Properties

Label 300.2.x.a.113.8
Level $300$
Weight $2$
Character 300.113
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 113.8
Character \(\chi\) \(=\) 300.113
Dual form 300.2.x.a.77.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.983962 + 1.42542i) q^{3} +(-2.12124 + 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(-1.06364 + 2.80512i) q^{9} +O(q^{10})\) \(q+(0.983962 + 1.42542i) q^{3} +(-2.12124 + 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(-1.06364 + 2.80512i) q^{9} +(-1.16772 + 1.60723i) q^{11} +(1.08607 + 0.172017i) q^{13} +(-3.09547 - 2.32767i) q^{15} +(-3.88627 + 1.98015i) q^{17} +(7.34866 + 2.38772i) q^{19} +(-3.39415 - 0.621890i) q^{21} +(0.596200 - 0.0944288i) q^{23} +(3.99936 - 3.00085i) q^{25} +(-5.04504 + 1.24400i) q^{27} +(-1.20411 - 3.70588i) q^{29} +(2.08371 - 6.41301i) q^{31} +(-3.43996 - 0.0830386i) q^{33} +(1.99181 - 3.98468i) q^{35} +(-1.00762 + 6.36188i) q^{37} +(0.823455 + 1.71736i) q^{39} +(4.90769 + 6.75485i) q^{41} +(2.08869 + 2.08869i) q^{43} +(0.272086 - 6.70268i) q^{45} +(1.27659 - 2.50545i) q^{47} +3.03101i q^{49} +(-6.64648 - 3.59117i) q^{51} +(9.48136 + 4.83099i) q^{53} +(1.34017 - 4.23529i) q^{55} +(3.82729 + 12.8243i) q^{57} +(11.0153 - 8.00310i) q^{59} +(-7.73999 - 5.62344i) q^{61} +(-2.45326 - 5.44999i) q^{63} +(-2.42549 + 0.403324i) q^{65} +(-5.76904 - 11.3224i) q^{67} +(0.721238 + 0.756920i) q^{69} +(-2.90043 + 0.942408i) q^{71} +(1.52706 + 9.64150i) q^{73} +(8.21269 + 2.74804i) q^{75} +(-0.619145 - 3.90913i) q^{77} +(8.77277 - 2.85044i) q^{79} +(-6.73735 - 5.96726i) q^{81} +(-1.61164 - 3.16301i) q^{83} +(6.84310 - 6.94927i) q^{85} +(4.09763 - 5.36281i) q^{87} +(-2.65779 - 1.93100i) q^{89} +(-1.77229 + 1.28765i) q^{91} +(11.1915 - 3.33999i) q^{93} +(-17.2772 + 0.133005i) q^{95} +(1.19966 + 0.611256i) q^{97} +(-3.26643 - 4.98510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 80q - 2q^{3} + 4q^{7} + 12q^{13} + 10q^{15} + 20q^{19} + 40q^{25} - 14q^{27} - 20q^{33} + 12q^{37} - 40q^{39} + 12q^{43} - 60q^{45} - 76q^{57} - 98q^{63} - 36q^{67} - 70q^{69} - 44q^{73} - 90q^{75} - 40q^{79} + 20q^{81} - 100q^{85} - 70q^{87} - 18q^{93} - 56q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\)

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
\(3\) 0.983962 + 1.42542i 0.568091 + 0.822966i
\(4\) 0 0
\(5\) −2.12124 + 0.707333i −0.948650 + 0.316329i
\(6\) 0 0
\(7\) −1.40872 + 1.40872i −0.532446 + 0.532446i −0.921300 0.388853i \(-0.872871\pi\)
0.388853 + 0.921300i \(0.372871\pi\)
\(8\) 0 0
\(9\) −1.06364 + 2.80512i −0.354546 + 0.935039i
\(10\) 0 0
\(11\) −1.16772 + 1.60723i −0.352081 + 0.484597i −0.947921 0.318506i \(-0.896819\pi\)
0.595840 + 0.803103i \(0.296819\pi\)
\(12\) 0 0
\(13\) 1.08607 + 0.172017i 0.301222 + 0.0477088i 0.305216 0.952283i \(-0.401271\pi\)
−0.00399423 + 0.999992i \(0.501271\pi\)
\(14\) 0 0
\(15\) −3.09547 2.32767i −0.799247 0.601003i
\(16\) 0 0
\(17\) −3.88627 + 1.98015i −0.942558 + 0.480257i −0.856565 0.516038i \(-0.827406\pi\)
−0.0859928 + 0.996296i \(0.527406\pi\)
\(18\) 0 0
\(19\) 7.34866 + 2.38772i 1.68590 + 0.547781i 0.986041 0.166502i \(-0.0532472\pi\)
0.699857 + 0.714283i \(0.253247\pi\)
\(20\) 0 0
\(21\) −3.39415 0.621890i −0.740663 0.135708i
\(22\) 0 0
\(23\) 0.596200 0.0944288i 0.124316 0.0196898i −0.0939663 0.995575i \(-0.529955\pi\)
0.218282 + 0.975886i \(0.429955\pi\)
\(24\) 0 0
\(25\) 3.99936 3.00085i 0.799872 0.600171i
\(26\) 0 0
\(27\) −5.04504 + 1.24400i −0.970919 + 0.239407i
\(28\) 0 0
\(29\) −1.20411 3.70588i −0.223598 0.688164i −0.998431 0.0559981i \(-0.982166\pi\)
0.774833 0.632166i \(-0.217834\pi\)
\(30\) 0 0
\(31\) 2.08371 6.41301i 0.374246 1.15181i −0.569740 0.821825i \(-0.692956\pi\)
0.943986 0.329986i \(-0.107044\pi\)
\(32\) 0 0
\(33\) −3.43996 0.0830386i −0.598821 0.0144552i
\(34\) 0 0
\(35\) 1.99181 3.98468i 0.336677 0.673533i
\(36\) 0 0
\(37\) −1.00762 + 6.36188i −0.165652 + 1.04589i 0.755063 + 0.655652i \(0.227606\pi\)
−0.920715 + 0.390235i \(0.872394\pi\)
\(38\) 0 0
\(39\) 0.823455 + 1.71736i 0.131858 + 0.274998i
\(40\) 0 0
\(41\) 4.90769 + 6.75485i 0.766452 + 1.05493i 0.996650 + 0.0817869i \(0.0260627\pi\)
−0.230198 + 0.973144i \(0.573937\pi\)
\(42\) 0 0
\(43\) 2.08869 + 2.08869i 0.318522 + 0.318522i 0.848199 0.529677i \(-0.177687\pi\)
−0.529677 + 0.848199i \(0.677687\pi\)
\(44\) 0 0
\(45\) 0.272086 6.70268i 0.0405602 0.999177i
\(46\) 0 0
\(47\) 1.27659 2.50545i 0.186210 0.365458i −0.778963 0.627070i \(-0.784254\pi\)
0.965173 + 0.261612i \(0.0842541\pi\)
\(48\) 0 0
\(49\) 3.03101i 0.433001i
\(50\) 0 0
\(51\) −6.64648 3.59117i −0.930694 0.502864i
\(52\) 0 0
\(53\) 9.48136 + 4.83099i 1.30236 + 0.663588i 0.961053 0.276362i \(-0.0891290\pi\)
0.341311 + 0.939950i \(0.389129\pi\)
\(54\) 0 0
\(55\) 1.34017 4.23529i 0.180709 0.571086i
\(56\) 0 0
\(57\) 3.82729 + 12.8243i 0.506937 + 1.69863i
\(58\) 0 0
\(59\) 11.0153 8.00310i 1.43407 1.04192i 0.444834 0.895613i \(-0.353263\pi\)
0.989240 0.146302i \(-0.0467372\pi\)
\(60\) 0 0
\(61\) −7.73999 5.62344i −0.991005 0.720007i −0.0308639 0.999524i \(-0.509826\pi\)
−0.960141 + 0.279516i \(0.909826\pi\)
\(62\) 0 0
\(63\) −2.45326 5.44999i −0.309081 0.686635i
\(64\) 0 0
\(65\) −2.42549 + 0.403324i −0.300845 + 0.0500262i
\(66\) 0 0
\(67\) −5.76904 11.3224i −0.704800 1.38325i −0.914137 0.405405i \(-0.867131\pi\)
0.209337 0.977844i \(-0.432869\pi\)
\(68\) 0 0
\(69\) 0.721238 + 0.756920i 0.0868269 + 0.0911225i
\(70\) 0 0
\(71\) −2.90043 + 0.942408i −0.344218 + 0.111843i −0.476024 0.879432i \(-0.657922\pi\)
0.131806 + 0.991276i \(0.457922\pi\)
\(72\) 0 0
\(73\) 1.52706 + 9.64150i 0.178729 + 1.12845i 0.900029 + 0.435829i \(0.143545\pi\)
−0.721300 + 0.692623i \(0.756455\pi\)
\(74\) 0 0
\(75\) 8.21269 + 2.74804i 0.948320 + 0.317316i
\(76\) 0 0
\(77\) −0.619145 3.90913i −0.0705581 0.445486i
\(78\) 0 0
\(79\) 8.77277 2.85044i 0.987013 0.320700i 0.229349 0.973344i \(-0.426340\pi\)
0.757665 + 0.652644i \(0.226340\pi\)
\(80\) 0 0
\(81\) −6.73735 5.96726i −0.748594 0.663029i
\(82\) 0 0
\(83\) −1.61164 3.16301i −0.176900 0.347186i 0.785483 0.618884i \(-0.212415\pi\)
−0.962383 + 0.271698i \(0.912415\pi\)
\(84\) 0 0
\(85\) 6.84310 6.94927i 0.742238 0.753755i
\(86\) 0 0
\(87\) 4.09763 5.36281i 0.439312 0.574953i
\(88\) 0 0
\(89\) −2.65779 1.93100i −0.281725 0.204685i 0.437944 0.899002i \(-0.355707\pi\)
−0.719670 + 0.694317i \(0.755707\pi\)
\(90\) 0 0
\(91\) −1.77229 + 1.28765i −0.185787 + 0.134982i
\(92\) 0 0
\(93\) 11.1915 3.33999i 1.16051 0.346341i
\(94\) 0 0
\(95\) −17.2772 + 0.133005i −1.77261 + 0.0136460i
\(96\) 0 0
\(97\) 1.19966 + 0.611256i 0.121807 + 0.0620636i 0.513832 0.857891i \(-0.328225\pi\)
−0.392025 + 0.919954i \(0.628225\pi\)
\(98\) 0 0
\(99\) −3.26643 4.98510i −0.328288 0.501021i
\(100\) 0 0
\(101\) 16.1183i 1.60383i −0.597435 0.801917i \(-0.703813\pi\)
0.597435 0.801917i \(-0.296187\pi\)
\(102\) 0 0
\(103\) −2.72904 + 5.35604i −0.268900 + 0.527746i −0.985487 0.169752i \(-0.945703\pi\)
0.716587 + 0.697498i \(0.245703\pi\)
\(104\) 0 0
\(105\) 7.63970 1.08161i 0.745558 0.105554i
\(106\) 0 0
\(107\) 5.18489 + 5.18489i 0.501242 + 0.501242i 0.911824 0.410582i \(-0.134674\pi\)
−0.410582 + 0.911824i \(0.634674\pi\)
\(108\) 0 0
\(109\) −2.24729 3.09313i −0.215251 0.296268i 0.687714 0.725982i \(-0.258614\pi\)
−0.902965 + 0.429714i \(0.858614\pi\)
\(110\) 0 0
\(111\) −10.0598 + 4.82356i −0.954835 + 0.457832i
\(112\) 0 0
\(113\) −2.96892 + 18.7450i −0.279292 + 1.76338i 0.305493 + 0.952194i \(0.401179\pi\)
−0.584786 + 0.811188i \(0.698821\pi\)
\(114\) 0 0
\(115\) −1.19789 + 0.622019i −0.111704 + 0.0580035i
\(116\) 0 0
\(117\) −1.63771 + 2.86359i −0.151407 + 0.264739i
\(118\) 0 0
\(119\) 2.68518 8.26415i 0.246150 0.757573i
\(120\) 0 0
\(121\) 2.17957 + 6.70804i 0.198143 + 0.609822i
\(122\) 0 0
\(123\) −4.79952 + 13.6420i −0.432758 + 1.23006i
\(124\) 0 0
\(125\) −6.36101 + 9.19443i −0.568946 + 0.822375i
\(126\) 0 0
\(127\) −1.51917 + 0.240614i −0.134805 + 0.0213510i −0.223472 0.974710i \(-0.571739\pi\)
0.0886673 + 0.996061i \(0.471739\pi\)
\(128\) 0 0
\(129\) −0.922067 + 5.03245i −0.0811835 + 0.443082i
\(130\) 0 0
\(131\) 9.46918 + 3.07672i 0.827326 + 0.268814i 0.691918 0.721976i \(-0.256766\pi\)
0.135407 + 0.990790i \(0.456766\pi\)
\(132\) 0 0
\(133\) −13.7158 + 6.98857i −1.18931 + 0.605986i
\(134\) 0 0
\(135\) 9.82185 6.20735i 0.845331 0.534243i
\(136\) 0 0
\(137\) −6.36073 1.00744i −0.543434 0.0860715i −0.121319 0.992614i \(-0.538712\pi\)
−0.422115 + 0.906542i \(0.638712\pi\)
\(138\) 0 0
\(139\) 1.21863 1.67731i 0.103363 0.142267i −0.754202 0.656642i \(-0.771976\pi\)
0.857565 + 0.514375i \(0.171976\pi\)
\(140\) 0 0
\(141\) 4.82744 0.645591i 0.406544 0.0543686i
\(142\) 0 0
\(143\) −1.54469 + 1.54469i −0.129174 + 0.129174i
\(144\) 0 0
\(145\) 5.17551 + 7.00937i 0.429803 + 0.582096i
\(146\) 0 0
\(147\) −4.32046 + 2.98240i −0.356346 + 0.245984i
\(148\) 0 0
\(149\) 6.16481 0.505041 0.252520 0.967592i \(-0.418741\pi\)
0.252520 + 0.967592i \(0.418741\pi\)
\(150\) 0 0
\(151\) −11.8069 −0.960833 −0.480417 0.877040i \(-0.659515\pi\)
−0.480417 + 0.877040i \(0.659515\pi\)
\(152\) 0 0
\(153\) −1.42097 13.0076i −0.114879 1.05160i
\(154\) 0 0
\(155\) 0.116070 + 15.0775i 0.00932298 + 1.21105i
\(156\) 0 0
\(157\) −8.22907 + 8.22907i −0.656751 + 0.656751i −0.954610 0.297859i \(-0.903728\pi\)
0.297859 + 0.954610i \(0.403728\pi\)
\(158\) 0 0
\(159\) 2.44310 + 18.2684i 0.193751 + 1.44878i
\(160\) 0 0
\(161\) −0.706855 + 0.972903i −0.0557080 + 0.0766755i
\(162\) 0 0
\(163\) 21.5564 + 3.41420i 1.68843 + 0.267421i 0.925413 0.378959i \(-0.123718\pi\)
0.763016 + 0.646380i \(0.223718\pi\)
\(164\) 0 0
\(165\) 7.35574 2.25706i 0.572644 0.175712i
\(166\) 0 0
\(167\) −12.8596 + 6.55227i −0.995102 + 0.507030i −0.874164 0.485630i \(-0.838590\pi\)
−0.120938 + 0.992660i \(0.538590\pi\)
\(168\) 0 0
\(169\) −11.2138 3.64358i −0.862598 0.280275i
\(170\) 0 0
\(171\) −14.5142 + 18.0742i −1.10993 + 1.38217i
\(172\) 0 0
\(173\) −5.05212 + 0.800177i −0.384106 + 0.0608364i −0.345501 0.938418i \(-0.612291\pi\)
−0.0386042 + 0.999255i \(0.512291\pi\)
\(174\) 0 0
\(175\) −1.40661 + 9.86135i −0.106330 + 0.745448i
\(176\) 0 0
\(177\) 22.2464 + 7.82671i 1.67214 + 0.588291i
\(178\) 0 0
\(179\) −2.20404 6.78334i −0.164738 0.507011i 0.834279 0.551342i \(-0.185884\pi\)
−0.999017 + 0.0443316i \(0.985884\pi\)
\(180\) 0 0
\(181\) −0.142407 + 0.438283i −0.0105850 + 0.0325773i −0.956210 0.292683i \(-0.905452\pi\)
0.945625 + 0.325260i \(0.105452\pi\)
\(182\) 0 0
\(183\) 0.399893 16.5660i 0.0295609 1.22459i
\(184\) 0 0
\(185\) −2.36256 14.2078i −0.173699 1.04458i
\(186\) 0 0
\(187\) 1.35551 8.55838i 0.0991250 0.625851i
\(188\) 0 0
\(189\) 5.35462 8.85950i 0.389491 0.644434i
\(190\) 0 0
\(191\) 15.1190 + 20.8095i 1.09397 + 1.50572i 0.843142 + 0.537691i \(0.180703\pi\)
0.250829 + 0.968031i \(0.419297\pi\)
\(192\) 0 0
\(193\) −16.8215 16.8215i −1.21084 1.21084i −0.970751 0.240087i \(-0.922824\pi\)
−0.240087 0.970751i \(-0.577176\pi\)
\(194\) 0 0
\(195\) −2.96150 3.06049i −0.212077 0.219166i
\(196\) 0 0
\(197\) 9.07122 17.8033i 0.646298 1.26843i −0.302681 0.953092i \(-0.597882\pi\)
0.948979 0.315339i \(-0.102118\pi\)
\(198\) 0 0
\(199\) 14.9399i 1.05906i 0.848291 + 0.529530i \(0.177632\pi\)
−0.848291 + 0.529530i \(0.822368\pi\)
\(200\) 0 0
\(201\) 10.4626 19.3641i 0.737976 1.36584i
\(202\) 0 0
\(203\) 6.91681 + 3.52429i 0.485465 + 0.247357i
\(204\) 0 0
\(205\) −15.1883 10.8573i −1.06080 0.758308i
\(206\) 0 0
\(207\) −0.369257 + 1.77285i −0.0256652 + 0.123221i
\(208\) 0 0
\(209\) −12.4188 + 9.02277i −0.859025 + 0.624118i
\(210\) 0 0
\(211\) 0.810432 + 0.588813i 0.0557925 + 0.0405356i 0.615332 0.788268i \(-0.289022\pi\)
−0.559539 + 0.828804i \(0.689022\pi\)
\(212\) 0 0
\(213\) −4.19724 3.20704i −0.287590 0.219743i
\(214\) 0 0
\(215\) −5.90802 2.95322i −0.402924 0.201408i
\(216\) 0 0
\(217\) 6.09877 + 11.9695i 0.414012 + 0.812544i
\(218\) 0 0
\(219\) −12.2406 + 11.6636i −0.827143 + 0.788151i
\(220\) 0 0
\(221\) −4.56138 + 1.48208i −0.306831 + 0.0996956i
\(222\) 0 0
\(223\) −3.95868 24.9941i −0.265093 1.67373i −0.657127 0.753780i \(-0.728228\pi\)
0.392034 0.919951i \(-0.371772\pi\)
\(224\) 0 0
\(225\) 4.16387 + 14.4105i 0.277591 + 0.960699i
\(226\) 0 0
\(227\) −3.09802 19.5601i −0.205623 1.29825i −0.847233 0.531221i \(-0.821733\pi\)
0.641610 0.767031i \(-0.278267\pi\)
\(228\) 0 0
\(229\) −18.2285 + 5.92281i −1.20458 + 0.391390i −0.841442 0.540347i \(-0.818293\pi\)
−0.363133 + 0.931737i \(0.618293\pi\)
\(230\) 0 0
\(231\) 4.96293 4.72897i 0.326537 0.311143i
\(232\) 0 0
\(233\) 5.12583 + 10.0600i 0.335804 + 0.659053i 0.995734 0.0922745i \(-0.0294137\pi\)
−0.659929 + 0.751328i \(0.729414\pi\)
\(234\) 0 0
\(235\) −0.935774 + 6.21765i −0.0610431 + 0.405595i
\(236\) 0 0
\(237\) 12.6951 + 9.70014i 0.824638 + 0.630092i
\(238\) 0 0
\(239\) 6.41867 + 4.66343i 0.415189 + 0.301652i 0.775699 0.631103i \(-0.217397\pi\)
−0.360510 + 0.932755i \(0.617397\pi\)
\(240\) 0 0
\(241\) 15.5433 11.2929i 1.00123 0.727439i 0.0388814 0.999244i \(-0.487621\pi\)
0.962352 + 0.271805i \(0.0876205\pi\)
\(242\) 0 0
\(243\) 1.87655 15.4751i 0.120381 0.992728i
\(244\) 0 0
\(245\) −2.14393 6.42952i −0.136971 0.410767i
\(246\) 0 0
\(247\) 7.57043 + 3.85733i 0.481695 + 0.245436i
\(248\) 0 0
\(249\) 2.92283 5.40954i 0.185227 0.342816i
\(250\) 0 0
\(251\) 16.7296i 1.05596i −0.849255 0.527982i \(-0.822949\pi\)
0.849255 0.527982i \(-0.177051\pi\)
\(252\) 0 0
\(253\) −0.544425 + 1.06849i −0.0342277 + 0.0671757i
\(254\) 0 0
\(255\) 16.6390 + 2.91646i 1.04197 + 0.182636i
\(256\) 0 0
\(257\) −14.2215 14.2215i −0.887111 0.887111i 0.107134 0.994245i \(-0.465833\pi\)
−0.994245 + 0.107134i \(0.965833\pi\)
\(258\) 0 0
\(259\) −7.54266 10.3816i −0.468678 0.645080i
\(260\) 0 0
\(261\) 11.6762 + 0.564039i 0.722736 + 0.0349132i
\(262\) 0 0
\(263\) −2.01269 + 12.7077i −0.124108 + 0.783587i 0.844602 + 0.535394i \(0.179837\pi\)
−0.968710 + 0.248193i \(0.920163\pi\)
\(264\) 0 0
\(265\) −23.5294 3.54124i −1.44540 0.217537i
\(266\) 0 0
\(267\) 0.137317 5.68849i 0.00840365 0.348130i
\(268\) 0 0
\(269\) 3.43765 10.5800i 0.209597 0.645074i −0.789896 0.613241i \(-0.789865\pi\)
0.999493 0.0318333i \(-0.0101346\pi\)
\(270\) 0 0
\(271\) 5.91811 + 18.2141i 0.359499 + 1.10643i 0.953354 + 0.301853i \(0.0976053\pi\)
−0.593855 + 0.804572i \(0.702395\pi\)
\(272\) 0 0
\(273\) −3.57930 1.25927i −0.216629 0.0762142i
\(274\) 0 0
\(275\) 0.152928 + 9.93204i 0.00922190 + 0.598924i
\(276\) 0 0
\(277\) −6.94071 + 1.09930i −0.417027 + 0.0660505i −0.361422 0.932402i \(-0.617709\pi\)
−0.0556046 + 0.998453i \(0.517709\pi\)
\(278\) 0 0
\(279\) 15.7729 + 12.6662i 0.944300 + 0.758305i
\(280\) 0 0
\(281\) 29.8705 + 9.70552i 1.78193 + 0.578983i 0.999066 0.0432145i \(-0.0137599\pi\)
0.782860 + 0.622197i \(0.213760\pi\)
\(282\) 0 0
\(283\) 13.6669 6.96363i 0.812412 0.413945i 0.00213954 0.999998i \(-0.499319\pi\)
0.810273 + 0.586053i \(0.199319\pi\)
\(284\) 0 0
\(285\) −17.1897 24.4964i −1.01823 1.45104i
\(286\) 0 0
\(287\) −16.4293 2.60214i −0.969789 0.153599i
\(288\) 0 0
\(289\) 1.18972 1.63751i 0.0699837 0.0963243i
\(290\) 0 0
\(291\) 0.309121 + 2.31147i 0.0181210 + 0.135501i
\(292\) 0 0
\(293\) 19.7002 19.7002i 1.15090 1.15090i 0.164528 0.986372i \(-0.447390\pi\)
0.986372 0.164528i \(-0.0526102\pi\)
\(294\) 0 0
\(295\) −17.7053 + 24.7681i −1.03085 + 1.44205i
\(296\) 0 0
\(297\) 3.89181 9.56117i 0.225826 0.554795i
\(298\) 0 0
\(299\) 0.663758 0.0383861
\(300\) 0 0
\(301\) −5.88476 −0.339192
\(302\) 0 0
\(303\) 22.9754 15.8598i 1.31990 0.911123i
\(304\) 0 0
\(305\) 20.3961 + 6.45393i 1.16788 + 0.369551i
\(306\) 0 0
\(307\) 16.0403 16.0403i 0.915468 0.915468i −0.0812272 0.996696i \(-0.525884\pi\)
0.996696 + 0.0812272i \(0.0258839\pi\)
\(308\) 0 0
\(309\) −10.3199 + 1.38011i −0.587077 + 0.0785119i
\(310\) 0 0
\(311\) 15.0505 20.7152i 0.853433 1.17465i −0.129663 0.991558i \(-0.541389\pi\)
0.983096 0.183092i \(-0.0586106\pi\)
\(312\) 0 0
\(313\) −0.120497 0.0190849i −0.00681092 0.00107874i 0.153028 0.988222i \(-0.451098\pi\)
−0.159839 + 0.987143i \(0.551098\pi\)
\(314\) 0 0
\(315\) 9.05892 + 9.82550i 0.510412 + 0.553604i
\(316\) 0 0
\(317\) 13.7216 6.99151i 0.770682 0.392682i −0.0239969 0.999712i \(-0.507639\pi\)
0.794679 + 0.607030i \(0.207639\pi\)
\(318\) 0 0
\(319\) 7.36226 + 2.39214i 0.412207 + 0.133934i
\(320\) 0 0
\(321\) −2.28891 + 12.4924i −0.127754 + 0.697256i
\(322\) 0 0
\(323\) −33.2869 + 5.27213i −1.85213 + 0.293349i
\(324\) 0 0
\(325\) 4.85978 2.57118i 0.269572 0.142623i
\(326\) 0 0
\(327\) 2.19776 6.24685i 0.121536 0.345452i
\(328\) 0 0
\(329\) 1.73112 + 5.32784i 0.0954398 + 0.293734i
\(330\) 0 0
\(331\) 0.542755 1.67043i 0.0298325 0.0918151i −0.935032 0.354564i \(-0.884629\pi\)
0.964864 + 0.262749i \(0.0846292\pi\)
\(332\) 0 0
\(333\) −16.7741 9.59324i −0.919213 0.525706i
\(334\) 0 0
\(335\) 20.2462 + 19.9369i 1.10617 + 1.08927i
\(336\) 0 0
\(337\) 1.61810 10.2163i 0.0881434 0.556516i −0.903610 0.428356i \(-0.859093\pi\)
0.991754 0.128160i \(-0.0409070\pi\)
\(338\) 0 0
\(339\) −29.6408 + 14.2124i −1.60987 + 0.771913i
\(340\) 0 0
\(341\) 7.87398 + 10.8376i 0.426400 + 0.586889i
\(342\) 0 0
\(343\) −14.1309 14.1309i −0.762997 0.762997i
\(344\) 0 0
\(345\) −2.06532 1.09546i −0.111193 0.0589774i
\(346\) 0 0
\(347\) −14.2252 + 27.9185i −0.763647 + 1.49874i 0.100189 + 0.994968i \(0.468055\pi\)
−0.863836 + 0.503773i \(0.831945\pi\)
\(348\) 0 0
\(349\) 16.4381i 0.879913i −0.898019 0.439956i \(-0.854994\pi\)
0.898019 0.439956i \(-0.145006\pi\)
\(350\) 0 0
\(351\) −5.69326 + 0.483235i −0.303884 + 0.0257932i
\(352\) 0 0
\(353\) −0.230966 0.117683i −0.0122931 0.00626364i 0.447833 0.894117i \(-0.352196\pi\)
−0.460126 + 0.887854i \(0.652196\pi\)
\(354\) 0 0
\(355\) 5.48593 4.05065i 0.291163 0.214986i
\(356\) 0 0
\(357\) 14.4220 4.30409i 0.763293 0.227797i
\(358\) 0 0
\(359\) 17.7312 12.8824i 0.935815 0.679909i −0.0115948 0.999933i \(-0.503691\pi\)
0.947410 + 0.320024i \(0.103691\pi\)
\(360\) 0 0
\(361\) 32.9302 + 23.9252i 1.73317 + 1.25922i
\(362\) 0 0
\(363\) −7.41715 + 9.70726i −0.389299 + 0.509499i
\(364\) 0 0
\(365\) −10.0590 19.3718i −0.526514 1.01397i
\(366\) 0 0
\(367\) 0.897351 + 1.76115i 0.0468413 + 0.0919313i 0.913241 0.407420i \(-0.133572\pi\)
−0.866399 + 0.499352i \(0.833572\pi\)
\(368\) 0 0
\(369\) −24.1681 + 6.58191i −1.25814 + 0.342641i
\(370\) 0 0
\(371\) −20.1621 + 6.55107i −1.04676 + 0.340114i
\(372\) 0 0
\(373\) 0.199978 + 1.26261i 0.0103545 + 0.0653755i 0.992325 0.123661i \(-0.0394635\pi\)
−0.981970 + 0.189037i \(0.939464\pi\)
\(374\) 0 0
\(375\) −19.3649 0.0201467i −0.999999 0.00104037i
\(376\) 0 0
\(377\) −0.670278 4.23197i −0.0345211 0.217958i
\(378\) 0 0
\(379\) −5.76610 + 1.87352i −0.296185 + 0.0962362i −0.453340 0.891338i \(-0.649768\pi\)
0.157155 + 0.987574i \(0.449768\pi\)
\(380\) 0 0
\(381\) −1.83778 1.92870i −0.0941525 0.0988105i
\(382\) 0 0
\(383\) −14.1048 27.6823i −0.720723 1.41450i −0.902294 0.431121i \(-0.858118\pi\)
0.181571 0.983378i \(-0.441882\pi\)
\(384\) 0 0
\(385\) 4.07841 + 7.85427i 0.207855 + 0.400291i
\(386\) 0 0
\(387\) −8.08062 + 3.63740i −0.410761 + 0.184900i
\(388\) 0 0
\(389\) −3.47117 2.52196i −0.175996 0.127868i 0.496300 0.868151i \(-0.334692\pi\)
−0.672296 + 0.740283i \(0.734692\pi\)
\(390\) 0 0
\(391\) −2.13001 + 1.54754i −0.107719 + 0.0782625i
\(392\) 0 0
\(393\) 4.93169 + 16.5249i 0.248771 + 0.833572i
\(394\) 0 0
\(395\) −16.5930 + 12.2518i −0.834883 + 0.616453i
\(396\) 0 0
\(397\) 13.0514 + 6.65001i 0.655030 + 0.333754i 0.749723 0.661752i \(-0.230187\pi\)
−0.0946927 + 0.995507i \(0.530187\pi\)
\(398\) 0 0
\(399\) −23.4575 12.6743i −1.17434 0.634511i
\(400\) 0 0
\(401\) 9.19743i 0.459297i −0.973274 0.229649i \(-0.926242\pi\)
0.973274 0.229649i \(-0.0737577\pi\)
\(402\) 0 0
\(403\) 3.36620 6.60655i 0.167683 0.329096i
\(404\) 0 0
\(405\) 18.5124 + 7.89246i 0.919889 + 0.392180i
\(406\) 0 0
\(407\) −9.04837 9.04837i −0.448511 0.448511i
\(408\) 0 0
\(409\) −14.8606 20.4539i −0.734809 1.01138i −0.998901 0.0468802i \(-0.985072\pi\)
0.264091 0.964498i \(-0.414928\pi\)
\(410\) 0 0
\(411\) −4.82269 10.0580i −0.237886 0.496124i
\(412\) 0 0
\(413\) −4.24338 + 26.7917i −0.208803 + 1.31833i
\(414\) 0 0
\(415\) 5.65598 + 5.56956i 0.277641 + 0.273399i
\(416\) 0 0
\(417\) 3.58995 + 0.0866593i 0.175801 + 0.00424372i
\(418\) 0 0
\(419\) −1.79122 + 5.51280i −0.0875066 + 0.269318i −0.985228 0.171245i \(-0.945221\pi\)
0.897722 + 0.440563i \(0.145221\pi\)
\(420\) 0 0
\(421\) 5.27994 + 16.2500i 0.257328 + 0.791975i 0.993362 + 0.115030i \(0.0366965\pi\)
−0.736034 + 0.676945i \(0.763304\pi\)
\(422\) 0 0
\(423\) 5.67025 + 6.24588i 0.275697 + 0.303685i
\(424\) 0 0
\(425\) −9.60043 + 19.5815i −0.465689 + 0.949840i
\(426\) 0 0
\(427\) 18.8253 2.98164i 0.911022 0.144292i
\(428\) 0 0
\(429\) −3.72176 0.681916i −0.179688 0.0329232i
\(430\) 0 0
\(431\) 7.18994 + 2.33615i 0.346327 + 0.112528i 0.477015 0.878895i \(-0.341719\pi\)
−0.130688 + 0.991424i \(0.541719\pi\)
\(432\) 0 0
\(433\) −4.16519 + 2.12227i −0.200166 + 0.101990i −0.551200 0.834373i \(-0.685830\pi\)
0.351034 + 0.936363i \(0.385830\pi\)
\(434\) 0 0
\(435\) −4.89878 + 14.2742i −0.234879 + 0.684396i
\(436\) 0 0
\(437\) 4.60674 + 0.729636i 0.220370 + 0.0349032i
\(438\) 0 0
\(439\) −3.13091 + 4.30933i −0.149430 + 0.205673i −0.877170 0.480181i \(-0.840571\pi\)
0.727739 + 0.685854i \(0.240571\pi\)
\(440\) 0 0
\(441\) −8.50233 3.22390i −0.404873 0.153519i
\(442\) 0 0
\(443\) −13.2529 + 13.2529i −0.629663 + 0.629663i −0.947983 0.318320i \(-0.896881\pi\)
0.318320 + 0.947983i \(0.396881\pi\)
\(444\) 0 0
\(445\) 7.00368 + 2.21618i 0.332006 + 0.105057i
\(446\) 0 0
\(447\) 6.06594 + 8.78744i 0.286909 + 0.415631i
\(448\) 0 0
\(449\) 0.687206 0.0324313 0.0162156 0.999869i \(-0.494838\pi\)
0.0162156 + 0.999869i \(0.494838\pi\)
\(450\) 0 0
\(451\) −16.5874 −0.781070
\(452\) 0 0
\(453\) −11.6176 16.8298i −0.545840 0.790733i
\(454\) 0 0
\(455\) 2.84867 3.98501i 0.133548 0.186820i
\(456\) 0 0
\(457\) 20.4930 20.4930i 0.958623 0.958623i −0.0405546 0.999177i \(-0.512912\pi\)
0.999177 + 0.0405546i \(0.0129125\pi\)
\(458\) 0 0
\(459\) 17.1431 14.8245i 0.800171 0.691946i
\(460\) 0 0
\(461\) −2.51720 + 3.46463i −0.117238 + 0.161364i −0.863603 0.504173i \(-0.831797\pi\)
0.746365 + 0.665537i \(0.231797\pi\)
\(462\) 0 0
\(463\) 29.9000 + 4.73569i 1.38957 + 0.220086i 0.805971 0.591955i \(-0.201644\pi\)
0.583599 + 0.812042i \(0.301644\pi\)
\(464\) 0 0
\(465\) −21.3775 + 15.0011i −0.991357 + 0.695659i
\(466\) 0 0
\(467\) 22.7856 11.6099i 1.05439 0.537241i 0.161205 0.986921i \(-0.448462\pi\)
0.893190 + 0.449680i \(0.148462\pi\)
\(468\) 0 0
\(469\) 24.0770 + 7.82310i 1.11177 + 0.361237i
\(470\) 0 0
\(471\) −19.8270 3.63278i −0.913578 0.167390i
\(472\) 0 0
\(473\) −5.79600 + 0.917996i −0.266500 + 0.0422095i
\(474\) 0 0
\(475\) 36.5551 12.5029i 1.67726 0.573672i
\(476\) 0 0
\(477\) −23.6362 + 21.4579i −1.08223 + 0.982489i
\(478\) 0 0
\(479\) 2.06837 + 6.36579i 0.0945063 + 0.290860i 0.987125 0.159953i \(-0.0511341\pi\)
−0.892618 + 0.450813i \(0.851134\pi\)
\(480\) 0 0
\(481\) −2.18870 + 6.73612i −0.0997960 + 0.307141i
\(482\) 0 0
\(483\) −2.08231 0.0502658i −0.0947485 0.00228717i
\(484\) 0 0
\(485\) −2.97713 0.448066i −0.135184 0.0203456i
\(486\) 0 0
\(487\) −2.38639 + 15.0671i −0.108138 + 0.682755i 0.872748 + 0.488171i \(0.162336\pi\)
−0.980886 + 0.194584i \(0.937664\pi\)
\(488\) 0 0
\(489\) 16.3440 + 34.0864i 0.739102 + 1.54144i
\(490\) 0 0
\(491\) −0.878303 1.20888i −0.0396373 0.0545560i 0.788738 0.614729i \(-0.210735\pi\)
−0.828376 + 0.560173i \(0.810735\pi\)
\(492\) 0 0
\(493\) 12.0177 + 12.0177i 0.541250 + 0.541250i
\(494\) 0 0
\(495\) 10.4550 + 8.26416i 0.469918 + 0.371446i
\(496\) 0 0
\(497\) 2.75831 5.41349i 0.123727 0.242828i
\(498\) 0 0
\(499\) 11.6309i 0.520672i 0.965518 + 0.260336i \(0.0838333\pi\)
−0.965518 + 0.260336i \(0.916167\pi\)
\(500\) 0 0
\(501\) −21.9930 11.8831i −0.982576 0.530896i
\(502\) 0 0
\(503\) 18.6581 + 9.50679i 0.831925 + 0.423887i 0.817444 0.576008i \(-0.195390\pi\)
0.0144808 + 0.999895i \(0.495390\pi\)
\(504\) 0 0
\(505\) 11.4010 + 34.1909i 0.507340 + 1.52148i
\(506\) 0 0
\(507\) −5.84030 19.5695i −0.259377 0.869111i
\(508\) 0 0
\(509\) −29.0463 + 21.1033i −1.28745 + 0.935389i −0.999751 0.0223311i \(-0.992891\pi\)
−0.287702 + 0.957720i \(0.592891\pi\)
\(510\) 0 0
\(511\) −15.7334 11.4310i −0.696004 0.505676i
\(512\) 0 0
\(513\) −40.0446 2.90447i −1.76801 0.128236i
\(514\) 0 0
\(515\) 2.00045 13.2918i 0.0881504 0.585707i
\(516\) 0 0
\(517\) 2.53613 + 4.97744i 0.111539 + 0.218907i
\(518\) 0 0
\(519\) −6.11168 6.41404i −0.268273 0.281545i
\(520\) 0 0
\(521\) −39.1289 + 12.7138i −1.71427 + 0.557000i −0.991035 0.133602i \(-0.957345\pi\)
−0.723235 + 0.690602i \(0.757345\pi\)
\(522\) 0 0
\(523\) 0.431314 + 2.72321i 0.0188601 + 0.119078i 0.995322 0.0966111i \(-0.0308003\pi\)
−0.976462 + 0.215689i \(0.930800\pi\)
\(524\) 0 0
\(525\) −15.4406 + 7.69817i −0.673883 + 0.335976i
\(526\) 0 0
\(527\) 4.60087 + 29.0488i 0.200417 + 1.26538i
\(528\) 0 0
\(529\) −21.5278 + 6.99479i −0.935990 + 0.304121i
\(530\) 0 0
\(531\) 10.7333 + 39.4117i 0.465786 + 1.71032i
\(532\) 0 0
\(533\) 4.16815 + 8.18045i 0.180542 + 0.354334i
\(534\) 0 0
\(535\) −14.6659 7.33097i −0.634060 0.316946i
\(536\) 0 0
\(537\) 7.50041 9.81623i 0.323667 0.423602i
\(538\) 0 0
\(539\) −4.87152 3.53937i −0.209831 0.152451i
\(540\) 0 0
\(541\) 17.6370 12.8140i 0.758273 0.550918i −0.140107 0.990136i \(-0.544745\pi\)
0.898380 + 0.439219i \(0.144745\pi\)
\(542\) 0 0
\(543\) −0.764860 + 0.228265i −0.0328233 + 0.00979577i
\(544\) 0 0
\(545\) 6.95492 + 4.97170i 0.297916 + 0.212964i
\(546\) 0 0
\(547\) −26.1267 13.3122i −1.11710 0.569189i −0.204834 0.978797i \(-0.565665\pi\)
−0.912262 + 0.409608i \(0.865665\pi\)
\(548\) 0 0
\(549\) 24.0069 15.7303i 1.02459 0.671352i
\(550\) 0 0
\(551\) 30.1083i 1.28266i
\(552\) 0 0
\(553\) −8.34290 + 16.3739i −0.354776 + 0.696287i
\(554\) 0 0
\(555\) 17.9275 17.3476i 0.760978 0.736365i
\(556\) 0 0
\(557\) −12.3449 12.3449i −0.523071 0.523071i 0.395427 0.918498i \(-0.370597\pi\)
−0.918498 + 0.395427i \(0.870597\pi\)
\(558\) 0 0
\(559\) 1.90917 + 2.62775i 0.0807494 + 0.111142i
\(560\) 0 0
\(561\) 13.5330 6.48894i 0.571366 0.273963i
\(562\) 0 0
\(563\) 6.59138 41.6164i 0.277794 1.75392i −0.315491 0.948928i \(-0.602169\pi\)
0.593285 0.804992i \(-0.297831\pi\)
\(564\) 0 0
\(565\) −6.96117 41.8628i −0.292859 1.76118i
\(566\) 0 0
\(567\) 17.8972 1.08484i 0.751614 0.0455590i
\(568\) 0 0
\(569\) −2.68424 + 8.26124i −0.112529 + 0.346329i −0.991424 0.130687i \(-0.958282\pi\)
0.878894 + 0.477016i \(0.158282\pi\)
\(570\) 0 0
\(571\) −3.08502 9.49470i −0.129104 0.397341i 0.865523 0.500870i \(-0.166987\pi\)
−0.994626 + 0.103529i \(0.966987\pi\)
\(572\) 0 0
\(573\) −14.7857 + 42.0266i −0.617683 + 1.75569i
\(574\) 0 0
\(575\) 2.10105 2.16676i 0.0876198 0.0903603i
\(576\) 0 0
\(577\) 10.6032 1.67937i 0.441415 0.0699133i 0.0682288 0.997670i \(-0.478265\pi\)
0.373186 + 0.927756i \(0.378265\pi\)
\(578\) 0 0
\(579\) 7.42598 40.5294i 0.308613 1.68435i
\(580\) 0 0
\(581\) 6.72615 + 2.18546i 0.279048 + 0.0906681i
\(582\) 0 0
\(583\) −18.8361 + 9.59746i −0.780110 + 0.397486i
\(584\) 0 0
\(585\) 1.44848 7.23278i 0.0598871 0.299039i
\(586\) 0 0
\(587\) 22.9124 + 3.62898i 0.945698 + 0.149784i 0.610191 0.792254i \(-0.291093\pi\)
0.335507 + 0.942038i \(0.391093\pi\)
\(588\) 0 0
\(589\) 30.6250 42.1517i 1.26188 1.73683i
\(590\) 0 0
\(591\) 34.3029 4.58745i 1.41103 0.188703i
\(592\) 0 0
\(593\) 6.63871 6.63871i 0.272619 0.272619i −0.557535 0.830154i \(-0.688253\pi\)
0.830154 + 0.557535i \(0.188253\pi\)
\(594\) 0 0
\(595\) 0.149574 + 19.4296i 0.00613194 + 0.796536i
\(596\) 0 0
\(597\) −21.2956 + 14.7003i −0.871570 + 0.601642i
\(598\) 0 0
\(599\) 3.40483 0.139118 0.0695588 0.997578i \(-0.477841\pi\)
0.0695588 + 0.997578i \(0.477841\pi\)
\(600\) 0 0
\(601\) 2.96693 0.121024 0.0605118 0.998167i \(-0.480727\pi\)
0.0605118 + 0.998167i \(0.480727\pi\)
\(602\) 0 0
\(603\) 37.8967 4.13991i 1.54327 0.168590i
\(604\) 0 0
\(605\) −9.36823 12.6877i −0.380873 0.515829i
\(606\) 0 0
\(607\) −11.7030 + 11.7030i −0.475010 + 0.475010i −0.903532 0.428521i \(-0.859035\pi\)
0.428521 + 0.903532i \(0.359035\pi\)
\(608\) 0 0
\(609\) 1.78229 + 13.3271i 0.0722218 + 0.540042i
\(610\) 0 0
\(611\) 1.81745 2.50150i 0.0735260 0.101200i
\(612\) 0 0
\(613\) 41.1420 + 6.51626i 1.66171 + 0.263189i 0.915440 0.402454i \(-0.131843\pi\)
0.746271 + 0.665643i \(0.231843\pi\)
\(614\) 0 0
\(615\) 0.531491 32.3329i 0.0214318 1.30379i
\(616\) 0 0
\(617\) −8.90536 + 4.53751i −0.358516 + 0.182673i −0.623966 0.781451i \(-0.714480\pi\)
0.265450 + 0.964125i \(0.414480\pi\)
\(618\) 0 0
\(619\) −0.701573 0.227955i −0.0281986 0.00916228i 0.294884 0.955533i \(-0.404719\pi\)
−0.323082 + 0.946371i \(0.604719\pi\)
\(620\) 0 0
\(621\) −2.89039 + 1.21807i −0.115987 + 0.0488794i
\(622\) 0 0
\(623\) 6.46432 1.02385i 0.258988 0.0410196i
\(624\) 0 0
\(625\) 6.98974 24.0030i 0.279590 0.960120i
\(626\) 0 0
\(627\) −25.0808 8.82390i −1.00163 0.352393i
\(628\) 0 0
\(629\) −8.68160 26.7192i −0.346158 1.06537i
\(630\) 0 0
\(631\) 7.30043 22.4684i 0.290626 0.894454i −0.694030 0.719946i \(-0.744167\pi\)
0.984656 0.174508i \(-0.0558334\pi\)
\(632\) 0 0
\(633\) −0.0418716 + 1.73458i −0.00166425 + 0.0689432i
\(634\) 0 0
\(635\) 3.05235 1.58496i 0.121129 0.0628973i
\(636\) 0 0
\(637\) −0.521384 + 3.29189i −0.0206580 + 0.130429i
\(638\) 0 0
\(639\) 0.441450 9.13843i 0.0174635 0.361511i
\(640\) 0 0
\(641\) −10.1942 14.0312i −0.402648 0.554198i 0.558758 0.829331i \(-0.311278\pi\)
−0.961406 + 0.275133i \(0.911278\pi\)
\(642\) 0 0
\(643\) −19.4481 19.4481i −0.766958 0.766958i 0.210612 0.977570i \(-0.432454\pi\)
−0.977570 + 0.210612i \(0.932454\pi\)
\(644\) 0 0
\(645\) −1.60369 11.3273i −0.0631452 0.446010i
\(646\) 0 0
\(647\) 0.917006 1.79973i 0.0360512 0.0707546i −0.872278 0.489010i \(-0.837358\pi\)
0.908330 + 0.418255i \(0.137358\pi\)
\(648\) 0 0
\(649\) 27.0495i 1.06179i
\(650\) 0 0
\(651\) −11.0606 + 20.4709i −0.433500 + 0.802316i
\(652\) 0 0
\(653\) 17.2019 + 8.76480i 0.673162 + 0.342993i 0.756934 0.653492i \(-0.226697\pi\)
−0.0837716 + 0.996485i \(0.526697\pi\)
\(654\) 0 0
\(655\) −22.2627 + 0.171384i −0.869876 + 0.00669653i
\(656\) 0 0
\(657\) −28.6698 5.97148i −1.11851 0.232970i
\(658\) 0 0
\(659\) 31.9956 23.2462i 1.24637 0.905543i 0.248367 0.968666i \(-0.420106\pi\)
0.998006 + 0.0631231i \(0.0201061\pi\)
\(660\) 0 0
\(661\) −29.5919 21.4997i −1.15099 0.836243i −0.162378 0.986729i \(-0.551916\pi\)
−0.988612 + 0.150486i \(0.951916\pi\)
\(662\) 0 0
\(663\) −6.60081 5.04356i −0.256354 0.195876i
\(664\) 0 0
\(665\) 24.1514 24.5261i 0.936552 0.951083i
\(666\) 0 0
\(667\) −1.06783 2.09574i −0.0413467 0.0811474i
\(668\) 0 0
\(669\) 31.7319 30.2360i 1.22683 1.16899i
\(670\) 0 0
\(671\) 18.0763 5.87334i 0.697827 0.226738i
\(672\) 0 0
\(673\) −4.75453 30.0189i −0.183274 1.15714i −0.892126 0.451787i \(-0.850787\pi\)
0.708852 0.705357i \(-0.249213\pi\)
\(674\) 0 0
\(675\) −16.4439 + 20.1146i −0.632926 + 0.774212i
\(676\) 0 0
\(677\) 4.63953 + 29.2929i 0.178312 + 1.12582i 0.900736 + 0.434366i \(0.143028\pi\)
−0.722425 + 0.691450i \(0.756972\pi\)
\(678\) 0 0
\(679\) −2.55107 + 0.828893i −0.0979011 + 0.0318100i
\(680\) 0 0
\(681\) 24.8331 23.6624i 0.951605 0.906745i
\(682\) 0 0
\(683\) −4.38498 8.60601i −0.167787 0.329300i 0.791768 0.610822i \(-0.209161\pi\)
−0.959555 + 0.281522i \(0.909161\pi\)
\(684\) 0 0
\(685\) 14.2053 2.36213i 0.542755 0.0902523i
\(686\) 0 0
\(687\) −26.3787 20.1555i −1.00641 0.768980i
\(688\) 0 0
\(689\) 9.46640 + 6.87775i 0.360641 + 0.262021i
\(690\) 0 0
\(691\) −9.38046 + 6.81530i −0.356849 + 0.259266i −0.751737 0.659463i \(-0.770784\pi\)
0.394887 + 0.918730i \(0.370784\pi\)
\(692\) 0 0
\(693\) 11.6241 + 2.42112i 0.441563 + 0.0919709i
\(694\) 0 0
\(695\) −1.39861 + 4.41996i −0.0530522 + 0.167659i
\(696\) 0 0
\(697\) −32.4482 16.5332i −1.22906 0.626239i
\(698\) 0 0
\(699\) −9.29611 + 17.2051i −0.351611 + 0.650758i
\(700\) 0 0
\(701\) 47.4850i 1.79348i 0.442556 + 0.896741i \(0.354072\pi\)
−0.442556 + 0.896741i \(0.645928\pi\)
\(702\) 0 0
\(703\) −22.5951 + 44.3454i −0.852190 + 1.67252i
\(704\) 0 0
\(705\) −9.78353 + 4.78406i −0.368469 + 0.180178i
\(706\) 0 0
\(707\) 22.7062 + 22.7062i 0.853956 + 0.853956i
\(708\) 0 0
\(709\) 24.5873 + 33.8414i 0.923394 + 1.27094i 0.962381 + 0.271703i \(0.0875867\pi\)
−0.0389877 + 0.999240i \(0.512413\pi\)
\(710\) 0 0
\(711\) −1.33523 + 27.6405i −0.0500749 + 1.03660i
\(712\) 0 0
\(713\) 0.636737 4.02020i 0.0238460 0.150558i
\(714\) 0 0
\(715\) 2.18406 4.36929i 0.0816792 0.163402i
\(716\) 0 0
\(717\) −0.331625 + 13.7379i −0.0123848 + 0.513052i
\(718\) 0 0
\(719\) −3.07429 + 9.46170i −0.114652 + 0.352862i −0.991874 0.127222i \(-0.959394\pi\)
0.877222 + 0.480084i \(0.159394\pi\)
\(720\) 0 0
\(721\) −3.70071 11.3896i −0.137822 0.424171i
\(722\) 0 0
\(723\) 31.3911 + 11.0440i 1.16745 + 0.410730i
\(724\) 0 0
\(725\) −15.9365 11.2078i −0.591866 0.416246i
\(726\) 0 0
\(727\) −34.3889 + 5.44666i −1.27541 + 0.202005i −0.757164 0.653225i \(-0.773416\pi\)
−0.518248 + 0.855230i \(0.673416\pi\)
\(728\) 0 0
\(729\) 23.9049 12.5520i 0.885368 0.464890i
\(730\) 0 0
\(731\) −12.2531 3.98128i −0.453198 0.147253i
\(732\) 0 0
\(733\) −11.5143 + 5.86682i −0.425290 + 0.216696i −0.653517 0.756912i \(-0.726707\pi\)
0.228227 + 0.973608i \(0.426707\pi\)
\(734\) 0 0
\(735\) 7.05520 9.38240i 0.260235 0.346075i
\(736\) 0 0
\(737\) 24.9343 + 3.94920i 0.918465 + 0.145471i
\(738\) 0 0
\(739\) 7.98551 10.9911i 0.293752 0.404315i −0.636476 0.771296i \(-0.719609\pi\)
0.930228 + 0.366981i \(0.119609\pi\)
\(740\) 0 0
\(741\) 1.95071 + 14.5865i 0.0716610 + 0.535848i
\(742\) 0 0
\(743\) 17.0201 17.0201i 0.624409 0.624409i −0.322247 0.946656i \(-0.604438\pi\)
0.946656 + 0.322247i \(0.104438\pi\)
\(744\) 0 0
\(745\) −13.0771 + 4.36057i −0.479107 + 0.159759i
\(746\) 0 0
\(747\) 10.5868 1.15652i 0.387351 0.0423149i
\(748\) 0 0
\(749\) −14.6081 −0.533769
\(750\) 0 0
\(751\) 4.62541 0.168784 0.0843918 0.996433i \(-0.473105\pi\)
0.0843918 + 0.996433i \(0.473105\pi\)
\(752\) 0 0
\(753\) 23.8467 16.4613i 0.869023 0.599884i
\(754\) 0 0
\(755\) 25.0454 8.35142i 0.911494 0.303939i
\(756\) 0 0
\(757\) −37.1450 + 37.1450i −1.35006 + 1.35006i −0.464471 + 0.885588i \(0.653756\pi\)
−0.885588 + 0.464471i \(0.846244\pi\)
\(758\) 0 0
\(759\) −2.05875 + 0.275324i −0.0747278 + 0.00999363i
\(760\) 0 0
\(761\) −2.00068 + 2.75371i −0.0725248 + 0.0998218i −0.843738 0.536755i \(-0.819650\pi\)
0.771214 + 0.636577i \(0.219650\pi\)
\(762\) 0 0
\(763\) 7.52316 + 1.19155i 0.272357 + 0.0431371i
\(764\) 0 0
\(765\) 12.2149 + 26.5872i 0.441632 + 0.961262i
\(766\) 0 0
\(767\) 13.3401 6.79711i 0.481682 0.245429i
\(768\) 0 0
\(769\) 25.5702 + 8.30827i 0.922086 + 0.299604i 0.731322 0.682032i \(-0.238904\pi\)
0.190764 + 0.981636i \(0.438904\pi\)
\(770\) 0 0
\(771\) 6.27817 34.2649i 0.226103 1.23402i
\(772\) 0 0
\(773\) 24.1237 3.82081i 0.867668 0.137425i 0.293298 0.956021i \(-0.405247\pi\)
0.574370 + 0.818596i \(0.305247\pi\)
\(774\) 0 0
\(775\) −10.9110 31.9009i −0.391935 1.14591i
\(776\) 0 0
\(777\) 7.37641 20.9665i 0.264627 0.752170i
\(778\) 0 0
\(779\) 19.9362 + 61.3573i 0.714288 + 2.19835i
\(780\) 0 0
\(781\) 1.87223 5.76213i 0.0669936 0.206185i
\(782\) 0 0
\(783\) 10.6849 + 17.1984i 0.381847 + 0.614621i
\(784\) 0 0
\(785\) 11.6352 23.2766i 0.415277 0.830776i
\(786\) 0 0
\(787\) −4.41590 + 27.8809i −0.157410 + 0.993846i 0.774873 + 0.632117i \(0.217814\pi\)
−0.932283 + 0.361730i \(0.882186\pi\)
\(788\) 0 0
\(789\) −20.0941 + 9.63491i −0.715370 + 0.343012i
\(790\) 0 0
\(791\) −22.2241 30.5889i −0.790198 1.08761i
\(792\) 0 0
\(793\) −7.43885 7.43885i −0.264161 0.264161i
\(794\) 0 0
\(795\) −18.1043 37.0237i −0.642093 1.31310i
\(796\) 0 0