Properties

Label 300.2.x.a.77.9
Level $300$
Weight $2$
Character 300.77
Analytic conductor $2.396$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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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 77.9
Character \(\chi\) \(=\) 300.77
Dual form 300.2.x.a.113.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.71199 - 0.262830i) q^{3} +(1.48454 - 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(2.86184 - 0.899925i) q^{9} +O(q^{10})\) \(q+(1.71199 - 0.262830i) q^{3} +(1.48454 - 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(2.86184 - 0.899925i) q^{9} +(-0.879848 - 1.21101i) q^{11} +(-5.29990 + 0.839422i) q^{13} +(2.10202 - 3.25292i) q^{15} +(6.61182 + 3.36889i) q^{17} +(-3.22097 + 1.04656i) q^{19} +(-0.484748 - 0.355717i) q^{21} +(-1.61050 - 0.255078i) q^{23} +(-0.592307 - 4.96479i) q^{25} +(4.66293 - 2.29284i) q^{27} +(-0.637623 + 1.96240i) q^{29} +(2.11791 + 6.51825i) q^{31} +(-1.82458 - 1.84199i) q^{33} +(-0.774858 + 0.0460576i) q^{35} +(1.18914 + 7.50792i) q^{37} +(-8.85278 + 2.83006i) q^{39} +(2.49942 - 3.44015i) q^{41} +(-3.03773 + 3.03773i) q^{43} +(2.74368 - 6.12146i) q^{45} +(-1.43370 - 2.81380i) q^{47} -6.87949i q^{49} +(12.2048 + 4.02974i) q^{51} +(-0.212713 + 0.108383i) q^{53} +(-3.33118 - 0.326527i) q^{55} +(-5.23920 + 2.63826i) q^{57} +(-2.57801 - 1.87303i) q^{59} +(3.40759 - 2.47576i) q^{61} +(-0.923378 - 0.481580i) q^{63} +(-6.46424 + 10.1085i) q^{65} +(-5.71895 + 11.2241i) q^{67} +(-2.82420 - 0.0134051i) q^{69} +(-15.0056 - 4.87563i) q^{71} +(-2.02219 + 12.7676i) q^{73} +(-2.31892 - 8.34402i) q^{75} +(-0.0812876 + 0.513230i) q^{77} +(-9.94456 - 3.23118i) q^{79} +(7.38027 - 5.15088i) q^{81} +(-6.61756 + 12.9877i) q^{83} +(15.4489 - 6.05486i) q^{85} +(-0.575829 + 3.52720i) q^{87} +(10.2231 - 7.42754i) q^{89} +(1.50698 + 1.09489i) q^{91} +(5.33903 + 10.6025i) q^{93} +(-3.03162 + 6.93965i) q^{95} +(2.73153 - 1.39178i) q^{97} +(-3.60780 - 2.67391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

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
\(3\) 1.71199 0.262830i 0.988420 0.151745i
\(4\) 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
\(9\) 2.86184 0.899925i 0.953947 0.299975i
\(10\) 0 0
\(11\) −0.879848 1.21101i −0.265284 0.365132i 0.655506 0.755190i \(-0.272455\pi\)
−0.920791 + 0.390057i \(0.872455\pi\)
\(12\) 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
\(15\) 2.10202 3.25292i 0.542739 0.839901i
\(16\) 0 0
\(17\) 6.61182 + 3.36889i 1.60360 + 0.817077i 0.999801 + 0.0199422i \(0.00634822\pi\)
0.603802 + 0.797134i \(0.293652\pi\)
\(18\) 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
\(21\) −0.484748 0.355717i −0.105781 0.0776239i
\(22\) 0 0
\(23\) −1.61050 0.255078i −0.335812 0.0531874i −0.0137486 0.999905i \(-0.504376\pi\)
−0.322063 + 0.946718i \(0.604376\pi\)
\(24\) 0 0
\(25\) −0.592307 4.96479i −0.118461 0.992959i
\(26\) 0 0
\(27\) 4.66293 2.29284i 0.897381 0.441257i
\(28\) 0 0
\(29\) −0.637623 + 1.96240i −0.118404 + 0.364409i −0.992642 0.121089i \(-0.961361\pi\)
0.874238 + 0.485497i \(0.161361\pi\)
\(30\) 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
\(33\) −1.82458 1.84199i −0.317619 0.320649i
\(34\) 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
\(39\) −8.85278 + 2.83006i −1.41758 + 0.453172i
\(40\) 0 0
\(41\) 2.49942 3.44015i 0.390343 0.537261i −0.567944 0.823067i \(-0.692261\pi\)
0.958288 + 0.285806i \(0.0922612\pi\)
\(42\) 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
\(45\) 2.74368 6.12146i 0.409003 0.912533i
\(46\) 0 0
\(47\) −1.43370 2.81380i −0.209127 0.410435i 0.762488 0.647002i \(-0.223978\pi\)
−0.971615 + 0.236567i \(0.923978\pi\)
\(48\) 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 −0.468539 0.883443i \(-0.655219\pi\)
0.439320 + 0.898330i \(0.355219\pi\)
\(54\) 0 0
\(55\) −3.33118 0.326527i −0.449176 0.0440289i
\(56\) 0 0
\(57\) −5.23920 + 2.63826i −0.693950 + 0.349446i
\(58\) 0 0
\(59\) −2.57801 1.87303i −0.335628 0.243848i 0.407187 0.913345i \(-0.366510\pi\)
−0.742815 + 0.669497i \(0.766510\pi\)
\(60\) 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
\(63\) −0.923378 0.481580i −0.116335 0.0606734i
\(64\) 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
\(69\) −2.82420 0.0134051i −0.339994 0.00161379i
\(70\) 0 0
\(71\) −15.0056 4.87563i −1.78084 0.578630i −0.781847 0.623471i \(-0.785722\pi\)
−0.998994 + 0.0448405i \(0.985722\pi\)
\(72\) 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
\(75\) −2.31892 8.34402i −0.267766 0.963484i
\(76\) 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
\(81\) 7.38027 5.15088i 0.820030 0.572320i
\(82\) 0 0
\(83\) −6.61756 + 12.9877i −0.726372 + 1.42559i 0.171434 + 0.985196i \(0.445160\pi\)
−0.897807 + 0.440390i \(0.854840\pi\)
\(84\) 0 0
\(85\) 15.4489 6.05486i 1.67566 0.656741i
\(86\) 0 0
\(87\) −0.575829 + 3.52720i −0.0617354 + 0.378156i
\(88\) 0 0
\(89\) 10.2231 7.42754i 1.08365 0.787318i 0.105335 0.994437i \(-0.466409\pi\)
0.978316 + 0.207119i \(0.0664086\pi\)
\(90\) 0 0
\(91\) 1.50698 + 1.09489i 0.157975 + 0.114775i
\(92\) 0 0
\(93\) 5.33903 + 10.6025i 0.553632 + 1.09943i
\(94\) 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 \(-0.965689\pi\)
0.994196 0.107584i \(-0.0343113\pi\)
\(102\) 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
\(105\) −1.31445 + 0.282506i −0.128277 + 0.0275697i
\(106\) 0 0
\(107\) 1.63321 1.63321i 0.157888 0.157888i −0.623742 0.781630i \(-0.714388\pi\)
0.781630 + 0.623742i \(0.214388\pi\)
\(108\) 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
\(111\) 4.00910 + 12.5410i 0.380527 + 1.19034i
\(112\) 0 0
\(113\) −0.695637 4.39208i −0.0654401 0.413172i −0.998562 0.0536118i \(-0.982927\pi\)
0.933122 0.359560i \(-0.117073\pi\)
\(114\) 0 0
\(115\) −2.81738 + 2.31436i −0.262722 + 0.215815i
\(116\) 0 0
\(117\) −14.4121 + 7.17181i −1.33240 + 0.663034i
\(118\) 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
\(123\) 3.37481 6.54643i 0.304296 0.590272i
\(124\) 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
\(129\) −4.40217 + 5.99898i −0.387590 + 0.528181i
\(130\) 0 0
\(131\) 18.1696 5.90366i 1.58748 0.515805i 0.623514 0.781812i \(-0.285705\pi\)
0.963971 + 0.266007i \(0.0857045\pi\)
\(132\) 0 0
\(133\) 1.04752 + 0.533739i 0.0908317 + 0.0462811i
\(134\) 0 0
\(135\) 3.08826 11.2010i 0.265795 0.964030i
\(136\) 0 0
\(137\) 13.6830 2.16717i 1.16902 0.185154i 0.458409 0.888741i \(-0.348420\pi\)
0.710609 + 0.703587i \(0.248420\pi\)
\(138\) 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
\(141\) −3.19404 4.44039i −0.268987 0.373948i
\(142\) 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
\(147\) −1.80813 11.7776i −0.149132 0.971404i
\(148\) 0 0
\(149\) 3.21507 0.263389 0.131695 0.991290i \(-0.457958\pi\)
0.131695 + 0.991290i \(0.457958\pi\)
\(150\) 0 0
\(151\) 13.2319 1.07680 0.538400 0.842689i \(-0.319029\pi\)
0.538400 + 0.842689i \(0.319029\pi\)
\(152\) 0 0
\(153\) 21.9537 + 3.69109i 1.77485 + 0.298407i
\(154\) 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
\(159\) −0.335677 + 0.241458i −0.0266209 + 0.0191488i
\(160\) 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
\(165\) −5.78877 + 0.316519i −0.450655 + 0.0246410i
\(166\) 0 0
\(167\) 9.23014 + 4.70299i 0.714249 + 0.363928i 0.773053 0.634341i \(-0.218729\pi\)
−0.0588037 + 0.998270i \(0.518729\pi\)
\(168\) 0 0
\(169\) 15.0206 4.88050i 1.15543 0.375423i
\(170\) 0 0
\(171\) −8.27607 + 5.89370i −0.632887 + 0.450703i
\(172\) 0 0
\(173\) −21.4566 3.39839i −1.63132 0.258375i −0.727440 0.686171i \(-0.759290\pi\)
−0.903875 + 0.427796i \(0.859290\pi\)
\(174\) 0 0
\(175\) −1.07329 + 1.36407i −0.0811329 + 0.103114i
\(176\) 0 0
\(177\) −4.90582 2.52904i −0.368744 0.190094i
\(178\) 0 0
\(179\) 5.69521 17.5280i 0.425680 1.31011i −0.476662 0.879087i \(-0.658153\pi\)
0.902342 0.431021i \(-0.141847\pi\)
\(180\) 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
\(183\) 5.18307 5.13410i 0.383143 0.379523i
\(184\) 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
\(189\) −1.70739 0.581770i −0.124194 0.0423176i
\(190\) 0 0
\(191\) 9.19912 12.6615i 0.665625 0.916154i −0.334026 0.942564i \(-0.608407\pi\)
0.999651 + 0.0264098i \(0.00840749\pi\)
\(192\) 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
\(195\) −8.40992 + 19.0047i −0.602247 + 1.36095i
\(196\) 0 0
\(197\) 6.50774 + 12.7722i 0.463657 + 0.909979i 0.997908 + 0.0646527i \(0.0205940\pi\)
−0.534250 + 0.845326i \(0.679406\pi\)
\(198\) 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
\(207\) −4.83854 + 0.719335i −0.336302 + 0.0499972i
\(208\) 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
\(213\) −26.9710 4.40311i −1.84802 0.301696i
\(214\) 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
\(219\) −0.106272 + 22.3895i −0.00718120 + 1.51294i
\(220\) 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
\(225\) −6.16303 13.6754i −0.410869 0.911695i
\(226\) 0 0
\(227\) 0.651345 4.11243i 0.0432313 0.272952i −0.956598 0.291410i \(-0.905876\pi\)
0.999830 + 0.0184580i \(0.00587571\pi\)
\(228\) 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
\(231\) −0.00427191 + 0.900010i −0.000281071 + 0.0592163i
\(232\) 0 0
\(233\) −6.67158 + 13.0937i −0.437070 + 0.857797i 0.562451 + 0.826831i \(0.309859\pi\)
−0.999520 + 0.0309667i \(0.990141\pi\)
\(234\) 0 0
\(235\) −6.83354 1.77979i −0.445771 0.116101i
\(236\) 0 0
\(237\) −17.8743 2.91804i −1.16106 0.189547i
\(238\) 0 0
\(239\) −5.39910 + 3.92267i −0.349239 + 0.253737i −0.748550 0.663079i \(-0.769249\pi\)
0.399311 + 0.916816i \(0.369249\pi\)
\(240\) 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
\(243\) 11.2812 10.7580i 0.723687 0.690128i
\(244\) 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 \(0.316744\pi\)
−0.544435 + 0.838803i \(0.683256\pi\)
\(252\) 0 0
\(253\) 1.10809 + 2.17475i 0.0696652 + 0.136726i
\(254\) 0 0
\(255\) 24.8569 14.4263i 1.55660 0.903409i
\(256\) 0 0
\(257\) −10.0358 + 10.0358i −0.626014 + 0.626014i −0.947063 0.321049i \(-0.895965\pi\)
0.321049 + 0.947063i \(0.395965\pi\)
\(258\) 0 0
\(259\) 1.55103 2.13481i 0.0963765 0.132651i
\(260\) 0 0
\(261\) −0.0587621 + 6.18989i −0.00363728 + 0.383145i
\(262\) 0 0
\(263\) −3.61785 22.8422i −0.223086 1.40851i −0.804040 0.594575i \(-0.797320\pi\)
0.580954 0.813937i \(-0.302680\pi\)
\(264\) 0 0
\(265\) −0.134546 + 0.516590i −0.00826508 + 0.0317339i
\(266\) 0 0
\(267\) 15.5498 15.4028i 0.951630 0.942639i
\(268\) 0 0
\(269\) −2.60045 8.00336i −0.158552 0.487974i 0.839951 0.542662i \(-0.182584\pi\)
−0.998503 + 0.0546882i \(0.982584\pi\)
\(270\) 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
\(273\) 2.86771 + 1.47836i 0.173562 + 0.0894744i
\(274\) 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
\(279\) 11.9270 + 16.7482i 0.714053 + 1.00269i
\(280\) 0 0
\(281\) −14.6137 + 4.74827i −0.871778 + 0.283258i −0.710539 0.703658i \(-0.751549\pi\)
−0.161239 + 0.986915i \(0.551549\pi\)
\(282\) 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
\(285\) −3.36617 + 12.6774i −0.199395 + 0.750946i
\(286\) 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
\(291\) 4.31056 3.10065i 0.252690 0.181764i
\(292\) 0 0
\(293\) −3.65414 3.65414i −0.213477 0.213477i 0.592266 0.805743i \(-0.298234\pi\)
−0.805743 + 0.592266i \(0.798234\pi\)
\(294\) 0 0
\(295\) −6.95917 + 1.53028i −0.405178 + 0.0890966i
\(296\) 0 0
\(297\) −6.87931 3.62948i −0.399178 0.210604i
\(298\) 0 0
\(299\) 8.74960 0.506003
\(300\) 0 0
\(301\) 1.49131 0.0859575
\(302\) 0 0
\(303\) −0.568343 3.70202i −0.0326505 0.212675i
\(304\) 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
\(309\) −14.3047 19.8866i −0.813767 1.13131i
\(310\) 0 0
\(311\) −13.3661 18.3969i −0.757922 1.04319i −0.997384 0.0722845i \(-0.976971\pi\)
0.239462 0.970906i \(-0.423029\pi\)
\(312\) 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
\(315\) −2.17607 + 0.829123i −0.122608 + 0.0467158i
\(316\) 0 0
\(317\) 2.91256 + 1.48402i 0.163586 + 0.0833510i 0.533866 0.845569i \(-0.320739\pi\)
−0.370281 + 0.928920i \(0.620739\pi\)
\(318\) 0 0
\(319\) 2.93749 0.954449i 0.164468 0.0534389i
\(320\) 0 0
\(321\) 2.36679 3.22530i 0.132101 0.180019i
\(322\) 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
\(327\) −3.41402 + 6.62249i −0.188796 + 0.366225i
\(328\) 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
\(333\) 10.1597 + 20.4163i 0.556747 + 1.11881i
\(334\) 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
\(339\) −2.34529 7.33638i −0.127379 0.398457i
\(340\) 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
\(345\) −4.21505 + 4.70265i −0.226931 + 0.253182i
\(346\) 0 0
\(347\) 0.905384 + 1.77692i 0.0486036 + 0.0953899i 0.914031 0.405645i \(-0.132953\pi\)
−0.865427 + 0.501035i \(0.832953\pi\)
\(348\) 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 −0.128853 0.991664i \(-0.541129\pi\)
0.726535 + 0.687129i \(0.241129\pi\)
\(354\) 0 0
\(355\) −30.4293 + 17.8539i −1.61502 + 0.947588i
\(356\) 0 0
\(357\) −2.00669 3.98501i −0.106205 0.210909i
\(358\) 0 0
\(359\) 14.9247 + 10.8434i 0.787695 + 0.572294i 0.907279 0.420530i \(-0.138156\pi\)
−0.119583 + 0.992824i \(0.538156\pi\)
\(360\) 0 0
\(361\) −6.09198 + 4.42609i −0.320631 + 0.232952i
\(362\) 0 0
\(363\) 2.44446 14.9734i 0.128301 0.785899i
\(364\) 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
\(369\) 4.05705 12.0945i 0.211202 0.629612i
\(370\) 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
\(375\) −17.3951 8.50936i −0.898281 0.439421i
\(376\) 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
\(381\) 16.4968 + 0.0783022i 0.845156 + 0.00401154i
\(382\) 0 0
\(383\) 2.02976 3.98364i 0.103716 0.203554i −0.833317 0.552796i \(-0.813561\pi\)
0.937033 + 0.349242i \(0.113561\pi\)
\(384\) 0 0
\(385\) 0.737533 + 0.897834i 0.0375882 + 0.0457579i
\(386\) 0 0
\(387\) −5.95978 + 11.4272i −0.302952 + 0.580879i
\(388\) 0 0
\(389\) 6.59921 4.79461i 0.334593 0.243096i −0.407784 0.913079i \(-0.633698\pi\)
0.742377 + 0.669982i \(0.233698\pi\)
\(390\) 0 0
\(391\) −9.78900 7.11213i −0.495051 0.359676i
\(392\) 0 0
\(393\) 29.5546 14.8825i 1.49083 0.750724i
\(394\) 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 \(0.273409\pi\)
−0.653241 + 0.757150i \(0.726591\pi\)
\(402\) 0 0
\(403\) −16.6963 32.7683i −0.831700 1.63230i
\(404\) 0 0
\(405\) 2.34312 19.9877i 0.116431 0.993199i
\(406\) 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
\(411\) 22.8556 7.30648i 1.12738 0.360402i
\(412\) 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
\(417\) −12.8631 12.9857i −0.629906 0.635915i
\(418\) 0 0
\(419\) −5.71751 17.5967i −0.279319 0.859655i −0.988044 0.154171i \(-0.950729\pi\)
0.708725 0.705484i \(-0.249271\pi\)
\(420\) 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
\(423\) −6.63524 6.76243i −0.322617 0.328801i
\(424\) 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
\(429\) 11.2163 + 8.23075i 0.541529 + 0.397384i
\(430\) 0 0
\(431\) 25.6284 8.32716i 1.23447 0.401105i 0.382141 0.924104i \(-0.375187\pi\)
0.852333 + 0.522999i \(0.175187\pi\)
\(432\) 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
\(435\) 5.04325 + 6.19914i 0.241805 + 0.297226i
\(436\) 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
\(441\) −6.19103 19.6880i −0.294811 0.937525i
\(442\) 0 0
\(443\) 26.4453 + 26.4453i 1.25645 + 1.25645i 0.952775 + 0.303677i \(0.0982142\pi\)
0.303677 + 0.952775i \(0.401786\pi\)
\(444\) 0 0
\(445\) 2.75649 28.1213i 0.130670 1.33308i
\(446\) 0 0
\(447\) 5.50418 0.845016i 0.260339 0.0399679i
\(448\) 0 0
\(449\) 18.7481 0.884779 0.442390 0.896823i \(-0.354131\pi\)
0.442390 + 0.896823i \(0.354131\pi\)
\(450\) 0 0
\(451\) −6.36515 −0.299723
\(452\) 0 0
\(453\) 22.6530 3.47774i 1.06433 0.163399i
\(454\) 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
\(459\) 38.5548 + 0.549035i 1.79958 + 0.0256268i
\(460\) 0 0
\(461\) 12.6563 + 17.4199i 0.589464 + 0.811328i 0.994693 0.102888i \(-0.0328082\pi\)
−0.405229 + 0.914215i \(0.632808\pi\)
\(462\) 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
\(465\) 25.6552 + 6.81209i 1.18973 + 0.315903i
\(466\) 0 0
\(467\) −26.7269 13.6180i −1.23677 0.630168i −0.291539 0.956559i \(-0.594167\pi\)
−0.945235 + 0.326391i \(0.894167\pi\)
\(468\) 0 0
\(469\) 4.15890 1.35131i 0.192040 0.0623977i
\(470\) 0 0
\(471\) −13.2340 9.71137i −0.609790 0.447476i
\(472\) 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
\(477\) −0.511214 + 0.501600i −0.0234069 + 0.0229667i
\(478\) 0 0
\(479\) 8.94946 27.5436i 0.408911 1.25850i −0.508673 0.860960i \(-0.669864\pi\)
0.917585 0.397540i \(-0.130136\pi\)
\(480\) 0 0
\(481\) −12.6046 38.7931i −0.574722 1.76881i
\(482\) 0 0
\(483\) 0.689950 + 0.696531i 0.0313938 + 0.0316932i
\(484\) 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
\(489\) 16.6247 5.31459i 0.751795 0.240334i
\(490\) 0 0
\(491\) 20.7228 28.5225i 0.935207 1.28720i −0.0225861 0.999745i \(-0.507190\pi\)
0.957793 0.287457i \(-0.0928100\pi\)
\(492\) 0 0
\(493\) −10.8270 + 10.8270i −0.487622 + 0.487622i
\(494\) 0 0
\(495\) −9.82715 + 2.06334i −0.441697 + 0.0927401i
\(496\) 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 −0.553307 0.832977i \(-0.686634\pi\)
0.348667 + 0.937247i \(0.386634\pi\)
\(504\) 0 0
\(505\) −3.61591 3.21016i −0.160906 0.142850i
\(506\) 0 0
\(507\) 24.4325 12.3032i 1.08508 0.546406i
\(508\) 0 0
\(509\) −22.3242 16.2195i −0.989502 0.718915i −0.0296898 0.999559i \(-0.509452\pi\)
−0.959812 + 0.280644i \(0.909452\pi\)
\(510\) 0 0
\(511\) 3.63036 2.63761i 0.160598 0.116681i
\(512\) 0 0
\(513\) −12.6195 + 12.2652i −0.557166 + 0.541521i
\(514\) 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
\(519\) −37.6268 0.178596i −1.65163 0.00783948i
\(520\) 0 0
\(521\) −12.0428 3.91295i −0.527606 0.171430i 0.0330883 0.999452i \(-0.489466\pi\)
−0.560694 + 0.828023i \(0.689466\pi\)
\(522\) 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
\(525\) −1.47894 + 2.61737i −0.0645464 + 0.114231i
\(526\) 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
\(531\) −9.06343 3.04031i −0.393319 0.131938i
\(532\) 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
\(537\) 5.14327 31.5048i 0.221948 1.35953i
\(538\) 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
\(543\) −2.22638 4.42126i −0.0955429 0.189735i
\(544\) 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
\(555\) 26.9223 + 11.9136i 1.14279 + 0.505705i
\(556\) 0 0
\(557\) 26.1957 26.1957i 1.10995 1.10995i 0.116791 0.993157i \(-0.462739\pi\)
0.993157 0.116791i \(-0.0372606\pi\)
\(558\) 0 0
\(559\) 13.5497 18.6496i 0.573093 0.788795i
\(560\) 0 0
\(561\) −5.85837 18.3257i −0.247340 0.773712i
\(562\) 0 0
\(563\) 0.227603 + 1.43703i 0.00959232 + 0.0605636i 0.992020 0.126079i \(-0.0402393\pi\)
−0.982428 + 0.186643i \(0.940239\pi\)
\(564\) 0 0
\(565\) −8.37701 5.35698i −0.352423 0.225370i
\(566\) 0 0
\(567\) −3.07595 0.547235i −0.129178 0.0229817i
\(568\) 0 0
\(569\) 7.83577 + 24.1160i 0.328493 + 1.01100i 0.969839 + 0.243745i \(0.0783761\pi\)
−0.641347 + 0.767251i \(0.721624\pi\)
\(570\) 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
\(573\) 12.4210 24.0942i 0.518895 1.00655i
\(574\) 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
\(579\) 10.4490 14.2392i 0.434245 0.591760i
\(580\) 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
\(585\) −9.40274 + 34.7462i −0.388756 + 1.43658i
\(586\) 0 0
\(587\) −27.7688 + 4.39815i −1.14614 + 0.181531i −0.700481 0.713671i \(-0.747031\pi\)
−0.445661 + 0.895202i \(0.647031\pi\)
\(588\) 0 0
\(589\) −13.6434 18.7785i −0.562167 0.773756i
\(590\) 0 0
\(591\) 14.4981 + 20.1554i 0.596373 + 0.829084i
\(592\) 0 0
\(593\) −16.3288 16.3288i −0.670545 0.670545i 0.287297 0.957842i \(-0.407243\pi\)
−0.957842 + 0.287297i \(0.907243\pi\)
\(594\) 0 0
\(595\) −5.27839 2.30589i −0.216393 0.0945322i
\(596\) 0 0
\(597\) 2.42920 + 15.8231i 0.0994207 + 0.647597i
\(598\) 0 0
\(599\) −37.1895 −1.51952 −0.759761 0.650202i \(-0.774684\pi\)
−0.759761 + 0.650202i \(0.774684\pi\)
\(600\) 0 0
\(601\) −4.85996 −0.198242 −0.0991209 0.995075i \(-0.531603\pi\)
−0.0991209 + 0.995075i \(0.531603\pi\)
\(602\) 0 0
\(603\) −6.26591 + 37.2682i −0.255168 + 1.51768i
\(604\) 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
\(609\) 1.00715 0.724456i 0.0408117 0.0293565i
\(610\) 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
\(615\) −5.93673 15.3617i −0.239392 0.619442i
\(616\) 0 0
\(617\) −9.21730 4.69645i −0.371075 0.189072i 0.258501 0.966011i \(-0.416771\pi\)
−0.629576 + 0.776939i \(0.716771\pi\)
\(618\) 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
\(621\) −8.09449 + 2.50321i −0.324821 + 0.100450i
\(622\) 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
\(627\) 7.80465 + 4.02345i 0.311688 + 0.160681i
\(628\) 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
\(633\) −13.0436 + 12.9203i −0.518435 + 0.513537i
\(634\) 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
\(639\) −47.3314 0.449328i −1.87240 0.0177751i
\(640\) 0 0
\(641\) −10.2750 + 14.1423i −0.405836 + 0.558586i −0.962197 0.272355i \(-0.912197\pi\)
0.556361 + 0.830941i \(0.312197\pi\)
\(642\) 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
\(645\) 3.49614 + 16.2669i 0.137660 + 0.640508i
\(646\) 0 0
\(647\) −10.7527 21.1033i −0.422730 0.829655i −0.999915 0.0130414i \(-0.995849\pi\)
0.577185 0.816614i \(-0.304151\pi\)
\(648\) 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 0.286309 0.958137i \(-0.407572\pi\)
0.943438 + 0.331550i \(0.107572\pi\)
\(654\) 0 0
\(655\) 17.1015 39.1468i 0.668210 1.52959i
\(656\) 0 0
\(657\) 5.70269 + 38.3586i 0.222483 + 1.49651i
\(658\) 0 0
\(659\) −3.78905 2.75290i −0.147600 0.107238i 0.511534 0.859263i \(-0.329077\pi\)
−0.659135 + 0.752025i \(0.729077\pi\)
\(660\) 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
\(663\) −68.0672 11.1122i −2.64351 0.431563i
\(664\) 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
\(669\) 0.0500518 10.5450i 0.00193511 0.407692i
\(670\) 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
\(675\) −14.1454 21.7924i −0.544455 0.838790i
\(676\) 0 0
\(677\) 1.90476 12.0262i 0.0732060 0.462204i −0.923668 0.383194i \(-0.874824\pi\)
0.996874 0.0790103i \(-0.0251760\pi\)
\(678\) 0 0
\(679\) −1.01213 0.328860i −0.0388418 0.0126205i
\(680\) 0 0
\(681\) 0.0342301 7.21165i 0.00131170 0.276351i
\(682\) 0 0
\(683\) 2.44981 4.80802i 0.0937393 0.183974i −0.839376 0.543551i \(-0.817079\pi\)
0.933115 + 0.359578i \(0.117079\pi\)
\(684\) 0 0
\(685\) 16.6890 26.0976i 0.637655 0.997136i
\(686\) 0 0
\(687\) 33.5558 + 5.47810i 1.28023 + 0.209003i
\(688\) 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
\(693\) 0.229236 + 1.54193i 0.00870795 + 0.0585732i
\(694\) 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 \(0.205022\pi\)
−0.799643 + 0.600475i \(0.794978\pi\)
\(702\) 0 0
\(703\) −11.6876 22.9382i −0.440807 0.865132i
\(704\) 0 0
\(705\) −12.1668 1.25094i −0.458227 0.0471130i
\(706\) 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
\(711\) −31.3676 0.297780i −1.17638 0.0111676i
\(712\) 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
\(717\) −8.21222 + 8.13463i −0.306691 + 0.303793i
\(718\) 0 0
\(719\) 10.7159 + 32.9803i 0.399637 + 1.22996i 0.925291 + 0.379258i \(0.123821\pi\)
−0.525654 + 0.850699i \(0.676179\pi\)
\(720\) 0 0
\(721\) −1.51718 + 4.66939i −0.0565027 + 0.173897i
\(722\) 0 0
\(723\) −36.6008 18.8684i −1.36120 0.701724i
\(724\) 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
\(729\) 16.4858 21.3827i 0.610584 0.791952i
\(730\) 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
\(735\) −22.3785 14.4608i −0.825442 0.533396i
\(736\) 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
\(741\) 25.5527 18.3804i 0.938701 0.675222i
\(742\) 0 0
\(743\) 15.7766 + 15.7766i 0.578787 + 0.578787i 0.934569 0.355782i \(-0.115785\pi\)
−0.355782 + 0.934569i \(0.615785\pi\)
\(744\) 0 0
\(745\) 4.77289 5.37615i 0.174865 0.196967i
\(746\) 0 0
\(747\) −7.25047 + 43.1241i −0.265281 + 1.57783i
\(748\) 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
\(753\) 6.98556 + 45.5018i 0.254568 + 1.65818i
\(754\) 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
\(759\) 2.46864 + 3.43192i 0.0896058 + 0.124571i
\(760\) 0 0
\(761\) −26.5073 36.4842i −0.960890 1.32255i −0.946517 0.322654i \(-0.895425\pi\)
−0.0143726 0.999897i \(-0.504575\pi\)
\(762\) 0 0
\(763\) 1.47489 0.233599i 0.0533945 0.00845686i
\(764\) 0 0
\(765\) 38.7633 31.2308i 1.40149 1.12915i
\(766\) 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
\(771\) −14.5435 + 19.8189i −0.523770 + 0.713759i
\(772\) 0 0
\(773\) −1.94871 0.308646i −0.0700904 0.0111012i 0.121291 0.992617i \(-0.461297\pi\)
−0.191381 + 0.981516i \(0.561297\pi\)
\(774\) 0 0
\(775\) 31.1073 14.3758i 1.11741 0.516393i
\(776\) 0 0
\(777\) 2.09427 4.06244i 0.0751314 0.145739i
\(778\) 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
\(783\) 1.52629 + 10.6125i 0.0545450 + 0.379260i
\(784\) 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
\(789\) −12.1974 38.1549i −0.434237 1.35835i
\(790\) 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
\(795\) −0.0945661 + 0.919761i −0.00335392 + 0.0326206i
\(796\) 0 0