Properties

Label 210.3.l.a.127.2
Level 210
Weight 3
Character 210.127
Analytic conductor 5.722
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.12745506816.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.2
Root \(-0.323042 - 0.323042i\) of \(x^{8} + 23 x^{4} + 1\)
Character \(\chi\) \(=\) 210.127
Dual form 210.3.l.a.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-0.578661 + 4.96640i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-0.578661 + 4.96640i) q^{5} -2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-5.54506 + 4.38774i) q^{10} -12.4065 q^{11} +(-2.44949 - 2.44949i) q^{12} +(3.13309 - 3.13309i) q^{13} +3.74166i q^{14} +(-5.37386 - 6.79129i) q^{15} -4.00000 q^{16} +(-5.80341 - 5.80341i) q^{17} +(3.00000 - 3.00000i) q^{18} +26.5813i q^{19} +(-9.93280 - 1.15732i) q^{20} -4.58258 q^{21} +(-12.4065 - 12.4065i) q^{22} +(-10.4235 + 10.4235i) q^{23} -4.89898i q^{24} +(-24.3303 - 5.74773i) q^{25} +6.26617 q^{26} +(3.67423 + 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} +14.5808i q^{29} +(1.41742 - 12.1652i) q^{30} +42.6563 q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.1948 - 15.1948i) q^{33} -11.6068i q^{34} +(-10.3739 + 8.20871i) q^{35} +6.00000 q^{36} +(11.9306 + 11.9306i) q^{37} +(-26.5813 + 26.5813i) q^{38} +7.67446i q^{39} +(-8.77548 - 11.0901i) q^{40} +37.5226 q^{41} +(-4.58258 - 4.58258i) q^{42} +(24.0083 - 24.0083i) q^{43} -24.8131i q^{44} +(14.8992 + 1.73598i) q^{45} -20.8470 q^{46} +(8.83609 + 8.83609i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(-18.5826 - 30.0780i) q^{50} +14.2154 q^{51} +(6.26617 + 6.26617i) q^{52} +(-1.97883 + 1.97883i) q^{53} +7.34847i q^{54} +(7.17918 - 61.6158i) q^{55} -7.48331 q^{56} +(-32.5553 - 32.5553i) q^{57} +(-14.5808 + 14.5808i) q^{58} +88.2651i q^{59} +(13.5826 - 10.7477i) q^{60} +102.471 q^{61} +(42.6563 + 42.6563i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(13.7472 + 17.3732i) q^{65} +30.3897 q^{66} +(-22.8107 - 22.8107i) q^{67} +(11.6068 - 11.6068i) q^{68} -25.5322i q^{69} +(-18.5826 - 2.16515i) q^{70} -10.7950 q^{71} +(6.00000 + 6.00000i) q^{72} +(80.4481 - 80.4481i) q^{73} +23.8612i q^{74} +(36.8379 - 22.7589i) q^{75} -53.1625 q^{76} +(-23.2105 - 23.2105i) q^{77} +(-7.67446 + 7.67446i) q^{78} +138.851i q^{79} +(2.31464 - 19.8656i) q^{80} -9.00000 q^{81} +(37.5226 + 37.5226i) q^{82} +(-96.0834 + 96.0834i) q^{83} -9.16515i q^{84} +(32.1803 - 25.4638i) q^{85} +48.0166 q^{86} +(-17.8578 - 17.8578i) q^{87} +(24.8131 - 24.8131i) q^{88} -3.29855i q^{89} +(13.1632 + 16.6352i) q^{90} +11.7229 q^{91} +(-20.8470 - 20.8470i) q^{92} +(-52.2431 + 52.2431i) q^{93} +17.6722i q^{94} +(-132.013 - 15.3815i) q^{95} +9.79796 q^{96} +(-88.5219 - 88.5219i) q^{97} +(-7.00000 + 7.00000i) q^{98} +37.2196i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 16q^{8} + O(q^{10}) \) \( 8q + 8q^{2} - 16q^{8} - 8q^{11} + 8q^{13} + 12q^{15} - 32q^{16} - 32q^{17} + 24q^{18} - 8q^{22} - 40q^{23} - 48q^{25} + 16q^{26} + 48q^{30} + 144q^{31} - 32q^{32} + 120q^{33} - 28q^{35} + 48q^{36} + 160q^{37} - 320q^{41} - 32q^{43} - 80q^{46} - 144q^{47} - 112q^{50} + 72q^{51} + 16q^{52} - 200q^{53} + 184q^{55} - 24q^{57} - 64q^{58} + 72q^{60} + 288q^{61} + 144q^{62} + 24q^{65} + 240q^{66} + 80q^{67} + 64q^{68} - 112q^{70} - 280q^{71} + 48q^{72} + 312q^{73} - 56q^{77} + 48q^{78} - 72q^{81} - 320q^{82} - 320q^{83} + 80q^{85} - 64q^{86} - 48q^{87} + 16q^{88} - 80q^{92} + 48q^{93} - 472q^{95} - 24q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(5\) −0.578661 + 4.96640i −0.115732 + 0.993280i
\(6\) −2.44949 −0.408248
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −5.54506 + 4.38774i −0.554506 + 0.438774i
\(11\) −12.4065 −1.12787 −0.563933 0.825820i \(-0.690712\pi\)
−0.563933 + 0.825820i \(0.690712\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) 3.13309 3.13309i 0.241007 0.241007i −0.576260 0.817267i \(-0.695488\pi\)
0.817267 + 0.576260i \(0.195488\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −5.37386 6.79129i −0.358258 0.452753i
\(16\) −4.00000 −0.250000
\(17\) −5.80341 5.80341i −0.341377 0.341377i 0.515508 0.856885i \(-0.327603\pi\)
−0.856885 + 0.515508i \(0.827603\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 26.5813i 1.39901i 0.714626 + 0.699507i \(0.246597\pi\)
−0.714626 + 0.699507i \(0.753403\pi\)
\(20\) −9.93280 1.15732i −0.496640 0.0578661i
\(21\) −4.58258 −0.218218
\(22\) −12.4065 12.4065i −0.563933 0.563933i
\(23\) −10.4235 + 10.4235i −0.453195 + 0.453195i −0.896414 0.443218i \(-0.853837\pi\)
0.443218 + 0.896414i \(0.353837\pi\)
\(24\) 4.89898i 0.204124i
\(25\) −24.3303 5.74773i −0.973212 0.229909i
\(26\) 6.26617 0.241007
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −3.74166 + 3.74166i −0.133631 + 0.133631i
\(29\) 14.5808i 0.502787i 0.967885 + 0.251393i \(0.0808888\pi\)
−0.967885 + 0.251393i \(0.919111\pi\)
\(30\) 1.41742 12.1652i 0.0472475 0.405505i
\(31\) 42.6563 1.37601 0.688005 0.725706i \(-0.258487\pi\)
0.688005 + 0.725706i \(0.258487\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 15.1948 15.1948i 0.460450 0.460450i
\(34\) 11.6068i 0.341377i
\(35\) −10.3739 + 8.20871i −0.296396 + 0.234535i
\(36\) 6.00000 0.166667
\(37\) 11.9306 + 11.9306i 0.322448 + 0.322448i 0.849706 0.527257i \(-0.176780\pi\)
−0.527257 + 0.849706i \(0.676780\pi\)
\(38\) −26.5813 + 26.5813i −0.699507 + 0.699507i
\(39\) 7.67446i 0.196781i
\(40\) −8.77548 11.0901i −0.219387 0.277253i
\(41\) 37.5226 0.915185 0.457593 0.889162i \(-0.348712\pi\)
0.457593 + 0.889162i \(0.348712\pi\)
\(42\) −4.58258 4.58258i −0.109109 0.109109i
\(43\) 24.0083 24.0083i 0.558332 0.558332i −0.370500 0.928832i \(-0.620814\pi\)
0.928832 + 0.370500i \(0.120814\pi\)
\(44\) 24.8131i 0.563933i
\(45\) 14.8992 + 1.73598i 0.331093 + 0.0385774i
\(46\) −20.8470 −0.453195
\(47\) 8.83609 + 8.83609i 0.188002 + 0.188002i 0.794832 0.606830i \(-0.207559\pi\)
−0.606830 + 0.794832i \(0.707559\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −18.5826 30.0780i −0.371652 0.601561i
\(51\) 14.2154 0.278733
\(52\) 6.26617 + 6.26617i 0.120503 + 0.120503i
\(53\) −1.97883 + 1.97883i −0.0373364 + 0.0373364i −0.725529 0.688192i \(-0.758405\pi\)
0.688192 + 0.725529i \(0.258405\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 7.17918 61.6158i 0.130530 1.12029i
\(56\) −7.48331 −0.133631
\(57\) −32.5553 32.5553i −0.571145 0.571145i
\(58\) −14.5808 + 14.5808i −0.251393 + 0.251393i
\(59\) 88.2651i 1.49602i 0.663688 + 0.748010i \(0.268990\pi\)
−0.663688 + 0.748010i \(0.731010\pi\)
\(60\) 13.5826 10.7477i 0.226376 0.179129i
\(61\) 102.471 1.67985 0.839924 0.542704i \(-0.182600\pi\)
0.839924 + 0.542704i \(0.182600\pi\)
\(62\) 42.6563 + 42.6563i 0.688005 + 0.688005i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) 13.7472 + 17.3732i 0.211495 + 0.267279i
\(66\) 30.3897 0.460450
\(67\) −22.8107 22.8107i −0.340458 0.340458i 0.516082 0.856539i \(-0.327390\pi\)
−0.856539 + 0.516082i \(0.827390\pi\)
\(68\) 11.6068 11.6068i 0.170688 0.170688i
\(69\) 25.5322i 0.370032i
\(70\) −18.5826 2.16515i −0.265465 0.0309307i
\(71\) −10.7950 −0.152042 −0.0760208 0.997106i \(-0.524222\pi\)
−0.0760208 + 0.997106i \(0.524222\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 80.4481 80.4481i 1.10203 1.10203i 0.107863 0.994166i \(-0.465599\pi\)
0.994166 0.107863i \(-0.0344007\pi\)
\(74\) 23.8612i 0.322448i
\(75\) 36.8379 22.7589i 0.491172 0.303452i
\(76\) −53.1625 −0.699507
\(77\) −23.2105 23.2105i −0.301435 0.301435i
\(78\) −7.67446 + 7.67446i −0.0983905 + 0.0983905i
\(79\) 138.851i 1.75761i 0.477180 + 0.878806i \(0.341659\pi\)
−0.477180 + 0.878806i \(0.658341\pi\)
\(80\) 2.31464 19.8656i 0.0289331 0.248320i
\(81\) −9.00000 −0.111111
\(82\) 37.5226 + 37.5226i 0.457593 + 0.457593i
\(83\) −96.0834 + 96.0834i −1.15763 + 1.15763i −0.172648 + 0.984984i \(0.555232\pi\)
−0.984984 + 0.172648i \(0.944768\pi\)
\(84\) 9.16515i 0.109109i
\(85\) 32.1803 25.4638i 0.378591 0.299575i
\(86\) 48.0166 0.558332
\(87\) −17.8578 17.8578i −0.205262 0.205262i
\(88\) 24.8131 24.8131i 0.281967 0.281967i
\(89\) 3.29855i 0.0370623i −0.999828 0.0185312i \(-0.994101\pi\)
0.999828 0.0185312i \(-0.00589899\pi\)
\(90\) 13.1632 + 16.6352i 0.146258 + 0.184835i
\(91\) 11.7229 0.128823
\(92\) −20.8470 20.8470i −0.226598 0.226598i
\(93\) −52.2431 + 52.2431i −0.561754 + 0.561754i
\(94\) 17.6722i 0.188002i
\(95\) −132.013 15.3815i −1.38961 0.161911i
\(96\) 9.79796 0.102062
\(97\) −88.5219 88.5219i −0.912597 0.912597i 0.0838786 0.996476i \(-0.473269\pi\)
−0.996476 + 0.0838786i \(0.973269\pi\)
\(98\) −7.00000 + 7.00000i −0.0714286 + 0.0714286i
\(99\) 37.2196i 0.375955i
\(100\) 11.4955 48.6606i 0.114955 0.486606i
\(101\) 142.067 1.40661 0.703304 0.710889i \(-0.251707\pi\)
0.703304 + 0.710889i \(0.251707\pi\)
\(102\) 14.2154 + 14.2154i 0.139367 + 0.139367i
\(103\) 60.4386 60.4386i 0.586782 0.586782i −0.349976 0.936759i \(-0.613810\pi\)
0.936759 + 0.349976i \(0.113810\pi\)
\(104\) 12.5323i 0.120503i
\(105\) 2.65176 22.7589i 0.0252548 0.216752i
\(106\) −3.95766 −0.0373364
\(107\) 78.7617 + 78.7617i 0.736091 + 0.736091i 0.971819 0.235728i \(-0.0757474\pi\)
−0.235728 + 0.971819i \(0.575747\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 102.684i 0.942053i −0.882119 0.471026i \(-0.843884\pi\)
0.882119 0.471026i \(-0.156116\pi\)
\(110\) 68.7950 54.4366i 0.625409 0.494879i
\(111\) −29.2239 −0.263278
\(112\) −7.48331 7.48331i −0.0668153 0.0668153i
\(113\) −34.2131 + 34.2131i −0.302771 + 0.302771i −0.842097 0.539326i \(-0.818679\pi\)
0.539326 + 0.842097i \(0.318679\pi\)
\(114\) 65.1105i 0.571145i
\(115\) −45.7356 57.7989i −0.397701 0.502599i
\(116\) −29.1616 −0.251393
\(117\) −9.39926 9.39926i −0.0803355 0.0803355i
\(118\) −88.2651 + 88.2651i −0.748010 + 0.748010i
\(119\) 21.7144i 0.182474i
\(120\) 24.3303 + 2.83485i 0.202753 + 0.0236237i
\(121\) 32.9220 0.272083
\(122\) 102.471 + 102.471i 0.839924 + 0.839924i
\(123\) −45.9556 + 45.9556i −0.373623 + 0.373623i
\(124\) 85.3126i 0.688005i
\(125\) 42.6245 117.508i 0.340996 0.940065i
\(126\) 11.2250 0.0890871
\(127\) −149.547 149.547i −1.17753 1.17753i −0.980371 0.197161i \(-0.936828\pi\)
−0.197161 0.980371i \(-0.563172\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 58.8080i 0.455876i
\(130\) −3.62599 + 31.1203i −0.0278922 + 0.239387i
\(131\) −93.4871 −0.713642 −0.356821 0.934173i \(-0.616139\pi\)
−0.356821 + 0.934173i \(0.616139\pi\)
\(132\) 30.3897 + 30.3897i 0.230225 + 0.230225i
\(133\) −49.7290 + 49.7290i −0.373902 + 0.373902i
\(134\) 45.6213i 0.340458i
\(135\) −20.3739 + 16.1216i −0.150918 + 0.119419i
\(136\) 23.2136 0.170688
\(137\) −66.0053 66.0053i −0.481790 0.481790i 0.423913 0.905703i \(-0.360656\pi\)
−0.905703 + 0.423913i \(0.860656\pi\)
\(138\) 25.5322 25.5322i 0.185016 0.185016i
\(139\) 111.764i 0.804059i 0.915627 + 0.402029i \(0.131695\pi\)
−0.915627 + 0.402029i \(0.868305\pi\)
\(140\) −16.4174 20.7477i −0.117267 0.148198i
\(141\) −21.6439 −0.153503
\(142\) −10.7950 10.7950i −0.0760208 0.0760208i
\(143\) −38.8707 + 38.8707i −0.271823 + 0.271823i
\(144\) 12.0000i 0.0833333i
\(145\) −72.4142 8.43735i −0.499408 0.0581886i
\(146\) 160.896 1.10203
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) −23.8612 + 23.8612i −0.161224 + 0.161224i
\(149\) 214.999i 1.44295i −0.692443 0.721473i \(-0.743465\pi\)
0.692443 0.721473i \(-0.256535\pi\)
\(150\) 59.5968 + 14.0790i 0.397312 + 0.0938600i
\(151\) −62.7527 −0.415581 −0.207790 0.978173i \(-0.566627\pi\)
−0.207790 + 0.978173i \(0.566627\pi\)
\(152\) −53.1625 53.1625i −0.349754 0.349754i
\(153\) −17.4102 + 17.4102i −0.113792 + 0.113792i
\(154\) 46.4210i 0.301435i
\(155\) −24.6835 + 211.848i −0.159249 + 1.36676i
\(156\) −15.3489 −0.0983905
\(157\) 181.318 + 181.318i 1.15489 + 1.15489i 0.985560 + 0.169329i \(0.0541601\pi\)
0.169329 + 0.985560i \(0.445840\pi\)
\(158\) −138.851 + 138.851i −0.878806 + 0.878806i
\(159\) 4.84712i 0.0304850i
\(160\) 22.1803 17.5510i 0.138627 0.109694i
\(161\) −39.0011 −0.242243
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −52.0026 + 52.0026i −0.319034 + 0.319034i −0.848396 0.529362i \(-0.822431\pi\)
0.529362 + 0.848396i \(0.322431\pi\)
\(164\) 75.0452i 0.457593i
\(165\) 66.6710 + 84.2563i 0.404067 + 0.510644i
\(166\) −192.167 −1.15763
\(167\) −153.475 153.475i −0.919013 0.919013i 0.0779443 0.996958i \(-0.475164\pi\)
−0.996958 + 0.0779443i \(0.975164\pi\)
\(168\) 9.16515 9.16515i 0.0545545 0.0545545i
\(169\) 149.368i 0.883832i
\(170\) 57.6441 + 6.71641i 0.339083 + 0.0395083i
\(171\) 79.7438 0.466338
\(172\) 48.0166 + 48.0166i 0.279166 + 0.279166i
\(173\) −86.7956 + 86.7956i −0.501708 + 0.501708i −0.911969 0.410260i \(-0.865438\pi\)
0.410260 + 0.911969i \(0.365438\pi\)
\(174\) 35.7156i 0.205262i
\(175\) −34.7648 56.2708i −0.198656 0.321548i
\(176\) 49.6261 0.281967
\(177\) −108.102 108.102i −0.610747 0.610747i
\(178\) 3.29855 3.29855i 0.0185312 0.0185312i
\(179\) 203.414i 1.13639i −0.822893 0.568196i \(-0.807641\pi\)
0.822893 0.568196i \(-0.192359\pi\)
\(180\) −3.47197 + 29.7984i −0.0192887 + 0.165547i
\(181\) −251.290 −1.38834 −0.694172 0.719810i \(-0.744229\pi\)
−0.694172 + 0.719810i \(0.744229\pi\)
\(182\) 11.7229 + 11.7229i 0.0644117 + 0.0644117i
\(183\) −125.500 + 125.500i −0.685795 + 0.685795i
\(184\) 41.6940i 0.226598i
\(185\) −66.1559 + 52.3483i −0.357599 + 0.282964i
\(186\) −104.486 −0.561754
\(187\) 72.0001 + 72.0001i 0.385027 + 0.385027i
\(188\) −17.6722 + 17.6722i −0.0940010 + 0.0940010i
\(189\) 13.7477i 0.0727393i
\(190\) −116.632 147.395i −0.613851 0.775762i
\(191\) 367.604 1.92463 0.962315 0.271938i \(-0.0876646\pi\)
0.962315 + 0.271938i \(0.0876646\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 95.7120 95.7120i 0.495917 0.495917i −0.414247 0.910164i \(-0.635955\pi\)
0.910164 + 0.414247i \(0.135955\pi\)
\(194\) 177.044i 0.912597i
\(195\) −38.1145 4.44091i −0.195459 0.0227739i
\(196\) −14.0000 −0.0714286
\(197\) −194.449 194.449i −0.987048 0.987048i 0.0128689 0.999917i \(-0.495904\pi\)
−0.999917 + 0.0128689i \(0.995904\pi\)
\(198\) −37.2196 + 37.2196i −0.187978 + 0.187978i
\(199\) 91.9043i 0.461831i 0.972974 + 0.230915i \(0.0741720\pi\)
−0.972974 + 0.230915i \(0.925828\pi\)
\(200\) 60.1561 37.1652i 0.300780 0.185826i
\(201\) 55.8745 0.277982
\(202\) 142.067 + 142.067i 0.703304 + 0.703304i
\(203\) −27.2782 + 27.2782i −0.134375 + 0.134375i
\(204\) 28.4308i 0.139367i
\(205\) −21.7129 + 186.352i −0.105916 + 0.909036i
\(206\) 120.877 0.586782
\(207\) 31.2705 + 31.2705i 0.151065 + 0.151065i
\(208\) −12.5323 + 12.5323i −0.0602517 + 0.0602517i
\(209\) 329.781i 1.57790i
\(210\) 25.4107 20.1072i 0.121003 0.0957484i
\(211\) 296.539 1.40540 0.702700 0.711486i \(-0.251978\pi\)
0.702700 + 0.711486i \(0.251978\pi\)
\(212\) −3.95766 3.95766i −0.0186682 0.0186682i
\(213\) 13.2211 13.2211i 0.0620707 0.0620707i
\(214\) 157.523i 0.736091i
\(215\) 105.342 + 133.127i 0.489963 + 0.619197i
\(216\) −14.6969 −0.0680414
\(217\) 79.8026 + 79.8026i 0.367754 + 0.367754i
\(218\) 102.684 102.684i 0.471026 0.471026i
\(219\) 197.057i 0.899803i
\(220\) 123.232 + 14.3584i 0.560144 + 0.0652652i
\(221\) −36.3651 −0.164548
\(222\) −29.2239 29.2239i −0.131639 0.131639i
\(223\) 99.7016 99.7016i 0.447092 0.447092i −0.447295 0.894387i \(-0.647612\pi\)
0.894387 + 0.447295i \(0.147612\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −17.2432 + 72.9909i −0.0766364 + 0.324404i
\(226\) −68.4262 −0.302771
\(227\) −45.7570 45.7570i −0.201573 0.201573i 0.599101 0.800674i \(-0.295525\pi\)
−0.800674 + 0.599101i \(0.795525\pi\)
\(228\) 65.1105 65.1105i 0.285573 0.285573i
\(229\) 248.102i 1.08342i 0.840567 + 0.541708i \(0.182222\pi\)
−0.840567 + 0.541708i \(0.817778\pi\)
\(230\) 12.0633 103.535i 0.0524493 0.450150i
\(231\) 56.8539 0.246121
\(232\) −29.1616 29.1616i −0.125697 0.125697i
\(233\) 306.481 306.481i 1.31537 1.31537i 0.397968 0.917399i \(-0.369716\pi\)
0.917399 0.397968i \(-0.130284\pi\)
\(234\) 18.7985i 0.0803355i
\(235\) −48.9967 + 38.7705i −0.208497 + 0.164981i
\(236\) −176.530 −0.748010
\(237\) −170.057 170.057i −0.717542 0.717542i
\(238\) 21.7144 21.7144i 0.0912368 0.0912368i
\(239\) 136.398i 0.570702i 0.958423 + 0.285351i \(0.0921102\pi\)
−0.958423 + 0.285351i \(0.907890\pi\)
\(240\) 21.4955 + 27.1652i 0.0895644 + 0.113188i
\(241\) 332.727 1.38061 0.690305 0.723519i \(-0.257477\pi\)
0.690305 + 0.723519i \(0.257477\pi\)
\(242\) 32.9220 + 32.9220i 0.136041 + 0.136041i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 204.941i 0.839924i
\(245\) −34.7648 4.05063i −0.141897 0.0165332i
\(246\) −91.9112 −0.373623
\(247\) 83.2814 + 83.2814i 0.337172 + 0.337172i
\(248\) −85.3126 + 85.3126i −0.344002 + 0.344002i
\(249\) 235.355i 0.945202i
\(250\) 160.133 74.8836i 0.640530 0.299534i
\(251\) 244.521 0.974186 0.487093 0.873350i \(-0.338057\pi\)
0.487093 + 0.873350i \(0.338057\pi\)
\(252\) 11.2250 + 11.2250i 0.0445435 + 0.0445435i
\(253\) 129.319 129.319i 0.511144 0.511144i
\(254\) 299.093i 1.17753i
\(255\) −8.22589 + 70.5993i −0.0322584 + 0.276860i
\(256\) 16.0000 0.0625000
\(257\) 102.592 + 102.592i 0.399191 + 0.399191i 0.877948 0.478756i \(-0.158912\pi\)
−0.478756 + 0.877948i \(0.658912\pi\)
\(258\) −58.8080 + 58.8080i −0.227938 + 0.227938i
\(259\) 44.6402i 0.172356i
\(260\) −34.7463 + 27.4943i −0.133640 + 0.105747i
\(261\) 43.7424 0.167596
\(262\) −93.4871 93.4871i −0.356821 0.356821i
\(263\) 253.841 253.841i 0.965174 0.965174i −0.0342400 0.999414i \(-0.510901\pi\)
0.999414 + 0.0342400i \(0.0109011\pi\)
\(264\) 60.7793i 0.230225i
\(265\) −8.68259 10.9727i −0.0327645 0.0414065i
\(266\) −99.4580 −0.373902
\(267\) 4.03988 + 4.03988i 0.0151306 + 0.0151306i
\(268\) 45.6213 45.6213i 0.170229 0.170229i
\(269\) 207.747i 0.772295i −0.922437 0.386147i \(-0.873806\pi\)
0.922437 0.386147i \(-0.126194\pi\)
\(270\) −36.4955 4.25227i −0.135168 0.0157492i
\(271\) −476.286 −1.75751 −0.878756 0.477270i \(-0.841626\pi\)
−0.878756 + 0.477270i \(0.841626\pi\)
\(272\) 23.2136 + 23.2136i 0.0853442 + 0.0853442i
\(273\) −14.3576 + 14.3576i −0.0525920 + 0.0525920i
\(274\) 132.011i 0.481790i
\(275\) 301.855 + 71.3094i 1.09765 + 0.259307i
\(276\) 51.0645 0.185016
\(277\) −9.67870 9.67870i −0.0349412 0.0349412i 0.689420 0.724362i \(-0.257865\pi\)
−0.724362 + 0.689420i \(0.757865\pi\)
\(278\) −111.764 + 111.764i −0.402029 + 0.402029i
\(279\) 127.969i 0.458670i
\(280\) 4.33030 37.1652i 0.0154654 0.132733i
\(281\) 101.463 0.361079 0.180540 0.983568i \(-0.442216\pi\)
0.180540 + 0.983568i \(0.442216\pi\)
\(282\) −21.6439 21.6439i −0.0767515 0.0767515i
\(283\) 276.026 276.026i 0.975358 0.975358i −0.0243452 0.999704i \(-0.507750\pi\)
0.999704 + 0.0243452i \(0.00775008\pi\)
\(284\) 21.5899i 0.0760208i
\(285\) 180.521 142.844i 0.633407 0.501207i
\(286\) −77.7415 −0.271823
\(287\) 70.1983 + 70.1983i 0.244594 + 0.244594i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 221.641i 0.766924i
\(290\) −63.9768 80.8515i −0.220610 0.278798i
\(291\) 216.834 0.745133
\(292\) 160.896 + 160.896i 0.551014 + 0.551014i
\(293\) 104.873 104.873i 0.357928 0.357928i −0.505121 0.863049i \(-0.668552\pi\)
0.863049 + 0.505121i \(0.168552\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) −438.360 51.0756i −1.48597 0.173138i
\(296\) −47.7224 −0.161224
\(297\) −45.5845 45.5845i −0.153483 0.153483i
\(298\) 214.999 214.999i 0.721473 0.721473i
\(299\) 65.3154i 0.218446i
\(300\) 45.5178 + 73.6758i 0.151726 + 0.245586i
\(301\) 89.8308 0.298441
\(302\) −62.7527 62.7527i −0.207790 0.207790i
\(303\) −173.996 + 173.996i −0.574245 + 0.574245i
\(304\) 106.325i 0.349754i
\(305\) −59.2958 + 508.911i −0.194412 + 1.66856i
\(306\) −34.8204 −0.113792
\(307\) 158.138 + 158.138i 0.515108 + 0.515108i 0.916087 0.400979i \(-0.131330\pi\)
−0.400979 + 0.916087i \(0.631330\pi\)
\(308\) 46.4210 46.4210i 0.150717 0.150717i
\(309\) 148.044i 0.479106i
\(310\) −236.532 + 187.165i −0.763006 + 0.603757i
\(311\) −519.537 −1.67054 −0.835269 0.549842i \(-0.814688\pi\)
−0.835269 + 0.549842i \(0.814688\pi\)
\(312\) −15.3489 15.3489i −0.0491953 0.0491953i
\(313\) 73.0852 73.0852i 0.233499 0.233499i −0.580653 0.814152i \(-0.697202\pi\)
0.814152 + 0.580653i \(0.197202\pi\)
\(314\) 362.635i 1.15489i
\(315\) 24.6261 + 31.1216i 0.0781782 + 0.0987987i
\(316\) −277.703 −0.878806
\(317\) 279.849 + 279.849i 0.882805 + 0.882805i 0.993819 0.111014i \(-0.0354098\pi\)
−0.111014 + 0.993819i \(0.535410\pi\)
\(318\) 4.84712 4.84712i 0.0152425 0.0152425i
\(319\) 180.897i 0.567076i
\(320\) 39.7312 + 4.62929i 0.124160 + 0.0144665i
\(321\) −192.926 −0.601016
\(322\) −39.0011 39.0011i −0.121122 0.121122i
\(323\) 154.262 154.262i 0.477591 0.477591i
\(324\) 18.0000i 0.0555556i
\(325\) −94.2371 + 58.2208i −0.289960 + 0.179141i
\(326\) −104.005 −0.319034
\(327\) 125.761 + 125.761i 0.384592 + 0.384592i
\(328\) −75.0452 + 75.0452i −0.228796 + 0.228796i
\(329\) 33.0616i 0.100491i
\(330\) −17.5853 + 150.927i −0.0532888 + 0.457356i
\(331\) −601.834 −1.81823 −0.909115 0.416546i \(-0.863241\pi\)
−0.909115 + 0.416546i \(0.863241\pi\)
\(332\) −192.167 192.167i −0.578816 0.578816i
\(333\) 35.7918 35.7918i 0.107483 0.107483i
\(334\) 306.950i 0.919013i
\(335\) 126.487 100.087i 0.377572 0.298768i
\(336\) 18.3303 0.0545545
\(337\) 17.0969 + 17.0969i 0.0507325 + 0.0507325i 0.732018 0.681285i \(-0.238579\pi\)
−0.681285 + 0.732018i \(0.738579\pi\)
\(338\) −149.368 + 149.368i −0.441916 + 0.441916i
\(339\) 83.8046i 0.247211i
\(340\) 50.9277 + 64.3605i 0.149787 + 0.189296i
\(341\) −529.217 −1.55195
\(342\) 79.7438 + 79.7438i 0.233169 + 0.233169i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 96.0331i 0.279166i
\(345\) 126.803 + 14.7745i 0.367546 + 0.0428247i
\(346\) −173.591 −0.501708
\(347\) 233.692 + 233.692i 0.673465 + 0.673465i 0.958513 0.285048i \(-0.0920095\pi\)
−0.285048 + 0.958513i \(0.592010\pi\)
\(348\) 35.7156 35.7156i 0.102631 0.102631i
\(349\) 399.184i 1.14379i 0.820326 + 0.571896i \(0.193792\pi\)
−0.820326 + 0.571896i \(0.806208\pi\)
\(350\) 21.5060 91.0357i 0.0614458 0.260102i
\(351\) 23.0234 0.0655937
\(352\) 49.6261 + 49.6261i 0.140983 + 0.140983i
\(353\) −137.005 + 137.005i −0.388117 + 0.388117i −0.874015 0.485898i \(-0.838493\pi\)
0.485898 + 0.874015i \(0.338493\pi\)
\(354\) 216.205i 0.610747i
\(355\) 6.24662 53.6121i 0.0175961 0.151020i
\(356\) 6.59709 0.0185312
\(357\) 26.5945 + 26.5945i 0.0744945 + 0.0744945i
\(358\) 203.414 203.414i 0.568196 0.568196i
\(359\) 473.333i 1.31848i 0.751934 + 0.659239i \(0.229121\pi\)
−0.751934 + 0.659239i \(0.770879\pi\)
\(360\) −33.2704 + 26.3264i −0.0924177 + 0.0731290i
\(361\) −345.564 −0.957241
\(362\) −251.290 251.290i −0.694172 0.694172i
\(363\) −40.3210 + 40.3210i −0.111077 + 0.111077i
\(364\) 23.4459i 0.0644117i
\(365\) 352.985 + 446.090i 0.967083 + 1.22216i
\(366\) −251.001 −0.685795
\(367\) −256.657 256.657i −0.699338 0.699338i 0.264930 0.964268i \(-0.414651\pi\)
−0.964268 + 0.264930i \(0.914651\pi\)
\(368\) 41.6940 41.6940i 0.113299 0.113299i
\(369\) 112.568i 0.305062i
\(370\) −118.504 13.8075i −0.320282 0.0373177i
\(371\) −7.40410 −0.0199571
\(372\) −104.486 104.486i −0.280877 0.280877i
\(373\) −278.764 + 278.764i −0.747355 + 0.747355i −0.973982 0.226627i \(-0.927230\pi\)
0.226627 + 0.973982i \(0.427230\pi\)
\(374\) 144.000i 0.385027i
\(375\) 91.7133 + 196.122i 0.244569 + 0.522991i
\(376\) −35.3444 −0.0940010
\(377\) 45.6830 + 45.6830i 0.121175 + 0.121175i
\(378\) −13.7477 + 13.7477i −0.0363696 + 0.0363696i
\(379\) 168.579i 0.444800i 0.974955 + 0.222400i \(0.0713891\pi\)
−0.974955 + 0.222400i \(0.928611\pi\)
\(380\) 30.7631 264.027i 0.0809555 0.694807i
\(381\) 366.313 0.961451
\(382\) 367.604 + 367.604i 0.962315 + 0.962315i
\(383\) −166.588 + 166.588i −0.434956 + 0.434956i −0.890310 0.455354i \(-0.849513\pi\)
0.455354 + 0.890310i \(0.349513\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 128.704 101.842i 0.334295 0.264524i
\(386\) 191.424 0.495917
\(387\) −72.0249 72.0249i −0.186111 0.186111i
\(388\) 177.044 177.044i 0.456299 0.456299i
\(389\) 73.9237i 0.190035i 0.995476 + 0.0950176i \(0.0302907\pi\)
−0.995476 + 0.0950176i \(0.969709\pi\)
\(390\) −33.6736 42.5554i −0.0863424 0.109116i
\(391\) 120.984 0.309421
\(392\) −14.0000 14.0000i −0.0357143 0.0357143i
\(393\) 114.498 114.498i 0.291343 0.291343i
\(394\) 388.897i 0.987048i
\(395\) −689.591 80.3478i −1.74580 0.203412i
\(396\) −74.4392 −0.187978
\(397\) 73.4533 + 73.4533i 0.185021 + 0.185021i 0.793540 0.608519i \(-0.208236\pi\)
−0.608519 + 0.793540i \(0.708236\pi\)
\(398\) −91.9043 + 91.9043i −0.230915 + 0.230915i
\(399\) 121.811i 0.305290i
\(400\) 97.3212 + 22.9909i 0.243303 + 0.0574773i
\(401\) −534.615 −1.33321 −0.666603 0.745413i \(-0.732252\pi\)
−0.666603 + 0.745413i \(0.732252\pi\)
\(402\) 55.8745 + 55.8745i 0.138991 + 0.138991i
\(403\) 133.646 133.646i 0.331627 0.331627i
\(404\) 284.135i 0.703304i
\(405\) 5.20795 44.6976i 0.0128591 0.110364i
\(406\) −54.5564 −0.134375
\(407\) −148.017 148.017i −0.363679 0.363679i
\(408\) −28.4308 + 28.4308i −0.0696833 + 0.0696833i
\(409\) 14.4205i 0.0352578i 0.999845 + 0.0176289i \(0.00561175\pi\)
−0.999845 + 0.0176289i \(0.994388\pi\)
\(410\) −208.065 + 164.639i −0.507476 + 0.401560i
\(411\) 161.679 0.393380
\(412\) 120.877 + 120.877i 0.293391 + 0.293391i
\(413\) −165.129 + 165.129i −0.399828 + 0.399828i
\(414\) 62.5410i 0.151065i
\(415\) −421.589 532.789i −1.01588 1.28383i
\(416\) −25.0647 −0.0602517
\(417\) −136.883 136.883i −0.328256 0.328256i
\(418\) 329.781 329.781i 0.788951 0.788951i
\(419\) 337.860i 0.806349i −0.915123 0.403174i \(-0.867907\pi\)
0.915123 0.403174i \(-0.132093\pi\)
\(420\) 45.5178 + 5.30352i 0.108376 + 0.0126274i
\(421\) 372.730 0.885345 0.442672 0.896683i \(-0.354031\pi\)
0.442672 + 0.896683i \(0.354031\pi\)
\(422\) 296.539 + 296.539i 0.702700 + 0.702700i
\(423\) 26.5083 26.5083i 0.0626673 0.0626673i
\(424\) 7.91531i 0.0186682i
\(425\) 107.842 + 174.555i 0.253746 + 0.410718i
\(426\) 26.4421 0.0620707
\(427\) 191.705 + 191.705i 0.448958 + 0.448958i
\(428\) −157.523 + 157.523i −0.368046 + 0.368046i
\(429\) 95.2134i 0.221943i
\(430\) −27.7853 + 238.470i −0.0646170 + 0.554580i
\(431\) −591.932 −1.37339 −0.686696 0.726944i \(-0.740940\pi\)
−0.686696 + 0.726944i \(0.740940\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −239.916 + 239.916i −0.554079 + 0.554079i −0.927615 0.373537i \(-0.878145\pi\)
0.373537 + 0.927615i \(0.378145\pi\)
\(434\) 159.605i 0.367754i
\(435\) 99.0225 78.3553i 0.227638 0.180127i
\(436\) 205.368 0.471026
\(437\) −277.070 277.070i −0.634027 0.634027i
\(438\) −197.057 + 197.057i −0.449901 + 0.449901i
\(439\) 243.928i 0.555644i −0.960633 0.277822i \(-0.910388\pi\)
0.960633 0.277822i \(-0.0896125\pi\)
\(440\) 108.873 + 137.590i 0.247439 + 0.312705i
\(441\) 21.0000 0.0476190
\(442\) −36.3651 36.3651i −0.0822741 0.0822741i
\(443\) 459.426 459.426i 1.03708 1.03708i 0.0377942 0.999286i \(-0.487967\pi\)
0.999286 0.0377942i \(-0.0120331\pi\)
\(444\) 58.4477i 0.131639i
\(445\) 16.3819 + 1.90874i 0.0368133 + 0.00428931i
\(446\) 199.403 0.447092
\(447\) 263.319 + 263.319i 0.589080 + 0.589080i
\(448\) 14.9666 14.9666i 0.0334077 0.0334077i
\(449\) 136.444i 0.303885i −0.988389 0.151943i \(-0.951447\pi\)
0.988389 0.151943i \(-0.0485529\pi\)
\(450\) −90.2341 + 55.7477i −0.200520 + 0.123884i
\(451\) −465.525 −1.03221
\(452\) −68.4262 68.4262i −0.151385 0.151385i
\(453\) 76.8561 76.8561i 0.169660 0.169660i
\(454\) 91.5140i 0.201573i
\(455\) −6.78361 + 58.2208i −0.0149090 + 0.127958i
\(456\) 130.221 0.285573
\(457\) 269.807 + 269.807i 0.590388 + 0.590388i 0.937736 0.347348i \(-0.112918\pi\)
−0.347348 + 0.937736i \(0.612918\pi\)
\(458\) −248.102 + 248.102i −0.541708 + 0.541708i
\(459\) 42.6461i 0.0929110i
\(460\) 115.598 91.4712i 0.251300 0.198850i
\(461\) −238.818 −0.518043 −0.259022 0.965872i \(-0.583400\pi\)
−0.259022 + 0.965872i \(0.583400\pi\)
\(462\) 56.8539 + 56.8539i 0.123060 + 0.123060i
\(463\) 308.280 308.280i 0.665831 0.665831i −0.290917 0.956748i \(-0.593960\pi\)
0.956748 + 0.290917i \(0.0939603\pi\)
\(464\) 58.3233i 0.125697i
\(465\) −229.229 289.691i −0.492966 0.622992i
\(466\) 612.961 1.31537
\(467\) 228.918 + 228.918i 0.490188 + 0.490188i 0.908365 0.418177i \(-0.137331\pi\)
−0.418177 + 0.908365i \(0.637331\pi\)
\(468\) 18.7985 18.7985i 0.0401678 0.0401678i
\(469\) 85.3497i 0.181982i
\(470\) −87.7672 10.2262i −0.186739 0.0217579i
\(471\) −444.135 −0.942963
\(472\) −176.530 176.530i −0.374005 0.374005i
\(473\) −297.860 + 297.860i −0.629724 + 0.629724i
\(474\) 340.115i 0.717542i
\(475\) 152.782 646.730i 0.321646 1.36154i
\(476\) 43.4287 0.0912368
\(477\) 5.93649 + 5.93649i 0.0124455 + 0.0124455i
\(478\) −136.398 + 136.398i −0.285351 + 0.285351i
\(479\) 342.177i 0.714357i 0.934036 + 0.357178i \(0.116261\pi\)
−0.934036 + 0.357178i \(0.883739\pi\)
\(480\) −5.66970 + 48.6606i −0.0118119 + 0.101376i
\(481\) 74.7591 0.155424
\(482\) 332.727 + 332.727i 0.690305 + 0.690305i
\(483\) 47.7665 47.7665i 0.0988953 0.0988953i
\(484\) 65.8440i 0.136041i
\(485\) 490.860 388.411i 1.01208 0.800848i
\(486\) 22.0454 0.0453609
\(487\) −456.499 456.499i −0.937370 0.937370i 0.0607814 0.998151i \(-0.480641\pi\)
−0.998151 + 0.0607814i \(0.980641\pi\)
\(488\) −204.941 + 204.941i −0.419962 + 0.419962i
\(489\) 127.380i 0.260491i
\(490\) −30.7142 38.8154i −0.0626820 0.0792152i
\(491\) 795.504 1.62017 0.810085 0.586312i \(-0.199421\pi\)
0.810085 + 0.586312i \(0.199421\pi\)
\(492\) −91.9112 91.9112i −0.186811 0.186811i
\(493\) 84.6184 84.6184i 0.171640 0.171640i
\(494\) 166.563i 0.337172i
\(495\) −184.847 21.5375i −0.373429 0.0435102i
\(496\) −170.625 −0.344002
\(497\) −20.1955 20.1955i −0.0406348 0.0406348i
\(498\) 235.355 235.355i 0.472601 0.472601i
\(499\) 145.240i 0.291062i −0.989354 0.145531i \(-0.953511\pi\)
0.989354 0.145531i \(-0.0464890\pi\)
\(500\) 235.016 + 85.2490i 0.470032 + 0.170498i
\(501\) 375.936 0.750371
\(502\) 244.521 + 244.521i 0.487093 + 0.487093i
\(503\) 169.609 169.609i 0.337195 0.337195i −0.518115 0.855311i \(-0.673366\pi\)
0.855311 + 0.518115i \(0.173366\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) −82.2089 + 705.564i −0.162790 + 1.39716i
\(506\) 258.639 0.511144
\(507\) −182.937 182.937i −0.360823 0.360823i
\(508\) 299.093 299.093i 0.588766 0.588766i
\(509\) 734.035i 1.44211i −0.692877 0.721056i \(-0.743657\pi\)
0.692877 0.721056i \(-0.256343\pi\)
\(510\) −78.8252 + 62.3734i −0.154559 + 0.122301i
\(511\) 301.009 0.589059
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −97.6658 + 97.6658i −0.190382 + 0.190382i
\(514\) 205.184i 0.399191i
\(515\) 265.189 + 335.136i 0.514930 + 0.650749i
\(516\) −117.616 −0.227938
\(517\) −109.625 109.625i −0.212041 0.212041i
\(518\) −44.6402 + 44.6402i −0.0861780 + 0.0861780i
\(519\) 212.605i 0.409643i
\(520\) −62.2407 7.25198i −0.119694 0.0139461i
\(521\) 96.5998 0.185412 0.0927061 0.995694i \(-0.470448\pi\)
0.0927061 + 0.995694i \(0.470448\pi\)
\(522\) 43.7424 + 43.7424i 0.0837978 + 0.0837978i
\(523\) 256.326 256.326i 0.490108 0.490108i −0.418232 0.908340i \(-0.637350\pi\)
0.908340 + 0.418232i \(0.137350\pi\)
\(524\) 186.974i 0.356821i
\(525\) 111.495 + 26.3394i 0.212372 + 0.0501703i
\(526\) 507.681 0.965174
\(527\) −247.552 247.552i −0.469738 0.469738i
\(528\) −60.7793 + 60.7793i −0.115112 + 0.115112i
\(529\) 311.702i 0.589228i
\(530\) 2.29014 19.6553i 0.00432102 0.0370855i
\(531\) 264.795 0.498673
\(532\) −99.4580 99.4580i −0.186951 0.186951i
\(533\) 117.562 117.562i 0.220566 0.220566i
\(534\) 8.07976i 0.0151306i
\(535\) −436.739 + 345.586i −0.816334 + 0.645955i
\(536\) 91.2426 0.170229
\(537\) 249.131 + 249.131i 0.463930 + 0.463930i
\(538\) 207.747 207.747i 0.386147 0.386147i
\(539\) 86.8457i 0.161124i
\(540\) −32.2432 40.7477i −0.0597096 0.0754588i
\(541\) −967.814 −1.78894 −0.894468 0.447133i \(-0.852445\pi\)
−0.894468 + 0.447133i \(0.852445\pi\)
\(542\) −476.286 476.286i −0.878756 0.878756i
\(543\) 307.766 307.766i 0.566789 0.566789i
\(544\) 46.4272i 0.0853442i
\(545\) 509.969 + 59.4191i 0.935723 + 0.109026i
\(546\) −28.7152 −0.0525920
\(547\) 107.907 + 107.907i 0.197271 + 0.197271i 0.798829 0.601558i \(-0.205453\pi\)
−0.601558 + 0.798829i \(0.705453\pi\)
\(548\) 132.011 132.011i 0.240895 0.240895i
\(549\) 307.412i 0.559949i
\(550\) 230.545 + 373.164i 0.419173 + 0.678480i
\(551\) −387.577 −0.703406
\(552\) 51.0645 + 51.0645i 0.0925081 + 0.0925081i
\(553\) −259.767 + 259.767i −0.469741 + 0.469741i
\(554\) 19.3574i 0.0349412i
\(555\) 16.9107 145.137i 0.0304697 0.261509i
\(556\) −223.528 −0.402029
\(557\) 106.902 + 106.902i 0.191925 + 0.191925i 0.796527 0.604603i \(-0.206668\pi\)
−0.604603 + 0.796527i \(0.706668\pi\)
\(558\) 127.969 127.969i 0.229335 0.229335i
\(559\) 150.440i 0.269123i
\(560\) 41.4955 32.8348i 0.0740990 0.0586337i
\(561\) −176.364 −0.314374
\(562\) 101.463 + 101.463i 0.180540 + 0.180540i
\(563\) −290.841 + 290.841i −0.516592 + 0.516592i −0.916539 0.399946i \(-0.869029\pi\)
0.399946 + 0.916539i \(0.369029\pi\)
\(564\) 43.2878i 0.0767515i
\(565\) −150.118 189.714i −0.265696 0.335777i
\(566\) 552.053 0.975358
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) 21.5899 21.5899i 0.0380104 0.0380104i
\(569\) 53.2185i 0.0935299i −0.998906 0.0467649i \(-0.985109\pi\)
0.998906 0.0467649i \(-0.0148912\pi\)
\(570\) 323.365 + 37.6769i 0.567307 + 0.0660999i
\(571\) 437.943 0.766976 0.383488 0.923546i \(-0.374723\pi\)
0.383488 + 0.923546i \(0.374723\pi\)
\(572\) −77.7415 77.7415i −0.135912 0.135912i
\(573\) −450.221 + 450.221i −0.785727 + 0.785727i
\(574\) 140.397i 0.244594i
\(575\) 313.518 193.695i 0.545249 0.336862i
\(576\) −24.0000 −0.0416667
\(577\) −219.701 219.701i −0.380764 0.380764i 0.490613 0.871377i \(-0.336773\pi\)
−0.871377 + 0.490613i \(0.836773\pi\)
\(578\) 221.641 221.641i 0.383462 0.383462i
\(579\) 234.446i 0.404915i
\(580\) 16.8747 144.828i 0.0290943 0.249704i
\(581\) −359.511 −0.618780
\(582\) 216.834 + 216.834i 0.372566 + 0.372566i
\(583\) 24.5504 24.5504i 0.0421105 0.0421105i
\(584\) 321.792i 0.551014i
\(585\) 52.1195 41.2415i 0.0890931 0.0704983i
\(586\) 209.746 0.357928
\(587\) 677.250 + 677.250i 1.15375 + 1.15375i 0.985795 + 0.167952i \(0.0537153\pi\)
0.167952 + 0.985795i \(0.446285\pi\)
\(588\) 17.1464 17.1464i 0.0291606 0.0291606i
\(589\) 1133.86i 1.92506i
\(590\) −387.285 489.436i −0.656415 0.829552i
\(591\) 476.300 0.805922
\(592\) −47.7224 47.7224i −0.0806121 0.0806121i
\(593\) −558.797 + 558.797i −0.942322 + 0.942322i −0.998425 0.0561035i \(-0.982132\pi\)
0.0561035 + 0.998425i \(0.482132\pi\)
\(594\) 91.1690i 0.153483i
\(595\) 107.842 + 12.5653i 0.181247 + 0.0211181i
\(596\) 429.998 0.721473
\(597\) −112.559 112.559i −0.188542 0.188542i
\(598\) −65.3154 + 65.3154i −0.109223 + 0.109223i
\(599\) 538.111i 0.898349i 0.893444 + 0.449175i \(0.148282\pi\)
−0.893444 + 0.449175i \(0.851718\pi\)
\(600\) −28.1580 + 119.194i −0.0469300 + 0.198656i
\(601\) 573.831 0.954793 0.477397 0.878688i \(-0.341580\pi\)
0.477397 + 0.878688i \(0.341580\pi\)
\(602\) 89.8308 + 89.8308i 0.149221 + 0.149221i
\(603\) −68.4320 + 68.4320i −0.113486 + 0.113486i
\(604\) 125.505i 0.207790i
\(605\) −19.0507 + 163.504i −0.0314887 + 0.270254i
\(606\) −347.993 −0.574245
\(607\) 409.542 + 409.542i 0.674699 + 0.674699i 0.958796 0.284097i \(-0.0916937\pi\)
−0.284097 + 0.958796i \(0.591694\pi\)
\(608\) 106.325 106.325i 0.174877 0.174877i
\(609\) 66.8177i 0.109717i
\(610\) −568.207 + 449.615i −0.931486 + 0.737074i
\(611\) 55.3685 0.0906195
\(612\) −34.8204 34.8204i −0.0568961 0.0568961i
\(613\) −571.915 + 571.915i −0.932977 + 0.932977i −0.997891 0.0649138i \(-0.979323\pi\)
0.0649138 + 0.997891i \(0.479323\pi\)
\(614\) 316.277i 0.515108i
\(615\) −201.641 254.827i −0.327872 0.414352i
\(616\) 92.8420 0.150717
\(617\) −479.790 479.790i −0.777617 0.777617i 0.201808 0.979425i \(-0.435318\pi\)
−0.979425 + 0.201808i \(0.935318\pi\)
\(618\) −148.044 + 148.044i −0.239553 + 0.239553i
\(619\) 308.772i 0.498824i −0.968398 0.249412i \(-0.919763\pi\)
0.968398 0.249412i \(-0.0802373\pi\)
\(620\) −423.697 49.3671i −0.683382 0.0796243i
\(621\) −76.5967 −0.123344
\(622\) −519.537 519.537i −0.835269 0.835269i
\(623\) 6.17102 6.17102i 0.00990532 0.00990532i
\(624\) 30.6978i 0.0491953i
\(625\) 558.927 + 279.688i 0.894284 + 0.447501i
\(626\) 146.170 0.233499
\(627\) 403.898 + 403.898i 0.644175 + 0.644175i
\(628\) −362.635 + 362.635i −0.577444 + 0.577444i
\(629\) 138.476i 0.220153i
\(630\) −6.49545 + 55.7477i −0.0103102 + 0.0884885i
\(631\) 876.945 1.38977 0.694885 0.719121i \(-0.255455\pi\)
0.694885 + 0.719121i \(0.255455\pi\)
\(632\) −277.703 277.703i −0.439403 0.439403i
\(633\) −363.185 + 363.185i −0.573752 + 0.573752i
\(634\) 559.698i 0.882805i
\(635\) 829.245 656.172i 1.30590 1.03334i
\(636\) 9.69424 0.0152425
\(637\) 21.9316 + 21.9316i 0.0344295 + 0.0344295i
\(638\) 180.897 180.897i 0.283538 0.283538i
\(639\) 32.3849i 0.0506805i
\(640\) 35.1019 + 44.3605i 0.0548468 + 0.0693133i
\(641\) 492.966 0.769057 0.384529 0.923113i \(-0.374364\pi\)
0.384529 + 0.923113i \(0.374364\pi\)
\(642\) −192.926 192.926i −0.300508 0.300508i
\(643\) −30.0997 + 30.0997i −0.0468114 + 0.0468114i −0.730125 0.683314i \(-0.760538\pi\)
0.683314 + 0.730125i \(0.260538\pi\)
\(644\) 78.0023i 0.121122i
\(645\) −292.064 34.0299i −0.452813 0.0527596i
\(646\) 308.524 0.477591
\(647\) −484.636 484.636i −0.749051 0.749051i 0.225250 0.974301i \(-0.427680\pi\)
−0.974301 + 0.225250i \(0.927680\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 1095.06i 1.68731i
\(650\) −152.458 36.0162i −0.234551 0.0554096i
\(651\) −195.476 −0.300270
\(652\) −104.005 104.005i −0.159517 0.159517i
\(653\) −113.485 + 113.485i −0.173791 + 0.173791i −0.788643 0.614852i \(-0.789216\pi\)
0.614852 + 0.788643i \(0.289216\pi\)
\(654\) 251.523i 0.384592i
\(655\) 54.0973 464.295i 0.0825914 0.708847i
\(656\) −150.090 −0.228796
\(657\) −241.344 241.344i −0.367343 0.367343i
\(658\) −33.0616 + 33.0616i −0.0502456 + 0.0502456i
\(659\) 625.067i 0.948509i 0.880388 + 0.474254i \(0.157282\pi\)
−0.880388 + 0.474254i \(0.842718\pi\)
\(660\) −168.513 + 133.342i −0.255322 + 0.202033i
\(661\) 608.913 0.921200 0.460600 0.887608i \(-0.347634\pi\)
0.460600 + 0.887608i \(0.347634\pi\)
\(662\) −601.834 601.834i −0.909115 0.909115i
\(663\) 44.5380 44.5380i 0.0671765 0.0671765i
\(664\) 384.334i 0.578816i
\(665\) −218.198 275.750i −0.328117 0.414662i
\(666\) 71.5835 0.107483
\(667\) −151.983 151.983i −0.227861 0.227861i
\(668\) 306.950 306.950i 0.459507 0.459507i
\(669\) 244.218i 0.365049i
\(670\) 226.574 + 26.3993i 0.338170 + 0.0394019i
\(671\) −1271.31 −1.89464
\(672\) 18.3303 + 18.3303i 0.0272772 + 0.0272772i
\(673\) −884.941 + 884.941i −1.31492 + 1.31492i −0.397179 + 0.917741i \(0.630011\pi\)
−0.917741 + 0.397179i \(0.869989\pi\)
\(674\) 34.1937i 0.0507325i
\(675\) −68.2767 110.514i −0.101151 0.163724i
\(676\) −298.735 −0.441916
\(677\) −390.548 390.548i −0.576881 0.576881i 0.357162 0.934043i \(-0.383745\pi\)
−0.934043 + 0.357162i \(0.883745\pi\)
\(678\) 83.8046 83.8046i 0.123606 0.123606i
\(679\) 331.219i 0.487804i
\(680\) −13.4328 + 115.288i −0.0197541 + 0.169541i
\(681\) 112.081 0.164583
\(682\) −529.217 529.217i −0.775977 0.775977i
\(683\) 869.027 869.027i 1.27237 1.27237i 0.327526 0.944842i \(-0.393785\pi\)
0.944842 0.327526i \(-0.106215\pi\)
\(684\) 159.488i 0.233169i
\(685\) 366.003 289.614i 0.534311 0.422794i
\(686\) −26.1916 −0.0381802
\(687\) −303.862 303.862i −0.442303 0.442303i
\(688\) −96.0331 + 96.0331i −0.139583 + 0.139583i
\(689\) 12.3997i 0.0179966i
\(690\) 112.029 + 141.578i 0.162361 + 0.205185i
\(691\) −148.448 −0.214831 −0.107415 0.994214i \(-0.534257\pi\)
−0.107415 + 0.994214i \(0.534257\pi\)
\(692\) −173.591 173.591i −0.250854 0.250854i
\(693\) −69.6315 + 69.6315i −0.100478 + 0.100478i
\(694\) 467.385i 0.673465i
\(695\) −555.066 64.6736i −0.798656 0.0930555i
\(696\) 71.4311 0.102631
\(697\) −217.759 217.759i −0.312423 0.312423i
\(698\) −399.184 + 399.184i −0.571896 + 0.571896i
\(699\) 750.721i 1.07399i
\(700\) 112.542 69.5296i 0.160774 0.0993280i
\(701\) 65.2652 0.0931029 0.0465515 0.998916i \(-0.485177\pi\)
0.0465515 + 0.998916i \(0.485177\pi\)
\(702\) 23.0234 + 23.0234i 0.0327968 + 0.0327968i
\(703\) −317.130 + 317.130i −0.451110 + 0.451110i
\(704\) 99.2522i 0.140983i
\(705\) 12.5245 107.492i 0.0177652 0.152472i
\(706\) −274.011 −0.388117
\(707\) 265.784 + 265.784i 0.375932 + 0.375932i
\(708\) 216.205 216.205i 0.305374 0.305374i
\(709\) 817.389i 1.15288i 0.817141 + 0.576438i \(0.195558\pi\)
−0.817141 + 0.576438i \(0.804442\pi\)
\(710\) 59.8587 47.3655i 0.0843080 0.0667119i
\(711\) 416.554 0.585870
\(712\) 6.59709 + 6.59709i 0.00926558 + 0.00926558i
\(713\) −444.628 + 444.628i −0.623601 + 0.623601i
\(714\) 53.1891i 0.0744945i
\(715\) −170.555 215.541i −0.238538 0.301455i
\(716\) 406.828 0.568196
\(717\) −167.052 167.052i −0.232988 0.232988i
\(718\) −473.333 + 473.333i −0.659239 + 0.659239i
\(719\) 1151.64i 1.60173i −0.598846 0.800864i \(-0.704374\pi\)
0.598846 0.800864i \(-0.295626\pi\)
\(720\) −59.5968 6.94393i −0.0827734 0.00964435i
\(721\) 226.141 0.313648
\(722\) −345.564 345.564i −0.478620 0.478620i
\(723\) −407.505 + 407.505i −0.563631 + 0.563631i
\(724\) 502.580i 0.694172i
\(725\) 83.8066 354.756i 0.115595 0.489318i
\(726\) −80.6421 −0.111077
\(727\) −82.3587 82.3587i −0.113286 0.113286i 0.648192 0.761477i \(-0.275526\pi\)
−0.761477 + 0.648192i \(0.775526\pi\)
\(728\) −23.4459 + 23.4459i −0.0322059 + 0.0322059i
\(729\) 27.0000i 0.0370370i
\(730\) −93.1043 + 799.075i −0.127540 + 1.09462i
\(731\) −278.660 −0.381203
\(732\) −251.001 251.001i −0.342897 0.342897i
\(733\) −482.749 + 482.749i −0.658593 + 0.658593i −0.955047 0.296454i \(-0.904196\pi\)
0.296454 + 0.955047i \(0.404196\pi\)
\(734\) 513.314i 0.699338i
\(735\) 47.5390 37.6170i 0.0646789 0.0511797i
\(736\) 83.3880 0.113299
\(737\) 283.001 + 283.001i 0.383991 + 0.383991i
\(738\) 112.568 112.568i 0.152531 0.152531i
\(739\) 430.657i 0.582757i −0.956608 0.291379i \(-0.905886\pi\)
0.956608 0.291379i \(-0.0941139\pi\)
\(740\) −104.697 132.312i −0.141482 0.178800i
\(741\) −203.997 −0.275300
\(742\) −7.40410 7.40410i −0.00997857 0.00997857i
\(743\) 902.316 902.316i 1.21442 1.21442i 0.244866 0.969557i \(-0.421256\pi\)
0.969557 0.244866i \(-0.0787438\pi\)
\(744\) 208.972i 0.280877i
\(745\) 1067.77 + 124.411i 1.43325 + 0.166995i
\(746\) −557.527 −0.747355
\(747\) 288.250 + 288.250i 0.385877 + 0.385877i
\(748\) −144.000 + 144.000i −0.192514 + 0.192514i
\(749\) 294.699i 0.393457i
\(750\) −104.408 + 287.835i −0.139211 + 0.383780i
\(751\) −262.783 −0.349910 −0.174955 0.984576i \(-0.555978\pi\)
−0.174955 + 0.984576i \(0.555978\pi\)
\(752\) −35.3444 35.3444i −0.0470005 0.0470005i
\(753\) −299.475 + 299.475i −0.397710 + 0.397710i
\(754\) 91.3659i 0.121175i
\(755\) 36.3126 311.655i 0.0480961 0.412788i
\(756\) −27.4955 −0.0363696
\(757\) −786.569 786.569i −1.03906 1.03906i −0.999205 0.0398555i \(-0.987310\pi\)
−0.0398555 0.999205i \(-0.512690\pi\)
\(758\) −168.579 + 168.579i −0.222400 + 0.222400i
\(759\) 316.767i 0.417347i
\(760\) 294.790 233.263i 0.387881 0.306926i
\(761\) 1469.36 1.93082 0.965412 0.260728i \(-0.0839627\pi\)
0.965412 + 0.260728i \(0.0839627\pi\)
\(762\) 366.313 + 366.313i 0.480725 + 0.480725i
\(763\) 192.104 192.104i 0.251774 0.251774i
\(764\) 735.208i 0.962315i
\(765\) −76.3915 96.5408i −0.0998582 0.126197i
\(766\) −333.177 −0.434956
\(767\) 276.542 + 276.542i 0.360551 + 0.360551i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 1018.45i 1.32439i 0.749333 + 0.662193i \(0.230374\pi\)
−0.749333 + 0.662193i \(0.769626\pi\)
\(770\) 230.545 + 26.8620i 0.299409 + 0.0348857i
\(771\) −251.299 −0.325938
\(772\) 191.424 + 191.424i 0.247958 + 0.247958i
\(773\) 570.658 570.658i 0.738238 0.738238i −0.233999 0.972237i \(-0.575181\pi\)
0.972237 + 0.233999i \(0.0751813\pi\)
\(774\) 144.050i 0.186111i
\(775\) −1037.84 245.177i −1.33915 0.316357i
\(776\) 354.088 0.456299
\(777\) −54.6728 54.6728i −0.0703640 0.0703640i
\(778\) −73.9237 + 73.9237i −0.0950176 + 0.0950176i
\(779\) 997.398i 1.28036i
\(780\) 8.88182 76.2289i 0.0113870 0.0977294i
\(781\) 133.928