4.43674 7.68466i 0.159270 0.275863i
\(777\) 0 0
\(778\) −20.8963 + 12.0645i −0.749169 + 0.432533i
\(779\) 37.0127 1.32612
\(780\) 0 0
\(781\) 18.0000 0.644091
\(782\) 0 0
\(783\) 0 0
\(784\) 0.157671 0.273094i 0.00563110 0.00975335i
\(785\) 8.36932i 0.298714i
\(786\) 0 0
\(787\) 3.84233 + 2.21837i 0.136964 + 0.0790763i 0.566916 0.823775i \(-0.308136\pi\)
−0.429952 + 0.902852i \(0.641470\pi\)
\(788\) 20.0540i 0.714393i
\(789\) 0 0
\(790\) 2.84233 + 4.92306i 0.101126 + 0.175155i
\(791\) −5.83583 + 3.36932i −0.207498 + 0.119799i