Properties

Label 690.3.k.a.277.3
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.3
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(3.78471 - 3.26741i) q^{5} -2.44949 q^{6} +(3.72268 + 3.72268i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(3.78471 - 3.26741i) q^{5} -2.44949 q^{6} +(3.72268 + 3.72268i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(7.05212 + 0.517301i) q^{10} +11.8026 q^{11} +(-2.44949 - 2.44949i) q^{12} +(17.6286 - 17.6286i) q^{13} +7.44536i q^{14} +(-0.633562 + 8.63705i) q^{15} -4.00000 q^{16} +(-20.6341 - 20.6341i) q^{17} +(3.00000 - 3.00000i) q^{18} -6.19835i q^{19} +(6.53482 + 7.56942i) q^{20} -9.11866 q^{21} +(11.8026 + 11.8026i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(3.64807 - 24.7324i) q^{25} +35.2571 q^{26} +(3.67423 + 3.67423i) q^{27} +(-7.44536 + 7.44536i) q^{28} +0.0875899i q^{29} +(-9.27061 + 8.00349i) q^{30} -0.753876 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-14.4552 + 14.4552i) q^{33} -41.2682i q^{34} +(26.2528 + 1.92575i) q^{35} +6.00000 q^{36} +(28.5265 + 28.5265i) q^{37} +(6.19835 - 6.19835i) q^{38} +43.1810i q^{39} +(-1.03460 + 14.1042i) q^{40} +57.1315 q^{41} +(-9.11866 - 9.11866i) q^{42} +(-1.66664 + 1.66664i) q^{43} +23.6052i q^{44} +(-9.80223 - 11.3541i) q^{45} -6.78233 q^{46} +(40.7708 + 40.7708i) q^{47} +(4.89898 - 4.89898i) q^{48} -21.2833i q^{49} +(28.3805 - 21.0843i) q^{50} +50.5430 q^{51} +(35.2571 + 35.2571i) q^{52} +(7.42708 - 7.42708i) q^{53} +7.34847i q^{54} +(44.6694 - 38.5639i) q^{55} -14.8907 q^{56} +(7.59140 + 7.59140i) q^{57} +(-0.0875899 + 0.0875899i) q^{58} +106.957i q^{59} +(-17.2741 - 1.26712i) q^{60} -91.1049 q^{61} +(-0.753876 - 0.753876i) q^{62} +(11.1680 - 11.1680i) q^{63} -8.00000i q^{64} +(9.11928 - 124.319i) q^{65} -28.9104 q^{66} +(22.3209 + 22.3209i) q^{67} +(41.2682 - 41.2682i) q^{68} -8.30662i q^{69} +(24.3270 + 28.1785i) q^{70} -123.707 q^{71} +(6.00000 + 6.00000i) q^{72} +(14.6619 - 14.6619i) q^{73} +57.0530i q^{74} +(25.8229 + 34.7588i) q^{75} +12.3967 q^{76} +(43.9373 + 43.9373i) q^{77} +(-43.1810 + 43.1810i) q^{78} -22.2431i q^{79} +(-15.1388 + 13.0696i) q^{80} -9.00000 q^{81} +(57.1315 + 57.1315i) q^{82} +(4.59002 - 4.59002i) q^{83} -18.2373i q^{84} +(-145.514 - 10.6741i) q^{85} -3.33329 q^{86} +(-0.107275 - 0.107275i) q^{87} +(-23.6052 + 23.6052i) q^{88} +30.0252i q^{89} +(1.55190 - 21.1564i) q^{90} +131.251 q^{91} +(-6.78233 - 6.78233i) q^{92} +(0.923306 - 0.923306i) q^{93} +81.5417i q^{94} +(-20.2525 - 23.4590i) q^{95} +9.79796 q^{96} +(120.850 + 120.850i) q^{97} +(21.2833 - 21.2833i) q^{98} -35.4078i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 3.78471 3.26741i 0.756942 0.653482i
\(6\) −2.44949 −0.408248
\(7\) 3.72268 + 3.72268i 0.531811 + 0.531811i 0.921111 0.389300i \(-0.127283\pi\)
−0.389300 + 0.921111i \(0.627283\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 7.05212 + 0.517301i 0.705212 + 0.0517301i
\(11\) 11.8026 1.07296 0.536482 0.843912i \(-0.319753\pi\)
0.536482 + 0.843912i \(0.319753\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 17.6286 17.6286i 1.35604 1.35604i 0.477305 0.878738i \(-0.341614\pi\)
0.878738 0.477305i \(-0.158386\pi\)
\(14\) 7.44536i 0.531811i
\(15\) −0.633562 + 8.63705i −0.0422375 + 0.575803i
\(16\) −4.00000 −0.250000
\(17\) −20.6341 20.6341i −1.21377 1.21377i −0.969777 0.243994i \(-0.921542\pi\)
−0.243994 0.969777i \(-0.578458\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 6.19835i 0.326229i −0.986607 0.163114i \(-0.947846\pi\)
0.986607 0.163114i \(-0.0521540\pi\)
\(20\) 6.53482 + 7.56942i 0.326741 + 0.378471i
\(21\) −9.11866 −0.434222
\(22\) 11.8026 + 11.8026i 0.536482 + 0.536482i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 3.64807 24.7324i 0.145923 0.989296i
\(26\) 35.2571 1.35604
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −7.44536 + 7.44536i −0.265906 + 0.265906i
\(29\) 0.0875899i 0.00302034i 0.999999 + 0.00151017i \(0.000480702\pi\)
−0.999999 + 0.00151017i \(0.999519\pi\)
\(30\) −9.27061 + 8.00349i −0.309020 + 0.266783i
\(31\) −0.753876 −0.0243186 −0.0121593 0.999926i \(-0.503871\pi\)
−0.0121593 + 0.999926i \(0.503871\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −14.4552 + 14.4552i −0.438036 + 0.438036i
\(34\) 41.2682i 1.21377i
\(35\) 26.2528 + 1.92575i 0.750079 + 0.0550213i
\(36\) 6.00000 0.166667
\(37\) 28.5265 + 28.5265i 0.770986 + 0.770986i 0.978279 0.207293i \(-0.0664652\pi\)
−0.207293 + 0.978279i \(0.566465\pi\)
\(38\) 6.19835 6.19835i 0.163114 0.163114i
\(39\) 43.1810i 1.10720i
\(40\) −1.03460 + 14.1042i −0.0258651 + 0.352606i
\(41\) 57.1315 1.39345 0.696725 0.717338i \(-0.254640\pi\)
0.696725 + 0.717338i \(0.254640\pi\)
\(42\) −9.11866 9.11866i −0.217111 0.217111i
\(43\) −1.66664 + 1.66664i −0.0387592 + 0.0387592i −0.726221 0.687462i \(-0.758725\pi\)
0.687462 + 0.726221i \(0.258725\pi\)
\(44\) 23.6052i 0.536482i
\(45\) −9.80223 11.3541i −0.217827 0.252314i
\(46\) −6.78233 −0.147442
\(47\) 40.7708 + 40.7708i 0.867464 + 0.867464i 0.992191 0.124727i \(-0.0398054\pi\)
−0.124727 + 0.992191i \(0.539805\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 21.2833i 0.434354i
\(50\) 28.3805 21.0843i 0.567609 0.421687i
\(51\) 50.5430 0.991040
\(52\) 35.2571 + 35.2571i 0.678021 + 0.678021i
\(53\) 7.42708 7.42708i 0.140134 0.140134i −0.633560 0.773694i \(-0.718407\pi\)
0.773694 + 0.633560i \(0.218407\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 44.6694 38.5639i 0.812172 0.701162i
\(56\) −14.8907 −0.265906
\(57\) 7.59140 + 7.59140i 0.133182 + 0.133182i
\(58\) −0.0875899 + 0.0875899i −0.00151017 + 0.00151017i
\(59\) 106.957i 1.81283i 0.422391 + 0.906413i \(0.361191\pi\)
−0.422391 + 0.906413i \(0.638809\pi\)
\(60\) −17.2741 1.26712i −0.287902 0.0211187i
\(61\) −91.1049 −1.49352 −0.746761 0.665092i \(-0.768392\pi\)
−0.746761 + 0.665092i \(0.768392\pi\)
\(62\) −0.753876 0.753876i −0.0121593 0.0121593i
\(63\) 11.1680 11.1680i 0.177270 0.177270i
\(64\) 8.00000i 0.125000i
\(65\) 9.11928 124.319i 0.140297 1.91260i
\(66\) −28.9104 −0.438036
\(67\) 22.3209 + 22.3209i 0.333148 + 0.333148i 0.853781 0.520633i \(-0.174304\pi\)
−0.520633 + 0.853781i \(0.674304\pi\)
\(68\) 41.2682 41.2682i 0.606885 0.606885i
\(69\) 8.30662i 0.120386i
\(70\) 24.3270 + 28.1785i 0.347529 + 0.402550i
\(71\) −123.707 −1.74235 −0.871177 0.490969i \(-0.836643\pi\)
−0.871177 + 0.490969i \(0.836643\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 14.6619 14.6619i 0.200848 0.200848i −0.599515 0.800363i \(-0.704640\pi\)
0.800363 + 0.599515i \(0.204640\pi\)
\(74\) 57.0530i 0.770986i
\(75\) 25.8229 + 34.7588i 0.344306 + 0.463451i
\(76\) 12.3967 0.163114
\(77\) 43.9373 + 43.9373i 0.570614 + 0.570614i
\(78\) −43.1810 + 43.1810i −0.553602 + 0.553602i
\(79\) 22.2431i 0.281558i −0.990041 0.140779i \(-0.955039\pi\)
0.990041 0.140779i \(-0.0449607\pi\)
\(80\) −15.1388 + 13.0696i −0.189236 + 0.163370i
\(81\) −9.00000 −0.111111
\(82\) 57.1315 + 57.1315i 0.696725 + 0.696725i
\(83\) 4.59002 4.59002i 0.0553014 0.0553014i −0.678915 0.734217i \(-0.737550\pi\)
0.734217 + 0.678915i \(0.237550\pi\)
\(84\) 18.2373i 0.217111i
\(85\) −145.514 10.6741i −1.71193 0.125577i
\(86\) −3.33329 −0.0387592
\(87\) −0.107275 0.107275i −0.00123305 0.00123305i
\(88\) −23.6052 + 23.6052i −0.268241 + 0.268241i
\(89\) 30.0252i 0.337361i 0.985671 + 0.168681i \(0.0539507\pi\)
−0.985671 + 0.168681i \(0.946049\pi\)
\(90\) 1.55190 21.1564i 0.0172434 0.235071i
\(91\) 131.251 1.44232
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 0.923306 0.923306i 0.00992802 0.00992802i
\(94\) 81.5417i 0.867464i
\(95\) −20.2525 23.4590i −0.213185 0.246936i
\(96\) 9.79796 0.102062
\(97\) 120.850 + 120.850i 1.24587 + 1.24587i 0.957526 + 0.288347i \(0.0931056\pi\)
0.288347 + 0.957526i \(0.406894\pi\)
\(98\) 21.2833 21.2833i 0.217177 0.217177i
\(99\) 35.4078i 0.357655i
\(100\) 49.4648 + 7.29614i 0.494648 + 0.0729614i
\(101\) −6.35681 −0.0629387 −0.0314693 0.999505i \(-0.510019\pi\)
−0.0314693 + 0.999505i \(0.510019\pi\)
\(102\) 50.5430 + 50.5430i 0.495520 + 0.495520i
\(103\) 128.811 128.811i 1.25059 1.25059i 0.295136 0.955455i \(-0.404635\pi\)
0.955455 0.295136i \(-0.0953649\pi\)
\(104\) 70.5142i 0.678021i
\(105\) −34.5115 + 29.7944i −0.328681 + 0.283756i
\(106\) 14.8542 0.140134
\(107\) 47.4520 + 47.4520i 0.443477 + 0.443477i 0.893179 0.449702i \(-0.148470\pi\)
−0.449702 + 0.893179i \(0.648470\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 145.890i 1.33844i 0.743062 + 0.669222i \(0.233373\pi\)
−0.743062 + 0.669222i \(0.766627\pi\)
\(110\) 83.2334 + 6.10550i 0.756667 + 0.0555046i
\(111\) −69.8754 −0.629508
\(112\) −14.8907 14.8907i −0.132953 0.132953i
\(113\) −94.3049 + 94.3049i −0.834557 + 0.834557i −0.988136 0.153580i \(-0.950920\pi\)
0.153580 + 0.988136i \(0.450920\pi\)
\(114\) 15.1828i 0.133182i
\(115\) −1.75425 + 23.9149i −0.0152544 + 0.207956i
\(116\) −0.175180 −0.00151017
\(117\) −52.8857 52.8857i −0.452014 0.452014i
\(118\) −106.957 + 106.957i −0.906413 + 0.906413i
\(119\) 153.628i 1.29099i
\(120\) −16.0070 18.5412i −0.133391 0.154510i
\(121\) 18.3014 0.151252
\(122\) −91.1049 91.1049i −0.746761 0.746761i
\(123\) −69.9715 + 69.9715i −0.568874 + 0.568874i
\(124\) 1.50775i 0.0121593i
\(125\) −67.0040 105.525i −0.536032 0.844198i
\(126\) 22.3361 0.177270
\(127\) 10.3220 + 10.3220i 0.0812757 + 0.0812757i 0.746576 0.665300i \(-0.231696\pi\)
−0.665300 + 0.746576i \(0.731696\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 4.08243i 0.0316467i
\(130\) 133.438 115.199i 1.02645 0.886149i
\(131\) −184.410 −1.40771 −0.703856 0.710343i \(-0.748540\pi\)
−0.703856 + 0.710343i \(0.748540\pi\)
\(132\) −28.9104 28.9104i −0.219018 0.219018i
\(133\) 23.0745 23.0745i 0.173492 0.173492i
\(134\) 44.6418i 0.333148i
\(135\) 25.9111 + 1.90069i 0.191934 + 0.0140792i
\(136\) 82.5364 0.606885
\(137\) −171.020 171.020i −1.24832 1.24832i −0.956461 0.291859i \(-0.905726\pi\)
−0.291859 0.956461i \(-0.594274\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 83.8444i 0.603197i 0.953435 + 0.301599i \(0.0975203\pi\)
−0.953435 + 0.301599i \(0.902480\pi\)
\(140\) −3.85149 + 52.5056i −0.0275107 + 0.375040i
\(141\) −99.8677 −0.708282
\(142\) −123.707 123.707i −0.871177 0.871177i
\(143\) 208.063 208.063i 1.45498 1.45498i
\(144\) 12.0000i 0.0833333i
\(145\) 0.286192 + 0.331502i 0.00197374 + 0.00228622i
\(146\) 29.3239 0.200848
\(147\) 26.0666 + 26.0666i 0.177324 + 0.177324i
\(148\) −57.0530 + 57.0530i −0.385493 + 0.385493i
\(149\) 117.040i 0.785504i −0.919644 0.392752i \(-0.871523\pi\)
0.919644 0.392752i \(-0.128477\pi\)
\(150\) −8.93591 + 60.5818i −0.0595728 + 0.403878i
\(151\) 39.9086 0.264295 0.132148 0.991230i \(-0.457813\pi\)
0.132148 + 0.991230i \(0.457813\pi\)
\(152\) 12.3967 + 12.3967i 0.0815572 + 0.0815572i
\(153\) −61.9023 + 61.9023i −0.404590 + 0.404590i
\(154\) 87.8746i 0.570614i
\(155\) −2.85320 + 2.46322i −0.0184078 + 0.0158918i
\(156\) −86.3619 −0.553602
\(157\) −56.3304 56.3304i −0.358793 0.358793i 0.504575 0.863368i \(-0.331649\pi\)
−0.863368 + 0.504575i \(0.831649\pi\)
\(158\) 22.2431 22.2431i 0.140779 0.140779i
\(159\) 18.1926i 0.114419i
\(160\) −28.2085 2.06921i −0.176303 0.0129325i
\(161\) −25.2484 −0.156823
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 104.950 104.950i 0.643867 0.643867i −0.307637 0.951504i \(-0.599538\pi\)
0.951504 + 0.307637i \(0.0995382\pi\)
\(164\) 114.263i 0.696725i
\(165\) −7.47768 + 101.940i −0.0453193 + 0.617816i
\(166\) 9.18003 0.0553014
\(167\) −173.661 173.661i −1.03989 1.03989i −0.999171 0.0407150i \(-0.987036\pi\)
−0.0407150 0.999171i \(-0.512964\pi\)
\(168\) 18.2373 18.2373i 0.108556 0.108556i
\(169\) 452.532i 2.67770i
\(170\) −134.840 156.188i −0.793177 0.918754i
\(171\) −18.5951 −0.108743
\(172\) −3.33329 3.33329i −0.0193796 0.0193796i
\(173\) −151.999 + 151.999i −0.878608 + 0.878608i −0.993391 0.114783i \(-0.963383\pi\)
0.114783 + 0.993391i \(0.463383\pi\)
\(174\) 0.214551i 0.00123305i
\(175\) 105.651 78.4902i 0.603722 0.448515i
\(176\) −47.2104 −0.268241
\(177\) −130.995 130.995i −0.740084 0.740084i
\(178\) −30.0252 + 30.0252i −0.168681 + 0.168681i
\(179\) 133.690i 0.746874i −0.927656 0.373437i \(-0.878179\pi\)
0.927656 0.373437i \(-0.121821\pi\)
\(180\) 22.7083 19.6045i 0.126157 0.108914i
\(181\) 269.565 1.48931 0.744655 0.667450i \(-0.232614\pi\)
0.744655 + 0.667450i \(0.232614\pi\)
\(182\) 131.251 + 131.251i 0.721159 + 0.721159i
\(183\) 111.580 111.580i 0.609728 0.609728i
\(184\) 13.5647i 0.0737210i
\(185\) 201.172 + 14.7568i 1.08742 + 0.0797665i
\(186\) 1.84661 0.00992802
\(187\) −243.536 243.536i −1.30233 1.30233i
\(188\) −81.5417 + 81.5417i −0.433732 + 0.433732i
\(189\) 27.3560i 0.144741i
\(190\) 3.20642 43.7115i 0.0168759 0.230061i
\(191\) −322.402 −1.68797 −0.843986 0.536366i \(-0.819797\pi\)
−0.843986 + 0.536366i \(0.819797\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −89.8376 + 89.8376i −0.465480 + 0.465480i −0.900447 0.434967i \(-0.856760\pi\)
0.434967 + 0.900447i \(0.356760\pi\)
\(194\) 241.699i 1.24587i
\(195\) 141.090 + 163.427i 0.723538 + 0.838090i
\(196\) 42.5666 0.217177
\(197\) −43.4072 43.4072i −0.220341 0.220341i 0.588301 0.808642i \(-0.299797\pi\)
−0.808642 + 0.588301i \(0.799797\pi\)
\(198\) 35.4078 35.4078i 0.178827 0.178827i
\(199\) 241.437i 1.21325i 0.794989 + 0.606624i \(0.207477\pi\)
−0.794989 + 0.606624i \(0.792523\pi\)
\(200\) 42.1687 + 56.7609i 0.210843 + 0.283805i
\(201\) −54.6749 −0.272014
\(202\) −6.35681 6.35681i −0.0314693 0.0314693i
\(203\) −0.326069 + 0.326069i −0.00160625 + 0.00160625i
\(204\) 101.086i 0.495520i
\(205\) 216.226 186.672i 1.05476 0.910595i
\(206\) 257.622 1.25059
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) −70.5142 + 70.5142i −0.339011 + 0.339011i
\(209\) 73.1567i 0.350032i
\(210\) −64.3059 4.71710i −0.306219 0.0224624i
\(211\) −52.1391 −0.247105 −0.123552 0.992338i \(-0.539429\pi\)
−0.123552 + 0.992338i \(0.539429\pi\)
\(212\) 14.8542 + 14.8542i 0.0700668 + 0.0700668i
\(213\) 151.510 151.510i 0.711313 0.711313i
\(214\) 94.9040i 0.443477i
\(215\) −0.862158 + 11.7534i −0.00401003 + 0.0546669i
\(216\) −14.6969 −0.0680414
\(217\) −2.80644 2.80644i −0.0129329 0.0129329i
\(218\) −145.890 + 145.890i −0.669222 + 0.669222i
\(219\) 35.9142i 0.163992i
\(220\) 77.1279 + 89.3389i 0.350581 + 0.406086i
\(221\) −727.499 −3.29185
\(222\) −69.8754 69.8754i −0.314754 0.314754i
\(223\) 280.452 280.452i 1.25763 1.25763i 0.305410 0.952221i \(-0.401206\pi\)
0.952221 0.305410i \(-0.0987935\pi\)
\(224\) 29.7814i 0.132953i
\(225\) −74.1972 10.9442i −0.329765 0.0486410i
\(226\) −188.610 −0.834557
\(227\) 144.396 + 144.396i 0.636105 + 0.636105i 0.949592 0.313487i \(-0.101497\pi\)
−0.313487 + 0.949592i \(0.601497\pi\)
\(228\) −15.1828 + 15.1828i −0.0665912 + 0.0665912i
\(229\) 362.796i 1.58426i 0.610351 + 0.792131i \(0.291028\pi\)
−0.610351 + 0.792131i \(0.708972\pi\)
\(230\) −25.6692 + 22.1606i −0.111605 + 0.0963506i
\(231\) −107.624 −0.465905
\(232\) −0.175180 0.175180i −0.000755085 0.000755085i
\(233\) −88.1385 + 88.1385i −0.378277 + 0.378277i −0.870480 0.492203i \(-0.836192\pi\)
0.492203 + 0.870480i \(0.336192\pi\)
\(234\) 105.771i 0.452014i
\(235\) 287.521 + 21.0908i 1.22349 + 0.0897481i
\(236\) −213.914 −0.906413
\(237\) 27.2421 + 27.2421i 0.114946 + 0.114946i
\(238\) 153.628 153.628i 0.645497 0.645497i
\(239\) 296.594i 1.24098i 0.784214 + 0.620490i \(0.213066\pi\)
−0.784214 + 0.620490i \(0.786934\pi\)
\(240\) 2.53425 34.5482i 0.0105594 0.143951i
\(241\) −286.041 −1.18689 −0.593445 0.804874i \(-0.702233\pi\)
−0.593445 + 0.804874i \(0.702233\pi\)
\(242\) 18.3014 + 18.3014i 0.0756258 + 0.0756258i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 182.210i 0.746761i
\(245\) −69.5413 80.5512i −0.283842 0.328780i
\(246\) −139.943 −0.568874
\(247\) −109.268 109.268i −0.442380 0.442380i
\(248\) 1.50775 1.50775i 0.00607965 0.00607965i
\(249\) 11.2432i 0.0451534i
\(250\) 38.5207 172.529i 0.154083 0.690115i
\(251\) 181.698 0.723897 0.361949 0.932198i \(-0.382112\pi\)
0.361949 + 0.932198i \(0.382112\pi\)
\(252\) 22.3361 + 22.3361i 0.0886352 + 0.0886352i
\(253\) −40.0246 + 40.0246i −0.158200 + 0.158200i
\(254\) 20.6440i 0.0812757i
\(255\) 191.291 165.145i 0.750160 0.647627i
\(256\) 16.0000 0.0625000
\(257\) 196.253 + 196.253i 0.763631 + 0.763631i 0.976977 0.213346i \(-0.0684361\pi\)
−0.213346 + 0.976977i \(0.568436\pi\)
\(258\) 4.08243 4.08243i 0.0158234 0.0158234i
\(259\) 212.390i 0.820039i
\(260\) 248.637 + 18.2386i 0.956298 + 0.0701483i
\(261\) 0.262770 0.00100678
\(262\) −184.410 184.410i −0.703856 0.703856i
\(263\) 231.129 231.129i 0.878816 0.878816i −0.114596 0.993412i \(-0.536557\pi\)
0.993412 + 0.114596i \(0.0365575\pi\)
\(264\) 57.8207i 0.219018i
\(265\) 3.84204 52.3767i 0.0144983 0.197648i
\(266\) 46.1489 0.173492
\(267\) −36.7732 36.7732i −0.137727 0.137727i
\(268\) −44.6418 + 44.6418i −0.166574 + 0.166574i
\(269\) 275.606i 1.02456i −0.858820 0.512278i \(-0.828802\pi\)
0.858820 0.512278i \(-0.171198\pi\)
\(270\) 24.0105 + 27.8118i 0.0889276 + 0.103007i
\(271\) −31.3910 −0.115834 −0.0579170 0.998321i \(-0.518446\pi\)
−0.0579170 + 0.998321i \(0.518446\pi\)
\(272\) 82.5364 + 82.5364i 0.303443 + 0.303443i
\(273\) −160.749 + 160.749i −0.588824 + 0.588824i
\(274\) 342.040i 1.24832i
\(275\) 43.0567 291.907i 0.156570 1.06148i
\(276\) 16.6132 0.0601929
\(277\) −15.9302 15.9302i −0.0575096 0.0575096i 0.677767 0.735277i \(-0.262948\pi\)
−0.735277 + 0.677767i \(0.762948\pi\)
\(278\) −83.8444 + 83.8444i −0.301599 + 0.301599i
\(279\) 2.26163i 0.00810619i
\(280\) −56.3571 + 48.6541i −0.201275 + 0.173765i
\(281\) −48.1708 −0.171426 −0.0857131 0.996320i \(-0.527317\pi\)
−0.0857131 + 0.996320i \(0.527317\pi\)
\(282\) −99.8677 99.8677i −0.354141 0.354141i
\(283\) −136.406 + 136.406i −0.482000 + 0.482000i −0.905770 0.423770i \(-0.860706\pi\)
0.423770 + 0.905770i \(0.360706\pi\)
\(284\) 247.414i 0.871177i
\(285\) 53.5355 + 3.92704i 0.187844 + 0.0137791i
\(286\) 416.126 1.45498
\(287\) 212.682 + 212.682i 0.741053 + 0.741053i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 562.532i 1.94648i
\(290\) −0.0453104 + 0.617694i −0.000156243 + 0.00212998i
\(291\) −296.020 −1.01725
\(292\) 29.3239 + 29.3239i 0.100424 + 0.100424i
\(293\) 96.8737 96.8737i 0.330627 0.330627i −0.522198 0.852825i \(-0.674888\pi\)
0.852825 + 0.522198i \(0.174888\pi\)
\(294\) 52.1333i 0.177324i
\(295\) 349.472 + 404.801i 1.18465 + 1.37221i
\(296\) −114.106 −0.385493
\(297\) 43.3655 + 43.3655i 0.146012 + 0.146012i
\(298\) 117.040 117.040i 0.392752 0.392752i
\(299\) 119.563i 0.399875i
\(300\) −69.5177 + 51.6458i −0.231726 + 0.172153i
\(301\) −12.4088 −0.0412251
\(302\) 39.9086 + 39.9086i 0.132148 + 0.132148i
\(303\) 7.78547 7.78547i 0.0256946 0.0256946i
\(304\) 24.7934i 0.0815572i
\(305\) −344.806 + 297.677i −1.13051 + 0.975990i
\(306\) −123.805 −0.404590
\(307\) 95.1467 + 95.1467i 0.309924 + 0.309924i 0.844880 0.534956i \(-0.179672\pi\)
−0.534956 + 0.844880i \(0.679672\pi\)
\(308\) −87.8746 + 87.8746i −0.285307 + 0.285307i
\(309\) 315.521i 1.02110i
\(310\) −5.31643 0.389981i −0.0171498 0.00125800i
\(311\) −374.486 −1.20414 −0.602068 0.798445i \(-0.705656\pi\)
−0.602068 + 0.798445i \(0.705656\pi\)
\(312\) −86.3619 86.3619i −0.276801 0.276801i
\(313\) 276.544 276.544i 0.883528 0.883528i −0.110363 0.993891i \(-0.535201\pi\)
0.993891 + 0.110363i \(0.0352015\pi\)
\(314\) 112.661i 0.358793i
\(315\) 5.77724 78.7583i 0.0183404 0.250026i
\(316\) 44.4862 0.140779
\(317\) 119.954 + 119.954i 0.378403 + 0.378403i 0.870526 0.492123i \(-0.163779\pi\)
−0.492123 + 0.870526i \(0.663779\pi\)
\(318\) −18.1926 + 18.1926i −0.0572093 + 0.0572093i
\(319\) 1.03379i 0.00324072i
\(320\) −26.1393 30.2777i −0.0816852 0.0946178i
\(321\) −116.233 −0.362097
\(322\) −25.2484 25.2484i −0.0784113 0.0784113i
\(323\) −127.897 + 127.897i −0.395967 + 0.395967i
\(324\) 18.0000i 0.0555556i
\(325\) −371.686 500.307i −1.14365 1.53941i
\(326\) 209.901 0.643867
\(327\) −178.679 178.679i −0.546418 0.546418i
\(328\) −114.263 + 114.263i −0.348363 + 0.348363i
\(329\) 303.553i 0.922655i
\(330\) −109.417 + 94.4620i −0.331568 + 0.286248i
\(331\) −28.1304 −0.0849862 −0.0424931 0.999097i \(-0.513530\pi\)
−0.0424931 + 0.999097i \(0.513530\pi\)
\(332\) 9.18003 + 9.18003i 0.0276507 + 0.0276507i
\(333\) 85.5795 85.5795i 0.256995 0.256995i
\(334\) 347.322i 1.03989i
\(335\) 157.410 + 11.5466i 0.469880 + 0.0344676i
\(336\) 36.4747 0.108556
\(337\) −3.26452 3.26452i −0.00968699 0.00968699i 0.702247 0.711934i \(-0.252180\pi\)
−0.711934 + 0.702247i \(0.752180\pi\)
\(338\) 452.532 452.532i 1.33885 1.33885i
\(339\) 230.999i 0.681413i
\(340\) 21.3481 291.028i 0.0627885 0.855966i
\(341\) −8.89770 −0.0260930
\(342\) −18.5951 18.5951i −0.0543715 0.0543715i
\(343\) 261.642 261.642i 0.762805 0.762805i
\(344\) 6.66658i 0.0193796i
\(345\) −27.1411 31.4382i −0.0786700 0.0911251i
\(346\) −303.998 −0.878608
\(347\) −298.180 298.180i −0.859309 0.859309i 0.131947 0.991257i \(-0.457877\pi\)
−0.991257 + 0.131947i \(0.957877\pi\)
\(348\) 0.214551 0.214551i 0.000616524 0.000616524i
\(349\) 330.198i 0.946127i −0.881028 0.473063i \(-0.843148\pi\)
0.881028 0.473063i \(-0.156852\pi\)
\(350\) 184.142 + 27.1612i 0.526119 + 0.0776034i
\(351\) 129.543 0.369068
\(352\) −47.2104 47.2104i −0.134120 0.134120i
\(353\) −121.953 + 121.953i −0.345476 + 0.345476i −0.858421 0.512946i \(-0.828554\pi\)
0.512946 + 0.858421i \(0.328554\pi\)
\(354\) 261.990i 0.740084i
\(355\) −468.196 + 404.202i −1.31886 + 1.13860i
\(356\) −60.0503 −0.168681
\(357\) 188.155 + 188.155i 0.527046 + 0.527046i
\(358\) 133.690 133.690i 0.373437 0.373437i
\(359\) 14.1715i 0.0394748i −0.999805 0.0197374i \(-0.993717\pi\)
0.999805 0.0197374i \(-0.00628302\pi\)
\(360\) 42.3127 + 3.10381i 0.117535 + 0.00862169i
\(361\) 322.580 0.893575
\(362\) 269.565 + 269.565i 0.744655 + 0.744655i
\(363\) −22.4146 + 22.4146i −0.0617482 + 0.0617482i
\(364\) 262.502i 0.721159i
\(365\) 7.58464 103.398i 0.0207798 0.283281i
\(366\) 223.160 0.609728
\(367\) −63.9505 63.9505i −0.174252 0.174252i 0.614593 0.788845i \(-0.289320\pi\)
−0.788845 + 0.614593i \(0.789320\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 171.394i 0.464483i
\(370\) 186.416 + 215.929i 0.503826 + 0.583592i
\(371\) 55.2973 0.149049
\(372\) 1.84661 + 1.84661i 0.00496401 + 0.00496401i
\(373\) −160.697 + 160.697i −0.430824 + 0.430824i −0.888909 0.458085i \(-0.848536\pi\)
0.458085 + 0.888909i \(0.348536\pi\)
\(374\) 487.072i 1.30233i
\(375\) 211.304 + 47.1781i 0.563476 + 0.125808i
\(376\) −163.083 −0.433732
\(377\) 1.54408 + 1.54408i 0.00409571 + 0.00409571i
\(378\) −27.3560 + 27.3560i −0.0723703 + 0.0723703i
\(379\) 201.845i 0.532573i −0.963894 0.266287i \(-0.914203\pi\)
0.963894 0.266287i \(-0.0857968\pi\)
\(380\) 46.9179 40.5051i 0.123468 0.106592i
\(381\) −25.2837 −0.0663613
\(382\) −322.402 322.402i −0.843986 0.843986i
\(383\) 177.891 177.891i 0.464466 0.464466i −0.435650 0.900116i \(-0.643481\pi\)
0.900116 + 0.435650i \(0.143481\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 309.851 + 22.7288i 0.804808 + 0.0590359i
\(386\) −179.675 −0.465480
\(387\) 4.99993 + 4.99993i 0.0129197 + 0.0129197i
\(388\) −241.699 + 241.699i −0.622936 + 0.622936i
\(389\) 501.474i 1.28914i 0.764547 + 0.644568i \(0.222963\pi\)
−0.764547 + 0.644568i \(0.777037\pi\)
\(390\) −22.3376 + 304.517i −0.0572758 + 0.780814i
\(391\) 139.947 0.357921
\(392\) 42.5666 + 42.5666i 0.108588 + 0.108588i
\(393\) 225.856 225.856i 0.574696 0.574696i
\(394\) 86.8144i 0.220341i
\(395\) −72.6773 84.1836i −0.183993 0.213123i
\(396\) 70.8156 0.178827
\(397\) −379.320 379.320i −0.955467 0.955467i 0.0435831 0.999050i \(-0.486123\pi\)
−0.999050 + 0.0435831i \(0.986123\pi\)
\(398\) −241.437 + 241.437i −0.606624 + 0.606624i
\(399\) 56.5207i 0.141656i
\(400\) −14.5923 + 98.9296i −0.0364807 + 0.247324i
\(401\) 179.175 0.446820 0.223410 0.974725i \(-0.428281\pi\)
0.223410 + 0.974725i \(0.428281\pi\)
\(402\) −54.6749 54.6749i −0.136007 0.136007i
\(403\) −13.2897 + 13.2897i −0.0329770 + 0.0329770i
\(404\) 12.7136i 0.0314693i
\(405\) −34.0624 + 29.4067i −0.0841047 + 0.0726091i
\(406\) −0.652138 −0.00160625
\(407\) 336.687 + 336.687i 0.827241 + 0.827241i
\(408\) −101.086 + 101.086i −0.247760 + 0.247760i
\(409\) 384.881i 0.941029i 0.882392 + 0.470514i \(0.155932\pi\)
−0.882392 + 0.470514i \(0.844068\pi\)
\(410\) 402.898 + 29.5542i 0.982678 + 0.0720834i
\(411\) 418.911 1.01925
\(412\) 257.622 + 257.622i 0.625296 + 0.625296i
\(413\) −398.166 + 398.166i −0.964082 + 0.964082i
\(414\) 20.3470i 0.0491473i
\(415\) 2.37442 32.3693i 0.00572150 0.0779984i
\(416\) −141.028 −0.339011
\(417\) −102.688 102.688i −0.246254 0.246254i
\(418\) 73.1567 73.1567i 0.175016 0.175016i
\(419\) 375.801i 0.896900i 0.893808 + 0.448450i \(0.148024\pi\)
−0.893808 + 0.448450i \(0.851976\pi\)
\(420\) −59.5888 69.0230i −0.141878 0.164341i
\(421\) 109.575 0.260274 0.130137 0.991496i \(-0.458458\pi\)
0.130137 + 0.991496i \(0.458458\pi\)
\(422\) −52.1391 52.1391i −0.123552 0.123552i
\(423\) 122.312 122.312i 0.289155 0.289155i
\(424\) 29.7083i 0.0700668i
\(425\) −585.606 + 435.056i −1.37790 + 1.02366i
\(426\) 303.019 0.711313
\(427\) −339.154 339.154i −0.794272 0.794272i
\(428\) −94.9040 + 94.9040i −0.221738 + 0.221738i
\(429\) 509.648i 1.18799i
\(430\) −12.6155 + 10.8912i −0.0293385 + 0.0253284i
\(431\) −720.493 −1.67168 −0.835839 0.548975i \(-0.815018\pi\)
−0.835839 + 0.548975i \(0.815018\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −10.2464 + 10.2464i −0.0236638 + 0.0236638i −0.718840 0.695176i \(-0.755326\pi\)
0.695176 + 0.718840i \(0.255326\pi\)
\(434\) 5.61288i 0.0129329i
\(435\) −0.756518 0.0554936i −0.00173912 0.000127572i
\(436\) −291.781 −0.669222
\(437\) 21.0196 + 21.0196i 0.0480998 + 0.0480998i
\(438\) −35.9142 + 35.9142i −0.0819960 + 0.0819960i
\(439\) 627.889i 1.43027i 0.698985 + 0.715136i \(0.253635\pi\)
−0.698985 + 0.715136i \(0.746365\pi\)
\(440\) −12.2110 + 166.467i −0.0277523 + 0.378334i
\(441\) −63.8500 −0.144785
\(442\) −727.499 727.499i −1.64593 1.64593i
\(443\) −253.351 + 253.351i −0.571898 + 0.571898i −0.932658 0.360761i \(-0.882517\pi\)
0.360761 + 0.932658i \(0.382517\pi\)
\(444\) 139.751i 0.314754i
\(445\) 98.1045 + 113.637i 0.220460 + 0.255363i
\(446\) 560.903 1.25763
\(447\) 143.344 + 143.344i 0.320681 + 0.320681i
\(448\) 29.7814 29.7814i 0.0664764 0.0664764i
\(449\) 86.2603i 0.192116i 0.995376 + 0.0960582i \(0.0306235\pi\)
−0.995376 + 0.0960582i \(0.969377\pi\)
\(450\) −63.2530 85.1414i −0.140562 0.189203i
\(451\) 674.300 1.49512
\(452\) −188.610 188.610i −0.417278 0.417278i
\(453\) −48.8778 + 48.8778i −0.107898 + 0.107898i
\(454\) 288.792i 0.636105i
\(455\) 496.747 428.850i 1.09175 0.942528i
\(456\) −30.3656 −0.0665912
\(457\) 302.229 + 302.229i 0.661333 + 0.661333i 0.955694 0.294361i \(-0.0951068\pi\)
−0.294361 + 0.955694i \(0.595107\pi\)
\(458\) −362.796 + 362.796i −0.792131 + 0.792131i
\(459\) 151.629i 0.330347i
\(460\) −47.8298 3.50851i −0.103978 0.00762719i
\(461\) −592.540 −1.28534 −0.642668 0.766145i \(-0.722172\pi\)
−0.642668 + 0.766145i \(0.722172\pi\)
\(462\) −107.624 107.624i −0.232952 0.232952i
\(463\) −210.922 + 210.922i −0.455554 + 0.455554i −0.897193 0.441639i \(-0.854397\pi\)
0.441639 + 0.897193i \(0.354397\pi\)
\(464\) 0.350360i 0.000755085i
\(465\) 0.477627 6.51126i 0.00102716 0.0140027i
\(466\) −176.277 −0.378277
\(467\) −75.0504 75.0504i −0.160707 0.160707i 0.622173 0.782880i \(-0.286250\pi\)
−0.782880 + 0.622173i \(0.786250\pi\)
\(468\) 105.771 105.771i 0.226007 0.226007i
\(469\) 166.187i 0.354344i
\(470\) 266.430 + 308.612i 0.566872 + 0.656620i
\(471\) 137.981 0.292953
\(472\) −213.914 213.914i −0.453207 0.453207i
\(473\) −19.6707 + 19.6707i −0.0415872 + 0.0415872i
\(474\) 54.4842i 0.114946i
\(475\) −153.300 22.6120i −0.322737 0.0476043i
\(476\) 307.257 0.645497
\(477\) −22.2813 22.2813i −0.0467112 0.0467112i
\(478\) −296.594 + 296.594i −0.620490 + 0.620490i
\(479\) 582.683i 1.21646i 0.793762 + 0.608229i \(0.208120\pi\)
−0.793762 + 0.608229i \(0.791880\pi\)
\(480\) 37.0824 32.0139i 0.0772551 0.0666957i
\(481\) 1005.76 2.09098
\(482\) −286.041 286.041i −0.593445 0.593445i
\(483\) 30.9229 30.9229i 0.0640226 0.0640226i
\(484\) 36.6029i 0.0756258i
\(485\) 852.246 + 62.5157i 1.75721 + 0.128898i
\(486\) 22.0454 0.0453609
\(487\) 324.456 + 324.456i 0.666234 + 0.666234i 0.956842 0.290608i \(-0.0938575\pi\)
−0.290608 + 0.956842i \(0.593858\pi\)
\(488\) 182.210 182.210i 0.373381 0.373381i
\(489\) 257.075i 0.525715i
\(490\) 11.0099 150.093i 0.0224692 0.306311i
\(491\) 371.828 0.757288 0.378644 0.925542i \(-0.376390\pi\)
0.378644 + 0.925542i \(0.376390\pi\)
\(492\) −139.943 139.943i −0.284437 0.284437i
\(493\) 1.80734 1.80734i 0.00366600 0.00366600i
\(494\) 218.536i 0.442380i
\(495\) −115.692 134.008i −0.233721 0.270724i
\(496\) 3.01550 0.00607965
\(497\) −460.522 460.522i −0.926604 0.926604i
\(498\) −11.2432 + 11.2432i −0.0225767 + 0.0225767i
\(499\) 116.928i 0.234325i −0.993113 0.117163i \(-0.962620\pi\)
0.993113 0.117163i \(-0.0373799\pi\)
\(500\) 211.049 134.008i 0.422099 0.268016i
\(501\) 425.381 0.849063
\(502\) 181.698 + 181.698i 0.361949 + 0.361949i
\(503\) −97.5611 + 97.5611i −0.193959 + 0.193959i −0.797404 0.603446i \(-0.793794\pi\)
0.603446 + 0.797404i \(0.293794\pi\)
\(504\) 44.6721i 0.0886352i
\(505\) −24.0587 + 20.7703i −0.0476410 + 0.0411293i
\(506\) −80.0491 −0.158200
\(507\) 554.236 + 554.236i 1.09317 + 1.09317i
\(508\) −20.6440 + 20.6440i −0.0406379 + 0.0406379i
\(509\) 442.972i 0.870278i −0.900363 0.435139i \(-0.856699\pi\)
0.900363 0.435139i \(-0.143301\pi\)
\(510\) 356.435 + 26.1460i 0.698893 + 0.0512666i
\(511\) 109.163 0.213627
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 22.7742 22.7742i 0.0443941 0.0443941i
\(514\) 392.506i 0.763631i
\(515\) 66.6340 908.390i 0.129386 1.76386i
\(516\) 8.16486 0.0158234
\(517\) 481.202 + 481.202i 0.930758 + 0.930758i
\(518\) −212.390 + 212.390i −0.410019 + 0.410019i
\(519\) 372.320i 0.717380i
\(520\) 230.399 + 266.876i 0.443075 + 0.513223i
\(521\) −666.249 −1.27879 −0.639394 0.768879i \(-0.720815\pi\)
−0.639394 + 0.768879i \(0.720815\pi\)
\(522\) 0.262770 + 0.262770i 0.000503390 + 0.000503390i
\(523\) −57.5211 + 57.5211i −0.109983 + 0.109983i −0.759957 0.649974i \(-0.774780\pi\)
0.649974 + 0.759957i \(0.274780\pi\)
\(524\) 368.821i 0.703856i
\(525\) −33.2655 + 225.526i −0.0633629 + 0.429574i
\(526\) 462.257 0.878816
\(527\) 15.5556 + 15.5556i 0.0295172 + 0.0295172i
\(528\) 57.8207 57.8207i 0.109509 0.109509i
\(529\) 23.0000i 0.0434783i
\(530\) 56.2187 48.5346i 0.106073 0.0915748i
\(531\) 320.870 0.604276
\(532\) 46.1489 + 46.1489i 0.0867461 + 0.0867461i
\(533\) 1007.15 1007.15i 1.88958 1.88958i
\(534\) 73.5464i 0.137727i
\(535\) 334.637 + 24.5470i 0.625490 + 0.0458822i
\(536\) −89.2837 −0.166574
\(537\) 163.737 + 163.737i 0.304910 + 0.304910i
\(538\) 275.606 275.606i 0.512278 0.512278i
\(539\) 251.199i 0.466046i
\(540\) −3.80137 + 51.8223i −0.00703958 + 0.0959672i
\(541\) 487.704 0.901487 0.450743 0.892654i \(-0.351159\pi\)
0.450743 + 0.892654i \(0.351159\pi\)
\(542\) −31.3910 31.3910i −0.0579170 0.0579170i
\(543\) −330.148 + 330.148i −0.608008 + 0.608008i
\(544\) 165.073i 0.303443i
\(545\) 476.684 + 552.153i 0.874650 + 1.01313i
\(546\) −321.498 −0.588824
\(547\) −151.290 151.290i −0.276582 0.276582i 0.555161 0.831743i \(-0.312657\pi\)
−0.831743 + 0.555161i \(0.812657\pi\)
\(548\) 342.040 342.040i 0.624160 0.624160i
\(549\) 273.315i 0.497841i
\(550\) 334.963 248.850i 0.609024 0.452454i
\(551\) 0.542913 0.000985323
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 82.8039 82.8039i 0.149736 0.149736i
\(554\) 31.8603i 0.0575096i
\(555\) −264.458 + 228.311i −0.476501 + 0.411372i
\(556\) −167.689 −0.301599
\(557\) −54.8204 54.8204i −0.0984208 0.0984208i 0.656182 0.754603i \(-0.272170\pi\)
−0.754603 + 0.656182i \(0.772170\pi\)
\(558\) −2.26163 + 2.26163i −0.00405310 + 0.00405310i
\(559\) 58.7611i 0.105118i
\(560\) −105.011 7.70299i −0.187520 0.0137553i
\(561\) 596.539 1.06335
\(562\) −48.1708 48.1708i −0.0857131 0.0857131i
\(563\) 393.961 393.961i 0.699753 0.699753i −0.264604 0.964357i \(-0.585241\pi\)
0.964357 + 0.264604i \(0.0852412\pi\)
\(564\) 199.735i 0.354141i
\(565\) −48.7841 + 665.050i −0.0863435 + 1.17708i
\(566\) −272.812 −0.482000
\(567\) −33.5041 33.5041i −0.0590901 0.0590901i
\(568\) 247.414 247.414i 0.435589 0.435589i
\(569\) 928.406i 1.63165i 0.578302 + 0.815823i \(0.303716\pi\)
−0.578302 + 0.815823i \(0.696284\pi\)
\(570\) 49.6084 + 57.4625i 0.0870323 + 0.100811i
\(571\) −817.767 −1.43217 −0.716083 0.698015i \(-0.754067\pi\)
−0.716083 + 0.698015i \(0.754067\pi\)
\(572\) 416.126 + 416.126i 0.727492 + 0.727492i
\(573\) 394.861 394.861i 0.689111 0.689111i
\(574\) 425.364i 0.741053i
\(575\) 71.5004 + 96.2429i 0.124349 + 0.167379i
\(576\) −24.0000 −0.0416667
\(577\) 259.934 + 259.934i 0.450491 + 0.450491i 0.895518 0.445026i \(-0.146806\pi\)
−0.445026 + 0.895518i \(0.646806\pi\)
\(578\) −562.532 + 562.532i −0.973240 + 0.973240i
\(579\) 220.056i 0.380063i
\(580\) −0.663005 + 0.572384i −0.00114311 + 0.000986869i
\(581\) 34.1743 0.0588198
\(582\) −296.020 296.020i −0.508625 0.508625i
\(583\) 87.6589 87.6589i 0.150358 0.150358i
\(584\) 58.6477i 0.100424i
\(585\) −372.956 27.3578i −0.637532 0.0467655i
\(586\) 193.747 0.330627
\(587\) 331.058 + 331.058i 0.563984 + 0.563984i 0.930437 0.366453i \(-0.119428\pi\)
−0.366453 + 0.930437i \(0.619428\pi\)
\(588\) −52.1333 + 52.1333i −0.0886620 + 0.0886620i
\(589\) 4.67279i 0.00793343i
\(590\) −55.3289 + 754.272i −0.0937778 + 1.27843i
\(591\) 106.325 0.179908
\(592\) −114.106 114.106i −0.192747 0.192747i
\(593\) 614.053 614.053i 1.03550 1.03550i 0.0361568 0.999346i \(-0.488488\pi\)
0.999346 0.0361568i \(-0.0115116\pi\)
\(594\) 86.7311i 0.146012i
\(595\) −501.967 581.439i −0.843641 0.977208i
\(596\) 234.080 0.392752
\(597\) −295.698 295.698i −0.495307 0.495307i
\(598\) −119.563 + 119.563i −0.199938 + 0.199938i
\(599\) 536.579i 0.895791i −0.894086 0.447895i \(-0.852174\pi\)
0.894086 0.447895i \(-0.147826\pi\)
\(600\) −121.164 17.8718i −0.201939 0.0297864i
\(601\) −764.010 −1.27123 −0.635616 0.772006i \(-0.719254\pi\)
−0.635616 + 0.772006i \(0.719254\pi\)
\(602\) −12.4088 12.4088i −0.0206126 0.0206126i
\(603\) 66.9628 66.9628i 0.111049 0.111049i
\(604\) 79.8172i 0.132148i
\(605\) 69.2657 59.7983i 0.114489 0.0988402i
\(606\) 15.5709 0.0256946
\(607\) −375.415 375.415i −0.618476 0.618476i 0.326665 0.945140i \(-0.394075\pi\)
−0.945140 + 0.326665i \(0.894075\pi\)
\(608\) −24.7934 + 24.7934i −0.0407786 + 0.0407786i
\(609\) 0.798703i 0.00131150i
\(610\) −642.483 47.1287i −1.05325 0.0772601i
\(611\) 1437.46 2.35264
\(612\) −123.805 123.805i −0.202295 0.202295i
\(613\) −195.776 + 195.776i −0.319374 + 0.319374i −0.848527 0.529153i \(-0.822510\pi\)
0.529153 + 0.848527i \(0.322510\pi\)
\(614\) 190.293i 0.309924i
\(615\) −36.1963 + 493.447i −0.0588558 + 0.802353i
\(616\) −175.749 −0.285307
\(617\) −124.149 124.149i −0.201214 0.201214i 0.599306 0.800520i \(-0.295443\pi\)
−0.800520 + 0.599306i \(0.795443\pi\)
\(618\) −315.521 + 315.521i −0.510552 + 0.510552i
\(619\) 144.829i 0.233972i −0.993134 0.116986i \(-0.962677\pi\)
0.993134 0.116986i \(-0.0373232\pi\)
\(620\) −4.92644 5.70641i −0.00794588 0.00920388i
\(621\) −24.9199 −0.0401286
\(622\) −374.486 374.486i −0.602068 0.602068i
\(623\) −111.774 + 111.774i −0.179413 + 0.179413i
\(624\) 172.724i 0.276801i
\(625\) −598.383 180.451i −0.957413 0.288722i
\(626\) 553.088 0.883528
\(627\) 89.5983 + 89.5983i 0.142900 + 0.142900i
\(628\) 112.661 112.661i 0.179396 0.179396i
\(629\) 1177.24i 1.87160i
\(630\) 84.5356 72.9811i 0.134183 0.115843i
\(631\) 990.046 1.56901 0.784506 0.620122i \(-0.212917\pi\)
0.784506 + 0.620122i \(0.212917\pi\)
\(632\) 44.4862 + 44.4862i 0.0703895 + 0.0703895i
\(633\) 63.8570 63.8570i 0.100880 0.100880i
\(634\) 239.907i 0.378403i
\(635\) 72.7921 + 5.33959i 0.114633 + 0.00840881i
\(636\) −36.3851 −0.0572093
\(637\) −375.194 375.194i −0.589002 0.589002i
\(638\) −1.03379 + 1.03379i −0.00162036 + 0.00162036i
\(639\) 371.121i 0.580785i
\(640\) 4.13841 56.4170i 0.00646627 0.0881515i
\(641\) −1189.18 −1.85519 −0.927595 0.373587i \(-0.878128\pi\)
−0.927595 + 0.373587i \(0.878128\pi\)
\(642\) −116.233 116.233i −0.181049 0.181049i
\(643\) 44.5224 44.5224i 0.0692416 0.0692416i −0.671638 0.740880i \(-0.734409\pi\)
0.740880 + 0.671638i \(0.234409\pi\)
\(644\) 50.4969i 0.0784113i
\(645\) −13.3390 15.4508i −0.0206806 0.0239547i
\(646\) −255.795 −0.395967
\(647\) 360.032 + 360.032i 0.556464 + 0.556464i 0.928299 0.371835i \(-0.121271\pi\)
−0.371835 + 0.928299i \(0.621271\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 1262.37i 1.94510i
\(650\) 128.620 871.993i 0.197878 1.34153i
\(651\) 6.87434 0.0105597
\(652\) 209.901 + 209.901i 0.321934 + 0.321934i
\(653\) 712.901 712.901i 1.09173 1.09173i 0.0963890 0.995344i \(-0.469271\pi\)
0.995344 0.0963890i \(-0.0307293\pi\)
\(654\) 357.357i 0.546418i
\(655\) −697.940 + 602.544i −1.06556 + 0.919914i
\(656\) −228.526 −0.348363
\(657\) −43.9858 43.9858i −0.0669495 0.0669495i
\(658\) −303.553 + 303.553i −0.461327 + 0.461327i
\(659\) 1012.88i 1.53699i 0.639854 + 0.768497i \(0.278995\pi\)
−0.639854 + 0.768497i \(0.721005\pi\)
\(660\) −203.879 14.9554i −0.308908 0.0226596i
\(661\) −913.639 −1.38221 −0.691104 0.722756i \(-0.742875\pi\)
−0.691104 + 0.722756i \(0.742875\pi\)
\(662\) −28.1304 28.1304i −0.0424931 0.0424931i
\(663\) 891.001 891.001i 1.34389 1.34389i
\(664\) 18.3601i 0.0276507i
\(665\) 11.9365 162.724i 0.0179496 0.244698i
\(666\) 171.159 0.256995
\(667\) −0.297032 0.297032i −0.000445325 0.000445325i
\(668\) 347.322 347.322i 0.519943 0.519943i
\(669\) 686.964i 1.02685i
\(670\) 145.863 + 168.956i 0.217706 + 0.252174i
\(671\) −1075.27 −1.60250
\(672\) 36.4747 + 36.4747i 0.0542778 + 0.0542778i
\(673\) −493.188 + 493.188i −0.732820 + 0.732820i −0.971178 0.238357i \(-0.923391\pi\)
0.238357 + 0.971178i \(0.423391\pi\)
\(674\) 6.52903i 0.00968699i
\(675\) 104.277 77.4688i 0.154484 0.114769i
\(676\) 905.064 1.33885
\(677\) −415.571 415.571i −0.613842 0.613842i 0.330103 0.943945i \(-0.392917\pi\)
−0.943945 + 0.330103i \(0.892917\pi\)
\(678\) 230.999 230.999i 0.340706 0.340706i
\(679\) 899.769i 1.32514i
\(680\) 312.376 269.680i 0.459377 0.396589i
\(681\) −353.696 −0.519378
\(682\) −8.89770 8.89770i −0.0130465 0.0130465i
\(683\) 236.634 236.634i 0.346463 0.346463i −0.512327 0.858790i \(-0.671217\pi\)
0.858790 + 0.512327i \(0.171217\pi\)
\(684\) 37.1901i 0.0543715i
\(685\) −1206.05 88.4688i −1.76066 0.129152i
\(686\) 523.284 0.762805
\(687\) −444.333 444.333i −0.646772 0.646772i
\(688\) 6.66658 6.66658i 0.00968979 0.00968979i
\(689\) 261.858i 0.380054i
\(690\) 4.29703 58.5793i 0.00622758 0.0848976i
\(691\) −81.6305 −0.118134 −0.0590670 0.998254i \(-0.518813\pi\)
−0.0590670 + 0.998254i \(0.518813\pi\)
\(692\) −303.998 303.998i −0.439304 0.439304i
\(693\) 131.812 131.812i 0.190205 0.190205i
\(694\) 596.361i 0.859309i
\(695\) 273.954 + 317.327i 0.394179 + 0.456586i
\(696\) 0.429101 0.000616524
\(697\) −1178.86 1178.86i −1.69133 1.69133i
\(698\) 330.198 330.198i 0.473063 0.473063i
\(699\) 215.894i 0.308862i
\(700\) 156.980 + 211.303i 0.224258 + 0.301861i
\(701\) 1277.39 1.82224 0.911122 0.412137i \(-0.135218\pi\)
0.911122 + 0.412137i \(0.135218\pi\)
\(702\) 129.543 + 129.543i 0.184534 + 0.184534i
\(703\) 176.817 176.817i 0.251518 0.251518i
\(704\) 94.4208i 0.134120i
\(705\) −377.970 + 326.309i −0.536128 + 0.462849i
\(706\) −243.906 −0.345476
\(707\) −23.6644 23.6644i −0.0334715 0.0334715i
\(708\) 261.990 261.990i 0.370042 0.370042i
\(709\) 1056.16i 1.48965i −0.667260 0.744825i \(-0.732533\pi\)
0.667260 0.744825i \(-0.267467\pi\)
\(710\) −872.398 63.9939i −1.22873 0.0901322i
\(711\) −66.7293 −0.0938527
\(712\) −60.0503 60.0503i −0.0843404 0.0843404i
\(713\) 2.55652 2.55652i 0.00358558 0.00358558i
\(714\) 376.311i 0.527046i
\(715\) 107.631 1467.28i 0.150533 2.05215i
\(716\) 267.381 0.373437
\(717\) −363.252 363.252i −0.506628 0.506628i
\(718\) 14.1715 14.1715i 0.0197374 0.0197374i
\(719\) 532.010i 0.739931i 0.929046 + 0.369965i \(0.120630\pi\)
−0.929046 + 0.369965i \(0.879370\pi\)
\(720\) 39.2089 + 45.4165i 0.0544568 + 0.0630785i
\(721\) 959.043 1.33016
\(722\) 322.580 + 322.580i 0.446787 + 0.446787i
\(723\) 350.327 350.327i 0.484546 0.484546i
\(724\) 539.130i 0.744655i
\(725\) 2.16631 + 0.319534i 0.00298801 + 0.000440737i
\(726\) −44.8292 −0.0617482
\(727\) 310.493 + 310.493i 0.427087 + 0.427087i 0.887635 0.460548i \(-0.152347\pi\)
−0.460548 + 0.887635i \(0.652347\pi\)
\(728\) −262.502 + 262.502i −0.360579 + 0.360579i
\(729\) 27.0000i 0.0370370i
\(730\) 110.982 95.8131i 0.152031 0.131251i
\(731\) 68.7794 0.0940895
\(732\) 223.160 + 223.160i 0.304864 + 0.304864i
\(733\) −737.954 + 737.954i −1.00676 + 1.00676i −0.00678219 + 0.999977i \(0.502159\pi\)
−0.999977 + 0.00678219i \(0.997841\pi\)
\(734\) 127.901i 0.174252i
\(735\) 183.825 + 13.4843i 0.250102 + 0.0183460i
\(736\) 27.1293 0.0368605
\(737\) 263.445 + 263.445i 0.357456 + 0.357456i
\(738\) 171.394 171.394i 0.232242 0.232242i
\(739\) 258.876i 0.350306i 0.984541 + 0.175153i \(0.0560421\pi\)
−0.984541 + 0.175153i \(0.943958\pi\)
\(740\) −29.5136 + 402.345i −0.0398832 + 0.543709i
\(741\) 267.651 0.361202
\(742\) 55.2973 + 55.2973i 0.0745247 + 0.0745247i
\(743\) −570.017 + 570.017i −0.767183 + 0.767183i −0.977610 0.210427i \(-0.932515\pi\)
0.210427 + 0.977610i \(0.432515\pi\)
\(744\) 3.69322i 0.00496401i
\(745\) −382.418 442.963i −0.513313 0.594581i
\(746\) −321.395 −0.430824
\(747\) −13.7700 13.7700i −0.0184338 0.0184338i
\(748\) 487.072 487.072i 0.651166 0.651166i
\(749\) 353.297i 0.471692i
\(750\) 164.126 + 258.482i 0.218834 + 0.344642i
\(751\) −739.550 −0.984754 −0.492377 0.870382i \(-0.663872\pi\)
−0.492377 + 0.870382i \(0.663872\pi\)
\(752\) −163.083 163.083i −0.216866 0.216866i
\(753\) −222.534 + 222.534i −0.295530 + 0.295530i
\(754\) 3.08817i 0.00409571i
\(755\) 151.042 130.398i 0.200056 0.172712i
\(756\) −54.7120 −0.0723703
\(757\) −383.596 383.596i −0.506732 0.506732i 0.406789 0.913522i \(-0.366648\pi\)
−0.913522 + 0.406789i \(0.866648\pi\)
\(758\) 201.845 201.845i 0.266287 0.266287i
\(759\) 98.0398i 0.129170i
\(760\) 87.4230 + 6.41283i 0.115030 + 0.00843793i
\(761\) −619.693 −0.814314 −0.407157 0.913358i \(-0.633480\pi\)
−0.407157 + 0.913358i \(0.633480\pi\)
\(762\) −25.2837 25.2837i −0.0331807 0.0331807i
\(763\) −543.103 + 543.103i −0.711800 + 0.711800i
\(764\) 644.805i 0.843986i
\(765\) −32.0222 + 436.543i −0.0418590 + 0.570644i
\(766\) 355.781 0.464466
\(767\) 1885.49 + 1885.49i 2.45827 + 2.45827i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 587.333i 0.763762i 0.924211 + 0.381881i \(0.124724\pi\)
−0.924211 + 0.381881i \(0.875276\pi\)
\(770\) 287.122 + 332.580i 0.372886 + 0.431922i
\(771\) −480.720 −0.623502
\(772\) −179.675 179.675i −0.232740 0.232740i
\(773\) 541.479 541.479i 0.700490 0.700490i −0.264026 0.964516i \(-0.585050\pi\)
0.964516 + 0.264026i \(0.0850504\pi\)
\(774\) 9.99987i 0.0129197i
\(775\) −2.75019 + 18.6452i −0.00354864 + 0.0240583i
\(776\) −483.399 −0.622936
\(777\) −260.124 260.124i −0.334779 0.334779i
\(778\) −501.474 + 501.474i −0.644568 + 0.644568i
\(779\)