Properties

Label 414.3.k.b.71.2
Level $414$
Weight $3$
Character 414.71
Analytic conductor $11.281$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 414.k (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.2806829445\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 71.2
Character \(\chi\) \(=\) 414.71
Dual form 414.3.k.b.35.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-0.172109 + 0.586151i) q^{5} +(-4.94341 + 5.70500i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})\) \(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-0.172109 + 0.586151i) q^{5} +(-4.94341 + 5.70500i) q^{7} +(2.79964 + 0.402527i) q^{8} +(-0.565759 - 0.652921i) q^{10} +(-8.63603 - 13.4379i) q^{11} +(11.0851 + 12.7929i) q^{13} +(-3.00767 - 10.2432i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(-1.90658 - 0.870706i) q^{17} +(-8.74546 - 19.1499i) q^{19} +(1.20936 - 0.173879i) q^{20} +22.5902 q^{22} +(-15.5903 - 16.9098i) q^{23} +(20.7174 + 13.3143i) q^{25} +(-23.6953 + 3.40687i) q^{26} +(14.4860 + 4.25348i) q^{28} +(-29.1843 - 13.3280i) q^{29} +(7.05976 - 49.1017i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(2.49363 - 1.60256i) q^{34} +(-2.49318 - 3.87947i) q^{35} +(-63.7823 + 18.7282i) q^{37} +(29.4695 + 4.23707i) q^{38} +(-0.717785 + 1.57173i) q^{40} +(13.4671 - 45.8648i) q^{41} +(-1.87890 - 13.0680i) q^{43} +(-17.2721 + 26.8758i) q^{44} +(32.0379 - 5.61903i) q^{46} -14.9396i q^{47} +(-1.13629 - 7.90309i) q^{49} +(-31.6803 + 14.4679i) q^{50} +(14.0638 - 30.7955i) q^{52} +(-51.4921 - 44.6182i) q^{53} +(9.36299 - 2.74922i) q^{55} +(-16.1362 + 13.9821i) q^{56} +(38.1703 - 24.5306i) q^{58} +(14.0463 - 12.1712i) q^{59} +(10.3773 - 72.1756i) q^{61} +(53.0191 + 45.9413i) q^{62} +(7.67594 + 2.25386i) q^{64} +(-9.40641 + 4.29577i) q^{65} +(77.1069 + 49.5536i) q^{67} +4.19198i q^{68} +6.52169 q^{70} +(48.0839 - 74.8200i) q^{71} +(30.7201 + 67.2676i) q^{73} +(26.4856 - 90.2018i) q^{74} +(-27.5727 + 31.8206i) q^{76} +(119.355 + 17.1606i) q^{77} +(-66.1732 - 76.3679i) q^{79} +(-1.32110 - 2.05567i) q^{80} +(44.2692 + 51.0894i) q^{82} +(36.5369 + 124.433i) q^{83} +(0.838506 - 0.967687i) q^{85} +(16.9838 + 7.75623i) q^{86} +(-18.7686 - 41.0976i) q^{88} +(-117.030 + 16.8263i) q^{89} -127.782 q^{91} +(-17.8106 + 42.4121i) q^{92} +(17.7738 + 11.4225i) q^{94} +(12.7299 - 1.83028i) q^{95} +(-104.624 - 30.7203i) q^{97} +(10.2712 + 4.69070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.764582 + 1.18971i −0.382291 + 0.594856i
\(3\) 0 0
\(4\) −0.830830 1.81926i −0.207708 0.454816i
\(5\) −0.172109 + 0.586151i −0.0344219 + 0.117230i −0.974912 0.222591i \(-0.928548\pi\)
0.940490 + 0.339821i \(0.110367\pi\)
\(6\) 0 0
\(7\) −4.94341 + 5.70500i −0.706202 + 0.815000i −0.989576 0.144009i \(-0.954001\pi\)
0.283375 + 0.959009i \(0.408546\pi\)
\(8\) 2.79964 + 0.402527i 0.349955 + 0.0503159i
\(9\) 0 0
\(10\) −0.565759 0.652921i −0.0565759 0.0652921i
\(11\) −8.63603 13.4379i −0.785093 1.22163i −0.971004 0.239063i \(-0.923160\pi\)
0.185911 0.982567i \(-0.440476\pi\)
\(12\) 0 0
\(13\) 11.0851 + 12.7929i 0.852701 + 0.984069i 0.999987 0.00502491i \(-0.00159949\pi\)
−0.147287 + 0.989094i \(0.547054\pi\)
\(14\) −3.00767 10.2432i −0.214833 0.731655i
\(15\) 0 0
\(16\) −2.61944 + 3.02300i −0.163715 + 0.188937i
\(17\) −1.90658 0.870706i −0.112152 0.0512180i 0.358549 0.933511i \(-0.383272\pi\)
−0.470701 + 0.882293i \(0.655999\pi\)
\(18\) 0 0
\(19\) −8.74546 19.1499i −0.460287 1.00789i −0.987422 0.158107i \(-0.949461\pi\)
0.527135 0.849782i \(-0.323266\pi\)
\(20\) 1.20936 0.173879i 0.0604678 0.00869396i
\(21\) 0 0
\(22\) 22.5902 1.02683
\(23\) −15.5903 16.9098i −0.677839 0.735210i
\(24\) 0 0
\(25\) 20.7174 + 13.3143i 0.828695 + 0.532570i
\(26\) −23.6953 + 3.40687i −0.911359 + 0.131034i
\(27\) 0 0
\(28\) 14.4860 + 4.25348i 0.517359 + 0.151910i
\(29\) −29.1843 13.3280i −1.00636 0.459587i −0.157108 0.987581i \(-0.550217\pi\)
−0.849248 + 0.527994i \(0.822944\pi\)
\(30\) 0 0
\(31\) 7.05976 49.1017i 0.227734 1.58393i −0.479885 0.877331i \(-0.659322\pi\)
0.707619 0.706594i \(-0.249769\pi\)
\(32\) −1.59372 5.42771i −0.0498038 0.169616i
\(33\) 0 0
\(34\) 2.49363 1.60256i 0.0733420 0.0471340i
\(35\) −2.49318 3.87947i −0.0712338 0.110842i
\(36\) 0 0
\(37\) −63.7823 + 18.7282i −1.72385 + 0.506167i −0.985705 0.168480i \(-0.946114\pi\)
−0.738141 + 0.674647i \(0.764296\pi\)
\(38\) 29.4695 + 4.23707i 0.775512 + 0.111502i
\(39\) 0 0
\(40\) −0.717785 + 1.57173i −0.0179446 + 0.0392933i
\(41\) 13.4671 45.8648i 0.328466 1.11865i −0.615369 0.788239i \(-0.710993\pi\)
0.943836 0.330415i \(-0.107189\pi\)
\(42\) 0 0
\(43\) −1.87890 13.0680i −0.0436954 0.303908i −0.999936 0.0113261i \(-0.996395\pi\)
0.956240 0.292582i \(-0.0945144\pi\)
\(44\) −17.2721 + 26.8758i −0.392547 + 0.610815i
\(45\) 0 0
\(46\) 32.0379 5.61903i 0.696476 0.122153i
\(47\) 14.9396i 0.317864i −0.987290 0.158932i \(-0.949195\pi\)
0.987290 0.158932i \(-0.0508051\pi\)
\(48\) 0 0
\(49\) −1.13629 7.90309i −0.0231897 0.161288i
\(50\) −31.6803 + 14.4679i −0.633605 + 0.289358i
\(51\) 0 0
\(52\) 14.0638 30.7955i 0.270458 0.592220i
\(53\) −51.4921 44.6182i −0.971549 0.841852i 0.0158867 0.999874i \(-0.494943\pi\)
−0.987436 + 0.158022i \(0.949488\pi\)
\(54\) 0 0
\(55\) 9.36299 2.74922i 0.170236 0.0499858i
\(56\) −16.1362 + 13.9821i −0.288146 + 0.249680i
\(57\) 0 0
\(58\) 38.1703 24.5306i 0.658109 0.422941i
\(59\) 14.0463 12.1712i 0.238073 0.206292i −0.527650 0.849462i \(-0.676927\pi\)
0.765723 + 0.643170i \(0.222381\pi\)
\(60\) 0 0
\(61\) 10.3773 72.1756i 0.170119 1.18321i −0.708510 0.705701i \(-0.750632\pi\)
0.878629 0.477505i \(-0.158459\pi\)
\(62\) 53.0191 + 45.9413i 0.855147 + 0.740989i
\(63\) 0 0
\(64\) 7.67594 + 2.25386i 0.119937 + 0.0352166i
\(65\) −9.40641 + 4.29577i −0.144714 + 0.0660887i
\(66\) 0 0
\(67\) 77.1069 + 49.5536i 1.15085 + 0.739605i 0.969808 0.243870i \(-0.0784171\pi\)
0.181041 + 0.983476i \(0.442053\pi\)
\(68\) 4.19198i 0.0616468i
\(69\) 0 0
\(70\) 6.52169 0.0931670
\(71\) 48.0839 74.8200i 0.677238 1.05380i −0.317187 0.948363i \(-0.602738\pi\)
0.994426 0.105441i \(-0.0336253\pi\)
\(72\) 0 0
\(73\) 30.7201 + 67.2676i 0.420823 + 0.921473i 0.994728 + 0.102551i \(0.0327006\pi\)
−0.573905 + 0.818922i \(0.694572\pi\)
\(74\) 26.4856 90.2018i 0.357914 1.21894i
\(75\) 0 0
\(76\) −27.5727 + 31.8206i −0.362799 + 0.418692i
\(77\) 119.355 + 17.1606i 1.55006 + 0.222865i
\(78\) 0 0
\(79\) −66.1732 76.3679i −0.837635 0.966683i 0.162163 0.986764i \(-0.448153\pi\)
−0.999798 + 0.0200812i \(0.993608\pi\)
\(80\) −1.32110 2.05567i −0.0165138 0.0256959i
\(81\) 0 0
\(82\) 44.2692 + 51.0894i 0.539868 + 0.623041i
\(83\) 36.5369 + 124.433i 0.440204 + 1.49920i 0.819042 + 0.573734i \(0.194506\pi\)
−0.378838 + 0.925463i \(0.623676\pi\)
\(84\) 0 0
\(85\) 0.838506 0.967687i 0.00986477 0.0113846i
\(86\) 16.9838 + 7.75623i 0.197486 + 0.0901887i
\(87\) 0 0
\(88\) −18.7686 41.0976i −0.213280 0.467018i
\(89\) −117.030 + 16.8263i −1.31494 + 0.189060i −0.763855 0.645388i \(-0.776696\pi\)
−0.551087 + 0.834448i \(0.685787\pi\)
\(90\) 0 0
\(91\) −127.782 −1.40419
\(92\) −17.8106 + 42.4121i −0.193593 + 0.461001i
\(93\) 0 0
\(94\) 17.7738 + 11.4225i 0.189083 + 0.121516i
\(95\) 12.7299 1.83028i 0.133999 0.0192661i
\(96\) 0 0
\(97\) −104.624 30.7203i −1.07860 0.316704i −0.306279 0.951942i \(-0.599084\pi\)
−0.772317 + 0.635238i \(0.780902\pi\)
\(98\) 10.2712 + 4.69070i 0.104808 + 0.0478643i
\(99\) 0 0
\(100\) 7.00952 48.7523i 0.0700952 0.487523i
\(101\) −10.4544 35.6043i −0.103509 0.352518i 0.891410 0.453197i \(-0.149717\pi\)
−0.994919 + 0.100679i \(0.967898\pi\)
\(102\) 0 0
\(103\) −23.7275 + 15.2487i −0.230364 + 0.148046i −0.650731 0.759308i \(-0.725538\pi\)
0.420367 + 0.907354i \(0.361901\pi\)
\(104\) 25.8848 + 40.2775i 0.248892 + 0.387284i
\(105\) 0 0
\(106\) 92.4527 27.1466i 0.872195 0.256100i
\(107\) 7.83849 + 1.12700i 0.0732569 + 0.0105328i 0.178846 0.983877i \(-0.442764\pi\)
−0.105589 + 0.994410i \(0.533673\pi\)
\(108\) 0 0
\(109\) −31.3193 + 68.5797i −0.287333 + 0.629172i −0.997169 0.0751954i \(-0.976042\pi\)
0.709836 + 0.704367i \(0.248769\pi\)
\(110\) −3.88799 + 13.2413i −0.0353453 + 0.120375i
\(111\) 0 0
\(112\) −4.29722 29.8879i −0.0383681 0.266856i
\(113\) −61.4969 + 95.6911i −0.544220 + 0.846824i −0.999042 0.0437590i \(-0.986067\pi\)
0.454822 + 0.890583i \(0.349703\pi\)
\(114\) 0 0
\(115\) 12.5949 6.22793i 0.109521 0.0541559i
\(116\) 64.1673i 0.553166i
\(117\) 0 0
\(118\) 3.74067 + 26.0170i 0.0317006 + 0.220483i
\(119\) 14.3924 6.57279i 0.120945 0.0552335i
\(120\) 0 0
\(121\) −55.7316 + 122.035i −0.460591 + 1.00855i
\(122\) 77.9339 + 67.5301i 0.638802 + 0.553526i
\(123\) 0 0
\(124\) −95.1944 + 27.9516i −0.767697 + 0.225416i
\(125\) −22.9119 + 19.8533i −0.183295 + 0.158826i
\(126\) 0 0
\(127\) −155.613 + 100.007i −1.22530 + 0.787454i −0.983153 0.182786i \(-0.941489\pi\)
−0.242149 + 0.970239i \(0.577852\pi\)
\(128\) −8.55033 + 7.40890i −0.0667995 + 0.0578821i
\(129\) 0 0
\(130\) 2.08125 14.4754i 0.0160096 0.111349i
\(131\) 83.5598 + 72.4050i 0.637861 + 0.552710i 0.912623 0.408803i \(-0.134054\pi\)
−0.274762 + 0.961512i \(0.588599\pi\)
\(132\) 0 0
\(133\) 152.482 + 44.7729i 1.14648 + 0.336638i
\(134\) −117.909 + 53.8472i −0.879918 + 0.401845i
\(135\) 0 0
\(136\) −4.98725 3.20511i −0.0366710 0.0235670i
\(137\) 39.3102i 0.286936i 0.989655 + 0.143468i \(0.0458254\pi\)
−0.989655 + 0.143468i \(0.954175\pi\)
\(138\) 0 0
\(139\) −54.3308 −0.390869 −0.195435 0.980717i \(-0.562612\pi\)
−0.195435 + 0.980717i \(0.562612\pi\)
\(140\) −4.98637 + 7.75894i −0.0356169 + 0.0554210i
\(141\) 0 0
\(142\) 52.2502 + 114.412i 0.367959 + 0.805719i
\(143\) 76.1786 259.441i 0.532718 1.81427i
\(144\) 0 0
\(145\) 12.8351 14.8125i 0.0885181 0.102155i
\(146\) −103.517 14.8835i −0.709021 0.101942i
\(147\) 0 0
\(148\) 87.0637 + 100.477i 0.588268 + 0.678898i
\(149\) 111.166 + 172.978i 0.746082 + 1.16093i 0.981950 + 0.189142i \(0.0605705\pi\)
−0.235867 + 0.971785i \(0.575793\pi\)
\(150\) 0 0
\(151\) 0.0601066 + 0.0693667i 0.000398057 + 0.000459382i 0.755949 0.654631i \(-0.227176\pi\)
−0.755551 + 0.655090i \(0.772631\pi\)
\(152\) −16.7758 57.1330i −0.110367 0.375875i
\(153\) 0 0
\(154\) −111.673 + 128.877i −0.725147 + 0.836865i
\(155\) 27.5659 + 12.5889i 0.177845 + 0.0812190i
\(156\) 0 0
\(157\) −70.3561 154.058i −0.448128 0.981264i −0.990035 0.140825i \(-0.955025\pi\)
0.541906 0.840439i \(-0.317703\pi\)
\(158\) 141.451 20.3375i 0.895257 0.128719i
\(159\) 0 0
\(160\) 3.45575 0.0215984
\(161\) 173.540 5.35044i 1.07789 0.0332325i
\(162\) 0 0
\(163\) 39.3079 + 25.2616i 0.241153 + 0.154979i 0.655635 0.755078i \(-0.272401\pi\)
−0.414482 + 0.910057i \(0.636037\pi\)
\(164\) −94.6291 + 13.6056i −0.577007 + 0.0829610i
\(165\) 0 0
\(166\) −175.975 51.6710i −1.06009 0.311271i
\(167\) −200.499 91.5647i −1.20059 0.548292i −0.288184 0.957575i \(-0.593051\pi\)
−0.912407 + 0.409283i \(0.865779\pi\)
\(168\) 0 0
\(169\) −16.7274 + 116.341i −0.0989785 + 0.688411i
\(170\) 0.510163 + 1.73746i 0.00300096 + 0.0102203i
\(171\) 0 0
\(172\) −22.2132 + 14.2755i −0.129146 + 0.0829973i
\(173\) −41.7879 65.0233i −0.241549 0.375857i 0.699220 0.714907i \(-0.253531\pi\)
−0.940768 + 0.339050i \(0.889895\pi\)
\(174\) 0 0
\(175\) −178.372 + 52.3749i −1.01927 + 0.299285i
\(176\) 63.2444 + 9.09317i 0.359343 + 0.0516657i
\(177\) 0 0
\(178\) 69.4603 152.097i 0.390227 0.854477i
\(179\) −86.3130 + 293.955i −0.482196 + 1.64221i 0.255304 + 0.966861i \(0.417824\pi\)
−0.737500 + 0.675347i \(0.763994\pi\)
\(180\) 0 0
\(181\) 21.7014 + 150.937i 0.119897 + 0.833905i 0.957666 + 0.287880i \(0.0929505\pi\)
−0.837769 + 0.546025i \(0.816140\pi\)
\(182\) 97.6996 152.023i 0.536811 0.835294i
\(183\) 0 0
\(184\) −36.8405 53.6169i −0.200220 0.291396i
\(185\) 40.6093i 0.219510i
\(186\) 0 0
\(187\) 4.76480 + 33.1399i 0.0254802 + 0.177219i
\(188\) −27.1791 + 12.4123i −0.144570 + 0.0660227i
\(189\) 0 0
\(190\) −7.55553 + 16.5443i −0.0397659 + 0.0870753i
\(191\) 128.443 + 111.296i 0.672474 + 0.582702i 0.922716 0.385481i \(-0.125965\pi\)
−0.250242 + 0.968183i \(0.580510\pi\)
\(192\) 0 0
\(193\) 201.175 59.0704i 1.04236 0.306064i 0.284633 0.958637i \(-0.408128\pi\)
0.757727 + 0.652572i \(0.226310\pi\)
\(194\) 116.542 100.984i 0.600731 0.520536i
\(195\) 0 0
\(196\) −13.4337 + 8.63334i −0.0685395 + 0.0440477i
\(197\) −157.681 + 136.631i −0.800411 + 0.693560i −0.955711 0.294307i \(-0.904911\pi\)
0.155300 + 0.987867i \(0.450366\pi\)
\(198\) 0 0
\(199\) 23.2484 161.696i 0.116826 0.812542i −0.844189 0.536046i \(-0.819917\pi\)
0.961015 0.276497i \(-0.0891735\pi\)
\(200\) 52.6418 + 45.6144i 0.263209 + 0.228072i
\(201\) 0 0
\(202\) 50.3521 + 14.7847i 0.249268 + 0.0731916i
\(203\) 220.307 100.611i 1.08525 0.495619i
\(204\) 0 0
\(205\) 24.5659 + 15.7875i 0.119834 + 0.0770123i
\(206\) 39.8878i 0.193630i
\(207\) 0 0
\(208\) −67.7097 −0.325527
\(209\) −181.809 + 282.900i −0.869897 + 1.35359i
\(210\) 0 0
\(211\) −75.5340 165.396i −0.357981 0.783870i −0.999854 0.0170588i \(-0.994570\pi\)
0.641873 0.766811i \(-0.278158\pi\)
\(212\) −38.3910 + 130.748i −0.181090 + 0.616735i
\(213\) 0 0
\(214\) −7.33398 + 8.46386i −0.0342709 + 0.0395508i
\(215\) 7.98322 + 1.14781i 0.0371312 + 0.00533867i
\(216\) 0 0
\(217\) 245.226 + 283.006i 1.13007 + 1.30417i
\(218\) −57.6440 89.6958i −0.264422 0.411449i
\(219\) 0 0
\(220\) −12.7806 14.7496i −0.0580937 0.0670437i
\(221\) −9.99580 34.0426i −0.0452299 0.154039i
\(222\) 0 0
\(223\) 138.419 159.744i 0.620711 0.716339i −0.355131 0.934817i \(-0.615564\pi\)
0.975842 + 0.218478i \(0.0701091\pi\)
\(224\) 38.8435 + 17.7392i 0.173409 + 0.0791930i
\(225\) 0 0
\(226\) −66.8254 146.327i −0.295688 0.647466i
\(227\) 8.76052 1.25957i 0.0385926 0.00554878i −0.122991 0.992408i \(-0.539249\pi\)
0.161584 + 0.986859i \(0.448340\pi\)
\(228\) 0 0
\(229\) 87.0830 0.380275 0.190138 0.981757i \(-0.439107\pi\)
0.190138 + 0.981757i \(0.439107\pi\)
\(230\) −2.22042 + 19.7461i −0.00965402 + 0.0858527i
\(231\) 0 0
\(232\) −76.3406 49.0611i −0.329054 0.211470i
\(233\) 184.632 26.5461i 0.792413 0.113932i 0.265790 0.964031i \(-0.414367\pi\)
0.526623 + 0.850099i \(0.323458\pi\)
\(234\) 0 0
\(235\) 8.75686 + 2.57125i 0.0372632 + 0.0109415i
\(236\) −33.8127 15.4418i −0.143274 0.0654312i
\(237\) 0 0
\(238\) −3.18444 + 22.1482i −0.0133800 + 0.0930598i
\(239\) −110.199 375.303i −0.461083 1.57030i −0.782051 0.623215i \(-0.785826\pi\)
0.320968 0.947090i \(-0.395992\pi\)
\(240\) 0 0
\(241\) 290.864 186.927i 1.20690 0.775630i 0.226766 0.973949i \(-0.427185\pi\)
0.980138 + 0.198319i \(0.0635482\pi\)
\(242\) −102.575 159.610i −0.423865 0.659547i
\(243\) 0 0
\(244\) −139.928 + 41.0866i −0.573476 + 0.168388i
\(245\) 4.82797 + 0.694157i 0.0197060 + 0.00283329i
\(246\) 0 0
\(247\) 148.038 324.158i 0.599344 1.31238i
\(248\) 39.5295 134.625i 0.159393 0.542843i
\(249\) 0 0
\(250\) −6.10167 42.4381i −0.0244067 0.169752i
\(251\) −49.5097 + 77.0387i −0.197250 + 0.306927i −0.925762 0.378106i \(-0.876576\pi\)
0.728513 + 0.685032i \(0.240212\pi\)
\(252\) 0 0
\(253\) −92.5947 + 355.535i −0.365987 + 1.40528i
\(254\) 261.598i 1.02991i
\(255\) 0 0
\(256\) −2.27704 15.8371i −0.00889468 0.0618638i
\(257\) 66.6840 30.4535i 0.259471 0.118496i −0.281433 0.959581i \(-0.590810\pi\)
0.540904 + 0.841085i \(0.318082\pi\)
\(258\) 0 0
\(259\) 208.458 456.459i 0.804857 1.76239i
\(260\) 15.6303 + 13.5437i 0.0601164 + 0.0520912i
\(261\) 0 0
\(262\) −150.029 + 44.0526i −0.572631 + 0.168140i
\(263\) −97.5024 + 84.4863i −0.370732 + 0.321241i −0.820223 0.572044i \(-0.806151\pi\)
0.449491 + 0.893285i \(0.351605\pi\)
\(264\) 0 0
\(265\) 35.0152 22.5029i 0.132133 0.0849167i
\(266\) −169.852 + 147.178i −0.638542 + 0.553300i
\(267\) 0 0
\(268\) 26.0883 181.448i 0.0973445 0.677046i
\(269\) −378.625 328.081i −1.40753 1.21963i −0.942444 0.334365i \(-0.891478\pi\)
−0.465085 0.885266i \(-0.653976\pi\)
\(270\) 0 0
\(271\) 158.019 + 46.3985i 0.583095 + 0.171212i 0.559959 0.828520i \(-0.310817\pi\)
0.0231356 + 0.999732i \(0.492635\pi\)
\(272\) 7.62632 3.48283i 0.0280380 0.0128045i
\(273\) 0 0
\(274\) −46.7679 30.0559i −0.170686 0.109693i
\(275\) 393.381i 1.43048i
\(276\) 0 0
\(277\) 3.54592 0.0128012 0.00640058 0.999980i \(-0.497963\pi\)
0.00640058 + 0.999980i \(0.497963\pi\)
\(278\) 41.5403 64.6380i 0.149426 0.232511i
\(279\) 0 0
\(280\) −5.41842 11.8647i −0.0193515 0.0423739i
\(281\) −30.2930 + 103.169i −0.107804 + 0.367148i −0.995670 0.0929542i \(-0.970369\pi\)
0.887866 + 0.460102i \(0.152187\pi\)
\(282\) 0 0
\(283\) 186.539 215.278i 0.659149 0.760699i −0.323489 0.946232i \(-0.604856\pi\)
0.982638 + 0.185533i \(0.0594013\pi\)
\(284\) −176.067 25.3146i −0.619954 0.0891360i
\(285\) 0 0
\(286\) 250.415 + 288.994i 0.875576 + 1.01047i
\(287\) 195.085 + 303.559i 0.679740 + 1.05770i
\(288\) 0 0
\(289\) −186.378 215.091i −0.644906 0.744261i
\(290\) 7.80914 + 26.5955i 0.0269281 + 0.0917086i
\(291\) 0 0
\(292\) 96.8543 111.776i 0.331693 0.382794i
\(293\) −214.858 98.1225i −0.733305 0.334889i 0.0135214 0.999909i \(-0.495696\pi\)
−0.746826 + 0.665020i \(0.768423\pi\)
\(294\) 0 0
\(295\) 4.71666 + 10.3280i 0.0159887 + 0.0350103i
\(296\) −186.106 + 26.7580i −0.628736 + 0.0903986i
\(297\) 0 0
\(298\) −290.790 −0.975805
\(299\) 43.5055 386.892i 0.145503 1.29395i
\(300\) 0 0
\(301\) 83.8414 + 53.8816i 0.278543 + 0.179009i
\(302\) −0.128483 + 0.0184730i −0.000425440 + 6.11690e-5i
\(303\) 0 0
\(304\) 80.7983 + 23.7245i 0.265784 + 0.0780412i
\(305\) 40.5197 + 18.5047i 0.132852 + 0.0606713i
\(306\) 0 0
\(307\) 42.6082 296.347i 0.138789 0.965299i −0.794779 0.606899i \(-0.792413\pi\)
0.933568 0.358400i \(-0.116678\pi\)
\(308\) −67.9438 231.395i −0.220597 0.751284i
\(309\) 0 0
\(310\) −36.0536 + 23.1703i −0.116302 + 0.0747428i
\(311\) 325.313 + 506.197i 1.04602 + 1.62764i 0.736087 + 0.676887i \(0.236672\pi\)
0.309937 + 0.950757i \(0.399692\pi\)
\(312\) 0 0
\(313\) 99.8401 29.3157i 0.318978 0.0936604i −0.118324 0.992975i \(-0.537752\pi\)
0.437302 + 0.899315i \(0.355934\pi\)
\(314\) 237.078 + 34.0867i 0.755026 + 0.108556i
\(315\) 0 0
\(316\) −83.9548 + 183.835i −0.265680 + 0.581757i
\(317\) −2.85982 + 9.73965i −0.00902151 + 0.0307244i −0.963881 0.266334i \(-0.914188\pi\)
0.954859 + 0.297059i \(0.0960057\pi\)
\(318\) 0 0
\(319\) 72.9355 + 507.278i 0.228638 + 1.59021i
\(320\) −2.64220 + 4.11135i −0.00825689 + 0.0128480i
\(321\) 0 0
\(322\) −126.320 + 210.553i −0.392298 + 0.653893i
\(323\) 44.1255i 0.136612i
\(324\) 0 0
\(325\) 59.3266 + 412.625i 0.182543 + 1.26962i
\(326\) −60.1081 + 27.4505i −0.184381 + 0.0842039i
\(327\) 0 0
\(328\) 56.1649 122.984i 0.171234 0.374951i
\(329\) 85.2305 + 73.8526i 0.259059 + 0.224476i
\(330\) 0 0
\(331\) −26.1640 + 7.68244i −0.0790453 + 0.0232098i −0.321016 0.947074i \(-0.604024\pi\)
0.241971 + 0.970284i \(0.422206\pi\)
\(332\) 196.021 169.853i 0.590425 0.511606i
\(333\) 0 0
\(334\) 262.233 168.527i 0.785130 0.504572i
\(335\) −42.3167 + 36.6676i −0.126318 + 0.109456i
\(336\) 0 0
\(337\) 71.7678 499.156i 0.212961 1.48118i −0.550236 0.835009i \(-0.685462\pi\)
0.763197 0.646166i \(-0.223629\pi\)
\(338\) −125.623 108.853i −0.371667 0.322051i
\(339\) 0 0
\(340\) −2.45713 0.721480i −0.00722686 0.00212200i
\(341\) −720.793 + 329.175i −2.11376 + 0.965323i
\(342\) 0 0
\(343\) −260.468 167.393i −0.759382 0.488025i
\(344\) 37.3421i 0.108553i
\(345\) 0 0
\(346\) 109.309 0.315923
\(347\) −45.4176 + 70.6712i −0.130886 + 0.203663i −0.900511 0.434834i \(-0.856807\pi\)
0.769624 + 0.638497i \(0.220444\pi\)
\(348\) 0 0
\(349\) 149.945 + 328.334i 0.429642 + 0.940786i 0.993385 + 0.114835i \(0.0366339\pi\)
−0.563742 + 0.825951i \(0.690639\pi\)
\(350\) 74.0693 252.257i 0.211626 0.720733i
\(351\) 0 0
\(352\) −59.1738 + 68.2902i −0.168107 + 0.194006i
\(353\) −305.290 43.8941i −0.864846 0.124346i −0.304407 0.952542i \(-0.598458\pi\)
−0.560439 + 0.828196i \(0.689367\pi\)
\(354\) 0 0
\(355\) 35.5801 + 41.0617i 0.100226 + 0.115667i
\(356\) 127.843 + 198.928i 0.359111 + 0.558787i
\(357\) 0 0
\(358\) −283.729 327.440i −0.792538 0.914638i
\(359\) −151.217 514.998i −0.421218 1.43454i −0.847911 0.530139i \(-0.822140\pi\)
0.426693 0.904397i \(-0.359679\pi\)
\(360\) 0 0
\(361\) −53.8301 + 62.1232i −0.149114 + 0.172086i
\(362\) −196.164 89.5851i −0.541889 0.247473i
\(363\) 0 0
\(364\) 106.165 + 232.469i 0.291662 + 0.638650i
\(365\) −44.7161 + 6.42921i −0.122510 + 0.0176143i
\(366\) 0 0
\(367\) −322.862 −0.879732 −0.439866 0.898064i \(-0.644974\pi\)
−0.439866 + 0.898064i \(0.644974\pi\)
\(368\) 91.9563 2.83512i 0.249881 0.00770413i
\(369\) 0 0
\(370\) 48.3134 + 31.0491i 0.130577 + 0.0839166i
\(371\) 509.093 73.1966i 1.37222 0.197295i
\(372\) 0 0
\(373\) 178.620 + 52.4476i 0.478874 + 0.140610i 0.512257 0.858832i \(-0.328810\pi\)
−0.0333822 + 0.999443i \(0.510628\pi\)
\(374\) −43.0701 19.6694i −0.115161 0.0525921i
\(375\) 0 0
\(376\) 6.01360 41.8255i 0.0159936 0.111238i
\(377\) −153.007 521.095i −0.405855 1.38221i
\(378\) 0 0
\(379\) −526.144 + 338.132i −1.38824 + 0.892169i −0.999573 0.0292080i \(-0.990701\pi\)
−0.388669 + 0.921377i \(0.627065\pi\)
\(380\) −13.9061 21.6384i −0.0365951 0.0569431i
\(381\) 0 0
\(382\) −230.615 + 67.7147i −0.603704 + 0.177264i
\(383\) −160.638 23.0963i −0.419421 0.0603036i −0.0706264 0.997503i \(-0.522500\pi\)
−0.348795 + 0.937199i \(0.613409\pi\)
\(384\) 0 0
\(385\) −30.6008 + 67.0064i −0.0794826 + 0.174043i
\(386\) −83.5382 + 284.505i −0.216420 + 0.737060i
\(387\) 0 0
\(388\) 31.0362 + 215.862i 0.0799902 + 0.556344i
\(389\) 14.4939 22.5529i 0.0372593 0.0579766i −0.822124 0.569308i \(-0.807211\pi\)
0.859384 + 0.511331i \(0.170848\pi\)
\(390\) 0 0
\(391\) 15.0007 + 45.8145i 0.0383649 + 0.117173i
\(392\) 22.5832i 0.0576102i
\(393\) 0 0
\(394\) −41.9920 292.061i −0.106579 0.741271i
\(395\) 56.1521 25.6438i 0.142157 0.0649211i
\(396\) 0 0
\(397\) −277.742 + 608.170i −0.699602 + 1.53191i 0.140851 + 0.990031i \(0.455016\pi\)
−0.840453 + 0.541884i \(0.817711\pi\)
\(398\) 174.596 + 151.289i 0.438684 + 0.380122i
\(399\) 0 0
\(400\) −94.5170 + 27.7527i −0.236292 + 0.0693817i
\(401\) 111.419 96.5453i 0.277853 0.240761i −0.504774 0.863251i \(-0.668424\pi\)
0.782628 + 0.622490i \(0.213879\pi\)
\(402\) 0 0
\(403\) 706.411 453.983i 1.75288 1.12651i
\(404\) −56.0878 + 48.6004i −0.138831 + 0.120298i
\(405\) 0 0
\(406\) −48.7446 + 339.026i −0.120061 + 0.835040i
\(407\) 802.493 + 695.364i 1.97173 + 1.70851i
\(408\) 0 0
\(409\) 603.563 + 177.222i 1.47570 + 0.433306i 0.917949 0.396699i \(-0.129844\pi\)
0.557756 + 0.830005i \(0.311663\pi\)
\(410\) −37.5652 + 17.1555i −0.0916225 + 0.0418426i
\(411\) 0 0
\(412\) 47.4550 + 30.4975i 0.115182 + 0.0740231i
\(413\) 140.302i 0.339713i
\(414\) 0 0
\(415\) −79.2250 −0.190904
\(416\) 51.7696 80.5551i 0.124446 0.193642i
\(417\) 0 0
\(418\) −197.562 432.600i −0.472636 1.03493i
\(419\) 79.0771 269.312i 0.188728 0.642749i −0.809707 0.586834i \(-0.800374\pi\)
0.998436 0.0559153i \(-0.0178077\pi\)
\(420\) 0 0
\(421\) 46.0397 53.1326i 0.109358 0.126206i −0.698432 0.715677i \(-0.746118\pi\)
0.807789 + 0.589471i \(0.200664\pi\)
\(422\) 254.526 + 36.5953i 0.603143 + 0.0867188i
\(423\) 0 0
\(424\) −126.199 145.642i −0.297640 0.343494i
\(425\) −27.9066 43.4235i −0.0656625 0.102173i
\(426\) 0 0
\(427\) 360.463 + 415.996i 0.844175 + 0.974230i
\(428\) −4.46213 15.1966i −0.0104255 0.0355062i
\(429\) 0 0
\(430\) −7.46939 + 8.62013i −0.0173707 + 0.0200468i
\(431\) 176.380 + 80.5499i 0.409234 + 0.186891i 0.609385 0.792874i \(-0.291416\pi\)
−0.200152 + 0.979765i \(0.564144\pi\)
\(432\) 0 0
\(433\) 24.7713 + 54.2417i 0.0572086 + 0.125269i 0.936077 0.351794i \(-0.114428\pi\)
−0.878869 + 0.477064i \(0.841701\pi\)
\(434\) −524.191 + 75.3672i −1.20781 + 0.173657i
\(435\) 0 0
\(436\) 150.786 0.345839
\(437\) −187.477 + 446.437i −0.429009 + 1.02159i
\(438\) 0 0
\(439\) −374.439 240.637i −0.852937 0.548149i 0.0395528 0.999217i \(-0.487407\pi\)
−0.892489 + 0.451068i \(0.851043\pi\)
\(440\) 27.3196 3.92797i 0.0620900 0.00892720i
\(441\) 0 0
\(442\) 48.1435 + 14.1362i 0.108922 + 0.0319823i
\(443\) −351.866 160.692i −0.794280 0.362736i −0.0234085 0.999726i \(-0.507452\pi\)
−0.770872 + 0.636990i \(0.780179\pi\)
\(444\) 0 0
\(445\) 10.2792 71.4931i 0.0230992 0.160659i
\(446\) 84.2166 + 286.815i 0.188826 + 0.643084i
\(447\) 0 0
\(448\) −50.8036 + 32.6495i −0.113401 + 0.0728784i
\(449\) 309.258 + 481.215i 0.688771 + 1.07175i 0.992881 + 0.119111i \(0.0380045\pi\)
−0.304110 + 0.952637i \(0.598359\pi\)
\(450\) 0 0
\(451\) −732.630 + 215.120i −1.62446 + 0.476984i
\(452\) 225.181 + 32.3761i 0.498188 + 0.0716286i
\(453\) 0 0
\(454\) −5.19960 + 11.3855i −0.0114529 + 0.0250783i
\(455\) 21.9924 74.8993i 0.0483350 0.164614i
\(456\) 0 0
\(457\) 44.9733 + 312.796i 0.0984099 + 0.684456i 0.977982 + 0.208690i \(0.0669199\pi\)
−0.879572 + 0.475766i \(0.842171\pi\)
\(458\) −66.5820 + 103.604i −0.145376 + 0.226209i
\(459\) 0 0
\(460\) −21.7945 17.7392i −0.0473794 0.0385634i
\(461\) 97.9527i 0.212479i 0.994341 + 0.106239i \(0.0338810\pi\)
−0.994341 + 0.106239i \(0.966119\pi\)
\(462\) 0 0
\(463\) −101.765 707.793i −0.219795 1.52871i −0.738792 0.673934i \(-0.764603\pi\)
0.518997 0.854776i \(-0.326306\pi\)
\(464\) 116.737 53.3121i 0.251589 0.114897i
\(465\) 0 0
\(466\) −109.584 + 239.956i −0.235159 + 0.514927i
\(467\) 8.39491 + 7.27423i 0.0179762 + 0.0155765i 0.663803 0.747908i \(-0.268942\pi\)
−0.645826 + 0.763484i \(0.723487\pi\)
\(468\) 0 0
\(469\) −663.874 + 194.931i −1.41551 + 0.415631i
\(470\) −9.75438 + 8.45222i −0.0207540 + 0.0179834i
\(471\) 0 0
\(472\) 44.2238 28.4209i 0.0936946 0.0602139i
\(473\) −159.381 + 138.104i −0.336958 + 0.291976i
\(474\) 0 0
\(475\) 73.7834 513.175i 0.155333 1.08037i
\(476\) −23.9153 20.7227i −0.0502422 0.0435351i
\(477\) 0 0
\(478\) 530.758 + 155.845i 1.11037 + 0.326035i
\(479\) −251.857 + 115.019i −0.525798 + 0.240124i −0.660586 0.750751i \(-0.729692\pi\)
0.134788 + 0.990874i \(0.456965\pi\)
\(480\) 0 0
\(481\) −946.621 608.356i −1.96803 1.26477i
\(482\) 488.965i 1.01445i
\(483\) 0 0
\(484\) 268.317 0.554375
\(485\) 36.0135 56.0380i 0.0742545 0.115542i
\(486\) 0 0
\(487\) −106.576 233.368i −0.218841 0.479195i 0.768089 0.640343i \(-0.221208\pi\)
−0.986930 + 0.161148i \(0.948480\pi\)
\(488\) 58.1053 197.888i 0.119068 0.405509i
\(489\) 0 0
\(490\) −4.51722 + 5.21315i −0.00921882 + 0.0106391i
\(491\) −661.544 95.1157i −1.34734 0.193718i −0.569403 0.822059i \(-0.692825\pi\)
−0.777938 + 0.628340i \(0.783734\pi\)
\(492\) 0 0
\(493\) 44.0375 + 50.8220i 0.0893255 + 0.103087i
\(494\) 272.468 + 423.968i 0.551554 + 0.858235i
\(495\) 0 0
\(496\) 129.942 + 149.961i 0.261979 + 0.302340i
\(497\) 189.150 + 644.185i 0.380583 + 1.29615i
\(498\) 0 0
\(499\) −595.865 + 687.665i −1.19412 + 1.37809i −0.286612 + 0.958047i \(0.592529\pi\)
−0.907506 + 0.420039i \(0.862016\pi\)
\(500\) 55.1543 + 25.1881i 0.110309 + 0.0503763i
\(501\) 0 0
\(502\) −53.7996 117.805i −0.107170 0.234671i
\(503\) 507.656 72.9899i 1.00926 0.145109i 0.382197 0.924081i \(-0.375168\pi\)
0.627059 + 0.778972i \(0.284258\pi\)
\(504\) 0 0
\(505\) 22.6688 0.0448887
\(506\) −352.188 381.997i −0.696024 0.754934i
\(507\) 0 0
\(508\) 311.227 + 200.013i 0.612651 + 0.393727i
\(509\) 732.401 105.303i 1.43890 0.206883i 0.621710 0.783248i \(-0.286438\pi\)
0.817192 + 0.576365i \(0.195529\pi\)
\(510\) 0 0
\(511\) −535.623 157.273i −1.04819 0.307775i
\(512\) 20.5826 + 9.39977i 0.0402004 + 0.0183589i
\(513\) 0 0
\(514\) −14.7544 + 102.619i −0.0287050 + 0.199648i
\(515\) −4.85434 16.5324i −0.00942590 0.0321017i
\(516\) 0 0
\(517\) −200.757 + 129.019i −0.388312 + 0.249553i
\(518\) 383.672 + 597.005i 0.740679 + 1.15252i
\(519\) 0 0
\(520\) −28.0637 + 8.24025i −0.0539687 + 0.0158466i
\(521\) 833.369 + 119.820i 1.59956 + 0.229982i 0.883627 0.468191i \(-0.155094\pi\)
0.715930 + 0.698172i \(0.246003\pi\)
\(522\) 0 0
\(523\) −146.409 + 320.591i −0.279941 + 0.612984i −0.996412 0.0846318i \(-0.973029\pi\)
0.716472 + 0.697616i \(0.245756\pi\)
\(524\) 62.2998 212.174i 0.118893 0.404911i
\(525\) 0 0
\(526\) −25.9659 180.597i −0.0493648 0.343339i
\(527\) −56.2132 + 87.4694i −0.106666 + 0.165976i
\(528\) 0 0
\(529\) −42.8849 + 527.259i −0.0810678 + 0.996709i
\(530\) 58.8634i 0.111063i
\(531\) 0 0
\(532\) −45.2333 314.605i −0.0850250 0.591362i
\(533\) 736.028 336.133i 1.38092 0.630643i
\(534\) 0 0
\(535\) −2.00967 + 4.40057i −0.00375640 + 0.00822536i
\(536\) 195.925 + 169.770i 0.365531 + 0.316734i
\(537\) 0 0
\(538\) 679.811 199.611i 1.26359 0.371023i
\(539\) −96.3881 + 83.5207i −0.178828 + 0.154955i
\(540\) 0 0
\(541\) 618.254 397.328i 1.14280 0.734432i 0.174606 0.984638i \(-0.444135\pi\)
0.968193 + 0.250206i \(0.0804985\pi\)
\(542\) −176.019 + 152.521i −0.324758 + 0.281405i
\(543\) 0 0
\(544\) −1.68739 + 11.7360i −0.00310181 + 0.0215736i
\(545\) −34.8077 30.1611i −0.0638674 0.0553414i
\(546\) 0 0
\(547\) 489.546 + 143.744i 0.894965 + 0.262785i 0.696700 0.717363i \(-0.254651\pi\)
0.198265 + 0.980148i \(0.436469\pi\)
\(548\) 71.5157 32.6601i 0.130503 0.0595988i
\(549\) 0 0
\(550\) 468.010 + 300.772i 0.850927 + 0.546858i
\(551\) 675.436i 1.22584i
\(552\) 0 0
\(553\) 762.801 1.37939
\(554\) −2.71115 + 4.21863i −0.00489377 + 0.00761485i
\(555\) 0 0
\(556\) 45.1397 + 98.8421i 0.0811865 + 0.177774i
\(557\) 219.818 748.631i 0.394646 1.34404i −0.487523 0.873110i \(-0.662100\pi\)
0.882169 0.470932i \(-0.156082\pi\)
\(558\) 0 0
\(559\) 146.350 168.897i 0.261807 0.302142i
\(560\) 18.2584 + 2.62516i 0.0326042 + 0.00468778i
\(561\) 0 0
\(562\) −99.5794 114.921i −0.177187 0.204485i
\(563\) −289.603 450.631i −0.514392 0.800410i 0.482766 0.875750i \(-0.339632\pi\)
−0.997158 + 0.0753397i \(0.975996\pi\)
\(564\) 0 0
\(565\) −45.5052 52.5158i −0.0805401 0.0929483i
\(566\) 113.494 + 386.525i 0.200520 + 0.682907i
\(567\) 0 0
\(568\) 164.735 190.114i 0.290026 0.334708i
\(569\) 428.118 + 195.515i 0.752404 + 0.343611i 0.754425 0.656387i \(-0.227916\pi\)
−0.00202080 + 0.999998i \(0.500643\pi\)
\(570\) 0 0
\(571\) −404.464 885.653i −0.708344 1.55106i −0.829552 0.558430i \(-0.811404\pi\)
0.121208 0.992627i \(-0.461323\pi\)
\(572\) −535.282 + 76.9620i −0.935809 + 0.134549i
\(573\) 0 0
\(574\) −510.306 −0.889035
\(575\) −97.8485 557.901i −0.170171 0.970262i
\(576\) 0 0
\(577\) −51.7096 33.2318i −0.0896181 0.0575940i 0.495064 0.868856i \(-0.335144\pi\)
−0.584682 + 0.811262i \(0.698781\pi\)
\(578\) 398.398 57.2810i 0.689270 0.0991021i
\(579\) 0 0
\(580\) −37.6117 11.0438i −0.0648478 0.0190410i
\(581\) −890.509 406.682i −1.53272 0.699969i
\(582\) 0 0
\(583\) −154.888 + 1077.27i −0.265674 + 1.84781i
\(584\) 58.9280 + 200.690i 0.100904 + 0.343648i
\(585\) 0 0
\(586\) 281.014 180.597i 0.479546 0.308186i
\(587\) 299.356 + 465.806i 0.509975 + 0.793537i 0.996798 0.0799637i \(-0.0254804\pi\)
−0.486822 + 0.873501i \(0.661844\pi\)
\(588\) 0 0
\(589\) −1002.03 + 294.223i −1.70124 + 0.499530i
\(590\) −15.8937 2.28516i −0.0269384 0.00387316i
\(591\) 0 0
\(592\) 110.459 241.871i 0.186586 0.408566i
\(593\) −182.114 + 620.224i −0.307107 + 1.04591i 0.650900 + 0.759164i \(0.274392\pi\)
−0.958007 + 0.286746i \(0.907426\pi\)
\(594\) 0 0
\(595\) 1.37558 + 9.56735i 0.00231189 + 0.0160796i
\(596\) 222.333 345.956i 0.373041 0.580463i
\(597\) 0 0
\(598\) 427.027 + 347.570i 0.714092 + 0.581221i
\(599\) 354.283i 0.591458i −0.955272 0.295729i \(-0.904437\pi\)
0.955272 0.295729i \(-0.0955625\pi\)
\(600\) 0 0
\(601\) −130.126 905.048i −0.216516 1.50590i −0.750761 0.660574i \(-0.770313\pi\)
0.534245 0.845330i \(-0.320596\pi\)
\(602\) −128.207 + 58.5502i −0.212969 + 0.0972595i
\(603\) 0 0
\(604\) 0.0762580 0.166982i 0.000126255 0.000276460i
\(605\) −61.9390 53.6705i −0.102379 0.0887115i
\(606\) 0 0
\(607\) 137.831 40.4708i 0.227069 0.0666735i −0.166219 0.986089i \(-0.553156\pi\)
0.393288 + 0.919415i \(0.371338\pi\)
\(608\) −90.0022 + 77.9874i −0.148030 + 0.128269i
\(609\) 0 0
\(610\) −52.9960 + 34.0584i −0.0868786 + 0.0558335i
\(611\) 191.121 165.607i 0.312800 0.271043i
\(612\) 0 0
\(613\) 59.5493 414.175i 0.0971441 0.675652i −0.881815 0.471595i \(-0.843678\pi\)
0.978959 0.204057i \(-0.0654126\pi\)
\(614\) 319.990 + 277.273i 0.521156 + 0.451584i
\(615\) 0 0
\(616\) 327.243 + 96.0871i 0.531238 + 0.155986i
\(617\) 13.5084 6.16907i 0.0218936 0.00999849i −0.404438 0.914565i \(-0.632533\pi\)
0.426332 + 0.904567i \(0.359806\pi\)
\(618\) 0 0
\(619\) 75.3876 + 48.4487i 0.121789 + 0.0782692i 0.600117 0.799912i \(-0.295121\pi\)
−0.478328 + 0.878181i \(0.658757\pi\)
\(620\) 60.6090i 0.0977564i
\(621\) 0 0
\(622\) −850.958 −1.36810
\(623\) 482.532 750.835i 0.774530 1.20519i
\(624\) 0 0
\(625\) 248.065 + 543.186i 0.396904 + 0.869098i
\(626\) −41.4586 + 141.195i −0.0662279 + 0.225551i
\(627\) 0 0
\(628\) −221.819 + 255.993i −0.353215 + 0.407632i
\(629\) 137.913 + 19.8289i 0.219257 + 0.0315244i
\(630\) 0 0
\(631\) 376.084 + 434.024i 0.596013 + 0.687835i 0.970968 0.239207i \(-0.0768876\pi\)
−0.374956 + 0.927043i \(0.622342\pi\)
\(632\) −154.521 240.439i −0.244495 0.380442i
\(633\) 0 0
\(634\) −9.40081 10.8491i −0.0148278 0.0171122i
\(635\) −31.8364 108.425i −0.0501361 0.170748i
\(636\) 0 0
\(637\) 88.5075 102.143i 0.138944 0.160350i
\(638\) −659.280 301.083i −1.03335 0.471917i
\(639\) 0 0
\(640\) −2.87114 6.28692i −0.00448616 0.00982332i
\(641\) −138.488 + 19.9116i −0.216050 + 0.0310633i −0.249490 0.968377i \(-0.580263\pi\)
0.0334397 + 0.999441i \(0.489354\pi\)
\(642\) 0 0
\(643\) −705.760 −1.09760 −0.548802 0.835952i \(-0.684916\pi\)
−0.548802 + 0.835952i \(0.684916\pi\)
\(644\) −153.916 311.270i −0.239000 0.483338i
\(645\) 0 0
\(646\) −52.4967 33.7376i −0.0812642 0.0522253i
\(647\) −646.467 + 92.9479i −0.999176 + 0.143660i −0.622446 0.782663i \(-0.713861\pi\)
−0.376731 + 0.926323i \(0.622952\pi\)
\(648\) 0 0
\(649\) −284.860 83.6425i −0.438922 0.128879i
\(650\) −536.265 244.904i −0.825024 0.376776i
\(651\) 0 0
\(652\) 13.2994 92.4995i 0.0203979 0.141870i
\(653\) −325.570 1108.79i −0.498576 1.69799i −0.696313 0.717739i \(-0.745177\pi\)
0.197737 0.980255i \(-0.436641\pi\)
\(654\) 0 0
\(655\) −56.8216 + 36.5170i −0.0867506 + 0.0557512i
\(656\) 103.373 + 160.851i 0.157581 + 0.245200i
\(657\) 0 0
\(658\) −153.029 + 44.9334i −0.232567 + 0.0682878i
\(659\) −239.530 34.4391i −0.363474 0.0522597i −0.0418416 0.999124i \(-0.513322\pi\)
−0.321633 + 0.946865i \(0.604232\pi\)
\(660\) 0 0
\(661\) −334.744 + 732.987i −0.506420 + 1.10891i 0.467909 + 0.883777i \(0.345008\pi\)
−0.974329 + 0.225129i \(0.927720\pi\)
\(662\) 10.8646 37.0015i 0.0164118 0.0558935i
\(663\) 0 0
\(664\) 52.2024 + 363.075i 0.0786180 + 0.546800i
\(665\) −52.4873 + 81.6719i −0.0789283 + 0.122815i
\(666\) 0 0
\(667\) 229.618 + 701.290i 0.344254 + 1.05141i
\(668\) 440.835i 0.659932i
\(669\) 0 0
\(670\) −11.2693 78.3800i −0.0168199 0.116985i
\(671\) −1059.51 + 483.861i −1.57900 + 0.721105i
\(672\) 0 0
\(673\) 481.489 1054.31i 0.715437 1.56659i −0.104754 0.994498i \(-0.533406\pi\)
0.820191 0.572090i \(-0.193867\pi\)
\(674\) 538.980 + 467.029i 0.799673 + 0.692921i
\(675\) 0 0
\(676\) 225.553 66.2284i 0.333659 0.0979711i
\(677\) −863.612 + 748.324i −1.27565 + 1.10535i −0.286553 + 0.958064i \(0.592509\pi\)
−0.989093 + 0.147289i \(0.952945\pi\)
\(678\) 0 0
\(679\) 692.458 445.016i 1.01982 0.655398i
\(680\) 2.73703 2.37165i 0.00402505 0.00348772i
\(681\) 0 0
\(682\) 159.481 1109.22i 0.233844 1.62642i
\(683\) 521.857 + 452.191i 0.764066 + 0.662067i 0.947063 0.321047i \(-0.104035\pi\)
−0.182998 + 0.983113i \(0.558580\pi\)
\(684\) 0 0
\(685\) −23.0417 6.76566i −0.0336376 0.00987688i
\(686\) 398.298 181.897i 0.580609 0.265155i
\(687\) 0 0
\(688\) 44.4263 + 28.5511i 0.0645732 + 0.0414987i
\(689\) 1153.33i 1.67392i
\(690\) 0 0
\(691\) −1178.18 −1.70504 −0.852518 0.522697i \(-0.824926\pi\)
−0.852518 + 0.522697i \(0.824926\pi\)
\(692\) −83.5758 + 130.047i −0.120774 + 0.187929i
\(693\) 0 0
\(694\) −49.3529 108.068i −0.0711137 0.155717i
\(695\) 9.35084 31.8460i 0.0134544 0.0458216i
\(696\) 0 0
\(697\) −65.6109 + 75.7191i −0.0941334 + 0.108636i
\(698\) −505.269 72.6467i −0.723881 0.104078i
\(699\) 0 0
\(700\) 243.481 + 280.992i 0.347830 + 0.401417i
\(701\) 12.6201 + 19.6373i 0.0180030 + 0.0280133i 0.850138 0.526559i \(-0.176518\pi\)
−0.832135 + 0.554573i \(0.812882\pi\)
\(702\) 0 0
\(703\) 916.447 + 1057.64i 1.30362 + 1.50446i
\(704\) −36.0025 122.613i −0.0511399 0.174166i
\(705\) 0 0
\(706\) 285.641 329.647i 0.404590 0.466922i
\(707\) 254.803 + 116.365i 0.360400 + 0.164589i
\(708\) 0 0
\(709\) −146.903 321.672i −0.207197 0.453699i 0.777293 0.629139i \(-0.216592\pi\)
−0.984490 + 0.175440i \(0.943865\pi\)
\(710\) −76.0555 + 10.9351i −0.107120 + 0.0154016i
\(711\) 0 0
\(712\) −334.414 −0.469683
\(713\) −940.365 + 646.131i −1.31888 + 0.906214i
\(714\) 0 0
\(715\) 138.960 + 89.3043i 0.194350 + 0.124901i
\(716\) 606.494 87.2006i 0.847058 0.121789i
\(717\) 0 0
\(718\) 728.318 + 213.853i 1.01437 + 0.297846i
\(719\) −283.132 129.302i −0.393786 0.179836i 0.208674 0.977985i \(-0.433085\pi\)
−0.602460 + 0.798149i \(0.705813\pi\)
\(720\) 0 0
\(721\) 30.3008 210.746i 0.0420260 0.292297i
\(722\) −32.7513 111.541i −0.0453618 0.154488i
\(723\) 0 0
\(724\) 256.564 164.884i 0.354370 0.227740i
\(725\) −427.170 664.690i −0.589200 0.916813i
\(726\) 0 0
\(727\) 1218.71 357.845i 1.67635 0.492221i 0.701052 0.713110i \(-0.252714\pi\)
0.975299 + 0.220888i \(0.0708957\pi\)
\(728\) −357.743 51.4356i −0.491405 0.0706533i
\(729\) 0 0
\(730\) 26.5402 58.1150i 0.0363565 0.0796096i
\(731\) −7.79615 + 26.5513i −0.0106650 + 0.0363218i
\(732\) 0 0
\(733\) 13.9279 + 96.8707i 0.0190012 + 0.132157i 0.997114 0.0759191i \(-0.0241891\pi\)
−0.978113 + 0.208076i \(0.933280\pi\)
\(734\) 246.854 384.112i 0.336313 0.523314i
\(735\) 0 0
\(736\) −66.9351 + 111.569i −0.0909445 + 0.151589i
\(737\) 1464.10i 1.98657i
\(738\) 0 0
\(739\) 35.9787 + 250.237i 0.0486856 + 0.338616i 0.999577 + 0.0290905i \(0.00926109\pi\)
−0.950891 + 0.309525i \(0.899830\pi\)
\(740\) −73.8791 + 33.7394i −0.0998366 + 0.0455938i
\(741\) 0 0
\(742\) −302.160 + 661.639i −0.407224 + 0.891697i
\(743\) −468.945 406.343i −0.631150 0.546895i 0.279462 0.960157i \(-0.409844\pi\)
−0.910612 + 0.413262i \(0.864389\pi\)
\(744\) 0 0
\(745\) −120.524 + 35.3890i −0.161777 + 0.0475021i
\(746\) −198.967 + 172.406i −0.266712 + 0.231107i
\(747\) 0 0
\(748\) 56.3315 36.2021i 0.0753096 0.0483985i
\(749\) −45.1785 + 39.1474i −0.0603184 + 0.0522662i
\(750\) 0 0
\(751\) −6.02299 + 41.8908i −0.00801996 + 0.0557801i −0.993438 0.114368i \(-0.963516\pi\)
0.985418 + 0.170148i \(0.0544247\pi\)
\(752\) 45.1624 + 39.1334i 0.0600564 + 0.0520392i
\(753\) 0 0
\(754\) 736.939 + 216.385i 0.977373 + 0.286983i
\(755\) −0.0510043 + 0.0232929i −6.75553e−5 + 3.08515e-5i
\(756\) 0 0
\(757\) −1098.71 706.097i −1.45140 0.932757i −0.999165 0.0408573i \(-0.986991\pi\)
−0.452233 0.891900i \(-0.649373\pi\)
\(758\) 884.489i 1.16687i
\(759\) 0 0
\(760\) 36.3758 0.0478629
\(761\) −421.286 + 655.533i −0.553595 + 0.861411i −0.999432 0.0337036i \(-0.989270\pi\)
0.445837 + 0.895114i \(0.352906\pi\)
\(762\) 0 0
\(763\) −236.423 517.695i −0.309860 0.678499i
\(764\) 95.7630 326.139i 0.125344 0.426883i
\(765\) 0 0
\(766\) 150.299 173.454i 0.196213 0.226442i
\(767\) 311.410 + 44.7740i 0.406010 + 0.0583755i
\(768\) 0 0
\(769\) 561.209 + 647.669i 0.729790 + 0.842223i 0.992448 0.122666i \(-0.0391444\pi\)
−0.262658 + 0.964889i \(0.584599\pi\)
\(770\) −56.3215 87.6380i −0.0731448 0.113816i
\(771\) 0 0
\(772\) −274.607 316.914i −0.355709 0.410510i
\(773\) −282.669 962.683i −0.365678 1.24539i −0.912826 0.408350i \(-0.866104\pi\)
0.547147 0.837036i \(-0.315714\pi\)
\(774\) 0 0
\(775\) 800.012 923.263i 1.03227 1.19131i
\(776\) −280.543 128.120i −0.361524 0.165103i
\(777\) 0 0
\(778\) 15.7497 + 34.4871i 0.0202438 + 0.0443278i
\(779\) −996.082 + 143.215i −1.27867 + 0.183845i
\(780\) 0 0
\(781\) −1420.68 −1.81905
\(782\) −65.9754 17.1825i −0.0843675 0.0219725i
\(783\) 0 0
\(784\) 26.8675 + 17.2667i 0.0342698 + 0.0220238i
\(785\) 102.410 14.7244i 0.130459 0.0187572i
\(786\) 0 0