Properties

Label 690.2.i.f.47.1
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.1
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.68613 - 0.396187i) q^{3} -1.00000i q^{4} +(2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68607 + 1.33605i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.68613 - 0.396187i) q^{3} -1.00000i q^{4} +(2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68607 + 1.33605i) q^{9} +(-0.965722 + 2.01677i) q^{10} +5.22806i q^{11} +(-0.396187 + 1.68613i) q^{12} +(2.60057 - 2.60057i) q^{13} +3.06963 q^{14} +(-3.85040 + 0.417606i) q^{15} -1.00000 q^{16} +(0.444150 - 0.444150i) q^{17} +(-2.84407 + 0.954611i) q^{18} -2.97966i q^{19} +(-0.743206 - 2.10894i) q^{20} +(2.79989 + 4.51979i) q^{21} +(-3.69679 - 3.69679i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-0.912127 - 1.47242i) q^{24} +(3.89529 - 3.13476i) q^{25} +3.67776i q^{26} +(-3.99974 - 3.31694i) q^{27} +(-2.17056 + 2.17056i) q^{28} +1.70734 q^{29} +(2.42735 - 3.01794i) q^{30} -5.25582 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.07129 - 8.81518i) q^{33} +0.628123i q^{34} +(-6.19075 - 2.96441i) q^{35} +(1.33605 - 2.68607i) q^{36} +(-2.75535 - 2.75535i) q^{37} +(2.10693 + 2.10693i) q^{38} +(-5.41521 + 3.35458i) q^{39} +(2.01677 + 0.965722i) q^{40} -6.96597i q^{41} +(-5.17579 - 1.21615i) q^{42} +(7.32093 - 7.32093i) q^{43} +5.22806 q^{44} +(6.65773 + 0.821342i) q^{45} +1.00000 q^{46} +(6.05572 - 6.05572i) q^{47} +(1.68613 + 0.396187i) q^{48} +2.42262i q^{49} +(-0.537774 + 4.97100i) q^{50} +(-0.924861 + 0.572928i) q^{51} +(-2.60057 - 2.60057i) q^{52} +(0.302305 + 0.302305i) q^{53} +(5.17367 - 0.482816i) q^{54} +(3.88553 + 11.0257i) q^{55} -3.06963i q^{56} +(-1.18050 + 5.02409i) q^{57} +(-1.20727 + 1.20727i) q^{58} +11.1739 q^{59} +(0.417606 + 3.85040i) q^{60} -1.40994 q^{61} +(3.71643 - 3.71643i) q^{62} +(-2.93030 - 8.73023i) q^{63} +1.00000i q^{64} +(3.55169 - 7.41721i) q^{65} +(4.76865 + 7.69790i) q^{66} +(3.64409 + 3.64409i) q^{67} +(-0.444150 - 0.444150i) q^{68} +(0.912127 + 1.47242i) q^{69} +(6.47368 - 2.28137i) q^{70} +4.61412i q^{71} +(0.954611 + 2.84407i) q^{72} +(0.698447 - 0.698447i) q^{73} +3.89665 q^{74} +(-7.80992 + 3.74235i) q^{75} -2.97966 q^{76} +(11.3478 - 11.3478i) q^{77} +(1.45708 - 6.20118i) q^{78} -11.7332i q^{79} +(-2.10894 + 0.743206i) q^{80} +(5.42996 + 7.17743i) q^{81} +(4.92569 + 4.92569i) q^{82} +(-9.38271 - 9.38271i) q^{83} +(4.51979 - 2.79989i) q^{84} +(0.606592 - 1.26678i) q^{85} +10.3534i q^{86} +(-2.87879 - 0.676425i) q^{87} +(-3.69679 + 3.69679i) q^{88} +3.53601 q^{89} +(-5.28850 + 4.12695i) q^{90} -11.2894 q^{91} +(-0.707107 + 0.707107i) q^{92} +(8.86201 + 2.08229i) q^{93} +8.56408i q^{94} +(-2.21450 - 6.28393i) q^{95} +(-1.47242 + 0.912127i) q^{96} +(-13.1840 - 13.1840i) q^{97} +(-1.71305 - 1.71305i) q^{98} +(-6.98493 + 14.0429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.68613 0.396187i −0.973488 0.228739i
\(4\) 1.00000i 0.500000i
\(5\) 2.10894 0.743206i 0.943148 0.332372i
\(6\) 1.47242 0.912127i 0.601113 0.372374i
\(7\) −2.17056 2.17056i −0.820393 0.820393i 0.165771 0.986164i \(-0.446989\pi\)
−0.986164 + 0.165771i \(0.946989\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.68607 + 1.33605i 0.895357 + 0.445349i
\(10\) −0.965722 + 2.01677i −0.305388 + 0.637760i
\(11\) 5.22806i 1.57632i 0.615472 + 0.788159i \(0.288966\pi\)
−0.615472 + 0.788159i \(0.711034\pi\)
\(12\) −0.396187 + 1.68613i −0.114369 + 0.486744i
\(13\) 2.60057 2.60057i 0.721268 0.721268i −0.247596 0.968863i \(-0.579641\pi\)
0.968863 + 0.247596i \(0.0796405\pi\)
\(14\) 3.06963 0.820393
\(15\) −3.85040 + 0.417606i −0.994170 + 0.107825i
\(16\) −1.00000 −0.250000
\(17\) 0.444150 0.444150i 0.107722 0.107722i −0.651191 0.758914i \(-0.725730\pi\)
0.758914 + 0.651191i \(0.225730\pi\)
\(18\) −2.84407 + 0.954611i −0.670353 + 0.225004i
\(19\) 2.97966i 0.683580i −0.939776 0.341790i \(-0.888967\pi\)
0.939776 0.341790i \(-0.111033\pi\)
\(20\) −0.743206 2.10894i −0.166186 0.471574i
\(21\) 2.79989 + 4.51979i 0.610987 + 0.986298i
\(22\) −3.69679 3.69679i −0.788159 0.788159i
\(23\) −0.707107 0.707107i −0.147442 0.147442i
\(24\) −0.912127 1.47242i −0.186187 0.300557i
\(25\) 3.89529 3.13476i 0.779058 0.626952i
\(26\) 3.67776i 0.721268i
\(27\) −3.99974 3.31694i −0.769751 0.638345i
\(28\) −2.17056 + 2.17056i −0.410196 + 0.410196i
\(29\) 1.70734 0.317044 0.158522 0.987355i \(-0.449327\pi\)
0.158522 + 0.987355i \(0.449327\pi\)
\(30\) 2.42735 3.01794i 0.443172 0.550998i
\(31\) −5.25582 −0.943974 −0.471987 0.881606i \(-0.656463\pi\)
−0.471987 + 0.881606i \(0.656463\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 2.07129 8.81518i 0.360565 1.53453i
\(34\) 0.628123i 0.107722i
\(35\) −6.19075 2.96441i −1.04643 0.501077i
\(36\) 1.33605 2.68607i 0.222674 0.447679i
\(37\) −2.75535 2.75535i −0.452977 0.452977i 0.443365 0.896341i \(-0.353785\pi\)
−0.896341 + 0.443365i \(0.853785\pi\)
\(38\) 2.10693 + 2.10693i 0.341790 + 0.341790i
\(39\) −5.41521 + 3.35458i −0.867127 + 0.537163i
\(40\) 2.01677 + 0.965722i 0.318880 + 0.152694i
\(41\) 6.96597i 1.08790i −0.839117 0.543951i \(-0.816928\pi\)
0.839117 0.543951i \(-0.183072\pi\)
\(42\) −5.17579 1.21615i −0.798642 0.187656i
\(43\) 7.32093 7.32093i 1.11643 1.11643i 0.124170 0.992261i \(-0.460373\pi\)
0.992261 0.124170i \(-0.0396268\pi\)
\(44\) 5.22806 0.788159
\(45\) 6.65773 + 0.821342i 0.992476 + 0.122438i
\(46\) 1.00000 0.147442
\(47\) 6.05572 6.05572i 0.883318 0.883318i −0.110553 0.993870i \(-0.535262\pi\)
0.993870 + 0.110553i \(0.0352621\pi\)
\(48\) 1.68613 + 0.396187i 0.243372 + 0.0571847i
\(49\) 2.42262i 0.346089i
\(50\) −0.537774 + 4.97100i −0.0760527 + 0.703005i
\(51\) −0.924861 + 0.572928i −0.129506 + 0.0802260i
\(52\) −2.60057 2.60057i −0.360634 0.360634i
\(53\) 0.302305 + 0.302305i 0.0415247 + 0.0415247i 0.727564 0.686040i \(-0.240652\pi\)
−0.686040 + 0.727564i \(0.740652\pi\)
\(54\) 5.17367 0.482816i 0.704048 0.0657029i
\(55\) 3.88553 + 11.0257i 0.523924 + 1.48670i
\(56\) 3.06963i 0.410196i
\(57\) −1.18050 + 5.02409i −0.156361 + 0.665457i
\(58\) −1.20727 + 1.20727i −0.158522 + 0.158522i
\(59\) 11.1739 1.45472 0.727359 0.686257i \(-0.240747\pi\)
0.727359 + 0.686257i \(0.240747\pi\)
\(60\) 0.417606 + 3.85040i 0.0539127 + 0.497085i
\(61\) −1.40994 −0.180525 −0.0902625 0.995918i \(-0.528771\pi\)
−0.0902625 + 0.995918i \(0.528771\pi\)
\(62\) 3.71643 3.71643i 0.471987 0.471987i
\(63\) −2.93030 8.73023i −0.369183 1.09991i
\(64\) 1.00000i 0.125000i
\(65\) 3.55169 7.41721i 0.440533 0.919991i
\(66\) 4.76865 + 7.69790i 0.586981 + 0.947546i
\(67\) 3.64409 + 3.64409i 0.445196 + 0.445196i 0.893754 0.448558i \(-0.148062\pi\)
−0.448558 + 0.893754i \(0.648062\pi\)
\(68\) −0.444150 0.444150i −0.0538611 0.0538611i
\(69\) 0.912127 + 1.47242i 0.109807 + 0.177259i
\(70\) 6.47368 2.28137i 0.773752 0.272676i
\(71\) 4.61412i 0.547596i 0.961787 + 0.273798i \(0.0882799\pi\)
−0.961787 + 0.273798i \(0.911720\pi\)
\(72\) 0.954611 + 2.84407i 0.112502 + 0.335177i
\(73\) 0.698447 0.698447i 0.0817471 0.0817471i −0.665051 0.746798i \(-0.731590\pi\)
0.746798 + 0.665051i \(0.231590\pi\)
\(74\) 3.89665 0.452977
\(75\) −7.80992 + 3.74235i −0.901811 + 0.432130i
\(76\) −2.97966 −0.341790
\(77\) 11.3478 11.3478i 1.29320 1.29320i
\(78\) 1.45708 6.20118i 0.164982 0.702145i
\(79\) 11.7332i 1.32009i −0.751225 0.660046i \(-0.770537\pi\)
0.751225 0.660046i \(-0.229463\pi\)
\(80\) −2.10894 + 0.743206i −0.235787 + 0.0830930i
\(81\) 5.42996 + 7.17743i 0.603329 + 0.797493i
\(82\) 4.92569 + 4.92569i 0.543951 + 0.543951i
\(83\) −9.38271 9.38271i −1.02989 1.02989i −0.999539 0.0303467i \(-0.990339\pi\)
−0.0303467 0.999539i \(-0.509661\pi\)
\(84\) 4.51979 2.79989i 0.493149 0.305493i
\(85\) 0.606592 1.26678i 0.0657942 0.137402i
\(86\) 10.3534i 1.11643i
\(87\) −2.87879 0.676425i −0.308639 0.0725204i
\(88\) −3.69679 + 3.69679i −0.394080 + 0.394080i
\(89\) 3.53601 0.374816 0.187408 0.982282i \(-0.439991\pi\)
0.187408 + 0.982282i \(0.439991\pi\)
\(90\) −5.28850 + 4.12695i −0.557457 + 0.435019i
\(91\) −11.2894 −1.18345
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) 8.86201 + 2.08229i 0.918947 + 0.215924i
\(94\) 8.56408i 0.883318i
\(95\) −2.21450 6.28393i −0.227203 0.644717i
\(96\) −1.47242 + 0.912127i −0.150278 + 0.0930936i
\(97\) −13.1840 13.1840i −1.33863 1.33863i −0.897391 0.441237i \(-0.854540\pi\)
−0.441237 0.897391i \(-0.645460\pi\)
\(98\) −1.71305 1.71305i −0.173044 0.173044i
\(99\) −6.98493 + 14.0429i −0.702012 + 1.41137i
\(100\) −3.13476 3.89529i −0.313476 0.389529i
\(101\) 10.8801i 1.08261i −0.840825 0.541306i \(-0.817930\pi\)
0.840825 0.541306i \(-0.182070\pi\)
\(102\) 0.248854 1.05910i 0.0246402 0.104866i
\(103\) −2.54969 + 2.54969i −0.251228 + 0.251228i −0.821474 0.570246i \(-0.806848\pi\)
0.570246 + 0.821474i \(0.306848\pi\)
\(104\) 3.67776 0.360634
\(105\) 9.26395 + 7.45108i 0.904069 + 0.727151i
\(106\) −0.427523 −0.0415247
\(107\) −9.52639 + 9.52639i −0.920950 + 0.920950i −0.997097 0.0761462i \(-0.975738\pi\)
0.0761462 + 0.997097i \(0.475738\pi\)
\(108\) −3.31694 + 3.99974i −0.319172 + 0.384875i
\(109\) 8.20451i 0.785849i 0.919571 + 0.392925i \(0.128537\pi\)
−0.919571 + 0.392925i \(0.871463\pi\)
\(110\) −10.5438 5.04885i −1.00531 0.481389i
\(111\) 3.55425 + 5.73752i 0.337354 + 0.544581i
\(112\) 2.17056 + 2.17056i 0.205098 + 0.205098i
\(113\) −0.453030 0.453030i −0.0426174 0.0426174i 0.685477 0.728094i \(-0.259594\pi\)
−0.728094 + 0.685477i \(0.759594\pi\)
\(114\) −2.71783 4.38731i −0.254548 0.410909i
\(115\) −2.01677 0.965722i −0.188065 0.0900541i
\(116\) 1.70734i 0.158522i
\(117\) 10.4598 3.51083i 0.967008 0.324576i
\(118\) −7.90115 + 7.90115i −0.727359 + 0.727359i
\(119\) −1.92810 −0.176749
\(120\) −3.01794 2.42735i −0.275499 0.221586i
\(121\) −16.3326 −1.48478
\(122\) 0.996981 0.996981i 0.0902625 0.0902625i
\(123\) −2.75983 + 11.7455i −0.248845 + 1.05906i
\(124\) 5.25582i 0.471987i
\(125\) 5.88517 9.50604i 0.526386 0.850246i
\(126\) 8.24524 + 4.10117i 0.734545 + 0.365361i
\(127\) 13.0705 + 13.0705i 1.15982 + 1.15982i 0.984514 + 0.175307i \(0.0560919\pi\)
0.175307 + 0.984514i \(0.443908\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −15.2445 + 9.44358i −1.34220 + 0.831461i
\(130\) 2.73333 + 7.75618i 0.239729 + 0.680262i
\(131\) 3.19088i 0.278788i 0.990237 + 0.139394i \(0.0445155\pi\)
−0.990237 + 0.139394i \(0.955484\pi\)
\(132\) −8.81518 2.07129i −0.767263 0.180283i
\(133\) −6.46751 + 6.46751i −0.560804 + 0.560804i
\(134\) −5.15352 −0.445196
\(135\) −10.9004 4.02260i −0.938157 0.346210i
\(136\) 0.628123 0.0538611
\(137\) −12.8044 + 12.8044i −1.09396 + 1.09396i −0.0988556 + 0.995102i \(0.531518\pi\)
−0.995102 + 0.0988556i \(0.968482\pi\)
\(138\) −1.68613 0.396187i −0.143533 0.0337257i
\(139\) 11.9592i 1.01437i −0.861839 0.507183i \(-0.830687\pi\)
0.861839 0.507183i \(-0.169313\pi\)
\(140\) −2.96441 + 6.19075i −0.250538 + 0.523214i
\(141\) −12.6099 + 7.81153i −1.06195 + 0.657850i
\(142\) −3.26268 3.26268i −0.273798 0.273798i
\(143\) 13.5959 + 13.5959i 1.13695 + 1.13695i
\(144\) −2.68607 1.33605i −0.223839 0.111337i
\(145\) 3.60068 1.26890i 0.299020 0.105377i
\(146\) 0.987754i 0.0817471i
\(147\) 0.959812 4.08486i 0.0791640 0.336913i
\(148\) −2.75535 + 2.75535i −0.226488 + 0.226488i
\(149\) 17.1561 1.40548 0.702740 0.711447i \(-0.251960\pi\)
0.702740 + 0.711447i \(0.251960\pi\)
\(150\) 2.87620 8.16869i 0.234841 0.666971i
\(151\) 16.9726 1.38121 0.690603 0.723234i \(-0.257345\pi\)
0.690603 + 0.723234i \(0.257345\pi\)
\(152\) 2.10693 2.10693i 0.170895 0.170895i
\(153\) 1.78642 0.599613i 0.144424 0.0484759i
\(154\) 16.0482i 1.29320i
\(155\) −11.0842 + 3.90616i −0.890308 + 0.313751i
\(156\) 3.35458 + 5.41521i 0.268582 + 0.433564i
\(157\) 11.7841 + 11.7841i 0.940473 + 0.940473i 0.998325 0.0578517i \(-0.0184251\pi\)
−0.0578517 + 0.998325i \(0.518425\pi\)
\(158\) 8.29665 + 8.29665i 0.660046 + 0.660046i
\(159\) −0.389956 0.629494i −0.0309255 0.0499221i
\(160\) 0.965722 2.01677i 0.0763470 0.159440i
\(161\) 3.06963i 0.241921i
\(162\) −8.91477 1.23565i −0.700411 0.0970821i
\(163\) 3.78878 3.78878i 0.296760 0.296760i −0.542983 0.839743i \(-0.682705\pi\)
0.839743 + 0.542983i \(0.182705\pi\)
\(164\) −6.96597 −0.543951
\(165\) −2.18327 20.1301i −0.169967 1.56713i
\(166\) 13.2692 1.02989
\(167\) −11.5545 + 11.5545i −0.894117 + 0.894117i −0.994908 0.100791i \(-0.967863\pi\)
0.100791 + 0.994908i \(0.467863\pi\)
\(168\) −1.21615 + 5.17579i −0.0938279 + 0.399321i
\(169\) 0.525898i 0.0404537i
\(170\) 0.466825 + 1.32468i 0.0358038 + 0.101598i
\(171\) 3.98096 8.00357i 0.304432 0.612048i
\(172\) −7.32093 7.32093i −0.558215 0.558215i
\(173\) −6.59928 6.59928i −0.501734 0.501734i 0.410242 0.911977i \(-0.365444\pi\)
−0.911977 + 0.410242i \(0.865444\pi\)
\(174\) 2.51392 1.55731i 0.190580 0.118059i
\(175\) −15.2591 1.65077i −1.15348 0.124786i
\(176\) 5.22806i 0.394080i
\(177\) −18.8407 4.42696i −1.41615 0.332751i
\(178\) −2.50034 + 2.50034i −0.187408 + 0.187408i
\(179\) −18.4232 −1.37702 −0.688508 0.725229i \(-0.741734\pi\)
−0.688508 + 0.725229i \(0.741734\pi\)
\(180\) 0.821342 6.65773i 0.0612192 0.496238i
\(181\) 4.84965 0.360472 0.180236 0.983623i \(-0.442314\pi\)
0.180236 + 0.983623i \(0.442314\pi\)
\(182\) 7.98278 7.98278i 0.591723 0.591723i
\(183\) 2.37735 + 0.558602i 0.175739 + 0.0412931i
\(184\) 1.00000i 0.0737210i
\(185\) −7.85867 3.76309i −0.577781 0.276668i
\(186\) −7.73879 + 4.79398i −0.567435 + 0.351512i
\(187\) 2.32204 + 2.32204i 0.169804 + 0.169804i
\(188\) −6.05572 6.05572i −0.441659 0.441659i
\(189\) 1.48207 + 15.8813i 0.107804 + 1.15519i
\(190\) 6.00929 + 2.87752i 0.435960 + 0.208757i
\(191\) 3.19418i 0.231123i −0.993300 0.115561i \(-0.963133\pi\)
0.993300 0.115561i \(-0.0368667\pi\)
\(192\) 0.396187 1.68613i 0.0285924 0.121686i
\(193\) −1.55053 + 1.55053i −0.111610 + 0.111610i −0.760706 0.649096i \(-0.775147\pi\)
0.649096 + 0.760706i \(0.275147\pi\)
\(194\) 18.6449 1.33863
\(195\) −8.92722 + 11.0992i −0.639291 + 0.794833i
\(196\) 2.42262 0.173044
\(197\) −16.0842 + 16.0842i −1.14595 + 1.14595i −0.158614 + 0.987341i \(0.550702\pi\)
−0.987341 + 0.158614i \(0.949298\pi\)
\(198\) −4.99076 14.8689i −0.354678 1.05669i
\(199\) 8.97499i 0.636220i −0.948054 0.318110i \(-0.896952\pi\)
0.948054 0.318110i \(-0.103048\pi\)
\(200\) 4.97100 + 0.537774i 0.351502 + 0.0380263i
\(201\) −4.70067 7.58815i −0.331559 0.535227i
\(202\) 7.69341 + 7.69341i 0.541306 + 0.541306i
\(203\) −3.70587 3.70587i −0.260101 0.260101i
\(204\) 0.572928 + 0.924861i 0.0401130 + 0.0647532i
\(205\) −5.17715 14.6908i −0.361588 1.02605i
\(206\) 3.60580i 0.251228i
\(207\) −0.954611 2.84407i −0.0663501 0.197676i
\(208\) −2.60057 + 2.60057i −0.180317 + 0.180317i
\(209\) 15.5778 1.07754
\(210\) −11.8193 + 1.28190i −0.815610 + 0.0884592i
\(211\) −0.301249 −0.0207388 −0.0103694 0.999946i \(-0.503301\pi\)
−0.0103694 + 0.999946i \(0.503301\pi\)
\(212\) 0.302305 0.302305i 0.0207624 0.0207624i
\(213\) 1.82806 7.78001i 0.125256 0.533078i
\(214\) 13.4723i 0.920950i
\(215\) 9.99846 20.8804i 0.681890 1.42403i
\(216\) −0.482816 5.17367i −0.0328515 0.352024i
\(217\) 11.4081 + 11.4081i 0.774430 + 0.774430i
\(218\) −5.80146 5.80146i −0.392925 0.392925i
\(219\) −1.45439 + 0.900957i −0.0982785 + 0.0608810i
\(220\) 11.0257 3.88553i 0.743351 0.261962i
\(221\) 2.31008i 0.155393i
\(222\) −6.57027 1.54381i −0.440967 0.103613i
\(223\) 12.8348 12.8348i 0.859480 0.859480i −0.131797 0.991277i \(-0.542075\pi\)
0.991277 + 0.131797i \(0.0420745\pi\)
\(224\) −3.06963 −0.205098
\(225\) 14.6512 3.21590i 0.976747 0.214394i
\(226\) 0.640680 0.0426174
\(227\) −9.96258 + 9.96258i −0.661239 + 0.661239i −0.955672 0.294433i \(-0.904869\pi\)
0.294433 + 0.955672i \(0.404869\pi\)
\(228\) 5.02409 + 1.18050i 0.332728 + 0.0781806i
\(229\) 17.6169i 1.16416i 0.813133 + 0.582079i \(0.197760\pi\)
−0.813133 + 0.582079i \(0.802240\pi\)
\(230\) 2.10894 0.743206i 0.139060 0.0490056i
\(231\) −23.6297 + 14.6380i −1.55472 + 0.963110i
\(232\) 1.20727 + 1.20727i 0.0792611 + 0.0792611i
\(233\) 1.50132 + 1.50132i 0.0983549 + 0.0983549i 0.754572 0.656217i \(-0.227844\pi\)
−0.656217 + 0.754572i \(0.727844\pi\)
\(234\) −4.91366 + 9.87872i −0.321216 + 0.645792i
\(235\) 8.27052 17.2718i 0.539509 1.12669i
\(236\) 11.1739i 0.727359i
\(237\) −4.64856 + 19.7838i −0.301956 + 1.28509i
\(238\) 1.36338 1.36338i 0.0883745 0.0883745i
\(239\) 24.3097 1.57246 0.786232 0.617932i \(-0.212029\pi\)
0.786232 + 0.617932i \(0.212029\pi\)
\(240\) 3.85040 0.417606i 0.248542 0.0269564i
\(241\) 23.8969 1.53933 0.769667 0.638445i \(-0.220422\pi\)
0.769667 + 0.638445i \(0.220422\pi\)
\(242\) 11.5489 11.5489i 0.742390 0.742390i
\(243\) −6.31201 14.2534i −0.404915 0.914354i
\(244\) 1.40994i 0.0902625i
\(245\) 1.80051 + 5.10918i 0.115030 + 0.326413i
\(246\) −6.35385 10.2568i −0.405107 0.653952i
\(247\) −7.74879 7.74879i −0.493044 0.493044i
\(248\) −3.71643 3.71643i −0.235993 0.235993i
\(249\) 12.1032 + 19.5378i 0.767007 + 1.23816i
\(250\) 2.56034 + 10.8832i 0.161930 + 0.688316i
\(251\) 22.5045i 1.42047i −0.703965 0.710234i \(-0.748589\pi\)
0.703965 0.710234i \(-0.251411\pi\)
\(252\) −8.73023 + 2.93030i −0.549953 + 0.184592i
\(253\) 3.69679 3.69679i 0.232415 0.232415i
\(254\) −18.4845 −1.15982
\(255\) −1.52468 + 1.89564i −0.0954789 + 0.118709i
\(256\) 1.00000 0.0625000
\(257\) −17.0064 + 17.0064i −1.06083 + 1.06083i −0.0628062 + 0.998026i \(0.520005\pi\)
−0.998026 + 0.0628062i \(0.979995\pi\)
\(258\) 4.10187 17.4571i 0.255371 1.08683i
\(259\) 11.9613i 0.743238i
\(260\) −7.41721 3.55169i −0.459996 0.220267i
\(261\) 4.58603 + 2.28108i 0.283868 + 0.141195i
\(262\) −2.25629 2.25629i −0.139394 0.139394i
\(263\) 17.9233 + 17.9233i 1.10520 + 1.10520i 0.993773 + 0.111428i \(0.0355425\pi\)
0.111428 + 0.993773i \(0.464458\pi\)
\(264\) 7.69790 4.76865i 0.473773 0.293490i
\(265\) 0.862218 + 0.412869i 0.0529656 + 0.0253623i
\(266\) 9.14644i 0.560804i
\(267\) −5.96217 1.40092i −0.364879 0.0857350i
\(268\) 3.64409 3.64409i 0.222598 0.222598i
\(269\) 17.9945 1.09714 0.548571 0.836104i \(-0.315172\pi\)
0.548571 + 0.836104i \(0.315172\pi\)
\(270\) 10.5522 4.86334i 0.642184 0.295973i
\(271\) −14.0280 −0.852139 −0.426070 0.904690i \(-0.640102\pi\)
−0.426070 + 0.904690i \(0.640102\pi\)
\(272\) −0.444150 + 0.444150i −0.0269305 + 0.0269305i
\(273\) 19.0353 + 4.47270i 1.15207 + 0.270700i
\(274\) 18.1082i 1.09396i
\(275\) 16.3887 + 20.3648i 0.988276 + 1.22804i
\(276\) 1.47242 0.912127i 0.0886293 0.0549036i
\(277\) −0.994150 0.994150i −0.0597327 0.0597327i 0.676609 0.736342i \(-0.263449\pi\)
−0.736342 + 0.676609i \(0.763449\pi\)
\(278\) 8.45642 + 8.45642i 0.507183 + 0.507183i
\(279\) −14.1175 7.02203i −0.845194 0.420398i
\(280\) −2.28137 6.47368i −0.136338 0.386876i
\(281\) 15.9968i 0.954291i 0.878824 + 0.477145i \(0.158328\pi\)
−0.878824 + 0.477145i \(0.841672\pi\)
\(282\) 3.39298 14.4402i 0.202049 0.859899i
\(283\) 21.3172 21.3172i 1.26718 1.26718i 0.319636 0.947540i \(-0.396439\pi\)
0.947540 0.319636i \(-0.103561\pi\)
\(284\) 4.61412 0.273798
\(285\) 1.24432 + 11.4729i 0.0737073 + 0.679594i
\(286\) −19.2275 −1.13695
\(287\) −15.1200 + 15.1200i −0.892507 + 0.892507i
\(288\) 2.84407 0.954611i 0.167588 0.0562510i
\(289\) 16.6055i 0.976792i
\(290\) −1.64881 + 3.44331i −0.0968216 + 0.202198i
\(291\) 17.0065 + 27.4532i 0.996941 + 1.60933i
\(292\) −0.698447 0.698447i −0.0408735 0.0408735i
\(293\) −4.08472 4.08472i −0.238632 0.238632i 0.577651 0.816284i \(-0.303969\pi\)
−0.816284 + 0.577651i \(0.803969\pi\)
\(294\) 2.20974 + 3.56712i 0.128875 + 0.208039i
\(295\) 23.5651 8.30452i 1.37202 0.483508i
\(296\) 3.89665i 0.226488i
\(297\) 17.3411 20.9109i 1.00623 1.21337i
\(298\) −12.1312 + 12.1312i −0.702740 + 0.702740i
\(299\) −3.67776 −0.212690
\(300\) 3.74235 + 7.80992i 0.216065 + 0.450906i
\(301\) −31.7810 −1.83182
\(302\) −12.0014 + 12.0014i −0.690603 + 0.690603i
\(303\) −4.31057 + 18.3453i −0.247636 + 1.05391i
\(304\) 2.97966i 0.170895i
\(305\) −2.97349 + 1.04788i −0.170262 + 0.0600014i
\(306\) −0.839202 + 1.68718i −0.0479740 + 0.0964498i
\(307\) 15.3903 + 15.3903i 0.878369 + 0.878369i 0.993366 0.114997i \(-0.0366858\pi\)
−0.114997 + 0.993366i \(0.536686\pi\)
\(308\) −11.3478 11.3478i −0.646600 0.646600i
\(309\) 5.30926 3.28895i 0.302033 0.187102i
\(310\) 5.07567 10.5998i 0.288278 0.602029i
\(311\) 19.9984i 1.13401i 0.823715 + 0.567004i \(0.191898\pi\)
−0.823715 + 0.567004i \(0.808102\pi\)
\(312\) −6.20118 1.45708i −0.351073 0.0824910i
\(313\) −21.4652 + 21.4652i −1.21329 + 1.21329i −0.243348 + 0.969939i \(0.578246\pi\)
−0.969939 + 0.243348i \(0.921754\pi\)
\(314\) −16.6652 −0.940473
\(315\) −12.6682 16.2337i −0.713773 0.914668i
\(316\) −11.7332 −0.660046
\(317\) 17.0015 17.0015i 0.954897 0.954897i −0.0441291 0.999026i \(-0.514051\pi\)
0.999026 + 0.0441291i \(0.0140513\pi\)
\(318\) 0.720860 + 0.169379i 0.0404238 + 0.00949832i
\(319\) 8.92605i 0.499763i
\(320\) 0.743206 + 2.10894i 0.0415465 + 0.117894i
\(321\) 19.8370 12.2885i 1.10719 0.685877i
\(322\) −2.17056 2.17056i −0.120960 0.120960i
\(323\) −1.32341 1.32341i −0.0736367 0.0736367i
\(324\) 7.17743 5.42996i 0.398746 0.301664i
\(325\) 1.97780 18.2821i 0.109709 1.01411i
\(326\) 5.35815i 0.296760i
\(327\) 3.25052 13.8339i 0.179754 0.765015i
\(328\) 4.92569 4.92569i 0.271975 0.271975i
\(329\) −26.2886 −1.44933
\(330\) 15.7780 + 12.6903i 0.868548 + 0.698580i
\(331\) −33.1267 −1.82081 −0.910404 0.413720i \(-0.864229\pi\)
−0.910404 + 0.413720i \(0.864229\pi\)
\(332\) −9.38271 + 9.38271i −0.514943 + 0.514943i
\(333\) −3.71979 11.0823i −0.203843 0.607309i
\(334\) 16.3406i 0.894117i
\(335\) 10.3935 + 4.97687i 0.567857 + 0.271915i
\(336\) −2.79989 4.51979i −0.152747 0.246575i
\(337\) −0.517894 0.517894i −0.0282115 0.0282115i 0.692860 0.721072i \(-0.256350\pi\)
−0.721072 + 0.692860i \(0.756350\pi\)
\(338\) 0.371866 + 0.371866i 0.0202269 + 0.0202269i
\(339\) 0.584382 + 0.943351i 0.0317393 + 0.0512358i
\(340\) −1.26678 0.606592i −0.0687009 0.0328971i
\(341\) 27.4777i 1.48800i
\(342\) 2.84441 + 8.47434i 0.153808 + 0.458240i
\(343\) −9.93545 + 9.93545i −0.536464 + 0.536464i
\(344\) 10.3534 0.558215
\(345\) 3.01794 + 2.42735i 0.162480 + 0.130684i
\(346\) 9.33280 0.501734
\(347\) 15.1025 15.1025i 0.810743 0.810743i −0.174003 0.984745i \(-0.555670\pi\)
0.984745 + 0.174003i \(0.0556701\pi\)
\(348\) −0.676425 + 2.87879i −0.0362602 + 0.154319i
\(349\) 1.81851i 0.0973424i 0.998815 + 0.0486712i \(0.0154986\pi\)
−0.998815 + 0.0486712i \(0.984501\pi\)
\(350\) 11.9571 9.62255i 0.639133 0.514347i
\(351\) −19.0275 + 1.77568i −1.01561 + 0.0947788i
\(352\) 3.69679 + 3.69679i 0.197040 + 0.197040i
\(353\) 16.7727 + 16.7727i 0.892723 + 0.892723i 0.994779 0.102056i \(-0.0325420\pi\)
−0.102056 + 0.994779i \(0.532542\pi\)
\(354\) 16.4527 10.1920i 0.874451 0.541700i
\(355\) 3.42925 + 9.73092i 0.182005 + 0.516464i
\(356\) 3.53601i 0.187408i
\(357\) 3.25103 + 0.763890i 0.172063 + 0.0404294i
\(358\) 13.0272 13.0272i 0.688508 0.688508i
\(359\) 3.97799 0.209950 0.104975 0.994475i \(-0.466524\pi\)
0.104975 + 0.994475i \(0.466524\pi\)
\(360\) 4.12695 + 5.28850i 0.217509 + 0.278729i
\(361\) 10.1217 0.532719
\(362\) −3.42922 + 3.42922i −0.180236 + 0.180236i
\(363\) 27.5388 + 6.47076i 1.44541 + 0.339627i
\(364\) 11.2894i 0.591723i
\(365\) 0.953896 1.99208i 0.0499292 0.104270i
\(366\) −2.07603 + 1.28605i −0.108516 + 0.0672229i
\(367\) −14.9574 14.9574i −0.780770 0.780770i 0.199191 0.979961i \(-0.436169\pi\)
−0.979961 + 0.199191i \(0.936169\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) 9.30686 18.7111i 0.484496 0.974061i
\(370\) 8.21783 2.89602i 0.427224 0.150557i
\(371\) 1.31234i 0.0681332i
\(372\) 2.08229 8.86201i 0.107962 0.459474i
\(373\) −3.78362 + 3.78362i −0.195909 + 0.195909i −0.798243 0.602335i \(-0.794237\pi\)
0.602335 + 0.798243i \(0.294237\pi\)
\(374\) −3.28386 −0.169804
\(375\) −13.6893 + 13.6968i −0.706914 + 0.707299i
\(376\) 8.56408 0.441659
\(377\) 4.44004 4.44004i 0.228674 0.228674i
\(378\) −12.2777 10.1818i −0.631498 0.523693i
\(379\) 0.706517i 0.0362913i −0.999835 0.0181457i \(-0.994224\pi\)
0.999835 0.0181457i \(-0.00577626\pi\)
\(380\) −6.28393 + 2.21450i −0.322359 + 0.113601i
\(381\) −16.8602 27.2170i −0.863776 1.39437i
\(382\) 2.25863 + 2.25863i 0.115561 + 0.115561i
\(383\) 22.6285 + 22.6285i 1.15626 + 1.15626i 0.985273 + 0.170991i \(0.0546968\pi\)
0.170991 + 0.985273i \(0.445303\pi\)
\(384\) 0.912127 + 1.47242i 0.0465468 + 0.0751392i
\(385\) 15.4981 32.3656i 0.789856 1.64950i
\(386\) 2.19279i 0.111610i
\(387\) 29.4456 9.88343i 1.49681 0.502403i
\(388\) −13.1840 + 13.1840i −0.669314 + 0.669314i
\(389\) 28.6741 1.45384 0.726918 0.686724i \(-0.240952\pi\)
0.726918 + 0.686724i \(0.240952\pi\)
\(390\) −1.53585 14.1608i −0.0777710 0.717062i
\(391\) −0.628123 −0.0317655
\(392\) −1.71305 + 1.71305i −0.0865222 + 0.0865222i
\(393\) 1.26419 5.38024i 0.0637697 0.271397i
\(394\) 22.7465i 1.14595i
\(395\) −8.72021 24.7447i −0.438762 1.24504i
\(396\) 14.0429 + 6.98493i 0.705684 + 0.351006i
\(397\) −4.16145 4.16145i −0.208857 0.208857i 0.594924 0.803782i \(-0.297182\pi\)
−0.803782 + 0.594924i \(0.797182\pi\)
\(398\) 6.34628 + 6.34628i 0.318110 + 0.318110i
\(399\) 13.4674 8.34272i 0.674214 0.417658i
\(400\) −3.89529 + 3.13476i −0.194764 + 0.156738i
\(401\) 7.43533i 0.371303i 0.982616 + 0.185651i \(0.0594395\pi\)
−0.982616 + 0.185651i \(0.940560\pi\)
\(402\) 8.68950 + 2.04176i 0.433393 + 0.101834i
\(403\) −13.6681 + 13.6681i −0.680858 + 0.680858i
\(404\) −10.8801 −0.541306
\(405\) 16.7858 + 11.1012i 0.834093 + 0.551624i
\(406\) 5.24089 0.260101
\(407\) 14.4051 14.4051i 0.714036 0.714036i
\(408\) −1.05910 0.248854i −0.0524331 0.0123201i
\(409\) 14.4432i 0.714170i −0.934072 0.357085i \(-0.883771\pi\)
0.934072 0.357085i \(-0.116229\pi\)
\(410\) 14.0488 + 6.72719i 0.693821 + 0.332232i
\(411\) 26.6629 16.5170i 1.31518 0.814724i
\(412\) 2.54969 + 2.54969i 0.125614 + 0.125614i
\(413\) −24.2536 24.2536i −1.19344 1.19344i
\(414\) 2.68607 + 1.33605i 0.132013 + 0.0656631i
\(415\) −26.7609 12.8143i −1.31364 0.629030i
\(416\) 3.67776i 0.180317i
\(417\) −4.73808 + 20.1648i −0.232025 + 0.987472i
\(418\) −11.0152 + 11.0152i −0.538770 + 0.538770i
\(419\) −4.96433 −0.242523 −0.121262 0.992621i \(-0.538694\pi\)
−0.121262 + 0.992621i \(0.538694\pi\)
\(420\) 7.45108 9.26395i 0.363575 0.452035i
\(421\) −38.1579 −1.85970 −0.929851 0.367938i \(-0.880064\pi\)
−0.929851 + 0.367938i \(0.880064\pi\)
\(422\) 0.213015 0.213015i 0.0103694 0.0103694i
\(423\) 24.3568 8.17537i 1.18427 0.397500i
\(424\) 0.427523i 0.0207624i
\(425\) 0.337788 3.12240i 0.0163851 0.151458i
\(426\) 4.20867 + 6.79393i 0.203911 + 0.329167i
\(427\) 3.06036 + 3.06036i 0.148101 + 0.148101i
\(428\) 9.52639 + 9.52639i 0.460475 + 0.460475i
\(429\) −17.5380 28.3110i −0.846740 1.36687i
\(430\) 7.69468 + 21.8346i 0.371070 + 1.05296i
\(431\) 28.1762i 1.35720i 0.734508 + 0.678600i \(0.237413\pi\)
−0.734508 + 0.678600i \(0.762587\pi\)
\(432\) 3.99974 + 3.31694i 0.192438 + 0.159586i
\(433\) 13.8540 13.8540i 0.665781 0.665781i −0.290956 0.956737i \(-0.593973\pi\)
0.956737 + 0.290956i \(0.0939732\pi\)
\(434\) −16.1334 −0.774430
\(435\) −6.57393 + 0.712994i −0.315196 + 0.0341855i
\(436\) 8.20451 0.392925
\(437\) −2.10693 + 2.10693i −0.100788 + 0.100788i
\(438\) 0.391335 1.66548i 0.0186987 0.0795798i
\(439\) 13.6748i 0.652661i 0.945256 + 0.326330i \(0.105812\pi\)
−0.945256 + 0.326330i \(0.894188\pi\)
\(440\) −5.04885 + 10.5438i −0.240694 + 0.502657i
\(441\) −3.23674 + 6.50734i −0.154130 + 0.309873i
\(442\) 1.63348 + 1.63348i 0.0776965 + 0.0776965i
\(443\) −24.2823 24.2823i −1.15369 1.15369i −0.985808 0.167879i \(-0.946308\pi\)
−0.167879 0.985808i \(-0.553692\pi\)
\(444\) 5.73752 3.55425i 0.272290 0.168677i
\(445\) 7.45724 2.62798i 0.353507 0.124578i
\(446\) 18.1511i 0.859480i
\(447\) −28.9274 6.79701i −1.36822 0.321488i
\(448\) 2.17056 2.17056i 0.102549 0.102549i
\(449\) −15.3176 −0.722883 −0.361442 0.932395i \(-0.617715\pi\)
−0.361442 + 0.932395i \(0.617715\pi\)
\(450\) −8.08598 + 12.6340i −0.381177 + 0.595570i
\(451\) 36.4185 1.71488
\(452\) −0.453030 + 0.453030i −0.0213087 + 0.0213087i
\(453\) −28.6179 6.72431i −1.34459 0.315936i
\(454\) 14.0892i 0.661239i
\(455\) −23.8086 + 8.39032i −1.11616 + 0.393344i
\(456\) −4.38731 + 2.71783i −0.205454 + 0.127274i
\(457\) 0.783829 + 0.783829i 0.0366660 + 0.0366660i 0.725202 0.688536i \(-0.241746\pi\)
−0.688536 + 0.725202i \(0.741746\pi\)
\(458\) −12.4570 12.4570i −0.582079 0.582079i
\(459\) −3.24970 + 0.303268i −0.151683 + 0.0141553i
\(460\) −0.965722 + 2.01677i −0.0450270 + 0.0940326i
\(461\) 29.9101i 1.39305i 0.717531 + 0.696527i \(0.245272\pi\)
−0.717531 + 0.696527i \(0.754728\pi\)
\(462\) 6.35809 27.0593i 0.295805 1.25891i
\(463\) 12.8240 12.8240i 0.595982 0.595982i −0.343259 0.939241i \(-0.611531\pi\)
0.939241 + 0.343259i \(0.111531\pi\)
\(464\) −1.70734 −0.0792611
\(465\) 20.2370 2.19487i 0.938470 0.101784i
\(466\) −2.12319 −0.0983549
\(467\) −27.4406 + 27.4406i −1.26980 + 1.26980i −0.323607 + 0.946192i \(0.604895\pi\)
−0.946192 + 0.323607i \(0.895105\pi\)
\(468\) −3.51083 10.4598i −0.162288 0.483504i
\(469\) 15.8194i 0.730472i
\(470\) 6.36488 + 18.0612i 0.293590 + 0.833100i
\(471\) −15.2008 24.5382i −0.700417 1.13066i
\(472\) 7.90115 + 7.90115i 0.363680 + 0.363680i
\(473\) 38.2742 + 38.2742i 1.75985 + 1.75985i
\(474\) −10.7022 17.2763i −0.491568 0.793525i
\(475\) −9.34051 11.6066i −0.428572 0.532548i
\(476\) 1.92810i 0.0883745i
\(477\) 0.408118 + 1.21590i 0.0186865 + 0.0556724i
\(478\) −17.1895 + 17.1895i −0.786232 + 0.786232i
\(479\) −15.9073 −0.726824 −0.363412 0.931629i \(-0.618388\pi\)
−0.363412 + 0.931629i \(0.618388\pi\)
\(480\) −2.42735 + 3.01794i −0.110793 + 0.137749i
\(481\) −14.3309 −0.653435
\(482\) −16.8977 + 16.8977i −0.769667 + 0.769667i
\(483\) 1.21615 5.17579i 0.0553367 0.235507i
\(484\) 16.3326i 0.742390i
\(485\) −37.6026 18.0058i −1.70745 0.817602i
\(486\) 14.5419 + 5.61539i 0.659635 + 0.254719i
\(487\) 17.8486 + 17.8486i 0.808797 + 0.808797i 0.984452 0.175655i \(-0.0562042\pi\)
−0.175655 + 0.984452i \(0.556204\pi\)
\(488\) −0.996981 0.996981i −0.0451312 0.0451312i
\(489\) −7.88945 + 4.88731i −0.356773 + 0.221012i
\(490\) −4.88588 2.33958i −0.220722 0.105691i
\(491\) 12.5148i 0.564787i −0.959299 0.282393i \(-0.908872\pi\)
0.959299 0.282393i \(-0.0911283\pi\)
\(492\) 11.7455 + 2.75983i 0.529530 + 0.124423i
\(493\) 0.758313 0.758313i 0.0341527 0.0341527i
\(494\) 10.9584 0.493044
\(495\) −4.29402 + 34.8070i −0.193002 + 1.56446i
\(496\) 5.25582 0.235993
\(497\) 10.0152 10.0152i 0.449243 0.449243i
\(498\) −22.3735 5.25707i −1.00258 0.235575i
\(499\) 26.3804i 1.18095i −0.807056 0.590474i \(-0.798941\pi\)
0.807056 0.590474i \(-0.201059\pi\)
\(500\) −9.50604 5.88517i −0.425123 0.263193i
\(501\) 24.0602 14.9047i 1.07493 0.665893i
\(502\) 15.9131 + 15.9131i 0.710234 + 0.710234i
\(503\) 9.48821 + 9.48821i 0.423059 + 0.423059i 0.886255 0.463197i \(-0.153298\pi\)
−0.463197 + 0.886255i \(0.653298\pi\)
\(504\) 4.10117 8.24524i 0.182681 0.367272i
\(505\) −8.08618 22.9456i −0.359830 1.02106i
\(506\) 5.22806i 0.232415i
\(507\) −0.208354 + 0.886733i −0.00925334 + 0.0393812i
\(508\) 13.0705 13.0705i 0.579911 0.579911i
\(509\) −14.3787 −0.637323 −0.318662 0.947869i \(-0.603233\pi\)
−0.318662 + 0.947869i \(0.603233\pi\)
\(510\) −0.262308 2.41853i −0.0116152 0.107094i
\(511\) −3.03204 −0.134129
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −9.88333 + 11.9179i −0.436360 + 0.526186i
\(514\) 24.0507i 1.06083i
\(515\) −3.48221 + 7.27210i −0.153444 + 0.320447i
\(516\) 9.44358 + 15.2445i 0.415730 + 0.671101i
\(517\) 31.6596 + 31.6596i 1.39239 + 1.39239i
\(518\) −8.45790 8.45790i −0.371619 0.371619i
\(519\) 8.51270 + 13.7418i 0.373666 + 0.603198i
\(520\) 7.75618 2.73333i 0.340131 0.119865i
\(521\) 12.6632i 0.554784i −0.960757 0.277392i \(-0.910530\pi\)
0.960757 0.277392i \(-0.0894701\pi\)
\(522\) −4.85578 + 1.62984i −0.212532 + 0.0713363i
\(523\) −9.41837 + 9.41837i −0.411836 + 0.411836i −0.882378 0.470541i \(-0.844059\pi\)
0.470541 + 0.882378i \(0.344059\pi\)
\(524\) 3.19088 0.139394
\(525\) 25.0748 + 8.82887i 1.09436 + 0.385324i
\(526\) −25.3474 −1.10520
\(527\) −2.33437 + 2.33437i −0.101687 + 0.101687i
\(528\) −2.07129 + 8.81518i −0.0901413 + 0.383632i
\(529\) 1.00000i 0.0434783i
\(530\) −0.901622 + 0.317738i −0.0391640 + 0.0138017i
\(531\) 30.0139 + 14.9289i 1.30249 + 0.647858i
\(532\) 6.46751 + 6.46751i 0.280402 + 0.280402i
\(533\) −18.1155 18.1155i −0.784668 0.784668i
\(534\) 5.20649 3.22529i 0.225307 0.139572i
\(535\) −13.0105 + 27.1707i −0.562495 + 1.17469i
\(536\) 5.15352i 0.222598i
\(537\) 31.0639 + 7.29904i 1.34051 + 0.314977i
\(538\) −12.7240 + 12.7240i −0.548571 + 0.548571i
\(539\) −12.6656 −0.545546
\(540\) −4.02260 + 10.9004i −0.173105 + 0.469078i
\(541\) 9.84624 0.423323 0.211661 0.977343i \(-0.432113\pi\)
0.211661 + 0.977343i \(0.432113\pi\)
\(542\) 9.91928 9.91928i 0.426070 0.426070i
\(543\) −8.17714 1.92137i −0.350915 0.0824538i
\(544\) 0.628123i 0.0269305i
\(545\) 6.09764 + 17.3028i 0.261194 + 0.741173i
\(546\) −16.6227 + 10.2973i −0.711385 + 0.440685i
\(547\) −24.2038 24.2038i −1.03488 1.03488i −0.999369 0.0355120i \(-0.988694\pi\)
−0.0355120 0.999369i \(-0.511306\pi\)
\(548\) 12.8044 + 12.8044i 0.546979 + 0.546979i
\(549\) −3.78721 1.88375i −0.161634 0.0803966i
\(550\) −25.9886 2.81151i −1.10816 0.119883i
\(551\) 5.08727i 0.216725i
\(552\) −0.396187 + 1.68613i −0.0168629 + 0.0717665i
\(553\) −25.4676 + 25.4676i −1.08299 + 1.08299i
\(554\) 1.40594 0.0597327
\(555\) 11.7599 + 9.45856i 0.499178 + 0.401494i
\(556\) −11.9592 −0.507183
\(557\) 19.7073 19.7073i 0.835026 0.835026i −0.153174 0.988199i \(-0.548949\pi\)
0.988199 + 0.153174i \(0.0489494\pi\)
\(558\) 14.9479 5.01727i 0.632796 0.212398i
\(559\) 38.0771i 1.61049i
\(560\) 6.19075 + 2.96441i 0.261607 + 0.125269i
\(561\) −2.99530 4.83523i −0.126462 0.204143i
\(562\) −11.3115 11.3115i −0.477145 0.477145i
\(563\) −6.01209 6.01209i −0.253379 0.253379i 0.568975 0.822355i \(-0.307340\pi\)
−0.822355 + 0.568975i \(0.807340\pi\)
\(564\) 7.81153 + 12.6099i 0.328925 + 0.530974i
\(565\) −1.29211 0.618719i −0.0543594 0.0260297i
\(566\) 30.1471i 1.26718i
\(567\) 3.79300 27.3650i 0.159291 1.14922i
\(568\) −3.26268 + 3.26268i −0.136899 + 0.136899i
\(569\) 1.31647 0.0551895 0.0275947 0.999619i \(-0.491215\pi\)
0.0275947 + 0.999619i \(0.491215\pi\)
\(570\) −8.99242 7.23268i −0.376651 0.302944i
\(571\) 17.5617 0.734934 0.367467 0.930036i \(-0.380225\pi\)
0.367467 + 0.930036i \(0.380225\pi\)
\(572\) 13.5959 13.5959i 0.568474 0.568474i
\(573\) −1.26549 + 5.38581i −0.0528668 + 0.224995i
\(574\) 21.3829i 0.892507i
\(575\) −4.97100 0.537774i −0.207305 0.0224267i
\(576\) −1.33605 + 2.68607i −0.0556686 + 0.111920i
\(577\) 16.0820 + 16.0820i 0.669504 + 0.669504i 0.957601 0.288097i \(-0.0930225\pi\)
−0.288097 + 0.957601i \(0.593023\pi\)
\(578\) −11.7418 11.7418i −0.488396 0.488396i
\(579\) 3.22871 2.00010i 0.134180 0.0831214i
\(580\) −1.26890 3.60068i −0.0526883 0.149510i
\(581\) 40.7314i 1.68982i
\(582\) −31.4378 7.38688i −1.30314 0.306196i
\(583\) −1.58046 + 1.58046i −0.0654562 + 0.0654562i
\(584\) 0.987754 0.0408735
\(585\) 19.4498 15.1779i 0.804152 0.627530i
\(586\) 5.77667 0.238632
\(587\) 9.61314 9.61314i 0.396777 0.396777i −0.480318 0.877095i \(-0.659479\pi\)
0.877095 + 0.480318i \(0.159479\pi\)
\(588\) −4.08486 0.959812i −0.168457 0.0395820i
\(589\) 15.6605i 0.645282i
\(590\) −10.7909 + 22.5353i −0.444254 + 0.927762i
\(591\) 33.4925 20.7478i 1.37770 0.853448i
\(592\) 2.75535 + 2.75535i 0.113244 + 0.113244i
\(593\) −12.3638 12.3638i −0.507719 0.507719i 0.406106 0.913826i \(-0.366886\pi\)
−0.913826 + 0.406106i \(0.866886\pi\)
\(594\) 2.52419 + 27.0483i 0.103569 + 1.10980i
\(595\) −4.06626 + 1.43298i −0.166701 + 0.0587464i
\(596\) 17.1561i 0.702740i
\(597\) −3.55578 + 15.1330i −0.145528 + 0.619353i
\(598\) 2.60057 2.60057i 0.106345 0.106345i
\(599\) −48.6613 −1.98825 −0.994123 0.108255i \(-0.965474\pi\)
−0.994123 + 0.108255i \(0.965474\pi\)
\(600\) −8.16869 2.87620i −0.333485 0.117420i
\(601\) −28.4823 −1.16182 −0.580909 0.813969i \(-0.697303\pi\)
−0.580909 + 0.813969i \(0.697303\pi\)
\(602\) 22.4725 22.4725i 0.915912 0.915912i
\(603\) 4.91961 + 14.6570i 0.200342 + 0.596877i
\(604\) 16.9726i 0.690603i
\(605\) −34.4445 + 12.1385i −1.40037 + 0.493499i
\(606\) −9.92406 16.0201i −0.403137 0.650773i
\(607\) 10.2267 + 10.2267i 0.415088 + 0.415088i 0.883507 0.468419i \(-0.155176\pi\)
−0.468419 + 0.883507i \(0.655176\pi\)
\(608\) −2.10693 2.10693i −0.0854475 0.0854475i
\(609\) 4.78036 + 7.71679i 0.193710 + 0.312700i
\(610\) 1.36161 2.84354i 0.0551302 0.115132i
\(611\) 31.4966i 1.27422i
\(612\) −0.599613 1.78642i −0.0242379 0.0722119i
\(613\) 4.21128 4.21128i 0.170092 0.170092i −0.616928 0.787020i \(-0.711623\pi\)
0.787020 + 0.616928i \(0.211623\pi\)
\(614\) −21.7651 −0.878369
\(615\) 2.90903 + 26.8218i 0.117304 + 1.08156i
\(616\) 16.0482 0.646600
\(617\) −1.18781 + 1.18781i −0.0478194 + 0.0478194i −0.730612 0.682793i \(-0.760765\pi\)
0.682793 + 0.730612i \(0.260765\pi\)
\(618\) −1.42857 + 6.07986i −0.0574657 + 0.244568i
\(619\) 9.65709i 0.388151i 0.980987 + 0.194076i \(0.0621707\pi\)
−0.980987 + 0.194076i \(0.937829\pi\)
\(620\) 3.90616 + 11.0842i 0.156875 + 0.445154i
\(621\) 0.482816 + 5.17367i 0.0193747 + 0.207612i
\(622\) −14.1410 14.1410i −0.567004 0.567004i
\(623\) −7.67510 7.67510i −0.307497 0.307497i
\(624\) 5.41521 3.35458i 0.216782 0.134291i
\(625\) 5.34654 24.4216i 0.213862 0.976864i
\(626\) 30.3564i 1.21329i
\(627\) −26.2662 6.17173i −1.04897 0.246475i
\(628\) 11.7841 11.7841i 0.470237 0.470237i
\(629\) −2.44758 −0.0975913
\(630\) 20.4368 + 2.52122i 0.814220 + 0.100448i
\(631\) −20.1398 −0.801754 −0.400877 0.916132i \(-0.631295\pi\)
−0.400877 + 0.916132i \(0.631295\pi\)
\(632\) 8.29665 8.29665i 0.330023 0.330023i
\(633\) 0.507945 + 0.119351i 0.0201890 + 0.00474377i
\(634\) 24.0437i 0.954897i
\(635\) 37.2791 + 17.8509i 1.47938 + 0.708391i
\(636\) −0.629494 + 0.389956i −0.0249611 + 0.0154627i
\(637\) 6.30019 + 6.30019i 0.249623 + 0.249623i
\(638\) −6.31167 6.31167i −0.249881 0.249881i
\(639\) −6.16468 + 12.3939i −0.243871 + 0.490294i
\(640\) −2.01677 0.965722i −0.0797200 0.0381735i
\(641\) 7.77971i 0.307280i −0.988127 0.153640i \(-0.950900\pi\)
0.988127 0.153640i \(-0.0490996\pi\)
\(642\) −5.33757 + 22.7161i −0.210657 + 0.896534i
\(643\) −22.1643 + 22.1643i −0.874075 + 0.874075i −0.992914 0.118838i \(-0.962083\pi\)
0.118838 + 0.992914i \(0.462083\pi\)
\(644\) 3.06963 0.120960
\(645\) −25.1313 + 31.2458i −0.989542 + 1.23030i
\(646\) 1.87159 0.0736367
\(647\) −7.24949 + 7.24949i −0.285007 + 0.285007i −0.835102 0.550095i \(-0.814591\pi\)
0.550095 + 0.835102i \(0.314591\pi\)
\(648\) −1.23565 + 8.91477i −0.0485410 + 0.350205i
\(649\) 58.4178i 2.29310i
\(650\) 11.5289 + 14.3259i 0.452200 + 0.561909i
\(651\) −14.7157 23.7552i −0.576756 0.931040i
\(652\) −3.78878 3.78878i −0.148380 0.148380i
\(653\) −18.2696 18.2696i −0.714944 0.714944i 0.252621 0.967565i \(-0.418707\pi\)
−0.967565 + 0.252621i \(0.918707\pi\)
\(654\) 7.48356 + 12.0805i 0.292630 + 0.472385i
\(655\) 2.37148 + 6.72938i 0.0926615 + 0.262939i
\(656\) 6.96597i 0.271975i
\(657\) 2.80924 0.942921i 0.109599 0.0367868i
\(658\) 18.5888 18.5888i 0.724667 0.724667i
\(659\) −23.0114 −0.896399 −0.448199 0.893934i \(-0.647934\pi\)
−0.448199 + 0.893934i \(0.647934\pi\)
\(660\) −20.1301 + 2.18327i −0.783564 + 0.0849836i
\(661\) −21.2264 −0.825611 −0.412806 0.910819i \(-0.635451\pi\)
−0.412806 + 0.910819i \(0.635451\pi\)
\(662\) 23.4241 23.4241i 0.910404 0.910404i
\(663\) −0.915226 + 3.89510i −0.0355444 + 0.151273i
\(664\) 13.2692i 0.514943i
\(665\) −8.83292 + 18.4463i −0.342526 + 0.715317i
\(666\) 10.4667 + 5.20611i 0.405576 + 0.201733i
\(667\) −1.20727 1.20727i −0.0467456 0.0467456i
\(668\) 11.5545 + 11.5545i 0.447058 + 0.447058i
\(669\) −26.7261 + 16.5561i −1.03329 + 0.640097i
\(670\) −10.8685 + 3.83013i −0.419886 + 0.147971i
\(671\) 7.37127i 0.284565i
\(672\) 5.17579 + 1.21615i 0.199661 + 0.0469139i
\(673\) −2.23113 + 2.23113i −0.0860038 + 0.0860038i −0.748800 0.662796i \(-0.769370\pi\)
0.662796 + 0.748800i \(0.269370\pi\)
\(674\) 0.732413 0.0282115
\(675\) −25.9780 0.382189i −0.999892 0.0147105i
\(676\) −0.525898 −0.0202269
\(677\) 8.73195 8.73195i 0.335596 0.335596i −0.519111 0.854707i \(-0.673737\pi\)
0.854707 + 0.519111i \(0.173737\pi\)
\(678\) −1.08027 0.253829i −0.0414876 0.00974826i
\(679\) 57.2330i 2.19640i
\(680\) 1.32468 0.466825i 0.0507990 0.0179019i
\(681\) 20.7453 12.8512i 0.794960 0.492457i
\(682\) 19.4297 + 19.4297i 0.744002 + 0.744002i
\(683\) −7.60796 7.60796i −0.291110 0.291110i 0.546408 0.837519i \(-0.315995\pi\)
−0.837519 + 0.546408i \(0.815995\pi\)
\(684\) −8.00357 3.98096i −0.306024 0.152216i
\(685\) −17.4875 + 36.5202i −0.668163 + 1.39536i
\(686\) 14.0509i 0.536464i
\(687\) 6.97959 29.7044i 0.266288 1.13329i
\(688\) −7.32093 + 7.32093i −0.279108 + 0.279108i
\(689\) 1.57233 0.0599009
\(690\) −3.85040 + 0.417606i −0.146582 + 0.0158980i
\(691\) 48.5623 1.84740 0.923698 0.383120i \(-0.125151\pi\)
0.923698 + 0.383120i \(0.125151\pi\)
\(692\) −6.59928 + 6.59928i −0.250867 + 0.250867i
\(693\) 45.6421 15.3198i 1.73380 0.581951i
\(694\) 21.3581i 0.810743i
\(695\) −8.88815 25.2213i −0.337147 0.956697i
\(696\) −1.55731 2.51392i −0.0590296 0.0952898i
\(697\) −3.09394 3.09394i −0.117191 0.117191i
\(698\) −1.28588 1.28588i −0.0486712 0.0486712i
\(699\) −1.93662 3.12623i −0.0732497 0.118245i
\(700\) −1.65077 + 15.2591i −0.0623931 + 0.576740i
\(701\) 18.5789i 0.701715i −0.936429 0.350858i \(-0.885890\pi\)
0.936429 0.350858i \(-0.114110\pi\)
\(702\) 12.1989 14.7101i 0.460417 0.555196i
\(703\) −8.21000 + 8.21000i −0.309646 + 0.309646i
\(704\) −5.22806 −0.197040
\(705\) −20.7881 + 25.8459i −0.782924 + 0.973412i
\(706\) −23.7202 −0.892723
\(707\) −23.6159 + 23.6159i −0.888168 + 0.888168i
\(708\) −4.42696 + 18.8407i −0.166375 + 0.708076i
\(709\) 40.6579i 1.52694i −0.645844 0.763469i \(-0.723495\pi\)
0.645844 0.763469i \(-0.276505\pi\)
\(710\) −9.30564 4.45596i −0.349235 0.167229i
\(711\) 15.6761 31.5163i 0.587901 1.18195i
\(712\) 2.50034 + 2.50034i 0.0937041 + 0.0937041i
\(713\) 3.71643 + 3.71643i 0.139181 + 0.139181i
\(714\) −2.83898 + 1.75868i −0.106246 + 0.0658168i
\(715\) 38.7776 + 18.5684i 1.45020 + 0.694420i
\(716\) 18.4232i 0.688508i
\(717\) −40.9893 9.63119i −1.53077 0.359683i
\(718\) −2.81286 + 2.81286i −0.104975 + 0.104975i
\(719\) 20.2760 0.756166 0.378083 0.925772i \(-0.376583\pi\)
0.378083 + 0.925772i \(0.376583\pi\)
\(720\) −6.65773 0.821342i −0.248119 0.0306096i
\(721\) 11.0685 0.412212
\(722\) −7.15709 + 7.15709i −0.266359 + 0.266359i
\(723\) −40.2933 9.46765i −1.49852 0.352106i
\(724\) 4.84965i 0.180236i
\(725\) 6.65057 5.35209i 0.246996 0.198772i
\(726\) −24.0484 + 14.8974i −0.892520 + 0.552894i
\(727\) 36.0659 + 36.0659i 1.33761 + 1.33761i 0.898370 + 0.439239i \(0.144752\pi\)
0.439239 + 0.898370i \(0.355248\pi\)
\(728\) −7.98278 7.98278i −0.295861 0.295861i
\(729\) 4.99586 + 26.5338i 0.185032 + 0.982733i
\(730\) 0.734105 + 2.08312i 0.0271704 + 0.0770996i
\(731\) 6.50318i 0.240529i
\(732\) 0.558602 2.37735i 0.0206465 0.0878694i
\(733\) −13.8202 + 13.8202i −0.510462 + 0.510462i −0.914668 0.404206i \(-0.867548\pi\)
0.404206 + 0.914668i \(0.367548\pi\)
\(734\) 21.1530 0.780770
\(735\) −1.01170 9.32807i −0.0373172 0.344071i
\(736\) −1.00000 −0.0368605
\(737\) −19.0515 + 19.0515i −0.701771 + 0.701771i
\(738\) 6.64980 + 19.8117i 0.244782 + 0.729278i
\(739\) 18.0843i 0.665240i −0.943061 0.332620i \(-0.892067\pi\)
0.943061 0.332620i \(-0.107933\pi\)
\(740\) −3.76309 + 7.85867i −0.138334 + 0.288891i
\(741\) 9.99550 + 16.1354i 0.367194 + 0.592751i
\(742\) 0.927963 + 0.927963i 0.0340666 + 0.0340666i
\(743\) 14.2366 + 14.2366i 0.522291 + 0.522291i 0.918263 0.395972i \(-0.129592\pi\)
−0.395972 + 0.918263i \(0.629592\pi\)
\(744\) 4.79398 + 7.73879i 0.175756 + 0.283718i
\(745\) 36.1812 12.7505i 1.32558 0.467142i
\(746\) 5.35085i 0.195909i
\(747\) −12.6669 37.7384i −0.463457 1.38077i
\(748\) 2.32204 2.32204i 0.0849022 0.0849022i
\(749\) 41.3551 1.51108
\(750\) −0.00527343 19.3649i −0.000192558 0.707107i
\(751\) 9.75271 0.355882 0.177941 0.984041i \(-0.443056\pi\)
0.177941 + 0.984041i \(0.443056\pi\)
\(752\) −6.05572 + 6.05572i −0.220829 + 0.220829i
\(753\) −8.91598 + 37.9454i −0.324916 + 1.38281i
\(754\) 6.27917i 0.228674i
\(755\) 35.7942 12.6141i 1.30268 0.459074i
\(756\) 15.8813 1.48207i 0.577596 0.0539022i
\(757\) 20.1653 + 20.1653i 0.732920 + 0.732920i 0.971197 0.238277i \(-0.0765827\pi\)
−0.238277 + 0.971197i \(0.576583\pi\)
\(758\) 0.499583 + 0.499583i 0.0181457 + 0.0181457i
\(759\) −7.69790 + 4.76865i −0.279416 + 0.173091i
\(760\) 2.87752 6.00929i 0.104379 0.217980i
\(761\) 1.55390i 0.0563288i −0.999603 0.0281644i \(-0.991034\pi\)
0.999603 0.0281644i \(-0.00896620\pi\)
\(762\) 31.1673 + 7.32333i 1.12907 + 0.265296i
\(763\) 17.8083 17.8083i 0.644705 0.644705i
\(764\) −3.19418 −0.115561
\(765\) 3.32183 2.59223i 0.120101 0.0937223i
\(766\) −32.0016 −1.15626
\(767\) 29.0585 29.0585i 1.04924 1.04924i
\(768\) −1.68613 0.396187i −0.0608430 0.0142962i
\(769\) 26.7080i 0.963116i −0.876414 0.481558i \(-0.840071\pi\)
0.876414 0.481558i \(-0.159929\pi\)
\(770\) 11.9271 + 33.8447i 0.429824 + 1.21968i
\(771\) 35.4128 21.9373i 1.27536 0.790053i
\(772\) 1.55053 + 1.55053i 0.0558050 + 0.0558050i
\(773\) 4.61426 + 4.61426i 0.165963 + 0.165963i 0.785202 0.619239i \(-0.212559\pi\)
−0.619239 + 0.785202i \(0.712559\pi\)
\(774\) −13.8326 + 27.8098i −0.497201 + 0.999604i
\(775\) −20.4730 + 16.4758i −0.735410 + 0.591827i
\(776\) 18.6449i 0.669314i
\(777\) 4.73891 20.1683i 0.170007 0.723533i
\(778\) −20.2757 + 20.2757i