Properties

Label 300.2.x.a.77.3
Level $300$
Weight $2$
Character 300.77
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.x (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 77.3
Character \(\chi\) \(=\) 300.77
Dual form 300.2.x.a.113.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.21892 + 1.23054i) q^{3} +(-1.48454 + 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(-0.0284784 - 2.99986i) q^{9} +O(q^{10})\) \(q+(-1.21892 + 1.23054i) q^{3} +(-1.48454 + 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(-0.0284784 - 2.99986i) q^{9} +(0.879848 + 1.21101i) q^{11} +(-5.29990 + 0.839422i) q^{13} +(-0.248153 - 3.86503i) q^{15} +(-6.61182 - 3.36889i) q^{17} +(-3.22097 + 1.04656i) q^{19} +(0.601255 - 0.00285386i) q^{21} +(1.61050 + 0.255078i) q^{23} +(-0.592307 - 4.96479i) q^{25} +(3.72618 + 3.62154i) q^{27} +(0.637623 - 1.96240i) q^{29} +(2.11791 + 6.51825i) q^{31} +(-2.56266 - 0.393426i) q^{33} +(0.774858 - 0.0460576i) q^{35} +(1.18914 + 7.50792i) q^{37} +(5.42720 - 7.54495i) q^{39} +(-2.49942 + 3.44015i) q^{41} +(-3.03773 + 3.03773i) q^{43} +(5.05856 + 4.40579i) q^{45} +(1.43370 + 2.81380i) q^{47} -6.87949i q^{49} +(12.2048 - 4.02974i) q^{51} +(0.212713 - 0.108383i) q^{53} +(-3.33118 - 0.326527i) q^{55} +(2.63826 - 5.23920i) q^{57} +(2.57801 + 1.87303i) q^{59} +(3.40759 - 2.47576i) q^{61} +(-0.729368 + 0.743349i) q^{63} +(6.46424 - 10.1085i) q^{65} +(-5.71895 + 11.2241i) q^{67} +(-2.27695 + 1.67087i) q^{69} +(15.0056 + 4.87563i) q^{71} +(-2.02219 + 12.7676i) q^{73} +(6.83137 + 5.32281i) q^{75} +(0.0812876 - 0.513230i) q^{77} +(-9.94456 - 3.23118i) q^{79} +(-8.99838 + 0.170863i) q^{81} +(6.61756 - 12.9877i) q^{83} +(15.4489 - 6.05486i) q^{85} +(1.63761 + 3.17663i) q^{87} +(-10.2231 + 7.42754i) q^{89} +(1.50698 + 1.09489i) q^{91} +(-10.6025 - 5.33903i) q^{93} +(3.03162 - 6.93965i) q^{95} +(2.73153 - 1.39178i) q^{97} +(3.60780 - 2.67391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\)

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 0
\(3\) −1.21892 + 1.23054i −0.703743 + 0.710455i
\(4\) 0 0
\(5\) −1.48454 + 1.67217i −0.663905 + 0.747817i
\(6\) 0 0
\(7\) −0.245464 0.245464i −0.0927767 0.0927767i 0.659195 0.751972i \(-0.270897\pi\)
−0.751972 + 0.659195i \(0.770897\pi\)
\(8\) 0 0
\(9\) −0.0284784 2.99986i −0.00949280 0.999955i
\(10\) 0 0
\(11\) 0.879848 + 1.21101i 0.265284 + 0.365132i 0.920791 0.390057i \(-0.127545\pi\)
−0.655506 + 0.755190i \(0.727545\pi\)
\(12\) 0 0
\(13\) −5.29990 + 0.839422i −1.46993 + 0.232814i −0.839469 0.543408i \(-0.817134\pi\)
−0.630460 + 0.776222i \(0.717134\pi\)
\(14\) 0 0
\(15\) −0.248153 3.86503i −0.0640727 0.997945i
\(16\) 0 0
\(17\) −6.61182 3.36889i −1.60360 0.817077i −0.999801 0.0199422i \(-0.993652\pi\)
−0.603802 0.797134i \(-0.706348\pi\)
\(18\) 0 0
\(19\) −3.22097 + 1.04656i −0.738940 + 0.240096i −0.654215 0.756308i \(-0.727001\pi\)
−0.0847246 + 0.996404i \(0.527001\pi\)
\(20\) 0 0
\(21\) 0.601255 0.00285386i 0.131205 0.000622763i
\(22\) 0 0
\(23\) 1.61050 + 0.255078i 0.335812 + 0.0531874i 0.322063 0.946718i \(-0.395624\pi\)
0.0137486 + 0.999905i \(0.495624\pi\)
\(24\) 0 0
\(25\) −0.592307 4.96479i −0.118461 0.992959i
\(26\) 0 0
\(27\) 3.72618 + 3.62154i 0.717104 + 0.696967i
\(28\) 0 0
\(29\) 0.637623 1.96240i 0.118404 0.364409i −0.874238 0.485497i \(-0.838639\pi\)
0.992642 + 0.121089i \(0.0386385\pi\)
\(30\) 0 0
\(31\) 2.11791 + 6.51825i 0.380387 + 1.17071i 0.939772 + 0.341803i \(0.111038\pi\)
−0.559384 + 0.828908i \(0.688962\pi\)
\(32\) 0 0
\(33\) −2.56266 0.393426i −0.446102 0.0684867i
\(34\) 0 0
\(35\) 0.774858 0.0460576i 0.130975 0.00778515i
\(36\) 0 0
\(37\) 1.18914 + 7.50792i 0.195493 + 1.23429i 0.868887 + 0.495010i \(0.164836\pi\)
−0.673394 + 0.739284i \(0.735164\pi\)
\(38\) 0 0
\(39\) 5.42720 7.54495i 0.869048 1.20816i
\(40\) 0 0
\(41\) −2.49942 + 3.44015i −0.390343 + 0.537261i −0.958288 0.285806i \(-0.907739\pi\)
0.567944 + 0.823067i \(0.307739\pi\)
\(42\) 0 0
\(43\) −3.03773 + 3.03773i −0.463250 + 0.463250i −0.899719 0.436469i \(-0.856229\pi\)
0.436469 + 0.899719i \(0.356229\pi\)
\(44\) 0 0
\(45\) 5.05856 + 4.40579i 0.754086 + 0.656776i
\(46\) 0 0
\(47\) 1.43370 + 2.81380i 0.209127 + 0.410435i 0.971615 0.236567i \(-0.0760223\pi\)
−0.762488 + 0.647002i \(0.776022\pi\)
\(48\) 0 0
\(49\) 6.87949i 0.982785i
\(50\) 0 0
\(51\) 12.2048 4.02974i 1.70902 0.564276i
\(52\) 0 0
\(53\) 0.212713 0.108383i 0.0292184 0.0148875i −0.439320 0.898330i \(-0.644781\pi\)
0.468539 + 0.883443i \(0.344781\pi\)
\(54\) 0 0
\(55\) −3.33118 0.326527i −0.449176 0.0440289i
\(56\) 0 0
\(57\) 2.63826 5.23920i 0.349446 0.693950i
\(58\) 0 0
\(59\) 2.57801 + 1.87303i 0.335628 + 0.243848i 0.742815 0.669497i \(-0.233490\pi\)
−0.407187 + 0.913345i \(0.633490\pi\)
\(60\) 0 0
\(61\) 3.40759 2.47576i 0.436297 0.316988i −0.347865 0.937545i \(-0.613093\pi\)
0.784162 + 0.620556i \(0.213093\pi\)
\(62\) 0 0
\(63\) −0.729368 + 0.743349i −0.0918918 + 0.0936532i
\(64\) 0 0
\(65\) 6.46424 10.1085i 0.801790 1.25380i
\(66\) 0 0
\(67\) −5.71895 + 11.2241i −0.698681 + 1.37124i 0.219709 + 0.975565i \(0.429489\pi\)
−0.918391 + 0.395674i \(0.870511\pi\)
\(68\) 0 0
\(69\) −2.27695 + 1.67087i −0.274113 + 0.201149i
\(70\) 0 0
\(71\) 15.0056 + 4.87563i 1.78084 + 0.578630i 0.998994 0.0448405i \(-0.0142780\pi\)
0.781847 + 0.623471i \(0.214278\pi\)
\(72\) 0 0
\(73\) −2.02219 + 12.7676i −0.236679 + 1.49433i 0.527625 + 0.849478i \(0.323083\pi\)
−0.764304 + 0.644856i \(0.776917\pi\)
\(74\) 0 0
\(75\) 6.83137 + 5.32281i 0.788819 + 0.614626i
\(76\) 0 0
\(77\) 0.0812876 0.513230i 0.00926358 0.0584879i
\(78\) 0 0
\(79\) −9.94456 3.23118i −1.11885 0.363536i −0.309521 0.950892i \(-0.600169\pi\)
−0.809329 + 0.587356i \(0.800169\pi\)
\(80\) 0 0
\(81\) −8.99838 + 0.170863i −0.999820 + 0.0189847i
\(82\) 0 0
\(83\) 6.61756 12.9877i 0.726372 1.42559i −0.171434 0.985196i \(-0.554840\pi\)
0.897807 0.440390i \(-0.145160\pi\)
\(84\) 0 0
\(85\) 15.4489 6.05486i 1.67566 0.656741i
\(86\) 0 0
\(87\) 1.63761 + 3.17663i 0.175570 + 0.340570i
\(88\) 0 0
\(89\) −10.2231 + 7.42754i −1.08365 + 0.787318i −0.978316 0.207119i \(-0.933591\pi\)
−0.105335 + 0.994437i \(0.533591\pi\)
\(90\) 0 0
\(91\) 1.50698 + 1.09489i 0.157975 + 0.114775i
\(92\) 0 0
\(93\) −10.6025 5.33903i −1.09943 0.553632i
\(94\) 0 0
\(95\) 3.03162 6.93965i 0.311038 0.711993i
\(96\) 0 0
\(97\) 2.73153 1.39178i 0.277345 0.141314i −0.309786 0.950806i \(-0.600257\pi\)
0.587131 + 0.809492i \(0.300257\pi\)
\(98\) 0 0
\(99\) 3.60780 2.67391i 0.362598 0.268738i
\(100\) 0 0
\(101\) 2.16240i 0.215167i 0.994196 + 0.107584i \(0.0343113\pi\)
−0.994196 + 0.107584i \(0.965689\pi\)
\(102\) 0 0
\(103\) −6.42093 12.6018i −0.632673 1.24169i −0.955432 0.295210i \(-0.904610\pi\)
0.322759 0.946481i \(-0.395390\pi\)
\(104\) 0 0
\(105\) −0.887812 + 1.00964i −0.0866416 + 0.0985305i
\(106\) 0 0
\(107\) −1.63321 + 1.63321i −0.157888 + 0.157888i −0.781630 0.623742i \(-0.785612\pi\)
0.623742 + 0.781630i \(0.285612\pi\)
\(108\) 0 0
\(109\) −2.52845 + 3.48012i −0.242182 + 0.333335i −0.912754 0.408509i \(-0.866049\pi\)
0.670572 + 0.741844i \(0.266049\pi\)
\(110\) 0 0
\(111\) −10.6883 7.68825i −1.01449 0.729736i
\(112\) 0 0
\(113\) 0.695637 + 4.39208i 0.0654401 + 0.413172i 0.998562 + 0.0536118i \(0.0170733\pi\)
−0.933122 + 0.359560i \(0.882927\pi\)
\(114\) 0 0
\(115\) −2.81738 + 2.31436i −0.262722 + 0.215815i
\(116\) 0 0
\(117\) 2.66909 + 15.8751i 0.246757 + 1.46765i
\(118\) 0 0
\(119\) 0.796023 + 2.44991i 0.0729713 + 0.224583i
\(120\) 0 0
\(121\) 2.70678 8.33062i 0.246071 0.757329i
\(122\) 0 0
\(123\) −1.18668 7.26890i −0.106999 0.655415i
\(124\) 0 0
\(125\) 9.18128 + 6.37997i 0.821199 + 0.570642i
\(126\) 0 0
\(127\) 9.40727 + 1.48997i 0.834760 + 0.132213i 0.559161 0.829059i \(-0.311124\pi\)
0.275600 + 0.961272i \(0.411124\pi\)
\(128\) 0 0
\(129\) −0.0353179 7.44081i −0.00310956 0.655127i
\(130\) 0 0
\(131\) −18.1696 + 5.90366i −1.58748 + 0.515805i −0.963971 0.266007i \(-0.914295\pi\)
−0.623514 + 0.781812i \(0.714295\pi\)
\(132\) 0 0
\(133\) 1.04752 + 0.533739i 0.0908317 + 0.0462811i
\(134\) 0 0
\(135\) −11.5875 + 0.854494i −0.997292 + 0.0735431i
\(136\) 0 0
\(137\) −13.6830 + 2.16717i −1.16902 + 0.185154i −0.710609 0.703587i \(-0.751580\pi\)
−0.458409 + 0.888741i \(0.651580\pi\)
\(138\) 0 0
\(139\) −6.20281 8.53743i −0.526115 0.724136i 0.460417 0.887703i \(-0.347700\pi\)
−0.986532 + 0.163567i \(0.947700\pi\)
\(140\) 0 0
\(141\) −5.21008 1.66556i −0.438768 0.140265i
\(142\) 0 0
\(143\) −5.67966 5.67966i −0.474957 0.474957i
\(144\) 0 0
\(145\) 2.33490 + 3.97947i 0.193903 + 0.330477i
\(146\) 0 0
\(147\) 8.46552 + 8.38554i 0.698225 + 0.691628i
\(148\) 0 0
\(149\) −3.21507 −0.263389 −0.131695 0.991290i \(-0.542042\pi\)
−0.131695 + 0.991290i \(0.542042\pi\)
\(150\) 0 0
\(151\) 13.2319 1.07680 0.538400 0.842689i \(-0.319029\pi\)
0.538400 + 0.842689i \(0.319029\pi\)
\(152\) 0 0
\(153\) −9.91793 + 19.9305i −0.801817 + 1.61129i
\(154\) 0 0
\(155\) −14.0437 6.13507i −1.12802 0.492781i
\(156\) 0 0
\(157\) −6.70136 6.70136i −0.534827 0.534827i 0.387178 0.922005i \(-0.373450\pi\)
−0.922005 + 0.387178i \(0.873450\pi\)
\(158\) 0 0
\(159\) −0.125910 + 0.393862i −0.00998531 + 0.0312353i
\(160\) 0 0
\(161\) −0.332707 0.457932i −0.0262210 0.0360901i
\(162\) 0 0
\(163\) 9.95274 1.57636i 0.779559 0.123470i 0.246042 0.969259i \(-0.420870\pi\)
0.533517 + 0.845789i \(0.320870\pi\)
\(164\) 0 0
\(165\) 4.46224 3.70115i 0.347385 0.288134i
\(166\) 0 0
\(167\) −9.23014 4.70299i −0.714249 0.363928i 0.0588037 0.998270i \(-0.481271\pi\)
−0.773053 + 0.634341i \(0.781271\pi\)
\(168\) 0 0
\(169\) 15.0206 4.88050i 1.15543 0.375423i
\(170\) 0 0
\(171\) 3.23125 + 9.63266i 0.247100 + 0.736628i
\(172\) 0 0
\(173\) 21.4566 + 3.39839i 1.63132 + 0.258375i 0.903875 0.427796i \(-0.140710\pi\)
0.727440 + 0.686171i \(0.240710\pi\)
\(174\) 0 0
\(175\) −1.07329 + 1.36407i −0.0811329 + 0.103114i
\(176\) 0 0
\(177\) −5.44722 + 0.889279i −0.409438 + 0.0668423i
\(178\) 0 0
\(179\) −5.69521 + 17.5280i −0.425680 + 1.31011i 0.476662 + 0.879087i \(0.341847\pi\)
−0.902342 + 0.431021i \(0.858153\pi\)
\(180\) 0 0
\(181\) −0.883167 2.71811i −0.0656453 0.202035i 0.912854 0.408287i \(-0.133874\pi\)
−0.978499 + 0.206251i \(0.933874\pi\)
\(182\) 0 0
\(183\) −1.10704 + 7.21094i −0.0818349 + 0.533048i
\(184\) 0 0
\(185\) −14.3198 9.15733i −1.05282 0.673260i
\(186\) 0 0
\(187\) −1.73765 10.9711i −0.127069 0.802285i
\(188\) 0 0
\(189\) −0.0256840 1.80360i −0.00186823 0.131193i
\(190\) 0 0
\(191\) −9.19912 + 12.6615i −0.665625 + 0.916154i −0.999651 0.0264098i \(-0.991593\pi\)
0.334026 + 0.942564i \(0.391593\pi\)
\(192\) 0 0
\(193\) 7.21036 7.21036i 0.519013 0.519013i −0.398260 0.917273i \(-0.630386\pi\)
0.917273 + 0.398260i \(0.130386\pi\)
\(194\) 0 0
\(195\) 4.55957 + 20.2760i 0.326518 + 1.45199i
\(196\) 0 0
\(197\) −6.50774 12.7722i −0.463657 0.909979i −0.997908 0.0646527i \(-0.979406\pi\)
0.534250 0.845326i \(-0.320594\pi\)
\(198\) 0 0
\(199\) 9.24251i 0.655184i 0.944819 + 0.327592i \(0.106237\pi\)
−0.944819 + 0.327592i \(0.893763\pi\)
\(200\) 0 0
\(201\) −6.84079 20.7187i −0.482512 1.46138i
\(202\) 0 0
\(203\) −0.638212 + 0.325185i −0.0447937 + 0.0228235i
\(204\) 0 0
\(205\) −2.04205 9.28647i −0.142623 0.648596i
\(206\) 0 0
\(207\) 0.719335 4.83854i 0.0499972 0.336302i
\(208\) 0 0
\(209\) −4.10135 2.97980i −0.283696 0.206117i
\(210\) 0 0
\(211\) −8.57544 + 6.23042i −0.590358 + 0.428920i −0.842443 0.538785i \(-0.818884\pi\)
0.252085 + 0.967705i \(0.418884\pi\)
\(212\) 0 0
\(213\) −24.2903 + 12.5221i −1.66434 + 0.858001i
\(214\) 0 0
\(215\) −0.569984 9.58923i −0.0388726 0.653980i
\(216\) 0 0
\(217\) 1.08012 2.11986i 0.0733237 0.143906i
\(218\) 0 0
\(219\) −13.2462 18.0510i −0.895096 1.21978i
\(220\) 0 0
\(221\) 37.8700 + 12.3047i 2.54741 + 0.827704i
\(222\) 0 0
\(223\) 0.952406 6.01326i 0.0637778 0.402677i −0.935060 0.354488i \(-0.884655\pi\)
0.998838 0.0481890i \(-0.0153450\pi\)
\(224\) 0 0
\(225\) −14.8768 + 1.91823i −0.991789 + 0.127882i
\(226\) 0 0
\(227\) −0.651345 + 4.11243i −0.0432313 + 0.272952i −0.999830 0.0184580i \(-0.994124\pi\)
0.956598 + 0.291410i \(0.0941243\pi\)
\(228\) 0 0
\(229\) 18.6691 + 6.06597i 1.23369 + 0.400851i 0.852051 0.523460i \(-0.175359\pi\)
0.381642 + 0.924310i \(0.375359\pi\)
\(230\) 0 0
\(231\) 0.532469 + 0.725613i 0.0350339 + 0.0477418i
\(232\) 0 0
\(233\) 6.67158 13.0937i 0.437070 0.857797i −0.562451 0.826831i \(-0.690141\pi\)
0.999520 0.0309667i \(-0.00985859\pi\)
\(234\) 0 0
\(235\) −6.83354 1.77979i −0.445771 0.116101i
\(236\) 0 0
\(237\) 16.0977 8.29867i 1.04566 0.539057i
\(238\) 0 0
\(239\) 5.39910 3.92267i 0.349239 0.253737i −0.399311 0.916816i \(-0.630751\pi\)
0.748550 + 0.663079i \(0.230751\pi\)
\(240\) 0 0
\(241\) −19.2337 13.9741i −1.23895 0.900153i −0.241426 0.970419i \(-0.577615\pi\)
−0.997528 + 0.0702665i \(0.977615\pi\)
\(242\) 0 0
\(243\) 10.7580 11.2812i 0.690128 0.723687i
\(244\) 0 0
\(245\) 11.5037 + 10.2129i 0.734944 + 0.652475i
\(246\) 0 0
\(247\) 16.1923 8.25039i 1.03029 0.524960i
\(248\) 0 0
\(249\) 7.91567 + 23.9741i 0.501635 + 1.51930i
\(250\) 0 0
\(251\) 26.5783i 1.67761i −0.544435 0.838803i \(-0.683256\pi\)
0.544435 0.838803i \(-0.316744\pi\)
\(252\) 0 0
\(253\) 1.10809 + 2.17475i 0.0696652 + 0.136726i
\(254\) 0 0
\(255\) −11.3801 + 26.3909i −0.712650 + 1.65266i
\(256\) 0 0
\(257\) 10.0358 10.0358i 0.626014 0.626014i −0.321049 0.947063i \(-0.604035\pi\)
0.947063 + 0.321049i \(0.104035\pi\)
\(258\) 0 0
\(259\) 1.55103 2.13481i 0.0963765 0.132651i
\(260\) 0 0
\(261\) −5.90510 1.85690i −0.365516 0.114939i
\(262\) 0 0
\(263\) 3.61785 + 22.8422i 0.223086 + 1.40851i 0.804040 + 0.594575i \(0.202680\pi\)
−0.580954 + 0.813937i \(0.697320\pi\)
\(264\) 0 0
\(265\) −0.134546 + 0.516590i −0.00826508 + 0.0317339i
\(266\) 0 0
\(267\) 3.32124 21.6336i 0.203257 1.32395i
\(268\) 0 0
\(269\) 2.60045 + 8.00336i 0.158552 + 0.487974i 0.998503 0.0546882i \(-0.0174165\pi\)
−0.839951 + 0.542662i \(0.817416\pi\)
\(270\) 0 0
\(271\) −7.11567 + 21.8998i −0.432246 + 1.33032i 0.463636 + 0.886026i \(0.346544\pi\)
−0.895882 + 0.444291i \(0.853456\pi\)
\(272\) 0 0
\(273\) −3.18420 + 0.519832i −0.192716 + 0.0314617i
\(274\) 0 0
\(275\) 5.49126 5.08555i 0.331135 0.306670i
\(276\) 0 0
\(277\) −11.0819 1.75520i −0.665845 0.105459i −0.185643 0.982617i \(-0.559437\pi\)
−0.480202 + 0.877158i \(0.659437\pi\)
\(278\) 0 0
\(279\) 19.4935 6.53906i 1.16705 0.391483i
\(280\) 0 0
\(281\) 14.6137 4.74827i 0.871778 0.283258i 0.161239 0.986915i \(-0.448451\pi\)
0.710539 + 0.703658i \(0.248451\pi\)
\(282\) 0 0
\(283\) 7.57810 + 3.86124i 0.450471 + 0.229527i 0.664481 0.747305i \(-0.268652\pi\)
−0.214010 + 0.976831i \(0.568652\pi\)
\(284\) 0 0
\(285\) 4.84425 + 12.1894i 0.286949 + 0.722038i
\(286\) 0 0
\(287\) 1.45795 0.230917i 0.0860600 0.0136306i
\(288\) 0 0
\(289\) 22.3744 + 30.7958i 1.31614 + 1.81152i
\(290\) 0 0
\(291\) −1.61686 + 5.05774i −0.0947820 + 0.296490i
\(292\) 0 0
\(293\) 3.65414 + 3.65414i 0.213477 + 0.213477i 0.805743 0.592266i \(-0.201766\pi\)
−0.592266 + 0.805743i \(0.701766\pi\)
\(294\) 0 0
\(295\) −6.95917 + 1.53028i −0.405178 + 0.0890966i
\(296\) 0 0
\(297\) −1.10724 + 7.69884i −0.0642488 + 0.446732i
\(298\) 0 0
\(299\) −8.74960 −0.506003
\(300\) 0 0
\(301\) 1.49131 0.0859575
\(302\) 0 0
\(303\) −2.66093 2.63579i −0.152867 0.151422i
\(304\) 0 0
\(305\) −0.918798 + 9.37342i −0.0526102 + 0.536721i
\(306\) 0 0
\(307\) 1.46729 + 1.46729i 0.0837427 + 0.0837427i 0.747737 0.663995i \(-0.231140\pi\)
−0.663995 + 0.747737i \(0.731140\pi\)
\(308\) 0 0
\(309\) 23.3337 + 7.45931i 1.32741 + 0.424345i
\(310\) 0 0
\(311\) 13.3661 + 18.3969i 0.757922 + 1.04319i 0.997384 + 0.0722845i \(0.0230290\pi\)
−0.239462 + 0.970906i \(0.576971\pi\)
\(312\) 0 0
\(313\) 22.0952 3.49953i 1.24889 0.197805i 0.503245 0.864144i \(-0.332139\pi\)
0.745649 + 0.666339i \(0.232139\pi\)
\(314\) 0 0
\(315\) −0.160233 2.32316i −0.00902811 0.130895i
\(316\) 0 0
\(317\) −2.91256 1.48402i −0.163586 0.0833510i 0.370281 0.928920i \(-0.379261\pi\)
−0.533866 + 0.845569i \(0.679261\pi\)
\(318\) 0 0
\(319\) 2.93749 0.954449i 0.164468 0.0534389i
\(320\) 0 0
\(321\) −0.0189883 4.00049i −0.00105983 0.223285i
\(322\) 0 0
\(323\) 24.8222 + 3.93145i 1.38114 + 0.218752i
\(324\) 0 0
\(325\) 7.30673 + 25.8157i 0.405305 + 1.43200i
\(326\) 0 0
\(327\) −1.20046 7.35335i −0.0663857 0.406641i
\(328\) 0 0
\(329\) 0.338764 1.04261i 0.0186767 0.0574809i
\(330\) 0 0
\(331\) −5.16968 15.9106i −0.284151 0.874527i −0.986652 0.162844i \(-0.947933\pi\)
0.702501 0.711683i \(-0.252067\pi\)
\(332\) 0 0
\(333\) 22.4889 3.78107i 1.23238 0.207201i
\(334\) 0 0
\(335\) −10.2786 26.2256i −0.561579 1.43286i
\(336\) 0 0
\(337\) −3.12579 19.7355i −0.170273 1.07506i −0.913744 0.406291i \(-0.866822\pi\)
0.743471 0.668768i \(-0.233178\pi\)
\(338\) 0 0
\(339\) −6.25257 4.49757i −0.339593 0.244275i
\(340\) 0 0
\(341\) −6.03020 + 8.29986i −0.326554 + 0.449463i
\(342\) 0 0
\(343\) −3.40692 + 3.40692i −0.183956 + 0.183956i
\(344\) 0 0
\(345\) 0.586233 6.28791i 0.0315617 0.338530i
\(346\) 0 0
\(347\) −0.905384 1.77692i −0.0486036 0.0953899i 0.865427 0.501035i \(-0.167047\pi\)
−0.914031 + 0.405645i \(0.867047\pi\)
\(348\) 0 0
\(349\) 19.7345i 1.05636i −0.849132 0.528181i \(-0.822874\pi\)
0.849132 0.528181i \(-0.177126\pi\)
\(350\) 0 0
\(351\) −22.7884 16.0660i −1.21635 0.857540i
\(352\) 0 0
\(353\) −11.2294 + 5.72168i −0.597682 + 0.304534i −0.726535 0.687129i \(-0.758871\pi\)
0.128853 + 0.991664i \(0.458871\pi\)
\(354\) 0 0
\(355\) −30.4293 + 17.8539i −1.61502 + 0.947588i
\(356\) 0 0
\(357\) −3.98501 2.00669i −0.210909 0.106205i
\(358\) 0 0
\(359\) −14.9247 10.8434i −0.787695 0.572294i 0.119583 0.992824i \(-0.461844\pi\)
−0.907279 + 0.420530i \(0.861844\pi\)
\(360\) 0 0
\(361\) −6.09198 + 4.42609i −0.320631 + 0.232952i
\(362\) 0 0
\(363\) 6.95185 + 13.4852i 0.364877 + 0.707787i
\(364\) 0 0
\(365\) −18.3476 22.3354i −0.960356 1.16909i
\(366\) 0 0
\(367\) 13.9237 27.3269i 0.726814 1.42645i −0.170636 0.985334i \(-0.554582\pi\)
0.897449 0.441118i \(-0.145418\pi\)
\(368\) 0 0
\(369\) 10.3912 + 7.39994i 0.540942 + 0.385225i
\(370\) 0 0
\(371\) −0.0788174 0.0256093i −0.00409200 0.00132957i
\(372\) 0 0
\(373\) −1.64265 + 10.3713i −0.0850532 + 0.537005i 0.907965 + 0.419046i \(0.137635\pi\)
−0.993018 + 0.117959i \(0.962365\pi\)
\(374\) 0 0
\(375\) −19.0421 + 3.52131i −0.983328 + 0.181840i
\(376\) 0 0
\(377\) −1.73206 + 10.9358i −0.0892055 + 0.563221i
\(378\) 0 0
\(379\) −18.0985 5.88056i −0.929657 0.302064i −0.195235 0.980757i \(-0.562547\pi\)
−0.734423 + 0.678693i \(0.762547\pi\)
\(380\) 0 0
\(381\) −13.3002 + 9.75992i −0.681388 + 0.500016i
\(382\) 0 0
\(383\) −2.02976 + 3.98364i −0.103716 + 0.203554i −0.937033 0.349242i \(-0.886439\pi\)
0.833317 + 0.552796i \(0.186439\pi\)
\(384\) 0 0
\(385\) 0.737533 + 0.897834i 0.0375882 + 0.0457579i
\(386\) 0 0
\(387\) 9.19929 + 9.02628i 0.467626 + 0.458831i
\(388\) 0 0
\(389\) −6.59921 + 4.79461i −0.334593 + 0.243096i −0.742377 0.669982i \(-0.766302\pi\)
0.407784 + 0.913079i \(0.366302\pi\)
\(390\) 0 0
\(391\) −9.78900 7.11213i −0.495051 0.359676i
\(392\) 0 0
\(393\) 14.8825 29.5546i 0.750724 1.49083i
\(394\) 0 0
\(395\) 20.1661 11.8322i 1.01467 0.595342i
\(396\) 0 0
\(397\) −27.6243 + 14.0753i −1.38642 + 0.706418i −0.978432 0.206568i \(-0.933771\pi\)
−0.407991 + 0.912986i \(0.633771\pi\)
\(398\) 0 0
\(399\) −1.93363 + 0.638438i −0.0968028 + 0.0319619i
\(400\) 0 0
\(401\) 30.3238i 1.51430i −0.653241 0.757150i \(-0.726591\pi\)
0.653241 0.757150i \(-0.273409\pi\)
\(402\) 0 0
\(403\) −16.6963 32.7683i −0.831700 1.63230i
\(404\) 0 0
\(405\) 13.0727 15.3005i 0.649588 0.760287i
\(406\) 0 0
\(407\) −8.04588 + 8.04588i −0.398819 + 0.398819i
\(408\) 0 0
\(409\) −23.2791 + 32.0409i −1.15108 + 1.58432i −0.411250 + 0.911523i \(0.634908\pi\)
−0.739826 + 0.672798i \(0.765092\pi\)
\(410\) 0 0
\(411\) 14.0117 19.4791i 0.691144 0.960835i
\(412\) 0 0
\(413\) −0.173046 1.09257i −0.00851503 0.0537618i
\(414\) 0 0
\(415\) 11.8936 + 30.3464i 0.583836 + 1.48965i
\(416\) 0 0
\(417\) 18.0664 + 2.77360i 0.884716 + 0.135824i
\(418\) 0 0
\(419\) 5.71751 + 17.5967i 0.279319 + 0.859655i 0.988044 + 0.154171i \(0.0492705\pi\)
−0.708725 + 0.705484i \(0.750729\pi\)
\(420\) 0 0
\(421\) −6.75964 + 20.8040i −0.329445 + 1.01393i 0.639949 + 0.768417i \(0.278955\pi\)
−0.969394 + 0.245510i \(0.921045\pi\)
\(422\) 0 0
\(423\) 8.40020 4.38105i 0.408432 0.213014i
\(424\) 0 0
\(425\) −12.8096 + 34.8218i −0.621358 + 1.68910i
\(426\) 0 0
\(427\) −1.44415 0.228731i −0.0698873 0.0110691i
\(428\) 0 0
\(429\) 13.9121 0.0660339i 0.671683 0.00318815i
\(430\) 0 0
\(431\) −25.6284 + 8.32716i −1.23447 + 0.401105i −0.852333 0.522999i \(-0.824813\pi\)
−0.382141 + 0.924104i \(0.624813\pi\)
\(432\) 0 0
\(433\) 0.736984 + 0.375512i 0.0354172 + 0.0180460i 0.471609 0.881808i \(-0.343673\pi\)
−0.436192 + 0.899854i \(0.643673\pi\)
\(434\) 0 0
\(435\) −7.74296 1.97745i −0.371246 0.0948116i
\(436\) 0 0
\(437\) −5.45431 + 0.863878i −0.260915 + 0.0413249i
\(438\) 0 0
\(439\) 11.6409 + 16.0224i 0.555591 + 0.764705i 0.990758 0.135645i \(-0.0433105\pi\)
−0.435167 + 0.900350i \(0.643311\pi\)
\(440\) 0 0
\(441\) −20.6376 + 0.195917i −0.982741 + 0.00932938i
\(442\) 0 0
\(443\) −26.4453 26.4453i −1.25645 1.25645i −0.952775 0.303677i \(-0.901786\pi\)
−0.303677 0.952775i \(-0.598214\pi\)
\(444\) 0 0
\(445\) 2.75649 28.1213i 0.130670 1.33308i
\(446\) 0 0
\(447\) 3.91891 3.95629i 0.185358 0.187126i
\(448\) 0 0
\(449\) −18.7481 −0.884779 −0.442390 0.896823i \(-0.645869\pi\)
−0.442390 + 0.896823i \(0.645869\pi\)
\(450\) 0 0
\(451\) −6.36515 −0.299723
\(452\) 0 0
\(453\) −16.1286 + 16.2825i −0.757790 + 0.765018i
\(454\) 0 0
\(455\) −4.06801 + 0.894533i −0.190711 + 0.0419364i
\(456\) 0 0
\(457\) 0.650828 + 0.650828i 0.0304444 + 0.0304444i 0.722165 0.691721i \(-0.243147\pi\)
−0.691721 + 0.722165i \(0.743147\pi\)
\(458\) 0 0
\(459\) −12.4362 36.4981i −0.580474 1.70359i
\(460\) 0 0
\(461\) −12.6563 17.4199i −0.589464 0.811328i 0.405229 0.914215i \(-0.367192\pi\)
−0.994693 + 0.102888i \(0.967192\pi\)
\(462\) 0 0
\(463\) 27.7819 4.40022i 1.29113 0.204495i 0.527172 0.849758i \(-0.323252\pi\)
0.763961 + 0.645263i \(0.223252\pi\)
\(464\) 0 0
\(465\) 24.6676 9.80328i 1.14393 0.454616i
\(466\) 0 0
\(467\) 26.7269 + 13.6180i 1.23677 + 0.630168i 0.945235 0.326391i \(-0.105833\pi\)
0.291539 + 0.956559i \(0.405833\pi\)
\(468\) 0 0
\(469\) 4.15890 1.35131i 0.192040 0.0623977i
\(470\) 0 0
\(471\) 16.4147 0.0779126i 0.756351 0.00359002i
\(472\) 0 0
\(473\) −6.35146 1.00597i −0.292040 0.0462546i
\(474\) 0 0
\(475\) 7.10373 + 15.3715i 0.325942 + 0.705295i
\(476\) 0 0
\(477\) −0.331191 0.635023i −0.0151642 0.0290757i
\(478\) 0 0
\(479\) −8.94946 + 27.5436i −0.408911 + 1.25850i 0.508673 + 0.860960i \(0.330136\pi\)
−0.917585 + 0.397540i \(0.869864\pi\)
\(480\) 0 0
\(481\) −12.6046 38.7931i −0.574722 1.76881i
\(482\) 0 0
\(483\) 0.969048 + 0.148771i 0.0440932 + 0.00676930i
\(484\) 0 0
\(485\) −1.72775 + 6.63374i −0.0784533 + 0.301223i
\(486\) 0 0
\(487\) 2.59886 + 16.4086i 0.117766 + 0.743544i 0.973931 + 0.226842i \(0.0728402\pi\)
−0.856166 + 0.516701i \(0.827160\pi\)
\(488\) 0 0
\(489\) −10.1918 + 14.1687i −0.460889 + 0.640732i
\(490\) 0 0
\(491\) −20.7228 + 28.5225i −0.935207 + 1.28720i 0.0225861 + 0.999745i \(0.492810\pi\)
−0.957793 + 0.287457i \(0.907190\pi\)
\(492\) 0 0
\(493\) −10.8270 + 10.8270i −0.487622 + 0.487622i
\(494\) 0 0
\(495\) −0.884671 + 10.0024i −0.0397630 + 0.449573i
\(496\) 0 0
\(497\) −2.48655 4.88013i −0.111537 0.218904i
\(498\) 0 0
\(499\) 3.09564i 0.138580i −0.997597 0.0692900i \(-0.977927\pi\)
0.997597 0.0692900i \(-0.0220734\pi\)
\(500\) 0 0
\(501\) 17.0380 5.62553i 0.761202 0.251330i
\(502\) 0 0
\(503\) 4.58961 2.33852i 0.204641 0.104270i −0.348667 0.937247i \(-0.613366\pi\)
0.553307 + 0.832977i \(0.313366\pi\)
\(504\) 0 0
\(505\) −3.61591 3.21016i −0.160906 0.142850i
\(506\) 0 0
\(507\) −12.3032 + 24.4325i −0.546406 + 1.08508i
\(508\) 0 0
\(509\) 22.3242 + 16.2195i 0.989502 + 0.718915i 0.959812 0.280644i \(-0.0905481\pi\)
0.0296898 + 0.999559i \(0.490548\pi\)
\(510\) 0 0
\(511\) 3.63036 2.63761i 0.160598 0.116681i
\(512\) 0 0
\(513\) −15.7920 7.76522i −0.697236 0.342843i
\(514\) 0 0
\(515\) 30.6044 + 7.97091i 1.34859 + 0.351240i
\(516\) 0 0
\(517\) −2.14609 + 4.21194i −0.0943850 + 0.185241i
\(518\) 0 0
\(519\) −30.3357 + 22.2609i −1.33159 + 0.977147i
\(520\) 0 0
\(521\) 12.0428 + 3.91295i 0.527606 + 0.171430i 0.560694 0.828023i \(-0.310534\pi\)
−0.0330883 + 0.999452i \(0.510534\pi\)
\(522\) 0 0
\(523\) −3.21583 + 20.3040i −0.140619 + 0.887831i 0.811999 + 0.583659i \(0.198380\pi\)
−0.952617 + 0.304172i \(0.901620\pi\)
\(524\) 0 0
\(525\) −0.370297 2.98342i −0.0161611 0.130207i
\(526\) 0 0
\(527\) 7.95605 50.2325i 0.346571 2.18816i
\(528\) 0 0
\(529\) −19.3457 6.28579i −0.841116 0.273295i
\(530\) 0 0
\(531\) 5.54542 7.78701i 0.240651 0.337927i
\(532\) 0 0
\(533\) 10.3589 20.3305i 0.448695 0.880613i
\(534\) 0 0
\(535\) −0.306447 5.15557i −0.0132489 0.222895i
\(536\) 0 0
\(537\) −14.6270 28.3735i −0.631204 1.22440i
\(538\) 0 0
\(539\) 8.33112 6.05291i 0.358847 0.260717i
\(540\) 0 0
\(541\) 23.2522 + 16.8937i 0.999689 + 0.726317i 0.962022 0.272974i \(-0.0880072\pi\)
0.0376677 + 0.999290i \(0.488007\pi\)
\(542\) 0 0
\(543\) 4.42126 + 2.22638i 0.189735 + 0.0955429i
\(544\) 0 0
\(545\) −2.06577 9.39436i −0.0884879 0.402410i
\(546\) 0 0
\(547\) −22.4858 + 11.4571i −0.961424 + 0.489870i −0.862961 0.505271i \(-0.831393\pi\)
−0.0984630 + 0.995141i \(0.531393\pi\)
\(548\) 0 0
\(549\) −7.52399 10.1518i −0.321116 0.433268i
\(550\) 0 0
\(551\) 6.98813i 0.297705i
\(552\) 0 0
\(553\) 1.64789 + 3.23417i 0.0700755 + 0.137531i
\(554\) 0 0
\(555\) 28.7232 6.45916i 1.21923 0.274176i
\(556\) 0 0
\(557\) −26.1957 + 26.1957i −1.10995 + 1.10995i −0.116791 + 0.993157i \(0.537261\pi\)
−0.993157 + 0.116791i \(0.962739\pi\)
\(558\) 0 0
\(559\) 13.5497 18.6496i 0.573093 0.788795i
\(560\) 0 0
\(561\) 15.6184 + 11.2346i 0.659411 + 0.474325i
\(562\) 0 0
\(563\) −0.227603 1.43703i −0.00959232 0.0605636i 0.982428 0.186643i \(-0.0597607\pi\)
−0.992020 + 0.126079i \(0.959761\pi\)
\(564\) 0 0
\(565\) −8.37701 5.35698i −0.352423 0.225370i
\(566\) 0 0
\(567\) 2.25072 + 2.16684i 0.0945213 + 0.0909986i
\(568\) 0 0
\(569\) −7.83577 24.1160i −0.328493 1.01100i −0.969839 0.243745i \(-0.921624\pi\)
0.641347 0.767251i \(-0.278376\pi\)
\(570\) 0 0
\(571\) −3.23704 + 9.96258i −0.135466 + 0.416921i −0.995662 0.0930420i \(-0.970341\pi\)
0.860196 + 0.509963i \(0.170341\pi\)
\(572\) 0 0
\(573\) −4.36757 26.7532i −0.182458 1.11763i
\(574\) 0 0
\(575\) 0.312499 8.14687i 0.0130321 0.339748i
\(576\) 0 0
\(577\) −12.5173 1.98255i −0.521102 0.0825345i −0.109658 0.993969i \(-0.534976\pi\)
−0.411444 + 0.911435i \(0.634976\pi\)
\(578\) 0 0
\(579\) 0.0838305 + 17.6615i 0.00348388 + 0.733987i
\(580\) 0 0
\(581\) −4.81239 + 1.56364i −0.199651 + 0.0648707i
\(582\) 0 0
\(583\) 0.318407 + 0.162237i 0.0131871 + 0.00671915i
\(584\) 0 0
\(585\) −30.5082 19.1040i −1.26136 0.789852i
\(586\) 0 0
\(587\) 27.7688 4.39815i 1.14614 0.181531i 0.445661 0.895202i \(-0.352969\pi\)
0.700481 + 0.713671i \(0.252969\pi\)
\(588\) 0 0
\(589\) −13.6434 18.7785i −0.562167 0.773756i
\(590\) 0 0
\(591\) 23.6491 + 7.56015i 0.972795 + 0.310983i
\(592\) 0 0
\(593\) 16.3288 + 16.3288i 0.670545 + 0.670545i 0.957842 0.287297i \(-0.0927567\pi\)
−0.287297 + 0.957842i \(0.592757\pi\)
\(594\) 0 0
\(595\) −5.27839 2.30589i −0.216393 0.0945322i
\(596\) 0 0
\(597\) −11.3733 11.2659i −0.465479 0.461081i
\(598\) 0 0
\(599\) 37.1895 1.51952 0.759761 0.650202i \(-0.225316\pi\)
0.759761 + 0.650202i \(0.225316\pi\)
\(600\) 0 0
\(601\) −4.85996 −0.198242 −0.0991209 0.995075i \(-0.531603\pi\)
−0.0991209 + 0.995075i \(0.531603\pi\)
\(602\) 0 0
\(603\) 33.8336 + 16.8364i 1.37781 + 0.685633i
\(604\) 0 0
\(605\) 9.91190 + 16.8933i 0.402976 + 0.686810i
\(606\) 0 0
\(607\) 17.8944 + 17.8944i 0.726313 + 0.726313i 0.969883 0.243570i \(-0.0783187\pi\)
−0.243570 + 0.969883i \(0.578319\pi\)
\(608\) 0 0
\(609\) 0.377773 1.18172i 0.0153081 0.0478858i
\(610\) 0 0
\(611\) −9.96046 13.7094i −0.402957 0.554623i
\(612\) 0 0
\(613\) −9.30092 + 1.47312i −0.375661 + 0.0594988i −0.341410 0.939914i \(-0.610904\pi\)
−0.0342506 + 0.999413i \(0.510904\pi\)
\(614\) 0 0
\(615\) 13.9165 + 8.80662i 0.561168 + 0.355117i
\(616\) 0 0
\(617\) 9.21730 + 4.69645i 0.371075 + 0.189072i 0.629576 0.776939i \(-0.283229\pi\)
−0.258501 + 0.966011i \(0.583229\pi\)
\(618\) 0 0
\(619\) −0.644785 + 0.209503i −0.0259161 + 0.00842065i −0.321946 0.946758i \(-0.604337\pi\)
0.296030 + 0.955179i \(0.404337\pi\)
\(620\) 0 0
\(621\) 5.07723 + 6.78296i 0.203742 + 0.272191i
\(622\) 0 0
\(623\) 4.33261 + 0.686218i 0.173582 + 0.0274927i
\(624\) 0 0
\(625\) −24.2983 + 5.88137i −0.971934 + 0.235255i
\(626\) 0 0
\(627\) 8.66598 1.41475i 0.346086 0.0564998i
\(628\) 0 0
\(629\) 17.4310 53.6471i 0.695020 2.13905i
\(630\) 0 0
\(631\) 7.71397 + 23.7411i 0.307088 + 0.945120i 0.978890 + 0.204389i \(0.0655207\pi\)
−0.671802 + 0.740731i \(0.734479\pi\)
\(632\) 0 0
\(633\) 2.78595 18.1468i 0.110732 0.721272i
\(634\) 0 0
\(635\) −16.4569 + 13.5187i −0.653072 + 0.536471i
\(636\) 0 0
\(637\) 5.77480 + 36.4607i 0.228806 + 1.44462i
\(638\) 0 0
\(639\) 14.1989 45.1537i 0.561699 1.78625i
\(640\) 0 0
\(641\) 10.2750 14.1423i 0.405836 0.558586i −0.556361 0.830941i \(-0.687803\pi\)
0.962197 + 0.272355i \(0.0878027\pi\)
\(642\) 0 0
\(643\) −11.1067 + 11.1067i −0.438005 + 0.438005i −0.891340 0.453335i \(-0.850234\pi\)
0.453335 + 0.891340i \(0.350234\pi\)
\(644\) 0 0
\(645\) 12.4947 + 10.9871i 0.491980 + 0.432616i
\(646\) 0 0
\(647\) 10.7527 + 21.1033i 0.422730 + 0.829655i 0.999915 + 0.0130414i \(0.00415134\pi\)
−0.577185 + 0.816614i \(0.695849\pi\)
\(648\) 0 0
\(649\) 4.76996i 0.187237i
\(650\) 0 0
\(651\) 1.29200 + 3.91308i 0.0506376 + 0.153366i
\(652\) 0 0
\(653\) −31.4248 + 16.0117i −1.22975 + 0.626587i −0.943438 0.331550i \(-0.892428\pi\)
−0.286309 + 0.958137i \(0.592428\pi\)
\(654\) 0 0
\(655\) 17.1015 39.1468i 0.668210 1.52959i
\(656\) 0 0
\(657\) 38.3586 + 5.70269i 1.49651 + 0.222483i
\(658\) 0 0
\(659\) 3.78905 + 2.75290i 0.147600 + 0.107238i 0.659135 0.752025i \(-0.270923\pi\)
−0.511534 + 0.859263i \(0.670923\pi\)
\(660\) 0 0
\(661\) 22.2635 16.1754i 0.865950 0.629149i −0.0635475 0.997979i \(-0.520241\pi\)
0.929497 + 0.368830i \(0.120241\pi\)
\(662\) 0 0
\(663\) −61.3019 + 31.6023i −2.38077 + 1.22733i
\(664\) 0 0
\(665\) −2.44759 + 0.959281i −0.0949134 + 0.0371993i
\(666\) 0 0
\(667\) 1.52746 2.99780i 0.0591433 0.116075i
\(668\) 0 0
\(669\) 6.23867 + 8.50164i 0.241201 + 0.328692i
\(670\) 0 0
\(671\) 5.99632 + 1.94832i 0.231485 + 0.0752142i
\(672\) 0 0
\(673\) −2.35183 + 14.8489i −0.0906565 + 0.572383i 0.899988 + 0.435915i \(0.143575\pi\)
−0.990644 + 0.136468i \(0.956425\pi\)
\(674\) 0 0
\(675\) 15.7732 20.6448i 0.607110 0.794618i
\(676\) 0 0
\(677\) −1.90476 + 12.0262i −0.0732060 + 0.462204i 0.923668 + 0.383194i \(0.125176\pi\)
−0.996874 + 0.0790103i \(0.974824\pi\)
\(678\) 0 0
\(679\) −1.01213 0.328860i −0.0388418 0.0126205i
\(680\) 0 0
\(681\) −4.26659 5.81423i −0.163496 0.222802i
\(682\) 0 0
\(683\) −2.44981 + 4.80802i −0.0937393 + 0.183974i −0.933115 0.359578i \(-0.882921\pi\)
0.839376 + 0.543551i \(0.182921\pi\)
\(684\) 0 0
\(685\) 16.6890 26.0976i 0.637655 0.997136i
\(686\) 0 0
\(687\) −30.2206 + 15.5793i −1.15299 + 0.594387i
\(688\) 0 0
\(689\) −1.03638 + 0.752974i −0.0394829 + 0.0286860i
\(690\) 0 0
\(691\) 16.6980 + 12.1318i 0.635223 + 0.461517i 0.858206 0.513306i \(-0.171579\pi\)
−0.222983 + 0.974822i \(0.571579\pi\)
\(692\) 0 0
\(693\) −1.54193 0.229236i −0.0585732 0.00870795i
\(694\) 0 0
\(695\) 23.4843 + 2.30197i 0.890811 + 0.0873188i
\(696\) 0 0
\(697\) 28.1152 14.3254i 1.06494 0.542614i
\(698\) 0 0
\(699\) 7.98028 + 24.1698i 0.301842 + 0.914187i
\(700\) 0 0
\(701\) 31.7969i 1.20095i −0.799643 0.600475i \(-0.794978\pi\)
0.799643 0.600475i \(-0.205022\pi\)
\(702\) 0 0
\(703\) −11.6876 22.9382i −0.440807 0.865132i
\(704\) 0 0
\(705\) 10.5196 6.23955i 0.396193 0.234995i
\(706\) 0 0
\(707\) 0.530792 0.530792i 0.0199625 0.0199625i
\(708\) 0 0
\(709\) −3.36185 + 4.62719i −0.126257 + 0.173778i −0.867466 0.497497i \(-0.834253\pi\)
0.741209 + 0.671274i \(0.234253\pi\)
\(710\) 0 0
\(711\) −9.40991 + 29.9243i −0.352899 + 1.12225i
\(712\) 0 0
\(713\) 1.74822 + 11.0379i 0.0654715 + 0.413371i
\(714\) 0 0
\(715\) 17.9290 1.06570i 0.670507 0.0398549i
\(716\) 0 0
\(717\) −1.75403 + 11.4252i −0.0655055 + 0.426684i
\(718\) 0 0
\(719\) −10.7159 32.9803i −0.399637 1.22996i −0.925291 0.379258i \(-0.876179\pi\)
0.525654 0.850699i \(-0.323821\pi\)
\(720\) 0 0
\(721\) −1.51718 + 4.66939i −0.0565027 + 0.173897i
\(722\) 0 0
\(723\) 40.6401 6.63465i 1.51142 0.246745i
\(724\) 0 0
\(725\) −10.1206 2.00332i −0.375869 0.0744015i
\(726\) 0 0
\(727\) 1.83595 + 0.290786i 0.0680916 + 0.0107847i 0.190387 0.981709i \(-0.439026\pi\)
−0.122296 + 0.992494i \(0.539026\pi\)
\(728\) 0 0
\(729\) 0.768825 + 26.9891i 0.0284750 + 0.999595i
\(730\) 0 0
\(731\) 30.3187 9.85116i 1.12138 0.364358i
\(732\) 0 0
\(733\) −35.2924 17.9824i −1.30355 0.664194i −0.342230 0.939616i \(-0.611182\pi\)
−0.961323 + 0.275423i \(0.911182\pi\)
\(734\) 0 0
\(735\) −26.5894 + 1.70716i −0.980766 + 0.0629697i
\(736\) 0 0
\(737\) −18.6242 + 2.94979i −0.686033 + 0.108657i
\(738\) 0 0
\(739\) −4.54039 6.24931i −0.167021 0.229885i 0.717300 0.696765i \(-0.245378\pi\)
−0.884321 + 0.466880i \(0.845378\pi\)
\(740\) 0 0
\(741\) −9.58462 + 29.9819i −0.352100 + 1.10141i
\(742\) 0 0
\(743\) −15.7766 15.7766i −0.578787 0.578787i 0.355782 0.934569i \(-0.384215\pi\)
−0.934569 + 0.355782i \(0.884215\pi\)
\(744\) 0 0
\(745\) 4.77289 5.37615i 0.174865 0.196967i
\(746\) 0 0
\(747\) −39.1498 19.4819i −1.43242 0.712807i
\(748\) 0 0
\(749\) 0.801789 0.0292967
\(750\) 0 0
\(751\) 21.4943 0.784340 0.392170 0.919893i \(-0.371725\pi\)
0.392170 + 0.919893i \(0.371725\pi\)
\(752\) 0 0
\(753\) 32.7058 + 32.3967i 1.19186 + 1.18060i
\(754\) 0 0
\(755\) −19.6433 + 22.1261i −0.714892 + 0.805250i
\(756\) 0 0
\(757\) 20.2676 + 20.2676i 0.736638 + 0.736638i 0.971926 0.235287i \(-0.0756031\pi\)
−0.235287 + 0.971926i \(0.575603\pi\)
\(758\) 0 0
\(759\) −4.02680 1.28729i −0.146164 0.0467257i
\(760\) 0 0
\(761\) 26.5073 + 36.4842i 0.960890 + 1.32255i 0.946517 + 0.322654i \(0.104575\pi\)
0.0143726 + 0.999897i \(0.495425\pi\)
\(762\) 0 0
\(763\) 1.47489 0.233599i 0.0533945 0.00845686i
\(764\) 0 0
\(765\) −18.6037 46.1720i −0.672618 1.66935i
\(766\) 0 0
\(767\) −15.2354 7.76285i −0.550120 0.280300i
\(768\) 0 0
\(769\) 20.9117 6.79462i 0.754095 0.245020i 0.0933528 0.995633i \(-0.470242\pi\)
0.660742 + 0.750613i \(0.270242\pi\)
\(770\) 0 0
\(771\) 0.116680 + 24.5822i 0.00420212 + 0.885307i
\(772\) 0 0
\(773\) 1.94871 + 0.308646i 0.0700904 + 0.0111012i 0.191381 0.981516i \(-0.438703\pi\)
−0.121291 + 0.992617i \(0.538703\pi\)
\(774\) 0 0
\(775\) 31.1073 14.3758i 1.11741 0.516393i
\(776\) 0 0
\(777\) 0.736401 + 4.51078i 0.0264182 + 0.161823i
\(778\) 0 0
\(779\) 4.45022 13.6964i 0.159446 0.490724i
\(780\) 0 0
\(781\) 7.29826 + 22.4617i 0.261152 + 0.803744i
\(782\) 0 0
\(783\) 9.48282 5.00308i 0.338888 0.178795i
\(784\) 0 0
\(785\) 21.1542 1.25741i 0.755027 0.0448788i
\(786\) 0 0
\(787\) −3.81634 24.0954i −0.136038 0.858909i −0.957455 0.288582i \(-0.906816\pi\)
0.821418 0.570327i \(-0.193184\pi\)
\(788\) 0 0
\(789\) −32.5182 23.3909i −1.15768 0.832737i
\(790\) 0 0
\(791\) 0.907344 1.24885i 0.0322614 0.0444041i
\(792\) 0 0
\(793\) −15.9817 + 15.9817i −0.567527 + 0.567527i
\(794\) 0 0
\(795\) −0.471687 0.795245i −0.0167290 0.0282044i
\(796\) 0 0