Properties

Label 690.2.i.f.323.1
Level $690$
Weight $2$
Character 690.323
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 323.1
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.f.47.1

$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 −0.986164 0.165771i \(-0.946989\pi\)
0.165771 + 0.986164i \(0.446989\pi\)
\(8\) 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 \(-0.711034\pi\)
0.615472 0.788159i \(-0.288966\pi\)
\(12\) −0.396187 1.68613i −0.114369 0.486744i
\(13\) 2.60057 + 2.60057i 0.721268 + 0.721268i 0.968863 0.247596i \(-0.0796405\pi\)
−0.247596 + 0.968863i \(0.579641\pi\)
\(14\) 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 0.758914 0.651191i \(-0.225730\pi\)
−0.651191 + 0.758914i \(0.725730\pi\)
\(18\) −2.84407 0.954611i −0.670353 0.225004i
\(19\) 2.97966i 0.683580i 0.939776 + 0.341790i \(0.111033\pi\)
−0.939776 + 0.341790i \(0.888967\pi\)
\(20\) −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 −0.896341 0.443365i \(-0.853785\pi\)
0.443365 + 0.896341i \(0.353785\pi\)
\(38\) 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 \(0.183072\pi\)
−0.839117 + 0.543951i \(0.816928\pi\)
\(42\) −5.17579 + 1.21615i −0.798642 + 0.187656i
\(43\) 7.32093 + 7.32093i 1.11643 + 1.11643i 0.992261 + 0.124170i \(0.0396268\pi\)
0.124170 + 0.992261i \(0.460373\pi\)
\(44\) 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 0.993870 0.110553i \(-0.0352621\pi\)
−0.110553 + 0.993870i \(0.535262\pi\)
\(48\) 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 −0.686040 0.727564i \(-0.740652\pi\)
0.727564 + 0.686040i \(0.240652\pi\)
\(54\) 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 −0.448558 0.893754i \(-0.648062\pi\)
0.893754 + 0.448558i \(0.148062\pi\)
\(68\) −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 \(-0.911720\pi\)
0.961787 0.273798i \(-0.0882799\pi\)
\(72\) 0.954611 2.84407i 0.112502 0.335177i
\(73\) 0.698447 + 0.698447i 0.0817471 + 0.0817471i 0.746798 0.665051i \(-0.231590\pi\)
−0.665051 + 0.746798i \(0.731590\pi\)
\(74\) 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 \(0.229463\pi\)
−0.751225 + 0.660046i \(0.770537\pi\)
\(80\) −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 −0.0303467 + 0.999539i \(0.509661\pi\)
−0.999539 + 0.0303467i \(0.990339\pi\)
\(84\) 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 −0.441237 + 0.897391i \(0.645460\pi\)
−0.897391 + 0.441237i \(0.854540\pi\)
\(98\) −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 \(0.182070\pi\)
−0.840825 + 0.541306i \(0.817930\pi\)
\(102\) 0.248854 + 1.05910i 0.0246402 + 0.104866i
\(103\) −2.54969 2.54969i −0.251228 0.251228i 0.570246 0.821474i \(-0.306848\pi\)
−0.821474 + 0.570246i \(0.806848\pi\)
\(104\) 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 0.0761462 0.997097i \(-0.475738\pi\)
−0.997097 + 0.0761462i \(0.975738\pi\)
\(108\) −3.31694 3.99974i −0.319172 0.384875i
\(109\) 8.20451i 0.785849i −0.919571 0.392925i \(-0.871463\pi\)
0.919571 0.392925i \(-0.128537\pi\)
\(110\) −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 −0.728094 0.685477i \(-0.759594\pi\)
0.685477 + 0.728094i \(0.259594\pi\)
\(114\) −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 0.175307 0.984514i \(-0.443908\pi\)
0.984514 0.175307i \(-0.0560919\pi\)
\(128\) −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 \(-0.955484\pi\)
0.990237 0.139394i \(-0.0445155\pi\)
\(132\) −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 −0.995102 0.0988556i \(-0.968482\pi\)
−0.0988556 0.995102i \(-0.531518\pi\)
\(138\) −1.68613 + 0.396187i −0.143533 + 0.0337257i
\(139\) 11.9592i 1.01437i 0.861839 + 0.507183i \(0.169313\pi\)
−0.861839 + 0.507183i \(0.830687\pi\)
\(140\) −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 −0.0578517 0.998325i \(-0.518425\pi\)
0.998325 + 0.0578517i \(0.0184251\pi\)
\(158\) 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 0.839743 0.542983i \(-0.182705\pi\)
−0.542983 + 0.839743i \(0.682705\pi\)
\(164\) −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 0.100791 0.994908i \(-0.467863\pi\)
−0.994908 + 0.100791i \(0.967863\pi\)
\(168\) −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 −0.911977 0.410242i \(-0.865444\pi\)
0.410242 + 0.911977i \(0.365444\pi\)
\(174\) 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 \(0.0368667\pi\)
−0.993300 + 0.115561i \(0.963133\pi\)
\(192\) 0.396187 + 1.68613i 0.0285924 + 0.121686i
\(193\) −1.55053 1.55053i −0.111610 0.111610i 0.649096 0.760706i \(-0.275147\pi\)
−0.760706 + 0.649096i \(0.775147\pi\)
\(194\) 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 −0.987341 0.158614i \(-0.949298\pi\)
−0.158614 0.987341i \(-0.550702\pi\)
\(198\) −4.99076 + 14.8689i −0.354678 + 1.05669i
\(199\) 8.97499i 0.636220i 0.948054 + 0.318110i \(0.103048\pi\)
−0.948054 + 0.318110i \(0.896952\pi\)
\(200\) 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 0.991277 0.131797i \(-0.0420745\pi\)
−0.131797 + 0.991277i \(0.542075\pi\)
\(224\) −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 0.294433 0.955672i \(-0.404869\pi\)
−0.955672 + 0.294433i \(0.904869\pi\)
\(228\) 5.02409 1.18050i 0.332728 0.0781806i
\(229\) 17.6169i 1.16416i −0.813133 0.582079i \(-0.802240\pi\)
0.813133 0.582079i \(-0.197760\pi\)
\(230\) 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 −0.656217 0.754572i \(-0.727844\pi\)
0.754572 + 0.656217i \(0.227844\pi\)
\(234\) −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 \(0.251411\pi\)
−0.703965 + 0.710234i \(0.748589\pi\)
\(252\) −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 −0.998026 0.0628062i \(-0.979995\pi\)
−0.0628062 0.998026i \(-0.520005\pi\)
\(258\) 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 0.111428 0.993773i \(-0.464458\pi\)
0.993773 0.111428i \(-0.0355425\pi\)
\(264\) 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 −0.736342 0.676609i \(-0.763449\pi\)
0.676609 + 0.736342i \(0.263449\pi\)
\(278\) 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 \(-0.841672\pi\)
0.878824 0.477145i \(-0.158328\pi\)
\(282\) 3.39298 + 14.4402i 0.202049 + 0.859899i
\(283\) 21.3172 + 21.3172i 1.26718 + 1.26718i 0.947540 + 0.319636i \(0.103561\pi\)
0.319636 + 0.947540i \(0.396439\pi\)
\(284\) 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 −0.816284 0.577651i \(-0.803969\pi\)
0.577651 + 0.816284i \(0.303969\pi\)
\(294\) 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 −0.114997 0.993366i \(-0.536686\pi\)
0.993366 + 0.114997i \(0.0366858\pi\)
\(308\) −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 \(-0.808102\pi\)
0.823715 0.567004i \(-0.191898\pi\)
\(312\) −6.20118 + 1.45708i −0.351073 + 0.0824910i
\(313\) −21.4652 21.4652i −1.21329 1.21329i −0.969939 0.243348i \(-0.921754\pi\)
−0.243348 0.969939i \(-0.578246\pi\)
\(314\) −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 0.999026 0.0441291i \(-0.0140513\pi\)
−0.0441291 + 0.999026i \(0.514051\pi\)
\(318\) 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 −0.721072 0.692860i \(-0.756350\pi\)
0.692860 + 0.721072i \(0.256350\pi\)
\(338\) 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 0.984745 0.174003i \(-0.0556701\pi\)
−0.174003 + 0.984745i \(0.555670\pi\)
\(348\) −0.676425 2.87879i −0.0362602 0.154319i
\(349\) 1.81851i 0.0973424i −0.998815 0.0486712i \(-0.984501\pi\)
0.998815 0.0486712i \(-0.0154986\pi\)
\(350\) 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 −0.102056 0.994779i \(-0.532542\pi\)
0.994779 + 0.102056i \(0.0325420\pi\)
\(354\) 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 −0.979961 0.199191i \(-0.936169\pi\)
0.199191 + 0.979961i \(0.436169\pi\)
\(368\) 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 0.602335 0.798243i \(-0.294237\pi\)
−0.798243 + 0.602335i \(0.794237\pi\)
\(374\) −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 \(0.00577626\pi\)
−0.999835 + 0.0181457i \(0.994224\pi\)
\(380\) −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 0.170991 0.985273i \(-0.445303\pi\)
0.985273 0.170991i \(-0.0546968\pi\)
\(384\) 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 −0.803782 0.594924i \(-0.797182\pi\)
0.594924 + 0.803782i \(0.297182\pi\)
\(398\) 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 \(-0.940560\pi\)
0.982616 0.185651i \(-0.0594395\pi\)
\(402\) 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 \(0.116229\pi\)
−0.934072 + 0.357085i \(0.883771\pi\)
\(410\) 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 \(-0.762587\pi\)
0.734508 0.678600i \(-0.237413\pi\)
\(432\) 3.99974 3.31694i 0.192438 0.159586i
\(433\) 13.8540 + 13.8540i 0.665781 + 0.665781i 0.956737 0.290956i \(-0.0939732\pi\)
−0.290956 + 0.956737i \(0.593973\pi\)
\(434\) −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 \(-0.894188\pi\)
0.945256 0.326330i \(-0.105812\pi\)
\(440\) −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 −0.167879 + 0.985808i \(0.553692\pi\)
−0.985808 + 0.167879i \(0.946308\pi\)
\(444\) 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 −0.688536 0.725202i \(-0.741746\pi\)
0.725202 + 0.688536i \(0.241746\pi\)
\(458\) −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 \(-0.754728\pi\)
0.717531 0.696527i \(-0.245272\pi\)
\(462\) 6.35809 + 27.0593i 0.295805 + 1.25891i
\(463\) 12.8240 + 12.8240i 0.595982 + 0.595982i 0.939241 0.343259i \(-0.111531\pi\)
−0.343259 + 0.939241i \(0.611531\pi\)
\(464\) −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 −0.946192 0.323607i \(-0.895105\pi\)
−0.323607 0.946192i \(-0.604895\pi\)
\(468\) −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 −0.175655 0.984452i \(-0.556204\pi\)
0.984452 + 0.175655i \(0.0562042\pi\)
\(488\) −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 \(0.0911283\pi\)
−0.959299 + 0.282393i \(0.908872\pi\)
\(492\) 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 \(0.201059\pi\)
−0.807056 + 0.590474i \(0.798941\pi\)
\(500\) −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 −0.463197 0.886255i \(-0.653298\pi\)
0.886255 + 0.463197i \(0.153298\pi\)
\(504\) 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 \(0.0894701\pi\)
−0.960757 + 0.277392i \(0.910530\pi\)
\(522\) −4.85578 1.62984i −0.212532 0.0713363i
\(523\) −9.41837 9.41837i −0.411836 0.411836i 0.470541 0.882378i \(-0.344059\pi\)
−0.882378 + 0.470541i \(0.844059\pi\)
\(524\) 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 −0.0355120 + 0.999369i \(0.511306\pi\)
−0.999369 + 0.0355120i \(0.988694\pi\)
\(548\) 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 0.988199 0.153174i \(-0.0489494\pi\)
−0.153174 + 0.988199i \(0.548949\pi\)
\(558\) 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 −0.822355 0.568975i \(-0.807340\pi\)
0.568975 + 0.822355i \(0.307340\pi\)
\(564\) 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 −0.288097 0.957601i \(-0.593023\pi\)
0.957601 + 0.288097i \(0.0930225\pi\)
\(578\) −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 0.877095 0.480318i \(-0.159479\pi\)
−0.480318 + 0.877095i \(0.659479\pi\)
\(588\) −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 −0.913826 0.406106i \(-0.866886\pi\)
0.406106 + 0.913826i \(0.366886\pi\)
\(594\) 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 −0.468419 0.883507i \(-0.655176\pi\)
0.883507 + 0.468419i \(0.155176\pi\)
\(608\) −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 0.787020 0.616928i \(-0.211623\pi\)
−0.616928 + 0.787020i \(0.711623\pi\)
\(614\) −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 0.682793 0.730612i \(-0.260765\pi\)
−0.730612 + 0.682793i \(0.760765\pi\)
\(618\) −1.42857 6.07986i −0.0574657 0.244568i
\(619\) 9.65709i 0.388151i −0.980987 0.194076i \(-0.937829\pi\)
0.980987 0.194076i \(-0.0621707\pi\)
\(620\) 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 \(0.0490996\pi\)
−0.988127 + 0.153640i \(0.950900\pi\)
\(642\) −5.33757 22.7161i −0.210657 0.896534i
\(643\) −22.1643 22.1643i −0.874075 0.874075i 0.118838 0.992914i \(-0.462083\pi\)
−0.992914 + 0.118838i \(0.962083\pi\)
\(644\) 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 0.550095 0.835102i \(-0.314591\pi\)
−0.835102 + 0.550095i \(0.814591\pi\)
\(648\) −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 −0.967565 0.252621i \(-0.918707\pi\)
0.252621 + 0.967565i \(0.418707\pi\)
\(654\) 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 0.662796 0.748800i \(-0.269370\pi\)
−0.748800 + 0.662796i \(0.769370\pi\)
\(674\) 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 0.854707 0.519111i \(-0.173737\pi\)
−0.519111 + 0.854707i \(0.673737\pi\)
\(678\) −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 −0.837519 0.546408i \(-0.815995\pi\)
0.546408 + 0.837519i \(0.315995\pi\)
\(684\) −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 \(0.114110\pi\)
−0.936429 + 0.350858i \(0.885890\pi\)
\(702\) 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 \(0.276505\pi\)
−0.645844 + 0.763469i \(0.723495\pi\)
\(710\) −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 0.439239 0.898370i \(-0.355248\pi\)
0.898370 0.439239i \(-0.144752\pi\)
\(728\) −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 0.404206 0.914668i \(-0.367548\pi\)
−0.914668 + 0.404206i \(0.867548\pi\)
\(734\) 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 \(0.107933\pi\)
−0.943061 + 0.332620i \(0.892067\pi\)
\(740\) −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 −0.395972 0.918263i \(-0.629592\pi\)
0.918263 + 0.395972i \(0.129592\pi\)
\(744\) 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 −0.238277 0.971197i \(-0.576583\pi\)
0.971197 + 0.238277i \(0.0765827\pi\)
\(758\) 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 \(0.00896620\pi\)
−0.999603 + 0.0281644i \(0.991034\pi\)
\(762\) 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 \(0.159929\pi\)
−0.876414 + 0.481558i \(0.840071\pi\)
\(770\) 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 −0.619239 0.785202i \(-0.712559\pi\)
0.785202 + 0.619239i \(0.212559\pi\)
\(774\) −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