Properties

Label 76.2.i.a.73.1
Level $76$
Weight $2$
Character 76.73
Analytic conductor $0.607$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} - 3969 x^{3} - 2088 x^{2} + 4446 x + 4161\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 73.1
Root \(-1.25236 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 76.73
Dual form 76.2.i.a.25.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.83638 + 1.03236i) q^{3} +(-0.658711 + 3.73574i) q^{5} +(-0.0695116 - 0.120398i) q^{7} +(4.68114 - 3.92794i) q^{9} +O(q^{10})\) \(q+(-2.83638 + 1.03236i) q^{3} +(-0.658711 + 3.73574i) q^{5} +(-0.0695116 - 0.120398i) q^{7} +(4.68114 - 3.92794i) q^{9} +(-0.350493 + 0.607072i) q^{11} +(-1.47751 - 0.537771i) q^{13} +(-1.98826 - 11.2760i) q^{15} +(2.88131 + 2.41771i) q^{17} +(4.28653 + 0.790990i) q^{19} +(0.321454 + 0.269732i) q^{21} +(1.02690 + 5.82385i) q^{23} +(-8.82337 - 3.21144i) q^{25} +(-4.69482 + 8.13166i) q^{27} +(5.28209 - 4.43220i) q^{29} +(1.43886 + 2.49217i) q^{31} +(0.367416 - 2.08372i) q^{33} +(0.495562 - 0.180370i) q^{35} -6.33018 q^{37} +4.74596 q^{39} +(-4.40018 + 1.60154i) q^{41} +(0.935226 - 5.30393i) q^{43} +(11.5902 + 20.0749i) q^{45} +(-1.42658 + 1.19704i) q^{47} +(3.49034 - 6.04544i) q^{49} +(-10.6684 - 3.88299i) q^{51} +(0.551093 + 3.12541i) q^{53} +(-2.03699 - 1.70923i) q^{55} +(-12.9748 + 2.18168i) q^{57} +(1.81608 + 1.52387i) q^{59} +(0.587398 + 3.33130i) q^{61} +(-0.798308 - 0.290560i) q^{63} +(2.98223 - 5.16537i) q^{65} +(7.61119 - 6.38655i) q^{67} +(-8.92496 - 15.4585i) q^{69} +(0.375070 - 2.12713i) q^{71} +(10.6967 - 3.89330i) q^{73} +28.3417 q^{75} +0.0974533 q^{77} +(7.36033 - 2.67894i) q^{79} +(1.73811 - 9.85732i) q^{81} +(-5.12849 - 8.88280i) q^{83} +(-10.9299 + 9.17125i) q^{85} +(-10.4064 + 18.0244i) q^{87} +(-12.2044 - 4.44204i) q^{89} +(0.0379580 + 0.215271i) q^{91} +(-6.65395 - 5.58333i) q^{93} +(-5.77852 + 15.4923i) q^{95} +(-0.581665 - 0.488075i) q^{97} +(0.743835 + 4.21850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + 3q^{11} - 9q^{13} - 15q^{15} - 3q^{17} - 12q^{19} - 15q^{21} - 12q^{23} - 18q^{25} - 9q^{27} + 27q^{29} + 6q^{31} + 48q^{33} + 33q^{35} - 12q^{37} + 60q^{39} + 3q^{41} + 27q^{43} + 24q^{45} - 15q^{47} + 9q^{49} - 33q^{51} - 21q^{53} - 27q^{55} - 42q^{57} - 48q^{59} - 6q^{61} - 9q^{63} - 33q^{65} + 24q^{67} - 33q^{69} + 30q^{73} + 42q^{75} + 24q^{77} + 3q^{79} + 3q^{81} + 3q^{83} - 42q^{85} - 18q^{87} - 18q^{89} - 24q^{91} - 78q^{93} + 9q^{95} + 12q^{97} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\)

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
\(3\) −2.83638 + 1.03236i −1.63758 + 0.596031i −0.986614 0.163073i \(-0.947859\pi\)
−0.650969 + 0.759105i \(0.725637\pi\)
\(4\) 0 0
\(5\) −0.658711 + 3.73574i −0.294585 + 1.67067i 0.374301 + 0.927307i \(0.377883\pi\)
−0.668886 + 0.743365i \(0.733228\pi\)
\(6\) 0 0
\(7\) −0.0695116 0.120398i −0.0262729 0.0455060i 0.852590 0.522580i \(-0.175031\pi\)
−0.878863 + 0.477074i \(0.841697\pi\)
\(8\) 0 0
\(9\) 4.68114 3.92794i 1.56038 1.30931i
\(10\) 0 0
\(11\) −0.350493 + 0.607072i −0.105678 + 0.183039i −0.914015 0.405681i \(-0.867034\pi\)
0.808337 + 0.588720i \(0.200368\pi\)
\(12\) 0 0
\(13\) −1.47751 0.537771i −0.409789 0.149151i 0.128896 0.991658i \(-0.458857\pi\)
−0.538685 + 0.842507i \(0.681079\pi\)
\(14\) 0 0
\(15\) −1.98826 11.2760i −0.513366 2.91145i
\(16\) 0 0
\(17\) 2.88131 + 2.41771i 0.698820 + 0.586380i 0.921438 0.388526i \(-0.127016\pi\)
−0.222617 + 0.974906i \(0.571460\pi\)
\(18\) 0 0
\(19\) 4.28653 + 0.790990i 0.983397 + 0.181466i
\(20\) 0 0
\(21\) 0.321454 + 0.269732i 0.0701471 + 0.0588604i
\(22\) 0 0
\(23\) 1.02690 + 5.82385i 0.214124 + 1.21436i 0.882421 + 0.470461i \(0.155912\pi\)
−0.668297 + 0.743895i \(0.732976\pi\)
\(24\) 0 0
\(25\) −8.82337 3.21144i −1.76467 0.642289i
\(26\) 0 0
\(27\) −4.69482 + 8.13166i −0.903518 + 1.56494i
\(28\) 0 0
\(29\) 5.28209 4.43220i 0.980860 0.823039i −0.00335912 0.999994i \(-0.501069\pi\)
0.984219 + 0.176955i \(0.0566248\pi\)
\(30\) 0 0
\(31\) 1.43886 + 2.49217i 0.258426 + 0.447608i 0.965821 0.259212i \(-0.0834627\pi\)
−0.707394 + 0.706819i \(0.750129\pi\)
\(32\) 0 0
\(33\) 0.367416 2.08372i 0.0639588 0.362729i
\(34\) 0 0
\(35\) 0.495562 0.180370i 0.0837653 0.0304881i
\(36\) 0 0
\(37\) −6.33018 −1.04067 −0.520337 0.853961i \(-0.674194\pi\)
−0.520337 + 0.853961i \(0.674194\pi\)
\(38\) 0 0
\(39\) 4.74596 0.759961
\(40\) 0 0
\(41\) −4.40018 + 1.60154i −0.687193 + 0.250118i −0.661933 0.749563i \(-0.730264\pi\)
−0.0252602 + 0.999681i \(0.508041\pi\)
\(42\) 0 0
\(43\) 0.935226 5.30393i 0.142621 0.808842i −0.826626 0.562751i \(-0.809743\pi\)
0.969247 0.246091i \(-0.0791461\pi\)
\(44\) 0 0
\(45\) 11.5902 + 20.0749i 1.72777 + 2.99259i
\(46\) 0 0
\(47\) −1.42658 + 1.19704i −0.208088 + 0.174607i −0.740875 0.671643i \(-0.765589\pi\)
0.532787 + 0.846249i \(0.321145\pi\)
\(48\) 0 0
\(49\) 3.49034 6.04544i 0.498619 0.863634i
\(50\) 0 0
\(51\) −10.6684 3.88299i −1.49388 0.543727i
\(52\) 0 0
\(53\) 0.551093 + 3.12541i 0.0756985 + 0.429307i 0.998979 + 0.0451806i \(0.0143863\pi\)
−0.923280 + 0.384127i \(0.874503\pi\)
\(54\) 0 0
\(55\) −2.03699 1.70923i −0.274667 0.230473i
\(56\) 0 0
\(57\) −12.9748 + 2.18168i −1.71855 + 0.288971i
\(58\) 0 0
\(59\) 1.81608 + 1.52387i 0.236433 + 0.198391i 0.753304 0.657672i \(-0.228459\pi\)
−0.516871 + 0.856063i \(0.672903\pi\)
\(60\) 0 0
\(61\) 0.587398 + 3.33130i 0.0752086 + 0.426529i 0.999043 + 0.0437370i \(0.0139264\pi\)
−0.923834 + 0.382792i \(0.874963\pi\)
\(62\) 0 0
\(63\) −0.798308 0.290560i −0.100577 0.0366072i
\(64\) 0 0
\(65\) 2.98223 5.16537i 0.369900 0.640685i
\(66\) 0 0
\(67\) 7.61119 6.38655i 0.929855 0.780241i −0.0459367 0.998944i \(-0.514627\pi\)
0.975791 + 0.218704i \(0.0701828\pi\)
\(68\) 0 0
\(69\) −8.92496 15.4585i −1.07444 1.86098i
\(70\) 0 0
\(71\) 0.375070 2.12713i 0.0445127 0.252444i −0.954429 0.298438i \(-0.903534\pi\)
0.998942 + 0.0459940i \(0.0146455\pi\)
\(72\) 0 0
\(73\) 10.6967 3.89330i 1.25196 0.455676i 0.370896 0.928674i \(-0.379051\pi\)
0.881063 + 0.472998i \(0.156828\pi\)
\(74\) 0 0
\(75\) 28.3417 3.27262
\(76\) 0 0
\(77\) 0.0974533 0.0111058
\(78\) 0 0
\(79\) 7.36033 2.67894i 0.828102 0.301404i 0.107022 0.994257i \(-0.465868\pi\)
0.721079 + 0.692852i \(0.243646\pi\)
\(80\) 0 0
\(81\) 1.73811 9.85732i 0.193123 1.09526i
\(82\) 0 0
\(83\) −5.12849 8.88280i −0.562925 0.975014i −0.997239 0.0742528i \(-0.976343\pi\)
0.434315 0.900761i \(-0.356991\pi\)
\(84\) 0 0
\(85\) −10.9299 + 9.17125i −1.18551 + 0.994761i
\(86\) 0 0
\(87\) −10.4064 + 18.0244i −1.11568 + 1.93242i
\(88\) 0 0
\(89\) −12.2044 4.44204i −1.29366 0.470856i −0.398737 0.917066i \(-0.630551\pi\)
−0.894928 + 0.446210i \(0.852773\pi\)
\(90\) 0 0
\(91\) 0.0379580 + 0.215271i 0.00397908 + 0.0225665i
\(92\) 0 0
\(93\) −6.65395 5.58333i −0.689983 0.578964i
\(94\) 0 0
\(95\) −5.77852 + 15.4923i −0.592863 + 1.58948i
\(96\) 0 0
\(97\) −0.581665 0.488075i −0.0590591 0.0495565i 0.612780 0.790253i \(-0.290051\pi\)
−0.671839 + 0.740697i \(0.734496\pi\)
\(98\) 0 0
\(99\) 0.743835 + 4.21850i 0.0747583 + 0.423975i
\(100\) 0 0
\(101\) 11.7847 + 4.28927i 1.17262 + 0.426798i 0.853589 0.520947i \(-0.174421\pi\)
0.319029 + 0.947745i \(0.396643\pi\)
\(102\) 0 0
\(103\) −4.32365 + 7.48879i −0.426022 + 0.737892i −0.996515 0.0834102i \(-0.973419\pi\)
0.570493 + 0.821302i \(0.306752\pi\)
\(104\) 0 0
\(105\) −1.21939 + 1.02319i −0.119001 + 0.0998534i
\(106\) 0 0
\(107\) 0.492451 + 0.852950i 0.0476070 + 0.0824578i 0.888847 0.458204i \(-0.151507\pi\)
−0.841240 + 0.540662i \(0.818174\pi\)
\(108\) 0 0
\(109\) −2.47482 + 14.0354i −0.237044 + 1.34435i 0.601221 + 0.799083i \(0.294681\pi\)
−0.838265 + 0.545263i \(0.816430\pi\)
\(110\) 0 0
\(111\) 17.9548 6.53500i 1.70419 0.620275i
\(112\) 0 0
\(113\) 2.86600 0.269611 0.134805 0.990872i \(-0.456959\pi\)
0.134805 + 0.990872i \(0.456959\pi\)
\(114\) 0 0
\(115\) −22.4328 −2.09187
\(116\) 0 0
\(117\) −9.02878 + 3.28621i −0.834711 + 0.303810i
\(118\) 0 0
\(119\) 0.0908016 0.514962i 0.00832377 0.0472065i
\(120\) 0 0
\(121\) 5.25431 + 9.10073i 0.477664 + 0.827339i
\(122\) 0 0
\(123\) 10.8272 9.08512i 0.976258 0.819177i
\(124\) 0 0
\(125\) 8.32575 14.4206i 0.744677 1.28982i
\(126\) 0 0
\(127\) 19.8223 + 7.21472i 1.75894 + 0.640203i 0.999941 0.0108860i \(-0.00346520\pi\)
0.759002 + 0.651089i \(0.225687\pi\)
\(128\) 0 0
\(129\) 2.82289 + 16.0094i 0.248542 + 1.40955i
\(130\) 0 0
\(131\) −7.87172 6.60516i −0.687756 0.577096i 0.230505 0.973071i \(-0.425962\pi\)
−0.918261 + 0.395975i \(0.870407\pi\)
\(132\) 0 0
\(133\) −0.202730 0.571071i −0.0175789 0.0495181i
\(134\) 0 0
\(135\) −27.2852 22.8950i −2.34834 1.97049i
\(136\) 0 0
\(137\) −2.08375 11.8175i −0.178027 1.00964i −0.934592 0.355722i \(-0.884235\pi\)
0.756565 0.653919i \(-0.226876\pi\)
\(138\) 0 0
\(139\) −9.67258 3.52053i −0.820417 0.298607i −0.102497 0.994733i \(-0.532683\pi\)
−0.717920 + 0.696126i \(0.754906\pi\)
\(140\) 0 0
\(141\) 2.81054 4.86800i 0.236690 0.409960i
\(142\) 0 0
\(143\) 0.844324 0.708472i 0.0706059 0.0592454i
\(144\) 0 0
\(145\) 13.0782 + 22.6520i 1.08608 + 1.88115i
\(146\) 0 0
\(147\) −3.65886 + 20.7504i −0.301777 + 1.71147i
\(148\) 0 0
\(149\) 3.52238 1.28204i 0.288565 0.105029i −0.193682 0.981064i \(-0.562043\pi\)
0.482247 + 0.876035i \(0.339821\pi\)
\(150\) 0 0
\(151\) −13.3866 −1.08939 −0.544693 0.838636i \(-0.683354\pi\)
−0.544693 + 0.838636i \(0.683354\pi\)
\(152\) 0 0
\(153\) 22.9844 1.85818
\(154\) 0 0
\(155\) −10.2579 + 3.73357i −0.823934 + 0.299888i
\(156\) 0 0
\(157\) 1.40711 7.98010i 0.112299 0.636881i −0.875753 0.482760i \(-0.839634\pi\)
0.988052 0.154121i \(-0.0492546\pi\)
\(158\) 0 0
\(159\) −4.78964 8.29590i −0.379843 0.657908i
\(160\) 0 0
\(161\) 0.629796 0.528461i 0.0496349 0.0416486i
\(162\) 0 0
\(163\) 4.12600 7.14644i 0.323173 0.559753i −0.657968 0.753046i \(-0.728584\pi\)
0.981141 + 0.193294i \(0.0619170\pi\)
\(164\) 0 0
\(165\) 7.54220 + 2.74514i 0.587159 + 0.213709i
\(166\) 0 0
\(167\) −2.04523 11.5991i −0.158264 0.897562i −0.955740 0.294211i \(-0.904943\pi\)
0.797476 0.603351i \(-0.206168\pi\)
\(168\) 0 0
\(169\) −8.06473 6.76711i −0.620364 0.520547i
\(170\) 0 0
\(171\) 23.1728 13.1345i 1.77207 1.00442i
\(172\) 0 0
\(173\) 7.17235 + 6.01832i 0.545304 + 0.457564i 0.873347 0.487098i \(-0.161945\pi\)
−0.328043 + 0.944663i \(0.606389\pi\)
\(174\) 0 0
\(175\) 0.226676 + 1.28555i 0.0171351 + 0.0971781i
\(176\) 0 0
\(177\) −6.72425 2.44743i −0.505426 0.183960i
\(178\) 0 0
\(179\) −4.64499 + 8.04536i −0.347183 + 0.601339i −0.985748 0.168229i \(-0.946195\pi\)
0.638565 + 0.769568i \(0.279528\pi\)
\(180\) 0 0
\(181\) −2.07659 + 1.74246i −0.154351 + 0.129516i −0.716693 0.697389i \(-0.754345\pi\)
0.562342 + 0.826905i \(0.309901\pi\)
\(182\) 0 0
\(183\) −5.10517 8.84242i −0.377385 0.653650i
\(184\) 0 0
\(185\) 4.16976 23.6479i 0.306567 1.73863i
\(186\) 0 0
\(187\) −2.47760 + 0.901773i −0.181180 + 0.0659441i
\(188\) 0 0
\(189\) 1.30538 0.0949522
\(190\) 0 0
\(191\) −18.8935 −1.36709 −0.683544 0.729910i \(-0.739562\pi\)
−0.683544 + 0.729910i \(0.739562\pi\)
\(192\) 0 0
\(193\) 20.0362 7.29258i 1.44224 0.524931i 0.501825 0.864969i \(-0.332662\pi\)
0.940412 + 0.340037i \(0.110440\pi\)
\(194\) 0 0
\(195\) −3.12622 + 17.7297i −0.223873 + 1.26965i
\(196\) 0 0
\(197\) −8.29055 14.3597i −0.590677 1.02308i −0.994141 0.108088i \(-0.965527\pi\)
0.403464 0.914996i \(-0.367806\pi\)
\(198\) 0 0
\(199\) 12.3943 10.4001i 0.878610 0.737241i −0.0872832 0.996184i \(-0.527819\pi\)
0.965893 + 0.258943i \(0.0833741\pi\)
\(200\) 0 0
\(201\) −14.9950 + 25.9721i −1.05767 + 1.83193i
\(202\) 0 0
\(203\) −0.900793 0.327862i −0.0632233 0.0230114i
\(204\) 0 0
\(205\) −3.08447 17.4929i −0.215428 1.22176i
\(206\) 0 0
\(207\) 27.6828 + 23.2286i 1.92409 + 1.61450i
\(208\) 0 0
\(209\) −1.98259 + 2.32499i −0.137138 + 0.160823i
\(210\) 0 0
\(211\) 20.1088 + 16.8733i 1.38434 + 1.16160i 0.967573 + 0.252592i \(0.0812831\pi\)
0.416772 + 0.909011i \(0.363161\pi\)
\(212\) 0 0
\(213\) 1.13212 + 6.42055i 0.0775713 + 0.439929i
\(214\) 0 0
\(215\) 19.1981 + 6.98752i 1.30930 + 0.476545i
\(216\) 0 0
\(217\) 0.200035 0.346470i 0.0135792 0.0235199i
\(218\) 0 0
\(219\) −26.3207 + 22.0857i −1.77859 + 1.49241i
\(220\) 0 0
\(221\) −2.95700 5.12168i −0.198910 0.344522i
\(222\) 0 0
\(223\) 0.397301 2.25321i 0.0266053 0.150886i −0.968611 0.248581i \(-0.920036\pi\)
0.995216 + 0.0976949i \(0.0311469\pi\)
\(224\) 0 0
\(225\) −53.9178 + 19.6245i −3.59452 + 1.30830i
\(226\) 0 0
\(227\) −17.4671 −1.15934 −0.579668 0.814853i \(-0.696818\pi\)
−0.579668 + 0.814853i \(0.696818\pi\)
\(228\) 0 0
\(229\) 8.14952 0.538536 0.269268 0.963065i \(-0.413218\pi\)
0.269268 + 0.963065i \(0.413218\pi\)
\(230\) 0 0
\(231\) −0.276414 + 0.100607i −0.0181867 + 0.00661943i
\(232\) 0 0
\(233\) −3.69185 + 20.9375i −0.241861 + 1.37166i 0.585810 + 0.810449i \(0.300777\pi\)
−0.827671 + 0.561214i \(0.810335\pi\)
\(234\) 0 0
\(235\) −3.53213 6.11783i −0.230411 0.399083i
\(236\) 0 0
\(237\) −18.1110 + 15.1970i −1.17644 + 0.987149i
\(238\) 0 0
\(239\) 10.3725 17.9657i 0.670941 1.16210i −0.306697 0.951807i \(-0.599224\pi\)
0.977638 0.210296i \(-0.0674429\pi\)
\(240\) 0 0
\(241\) −18.7960 6.84119i −1.21076 0.440680i −0.343791 0.939046i \(-0.611711\pi\)
−0.866966 + 0.498367i \(0.833933\pi\)
\(242\) 0 0
\(243\) 0.354850 + 2.01245i 0.0227636 + 0.129099i
\(244\) 0 0
\(245\) 20.2851 + 17.0212i 1.29596 + 1.08744i
\(246\) 0 0
\(247\) −5.90804 3.47387i −0.375919 0.221037i
\(248\) 0 0
\(249\) 23.7165 + 19.9005i 1.50297 + 1.26115i
\(250\) 0 0
\(251\) −1.27528 7.23245i −0.0804948 0.456508i −0.998238 0.0593346i \(-0.981102\pi\)
0.917743 0.397174i \(-0.130009\pi\)
\(252\) 0 0
\(253\) −3.89541 1.41781i −0.244903 0.0891372i
\(254\) 0 0
\(255\) 21.5332 37.2966i 1.34846 2.33561i
\(256\) 0 0
\(257\) 20.7914 17.4460i 1.29693 1.08825i 0.306265 0.951946i \(-0.400921\pi\)
0.990666 0.136308i \(-0.0435238\pi\)
\(258\) 0 0
\(259\) 0.440021 + 0.762139i 0.0273416 + 0.0473570i
\(260\) 0 0
\(261\) 7.31677 41.4955i 0.452897 2.56851i
\(262\) 0 0
\(263\) −20.3152 + 7.39413i −1.25269 + 0.455941i −0.881309 0.472540i \(-0.843337\pi\)
−0.371379 + 0.928481i \(0.621115\pi\)
\(264\) 0 0
\(265\) −12.0387 −0.739532
\(266\) 0 0
\(267\) 39.2021 2.39913
\(268\) 0 0
\(269\) −5.63396 + 2.05060i −0.343509 + 0.125027i −0.508013 0.861349i \(-0.669620\pi\)
0.164504 + 0.986376i \(0.447398\pi\)
\(270\) 0 0
\(271\) −4.11091 + 23.3141i −0.249720 + 1.41623i 0.559551 + 0.828796i \(0.310974\pi\)
−0.809271 + 0.587436i \(0.800137\pi\)
\(272\) 0 0
\(273\) −0.329899 0.571402i −0.0199664 0.0345828i
\(274\) 0 0
\(275\) 5.04211 4.23083i 0.304050 0.255129i
\(276\) 0 0
\(277\) 4.74294 8.21502i 0.284976 0.493593i −0.687628 0.726064i \(-0.741348\pi\)
0.972603 + 0.232471i \(0.0746811\pi\)
\(278\) 0 0
\(279\) 16.5246 + 6.01446i 0.989302 + 0.360076i
\(280\) 0 0
\(281\) 4.22110 + 23.9391i 0.251810 + 1.42808i 0.804131 + 0.594453i \(0.202631\pi\)
−0.552321 + 0.833632i \(0.686258\pi\)
\(282\) 0 0
\(283\) −8.94917 7.50925i −0.531973 0.446378i 0.336809 0.941573i \(-0.390652\pi\)
−0.868782 + 0.495195i \(0.835097\pi\)
\(284\) 0 0
\(285\) 0.396453 49.9075i 0.0234839 2.95627i
\(286\) 0 0
\(287\) 0.498685 + 0.418446i 0.0294364 + 0.0247001i
\(288\) 0 0
\(289\) −0.495374 2.80941i −0.0291397 0.165259i
\(290\) 0 0
\(291\) 2.15369 + 0.783879i 0.126251 + 0.0459518i
\(292\) 0 0
\(293\) −7.01571 + 12.1516i −0.409862 + 0.709902i −0.994874 0.101122i \(-0.967757\pi\)
0.585012 + 0.811025i \(0.301090\pi\)
\(294\) 0 0
\(295\) −6.88905 + 5.78060i −0.401096 + 0.336559i
\(296\) 0 0
\(297\) −3.29100 5.70018i −0.190963 0.330758i
\(298\) 0 0
\(299\) 1.61464 9.15705i 0.0933768 0.529566i
\(300\) 0 0
\(301\) −0.703590 + 0.256086i −0.0405543 + 0.0147605i
\(302\) 0 0
\(303\) −37.8538 −2.17464
\(304\) 0 0
\(305\) −12.8318 −0.734746
\(306\) 0 0
\(307\) 0.522125 0.190038i 0.0297993 0.0108460i −0.327078 0.944998i \(-0.606064\pi\)
0.356877 + 0.934151i \(0.383842\pi\)
\(308\) 0 0
\(309\) 4.53241 25.7046i 0.257840 1.46228i
\(310\) 0 0
\(311\) 7.89478 + 13.6742i 0.447672 + 0.775390i 0.998234 0.0594037i \(-0.0189199\pi\)
−0.550562 + 0.834794i \(0.685587\pi\)
\(312\) 0 0
\(313\) −17.4399 + 14.6338i −0.985763 + 0.827153i −0.984949 0.172846i \(-0.944704\pi\)
−0.000814014 1.00000i \(0.500259\pi\)
\(314\) 0 0
\(315\) 1.61131 2.79087i 0.0907871 0.157248i
\(316\) 0 0
\(317\) 17.8284 + 6.48900i 1.00134 + 0.364458i 0.790102 0.612976i \(-0.210028\pi\)
0.211240 + 0.977434i \(0.432250\pi\)
\(318\) 0 0
\(319\) 0.839328 + 4.76006i 0.0469933 + 0.266512i
\(320\) 0 0
\(321\) −2.27733 1.91090i −0.127108 0.106656i
\(322\) 0 0
\(323\) 10.4384 + 12.6427i 0.580810 + 0.703456i
\(324\) 0 0
\(325\) 11.3096 + 9.48991i 0.627345 + 0.526405i
\(326\) 0 0
\(327\) −7.47001 42.3645i −0.413092 2.34276i
\(328\) 0 0
\(329\) 0.243285 + 0.0885485i 0.0134127 + 0.00488184i
\(330\) 0 0
\(331\) 7.38160 12.7853i 0.405729 0.702744i −0.588677 0.808368i \(-0.700351\pi\)
0.994406 + 0.105625i \(0.0336843\pi\)
\(332\) 0 0
\(333\) −29.6324 + 24.8646i −1.62385 + 1.36257i
\(334\) 0 0
\(335\) 18.8449 + 32.6403i 1.02961 + 1.78333i
\(336\) 0 0
\(337\) −1.43116 + 8.11649i −0.0779601 + 0.442134i 0.920695 + 0.390283i \(0.127623\pi\)
−0.998655 + 0.0518502i \(0.983488\pi\)
\(338\) 0 0
\(339\) −8.12906 + 2.95874i −0.441510 + 0.160697i
\(340\) 0 0
\(341\) −2.01724 −0.109240
\(342\) 0 0
\(343\) −1.94364 −0.104947
\(344\) 0 0
\(345\) 63.6278 23.1586i 3.42561 1.24682i
\(346\) 0 0
\(347\) 3.39699 19.2653i 0.182360 1.03421i −0.746941 0.664891i \(-0.768478\pi\)
0.929301 0.369324i \(-0.120411\pi\)
\(348\) 0 0
\(349\) −12.8829 22.3139i −0.689607 1.19443i −0.971965 0.235126i \(-0.924450\pi\)
0.282358 0.959309i \(-0.408884\pi\)
\(350\) 0 0
\(351\) 11.3096 9.48991i 0.603663 0.506534i
\(352\) 0 0
\(353\) 0.712979 1.23492i 0.0379480 0.0657279i −0.846428 0.532504i \(-0.821251\pi\)
0.884376 + 0.466776i \(0.154585\pi\)
\(354\) 0 0
\(355\) 7.69934 + 2.80233i 0.408638 + 0.148732i
\(356\) 0 0
\(357\) 0.274076 + 1.55436i 0.0145057 + 0.0822657i
\(358\) 0 0
\(359\) 7.55106 + 6.33609i 0.398530 + 0.334406i 0.819925 0.572471i \(-0.194015\pi\)
−0.421395 + 0.906877i \(0.638460\pi\)
\(360\) 0 0
\(361\) 17.7487 + 6.78120i 0.934141 + 0.356905i
\(362\) 0 0
\(363\) −24.2984 20.3888i −1.27534 1.07013i
\(364\) 0 0
\(365\) 7.49827 + 42.5248i 0.392477 + 2.22585i
\(366\) 0 0
\(367\) −10.7351 3.90726i −0.560368 0.203957i 0.0462791 0.998929i \(-0.485264\pi\)
−0.606647 + 0.794971i \(0.707486\pi\)
\(368\) 0 0
\(369\) −14.3071 + 24.7807i −0.744799 + 1.29003i
\(370\) 0 0
\(371\) 0.337984 0.283602i 0.0175473 0.0147239i
\(372\) 0 0
\(373\) −13.3194 23.0699i −0.689653 1.19451i −0.971950 0.235187i \(-0.924430\pi\)
0.282297 0.959327i \(-0.408903\pi\)
\(374\) 0 0
\(375\) −8.72773 + 49.4974i −0.450698 + 2.55604i
\(376\) 0 0
\(377\) −10.1879 + 3.70808i −0.524702 + 0.190976i
\(378\) 0 0
\(379\) 19.8016 1.01714 0.508569 0.861021i \(-0.330174\pi\)
0.508569 + 0.861021i \(0.330174\pi\)
\(380\) 0 0
\(381\) −63.6716 −3.26199
\(382\) 0 0
\(383\) −16.8435 + 6.13052i −0.860661 + 0.313255i −0.734379 0.678739i \(-0.762527\pi\)
−0.126282 + 0.991994i \(0.540304\pi\)
\(384\) 0 0
\(385\) −0.0641936 + 0.364060i −0.00327161 + 0.0185542i
\(386\) 0 0
\(387\) −16.4556 28.5019i −0.836485 1.44884i
\(388\) 0 0
\(389\) −16.4626 + 13.8137i −0.834685 + 0.700384i −0.956362 0.292186i \(-0.905617\pi\)
0.121676 + 0.992570i \(0.461173\pi\)
\(390\) 0 0
\(391\) −11.1215 + 19.2631i −0.562440 + 0.974175i
\(392\) 0 0
\(393\) 29.1461 + 10.6083i 1.47022 + 0.535118i
\(394\) 0 0
\(395\) 5.15949 + 29.2609i 0.259602 + 1.47228i
\(396\) 0 0
\(397\) 4.26129 + 3.57565i 0.213868 + 0.179457i 0.743428 0.668816i \(-0.233199\pi\)
−0.529560 + 0.848272i \(0.677643\pi\)
\(398\) 0 0
\(399\) 1.16457 + 1.41048i 0.0583013 + 0.0706124i
\(400\) 0 0
\(401\) −27.9884 23.4850i −1.39767 1.17279i −0.962121 0.272621i \(-0.912109\pi\)
−0.435550 0.900164i \(-0.643446\pi\)
\(402\) 0 0
\(403\) −0.785713 4.45600i −0.0391391 0.221969i
\(404\) 0 0
\(405\) 35.6794 + 12.9863i 1.77293 + 0.645292i
\(406\) 0 0
\(407\) 2.21868 3.84287i 0.109976 0.190484i
\(408\) 0 0
\(409\) −0.581665 + 0.488075i −0.0287615 + 0.0241338i −0.657055 0.753843i \(-0.728198\pi\)
0.628294 + 0.777976i \(0.283754\pi\)
\(410\) 0 0
\(411\) 18.1102 + 31.3678i 0.893311 + 1.54726i
\(412\) 0 0
\(413\) 0.0572319 0.324578i 0.00281620 0.0159714i
\(414\) 0 0
\(415\) 36.5620 13.3075i 1.79476 0.653238i
\(416\) 0 0
\(417\) 31.0695 1.52148
\(418\) 0 0
\(419\) 16.2619 0.794446 0.397223 0.917722i \(-0.369974\pi\)
0.397223 + 0.917722i \(0.369974\pi\)
\(420\) 0 0
\(421\) −14.1059 + 5.13414i −0.687481 + 0.250223i −0.662056 0.749454i \(-0.730316\pi\)
−0.0254245 + 0.999677i \(0.508094\pi\)
\(422\) 0 0
\(423\) −1.97610 + 11.2070i −0.0960814 + 0.544905i
\(424\) 0 0
\(425\) −17.6585 30.5855i −0.856565 1.48361i
\(426\) 0 0
\(427\) 0.360250 0.302285i 0.0174337 0.0146286i
\(428\) 0 0
\(429\) −1.66342 + 2.88114i −0.0803109 + 0.139103i
\(430\) 0 0
\(431\) −9.41358 3.42626i −0.453436 0.165037i 0.105198 0.994451i \(-0.466452\pi\)
−0.558634 + 0.829414i \(0.688674\pi\)
\(432\) 0 0
\(433\) 0.711701 + 4.03626i 0.0342022 + 0.193970i 0.997122 0.0758190i \(-0.0241571\pi\)
−0.962919 + 0.269789i \(0.913046\pi\)
\(434\) 0 0
\(435\) −60.4796 50.7484i −2.89977 2.43320i
\(436\) 0 0
\(437\) −0.204761 + 25.7764i −0.00979506 + 1.23305i
\(438\) 0 0
\(439\) −4.00981 3.36463i −0.191378 0.160585i 0.542064 0.840337i \(-0.317643\pi\)
−0.733442 + 0.679752i \(0.762087\pi\)
\(440\) 0 0
\(441\) −7.40738 42.0094i −0.352733 2.00045i
\(442\) 0 0
\(443\) 31.8347 + 11.5869i 1.51251 + 0.550509i 0.959265 0.282508i \(-0.0911665\pi\)
0.553247 + 0.833017i \(0.313389\pi\)
\(444\) 0 0
\(445\) 24.6335 42.6664i 1.16774 2.02258i
\(446\) 0 0
\(447\) −8.66727 + 7.27271i −0.409948 + 0.343987i
\(448\) 0 0
\(449\) 0.545695 + 0.945172i 0.0257530 + 0.0446054i 0.878615 0.477531i \(-0.158468\pi\)
−0.852862 + 0.522137i \(0.825135\pi\)
\(450\) 0 0
\(451\) 0.569986 3.23255i 0.0268396 0.152215i
\(452\) 0 0
\(453\) 37.9694 13.8197i 1.78396 0.649308i
\(454\) 0 0
\(455\) −0.829198 −0.0388734
\(456\) 0 0
\(457\) 16.9280 0.791858 0.395929 0.918281i \(-0.370423\pi\)
0.395929 + 0.918281i \(0.370423\pi\)
\(458\) 0 0
\(459\) −33.1872 + 12.0792i −1.54905 + 0.563806i
\(460\) 0 0
\(461\) 1.62318 9.20551i 0.0755991 0.428744i −0.923393 0.383856i \(-0.874596\pi\)
0.998992 0.0448876i \(-0.0142930\pi\)
\(462\) 0 0
\(463\) −3.80227 6.58572i −0.176706 0.306064i 0.764044 0.645164i \(-0.223211\pi\)
−0.940750 + 0.339100i \(0.889878\pi\)
\(464\) 0 0
\(465\) 25.2409 21.1796i 1.17052 0.982181i
\(466\) 0 0
\(467\) 17.7403 30.7272i 0.820925 1.42188i −0.0840686 0.996460i \(-0.526792\pi\)
0.904994 0.425424i \(-0.139875\pi\)
\(468\) 0 0
\(469\) −1.29799 0.472430i −0.0599357 0.0218148i
\(470\) 0 0
\(471\) 4.24722 + 24.0872i 0.195702 + 1.10988i
\(472\) 0 0
\(473\) 2.89208 + 2.42674i 0.132978 + 0.111582i
\(474\) 0 0
\(475\) −35.2814 20.7451i −1.61882 0.951853i
\(476\) 0 0
\(477\) 14.8561 + 12.4658i 0.680216 + 0.570769i
\(478\) 0 0
\(479\) −4.87224 27.6318i −0.222618 1.26253i −0.867186 0.497984i \(-0.834074\pi\)
0.644568 0.764547i \(-0.277037\pi\)
\(480\) 0 0
\(481\) 9.35293 + 3.40419i 0.426457 + 0.155218i
\(482\) 0 0
\(483\) −1.24078 + 2.14909i −0.0564573 + 0.0977870i
\(484\) 0 0
\(485\) 2.20647 1.85145i 0.100191 0.0840699i
\(486\) 0 0
\(487\) −21.5368 37.3029i −0.975926 1.69035i −0.676844 0.736126i \(-0.736653\pi\)
−0.299082 0.954228i \(-0.596680\pi\)
\(488\) 0 0
\(489\) −4.32521 + 24.5295i −0.195593 + 1.10926i
\(490\) 0 0
\(491\) 17.4166 6.33912i 0.786000 0.286080i 0.0823275 0.996605i \(-0.473765\pi\)
0.703672 + 0.710525i \(0.251542\pi\)
\(492\) 0 0
\(493\) 25.9351 1.16806
\(494\) 0 0
\(495\) −16.2492 −0.730346
\(496\) 0 0
\(497\) −0.282173 + 0.102703i −0.0126572 + 0.00460684i
\(498\) 0 0
\(499\) −7.54046 + 42.7641i −0.337557 + 1.91438i 0.0628031 + 0.998026i \(0.479996\pi\)
−0.400361 + 0.916358i \(0.631115\pi\)
\(500\) 0 0
\(501\) 17.7754 + 30.7879i 0.794146 + 1.37550i
\(502\) 0 0
\(503\) −0.819590 + 0.687718i −0.0365437 + 0.0306638i −0.660877 0.750495i \(-0.729815\pi\)
0.624333 + 0.781158i \(0.285371\pi\)
\(504\) 0 0
\(505\) −23.7863 + 41.1990i −1.05847 + 1.83333i
\(506\) 0 0
\(507\) 29.8607 + 10.8684i 1.32616 + 0.482682i
\(508\) 0 0
\(509\) 1.01402 + 5.75077i 0.0449455 + 0.254899i 0.998999 0.0447386i \(-0.0142455\pi\)
−0.954053 + 0.299637i \(0.903134\pi\)
\(510\) 0 0
\(511\) −1.21229 1.01723i −0.0536286 0.0449998i
\(512\) 0 0
\(513\) −26.5565 + 31.1431i −1.17250 + 1.37500i
\(514\) 0 0
\(515\) −25.1281 21.0850i −1.10728 0.929116i
\(516\) 0 0
\(517\) −0.226684 1.28559i −0.00996957 0.0565402i
\(518\) 0 0
\(519\) −26.5565 9.66579i −1.16570 0.424281i
\(520\) 0 0
\(521\) 5.78321 10.0168i 0.253367 0.438844i −0.711084 0.703107i \(-0.751795\pi\)
0.964451 + 0.264263i \(0.0851287\pi\)
\(522\) 0 0
\(523\) 2.87535 2.41270i 0.125730 0.105500i −0.577754 0.816211i \(-0.696071\pi\)
0.703485 + 0.710710i \(0.251626\pi\)
\(524\) 0 0
\(525\) −1.97008 3.41228i −0.0859814 0.148924i
\(526\) 0 0
\(527\) −1.87955 + 10.6595i −0.0818745 + 0.464333i
\(528\) 0 0
\(529\) −11.2497 + 4.09457i −0.489119 + 0.178025i
\(530\) 0 0
\(531\) 14.4870 0.628681
\(532\) 0 0
\(533\) 7.36259 0.318909
\(534\) 0 0
\(535\) −3.51078 + 1.27782i −0.151784 + 0.0552450i
\(536\) 0 0
\(537\) 4.86926 27.6150i 0.210124 1.19167i
\(538\) 0 0
\(539\) 2.44668 + 4.23777i 0.105386 + 0.182534i
\(540\) 0 0
\(541\) −11.2927 + 9.47568i −0.485510 + 0.407391i −0.852414 0.522867i \(-0.824862\pi\)
0.366904 + 0.930259i \(0.380418\pi\)
\(542\) 0 0
\(543\) 4.09114 7.08606i 0.175568 0.304092i
\(544\) 0 0
\(545\) −50.8023 18.4905i −2.17613 0.792047i
\(546\) 0 0
\(547\) −1.35734 7.69785i −0.0580356 0.329136i 0.941942 0.335775i \(-0.108998\pi\)
−0.999978 + 0.00663836i \(0.997887\pi\)
\(548\) 0 0
\(549\) 15.8348 + 13.2870i 0.675814 + 0.567076i
\(550\) 0 0
\(551\) 26.1477 14.8207i 1.11393 0.631382i
\(552\) 0 0
\(553\) −0.834166 0.699949i −0.0354724 0.0297648i
\(554\) 0 0
\(555\) 12.5860 + 71.3790i 0.534248 + 3.02987i
\(556\) 0 0
\(557\) −0.775402 0.282223i −0.0328549 0.0119582i 0.325540 0.945528i \(-0.394454\pi\)
−0.358395 + 0.933570i \(0.616676\pi\)
\(558\) 0 0
\(559\) −4.23411 + 7.33370i −0.179084 + 0.310182i
\(560\) 0 0
\(561\) 6.09645 5.11553i 0.257393 0.215978i
\(562\) 0 0
\(563\) 2.41715 + 4.18662i 0.101871 + 0.176445i 0.912455 0.409176i \(-0.134184\pi\)
−0.810585 + 0.585621i \(0.800851\pi\)
\(564\) 0 0
\(565\) −1.88787 + 10.7066i −0.0794232 + 0.450431i
\(566\) 0 0
\(567\) −1.30762 + 0.475933i −0.0549147 + 0.0199873i
\(568\) 0 0
\(569\) −20.7045 −0.867977 −0.433989 0.900918i \(-0.642894\pi\)
−0.433989 + 0.900918i \(0.642894\pi\)
\(570\) 0 0
\(571\) −8.15233 −0.341164 −0.170582 0.985343i \(-0.554565\pi\)
−0.170582 + 0.985343i \(0.554565\pi\)
\(572\) 0 0
\(573\) 53.5891 19.5048i 2.23872 0.814827i
\(574\) 0 0
\(575\) 9.64223 54.6838i 0.402109 2.28047i
\(576\) 0 0
\(577\) 2.61121 + 4.52275i 0.108706 + 0.188285i 0.915246 0.402895i \(-0.131996\pi\)
−0.806540 + 0.591179i \(0.798663\pi\)
\(578\) 0 0
\(579\) −49.3017 + 41.3690i −2.04891 + 1.71924i
\(580\) 0 0
\(581\) −0.712979 + 1.23492i −0.0295793 + 0.0512329i
\(582\) 0 0
\(583\) −2.09050 0.760879i −0.0865796 0.0315124i
\(584\) 0 0
\(585\) −6.32905 35.8938i −0.261674 1.48403i
\(586\) 0 0
\(587\) 4.74153 + 3.97861i 0.195704 + 0.164215i 0.735374 0.677662i \(-0.237007\pi\)
−0.539670 + 0.841877i \(0.681451\pi\)
\(588\) 0 0
\(589\) 4.19642 + 11.8209i 0.172910 + 0.487072i
\(590\) 0 0
\(591\) 38.3394 + 32.1706i 1.57707 + 1.32332i
\(592\) 0 0
\(593\) 2.92199 + 16.5715i 0.119992 + 0.680508i 0.984157 + 0.177300i \(0.0567361\pi\)
−0.864165 + 0.503209i \(0.832153\pi\)
\(594\) 0 0
\(595\) 1.86395 + 0.678422i 0.0764145 + 0.0278126i
\(596\) 0 0
\(597\) −24.4184 + 42.2938i −0.999377 + 1.73097i
\(598\) 0 0
\(599\) 26.5345 22.2651i 1.08417 0.909726i 0.0879086 0.996129i \(-0.471982\pi\)
0.996260 + 0.0864028i \(0.0275372\pi\)
\(600\) 0 0
\(601\) 10.0714 + 17.4442i 0.410822 + 0.711564i 0.994980 0.100076i \(-0.0319085\pi\)
−0.584158 + 0.811640i \(0.698575\pi\)
\(602\) 0 0
\(603\) 10.5430 59.7926i 0.429346 2.43494i
\(604\) 0 0
\(605\) −37.4590 + 13.6340i −1.52293 + 0.554300i
\(606\) 0 0
\(607\) 30.9282 1.25534 0.627668 0.778481i \(-0.284010\pi\)
0.627668 + 0.778481i \(0.284010\pi\)
\(608\) 0 0
\(609\) 2.89346 0.117249
\(610\) 0 0
\(611\) 2.75153 1.00147i 0.111315 0.0405153i
\(612\) 0 0
\(613\) 1.55289 8.80687i 0.0627206 0.355706i −0.937254 0.348646i \(-0.886642\pi\)
0.999975 0.00706025i \(-0.00224737\pi\)
\(614\) 0 0
\(615\) 26.8076 + 46.4321i 1.08099 + 1.87232i
\(616\) 0 0
\(617\) 16.4246 13.7819i 0.661230 0.554838i −0.249225 0.968446i \(-0.580176\pi\)
0.910455 + 0.413607i \(0.135731\pi\)
\(618\) 0 0
\(619\) −12.7984 + 22.1675i −0.514413 + 0.890989i 0.485448 + 0.874266i \(0.338657\pi\)
−0.999860 + 0.0167229i \(0.994677\pi\)
\(620\) 0 0
\(621\) −52.1787 18.9915i −2.09386 0.762102i
\(622\) 0 0
\(623\) 0.313537 + 1.77816i 0.0125616 + 0.0712403i
\(624\) 0 0
\(625\) 12.4230 + 10.4241i 0.496919 + 0.416965i
\(626\) 0 0
\(627\) 3.22314 8.64129i 0.128720 0.345100i
\(628\) 0 0
\(629\) −18.2392 15.3045i −0.727245 0.610231i
\(630\) 0 0
\(631\) −0.493858 2.80081i −0.0196602 0.111498i 0.973398 0.229119i \(-0.0735845\pi\)
−0.993059 + 0.117621i \(0.962473\pi\)
\(632\) 0 0
\(633\) −74.4553 27.0995i −2.95933 1.07711i
\(634\) 0 0
\(635\) −40.0094 + 69.2984i −1.58773 + 2.75002i
\(636\) 0 0
\(637\) −8.40808 + 7.05522i −0.333140 + 0.279538i
\(638\) 0 0
\(639\) −6.59948 11.4306i −0.261072 0.452189i
\(640\) 0 0
\(641\) 8.07050 45.7701i 0.318765 1.80781i −0.231518 0.972831i \(-0.574369\pi\)
0.550283 0.834978i \(-0.314520\pi\)
\(642\) 0 0
\(643\) −8.80807 + 3.20587i −0.347356 + 0.126427i −0.509806 0.860290i \(-0.670283\pi\)
0.162450 + 0.986717i \(0.448061\pi\)
\(644\) 0 0
\(645\) −61.6665 −2.42812
\(646\) 0 0
\(647\) −5.27319 −0.207311 −0.103655 0.994613i \(-0.533054\pi\)
−0.103655 + 0.994613i \(0.533054\pi\)
\(648\) 0 0
\(649\) −1.56162 + 0.568383i −0.0612990 + 0.0223110i
\(650\) 0 0
\(651\) −0.209693 + 1.18923i −0.00821851 + 0.0466095i
\(652\) 0 0
\(653\) 21.0269 + 36.4197i 0.822848 + 1.42521i 0.903553 + 0.428476i \(0.140949\pi\)
−0.0807056 + 0.996738i \(0.525717\pi\)
\(654\) 0 0
\(655\) 29.8603 25.0558i 1.16674 0.979011i
\(656\) 0 0
\(657\) 34.7803 60.2412i 1.35691 2.35023i
\(658\) 0 0
\(659\) 31.5671 + 11.4895i 1.22968 + 0.447567i 0.873488 0.486846i \(-0.161853\pi\)
0.356192 + 0.934413i \(0.384075\pi\)
\(660\) 0 0
\(661\) −3.70331 21.0025i −0.144042 0.816903i −0.968131 0.250443i \(-0.919424\pi\)
0.824089 0.566460i \(-0.191687\pi\)
\(662\) 0 0
\(663\) 13.6746 + 11.4743i 0.531077 + 0.445626i
\(664\) 0 0
\(665\) 2.26691 0.381176i 0.0879071 0.0147814i
\(666\) 0 0
\(667\) 31.2366 + 26.2107i 1.20949 + 1.01488i
\(668\) 0 0
\(669\) 1.19922 + 6.80110i 0.0463644 + 0.262946i
\(670\) 0 0
\(671\) −2.22822 0.811004i −0.0860193 0.0313085i
\(672\) 0 0
\(673\) 16.8335 29.1564i 0.648882 1.12390i −0.334508 0.942393i \(-0.608570\pi\)
0.983390 0.181504i \(-0.0580964\pi\)
\(674\) 0 0
\(675\) 67.5385 56.6715i 2.59956 2.18129i
\(676\) 0 0
\(677\) −16.2965 28.2264i −0.626327 1.08483i −0.988283 0.152635i \(-0.951224\pi\)
0.361956 0.932195i \(-0.382109\pi\)
\(678\) 0 0
\(679\) −0.0183306 + 0.103958i −0.000703464 + 0.00398954i
\(680\) 0 0
\(681\) 49.5434 18.0323i 1.89851 0.691000i
\(682\) 0 0
\(683\) −29.1071 −1.11375 −0.556875 0.830596i \(-0.688000\pi\)
−0.556875 + 0.830596i \(0.688000\pi\)
\(684\) 0 0
\(685\) 45.5198 1.73922
\(686\) 0 0
\(687\) −23.1151 + 8.41321i −0.881897 + 0.320984i
\(688\) 0 0
\(689\) 0.866505 4.91419i 0.0330112 0.187216i
\(690\) 0 0
\(691\) 17.4572 + 30.2367i 0.664102 + 1.15026i 0.979528 + 0.201309i \(0.0645195\pi\)
−0.315425 + 0.948950i \(0.602147\pi\)
\(692\) 0 0
\(693\) 0.456192 0.382791i 0.0173293 0.0145410i
\(694\) 0 0
\(695\) 19.5232 33.8152i 0.740558 1.28268i
\(696\) 0 0
\(697\) −16.5503 6.02383i −0.626889 0.228169i
\(698\) 0 0
\(699\) −11.1435 63.1980i −0.421486 2.39037i
\(700\) 0 0
\(701\) 1.84929 + 1.55174i 0.0698467 + 0.0586084i 0.677043 0.735944i \(-0.263261\pi\)
−0.607196 + 0.794552i \(0.707706\pi\)
\(702\) 0 0
\(703\) −27.1345 5.00711i −1.02340 0.188847i
\(704\) 0 0
\(705\) 16.3342 + 13.7061i 0.615183 + 0.516200i
\(706\) 0 0
\(707\) −0.302753 1.71700i −0.0113862 0.0645744i
\(708\) 0 0
\(709\) −4.00623 1.45815i −0.150457 0.0547619i 0.265694 0.964057i \(-0.414399\pi\)
−0.416151 + 0.909296i \(0.636621\pi\)
\(710\) 0 0
\(711\) 23.9320 41.4514i 0.897519 1.55455i
\(712\) 0 0
\(713\) −13.0365 + 10.9389i −0.488220 + 0.409665i
\(714\) 0 0
\(715\) 2.09050 + 3.62085i 0.0781802 + 0.135412i
\(716\) 0 0
\(717\) −10.8733 + 61.6656i −0.406071 + 2.30294i
\(718\) 0 0
\(719\) −27.5194 + 10.0162i −1.02630 + 0.373543i −0.799671 0.600438i \(-0.794993\pi\)
−0.226630 + 0.973981i \(0.572771\pi\)
\(720\) 0 0
\(721\) 1.20218 0.0447714
\(722\) 0 0
\(723\) 60.3751 2.24537
\(724\) 0 0
\(725\) −60.8396 + 22.1438i −2.25953 + 0.822400i
\(726\) 0 0
\(727\) −7.25564 + 41.1488i −0.269097 + 1.52612i 0.488013 + 0.872836i \(0.337722\pi\)
−0.757110 + 0.653287i \(0.773389\pi\)
\(728\) 0 0
\(729\) 11.9300 + 20.6634i 0.441852 + 0.765311i
\(730\) 0 0
\(731\) 15.5180 13.0212i 0.573955 0.481605i
\(732\) 0 0
\(733\) −1.63173 + 2.82624i −0.0602693 + 0.104390i −0.894586 0.446896i \(-0.852529\pi\)
0.834316 + 0.551286i \(0.185863\pi\)
\(734\) 0 0
\(735\) −75.1080 27.3371i −2.77040 1.00834i
\(736\) 0 0
\(737\) 1.20942 + 6.85898i 0.0445496 + 0.252654i
\(738\) 0 0
\(739\) 3.24786 + 2.72528i 0.119474 + 0.100251i 0.700567 0.713586i \(-0.252930\pi\)
−0.581093 + 0.813837i \(0.697375\pi\)
\(740\) 0 0
\(741\) 20.3437 + 3.75400i 0.747344 + 0.137907i
\(742\) 0 0
\(743\) −12.3449 10.3586i −0.452889 0.380019i 0.387618 0.921820i \(-0.373298\pi\)
−0.840507 + 0.541801i \(0.817742\pi\)
\(744\) 0 0
\(745\) 2.46914 + 14.0032i 0.0904623 + 0.513037i
\(746\) 0 0
\(747\) −58.8982 21.4372i −2.15497 0.784346i
\(748\) 0 0
\(749\) 0.0684621 0.118580i 0.00250155 0.00433281i
\(750\) 0 0
\(751\) −26.4072 + 22.1583i −0.963614 + 0.808568i −0.981537 0.191271i \(-0.938739\pi\)
0.0179232 + 0.999839i \(0.494295\pi\)
\(752\) 0 0
\(753\) 11.0836 + 19.1974i 0.403910 + 0.699593i
\(754\) 0 0
\(755\) 8.81790 50.0088i 0.320916 1.82001i
\(756\) 0 0
\(757\) −23.7846 + 8.65689i −0.864466 + 0.314640i −0.735924 0.677064i \(-0.763252\pi\)
−0.128542 + 0.991704i \(0.541030\pi\)
\(758\) 0 0
\(759\) 12.5125 0.454177
\(760\) 0 0
\(761\) −13.6889 −0.496223 −0.248111 0.968731i \(-0.579810\pi\)
−0.248111 + 0.968731i \(0.579810\pi\)
\(762\) 0 0
\(763\) 1.86186 0.677660i 0.0674037 0.0245329i
\(764\) 0 0
\(765\) −15.1401 + 85.8637i −0.547391 + 3.10441i
\(766\) 0 0
\(767\) −1.86379 3.22817i −0.0672974 0.116563i
\(768\) 0 0
\(769\) 26.4169 22.1664i 0.952616 0.799340i −0.0271198 0.999632i \(-0.508634\pi\)
0.979736 + 0.200292i \(0.0641891\pi\)
\(770\) 0 0
\(771\) −40.9617 + 70.9477i −1.47520 + 2.55512i
\(772\) 0 0
\(773\) 45.5996 + 16.5969i 1.64010 + 0.596948i 0.987057 0.160371i \(-0.0512689\pi\)
0.653045 + 0.757319i \(0.273491\pi\)
\(774\) 0 0
\(775\) −4.69209 26.6102i −0.168545 0.955866i
\(776\) 0 0
\(777\) −2.03486 1.70745i −0.0730003 0.0612545i
\(778\) 0 0
\(779\) −20.1283 + 3.38453i −0.721172 + 0.121263i
\(780\) 0 0
\(781\) 1.15986 + 0.973239i 0.0415031 + 0.0348252i
\(782\) 0 0
\(783\) 11.2427 + 63.7606i 0.401782 + 2.27862i
\(784\) 0 0
\(785\) 28.8847 + 10.5132i 1.03094 + 0.375231i
\(786\) 0 0
\(787\) −23.4705 + 40.6521i −0.836633 + 1.44909i 0.0560615 + 0.998427i \(0.482146\pi\)
−0.892694 + 0.450663i \(0.851188\pi\)
\(788\) 0 0
\(789\) 49.9882 41.9451i 1.77963 1.49328i
\(790\) 0 0
\(791\) −0.199220 0.345060i −0.00708346 0.0122689i
\(792\) 0 0
\(793\) 0.923588 5.23793i 0.0327976 0.186004i
\(794\) 0 0