Properties

Label 525.2.j.b.407.7
Level 525
Weight 2
Character 525.407
Analytic conductor 4.192
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 407.7
Character \(\chi\) \(=\) 525.407
Dual form 525.2.j.b.218.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.260263 - 0.260263i) q^{2} +(1.52191 + 0.826909i) q^{3} +1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.00579 + 1.00579i) q^{8} +(1.63244 + 2.51697i) q^{9} +O(q^{10})\) \(q+(0.260263 - 0.260263i) q^{2} +(1.52191 + 0.826909i) q^{3} +1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.00579 + 1.00579i) q^{8} +(1.63244 + 2.51697i) q^{9} +3.38750i q^{11} +(-1.54179 + 2.83765i) q^{12} +(-1.59420 + 1.59420i) q^{13} -0.368068 q^{14} -3.20551 q^{16} +(0.140684 - 0.140684i) q^{17} +(1.07994 + 0.230209i) q^{18} -7.34691i q^{19} +(-0.491443 - 1.66087i) q^{21} +(0.881641 + 0.881641i) q^{22} +(2.21444 + 2.21444i) q^{23} +(0.699032 + 2.36243i) q^{24} +0.829822i q^{26} +(0.403134 + 5.18049i) q^{27} +(1.31842 - 1.31842i) q^{28} +9.49165 q^{29} +0.922582 q^{31} +(-2.84586 + 2.84586i) q^{32} +(-2.80115 + 5.15548i) q^{33} -0.0732300i q^{34} +(-4.69295 + 3.04373i) q^{36} +(-5.91558 - 5.91558i) q^{37} +(-1.91213 - 1.91213i) q^{38} +(-3.74449 + 1.10797i) q^{39} -1.39256i q^{41} +(-0.560167 - 0.304359i) q^{42} +(-0.864526 + 0.864526i) q^{43} -6.31608 q^{44} +1.15267 q^{46} +(0.651346 - 0.651346i) q^{47} +(-4.87851 - 2.65066i) q^{48} +1.00000i q^{49} +(0.330443 - 0.0977764i) q^{51} +(-2.97242 - 2.97242i) q^{52} +(6.54108 + 6.54108i) q^{53} +(1.45321 + 1.24337i) q^{54} -1.42241i q^{56} +(6.07522 - 11.1814i) q^{57} +(2.47033 - 2.47033i) q^{58} +6.25032 q^{59} +1.83261 q^{61} +(0.240114 - 0.240114i) q^{62} +(0.625454 - 2.93408i) q^{63} -4.92967i q^{64} +(0.612745 + 2.07082i) q^{66} +(0.815500 + 0.815500i) q^{67} +(0.262310 + 0.262310i) q^{68} +(1.53904 + 5.20132i) q^{69} -9.77651i q^{71} +(-0.889650 + 4.17345i) q^{72} +(4.80768 - 4.80768i) q^{73} -3.07921 q^{74} +13.6985 q^{76} +(2.39532 - 2.39532i) q^{77} +(-0.686187 + 1.26292i) q^{78} -3.41711i q^{79} +(-3.67026 + 8.21761i) q^{81} +(-0.362432 - 0.362432i) q^{82} +(-6.26911 - 6.26911i) q^{83} +(3.09673 - 0.916307i) q^{84} +0.450009i q^{86} +(14.4455 + 7.84873i) q^{87} +(-3.40712 + 3.40712i) q^{88} -12.3767 q^{89} +2.25454 q^{91} +(-4.12888 + 4.12888i) q^{92} +(1.40409 + 0.762891i) q^{93} -0.339043i q^{94} +(-6.68443 + 1.97789i) q^{96} +(6.71326 + 6.71326i) q^{97} +(0.260263 + 0.260263i) q^{98} +(-8.52622 + 5.52990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{3} + O(q^{10}) \) \( 24q + 4q^{3} - 16q^{12} + 8q^{13} - 16q^{16} + 20q^{18} + 4q^{21} - 8q^{22} + 16q^{27} - 28q^{33} + 16q^{36} + 16q^{37} + 20q^{42} + 40q^{43} - 64q^{46} - 16q^{48} - 20q^{51} - 4q^{57} - 40q^{58} + 32q^{61} + 8q^{63} - 16q^{66} - 24q^{67} + 8q^{72} - 32q^{73} + 32q^{76} - 60q^{78} + 52q^{81} + 80q^{82} - 4q^{87} - 96q^{88} - 24q^{91} + 76q^{93} - 96q^{96} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.260263 0.260263i 0.184034 0.184034i −0.609077 0.793111i \(-0.708460\pi\)
0.793111 + 0.609077i \(0.208460\pi\)
\(3\) 1.52191 + 0.826909i 0.878677 + 0.477416i
\(4\) 1.86453i 0.932263i
\(5\) 0 0
\(6\) 0.611312 0.180884i 0.249567 0.0738457i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 1.00579 + 1.00579i 0.355602 + 0.355602i
\(9\) 1.63244 + 2.51697i 0.544148 + 0.838989i
\(10\) 0 0
\(11\) 3.38750i 1.02137i 0.859768 + 0.510684i \(0.170608\pi\)
−0.859768 + 0.510684i \(0.829392\pi\)
\(12\) −1.54179 + 2.83765i −0.445077 + 0.819158i
\(13\) −1.59420 + 1.59420i −0.442151 + 0.442151i −0.892734 0.450583i \(-0.851216\pi\)
0.450583 + 0.892734i \(0.351216\pi\)
\(14\) −0.368068 −0.0983703
\(15\) 0 0
\(16\) −3.20551 −0.801377
\(17\) 0.140684 0.140684i 0.0341210 0.0341210i −0.689840 0.723961i \(-0.742319\pi\)
0.723961 + 0.689840i \(0.242319\pi\)
\(18\) 1.07994 + 0.230209i 0.254544 + 0.0542609i
\(19\) 7.34691i 1.68550i −0.538308 0.842748i \(-0.680936\pi\)
0.538308 0.842748i \(-0.319064\pi\)
\(20\) 0 0
\(21\) −0.491443 1.66087i −0.107242 0.362431i
\(22\) 0.881641 + 0.881641i 0.187966 + 0.187966i
\(23\) 2.21444 + 2.21444i 0.461742 + 0.461742i 0.899226 0.437484i \(-0.144130\pi\)
−0.437484 + 0.899226i \(0.644130\pi\)
\(24\) 0.699032 + 2.36243i 0.142689 + 0.482229i
\(25\) 0 0
\(26\) 0.829822i 0.162741i
\(27\) 0.403134 + 5.18049i 0.0775831 + 0.996986i
\(28\) 1.31842 1.31842i 0.249158 0.249158i
\(29\) 9.49165 1.76256 0.881278 0.472598i \(-0.156684\pi\)
0.881278 + 0.472598i \(0.156684\pi\)
\(30\) 0 0
\(31\) 0.922582 0.165701 0.0828503 0.996562i \(-0.473598\pi\)
0.0828503 + 0.996562i \(0.473598\pi\)
\(32\) −2.84586 + 2.84586i −0.503083 + 0.503083i
\(33\) −2.80115 + 5.15548i −0.487618 + 0.897454i
\(34\) 0.0732300i 0.0125588i
\(35\) 0 0
\(36\) −4.69295 + 3.04373i −0.782159 + 0.507289i
\(37\) −5.91558 5.91558i −0.972515 0.972515i 0.0271173 0.999632i \(-0.491367\pi\)
−0.999632 + 0.0271173i \(0.991367\pi\)
\(38\) −1.91213 1.91213i −0.310188 0.310188i
\(39\) −3.74449 + 1.10797i −0.599598 + 0.177418i
\(40\) 0 0
\(41\) 1.39256i 0.217481i −0.994070 0.108741i \(-0.965318\pi\)
0.994070 0.108741i \(-0.0346818\pi\)
\(42\) −0.560167 0.304359i −0.0864357 0.0469636i
\(43\) −0.864526 + 0.864526i −0.131839 + 0.131839i −0.769947 0.638108i \(-0.779717\pi\)
0.638108 + 0.769947i \(0.279717\pi\)
\(44\) −6.31608 −0.952184
\(45\) 0 0
\(46\) 1.15267 0.169952
\(47\) 0.651346 0.651346i 0.0950085 0.0950085i −0.658005 0.753014i \(-0.728599\pi\)
0.753014 + 0.658005i \(0.228599\pi\)
\(48\) −4.87851 2.65066i −0.704152 0.382591i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0.330443 0.0977764i 0.0462713 0.0136914i
\(52\) −2.97242 2.97242i −0.412201 0.412201i
\(53\) 6.54108 + 6.54108i 0.898486 + 0.898486i 0.995302 0.0968158i \(-0.0308658\pi\)
−0.0968158 + 0.995302i \(0.530866\pi\)
\(54\) 1.45321 + 1.24337i 0.197757 + 0.169201i
\(55\) 0 0
\(56\) 1.42241i 0.190077i
\(57\) 6.07522 11.1814i 0.804683 1.48101i
\(58\) 2.47033 2.47033i 0.324370 0.324370i
\(59\) 6.25032 0.813722 0.406861 0.913490i \(-0.366623\pi\)
0.406861 + 0.913490i \(0.366623\pi\)
\(60\) 0 0
\(61\) 1.83261 0.234642 0.117321 0.993094i \(-0.462569\pi\)
0.117321 + 0.993094i \(0.462569\pi\)
\(62\) 0.240114 0.240114i 0.0304945 0.0304945i
\(63\) 0.625454 2.93408i 0.0787998 0.369659i
\(64\) 4.92967i 0.616209i
\(65\) 0 0
\(66\) 0.612745 + 2.07082i 0.0754237 + 0.254900i
\(67\) 0.815500 + 0.815500i 0.0996292 + 0.0996292i 0.755165 0.655535i \(-0.227557\pi\)
−0.655535 + 0.755165i \(0.727557\pi\)
\(68\) 0.262310 + 0.262310i 0.0318097 + 0.0318097i
\(69\) 1.53904 + 5.20132i 0.185279 + 0.626166i
\(70\) 0 0
\(71\) 9.77651i 1.16026i −0.814524 0.580129i \(-0.803002\pi\)
0.814524 0.580129i \(-0.196998\pi\)
\(72\) −0.889650 + 4.17345i −0.104846 + 0.491846i
\(73\) 4.80768 4.80768i 0.562697 0.562697i −0.367376 0.930073i \(-0.619744\pi\)
0.930073 + 0.367376i \(0.119744\pi\)
\(74\) −3.07921 −0.357951
\(75\) 0 0
\(76\) 13.6985 1.57133
\(77\) 2.39532 2.39532i 0.272972 0.272972i
\(78\) −0.686187 + 1.26292i −0.0776954 + 0.142997i
\(79\) 3.41711i 0.384455i −0.981350 0.192228i \(-0.938429\pi\)
0.981350 0.192228i \(-0.0615712\pi\)
\(80\) 0 0
\(81\) −3.67026 + 8.21761i −0.407807 + 0.913068i
\(82\) −0.362432 0.362432i −0.0400239 0.0400239i
\(83\) −6.26911 6.26911i −0.688124 0.688124i 0.273693 0.961817i \(-0.411755\pi\)
−0.961817 + 0.273693i \(0.911755\pi\)
\(84\) 3.09673 0.916307i 0.337881 0.0999773i
\(85\) 0 0
\(86\) 0.450009i 0.0485257i
\(87\) 14.4455 + 7.84873i 1.54872 + 0.841473i
\(88\) −3.40712 + 3.40712i −0.363201 + 0.363201i
\(89\) −12.3767 −1.31192 −0.655962 0.754794i \(-0.727737\pi\)
−0.655962 + 0.754794i \(0.727737\pi\)
\(90\) 0 0
\(91\) 2.25454 0.236340
\(92\) −4.12888 + 4.12888i −0.430465 + 0.430465i
\(93\) 1.40409 + 0.762891i 0.145597 + 0.0791082i
\(94\) 0.339043i 0.0349696i
\(95\) 0 0
\(96\) −6.68443 + 1.97789i −0.682227 + 0.201867i
\(97\) 6.71326 + 6.71326i 0.681628 + 0.681628i 0.960367 0.278739i \(-0.0899164\pi\)
−0.278739 + 0.960367i \(0.589916\pi\)
\(98\) 0.260263 + 0.260263i 0.0262906 + 0.0262906i
\(99\) −8.52622 + 5.52990i −0.856918 + 0.555775i
\(100\) 0 0
\(101\) 12.4523i 1.23905i −0.784976 0.619526i \(-0.787325\pi\)
0.784976 0.619526i \(-0.212675\pi\)
\(102\) 0.0605545 0.111450i 0.00599579 0.0110352i
\(103\) 9.78924 9.78924i 0.964563 0.964563i −0.0348303 0.999393i \(-0.511089\pi\)
0.999393 + 0.0348303i \(0.0110891\pi\)
\(104\) −3.20687 −0.314459
\(105\) 0 0
\(106\) 3.40481 0.330704
\(107\) 5.21866 5.21866i 0.504507 0.504507i −0.408328 0.912835i \(-0.633888\pi\)
0.912835 + 0.408328i \(0.133888\pi\)
\(108\) −9.65916 + 0.751653i −0.929453 + 0.0723279i
\(109\) 6.67661i 0.639504i −0.947501 0.319752i \(-0.896400\pi\)
0.947501 0.319752i \(-0.103600\pi\)
\(110\) 0 0
\(111\) −4.11135 13.8946i −0.390233 1.31882i
\(112\) 2.26664 + 2.26664i 0.214177 + 0.214177i
\(113\) −8.23451 8.23451i −0.774637 0.774637i 0.204276 0.978913i \(-0.434516\pi\)
−0.978913 + 0.204276i \(0.934516\pi\)
\(114\) −1.32894 4.49125i −0.124467 0.420644i
\(115\) 0 0
\(116\) 17.6974i 1.64317i
\(117\) −6.61498 1.41011i −0.611555 0.130365i
\(118\) 1.62673 1.62673i 0.149752 0.149752i
\(119\) −0.198958 −0.0182384
\(120\) 0 0
\(121\) −0.475134 −0.0431940
\(122\) 0.476962 0.476962i 0.0431821 0.0431821i
\(123\) 1.15152 2.11936i 0.103829 0.191096i
\(124\) 1.72018i 0.154477i
\(125\) 0 0
\(126\) −0.600850 0.926415i −0.0535279 0.0825316i
\(127\) −1.88180 1.88180i −0.166983 0.166983i 0.618669 0.785652i \(-0.287672\pi\)
−0.785652 + 0.618669i \(0.787672\pi\)
\(128\) −6.97474 6.97474i −0.616486 0.616486i
\(129\) −2.03062 + 0.600850i −0.178786 + 0.0529019i
\(130\) 0 0
\(131\) 8.97080i 0.783783i 0.920012 + 0.391891i \(0.128179\pi\)
−0.920012 + 0.391891i \(0.871821\pi\)
\(132\) −9.61252 5.22282i −0.836663 0.454588i
\(133\) −5.19505 + 5.19505i −0.450468 + 0.450468i
\(134\) 0.424489 0.0366703
\(135\) 0 0
\(136\) 0.282999 0.0242670
\(137\) −6.49538 + 6.49538i −0.554938 + 0.554938i −0.927862 0.372924i \(-0.878355\pi\)
0.372924 + 0.927862i \(0.378355\pi\)
\(138\) 1.75427 + 0.953156i 0.149333 + 0.0811380i
\(139\) 1.83916i 0.155995i 0.996954 + 0.0779976i \(0.0248526\pi\)
−0.996954 + 0.0779976i \(0.975147\pi\)
\(140\) 0 0
\(141\) 1.52990 0.452688i 0.128840 0.0381232i
\(142\) −2.54447 2.54447i −0.213527 0.213527i
\(143\) −5.40034 5.40034i −0.451599 0.451599i
\(144\) −5.23281 8.06817i −0.436068 0.672347i
\(145\) 0 0
\(146\) 2.50253i 0.207110i
\(147\) −0.826909 + 1.52191i −0.0682023 + 0.125525i
\(148\) 11.0297 11.0297i 0.906640 0.906640i
\(149\) 0.987227 0.0808768 0.0404384 0.999182i \(-0.487125\pi\)
0.0404384 + 0.999182i \(0.487125\pi\)
\(150\) 0 0
\(151\) −8.71084 −0.708878 −0.354439 0.935079i \(-0.615328\pi\)
−0.354439 + 0.935079i \(0.615328\pi\)
\(152\) 7.38948 7.38948i 0.599366 0.599366i
\(153\) 0.583758 + 0.124439i 0.0471940 + 0.0100603i
\(154\) 1.24683i 0.100472i
\(155\) 0 0
\(156\) −2.06585 6.98169i −0.165400 0.558983i
\(157\) −5.26306 5.26306i −0.420038 0.420038i 0.465179 0.885217i \(-0.345990\pi\)
−0.885217 + 0.465179i \(0.845990\pi\)
\(158\) −0.889349 0.889349i −0.0707528 0.0707528i
\(159\) 4.54608 + 15.3638i 0.360528 + 1.21843i
\(160\) 0 0
\(161\) 3.13169i 0.246812i
\(162\) 1.18351 + 3.09398i 0.0929853 + 0.243086i
\(163\) −14.1511 + 14.1511i −1.10840 + 1.10840i −0.115041 + 0.993361i \(0.536700\pi\)
−0.993361 + 0.115041i \(0.963300\pi\)
\(164\) 2.59646 0.202750
\(165\) 0 0
\(166\) −3.26324 −0.253276
\(167\) 17.4876 17.4876i 1.35323 1.35323i 0.471215 0.882018i \(-0.343816\pi\)
0.882018 0.471215i \(-0.156184\pi\)
\(168\) 1.17620 2.16478i 0.0907459 0.167017i
\(169\) 7.91707i 0.609005i
\(170\) 0 0
\(171\) 18.4919 11.9934i 1.41411 0.917159i
\(172\) −1.61193 1.61193i −0.122909 0.122909i
\(173\) 10.8767 + 10.8767i 0.826942 + 0.826942i 0.987093 0.160150i \(-0.0511979\pi\)
−0.160150 + 0.987093i \(0.551198\pi\)
\(174\) 5.80236 1.71689i 0.439876 0.130157i
\(175\) 0 0
\(176\) 10.8587i 0.818502i
\(177\) 9.51244 + 5.16844i 0.714999 + 0.388484i
\(178\) −3.22119 + 3.22119i −0.241439 + 0.241439i
\(179\) −17.6524 −1.31941 −0.659703 0.751527i \(-0.729318\pi\)
−0.659703 + 0.751527i \(0.729318\pi\)
\(180\) 0 0
\(181\) −11.9237 −0.886282 −0.443141 0.896452i \(-0.646136\pi\)
−0.443141 + 0.896452i \(0.646136\pi\)
\(182\) 0.586773 0.586773i 0.0434945 0.0434945i
\(183\) 2.78908 + 1.51541i 0.206175 + 0.112022i
\(184\) 4.45454i 0.328393i
\(185\) 0 0
\(186\) 0.563986 0.166881i 0.0413534 0.0122363i
\(187\) 0.476568 + 0.476568i 0.0348501 + 0.0348501i
\(188\) 1.21445 + 1.21445i 0.0885729 + 0.0885729i
\(189\) 3.37810 3.94822i 0.245721 0.287191i
\(190\) 0 0
\(191\) 17.7849i 1.28687i 0.765501 + 0.643435i \(0.222491\pi\)
−0.765501 + 0.643435i \(0.777509\pi\)
\(192\) 4.07639 7.50253i 0.294188 0.541449i
\(193\) −14.3394 + 14.3394i −1.03217 + 1.03217i −0.0327052 + 0.999465i \(0.510412\pi\)
−0.999465 + 0.0327052i \(0.989588\pi\)
\(194\) 3.49443 0.250885
\(195\) 0 0
\(196\) −1.86453 −0.133180
\(197\) −4.10678 + 4.10678i −0.292596 + 0.292596i −0.838105 0.545509i \(-0.816336\pi\)
0.545509 + 0.838105i \(0.316336\pi\)
\(198\) −0.779834 + 3.65829i −0.0554204 + 0.259983i
\(199\) 13.4148i 0.950949i −0.879730 0.475474i \(-0.842276\pi\)
0.879730 0.475474i \(-0.157724\pi\)
\(200\) 0 0
\(201\) 0.566776 + 1.91547i 0.0399773 + 0.135107i
\(202\) −3.24088 3.24088i −0.228027 0.228027i
\(203\) −6.71161 6.71161i −0.471063 0.471063i
\(204\) 0.182307 + 0.616119i 0.0127640 + 0.0431370i
\(205\) 0 0
\(206\) 5.09556i 0.355025i
\(207\) −1.95873 + 9.18861i −0.136141 + 0.638653i
\(208\) 5.11022 5.11022i 0.354330 0.354330i
\(209\) 24.8876 1.72151
\(210\) 0 0
\(211\) 8.11525 0.558677 0.279338 0.960193i \(-0.409885\pi\)
0.279338 + 0.960193i \(0.409885\pi\)
\(212\) −12.1960 + 12.1960i −0.837626 + 0.837626i
\(213\) 8.08429 14.8790i 0.553926 1.01949i
\(214\) 2.71645i 0.185693i
\(215\) 0 0
\(216\) −4.80504 + 5.61598i −0.326941 + 0.382119i
\(217\) −0.652364 0.652364i −0.0442854 0.0442854i
\(218\) −1.73768 1.73768i −0.117690 0.117690i
\(219\) 11.2924 3.34136i 0.763069 0.225788i
\(220\) 0 0
\(221\) 0.448558i 0.0301732i
\(222\) −4.68630 2.54623i −0.314524 0.170892i
\(223\) 11.5431 11.5431i 0.772984 0.772984i −0.205643 0.978627i \(-0.565928\pi\)
0.978627 + 0.205643i \(0.0659285\pi\)
\(224\) 4.02466 0.268909
\(225\) 0 0
\(226\) −4.28628 −0.285119
\(227\) −7.04578 + 7.04578i −0.467645 + 0.467645i −0.901151 0.433506i \(-0.857276\pi\)
0.433506 + 0.901151i \(0.357276\pi\)
\(228\) 20.8479 + 11.3274i 1.38069 + 0.750176i
\(229\) 4.80117i 0.317270i −0.987337 0.158635i \(-0.949291\pi\)
0.987337 0.158635i \(-0.0507093\pi\)
\(230\) 0 0
\(231\) 5.62619 1.66476i 0.370176 0.109533i
\(232\) 9.54665 + 9.54665i 0.626768 + 0.626768i
\(233\) 14.2791 + 14.2791i 0.935455 + 0.935455i 0.998040 0.0625851i \(-0.0199345\pi\)
−0.0625851 + 0.998040i \(0.519934\pi\)
\(234\) −2.08864 + 1.35464i −0.136538 + 0.0885554i
\(235\) 0 0
\(236\) 11.6539i 0.758603i
\(237\) 2.82564 5.20055i 0.183545 0.337812i
\(238\) −0.0517814 + 0.0517814i −0.00335649 + 0.00335649i
\(239\) −12.8618 −0.831961 −0.415981 0.909373i \(-0.636562\pi\)
−0.415981 + 0.909373i \(0.636562\pi\)
\(240\) 0 0
\(241\) −16.1856 −1.04261 −0.521304 0.853371i \(-0.674554\pi\)
−0.521304 + 0.853371i \(0.674554\pi\)
\(242\) −0.123660 + 0.123660i −0.00794917 + 0.00794917i
\(243\) −12.3810 + 9.47153i −0.794244 + 0.607599i
\(244\) 3.41696i 0.218748i
\(245\) 0 0
\(246\) −0.251892 0.851289i −0.0160601 0.0542762i
\(247\) 11.7124 + 11.7124i 0.745243 + 0.745243i
\(248\) 0.927928 + 0.927928i 0.0589235 + 0.0589235i
\(249\) −4.35706 14.7250i −0.276117 0.933160i
\(250\) 0 0
\(251\) 8.02862i 0.506762i −0.967367 0.253381i \(-0.918457\pi\)
0.967367 0.253381i \(-0.0815426\pi\)
\(252\) 5.47066 + 1.16618i 0.344619 + 0.0734621i
\(253\) −7.50140 + 7.50140i −0.471609 + 0.471609i
\(254\) −0.979525 −0.0614609
\(255\) 0 0
\(256\) 6.22880 0.389300
\(257\) −16.6108 + 16.6108i −1.03615 + 1.03615i −0.0368323 + 0.999321i \(0.511727\pi\)
−0.999321 + 0.0368323i \(0.988273\pi\)
\(258\) −0.372116 + 0.684874i −0.0231669 + 0.0426384i
\(259\) 8.36589i 0.519831i
\(260\) 0 0
\(261\) 15.4946 + 23.8902i 0.959091 + 1.47877i
\(262\) 2.33477 + 2.33477i 0.144243 + 0.144243i
\(263\) 13.8361 + 13.8361i 0.853173 + 0.853173i 0.990523 0.137350i \(-0.0438584\pi\)
−0.137350 + 0.990523i \(0.543858\pi\)
\(264\) −8.00273 + 2.36797i −0.492534 + 0.145738i
\(265\) 0 0
\(266\) 2.70416i 0.165803i
\(267\) −18.8362 10.2344i −1.15276 0.626334i
\(268\) −1.52052 + 1.52052i −0.0928806 + 0.0928806i
\(269\) 11.4632 0.698925 0.349463 0.936950i \(-0.386364\pi\)
0.349463 + 0.936950i \(0.386364\pi\)
\(270\) 0 0
\(271\) 8.42276 0.511646 0.255823 0.966724i \(-0.417654\pi\)
0.255823 + 0.966724i \(0.417654\pi\)
\(272\) −0.450965 + 0.450965i −0.0273438 + 0.0273438i
\(273\) 3.43121 + 1.86430i 0.207666 + 0.112832i
\(274\) 3.38102i 0.204255i
\(275\) 0 0
\(276\) −9.69800 + 2.86959i −0.583751 + 0.172729i
\(277\) −12.7307 12.7307i −0.764914 0.764914i 0.212293 0.977206i \(-0.431907\pi\)
−0.977206 + 0.212293i \(0.931907\pi\)
\(278\) 0.478665 + 0.478665i 0.0287084 + 0.0287084i
\(279\) 1.50606 + 2.32211i 0.0901656 + 0.139021i
\(280\) 0 0
\(281\) 4.41251i 0.263228i 0.991301 + 0.131614i \(0.0420160\pi\)
−0.991301 + 0.131614i \(0.957984\pi\)
\(282\) 0.280357 0.515994i 0.0166950 0.0307270i
\(283\) −2.07246 + 2.07246i −0.123195 + 0.123195i −0.766016 0.642821i \(-0.777764\pi\)
0.642821 + 0.766016i \(0.277764\pi\)
\(284\) 18.2286 1.08167
\(285\) 0 0
\(286\) −2.81102 −0.166219
\(287\) −0.984688 + 0.984688i −0.0581243 + 0.0581243i
\(288\) −11.8087 2.51724i −0.695832 0.148330i
\(289\) 16.9604i 0.997672i
\(290\) 0 0
\(291\) 4.66575 + 15.7683i 0.273511 + 0.924352i
\(292\) 8.96405 + 8.96405i 0.524581 + 0.524581i
\(293\) 7.37595 + 7.37595i 0.430908 + 0.430908i 0.888937 0.458029i \(-0.151445\pi\)
−0.458029 + 0.888937i \(0.651445\pi\)
\(294\) 0.180884 + 0.611312i 0.0105494 + 0.0356525i
\(295\) 0 0
\(296\) 11.8997i 0.691656i
\(297\) −17.5489 + 1.36561i −1.01829 + 0.0792410i
\(298\) 0.256939 0.256939i 0.0148841 0.0148841i
\(299\) −7.06050 −0.408319
\(300\) 0 0
\(301\) 1.22262 0.0704709
\(302\) −2.26711 + 2.26711i −0.130458 + 0.130458i
\(303\) 10.2969 18.9513i 0.591543 1.08873i
\(304\) 23.5506i 1.35072i
\(305\) 0 0
\(306\) 0.184318 0.119544i 0.0105367 0.00683386i
\(307\) −11.3608 11.3608i −0.648396 0.648396i 0.304209 0.952605i \(-0.401608\pi\)
−0.952605 + 0.304209i \(0.901608\pi\)
\(308\) 4.46614 + 4.46614i 0.254482 + 0.254482i
\(309\) 22.9932 6.80357i 1.30804 0.387042i
\(310\) 0 0
\(311\) 8.94291i 0.507106i 0.967322 + 0.253553i \(0.0815992\pi\)
−0.967322 + 0.253553i \(0.918401\pi\)
\(312\) −4.88058 2.65179i −0.276308 0.150128i
\(313\) −4.52473 + 4.52473i −0.255753 + 0.255753i −0.823324 0.567571i \(-0.807883\pi\)
0.567571 + 0.823324i \(0.307883\pi\)
\(314\) −2.73956 −0.154602
\(315\) 0 0
\(316\) 6.37130 0.358414
\(317\) −1.78453 + 1.78453i −0.100229 + 0.100229i −0.755443 0.655214i \(-0.772578\pi\)
0.655214 + 0.755443i \(0.272578\pi\)
\(318\) 5.18182 + 2.81546i 0.290582 + 0.157883i
\(319\) 32.1529i 1.80022i
\(320\) 0 0
\(321\) 12.2577 3.62699i 0.684158 0.202439i
\(322\) −0.815063 0.815063i −0.0454217 0.0454217i
\(323\) −1.03360 1.03360i −0.0575108 0.0575108i
\(324\) −15.3220 6.84330i −0.851220 0.380183i
\(325\) 0 0
\(326\) 7.36604i 0.407967i
\(327\) 5.52095 10.1612i 0.305309 0.561917i
\(328\) 1.40063 1.40063i 0.0773368 0.0773368i
\(329\) −0.921142 −0.0507842
\(330\) 0 0
\(331\) −3.61857 −0.198895 −0.0994474 0.995043i \(-0.531707\pi\)
−0.0994474 + 0.995043i \(0.531707\pi\)
\(332\) 11.6889 11.6889i 0.641512 0.641512i
\(333\) 5.23248 24.5462i 0.286738 1.34512i
\(334\) 9.10277i 0.498082i
\(335\) 0 0
\(336\) 1.57532 + 5.32393i 0.0859410 + 0.290444i
\(337\) 17.0941 + 17.0941i 0.931175 + 0.931175i 0.997779 0.0666042i \(-0.0212165\pi\)
−0.0666042 + 0.997779i \(0.521216\pi\)
\(338\) 2.06052 + 2.06052i 0.112078 + 0.112078i
\(339\) −5.72302 19.3414i −0.310832 1.05048i
\(340\) 0 0
\(341\) 3.12524i 0.169241i
\(342\) 1.69133 7.93421i 0.0914565 0.429033i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −1.73907 −0.0937644
\(345\) 0 0
\(346\) 5.66162 0.304371
\(347\) 5.48573 5.48573i 0.294489 0.294489i −0.544361 0.838851i \(-0.683228\pi\)
0.838851 + 0.544361i \(0.183228\pi\)
\(348\) −14.6342 + 26.9340i −0.784474 + 1.44381i
\(349\) 14.8272i 0.793681i −0.917888 0.396841i \(-0.870107\pi\)
0.917888 0.396841i \(-0.129893\pi\)
\(350\) 0 0
\(351\) −8.90140 7.61605i −0.475122 0.406515i
\(352\) −9.64036 9.64036i −0.513833 0.513833i
\(353\) 7.55570 + 7.55570i 0.402149 + 0.402149i 0.878990 0.476841i \(-0.158218\pi\)
−0.476841 + 0.878990i \(0.658218\pi\)
\(354\) 3.82089 1.13058i 0.203078 0.0600898i
\(355\) 0 0
\(356\) 23.0766i 1.22306i
\(357\) −0.302797 0.164520i −0.0160257 0.00870732i
\(358\) −4.59428 + 4.59428i −0.242815 + 0.242815i
\(359\) 6.09504 0.321684 0.160842 0.986980i \(-0.448579\pi\)
0.160842 + 0.986980i \(0.448579\pi\)
\(360\) 0 0
\(361\) −34.9770 −1.84090
\(362\) −3.10330 + 3.10330i −0.163106 + 0.163106i
\(363\) −0.723114 0.392893i −0.0379536 0.0206215i
\(364\) 4.20364i 0.220331i
\(365\) 0 0
\(366\) 1.12030 0.331491i 0.0585590 0.0173273i
\(367\) −3.52753 3.52753i −0.184136 0.184136i 0.609019 0.793155i \(-0.291563\pi\)
−0.793155 + 0.609019i \(0.791563\pi\)
\(368\) −7.09840 7.09840i −0.370030 0.370030i
\(369\) 3.50503 2.27327i 0.182465 0.118342i
\(370\) 0 0
\(371\) 9.25048i 0.480261i
\(372\) −1.42243 + 2.61796i −0.0737496 + 0.135735i
\(373\) 7.07089 7.07089i 0.366117 0.366117i −0.499942 0.866059i \(-0.666645\pi\)
0.866059 + 0.499942i \(0.166645\pi\)
\(374\) 0.248066 0.0128272
\(375\) 0 0
\(376\) 1.31024 0.0675704
\(377\) −15.1316 + 15.1316i −0.779315 + 0.779315i
\(378\) −0.148381 1.90677i −0.00763187 0.0980738i
\(379\) 21.4715i 1.10292i −0.834202 0.551459i \(-0.814071\pi\)
0.834202 0.551459i \(-0.185929\pi\)
\(380\) 0 0
\(381\) −1.30786 4.42001i −0.0670036 0.226444i
\(382\) 4.62875 + 4.62875i 0.236828 + 0.236828i
\(383\) −14.6559 14.6559i −0.748882 0.748882i 0.225388 0.974269i \(-0.427635\pi\)
−0.974269 + 0.225388i \(0.927635\pi\)
\(384\) −4.84748 16.3824i −0.247372 0.836012i
\(385\) 0 0
\(386\) 7.46402i 0.379909i
\(387\) −3.58727 0.764695i −0.182351 0.0388716i
\(388\) −12.5170 + 12.5170i −0.635457 + 0.635457i
\(389\) −13.6323 −0.691185 −0.345592 0.938385i \(-0.612322\pi\)
−0.345592 + 0.938385i \(0.612322\pi\)
\(390\) 0 0
\(391\) 0.623074 0.0315102
\(392\) −1.00579 + 1.00579i −0.0508003 + 0.0508003i
\(393\) −7.41804 + 13.6528i −0.374190 + 0.688692i
\(394\) 2.13769i 0.107695i
\(395\) 0 0
\(396\) −10.3106 15.8974i −0.518129 0.798873i
\(397\) 24.5632 + 24.5632i 1.23279 + 1.23279i 0.962886 + 0.269907i \(0.0869929\pi\)
0.269907 + 0.962886i \(0.413007\pi\)
\(398\) −3.49137 3.49137i −0.175007 0.175007i
\(399\) −12.2022 + 3.61058i −0.610876 + 0.180755i
\(400\) 0 0
\(401\) 15.5011i 0.774088i −0.922061 0.387044i \(-0.873496\pi\)
0.922061 0.387044i \(-0.126504\pi\)
\(402\) 0.646036 + 0.351014i 0.0322214 + 0.0175070i
\(403\) −1.47078 + 1.47078i −0.0732647 + 0.0732647i
\(404\) 23.2177 1.15512
\(405\) 0 0
\(406\) −3.49357 −0.173383
\(407\) 20.0390 20.0390i 0.993296 0.993296i
\(408\) 0.430700 + 0.234015i 0.0213228 + 0.0115854i
\(409\) 32.0414i 1.58434i 0.610298 + 0.792172i \(0.291050\pi\)
−0.610298 + 0.792172i \(0.708950\pi\)
\(410\) 0 0
\(411\) −15.2565 + 4.51432i −0.752547 + 0.222675i
\(412\) 18.2523 + 18.2523i 0.899226 + 0.899226i
\(413\) −4.41964 4.41964i −0.217476 0.217476i
\(414\) 1.88167 + 2.90124i 0.0924792 + 0.142588i
\(415\) 0 0
\(416\) 9.07374i 0.444877i
\(417\) −1.52081 + 2.79904i −0.0744746 + 0.137069i
\(418\) 6.47733 6.47733i 0.316817 0.316817i
\(419\) 5.95062 0.290707 0.145353 0.989380i \(-0.453568\pi\)
0.145353 + 0.989380i \(0.453568\pi\)
\(420\) 0 0
\(421\) −10.6388 −0.518504 −0.259252 0.965810i \(-0.583476\pi\)
−0.259252 + 0.965810i \(0.583476\pi\)
\(422\) 2.11210 2.11210i 0.102816 0.102816i
\(423\) 2.70270 + 0.576132i 0.131410 + 0.0280125i
\(424\) 13.1580i 0.639007i
\(425\) 0 0
\(426\) −1.76842 5.97650i −0.0856801 0.289563i
\(427\) −1.29585 1.29585i −0.0627108 0.0627108i
\(428\) 9.73032 + 9.73032i 0.470333 + 0.470333i
\(429\) −3.75326 12.6844i −0.181209 0.612410i
\(430\) 0 0
\(431\) 11.2739i 0.543045i −0.962432 0.271523i \(-0.912473\pi\)
0.962432 0.271523i \(-0.0875271\pi\)
\(432\) −1.29225 16.6061i −0.0621733 0.798962i
\(433\) −9.75098 + 9.75098i −0.468602 + 0.468602i −0.901462 0.432859i \(-0.857505\pi\)
0.432859 + 0.901462i \(0.357505\pi\)
\(434\) −0.339573 −0.0163000
\(435\) 0 0
\(436\) 12.4487 0.596185
\(437\) 16.2693 16.2693i 0.778265 0.778265i
\(438\) 2.06936 3.80863i 0.0988779 0.181983i
\(439\) 28.4375i 1.35725i −0.734485 0.678625i \(-0.762576\pi\)
0.734485 0.678625i \(-0.237424\pi\)
\(440\) 0 0
\(441\) −2.51697 + 1.63244i −0.119856 + 0.0777354i
\(442\) 0.116743 + 0.116743i 0.00555290 + 0.00555290i
\(443\) −19.2121 19.2121i −0.912796 0.912796i 0.0836955 0.996491i \(-0.473328\pi\)
−0.996491 + 0.0836955i \(0.973328\pi\)
\(444\) 25.9069 7.66573i 1.22949 0.363799i
\(445\) 0 0
\(446\) 6.00850i 0.284511i
\(447\) 1.50247 + 0.816347i 0.0710646 + 0.0386119i
\(448\) −3.48580 + 3.48580i −0.164689 + 0.164689i
\(449\) 2.40628 0.113559 0.0567796 0.998387i \(-0.481917\pi\)
0.0567796 + 0.998387i \(0.481917\pi\)
\(450\) 0 0
\(451\) 4.71729 0.222129
\(452\) 15.3534 15.3534i 0.722166 0.722166i
\(453\) −13.2572 7.20307i −0.622875 0.338430i
\(454\) 3.66752i 0.172125i
\(455\) 0 0
\(456\) 17.3566 5.13572i 0.812796 0.240502i
\(457\) −6.21588 6.21588i −0.290767 0.290767i 0.546617 0.837383i \(-0.315916\pi\)
−0.837383 + 0.546617i \(0.815916\pi\)
\(458\) −1.24957 1.24957i −0.0583884 0.0583884i
\(459\) 0.785529 + 0.672100i 0.0366654 + 0.0313709i
\(460\) 0 0
\(461\) 35.4227i 1.64980i 0.565278 + 0.824900i \(0.308769\pi\)
−0.565278 + 0.824900i \(0.691231\pi\)
\(462\) 1.03101 1.89757i 0.0479671 0.0882827i
\(463\) 20.0869 20.0869i 0.933519 0.933519i −0.0644045 0.997924i \(-0.520515\pi\)
0.997924 + 0.0644045i \(0.0205148\pi\)
\(464\) −30.4256 −1.41247
\(465\) 0 0
\(466\) 7.43265 0.344311
\(467\) −5.80567 + 5.80567i −0.268654 + 0.268654i −0.828558 0.559903i \(-0.810838\pi\)
0.559903 + 0.828558i \(0.310838\pi\)
\(468\) 2.62918 12.3338i 0.121534 0.570130i
\(469\) 1.15329i 0.0532540i
\(470\) 0 0
\(471\) −3.65785 12.3620i −0.168545 0.569610i
\(472\) 6.28653 + 6.28653i 0.289361 + 0.289361i
\(473\) −2.92858 2.92858i −0.134656 0.134656i
\(474\) −0.618102 2.08892i −0.0283904 0.0959475i
\(475\) 0 0
\(476\) 0.370962i 0.0170030i
\(477\) −5.78575 + 27.1416i −0.264911 + 1.24273i
\(478\) −3.34746 + 3.34746i −0.153109 + 0.153109i
\(479\) −40.3829 −1.84514 −0.922571 0.385828i \(-0.873916\pi\)
−0.922571 + 0.385828i \(0.873916\pi\)
\(480\) 0 0
\(481\) 18.8612 0.859997
\(482\) −4.21252 + 4.21252i −0.191875 + 0.191875i
\(483\) 2.58962 4.76616i 0.117832 0.216868i
\(484\) 0.885900i 0.0402682i
\(485\) 0 0
\(486\) −0.757238 + 5.68742i −0.0343490 + 0.257987i
\(487\) −19.7983 19.7983i −0.897147 0.897147i 0.0980363 0.995183i \(-0.468744\pi\)
−0.995183 + 0.0980363i \(0.968744\pi\)
\(488\) 1.84323 + 1.84323i 0.0834393 + 0.0834393i
\(489\) −33.2385 + 9.83510i −1.50310 + 0.444759i
\(490\) 0 0
\(491\) 36.6924i 1.65590i 0.560798 + 0.827952i \(0.310494\pi\)
−0.560798 + 0.827952i \(0.689506\pi\)
\(492\) 3.95159 + 2.14704i 0.178152 + 0.0967960i
\(493\) 1.33533 1.33533i 0.0601402 0.0601402i
\(494\) 6.09662 0.274300
\(495\) 0 0
\(496\) −2.95735 −0.132789
\(497\) −6.91304 + 6.91304i −0.310092 + 0.310092i
\(498\) −4.96636 2.69840i −0.222548 0.120918i
\(499\) 7.62548i 0.341363i 0.985326 + 0.170682i \(0.0545970\pi\)
−0.985326 + 0.170682i \(0.945403\pi\)
\(500\) 0 0
\(501\) 41.0753 12.1540i 1.83511 0.543000i
\(502\) −2.08955 2.08955i −0.0932614 0.0932614i
\(503\) −15.7533 15.7533i −0.702406 0.702406i 0.262521 0.964926i \(-0.415446\pi\)
−0.964926 + 0.262521i \(0.915446\pi\)
\(504\) 3.58016 2.32200i 0.159473 0.103430i
\(505\) 0 0
\(506\) 3.90468i 0.173584i
\(507\) −6.54670 + 12.0491i −0.290749 + 0.535119i
\(508\) 3.50866 3.50866i 0.155672 0.155672i
\(509\) −14.4091 −0.638673 −0.319336 0.947641i \(-0.603460\pi\)
−0.319336 + 0.947641i \(0.603460\pi\)
\(510\) 0 0
\(511\) −6.79909 −0.300774
\(512\) 15.5706 15.5706i 0.688130 0.688130i
\(513\) 38.0606 2.96178i 1.68042 0.130766i
\(514\) 8.64637i 0.381375i
\(515\) 0 0
\(516\) −1.12030 3.78614i −0.0493185 0.166676i
\(517\) 2.20643 + 2.20643i 0.0970387 + 0.0970387i
\(518\) 2.17733 + 2.17733i 0.0956666 + 0.0956666i
\(519\) 7.55938 + 25.5475i 0.331820 + 1.12141i
\(520\) 0 0
\(521\) 25.3850i 1.11214i 0.831136 + 0.556069i \(0.187691\pi\)
−0.831136 + 0.556069i \(0.812309\pi\)
\(522\) 10.2504 + 2.18507i 0.448648 + 0.0956378i
\(523\) 16.0464 16.0464i 0.701661 0.701661i −0.263106 0.964767i \(-0.584747\pi\)
0.964767 + 0.263106i \(0.0847470\pi\)
\(524\) −16.7263 −0.730692
\(525\) 0 0
\(526\) 7.20208 0.314026
\(527\) 0.129793 0.129793i 0.00565387 0.00565387i
\(528\) 8.97912 16.5259i 0.390766 0.719199i
\(529\) 13.1925i 0.573588i
\(530\) 0 0
\(531\) 10.2033 + 15.7318i 0.442785 + 0.682704i
\(532\) −9.68630 9.68630i −0.419954 0.419954i
\(533\) 2.22002 + 2.22002i 0.0961595 + 0.0961595i
\(534\) −7.56601 + 2.23874i −0.327413 + 0.0968799i
\(535\) 0 0
\(536\) 1.64045i 0.0708567i
\(537\) −26.8655 14.5970i −1.15933 0.629905i
\(538\) 2.98346 2.98346i 0.128626 0.128626i
\(539\) −3.38750 −0.145910
\(540\) 0 0
\(541\) −26.9427 −1.15836 −0.579178 0.815201i \(-0.696626\pi\)
−0.579178 + 0.815201i \(0.696626\pi\)
\(542\) 2.19213 2.19213i 0.0941602 0.0941602i
\(543\) −18.1468 9.85981i −0.778756 0.423125i
\(544\) 0.800738i 0.0343313i
\(545\) 0 0
\(546\) 1.37823 0.407810i 0.0589826 0.0174527i
\(547\) −17.9286 17.9286i −0.766572 0.766572i 0.210929 0.977501i \(-0.432351\pi\)
−0.977501 + 0.210929i \(0.932351\pi\)
\(548\) −12.1108 12.1108i −0.517348 0.517348i
\(549\) 2.99164 + 4.61263i 0.127680 + 0.196862i
\(550\) 0 0
\(551\) 69.7343i 2.97078i
\(552\) −3.68350 + 6.77942i −0.156780 + 0.288551i
\(553\) −2.41627 + 2.41627i −0.102750 + 0.102750i
\(554\) −6.62667 −0.281540
\(555\) 0 0
\(556\) −3.42915 −0.145428
\(557\) −5.15944 + 5.15944i −0.218613 + 0.218613i −0.807914 0.589301i \(-0.799403\pi\)
0.589301 + 0.807914i \(0.299403\pi\)
\(558\) 0.996333 + 0.212387i 0.0421781 + 0.00899106i
\(559\) 2.75645i 0.116585i
\(560\) 0 0
\(561\) 0.331217 + 1.11937i 0.0139840 + 0.0472600i
\(562\) 1.14841 + 1.14841i 0.0484429 + 0.0484429i
\(563\) −23.2548 23.2548i −0.980072 0.980072i 0.0197332 0.999805i \(-0.493718\pi\)
−0.999805 + 0.0197332i \(0.993718\pi\)
\(564\) 0.844049 + 2.85253i 0.0355409 + 0.120113i
\(565\) 0 0
\(566\) 1.07877i 0.0453442i
\(567\) 8.40600 3.21547i 0.353019 0.135037i
\(568\) 9.83316 9.83316i 0.412590 0.412590i
\(569\) 45.1914 1.89452 0.947260 0.320466i \(-0.103839\pi\)
0.947260 + 0.320466i \(0.103839\pi\)
\(570\) 0 0
\(571\) 15.2468 0.638059 0.319029 0.947745i \(-0.396643\pi\)
0.319029 + 0.947745i \(0.396643\pi\)
\(572\) 10.0691 10.0691i 0.421009 0.421009i
\(573\) −14.7065 + 27.0671i −0.614372 + 1.13074i
\(574\) 0.512556i 0.0213937i
\(575\) 0 0
\(576\) 12.4078 8.04741i 0.516993 0.335309i
\(577\) 6.12177 + 6.12177i 0.254853 + 0.254853i 0.822957 0.568104i \(-0.192323\pi\)
−0.568104 + 0.822957i \(0.692323\pi\)
\(578\) 4.41417 + 4.41417i 0.183605 + 0.183605i
\(579\) −33.6806 + 9.96593i −1.39972 + 0.414170i
\(580\) 0 0
\(581\) 8.86586i 0.367818i
\(582\) 5.31822 + 2.88958i 0.220447 + 0.119777i
\(583\) −22.1579 + 22.1579i −0.917686 + 0.917686i
\(584\) 9.67107 0.400192
\(585\) 0 0
\(586\) 3.83938 0.158603
\(587\) −3.77086 + 3.77086i −0.155640 + 0.155640i −0.780632 0.624992i \(-0.785102\pi\)
0.624992 + 0.780632i \(0.285102\pi\)
\(588\) −2.83765 1.54179i −0.117023 0.0635825i
\(589\) 6.77812i 0.279288i
\(590\) 0 0
\(591\) −9.64610 + 2.85423i −0.396787 + 0.117407i
\(592\) 18.9624 + 18.9624i 0.779352 + 0.779352i
\(593\) −8.38017 8.38017i −0.344132 0.344132i 0.513786 0.857918i \(-0.328242\pi\)
−0.857918 + 0.513786i \(0.828242\pi\)
\(594\) −4.21191 + 4.92275i −0.172817 + 0.201983i
\(595\) 0 0
\(596\) 1.84071i 0.0753985i
\(597\) 11.0928 20.4161i 0.453998 0.835577i
\(598\) −1.83759 + 1.83759i −0.0751446 + 0.0751446i
\(599\) 6.75588 0.276038 0.138019 0.990430i \(-0.455927\pi\)
0.138019 + 0.990430i \(0.455927\pi\)
\(600\) 0 0
\(601\) 21.2564 0.867068 0.433534 0.901137i \(-0.357266\pi\)
0.433534 + 0.901137i \(0.357266\pi\)
\(602\) 0.318204 0.318204i 0.0129690 0.0129690i
\(603\) −0.721331 + 3.38385i −0.0293749 + 0.137801i
\(604\) 16.2416i 0.660861i
\(605\) 0 0
\(606\) −2.25243 7.61225i −0.0914986 0.309227i
\(607\) −2.72491 2.72491i −0.110601 0.110601i 0.649641 0.760241i \(-0.274919\pi\)
−0.760241 + 0.649641i \(0.774919\pi\)
\(608\) 20.9083 + 20.9083i 0.847944 + 0.847944i
\(609\) −4.66460 15.7644i −0.189019 0.638805i
\(610\) 0 0
\(611\) 2.07675i 0.0840162i
\(612\) −0.232020 + 1.08843i −0.00937884 + 0.0439972i
\(613\) −15.6232 + 15.6232i −0.631017 + 0.631017i −0.948323 0.317306i \(-0.897222\pi\)
0.317306 + 0.948323i \(0.397222\pi\)
\(614\) −5.91361 −0.238654
\(615\) 0 0
\(616\) 4.81840 0.194139
\(617\) 5.47009 5.47009i 0.220218 0.220218i −0.588373 0.808590i \(-0.700231\pi\)
0.808590 + 0.588373i \(0.200231\pi\)
\(618\) 4.21357 7.75500i 0.169494 0.311952i
\(619\) 42.9951i 1.72812i −0.503389 0.864060i \(-0.667914\pi\)
0.503389 0.864060i \(-0.332086\pi\)
\(620\) 0 0
\(621\) −10.5792 + 12.3646i −0.424527 + 0.496174i
\(622\) 2.32751 + 2.32751i 0.0933247 + 0.0933247i
\(623\) 8.75163 + 8.75163i 0.350627 + 0.350627i
\(624\) 12.0030 3.55162i 0.480504 0.142179i
\(625\) 0 0
\(626\) 2.35524i 0.0941344i
\(627\) 37.8768 + 20.5798i 1.51265 + 0.821878i
\(628\) 9.81311 9.81311i 0.391586 0.391586i
\(629\) −1.66446 −0.0663664
\(630\) 0 0
\(631\) −38.0091 −1.51312 −0.756560 0.653925i \(-0.773121\pi\)
−0.756560 + 0.653925i \(0.773121\pi\)
\(632\) 3.43691 3.43691i 0.136713 0.136713i
\(633\) 12.3507 + 6.71057i 0.490897 + 0.266721i
\(634\) 0.928896i 0.0368912i
\(635\) 0 0
\(636\) −28.6463 + 8.47629i −1.13590 + 0.336107i
\(637\) −1.59420 1.59420i −0.0631644 0.0631644i
\(638\) 8.36823 + 8.36823i 0.331301 + 0.331301i
\(639\) 24.6072 15.9596i 0.973445 0.631352i
\(640\) 0 0
\(641\) 30.8009i 1.21656i −0.793721 0.608282i \(-0.791859\pi\)
0.793721 0.608282i \(-0.208141\pi\)
\(642\) 2.24626 4.13420i 0.0886527 0.163164i
\(643\) 6.17366 6.17366i 0.243465 0.243465i −0.574817 0.818282i \(-0.694927\pi\)
0.818282 + 0.574817i \(0.194927\pi\)
\(644\) 5.83911 0.230093
\(645\) 0 0
\(646\) −0.538014 −0.0211679
\(647\) −23.4296 + 23.4296i −0.921112 + 0.921112i −0.997108 0.0759964i \(-0.975786\pi\)
0.0759964 + 0.997108i \(0.475786\pi\)
\(648\) −11.9568 + 4.57370i −0.469706 + 0.179672i
\(649\) 21.1729i 0.831110i
\(650\) 0 0
\(651\) −0.453396 1.53229i −0.0177700 0.0600551i
\(652\) −26.3851 26.3851i −1.03332 1.03332i
\(653\) 17.1928 + 17.1928i 0.672805 + 0.672805i 0.958362 0.285557i \(-0.0921786\pi\)
−0.285557 + 0.958362i \(0.592179\pi\)
\(654\) −1.20769 4.08150i −0.0472246 0.159599i
\(655\) 0 0
\(656\) 4.46386i 0.174285i
\(657\) 19.9490 + 4.25252i 0.778286 + 0.165906i
\(658\) −0.239739 + 0.239739i −0.00934601 + 0.00934601i
\(659\) −0.0375362 −0.00146220 −0.000731101 1.00000i \(-0.500233\pi\)
−0.000731101 1.00000i \(0.500233\pi\)
\(660\) 0 0
\(661\) 19.6937 0.765995 0.382998 0.923749i \(-0.374892\pi\)
0.382998 + 0.923749i \(0.374892\pi\)
\(662\) −0.941782 + 0.941782i −0.0366034 + 0.0366034i
\(663\) −0.370916 + 0.682666i −0.0144052 + 0.0265125i
\(664\) 12.6109i 0.489396i
\(665\) 0 0
\(666\) −5.02664 7.75029i −0.194778 0.300318i
\(667\) 21.0187 + 21.0187i 0.813846 + 0.813846i
\(668\) 32.6061 + 32.6061i 1.26157 + 1.26157i
\(669\) 27.1127 8.02252i 1.04824 0.310169i
\(670\) 0 0
\(671\) 6.20798i 0.239656i
\(672\) 6.12519 + 3.32803i 0.236284 + 0.128381i
\(673\) 4.33276 4.33276i 0.167016 0.167016i −0.618651 0.785666i \(-0.712320\pi\)
0.785666 + 0.618651i \(0.212320\pi\)
\(674\) 8.89793 0.342736
\(675\) 0 0
\(676\) −14.7616 −0.567753
\(677\) 3.64637 3.64637i 0.140142 0.140142i −0.633556 0.773697i \(-0.718405\pi\)
0.773697 + 0.633556i \(0.218405\pi\)
\(678\) −6.52335 3.54436i −0.250528 0.136120i
\(679\) 9.49398i 0.364346i
\(680\) 0 0
\(681\) −16.5493 + 4.89685i −0.634170 + 0.187648i
\(682\) 0.813386 + 0.813386i 0.0311462 + 0.0311462i
\(683\) −33.7536 33.7536i −1.29155 1.29155i −0.933830 0.357718i \(-0.883555\pi\)
−0.357718 0.933830i \(-0.616445\pi\)
\(684\) 22.3620 + 34.4787i 0.855033 + 1.31833i
\(685\) 0 0
\(686\) 0.368068i 0.0140529i
\(687\) 3.97013 7.30696i 0.151470 0.278778i
\(688\) 2.77125 2.77125i 0.105653 0.105653i
\(689\) −20.8555 −0.794533
\(690\) 0 0
\(691\) −12.2184 −0.464812 −0.232406 0.972619i \(-0.574660\pi\)
−0.232406 + 0.972619i \(0.574660\pi\)
\(692\) −20.2799 + 20.2799i −0.770928 + 0.770928i
\(693\) 9.93918 + 2.11872i 0.377558 + 0.0804836i
\(694\) 2.85547i 0.108392i
\(695\) 0 0
\(696\) 6.63497 + 22.4234i 0.251498 + 0.849956i
\(697\) −0.195912 0.195912i −0.00742068 0.00742068i
\(698\) −3.85897 3.85897i −0.146064 0.146064i
\(699\) 9.92404 + 33.5391i 0.375362 + 1.26856i
\(700\) 0 0
\(701\) 21.7907i 0.823024i −0.911404 0.411512i \(-0.865001\pi\)
0.911404 0.411512i \(-0.134999\pi\)
\(702\) −4.29889 + 0.334529i −0.162251 + 0.0126260i
\(703\) −43.4612 + 43.4612i −1.63917 + 1.63917i
\(704\) 16.6992 0.629377
\(705\) 0 0
\(706\) 3.93294 0.148018
\(707\) −8.80511 + 8.80511i −0.331150 + 0.331150i
\(708\) −9.63670 + 17.7362i −0.362169 + 0.666567i
\(709\) 14.1622i 0.531874i 0.963990 + 0.265937i \(0.0856814\pi\)
−0.963990 + 0.265937i \(0.914319\pi\)
\(710\) 0 0
\(711\) 8.60077 5.57825i 0.322554 0.209201i
\(712\) −12.4484 12.4484i −0.466523 0.466523i
\(713\) 2.04300 + 2.04300i 0.0765110 + 0.0765110i
\(714\) −0.121625 + 0.0359883i −0.00455172 + 0.00134683i
\(715\) 0 0
\(716\) 32.9134i 1.23003i
\(717\) −19.5746 10.6355i −0.731026 0.397192i
\(718\) 1.58632 1.58632i 0.0592008 0.0592008i
\(719\) 39.3153 1.46621 0.733106 0.680114i \(-0.238070\pi\)
0.733106 + 0.680114i \(0.238070\pi\)
\(720\) 0 0
\(721\) −13.8441 −0.515581
\(722\) −9.10324 + 9.10324i −0.338787 + 0.338787i
\(723\) −24.6331 13.3840i −0.916115 0.497757i
\(724\) 22.2320i 0.826248i
\(725\) 0 0
\(726\) −0.290455 + 0.0859443i −0.0107798 + 0.00318969i
\(727\) −10.0141 10.0141i −0.371403 0.371403i 0.496585 0.867988i \(-0.334587\pi\)
−0.867988 + 0.496585i \(0.834587\pi\)
\(728\) 2.26760 + 2.26760i 0.0840428 + 0.0840428i
\(729\) −26.6750 + 4.17686i −0.987962 + 0.154699i
\(730\) 0 0
\(731\) 0.243251i 0.00899695i
\(732\) −2.82551 + 5.20032i −0.104434 + 0.192209i
\(733\) 30.5737 30.5737i 1.12926 1.12926i 0.138967 0.990297i \(-0.455622\pi\)
0.990297 0.138967i \(-0.0443783\pi\)
\(734\) −1.83618 −0.0677745
\(735\) 0 0
\(736\) −12.6040 −0.464589
\(737\) −2.76250 + 2.76250i −0.101758 + 0.101758i
\(738\) 0.320580 1.50388i 0.0118007 0.0553586i
\(739\) 16.1095i 0.592598i −0.955095 0.296299i \(-0.904247\pi\)
0.955095 0.296299i \(-0.0957525\pi\)
\(740\) 0 0
\(741\) 8.14019 + 27.5104i 0.299037 + 1.01062i
\(742\) −2.40756 2.40756i −0.0883844 0.0883844i
\(743\) 23.1679 + 23.1679i 0.849946 + 0.849946i 0.990126 0.140180i \(-0.0447681\pi\)
−0.140180 + 0.990126i \(0.544768\pi\)
\(744\) 0.644914 + 2.17954i 0.0236437 + 0.0799057i
\(745\) 0 0
\(746\) 3.68059i 0.134756i
\(747\) 5.54518 26.0131i 0.202888 0.951770i
\(748\) −0.888574 + 0.888574i −0.0324895 + 0.0324895i
\(749\) −7.38030 −0.269670
\(750\) 0 0
\(751\) 28.7540 1.04925 0.524625 0.851334i \(-0.324206\pi\)
0.524625 + 0.851334i \(0.324206\pi\)
\(752\) −2.08789 + 2.08789i −0.0761377 + 0.0761377i
\(753\) 6.63894 12.2189i 0.241936 0.445280i
\(754\) 7.87638i 0.286841i
\(755\) 0 0
\(756\) 7.36156 + 6.29856i 0.267737 + 0.229076i
\(757\) 1.29026 + 1.29026i 0.0468952 + 0.0468952i 0.730166 0.683270i \(-0.239443\pi\)
−0.683270 + 0.730166i \(0.739443\pi\)
\(758\) −5.58825 5.58825i −0.202974 0.202974i
\(759\) −17.6195 + 5.21351i −0.639546 + 0.189238i
\(760\) 0 0
\(761\) 33.9969i 1.23239i 0.787596 + 0.616193i \(0.211326\pi\)
−0.787596 + 0.616193i \(0.788674\pi\)
\(762\) −1.49075 0.809978i −0.0540043 0.0293424i
\(763\) −4.72108 + 4.72108i −0.170915 + 0.170915i
\(764\) −33.1604 −1.19970
\(765\) 0 0
\(766\) −7.62879 −0.275639
\(767\) −9.96424 + 9.96424i −0.359788 + 0.359788i
\(768\) 9.47970 + 5.15065i 0.342069 + 0.185858i
\(769\) 21.4206i 0.772448i 0.922405 + 0.386224i \(0.126221\pi\)
−0.922405 + 0.386224i \(0.873779\pi\)
\(770\) 0 0
\(771\) −39.0158 + 11.5446i −1.40512 + 0.415768i
\(772\) −26.7361 26.7361i −0.962254 0.962254i
\(773\) 9.50533 + 9.50533i 0.341883 + 0.341883i 0.857075 0.515192i \(-0.172279\pi\)
−0.515192 + 0.857075i \(0.672279\pi\)
\(774\) −1.13266 + 0.734614i −0.0407125 + 0.0264051i
\(775\) 0 0
\(776\) 13.5043i 0.484777i
\(777\) −6.91783 + 12.7322i −0.248176 + 0.456764i
\(778\)