Properties

Label 690.2.i.f.47.12
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 47.12
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.396187 + 1.68613i) q^{3} -1.00000i q^{4} +(-2.10894 + 0.743206i) q^{5} +(1.47242 + 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.68607 + 1.33605i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.396187 + 1.68613i) 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} +(1.68613 - 0.396187i) q^{12} +(2.60057 - 2.60057i) q^{13} -3.06963 q^{14} +(-2.08868 - 3.26151i) q^{15} -1.00000 q^{16} +(-0.444150 + 0.444150i) q^{17} +(-0.954611 + 2.84407i) 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} +(-3.31694 - 3.99974i) q^{27} +(-2.17056 + 2.17056i) q^{28} -1.70734 q^{29} +(-3.78315 - 0.829313i) q^{30} -5.25582 q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.81518 - 2.07129i) 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} +(-1.21615 - 5.17579i) q^{42} +(7.32093 - 7.32093i) q^{43} -5.22806 q^{44} +(4.67181 - 4.81395i) q^{45} +1.00000 q^{46} +(-6.05572 + 6.05572i) q^{47} +(-0.396187 - 1.68613i) 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} +(5.02409 - 1.18050i) q^{57} +(-1.20727 + 1.20727i) q^{58} -11.1739 q^{59} +(-3.26151 + 2.08868i) q^{60} -1.40994 q^{61} +(-3.71643 + 3.71643i) q^{62} +(8.73023 + 2.93030i) 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} +(2.84407 + 0.954611i) q^{72} +(0.698447 - 0.698447i) q^{73} -3.89665 q^{74} +(6.82888 + 5.32601i) q^{75} -2.97966 q^{76} +(-11.3478 + 11.3478i) q^{77} +(6.20118 - 1.45708i) 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} +(-0.676425 - 2.87879i) q^{87} +(-3.69679 + 3.69679i) q^{88} -3.53601 q^{89} +(-0.100507 - 6.70745i) q^{90} -11.2894 q^{91} +(0.707107 - 0.707107i) q^{92} +(-2.08229 - 8.86201i) 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
\(3\) 0.396187 + 1.68613i 0.228739 + 0.973488i
\(4\) 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 \(-0.711034\pi\)
0.615472 0.788159i \(-0.288966\pi\)
\(12\) 1.68613 0.396187i 0.486744 0.114369i
\(13\) 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
\(15\) −2.08868 3.26151i −0.539295 0.842117i
\(16\) −1.00000 −0.250000
\(17\) −0.444150 + 0.444150i −0.107722 + 0.107722i −0.758914 0.651191i \(-0.774270\pi\)
0.651191 + 0.758914i \(0.274270\pi\)
\(18\) −0.954611 + 2.84407i −0.225004 + 0.670353i
\(19\) 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
\(27\) −3.31694 3.99974i −0.638345 0.769751i
\(28\) −2.17056 + 2.17056i −0.410196 + 0.410196i
\(29\) −1.70734 −0.317044 −0.158522 0.987355i \(-0.550673\pi\)
−0.158522 + 0.987355i \(0.550673\pi\)
\(30\) −3.78315 0.829313i −0.690706 0.151411i
\(31\) −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
\(33\) 8.81518 2.07129i 1.53453 0.360565i
\(34\) 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 \(0.183072\pi\)
−0.839117 + 0.543951i \(0.816928\pi\)
\(42\) −1.21615 5.17579i −0.187656 0.798642i
\(43\) 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
\(45\) 4.67181 4.81395i 0.696433 0.717622i
\(46\) 1.00000 0.147442
\(47\) −6.05572 + 6.05572i −0.883318 + 0.883318i −0.993870 0.110553i \(-0.964738\pi\)
0.110553 + 0.993870i \(0.464738\pi\)
\(48\) −0.396187 1.68613i −0.0571847 0.243372i
\(49\) 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 \(-0.259348\pi\)
−0.727564 + 0.686040i \(0.759348\pi\)
\(54\) −5.17367 0.482816i −0.704048 0.0657029i
\(55\) 3.88553 + 11.0257i 0.523924 + 1.48670i
\(56\) 3.06963i 0.410196i
\(57\) 5.02409 1.18050i 0.665457 0.156361i
\(58\) −1.20727 + 1.20727i −0.158522 + 0.158522i
\(59\) −11.1739 −1.45472 −0.727359 0.686257i \(-0.759253\pi\)
−0.727359 + 0.686257i \(0.759253\pi\)
\(60\) −3.26151 + 2.08868i −0.421059 + 0.269647i
\(61\) −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
\(63\) 8.73023 + 2.93030i 1.09991 + 0.369183i
\(64\) 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 \(-0.911720\pi\)
0.961787 0.273798i \(-0.0882799\pi\)
\(72\) 2.84407 + 0.954611i 0.335177 + 0.112502i
\(73\) 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
\(75\) 6.82888 + 5.32601i 0.788531 + 0.614995i
\(76\) −2.97966 −0.341790
\(77\) −11.3478 + 11.3478i −1.29320 + 1.29320i
\(78\) 6.20118 1.45708i 0.702145 0.164982i
\(79\) 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 \(0.00966113\pi\)
0.0303467 + 0.999539i \(0.490339\pi\)
\(84\) −4.51979 2.79989i −0.493149 0.305493i
\(85\) 0.606592 1.26678i 0.0657942 0.137402i
\(86\) 10.3534i 1.11643i
\(87\) −0.676425 2.87879i −0.0725204 0.308639i
\(88\) −3.69679 + 3.69679i −0.394080 + 0.394080i
\(89\) −3.53601 −0.374816 −0.187408 0.982282i \(-0.560009\pi\)
−0.187408 + 0.982282i \(0.560009\pi\)
\(90\) −0.100507 6.70745i −0.0105944 0.707027i
\(91\) −11.2894 −1.18345
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) −2.08229 8.86201i −0.215924 0.918947i
\(94\) 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 \(0.182070\pi\)
−0.840825 + 0.541306i \(0.817930\pi\)
\(102\) −1.05910 + 0.248854i −0.104866 + 0.0246402i
\(103\) −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
\(105\) −2.54568 + 11.6129i −0.248433 + 1.13330i
\(106\) −0.427523 −0.0415247
\(107\) 9.52639 9.52639i 0.920950 0.920950i −0.0761462 0.997097i \(-0.524262\pi\)
0.997097 + 0.0761462i \(0.0242616\pi\)
\(108\) −3.99974 + 3.31694i −0.384875 + 0.319172i
\(109\) 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 0.728094 0.685477i \(-0.240406\pi\)
−0.685477 + 0.728094i \(0.740406\pi\)
\(114\) 2.71783 4.38731i 0.254548 0.410909i
\(115\) −2.01677 0.965722i −0.188065 0.0900541i
\(116\) 1.70734i 0.158522i
\(117\) −3.51083 + 10.4598i −0.324576 + 0.967008i
\(118\) −7.90115 + 7.90115i −0.727359 + 0.727359i
\(119\) 1.92810 0.176749
\(120\) −0.829313 + 3.78315i −0.0757056 + 0.345353i
\(121\) −16.3326 −1.48478
\(122\) −0.996981 + 0.996981i −0.0902625 + 0.0902625i
\(123\) −11.7455 + 2.75983i −1.05906 + 0.248845i
\(124\) 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 \(-0.955484\pi\)
0.990237 0.139394i \(-0.0445155\pi\)
\(132\) −2.07129 8.81518i −0.180283 0.767263i
\(133\) −6.46751 + 6.46751i −0.560804 + 0.560804i
\(134\) 5.15352 0.445196
\(135\) 9.96787 + 5.97006i 0.857897 + 0.513821i
\(136\) 0.628123 0.0538611
\(137\) 12.8044 12.8044i 1.09396 1.09396i 0.0988556 0.995102i \(-0.468482\pi\)
0.995102 0.0988556i \(-0.0315182\pi\)
\(138\) 0.396187 + 1.68613i 0.0337257 + 0.143533i
\(139\) 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
\(147\) −4.08486 + 0.959812i −0.336913 + 0.0791640i
\(148\) −2.75535 + 2.75535i −0.226488 + 0.226488i
\(149\) −17.1561 −1.40548 −0.702740 0.711447i \(-0.748040\pi\)
−0.702740 + 0.711447i \(0.748040\pi\)
\(150\) 8.59481 1.06269i 0.701763 0.0867682i
\(151\) 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
\(153\) 0.599613 1.78642i 0.0484759 0.144424i
\(154\) 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
\(162\) −1.23565 8.91477i −0.0970821 0.700411i
\(163\) 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
\(165\) −17.0513 + 10.9197i −1.32744 + 0.850100i
\(166\) 13.2692 1.02989
\(167\) 11.5545 11.5545i 0.894117 0.894117i −0.100791 0.994908i \(-0.532137\pi\)
0.994908 + 0.100791i \(0.0321372\pi\)
\(168\) −5.17579 + 1.21615i −0.399321 + 0.0938279i
\(169\) 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 \(-0.134556\pi\)
−0.410242 + 0.911977i \(0.634556\pi\)
\(174\) −2.51392 1.55731i −0.190580 0.118059i
\(175\) −15.2591 1.65077i −1.15348 0.124786i
\(176\) 5.22806i 0.394080i
\(177\) −4.42696 18.8407i −0.332751 1.41615i
\(178\) −2.50034 + 2.50034i −0.187408 + 0.187408i
\(179\) 18.4232 1.37702 0.688508 0.725229i \(-0.258266\pi\)
0.688508 + 0.725229i \(0.258266\pi\)
\(180\) −4.81395 4.67181i −0.358811 0.348217i
\(181\) 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
\(183\) −0.558602 2.37735i −0.0412931 0.175739i
\(184\) 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 \(0.963133\pi\)
\(192\) −1.68613 + 0.396187i −0.121686 + 0.0285924i
\(193\) −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
\(195\) −13.9135 3.05001i −0.996368 0.218416i
\(196\) 2.42262 0.173044
\(197\) 16.0842 16.0842i 1.14595 1.14595i 0.158614 0.987341i \(-0.449298\pi\)
0.987341 0.158614i \(-0.0507025\pi\)
\(198\) 14.8689 + 4.99076i 1.05669 + 0.354678i
\(199\) 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
\(207\) −2.84407 0.954611i −0.197676 0.0663501i
\(208\) −2.60057 + 2.60057i −0.180317 + 0.180317i
\(209\) −15.5778 −1.07754
\(210\) 6.41147 + 10.0116i 0.442434 + 0.690867i
\(211\) −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
\(213\) 7.78001 1.82806i 0.533078 0.125256i
\(214\) 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
\(222\) −1.54381 6.57027i −0.103613 0.440967i
\(223\) 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
\(225\) −6.27483 + 13.6245i −0.418322 + 0.908299i
\(226\) 0.640680 0.0426174
\(227\) 9.96258 9.96258i 0.661239 0.661239i −0.294433 0.955672i \(-0.595131\pi\)
0.955672 + 0.294433i \(0.0951307\pi\)
\(228\) −1.18050 5.02409i −0.0781806 0.332728i
\(229\) 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 0.656217 0.754572i \(-0.272156\pi\)
−0.754572 + 0.656217i \(0.772156\pi\)
\(234\) 4.91366 + 9.87872i 0.321216 + 0.645792i
\(235\) 8.27052 17.2718i 0.539509 1.12669i
\(236\) 11.1739i 0.727359i
\(237\) 19.7838 4.64856i 1.28509 0.301956i
\(238\) 1.36338 1.36338i 0.0883745 0.0883745i
\(239\) −24.3097 −1.57246 −0.786232 0.617932i \(-0.787971\pi\)
−0.786232 + 0.617932i \(0.787971\pi\)
\(240\) 2.08868 + 3.26151i 0.134824 + 0.210529i
\(241\) 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
\(243\) 14.2534 + 6.31201i 0.914354 + 0.404915i
\(244\) 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 \(0.748589\pi\)
\(252\) 2.93030 8.73023i 0.184592 0.549953i
\(253\) 3.69679 3.69679i 0.232415 0.232415i
\(254\) 18.4845 1.15982
\(255\) 2.37628 + 0.520910i 0.148809 + 0.0326207i
\(256\) 1.00000 0.0625000
\(257\) 17.0064 17.0064i 1.06083 1.06083i 0.0628062 0.998026i \(-0.479995\pi\)
0.998026 0.0628062i \(-0.0200050\pi\)
\(258\) 17.4571 4.10187i 1.08683 0.255371i
\(259\) 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 \(-0.964458\pi\)
−0.111428 0.993773i \(-0.535542\pi\)
\(264\) −7.69790 4.76865i −0.473773 0.293490i
\(265\) 0.862218 + 0.412869i 0.0529656 + 0.0253623i
\(266\) 9.14644i 0.560804i
\(267\) −1.40092 5.96217i −0.0857350 0.364879i
\(268\) 3.64409 3.64409i 0.222598 0.222598i
\(269\) −17.9945 −1.09714 −0.548571 0.836104i \(-0.684828\pi\)
−0.548571 + 0.836104i \(0.684828\pi\)
\(270\) 11.2698 2.82688i 0.685859 0.172038i
\(271\) −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
\(273\) −4.47270 19.0353i −0.270700 1.15207i
\(274\) 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 \(-0.841672\pi\)
0.878824 0.477145i \(-0.158328\pi\)
\(282\) −14.4402 + 3.39298i −0.859899 + 0.202049i
\(283\) 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
\(285\) −9.71816 + 6.22355i −0.575654 + 0.368651i
\(286\) −19.2275 −1.13695
\(287\) 15.1200 15.1200i 0.892507 0.892507i
\(288\) 0.954611 2.84407i 0.0562510 0.167588i
\(289\) 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 \(-0.196031\pi\)
−0.577651 + 0.816284i \(0.696031\pi\)
\(294\) −2.20974 + 3.56712i −0.128875 + 0.208039i
\(295\) 23.5651 8.30452i 1.37202 0.483508i
\(296\) 3.89665i 0.226488i
\(297\) −20.9109 + 17.3411i −1.21337 + 1.00623i
\(298\) −12.1312 + 12.1312i −0.702740 + 0.702740i
\(299\) 3.67776 0.212690
\(300\) 5.32601 6.82888i 0.307497 0.394266i
\(301\) −31.7810 −1.83182
\(302\) 12.0014 12.0014i 0.690603 0.690603i
\(303\) −18.3453 + 4.31057i −1.05391 + 0.247636i
\(304\) 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 \(-0.808102\pi\)
0.823715 0.567004i \(-0.191898\pi\)
\(312\) −1.45708 6.20118i −0.0824910 0.351073i
\(313\) −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
\(315\) −20.5894 + 0.308520i −1.16008 + 0.0173831i
\(316\) −11.7332 −0.660046
\(317\) −17.0015 + 17.0015i −0.954897 + 0.954897i −0.999026 0.0441291i \(-0.985949\pi\)
0.0441291 + 0.999026i \(0.485949\pi\)
\(318\) −0.169379 0.720860i −0.00949832 0.0404238i
\(319\) 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
\(327\) −13.8339 + 3.25052i −0.765015 + 0.179754i
\(328\) 4.92569 4.92569i 0.271975 0.271975i
\(329\) 26.2886 1.44933
\(330\) −4.33569 + 19.7785i −0.238672 + 1.08877i
\(331\) −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
\(333\) 11.0823 + 3.71979i 0.607309 + 0.203843i
\(334\) 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
\(342\) 8.47434 + 2.84441i 0.458240 + 0.153808i
\(343\) −9.93545 + 9.93545i −0.536464 + 0.536464i
\(344\) −10.3534 −0.558215
\(345\) 0.829313 3.78315i 0.0446487 0.203678i
\(346\) 9.33280 0.501734
\(347\) −15.1025 + 15.1025i −0.810743 + 0.810743i −0.984745 0.174003i \(-0.944330\pi\)
0.174003 + 0.984745i \(0.444330\pi\)
\(348\) −2.87879 + 0.676425i −0.154319 + 0.0362602i
\(349\) 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 0.102056 0.994779i \(-0.467458\pi\)
−0.994779 + 0.102056i \(0.967458\pi\)
\(354\) −16.4527 10.1920i −0.874451 0.541700i
\(355\) 3.42925 + 9.73092i 0.182005 + 0.516464i
\(356\) 3.53601i 0.187408i
\(357\) 0.763890 + 3.25103i 0.0404294 + 0.172063i
\(358\) 13.0272 13.0272i 0.688508 0.688508i
\(359\) −3.97799 −0.209950 −0.104975 0.994475i \(-0.533476\pi\)
−0.104975 + 0.994475i \(0.533476\pi\)
\(360\) −6.70745 + 0.100507i −0.353514 + 0.00529720i
\(361\) 10.1217 0.532719
\(362\) 3.42922 3.42922i 0.180236 0.180236i
\(363\) −6.47076 27.5388i −0.339627 1.44541i
\(364\) 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
\(372\) −8.86201 + 2.08229i −0.459474 + 0.107962i
\(373\) −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
\(375\) −18.3601 6.15699i −0.948109 0.317946i
\(376\) 8.56408 0.441659
\(377\) −4.44004 + 4.44004i −0.228674 + 0.228674i
\(378\) 10.1818 + 12.2777i 0.523693 + 0.631498i
\(379\) 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 \(-0.945303\pi\)
−0.170991 0.985273i \(-0.554697\pi\)
\(384\) −0.912127 + 1.47242i −0.0465468 + 0.0751392i
\(385\) 15.4981 32.3656i 0.789856 1.64950i
\(386\) 2.19279i 0.111610i
\(387\) −9.88343 + 29.4456i −0.502403 + 1.49681i
\(388\) −13.1840 + 13.1840i −0.669314 + 0.669314i
\(389\) −28.6741 −1.45384 −0.726918 0.686724i \(-0.759048\pi\)
−0.726918 + 0.686724i \(0.759048\pi\)
\(390\) −11.9950 + 7.68166i −0.607392 + 0.388976i
\(391\) −0.628123 −0.0317655
\(392\) 1.71305 1.71305i 0.0865222 0.0865222i
\(393\) 5.38024 1.26419i 0.271397 0.0637697i
\(394\) 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 \(-0.940560\pi\)
0.982616 0.185651i \(-0.0594395\pi\)
\(402\) 2.04176 + 8.68950i 0.101834 + 0.433393i
\(403\) −13.6681 + 13.6681i −0.680858 + 0.680858i
\(404\) 10.8801 0.541306
\(405\) −6.11716 + 19.1724i −0.303964 + 0.952683i
\(406\) 5.24089 0.260101
\(407\) −14.4051 + 14.4051i −0.714036 + 0.714036i
\(408\) 0.248854 + 1.05910i 0.0123201 + 0.0524331i
\(409\) 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
\(417\) 20.1648 4.73808i 0.987472 0.232025i
\(418\) −11.0152 + 11.0152i −0.538770 + 0.538770i
\(419\) 4.96433 0.242523 0.121262 0.992621i \(-0.461306\pi\)
0.121262 + 0.992621i \(0.461306\pi\)
\(420\) 11.6129 + 2.54568i 0.566650 + 0.124217i
\(421\) −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
\(423\) 8.17537 24.3568i 0.397500 1.18427i
\(424\) 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 \(-0.237413\pi\)
\(432\) 3.31694 + 3.99974i 0.159586 + 0.192438i
\(433\) 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
\(435\) 3.56608 + 5.56849i 0.170980 + 0.266988i
\(436\) 8.20451 0.392925
\(437\) 2.10693 2.10693i 0.100788 0.100788i
\(438\) 1.66548 0.391335i 0.0795798 0.0186987i
\(439\) 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 \(0.0536919\pi\)
0.167879 + 0.985808i \(0.446308\pi\)
\(444\) −5.73752 3.55425i −0.272290 0.168677i
\(445\) 7.45724 2.62798i 0.353507 0.124578i
\(446\) 18.1511i 0.859480i
\(447\) −6.79701 28.9274i −0.321488 1.36822i
\(448\) 2.17056 2.17056i 0.102549 0.102549i
\(449\) 15.3176 0.722883 0.361442 0.932395i \(-0.382285\pi\)
0.361442 + 0.932395i \(0.382285\pi\)
\(450\) 5.19699 + 14.0709i 0.244988 + 0.663310i
\(451\) 36.4185 1.71488
\(452\) 0.453030 0.453030i 0.0213087 0.0213087i
\(453\) 6.72431 + 28.6179i 0.315936 + 1.34459i
\(454\) 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 \(-0.754728\pi\)
0.717531 0.696527i \(-0.245272\pi\)
\(462\) −27.0593 + 6.35809i −1.25891 + 0.295805i
\(463\) 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
\(465\) 10.9777 + 17.1419i 0.509080 + 0.794937i
\(466\) −2.12319 −0.0983549
\(467\) 27.4406 27.4406i 1.26980 1.26980i 0.323607 0.946192i \(-0.395105\pi\)
0.946192 0.323607i \(-0.104895\pi\)
\(468\) 10.4598 + 3.51083i 0.483504 + 0.162288i
\(469\) 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
\(477\) 1.21590 + 0.408118i 0.0556724 + 0.0186865i
\(478\) −17.1895 + 17.1895i −0.786232 + 0.786232i
\(479\) 15.9073 0.726824 0.363412 0.931629i \(-0.381612\pi\)
0.363412 + 0.931629i \(0.381612\pi\)
\(480\) 3.78315 + 0.829313i 0.172676 + 0.0378528i
\(481\) −14.3309 −0.653435
\(482\) 16.8977 16.8977i 0.769667 0.769667i
\(483\) 5.17579 1.21615i 0.235507 0.0553367i
\(484\) 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 \(0.0911283\pi\)
−0.959299 + 0.282393i \(0.908872\pi\)
\(492\) 2.75983 + 11.7455i 0.124423 + 0.529530i
\(493\) 0.758313 0.758313i 0.0341527 0.0341527i
\(494\) −10.9584 −0.493044
\(495\) −25.1676 24.4245i −1.13120 1.09780i
\(496\) 5.25582 0.235993
\(497\) −10.0152 + 10.0152i −0.449243 + 0.449243i
\(498\) 5.25707 + 22.3735i 0.235575 + 1.00258i
\(499\) 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 0.463197 0.886255i \(-0.346702\pi\)
−0.886255 + 0.463197i \(0.846702\pi\)
\(504\) −4.10117 8.24524i −0.182681 0.367272i
\(505\) −8.08618 22.9456i −0.359830 1.02106i
\(506\) 5.22806i 0.232415i
\(507\) 0.886733 0.208354i 0.0393812 0.00925334i
\(508\) 13.0705 13.0705i 0.579911 0.579911i
\(509\) 14.3787 0.637323 0.318662 0.947869i \(-0.396767\pi\)
0.318662 + 0.947869i \(0.396767\pi\)
\(510\) 2.04863 1.31195i 0.0907147 0.0580940i
\(511\) −3.03204 −0.134129
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −11.9179 + 9.88333i −0.526186 + 0.436360i
\(514\) 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 \(0.910530\pi\)
\(522\) 1.62984 4.85578i 0.0713363 0.212532i
\(523\) −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
\(525\) −3.26206 26.3829i −0.142368 1.15144i
\(526\) −25.3474 −1.10520
\(527\) 2.33437 2.33437i 0.101687 0.101687i
\(528\) −8.81518 + 2.07129i −0.383632 + 0.0901413i
\(529\) 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
\(537\) 7.29904 + 31.0639i 0.314977 + 1.34051i
\(538\) −12.7240 + 12.7240i −0.548571 + 0.548571i
\(539\) 12.6656 0.545546
\(540\) 5.97006 9.96787i 0.256911 0.428949i
\(541\) 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
\(543\) 1.92137 + 8.17714i 0.0824538 + 0.350915i
\(544\) 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
\(552\) 1.68613 0.396187i 0.0717665 0.0168629i
\(553\) −25.4676 + 25.4676i −1.08299 + 1.08299i
\(554\) −1.40594 −0.0597327
\(555\) −3.23155 + 14.7416i −0.137171 + 0.625748i
\(556\) −11.9592 −0.507183
\(557\) −19.7073 + 19.7073i −0.835026 + 0.835026i −0.988199 0.153174i \(-0.951051\pi\)
0.153174 + 0.988199i \(0.451051\pi\)
\(558\) 5.01727 14.9479i 0.212398 0.632796i
\(559\) 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 \(-0.192660\pi\)
−0.568975 + 0.822355i \(0.692660\pi\)
\(564\) −7.81153 + 12.6099i −0.328925 + 0.530974i
\(565\) −1.29211 0.618719i −0.0543594 0.0260297i
\(566\) 30.1471i 1.26718i
\(567\) −27.3650 + 3.79300i −1.14922 + 0.159291i
\(568\) −3.26268 + 3.26268i −0.136899 + 0.136899i
\(569\) −1.31647 −0.0551895 −0.0275947 0.999619i \(-0.508785\pi\)
−0.0275947 + 0.999619i \(0.508785\pi\)
\(570\) −2.47107 + 11.2725i −0.103502 + 0.472153i
\(571\) 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
\(573\) −5.38581 + 1.26549i −0.224995 + 0.0528668i
\(574\) 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
\(582\) −7.38688 31.4378i −0.306196 1.30314i
\(583\) −1.58046 + 1.58046i −0.0654562 + 0.0654562i
\(584\) −0.987754 −0.0408735
\(585\) −0.369642 24.6684i −0.0152828 1.01991i
\(586\) 5.77667 0.238632
\(587\) −9.61314 + 9.61314i −0.396777 + 0.396777i −0.877095 0.480318i \(-0.840521\pi\)
0.480318 + 0.877095i \(0.340521\pi\)
\(588\) 0.959812 + 4.08486i 0.0395820 + 0.168457i
\(589\) 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 \(-0.133114\pi\)
−0.406106 + 0.913826i \(0.633114\pi\)
\(594\) −2.52419 + 27.0483i −0.103569 + 1.10980i
\(595\) −4.06626 + 1.43298i −0.166701 + 0.0587464i
\(596\) 17.1561i 0.702740i
\(597\) 15.1330 3.55578i 0.619353 0.145528i
\(598\) 2.60057 2.60057i 0.106345 0.106345i
\(599\) 48.6613 1.98825 0.994123 0.108255i \(-0.0345263\pi\)
0.994123 + 0.108255i \(0.0345263\pi\)
\(600\) −1.06269 8.59481i −0.0433841 0.350881i
\(601\) −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
\(603\) −14.6570 4.91961i −0.596877 0.200342i
\(604\) 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
\(612\) −1.78642 0.599613i −0.0722119 0.0242379i
\(613\) 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
\(615\) 22.7196 14.5497i 0.916141 0.586700i
\(616\) 16.0482 0.646600
\(617\) 1.18781 1.18781i 0.0478194 0.0478194i −0.682793 0.730612i \(-0.739235\pi\)
0.730612 + 0.682793i \(0.239235\pi\)
\(618\) −6.07986 + 1.42857i −0.244568 + 0.0574657i
\(619\) 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
\(627\) −6.17173 26.2662i −0.246475 1.04897i
\(628\) 11.7841 11.7841i 0.470237 0.470237i
\(629\) 2.44758 0.0975913
\(630\) −14.3407 + 14.7771i −0.571349 + 0.588732i
\(631\) −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
\(633\) −0.119351 0.507945i −0.00474377 0.0201890i
\(634\) 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 \(0.950900\pi\)
\(642\) 22.7161 5.33757i 0.896534 0.210657i
\(643\) −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
\(645\) −39.1683 8.58617i −1.54225 0.338080i
\(646\) 1.87159 0.0736367
\(647\) 7.24949 7.24949i 0.285007 0.285007i −0.550095 0.835102i \(-0.685409\pi\)
0.835102 + 0.550095i \(0.185409\pi\)
\(648\) −8.91477 + 1.23565i −0.350205 + 0.0485410i
\(649\) 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 \(-0.0812926\pi\)
−0.252621 + 0.967565i \(0.581293\pi\)
\(654\) −7.48356 + 12.0805i −0.292630 + 0.472385i
\(655\) 2.37148 + 6.72938i 0.0926615 + 0.262939i
\(656\) 6.96597i 0.271975i
\(657\) −0.942921 + 2.80924i −0.0367868 + 0.109599i
\(658\) 18.5888 18.5888i 0.724667 0.724667i
\(659\) 23.0114 0.896399 0.448199 0.893934i \(-0.352066\pi\)
0.448199 + 0.893934i \(0.352066\pi\)
\(660\) 10.9197 + 17.0513i 0.425050 + 0.663722i
\(661\) −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
\(663\) −3.89510 + 0.915226i −0.151273 + 0.0355444i
\(664\) 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
\(672\) 1.21615 + 5.17579i 0.0469139 + 0.199661i
\(673\) −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
\(675\) −25.4587 5.18234i −0.979904 0.199468i
\(676\) −0.525898 −0.0202269
\(677\) −8.73195 + 8.73195i −0.335596 + 0.335596i −0.854707 0.519111i \(-0.826263\pi\)
0.519111 + 0.854707i \(0.326263\pi\)
\(678\) 0.253829 + 1.08027i 0.00974826 + 0.0414876i
\(679\) 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 \(-0.184005\pi\)
−0.546408 + 0.837519i \(0.684005\pi\)
\(684\) 8.00357 3.98096i 0.306024 0.152216i
\(685\) −17.4875 + 36.5202i −0.668163 + 1.39536i
\(686\) 14.0509i 0.536464i
\(687\) −29.7044 + 6.97959i −1.13329 + 0.266288i
\(688\) −7.32093 + 7.32093i −0.279108 + 0.279108i
\(689\) −1.57233 −0.0599009
\(690\) −2.08868 3.26151i −0.0795147 0.124163i
\(691\) 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
\(693\) 15.3198 45.6421i 0.581951 1.73380i
\(694\) 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 \(0.885890\pi\)
\(702\) −14.7101 + 12.1989i −0.555196 + 0.460417i
\(703\) −8.21000 + 8.21000i −0.309646 + 0.309646i
\(704\) 5.22806 0.197040
\(705\) 32.3992 + 7.10230i 1.22023 + 0.267488i
\(706\) −23.7202 −0.892723
\(707\) 23.6159 23.6159i 0.888168 0.888168i
\(708\) −18.8407 + 4.42696i −0.708076 + 0.166375i
\(709\) 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
\(717\) −9.63119 40.9893i −0.359683 1.53077i
\(718\) −2.81286 + 2.81286i −0.104975 + 0.104975i
\(719\) −20.2760 −0.756166 −0.378083 0.925772i \(-0.623417\pi\)
−0.378083 + 0.925772i \(0.623417\pi\)
\(720\) −4.67181 + 4.81395i −0.174108 + 0.179405i
\(721\) 11.0685 0.412212
\(722\) 7.15709 7.15709i 0.266359 0.266359i
\(723\) 9.46765 + 40.2933i 0.352106 + 1.49852i
\(724\) 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
\(732\) −2.37735 + 0.558602i −0.0878694 + 0.0206465i
\(733\) −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
\(735\) 7.90140 5.06008i 0.291447 0.186644i
\(736\) −1.00000 −0.0368605
\(737\) 19.0515 19.0515i 0.701771 0.701771i
\(738\) −19.8117 6.64980i −0.729278 0.244782i
\(739\) 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 0.395972 0.918263i \(-0.370408\pi\)
−0.918263 + 0.395972i \(0.870408\pi\)
\(744\) −4.79398 + 7.73879i −0.175756 + 0.283718i
\(745\) 36.1812 12.7505i 1.32558 0.467142i
\(746\) 5.35085i 0.195909i
\(747\) −37.7384 12.6669i −1.38077 0.463457i
\(748\) 2.32204 2.32204i 0.0849022 0.0849022i
\(749\) −41.3551 −1.51108
\(750\) −17.3362 + 8.62887i −0.633027 + 0.315082i
\(751\) 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
\(753\) −37.9454 + 8.91598i −1.38281 + 0.324916i
\(754\) 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 \(0.00896620\pi\)
−0.999603 + 0.0281644i \(0.991034\pi\)
\(762\) 7.32333 + 31.1673i 0.265296 + 1.12907i
\(763\) 17.8083 17.8083i 0.644705 0.644705i
\(764\) 3.19418 0.115561
\(765\) 0.0631309 + 4.21310i 0.00228250 + 0.152325i
\(766\) −32.0016 −1.15626
\(767\) −29.0585 + 29.0585i −1.04924 + 1.04924i
\(768\) 0.396187 + 1.68613i 0.0142962 + 0.0608430i
\(769\) 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 0.619239 0.785202i \(-0.287441\pi\)
−0.785202 + 0.619239i \(0.787441\pi\)
\(774\) 13.8326 + 27.8098i 0.497201 + 0.999604i
\(775\) −20.4730 + 16.4758i −0.735410 + 0.591827i
\(776\) 18.6449i 0.669314i
\(777\) −20.1683 + 4.73891i −0.723533 + 0.170007i